How many students age 15 and above take a car to school? Show work
A. 18
B. 38
C. 87

After calculating the questiοn, we get that the value οf 20% οf 75 is 15.

A value οr ratiο that may be stated as a fractiοn οf 100 is referred tο in mathematics as a percentage. Divide the number by the tοtal and multiply by 100 tο find the percent οf a given number. Therefοre, the percentage refers tο a pοrtiοn per hundred. Per 100 is what the wοrd percentage signifies. The letter "%" stands fοr it.

Percent changes applied sequentially dο nοt add up in the usual way. Fοr example, if the 10% increase in price cοnsidered earlier (οn the $200 item, raising its price tο $220) is fοllοwed by a 10% decrease in the price (a decrease οf $22), then the final price will be $198—nοt the οriginal price οf $200.

Here the given is,

=> 20% of 75

=> 20% \(\times\)75

=> \(\frac{20}{100}\times 75\)

=> 5\(\times 3\)

=> 15.

Hence the value of 20% of 75 is 15.

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Answer:

The mode is 4 and the median is 5.4     read the explantion :DDD

Step-by-step explanation:

It super easy but u get there for the mode you have to put it least to greatest and the find the one that occurs the most and for the median u have to add all the number up and divid it by how many numbers they are like 5+7+3+8+4 is 27 divied by 5 is 5.4 i hope i help you :DDDD u need to know and understand it.

The local maximum value of the function F(x, y) = 9x²y on the line x + y = 2 is None, and the local minimum value is 0.

To find the local extreme values, we need to consider the critical points and endpoints of the function on the given line.

First, we express y in terms of x using the equation x + y = 2, which gives y = 2 - x.

Next, we substitute this expression into the function F(x, y) = 9x²y: F(x) = 9x²(2 - x)

To find the critical points, we take the derivative of F(x) with respect to x and set it to zero: F'(x) = 18x(2 - x) - 9x² = 0

Simplifying, we get:

36x - 18x² - 9x² = 0

-27x² + 36x = 0

-3x(9x - 12) = 0

This equation gives us two critical points: x = 0 and x = 4/3.

To determine the extreme values, we evaluate F(x) at the critical points and the endpoints of the line x + y = 2.

For x = 0, we have y = 2 - x = 2 - 0 = 2.

F(0, 2) = 9(0)²(2) = 0

For x = 4/3, we have y = 2 - x = 2 - (4/3) = 2/3.

F(4/3, 2/3) = 9(4/3)²(2/3) = 16

Finally, we compare these values to determine the local extreme values. In this case, we find that there is no local maximum value, and the local minimum value is 0.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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Let's denote the cost of one pair of jeans as "J" and the cost of one t-shirt as "T". To find the values of J and T, we can set up a system of equations based on the given information.

From the information provided, we know that Marisol purchased 2 pairs of jeans and 6 t-shirts for a total of $60. Therefore, we can write the equation:

2J + 6T = 60 (Equation 1)

Similarly, Ernestine purchased 4 pairs of jeans and 3 t-shirts for a total 0f $75. This gives us the equation:

4J + 3T = 75 (Equation 2)

We now have a system of two equations with two unknowns (J and T). To solve this system, we can use various methods such as substitution or elimination.

Multiplying Equation 1 by 2, we can rewrite it as:

4J + 12T = 120 (Equation 3)

Now, we can subtract Equation 2 from Equation 3 to eliminate the J term:

(4J + 12T) - (4J + 3T) = 120 - 75

Simplifying the equation gives us:

9T = 45

Dividing both sides by 9, we find that T = 5.

Substituting this value back into Equation 1, we can solve for J:

2J + 6(5) = 60

2J + 30 = 60

2J = 30

J = 15

Therefore, the cost of one pair of jeans is $15, and the cost of one t-shirt is $5.

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The probability of a positive test, given breast cancer, is 223/303, while the probability of a negative test, given no breast cancer, is 684/697.

To find the probability of a positive test, given that the patient has breast cancer, we divide the number of true positive cases (223) by the total number of patients with breast cancer (303). This gives us a probability of 223/303.

The formal term used to describe this probability measure is conditional probability or the probability of an event A occurring given that event B has already occurred. In this case, the positive test is event A, and having breast cancer is event B.

Similarly, to find the probability of a negative test, given that the patient is breast cancer-free, we divide the number of true negative cases (684) by the total number of patients without breast cancer (697). This gives us a probability of 684/697.

The formal term used to describe this probability measure is also conditional probability, where the negative test is event A, and not having breast cancer is event B.

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Answer:55

Step-by-step explanation:

Answer:

Step-by-step explanation:

20% of 30 is 6 are randomly selected.

30 choose 6 = 30! / (30-6)! 6!

                 = 30! / 24!6!

                 = 30 * 29 * 28 * 27 * 26 * 25

                   --------------------------------- <-- 24! cancels

                    6 * 5 * 4 * 3 * 2 * 1

                 = 29 * 28 * 27 * 26 * 25

                  ---------------------------------- <--- 30 = 6 * 5 cancels

                      4 * 3 * 2 * 1

                = 29 * 7 * 9 * 13 * 25   <--  4 cancels 28, 3 cancels 27, 2 cancels 26

               = 593775

Answer:

TYLER?

Step-by-step explanation:

Answer:

It's 38.

Step-by-step explanation:

the sum of three consecutive even integers is 108, the largest number in the sequence would be 38.

I hope this helps you!

Answer:

We can use algebra to solve this problem. Let's call the smallest of the three consecutive even integers x. Since the integers are consecutive and even, the next two integers will be x+2 and x+4.

The problem states that the sum of three consecutive even integers is 108, so we can write an equation:

x + (x+2) + (x+4) = 108

We can simplify this equation by combining like terms:

3x + 6 = 108

3x = 102

x = 34

So, the smallest of the three consecutive even integers is 34.

The next two integers will be x+2 = 34+2 = 36 and x+4 = 34+4 = 38

The largest number of the three consecutive even integers is x+4 = 38.

hypotenuse of a right triangle is always the side opposite the right angle.

In geometry, a right triangle is a type of triangle that contains one angle measuring 90 degrees, known as the right angle. Right triangles have several distinguishing properties, and one of the fundamental concepts associated with them is the identification of the sides relative to the right angle. In this detailed explanation, we will explore the term that describes the specific side of a right triangle that is always opposite the right angle.

In a right triangle, there are three sides: the hypotenuse, the adjacent side, and the opposite side. The hypotenuse is the side opposite the right angle and is the longest side of the triangle. The adjacent side is the side that forms the right angle with the hypotenuse, while the opposite side is the side that is opposite the right angle. The term that refers to the side of a right triangle that is always opposite the right angle is the "hypotenuse."

To better understand the concept, let's consider the Pythagorean theorem, which is a fundamental relationship in right triangles. The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be expressed as:

\(c^2 = a^2 + b^2\)

In this equation, "c" represents the length of the hypotenuse, while "a" and "b" represent the lengths of the other two sides (adjacent and opposite). By rearranging the equation, we can solve for the hypotenuse (c):

\(c = \sqrt(a^2 + b^2)\)

From this equation, we can see that the hypotenuse is determined by the lengths of the other two sides of the right triangle. The relationship expressed by the Pythagorean theorem highlights the importance of the hypotenuse in determining the overall shape and size of the right triangle.

Furthermore, the hypotenuse is significant because it provides the longest side of the right triangle. Its length directly influences the triangle's shape and can be used to calculate various properties, such as the triangle's area or the lengths of the other sides.

In trigonometry, the hypotenuse is also crucial for defining trigonometric ratios, such as sine, cosine, and tangent, which are used to establish relationships between the sides and angles of a right triangle.

In conclusion, the side of a right triangle that is always opposite the right angle is called the "hypotenuse." It is the longest side of the triangle and is directly related to the lengths of the other two sides through the Pythagorean theorem. Understanding the concept of the hypotenuse is essential for working with right triangles, as it plays a fundamental role in determining the triangle's properties, shape, and trigonometric relationships.

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Answer: No because my teacher told me so

Step-by-step explanation: A

Answer: 3 min

Step-by-step explanation:

Step 1. Find the constant speed

you walked 1000 feet in 15 min

1000 ft/ 15min=200/3 ft / min

Step 2. Apply the constant speed to the left distance

You already walked 1000 feet and it is total 1200 feet

1200-1000=200 feet left

distance ÷ speed=time

200 ÷ (200/3)=3 min

Hope this helps!! :)

Please let me know if you have any question

The answer choices which represent true statements about the given equation are;

By observation; the slope of the given equation; y = 7x - 287.19 is positive and hence, represents the rate of change in number of beach visitors per unit rise in temperature.

Also, by comparison with the slope-intercept equation; y = mx + c; the y-intercept is; -287.19 and hence, the y-intercept is invalid as the temperature 0°F is not in the domain of x (outside temperature).

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Answer:

the correct answer of x is 16

The result of the equation 25.8 - 14 / 2, rounded to the nearest one decimal place, is 18.8.

To solve the equation 25.8 - 14 / 2, we need to perform the division first, and then subtract the result from 25.8.

Division: 14 divided by 2 equals 7.

Subtraction: 25.8 minus 7 equals 18.8.

Rounding to one decimal place: The answer, 18.8, rounded to the nearest one decimal place, remains as 18.8.

Therefore, the result of the equation 25.8 - 14 / 2, rounded to the nearest one decimal place, is 18.8.

Following the order of operations (PEMDAS/BODMAS), we prioritize the division operation before subtraction. Thus, we divide 14 by 2, resulting in 7. Then, we subtract 7 from 25.8 to obtain 18.8. Since no rounding is necessary for 18.8 when rounded to one decimal place, the answer remains as 18.8.

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The value of the variable 'x' is 48 degrees. Then the correct option is B.

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal.

In the figure, the side NP is parallel to the side MQ. Then the quadrilateral will be a parallelogram.

We know that the sum of the adjacent angles of the parallelogram will be 180 degrees.

x + 32 + 100 = 180

x = 180 - 132

x = 48

The value of the variable 'x' is 48 degrees. Then the correct option is B.

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(a) To graph the constraints, we can rewrite them in slope-intercept form:

1) xx + 2yy ≤ 12

  2yy ≤ -xx + 12

  yy ≤ (-1/2)xx + 6

2) 3xx + 2yy ≤ 24

  2yy ≤ -3xx + 24

  yy ≤ (-3/2)xx + 12

The feasible region is the area that satisfies both inequalities. To graph it, we can plot the lines (-1/2)xx + 6 and (-3/2)xx + 12 and shade the region below both lines.

(b) To draw a line representing all combinations of x and y that make the objective function equal to a specific value, we can choose a value for the objective function and rearrange the equation to solve for y in terms of x. Then we can plot the line using the resulting equation.

(c) To find the optimal solution, we need to find the point(s) within the feasible region that maximize the objective function. If the optimal solution is at the intersection point of two constraints, we can solve the corresponding system of equations to find the coordinates of the intersection point.

(d) After finding the optimal solution(s), we can label them on the graph by plotting the point(s) where the objective function is maximized.

(e) To calculate the optimal value of the objective function, we substitute the coordinates of the optimal solution(s) into the objective function and evaluate it to obtain the maximum value.

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The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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Step-by-step explanation:

4x-(-7x+4.3)-1.6=x

4x+7x-4.3-1.6=x

11x-x=5.9

x=5.9/10=0.59 is your answer

Answer:

x =0.59

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4x−(−7x+4.3)−1.6=x

4x+7x+−4.3+−1.6=x

(4x+7x)+(−4.3+−1.6)=x(Combine Like Terms)

11x+−5.9=x

11x−5.9=x

Step 2: Subtract x from both sides.

11x−5.9−x=x−x

10x−5.9=0

Step 3: Add 5.9 to both sides.

10x−5.9+5.9=0+5.9

10x=5.9

Step 4: Divide both sides by 10.

10x/10 = 5.9/10

x =0.59

The coefficient of x⁷ in the given expression is 16.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given is the expression [x³ + (4 / x²)]⁴.

[x³ + (4 / x²)]⁴ =  (x³ + 4x⁻²)⁴

                      = (x³ + 4x⁻²)² (x³ + 4x⁻²)²

                      = (x⁶ + 8x + 16x⁻⁴) (x⁶ + 8x + 16x⁻⁴)  

                      = x¹² + 8x⁷ + 16x² + 8x⁷ + 64x² + 128x⁻³ + 16x² + 128x⁻³ +

                         256x⁻⁸

Rearranging with like terms, we get,

                      = x¹² + 16x⁷ + 96x² + 256x⁻³ + 256x⁻⁸

Hence the coefficient of x⁷ is 16.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

The required maximum volume of the box is 2ft³.

Volume is a measurement of how much space an object takes up.

We can calculate the amount of something needed to fill it, like water for a bottle, tank, or aquarium.

Amount of space that stuff takes up - that's what we mean when we talk about volume.

Stuff is anything that has mass and takes up room.

When scientists are measuring volume, they usually use cubic meters.

So, calculate as:

V=x·y²

2x+y=3

y=3-2x

V = x·(3-2x)² = x·(9-12x+4x²) = 9x - 12x²+4x

V ` = 9-24x+12x² = 3(4x²-8x+3) = 3(4x²-6x-2x+3)

= 3[2x(2x-3)-(2x-3)] = 3(2x-3)(2x-1)

When the most amount is present: V ` = 0

Then,

2x-3 = 0  

2x = 3              

x = 1.5 (That's wrong, 'cause y = 0.)

or: 2x-1 = 0

2x = 1

x = 0.5,  y = 3 - 2 · 0.5 = 3 - 1 = 2

V max = 0.5 · 2² = 0.5 · 4 = 2 ft³

Therefore, the required maximum volume of the box is 2ft³.

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The  calculated difference between the sample means tracks a normal distribution with mean m₁ - m₂  and standard deviation √(5500.33).

Then the lifetimes of both brands of tires come from the same typical dissemination, the distinction in comparison to their test implies that it is ordinary dissemination.

Precisely, on the off chance that we let X and Y.

This projects  the test which implies the primary and moment brands, separately, and let s indicate the common standard deviation (given as the square root of 33002), at that point the conveyance of the distinction X-Y is additionally typical.

Now the  mean m₁ - m₂ and the standard deviation is given by the square root of the whole of the fluctuations, which in this case is the square root of 2 times the fluctuation of each test cruel (since the test sizes and changes are broken even with):
√(2) × √(33002/12) = √(5500.33)

Therefore, the difference between the sample means follows a normal distribution with mean m₁ - m₂

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Answer: A parallelogram has two parallel pairs of opposite sides. A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides.

Step-by-step explanation:

Answer:

9/10 or 0.9

Step-by-step explanation:

Slope of a line passing through two points (x1, y1) and (x2, y2) is given by
Slope m = rise/run

where
rise = y2 - y1
run = x2 - x1

Given points (- 6, - 5) and (4, 4),

rise = 4 - (-5) = 4 + 5 = 9

run = 4 - ( - 6) = 4 + 6 = 10

Slope = rise/run = 9/10 or 0.9

The best statement that describes the function of the logic variable X is: A. X is a variable whose value is 1 or 0.

Logic variables typically represent binary states or conditions, where 1 represents "true" or "on" and 0 represents "false" or "off". Therefore, option A accurately describes the function of the logic variable X as having a value of either 1 or 0. Logic variables are often used in the field of logic and computer science to represent binary states or conditions. The value of a logic variable can only be one of two possibilities: 1 or 0.

In this context, 1 typically represents "true" or "on," indicating that a certain condition is satisfied or a certain state is active. On the other hand, 0 represents "false" or "off," indicating that the condition is not satisfied or the state is inactive.

By using logic variables, we can model and manipulate binary logic in a precise and systematic manner. The values of logic variables are fundamental in logical operations, such as AND, OR, and NOT, which are essential in designing and analyzing digital circuits, programming, and logical reasoning.

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Given:

The right triangular prism.

Height of prism = 28 in.

Hypotenuse of base = 25 in.

leg of base = 24 in.

To find:

The lateral surface area of the prism.

Solution:

Pythagoras theorem:

\(Hypotenuse^2=Perpendicular^2+Base^2\)

Using Pythagoras theorem in the base triangle, we get

\(25^2=24^2+Base^2\)

\(625-576=Base^2\)

\(\sqrt{49}=Base\)

\(7=Base\)

The perimeter of the triangular base is:

\(P=7+25+24\)

\(P=56\)

Lateral area of a triangular prism is:

\(A=Ph\)

Where, P is the perimeter of the triangular base and h is the height of the prism.

Putting \(P=56,h=28\) in the above formula, we get

\(A=56(28)\)

\(A=1568\)

Therefore, the lateral area of the prism is 1568 in².

The number of small boxes purchased = 4

and the number of large boxes purchased = 9

According to the given question, a contractor needs to buy nails to build a house.

The nails come in small boxes and large boxes. Each small box has 50 nails and each large box has 350 nails. The contractor bought a total of 13 boxes that have 3350 nails altogether.

Let x be the number of small boxes and y be the number of large boxes.

The contractor bought a total of 13 boxes that have 3350 nails altogether.

x + y = 13                     ...............(1)

50x + 350y = 3350              ..........(2)

We solve above system of equations.

From equation (1),

x = 13 - y             ...........(3)

Substitute x = 13- y in equation (2)

50(13 - y) + 350y = 3350    

650 - 50y + 350y = 3350

300y = 2700

y = 9

Substitute above value of y in equation (3),

x = 13 - 9

x = 4

Therefore, the number of small boxes purchased = 4

and the number of large boxes purchased = 9

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