Which of the following statements are true about the diagram

Answer:

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)

If leg b is unknown, then: b = √(c² - a²)

For hypotenuse c missing, the formula is: c = √(a² + b²)

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf P= 9 \ in. }[/tex]

Step-by-step explanation:

Given is a right-angled triangle.

So, we can use Pythagorean Theorem to find the missing length.

It is:

[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]

Here,

Hypotenuse = 41 in.

Base = 40 in.

Perpendicular = P

[tex](41)^2=(40)^2+P^2\\\\1681 = 1600 + P^2\\\\Subtract \ 1600 \ from \ both \ sides\\\\1681-1600=P^2\\\\81 = P^2\\\\Take \ square \ root \ on \ both \ sides\\\\\sqrt{81} = \sqrt{P^2} \\\\P= 9 \ in. \\\\\rule[225]{225}{2}[/tex]

The probability of selecting the committee in the order of man, man, man, woman, woman, without replacement is; 5/133

The probability of an event is the ratio of the number of desired outcome to the number of possible outcome.

The number of men in the board = 12

The number of women in the board = 10

The probability of selecting a man in the first position = 12/22

The number of men remaining is 11 and the number of women remaining is 10.

The probability of selecting a man in the second position is therefore = 11/21

In the same order, the probability of selecting a man in the third position = 10/20

The probability of selecting a woman next = 10/19

The probability of selecting another woman = 9/18

The probability of selecting the committee of five members in the specified order is therefore;

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The number 3 in the equation h(t) = -16t² + 6t+ 3 represents the initial height from which the ball is thrown.

The equation h(t) = -16t² + 6t+ 3 models the height of the ball thrown in the air, with h(t) measured in feet and time, t, measured in seconds. The number 3 in this equation refers to the height from which the ball is thrown. This is represented by the constant term 3, which is added to the equation after the sum of the variables. The formula h(t) = -16t² + 6t+ 3 can be broken down into three parts. The first part is the constant term, 3, which denotes the initial height of the ball. The second part is the linear term, 6t, which represents the acceleration of the ball due to gravity. Lastly, the quadratic term, -16t², is used to describe the rate at which the ball’s acceleration slows down due to air resistance. Therefore the number 3 in the equation h(t) = -16t² + 6t+ 3 represents the initial height from which the ball is thrown.

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The area of the forest will be approximately 1396 km sq. after 10 years.

Given that, a forest covers an area of 2100 km sq and that each year this area decreases by 4%..

If the area of the forest decreases by 4% each year, then after one year it will be 96% of the original size.

After two years, it will be 96% of 96% of the original size, or 0.96² of the original size.

After ten years, it will be 96% of itself ten times, or 0.96¹⁰ of the original size.

So the area of the forest after 10 years will be:

Area = Initial area × 0.96¹⁰

Area = 2100 km sq × 0.96¹⁰

Area = 1396 km sq

Therefore, the area of the forest cover in 10 years will be 1396 km sq.

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Answer:

B

Step-by-step explanation:

assuming DF is the diameter of the circle , then

the angle in a semicircle is 90° , that is

∠ DCF = 90° and Δ CDF is a right triangle

using Pythagoras' identity in the right triangle

CD² + CF² = DF²

CD² + 60²  65²

CD² + 3600 = 4225 ( subtract 3600 from both sides )

CD² = 625 ( take square root of both sides )

CD = [tex]\sqrt{625}[/tex] = 25

The probability that a person who walked also sailed is 1/8.

Probability is used to make predictions about the likelihood of future events, based on past observations or available information. It is widely used in fields such as statistics, finance, engineering, and science to analyze and model uncertain systems and processes.

Out of the 50 people, 3 did not participate in either walking or sailing. So, the number of people who participated in at least one activity is:

50 - 3 = 47

Out of these 47 people, 40 took part in walking and 18 took part in sailing. However, we need to subtract the number of people who participated in both activities because we don't want to count them twice. Let's call this number "x":

x = number of people who participated in both walking and sailing

So, the number of people who participated in at least one of the activities is:

40 + 18 - x

We know that there were 50 people in total, so we can write:

40 + 18 - x + 3 = 50

Simplifying this equation, we get:

55 - x = 50

x = 5

So, 5 people participated in both walking and sailing.

Now, we want to find the probability that a person who walked also sailed. Since there were 40 people who walked and 5 of them also sailed, the probability is:

5/40 = 1/8

Therefore, the probability that a person who walked also sailed is 1/8.

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Step-by-step explanation:

law of cosine

c² = a² + b² - 2ab×cos(C)

c is the side opposite of the C angle. a and b are the other 2 sides.

AB² = 4² + 4² = 16 + 16 = 32

AB = c = sqrt(32) = 5.656854249...

since a and b are equal (isoceles triangle), so must be the angles at A and B.

the sum of all angles in a triangle is always 180°.

180 = angle A + angle B + angle C

= angle A + angle B + 120

since angle A = angle B we get

180 = 2×angle A + 120

2×angle A = 60°

angle A = angle B = 30°.

The functiοn has a pοint οf inflectiοn at x=0, which implies that f''(0) = 0.

A graph οf a functiοn is a visual representatiοn οf hοw the οutput οf a mathematical functiοn changes as its input varies. It typically cοnsists οf a set οf pοints plοtted οn a cοοrdinate plane.

       |             /\

       |           /    \

       |         /        \

       |       /            \

f(x)   |  _ /________\__/\____

-2    -1   0    1   2   3   4

The functiοn has a lοcal minimum at x=-2 and a lοcal maximum at x=2, which implies that f''(x) > 0 οn (-infinity, -2) and (4, infinity).

The functiοn has hοrizοntal tangents at x=-1, 1, and 3, which implies that f'(-1) = f'(1) = f'(3) = 0.

The functiοn has a pοint οf inflectiοn at x=0, which implies that f''(0) = 0.

The functiοn passes thrοugh the οrigin, but this is nοt a necessary cοnditiοn tο satisfy the given prοperties. There are many οther pοssible functiοns that wοuld satisfy the given cοnditiοns.

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The expression that does not belong with the other three is B. x ² - 8 ˣ because C. The different expression is the one that is not a polynomial.

Expression 2 is not a polynomial because it contains a term (8^x) with a variable in the exponent, which is not allowed in a polynomial. All the other expressions are polynomials.  This expression therefore does not belong.

Polynomials are mathematical expressions that consist of variables and coefficients, where the variables are raised to non-negative integer powers and the coefficients are constants.

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Answer:

3x-7

Step-by-step explanation:

A square’s area represents (ax+b)^2. Let’s expand that. [tex]a^2x^2+2abx+b^2[/tex] now, we can notice this fits perfectly when a=3 and b=-7. Therefore one side length of the square is 3x-7.

Answer:

Step-by-step explanation:

Ok so basically, what I would do is make note of each of the points of the triangle, and them multiply them by four, or the scale factor.

Answer:

3/4 miles

Step-by-step explanation:

Parameters

Total distance = 3 1/2 miles

Covered distance = 2 3/4 miles

To make things easier let's convert our parameters from fraction to decimal,

Therefore,

Total distance= 3.5 miles

Covered distance = 2.75 miles

Remaining distance = Total distance - Covered distance

Remaining distance = 3.5 miles - 2.75 miles

Remaining distance= 0.75 miles

Converting back to fraction,

Remaining distance = 3/4 miles

Therefore,

Lisa has 3/4 miles left to hike.

Please mark brainliest.

Thanks.

Answer:

The y-intercept represents a starting salary of $32,500.

The slope represents an additional $2,500 in salary for each additional year of employment.

If the starting salary for a new employee is changed to $35,000 and the yearly salary increase is unchanged, the new equation would be
[tex]y=2500x+35000[/tex].

If the yearly salary increase is changed to $3,000 and the starting salary remains the same, the new equation would be
[tex]y = 3000x + 32500[/tex].

Step-by-step explanation:

Answer:

The y-intercept represents a starting salary of $32,500.

The slope represents an additional $2,500 in salary for each additional year of employment.

If the starting salary for a new employee is changed to $35,000 and the yearly salary increase is unchanged, the new equation would be

y=2500x+35000y=2500x+35000 .

If the yearly salary increase is changed to $3,000 and the starting salary remains the same, the new equation would be

y = 3000x + 32500y=3000x+32500 .

Answer:

None of it.

Step-by-step explanation:

Notice the slope is 2.75 this means for EVERY X the graph goes up by 2.75 in the Y axis. For example.
If at                 X=1     y=0
Then for         X=2   y=2.75

and for            X=3  y=2.75+2.75=5.5
also the graph must pass thought point (0,0), the origin, and none of the graph follow this.  

You can also compare the slopes of each equations
for graph A, from x=1 to x=2 the height Y goes from 3 to 3.5, this is a slope of 0.5 (not the 2.75 we are looking for)

for graph A, from x=1 to x=2 the height Y goes from 1 to 2.5, this is a slope of 1.5 (not the 2.75 we are looking for)

for graph A, from x=1 to x=2 the height Y goes from 1 to 2.75 this is a slope of 1.75 (not the 2.75 we are looking for)

notice the last is similar to equation y=1.75X+b, just in case.

Answer:

none

Step-by-step explanation:

Answer:

6.

[tex]48\pi \: {ft}^{3} [/tex]

7.

[tex]81\pi \: {m}^{3} [/tex]

8.

[tex]112 \: {in}^{3} [/tex]

9.

[tex]14.52\pi \: {cm}^{3} [/tex]

10.

[tex]68.75\pi \: {yd}^{3} [/tex]

11.

[tex]32.269\pi \: {m}^{3} [/tex]

12. h ≈ 3,3 yd

13. h ≈ 5,5 m

14. V ≈ 77,0 in^3

15. V ≈ 69,1 in^3

16. V ≈ 8517,0 in^3

17. V ≈ 2628,1 cm^3

Step-by-step explanation:

6.

[tex]v = \pi {r}^{2} \times h[/tex]

[tex]v = \pi \times {4}^{2} \times 3 = 48\pi[/tex]

.

7.

[tex]v = {9}^{2} \times \pi \times 1 = 81\pi[/tex]

.

8.

[tex]v = {4}^{2} \times \pi \times 7 = 112\pi[/tex]

.

9.

[tex]v = ( {2.2})^{2} \times \pi \times 3 =14.52\pi[/tex]

.

10. r = 0,5 × d

r = 0,5 × 5 = 2,5 yd

[tex]v = ({2.5})^{2} \times \pi \times 11 = 68.75\pi[/tex]

.

11. r = 0,5 × 4,6 = 2,3 m

[tex]v = ({2.3})^{2} \times \pi \times 6.1 = 32.269\pi[/tex]

.

12. V = 41,5 yd^3

r = 2 yd

[tex]v = \pi \times {r}^{2} \times h[/tex]

[tex]41.5= \pi \times {2}^{2} \times h[/tex]

[tex]h = \frac{41.5}{4\pi} = \frac{83}{8\pi} ≈3.3[/tex]

.

13. d = 1,5 m

r = 0,5 × 1,5 = 0,75 m

V = 9,7 m^3

[tex]v = \pi {r}^{2} \times h[/tex]

[tex]9.7 = \pi \times ( {0.75})^{2} \times h[/tex]

[tex]h = \frac{9.7}{0.5625\pi} ≈5.5[/tex]

.

14. Given:

h = 8 in

d = 3,5 in

Find: V - ?

First, let's find the radius:

r = 0,5 × 3,5 = 1,75

[tex]v = \pi {r}^{2} \times h[/tex]

[tex]v = \pi \times( {1.75})^{2} \times 8 =24.5\pi≈77.0[/tex]

.

15 Given:

h = 5,5 in

d = 4 in

Find: V - ?

First, let's find the radius:

r = 0,5 × 4 = 2 in

[tex]v = \pi {r}^{2} \times h[/tex]

[tex]v = \pi \times {2}^{2} \times 5.5 = 22\pi≈69.1[/tex]

.

16. This figure contains 2 cilinders and one rectangular prism

First, let's find the volume of 2 cilinders (r = 0,5 × 25 = 12,5 in)

[tex]v(both \: cilinders) = (\pi \times ({12.5})^{2} \times 4 ) \times 2= 1250\pi[/tex]

[tex]v(prism) = 30 \times 17 \times 9 = 4590[/tex]

[tex]v(total) = 1250\pi + 4590≈8517.0[/tex]

.

17. This figure contains one rectangular prism and two semi-cilinders

First, let's find the volume of 2 semi-cilinders (it counts as one cilinder, since there's 2 identical halves, also r = 0,5 × 8 = 4):

[tex]v(cilinder) = \pi \times {4}^{2} \times 23 = 368\pi[/tex]

[tex]v(prism) = 23 \times 8 \times 8 = 1472[/tex]

[tex]v(total) = 368\pi + 1472≈2628.1[/tex]

In the rectangle , the cοοrdinate οf b is (0,2).

A quadrilateral with fοur equal vertices and parallel sides is knοwn as a rectangle. Because οf this, it is alsο knοwn as an equiangular quadrilateral.

The term "parallelοgram" can alsο be used tο describe a rectangle because the οppοsing sides are equal and parallel.

Here In the given rectange abcd,  Let cοοrdinates οf b be (x, y)

then, ac and bd are diagοnals οf the rectangle.

Coordinates of midpoints of ac and bd must be same.

Coordinates of midpoint of ac = [tex](\frac{6-2}{2},\frac{-8+4}{2})[/tex] = [tex](\frac{4}{2},\frac{-4}{2})[/tex] = (2,-2)

Coordinates of midpoint of bd = [tex](\frac{x+4}{2},\frac{y-6}{2}) = (2,-2)[/tex]

=> [tex]\frac{x+4}{2}=2 , \frac{y-6}{2}=-2[/tex]

=> x+4=4 , y-6=-4

=> x=4-4, y=-4+6

=> x=0,y=2

Hence the coordinate of b is (0,2).

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Answer:

21

Step-by-step explanation:

2 1/3 ×9=7/3  × 9=21

To solve this problem, we need to first determine how long it will take for Justin's money to triple in value. We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

For Justin, we have:

P = $940

r = 0.07625

n = 12 (monthly compounding)

t = unknown

We want to solve for t when A = 3P = $2820. We can rearrange the formula and plug in the values:

A = P(1 + r/n)^(nt)

3P = P(1 + r/n)^(nt)

3 = (1 + 0.07625/12)^(12t)

ln(3) = 12t * ln(1 + 0.07625/12)

t = ln(3) / (12 * ln(1 + 0.07625/12))

t ≈ 15.8 years

So it will take Justin about 15.8 years for his money to triple in value.

Now we can use the same formula to find how much money Hailey will have in her account after 15.8 years:

P = $940

r = 0.0825

n = 4 (quarterly compounding)

t = 15.8

A = P(1 + r/n)^(nt)

A = $940(1 + 0.0825/4)^(4*15.8)

A ≈ $3501

Therefore, Hailey will have about $3,501 in her account when Justin's money has tripled in value

Answer:

the answer is 1/3*9/4

Answer:  1/3*9/4

Step-by-step explanation: I did a test.

Answer:

the limit of sin(1/θ) as θ approaches 0 is equal to 0.

Step-by-step explanation:

To evaluate this limit:

lim θ→0 sin(1/θ)

we can use the squeeze theorem. First, we note that -1 ≤ sin(1/θ) ≤ 1 for all values of θ, since the sine function oscillates between -1 and 1.

Next, we consider the limit of two other functions, -1/|θ| and 1/|θ|, as θ approaches 0:

lim θ→0 -1/|θ| = -∞

lim θ→0 1/|θ| = ∞

Since sin(1/θ) is always between -1/|θ| and 1/|θ|, we can apply the squeeze theorem to conclude that:

lim θ→0 sin(1/θ) = 0

Therefore, the limit of sin(1/θ) as θ approaches 0 is equal to 0.

Bobbi owes a total of $10,455.75 in taxes.

Taxes are compulsory financial charges imposed by governments on individuals or entities based on income, property, or goods/services.

To compute the tax owed by Bobbi, we can use the following steps:

Calculate Bobbi's taxable income by subtracting the standard deduction and personal exemption from her total income:

Taxable income = $68,000 - $6,350 (standard deduction) - $4,050 (personal exemption) = $57,600

Determine the tax bracket in which Bobbi's taxable income falls:

Bobbi's taxable income of $57,600 falls in the 25% tax bracket.

Calculate the tax owed by Bobbi by applying the marginal tax rates to her taxable income. We can use the following formula:

Tax owed = (Taxable income - Previous tax bracket limit) x Marginal tax rate + Previous tax amount

In Bobbi's case, we need to calculate the tax owed in three steps, since her taxable income falls in the 10%, 15%, and 25% tax brackets:

For the first $9,325 of her taxable income, Bobbi owes 10% in taxes:

Tax owed = ($9,325 - $0) x 0.10 + $0 = $932.50

For the next $28,625 of her taxable income (up to $37,950), Bobbi owes 15% in taxes:

Tax owed = ($37,950 - $9,325) x 0.15 + $932.50 = $3,825.75

For the remaining $19,650 of her taxable income (up to $57,600), Bobbi owes 25% in taxes:

Tax owed = ($57,600 - $37,950) x 0.25 + $3,825.75 = $5,697.50

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Answer: B: y=5x-5

Step-by-step explanation:

Using the multiplication operation, the total quantity that the 27 horses consume in 8 weeks is 1,944 pounds.

The multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication operation involves the multiplicand (the number multiplied), the multiplier (the number multiplying), and the product (the result).

The number of horses in a stable = 27

The quantity of food eaten per horse per week = 9 pounds.

The number of weeks involved = 8 weeks.

The total quantity eaten by the 27 horses in 8 weeks = 1,944 pounds (27 x 9 x 8)

With multiplication, we can conclude that the total quantity is 1,944 pounds.

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A stable has 27 horses. Each one eats 9 pounds per week.  How many pounds will the horses eat in 8 weeks?

The linear equation that can be given for squirrel y is the value of 12x.

According to the question,

Animal            Mouse       Squirrel

Speed(mph)         8                12

SInce "x" the time goes along with x-axis and "y" is  the distance covered by the animal.

The mouse time and distance would plot the graph (1,8)(2,16)(3,24)....

The squirrel time and distance would plot the graph (1,12)(2,24)(3,36)....

Let us consider the track is a straight line and the shorter distance is 50 meters.

The formula for straight line equation y = mx + b  where 'b' is the base value, 'x' is the time and 'y' is the distance.

The linear equation for squirrel y = 12x+b and the squirrel starts at 0 meters per hour. so the equation becomes y = 12x.

The linear equation for mouse y = 8x + b  and the mouse starts at 0 meters.  so the equation becomes y = 8x.

Distance covered by the mouse and the squirrel at time x = 3 we can find the distance covered by the mouse and the squirrel.

y =12x

y = 12(3)

y = 36.

The distance covered by the squirrel is 36km at time 3hours.

For mouse, at time x = 3 hours.

y = 8(3)

y=24.

The distance covered by the squirrel is 24km at time 3hours.

Hence, The linear equation for squirrel y = 12x.

The linear equation for mouse  y = 8x

The distance covered by the squirrel is 36km at time 3hours.

The distance covered by the squirrel is 24km at time 3hours.

Thus:

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The ratio of those who finished the race to those that entered will be 8:9.

What is ratio?

For evaluating the relationship between two numbers or quantities, we employ the ratio formula. The general manner of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is interpreted as 'a is to b'.

A ratio describes how much of one quantity is necessary in relation to another. It is possible to combine and express the two terms in the ratio in their simplest form.

Given : total people entered = 18

           people didn't finish = 2

So, people who finished = total people entered - people didn't finish

                                         = 18 - 2

                                         = 16

Hence, Ratio required = people who finished race / people who entered

                                     = 16 / 18

                                     = 8/9

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The indicated z-score is 0.84.

The standard normal distribution, also known as the Gaussian distribution or the bell curve, is a probability distribution that describes a set of data points that are normally distributed around the mean with a known variance. It is characterized by its mean, which is 0, and its standard deviation, which is 1. The shape of the distribution is symmetric and bell-shaped, with the highest probability density occurring at the mean.

From the given information, we know that the shaded area under the curve is 0.1949. This area corresponds to the probability that a random variable from a standard normal distribution falls between the mean and some unknown value, which we'll call "z".

Looking up the standard normal distribution table or using a calculator, we find that the z-score corresponding to an area of 0.1949 is approximately 0.84.

Therefore, the indicated z-score is 0.84.

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The area of the shaded portion is solved to be

The area of the shaded portion is solved by finding the whole area  of the triangle and subtracting the area of the circle

Area of the whole shape

The shape is a triangle and the area of the triangle is

= 0.5 * base * height

where

base = 40 km

height = 27 km

plugging in the values

Area = 0.5 * 40 * 27

Area = 540 square km

Area of the circle

= π * radius^2

= 3.142 * 6^2

= 113.112 square km

Area of the shaded portion is

= 540 - 113.112

= 426.888

= 426.89 km²

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Answer:

2.5

Step-by-step explanation:

If the areas stay the same, then 10*5=20*h

So, 20h=50

h=2.5