Answer:
7 ( 3 + 8)
Explanation:
First, let's find the greatest common factor between 21 and 56.
So, the factors of 21 and 56 are:
21: 1, 3, 7, 21
56: 1, 2, 4, 7, 8, 14, 28, 56
Then, the common factors are 1 and 7 and the greatest is 7. It means that the GCF of 21 and 56 is 7
Now, we need to write 21 and 56 as a product that includes the number 7 as:
21 = 7 x 3
56 = 7 x 8
Therefore, the sum of 21 and 56 can be written as:
21 + 56
(7 x 3) + (7 x 8)
So, applying the distributive property, we get:
(7 x 3) + (7 x 8) = 7 ( 3 + 8 )
Therefore, the answer is 7(3 + 8)
Because 7 is the GCF and 3 and 8 are two number with no common factor
Factor the quadratic expressionx^2 + 5x - 14
Solution:
Given:
[tex]x^2+5x-14[/tex]Using the product-sum to factor the expression, the middle term is split;
[tex]\begin{gathered} x^2+7x-2x-14 \\ \\ Grouping\text{ the terms;} \\ (x^2+7x)(-2x-14) \\ \\ Factor\text{ out the terms;} \\ x(x+7)-2(x+7) \\ =(x-2)(x+7) \end{gathered}[/tex]Therefore, the factored term is;
[tex](x-2)(x+7)[/tex]
use the graph to find when f(x)
x > -7
Explanations:For the graph g(x), select two points on the line
(-7, 4) and (-2, 8)
That is, x₁ = -7, y₁ = 4, x₂ = -2, y₂ = 8
The slope of the line is given as:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{8-4}{-2-(-7)} \\ m\text{ = }\frac{4}{5} \end{gathered}[/tex]The equation of a line is given as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = }\frac{4}{5}(x-(-7)) \\ y\text{ - 4 = }\frac{4}{5}(x+7) \\ y-4=\frac{4}{5}x+\frac{28}{5} \\ y\text{ = }\frac{4}{5}x+\frac{28}{5}+4 \\ y\text{ = }\frac{4}{5}x\text{ + }\frac{48}{5} \\ y\text{ = }0.8x+9.6 \\ g(x)\text{ = 0.8x+9.6} \end{gathered}[/tex]For the graph f(x):
Select the points (-7, 4) and (-3, 2)
[tex]\begin{gathered} m\text{ = }\frac{2-4}{-3-(-7)} \\ m\text{ = }\frac{-2}{4} \\ m\text{ = -0.5} \end{gathered}[/tex]The equation of the line is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = -0.5(x - (-7)} \\ y\text{ - 4 = -0.5(x + 7)} \\ y\text{ - 4 = -0.5x - }3.5 \\ y\text{ = -0.5x - 3.5 + 4} \\ y\text{ = -0.5x + 0.5} \\ f(x)\text{ = -0.5x + 0.5} \end{gathered}[/tex]f(x) < g(x)
-0.5x + 0.5 < 0.8x + 9.6
-0.5x - 0.8x < 9.6 - 0.5
-1.3x < 9.1
-x < 9.1 / 1.3
-x < 7
x > -7
T+a/N=F I need to solve for a.
Find the length of PQ. The endpoints are P(-2,-1) and Q(2,4)
Morgy, this is the solution:
Point P = (-2, -1)
Point Q = (2, 4)
Let's use the formula to calculate the distance, this way:
d = √(2 - -2)² + (4 - -1)²
d = √4² + 5²
d = √16 + 25
d = √41
d = 6.403
In consequence, the lenght of PQ is 6.403 units
Jina is ordering 4 bags of cat food from Canada. Each bag has a mass of 2.5 kg. To determine the shipping costs, Jina needs to know the total weight in pounds. What is the weight of the cat food in pounds? USE 1kg=2.2lb AND DON'T ROUND ANY COMPUTATIONS.
Answer
22 lb
Step-by-step explanation
Given that 1 bag weighs 2.5 kg, then 4 bags will weigh:
[tex]4\times2.5\text{ kg}=10\text{ kg}[/tex]Using the conversion factor: 1 kg = 2.2 lb, 10 kg are equivalent to:
[tex]10\text{ kg}=10\text{ kg}\times\frac{2.2\text{ lb}}{1\text{ kg}}=22\text{ lb}[/tex]Answer:
22 pounds
Step-by-step explanation:
Jina is ordering 4 bags, each of them weighs 2.5 kgs. Let's first find each bag's weight in lbs:
[tex]2.5kg*2.2lb = 5.5 lbs[/tex]
Now, to find the total mass of cat food, let's multiply each bag's weight to the number of bags:
[tex]5.5lbs * 4 = 22 lbs[/tex]
Jason wants to dine at five different restaurants during a summer getaway. If two of nineavailable restaurants serve seafood, find the number of ways that at least one of theselected restaurants will serve seafood given the following conditions.a) The order of selection is important.b) The order of selection is not important.
Solution
Explanation:
If order is important, permutations can be used to find the number of ways the event can take place
Number of ways to select any 5 out of 8 in a particular order = 8P5
In this case, "at least one" is complement of "fewer than one" (that is 0). Thus, four restaurants that are not serving seafood can be chosen from five restaurants in
[tex]8P_5=6720[/tex]Number of restaurants serving seafood = 2 , Number of restaurants not serving seafood = 3
Number of selections in which all restaurants do not serve seafood = 5P3 = 20
Number of ways such that at least one of the selected restaurants will serve seafood = Total number of selections - Number of selections in which all restaurants do not serve seafood
[tex]6720-20=6700[/tex]marlo has a photogrph this is 5 inches wide and 7 inches tall.he wants to enlarge the photo to fit in a frame that is 32 inches tall.if the length and width will be scaled proportionally,what is the width of the frame for the enlarged photo?round to one decimal place.
Given: a photograph is 5 inches wide and 7 inches tall.
He wants to enlarge the photo to fit in a frame that is 32 inches tall.
So, the length and the width will be scaled proportionally
So, the scale factor = r= new length over the lod length
[tex]r=\frac{32}{7}[/tex]It must be the same ratio: new width to old width
Let the new wide = x
so,
[tex]\frac{x}{5}=\frac{32}{7}[/tex]solve for x:
[tex]x=\frac{32}{7}\cdot5=\frac{160}{7}=22\frac{6}{7}in[/tex]So, the answer will be: the new width = 22 6/7 inches
Hello I need help with This , I am studying but I just don’t understand this
Explanation:
Concept:
The product of two matrices is undefined whenever the rows of the first matrix (reading right to left) do not match the column of the second matrix. However, say that I would need (for some reason) to multiply a 3x3 matrix by a 2x3 one.
Hence,
The final answer is OPTION C
I just am having trouble solving the equation. Can you help me?
Given:
[tex]h(x)=x^2-1[/tex]Required:
To calculate which option is correct
Explanation:
According to the formula for the average rate of change of the function:
[tex]\begin{gathered} \frac{\Delta y}{\Delta x}=(f^1(x_1)+f^1(x_2))\text{ divide by 2} \\ \\ So,\text{ -3}\leq x\leq1,\frac{\Delta y}{\Delta x}=\frac{-6+2}{2}=-2 \\ \\ it\text{ has a negative rate of change.} \end{gathered}[/tex]Required answer:
Option C
Find the final hourly wage if a $14.00 starting wage is increased by 5.5% each year for 10 years. The final hourly wage is $____Round your answer to the nearest cent.
Answer: $23.91
The exponential growth formula goes by:
[tex]y=a(1+r)^x[/tex]Where:
a = present value
r = rate
x = time
From the given, we know that:
a = $14.00
r = 5.5% = 0.055
x = 10
Substitute these to the equation:
[tex]\begin{gathered} y=a(1+r)^x \\ y=14.00(1+0.055)^{10} \\ y=23.9140 \\ y=23.91 \end{gathered}[/tex]I have the picture of the jersey and I will give it to you when we start :)
Print it :
$21 per jersey
x = number of jerseys
y = total cost
y= 21x
Top print
Setting up cost = $45
$18 per jersey
y= 45+18x
Equal both costs:
21x = 45 + 18x
Solve for x:
21x-18x =45
3x =45
x =45/3
x=15
when 15 jerseys are bought, both companies have the same cost.
If he bought more than 15 ( for example 20)
Print it = 21x = 21 (20)= 420
Top print = 45 +18 (20) = 405
Less than 15 jerseys ( ex: 10)
PRINT IT = 21 (10) = $210
TOP PRINT = 45+18(10) = $225
1.
When he buys more than 15 jerseys, he should choose TOP PRINT.
When he buys less than 15 jerseys, he should choose PRINT IT
2. set up one-off set up cost less than TOP PRINT = ex = 15
And a cost per shirt higher than TOP PRINT and less than PRINT IT = ex = 20 ( the slope value must be between 18 and 21 )
The head of public safety notices that the average driving speed at a particular intersection averages 35 mph with a standard deviation of 7.5 mph. After a school speed limit sign of 20 mph is placed at the intersection, the first 40 cars travel past at an average speed of 32 mph. Using the .01 alpha level, was there a significant change in driving speed?figure the effect size
First, we have to define the system of hypothesis
[tex]\begin{gathered} H_0\colon\mu=35 \\ H_a\colon\mu\ne35 \end{gathered}[/tex]Then, we find the statistic test value
[tex]\frac{\sqrt[]{n}\cdot(\bar{x}-\mu)}{\sigma}[/tex]It's important to know that this situation models a standard normal distribution.
Replacing the given information, we have
[tex]\frac{\sqrt[]{40}\cdot|32-35|}{7.5}=\frac{|-3|\cdot\sqrt[]{40}}{7.5}=2.5[/tex]This value allows us to deduct that the null hypothesis can't be rejected because the test statistic is not greater than 2.57583, it's equal. It's important to consider that this value refers to 0.5% of the distribution (two tales).
Hence, there's no significant evidence to reject the null hypothesis.Find the slope of the line between the points (3,-8)(2,-3)
Slope = -5
Explanations:The formula for calculating the slope of a line is expressed as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are the coordinates of the line.
Given the coordinates (3,-8) and (2,-3), the slope of the line is expressed as:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{-3-\left(-8\right)}{2-3} \\ m=\frac{-3+8}{-1} \\ m=\frac{5}{-1} \\ m=-5 \end{gathered}[/tex]Hence the slope of the line between the points (3,-8) and (2,-3) is -5
What is 280 decreased by 47.2 %? Round your answer to two decimal places if needed.
Given:
The original number given is 280.
Required:
The number is to be obtained by decreasing the original number by 47.2 %.
Explanation:
47.2% of the original number is calculated as,
[tex]\begin{gathered} 47.2\text{ \% of 280 = }\frac{47.2}{100}\times280 \\ 47.2\text{ \% of 280 = }\frac{47.2\times280}{100} \\ 47.2\text{ \% of 280 = 132.16} \end{gathered}[/tex]The new number obtained is calculated as,
[tex]\begin{gathered} New\text{ number = 280 - 132.16} \\ New\text{ number = 147.84} \end{gathered}[/tex]Answer:
Thus the number obtained by decreasing 280 by 47.2% is 147.84.
A twelve-sised die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number less than 4?
Explanation:
There are 3 posible outcomes with a number less than 4: 1, 2 & 3. This is the numerator
The total posible outcomes is 12. This is the denominator
Now we have to write and simplify the fraction:
[tex]\frac{3}{12}=\frac{1}{4}=0.25[/tex]Answer:
The probability of rolling a number less than 4 is 1/4
Each individual letter of the word Wisconsin is placed on a piece of paper, and all 9 pieces of paper are placed in a hat. If one letter is selected at random from the hat, find the probability that a consonant is selected.P(consonant)-(Type a fraction. Simplify your answer.)
GIVEN:
We are told that all the individual letters of the word WISCONSIN are placed on a piece of paper. Then all nine pieces of paper are placed in a hat.
Required;
Find the probability that a letter chosen at random is a consonant.
Step-by-step solution;
The probability of an event is given by the formula;
[tex]P[event]=\frac{number\text{ }of\text{ }required\text{ }outcomes}{number\text{ }of\text{ }all\text{ }possible\text{ }outcomes}[/tex]The number of all possible outcomes is the total number of letters that stands a chance of being selected, and that is 9. The number of required outcomes for this experiment is 6 (that is, 6 consonants).
Therefore, the probability of selecting a consonant by random is;
[tex]\begin{gathered} P[consonant]=\frac{6}{9} \\ \\ P[consonant]=\frac{2}{3} \end{gathered}[/tex]ANSWER:
The probability of selecting a consonant is;
[tex]P[consonant]=\frac{2}{3}[/tex]The seniors and juniors at sweet valley high school are going on a trip to Busch gardens. The seniors filled 12 Van's and 13 buses with 564 total students. The juniors filled 6 Van's and 13 buses with 492 students. How many students were in each van? in each bus?
The seniors and juniors at sweet valley high school are going on a trip to Busch gardens. The seniors filled 12 Van's and 13 buses with 564 total students. The juniors filled 6 Van's and 13 buses with 492 students. How many students were in each van? in each bus?
step 1
Seniors
Let
x -----> number of students in vans
y -----> number of students in bus
we have
12x+13y=564
Juniors
6x+13y=492
solve the system of equations
Solve by graphing
the solution is the intersection point both graphs
see the attached figure
the solution is the point (12,32)
therefore
In each Vans there are 12 students and in each bus there are 32 studentsWhat is the image of the point (4,0) after a rotation of 90° counterclockwise aboutthe origin?
To rotate a point 90º counterclockwise you have to invert the place fo the coordinates, for example:
(x,y) → (y,x)
Then you have to change the sign of the
use the function p=20g to find the value of p when g =8
To find the value of p when g = 8 you have to replace g = 8 into the equation, as follows
p = 20g
p = 20(8)
p = 160
some help and I need an answer asap explain it to me pls
a)
[tex]\begin{gathered} \frac{29}{4}\text{cups of yellow}\rightarrow\frac{29}{16}cups\text{ of blue } \\ 1\text{ yellow cup}\rightarrow\frac{29}{16}\div\frac{29}{4}=\frac{29}{16}\times\frac{4}{29}=\frac{4}{16}=\frac{1}{4}cups\text{ of blue paint} \end{gathered}[/tex]So therefore 1/4 cups of blue paint will be used for 1 cup of yellow paint.
b) So for this we will assume this relationship:
[tex]\begin{gathered} x=ky \\ \text{where k is the constant of proportionality:} \\ x=\frac{35}{8} \\ y=\frac{35}{2} \end{gathered}[/tex]So substituting the values of and y into the equation above:
[tex]\begin{gathered} \frac{35}{8}=k\times\frac{35}{2} \\ \frac{35}{8}\div\frac{35}{2}=k \\ \frac{1}{4}=k \\ \text{The constant of proportionality that relates the quantities x and y is:} \\ \frac{1}{4} \end{gathered}[/tex]how do u graph the solutions for b>5
Given
We have already used the number line on which we have represented numbers as points on a line.
For b>5
Study the diagram of circle L, where RS is tangent to circle L at point S.Also, RS = 24, RL = 26, and LS is a radius.What is the length of the radius, r?
From the figure given,
Where RS is perpedicular to the radius LS and L is the centre of the circle,
Given that
[tex]\begin{gathered} RS=24\text{ units} \\ RL=26\text{ units and } \\ LS=r\text{ units} \end{gathered}[/tex]The formula to find the value of r is the Pythagorean theorem, which is given as
[tex](\text{HYP)}^2=(OPP)^2+(\text{ADJ)}^2[/tex]Where
[tex]\begin{gathered} \text{HYP=RL}=26\text{ units} \\ OPP=RS=24\text{ units} \\ \text{ADJ=LS}=r\text{ units} \end{gathered}[/tex]Substitute the values into the formula of the Pythagorean theorem
[tex]\begin{gathered} (RL)^2=(RS)^2+(LS)^2 \\ 26^2=24^2+r^2 \\ 676=576+r^2 \\ \text{Collect like terms} \\ r^2=676-576 \\ r^2=100 \\ \text{Square root of both sides} \\ \sqrt[]{r^2}=\sqrt[]{100} \\ r=10\text{ units} \end{gathered}[/tex]Hence, the length of radius, r is 10 units
5. The custodians at school must sanitize all the desks in the building each night. If there are 3,500 desks in the entire school building and the custodians have cleaned 1,400 desks by the time Ms. Burlingame leaves at 3:30pm, what percent of the desks have the custodians cleaned?
The cleaned desks is 40%.
Given:
Total number of desks is, N = 3500.
Number of desks cleaned is, C = 1400.
The objective is to find the percentage of cleaned desks.
Consider the percentage as x.
Then, the equation can be represented as,
[tex]\begin{gathered} \frac{x}{100}\cdot3500=1400 \\ \frac{x}{100}=\frac{1400}{3500} \\ x=\frac{14}{35}\cdot100 \\ x=40 \end{gathered}[/tex]Hence, the percentage of cleaned desks is 40%.
Reny establishes a loan for an $8,000 vacation package to Transylvania. The vacation company charges 5.5% simple interest. Reny plans to pay back the loan over 1.5 years.How much interest will Reny pay?
SOLUTION
We are asked how much interest will Reny pay after getting a loan of $8,000 at an interest rate of 5.5% for 1.5 years
We will apply the simple interest formula
[tex]\begin{gathered} I=\frac{P\times R\times T}{100} \\ \text{Where I = interest } \\ P=\text{ principal, that is loan collected = 8,000} \\ R=\text{interest rate = 5.5\%} \\ T\text{ = time in years = 1.5 years } \end{gathered}[/tex]Substituting the values we have
[tex]\begin{gathered} I=\frac{P\times R\times T}{100} \\ I=\frac{8000\times5.5\times1.5}{100} \\ I=80\times5.5\times1.5 \\ I=660\text{ dollars } \end{gathered}[/tex]Hence, the answer is $660
Please solve the problem step by step, to check my final answers.
We are asked to determine the future value and the time for a quarterly compounded interest. To do that we will use the following formula:
[tex]A=P(1+\frac{r}{400})^{4t}[/tex]Where:
[tex]\begin{gathered} A=\text{ future value} \\ P=\text{ initial value} \\ r=\text{ interest rate} \\ t=\text{ time} \end{gathered}[/tex]Part A. We are asked to determine the time in 7 years. To do that we will substitute the value of "t = 7" and "r = 2", we get:
[tex]A=4000(1+\frac{2}{400})^{(4)(7)}[/tex]Solving the operations:
[tex]A=4599.49[/tex]Therefore, in 7 years there will be the amount of $4599.49
Part B. We are asked to determine the time to get the amount of $5000. To do that we will substitute the value of "A = 5000", and we get:
[tex]5000=4000(1+\frac{2}{400})^{4t}[/tex]Now, we solve for "t". First, we divide both sides by 4000:
[tex]\frac{5000}{4000}=(1+\frac{2}{400})^{4t}[/tex]Now, we take the natural logarithm to both sides:
[tex]\ln(\frac{5000}{4000})=\ln(1+\frac{2}{400})^{4t}[/tex]Now, we use the following property of logarithms:
[tex]\ln x^y=y\ln x[/tex]Applying the property we get:
[tex]\operatorname{\ln}(\frac{5,000}{4,000})=4t\operatorname{\ln}(1+\frac{2}{400})[/tex]Now, we divide both sides by the natural logarithm and by 4:
[tex]\frac{1}{4}\frac{\ln(\frac{5000}{4000})}{\ln(1+\frac{2}{400})}=t[/tex]Solving the operations:
[tex]11.19=t[/tex]Therefore, the amount of 5000 will be obtained after 11.19 years.
Which of the following is a continuous random variable?A. P = number of points scored by Stephen Curry in a gaB. T = winning time in the men's 100-meter dash at the 2016 Olympicsc. H = the number of hats sold on Tuesdayd. X = number of incoming flights at the local airport
A continuous random variable is a random variable where the data can take infinitely many values. For example, a random variable measuring the time taken for something to be done is continuous since there is an infinite number of possible times that can be taken.
Time has no specific integer of values and it is continuous, while the other variables like number of points, number of hats, number of incoming flights can have discrete values and as such are called a discrete variable
With this, we can therefore say that the correct option of an example of a continuous random variable will be
T= WINNING TIME IN THE 100-METER DASH AT THE 2016 OLYMPICS
THE CORRECT OPTION WILL BE OPTION B
can the given information be used to prove triangle ABC is congruent to triangle EDC explain your reasoning
SOLUTION:
Case: Congruence
Method:
Compare the triangles
[tex]\frac{15}{10}\equiv\frac{12}{8}\ne\frac{21}{12}[/tex]Final answer:
The scale factor is not consistent
Hence the given information cannot be used to prove triangle ABC is congruent to triangle EDC.
Which of the following would be a good name for the function that takes the pages in areading assignment and returns the time needed to ocomplete it A. Time(pages) B. Cost(time C. Time(cost) D. Pages(time) E Year(time) F Time(year)
A function is expressed as
f(
A rectangular swimming pool with a length of 18 meters and a width of 6 meters is surrounded by a concrete patio. The patio is a uniform 3 meters width around the entire pool. What is the area of the patio?
The area of the combined patio and swimming pool is
[tex]\begin{gathered} (18\text{ m}+3\text{ m})(6\text{ m}+3\text{ m}) \\ =(21\text{ m})(9\text{ m}) \\ =189\text{ m}^2 \end{gathered}[/tex]The area of the swimming pool is
[tex](18\text{ m})(6\text{ m})=108\text{ m}^2[/tex]Subtract the combined area to the area of the swimming pool and we get
[tex]189\text{ m}^2-108\text{ m}^2=81\text{ m}^2[/tex]Therefore, the area of the patio is 81 square meters.
I’m confused and stuck in these 4 questions. Can you please help me?
Answer:
1. 32.2 square inches (A)
2. 21.4 inches (H)
3. 14.5 inches (I)
4. 15.2 square inches (E)
AHIE
Explanation:
1. Given the diameter of the closed paint can's lid as 6.4 inches, the radius(r) will be;
[tex]\text{radius(r) }=\frac{Diameter}{2}=\frac{6.4}{2}=3.2\text{ inches}[/tex]We can now go ahead and determine the area(A) of the closed paint can's lid using the below formula;
[tex]A=\pi\cdot r^2=3.14\cdot(3.2)^2=3.14\cdot10.24=32.2in^2[/tex]So the area of the closed paint can's lid is 32.2 inches squared (A)
2. Given the radius of the closed paint can as 3.4 inches, the can's circumference(C) can be determined using the below formula;
[tex]C=2\pi r=2\cdot3.14\cdot3.4=21.4\text{ inches}[/tex]So the circumference of the can is 21.4 inches (H)
3. Given the diameter(d) of the open paint can as 4.6 inches, then we can determine its circumference(C) using the below formula;
[tex]C=\pi d=3.14\cdot4.6=14.5\text{ inches}[/tex]So the circumference of the open paint can is 14.5 inches (I)
4. Given the diameter(d) of the open paint can's lid as 4.4 inches, the radius(r) will be;
[tex]r=\frac{d}{2}=\frac{4.4}{2}=2.2\text{ inches}[/tex]We can go ahead and determine the area(A) of lid using the below formula;
[tex]A=\pi\cdot r^2=3.14\cdot(2.2)^2=3.14\cdot4.84=15.2\text{ squared inches}[/tex]So the area of the lid is 15.2 square inches (E)