100 Points! Algebra question. Photo attached. Graph the function. Thank you!

The surface area of the composite solid is 255 square inches.

We will compute the surface area of each component and then add them together to find the surface area of the composite solid.

First, the surface area of the square prism:

Given: The square prism has a width, length, and height of 5 inches each.

Formula for the surface area of a rectangular prism: 2lw + 2lh + 2wh

Surface area of the prism = 2(5 * 5) + 2(5 * 5) + 2(5 * 5)

= 2(25) + 2(25) + 2(25)

= 50 + 50 + 50

= 150 square inches

Next, the surface area of the square pyramid at the bottom:

Given: The slant height of the pyramid on the bottom of the prism = 7.5 inches.

The base of the pyramid is a square with a side length of 5 inches.

Formula to find the lateral surface area of a square pyramid: (perimeter of base) * slant height / 2.

The base is a square, the perimeter is 4 times the side length.

Lateral surface area of the bottom pyramid = (4 * 5) * 7.5 / 2

= 20 * 7.5 / 2

= 150 / 2

= 75 square inches

Then, the Surface area of the square pyramid at the top:

Given: The height of the pyramid on top of the prism = 3 inches.

The base of the pyramid is a square with a side length of 5 inches.

Lateral surface area of the top pyramid = (4 * 5) * 3 / 2

= 20 * 3 / 2

= 60 / 2

= 30 square inches

Finally, we shall find the total surface area by summing up the surface areas of each component in this way:

Total surface area = Surface area of the prism + Surface area of the bottom pyramid + Surface area of the top pyramid

= 150 + 75 + 30

= 255 square inches

Therefore, the surface area of the composite solid = 255 square inches.

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The Interquartile range for the given data set is 51.

The interquartile range for a given data set, the values of the first quartile (Q1) and the third quartile (Q3). The interquartile range is the difference between Q3 and Q1.

First, let's arrange the data set in ascending order:

4, 5, 6, 27, 27, 41, 48, 54, 64, 71, 78, 79

To find Q1, which represents the lower quartile, we need to locate the median of the lower half of the data set. Since the data set has 12 values, the lower half consists of the first 6 values:

4, 5, 6, 27, 27, 41

The median of this lower half is the average of the middle two values, which are 6 and 27:

Q1 = (6 + 27) / 2 = 33 / 2 = 16.5

To find Q3, the upper quartile, we need to locate the median of the upper half of the data set. Again, since the data set has 12 values, the upper half consists of the last 6 values:

48, 54, 64, 71, 78, 79

The median of this upper half is the average of the middle two values, which are 64 and 71:

Q3 = (64 + 71) / 2 = 135 / 2 = 67.5

Finally, we can calculate the interquartile range by subtracting Q1 from Q3:

Interquartile range = Q3 - Q1 = 67.5 - 16.5 = 51

Therefore, the interquartile range for the given data set is 51.

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The volume of the storage nook is 24 cubic feet.

To find the area of 8 puzzles, we multiply the area of one puzzle by 8:

Area of 8 puzzles = 1 square foot * 8 = 8 square feet

Now, to find the volume of the storage nook, we multiply the area of the floor by its height:

Volume of the nook = Area of the floor * Height

= 8 square feet * 3 feet

= 24 cubic feet

Hence, the volume of the storage nook is 24 cubic feet.

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The inequality states that Jayda's age (j) is greater than 12 i.e., j > 12.

Let j represent Jayda's age.

Since Jayda is older than her 12-year-old sister, we can write the inequality:

j > 12

Thus, the inequality states that Jayda's age (j) is greater than 12.

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Answer:

 y = 4.87x + 2.28 Is the answer

Step-by-step explanation:

( i see a little bit of part b but do not see the FULL QUESTION which is a problem and i cannot answer.. )

using a:

THE ULTIMATE LINEAR REGRESSION CACLAULTOR

yes it is the epic i get:

y = 4.87x + 2.28

Nothing more noting less ikr

y = 4.87x + 2.28 Being the answer

Answer:

84°

Step-by-step explanation:

opposite angles in a cyclic quadrilateral (4-sided shape) add up to 180.

c + 96 = 180

c = 180 - 96 = 84°

The solution is : the percentage of cars that are driving less than 45 mi/hr is 2.3%

Here, we have,

Since the speeds of cars are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = speeds of cars

µ = mean speed

σ = standard deviation

From the information given,

µ = 55 mi/hr

σ = 5 mi/hr

The probability that a car is driving less than 45 mi/hr is expressed as

P(x < 45)

For x = 45

z = (45 - 55)/5 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

Therefore, the percentage of cars that are driving less than 45 mi/hr is

0.023 × 100 = 2.3%

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The values of the composite functions are

(1) (f + g)(x) = 4x² + 2x - 2

(2) (fg)(x) = 8x³ - 4x² - 2x + 1

(3) (fⁿ)(x) = (4x² - 1)ⁿ

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

f(x) = 4x² - 1

g(x) = 2x - 1

Using the above as a guide, we have the following:

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 4x² - 1 + 2x - 1

Evaluate the like terms

(f + g)(x) = 4x² + 2x - 2

(fg)(x) = f(x) * g(x)

(fg)(x) = (4x² - 1) * (2x - 1)

Evaluate the products

(fg)(x) = 8x³ - 4x² - 2x + 1

(fⁿ)(x) = (f(x))ⁿ

So, we have

(fⁿ)(x) = (4x² - 1)ⁿ

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The statement Y = {u: (z X)uez) = U{z: zEX}=UX, means that the set Y is the union of all the sets z that are elements of X. In other words, Y is the set of all elements that are in at least one of the sets in X.

The statement can be broken down into two parts:

The first part, Y = {u: (z X)uez), says that Y is the set of all elements u such that u is an element of at least one set z that is an element of X.

The second part, U{z: zEX}=UX, says that the union of all the sets z that are elements of X is equal to the set UX.

The two parts of the statement can be combined to say that Y is the union of all the sets z that are elements of X.

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The value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.

(2x - 13) + 123 = 180° {supplementary angles}

2x - 13 + 123 = 180°

2x + 110 = 180

2x = 180 - 110 {collect like terms}

2x = 70

x = 70/2 {divide through by 2}

x = 35

Therefore, the value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3

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Step-by-step explanation:

For some side x, we are given two angles so let use law of sines

We don't know the angle opposite of the x side so we using the triangle interior property

[tex]120 + 51 + x = 180[/tex]

[tex]x = 9[/tex]

So the missing angle is 9.

The law of sines formula is that

[tex] \frac{a}{ \sin( \alpha ) } = \frac{b}{ \sin( \beta ) } [/tex]

where a and b are side lengths.

And alpha, and Beta are angles that are OPPOSITE of the side lengths, a and b, respectively

Let a be 25,

therefore alpha is 120

Let b be x,

therefore beta is 9.

[tex] \frac{25}{ \sin(120) } = \frac{x}{ \sin(9) } [/tex]

Solving for x.

[tex]25 \times \frac{ \sin(9) }{ \sin(120) } = x[/tex]

[tex]x = 4.51587[/tex]

Round if needed so our answer is

[tex]x = 4.5[/tex]

The rate is 5.2%

After 10 years, the money will amount to  £4150.

We know that the compound interest can be obtained from;

[tex]A = P(1 + r/n)^{nt}[/tex]

The rate is obtained from;

I = A - P

I = interest

A = amount

P = principal

r = rate

n = Number of times compounded

t = time in years

Then;

I = £2630.00 -  £2500.00

I = £130

I = PRT/100

130 = 2500 * R * 1/100

R = 130 * 100/2500

R = 5.2%

After 10 years;

[tex]A = 2500 ( 1 + 0.052)^{10}[/tex]

A = £4150

Thus this is the amount after 10 years

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The values of the angles x and y are ∠x = 110 and ∠y = 70

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

The lines (parallel, transversal and others)

The measure of angle 1 is calculated as

∠1 = 180 - 140 -- angle on a straight line

So, we have

∠1 = 40

Next, we have

∠2 = 180 - 40 - 80 --- corresponding angles

So, we have

∠2 = 60

This means that

∠y = 180 - 60 - 50 -- angle on a straight line

So, we have

∠y = 70

This also means that

∠x = 180 - 60 - 10 -- angle in a triangle

So, we have

∠x = 110

Hence, the values of x and y are ∠x = 110 and ∠y = 70

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Answer:

24

Step-by-step explanation:

For this problem, substitute the value -3 for x and solve. It would look like this:

[tex]4(-3)^2+2(-3)-6[/tex]

Using the order of operations (PEMDAS) we solve the exponent first.

[tex]-3^2=9[/tex]

Then solve the multiplication parts.

[tex]4(9)+2(-3)-6\\4*9=36[/tex]and        [tex]2*(-3)=-6[/tex]

Finally subtract to get the answer.

[tex]36-6-6=24[/tex]

Function graph that has y- intercept of 3 is g(x) = 3[tex](\frac{1}{4}) ^{x}[/tex].

y- intercept will be 3 when we will put value of x = 0 and y will be 3 that graph will have y intercept 3

A) h(x) = 5[tex](2)^{x}[/tex]

when x = 0

Any number with zero power is always 1

h(x) = 5

B) h(x) = 5[tex](0.5)^{x}[/tex] + 0.5

when x = 0

h(x) = 5 + 0.5

h(x) = 5.5

C) g(x) = 3[tex](\frac{1}{4}) ^{x}[/tex]

when x = 0

g(x) = 3

Here we get y intercept as 3.

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Explanation:

The error is 42-40 = 2 meters

Divide this over the actual width

2/42 = 0.0476 = 4.76% approximately

This rounds to 5%

Answer:

D. 5%

Step-by-step explanation:

Percent Error = (|40 - 42| / 42) × 100

Percent Error = (2 / 42) × 100

Percent Error ≈ 4.76%

Answer:

KL = 7, so B is the correct answer.

The equation for each circle is given as follows:

36) (x - 2)² + (y - 15)² = 4.

37) (x + 8)² + (y + 18)² = 25.

38) (x - 11)² + (y + 9)² = 49.

39) (x - 13)² + (y + 8)² = 36.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

For item 36, the center is given as follows:

(-3, 11)

After the translation, the center will be given as follows:

(2, 15)

Hence the equation is given as follows:

(x - 2)² + (y - 15)² = 4.

For item 37, the center is given as follows:

(-3, -14)

After the translation, the center will be given as follows:

(-8, -18)

Hence the equation is given as follows:

(x + 8)² + (y + 18)² = 25.

For item 38, the center is given as follows:

(11, -9).

Hence:

(x - 11)² + (y + 9)² = r².

Point (18, -9) is on the circle, hence the radius squared is obtained as follows:

r² = (18 - 11)² + (-9 + 9)²

r² = 49.

Hence the equation is:

(x - 11)² + (y + 9)² = 49.

For item 39, the center is given as follows:

(13, -8).

Hence the equation is:

(x - 13)² + (y + 8)² = r².

Point (7, -8) is on the circumference of the circle, hence the radius squared is obtained as follows:

r² = (7 - 13)² + (-8 + 8)²

r² = 36.

Hence the equation is given as follows:

(x - 13)² + (y + 8)² = 36.

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The solution of the inequality equation is determined as y > 3.

A solution for an inequality in y is a number such that when we substitute that number for y we have a true statement.

For the given inequality equation, which is;

y + 5 > 8

The solution of the inequality equation is calculated as follows;

y + 5 > 8

Subtract 5 from both sides of the equation as shown below;

y + 5 - 5 > 8 - 5

y > 3

The solution of the inequality equation is determined as 3, so we can conclude that any value less than  3 is not true and the proposed solution of 1 is not true or correct for the inequality equation.

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Answer:

area=20ft^2

Step-by-step explanation:

3ft×4ft=12ft^2

12ft÷2=6ft is the area of the smaller triangle

7ft×4ft=28ft^2

28ft÷2=14ft is the area of the larger triangle

6ft+14ft=20ft^2

Answer:

the solution set is { - 7, - 3 }

Step-by-step explanation:

(x + 3)(x + 7) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

x + 7 = 0 ( subtract 7 from both sides )

x = - 7

solution set is { - 7, - 3 }

Part A:

To find out how much leftover pizza Brad had, we need to add up the fractions of each type of pizza:

1/2 cheese pizza + 3/4 sausage pizza + 2/6 pepperoni pizza

We can simplify the fractions by finding a common denominator:

1/2 = 3/6

3/4 = 4.5/6

2/6 = 2/6

Now, we can add the fractions:

3/6 + 4.5/6 + 2/6 = 9.5/6

This means Brad had 9.5/6 of a pizza leftover.

Part B:

Steve had 2/3 of a pizza. To compare this to Brad's leftover pizza, we need to convert Brad's leftover pizza to a fraction with the same denominator as 2/3:

9.5/6 = 9/6 + 0.5/6 = 3/2 + 1/12 = 19/12

Now we can compare:

19/12 - 2/3 = 38/12 - 8/12 = 30/12 = 2.5

This means Brad has 2.5 more pizzas than Steve.

The probability that exactly 1 buyer would prefer green P ( A ) = 0.1854

Given data ,

A researcher wishes to conduct a study of the color preferences of new car buyers

And , 30 % of this population prefers the color green

where 20 buyers are randomly selected

Now , binomial distribution problem with n = 20, p = 0.30 and we want to find the probability of exactly 1 buyer preferring green.

The formula for the probability mass function of a binomial distribution is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) = n! / (k! * (n-k)!)

Plugging in the values, we get:

P(X = 1) = (20 choose 1) * 0.30¹ * 0.70¹⁹

= 20 * 0.30 * 0.70¹⁹

= 0.1854 (rounded to four decimal places)

Hence , the probability that exactly 1 buyer would prefer green is 0.1854

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Answer:

The circle's circumference is approximately 106.81 centimeters.

Explanation:

The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is pi (approximately 3.14), and r is the radius of the circle.

So, for a circle with a radius of 17 centimeters, its circumference can be found by:

C = 2πr

C = 2 x 3.14 x 17

C ≈ 106.81 cm

Therefore, the circumference of the circle is approximately 106.81 centimeters.

Answer: $383.33 per month for the next 4 years

Step-by-step explanation:

The correct answer is save $383.33 per month for the next 4 years. Tuition for one year at a state university is about $12,500, and Greg would like to attend this university. His parents will give him $4,600 for his first year of tuition, so he must save the remaining $7,900. To have enough money to pay for his first year of tuition, Greg must save $383.33 per month for the next 4 years. This is the minimum amount of money he must save, as the other plans require him to save more money than necessary.

Sorry if this is wrong btw fr fr.

Answer:164.58 (D)

Step-by-step explanation:

12,500-4600= 7900

12 months x 4 years makes 48 months, so 7900/48 = 164.58 per month

The solution is: In 86400 ways can the station air the movie marathon.

Given:

Number of total movies = 11

Number of science fiction movie = 6

Number of horror movie = 5

Computation:

Number of science fiction movies way air = 6!

so, we get,

Number of science fiction movies way air = 720

Number of horror movies way air = 5!

so, we have,

Number of horror movies way air = 120

The number of ways the station air the movie marathon is:

720 * 120

=86400

so, we get,

Final answer is 86400 ways.

Hence, The solution is: In 86400 ways can the station air the movie marathon.

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The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.

We have,

We see that there are 10 marbles.

Now,

Number of blue marbles = 2

Number of green marbles = 4

Now,

The probability of picking a blue marble first is 2/10, as there are 2 blue marbles out of 10 in total.

After picking a blue marble, there will be 9 marbles left in the bag.

The probability of picking a green marble second, without replacing the blue one, is 4/9, as there are 4 green marbles remaining out of the 9 marbles in total.

Now,

P(blue marble and green marble) = P(blue marble) x P(green marble)

= (2/10) x (4/9)

= 8/90

= 4/45.

Therefore,

The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.

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Answer:

(a) 44 (4 + 4 = 8), 62 (6 + 2 = 8)

(b) 165 (1 + 6 + 5 = 12)

The vertical asymptote of the equation does not exist, the horizontal asymptote of the equation is 1.

To calculate vertical asymptote,

Putting the denominator equal to zero,

x²+2x+3 = 0

Using Quadratic formulae,

b² - 4ac

where,

b = 2

a = 1

c = 3

putting value,

4-12 = -8<0

therefore, the solution is negative

Hence, no vertical asymptote of the given equation exists,

To calculate the horizontal asymptote,

the degrees of the numerator and denominator are the same. we can compare the coefficients of the highest power terms.

The coefficient of x² in the numerator is 1

Hence, the horizontal asymptote is y = 1.

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