15. Matthew and some friends are going to a concert. They hire a car service for $60 to
drive them to a restaurant for dinner and then to the concert. They divide the $75 cost
of the dinner equally. However, since Matthew's dad provided concert tickets for the
group, the friends agree that Matthew doesn't have to help pay for the car service.
The friends divide this cost equally among themselves. If each friend spends a total of
$30, how many friends went to the concert with Matthew?
A4
B5
C6
D7

The corresponding z-score is -1.80 (rounded to two decimal places).  The x value corresponding to z = -0.25 is x = μ - 1.697 = μ - 1.80 * (12 / sqrt(50)).

To find the x value corresponding to z = -0.25, we need to use the standard normal distribution table or calculator. First, we calculate the z-score:
z = (x - μ) / (s / sqrt(n))
where μ is the population mean (which we don't know), s is the sample standard deviation, n is the sample size, and x is the value we want to find. Rearranging this formula, we get:
x = μ + z * (s / sqrt(n))
Substituting the given values, we get:
x = μ + (-0.25) * (12 / sqrt(50))
x = μ - 1.697
Now we need to find the corresponding value of x from the standard normal distribution table or calculator. Looking up -1.697 in the table, we find that the corresponding area is 0.0445. Since we're looking for the left-tail area (z < 0), we subtract this area from 0.5 (the total area under the curve):
0.5 - 0.0445 = 0.4555
Looking up 0.4555 in the table (or using a calculator), Therefore, the x value corresponding to z = -0.25 is:
x = μ - 1.697 = μ - 1.80 * (12 / sqrt(50))

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Answer:

$12.50

Step-by-step explanation:

100%-20% -> $10

80% -> $10

100% -> \(\frac{100}{80}\) × $10 = $12.50

Answer:

The original price was $12

A monomial function that has a minimum value is y = 5x^10

In this question, we have been given four monomial functions.

y = 5x^10

y = -4x^11

y = -x^12

y = 6x

we need  to find a monomial function that has a minimum value.

For function y = 5x^10, as x > 0 increases, f(x) increases. And as x < 0 decreases, f(x) increases.

We know that for even, positive monomial function if coefficient > 0 and exponent is even then a monomial has a minimum value.

Therefore, a monomial function that has a minimum value is y = 5x^10

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Answer:

for each centimeter its $4

Step-by-step explanation:

10 divided by 2.5 is 4

1 = 4

2 = 8

2.5 equals 4 divided by 2 so 8 + 2 = 10

The sum of all 3-digit multiples of 10 is 49500.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

The first 3-digit number divisible by 10 is 100, and the last 3-digit number divisible by 10 is 990.

The total number of such digits are,

= (990 - 10)/10 + 1.

= 980/10 + 1.

= 98 + 1.

= 99.

We know sum of an arithmetic series when the first term and the last term is given is,

= [n(a + l)/]2.

= [99(10 + 990)]/2.

= (990 + 98,010)/2.

= 49500.

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The fraction of pizza that Shroff ate is 2/3 of a pizza.

The Greatest Common Factor (GCF) is the largest number that divides evenly into two or more integers. It is also known as the Greatest Common Divisor (GCD).

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by that number.

The GCD of 52 and 78 is 26 (because 26 is the largest number that divides evenly into both 52 and 78).

So, to simplify the fraction, we divide both the numerator and denominator by 26:

52/78 = (52 ÷ 26) / (78 ÷ 26) = 2/3

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The expression that represent the area of the figure is  (3 x 2) + (3 x 4).

The area of the rectangle can be found as follows:

area of a rectangle  = lw

where

Therefore, the expression that represent the area of the figure is as follows:

area of the figure = lw

l = 6 ft

w = 3 ft

area of the figure = 6 × 3 = 18 ft²

or

area of the figure = (3 x 2) + (3 x 4) ft²

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The value of the triple integral is (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)] where E is bounded by the parabolic cylinder z=16−y2z=16−y2 and the planes z=0,x=4, and x=−4.

To evaluate the triple integral ∭E \(x^8 e^y\) dV, where E is bounded by the parabolic cylinder z=16−y² and the planes z = 0,x = 4, and x = −4, we can use the cylindrical coordinate system. Here are the steps to solve the integral:

Write down the limits of integration for each variable:

For ρ, the radial distance from the z-axis, the limits are 0 to 4.

For φ, the angle in the xy-plane, the limits are 0 to 2π.

For z, the height, the limits are 0 to 16 - y² for the parabolic cylinder, and 0 to the plane z = 0.

Write the integral using cylindrical coordinates:

∭E \(x^8 e^y\) dV = ∫\(0^4\) ∫0²π ∫\(0^{(16-y^2)\) (\(\rho^9\) \(cos^8\) φ) (\(e^y\)) ρ dρ dφ dz

Evaluate the integral:

∫0²π ∫\(0^4\)(16-y²) (\(\rho^9\) \(cos^8\) φ) (\(e^y\)) ρ dρ dφ dz

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) dφ ∫\(0^{(16-y^2)}\)(\(\rho^{10\) \(e^y\)) dρ dz

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) [\((16-y^2)^{11}\) / 11 \(e^y\)] dy dφ

= ∫\(0^4\) ∫0²π (\(cos^8\) φ) [(\(16^{11}\) / 11) \(e^y\) - (11/11) y² (\(16^{10}\)) \(e^y\) + (55/11) \(y^4\) (\(16^9\)) \(e^y\) - ...] dφ

= ∫\(0^4\) (\(16^{11}\) / 11) \(e^y\) [(\(cos^8\) φ) (2π)] dy

= (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)]

Therefore, the value of the triple integral is (\(16^{11}\) / 11) [(\(e^{16}\) - 1) (\(cos^8\) φ) (2π)].

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Answer:

3

Step-by-step explanation:

6x - 2x + 12 - 8x = 6x + 6 / 10

= 4x + 12 - 8x = 6x + 6 / 10

= 120 - 40x = 6x + 6

= 120 - 40x - 6x - 6

= - 46x = -114

= x = 114 / 46

= 2.47 ~~ 3.

The slope of all the given options  are equal and it is equal to slope of given equation .

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.

Given

Equation of a given line is x+2 y=6

Lets find out slope m by writing the equation in \($y= \mathbf{m}+\mathbf{b}$\) form

\($$\begin{aligned}& x+2 y=6 \\& 2 y=-x+6 \\& y=\frac{-1}{2} x+6\end{aligned}$$\)

The slope of the line is \($\frac{-1}{2}$\)

Now we find slope of each option using formula \($m=\frac{y_2-y_1}{x_2-x_1}$\)

Lets pick two points from the graph to find out slope

Pick (0,3) and (6,0)

\($$\begin{aligned}& m=\frac{y_2-y_1}{x_2-x_1} \\& m=\frac{0-3}{6-0}=\frac{-1}{2}\end{aligned}$$\)

Now pick two points from option \($\mathbf{B}$\) to find slope

(-10,-3) and (0,-8)

\(m=\frac{-8+3}{0+10}=\frac{-1}{2}$$\)

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Answer:

four x plus three divided by two

Step-by-step explanation:

450 gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25% sugar by volume. Let x be the number of gallons of solution X that need to be added. We need to find the value of x that will result in a solution that is 25% sugar by volume.

To do this, we can set up an equation:0.2x + 0.4(150) = 0.25(x + 150)

This equation is based on the fact that the amount of sugar in the final solution must be equal to 25% of the total volume of the final solution. The left side of the equation represents the amount of sugar in the initial mixture (0.4 represents the 40% sugar in solution Y), and the right side represents the amount of sugar in the final mixture. We can simplify this equation:

0.2x + 60 = 0.25x + 37.5

Subtract 0.2x from both sides:

60 = 0.05x + 37.5

Subtract 37.5 from both sides:

22.5 = 0.05x

Divide both sides by 0.05:

x = 450

Therefore, 450 gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25% sugar by volume.

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The odds that a woman will get divorced from her first marriage by the time she is 40 depend on various factors such as location, cultural norms, socioeconomic status, and individual circumstances.

Therefore, a specific value cannot be provided without more information about the population being studied.

However, according to statistics from the United States Census Bureau, the estimated probability of a first marriage ending in divorce by the 20th wedding anniversary is about 52%. This suggests that the odds of a woman getting divorced from her first marriage before age 40 are relatively high.

It's worth noting that divorce rates and probabilities can vary widely based on factors such as age, education level, income, and race/ethnicity. Additionally, divorce is a complex and often emotionally charged issue that is influenced by a wide range of individual and societal factors.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

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Answer:

40%

Step-by-step explanation:

The value of x is -1. Option B

From the information given, we have the equation as;

2x - 10/ 4 = 3x

Where;

Let's simplify the equation

cross multiply

2x - 10 = 3x × 4

2x - 10 = 12x

collect like terms

2x - 12x = 10

-10x = 10

Divide both sides by the coefficient of x

x = 10/ -10

x = -1

Thus, the value of x is -1. Option B

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Answer:

2 : 1

Explanation:

\(\sf area \ of \ sector: \dfrac{\theta}{360} \pi r^2\)

1st sector:

\(\sf \rightarrow area: \dfrac{80}{360} \pi (8)^2 = 44.68 \ cm^2\)

2nd sector:

\(\sf \rightarrow area: \dfrac{160}{360} \pi (4)^2 = 22.34 \ cm^2\)

Ratio of 1st sector to 2nd sector:

44.68 : 22.34

2 : 1

Answer:

800

Step-by-step explanation:

If you multiply 1 tenth by 80 you will get 800 over 1.

800/1

800/1 = 800.

As RS=TU and ST=UR by distance formula, The given quadrilateral RSTU is rectangle and The diagonals RT=US so they are equal and bisect each other at right angle.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.

Here,

Calculate the length of sides by distance formula.

RS=√(y2-y1)²+(x2-x1)²

=√(2-4)²+(-2-2)²

=√4+8

=√(12

=2√3 units

ST=√(y2-y1)²+(x2-x1)²

=√(0-2)²+(-1-(-2))²

=√(4+1)

=√5 units

TU=√(y2-y1)²+(x2-x1)²

=√(2-0)²+(3-(-1))²

=√(4+8)

=√12

=2√3 units

UR=√(y2-y1)²+(x2-x1)²

=√(4-2)²+(3-2)²

=√(4+1)

=√5 units

RT=√(y2-y1)²+(x2-x1)²

=√(0-4)²+(-1-2)²

=√(16+9)

=√25

=5 units

US=√(y2-y1)²+(x2-x1)²

=√(2-2)²+(-2-3)²

=√(0+25)

=√25

=5 units

Because the given quadrilaterals, RS=TU and ST=UR, are rectangles and the diagonals, RT=US, are equal and at right angles to one another, according to the distance formula.

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Answer:

120 cubic cm

Step-by-step explanation:

formula is b*h. the base can be found by l*w/2. the area of the base is 12. 12*10 is 120 cm

Answer:

\(120 cm^3\)

Step-by-step explanation:

area of triangular base times the height will give the volume

(1/2 × 6 × 4)(10)

12×10 = \(120 cm^3\)

Answer:

5

Step-by-step explanation:

Slope intercept form is y = mx + b

M is the slope

5 is the m

Answer:

5

Step-by-step explanation:

When your trying to find the slope of something you need to use slope intercept form.

Answer:

4 Containers needed to Fill 3 Two lbs Bags Of Candy .

Step-by-step explanation:

According to Question, We have    

2 lbs Bag Of Candy Used To Fill Container That hold \(1\frac{1}{2}\) lbs Each .

Now There are 4 Container of Capacity \(1\frac{1}{2}\)  lbs Needed To fill Exactly 3 two lbs Bags .

Thus 4 containers have Total capacity Of 6 lbs . Which Is Easily Filled By The 3 two lbs Bags . ( Without Any Loss )

Using translation concepts, the graph of a translated function of \(y = \sqrt{x}\) is given by:

On a coordinate plane, a curve starts in quadrant 3 and then increases into quadrant 1. It crosses the y-axis at (0, negative 2) and crosses the x-axis at (1.5, 0).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

\(y = \sqrt{x}\) starts at (0,0) and in it's entirety, is in quadrant 1. When it is shifted down and left, it will start on quadrant 3 and increase into quadrant 1, hence the correct option is given by:

On a coordinate plane, a curve starts in quadrant 3 and then increases into quadrant 1. It crosses the y-axis at (0, negative 2) and crosses the x-axis at (1.5, 0).

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Answer:

A

Step-by-step explanation:

I took it

The appropriate nonparametric test for the given research is; One sample Wilcoxon signed rank test.

A non-parametric test is also called a distribution-free test and it unlike the parametric test, it is usually based on fewer assumptions. Thus, there is typically no need for key parameters like median, mean deviation, mean e.t.c.

Now, the types of Non parametric tests are;

In this question, we do not know the distribution of X.

where;

X is the time it takes to walk across a presumably scary portion of campus.

However, we know that X is continuous and so we will use the One sample Wilcoxon signed rank test.

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The rate at which the snake  ganing weight is  is dw/dt = k * 0.3

To find the rate at which the snake is gaining weight, we can use the given information about its length and growth rate.

Given:

Length of the snake (x) = 0 meters

Growth rate of the snake (dx/dt) = 0.3 meters/year

We know that the weight of the snake is directly proportional to its length. Let's assume the weight of the snake (w) is given by the formula:

w = k * x

where k is a constant.

To find the rate at which the snake is gaining weight (dw/dt), we need to differentiate the equation with respect to time (t):

dw/dt = d(kx)/dt

Using the product rule of differentiation, we have:

dw/dt = k * dx/dt

Substituting the given value for the growth rate (dx/dt = 0.3 meters/year):

dw/dt = k * 0.3

To determine the value of k, we need additional information or assumptions. Without that information, we cannot determine the specific weight gain rate in grams per year.

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Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

1/4 inches

Step-by-step explanation:

Answer:

1/4 inches is smaller than 1/2 inches

1/4 inches in cm= 0.635

Step-by-step explanation:

The solution to the original equation is approximately 1.4422.

To continue with the bounds found in part d, we need to use the interval [1.4, 1.5] as the initial approximation for the next iteration. Using the Newton-Raphson method, we get the following approximations:

- Iteration 2: x1 = 1.4428
- Iteration 3: x2 = 1.4422

Based on these two iterations, we can conclude that the solution to the original equation is approximately 1.4422. This is because the difference between the approximations in the last two iterations is only 0.0006, which is a small enough difference to suggest that the approximation has converged to a solution.

In other words, the Newton-Raphson method has been successful in finding a solution to the equation f(x) = x^3 - x^2 - x - 1 = 0 within the given interval [1.4, 1.5]. The method works by using the tangent line to the graph of f(x) at each iteration to approximate the root of the equation. By repeating this process, we are able to get closer and closer to the actual solution.  

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