The statement that express 9(x + 7) is product of constant factors 9 and x + 7. The Option B.
What does the expression 9(x + 7) represent?The expression 9(x + 7) represents the product of constant factors 9 and x + 7. To evaluate the expression, you would distribute the 9 to both terms inside the parentheses, resulting in 9x + 63.
This expression can also be written as a 2-term factor of 9 and x + 7. It is important to understand the different terms and factors in an expression to simplify and solve equations.
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I NEED HELP ASAP IT'S DUE IN 20MIN
Question 2
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 5
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Question 7
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sports Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 9
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.
2. The appropriate measure of center for the given data is the median, and it equals 19.
5. We can predict that there were about 169 principals in attendance at the conference.
6. The best graphical representation for the teacher's data would be a bar graph.
7. A histogram is used to display continuous data, while a bar graph is used to display categorical data.
8. The correct circle graph to represent the data is titled "New York City Visitor's Transportation"
9. We can predict that the college will need about 1440 scoops of ice cream.
Median, bar chart, histogramAnswer 2:
The appropriate measure of center for the given data is the median, and it equals 19. We can determine this from the box plot since the line inside the box represents the median of the data, and the box itself represents the middle 50% of the data. Since the box extends from 17 to 21, we know that half of the data falls below 19 and half above, making it the median. The mean is not a good measure of center for this data because it can be influenced by outliers, which are present in this dataset.
Answer 5:
Since we know that 15 out of 80 people in the exhibit room were principals, we can assume that about 15/80 (or about 0.1875) of the attendees were principals. To estimate the number of principals in attendance, we can multiply this fraction by the total number of attendees:
0.1875 x 900 ≈ 169
Therefore, we can predict that there were about 169 principals in attendance at the conference.
Answer 6:
The best graphical representation for the teacher's data would be a bar graph. A bar graph is a useful way to display categorical data, such as the subject preferences of the students. Each subject can be represented by a bar, with the height of the bar representing the frequency or percentage of students who prefer that subject.
Answer 7:
The correct graph to display the data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students". The bars should be labeled "Basketball" with a value of 17, "Baseball" with a value of 12, "Soccer" with a value of 27, and "Tennis" with a value of 44. A histogram is used to display continuous data, while a bar graph is used to display categorical data.
Answer 8:
The correct circle graph to represent the data is titled "New York City Visitor's Transportation" and has five sections labeled "Walk" at 30%, "Bicycle" at 6%, "Car Service" at 11.25%, "Bus" at 7.5%, and "Subway" at 20.25%. To calculate the percentages, we can divide the number of visitors for each mode of transportation by the total number of visitors (i.e., 300), then multiply by 100% to get the percentage.
Answer 9:
To estimate the number of students who prefer ice cream, we can add up the number of students who chose ice cream, which is 81. Then, we can set up a proportion:
81/225 = x/4000
where x represents the number of students who prefer ice cream out of the total population of 4000. Solving for x, we get:
x = 81 x 4000 / 225 = 1440
Therefore, we can predict that the college will need about 1440 scoops of ice cream.
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If you have a 19 out of 30 what would be the percentage?
Answer:
63.3%
Step-by-step explanation:
30 divided by 100 and then multiplied by 19 gives u the answer
Which table represents a function?
Answer:
Table 4 represents a function because each x-value corresponds to exactly one y-value.
Please help me with this homework
Answer:
14
Step-by-step explanation:
c = 2[tex]\pi r[/tex]
c = 2[tex]\pi[/tex]7
x = 14[tex]\pi[/tex]
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highway accidents: dui the u.s. department of transportation, national highway traffic safety administration, reported that 77% of all fatally injured automobile drivers were intoxicated. a random sample of 27 records of automobile driver fatalities in kit carson county, colorado, showed that section 8.3 testing a proportion p 479 15 involved an intoxicated driver. do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in kit carson county? use a 5 0.01.
The highway accident evidence to reject the null hypothesis that the population proportion is equal to 77%.
No, these data do not indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County.
The sample proportion of 15 out of 27 is 56.25%, which is not significantly different from the population proportion of 77%.
The p value for this test is 0.788, which is greater than the alpha level of 0.01.
The p value of this test indicates that the sample proportion of 15 out of 27 (56.25%) is not significantly different from the population proportion of 77%.
This means that there is not enough evidence to reject the null hypothesis that the population proportion is equal to 77%.
The p value of 0.788 is greater than the alpha level of 0.01, meaning that the results of this test are not statistically significant enough to support the alternative hypothesis that the population proportion is less than 77%.
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Approximate the volume of a sphere with a radius of 7 feet, both in terms of pie and to the nearest tenth.
The volume of the sphere with a radius of 7 feet is therefore 1436.8 cubic feet when expressed in terms of pi and rounded to the closest tenth (or about 1436.76 cubic feet).
what is volume ?The volume of such a three-dimensional object is the amount of space it takes up in algebra and geometry. It is a description of an object's capacity and, depending on the situation, may be stated in terms of cubic metres, cubic centimetres, litres, or gallons. A cube's volume, for instance, can be determined by adding up its length, width, and height. An equation for calculating a cube's volume is: V = l × w × h where V indicates for volume, l for length, w for width, and h for height.
given
The following equation determines a sphere's volume:
[tex]V = (4/3)\pi r^3[/tex]
where r denotes the sphere's radius.
If we substitute r = 7 feet, we obtain:
[tex]V = (4/3)\pi (7 feet)^3[/tex]
Using V, 1436.76 cubic feet (3.14159)
To the nearest tenth, we round and obtain:
1436.8 cubic feet equals V.
The volume of the sphere with a radius of 7 feet is therefore 1436.8 cubic feet when expressed in terms of pi and rounded to the closest tenth (or about 1436.76 cubic feet).
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Suppose money grows according to the simple interest accumulation function a(t) = 1. 05t. How much money would you need to invest at time 3 in order to have $3,200 at time 8?
$2,560 needs to be invested at time 3 in order to have $3,200 at time 8.
Since the money grows according to the simple interest accumulation function a(t) = 1.05t, the amount of money A at time t, given an initial amount P, can be calculated using the formula:
A = P + Pr(t)
where r is the interest rate (in this case, 5% or 0.05) and t is the time period (measured in years).
To determine how much money needs to be invested at time 3 to have $3,200 at time 8, we can use the above formula and solve for P:
3200 = P + Pr(8-3)
3200 = P + 5P(0.05)
3200 = P + 0.25P
3200 = 1.25P
P = 3200 / 1.25
P = 2560
Therefore, an initial investment of $2,560 at time 3 would be needed to have $3,200 at time 8, assuming a simple interest accumulation function with an interest rate of 5%.
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5 out of 7 questions. PLEASE help me.
Answer:
5 units is the distance
Step-by-step explanation:
7,2 is point c
7,7 is point d
7 - 7 = 0
7 - 2 = 5
5 is the answer
Between which two integers does 7/3 lie Answer A 4 and 5 Answer B 1 and 2 Answer C 2 and 3 Answer D 3 and 4
We can conclude that 7/3 lies between the integers 2 and 3. So, correct option is C,
To determine between which two integers 7/3 lies, we can use division and rounding.
Dividing 7 by 3 gives 2 with a remainder of 1. Therefore, we can express 7/3 as the sum of 2 and a fraction:
7/3 = 2 + 1/3
Since the fraction 1/3 is less than 1/2, we can round down to 2. Therefore, we can conclude that 7/3 lies between the integers 2 and 3.
This question requires us to determine between which two integers the fraction 7/3 lies. One approach to solving this is to perform long division, which gives us a quotient of 2 with a remainder of 1. We can express 7/3 as the sum of the quotient and the fraction 1/3. Since 1/3 is less than 1/2, we round down to the nearest integer, which in this case is 2.
Answer C, 2 and 3, is the correct answer.
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in order to determine whether or not there is a significant difference between the hourly wages of two companies, two independent random samples were selected and the following statistics were calculated. company a company b sample size 80 60 sample mean $6.75 $6.25 population standard deviation $1.00 $0.95 refer to exhibit 10-8. the value of the test statistic is . a. 3.01 b. 1.645 c. 2.75 d. .098
The value of the test statistic is approximately 2.84. Its significance can't be determined.
To determine whether or not there is a significant difference between the hourly wages of two companies, we need to conduct a hypothesis test.
The null hypothesis states that there is no significant difference between the hourly wages of the two companies, while the alternative hypothesis states that there is a significant difference.
The test statistic for this hypothesis test is calculated using the formula:
[tex]t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^(1/2)[/tex]
where x1, x2 are the sample means for companies A and B, s1 and s2 are the sample standard deviations for companies A and B, and n1 and n2 are the sample sizes for companies A and B.
Plugging in given values, we get:
[tex]t = (6.75 - 6.25) / [(1^2/80) + (0.95^2/60)]^(1/2)[/tex]
t = 0.5 / 0.1759
t = 2.8437
Without knowing the significance level or the degrees of freedom, we cannot determine whether or not the test statistic is statistically significant.
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The value of the test statistic is 2.75.
To determine the test statistic for comparing the hourly wages of two companies, the researcher would need to conduct a two-sample t-test with equal variances.
The formula for the test statistic is:
[tex]t = (\bar x1 - \barx2) / [s_p \times \sqrt(1/n1 + 1/n2)][/tex]
where:
[tex]\bar x1[/tex] and[tex]\bar x2[/tex] are the sample means for Company A and Company B, respectively
[tex]s_p[/tex] is the pooled standard deviation of the two samples, calculated as:
[tex]s_p = sqrt [((n1 - 1) \times s1^2 + (n2 - 1) \times s2^2) / (n1 + n2 - 2)][/tex]
n1 and n2 are the sample sizes for Company A and Company B, respectively
s1 and s2 are the sample standard deviations for Company A and Company B, respectively.
Plugging in the given values, we get:
[tex]t = (6.75 - 6.25) / [\sqrt(((80-1)\times 1^2 + (60-1)\times 0.95^2)/(80+60-2)) \times \sqrt(1/80 + 1/60)][/tex]
[tex]t = 2.75[/tex]
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can yall help me with this question this would rlly help me out!
Answer:
59.5[tex]cm^{2}[/tex]
Step-by-step explanation:
You have two shape: a square and a triangle
Square:
The area of a square is the sides squared
a = [tex]s^{2}[/tex] The side length is 7 (7 x 7 = 49)
a = [tex]7^{2}[/tex]
a = 49
Triangle:
a [tex]\frac{bh}{2}[/tex] The base times the height divided by 2
The base is 7 and the height is 3.
a = [tex]\frac{7x3}{2}[/tex] = [tex]\frac{21}{2}[/tex] = 10.5
Add the two areas together: 49 + 10.5 = 59.5
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
The correct answer is option b. Burger Quick, because it has a larger mean.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to gather, analyze, and interpret data from various fields, including business, economics, medicine, engineering, psychology, and social sciences. Statistics allows researchers and analysts to draw conclusions and make predictions based on data, and is used in a wide range of applications, from designing experiments and conducting surveys to testing hypotheses and making decisions based on data-driven insights.
Burger Quick typically has more wait time, because it has a larger interquartile range (IQR) and a larger upper whisker on the box plot, indicating that there is more variability in the wait times and some customers have experienced longer wait times. Although the median wait time for Burger Quick is also larger, it is the IQR and upper whisker that provide more evidence for the longer wait times. The mean is not shown on the box plot and therefore cannot be used to determine which drive-thru typically has more wait time.
Therefore, the correct answer is option b. Burger Quick, because it has a larger mean.
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Find the missing measures in each diagram.
Answer:
X = 65°
Y = 75°
Z = 65°
Step-by-step explanation:
Hello!
Angle Y and the angle measuring 75 degrees are corresponding angles, and corresponding angles are congruent to each other in degree measure.
There is also another set of corresponding angles, and those are Angle Z and Angle X.
Since Angle Y and 75° are corresponding, we can state that Angle Y is also 75°. We can now find Angle Z by subtracting 40° and 75° from 180°. This is because the sum of angles in a triangle is 180°.
Angle Z:180° - 40° - 75°180°-115°65°The measure of Angle Z is 65°. We know that Z and X are corresponding, so X is also 65°.
Kayla has three different sizes of plates. 7.G.4
Part A: The table shows the circumferences of the plates. Find the radius
and diameter for each plate. Use 3.14 for T.
43.96
28.26
Circumference (in.)
Radius (in.)
Diameter (in.)
21.98
Part B: How did you find the radius and the diameter of each plate?
So the radius and diameter for each plate are:
Plate 1: radius ≈ 7 in., diameter ≈ 14 in.
Plate 2: radius ≈ 4.5 in., diameter ≈ 9 in.
Plate 3: radius ≈ 3.5 in., diameter ≈ 7 in.
What is circumference?Circumference is the distance around the edge of a circle. It is the total length of the boundary of a circle. It is also referred to as the perimeter of a circle. The circumference of a circle can be calculated using the formula: C = 2πr where C is the circumference, r is the radius of the circle, and π is a mathematical constant with an approximate value of 3.14. The circumference of a circle is directly proportional to its radius; that is, as the radius of a circle increases, the circumference also increases.
Here,
Part A:
To find the radius and diameter of each plate, we can use the formula for the circumference of a circle:
C = 2πr
where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:
r = C / 2π
Using the given circumferences and the value of π as 3.14, we can find the radius for each plate:
Plate 1:
C = 43.96 in.
r = 43.96 / (2 x 3.14) ≈ 7 in.
d = 2r ≈ 14 in.
Plate 2:
C = 28.26 in.
r = 28.26 / (2 x 3.14) ≈ 4.5 in.
d = 2r ≈ 9 in.
Plate 3:
C = 21.98 in.
r = 21.98 / (2 x 3.14) ≈ 3.5 in.
d = 2r ≈ 7 in.
So the radius and diameter for each plate are:
Plate 1: radius ≈ 7 in., diameter ≈ 14 in.
Plate 2: radius ≈ 4.5 in., diameter ≈ 9 in.
Plate 3: radius ≈ 3.5 in., diameter ≈ 7 in.
Part B:
To find the radius and diameter of each plate, we used the formula for the circumference of a circle and rearranged it to solve for the radius. We then used the formula for the diameter of a circle, which is simply twice the radius, to find the diameter. We also used the value of π as 3.14 in our calculations.
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What is the value of the expression 8w−4j2 when w=0. 25 and j=0. 5?
The value of the expression 8w - 4j² when w = 0.25 and j = 0.5 is 1.
The expression 8w - 4j² is a combination of variables, w and j, and a constant, 8 and 4. In order to evaluate the expression when w = 0.25 and j = 0.5, we substitute these values for w and j in the expression and perform the necessary calculations.
First, we substitute w = 0.25 and j = 0.5 in the expression:
8(0.25) - 4(0.5)²
Next, we simplify the expression by performing the calculations in the parentheses first. Since 0.5² = 0.25, we can simplify 4(0.5)² to 4(0.25) = 1. We can then simplify 8(0.25) - 4(0.5)² to:
= 2 - 1
= 1
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The given question is incomplete, the complete question is:
What is the value of the expression 8w−4j² when w=0. 25 and j=0. 5?
Sarah and Nathan each picked a bucket of strawberries. Sarah picked 4 1/4 pounds, and Nathan picked 3 3/4 pounds. How many pounds did they pick altogether?
8 pounds
8, 1/2, pounds
7 1/2 pounds
7 pounds
Answer:
8 pounds
Step-by-step explanation:
Simply add the fractions. Think of mixed fractions as whole numbers + fractions.
[tex]4\frac{1}{4} =\\4+\frac{1}{4} \\\\\\3\frac{3}{4} =\\3+\frac{3}{4}[/tex]
Now, add all the terms together:
[tex]4+\frac{1}{4}+3+\frac{3}{4} =\\\\ 7+\frac{4}{4}[/tex]
4/4 can be rewritten as 1, so we have:
[tex]7+\frac{4}{4} =\\\\ 7+1= \\\\8[/tex]
Thus, Sarah and Nathan picked 8 pounds of strawberries altogether.
The Gabrielsons ran a family relay race. The distance run by each family member (in kilometers) is listed below.
11
,
4
,
8
,
2
,
5
11,4,8,2,5
The Gabrielsons ran a total of 30 kilometers in the family relay race.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
It seems that there are five family members who participated in the relay race, and the distance run by each of them in kilometers is listed as follows:
11, 4, 8, 2, 5
To find the total distance run by the family, we simply add up the distances:
11 + 4 + 8 + 2 + 5 = 30
Therefore, the Gabrielsons ran a total of 30 kilometers in the family relay race.
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# 15) A boat is heading towards a lighthouse, where Jeriel is watching from a vertical distance of
113 feet above the water. Jeriel measures an angle of depression to the boat at point A to be
8°. At some later time, Jeriel takes another measurement and finds the angle of depression to
the boat (now at point B) to be 52°. Find the distance from point A to point B. Round your
answer to the nearest tenth of a foot if necessary.
the distance between point A and point B is approximately 777.9 feet.
what is distance ?
Distance is a numerical measurement of how far apart two objects or points are from each other. It is a fundamental concept in mathematics and physics, and it can be defined in different ways depending on the context.
In the given question,
Let's denote the distance between Jeriel and point A as x, and the distance between Jeriel and point B as y. We want to find the distance between point A and point B, which we can call d.
From the first measurement, we can draw a right triangle with one leg of length x, another leg of length 113, and an acute angle of 8 degrees. The angle opposite the leg of length 113 is 90 degrees minus 8 degrees, or 82 degrees. We can use tangent to find x:
tan(8) = 113/x
x = 113/tan(8)
x =802.5
From the second measurement, we can draw another right triangle with one leg of length y, another leg of length 113, and an acute angle of 52 degrees. The angle opposite the leg of length 113 is 90 degrees minus 52 degrees, or 38 degrees. We can use tangent to find y:
tan(52) = 113/y
y = 113/tan(52)
y =72.4
Now we can use the Law of Cosines to find d:
d² = x² + y² - 2xy cos(130)
where 130 degrees is the angle between the sides of length x and y. We can simplify this equation and substitute the values we found for x and y:
d² = (802.5)² + (72.4)² - 2(802.5)(72.4) cos(130)
d =777.9
Therefore, the distance between point A and point B is approximately 777.9 feet.
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Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. −9. 5 − (−8) − 6. 5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. Then, show your work, and represent the answer as a single rational number
The value of the expression as a single rational number is -8.
Kent was likely referring to the idea that subtracting a negative number is the same as adding a positive number. Specifically, to subtract a negative number, we can add the opposite of that number (i.e., the positive version of that number). In this case, we can rewrite the expression as:
= -9.5 - (-8) - 6.5
= -9.5 + 8 - 6.5 (replacing -(-8) with its positive equivalent 8)
= (-9.5 - 6.5) + 8 (grouping like terms)
= -16 + 8 (simplifying)
= -8
Therefore, the value of the expression is -8, which is a single rational number.
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at my office, $16$ people own cats, $8$ people own dogs, and $5$ people own both cats and dogs. how many people own a cat or a dog?
There are 19 people who own a cat or a dog.
What is number refers to?A number is a mathematical object used to represent quantity, measurement, or a count of something. It can be an integer (whole number), a rational number (fraction), an irrational number (such as pi), or a real number (which includes all rational and irrational numbers).
To find the number of people who own a cat or a dog, we need to add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs.
Let's start by finding the number of people who own only cats. We know that 16 people own cats, and 5 people own both cats and dogs. Therefore, the number of people who own only cats is:
16 - 5 = 11
Next, let's find the number of people who own only dogs. We know that 8 people own dogs, and 5 people own both cats and dogs. Therefore, the number of people who own only dogs is:
8 - 5 = 3
Finally, we can add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs:
11 + 3 + 5 = 19
So, there are 19 people who own a cat or a dog.
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11. three players on a baseball team are only permitted to pitch. the remaining 12 players are multitalented and can play any of the 8 remaining positions. how many baseball teams of nine can be formed?
There are 302,702,400 possible baseball teams of nine that can be formed with three designated pitchers and 12 multitalented players who can play any of the remaining positions.
Since three players are designated as pitchers, we need to choose three players out of the total 15 players on the team. This can be done in C(15, 3) ways, where C(n, r) represents the number of combinations of r objects selected from a set of n objects.
For the remaining six positions, any of the 12 multitalented players can be assigned to any of the positions, which means that there are 12 choices for the first position, 11 choices for the second position, and so on, down to 7 choices for the sixth position.
Therefore, the total number of baseball teams of nine that can be formed is:
C(15, 3) x 12 x 11 x 10 x 9 x 8 x 7
which simplifies to:
(15 x 14 x 13 / 3 x 2 x 1) x (12 x 11 x 10 x 9 x 8 x 7)
= 455 x 665,280
= 302,702,400
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Find the measures of angle and B. Round to the nearest degree.
The measure of angle A and angle B are 30° and 60° respectively.
What is the measure of angle A and angle B?The figure in the image is a right-triangle.
To find the measure of angle A and angle B, we use the trigonometric ratio.
Solving for the measure of angle A:
sinθ = opposite / hypotenuse
opposite of angle A = 8
hypotenuse = 16
Plug in the values
sinθ = 8/16
sinθ = 1/2
θ = sin⁻¹( 1/2 )
θ = 30°
Solving for angle B
cosB = adjacent / Hypotenuse
adjeacent of angle B = 8
Hypotenuse = 16
Plug in the given values
cosB = 8/16
cosB = 1/2
B = cos⁻¹( 1/2 )
B = 60°
Therefore angle A is 30 degrees and angle B is 60 degree.
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the town mouse and the country mouse
1. The characters in "The Town Mouse and the Country Mouse" are two mice who are cousins. The town mouse is described as elegant, refined, and sophisticated, while the country mouse is simple and unsophisticated.
2. The main idea of the story is that one should be content with their simple life rather than crave for a luxurious life full of dangers and uncertainties.
What is The Town Mouse and The Country Mouse?"The Town Mouse and the Country Mouse" is a fable, a short story that teaches a moral or lesson. It tells the story of two cousins, a town mouse and a country mouse, who visit each other's homes and experience each other's way of life. The town mouse lives in luxury and eats rich food, but is always in danger from the cat, while the country mouse lives a simple life but is safe and content.
3. The sequence of events in the story is as follows:
The country mouse invites the town mouse to visit him in the countryside.The town mouse accepts the invitation and visits the country mouse.The country mouse serves the town mouse simple food, which the town mouse finds unappetizing.The town mouse invites the country mouse to visit him in the town.The country mouse accepts the invitation and visits the town.The town mouse serves the country mouse luxurious food, but they both get scared and run away when the cat appears.The country mouse returns to his simple life, realizing that it's better to be safe and content than to live in luxury but in constant danger.4. Important details in the story include the description of the town and country mice, the differences in their lifestyles, and their reactions to each other's homes. These details are important because they emphasize the theme of the story, which is that it's better to be content with one's simple life than to crave for a luxurious but dangerous life.
5. I think "The Town Mouse and the Country Mouse" is a great story because it teaches an important lesson in a fun and engaging way. The characters are well-developed, and the plot is entertaining, making it easy for readers to understand the message.
6. One question I have about the writing is whether the author intended the story to be a commentary on social class and wealth.
7. A fable is a short story that teaches a moral or lesson. Fables usually feature animals or other non-human characters that can talk and behave like humans.
8. The moral of "The Town Mouse and the Country Mouse" is that it's better to be content with a simple life than to crave for luxury and danger. The story shows that the country mouse is happier and safer in his simple life than the town mouse, who is always in danger despite his luxurious lifestyle. This lesson teaches readers to be satisfied with what they have rather than always craving for more.
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town mouse and country mouse are cousins, the town mouse is working hard, (keep up the good work bud,) and the city mouse is relaxing, one day, town mouse was invited to city mouse’s city, they were relaxing, and then, a dog almost killed the mouses.
marvin company sells pens ($6) and flashlights ($10). if total sales were $624 and customers bought 7 times as many pens as flashlights, what would be the number of pens sold?
If total sales were $624 and customers bought 7 times as many pens as flashlights, then the number of pens sold is 84.
Let's start by assigning variables to represent the unknown quantities.
Let x be the number of flashlights sold.
Then, since "customers bought 7 times as many pens as flashlights," the number of pens sold would be 7x.
The total sales can be expressed as the sum of the sales of each item:
10x (sales from flashlights) + 6(7x) (sales from pens) = 624
Simplifying this equation
10x + 42x = 624
52x = 624
x = 12
So, the number of flashlights sold is 12.
And the number of pens sold would be 7x = 7(12) = 84.
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Calculate the lengths of the 2 unlabeled sides.
Leave your answer in exact form.
Answer:
BC=4
AC=[tex]4\sqrt{2}[/tex]
To help determine what types of clubs to offer at harding middle school the principal surveyed fifty 8th grades. Does the sampl fairly represent the population ? explain
To determine if the sample fairly represents the population, we need to consider whether the sample is representative and whether there is any bias present in the sampling process.
If the principal surveyed fifty 8th graders in a way that ensures that each 8th grader in the population has an equal chance of being selected, then the sample can be considered representative. This means that the sample accurately reflects the characteristics of the population, and any conclusions drawn from the sample can be applied to the population.
However, if the sampling process was biased in some way, the sample may not be representative of the population. For example, if the principal only surveyed 8th graders in one class or in one particular group, the sample may not be representative of the entire 8th-grade population at Harding Middle School. In this case, any conclusions drawn from the sample may not accurately reflect the entire population.
Therefore, the key factor in determining whether the sample fairly represents the population is the sampling method used. If the sampling method is random and unbiased, then the sample can be considered representative of the population.
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3. In raising a 7000 N motorcycle with a pulley system, the workers note that for every 3 m of rope pulled down- ward, the piano rises 0. 3 m. Show that 700 N is required to lift the motorcycle
If workers note that for every "3 m" of rope pulled down-ward, the piano rises 0.3 m, then we have shown that 700 N is required force to lift the motorcycle.
The term "Mechanical advantage" (MA) is defined as ratio of "output-force" to "input-force" in a machine.
In this case, the output force is the weight of the motorcycle (7000 N) and the input force is the force applied to pull the rope downward.
We use the formula for mechanical advantage in a pulley system, which is given by:
⇒ MA = (distance moved by the effort) / (distance moved by the load),
In this case, the distance moved by the effort is 3 m, and
The distance moved by the load is 0.3 m,
Substituting the values,
We get,
⇒ MA = 3/0.3,
⇒ MA = 10,
So, mechanical advantage of "pulley-system" is 10.
Now, we use mechanical advantage to calculate the required force to lift the motorcycle.
Since mechanical advantage is defined as the ratio of output force to input force, we can rearrange the formula as:
⇒ Input force = (Output force)/(Mechanical advantage),
Substituting values for "output-force" as 7000 N and "mechanical-advantage" as 10,
We get,
⇒ Input force = 7000/10,
⇒ 700 N,
Therefore, the required force to lift motorcycle is 700 N.
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The area of a semicircle is 1. 2717 square meters. What is the semicircles diameter
The diameter of the semicircle for the given area of the semicircle 1. 2717 square meters is equal to 1.8 meters.
Area of a semicircle = 1. 2717 square meters
The area of a semicircle is given by the formula,
A = πr^2 / 2
where A is the area
And r is the radius of the semicircle.
Rearrange the formula to solve for r,
r = √(2A/π)
Substituting the given value of A = 1.2717 square meters into this formula, we get,
⇒ r = √(2 × 1.2717 / π)
⇒ r = 0.9 meters
Since the diameter of a semicircle is twice the radius,
The diameter of this semicircle is equal to,
d = 2r
= 2 × 0.9
= 1.8 meters
Therefore, the diameter of the semicircle is equal to 1.8meters.
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The ratio of the lengths of the edges of two cubes is #. What is the ratio of their
surtace areas?
The ratio of their surface areas is x^2
What is the ratio of their surface areas?Let's assume that the lengths of the edges of the first cube are a, and the lengths of the edges of the second cube are bx, where b is a constant.
The surface area of a cube is given by the formula A = 6a^2, where a is the length of an edge.
Therefore, the surface area of the first cube is 6a^2 and the surface area of the second cube is 6(bx)^2 = 6b^2x^2.
The ratio of their surface areas is:
(6b^2x^2) / (6a^2) = b^2x^2 / a^2
Since the ratio of the lengths of the edges of the two cubes is x, we have:
a / bx = 1 / x
Solving for a, we get:
a = bx^2
Substituting this value into the ratio of their surface areas, we get:
(b^2x^2) / (bx^2)^2 = (b^2x^2) / b^2x^4 = x^2
Therefore, the ratio of the surface areas of the two cubes is x^2.
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In circle C, FG and FE are tangent segments, m
Choose the two answers that represent the angle measures of the central and circumscribed angles.
The angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
What is angle?Angle is a geometric term used to describe the measure between two lines or surfaces that intersect each other. It is measured in degrees, and is typically represented by the Greek letter θ (theta). Angles can be acute, obtuse, right, reflex, or straight. Acute angles are angles that are less than 90°, obtuse angles are angles that are greater than 90°, and right angles are angles that measure exactly 90°. Reflex angles are angles that measure greater than 180°, and straight angles measure exactly 180°.
The two correct answers are 83° and 79°. The angle measure of the central angle GFE is 3x + 11. Therefore, 3x + 11 = 83°, and x = 26. The angle measure of the circumscribed angle GCE is 5x - 23. Therefore, 5x - 23 = 79°, and x = 26. As both equations have the same value for x, the two angle measures are 83° and 79°.
In conclusion, the angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
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