The price at which twenty percent of the BBQs would cost more is $542 and it follows a normal distribution.
In this case, we are given that the price of BBQs at a large hardware store follows a normal distribution with a mean of $500 and a standard deviation of $50. We want to find the price at which twenty percent of the BBQs would cost more.
To solve this problem, we need to find the value, denoted as x, for which 20% of the BBQs are priced higher. This can be done by finding the z-score corresponding to the 20th percentile and then converting it back to the original scale.
The z-score is calculated using the formula:
z = (x - μ) / σ,
where μ is the mean and σ is the standard deviation.
To find the z-score corresponding to the 20th percentile, we can use a standard normal distribution table or a statistical calculator. The z-score corresponding to the 20th percentile is approximately -0.84.
Now we can use the z-score to find the corresponding value in the original scale:
-0.84 = (x - 500) / 50.
Solving for x, we get:
-0.84 * 50 = x - 500,
-42 = x - 500,
x = 500 - 42,
x = 458.
So, twenty percent of the BBQs would cost more than $458. However, since we need to choose from the given options, the closest price to $458 is $459.
Therefore, the answer is $459.
To know more about normal distribution, refer here:
https://brainly.com/question/31327019#
#SPJ11
a pair of dice is rolled, and the number that appears uppermost on each die is observed. refer to this experiment and find the probability of the given event. (enter your answer as a fraction.)
If a pair of dice is rolled, and the number that appears uppermost on each die is observed, the probability of the sum of the numbers being either 7 or 11 is 2/9.
To find the probability of the sum of the numbers rolled on a pair of dice being either 7 or 11, we need to determine the number of favorable outcomes and the total number of possible outcomes.
There are six possible outcomes for each die, ranging from 1 to 6. Since we are rolling two dice, the total number of possible outcomes is 6 multiplied by 6, which is 36.
To calculate the number of favorable outcomes, we need to determine the combinations that result in a sum of either 7 or 11.
For the sum of 7, there are six possible combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).
For the sum of 11, there are two possible combinations: (5, 6) and (6, 5).
Therefore, the number of favorable outcomes is 6 + 2 = 8.
The probability of the sum of the numbers being either 7 or 11 is given by the ratio of favorable outcomes to the total number of outcomes:
P(sum is 7 or 11) = favorable outcomes / total outcomes = 8/36 = 2/9.
To learn more about probability click on,
https://brainly.com/question/14536671
#SPJ4
Complete question is:
A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)
The sum of the numbers is either 7 or 11.
I need help quick please
i’ll tell you on discord, add me there my user is ri#0511
Answer: 0.1562 I believe
Can you give me the answer to this
Answer: I think A
Step-by-step explanation:
Let a € (-1,1). Evaluate TT cos 20 de. 1-2a cos 0 + a2 d0
The value of the given integral is 2π [sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) (1/2) [sin(22e)/22 + sin(18e)/18] + C]
To evaluate the given expression:
∫∫ cos(20e) (1 - 2a cos(e) + a²) de dθ
We need to integrate with respect to both e and θ.
First, let's integrate with respect to e:
∫ cos(20e) (1 - 2a cos(e) + a²) de
Using the power reduction formula for cosine, we can rewrite the integrand:
= ∫ cos(20e) (1 - a² + a² cos²(e) - 2a cos(e)) de
= ∫ cos(20e) (1 - a² - a² sin²(e)) de
Now, we can integrate term by term:
= ∫ cos(20e) de - a² ∫ cos(20e) sin²(e) de - a² ∫ cos(20e) de
The first and third integrals are straightforward to evaluate:
= ∫ cos(20e) de - a² ∫ cos(20e) de - a² ∫ cos(20e) sin²(e) de
= sin(20e) - a² sin(20e) - a² ∫ cos(20e) sin²(e) de
Now, let's evaluate the remaining integral with respect to e:
= sin(20e) - a² sin(20e) - a² ∫ cos(20e) sin²(e) de
Using the trigonometric identity sin²(e) = (1 - cos(2e))/2, we can simplify the integrand:
= sin(20e) - a² sin(20e) - a² ∫ cos(20e) ((1 - cos(2e))/2) de
= sin(20e) - a² sin(20e) - (a²/2) ∫ cos(20e) - cos(20e) cos(2e) de
= sin(20e) - a² sin(20e) - (a²/2) ∫ cos(20e) de + (a²/2) ∫ cos(20e) cos(2e) de
Integrating the first term gives:
= sin(20e) - a² sin(20e) - (a²/2) ∫ cos(20e) de + (a²/2) ∫ cos(20e) cos(2e) de
= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) ∫ cos(20e) cos(2e) de
Next, let's evaluate the remaining integral with respect to e:
= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) ∫ cos(20e) cos(2e) de
Using the trigonometric identity cos(a) cos(b) = (1/2) [cos(a + b) + cos(a - b)], we can simplify the integrand:
= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) ∫ (1/2) [cos(20e + 2e) + cos(20e - 2e)] de
= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) (1/2) [∫ cos(22e) de + ∫ cos(18e) de]
= sin(20e) - a² sin(20e) - (a²/2) sin(20e) + (a²/2) (1/2) [sin(22e)/22 + sin(18e)/18] + C
where C is the constant of integration.
Now, we have the integral with respect to e evaluated. To find the final result, we need to integrate with respect to θ. However, we don't have any dependence on θ in the original expression. Therefore, we can simply multiply the result obtained above by 2π, as we're integrating over the entire range of θ.
To know more about integral, refer to the link below:
https://brainly.com/question/31059545#
#SPJ11
Complete question:
A filing cabinet is 2 yards long by 2 feet wide by 48 inches high. What is the volume of the filing cabinet in cubic inches? Enter your answer in the box.
Answer:
82944 in^3
Step-by-step explanation:
Volume = length x breadth x height
Before volume can be calculated, feet and yards needs to be converted to inches
1 yard = 36 inches
2 x 36 = 72 inches
1 foot = 12 inches
2 x 12 = 24 inches
Volume = 72 x 48 x 24 = 82944 in^3
Using the Excel file Weddings, apply the Excel Regression tool using the wedding cost as the dependent variable and attendance as the independent variable. Interpret all key regression results, hypothesis tests, and confidence intervals in the output. Analyze the residuals to determine if the assumptions underlying the regression analysis are valid. Use the standard residuals to determine if any possible outliers exist. If a couple is planning a wedding for 175 guests, how much should they budget?
Using the Excel Regression tool on the Weddings dataset with wedding cost as the dependent variable and attendance as the independent variable, the key regression results, hypothesis tests, and confidence intervals should be interpreted.
After applying the Excel Regression tool with wedding cost as the dependent variable and attendance as the independent variable, the key regression results should be examined. These results typically include coefficients, standard errors, t-values, p-values, and confidence intervals. The coefficient for the independent variable (attendance) represents the estimated change in the wedding cost for each unit increase in attendance. Hypothesis tests and confidence intervals help assess the statistical significance and precision of the estimated coefficients. The t-value indicates the strength of evidence against the null hypothesis of no relationship between the variables, and the p-value indicates the probability of observing the estimated coefficient under the null hypothesis. Lower p-values suggest stronger evidence against the null hypothesis. To validate the assumptions of the regression analysis, the residuals (the differences between the observed and predicted values) should be analyzed. Residual plots can be examined to check for patterns or deviations from assumptions, such as linearity, independence, and constant variance. Outliers can be identified by examining the standardized residuals. Values with high absolute values indicate potential outliers. To estimate the budget for a wedding with 175 guests, the regression model can be used to predict the corresponding cost. The attendance value of 175 can be plugged into the regression equation, and the predicted wedding cost can be obtained.
To know more about regression here: brainly.com/question/32505018
#SPJ11
6р + 22 – 10
Help me please
Answer:
P = -2
Step-by-step explanation:
6p +22 =10
-22 -22
6p= -12
6 6
p= -2
Im pretty sure thats it.
if you want to be 99onfident of estimating the population mean to within a sampling error of ±3 and the standard deviation is assumed to be 14, what sample size is required?
The sample size required is_________
The sample size required is 357.
Here's how to solve the problem:
Given that we need to be 99% confident of estimating the population mean to within a sampling error of ±3.
So, the margin of error (E) = 3 z-score for 99% confidence level = 2.58 (from standard normal distribution table)
The formula for sample size is:n = [z² * σ²] / E²
Where, n = sample size, σ = standard deviation of the population,
E = margin of error, and z = z-score
For a 99% confidence level, the z-score = 2.58
Substitute the given values in the formula:n = [2.58² * 14²] / 3²= 357.15≈ 357
Therefore, the sample size required is 357.
To know more about the sample size visit:
https://brainly.in/question/21388207?
#SPJ11
Which of the following is typical of the starting work geometry in sheet metal processes: (a) high volume to area ratio or (b) low volume to area ratio?
The correct answer is (b) low volume to area ratio is typical of the starting work geometry in sheet metal processes.
Explanation: Sheet metal processing is the method of shaping metal objects to create complex shapes and designs.
Cutting, punching, stamping, and forming are the most common sheet metal processes.
The workpiece's original shape and size are critical considerations in sheet metal processing.
The workpiece's geometry plays an important role in sheet metal processes.
The term volume-to-area ratio refers to the quantity of metal in a part divided by the surface area of that part.
The ratio is low in the case of sheet metal processing. Sheet metal workpieces have a high surface area-to-volume ratio.
This is due to the fact that sheet metal workpieces are often quite thin.
Because of this, sheet metal workpieces are lightweight.
Furthermore, thin sheets are more pliable and can be easily formed into various forms.
This geometry is ideal for sheet metal work since it allows for greater flexibility during processing.
In sheet metal processing, low volume-to-area ratios are typical of the starting work geometry.
Visit here to learn more about ratio brainly.com/question/13419413
#SPJ11
The null hypothesis is that 30% people are unemployed in Karachi city. In a sample of 100 people, 35 are unemployed. Test the hypothesis with the alternative hypothesis is not equal to 30%. What is the p-value?
After testing hypothesis with alternative-hypothesis is not equal to 30%, the p-value is 0.278.
To test the hypothesis that proportion of unemployed people in Karachi city is not equal to 30%, we perform a two-tailed test using binomial distribution.
The null-hypothesis (H₀) is that the proportion of unemployed people is 30% (p = 0.30), and the alternative-hypothesis (H₁) is that the proportion is not equal to 30% (p ≠ 0.30),
We have a sample of 100 people, and 35 of them are unemployed. we will calculate "test-statistic" "z-score" and use it to find p-value,
The "test-statistic" formula for "two-tailed" test is :
z = (p' - p₀)/√((p₀ × (1 - p₀))/n),
where p' = sample proportion, p₀ = hypothesized-proportion under the null-hypothesis, and n = sample-size,
In this case, p' = 35/100 = 0.35, p₀ = 0.30, and n = 100,
Calculating the test statistic:
z = (0.35 - 0.30)/√((0.30 × (1 - 0.30)) / 100)
= 0.05/√((0.30 * 0.70) / 100)
≈ 0.05/√(0.21 / 100)
≈ 0.05/√(0.0021)
≈ 0.05/0.0458258
≈ 1.0905
To find the p-value, we calculate probability of obtaining "test-statistic" as extreme as 1.0905 in a two-tailed test.
We know that the cumulative-probability (area) to left of 1.0905 is approximately 0.861.
Since this is a two-tailed test, we double this probability to get "p-value":
So, p-value = 2 × (1 - 0.861),
= 2 × 0.139,
= 0.278
Therefore, the p-value for hypothesis test is 0.278.
Learn more about P Value here
https://brainly.com/question/28197808
#SPJ4
shoes
11 cm
8.8 cm
18.4 cm
Evaluate for f(8), show all your work: f(x)=x2+10
Answer:
[tex]f(8)=74[/tex]
Step-by-step explanation:
[tex]f(8)=8^2+10=64+10=74[/tex]
Determine an expression for dy/d x = y' if [1+y]²-x+y=4 10.
The integration method you must use here is
Logarithmic q_23 = 1 Implicit q_23 = 2 Product rule q_23 = 3
The simplified expression for y' = 1/q_24y + q_25
The required expression is: y' = (1/2)(1-y)/(1+y)
Given [1 + y]² - x + y = 4 10. We need to determine an expression for dy/dx = y'.
Simplification of the given expression:
[1 + y]² + y - 4 10 = x
Differentiating w.r.t x by using the chain rule, we get:
(2[1 + y])*(dy/dx) + dy/dx + 1 = 0
(dy/dx)[2(1 + y) + 1] = - 1 - [1 + y]²
(dy/dx) = [- 1 - (1 + y)²]/[2(1 + y)]
The given expression is [1+y]²-x+y=4 10. We need to determine an expression for dy/d x = y'.
Differentiating the given equation with respect to x, we get:
2(1+y).dy/dx - 1 + dy/dx = 0
dy/dx(2+2y) = 1 - y(2+dy/dx)
dy/dx(2+2y) = (1-y)(2+dy/dx)
dy/dx = (1-y)/(2+2y)
dy/dx = (1/2)(1-y)/(1+y)
Hence, the required expression is: y' = (1/2)(1-y)/(1+y)
Learn more about chain rule here:
https://brainly.com/question/31585086
#SPJ11
Consider the first three terms of the sequence below.
14000, 12600, 11340
Complete a recursively-defined function to describe this sequence.
f(1) = _____
f(n) = f(n - 1) · ___, for n ≥ 2
The next term in the sequence is ____.
Answer:
f(1) = 14000
f(n) = f(n - 1) · 0.9 , for n ≥ 2
The next term in the sequence is 10206 .
Step-by-step explanation:
First we try to find the type of sequence it is.
Is there a common difference?
12600 - 14000 = -1400
11340 - 12600 = -1260
There is no common difference, so it is not an arithmetic sequence.
12600/14000 = 0.9
11340/12600 = 0.9
There is a common ratio, so this is a geometric sequence.
Each term is 0.9 times the previous term.
The next term is:
11340 * 0.9 = 10206
Answer:
f(1) = 14000
f(n) = f(n - 1) · 0.9 , for n ≥ 2
The next term in the sequence is 10206 .
a)Estimate a model relating annual salary to firm sales and market value. Make the
model of constant elasticity variety for both independent variables. Write the results
out in equation form (s.e. under parameter estimates). summary (lm(formula= salary ∼ sales + mktval, data = ceosal2)) Call: lm(formula = salary sales + mktval, data = ceosal2) Residuals: Coefficients: segnitr. coues: v Residual standard error: 535.9 on 174 degrees of freedom Multiple R-squared: 0.1777, Adjusted R-squared: 0.1682 F-statistic: 18.8 on 2 and 174 DF, p-value: 4.065e−08 > lm(formula = lsalary ∼ lsales + lmktval, data = ceosal2) Call: lm(formula = lsalary ∼ lsales + lmktval, data = ceosal2) Coefficients: (Intercept) 4.6209
Lsales 0.1621
Lmktval 0.1067
b) A friend of yours is about to start as a CEO at a firm. She is thinking of asking for
$500.000 as annual salaries. The firm sales last year was $5.000.000 and the market
value of the firm is $20 million. According to your model from part (a) would she be
asking too much? What are the expected salaries according to the model?
a) The estimated model relating annual salary to firm sales and market value, in equation form, is: Salary = 4.6209 + 0.1621 * log(sales) + 0.1067 * log(mktval), where log denotes the natural logarithm.
b) Calculating this expression will give us the expected salary according to the model. If the expected salary is higher than $500,000, then your friend would be asking too much.
a) The estimated model relating annual salary to firm sales and market value, in equation form, is:
Salary = 4.6209 + 0.1621 * log(sales) + 0.1067 * log(mktval)
where log denotes the natural logarithm.
b) To determine if your friend would be asking too much for an annual salary of $500,000, we need to plug the values of firm sales and market value into the model and calculate the expected salary.
Using the given values:
- Firm sales (sales) = $5,000,000
- Market value (mktval) = $20,000,000
We first need to take the logarithm of the sales and market value:
log(sales) = log(5,000,000)
log(mktval) = log(20,000,000)
Then, we can substitute these values into the equation:
Expected Salary = 4.6209 + 0.1621 * log(5,000,000) + 0.1067 * log(20,000,000)
Calculating this expression will give us the expected salary according to the model. If the expected salary is higher than $500,000, then your friend would be asking too much.
Note: Make sure to use the natural logarithm (ln) in the calculations.
Visit here to learn more about market value brainly.com/question/28320555
#SPJ11
ASAP PLEASE
Type in your response.
What is the area of kite ABCD?
sq yd
Answer:
51.5?
Step-by-step explanation:
I think it's just length times width divided by 2
The area of the kite ABCD is 51.56 square yards.
What is the area of the kite?A kite's area is the amount of space enclosed or surrounded by a kite in a two-dimensional plane.
A kite's area equals half the product of its diagonal lengths. The formula for calculating a kite's area is:
Area = 1/2 × d₁ × d₂
Where d₁ and d₂ are long and short diagonals of a kite.
Here, AC = 12.5 yards and BD = 8.25 yards
Substitute the values of d₁ = 12.5 yards and d₂ in the formula of the kite's area:
The area of the kite = 1/2 × 12.5 × 8.25
The area of the kite = 51.5625
The area of the kite ≈ 51.56 square yards
Thus, the area of the kite ABCD is 51.56 square yards.
Learn more about the area of the kite here:
https://brainly.com/question/2292872
#SPJ7
Multiply the additive inverse of -1/14 with the multiplicative inverse of 21/49.
Chapter : Rational Numbers
Answer:
1/6
Step-by-step explanation:
When we talk of additive inverse, we mean the value we will add to a certain number to give 0
for example, the additive inverse of 4 is -4
Hence, the additive inverse of -1/14 is 1/14
The
multiplicative inverse is the number multiplied by another that gives 1
For example, the multiplicative inverse of 4 is 1/4
Thus, we have it that;
multiplicative inverse of 21/49 is 49/21
multiplying;
1/14 * 49/21 = 1/6
Answer:
Answer:
1/6
Step-by-step explanation:
When we talk of additive inverse, we mean the value we will add to a certain number to give 0
for example, the additive inverse of 4 is -4
Hence, the additive inverse of -1/14 is 1/14
The
multiplicative inverse is the number multiplied by another that gives 1
For example, the multiplicative inverse of 4 is 1/4
Step-by-step explanation:
Given the following sets, find the set (A U B) O (AUC). U = {1, 2, 3, ..., 10) 3 , A = {1, 2, 3, 7} B = {1, 3, 10} C = {1, 2, 3, 6, 8}
The set (A U B) O (AUC) is {1, 2, 3, 6, 7, 8, 10}.
The following steps can be used to find the set (A U B) O (AUC):
Step 1: Find A U B {1, 2, 3, 7} U {1, 3, 10} = {1, 2, 3, 7, 10}
Step 2: Find (A U B) U C({1, 2, 3, 7, 10} U {1, 2, 3, 6, 8}) = {1, 2, 3, 6, 7, 8, 10}
A set is a group of things. The objects (or elements) that make up a set are often listed within curly brackets, and sets are typically identified by a letter. It's important to keep in mind that a set is an unordered collection of objects, meaning that it doesn't matter what order the elements are listed in. are viewed as being equivalent.
Know more about set here:
https://brainly.com/question/31656454
#SPJ11
tyler wants to buy a new television that costs $312.
Answer:
ummm is there more to the problem?!
Cool.... the question???
Which answer choice below lists only personal financial assets?
А
car, savings, mortgage loan
B
personal savings, college fund, 401K retirement fund
C
credit cards, home equity loan, retirement fund
D
boat, personal loans, savings
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
volume of a cylinder that has a diameter of 16 and a height of 7
Answer:
volume of a cylinder = 1408
hope this answer helps you...
Answer:
1407.616
Step-by-step explanation:
Volume of cylinder=πr²h
V=3.142×8×8×7
V=1407.616
NOTE: radius =diameter/2=16/2
giving 8.
Find the volume of the cylinder whose base area is (4x)2 and height is (5x)2.
Answer:
Step-by-step explanation:
The computation of the volume of the cylinder is shown below:
As we know that
The Volume of the cylinder is
= base × height
= (4x)^2 + (5x)^2
=16x^2 + 25x^2
= 41x^3
Hence, the volume of the cylinder is 41x^3
The volume of the cylinder will be [tex]20x^2[/tex] .
What is volume ?Volume is the amount of space that something contains or fills.
Volume [tex]=Length*Breadth*Height[/tex]
We have,
Base area [tex]=(4x)^2[/tex]
Height [tex]= (5x)^2[/tex]
So,
Volume of the cylinder [tex]=Base\ Area*Height[/tex]
[tex]= (4x)^2* (5x)^2[/tex]
Volume of the cylinder [tex]=20x^2[/tex]
Hence, we can say that the volume of the cylinder will be [tex]20x^2[/tex] .
To know more about volume of the cylinder click here
https://brainly.com/question/16134180
#SPJ3
At what number of days will the cost of attendance be the same for both preschools?
Answer:
Forgot the pic ?
Step-by-step explanation:
π (pi) is an unending decimal. Find the Circumference of the circle below using exact π (pi).
Step-by-step explanation:
Given radius, r = 5,
Circumference of Circle, C
[tex] = 2\pi \: r \\ = 2\pi(5) \\ = 10\pi \: units[/tex]
Answer:
[tex]10\pi[/tex]
Step-by-step explanation:
As the hint below says:
[tex]C = 2\pi r[/tex]
We also know that
r = 5
So thus:
[tex]C = 2 \pi \cdot 5 = 10\pi[/tex]
For women aged 18-24. systolic blood pressures (in mm Hg) are normally distributed with a mean of 114 8 and a standard deviation of 13.1. If 23 women aged 18-24 are randomly selected, find the probability that their mean systolic blood pressure is between 119 and 122.
The probability that their mean systolic blood pressure is between 119 and 122 is 0.0807.
The given distribution is normal.
So, the formula for the standardized random variable, z can be used.
Here,Mean of the given distribution, μ = 114.8
Standard deviation of the given distribution, σ = 13.1
Number of women aged 18-24 randomly selected, n = 23
Let X be the mean systolic blood pressure of 23 randomly selected women aged 18-24.
P(X is between 119 and 122) = P((X-μ)/σ is between (119-μ)/(σ/√n) and (122-μ)/(σ/√n))
= P((X-μ)/σ is between (119-114.8)/(13.1/√23) and (122-114.8)/(13.1/√23))
= P((X-μ)/σ is between 1.35 and 2.45)
Using standard normal distribution table,P(1.35 < z < 2.45)= P(z < 2.45) - P(z < 1.35)≈ 0.9922 - 0.9115= 0.0807
Thus, the probability that the mean systolic blood pressure of the randomly selected 23 women aged 18-24 is between 119 and 122 is approximately equal to 0.0807.
#SPJ11
Let us know moree about probability: https://brainly.com/question/11034287
hi hottie, pls help me !
Mrs. St. Louis purchased an iPhone 12 Pro. The decreasing value of her phone, after t years, is modeled by the function V(t)=1,200(0.65)^t
Fill in the numbers from the options to correctly complete the statements interpreting this function.
The phone initially cost $______
The value of the phone is depreciating at a rate of _____ % each year.
Answer:
1200
0.65
The answers are in the function
I WILL MARK BRAINLIEST
Answer:
A.
Step-by-step explanation:
It is commonly recognized that a poor environment (for example, poverty, low educational level of parents) and the presence of stressors (for example divorce of parents, abuse) are associated with lower IQs in children. Recent research indicates that a child's IQ is related to the number of such risk factors in the children's background, regardless of which specific factors are present. Below are the numbers of risk factors and the IQs of 12 children.
Child
Risk factors (x)
IQ (y)
A
3
112
B
6
82
C
0
105
D
5
102
E
1
115
F
1
101
G
5
94
H
4
89
I
3
98
J
3
109
K
4
91
L
2
107
A. Draw a scatterplot of the data. What does the plot tell you? Determine the regression equation. Be sure to include an interpretation of each parameter in the regression equation.
B. What IQ do you predict for James, who has 5 risk factors, versus Elizabeth, who has only 2?
A) The scatterplot of the data is as follows:What can we interpret from the scatterplot of the given data?We can observe that the higher the number of risk factors, the lower the IQ of the children. This fact is supported by the trend line that shows a negative correlation. This is what the plot is telling us.A regression equation is given by the formula: $y=\beta_0+\beta_1x$Where, $y$ is the IQ of the child, $x$ is the number of risk factors, $\beta_0$ is the y-intercept and $\beta_1$ is the slope of the line.Both $\beta_0$ and $\beta_1$ can be calculated using the following formulae: $$\beta_1=r_{xy}\frac{s_y}{s_x}$$$$\beta_0=\bar{y}-\beta_1\bar{x}$$Where, $r_{xy}$ is the correlation coefficient between $x$ and $y$, $s_x$ and $s_y$ are the standard deviations of $x$ and $y$ respectively, and $\bar{x}$ and $\bar{y}$ are the means of $x$ and $y$ respectively.From the scatterplot, we can observe that $r_{xy}$ is negative. Therefore, there exists a negative correlation between $x$ and $y$.Let us calculate the values of $\beta_1$, $\beta_0$ using the above formulae.$$r_{xy}=\frac{\sum(x-\bar{x})(y-\bar{y})}{\sqrt{\sum(x-\bar{x})^2\sum(y-\bar{y})^2}}$$$$r_{xy}=\frac{(3)(112)+(6)(82)+(0)(105)+(5)(102)+(1)(115)+(1)(101)+(5)(94)+(4)(89)+(3)(98)+(3)(109)+(4)(91)+(2)(107)}{\sqrt{(3^2+6^2+0^2+5^2+1^2+1^2+5^2+4^2+3^2+3^2+4^2+2^2)(112^2+82^2+105^2+102^2+115^2+101^2+94^2+89^2+98^2+109^2+91^2+107^2)}}$$$$r_{xy}=-0.835$$Now, let's calculate the standard deviations of $x$ and $y$:$$s_x=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}$$$$s_y=\sqrt{\frac{\sum(y-\bar{y})^2}{n-1}}$$$$s_x=\sqrt{\frac{(3-2)^2+(6-2)^2+(0-2)^2+(5-2)^2+(1-2)^2+(1-2)^2+(5-2)^2+(4-2)^2+(3-2)^2+(3-2)^2+(4-2)^2+(2-2)^2}{12-1}}$$$$s_x=\sqrt{\frac{44}{11}}=2$$$$s_y=\sqrt{\frac{\sum(y-\bar{y})^2}{n-1}}$$$$s_y=\sqrt{\frac{(112-99.17)^2+(82-99.17)^2+(105-99.17)^2+(102-99.17)^2+(115-99.17)^2+(101-99.17)^2+(94-99.17)^2+(89-99.17)^2+(98-99.17)^2+(109-99.17)^2+(91-99.17)^2+(107-99.17)^2}{12-1}}$$$$s_y=\sqrt{\frac{5626.1}{11}}=9.025$$Finally, let's calculate $\beta_1$ and $\beta_0$:$$\beta_1=r_{xy}\frac{s_y}{s_x}$$$$\beta_1=-0.835\frac{9.025}{2}=-3.762$$$$\beta_0=\bar{y}-\beta_1\bar{x}$$$$\beta_0=99.17-(-3.762)(3.08)=112.91$$Therefore, the regression equation is $y=112.91-3.762x$.Here, $\beta_0=112.91$ represents the expected IQ of a child with zero risk factors, while $\beta_1=-3.762$ represents the decrease in IQ per risk factor.B) James has 5 risk factors. Substituting $x=5$ in the regression equation, we get:$$y=112.91-3.762x$$$$y=112.91-3.762(5)$$$$y=93.13$$Therefore, the IQ predicted for James is $93.13$.Similarly, Elizabeth has 2 risk factors. Substituting $x=2$ in the regression equation, we get:$$y=112.91-3.762x$$$$y=112.91-3.762(2)$$$$y=105.39$$Therefore, the IQ predicted for Elizabeth is $105.39$.
ASAP HELP MATH!!!!!!!! 1st PERSON GETS BRAINLIEST
WILL GIVE BRAINLIEST FOR BEST ANSWER NO LINKS!!!!*Use the data from the dot plot below to answer the question. The data shows games of a soccer season and the number of goals scored in each game.
Which goals were scored the fewest amount of times during the soccer season?
Question 5 options:
3
0, 7
1, 4, 5, 6
2
0, 7
0 and 7 have the least amount of dots.