why do terms have to be like terms?

The variance V[aX+b] of a random variable X with real numbers a and b simplifies to a^2 * V[X].

Here's a step-by-step explanation:

1. Recall the definition of variance: V[Y] = E[(Y - E[Y])^2], where Y is a random variable and E[Y] represents its expected value.
2. Substitute Y with aX+b: V[aX+b] = E[((aX+b) - E[aX+b])^2].
3. Apply the linearity of expectation: E[aX+b] = aE[X] + b.
4. Substitute this back into the variance equation: V[aX+b] = E[((aX+b) - (aE[X] + b))^2].
5. Simplify the expression inside the expectation: (aX+b) - (aE[X] + b) = a(X-E[X]).
6. Square the simplified expression: (a(X-E[X]))^2 = a^2 * (X-E[X])^2.
7. Use the fact that E[aZ] = a * E[Z], where Z is a random variable: E[a^2 * (X-E[X])^2] = a^2 * E[(X-E[X])^2].
8. Recall that E[(X-E[X])^2] = V[X], so the final answer is: V[aX+b] = a^2 * V[X].

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Answer:

56

Step-by-step explanation:

Answer:

k=56

Step-by-step explanation:

100-44=56

100-56=44

Answer:

3 2/3

Step-by-step explanation:

Do the multiplications and then convert the denominator to the same number.  Then add the fractions/numbers.

1 5/6 = 11/6

1 5/6 * 2 * 3/4 + 1 5/6 * 1 * 3/4​

(11/6)*(2)*(3/4) + (11/6)*(1)*(3/4)

(11/6)*[(2)*(3/4) + (1)*(3/4)]       [Factor out (11/6) to make it easier to calculate, if you want]

((11/6)*(6/4) + (11/6)*(3/4))

(66/24) + (22/24)                 [The denominators are now both 24, so the numerators may be added]

88/24 = 3 (16/24) or 3 2/3

(11/6)*(2)*(3/4)

(11/6)*(1)*(3/4)

1. In 2008, there were approximately 28.2 million live Christmas trees sold in the U.S

2. The linear regression equation that models the set of data above is C = 0.28t + 27.28.

3. From 2004 to 2011, the number of Christmas trees sold in the U.S. increased by approximately 0.28 million trees each year.

4. In 2008, there were approximately 28.4 million live Christmas trees sold in the U.S.

5. Why is this the case: A. The data are not perfectly linear. The regression equation gives only an approximation.

By using the data values in the table, the number of live Christmas trees that were sold in the year 2008 can be calculated as follows;

t = 0 + (2008 - 2004) years.

t = 4 years.

At t = 4 years on the table, approximately 28.2 million live Christmas trees sold in the U.S.

Part 2.

Based on the table, we can logically deduce that the y-intercept or initial value is (0, 27.1).

y = mx + b ≡ C = mt + b

b = (547.6 - 538.6)/(105 - 72.2)

b = 0.28

Therefore, the required linear regression equation is given by;

C = 0.28t + 27.28

Part 3.

Based on the slope of the above linear regression equation, the number of Christmas trees sold in the U.S. from 2004 to 2011 increased by approximately 0.28 million trees each year.

Part 4.

For the number of live Christmas trees sold in year 2008, we have:

C(4) = 0.28(4) + 27.28

C(4) = 28.4 million.

Part 5.

The answers to parts 1 and 4 are different because the data set do not have a perfectly linear relationship and the linear regression equation gives only an approximated value, not an exact value.

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As long as Glenda's process follows these criteria, it will be a binomial experiment.

Glenda's process of checking computer monitors for defects to be considered a binomial experiment, it must meet the following criteria:
1. Fixed number of trials (n): Glenda must check a fixed number of monitors, such as 50 or 100.
2. Only two possible outcomes: Each monitor can either be defective (success) or not defective (failure).
3. Independent trials: The outcome of one trial (checking one monitor) does not affect the outcome of any other trials.
4. Constant probability of success (p): The probability of finding a defective monitor should remain constant at 0.5% (0.005) for all trials.
As long as Glenda's process follows these criteria, it will be a binomial experiment.

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The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

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Draw a flower

Draw a cupcake

Draw a butterfly

Draw a tree

Draw a cartoon character

Draw a heart

Draw a cat

Draw a sun

Draw a bird

Draw a landscape

Draw a cloud

Draw a house

Draw a star

Draw a fish

Draw a snowman

Draw a rainbow

Draw a car

Draw a dog

Draw a person

Draw a fruit

Remember, practice makes perfect! So, keep practicing and exploring your creativity.

Answer: sm1 took my answer down but yes draw a cartoon character or something similar to an old school drawing try giving the character a new look something u never drawn before

Step-by-step explanation:

Answer:

\( \frac{8}{3} \)

Step-by-step explanation:

\( - 2 \frac{1}{3} - ( - 5)\)

convert mixed fraction into improper fraction.

\( - \frac{7}{3} + ( - 5)\)

calculate the sum of the fraction:

\( \frac{8}{3} \)

Answer:

X=6

Y= - 1

Step-by-step explanation:

X-y =7

X+y =5 cross - y and y

_______

X+x =7 +5

2x= 12

X= 12/2

X= 6

Replace X in first equation:

X - y =7

6 - y =7

6 - 7 =y

y = - 1

Hope this helps you.. Good Luck!

Answer:

See below.

Step-by-step explanation:

The cubic root of 49 is 3.66, so the dot should go between 3 and 4, a little closer to 4 than to 3.

She thought the problem was square root of 49 which is 7 and placed a dot on the 7.

1.5 doller = 100* $ 1.5  = 150 peniess

After 50 minutes = 20 gallons of water

Solution :

Pennies :

The dollar is the United States' 100-cent coin. It takes 100 pennies to equal a dollar

1. Girl deposit 5 pennies for each day

which means after 10 days = 50 pennies

Her sister gave her 3 pennies = 53 pennies total she has

To make the $1.50  into her piggy beg

She needs how many pinnies to do so.

1 doller = 100 pennies

1.5 doller = 100* $ 1.5  = 150 peniess

2.

Gallons :

A gallon of water by definition is 128 fluid ounces in the United States. Water bottles can vary in size, but the total number of bottles making up 128 ounces can fit in a gallon. For example, if the water bottle is 16 ounces in size, then 8 of these make up a gallon.

pool capacity = 1500 gallons of water

then

every 5 minutes = 2 gallons of water

then,

after 50 minutes = 2*10 gallons of water

= 20 gallons of water

After 50 minutes = 20 gallons of water

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the researcher can conclude that private hospitals pay more than government-owned hospitals based on the sample data.

To test whether private hospitals pay more than government-owned hospitals, we can use a two-sample t-test with equal variances.

The null hypothesis is that there is no difference in mean salary between the two groups:

H0: μprivate = μgovernment

The alternative hypothesis is that private hospitals pay more than government-owned hospitals:

Ha: μprivate > μgovernment

We can use a significance level of 0.01, which corresponds to a critical value of t = 2.364 (with degrees of freedom = 898).

First, we need to calculate the pooled standard deviation:

Sp = sqrt(((n private - 1)s^2private + (n government - 1)s^2government) / (n private + n government - 2))

where n private and n government are the sample sizes, s^2private and s^2government are the sample variances, and s^2pooled is the pooled variance.

Plugging in the values, we get:

Sp = sqrt(((100-1) * 186^2 + (800-1) * 176^2) / (100 + 800 - 2)) = 176.43

Next, we calculate the test statistic:

t = (x(bar)private - x(bar)government) / (Sp * sqrt(1/n private + 1/n government))

where x(bar)private and x(bar)government are the sample means.

Plugging in the values, we get:

t = (26,800 - 25,400) / (176.43 * sqrt(1/100 + 1/800)) = 3.14

Since our test statistic (3.14) is greater than the critical value (2.364), we reject the null hypothesis and conclude that private hospitals pay more than government-owned hospitals at a significance level of 0.01.

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Answer:  7 Courts

Step-by-step explanation: One US gallon equals for US courts, so 1 3/4 x 4 is seven

Answer: 7

Step-by-step explanation:

3/4 as a decimal is .75

The exact solution of this equation involves solving a quadratic equation, which may not result in a simple integer value for x.

To find the point (x, y) on the function f(x) = 6 - 7x that is closest to the point (-10, -4), we need to minimize the distance between the two points.

The distance between two points (x1, y1) and (x2, y2) is given by the formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, we want to minimize the distance between the point (-10, -4) and any point on the function f(x) = 6 - 7x. So we can set up the distance equation:

d = sqrt((-10 - x)^2 + (-4 - (6 - 7x))^2)

To find the point (x, y) that minimizes the distance, we can find the value of x that minimizes the distance equation. Let's differentiate the distance equation with respect to x and set it equal to zero to find the critical point:

d' = 0

Differentiating and simplifying the equation, we get:

(-10 - x) + (-4 - (6 - 7x))(-7) = 0

Solving this equation will give us the value of x at the closest point. Plugging this x-value into the function f(x) = 6 - 7x will give us the corresponding y-value.

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Answer:

I believe the first one

Step-by-step explanation:

Sample Parameter: The population's weight and the average weight of the cereal box The grain on the line's average weight is the parameter.

The value that consistently appears in a given set is known as the mode in statistics. The mode or modal value is the value or number that appears most frequently in a data set and has a high frequency. Along with mean and median, there are three other ways to measure central tendency. The mode can be calculated quite easily. After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group.

given

Example: 50th box of cereal

All cereal boxes are lined up in the population

Example Parameter: The cereal box's average weight

Population metric: The cereal on the line's average weight

Sample Parameter: The population's weight and the average weight of the cereal box The grain on the line's average weight is the parameter.

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Answer:

2m-8+1=2m-7

Step-by-step explanation:

Answer:Okay, so the first thing to do here is show you that any number can be a fraction if you use a 1 as the denominator. Take a look:

1.80

1

What we really want to do though, is get rid of the decimal places completely so that the numerator in our fraction is a whole number. To do this, we have to count the numbers after the decimal point, which in this case is 80.

To get a whole fraction we need to multiply both the numerator and the denominator by 10 if there is one number after the decimal point, 100 if there are two numbers, 1,000 if it's three numbers and 10,000 if it's...well, you get the idea!

In our case 80 is 2 digits long so we need to multiply the numerator and denominator by 100.

Now we just need to do that multiplication to get our whole fraction:

1.80 x 100

1 x 100

=

180

100

The next step is to simplify this fraction and, to do that, we need to find the greatest common factor (GCF). This is sometimes also known as:

Greatest Common Divisor (GCD)

Highest Common Factor (HCF)

Greatest Common Denominator (GCD)

The GCF can be a bit complicated to work out by hand but you can use our handy GCF calculator to figure it out.

In the case of 180 and 100, the greatest common divisor is 20. This means that to simplify the fraction we can divide by the numerator and the denominator by 20 and we get:

180/20

100/20

=

9

5

And there you have it! In just a few short steps we have figured out what 1.80 is as a fraction. The complete answer for your enjoyment is below:

1 4/5

Note: because 180 is greater than 100 we have simplified this fraction even further to a mixed fraction.

Step-by-step explanation:

To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.

Distance Formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the distance formula, we can calculate the lengths of the three sides of the triangle:

Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68

Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34

Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34

Slope Formula:

The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)

Using the slope formula, we can calculate the slopes of the three sides of the triangle:

Slope AB:

m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4

Slope BC:

m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5

Slope AC:

m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3

From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.

Therefore, triangle ABC is an isosceles right triangle.

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Answer:

2/3

Step-by-step explanation:

1/3 x 2/1 = 2/3

Answer:

   2/3

Step-by-step explanation:

so what you do is switch the numerators and deno. (1/3 1/2)turns into 3/1 and 2/1 you multiple both top and bottom numbers and boom!!

(simplify if need)

Answer:9

Step-by-step explanation:

she went up 20 instead of 2

two buses leave towns miles apart at the same time and travel toward each other. then the Rate of first bus = 72 mph and Rate of second bus  = 62 mph

let first bust travels at x mph

then,  2nd but will travel at ( x - 10) mph

distance travelled by first bus in 2 hours = 2x

distance travelled by 2nd but in 2 hours = 2( x- 10) = 2x - 20

distance between the two is 268 miles

so we can write

2x + 2x - 20 = 268

4x = 288

x = 288 / 4 = 72 mph

rate of first bus = 72 mph

and second bus = 72 - 10 = 62 mph

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First let's translate these words algebraically and form an equation:

Let oranges be x and apples be y, \(2.29x+1.69y\)

a. coefficients are the constants multiplied by the variable, they represent the price of both oranges and apples.

b. I am assuming that the terms here represent how much he paid for the pounds of oranges and apples he bought in total.

The confidence coefficients for the given scenarios can be determined using the t-table, which provides critical values for different levels of confidence and degrees of freedom.

For n = 12 with 95% confidence: The degrees of freedom (df) is n - 1 = 12 - 1 = 11. Looking up the t-table for df = 11 and a confidence level of 95%, the confidence coefficient is approximately 2.201.

For n = 15 with 95% confidence: The degrees of freedom is df = 15 - 1 = 14. Referring to the t-table for df = 14 and a confidence level of 95%, the confidence coefficient is approximately 2.145.

For n = 21 with 96% confidence: The degrees of freedom is df = 21 - 1 = 20. Consulting the t-table for df = 20 and a confidence level of 96%, the confidence coefficient is approximately 2.528.

For n = 27 with 92% confidence: The degrees of freedom is df = 27 - 1 = 26. Checking the t-table for df = 26 and a confidence level of 92%, the confidence coefficient is approximately 1.708.

These confidence coefficients represent the critical values that determine the range of values within which the population parameter is estimated with the specified level of confidence.

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Answer:

carrect answer is : multiply 40x20

Answer:

D. Multiply 40 x 8

Step-by-step explanation:

Answer:

Long wings: 0

Short wings: 100

Step-by-step explanation:

Genotype of the flies: ww

The cross will yield the genotype ww and the flies will express the recessive phenotype which is short wings.

The probability for long wings will be 0 as there is no dominant allele present. The probability for short wings will be 100 as all the flies will have short wings.

Hope that helps.

Answer:

Step-by-step explanation:

138° - 80° = 58°

The polar curve r = 4 - 4sinθ, 0 ≤ θ < 2π has vertical tangent lines at θ = π/6 and θ = 7π/6.

To find the points where the polar curve has a vertical tangent line, we need to determine the values of θ for which the derivative of r with respect to θ, dr/dθ, is equal to infinity.

The derivative of r with respect to θ can be found using the chain rule of calculus. We have:

dr/dθ = d(4 - 4sinθ)/dθ

Differentiating the expression, we get:

dr/dθ = -4cosθ

For a vertical tangent line, the slope of the tangent line should be infinite, which means the derivative dr/dθ should be equal to infinity. Therefore, we set -4cosθ equal to infinity and solve for θ:

-4cosθ = ∞

Since the cosine function oscillates between -1 and 1, it never attains the value of infinity. However, there are two specific values of θ for which the cosine is equal to zero, resulting in the derivative being undefined (i.e., vertical tangent lines). These values are:

θ = π/2 + 2πk, where k is an integer

Converting these values to the range 0 ≤ θ < 2π, we have:

θ = π/2 and θ = 3π/2

Substituting these values back into the polar equation, we find the corresponding points on the curve:

For θ = π/2:

r = 4 - 4sin(π/2) = 4 - 4(1) = 0

For θ = 3π/2:

r = 4 - 4sin(3π/2) = 4 - 4(-1) = 8

Therefore, the polar curve r = 4 - 4sinθ has vertical tangent lines at the points (0, π/2) and (8, 3π/2).

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Answer:

3, 4, and 5 by 8.

Step-by-step explanation:

I created a Pythagorean triple of (24, 32, 40) by multiplying the known Pythagorean triples 3, 4, and 5 by 8.