A rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The worker holds the rope at the same height as the connection point between the rope and weight. The distance from the connection point to the ceiling is 30 ft. Suppose the worker stands directly next to the weight (i.e., a total rope length of 60 ft) and begins to walk away at a constant rate of 2 ft/s. How fast is the weight rising when the worker has walked:

Answer: Tiffany 15mph, Maggie 20mph

Step-by-step explanation:

Set up the equation 4((x+5) + x) = 140. x+5 represents how many miles Maggie covered in one hour. x represents how much Tiffany traveled in one hour. 140 is the number of miles in total. 4 is the number of hours in total.

Simplify the equation.

(x+5) + x = 35    Divide both sides by 4

2x+5 = 35         Combine like terms

2x = 30              Subtract 5 from both sides

x = 15                 Divide both sides by 2

Tiffany traveled 15mph, while Maggie traveled 15+5=20mph.

Answer:

1 + 4x

Step-by-step explanation:

Let's break this down.

"The sum of one" means that something is being added to the number one:

1 +

"and" whatever comes after the word 'and' will be added to the number one

"the product of 4 and a number x" this means that the number four and the variable x are being multiplied:

4x

Put it together:

1 + 4x

Therefore, the expression is 1 + 4x.

Answer:

height = 6 mm

Step-by-step explanation:

The prism is a rectangular prism. The base area of the prism is 24 mm². The volume of the prism is given as 144 mm³.

The height of the prism can be solved as follows.

Volume of the rectangular prism = Bh

where

B = base area

h = height

Volume = 144 mm³

B = 24 mm²

volume = Bh

144 = 24 × h

144 = 24h

divide both sides by 24

h = 144/24

h = 6 mm

Answer:

c

Step-by-step explanation:

edg 2022

Answer:

80

Step-by-step explanation:

17+13=30

22+23+5=50

30+50=80

Answer:

80 cards

Step-by-step explanation:

23+5=28

13+17=30

28+30=58

58+22=80

Answer:

8

Step-by-step explanation:

y²+by+16= (y+4)²

y²+by+16= y²+2*4*y+4²

y²+by+16= y²+8y+16

by=8y

b=8

Answer:

100+70+8+0.2+0.05. is the answer

Answer:

178.25 as a fraction is 178 1/4 or 713 / 4

Step-by-step explanation:

hope it works out !!

Answer:

(-1,4)

Step-by-step explanation:

Divide each imput by 4

The required image of the given point (-4, 12) dilation by a scale factor of 1/4 and centered at the origin is (1, -3).

Given that,
To determine the image of  (-4,12) after dilation by a scale factor of 1/4 centered at the origin.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Coordinate, is represented as the values on the x-axis and y-axis of the graph

Here,
For the point, we have a dilation factor of 1/4,
So dilated coordinate,
= (1/4 * - 4 ,   1/4 * 12)
= (-1 , 3)
To form the image across the origin
= - (-1, 3)
= (1, -3)

Thus, the required image of the given point (-4, 12) with a scale factor of 1/4 and centered at the origin is (1, -3).

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Answer:

The correct answer would be D) 4.8x + 1.2 = 3.6; x = 0.5 mile

Step-by-step explanation:

This is because laps would be the dependent variable, so we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant. Now we can solve to make sure this is the right equation.

4.8x + 1.2 = 3.6

4.8x = 2.4

x = 0.5

Answer:

D) 4.8x + 1.2 = 3.6; x = 0.5 miles

Answer:

226 cm^3

The mass of plastic used to make cylinder is greater

Step-by-step explanation:

Given:-

- The density of cone material, ρc = 1.4 g / cm^3

- The density of cylinder material, ρl = 0.8 g / cm^3

Solution:-

- To determine the volume of plastic that remains in the cylinder after gouging out a hemispherical amount of material.

- We will first consider a solid cylinder with length ( L = 10 cm ) and diameter ( d = 6 cm ). The volume of a cylinder is expressed as follows:

                                  [tex]V_L =\pi \frac{d^2}{4} * L[/tex]

- Determine the volume of complete cylindrical body as follows:

                                 [tex]V_L = \pi \frac{(6)^2}{4} * 10\\\\V_L = 90\pi cm^3\\[/tex]

- Where the volume of hemisphere with diameter ( d = 6 cm ) is given by:

                                 [tex]V_h = \frac{\pi }{12}*d^3[/tex]

- Determine the volume of hemisphere gouged out as follows:

                                 [tex]V_h = \frac{\pi }{12}*6^3\\\\V_h = 18\pi cm^3[/tex]

- Apply the principle of super-position and subtract the volume of hemisphere from the cylinder as follows to the nearest ( cm^3 ):

                               [tex]V = V_L - V_h\\\\V = 90\pi - 18\pi \\\\V = 226 cm^3[/tex]

Answer: The amount of volume that remains in the cylinder is 226 cm^3

- The volume of cone with base diameter ( d = 6 cm ) and height ( h = 5 cm ) is expressed as follows:

                               [tex]V_c = \frac{\pi }{12} *d^2 * h[/tex]

- Determine the volume of cone:

                              [tex]V_c = \frac{\pi }{12} *6^2 * 5\\\\V_c = 15\pi cm^3[/tex]

- The mass of plastic for the cylinder and the cone can be evaluated using their respective densities and volumes as follows:

                             [tex]m_i = p_i * V_i[/tex]

- The mass of plastic used to make the cylinder ( after removing hemispherical amount ) is:

                           [tex]m_L = p_L * V\\\\m_L = 0.8 * 226\\\\m_L = 180.8 g[/tex]

- Similarly the mass of plastic used to make the cone would be:

                           [tex]m_c = p_c * V_c\\\\m_c = 1.4 * 15\pi \\\\m_c = 65.973 g[/tex]

Answer: The total weight of the cylinder ( m_l = 180.8 g ) is greater than the total weight of the cone ( m_c = 66 g ).

The volume of the remaining plastic in the cylinder is large, which

makes the weight much larger than the weight of the cone.

Responses:

Density of the plastic for the cone = 1.4 g/cm³

Density of the plastic used for the cylinder = 0.8 g/cm³

From a similar question, we have;

Height of the cylinder = 10 cm

Diameter of the cylinder = 6 cm

Height of the cone = 5 cm

(a) Radius of the cylinder, r = 6 cm ÷ 2 = 3 cm

Volume of a cylinder = π·r²·h

Volume of a hemisphere = [tex]\mathbf{\frac{2}{3}}[/tex] × π×  r³

Volume of the cylinder after it has been hollowed out, V, is therefore;

Which gives;

[tex]V = \pi \times 3^2 \times 10 - \frac{2}{3} \times \pi \times 3^3 \approx \mathbf{ 226}[/tex]

(b) Volume of the cone = [tex]\mathbf{\frac{1}{3}}[/tex] × π × 3² × 5 ≈ 47.1

Mass of the cone = 47.1 cm³ × 1.4 g/cm³ ≈ 66 g

Mass of the hollowed cylinder ≈ 226 cm³ × 0.8 g/cm³ = 180.8 g

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Answer:

Step-by-step explanation:

To find the right answer, we just need to replace the given root in each expression and see which one gives zero.

[tex]f(x)=4x^{4} -7x^{2} +x+25\\f(-\frac{2}{5})= 4(-\frac{2}{5})^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+25=\frac{64}{625}-\frac{28}{25} -\frac{2}{5} +25 \approx 23.58[/tex]

[tex]f(x)=9x^{4}-7x^{2} +x+10=9(-\frac{2}{5} )^{4} -7(-\frac{2}{5} )^{2} +\frac{2}{5} +10 \approx 9.5[/tex]

[tex]f(x)=10x^{4}-7x^{2} +x+9=10(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+9 \approx 7.7[/tex]

[tex]f(x)=25x^{4}-7x^{2} +x+4=25(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+4 \approx 3.12[/tex]

Therefore, neither expression satisfies the given rational root.

Answer:

D. f(x) = 25x^4 - 7x^2 + x + 4.

Step-by-step explanation:

The correct answer to your question is D.

Answer:

57°

Step-by-step explanation:

According to theorem, "any two angles in the same segment of the circle are equal"

So,

m<BED = 57°

Answer:

b. The engineer who weighed the rod 25 times.

Step-by-step explanation:

Hello!

Full text:

Length of a rod: Engineers on the Bay Bridge are measuring tower rods to find out if any rods have been corroded from salt water. There are rods on the east and west sides of the bridge span. One engineer plans to measure the length of an eastern rod 25 times and then calculate the average of the 25 measurements to estimate the true length of the eastern rod. A different engineer plans to measure the length of a western rod 20 times and then calculate the average of the 20 measurements to estimate the true length of the western rod.

Suppose the engineers construct a 90% confidence interval for the true length of their rods. Whose interval do you expect to be more precise (narrower)?

a. Both confidence intervals would be equally precise.

b. The engineer who weighed the rod 25 times.

c. The engineer who weighed the rod 20 times.

X₁: Length of an eastern rod of the Bay Bridge

n₁= 25

X₂: Length of a western rod of the Bay Bridge

n₂= 20

Both Engineers will use their samples to estimate the population average length of the rods using a 90% CI.

Assuming the standard normal distribution, the confidence interval will be centered in the estimated mean.

X[bar] ± [tex]Z_{1-\alpha /2}[/tex]*(σ/√n)

And the width is determined by the semi amplitude:

↓d= [tex]Z_{1-\alpha /2}[/tex]*(σ/√↑n)

As you can see the sample size has an indirect relationship with the semi amplitude of the interval. This means, when the sample size increases, the semi amplitude decreases, and if the sample size decreases, the semi amplitude increases. Naturally this is leaving all other elements of the equation constant, this means, using the same confidence level and the same population standard deviation.

Since the first engineer took the larger sample, he's confidence interval will be narrower and more accurate.

Hope this helps!

Answer:

Height of this missing bar would be 1

Step-by-step explanation:

Since there is 1 and only 1 quantity between 80-99.

Answer:

1

There is 1 number that is between 80 and 99 which is 99 so there should be 1 bar.

Step-by-step explanation:

First check for the critical points of f by checking where the first-order derivatives vanish.

[tex]\dfrac{\partial f}{\partial x}=4x-4=0\implies x=1[/tex]

[tex]\dfrac{\partial f}{\partial y}=2y-4=0\implies y=2[/tex]

Notice how the point (1, 2) lies on the line y = 2x ; at this point, we get a value of f(1, 2) = -5 (MIN).

Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2). We already checked the last one. We find f(0, 0) = 1 (MAX) and f(0, 2) = -3.

Now check on the boundary lines themselves. If x = 0, then

[tex]f(0,y)=y^2-4y+1=(y-2)^2-3[/tex]

which has a maximum value of -3 when y = 2 (so we get the same critical point as before).

If y = 2, then

[tex]f(x, 2)=2x^2-4x-3=2(x-1)^2-5[/tex]

with a maximum of -5 when x = 1.

If y = 2x, then

[tex]f(x,2x)=6x^2-12x+1=6(x-1)^2-5[/tex]

with the same maximum of -5 when x = 1.

This question is based on the absolute maximum and absolute minimum.

We get this by differentiating the terms.

Given:

f(x,y) =   [tex]2x^{2} - 4x + y^2 - 4y +1[/tex], bounded by the lines x=0,y=2,y=2x in the first quadrant,bounded by the lines x=0,y=2,y=2x in the first quadrant.

We need to determined the absolute maximum and absolute minimum of the function.

Now, partial differentiating wrt x and y.

[tex]\dfrac{\partial f}{ \partial x} = 4x -4 = 0 \Rightarrow x= 1 \\\dfrac{\partial f}{ \partial y} = 2y - 4 = 0 \Rightarrow y = 2[/tex]

Now, point (1, 2) lies on the line y = 2x ; at this point, we get a value of

f(1, 2) = -5 (MIN).

Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2).

Now, find f(0, 0) = 1 (MAX) and f(0, 2) = -3.

Now check on the boundary lines themselves.

If x = 0, then we get,

[tex]f(0,y) = y^2 - 4y +1 = ( y-2)^2 -3\\[/tex]

which has a maximum value of -3 when y = 2 (so we get the same critical point as before).

If y = 2, then we get,

f(x,2) = [tex]2x^2-4x -3 = 2(x-1)^2 -5[/tex] with a maximum of -5 when x = 1.

If y = 2x, then we get,

f(x,2x) = [tex]6x^2 -12x +1 = 6(x-1)^2 -5[/tex] with the same maximum of -5 when     x = 1.

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Answer:

Step-by-step explanation:

[tex]a = 5 ,\\b = - 2 \\ c = - 2 \\ 2b - 3ac=?\\2(-2) -3(5)(-2)\\-4 +30\\= 26[/tex]

Answer:

-34

Step-by-step explanation:

2x-2-3(4)(-2)

which is -34

Answer:

1607.68 square miles

Step-by-step explanation:

use pi r squared

Answer:

Step-by-step explanation:

diameter = 64  miles

r =64/2 = 32 miles

Area of semicircle = πr²/2

                              = 3.14*32*32/2

                             = 1607.68 sq.miles

Answer:

The percentage would be 20% (5x20=100)

Step-by-step explanation:

Answer:

The answer is 3.01 x 10’23

Step-by-step explanation:

I got the answer to wrong and guessed the first one and it was correct

Answer:

The sample size required is 289.

Step-by-step explanation:

Let p be population proportion of people that would buy the product.

It is provided that the nationwide poll on this type of product and price was run earlier this year, with percentages running from 75% to 80%.

Assume that the sample proportion of people that would buy the product is, [tex]\hat p=0.75[/tex].

A 95% Confidence Interval is to be constructed with a margin of error of 5%.

We need to determine the sample size required for the 95% Confidence Interval to be within 5% of the actual value.

The formula to compute the margin of error for a (1 - α)% confidence interval of population proportion is:

[tex]MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

The critical value of z for 95% confidence interval is,

z = 1.96.

Compute the sample size required as follows:

[tex]MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

      [tex]n=[\frac{z_{\alpha/2}\ \sqrt{\hat p(1-\hat p)} }{MOE}]^{2}[/tex]

         [tex]=[\frac{1.96\cdot \sqrt{0.75(1-0.75)} }{0.05}]^{2}\\\\=(16.9741)^{2}\\\\=288.12007081\\\\\approx 289[/tex]

Thus, the sample size required is 289.

Answer:

Please see steps below

Step-by-step explanation:

In order to factor by grouping, we divide the four terms given into two groups, and extract on each group any common factor  we can.

In our example, we can select the terms: [tex]w^2[/tex]  and [tex]w[/tex] as one of our groups, and [tex]3w[/tex] and 3 in the other group. Then we re-organize the expression as:

[tex](w^2+w)+(3x+3)[/tex]

Now we extract from the first binomial group, the factor [tex]w[/tex] as a common factor of both terms, and from the second group we extract the factor "3" as common factor of those two terms:

[tex](w^2+w)+(3x+3)\\w(w+1)+3(w+1)[/tex]

We notice now that after the extraction, we are left with two exactly equal binomial factors [tex](w+1)[/tex] that appeared in the first group and in the second group. We proceed then to extract it as common factor for the two groups:

[tex]w(w+1)+3(w+1)\\(w+1)(w+3)[/tex]

this last product of two binomials ([tex](w+1)\,(w+3)[/tex] is the result of factoring the original expression.

Answer:

C

Step-by-step explanation:

It's of the shape of a cone

Answer:

4

Step-by-step explanation:

A=P0(1+rt).

We know that A=$3,500,P0=$2,800 and r=7.5%=0.075, so we can rearrange the formula for A to get an explicit expression for t:

A=P0(1+rt)⟹t=A−P0P0r,

and substituting the known quantities gives

r=$3,500−$2,800$2,800×0.075=3.33,

which means, since the interest is paid annually, that she must wait four years for the total investment to exceed $3,500.

Answer:

48x>+2

Step-by-step explanation:

Answer:

B and F

Step-by-step explanation:

When we'll slice a triangular prism, a square and triangle would be formed

Answer:

Step-by-step explanation:

20 sin^4x

=5(4sin^4 x)

=5(2sin²x)²

=5(1-cos 2x)²

=5(1-4cos2x+cos²(2x))

=5[1-4cos(2x)+{1+cos (4x)}/2]

=5/2[2-8cos(2x)+1+cos(4x)]

=5/2[3-8cos (2x)+cos (4x)]

Answer:

Step-by-step explanation:

Given: DE║BC

To prove: [tex]\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}[/tex]

                Statements                           Reasons

1). DE║BC                                   1). Given

2). ∠1 ≅ ∠4, ∠3 ≅ ∠4                2). Corresponding angles theorem

3). ΔADE ~ ΔABC                      3). AA Similarity theorem

4). [tex]\frac{\text{AB}}{\text{AD}}=\frac{\text{AC}}{\text{AE}}[/tex]                                4). Corresponding sides are proportional

5). [tex]\frac{\text{AD+DB}}{\text{AD}}=\frac{\text{AE+EC}}{AE}[/tex]                   5). Segment addition postulate

6). [tex]1+\frac{\text{DB}}{\text{AD}}=1+\frac{\text{EC}}{\text{AE}}[/tex]                   6). [tex]\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}[/tex]

7). [tex]\frac{\text{DB}}{\text{AD}}=\frac{\text{EC}}{\text{AE}}[/tex]                                7). Subtract 1 from both sides

8). [tex]\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}[/tex]                               8). Take the reciprocal of both sides

Answer:

The answer is C :,)

Step-by-step explanation:

Answer:

The answer to your question is c

Step-by-step explanation:

Because the years have to increase for it to grow.