A utility pole is 40 feet tall. If 5% feet is cut
off the top, find the height of the pole.

Answer:

A”(-3, -18) B” (0, -27) C” (-12, -30)

Step-by-step explanation:

Two transformations have been listed beneath the graph. Complete them in order to get the solution.

The first transformation is a translation. A translation involves moving the shape across the graph without altering its form. To receive the coordinates for this. Add the <-3, -8> given to coordinates A, B, and C. Which should result in the following: A (-1, -6) B (0, -9) C (-4, -10)

Now complete the second transformation, which is a dilation. Dilations happen when a shape is either made smaller or larger by a set number. To complete the second transformation: take the number given: “3” and multiply each number in the coordinate sets you got after the first transformation by this number.

Which should result in: A”(-3, -18) B” (0, -27) C” (-12, -30)

Answer:

Yes

Step-by-step explanation:

The numbers both multiplied by 10

3 -6

30-60

The rate which the mulch is being applied is 250,000 cm^3/cm^2

The statement is given as

Rita is applying 250,000 cm^3 of mulch per m^2 of the garden space

This means that the rate is

Rate = Volume of mulch/Area of garden space

Substitute the known values in the above equation

So, we have

Rate = 250,000 cm^3/cm^2

Hence, the rate which the mulch is being applied is 250,000 cm^3/cm^2

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Answer:

108 inches

Step-by-step explanation:

6X6X3

Answer:

y= mx + c

Step-by-step explanation:

y=mx+c

y= -2x+c

-5 = -2(3) +c

-5 = -6 +c

-5 + 6 = c

1 = c

therfore equation is y = -2x + 1

The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.

First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.

Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.

Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:

1/2 = 3/6

x/6

Now we need to find the value of x that makes the sum of the fractions equal to 19/3:

3/6 + x/6 = 19/3

To solve for x, we can multiply both sides by 6:

3 + x = 38/3

Then, we can subtract 3 from both sides:

x = 29/3

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The degree of a polynomial is the highest exponent of its variable. When multiplying monomials and binomials, we add the exponents of the variables to get the degree of the resulting polynomial.

However, the degree of the product can be different from the degree of the factors because of the distributive property of multiplication.

When we multiply a monomial by a binomial, we need to distribute the monomial to each term of the binomial. This results in new terms that may have different degrees than the original terms. For example, when multiplying the monomial x^2 by the binomial (2x + 3), we get:

x²(2x + 3) = 2x³ + 3x²

The degree of the monomial x² is 2, and the degree of the binomial (2x + 3) is 1. However, the degree of the resulting polynomial 2x³ + 3x² is 3 because the term 2x³ has a higher degree than any of the original terms.

Similarly, when we multiply two binomials, we need to distribute each term of one binomial to each term of the other binomial. This can also result in new terms with different degrees than the original terms.

Therefore, the degree of the product can be different from the degree of the factors when multiplying monomials and binomials because of the distributive property of multiplication.

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Answer:

Step-by-step explanation:

We will need to rewrite the Pythagorean Theorem

A^2 + B^2 = C^2

Substitute. tIn this case:

18^2 + x^2 = 82^2

Subtract 18^2

x^2 = 82^2 - 18^2

In order to get x alone, take the root:

x = sqrt(82^2 - 18^2)

And solve:

x = 80

The magnetic force that the wire exerts on the point charge is in the negative z-direction.

When a current-carrying wire and a moving point charge are placed in a magnetic field, a magnetic force is exerted on the moving charge due to the interaction between the magnetic field and the charge's velocity. According to the right-hand rule, the direction of the magnetic force is perpendicular to both the velocity of the moving charge and the magnetic field created by the current-carrying wire.

In this scenario, the wire carrying current in the positive y-direction generates a magnetic field that circulates around the wire. The point charge moving along the x-axis in the positive x-direction experiences a magnetic force directed perpendicularly to both the velocity (positive x-direction) and the magnetic field (circulating around the wire). Applying the right-hand rule, the magnetic force is found to be in the negative z-direction, which is downward and perpendicular to the x and y axes.

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Answer:

Answer is 11. You have to add the 4 and 7.

In rectangles all sides are either perpendicular or parallel, so you know that the missing side is equal to the bottom 2 horizontal sides added up.

4 + 7 = 11.

The missing side is 11cm.

Answer:

3^6

hope it's helpful.

thanks

Answer:

-4

Step-by-step explanation:

Subtract 1 - 5 = -4...

Since 1 is less than 5, we know that the difference is negative, so we can rewrite this expression as -(5-1).

5 - 1 = 4, so - (5-1) = -4.

Answer:

1-(5) is 1-5 = -4

Step-by-step explanation:

one subtracted by 5 will offer an negative number, -4.

Answer:

x = 5

Step-by-step explanation:

30 divided by 6 equals x

30/6 = 5

so x = 5

Answer:

X= 5

Step-by-step explanation:

6x=30

or, x=30/6
Therefore, x=5

Answer:

\(m=\frac{-5}{3}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point C(-2, 4)

Point D(1, -1)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

After rotation the coordinate i (4,-4) and the error is in Step 2.

What is rotation of coordinates?

Every point in a preimage is transformed in a plane by rotation, which revolves a fixed point in a specific direction and at a specific angle for each point. The center of rotation is the fixed point.

The term for the amount of rotation is the angle of rotation, and it is expressed in degrees.

Here, Rotating a figure 270 degrees clockwise is the same as rotating it 90 degrees anticlockwise.

The formula would now be (x, y) = (-y, x)

The given B is (3,-1) then

step 1: (3,-1) -> (3-2,-1-5) -> (1,-6)

Step 2:(1,-6) -> (-(-6),1) -> (6,1)

Step 3: (6,1) -> (6-2,1-5) -> (4,-4)

Hence after rotation the coordinate is (4,-4) . The error is in step2.

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Answer:

55%

Step-by-step explanation:

We need to first find the total length of the side.

let remaining length be x

perimeter= 40cm

4 (s)=perimeter

4(7+x)=40

28+4x=40

4x=40-28=12

4x=12

x=12/4=3

total length= 7+3= 10cm

4+y= 10=

y=6

therefore, area of square= s*s= 10*10=100cm²

find areas of the two triangles (unshaded).

1/2*3*10= 15cm²

1/2*6*10= 30 cm²

15/100*100= 15%

30/100*100= 30%

shaded percentage= 100-(15+30)

= 100-45

= 55%

Answer:

670000

Step-by-step explanation:

67 * 10^4

67 * (10*10*10*10)

= 670000

Answer:

670,000

Step-by-step explanation:

You'd do 10^4 first which is 10,000.

Then multiply 10,000 by 67.

67*1 is 67. Add the 4 zeros and you get...

670,000

Answer:

The correct options are;

The equation of the function is 2·y = -25·x + 200

The equation of the function is y = -25/2·x  + 100

The x-intercept of the function is (8, 0)

Step-by-step explanation:

From the graph of the function, the y-intercept is observed at (0, 100), the x-intercept occurs at (8, 0)

Therefore, we have the slope, m given by the following relation

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Where:

y₁ = 100

x₁ = 0

y₂ = 0

x₂ = 8

Which gives;

\(m =\dfrac{0-100}{8-0} = -12.5\)

The equation in slope can be found as follows

y - 100 = -12.5×(x - 0)

y = -12.5·x  + 100 = -25/2·x  + 100

Multiplying by 2 gives;

2·y = -25·x + 200

25·x + 2·y =  200

Therefore, the correct options are;

The equation of the function is 2·y = -25·x + 200

The equation of the function is y = -25/2·x  + 100

The x-intercept of the function is (8, 0).

Answer:

    The x-intercept for the function is (8,0).

   The equation of the function is 25x + 2y = 200.

   The equation of the function is y =-25/2 x + 100.

Step-by-step explanation:

The probability that it takes 4 shots for the marksman to hit the long-range target is approximately 0.1466, or 14.66%.

To calculate the probability that it takes 4 shots for the marksman to hit the long-range target, we assume each shot is independent and has a success probability of 0.623. The probability of hitting the target on the fourth shot can be calculated using the binomial distribution. The formula for the probability mass function (PMF) of the binomial distribution is:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of exactly k successes,

n is the number of trials,

k is the number of successful trials,

p is the probability of success on a single trial, and

C(n, k) is the binomial coefficient, given by C(n, k) = n! / (k! * (n - k)!)

In this case, n = 4 (the number of shots), k = 4 (the number of successful shots), and p = 0.623 (the probability of hitting the target on each shot). Substituting these values into the formula, we can calculate the probability:

P(X = 4) = C(4, 4) * 0.623^4 * (1 - 0.623)^(4 - 4)

C(4, 4) = 4! / (4! * (4 - 4)!) = 1

P(X = 4) = 1 * 0.623^4 * (1 - 0.623)^(4 - 4)

= 1 * 0.623^4 * 1

= 0.623^4

= 0.1466

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Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

The dimensions of the box that minimize the cost are: Length = Width = 2^(1/3) ft and Height = 1/(2^(2/3)) ft, We can also compute the minimum cost as: Cost = 4 × 2^(2/3) + 8 × 2^(1/3) ≈ $10.42

To find the dimensions of the box that will minimize the cost, we need to use optimization techniques. Let's start by defining the variables:

Let L be the length of the base of the box.
Let W be the width of the base of the box.
Let H be the height of the box.

The volume of the box is given as 4 ft3, so we have:

L × W × H = 4

We want to minimize the cost of the box, which is given by:

Cost = (2LH + 2WH) × 2 + LW × 4

where the first term represents the cost of the sides (which have a height of H and a length of L or W) and the second term represents the cost of the bottom (which has an area of LW).

Now, we can use the volume equation to solve for one of the variables in terms of the other two. For example, we can solve for H:

H = 4/(LW)

Substituting this into the cost equation, we get:

Cost = 4L + 4W + 16/(LW)

To find the dimensions that minimize the cost, we need to find the critical points of this function. Taking the partial derivatives with respect to L and W, we get:

dCost/dL = 4 - 16/(L^2W)
dCost/dW = 4 - 16/(LW^2)

Setting these equal to zero and solving for L and W, we get:

L = W = 2^(1/3)

(Note that we need to check that this is a minimum by verifying that the second partial derivatives are positive.)

Substituting these values into the volume equation, we get:

H = 1/(2^(2/3))

Therefore, the dimensions of the box that minimize the cost are:

Length = Width = 2^(1/3) ft
Height = 1/(2^(2/3)) ft

We can also compute the minimum cost as:
Cost = 4 × 2^(2/3) + 8 × 2^(1/3) ≈ $10.42

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Answer:

$1,640

Step-by-step explanation:

Total  Amount = Principal Amount + Interest Earned

Interest Earned = Principal * Interest Rate (as a decimal) * time (in years)

Interest = 1000(.04)(16) which equals $640

Add $640 to the principal of $1000 and  George will receive $1,640 on his 16th birthday

The average value of the step function u(x) on [-1,1] is 1/2, is 1/2

A step function (also called as staircase function) is defined as a piecewise constant function, that has only a finite number of pieces. In other words, a function on the real numbers can be described as a finite linear combination of indicator functions of given intervals.

The average value of the step function u(x) on the interval [-1,1] can be calculated by integrating u(x) over the given interval and dividing the result by the length of the interval.

We have:

∫[-1,1] u(x)dx = ∫[-1,0] 0dx + ∫[0,1] 1dx = 1 - 0 = 1

Therefore, the average value of u(x) is = (1/2)(1 - 0) = 1/2

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S + R represents the total trips done by these trucks.

Volume is defined as the amount of space occupied by an object that is bound by a boundary. It must be noted that the volume is a mathematical term that is only applicable to 3D (three-dimensional) objects or spaces. As such, the units commonly used for volume are cubic units, that is, m3, cm3, in3, etc.

Two dump trucks hauling rock to a construction site is given by the expression. xS + yR

S +R

Truck 1 can haul x cubic yards

Truck 2 can haul y cubic yards.

Truck 1 makes P trips to the construction site, while truck 2 makes R trips.

Hence the trips made by truck 1 and truck 2 should be the addition of the trips made by the trucks individually.

So the total trips is represented by S + R

Therefore, S + R represents the total trips done by these trucks.

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The functions best models this scenario is:

C(x) = 3.45x ,   x<4

         3.00x+1,   x≥4

Given:

A local city park rents kayaks for $3.45 per hour. If a customer rents for four or more hours, the cost is only $3 per hour, plus a $1 processing fee.

If C(x) represents the total cost and x represents the number of rental hours.

If customer parks for 1 hour

C(x) = 3.45*1

= 3.45

for 2 hour

C(x) = 3.45*2

= 6.70

Until 3 hour the price per hour is 3.45

so C(x) = 3.45x ,   x<4

If x = 4 hour

C(x) = 3*4 + 1

= 12+1

= 13

If 4 hour or more the price per hour is 3.00

so C(x) = 3.00x+1 , x ≥5

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Hope it helps.

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Answer:

estimate = 61

real answer = 61.1428571429

Step-by-step explanation:

The null and alternative hypotheses are:

H0: β1 = 0 (The slope is not significant.)

H1: β1 ≠ 0 (The slope is significant.)

Here,β1=0.0943seβ1=0.107α=0.05

Test the slope significance and find the t-test statistic.

We need to find the t-test statistic so that we can compare it with the t-distribution, whose distributional properties we know, to determine if we can reject or fail to reject the null hypothesis.t-test statistic is calculated by dividing the value of β1 by its standard error (seβ1) and taking the absolute value of this quotient.

t-test statistic = | β1/seβ1 | = |0.0943/0.107| = 0.881

The degrees of freedom (df) associated with this t-test are df = n - 2, where n is the sample size for the explanatory variable x.

In this problem, the decision rule and conclusion are as follows:

Decision Rule: Reject the null hypothesis if |t-test statistic| > tc where tc is the critical value obtained from the t-distribution with df degrees of freedom and a significance level of α/2 in each tail.

Conclusion: The slope is not significant if we fail to reject the null hypothesis, but the slope is significant if we reject the null hypothesis. Since the t-test statistic (0.881) is less than the critical value (1.987), we fail to reject the null hypothesis. Therefore, we conclude that the slope is not significant.

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The height of the statue is of 35 feet, applying similarity of triangles.

Similar triangles are triangles that have congruent angle measures, thus the measures of their side lengths are proportional. This relation can be proven from the law of sines.

In the context of this problem, there are two similar right triangles, in which:

Hence the following proportional relationship is established:

5/x = 12/84

Applying cross multiplication, it is found that:

12x = 84 x 5

Simplifying by 12, the expression is written as follows:

x = 7 x 5 (as 84/12 = 7).

x = 35 feet, which is the height of the statue.

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Answer:

Step-by-step explanation:

25 = 5 * 5

36 = 2*2*3*3

117 = 3*3*13

3825 = 5*5*3*3*17