Find the value of f (-1).

The angle of depression at which Beatrice sees the boat is 83.35°.

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Check the attached image for the sketch of triangle ABC.

From the sketch, the angle of depression is represented with x:

tan x = 600/70   (tan = opposite/adjacent)

x = tan⁻¹(600/70)

x = 83.35°

Therefore, the angle of depression at which Beatrice sees the boat is 83.35°.

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Answer:

The surface area of a rectangular prism is given by the formula:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively. We are given that the surface area of the prism is 1,060 cm², and that the base has measurements 8 cm and 10 cm.

Substituting these values into the formula, we get:

1060 = 2(8)(10) + 2(8)h + 2(10)h

Simplifying and solving for h, we get:

1060 = 160 + 16h + 20h

1060 = 160 + 36h

900 = 36h

h = 25

Therefore, the height of the prism is 25 cm.

Step-by-step explanation:

Answer: Part A) 3,141.59 Part B) 75.40

Step-by-step explanation:

Sorry if this is wrong.

The breadth and error margin of the confidence interval will rise when the confidence level is raised from 95% to 98%.

We are more certain that the genuine population mean falls inside the interval if the confidence level is larger. The range of feasible values for the population means will be broader since we need to widen the interval in order to reach this higher degree of confidence.

Since the margin of error equals half of the interval's breadth, it is directly proportional to the interval's width. The margin of error will therefore expand as the confidence level does as well.

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The length of the third side of the triangle is 10.7 feet.

Patricia is building a garden in her backyard that is shaped like a triangle. She has already built two sides of the garden  and they have length of 6 feet and 7 feet.

She wants to find the length of the third side. The angles between the the built sides is 110 degrees.

Therefore, let's find the third sides using the included angle and the two known sides.

using cosine rules,

c² = a² + b² - 2ab cos C

c² = 6² + 7² - 2(6)(7) cos 110

c² = 36 + 49 - 84 cos 110°

c² = 85 - 84(-0.34202014332)

c² = 85 + 28.7296920394

c = √113.729

c = 10.6643799632

c = 10.7 feet

Therefore,

third side of the triangle = 10.7 feet

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Answer: 6.5

Step-by-step explanation:

26/4 = 6.5 hours

The probability that you will get a 15-inch monitor = 1/3

We know that probability of event is the ratio of number of possible outcomes of event A and the total number of outcomes.

Let us assume that event A = you will get a 15-inch monitor

The number of favourable outcomes for event A are 2

So, n(A) = 2

The sample space for this experiment would be,

n(S) = 6

Using the definition of probability, the required proabability would be,

P(A) = n(A) / n(S)

P(A) = 2/6

P(A) = 1/3

Therefore, the required probability = 1/3

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Answer:

56% Caesar

Step-by-step explanation:

The only salads sold were Caesar and it is majority

The monthly payment will be $618.71

We know that the formula for the loans are:

[tex]P_0=\frac{d(1-(1+\frac{r}{k} )^{-Nk})}{\frac{r}{k}}[/tex]

where

P₀ is principal

d is monthly payment, annual payment

r is the annual interest rate in decimal form.

k is the number of compounding periods in one year.

and N is the length of the loan, in years.

Here, P₀ =  $32,000

r = 0.06

N = 5

k = 12

Using above formula of loan we need to find value of d.

[tex]P_0=\frac{d(1-(1+\frac{r}{k} )^{-Nk})}{\frac{r}{k}} \\\\32000 =\frac{d(1-(1+\frac{0.06}{12} )^{-60})}{\frac{0.06}{12}}\\\\32,000 =\frac{d(1-(1+0.005)^{-60})}{0.005} \\\\32000\times 0.05=d(1-(1.005)^{-60})\\\\160=d\times (1-0.7414)\\\\d = 160/0.2586\\\\d=618.72[/tex]

Therefore, the monthly payment = $618.71

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Answer:

32

Step-by-step explanation:

in the word problem “256 chairs in the cafeteria. this is 8 times the chairs in the library.” Which means 8 times the number of chairs in the library equals the number of chairs in the cafeteria.

L = library

8 x L = 256

to find L divided 256 by 8

256/8 = 32

L = 32

Check the answer

8 x 32 = 256

The circumference of the lollipop is 12.57 inches.

Circumference is the measurement of the distance around the outer edge of a closed curve, particularly a circle. It is the total length of the curve that makes up the boundary of the circle.

The circumference of the circle is given by the formula;

Circumference = 2 × π × radius

where π (pi) is the mathematical constant approximately equal to 3.14159265359...

Given that the radius of the round lollipop is 2 inches, we can substitute this value into the formula;

Circumference = 2 × π × 2

Using the approximate value of π as 3.14159265359..., we can calculate the circumference;

Circumference = 2 × 3.141592 × 2

Circumference ≈ 12.56

Therefore, the circumference of the lollipop is approximately 12.57 inches.

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The equation for contribution for each student is 185.5/14 = 13.25.

Price of new easel= $129

Set of blank canvases = $ 46

Sales tax = $ 10.50

So, the total amount is

= 129 + 46 + 10.5

= 185.5

Then, each student contribute

= 185.5 / 14

= 13.25

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The proportion Max can use to find how many quarts of lemonade is 2 gallons divided by 4 quarts per gallon equals 8 quarts.

Max can use the following proportion to calculate how many quarts of lemonade he made:

1 gallon equals 4 quarts

Max can calculate the number of quarts by multiplying 2 by 4 because he made 2 gallons of lemonade:

2 gallons divided by 4 quarts per gallon equals 8 quarts

As a result, Max created 8 pints of lemonade.

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For 3 personal training session both gym cost same.

We have,

At Silver gym, membership is $25 per month and personal training sessions are $30 each.

At Fit Factor, membership is $65 per month, the and personal training sessions are $20 each.

let the number of personal session be x.

So, 25+ 30x = 65 + 20x

30x - 20x = 65 - 25

10x = 30

x= 3 sessions

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Answer:

√(6 + 9 +12) = √27 = 3√3

√(-6 + 9 + 12) = √15 = √3√5

√(6 - 9 + 12) = √9 = 3

√(6 + 9 - 12) = √3

(1/4)(3√3)(√3√5)(3)(√3)

= (1/4)(27√3)(√5) = (27√15)/4 = 26.1

Answer:correct answer is 26.1

Step-by-step explanation:

Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is given by:

A = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter, which is half the perimeter of the triangle:

s = (a + b + c) / 2

In this case, the side lengths are a = 6, b = 9, and c = 12. Therefore, the semiperimeter is:

s = (6 + 9 + 12) / 2 = 27 / 2

Using Heron's formula, we can now calculate the area of the triangle:

The horizontal and vertical translations that map triangle XYZ onto its image, triangle X'Y'Z' include the following: C. right 3; down 5.

In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In order to map the two triangles, we would have to apply a vertical translation to f(x) by 5 units down and a horizontal translation by 3 units right.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

0.38 degrees.

Step-by-step explanation:

C = 2π(53) = 106π km

The train is traveling at a speed of 44 km/h, which is equivalent to (44/60) km/min since there are 60 minutes in an hour.

d = (44/60) km/min

θ = (d / C) x 360°

θ = [(44/60) / (106π)] x 360°

θ ≈ 0.38°

Therefore, the angle through which the train turns in 1 minute is approximately 0.38 degrees.

The class that contains the 80 th percentile is d) 32-34.

First, find the total frequency of the income :

Total frequency = 2 + 11 + 8 + 5 + 4 = 30

The position of the number at the 80 th percentile would then be :

= 30 x 80 %

= 24 th position

The cumulative frequency of :

26 - 28 =  2

28  - 30 : 2 + 11 = 13

30 - 32 : 13 + 8 = 21

This then means that the 24 th position is in the next interval of 32 - 34.

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Answer:

3.14 (24 square) (2.5)

Step-by-step explanation:

3.14 24 square 2.5

X radius squared X height???

The answers are (-8, 5) and (-8, -5)

Given that, the point (8, 5) is on the graph of an even function, we need to find the other point must also be on the graph,

A function f(x) is said to be an even function if it satisfies the following equation: f(−x) = f(x)

A function satisfying this equation has a graph that is symmetric about the y-axis.

So, if the point (8, 5) is on the graph of an even function, the (-8, 5) must also be on the graph of the function.

Also, the point (8, 5) is on the graph of an odd function,

The graph of an odd function is symmetrical about the origin. Therefore, an odd function satisfies the following condition:

-f(x) = f(-x),

Therefore,

(8, 5) = (-8, -5)

Hence, the answers are (-8, 5) and (-8, -5)

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Answer:

A) oblique hexagonal prism

Step-by-step explanation:

Answer:

right hexagonal prism

Step-by-step explanation:

as seen on the Image below the left one is a right hexagonal prism and the right one is a oblique hexagonal prism.

Answer:

- angle T is congruent to angle U (given)

- NS is congruent to SH (given)

- angle TSN is congruent to USH (vertical angles are congruent)

So triangle TNS is congruent to triangle UHS by AAS.

The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

We have the 4 functions as shown in the image attached.

The y - intercept is the point where the graph intercepts the y - axis.

Function [1] -

y = 4 + 2x

y - intercept is 4

Function [2] -

y = 5ˣ + 1

y - intercept is 2.

Function [3] -

the y-intercept is 1.

Function [4] -

the y - intercept is at -1.

Therefore, the greatest y-intercept is of function -

f(x) = 2x + 4

and the least y-intercept is of the function shown in graph [4] or function [4].

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Answer:

Carlos puts $3 into his bank account and it grows by 50% each year

f(x)=4^x+1

(The Table)

(The Graph)

The probability that Mia and Lia place in 1st or 2nd is 99/2450. There are two possible scenarios in which Mia and Lia can place in 1st or 2nd: Mia places 1st and Lia places 2nd, or Mia places 2nd and Lia places 1st. The probability of the first scenario is (1/50) * (1/49) = 1/2450. The probability of the second scenario is also (1/50) * (1/49) = 1/2450. Since these two scenarios are mutually exclusive, we can add their probabilities to find the total probability: 1/2450 + 1/2450 = 2/2450. However, we must also account for the fact that there are 49 other people who could place in 3rd. So the final probability is (2/2450) * 49 = 98/2450. Adding the probability that neither Mia nor Lia place in 3rd (1/2450), we get 98/2450 + 1/2450 = 99/2450.

Received message. The probability that Mia and Lia place in 1st or 2nd is **99/2450**. There are two possible scenarios in which Mia and Lia can place in 1st or 2nd: Mia places 1st and Lia places 2nd, or Mia places 2nd and Lia places 1st. The probability of the first scenario is `(1/50) * (1/49) = 1/2450`. The probability of the second scenario is also `(1/50) * (1/49) = 1/2450`. Since these two scenarios are mutually exclusive, we can add their probabilities to find the total probability: `1/2450 + 1/2450 = 2/2450`. However, we must also account for the fact that there are `49` other people who could place in 3rd. So the final probability is `(2/2450) * 49 = 98/2450`. Adding the probability that neither Mia nor Lia place in 3rd (`1/2450`), we get `98/2450 + 1/2450 = 99/2450`.

Yes, The argument is valid.

Now, We have;

(∀x) (∃y) (p(x, y) ⇒ r(x))

Means that for any integer x, there exists an integer y such that if x is a factor of y, then x is prime.

(∀x)(∀y)(∀z)(¬q(x, y, z)) means that for any integers x, y, and z, the greatest common factor of x and y is not z.

(∃x)(∀y)(p(x, y) ∨ r(x)) means that there exists an integer x such that for any integer y, either x is a factor of y or x is prime.

Therefore, (∀y)(∃z)(∃x)q(x, y, z) means that for any integer y, there exists integers z and x such that the greatest common factor of x and y is z.

To see why this conclusion follows, consider that if (∀y)(∃z)(∃x)q(x, y, z) were false, then there would be some integer y such that for all integers z and x, the greatest common factor of x and y is not z.

However, this would contradict (∀x)(∀y)(∀z)(¬q(x, y, z)), which states that for any integers x, y, and z, the greatest common factor of x and y is not z.

Therefore, the argument is valid.

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The likelihood that they will choose to work in an animal shelter for each of the six options they choose is around 0.2214 or 22.14%

The probability is given as,

P = (Favorable event) / (Total event)

The likelihood of choosing an opportunity at an animal shelter is 7/9. If each chance is equally likely to be chosen, the likelihood of choosing six in a row from an animal shelter may be estimated by multiplying the likelihood of choosing one opportunity by itself six times:

P = (7/9) x (7/9) x (7/9) x (7/9)

P = (7/9)⁶

P = 0.2214 or 22.14%

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The rule of the function table is,

⇒ y = 1/2x

Now, We have to given that;

Table is shown in image.

Let two points on the table is, (24, 12) and (12, 6)

Hence, We get;

The equation for table is,

y - 12 = (6 - 12) / (12 - 24) (x - 24)

y - 12 = - 6/-12 (x - 24)

y - 12 = 1/2 (x - 24)

y - 12 = 1/2x - 12

y = 1/2x

Thus, The rule of the function table is,

⇒ y = 1/2x

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Answer:

Step-by-step explanation:

Answer:

2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2

B is the correct answer.