A one lane highway runs through a tunnel in the shape of one half a sine curve cycle

Answer:

jhshejwjabsgsgshshsnsjs

Answer:

Step-by-step explanation:

Put the equation into center-radius form.

x² + y² + 8x - 12y + 24 = 0

x² + y² + 8x - 12y = -24

(x²+8x) + (y²-12y) = -24

(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24

(x+4)² + (y-6)² = 28

Center: (-4,6)

radius: √28

Answer:

Option C

Step-by-step explanation:

thankful that there are graphing tools. see screenshot

Answer: C

<BFE is 148 degrees

Step-by-step explanation:

We have angles <BFC (57 degrees) and <CFD (34 degrees), but what is <DFE?

1. The angle symbol in the vertexes shows that <BFC is congruent to <DFE, meaning that they are the same

2. Knowing this, we can safely say that <DFE is equal to 57 degrees because <BFC is also 57 degrees.

3. Now, we have all the angles we need to find out <BFE.

4. <BFC+<CFD+<DFE=<BFE

5. Substitute to get

57+34+57=<BFE

91+57=<BFE

148=<BFE

6. Now we know that the answer is 148 degrees.

Answer:

[tex]\displaystyle 51[/tex]

General Formulas and Concepts:

Algebra I

Algebra II

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Addition/Subtraction]:                                                                   [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]

Limit Property [Multiplied Constant]:                                                                     [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.[/tex]

Step 2: Solve

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

Answer:

12

Step-by-step explanation:

Scale factor of 4

CD = 3

3 · 4 = 12

Length of C'D' is 12 units

Answer:

12 units

Step-by-step explanation:

The original segment CD = 3 units

Scale factor is 4.

3 x 4 = 12

Answer:

In picture.

Step-by-step explanation:

To do this answer, you need to count the boxes up to the mirror line. This will give us the exact place to draw the triangle.

The picture below is the answer.

y'' - 6y' + 9y = 0

If y = C₁ exp(3x) + C₂ x exp(3x), then

y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))

y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))

Substituting these into the DE gives

(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))

… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))

… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))

= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))

… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))

… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)

= 0

so the provided solution does satisfy the DE.

Answer: $40 / $80

Step-by-step explanation: 40$ if it's $8 for BOTH per hour, or if it's $8 for ONE per hour it's $80

Answer:

A president, a vice president, and a secretary can be selected in 60 ways.

Step-by-step explanation:

The order in which the people are chosen is important(first president, second vice president and third secretary), which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

3 students from a set of 5, so:

[tex]P_{(5,3)} = \frac{5!}{2!} = 5*4*3 = 60[/tex]

A president, a vice president, and a secretary can be selected in 60 ways.

Tanθ =sin /cos

tan θ = 5/2 / y

tan (30°) = 5/2 /y

[tex]y = \frac{5 \sqrt{3} }{2} [/tex]

y=4.33

Answer:

f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.

Step-by-step explanation:

The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.

* if x>1, then x-1>0.

* Also since the parabola opens up, then y>5.

So let's solve y=(x-1)^2+5 for x.

Subtract 5 on both sides:

y-5=(x-1)^2

Take square root of both sides:

Plus/minus sqrt(y-5)=x-1

We want x-1>0:

Sqrt(y-5)=x-1

Add 1 on both sides:

Sqrt(y-5)+1=x

Swap x and y:

Sqrt(x-5)+1=y

x>5

y>1

Answer:

251.5 cm

Step-by-step explanation:

1 m = 100 cm

1 cm = 10 mm

2 m + 50 cm + 15 mm =

= 2 m * (100 cm)/m + 50 cm + 15 mm * (1 cm)/(10 mm)

= 200 cm + 50 cm + 1.5 cm

= 251.5 cm

Answer:

35

Step-by-step explanation:

y = 35x+23 is in the form

y = mx+b  where m is the slope and b is the y intercept

The slope can also be called the rate of change

35 is the slope

Answer:

0.3736

Step-by-step explanation:

46.7 percent of  [tex]\frac{4}{5}[/tex] is 0.3736.

To find 46.7% of [tex]\frac{4}{5}[/tex].

So,

[tex]\frac{46.7}{100}[/tex] × [tex]\frac{4}{5}[/tex]

[tex]\frac{0.467}{100}[/tex] × [tex]\frac{4}{5}[/tex]

⇒ [tex]0.3736[/tex]

Therefore,  46.7% of  [tex]\frac{4}{5}[/tex] is 0.3736.

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9514 1404 393

Answer:

  arithmetic; common difference of 5

Step-by-step explanation:

It usually works well to check differences first. Here, they are ...

  8 -3 = 5

  13 -8 = 5

These are the same value, so the sequence is arithmetic with a common difference of 5.

Answer:

y = 3

Step-by-step explanation:

6sin(30) = 3

Answer:

The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].

Step-by-step explanation:

Vectorially speaking, the translation of a point can be defined by the following expression:

[tex]V'(x,y) = V(x,y) + T(x,y)[/tex] (1)

Where:

[tex]V(x,y)[/tex] - Original point.

[tex]V'(x,y)[/tex] - Translated point.

[tex]T(x,y)[/tex] - Translation vector.

If we know that [tex]A(x,y) = (-3,4)[/tex], [tex]B(x,y) = (0,1)[/tex], [tex]C(x,y) = (-4,1)[/tex] and [tex]T(x,y) = (6, -4)[/tex], then the resulting points are:

[tex]A'(x,y) = (-3, 4) + (6, -4)[/tex]

[tex]A'(x,y) = (3, 0)[/tex]

[tex]B'(x,y) = (0,1) + (6, -4)[/tex]

[tex]B'(x,y) = (6, -3)[/tex]

[tex]C'(x,y) = (-4, 1) + (6, -4)[/tex]

[tex]C'(x,y) = (2, -3)[/tex]

The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].

Answer:

A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum.

Step-by-step explanation:

Two workers finished a job in 7.5 days.

How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

let t = time required by one worker to complete the job alone

then

(t+8) = time required by the other worker (shirker)

let the completed job = 1

A typical shared work equation

7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1

multiply by t(t+8), cancel the denominators, and you have

7.5(t+8) + 7.5t = t(t+8)

7.5t + 60 + 7.5t = t^2 + 8t

15t + 60 = t^2 + 8t

form a quadratic equation on the right

0 = t^2 + 8t - 15t - 60

t^2 - 7t - 60 = 0

Factor easily to

(t-12) (t+5) = 0

the positive solution is all we want here

t = 12 days, the first guy working alone

then

the shirker would struggle thru the job in 20 days.

Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15

Step-by-step explanation:

minus sign ironically makes it go to the right

because the function crosses the y axis at -13

It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of  transformation, we have to compare the two equations and look for changes.

In the equation y = x - 13, we subtract 13 from the value of x.

This means that the graph of y = x is shifted 13 units downwards,

since every point on the graph has 13 subtracted from its y-coordinate.

Hence,  It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

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Answer:

20'×15 in 54 inches

Step-by-step explanation:

The Best as a pool should be rectangular in shape and 54inches deep for safety of life's

The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = [tex]\pi r^{2}[/tex]h

The volume of the cylindrical pool that has a 3.3 m radius and is 1.8 m deep is;

=  [tex]\pi r^{2}[/tex]h

[tex]= 3.14 (3.3)^2 (1.8)\\\\= 61.55 m^3[/tex]

The volume of the rectangular pool that is 20' x 15' in 54 inches deep ;

V = 20 x 15 x 54

V = 16,200 cubic meter.

The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.

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Answer:

5:12

Step-by-step explanation:

125:300 simplified = 5:12

I hope this helps

More information pleaseeeeeeee

Answer:

Given E(t)=1100(100-t)+580(100-t)^2

Put t = 99.5, we get

E(99.5)=1100(100-99.5)+580(100-99.5)^2

E(99.5)=1100(0.5)+580(0.5)^2

E(99.5)=1100(0.5)+580(0.25)

E(99.5)=550+145

E(99.5)=695m

Step-by-step explanation:

It can be concluded that -

E(99.5) = 695

E(100) = 0

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as follows -

E(t) = 1100(100 - t) + 580(100 - t)²

The given function is -

E(t) = 1100(100 - t) + 580(100 - t)²

At → E(99.5)

E(99.5) = 1100(100 - t) + 580(100 - t)²

E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²

E(99.5) = 1100(0.5) + 580(0.5)²

E(99.5) = 550 + 145

E(99.5) = 695

At → E(100)

E(100) = 1100(100 - t) + 580(100 - t)²

E(100) = 1100(100 - 100) + 580(100 - 100)²

E(100) = 0

Therefore, it can be concluded that -

E(99.5) = 695

E(100) = 0

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Answer:

a)

The null hypothesis is: [tex]H_0: p_M - p_W = 0[/tex]

The alternative hypothesis is: [tex]H_1: p_M - p_W > 0[/tex]

b) For men is of 0.49 and for women is of 0.36.

c) The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Men:

98 out of 200, so:

[tex]p_M = \frac{98}{200} = 0.49[/tex]

[tex]s_M = \sqrt{\frac{0.49*0.51}{200}} = 0.0353[/tex]

Women:

72 out of 200, so:

[tex]p_W = \frac{72}{200} = 0.36[/tex]

[tex]s_W = \sqrt{\frac{0.36*0.64}{200}} = 0.0339[/tex]

a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.

At the null hypothesis, we test if the proportion are similar, that is, if the subtraction of the proportions is 0, so:

[tex]H_0: p_M - p_W = 0[/tex]

At the alternative hypothesis, we test if the proportion of men is greater, that is, the subtraction is greater than 0, so:

[tex]H_1: p_M - p_W > 0[/tex]

b. What is the sample proportion for men? For women?

For men is of 0.49 and for women is of 0.36.

c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?

From the sample, we have that:

[tex]X = p_M - p_W = 0.49 - 0.36 = 0.13[/tex]

[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0353^2 + 0.0339^2} = 0.0489[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error, so:

[tex]z = \frac{0.13 - 0}{0.0489}[/tex]

[tex]z = 2.66[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference above 0.13, which is the p-value of z = 2.66.

Looking at the z-table, z = 2.66 has a p-value of 0.9961.

1 - 0.9961 = 0.0039.

The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

Answer:

[tex]\angle P[/tex]

Step-by-step explanation:

Given

[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]

[tex]PQ = 20[/tex]     [tex]QR = 16[/tex]    [tex]PR = 12[/tex]

[tex]ST = 30[/tex]       [tex]TU = 34[/tex]    [tex]SU = 16[/tex]

See attachment

Required

Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]

Considering [tex]\triangle PQR[/tex]

We have:

[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse

So, we have:

[tex]\sin(P) = \frac{16}{20}[/tex]

Divide by 4

[tex]\sin(P) = \frac{4}{5}[/tex]

Hence:

[tex]\angle P[/tex] is correct

Answer:

A or <P

Step-by-step explanation:

on edge 2021

Answer:

Step-by-step explanation:

the arrows from the picture tells us that TV is parallel to RS

since TS is a transversal that cuts the 2 parallel lines TV and RS than ∠S =x

(alternate interior angles)

sum of angles in a Δ is 180° so x+x+2x = 180°, 4x =180°, x= 45°

2x = 45*2 = 90°

Answer:

135

Step-by-step explanation:

Given that :

Total score obtained by Peter, Jan and Maxim = 269

Let :

Peter's score = x

Jan's score = y

Maxim's score = z

x + y + z = 269

x > (y + z)

For x to be greater Than y + z ;

Then x > (269 / 2) ; x > 134.5

The least possible x score is 135

Hence, Peter's least possible score is 135.

Answer:

C

Step-by-step explanation:

The graph has asymptotes at x = 2 and x = -1 corresponding to the denominator of option C.