9 Salvatore is making some back-to-school packs for his teacher. He has 96 pencils and 80 erasers. He wants each pack to be the same, and he wants to use all of the pencils and erasers. Find the greatest common factor of 96 and 80 to figure out how many packs he can make. How many pencils and erasers will be in each one?​

The reliability of a study using multiple regression analysis depends on a, b, and c, but not d.

Regression analysis depends on Omitted variable bias refers to the problem of leaving out important variables from the regression model that could affect the dependent variable. This can lead to biased and inconsistent estimates of the regression coefficients.

Errors-in-variables refer to measurement errors in the independent or dependent variables. These errors can result in biased and inconsistent estimates of the regression coefficients.

Homoskedasticity in the error term refers to the condition where the variance of the error term is constant across all values of the independent variables. This is important because it ensures that the regression coefficients are unbiased and efficient.

External validity refers to the ability to generalize the findings of a study to other populations or settings. While important for the overall usefulness of the study, it does not affect the reliability of the multiple regression analysis itself. So, regression analysis depends on a,b,c but not on d.

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Answer:

x = 44/7

Step-by-step explanation:

7x+3 = 47

Subtract 3 from each side

7x+3-3 = 47-3

7x = 44

Divide by 7

7x/7 = 44/7

x = 44/7

Answer:

-9a -5b

Step-by-step explanation:

Answer:

-9a - 5b

Step-by-step explanation:

Step 1. Collect like Terms

-13a + 5b + 4a - 10b  (-13a + 4a = -9a)

-9a + 5b - 10b (5b - 10b = -5b)

Leaves you with -9a - 5b

The sample size increases, the probability of obtaining a sample mean less than 3500 decreases. The mean of the sample mean distribution is equal to the population mean, which is 7500.

a) The probability that, on a single test, x is less than 3500 can be calculated using the standard normal distribution. We need to standardize the value using the z-score formula: z = (x - μ) / σ. Substituting the given values, we get z = (3500 - 7500) / 1750 ≈ -2.286.

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -2.286. The probability is approximately 0.0116, or 1.16%. Therefore, there is a 1.16% chance that a single test result will be less than 3500, indicating leukopenia.

(b) When the doctor uses the average x (sample mean) for two tests taken about a week apart, the probability distribution of x (sample mean) follows a normal distribution. The mean of the sample mean distribution is equal to the population mean, which is 7500. The standard deviation of the sample mean distribution is equal to the population standard deviation divided by the square root of the sample size. In this case, the sample size is 2.

The probability distribution of x (sample mean) < 3500 can be calculated by standardizing the value using the z-score formula and then finding the corresponding probability from the standard normal distribution table or a calculator. With two tests, the probability distribution will be narrower compared to a single test. The exact probability depends on the specific value of the sample mean and the standard deviation of the sample mean distribution.

(c) When considering three tests taken a week apart, the process is similar to part (b). The mean of the sample mean distribution remains the same at 7500, but the standard deviation of the sample mean distribution is now divided by the square root of 3, since the sample size is 3. As the sample size increases, the standard deviation of the sample mean distribution decreases, resulting in a narrower distribution.

The probability distribution of x (sample mean) < 3500 can be calculated using the z-score formula and finding the corresponding probability from the standard normal distribution table or a calculator. With three tests, the probability distribution will be even narrower compared to two tests.

In summary, as the sample size increases, the probability of obtaining a sample mean less than 3500 decreases. With more tests, we can have greater confidence in the accuracy of the sample mean and draw stronger conclusions about the individual's condition. If a person had a sample mean less than 3500 based on three tests, it would indicate a higher level of certainty about the presence of leukopenia, potentially leading to further investigation or treatment options.

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Answer: 7 tens and 6 ones

Step-by-step explanation: 76 is two numbers, with a 7 in the tens place and a 6 in the ones place.

76 can be represented as 7 tens and 6 ones or as 6 tens and 16 ones. This involves understanding the place value of digits in a number and knowing that a ten can be broken down into ones.

The number 76 can be broken down into tens and ones in multiple ways. First, let's understand what tens and ones mean in the context of a number. In the number 76, '7' is the tens place, and '6' is the ones place, meaning there are 7 tens (70) and 6 ones (6) making up 76.

One way to show 76 with tens and ones is to say that there are 7 tens and 6 ones. This is a very direct method where we just count the number of tens and ones in the number.

Another way we could break down 76 is to say there are 6 tens and 16 ones. This method involves taking one of the tens and breaking it down into 10 ones, giving us a total of 6 tens and 16 ones.

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Answer:

192

Step-by-step explanation:

Apply the geometric mean formula to solve for x, which is the altitude of the right triangle.

The formula is:

h = √(mn)

h = x = ?

m = 144

n = 400 - 144 = 256

Substitute

h = √(256*144)

h = √36,864

h = 192

Therefore, x = 192

Answer:

y = -3x - 2, the slope is -3 and the y-intercept is -2

Step-by-step explanation:

2y +4 = -6x and minus the four to get 2y alone

Then divide -4 and -6x by 2 to get y = -3x and -2

The correct answer is d. the zeros are neither positive nor negative. The student included these in the interval over which the function is positive, which is incorrect.

The statement indicates that the zeros of the function are neither positive nor negative. This means that the function changes sign at the zeros, crossing the x-axis from either the positive side to the negative side or vice versa.

If the student included these zeros in the interval over which the function is positive, it would be incorrect because the function should be positive on one side of the zero and negative on the other side.

Similarly, if the student included these zeros in the interval over which the function is negative, it would also be incorrect because the function should be negative on one side of the zero and positive on the other side.

The correct statement is d. the zeros are neither positive nor negative. The student including these zeros in the interval over which the function is positive is incorrect. The function changes sign at the zeros, and it is important to consider both the positive and negative intervals correctly when determining the intervals of positivity and negativity for the function.

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The outward flux of the vector field F across the boundary of the region D, which is the cube bounded by the planes x = ±1, y = ±1, and ±1, can be found using the divergence theorem.

The outward flux is the integral of the divergence of F over the volume enclosed by the boundary surface.The first step is to calculate the divergence of F. The divergence of a vector field F = P i + Q j + R k is given by div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z. In this case, div(F) = ∂/∂x(5y - 4x) + ∂/∂y(-4z - 5y) + ∂/∂z(-3y - 2x). Simplifying these partial derivatives, we have div(F) = -4 - 2 - 3 = -9.

Applying the divergence theorem, we can relate the flux of F across the boundary surface to the triple integral of the divergence of F over the volume enclosed by the surface. Since D is a cube with sides of length 2, the volume enclosed by the surface is 2^3 = 8.

Therefore, the outward flux of F across the boundary of D is given by ∬S F · dS = ∭V div(F) dV = -9 * 8 = -72. The negative sign indicates that the flux is inward.

In summary, the outward flux of the vector field F across the boundary of the cube D, as described by the given vector components, is -72. This means that the vector field is predominantly flowing inward through the boundary of the cube.

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The equation of the quadratic equation is y = x² - 7x + 10.

What is x-intercept of a graph?

The points where a line crosses x- axis  and y- axis are known as the x-intercept and the y-intercept, respectively.

Given that the x-intercepts of the graph are 2 and 5.

If a and b x-intercepts of a graph, then the equation of the graph is y = A(x -a)(x - b).

Assume the equation of the quadratic equation will be y = A(x -2)(x - 5).

The graph is passes through the point (4, -2).

Putting x = 4 and y = -2 in the equation y = A(x -2)(x - 5)

-2 = A(4 -2)(4 - 5)

-2 = -2A

A = 1

The equation of the quadratic equation is y = (x -2)(x - 5)

y = x² - 7x + 10.

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Answer:

Your input: find the distance between P=(−3,11)

P

=

(

−

3

,

11

)

and Q=(−6,4)

Q

=

(

−

6

,

4

)

.

The distance between two points is d=(x2−x1)2+(y2−y1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√

d

=

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

.

We have that x1=−3

x

1

=

−

3

, y1=11

y

1

=

11

, x2=−6

x

2

=

−

6

, y2=4

y

2

=

4

.

So, d=(−6−(−3))2+(4−(11))2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=58‾‾‾√

d

=

(

−

6

−

(

−

3

)

)

2

+

(

4

−

(

11

)

)

2

=

58

.

Answer: d=58‾‾‾√≈7.61577310586391

d

=

58

≈

7.61577310586391

.

Step-by-step explanation:

Hey! Got this off of someone else ages ago.. hope this helps tho

Answer:

domain: [-3,2]

range: [-3,2]

Step-by-step explanation:

domain: all possible x values *maximum values of x

range: all possible y values *maximum values of x

brackets means the max while parenthesis mean infinite

Answer:

0.006 km

Step-by-step explanation:

600 cm to km

we have to divide by 100000

=> 600/100000

=>6/10000

=>0.006 km

9514 1404 393

Answer:

  each equation can be transformed to the other

Step-by-step explanation:

Starting with the given equation, we can subtract 4, then multiply by 2:

  x + 5 = 15

  x + 5 - 4 = 15 - 4

  x + 1 = 11

  2(x + 1) = 2(11)

  2(x +1) = 22 . . . an equivalent equation

The properties of equality allow one equation to be transformed into the other.

Answer:

39.512195122

Step-by-step explanation:

You divide 162 by 4.1, you can use a calculator to help solve. If needed to be rounded it is 40

Priya's equation for p(x) is not correct. The correct equation for horizontally stretching f(x) by a factor of 5 is\($$p(x) = f\left(\frac{x}{5}\right) = \left(\frac{x}{5}\right)^2 + 3 = \frac{x^2}{25} + 3$$\)

We are given the original function $f(x)$ and the proposed new function p(x), which is obtained by horizontally stretching $f(x)$ by a factor of 5. The proposed equation for p(x) is:

p(x) = f(5x)

And we are also given a specific expression for $f(x)$:

\($$f(x) = x^2 + 3$$\)

To check whether Priya's equation for p(x) is correct, we need to substitute f(5x) with its expression in terms of $x$ and simplify:

\($$p(x) = f(5x) = (5x)^2 + 3 = 25x^2 + 3$$\)

So Priya's equation for p(x) is not correct. The correct equation for horizontally stretching f(x) by a factor of 5 is:

\($$p(x) = f\left(\frac{x}{5}\right) = \left(\frac{x}{5}\right)^2 + 3 = \frac{x^2}{25} + 3$$\)

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Answer:

$33,600

Step-by-step explanation:

2,800 x 12

answer:

it's a function

step-by-step explanation:

according to g00gle- in mathematics, a function is a binary relation between two sets that associates to each element of the first set exactly one element of the second set. typical examples are functions from integers to integers, or from real numbers to real numbers.

but the simple definition is that a function is when the x value isn't being repeated. and since in your case it isn't, the table is a function

another way to solve-

for this, we will put the pairs into a graph then perform the line test-

as you can see each point has its own individual line, therefore, meaning it passed the vertical line test

good luck :)

i hope this helps

brainliest would be highly appreciated

have a nice day!

Answer:

419.999999994 =420

Step-by-step explanation:

Its all in the equations lol

Answer:

-108x³ + 115x² + 149x - 32

Step-by-step explanation:

[(5x + 3)(8x + 6)] + [(-9x + 10) (12x² + 5x-5)]

= (5x + 3) (8x + 6) + (-9x + 10) ( 12x² + 5x - 5)

= 40x² + 54x + 18 - 108x³ + 75x² + 95x - 50

= -108x³ + 115x² + 149x - 32

So, the answer is -108x³ + 115x² + 149x - 32

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

In this experiment, the dependent variable would be the amount of fruit production by tomato plants.

The dependent variable is the variable that is measured or observed in an experiment. It is the outcome or response that is influenced by the independent variable, which is the variable that is manipulated or controlled by the researcher. In this case, the independent variable would be the brand of fertilizer.

By testing different brands of fertilizer and measuring the resulting fruit production, the researcher can determine the impact of each brand on the tomato plants' yield. The dependent variable, which is the amount of fruit production, will vary based on the different levels or variations of the independent variable (i.e., different brands of fertilizer).

By analyzing the data collected on fruit production for each brand of fertilizer, the researcher can identify which brand yields the greatest amount of fruit. This information can be used to make informed decisions on the most effective fertilizer brand for maximizing tomato plant productivity.

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Answer:

r < 3

Step-by-step explanation:

Step 1: Write out inequality

5r + 2 < 17

Step 2: Subtract 2 on both sides

5r + 2 - 2 < 17 - 2

5r < 15

Step 3: Divide both sides by 5

5r/5 < 15/5

r < 3

In this case, r has to be smaller than 3. So anything like -2, -15, or even -12413573875942 works as r, as long as it's smaller than 3.

Answer:

sin of 90 is 1

Step-by-step explanation:

sin is the y axis coordinate and the coordinates of 90° on unit circle is (0,1)

Answer:

Scalene Triangle

Step-by-step explanation:

To classify the triangle we have to find the lengths of each side.

Side AB

d= √  (−1−(−3))2+(4−2)2√  

d= √  (2)2+(2)2

d= √  4+4

d=√  8

d=2.828427 approximately 2.8

Side BC

d= √  (3−(−1))2+(−4−4)2

d= √  (4)2+(−8)2

d= √  16+64

d=8–√0

d=8.944272 approximately 8.9

Side AC

d=  √  (3−(−3))2+(−4−2)2

d=  √  (6)2+(−6)2

d=  √  36+36

d=  √  7 2

d=8.485281 approximately 8.5

Since no sides are the same length, it is a scalene triangle.

I hope this helps!

the sequence converges to ln(3) as n approaches infinity.

What is sequence?

In mathematics, a sequence is an ordered list of numbers, typically arranged in a specific pattern or following a certain rule.

To determine whether the sequence given by an = ln(3n² + 7) − ln(n² + 7) converges or diverges, we need to examine the behavior of the sequence as n approaches infinity.

Taking the limit as n approaches infinity, we have:

lim(n→∞) ln(3n² + 7) − ln(n² + 7)

We can simplify this expression by using properties of logarithms:

lim(n→∞) ln((3n² + 7)/(n² + 7))

Now, let's consider the ratio inside the logarithm:

(3n² + 7)/(n² + 7)

As n approaches infinity, the dominant term in the numerator and denominator will be the highest power of n. In this case, it is the term 3n²/n². Taking the limit of this term:

lim(n→∞) (3n² + 7)/(n² + 7) = 3

Thus, the ratio inside the logarithm converges to 3 as n approaches infinity.

Returning to the original expression, we have:

lim(n→∞) ln((3n² + 7)/(n² + 7))

Since the ratio inside the logarithm converges to 3, we can rewrite the expression as:

ln(3)

Therefore, the limit of the sequence is:

lim(n→∞) an = ln(3)

Hence, the sequence converges to ln(3) as n approaches infinity.

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The number of children are there in the given scenario are 400.

Given that, the ratio of children to adults on a school trip is initially 10:1.

Here, the given ratio can be written as 10x:1x

5 more children and 5 more adults join the trip so that the ratio is now 9:1

10x+5:1x+5

The new ratio is (10x+5)/(x+5) = 9/1

10x+5=9(x+5)

10x+5=9x+45

10x-9x=45-5

x=40

So, the number of children =10x=400

Therefore, the number of children are there in the given scenario are 400.

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The net magnetic field at point P is zero, as the magnetic fields produced by the two equal currents in opposite directions cancel out. A third wire at P would experience zero force due to the net zero magnetic field at P.

To construct a vector diagram showing the net magnetic field vector at point P, we can use the right-hand rule for determining the direction of the magnetic field around a current-carrying wire.

If we curl the fingers of our right hand in the direction of the current in the first wire, which is out of the page, the thumb points in the direction of the magnetic field at point P due to the first wire. Similarly, in the opposite direction to the magnetic field at point P due to the second wire.

Since the magnetic fields they produce at P have equal magnitudes but opposite directions. Therefore, the net magnetic field at P is zero,

If a third wire carrying equal current into the plane of the paper were located at P, the direction of the force on this wire would be perpendicular to both the magnetic field produced by the other two wires and the direction of the current in the third wire.

Since the net magnetic field at P is zero, the vector product of the current in the third wire and the magnetic field is also zero, and there is no force on the third wire.

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The way to determine the exponential regression equation and the value of the correlation coefficient, r, is given below.

Step 1: Collect your data

Gather the data for the variables you want to analyze.

Step 2: Plot the data on a graph

Create a scatter plot of the data to see if there is any relationship between the variables. If the data appears to have an exponential relationship, then an exponential regression analysis may be appropriate.

Step 3: Use logarithmic transformation

To create a linear relationship between the variables, take the natural logarithm of both the x and y variables.

Step 4: Calculate the regression equation

Use linear regression techniques to find the equation of the line that best fits the transformed data. The equation will be in the form of y = a + bx.

Step 5: Convert back to exponential form

Convert the equation back to its exponential form by taking the exponential function of both sides of the equation. The equation will now be in the form of y = Ae^(bx).

Step 6: Calculate the correlation coefficient

Calculate the correlation coefficient, r, between the original x and y variables. This will tell you the strength and direction of the relationship between the variables.

An overview is given as your information is incomplete.

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