the long jump distance of four students are listed in the table below. How much farther did the student with the longest distance jump than the student with the shortest distance.
Joe 6.25
Shakira 4.37
Jackson 5.85
Chelsey 4.20

Answer:

E

Step-by-step explanation:

using the Sine rule in Δ ABC

\(\frac{a}{sinA}\) = \(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

where a is the side opposite ∠ A , b opposite ∠ B , c opposite ∠ C

we require to calculate ∠ C

∠ C = 180° - (64 + 85)° = 180° - 149° = 31°

then to find a , using

\(\frac{a}{sinA}\) = \(\frac{c}{sinC}\)

\(\frac{a}{sin64}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

a × sin31° = 9.3 × sin64° ( divide both sides by sin31° )

a = \(\frac{9.3sin64}{sin31}\) ≈ 16.23 ( to 2 decimal places )

then to find b , using

\(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

\(\frac{b}{sin85}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

b × sin31° = 9.3 × sin85° ( divide both sides by sin31° )

b = \(\frac{9.3sin85}{sin31}\) ≈ 17.99 ( to 2 decimal places )

You have some missing symbols, so I'm guessing that the integral reads

\(\displaystyle \int_C (x-9y) \, dx - x^2 \, dy\)

where C is composed of the two line segments,

• C₁ = {(9t, t) : 0 ≤ t ≤ 1}

• C₂ = {(9 + t, 1 - t) : 0 ≤ t ≤ 1}

The integrals over each path are

\(\displaystyle \int_{C_1} (x-9y) \, dx - x^2 \, dy = \int_0^1 (9t - 9\cdot t) (9 \, dt) - (9t)^2 \, dt\)

\(\displaystyle \cdots = -81 \int_0^1 t^2 \, dt\)

\(\displaystyle \cdots = -\frac{81}3 (1^3 - 0^3) = -27\)

and

\(\displaystyle \int_{C_2} (x-9y) \, dx - x^2 \, dy = \int_0^1 ((9 + t) - 9(1 - t)) \, dt - (9 + t)^2 (-dt)\)

\(\displaystyle \cdots = \int_0^1 (81 + 28t + t^2) \, dt\)

\(\displaystyle \cdots = 81 (1 - 0) + 14 (1^2 - 0^2) + \frac13 (1^3 - 0^3) = \frac{286}3\)

Then the overall line integral has a value of

\(\displaystyle \int_C (x-9y) \, dx - x^2 \, dy = -27 + \frac{286}3 = \boxed{\frac{205}3}\)

Answer:

  5.5 units

Step-by-step explanation:

Arc length is given by ...

  s = rθ

  s = (3.5)(π/2) ≈ 5.5 . . . units

Answer:

0.03593

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = 17,340

μ is the population mean = 15,000

σ is the population standard deviation = 1300

z score:

z = 17340 - 15000/1300

z =1.8

Probability value from Z-Table:

P(x<17340) = 0.96407

P(x >17340) = 1 - P(x<17340)

= 1 - 0.96407

= 0.03593

The probability that the life span of the monitor will be more than 17,340 hours is 0.03593

Whenever we have "AND" in a probability question, it means "x" [multiplication].

When we have "OR" in a probability question, it means "+" [addition].

Here, we want Probability of Quarter [P(q)] OR Probability of Dime [P(d)].

So, we will add the individual probabilities.

Now,

Total Coins = 7 + 11 + 8 + 15 = 41

Number of Quarters = 7

Number of Dimes = 11

So, we find individual probabilities:

P(q) = 7/41

and

P(d) = 11/41

Now, we add them up:

To get percentage, we do the division and multiply by 100.

18 divided by 41 = 0.4390

Multiply by 100:

0.4390 * 100 = 43.90%

Answer: We can conclude that at least one of the population means has a different value than the other population means.

Step-by-step explanation:

When the null hypothesis is rejected for an analysis of variance, we can then conclude that at least one of the population proportions has a different value.

For one-way analysis of variance, it should be noted that the null hypothesis is rejected when there is sufficient evidence which is used in making the conclusion that not all the means are equal and that there is a different value.

The possible shapes of the fencing are a parallelogram and a rectangle.

Given that, a worker fences in a construction site using four pieces of fencing that have lengths of 20, yards 16, yards, 20 yards, and 16 yards.

We need to tell possible four-sided shapes that the worker can enclose with the fencing.

So, we can see that, the pair of sides are equal,

Which is condition in a parallelogram and a rectangle.

Hence, the possible shapes of the fencing are a parallelogram and a rectangle.

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Answer:

6) = 55

7) = 68

8) = 148

9) = 102

10) = 38

5) = 48

4) =30

3) = 10

2) = 6

1) =4

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

-7

Step-by-step explanation:

Remember y = mx + b and m is the slope. Just convert to this form and identify the m.

y-3=- 7(x-2)

y - 3 = -7x + 14

y = -7x + 17

While problem and solution essays are considered expository (writing that exposes facts) in nature, they are persuasive in nature because they call for a solution to a problem.

What is the problem?

A mathematical problem is one that can be modeled, examined, and potentially resolved using mathematical techniques. This can be a practical issue, like figuring out the orbits of the planets in our solar system, or a more theoretical issue, like Hilbert's problems.

The expository essay is a type of essay that calls for the student to research a topic, assess the evidence, elaborate on the topic, and present an argument about the topic in a clear and succinct manner. This can be done by using examples, definitions, comparisons, cause and effect analyses, and more.

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Answer: 10x^3 + 2x^2 -12x

Step-by-step explanation:

Answer: \(10x^{3} + 2x^2 - 12x\)

Step-by-step explanation:

2x(5x^2 + x - 6)

10x^3 + 2x^2 - 12x

Answer:

Infinite, any number

Step-by-step explanation:

Simplify

30 - 3x = 30 - 3x

The graph of the function g(x) = x + 3 is a straight line that passes through the point (0, 3) on the y-axis and has a slope of 1.

To understand how to plot the graph, let's consider a few points on the line.

We can choose any values for x and calculate the corresponding values for g(x).

Let's start with x = 0.

Substituting this value into the function, we get g(0) = 0 + 3 = 3.

So, the point (0, 3) is on the graph.

Next, let's choose x = 1.

Substituting this value into the function, we get g(1) = 1 + 3 = 4.

This gives us another point on the line, (1, 4).

Similarly, we can choose more values for x and calculate the corresponding values for g(x).

For example, if we let x = -1, we get g(-1) = -1 + 3 = 2, giving us the point (-1, 2).

By connecting these points and extending the line in both directions, we obtain a straight line that represents the graph of g(x) = x + 3.

The line has a positive slope of 1, which means it rises by 1 unit vertically for every 1 unit it moves horizontally.

Overall, the graph of g(x) = x + 3 is a straight line that passes through the point (0, 3) and has a slope of 1.

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62 square yards is the area of the figure.

Area is the measure of a region's size on a surface and the area of a plane region or plane area refers to the area of a shape

In the given figure there are three rectangle in that two are smaller rectangles squares.

The rectangle has length of 10 yd and width of 5 yd.

Area of rectangle (Large)=10×5

=50 square yds

The side length of smaller rectangle is 3 yards and width is 2 yd

Area of rectangle (small)=3×2

6 square yds.

As there are two smaller rectangles, then area will be 2(6)=12 yards.

Now total area = 50+12

=62 square yards.

Hence, the area of the figure is 62 square yards.

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Answer:

ydsrggg

Step-by-step explanation:

Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

Answer:

(7x+5) is the length of the square

Step-by-step explanation:

(a+b)^2

= a^2 + 2ab + B^2

Substituite values in and you will find this

Answer:

Propaganda: ideas or statements spread to promote one side's views and present an opposing side negatively.

Front: the front lines where combat between opposing armies occurs.

Free enterprise system: an economic system characterized by private or corporate ownership of capital goods.

Allied Forces: the military alliance of the USA, Britain, France, and other countries during WWII.

Axis Powers: Germany, Italy, Japan.

Answer:

an equation is said to have no real solutions when value of x < 0

Step-by-step explanation:

here,

(x-4) 2= -9

2x - 8 = -9

2x = -1

x = -1/2

which is less than 0

The equation (x – 4)² = -9 has no real roots.

The solution of a quadratic equation is the value of the variable for which the expression becomes true.

Given,

          (x – 4)² = -9

The LHS of the equation is either positive or zero.

But, the RHS of the equation is a negative value.

Therefore, RHS and LHS can never be equal.

Hence, the equation (x – 4)² = -9 has no real roots.

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Answer:

8

Step-by-step explanation:

Let,

x1 = 0

x2 = 1

y1 = 18

y2 = 26

Formula : -

Slope = ( y2 - y1 ) / ( x2 - x1 )

Slope = ( 26 - 18 ) / ( 1 - 0 )

= 8 / 1

Slope = 8

Answer: 25650

Step-by-step explanation: 10% of 28500 is well 2850

28500-2850=25650

(if only i could get good rates on my car)

Answer:

Option 4 is the correct answer

Step-by-step explanation:

4. Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.

Answer:

\(y=-\dfrac{1}{2}x-3\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}\)

Given equation:

\(y=-\dfrac{1}{2}x+1\)

Parallel lines have the same slope.

Therefore, the slope of the line parallel to the given equation is:

\(m=-\dfrac{1}{2}\)

Substitute the found slope and given point (-4, -1) into the point-slope formula:

\(\implies y-(-1)=-\dfrac{1}{2}(x-(-4))\)

\(\implies y+1=-\dfrac{1}{2}(x+4)\)

\(\implies y+1=-\dfrac{1}{2}x-2\)

\(\implies y=-\dfrac{1}{2}x-3\)

Therefore, the equation of the line passing through (-4, -1) and parallel to the given equation is:

\(\boxed{y=-\dfrac{1}{2}x-3}\)

The interest for Part 1 is approximately $385.10.

The interest for Part 2 is approximately $709.31.

The formula is as follows:

Interest is calculated as follows: Principal * Rate * Time

Where

Part 1:

$132,000 is the principal.

(Decimal) Rate = 12% = 0.12

Time = 8 days/365 days.

How much interest is there in Part 1?

Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10

Therefore, the interest for Part 1 is approximately $385.10.

Part 2:

$106,750 as the principal

(Decimal) Rate = 12% = 0.12

Time = 20 days / 365 days.

How much interest will there be in Part 2

Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31

Therefore, the interest for Part 2 is approximately $709.31.

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The percentage of our new facility's seating is full will be 76%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

Our new training room can seat 150 employees.

If 6 tables consisting of 6 chairs are now taken.

Then the number of occupied seats by tables will be

⇒ 6 x 6

⇒ 36

Then the percentage of our new facility's seating is full will be

P = [(150 - 36) / 150]  x 100

P = (114/150) x 100

P = 0.76 x 100

P = 76%

The percentage of our new facility's seating is full will be 76%.

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so the solutions are x=4/5 and x=2/3.

Answer:

Here's a step-by-step explanation of how to find x in the equation 2x + 7 = -15:

First, we want to isolate the variable (x) on one side of the equation. To do this, we need to get rid of the constant (7) on the same side as x.

To cancel out the 7, we need to subtract 7 from both sides of the equation. This gives us:

2x + 7 - 7 = -15 - 7

Simplifying, we get:

2x = -22

Now we want to isolate x completely, so we need to get rid of the coefficient (2) that's multiplied with x.

To cancel out the 2, we can divide both sides of the equation by 2. This gives us:

2x/2 = -22/2

Simplifying, we get:

x = -11

So the solution to the equation 2x + 7 = -15 is x = -11.

Answer:

-11

Step-by-step explanation:

The key to this is to work backwards

You start with -15, and you know that you're adding 7 to get -15

So you take the 7 out of the equation by subtracting it from -15

-15 - 7 = -22

Now your new equation is:

2x = -22

2 times what equals 22? 11 right?

So 2 times -11 would equal -22

Which means that...

x = -11

Hope this helps! :)

Answer:

Investment is a source of Income.

Self Employment Income

Answer: Business ownership

Step-by-step explanation: took the quiz

Answer:

1

Step-by-step explanation:

h

Answer:

I know it is 1

Step-by-step explanation: