Owen stops at a gas station. He pays for gas and a car wash. The graph shows the total cost of
Owen's stop at the gas station, y, as a function of the number of gallons of gas, z.

Answer:

Step-by-step explanation:50/20= $2.05

Answer:

they tiped $10

Step-by-step explanation:

10% = $5

20% = $10

The point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.

For an angle \(\theta\) the unit circle is a circle with radius 1 containing the following set of points: \((\cos{\theta}, \sin{\theta})\).

The angle for this problem is given as follows:

-4pi/3.

Hence the sine and the cosine are given as follows:

Hence the point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.

(the equation of the unit circle is x² + y² = 1).

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The transformation that mapped ∆ABC onto ∆A′B′C′ is a reflection over the x-axis. The coordinate of B'' would be same as that of B'.

We are given the coordinates as;

∆ABC; A(-6, 2), B(-2, 6), C(-4, 2).

∆A′B′C; A'(-6, - 2), B (-2, -6), C (-4, -2).

A) Now, we are told that ∆ABC was transformed to

∆A′B′C. From the given coordinates, we see that only the y coordinate sign changed after the transformation. Thus, the transformation that mapped ∆ABC onto ∆A′B′C′ is a reflection over the x-axis.

B) Now, ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″. Since the line x = -2 is vertical and the coordinate of B' in ∆A′B′C′ has an x - coordinate of -2, then it means the coordinate of B'' would be same as that of B'

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The cylinder should make approximately 0.3097 revolutions per second in order for the clothes to lose contact with the wall at an angle of 54.0°.

To determine the required number of revolutions per second for the cylinder in order for the clothes to lose contact with the wall at a specific angle, we can use the concept of centripetal acceleration.

The centripetal acceleration experienced by an object moving in a circular path of radius r at a speed v is given by the formula:

\(a = v^2 / r\)

In this case, when the clothes lose contact with the wall, the net force acting on them is the gravitational force pulling them downward, which can be expressed as:

mg = m * g

Since the gravitational force provides the centripetal force for the clothes, we can equate the centripetal acceleration to the gravitational acceleration:

v^2 / r = g

To solve for the speed v, we need to find the circumference of the circular path. The circumference C can be calculated as:

C = 2πr

Substituting this into the equation above, we have:

v^2 / (2πr) = g

Now, we need to find the required speed v when the clothes lose contact with the wall at an angle of θ = 54.0°. We can use the angle θ to find the arc length traveled by the clothes on the circular path.

The arc length s can be calculated as:

s = θ * r

Substituting the given values, we have:

s = (54.0°) * (0.512 m)

Next, we can calculate the time it takes for the clothes to traverse the arc length s at the required speed v. The time t can be calculated as:

t = s / v

Now, since we want to find the number of revolutions per second, we need to convert the time t into seconds per revolution (s/rev). Since each revolution covers the circumference C, the time for one revolution is:

t_rev = C / v

Finally, the number of revolutions per second is given by the reciprocal of the time for one revolution:

Rev/s = 1 / t_rev

Let's calculate the required number of revolutions per second using the given values. Assuming the acceleration due to gravity is approximately 9.8 m/s²:

r = 0.512 m (radius)

θ = 54.0° (angle)

g = 9.8 m/s² (acceleration due to gravity)

First, calculate the arc length s:

s = (54.0°) * (0.512 m) = 27.648 m

Next, calculate the required speed v using the centripetal acceleration equation:

v^2 / (2πr) = g

v^2 / (2π * 0.512 m) = 9.8 m/s²

v^2 = (2π * 0.512 m) * (9.8 m/s²)

v^2 = 10.0384 m²/s²

v ≈ 3.1687 m/s

Now, calculate the time for one revolution:

t_rev = (2π * 0.512 m) / (3.1687 m/s) ≈ 3.2321 s/rev

Finally, calculate the number of revolutions per second:

Rev/s = 1 / (3.2321 s/rev) ≈ 0.3097 rev/s

Therefore, the cylinder should make approximately 0.3097 revolutions per second in order for the clothes to lose contact with the wall at an angle of 54.0°.

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The numerator for the given rational expression is 3 + 5k.

In the given rational expression, (3 + 5k) represents the numerator. The numerator is the part of the fraction that is located above the division line or the horizontal bar.

In this case, the expression 3 + 5k is the numerator because it is the sum of 3 and 5k. The term 3 is a constant, and 5k represents the product of 5 and k, which is a variable.

The numerator consists of the terms 3 and 5k, which are combined using addition (+). Therefore, the numerator can be written as 3 + 5k.

To clarify, the numerator is the value that contributes to the overall value of the fraction. In this case, it is the sum of 3 and 5k.

Hence, the correct answer for the numerator of the given rational expression (3 + 5k) / (74/k^2) is 3 + 5k.

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A researcher is using a one-way between-subjects ANOVA with k = 5 groups and N = 80 total participants. The degrees of freedom between-groups (df_ between) can be calculated using the formula:

df_ between = k - 1 = 5 - 1 = 4.

Analysis of variance (ANOVA) is an analytical tool used in statistics that divides all the variability in the data set into two parts as systematic and random. While systematic factors affect a particular data set statistically, random factors do not. Analysts use the ANOVA test to determine the effects of independent variables on variables in a regression study.

The t-test and z-test methods developed in the 20th century were used in statistical analysis until Ronald Fisher developed the ANOVA method in 1918. ANOVA, also known as Fisher's method of variance analysis, is an extension of the t and z test.

To calculate the degrees of freedom between-groups for a one-way between-subjects ANOVA, we use the formula df_ between = k - 1, where k is the number of groups (levels of the independent variable).
In this case, k = 5, so df_ between = 5 - 1 = 4.

It's important to note that the degrees of freedom within-groups can be calculated using the formula df_ within = N - k, where N is the total sample size.
In this case, N = 80, so df_ within = 80 - 5 = 75.

So, the correct answer is d. 4.

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The salesman's actual profit earnings after suffering a 5% loss due to damages when assembling the computer is $14,820.

Let's first calculate the original cost price of the computer to the salesman. We know that the salesman sold the computer for $15,600 and made a profit of 25%, which means that the selling price is 125% of the cost price.

Let the cost price of the computer be x.

Selling price = 125% of cost price

$15,600 = 1.25x

Solving for x, we get:

x = $12,480

So, the salesman's cost price of the computer was $12,480.

Now, the salesman suffered a loss of 5% due to damages when assembling the computer.

Loss = 5% of cost price

Loss = 5% of $12,480

Loss = $624

So, the actual earnings of the salesman after the loss is: $15,600 - $624 = $14,820.

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your answer is correct.

Answer:

y = -11x + 9

Step-by-step explanation:

m = -11

x = -1

y = 20

Plug those values into the equation to find b: y = mx + b

20 = (-11)(-1) + b

---> b = 9

Plus m = -11 and b = 9 into y = mx + b

---> y = -11x + 9

No, it is not possible to form a triangle with the given measures of angle a equals pi over 6 and c = 18, and a = 9.

It is not possible to create a triangle if the measure of angle a equals pi over 6 and c = 18, and a = 9. In order for a triangle to be formed, the sum of the measures of all three angles must be equal to 180 degrees. Since the measure of angle a is given as pi over 6, which is approximately 30 degrees, the sum of the measures of the three angles would be 30 + x + y = 180, where x and y represent the measures of the other two angles.

Additionally the sum of the two shorter sides of a triangle should be greater than the longest side, it can be inferred that the side c = 18 is the longest side of the triangle, and the sides a = 9 and b = x + y should be the shorter sides, but since 9 + 9 < 18 we can conclude that is not possible to create a triangle with these measures.

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Answer: 1 triangle

Step-by-step explanation: TRUST ME IT IS CORRECT!!

1 TRIANGLE!

Answer: it’s 1/5

Step-by-step explanation:

We can use the Pythagorean identity one more time to get:

cos^2(a)t + cos^2(B) + cos^2(y) = 1

What is Trigonometry ?

Trigonometry is the branch of mathematics that studies the relationships between the sides and angles of triangles. Trigonometry is found throughout geometry because every shape with equal sides can be broken down into a collection of triangles.

The identity you want to prove is:

cos^2(a)t cos^2(B) + cos^2(y) = 1

We can start by using the Pythagorean identity for sine and cosine:

sin^2(x) + cos^2(x) = 1

cos^2(x) = 1 - sin^2(x)

We can use this identity to substitute for cos^2(a)t and cos^2(B):

cos^2(a)t cos^2(B) = (1 - sin^2(a)t)(1 - sin^2(B))

Expanding this expression, we get:

cos^2(a)t cos^2(B) = 1 - sin^2(a)t - sin^2(B) + sin^2(a)t sin^2(B)

Now we can substitute this expression back into the original identity:

cos^2(a)t cos^2(B) + cos^2(y) = 1

(1 - sin^2(a)t)(1 - sin^2(B)) + cos^2(y) = 1

Expanding the left side and simplifying, we get:

1 - sin^2(a)t - sin^2(B) + sin^2(a)t sin^2(B) + cos^2(y) = 1

sin^2(a)t sin^2(B) + cos^2(y) = sin^2(a)t + sin^2(B)

Now we can use the Pythagorean identity again:

sin^2(a)t + sin^2(B) = 1 - cos^2(a)t - cos^2(B)

Substituting this expression, we get:

sin^2(a)t sin^2(B) + cos^2(y) = 1 - cos^2(a)t - cos^2(B)

Finally, we can use the Pythagorean identity one more time to get:

cos^2(a)t + cos^2(B) + cos^2(y) = 1

which is the identity we wanted to prove.

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Answer:

This is an equation for a parabola. All parabolas are functions.

answer: function

Step-by-step explanation:

Answer:

x= -74 or -84

Step-by-step explanation:

x^2+3x+37=-7x

x^2+3x+7x+37=0

x^2+10x+37=0

this convert to following

\(( - b + - \sqrt{ {b}^{2} } - 4 \times a \times c) \div 2 \times a\)

-b= -(10), a= 1, c =37

according to that

x= -74 or x= -84

The different percentages are, 42%, 21% and 63%.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The word "percent" is used to symbolize it.

There is no dimension to percentages. As a result, it is known as a dimensionless number. We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Now, according to the given information, the double number line shows that 42 people watched Deon's new video today.

Now, we are to find,

100% of 42 people.

This is, (100/100)*42 = 42%.

Again, 50% of 42 people is,

(50/100)*42 = 21%.

Again, 150% of 42 people is,

(150/100)*42 = 63%.

Hence, the percentages are, 42%, 21% and 63%.

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Answer:

Answers are in the explaination.

Step-by-step explanation:

100% of 42 people answer is 42

50% of 42 people answer is 21

150% of 42 people answer is 63

B = PAKP⁻¹ holds for k + 1. By induction, we conclude that B = PAKP⁻¹ for all integers k, positive and negative.

Let's prove that if B = PAP⁻¹ for some invertible matrix P, then B = PAKP⁻¹ for all integers k, positive and negative.

Let P be an invertible matrix, and let B = PAP⁻¹. Now, consider an arbitrary integer k, positive or negative. Our goal is to show that B = PAKP⁻¹. We will proceed by induction on k.

Base case: k = 0.

In this case, P⁰ = I, where I represents the identity matrix. Thus, B = P⁰AP⁰⁻¹ = AI = A = P⁰AP⁰⁻¹ = PAP⁻¹. Hence, B = PAKP⁻¹ holds for k = 0.

Induction step:

Assume that B = PAKP⁻¹ holds for some integer k. We aim to show that B = PA(k+1)P⁻¹ also holds. Using the induction hypothesis, we have B = PAKP⁻¹. Multiplying both sides by A, we obtain AB = PAKAP⁻¹ = PA(k+1)P⁻¹. Then, multiplying both sides by P⁻¹, we get B = PAKP⁻¹ = PA(k+1)P⁻¹.

Therefore, B = PAKP⁻¹ holds for k + 1. By induction, we conclude that B = PAKP⁻¹ for all integers k, positive and negative.

In summary, we have shown that B = PAKP⁻¹ for all integers k, positive and negative.

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The type of sampling described in the scenario is c. Cluster sampling.

Cluster sampling involves dividing the population into clusters or groups and randomly selecting some of these clusters. In this case, the state is subdivided into counties, which act as the clusters. Seven counties are selected at random, and further sampling is concentrated on these seven counties.

Cluster sampling is commonly used when it is not feasible or practical to directly sample individuals from the entire population. Instead, clusters or groups are randomly selected, and then a sample is taken from each of these clusters. This approach can be more efficient and cost-effective compared to other sampling methods, especially when the clusters are internally heterogeneous.

In this scenario, the initial random selection of the seven counties represents the cluster sampling, as subsequent sampling is focused on these specific clusters.

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The observed odds ratio (the observed association between migraine headache and cell phone use) is OR = 1.23.

An investigator is studying the association between cell phone use and migraine headaches.

100 cases (migraine patients) and 100 controls (people who don't suffer from migraine), and asks each group how many hours they use their cell phones per day, on average.

To calculate odd ratio ( exposure is cell phone as to check cell phone use on migraine)

Odds of disease in exposed = 60/55= 1.09

Odd of disease in non exposed = 40/45 = 0.88

Thus the odds ratio will be = 1.09:0.88

=> Odds of disease in exposed / odds of disease in non exposed = 1.09/ 0.88 = 1.23

= OR = 1.23

Hence the answer is the observed odds ratio (the observed association between migraine headache and cell phone use) is OR = 1.23.

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Answer:

its is a

Step-by-step explanation:

EDGE 2021

Point A Represents (3,-5π/3). Option A is correct.

A pair of coordinates that identify a point's location in a plane; the first is the distance (r) from the point to the origin and the second is the angle (Θ) that this line makes with a fixed-line.

Point A Represents (3,-5π/3).

The radius of all the points from the center of the circle is 3 units.

The angle in the polar coordinate in the clockwise direction is taken as negative and the anticlockwise direction is positive.

The given angle is;

-5π/3

In order to get the position of the angle from the x-axis the angle should be added by 2π as;

Θ = 2π-5π/3

Θ = π/3

The angle is calculated clockwise. From the digrame point, A represents the angle  π/3.

Point A Represents (3,-5π/3).

Hence, option A is correct.

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Answer:

The answer is 36

Step-by-step explanation:

Brainlest pls :)

Answer:

jgdnh svfbbth1f we ra r ti

Answer:

Step-by-step explanation:

f(x) = 0

Step-by-step explanation:

The denominator has a higher degree than the numerator, so the horizontal asymptote is f(x) = 0.

f(x) = (x^2 + x - 2) / (x^2 - 3x - 4)

Domain is all real numbers except the valus of x for which x^2 - 3x - 4 = 0

(x + 1)(x - 4) = 0

x = -1, x = 4

Domain is all real numbers except x = -1 and x = 4.  (-∞, -1) ∪ (-1, 4) ∪ (4, ∞)

Range is all real numbers

x-intercepts are the values of x for which x^2 + x - 2 = 0

(x - 1)(x + 2) = 0

x = 1, x = -2

x-intercepts are x = 1 and x = -2

y-intercept is y = 1/2

It has no Horizontal asymptotes

Vertical asymptotes are x = -1, x = 4

Answer:

Median is 5

Step-by-step explanation:

There are 15 data points and and 15 is 7 + 7 + 1, so the eighth data point would be your median because it is in the exact middle. If you count it out the answer is 5.

Answer:

19/3 (6 1/3)

Step-by-step explanation:

According to the question we have  approximately 99.74 percent of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

To answer this question, we will use the normal distribution formula and z-score.

First, we need to find the z-score for the lower limit of $1.20:

z = (1.20 - 1.50) / 0.10 = -3

Next, we need to find the z-score for the upper limit of $1.80:

z = (1.80 - 1.50) / 0.10 = 3

Now, we can use a z-table to find the area under the curve between these two z-scores.

The area to the left of z = -3 is 0.0013, and the area to the left of z = 3 is 0.9987.

To find the area between these two z-scores, we subtract the area to the left of z = -3 from the area to the left of z = 3:

0.9987 - 0.0013 = 0.9974

Therefore, approximately 99.74% of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

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The straight-line distance and the shortest distance between point X and point Y will be 2,260 m and 2,361.78, respectively.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The distance between streets is around 80 m and the distance between avenues is around 260 m, as shown below.

The straight-line distance between point X and point Y will be given as,

⇒ (24 - 15) x 260 + (9 - 5) x 80

⇒ 2,340 + 320

⇒ 2,260 m

The shortest distance along the roads to get from point X to point Y will be given as,

D² = (2,340)² + (320)²

D² = 5,475,600 + 102,400

D² = 5,578,000

D = 2,361.78 meters

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The complete question is attached below.

I will be making 7200 dollars at the end of the day

There are 24 hours in a day

Convert 24 hours to minutes

60 minutes = 1 hour

x= 24

Cross multiply

x= 1440 minutes

The amount made every 10 minutes is 50 dollars

50 dollars = 10 minutes

y= 1440

Cross multiply

10 × y= 1440 × 50

10y= 72000

divide both sides by the coefficient of y which is 10

10y/10= 72000/10

y= 7200

Hence 7200 dollars will be made at the end of the day

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