The table represents a quadratic function C(t).


t C(t)
−2 7
−1 4
0 3
1 4
2 7

What is the equation of C(t)?
C(t) = −(t − 3)2
C(t) = (t − 3)2
C(t) = −t2 + 3
C(t) = t2 + 3

The height of cuboid is 5.412 unit.

TSA of cuboid is 96 unit².

Volume of Cuboid is 61.704 unit³

We have,

LSA of cuboid = 72 square unit

width = 3

length = 4

So, LSA of cuboid = 72 square unit

2h(l+b) = 72

2h(4+3) = 72

14h = 72

h = 72/14

h= 5.142

Now, TSA of cuboid

= 2(lw + wh + lh)

= 2 (12 + 20.568 + 15.426)

= 95.988

= 96 unit²

Now, Volume of Cuboid

= l w h

= 4 x 3 x 5.142

= 61.704 unit³

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Answer:15/17 or 0.88

Step-by-step explanation:

The probability that exactly three of their seven children will have the given trait is 0.073.

To solve this problem, we can use the binomial probability formula. The probability of exactly k successes in n trials, where the probability of success is p, is given by:

P(X = k) = C(n, k) . [tex]p^k[/tex] . (1 - [tex]p)^(n - k)[/tex]

In this case, the probability of a child having the trait is p = 3/4, and we want to find the probability of exactly 3 children having the trait out of 7 children, so k = 3 and n = 7.

Using the formula:

P(3) = 7! / 4! 3! x (3/4)³ x (1-3/4)⁴

P(3) = 35 x 27/64 x 1/256

P(3) ≈ 0.073

Therefore, the probability that exactly three of their seven children will have the given trait is 0.073.

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Answer:

106°

Step-by-step explanation:

Since segment WY is a diameter, m<X = 90°.

m<W + m<X + m<Y = 180°

m<W + 90° + 37° = 180°

m<W = 53°

m(arc)XY = 2 × m<W = 2 × 53° = 106°

The answer would be C - "Cheetah B has a higher ratio of miles per minute than Cheetah A because 17 over 8 is less than 56 over 20."

also "get it right please" ?! how rude

The calculated number of miles run is 24 miles

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

The graph is a proportional graph with the points

(x, y) = (10, 1)

So, the equation of the graph is

y = x/10

At 4 hours, the value of x is

x = 4 * 60

So, we have

y = 4 * 60/10

Evaluate

y = 24

Hence, the number of miles run is 24 miles

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Answer:

A = (1/2)Pa = Pa/2 You can multiply both sides by 2 to eliminate the fraction on the right side: 2A = 2 (Pa/ 2) = Pa Then divide both sides by a (or multiply both sides by 1/a) to leave P alone on the right side: (2A) (1/a) = 2A/a = (P a) (1/ a) = P

Step-by-step explanation:

have a nice day.

To solve this problem, we can use the formula:

Total = n(A) + n(B) + n(C) - n(A and B) - n(A and C) - n(B and C) + n(A and B and C)

where:

n(A) = number of people who liked Nepali

n(B) = number of people who liked English

n(C) = number of people who liked Hindi

n(A and B) = number of people who liked both Nepali and English

n(A and C) = number of people who liked both Nepali and Hindi

n(B and C) = number of people who liked both English and Hindi

n(A and B and C) = number of people who liked all three languages

From the given information in the problem, we have:

n(A) = 50

n(B) = 40

n(C) = 30

n(A and B) = 11

n(A and C) = 19

n(B and C) = 13

n(A and B and C) = 6

We can now substitute these values into the formula:

Total = 50 + 40 + 30 - 11 - 19 - 13 + 6

Total = 73

ANSWER: Therefore, there were a total of 73 people who liked at least one of the three languages.

By using the given graph of the function​ f, the key features include the following:

​(a) the​ y-intercept is (0, 10).

​(b) its domain is [-∞, ∞] and the range is [0, ∞].

​(c) it is​ increasing over the interval [-∞, ∞].

​(d) The function is​ even.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the graph, we would calculate the value of a and b as follows;

f(x) = a(b)^x

10 = a(b)⁰

a = 10

Next, we would determine value of b as follows;

12 = 10(b)¹

12 = 10b

b = 12/10

b = 1.2

Therefore, the required exponential function is given by;

[tex]y = 10(1.2)^x[/tex]

Part a.

When x = 0, the y-intercept can be determined as follows;

[tex]y = 10(1.2)^0[/tex]

y = 10(1)

y = 10.

Part b.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞].

Range = [0, ∞] or {y | y ≥ 0}

Part c.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce that the exponential function is always increasing over the interval [-∞, ∞].

Part d.

In conclusion, this exponential function is an even function because it is symmetric with respect to the y-coordinate (y-axis).

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The location of L″ is (-5, 0).

To find the location of L″, we first need to apply the first translation rule to the coordinates of trapezoid JKLM:

J': (x, y) → (x + 3, y - 3) => J'(-2+3, 1-3) = J(1, -2)

K': (x, y) → (x + 3, y - 3) => K'(1+3, 1-3) = K(4, -2)

L': (x, y) → (x + 3, y - 3) => L'(3+3, -2-3) = L(6, -5)

M': (x, y) → (x + 3, y - 3) => M'(-4+3, 2-3) = M(-1, -1)

Now, we need to apply the second translation rule to the coordinates of J', K', L', and M':

J'': (x, y) → (x - 1, y + 1) => J''(1-1, -2+1) = J''(0, -1)

K'': (x, y) → (x - 1, y + 1) => K''(4-1, -2+1) = K''(3, -1)

L'': (x, y) → (x - 1, y + 1) => L''(6-1, -5+1) = L''(5, -4)

M'': (x, y) → (x - 1, y + 1) => M''(-1-1, -1+1) = M''(-2, 0)

Therefore, the location of L″ is (-5, 0).

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Answer:

(5,-4)

Step-by-step explanation:

24-gon is the regular polygons has a perimeter that would be closest to circumference of a circle with the same radius

The closer a regular polygon's range of facets is to infinity, the closer its perimeter will be to the circumference of a circle with the identical radius.

Therefore, the answer is the 24-gon, which has greater facets than the octagon and the dodecagon but fewer facets than the 15-gon.

This makes the 24 - gon the most appropriate answer isnce it has more faces

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The regular polygons which has a perimeter that would be closest to the circumference of a circle with same radius is a; 24-gon.

It follows from the task content that the regular polygon which would have a perimeter closest to circumference of a circle with the same radius is to be determined.

By observation, the greater the number of sides of a regular polygon, the greater is its perimeter and the closer is its perimeter to the circumference of a circle with same radius.

Therefore, the answer choice which is correct is; 24-gon.

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Answer:

Step-by-step explanation:

let m = mean

s= standard deviation

to find zscore = (value-m)/s

1.)

((m-1.5s)-m)/s = -1.5

in fact, if it's n standard deviations ABOVE the mean, your zscore is n

if it's n standard deviations BELOW the mean, your zscore is -n

2.)

((m+1.7s)-m)/s= 1.7

3.)

(m-m)/s= 0

1. Statement 1 is false because the + sign in logarithm laws stands for multiplication

2. The value of x is not a solution

3. In logarithmic form we can write; log10 0.0001 = -4

A set of guidelines called the laws of logarithms governs how to work with and simplify logarithmic expressions. These principles are useful for performing numerous mathematical operations involving logarithms as well as for solving logarithmic equations and simplifying complex logarithmic statements.

1. log3(a + b) ought to be the same as log3(a * b)

2. We have that;

[tex]3^{2x - 5} = 27[/tex]

Writing in the same base;

[tex]3^{2x - 5 } = 3^3[/tex]

2x - 5 = 3

2x = 3 + 5

2x = 8

x = 4

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Answer:

Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

Step-by-step explanation:

Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

There is a 48% chance of selecting a club or a face card from a standard 52-card deck.

To find the probability of picking a club or a face card from a standard 52-card deck, we need to determine the number of favorable outcomes (cards that are either clubs or face cards) and divide it by the total number of possible outcomes (all the cards in the deck).

There are 13 clubs in a deck, as there is one club for each rank (Ace, 2, 3, ..., 10, Jack, Queen, King). Additionally, there are 12 face cards (Jack, Queen, and King) in each suit, including clubs. So, the number of favorable outcomes is 13 (clubs) + 12 (face cards in clubs) = 25.

The total number of cards in a deck is 52.

Therefore, the probability of picking a club or a face card is 25/52 ≈ 0.48 (rounded to two decimal places).

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Answer:2.381 cm.

Step-by-step explanation:

The volume of the gold bar can be calculated using the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

We know the length and width of the bar, so we can substitute those values:

Volume = 23.5 cm x 28 cm x Height

We can then solve for the height by rearranging the equation:

Height = Volume / (Length x Width)

To find the volume, we can use the density of gold and the mass of the bar:

Density = Mass / Volume

Volume = Mass / Density

Substituting the values we have:

Volume = 43,892.5 g / 27.2 g/cm³

Volume = 1610.049 cm³

Now we can substitute the volume into the equation we derived earlier to solve for the height:

Height = 1610.049 cm³ / (23.5 cm x 28 cm)

Height = 2.381 cm

Therefore, the height of the gold bar is approximately 2.381 cm.

We can see that (a^2+b^2)(x+y) - (a^2y+b^2x) simplifies to zero, which means the expression is true. Therefore, the polynomial identity (a^2+b^2)(x+y) - (a^2y+b^2x) holds.

To verify the polynomial identity (a^2+b^2)(x+y) - (a^2y+b^2x), we need to simplify the expression on both sides and show that they are equal.

Expanding (a^2+b^2)(x+y) using the distributive property, we get:

(a^2+b^2)(x+y) = a^2x + a^2y + b^2x + b^2y

Expanding (a^2y+b^2x), we have:

(a^2y+b^2x)

Now, let's subtract (a^2y+b^2x) from (a^2x + a^2y + b^2x + b^2y):

(a^2x + a^2y + b^2x + b^2y) - (a^2y+b^2x)

We can observe that the terms involving 'x' and 'y' cancel each other out:

(a^2x - b^2x) + (a^2y - a^2y) + (b^2y - b^2y)

= 0 + 0 + 0

= 0

We can see that (a^2+b^2)(x+y) - (a^2y+b^2x) is being simplified to zero, which means that the expression is true. Therefore, the polynomial identity (a^2+b^2)(x+y) - (a^2y+b^2x) holds.

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The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.

To calculate the expected value for the game, we need to multiply each outcome by its respective probability and then sum them up.

Let's calculate the expected value for each outcome:

Outcome 1: Roll a 1 and receive $55.

The probability of rolling a 1 on a fair die is 1/6.

Expected value = (1/6) × $55 = $9.17

Outcome 2: Roll a 2 and receive $10.

The probability of rolling a 2 on a fair die is 1/6.

Expected value = (1/6) × $10 = $1.67

Outcome 3: Roll a 3 and win nothing.

The probability of rolling a 3 on a fair die is 1/6.

Expected value = (1/6) × $0 = $0

Outcome 4: Roll a 4 or 5 and pay Señor Rick $35.

The probability of rolling a 4 or 5 on a fair die is 2/6 or 1/3.

Expected value = (1/3) × (-$35) = -$11.67 (negative because you have to pay)

Outcome 5: Roll a 6 and pay Señor Rick $25.

The probability of rolling a 6 on a fair die is 1/6.

Expected value = (1/6) × (-$25) = -$4.17 (negative because you have to pay)

Now, let's sum up the expected values:

Expected value = $9.17 + $1.67 + $0 - $11.67 - $4.17

= -$4.00

The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.

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The length of the other diagonal of the kite is: 50 cm

We want to find the area of the given kite but It should be noted that:

The hypotenuse is usually the slanted line part in a triangle.

Area of a kite = pq/2

where:

p and q are diagonals

We are given:

Area of Kite = 180 cm²

Length of diagonal = 16 cm

Thus:

16q = 180

q = 180/16

q = 50 cm

This gives us the length of the other diagonal of the kite

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Answer:

the length of C is 6, the length of D is 9,

Step-by-step explanation:

a. The rate of change of the relation is 2.

b. The value of n is 14.5.

In Mathematics and Geometry, the rate of change (slope) of any straight line can be determined by using this mathematical equation;

Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope) = rise/run

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the rate of change (slope) of a line, we have the following;

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope) = (10 + 1)/(3.5 + 2)

Rate of change (slope) = 11/5.5

Rate of change (slope) = 2

Part b.

Next, we would determine the value of n as follows;

2 = (43 - 32)/(20 - n)

2(20 - n) = 11

40 - 2n = 11

2n = 29

n = 14.5

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In a right angled triangle, the base is 17 and the angle between base and hypotenuse is 29°, then the hypotenuse x is equal to 19.4 after rounding off to the nearest tenth.

From the given figure, we have to find the missing length x

In the figure we can see that,

For the angle, θ = 29°

Base = 17

and, hypotenuse = x

We know that by the cosine of the angle in the given triangle can be written as,

cos θ = [tex]\frac{base}{hypotenuse}[/tex]

⇒ cos 29° = [tex]\frac{17}{x}[/tex]

⇒ x = [tex]\frac{17}{cos \ 29\textdegree}[/tex]

⇒ x = 19.437

Rounding to the nearest tenth, x = 19.4

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Given fraction:- 11.454545... can be expressed as the ratio 1155/100. However, this fraction is not in its simplest form because both the numerator and denominator have a common factor of 5. A ratio of two integers in simplest form is 231/20.

Let x = 11.454545...

Multiplying both sides of this equation by 100 gives:

100x = 1145.454545...

Subtracting x from both sides gives:

99x = 1145

Dividing both sides by 99 gives:

x = 11.55

Therefore, 11.454545... can be expressed as the ratio 1155/100. However, this fraction is not in its simplest form because both the numerator and denominator have a common factor of 5. Dividing both the numerator and denominator by 5 gives the simplest form of the fraction:

1155/100 = 231/20

Hence, 11.454545... as a ratio of two integers in simplest form is 231/20.

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Answer:

Hope this helps ^^

Step-by-step explanation:

Part A: To determine the values where the pogo stick's spring will be equal to its non-compressed length, we set the function equal to zero:

f(θ) = 2cos(θ) + √3

To find the values of θ that satisfy this equation, we solve:

2cos(θ) + √3 = 0

Subtracting √3 from both sides:

2cos(θ) = -√3

Dividing by 2:

cos(θ) = -√3/2

Using the unit circle, we can find the angles where cosine is equal to -√3/2. These angles are π/6 and 11π/6.

Therefore, the values where the pogo stick's spring will be equal to its non-compressed length are θ = π/6 and 11π/6.

Part B: If the angle θ is doubled, that is, θ becomes 2θ, we substitute 2θ into the original function:

f(2θ) = 2cos(2θ) + √3

Using the double angle formula for cosine:

f(2θ) = 2(2cos²(θ) - 1) + √3

Expanding and simplifying:

f(2θ) = 4cos²(θ) - 2 + √3

Comparing this to the original function f(θ), we see that the new function has the same form but with different coefficients. The solutions for f(2θ) in the interval [0, 2π) will be the same as the solutions for f(θ), but they will occur at double the angles. In other words, if θ is a solution for f(θ), then 2θ will be a solution for f(2θ).

Part C: To find the times when the lengths of the springs from the original pogo stick and the toddler's pogo stick are equal, we set the two functions equal to each other:

f(θ) = g(θ)

2cos(θ) + √3 = 1 - sin²(θ) + √3

Rearranging the equation:

sin²(θ) + 2cos(θ) = 0

Using the Pythagorean identity sin²(θ) = 1 - cos²(θ), we substitute:

1 - cos²(θ) + 2cos(θ) = 0

Rearranging and simplifying:

cos²(θ) - 2cos(θ) + 1 = 0

Factoring:

(cos(θ) - 1)² = 0

Taking the square root:

cos(θ) - 1 = 0

cos(θ) = 1

This occurs when θ is a multiple of 2π.

Therefore, the lengths of the springs from the original pogo stick and the toddler's pogo stick are equal at θ = 2πn, where n is an integer.

The area of the region that lies inside both curves is 11π/3 - 9√3/2 square units.

The area of the region that lies inside both curves first need to find the points of intersection.

The two equations equal to each other and solve for θ:

6sin(2θ) = 6sin(θ)

Dividing both sides by 6 get:

sin(2θ) = sin(θ)

The identity sin(2θ) = 2sin(θ)cos(θ) can rewrite this as:

2sin(θ)cos(θ) = sin(θ)

Dividing both sides by sin(θ) we get:

2cos(θ) = 1

Solving for θ we get:

θ = π/3, 5π/3

The area of the region by integrating the function r with respect to θ from θ = π/3 to θ = 5π/3:

A = ∫[π/3, 5π/3] 1/2 r² dθ

r = 6sin(2θ) when 0 ≤ θ ≤ π and r = 6sin(θ) when π ≤ θ ≤ 2π.

Substituting the appropriate values of r and integrating, we get:

A = ∫[π/3, π] 1/2 (6sin(2θ))² dθ + ∫[π, 5π/3] 1/2 (6sin(θ))² dθ

= ∫[π/3, π] 27sin²(2θ) dθ + ∫[π, 5π/3] 18sin²(θ) dθ

= [9θ - 3/4 sin(4θ)]π/3π + [6θ - 9/2 cos(2θ)]π/5π

= (π/3)[9π/2 - 3√3] + (2π/3)[5 - 9√3/2]

= 11π/3 - 9√3/2

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The values of x for the lengths of the similar shapes are: (3). x = 10, (4). x = 6, (6). x = 35, and (7). x = 60

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other.

(3). PN/PR = PM/PQ

(x + 8)/(3x - 9) = 24/28

28(x + 8) = 24(3x - 9) {cross multiplication}

72x - 28x = 224 + 216 {open brackets and collect like terms}

44x = 440

x = 440/44

x = 10

(4). FE/BD = FG/BC

(5x - 2)/42 = (4x + 2)/39

39(5x - 2) = 42(4x + 2) {cross multiplication}

195x - 168x = 84 + 78 open brackets and collect like terms}

27x = 162

x = 162/27

x = 6

(6). DE/AB = EF/BC

25/x = 20/28

x = (25 × 28)/20 {cross multiplication}

x = 35

(7). YZ/RS = ZW/SP

32/x = 40/75

x = (32 × 75)/40 {cross multiplication}

x = 69

Therefore, the values of x for the lengths of the similar shapes are: (3). x = 10, (4). x = 6, (6). x = 35, and (7). x = 60

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Answer:

1.57ft

Step-by-step explanation:

The circumference is twice the radius times pi.

C=2πr

C=2·π·5

C=10π

C=31.4159265359

We know that KL is 18° of that (180-162).

So we get the formula

31.4159265359÷360x18=1.57

The city's popuation grew by approximately 2.56% from 2010 to 2020

Considering the percentage in bits

From 2010 to 2015

Population growth = 7.4% of 175 000 = 0.074 * 175,000 = 12,950

New population in 2015 = 175 000 + 12,950 = 187,950

From 2015 to 2020

population decrease = 4.5% of 187 950 = 0.045 * 187,950 = 8,462.75

new population in 2020 = 187 950 - 8,463 = 179,487

overall percent change in the population

Percent change = (New population - Initial population) / Initial population * 100

Percent change = (179,487 - 175,000) / 175,000 * 100

Percent change = 4,487 / 175,000 * 100

Percent change ≈ 2.56

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The perimeter of the sandbox is 28 feet. a.

The width of the rectangular sandbox using the given area and length and then use the formula for the perimeter of a rectangle to find the perimeter.

Let's start by using the formula for the area of a rectangle to find the width:

Area = length × width

The area of the sandbox is 45 square feet and the length is 5 feet can substitute these values into the formula and solve for the width:

45 = 5 × width

Dividing both sides by 5, we get:

width = 9 feet

Now that we know the width and length of the sandbox can use the formula for the perimeter of a rectangle:

Perimeter = 2 × length + 2 × width

Substituting the values we found earlier get:

Perimeter = 2 × 5 + 2 × 9

Simplifying, we get:

Perimeter = 10 + 18

Perimeter = 28 feet

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