Random sample of 250 students taken with a population of 7500 surveyed about their majors. In the sample, 75 students were Art majors. How many students in total population are are Art majors?

Using the Pythagorean theorem, we can find the length of HG:

HG² = HI² + IG²

Therefore, the length of HG is 5sqrt(3) units.

The Pythagorean Theorem is a mathematical formula that states in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Length is a measurement of the extent of something along its longest dimension, from one end to the other. It is often expressed in units such as meters, feet, or inches.

According to the given information:

To calculate the length of HG, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its two legs.

First, we can identify that triangle HGN is a right triangle, with HG being the hypotenuse. Using the Pythagorean theorem, we have:

(HG)² = (NG)² + (NH)²

We can also identify that triangle INH is also a right triangle, with IN being the hypotenuse. Using the Pythagorean theorem, we have:

(IN)² = (NH)² + (NI)²

Substituting (NH)^2 from the second equation into the first equation, we get:

(HG)² = (NG)² + (IN)² - (NI)²

Plugging in the values given in the diagram, we get:

(HG)² = 5² + 9² - 3²

(HG)² = 61

HG = √61

Therefore, the length of HG is the square root of 61.

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Another equivalent equation to the equation (4x • 7)(5x • 9) is 28x(45x) respectively.

Equivalent equations in algebra are those that have equivalent roots or solutions.

In order to produce an equivalent equation, the same quantity or expression must be added to or subtracted from both sides of the original equation.

If you multiply or divide an equation's two sides by the same non-zero number, the results are identical.

If x4=2x+7, we can add 4 to both sides to get the following equation, which is equivalent: x4+4=2x+7+4.

So, we have the equation:

(4x • 7)(5x • 9)

Then, another equation that will be equivalent to the given equation can be:

(4x • 7)(5x • 9)

(28x)(45x )

Then,

28x(45x)

So,

(4x • 7)(5x • 9) = 28x(45x)

Therefore, another equivalent equation to the equation (4x • 7)(5x • 9) is 28x(45x) respectively.

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The line plot representing the values on the number line can be presented as follows;

[tex]{}[/tex]         ×

[tex]{}[/tex]         ×                             ×

[tex]{}[/tex]         ×      ×                     ×      ×

<-|------|------|------|------|------|------|------|------|->

 [tex]{}[/tex]0     1/8    1/4          1/2   5/8  3/4           1

A line plot is a graph displaying data as points above a number, which indicates the frequency of the data.

The values in the fraction can be expressed as follows;

5/8, 5/8, 1/4, 1/8, 1/8, 3/4, 1/8

The values that are repeated can be excluded to get;

Values to be represented are; 5/8, 1/4, 1/8, 3/4

The above fractions can be expressed as fractions with a denominator of 8 as follows;

5/8, 1/4, 1/8, 3/4 = 5/8, 2/8, 1/8, 6/8

The fractions can be arranged in increasing order as follows;

5/8, 2/8, 1/8, 6/8; 1/8, 2/8, 5/8, 6/8

The fractions 1/8, 2/8, 5/8, 6/8, can therefore, be entered into the number line as follows;

<-|------|------|------|------|------|------|------|------|->

 0[tex]{}[/tex]    1/8   2/8          1/2    5/8  6/8           1

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Answer: B. 12

Step-by-step explanation:

1) Alan can make 2.5 cookies per min

2) Abi can make 8/3 which is 2.7.

3) overall, 5.2 cookies per minute can be made.

multiple 5.2 x 6 and you get around 31.5?

then subtract =1. you have 30.5, now add onto that number 31.5, which is another 6 minutes. since you're still only subtracting 1, the answer would be above 60, which is 5 dozen, and it only took 12 mins

If the width of a rectangle with perimeter P is 6 units, its length would be equal to L = P/2 - 6.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + 6)

P = 2L + 12

P - 12 = 2L

L = (P - 12)/2

L = P/2 - 6.

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Answer:

Area of a rectangle = Length x Width

Step-by-step explanation:

Length = 25 cm

Width = 8 cm

25 x 8 = 200

So the area of a rectangle = 60 cm^2

Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.

Standard deviation (σ) = √(variance) = √(121) = 11

Now, we can calculate the z-score for Dr. Baker's average of 169 using the formula:

z = (X - μ) / σ

z = (169 - 158) / 11

z = 11 / 11

z = 1

Dr. Baker's z-score is 1, meaning his performance is one standard deviation above the mean.

The area to the left (or the cumulative probability) is approximately 0.8413

1 - 0.8413 = 0.1587

Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.

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Answer:

To convert 5.25 to a fraction, we can first note that the decimal represents the number 5 units and 25 hundredths. We can write this as:

5.25 = 5 + 0.25

Next, we can convert the decimal 0.25 to a fraction by recognizing that it is equivalent to 25/100 or 1/4. Therefore:

5.25 = 5 + 1/4

We can then combine the whole number 5 with the fraction 1/4 by finding a common denominator:

5 + 1/4 = 20/4 + 1/4 = 21/4

Therefore, 5.25 as a fraction in simplest form is 21/4.

Answer:

i believe it should be

5 1/4

i apologize if wrong, it depends on the ratio (you didnt include it)

If Mrs. Lang has x students in each of her 5 classes, then she has a total of 5x students.

Ms. Easter has 4 less students in each of her classes, so she has x - 4 students in each of her 5 classes.

To find out how many students are in all of Ms. Easter's classes, we can use the expression:

5(x - 4)

This simplifies to:

5x - 20

Therefore, there are 5x - 20 students in all of Ms. Easter's classes.

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Answer:

131072

Step-by-step explanation:

Answer: The answer is 131072.

Step-by-step explanation:

Using a calculator, we find that [tex]2^{17}=\boxed{131072}.[/tex]

Answer:

mark me as brainliest

Step-by-step explanation:

common stocks

Therefore, you are three times more likely to be on time than be late if you take Route C to school.

Relative frequency is a statistical term that refers to the proportion or percentage of times an event or a particular value occurs within a larger set of data. It is calculated by dividing the number of times the event or value occurs by the total number of observations in the data set.

Here,

To determine how many times more likely you are to be on time than late if you take Route C, we need to compare the heights of the green and red bars for Route C. From the graph, we can see that the green bar (representing on-time arrivals) is approximately three times taller than the red bar (representing late arrivals) for Route C.

To calculate how many times more likely you are to be on time than late if you take Route C, we need to find the ratio of the heights of the green and red bars:

Ratio = height of green bar / height of red bar

Looking at the segmented bar graph, we can see that the height of the green bar for Route C is approximately 0.45, and the height of the red bar is approximately 0.15.

Ratio = 0.45 / 0.15

= 3

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The vertical line at x=0 represents the boundary of the inequality, and the shaded region to the left of the line represents the solution set of the inequality, x < 0.

Explain the term inequality

Inequality refers to the unequal distribution of resources, opportunities, and rewards among individuals or groups within a society. It can be based on factors such as race, gender, income, education, and social status, leading to disparities in outcomes and experiences.

According to the given information

Start by simplifying the inequality using the distributive property and combining like terms:

4(x-1) - 2x < 6 - 5(x+2)

4x - 4 - 2x < 6 - 5x - 10

2x - 4 < -5x - 4

2x + 5x < 4 - 4

7x < 0

x < 0

So the solution to the inequality is x < 0.

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The statement, "t is not less than 7" as an inequality is E. t ≥ 7.

The statement, " the negative of z is not greater than 8" is A. - z ≤ 8 .

The statement "t is not less than 7" means that t can be equal to 7 or greater than 7, so we can write this as:

t ≥ 7

Therefore, the correct inequality for the statement is t ≥ 7.

Similarly, the statement "the negative of z is not greater than 8" means that the opposite of z, which is -z, can be equal to -8 or less than -8, so we can write this as:

-z ≤ 8

Multiplying both sides of the inequality by -1 gives:

z ≥ -8

Therefore, the correct inequality for the statement is z ≥ -8.

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Answer:

e) The correct option is: t≥7

The phrase "t is not less than 7" means that t can be equal to 7 or any value greater than 7, but it cannot be less than 7. Therefore, we use the greater than or equal to a symbol (≥) to represent this statement.

here's an explanation of each option:

t * 7a^2 ≥ 7 * 7a^2

49a^2

t * 7a^2 ≥ 49a^2

Note that this inequality is equivalent to t ≥ 7, which is what we started with.

f) The correct option is:-z ≤ 8

The phrase "the negative of z is not greater than 8" means that -z cannot be greater than 8. In other words, -z is less than or equal to 8. To express this as an inequality, we use the less than or equal symbol (≤) and write "-z ≤ 8".
here's an explanation of each option:

Note that only the first option (-z ≤ 8) accurately represents the original statement "The negative of z is not greater than 8". The other options either represent a different statement or contradict the original statement.

The statement "the negative of z is not greater than 8" can be expressed as an inequality in terms of 7a^2 as follows:

-z ≤ 8

z ≥ -8

7a^2 * z ≥ -8 * 7a^2

-56a^2

7a^2 * z ≥ -56a^2

So, the statement "the negative of z is not greater than 8" can be expressed as the inequality 7a^2 * z ≥ -56a^2.

The model is 64.62 inches tall. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." In mathematics, operations like division, multiplication, addition, and subtraction come first, followed by operations like quotient, product, sum, and difference.

We are given that height of tower is 1454 feet and the scale is given as follows:

2 inches = 45 feet

Now, using the division operation, we get

⇒ Height of the model = 1,454 ÷ 45

⇒ Height of the model = 32.31

Now, using the multiplication operation, we get

⇒ Height of the model = 32.31 * 2

⇒ Height of the model = 64.62 inches

Hence, the model is 64.62 inches tall.

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The correct question has been attached below.

Clara's and Stefan's pizzas did not have the same ratio of pepperoni pieces to ham pieces.

For Clara,

The number of pepperoni pieces = 4

The number of ham pieces = 6

The ratio = 4:6 = 2:3

For Stefan,

The number of pepperoni piece = 6

The number of ham piece = 10

The ratio = 6:10 = 3:5

Therefore the ratio of Clara's and Stefan's pizzas is not the same.

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Answer:

200

Step-by-step explanation:

Turn the 31% back to a decimal = 0.31

62/ x = 0.31

multiply each side of the equation by x to cancel it out from under the fraction

62 = 0.31x

divide each side by 0.31 to have to x alone

200 = x

Check work:

62/200 = 0.31 x 100 = 31%

We can start by isolating the secant term and then taking the inverse cosine of both sides. Remember that the inverse cosine function only gives results on the interval [0,π], so we will need to adjust our solutions accordingly:

2sec(θ) + 3 = 0

2sec(θ) = -3

sec(θ) = -3/2

cos(θ) = -2/3

θ = ±cos⁻¹(-2/3)

Using a calculator, we find:

θ ≈ 2.302, 4.981 radians

However, we need to adjust these solutions to be within the interval [0,2π). Since cos(x) = cos(2π - x), we can add 2π to the negative solution to get an equivalent positive solution:

θ ≈ 2.302, 7.438 radians

Rounding to the nearest thousandth, we get:

θ ≈ 2.302, 7.438 radians

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The surface area of the solid created upon dilation is equal to 36 units².

In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):

SA = 2πrh + 2πr²

Where:

By substituting the given parameters into the formula for the surface area (SA) of a cylinder, we have the following;

Surface area = 2πrh + 2πr²

Surface area = 2(π)(9)(9) + 2(π)(9²)

Surface area = 324π units²

After applying a dilation with a scale factor of 1/3, the surface area of the cylinder is given by;

Surface area = 324π × (1/3)²

Surface area = 324π × 1/9

Surface area = 36 units²

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Answer: $702.39

Step-by-step explanation: To find the total cost of the laptop with sales tax included, we need to add the sales tax to the listed price.

First, we need to calculate the amount of sales tax.

Sales tax = 9.75% of 639.99

Sales tax = 0.0975 x 639.99

Sales tax = 62.40

Now we can find the total cost of the laptop with sales tax included:

Total cost = listed price + sales tax

Total cost = 639.99 + 62.40

Total cost = 702.39

Therefore, the total cost of the laptop with sales tax included is $702.39.

Answer:2.86.

Step-by-step explanation:

We can use the geometric distribution to solve this problem. The geometric distribution models the number of trials needed to achieve the first success in a sequence of independent trials with a constant probability of success.In this case, the probability of success (the teacher tripping over the cords) is 0.35. Therefore, the expected value or mean of the geometric distribution is 1/0.35 ≈ 2.86.So, on average, students need to wait for 2.86 periods until the teacher trips over the cords in her classroom.Therefore, the answer is 2.86.

x2−1x5=(x−a)2+b2−15=(−)2+

Answer:

7 ÷ 2 = 3.5, so 2:7 = 1:3.5 (1 to 3.5).

Answer:

1 : 3.5

Step-by-step explanation:

2: 7 written in the ratio 1 : n...

2:7

1:n

To get to 1 from 2 you have to divide by 2.

So do the same for 7.

Therefore the answer is 1: 3.5

Given that the coordinates of the three vertices of a square are (4, 14), (10, 14), and (4,8).

The missing coordinate will be at (10,8) on the coordinate plane for the given square.

A vertex is a location in geometry where two or more line segments converge. Vertices are the corners of two-dimensional forms such as squares and triangles. Vertices are the places where three or more faces of a three-dimensional shape, such as a cube or a pyramid, meet.

Four of a square's vertices have the coordinates (4,14), (10,14), and (4,8).

The length of one of the square's sides may be determined using the distance formula, and the length can then be used to determine the coordinates of the missing vertex.

We know that one side of the square has a length of 6 units since the distance between (4,14) and (10,14) is 6 units.

We know that the missing vertex must be 6 units away from (4,8) in the y-direction since the square is symmetric.

The missing vertex therefore has the coordinates (10,8).

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The missing coordinate will be at (10,8) on the coordinate plane for the given square.

A vertex is a location in geometry where two or more line segments converge. Vertices are the corners of two-dimensional forms such as squares and triangles. Vertices are the places where three or more faces of a three-dimensional shape, such as a cube or a pyramid, meet.

Four of a square's vertices have the coordinates (4,14), (10,14), and (4,8).

The length of one of the square's sides may be determined using the distance formula, and the length can then be used to determine the coordinates of the missing vertex.

We know that one side of the square has a length of 6 units since the distance between (4,14) and (10,14) is 6 units.

We know that the missing vertex must be 6 units away from (4,8) in the y-direction since the square is symmetric.

The missing vertex therefore has the coordinates (10,8).

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The relative change from 1995 to 2000 is -63.92%, indicating a decrease in price of approximately 63.92%.

To calculate the relative change from 1995 to 2000, we need to find the difference between the prices in those two years, and then express that difference as a percentage of the price in 1995.

Price in 1995 = $351.94

Price in 2000 = $349.69

Difference = Price in 2000 - Price in 1995

Difference = $349.69 - $351.94

Difference = -$2.25

The negative sign indicates a decrease in price from 1995 to 2000.

Now, we can calculate the relative change as a percentage:

Relative change = (Difference / Price in 1995) * 100

Relative change = (-$2.25 / $351.94) * 100

Relative change = -0.6392 * 100

Relative change = -63.92%

Therefore, the relative change from 1995 to 2000 is -63.92%, indicating a decrease in price of approximately 63.92%.

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The graph of the piecewise function can be seen in the image attached below where (x+2)² terminates at x = -1,  |x - 1| between the interval of x = -1 to x = 1, and  [tex]-\sqrt[3]{x}[/tex] from +x-axis to infinity [tex]\infty[/tex]

A piecewise function is a type of function that has different expressions or formulas for different parts or intervals of its domain. This means that the formula that defines the function changes depending on which part of the domain we are looking at.

Now, to graph the piecewise function, we need to start by identifying the different intervals on which the function is defined and the corresponding expressions that define the function on each interval.

If we have a piecewise function f(x) defined as:

The graph of the piecewise function can be seen in the image attached below.

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Step-by-step explanation:

The number of non square numbers between 12square and 13square are

a. reflexive, symmetric, and transitive only
b. congruence and midpoint.

A segment proof is a type of proof that shows the steps used to establish the congruence or equality of two line segments. The goal of a segment proof is to provide a clear and logical argument that demonstrates why the two segments are equal or congruent.
Segment proofs typically involve using a combination of definitions, postulates, and theorems to justify each step of the argument. For example, to prove that two line segments are congruent, one might use the segment addition postulate, the definition of congruence, and the reflexive, symmetric, and transitive properties of congruence.

The appropriate matching is:

1. Segment proofs include the following definitions as justifications/reasons: ⇔ reflexive, symmetric, and transitive only

2. Segment proofs include the following as congruence of segments: ⇔ congruence and midpoint.

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Answer:

28

Step-by-step explanation:

you first do the 4x4=16 then 4x3=12 then do 16+12=28