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the expression equivalent to f(p+r) is 5p + 5r.

The expression equivalent to f(p+r), where f(x) = 5x, is 5p + 5r. To understand this, we substitute (p+r) into the function f(x):

f(p+r) = 5(p+r)

Next, we distribute the 5 to both p and r:

f(p+r) = 5p + 5r

This equivalent expression arises from the definition of f(x) = 5x, where the function multiplies any given input x by 5. In this case, we substitute (p+r) into the function, resulting in 5 multiplied by the sum of p and r. Consequently, the expression 5p + 5r represents the value obtained by applying the function f to the sum of p and r. It is important to note that the function f(x) = 5x implies a linear relationship, where the function scales the input by a factor of 5.

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Answer:

She would have 5 muffins left over

Step-by-step explanation:

The perimeter of the square is a rational number of meters. However, the product of a rational number and an irrational number is always irrational.

If the area of a square is 7 square meters, then each side of the square is √7 meters long. The perimeter of the square is simply the sum of the four sides, which is 4√7 meters.

To determine whether 4√7 is a rational or irrational number, we need to check if √7 is rational or irrational. Since √7 is not a perfect square, it cannot be expressed as a fraction of two integers. Therefore, √7 is an irrational number.

However, the product of a rational number and an irrational number is always irrational. Since 4 is a rational number and √7 is irrational, the product 4√7 is also an irrational number.

Therefore, the perimeter of the square is an irrational number of meters.

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Answer:

see below

Step-by-step explanation:

y= -3x+4

Let x = -4

y= -3(-4) +4 = 12 +4 = 16

Let x = -0

y= -3(0) +4 = 0 +4 = 4

Let x = 4

y= -3(4) +4 = -12 +4 = -8

Let x = 8

y= -3(8) +4 = -24 +4 = -20

The intersection points are (0, 0) and (1, 1) and the area between the graphs of the two functions is -1/3 in fraction form.

To find the intersection points of the functions \(y = x^2\) and \(y = x^{(1/2)}\), we set them equal to each other and solve for x:

\(x^2 = x^{(1/2)}\)

Taking the square root of both sides:

\(x^{(2/2)} = x^{(1/4)}\)

\(x = x^{(1/4)}\)

To eliminate the fractional exponent, we can raise both sides to the fourth power:

\(x^4 = (x^{(1/4)})^4\)

\(x^4 = x\)

Now, we can solve this equation:

\(x^4 - x = 0\)

Factoring out x:

\(x(x^3 - 1) = 0\)

Setting each factor equal to zero:

x = 0

\(x^3 - 1 = 0\)

Solving the second equation:

\(x^3 = 1\)

Taking the cube root of both sides:

x = 1

Therefore, the intersection points are (0, 0) and (1, 1).

To calculate the area between the graphs of the two functions, we integrate the difference of the two functions over the interval where they intersect.

The area is given by:

\(\int\limits^a_b {(x^2 - x^{(1/2)})} \, dx \\\)

We already found the intersection points to be a = 0 and b = 1. Now, let's evaluate the integral:

\(∫[0,1] dx\\\\\int\limits^1_0 {(x^2 - x^{(1/2)})} \, dx\)

\(= [x^3/3 - (2/3)x^{(3/2)}]\) evaluated from 0 to 1

= [(1/3) - (2/3)] - [(0/3) - (0/3)]

= (1/3) - (2/3)

= -1/3

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Answer: 1/5 or 20%

Step-by-step explanation:

4 red + 9 blue + 7 white = 20 total

neither blue nor white means it has to be red so 4/20 or 1/5

Answer:

Elimination

Step-by-step explanation:

Elimination is a process which involves complete removal of one of the variables in a given equation, so as to first determine the value of the other variable.

For example in solving a simultaneous equation, applying the elimination method is easily understood, straight forward and simple to use. Once the logic behind the process is well understood and followed, errors can easily be avoided.

Therefore my favorite way of solving an equation would be by applying the elimination method because it is easy and direct to apply.

When choosing between two unbiased estimators of a population parameter, the one with the lower standard deviation is generally preferred as it indicates that the estimator is more precise. The correct answer is option d.

In other words, the variance of the estimator is smaller, meaning that the estimator is less likely to deviate far from the true value of the population parameter.

An estimator with a larger standard deviation, on the other hand, is less precise and is more likely to produce estimates that are farther from the true value. Therefore, it is important to consider the variability of the estimators when choosing between them.

It is worth noting, however, that the standard deviation alone is not sufficient to fully compare and evaluate two estimators. Other properties such as bias, efficiency, and robustness must also be taken into account depending on the specific context and requirements of the problem at hand.

The correct answer is option d.

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Her dexterity improved due to Increased myelination of the central nervous system.

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Answer and Step-by-step explanation:

3 x 2 - x = ? Well, if you simplify it's just 5x. But, if you are trying to solve this then you have to know what x is or what your answer is. But, if you're trying to solve 3 x 2 = x then x would equal 6. Of course, if you know the answer or what x equals then plug it in as such, let's say x = 2 then you would plug 2 in for x and solve, 3 x 2 = 6 - 2 = 4. But, if you are trying to solve for x then look at the answer, let's say it is 24 so, 3 x 2 - x = 24, x would equal -18.

Hope this helped you out! Have a wonderful day!

**Note, I didn't understand what you were asking, that's why I went into so much detail to help you out. Please, be clearer with your questions. Make sure you got all the whole question in there! Thank you!**

Answer:

1 ft / 0.3048 m

Step-by-step explanation:

The diameter of the circle is 396 units

The diameter is the length of the line through the center that touches two points on the edge of the circle.

A diameter is twice the radius of a circle.All diameters are segment but not all segments are diameter.

length of an arc = tetha/360 × πd

l = 80/360 × π d

88π = 80/360 × π d

80d = 88× 360

80d = 31680

divide both sides by 80

d = 31680/ 80

d = 396 units

therefore the diameter of the circle is 396 units

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The general Coordinates of the rectangle's vertices can be expressed using the relative distances and the given vertex (-1, 4).

To draw a rectangle with one vertex at (-1, 4), we need to determine the positions of the other three vertices based on the properties of a rectangle. A rectangle has four right angles, and its opposite sides are parallel and equal in length.

the given vertex as A(-1, 4). To construct the rectangle, we can determine the positions of the other three vertices using the following properties:

1. Opposite sides are parallel: We can draw a line segment parallel to the x-axis from point A to determine the position of the opposite vertex.

2. Equal sides: We can draw a line segment parallel to the y-axis from point A to determine the position of the other two vertices.

the vertices of the rectangle:

A (-1, 4): Given vertex

B (x, 4): Opposite vertex along the x-axis

C (x, y): Vertex along the y-axis

D (-1, y): Opposite vertex along the y-axis

The coordinates of the remaining vertices, we need to determine the values of x and y. Since the opposite sides of a rectangle are equal in length, we can set the length of the rectangle as the distance between points A and B, or the distance between points A and D.

the length of the rectangle as 'L' units. The distance between A and B is L units, which means the x-coordinate of point B is -1 + L.

Similarly, the distance between A and D is also L units, which means the y-coordinate of point D is 4 + L.

Thus, the coordinates of the rectangle's vertices are:

A (-1, 4)

B (-1 + L, 4)

C (-1 + L, 4 + L)

D (-1, 4 + L)

The exact values of L or the specific size of the rectangle are not provided, so we cannot determine the precise coordinates without additional information.

However, the general coordinates of the rectangle's vertices can be expressed using the relative distances and the given vertex (-1, 4).

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Given: \(\textsf{Decreased by 20\%, Decreased price is \$476}\)

Find:  \(\textsf{Original price}\)

Solution: Looking at the information given and what we need to determine this can simply be done by first creating an expression and inputting the values. We would then simplify the left side and then divide both sides by 0.8 which would isolate the original price and give us the value.

Create an expression

Simplify the parenthesis

Divide both sides by 0.8

After creating the expression and solving for the unknown we were able to determine that the best answer would be option C, $595.

Using the Pythagoras theorem, the length of the unknown diagonal of the rhombus can be calculated

The diagonals of a rhombus are line segments  drawn between  opposite vertices of the rhombus. The properties of the diagonals of a rhombus are listed below.

The diagonals of a rhombus bisect each other at right angles.

The diagonals of a rhombus may not be  equal.

Two diagonals divide the rhombus into four congruent right triangles.

The length of the diagonals can be calculated by various methods, such as the Pythagorean theorem or  the area of ​​a rhombus.

Example 1: Find the length of the diagonal of a rhombus if the area is 54 units2, and one diagonal is 6 units.

The area of the rhombus = 54 square units; one diagonal (q) = 6 units

We will use the formula for the diagonal of rhombus, p = (2 × Area)/q, where 'p' and 'q' are the two diagonals of the rhombus. Substituting the values, p = (2 × 54)/6 = 18 units.

Answer: Therefore, the length of the unknown diagonal is 18 units.

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The income you need to afford a $425,000 house is largely dependent on your debt-to-income ratio, credit score, and down payment. However, a general rule of thumb is to have an annual income that is at least three times the purchase price of the home, which in this case would be $1,275,000.

To more accurately determine the income needed to afford a $425,000 house, consider factors such as the interest rate on the mortgage, property taxes, homeowners insurance, and any homeowner association fees.

These additional expenses can significantly impact your monthly mortgage payment and thus your income requirements.
It's important to keep in mind that lenders have varying criteria when determining mortgage eligibility and income requirements, so it's best to speak with a mortgage professional to get a more accurate estimate based on your individual circumstances.

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Answer:

well if you think about it the answer you see is in the points

Step-by-step explanation:

and the data comes from the scatterplot so try to see it and remember to chose b or c ok  

You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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Answer:

2=0.55x+1.2y+zp

Step-by-step explanation:

The equation that relates x, y, z and p is 2=0.55x+1.2y+zp.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have,

Bananas       0.55    55$ / Kg   x Kg

Cantaloupes 1.21       y$ / Kg      2 Kg

Milk                              z $/ l

Total cost = $2

So, the price of banana for x Kg = 0.55 x

and, for Cantaloupes = 1.2y

and, for milk = zp

Then, the equation can be framed as

2=0.55x+1.2y+zp

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Yes, the data indicate that the machinery should be repaired and the hypotheses are stated.

In this scenario, the null hypothesis is that the machinery is not producing more than 10% defective items, while the alternative hypothesis is that it is producing more than 10% defectives. We can represent these hypotheses as follows:

H0: The machinery is not producing more than 10% defectives.

Ha: The machinery is producing more than 10% defectives.

To test the hypothesis, we will use a statistical test called the one-sample proportion test. This test compares the sample proportion to a hypothesized population proportion. In this case, the hypothesized proportion is 0.10 (10% defectives).

Using the one-sample proportion test, we can calculate a p-value, which is the probability of obtaining a sample proportion as extreme as the one observed or more extreme, assuming the null hypothesis is true. If the p-value is less than the significance level, we reject the null hypothesis in favor of the alternative hypothesis.

In this scenario, the sample proportion is 0.15 (15 defectives out of 100 items), and the hypothesized population proportion is 0.10 (10% defectives). Using a one-tailed test with a significance level of 0.05, we can calculate the p-value as 0.0347.

Since the p-value is less than the significance level, we reject the null hypothesis and conclude that the machinery is producing more than 10% defectives. Therefore, the machinery should be repaired to reduce the defect rate.

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the graph that adequately fits the description would be a pictograph

because shows a symbol for a word or phrase

The curve of intersection between the cylinder x^2 + y^2 = 1 and the plane y + z = 2 is a circle lying on the plane y + z = 2. The parametric equations for this curve are x = cos(θ), y = sin(θ), and z = 2 - sin(θ), where θ is the parameter representing points on the circle.

To find the parametric equations for the curve of intersection between the cylinder and the plane, we can start by parameterizing the cylinder using the angle θ. Since the equation x^2 + y^2 = 1 represents a circle in the x-y plane with radius 1, we can use θ as a parameter to represent points on this circle.

The parametric equations for the cylinder are:

x = cos(θ)

y = sin(θ)

z = 2 - y

Next, we substitute these equations into the plane equation y + z = 2 to determine the intersection points. By substituting y and z, we have sin(θ) + 2 - sin(θ) = 2, which simplifies to sin(θ) - sin(θ) = 0. This implies that the plane equation is satisfied for any value of θ.

Therefore, the intersection between the cylinder and the plane is the entire cylinder itself, lying on the plane y + z = 2. The parametric equations for the curve of intersection are x = cos(θ), y = sin(θ), and z = 2 - sin(θ).

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Answer:

\(\sf \dfrac{1}{8}\)

Step-by-step explanation:

Spinner choices:  Red, Green, Yellow, Blue

Coin choices: Heads, Tails

\(\large\begin{array}{| c | c | c | c | c |}\cline{1-5} & \sf Red & \sf Green & \sf Yellow & \sf Blue\\\cline{1-5} \sf Heads & RH & GH &YH & BH \\\cline{1-5} \sf Tails &RT & GT& YT& BT\\\cline{1-5}\end{array}\)

\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)

\(\implies \sf P(blue)=\dfrac{1}{4}\)

\(\implies \sf P(heads)=\dfrac{1}{2}\)

\(\implies \sf P(blue)\:and\:P(heads)=\dfrac{1}{4} \times \dfrac{1}{2}=\dfrac{1}{8}\)

The value of x using Pythagoras theorem is: x = √118 mi

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

Thus:

x = √(12² - (√26)²)

x = √(144 - 26)

x = √118 mi

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Answer:

Option 1 -  7⁵

Step-by-step explanation:

When dividing numbers that have the same base number (7), you subtract bottom exponent from the top exponent.  So exponent  8 - 3 = 5

You keep the same base number and use the resultant exponent.

7⁵

Answer:

it C

Step-by-step explanation:

Answer:

g(x)= -2 x+1

Step-by-step explanation:

g(x)= -2 x+1

there isnt much for my to explain, sorry.

The three positive numbers whose sum is 21 and whose product is maximal are 7, 7, and 7. So, the answer is: 7, 7, 7.

To find three positive numbers whose sum is 21 and whose product is maximal, we have to use the concept of AM-GM inequality.

The AM-GM inequality states that for any set of positive real numbers, the arithmetic mean of these numbers is always greater than or equal to the geometric mean of these numbers. To maximize the product of the three positive numbers whose sum is 21, we let all three numbers be equal. Therefore:

Let the three numbers be a, b, and c.

So, a = b = c.

The sum of the three numbers is 21,

so: a + b + c = 21

We have a = b = c.

Then we substitute to obtain:

3a = 21

a = 7

Therefore, the three positive numbers whose sum is 21 and whose product is maximal are 7, 7, and 7. So, the answer is: 7, 7, 7.

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Answer:

84

Step-by-step explanation:

Splitting the figure into smaller shapes will be pretty tedious, so we'll just make it into large square that encompasses this shape and subtract the missing areas. If we find the area of the large square, we get 196. The missing parts are 64 (top left corner) and 48 (bottom right). Therefore, the area is 196 - 64 - 48 = 84

By considering the planet's diameter as the distance from its center, we can determine the gravitational acceleration at that altitude. At an altitude equal to the planet's diameter, the gravitational acceleration would be 3.825 m/s² on this hypothetical planet.

The inverse square law of gravity states that the gravitational force decreases as the square of the distance from the center of mass increases.

Since the diameter of the planet is equal to twice the radius, the altitude equal to the planet's diameter is equivalent to being at a distance twice the radius away from the center of mass.

Let's denote the planet's surface gravitational acceleration as "g" and the radius as "R".

Using the inverse square law, we can calculate the gravitational acceleration at an altitude equal to the planet's diameter as follows:

g_altitude = g * (R / (2R))²

= g * (1/4)

= g/4

= 15.3 m/s² / 4

= 3.825 m/s²

Therefore, at an altitude equal to the planet's diameter, the gravitational acceleration would be 3.825 m/s² on this hypothetical planet.

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