What are the X - and y-intercepts of the equation 7x + 3y = 21 ?

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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Answer:

4 minutes

Hope this helps!!! :)

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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\(2 - \sqrt{1} \\ = 2 - 1 \\ = 1\)

Answer:

I dunno if this is the right answer but I tried my best

the answer is 140

??????

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Answer:

if i have 19

Step-by-step explanation:

the solution to the system of equations is x = -1.3478, y = -1, and z = 1.

To solve the system of equations using Cramer's rule, we need to find the determinants of the coefficient matrix, the matrix with x coefficients, and the matrix with y coefficients.

The coefficient matrix:

3 1 2

2 -3 -1

1 2 1

The matrix with x coefficients:

3 1 2

-3 -3 -1

4 2 1

The matrix with y coefficients:

3 3 2

2 -3 -1

1 4 1

The determinant of the coefficient matrix is:

| 3 1 2 |

| 2 -3 -1 |

| 1 2 1 | = 3(2(-1) - (-3)(2)) - 1(2(-1) - (-3)(1)) + 2(2(2) - (-3)(1)) = 23

The determinant of the matrix with x coefficients is:

| 3 1 2 |

| -3 -3 -1 |

| 4 2 1 | = 3(-3(1) - 2(-1)) - 1(-3(4) - 2(1)) + 2(2(3) - (-3)(-3)) = -31

The determinant of the matrix with y coefficients is:

| 3 3 2 |

| 2 -3 -1 |

| 1 4 1 | = 3(-3(-1) - 4(-1)) - 3(2(1) - (-1)(1)) + 2(2(-4) - (-3)(1)) = -23

Now, we can find the values of x, y, and z as follows:

x = det(x coefficients) / det(coefficient matrix) = (-31) / 23 = -1.3478

y = det(y coefficients) / det(coefficient matrix) = (-23) / 23 = -1

z = (det(coefficients matrix)) / det(coefficient matrix) = 1

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Answer: 33

Step-by-step explanation:

Answer:

-0.13157894736

Step-by-step explanation:

Answer:

SOH CAH TOA........... Cosine=Adj/hypotenuse...... ***Cosine X=15/39 ****

SOH CAH TOA......... Sine= Opp/hypotenuse..... ***Sine Z=30/40***

Step-by-step explanation:

SOH CAH TOA........... Cosine=Adj/hypotenuse...... ***Cosine X=15/39 ****

SOH CAH TOA......... Sine= Opp/hypotenuse..... ***Sine Z=30/40***

Answer:

the actual answer is D

Step-by-step explanation:

they are congruent lol, i also took the unit test and got 100 on edge

The transformation should be used that  ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.

A transformation that does not change the size or shape of a figure. The rigid transformation could be in the form of rotations, reflections, and even the translations.

Therefore, we can conclude that The transformation should be used that  ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.

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The value of P0.05 < 0.19658. We do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.

According to the question we will set up Hypothesis

Null,  H0: U=26

Alternate, H1: U<26

Test Statistic

Population Mean(U)=26

Sample X(Mean)=24.4

Standard Deviation(S.D)=9.2

Number (n)=25

we use Test Statistic (t) = x-U/(s.d/√(n))

to =24.4-26/(9.2/√(25))

to =-0.87

| to | =0.87

Critical Value

The Value of |t α| with n-1 = 24 d.f is 1.711

We got |to| =0.87  & | t α | =1.711

According to this, we have to make a decision

Hence Value of  |to | < | t α |

P-Value: Left Tail -Ha : ( P < -0.8696 ) = 0.19658

Hence Value of P0.05 < 0.19658

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The scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

What is dilation?

A dilation is a transformation that creates an image that has the same shape as the original but is larger.

• An enlargement is a dilation that produces a larger image.

• A reduction is a dilation that produces a smaller image.

• A dilation expands or contracts the original figure.

A dilation is a stretch or a shrink in the size and location of a figure or point.

The scale factor in a dilation is the amount by which the figure is stretched or shrunk.

The center of dilation is a reference point used to appropriately scale the dilation of a figure. Given a point on the pre-image, \((x_1, y_1)\)and a corresponding point on the dilated image \((x_2, y_2)\)and the scale factor,

k, the location of the center of dilation, \((x_0,y_0)\) is

\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\)

Hence, the scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

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Answer:

Given the equation 2y-40=-18 to simplify the equation further we need to first add 40 to both sides of the equation thereby justifying the addition property as shown;

2y-40 + 40 =-18+40

2y = 40-18

2y = 22

We will also apply the division property here. Division property is used when both sides of an equation is divided by a number without affecting the equality rule.

Dividing the resulting equation by 2:

2y/2 = 22/2

y = 11

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

I used the calculator heheh

Hope It Helps

Answer:

5. x=80°, y= 80°

Step-by-step explanation:

5.x=80 (Vertically opposite angle V.O.A)

y=80 (alternate angle)

Answer:

Liz scored more because she would score 94%, while Austin only scored 92%

Answer:

y=.1x+3 I think that is the answer

Answer:

y=0.1x+3

Step-by-step explanation:

The slope is 0.1, (Y2-Y1/X2-X1) --> (2.5-3)/(-5-0)= -0.5/-5=0.1

The y-intercept is 3

y=0.1x+3

A) True. The source term in a partial differential equation (PDE) represents a forcing function or external input to the system being modeled.

A) True. The source term in a partial differential equation (PDE) represents a forcing function or external input to the system being modeled. In the finite element method (FEM), the PDE is discretized into a set of algebraic equations, and the source term appears in each of these equations.

Specifically, for each algebraic equation resulting from the discretization of the PDE, the source term contributes to the coefficient of the dependent variable on the left-hand side of the equation, and it is taken to the right-hand side of the equation. The resulting coefficient and right-hand side term are then used to construct the corresponding row of the global coefficient matrix and the right-hand side vector, respectively.

Therefore, the source term affects all algebraic equations in the finite element method and is an essential component of the mathematical model. Changing the source term will affect the solution obtained from the ANSYS solver and can result in a different physical behavior of the system being modeled.

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Answer:

f

Step-by-step explanation:

bc i guessed

A system of three linear equations: for the total number of tickets sold is 215 is f + s + t = 215, for the total revenue from ticket sales is $1214 is 7f + 5.25s + 5.5t = 1214, for three times as many senior citizen tickets were sold as full-price tickets is s = 3f.  

There were approximately 11 full-price tickets sold. There were 33 senior citizen tickets sold. There were 171 student tickets sold.

Let f, s, t be the number of full-price tickets sold, senior citizen tickets sold, student tickets sold.

Firstly, write a system of three linear equations based on the given information and mark the equation number.

f + s + t = 215      (1)        (the total number of tickets sold is 215)

7f + 5.25s + 5.5t = 1214   (2)  (the total revenue from ticket sales is $1214)

s = 3f          (3)           (three times as many senior citizen tickets were sold as full-price tickets)

solve this system by substitution. Using equation (3), we can substitute 3f for s in equations (1) and (2):

f + 3f + t = 215

7f + 5.25(3f) + 5.5t = 1214

Simplifying these equations gives:

4f + t = 215           (4)

24.75f + 5.5t = 1214   (5)

We can solve equation (4) for t to get:

t = 215 - 4f

We can substitute this expression for t in equation (5) and solve for f:

24.75f + 5.5(215 - 4f) = 1214

24.75f + 1182.5 - 22f = 1214

2.75f = 31.5

f = 11.45 ≈ 11

Therefore, approximately 11 full-price tickets were sold. Using equation (3), we can find the number of senior citizen tickets sold:

s = 3f = 3(11) = 33

Therefore, 33 senior citizen tickets were sold. Finally, we can use equation (1) to find the number of student tickets sold:

f + s + t = 215

11 + 33 + t = 215

t = 171

Therefore, 171 student tickets were sold.

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A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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Answer:

5?

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The median value is in the middle.

The experimental probability of landing on a number greater than 4 is 0.25 or 25%.

To find this probability, we need to determine the number of successful outcomes (landing on a number greater than 4) and divide that by the total number of trials (60).

The successful outcomes are 5 and 6, with a frequency of 10 and 8 respectively. To add these two frequencies together, we can use 10 + 8 = 18.

So, the experimental probability is 18/60 = 0.3 or 25%.

It's important to note that experimental probability is based on the outcomes of an experiment or a sample and it may not be the same as a theoretical probability which is based on the ratio of favorable outcomes to the total number of outcomes in a theoretical model.

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the answer in fraction form is 18/60

if thats what you are looking for.

In an incidence geometry with the additional axiom that every line has exactly three points lying on it, the minimum number of points required is 4.

This is because a line must have at least two-points to exist, and if it has only two points, it is not possible to have another point lying on it (since every line must have exactly three points).

Hence, there must be at least 4-points to create two lines such that each line contains exactly three points.

Also, with 4 points, it is possible to create 6 lines such that each line contains exactly 3 points, forming a configuration known as the Fano-plane, which is the smallest example of an incidence geometry that satisfies the given axiom.

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Answer:

The expression for the area is;

Explanation:

Given that the length of the rectangle is 3 and the width is (7-4x);

Recall that the area of rectangle can be calculated by multiplying its length by the width.

So, the expression for the area of the given rectangle is;

Therefore, the expression for the area is;

a. The point estimate of the population mean is 7.8.

b. The point estimate of the population standard deviation is 3.9 (to 1 decimal place).

In statistics, a point estimate is a single value that is used to estimate an unknown parameter of a population based on sample data. In this case, we are given a simple random sample with the following data points: 2, 8, 11, 7, and 11.

Therefore, the sample mean is 39/5 = 7.8. This means that, based on the given sample, we estimate the population mean to be 7.8.

First, we calculate the deviations from the sample mean for each data point: (-5.8), 0.2, 3.2, (-0.8), and 3.2. Squaring these deviations gives us: 33.64, 0.04, 10.24, 0.64, and 10.24.

Taking the average of these squared deviations gives us a variance of (33.64 + 0.04 + 10.24 + 0.64 + 10.24)/5 = 10.76. Finally, taking the square root of the variance, we find the sample standard deviation to be approximately 3.3 (rounded to 1 decimal place).

Therefore, the point estimate of the population standard deviation is 3.9 (to 1 decimal place).

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