ben and chris start at the same time from places 96miles apart to cycle toward each other, ben at 16mph and chris at 12mph. if ben rests for 1/2 hour on the way, after how many hours will they meet?

Answer:

Step-by-step explanation

the answer is

The cost of the event at Skate Fest can be represented as 200 + 3x. The cost of the event at Roller Rama can be represented as 5x.

The cost of the event at Skate Fest can be represented by the mathematical expression 200 + 3x, where x is the number of students attending the event. This represents the fixed fee of $200 plus an additional $3 for each skater.

The cost of the event at Roller Rama can be represented by the mathematical expression 5x, where x is the number of students attending the event. This represents $5 per skater.

By comparing these two expressions, the director can determine which skating rink is more cost-effective based on the number of students attending the event.

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In linear equation, 80 cups of water will yonni need to replace all the water in the fish tank.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Now, as we know:

1 quart  = 0.25 gallons

⇒ 4 pints =  1  gallons

⇒ 8 pints =  2 gallons

Also, 1 pint  = 0.5 quart

⇒ 2 pints =  1 quarts

⇒ 8 pints =  4 quarts

⇒ 16 pints =  8 quarts

Again,  1 cup = 0.5 pint

⇒ 2 cup  = 1  pint

⇒ 32 cup  = 16  pints

so 16 * 5 = 80 cups

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Answer:212

Step-by-step explanation:

$2000 - $200 = $1800

$1800/$8.50 = 211.76 round up to 212

Answer:

that answer should be wrong?

Answer:

-84

Step-by-step explanation:

To simplify the expression 20^2 - 22^2, we'll first square both 20 and 22:

20^2 = 20 * 20 = 400

22^2 = 22 * 22 = 484

Now, we can substitute these values back into the original expression:

400 - 484 = -84

So 20^2 - 22^2 = -84.

The race is 40 miles long, since there are two repair and two water stations evenly spaced between the start and finish lines, and the third water station is located 8 miles after the first repair station.

The race is 40 miles long because the start and finish lines are 20 miles apart, and there are evenly spaced water and repair stations between them. The figure indicates that the first repair station is located at the start line, and the second repair station is 20 miles after the start line. The first water station is located 8 miles after the first repair station, and the second water station is located 16 miles after the second repair station. Therefore, the third water station is located 8 miles after the first repair station. Since there are two repair and two water stations evenly spaced between the start and finish lines, the race is 40 miles long.

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Answer:

X < 3

Step-by-step explanation:

2x-1<x+2

2x - x < 2 + 1

X < 3

Answer:

20 - (6 + b)

Step-by-step explanation:

ur mom

The piece of information which would have to be marked on the triangle to show congruence by the HL theorem is ac = dc which is denoted as option C.

It states that 'if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.'

In triangle  ABC and triangle EDC, hypotenuses of triangles are AB and DE respectively.To use HL hypotenuse and one leg of triangles must be equal which means that :

AB = DE (hypotenuse)

AC = DC  (leg)

This means that the additional information  which  will allow you to prove the triangles congruent by the HL Theorem is AC = DC.

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The full question is:

What additional information will allow you to prove the triangles congruent by the HL Theorem?

choices

A = E

bce= 90

ac = dc

ac=bd

Emma's total test score for the class is 156.5 out of 100.

We can calculate Emma's total score by considering the weight of each component of her grade and adding them up.

First, we can find the total score from the three tests:

(71 + 75 + 79) * 0.15 * 3 = 101.55

Next, we can find the score from the project:

85 * 0.10 = 8.5

Next, we can find the score from the final:

80 * 0.20 = 16

Finally, we can find the score from the homework:

87 * 0.35 = 30.45

The total score is the sum of all these components:

101.55 + 8.5 + 16 + 30.45 = 156.5

So, Emma's total score for the class is 156.5 out of 100.

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The quadratic function from the given graph is g(x)= -1/2 x². Therefore, option A is the correct answer.

A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.

The given function is f(x)=x².

From the given figure, graph of f(x) is

Direction: Opens Up

Vertex: (0, 0)

Focus: (0, 1/4)

Axis of symmetry: x=0

Directrix: y= -1/4

Direction: Opens Up

Vertex: (0, 0)

Focus: (0, -1/2)

Axis of symmetry: x=0

Directrix: y=1/2

So, the function is g(x)= -1/2 x²

Therefore, option A is the correct answer.

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the value of a will be 15 in equation 3 a plus b equals 54 when b equals 9.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, equation 3 a plus b equals 54 when b equals 9

In numerical form,

3a + b = 54

and b = 9

Comparing these equations

3a + 9 = 54

3a = 45

a = 15

Therefore, the value of a will be 15 in equation 3 a plus b equals 54 when b equals 9.

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The missing values of Deviation of July is 289.17, August is 339.17, September is 14800.17, whereas, October, November and December are -65.83, 10690.17 and -480.83 respectively.

When determining the standard deviation: By combining the data points and dividing the result by the number of data points, you may determine the mean, or average, of the data points. Each data point's mean should be subtracted, and the results should then be squared.

Month               sales                          Average                           Deviation:

July                    $1,750                      1,460.83                                     289.17

August              $1,800                      1,460.83                                      339.17

September        $1,6251,                   1,460.83                                  14800.17

October            $1,395                      1,460.83                                      -65.83

November        $1, 2151                     1,460.83                                  10690.17

December           $980                      1,460.83                                   -480.83

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The results of this test will be used to determine if the average tenure of U.S. workers is significantly different from the stated 4.6 years. If the results are statistically significant, then we can reject the null hypothesis and conclude that the average tenure of U.S. workers is 4.6 years.

Hypothesis: The average tenure of U.S. workers is 4.6 years

Null Hypothesis: The average tenure of U.S. workers is not 4.6 years

Alternative Hypothesis: The average tenure of U.S. workers is 4.6 years

Test Statistic: One-sample t-test

Significance Level: α = 0.05

The purpose of this one-sample t-test is to determine whether the average tenure of U.S. workers is 4.6 years. The null hypothesis states that the average tenure of U.S. workers is not 4.6 years, while the alternative hypothesis states that the average is 4.6 years. The significance level for this test will be set at α = 0.05. The test statistic is a one-sample t-test, which is used to compare the mean of a sample to a known population mean. The results of this test will be used to determine if the average tenure of U.S. workers is significantly different from the stated 4.6 years. If the results are statistically significant, then we can reject the null hypothesis and conclude that the average tenure of U.S. workers is 4.6 years.

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The solution to equation is sinx.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

Given;

The equation cosine of the quantity x plus 3 times pi over 2

Using the expression for the cosine of a sum of angles:

cos(a + B): = cos a cos B - sin a sin ß

we have:

cos(x+3pi/2)

=cos(3pi/2)cosx- sin(3pi/2)sinx

=sinx

Therefore, the solution of trigonometric equation will be sinx

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The number increase by a percentage of 76.29 over the given period of time.

To calculate the percent increase, we need to find the difference between the two values and divide that by the original value, then multiply by 100 to express the answer as a percentage:

If in 1995, a total of 945477 graduating seniors took the exam, and in 2012, the number of graduating seniors taking the ACT exam was 1666809, then the percent increase from 1995 to 2012 is:

(1666809 - 945477) / 945477 = 0.7629 x 100 = 76.29%

Therefore, the number of graduating seniors taking the ACT exam increased by 76.29% between 1995 and 2012.

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Since there are 20 students, and only 14 cookies, it is practically impossible for each student to get one whole cookie.

If there are 20 students and only 14 cookies, it is not possible for every student to get one cookie equally.

Dividing 14 cookies equally among 20 students means each student would get only 0.7 cookies, which is not possible since cookies are discrete objects.

In this scenario, the best solution would be to divide the 14 cookies as equally as possible among the 20 students, with some students getting one cookie and others getting none. This is known as an unequal distribution and is the fairest solution in such a scenario.

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Luis is  9.43 km from the starting point.

Let us assume that x represents the distance between the starting point and end point.

Let m be the east side distance and n be the northside diatnce.

Using Pythagoras theorem we find the distance between the starting point and end point i.e., the value of x.

x² = m² + n²

x = [tex]\sqrt{m^2+n^2}[/tex]

x = [tex]\sqrt{5^2+8^2}[/tex]

x = 9.43 km

Therefore, he is  9.43 km from the starting point.

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The complete question is:

Luis walks 5 kilometer due to east and 8 kilometer due to north. How far is he from the starting point?

Answer:

Step-by-step explanation:

To find the standard deviation of the population, we first need to find the mean of the population.

Mean = (28 + 28 + 29 + 31 + 28 + 24) / 6 = 28

Next, we need to find the variance of the population.

Variance = [(28 - 28)^2 + (28 - 28)^2 + (29 - 28)^2 + (31 - 28)^2 + (28 - 28)^2 + (24 - 28)^2] / 6

Variance = (0 + 0 + 1 + 9 + 0 + 16) / 6 = 2.67

Finally, we can find the standard deviation of the population by taking the square root of the variance.

Standard deviation = sqrt(2.67) ≈ 1.63

Therefore, the standard deviation of the population is approximately 1.63 seconds.

The angles m∠APE and m∠EPD are complementary angles and so the measure of angle m∠EPD is equal to 20° which makes option D correct.

In geometry, if two angles are said to be complementary, then the total of their sum is equal to 90°.

The angles m∠APE and m∠EPD are complementary angles so we evaluate for the angle m∠EPD as follows:

m∠APE + m∠EPD = 90°

70° + m∠EPD = 90°

m∠EPD = 90° - 70° {subtract 70° from both sides}

m∠EPD = 20°.

Therefore, the measure of angle m∠EPD is equal to 20°.

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Answer:

4 feet

Step-by-step explanation:

I'll use ratios:

10 feet tall is to 5 foot shadow  as  x feet tall is to 2 foot shadow

 or

10 / 5 = x /2    Multiply both sides of the equation by 2

20 / 5 = x  = 4 feet tall

The height of other tree is 4 foot.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

10 feet tall cats a shadow of 5 foot.

let x feet casts a shadow of 2 foot.

Using proportion

10/ 5 = x / 2

2 = x/2

x = 4 feet.

Thus, the 4 feet tall tree casts a shadow of 2 foot.

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Answer:

The answer is 24%

Step-by-step explanation:

Your welcome have a nice day!

Just evaluate the line in the values of the point and check if the equation is true or not.

So let's say line l has an equaiton known:

y = a*x +b

To check if a point is on the line, just replace the values of the point on the line equation, if the equation is true, then that point belongs to the line, if don't, then the point does not belong to the line.

That is the only way to check that.

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Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

What is Distance?

Distance is defined as the space between two points in space.

To find out how far Jake will have traveled after 3 hours, we can use the formula:

distance = speed x time

where speed is the rate at which Jake is traveling and time is the duration of the travel. In this case, the speed is 12 mph and the time is 3 hours.

So, the distance traveled after 3 hours is:

distance = 12 mph x 3 hours = 36 miles

Therefore, Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

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Answer:

1. 62.8

2. 3.14

Step-by-step explanation:

It is important to note that the circumference formula is pi times 2 times radius. Radius for bigger circle is 10 so its circumference would be 62.8 (3.14 times 2 times 10) where was the radius for small circle is 31.4 (3.14 times 2 times 5) so subtract 31.4 from 62.8 and you get your answer.

Answer:

When h(x)=0, x=4

Step-by-step explanation:

If: h(x)=-x+4

And: h(x)=0

—> We set the equation equal to 0

—>  -x+4=0

X=4

Answer:

              When h(x) = 0, x would equal 4.

Step-by-step explanation:

              Since we know the h(x) function is h(x) = -x + 4, when we're looking for a specific value for the function, we can replace the h(x) with the value we are setting the function equal to. In this case, 0 would replace h(x), and we would have a simple algebraic equation: -x + 4 = 0. Now we can solve for x, which will be equal to -x + 4 = 0 ⇒ -x = -4 ⇒ x = 4. Therefore, when h(x) equals 0, x would be equivalent to 4.

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KN is 6 units long, AL is 6 units long, AR is 10 units long, and RG is 4 units long.

A line segment is a section of a straight line that is bounded by two different end points and contains every point on the line between them. The Euclidean distance between the ends of a line segment determines its length. A line segment has endpoints, but a line can be extended forever on both ends. A line segment is a section of a line that links two places known as the line's endpoints. It is possible to measure the distance between two places. Because line segments have a fixed length, they may be used to create the sides of any polygon.

Here,

They are equal in ratio.

4/8=x/12

x=6 units

4/8=3/y

y=6 units

4/8=5/z

z=10 units

4/8=2/p

p=4 units

The length of line segment KN is 6 units, AL is 6 units, AR is 10 units and  RG is 4 units.

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The angle of elevation at which Luke shoots the squirt gun is 25.641°

A frequently used idea in relation to height and distance is the angle of elevation, particularly in trigonometry. It is described as a relationship between an oblique line from the observer's eye to an item above his eye and the horizontal plane. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.

Given that, the height of Luke is 6 ft .

the height of squirt gun from the ground is 30ft.

So, the height of squirt gun from the Luke's eye is 30-6 = 24 ft

The horizontal distance of Luke from Alex's building is 50 feet .

Let the angle of elevation is θ.

tan θ = the height of squirt gun from the Luke's eye / The horizontal distance of Luke from Alex's building

tan θ = 24/50

tan θ = 0.48

θ = tan⁻¹ 0.48

θ = 25.641°

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The system of equations to find the number of each type of test is t + f = 28 and 2t + 4f = 100

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The slope intercept form of the linear equation is:

y = mx + b

where m is the slope and b is the initial value.

Let t represent the number of 2 point questions and f represent the number of 4 point question.

Mr. Evans is giving a 28-question test, hence

t + f = 28      (1)

The entire test is worth 100 points., therefore:

2t + 4f = 100    (2)

From both equations:

t = 6, f = 22

The test had 6 number of 2 point questions and 22 number of 4 point question.

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Answer:

50%

Step-by-step explanation:

50% = 0.5

$90000 times 0.5 = $45000

So, 50% of $90000 is equal to $45000

Answer: 50%

Hope this helps :)

Step-by-step explanation:

45,000 / 90,000 = .5 (50 out of 100)

45 * 2 = 90