Answer: x-intercept is (3/2, 0), y-intercept is (0, -3)
Step-by-step explanation:
Kira will run less than 29 miles this week. So far, she has run 12 miles. What are the possible numbers of additional miles she will run? Use t the number of additional miles she will run. Write your answer as an inequality solved for .
Answer:
t < 17
Step-by-step explanation:
If Kira has already run 12 miles and she will run less than 29 miles this week, then the total number of additional miles she will run is less than 29 - 12 = 17 miles. So, the inequality that represents the possible number of additional miles Kira will run is t < 17.
Starting at noon the temperature changed steadily at a rate of -0. 8°C every hour how many hours does it take for the temperature to change by -4. 4°C
Number of hours does it take for the temperature to change by -4. 4°C is 5.5 hours
To solve this problem, we can use the formula for finding the change in temperature
Change in temperature = rate of change × time
where the rate of change is -0.8°C per hour and the change in temperature we want to find is -4.4°C. So, we can plug in these values and solve for time
-4.4°C = (-0.8°C / hour) × time
Dividing both sides by -0.8°C / hour, we get
time = 5.5 hours
Therefore, it will take 5.5 hours for the temperature to change by -4.4°C.
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12' of framing materical can be used to make a rectangular window with a semicircle top. what are the dimensions for the largest area
The dimension for the largest area is 181 sq ft.
The rectangle has width. [tex]$w$[/tex] and height [tex]$h$[/tex],and let the radius of the semicircle be [tex]$r$[/tex]. We want to maximize the area [tex]$A$[/tex] of the window, which is given by:
[tex]A= 21 \pi r 2 +wh[/tex]
We also have the constraint that the total length of framing material is 12 feet:
[tex]2r+2w+h=12[/tex]
Solving this equation for [tex]$h$[/tex] we get:
[tex]h=12-2r-2w[/tex]
Substituting this expression for [tex]$h$[/tex] into the equation for [tex]$A$[/tex], we get:
[tex]A= 21 \pi r ^2+w(12-2r-2w)[/tex]
Expanding this expression, we get:
[tex]A= 21\pi r^2 +12w-2rw-2w^2[/tex]
To find the values of [tex]$r$[/tex], [tex]$w$[/tex], and [tex]$h$[/tex] that maximize[tex]$A$[/tex], we take the partial derivatives of [tex]$A$[/tex] with respect to each variable, set them equal to zero, and solve for the variables.
We get:
[tex]\partial r/\partial A=\pi r-2w=0 \Rightarrow r= 2w/\pi[/tex]
[tex]\partial w/\partial A=12-2r-4w=0 \Rightarroww= (6-r)/2= (6-2w/\pi)/2=3- w/\pi[/tex]
Substituting the expression for [tex]$w$[/tex] into the equation for [tex]$r$[/tex], we get:
[tex]r= 2/\pi (3-w/\pi )= 6/\pi - 2/\pi^2w[/tex]
Substituting these expressions for [tex]$r$[/tex] and [tex]$w$[/tex] into the equation for [tex]$h$[/tex], we get:
[tex]h=12-2r-2w=12- (4/\pi)w[/tex]
So the dimensions that maximize the area are:
[tex]w= \pi/2,r= 3\pi /4 ,h= (48-8\pi) / \pi[/tex]
The area of the window is:
[tex]A= (1/2)\pir^2 +wh= (1/2)\pi ( 3\pi/4)^2 + (\pi/2)\cdot (48-8\pi)/\pi = 9\pi/8+24-4\pi\approx 18.1 sq ft[/tex]
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Therefore, the dimensions of the largest area rectangular window with a semicircle top that can be made with 12' of framing material are approximately 1.55' * 3.38'. The maximum area is: Area = 4.82 square feet.
To find the dimensions for the largest area of a rectangular window with a semicircle top using 12' of framing material, we need to use optimization techniques.
Let's denote the width of the rectangular window as "w" and the height of the rectangular portion as "h". We also know that the semicircle top will have a radius equal to the width of the rectangular portion, so its diameter will be 2w.
The perimeter of the window is given by:
Perimeter = 2w + h +[tex]\pi w[/tex]
Since we have 12' of framing material available, we can write:
2w + h + [tex]\pi w[/tex] = 12
We can rearrange this equation to solve for h:
h = 12 - 2w - [tex]\pi w[/tex]
The area of the window is given by:
Area = w * h + 1/2 * [tex]\pi w^2[/tex]
Substituting the expression for h from the perimeter equation, we get:
Area = w(12 - 2w - [tex]\pi w[/tex]) + 1/2 * [tex]\pi w^2[/tex]
Expanding and simplifying, we get:
Area = 12w - [tex]2\pi w^2[/tex] - [tex]w^2[/tex]
To find the dimensions that maximize the area, we need to take the derivative of the area equation with respect to w and set it equal to zero:
d(Area)/dw = 12 - [tex]4\pi w[/tex] - 2w = 0
Solving for w, we get:
w = 12/(4\pi+2) ≈ 1.55'
Substituting this value back into the perimeter equation, we can find the height:
h = 12 - 2w - \piw ≈ 3.38'
Therefore, the dimensions of the largest area rectangular window with a semicircle top that can be made with 12' of framing material are approximately 1.55' * 3.38'. The maximum area is:
Area ≈ 4.82 square feet.
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Complete the statement. The ratio of MM'/MM" is x/3
The value of x is 1.
What is a line segment?
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Here, we have
Given:
The ratio of MM'/MM" is x/3.
We have to find the value of x.
MM' = 3 blocks
MM" = 9 blocks
MM'/MM" = 3/9 = 1/3 = x/3
x = 1
Hence, the value of x is 1.
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this table lists the lengths, to the nearest inch, of a random sample of 21 2121 brown bullhead fish. the outlier measurement of 24 2424 inches is an error. of the mean, median, and range of the values listed, which will change the most if the 24 2424-inch measurement is removed from the data?
The range will change the most, if the 24-inch measurement is removed from the data.
The correct answer is an option (c)
Consider the table with outlier 24.
The mean of this sample of 21 brown bullhead fish would be,
x₁ = (8 + (3 × 9) + (2 × 10) + (2 × 11) + (4 × 12) + (3 × 13) + (2 × 14) + (2 × 15) + 16 + 24) / 21
x₁ = 262/21
x₁ = 12.476
And the median would be,
m₁ = 12
And the range would be,
R₁ = 24 - 8
R₁ = 16
If we remove outlier 24 then,
mean x₂ = 11.9
median m₂ = 12
range R₂ = 16 - 8
= 8
Therefore, the range will change the most.
The correct answer is an option (c)
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The complete question is:
The table lists the lengths, to the nearest inch, of a random sample of 21 brown bullhead fish. The outlier measurement of 24 inches is an error. Of the mean, median, and range of the values listed, which will change the most if the 24-inch measurement is removed from the data?
a) mean
b) median
c) range
d) They will all change by the same amount.
the poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.truefalse
The Poisson distribution is applied to events where the probability of occurrence of a certain number of events in a fixed interval of time, space, or distance is small but not necessarily "very small". False.
The Poisson distribution is used to model events that occur randomly and independently over a continuous or discrete interval of time, space, or distance, such as the number of phone calls received at a call center in an hour, the number of cars passing through a toll booth in a given time period, or the number of emails received per day. The Poisson distribution is characterized by a discrete probability mass function that describes the probability of a certain number of events occurring in a given interval, and it is widely used in probability theory and statistics for modeling events with low to moderate occurrence rates.
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The poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.
Given statement is False.
Because, The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is not necessarily very small, but rather where the events occur randomly and independently at a constant average rate.
The Poisson distribution models the number of events that occur in a fixed time interval or within a certain area or volume of space, assuming that the events occur independently of each other and at a constant average rate. It is used in many fields, such as biology, physics, economics, and engineering, to model the occurrence of rare or common events.
The Poisson distribution has several important properties, including:
Its mean is equal to λ, and its variance is also equal to λ.
It is a discrete distribution, meaning that it models only whole numbers of events.
It is often used to model rare or unusual events, but can also be used for events that occur frequently, as long as they occur independently at a constant average rate.
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How much more energetic was the Tohoku earthquake? (Give your answer as a ratio of the energies. )
So the Tohoku earthquake was about 2.25 times more energetic than the Northridge earthquake.
What is earthquake?An earthquake is a shaking or trembling of the earth's crust caused by the sudden release of energy in the Earth's lithosphere, usually by the movement of tectonic plates or by volcanic activity. Earthquakes can cause significant damage to buildings and infrastructure, trigger landslides and tsunamis, and have other destructive consequences. They are one of the most powerful and unpredictable natural phenomena on the planet.
In the given question,
The Tohoku earthquake had an energy release equivalent to about 3.6 x 10¹⁴ joules, while the Northridge earthquake had an energy release equivalent to about 1.6 x 10¹⁴ joules. Therefore, the ratio of the energies is:
Tohoku earthquake energy / Northridge earthquake energy = (3.6 x 10¹⁴J) / (1.6 x 10¹⁴ J) = 2.25
So the Tohoku earthquake was about 2.25 times more energetic than the Northridge earthquake.
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How will the mean be affected if 68 is added to the data set below?
58,60,62,64,66
A.
The mean will increase by 5.
B.
The mean will increase by 1.
C.
The mean will not change.
D.
The mean will decrease by 1.
Answer:
b
Step-by-step explanation:
in order to find the mean you have find the sum of the numbers and divide them by the amount of numbers.without 68 the sum is 310 divide it by 5 and tge answer is 62.however if you add 68 the sum is 378 divide it by 6 and the answer is 63.
therefore the answer increased by 1.
hope this helps :)
Joey deposits $6000 each into the two savings accounts described below. If he doesn’t make any other deposits or withdrawals, find the combined amount of accounts after 10 years.
Account 1
3.5% annual simple interest
Account 2
3.5% annual compound interest
The combined amount in both accounts after 10 years is $16,869.58
What is formula of simple interest and compound interest ?To solve the problem, we need to use the following formulas:
Simple Interest = Principal x Rate x Time
Compound Interest = [tex]Principal * (1 + Rate/ n)^{n * Time}[/tex]
where:
Principal = the initial deposit
Rate = the interest rate (in decimal form)
Time = the number of years
n = the number of times interest is compounded per year
For Account 1:
Simple Interest = Principal x Rate x Time
= $6000 x 0.035 x 10
= $2100
The amount in Account 1 after 10 years will be the initial deposit plus the interest earned:
= $6000 + $2100
= $8100
For Account 2:
Since the interest is compounded annually, n = 1.
Compound Interest = [tex]Principal * (1 + Rate/ n)^{n * Time}[/tex]
= [tex]6000 *(1 + 0.035/1)^{1 * 10}\\= $6000 (1.035)^{10}\\= $8769.58[/tex]
After ten years, the amount in Account 2 will be $8769.58.
After ten years, the combined amount in both accounts will be:
$8100 minus $8769.58 equals $16869.58, resulting in a total of $16,869.58 in both accounts after ten years.
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Distance between (7,-2) and (-1,-1)
Answer: The distance formula between two points (x1, y1) and (x2, y2) is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the distance between (7, -2) and (-1, -1):
d = sqrt((-1 - 7)^2 + (-1 - (-2))^2)
= sqrt((-8)^2 + (1)^2)
= sqrt(64 + 1)
= sqrt(65)
Therefore, the distance between (7, -2) and (-1, -1) is sqrt(65), or approximately 8.06 units.
Step-by-step explanation:
how to solve Systems of equations with substitution: -3x-4y=-2 & y=2x-5
PLEASE HELPPP I NEED THIS BEFORE TW BY 11:59 PLSSSSSSSSSSSSS HELPPPPPPPP
Answer:
5x+20
Step-by-step explanation:
you are given that y=2x-5 so you can substitue that for the y value.
-3x-4(2x-5) is your new equation. You can further simply it and you will get:
-3x+8x+20
5x+20
a machine that is programmed to package 1.30 pounds of cereal is being tested for its accuracy in a sample of 43 cereal boxes, the sample mean filling weight is calculated as 1.32 pounds. the population standard deviation is known to be 0.06 pounds. find the 95% confidence interval for the mean.
The 95% confidence interval for the mean filling weight of the cereal boxes is (1.300, 1.340) pounds.
To find the 95% confidence interval for the mean filling weight of the cereal boxes, we can use the formula
CI = x ± z × (σ/√n)
where:
x = sample mean filling weight = 1.32 pounds
σ = population standard deviation = 0.06 pounds
n = sample size = 43
z = z-score corresponding to the desired level of confidence (95% in this case)
To find the z-score, we can use a standard normal distribution table or calculator. For a 95% confidence level, the z-score is 1.96.
Plugging in the values, we get
CI = 1.32 ± 1.96×(0.06/√43)
CI = 1.32 ± 0.020
Therefore, the 95% confidence interval for the mean filling weight of the cereal boxes is (1.300, 1.340) pounds. This means that we can be 95% confident that the true population mean filling weight falls within this range.
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a study was conducted to determine if drinking a cup of tea before bedtime helped with falling asleep faster. after randomly assigning 50 people to one group that received tea before bedtime and 50 other people to a group that did not receive tea before bedtime, the researcher then compared the amount of time it took for each person to fall asleep. what is the explanatory variable? the 50 individuals in both groups the amount of time it took to fall asleep if a subject received tea and how long it took for that individual to fall asleep if subject received tea
The explanatory variable is whether or not a subject received tea before bedtime.
The theory behind this study is that drinking tea before bedtime may help with falling asleep faster.
Participants were randomly assigned to one group that received tea before bedtime and the other group that did not receive tea before bedtime.
The researcher then monitored the amount of time it took for each person to fall asleep.
The explanatory variable of this study is whether or not a subject received tea before bedtime, and the goal is to compare the amount of time it takes for each person to fall asleep depending on if they received tea before bedtime.
The results of this study will help determine if drinking tea before bedtime is an effective way to fall asleep faster.
The goal is to test whether or not this is true by comparing the amount of time it takes for each person to fall asleep depending on if they received tea before bedtime.
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Calculate the slope of the line between pairs of points in each of the tables to determine which table represents a linear function? A. B. C. D.
Answer:
Table D represents the linear function
y = x + 1.
Please help me with this homework
Answer: Area = 144 π cm²
Step-by-step explanation:
We can use this formula to find the area of a circle:
➜ r is equal to the radius, also known as half the width of a circle.
A = πr²
We will substitute our known values and solve for C by multiplying. Since the answer option includes π in our units, we do not multiply this into the 144.
A = πr²
A = π(12)²
A = 144 π cm²
a number g multiplied by 67
Answer:
67g
Step-by-step explanation:
the correct form of g multiplied by 67 is 67g
a sample consists of n observations which are sorted into k frequency bins. what is the degrees of freedom for a chi-square goodness-of-fit test?
For a chi-square goodness-of-fit test with n observations sorted into k frequency bins, the degrees of freedom are equal to (k - 1).
The degrees of freedom for a chi-square goodness-of-fit test in this scenario would be (k-1) since there are k frequency bins and the total frequency is fixed (n). The chi-square test compares the observed frequencies with the expected frequencies in each bin, and the difference between these frequencies is used to calculate the test statistic. The degrees of freedom determine the critical value of the test statistic and are based on the number of independent pieces of information used to estimate the expected frequencies.
Hi! I'd be happy to help you with your question. In a chi-square goodness-of-fit test, the degrees of freedom can be calculated using the given terms: observations, frequency, and chi-square. Here's the step-by-step explanation:
1. You have a sample consisting of n observations.
2. These observations are sorted into k frequency bins.
3. The chi-square goodness-of-fit test is used to determine how well the observed frequencies match the expected frequencies.
To calculate the degrees of freedom for this test, use the following formula:
Degrees of freedom = (k - 1)
Where k is the number of frequency bins.
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The degrees of freedom (df) for a chi-square goodness-of-fit test in this scenario is k-1.
The chi-square goodness-of-fit test is used to test whether a set of observed frequencies fits a theoretical distribution.
The observed frequencies are sorted into k bins.
The test statistic is calculated by comparing the observed frequencies to the expected frequencies under the theoretical distribution, and summing the squared differences divided by the expected frequencies.
The degrees of freedom for the chi-square goodness-of-fit test is calculated as (k-1), where k is the number of frequency bins.
This is because once we have chosen the observed frequencies for k-1 of the bins, the frequency for the last bin is completely determined by the total number of observations and the frequencies in the other k-1 bins.
So, we only have (k-1) degrees of freedom to choose the observed frequencies independently.
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Using the graph, determine the coordinates of the vertex of the parabola.
Based on the information given, the vertex of the parabola can be found using the coordinates of the turning point (also known as the vertex).
What is the explanation for the above response?The vertex is located at (4,-4), which means that the value of x is 4 and the value of y is -4. Therefore, the coordinates of the vertex are (4,-4).
The fact that the curve is on the upper and lower quadrants of the right side of the cartesian coordinate system suggests that the parabola opens upwards.
Also, since the curve meets the x-axis at two points, this indicates that the parabola intersects the x-axis at those two points, which are (2,0) and (6,0).
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Joe solved the equation 3+x/2=10 and justified each step as shown.
Explain in words Joe’s error and fix his mistake.
Step Justification
3+x/2=10 Given equation
x/2=7 Multiplication Property of Equality
x = 14 Subtraction Property of Equality
The correct solution for the given equation is x = 17.
What is distributive property?The distributive property is a mathematical property that relates multiplication and addition or subtraction. It states that multiplying a number by a sum (or difference) is equivalent to multiplying the number by each term of the sum (or difference) and then adding (or subtracting) the results.
According to question:Joe's error is due to not using the order of operations correctly. In step 2, he did not use parentheses to isolate the x term before dividing by 2. Instead, he divided both 3 and x by 2, resulting in x/2 = 7.
To fix Joe's mistake, we need to apply the distributive property by adding parentheses around the numerator of the left-hand side of the equation, like this:
(3 + x)/2 = 10
Then we can multiply both sides by 2 to eliminate the fraction:
3 + x = 20
Finally, we can solve for x by subtracting 3 from both sides:
x = 17
Therefore, the correct solution is x = 17.
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John has 10 ribbons, each measured 3 ½ inches long. How long are the 10 ribbons placed end to end?
The total length of all 10 ribbons is 35 inches when they are placed end to end.
What are inches?Inches are a unit of length in the imperial system of measurement, which is primarily used in the United States, the United Kingdom, and some other countries. One inch is equal to 1/12 of a foot or 2.54 centimeters.
The inch is commonly used to measure the length or distance of small objects, such as the size of a computer screen, the length of a pencil, or the height of a person. Inches are also used to measure the dimensions of larger objects, such as the width of a door or the size of a piece of furniture.
According to the given informationIf John has 10 ribbons, each measuring 3 ½ inches long, we can find the total length of all the ribbons by multiplying the length of one ribbon by the number of ribbons:
Total length = 10 × 3 ½ inches
To multiply a whole number and a mixed number, we can first convert the mixed number to an improper fraction, then multiply:
Total length = 10 × (7/2) inches
Total length = 35 inches
Therefore, the 10 ribbons, placed end to end, would be 35 inches long.
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Find the value of x .
J
30°
M
to
K
(2x - 30)°
[
The value of x in the Intersecting chords is 15
Finding the value of x .From the question, we have the following parameters that can be used in our computation:
Intersecting chords
The value of x is then calculated as
x = 1/2(30 - 2x + 30)
So, we have
2x = 30 - 2x + 30
Evaluate the like terms
4x = 60
Divide
x = 15
Hence, the value of x is 15
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which of the following null hypothesis statistical tests require calculating degrees of freedom? group of answer choices all of the above two-sample t-test chi-squared one-sample t-test
The two null hypothesis that are correct answer are two-sample t-test and one-sample t-test.
Among the group of answer choices provided, the tests that require calculating degrees of freedom are the two-sample t-test and the one-sample t-test. Both of these tests belong to the t-test family and involve using degrees of freedom to determine the critical t-value.
In summary:
- Null hypothesis: The assumption that there is no significant difference between the sample and population or between two samples.
- T-test: A statistical test used to determine if there is a significant difference between the means of two groups or between a sample and population mean.
- Degrees of freedom: A value used in statistical tests that represents the number of independent values in a data set, which can affect the outcome of the test.
So answer is: two-sample t-test and one-sample t-test.
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The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-
sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also
requires degrees of freedom, but it is not a test for a null hypothesis.
The correct answer is: all of the above.
All these tests require calculating degrees of freedom:
1. Two-sample t-test:
Degrees of freedom are calculated using the formula (n1 + n2) - 2, where n1 and n2 are the sample sizes of the two
groups being compared.
2. Chi-squared test:
Degrees of freedom are calculated using the formula (rows - 1) * (columns - 1), where rows and columns represent the
number of categories in the data.
3. One-sample t-test:
Degrees of freedom are calculated using the formula n - 1, where n is the sample size.
The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-
sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also
requires degrees of freedom, but it is not a test for a null hypothesis.
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Indicate the method you would use to prove the two triangles congruent if new method applies, enter none. SSS, ASA, AAS, SAS, none.
The two triangles are congruent based on the ASA Congruence Postulate.
What is the ASA Congruence Postulate?The ASA Congruence Postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
The image shown above shows two triangles that has three pairs of congruent triangles and a pair of corresponding congruent sides.
Therefore, both triangles are congruent by the ASA Congruence Postulate.
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10. Sarah has a new job of slicing and
stocking the lunchmeat in a deli case.
She keeps track of how many pounds
she puts in the case, while her manager
keeps track of the number of pounds
they sell from the case.
Sarah's List
6
10.60
Day
143.46 1
2
3
bropez
10
bro
Day
Number of Pounds
Added to Case
0.5
10
0.5
10de
2
erit
aby
List ole qu zmlwz
Manager's List
Number of Pounds Soldot
exom S
from Case
wan 11 svib ed EdW
24/4
3
If there were 12 pounds in the case
when Sarah started on Day 1, how
many pounds will be in the case at the
start of Day 4?
The total number of pounds in the case at the start of Day 4 would be 12.50 pounds found by using an arithmetic operation.
What is the arithmetic operation?Arithmetic operations refer to the basic mathematical operations used to perform calculations involving numbers. These operations include Addition, Subtraction, Multiplication, Division, Exponential, Modulo.
According to the given information:
Based on the information provided, Sarah's list shows the number of pounds she added to the deli case each day. According to her list:
Day 1: 6 pounds
Day 2: 10.60 pounds
Day 3: 0.5 pounds
So the total number of pounds Sarah added to the case from Day 1 to Day 3 is 6 + 10.60 + 0.5 = 17.10 pounds.
Since Sarah's manager's list shows the number of pounds sold from the case each day, and no information about the pounds sold on Day 4 is given, we can assume that no pounds were sold on Day 4.
Therefore, at the start of Day 4, the total number of pounds in the case would be the initial 12 pounds plus the pounds added by Sarah on Day 3, which is 0.5 pounds. So the total number of pounds in the case at the start of Day 4 would be 12 + 0.5 = 12.50 pounds.
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For the function 8-(x-3)^2,
state the domain
The domain of the function 8 - [tex](x-3)^{2}[/tex] is R which is all the real numbers.
What is domain of a function?
The set or grouping of all potential values that may be used in the function is known as the domain.
We are given a function as 8 - [tex](x-3)^{2}[/tex].
Now, in order to find the domain, we need to find the values where the function is not defined for a value of x.
But, there is no such value for x where the function is not defined.
This means that all values of x give an output.
So, the domain is the set of all the real numbers.
Hence, the domain of the given function is R.
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What is the answer and how do I get there?
The value of the missing side length is 2√6. Option C
How to determine the value
We have that the six trigonometric identities are;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
Using the tangent identity,
tan 60 = 6√6/y
find the value
y = 6√6 /√3
Using the sine identity
sin 45 = 6√6 /√3/x
sin45 =6√18/3 × 1/x
√2/2x = 6√18/3
x = 2√18/√2
x = 2√36
x = 2√6
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a plane cuts through a sphere with diameter 20 cm, but the closest it gets to the center is 3 cm. what is the area of the intersection of the sphere and the plane in sq cm?
The area of the intersection of the sphere and the plane in sq cm is 286.46 square centimeters.
The sphere is divided into two equal halves by the plane. The closest point on the plane is 3 cm away from the sphere's center. As a result, a right triangle is formed, with one leg equal to the sphere's radius and the other to the sphere's radius from the plane.
We may calculate the radius of the sphere using the Pythagorean theorem:
r^2 = (20/2)^2 - 3^2
r = sqrt(91) 9.54 cm and r2 = 91
A circle with a radius of 9.54 cm forms the point where the sphere and the plane cross. Its area is therefore: A = r2 A = (9.54)2 A 286.46 sq cm.
The sphere and plane's intersection therefore has a surface area of about 286.46 square centimeters.
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Establishing causality is often a main focus of statistical studies. What is the best type of study to conduct to establish causality? Use the situation in this task to support your answer.
The best type of study to establish causality is a randomized controlled experiment.
What is the best type of study to conduct to establish causality?In this type of study, participants are randomly assigned to different groups, and at least one group is given a specific treatment or intervention, while the other group(s) serve as a control group. By randomly assigning participants to groups, researchers can control for potential confounding variables that could impact the results.
For example, let's say we want to determine if a new medication reduces blood pressure. In a randomized controlled experiment, we could randomly assign some participants to receive the medication and others to receive a placebo. This would allow us to compare the effects of the medication on blood pressure to the effects of the placebo, while controlling for other variables that could impact blood pressure.
In contrast, observational studies, such as cohort studies or case-control studies, can only establish correlations between variables, not causation. This is because researchers do not have control over the variables being studied, and there may be other factors that are influencing the relationship between the variables.
Therefore, to establish causality, a randomized controlled experiment is the best type of study to conduct.
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A chef used some bouillon cubes when making chicken noodle soup. The volume of each of the bouillon cubes was 1/27
cubic inch. How long was an edge of one of the bouillon cubes that the chef used?
Answer: 1/3
Step-by-step explanation:
1/3x1/3x1/3=1/27
Which of the following functions is graphed below?
Note that the function that is graphed below is y = x + 7.
What is the explanation for the above response?The equation y = x + 7 represents a linear function, where x is the independent variable and y is the dependent variable.
It has a slope of 1, which means that for every unit increase in x, y increases by 1. The y-intercept is 7, which is the value of y when x is zero. This equation can be graphed as a straight line on a coordinate plane, with a positive slope and y-intercept of (0, 7).
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