Subtract: (-137° + 6) - (-43°) Your answer should be in simplest terms. Enter the correct answer.​

The bottom of the ladder is sliding along the ground at a rate of 20 feet per second when it is 5 feet away from the base of the wall.

Let's denote the distance between the base of the ladder and the wall as x and the distance between the top of the ladder and the ground as y. Then we can use the Pythagorean theorem to relate x and y

x² + y² = 21²

We want to find how fast the bottom of the ladder (x) is sliding along the ground, which is the rate of change of x with respect to time. Let's call this rate dx/dt.

We are given that the top of the ladder is slipping down the wall at a rate of 5 feet per second, which means that the rate of change of y with respect to time (dy/dt) is -5. The negative sign indicates that y is decreasing.

We want to find the value of dx/dt when x = 5. To do this, we need to relate x, y, dx/dt, and dy/dt using implicit differentiation

2x(dx/dt) + 2y(dy/dt) = 0

Simplifying this expression, we get

dx/dt = -(y/x) × dy/dt

We can substitute the values we know into this equation

dx/dt = -(y/x) × (-5) = 5y/x

To find y when x = 5, we can use the Pythagorean theorem

5² + y² = 21²

y = √(21² - 5²) = 20

Substituting this into the equation for dx/dt, we get

dx/dt = 5y/x = 5(20)/5 = 20

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A simple random sampling method might select any 20 customers when preparing a representative sample from a list of 200 customers who complained about errors in their statements.

Simple random sampling involves selecting a subset of individuals from a larger population in such a way that every individual has an equal chance of being chosen. In this scenario, the researcher would assign a unique identifier to each customer on the list and then use a random number generator or a randomization technique to select 20 customers from the list. This ensures that each customer has an equal probability of being included in the sample.

By using simple random sampling, the researcher can reduce bias and ensure that the selected sample is representative of the larger population. This method allows for unbiased generalizations and provides a fair representation of the views and experiences of the customers who complained about errors in their statements.

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According to the given image, with the help of a protractor, we can conclude that ∠NCD represents an angle of 50°.

An instrument for measuring angles is a protractor, which is often made of transparent plastic or glass.

Protractors might be straightforward half-discs or complete circles. Protractors with more complex features, like the bevel protractor, include one or two swinging arms that can be used to measure angles.

Most protractors use degrees (°) to express angles.

Protractors with radian scales calculate angles.

The majority of protractors have 180 equal segments.

Degrees are further subdivided into arcminutes by some precision protractors.

They are employed in geometry, engineering, and mechanics.

So, in the given image the proctor is measuring the angle of 50°.

Therefore, according to the given image, with the help of a protractor, we can conclude that ∠NCD represents an angle of 50°.

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Answer:

5 choose 4

\(=\frac{5!}{4!\left(5-4\right)!}\) = 5

Step-by-step explanation:

Answer:

5/16=s/32

Step-by-step explanation:

What we know:

- a school team has 80 swimmers

The ratio of 7th grade swimmers to every swimmer in their school (counting all the grades) is 5:16. Write a proportion of this for a value of s.

a ratio can also be expressed in a fraction by simply putting it from x:y to x/y

so, the ratio 5:16 can also be expressed as 5/16.

note: let sgs represent seventh grade swimmers.

also, let x represent the value of the equivalent amount of swimmers (in the denominator that serves as a value for the proportion of 5/16.

we need to find:

5 sgs/16 swimmers = s amount of sgs/x

5/16=s/x

equivalent fractions could literally be anything, just multiply that ratio by a value equal to one; ex 4/4, or 16/16, or 2/2.

the simplest proportion is to multiply 5/16 by 2/2.

5/16*(2/2)=s/x

10/32=s/x

so s=10 and x=32 but we only need to know x cuz your problem doesn't have a box to answer the s=10.

so... 5/16=s/32.

ANSWER

The short piece is 10 meters long and the long piece is 33 meters long

EXPLANATION

Let the length of the shorter piece be x.

Let the length of the longer piece be y.

We have that the total length of the banner is 43 meters. This means that:

x + y = 43 ___(1)

The short piece is 23 meters shorter than the long piece. This means that:

x = y - 23 _____(2)

Now, we have a system of two simultaneous equations:

x + y = 43

x = y - 23

We can solve this by substitution.

Substitute the second equation into the first equation.

That is:

y - 23 + y = 43

Collect like terms:

y + y = 43 + 23

2y = 66

Divide through by 2:

y = 66 / 2

y = 33 m

Recall that:

x = y - 23

Therefore:

x = 33 - 23

x = 10 m

Therefore, the short piece is 10 meters long and the long piece is 33 meters long.

y=4x+7

First we need to figure out the slope. We can do that using the equation (y2-y1)/(x2-x1). Substitute your numbers in for the xs and ys:

(-9-7)/(-4-0)=

-16/-4=

4

Now that we have the slope, we can figure out the intercept by using the equation y=mx+b and substituting one of the points in for x and y, the slope in for m, and solving for b.

I’m going to use (0,7) as it will be faster:

7=4(0)+b

7=0+b

7=b

The full equation will then be:

y=4x+7

Answer:

D. 0

Step-by-step explanation:

Answer:

d. 0

Step-by-step explanation:

−(−x)3 − x3

(remove parentheses)

x * 3 -x *3

(eliminated opposites)

0

(your answer)

Answer:

it gonna be $6,427.94 which is D

Step-by-step explanation:

The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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Answer:

should look like this

Step-by-step explanation:

equations are y=x  and  y = -x if needed

The equation of the lines are y = x and y = x - 2

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept

The equation of a line passing through the point (2, 2) with a slope of 1 is:

\(y-y_1=m(x-x_1)\\\\y-2=1(x-2)\\\\y = x\)

The equation of a line passing through the point (1, -1) with a slope of 1 is:

\(y-y_1=m(x-x_1)\\\\y-(-1)=1(x-1)\\\\y = x-2\)

Therefore both lines have equation of y = x and y = x - 2. The graphs of the lines are attached.

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Answer:

9/40= 0.225 (experimental probability for white)

(b) because the spinner has 10 sections but there has only been 3 outcomes. If the spinner has 3 sections the changes of white would be 0.333.

2. Is correct, the more times you spin the closer you’ll get to the theoretical probability.

Step-by-step explanation:

a.  The marginal pdf f1(x) of X is 0

b. the conditional pdf f2(y∨x) is 0

c. The  P(Y>13∨X=x) for any x>13 is  0

a. To find the marginal pdf f1(x) of X, we integrate f(x,y) over y from 0 to x:

f1(x) = ∫ f(x,y) dy from 0 to x

= ∫ 15xy^2 dy from 0 to x

= 5x^4

So, f1(x) = 5x^4 for 0 ≤ x ≤ 1, and f1(x) = 0 otherwise.

b. To find the conditional pdf f2(y∨x), we use the formula:

f2(y∨x) = f(x,y) / f1(x)

So, we have:

f2(y∨x) = 15xy^2 / (5x^4) = 3y^2 / x^3 for 0 ≤ y ≤ x ≤ 1, and f2(y∨x) = 0 otherwise.

c. To find P(Y > 13 ∨ X = x) for any x > 0, we need to integrate the joint pdf f(x,y) over the region where y > 13 and x = x. This region is a triangular region with vertices at (x,13), (x,x), and (1,x). So, we have:

P(Y > 13 ∨ X = x) = ∫∫ f(x,y) dy dx over the triangular region

= ∫ x∫13^x 15xy^2 dy dx / (5x^4)

= ∫ x [(13x^3)/2 - (x^4)/4] dx / (5x^4)

= 15/8 - (13/8)x

So, P(Y > 13 ∨ X = x) = 15/8 - (13/8)x for 0 < x ≤ 1, and P(Y > 13 ∨ X = x) = 0 otherwise.

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Answer:

I shall assist thee.

Step-by-step explanation:

Being me, I would say the answer is A. or B. But i'd prolly go with A tbh.

And oofers on me if this ain't what you need.

\(\huge\text{Hey there!}\)

\(\mathsf{f(x) = -3x}\\\\\mathsf{f(x) = -3(5)}\\\\\textsf{Picture your equation is showing you: }\mathsf{-3\times5}\textsf{ and that should give you the answer}\\\textsf{for your function \boxed{\mathsf{f(x)}} also known as your y-value}\\\\\mathsf{f(x) = -3\times5}\\\\\mathsf{f(x) =-15}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{x = -15}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

15/16

Step-by-step explanation:

just divide the fraction. or other is 0.9375

Answer:

0.9375

Step-by-step explanation:

Answer:

164.6

Step-by-step explanation:   i'm a human calculator

Answer:

164.6

Step-by-step explanation:

Divide 987.6 by 6 = 987.6/6= 164.6

Answer:

Well we are going to use the formula of a trapezoid.

What'd given is that two bases are 5 and 10 and the height is 6

add the two bases: 10 + 5 = 15 multiply it by 6 = 15 x 6 = 90 then divide by 2 = 45 since she is making 4 multiply it by 4,

45 x 4 = 180 fabric she needs.

The result of inverse trigonometric function are: cos, tan^-1, sin, tan^-1(5), sin^-1, tan^-1(-1), sin^-1(1), cos, sin, cos^-1(0), tan(13), sin^-1(1), cos, cos^-1.

Inverse trigonometric functions are used to determine the angle measures of a right triangle given the length of two sides. In this problem, we are matching the inverse tangent solutions to the corresponding trigonometric problems. The inverse tangent function, tan^-1(x), gives the angle whose tangent is x.

Therefore, matching tan^-1(1/6) with problem number 2 means finding the angle whose tangent is 1/6. Similarly, matching cos^-1(0.5) with problem number 10 means finding the angle whose cosine is 0.5. The other inverse trigonometric functions, such as sin^-1(x) and cos^-1(x), give the angles whose sine and cosine are x, respectively.

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Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

The probability that at most a fifth of the buyers would prefer green is approximately 0.0198

This problem can be solved by using the binomial distribution. Let X be the number of buyers out of 15 who prefer green. Then X follows a binomial distribution with parameters n = 15 and p = 0.6.

We want to find the probability that at most a fifth of the buyers would prefer green. This means we want to find P(X ≤ 3), since a fifth of 15 is 3.

Using the binomial probability formula, we have

P(X ≤ 3) = Σ P(X = k) for k = 0 to 3

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (15 choose 0) (0.6)⁰ (0.4)¹⁵ + (15 choose 1) (0.6)¹(0.4)¹⁴ + (15 choose 2) (0.6)² (0.4)¹³ + (15 choose 3) (0.6)³ (0.4)¹²

= 0.0000265 + 0.000397 + 0.00312 + 0.0163

Add the number

= 0.0198

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the total decrease in value of the machine in the second 5 years after it was bought is $35000. option B is correct.

To find the total decrease in value of the machine in the second 5 years after it was bought, we need to integrate the rate of change of value over that time period.

Given that the rate at which the value changes is 500(t - 12) dollars per year, we can integrate this expression over the interval t = 12 to t = 17 (second 5 years).

The integral of 500(t - 12) with respect to t is:

∫[0 to 10] 500(t - 12) dt

= 500 ∫[0 to 10] (t - 12) dt

= 500 [(t²/2 - 12t) | [0 to 10]

= 500 [(10²/2 - 12*10) - (0²/2 - 12*0)]

= 500 [(50 - 120) - 0]

= 500 [-70]

= - 350000

Therefore, the total decrease in value of the machine in the second 5 years after it was bought is $35000. option B is correct.

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Answer:

29

Step-by-step explanation:

-3 1/3 • -8 7/10

-10/3 • -87/10

870/30

29

Answer:So for an isosceles right triangle with side length a , the hypotenuse has a length of a√2 . Similarly, if the hypotenuse of an isosceles right triangle has length of a , the legs have a length of a√2ora√22 each

Step-by-step explanation:

An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.

FOR EXAMPLE What is the length of the legs of an isosceles right triangle if the hypotenuse is 8 units?

2 Answers By Expert Tutors. For an isoceles right trangle, the legs each have length x and the hypotenuse has length x √2. Therefore, since the hypotenuse has length 8√2, the legs must each be of length 8.

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Have a GREAT day!!!

Answer:

C

Step-by-step explanation:

Don't worry about the volume to start with. Just look at the area of the top or bottom.

The hole has a 4 inch diameter

d = 4

r = d/2

r = 2

Area = pi r^2

Area = pi * 2^2

Area = 4 pi

Now find the area of the top (or bottom) if the circle was not there.

L = 8

W = 6

Area = L * W

Area = 8 * 6

Area = 48

Now take away the area of the circle.

Area Top = 48 - 4 * pi

Area Top = 48 - 12.56

Area Top = 35.44

Finally, Find the volume

Volume = area of the top * height

Volume = 35.44 * 15

Volume = 531.6