An athlete runs 1/3 of a mile every 1/20 hour. At this rate, how far does the athlete run per hour?

The quadratic function that only has one root at 3 and passes through the point (0,4) is: f(x) = (4/9)(x - 3)^2

A quadratic equation is a polynomial equation of degree 2, meaning that the highest exponent of the variable is 2. It has the general form:

ax^2 + bx + c = 0

If a quadratic function has only one root at 3, then it must be of the form:

f(x) = a(x - 3)^2

where a is a constant. This is because a quadratic function with only one root must have a double root, meaning that the parabola only touches the x-axis at that point and does not cross it. And a quadratic function with vertex at (3,0) and opening upwards satisfies this condition.

To determine the value of a, we can use any additional information that may be provided, such as the value of the function at another point. For example, if we know that f(0) = 4, then we can substitute these values into the equation to get:

4 = a(0 - 3)^2

4 = 9a

a = 4/9

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The quadratic function that has only one root at 3 and passes through (0,4) is: [tex]f(x)=(\frac{4}{9} )(x-3)^{2}[/tex]

A quadratic equation is a second-degree algebraic problem in x. In its standard form, the quadratic equation is [tex]ax^2+bx+c=0[/tex], where an as well as b are the coefficients, x is the variable, and c is the value of the constant component. The essential requirement for a formula to be a quadratic equation is that the coefficient of [tex]x^2[/tex] is not zero (a 0). When writing an equation with quadratic equations in conventional format, the [tex]x^2[/tex] term comes first, then the x term, and lastly the constant term.

A quadratic equation is a polynomial expression of degree 2, which means that the variable's greatest exponent is 2. It takes the following basic form:

[tex]ax^2+bx+c=0[/tex]

If the quadratic function has only one root at 3, it must have the following form:

[tex]f(x)=a(x-3)^2[/tex]

This requirement is satisfied by a quadratic function with a vertex at (3,0) and an opening upwards.

We know that f(0) = 4, so we can plug these numbers into the equation to get:

[tex]4=a(0-3)^2[/tex]

simplify the above equation

4 = 9a

The value is,

a = 4/9

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Answer:

To summarize the typical daily revenue of the food truck now, we would use the new mean of the daily revenue, which takes into account the new sale of $7,100. We can add this new value to the previous sum of daily revenues and divide the total by the number of days to find the new mean:

New mean = (total sum of daily revenues + $7,100) / (number of days + 1)

This would give us the updated measure of center that reflects the new data point.

The mean daily revenue of the food truck now is $6,550.

The average is calculated as the product of all values divided by all possible values. It can also be described as mean. The mean in statistics is the average value for the particular sample or collection of data. It is determined by dividing the sum of the total number of observations by the total number of observations.

To summarize the typical daily revenue of the food truck now, we would use the mean as the measure of the center.

We can calculate the mean daily revenue by adding the daily revenues from the two days ($6,000 + $7,100 = $13,100) and dividing by the number of days (2).

Mean daily revenue = (Total revenue) / (Number of days) = $13,100 / 2 = $6,550

Therefore, the mean daily revenue of the food truck now is $6,550.

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The larger sample size also reduces the impact of individual outliers, which could potentially skew the results. Therefore, increasing the sample size will result in more reliable results, and a smaller error bound and confidence interval.

The error bound (E) for the sample size of 35 community colleges is calculated using the formula: E =[tex]1.96 * √[p*(1-p)/n].[/tex]

With n = 35, p = 0.5 (assuming the mean of the enrollment figures is 0.5), the error bound is calculated to be E = 0.823.

If the sample size is increased to 500 community colleges, the error bound would be reduced to 0.338. This is because the larger the sample size, the smaller the error bound. The confidence interval would also be reduced, since it is directly proportional to the error bound.

In practical terms, a larger sample size means more reliable results. This is because when the sample size is increased, the results tend to be more representative of the entire population, leading to more accurate conclusions.

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The distance from the tower to the ground anchor is approximately 2091.36 meters.

We can use trigonometry to solve this problem. Let's call the distance from the tower to the ground anchor "x". We can draw a right triangle with the tower as the vertical side, the guy wire as the hypotenuse, and the distance we're trying to find as the horizontal side.

The angle between the tower and the guy wire is 15 degrees, so the angle between the guy wire and the horizontal is 90 - 15 = 75 degrees.

Using the trigonometric function tangent, we can set up the following equation

tan(75) = x / 500

We can solve for x by multiplying both sides by 500 and taking the tangent of 75 degrees

x = 500 × tan(75)

x ≈ 2091.36 meters

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In the following question, Welch's t-test is used to compare the means of two populations with unequal variances. It is a variation of the standard Student's t-test, which is used when the variances are assumed to be equal.

Welch's t-test is generally used when the sample sizes are small and the variances are significantly different.

The distributional assumptions that are needed for Welch's t-test include:

Normality - The data from each population must be normally distributed, although this assumption is not always strictly required for the test to be valid.

Equal variances - The variances of the two populations must be equal. In practice, this assumption is often difficult to satisfy, particularly when the sample sizes are small. Welch's t-test does not require the assumption of equal variances.

Independence - The samples from each population must be independent of each other. This means that the observations in one sample should not be related to the observations in the other sample.

Welch's t-test is a parametric test, which means that it is based on assumptions about the underlying distribution of the data. If the distributional assumptions are not met, then the test may not be valid. In such cases, non-parametric tests may be used instead, such as the Wilcoxon rank-sum test.

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If the length of the garden is 4 meters and 52 meters of fencing is required to completely enclose it, the width of the garden is 22 meters.

To find the width of the garden, we need to use the formula for the perimeter of a rectangle, which is:

P = 2l + 2w

Where:

P = perimeter of the rectangle

l = length of the rectangle

w = width of the rectangle

We know that the length of the garden is 4 meters and the perimeter is 52 meters, so we can plug in the values and solve for the width:

52 = 2(4) + 2w

52 = 8 + 2w

44 = 2w

w = 22

To verify our answer, we can check if the perimeter using this width is indeed 52 meters:

P = 2l + 2w = 2(4) + 2(22) = 8 + 44 = 52

As expected, the perimeter is 52 meters. This means that if we fence in the garden with a width of 22 meters and a length of 4 meters, we will require 52 meters of fencing to completely enclose it.

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The total interest earned on a savings bond over 24 quarters with a principal investment of $37,000 and an interest rate of 1.125% per quarter, the savings bond has earned a total interest of $9,990.

The savings bond earns 1.125%/quarter, so its quarterly interest rate is 0.01125. The amount of interest earned in one quarter is the product of the interest rate and the principal amount, which is:

To calculate the interest earned in one quarter, we multiply the principal amount by the interest rate expressed as a decimal.

Interest earned in one quarter = 0.01125 x $37,000 = $416.25

In this case, the interest earned in one quarter is $416.25.

To find the total interest earned over 24 quarters, we multiply the interest earned in one quarter by the number of quarters, which is 24.

After 24 quarters, the total interest earned is:

Total interest earned = 24 x $416.25 = $9,990

Therefore, the savings bond has earned a total interest of $9,990 after 24 quarters.

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The lowest score a student could have received and still have passed the quiz with a normally distributed class is 55.

This is because the upper 35% of a normally distributed class corresponds to a score of 1.5 standard deviations above the mean. Since the mean was 70 and the standard deviation was 10, that would mean the lowest score a student could have received and still have passed the quiz is 70 + (1.5 * 10) = 70 + 15 = 55.

In summary,
1. Start with the mean of the quiz which is 70.
2. Add 1.5 standard deviations which is 1.5 * 10 = 15.
3. The result is the lowest score a student could have received and still have passed the quiz which is 70 + 15 = 55.

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Vanessa's vertical climb rate is 0.2 feet per foot of horizontal distance. When she walks 65 feet horizontally up the hill and climbs an additional 25 feet, her total vertical climb will be 21 feet.

For every 40 feet of horizontal distance Vanessa walks, she climbs 8 feet vertically. So her vertical climb rate is 8/40 = 0.2 feet per foot of horizontal distance.

If she walks an additional 25 feet up the hill, her total horizontal distance traveled will be 40 + 25 = 65 feet.

Therefore, her total vertical climb will be 0.2 times her total horizontal distance:

8 + (0.2 * 65) = 8 + 13 = 21 feet

So, Vanessa will have climbed a total of 21 feet vertically after walking 65 feet horizontally up the hill.

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There are a total of 48 soccer games in the season.

Since there are 3 soccer games in a month, there will be 12 games in a season (3 games/month x 4 months). Since 8 games are played at night and assuming that all games are played either during the day or at night, we can calculate the number of games played during the day as:

Number of day games = Total number of games - Number of night games

= 12 games/month x 4 months - 8 night games/month x 4 months

= 48 games - 32 games

= 16 games

Therefore, the total number of games in the season is:

Total number of games = Number of day games + Number of night games

= 16 games + 32 games

= 48 games

So, there are 48 soccer games in the season.


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Answer:

$510,000

Step-by-step explanation:

Since we are rounding to the nearest thousand, we can use the hundreds place to determine the if we need to round down or up.

Remember, 4 or less, round down. 5 or more, round up.

Since the hundreds digit is 4, we do not need to round.

We only need to change the rest of the digits to 0.

So, our answer would be $510,000.

As per integration, the height of the water in the barrel at time = 2 hours is 1.672 feet (option C).

The formula is r(t) = 47-15, where t is the time in hours since the rain began. This formula tells us how fast the water level is changing at any given time t.

In this case, we're asked to find the height of the water in the barrel at t = 2 hours, given that the height at t = 1 hour is 0.75 feet. To solve this problem, we'll integrate the rate formula from t = 1 to t = 2, and add the starting height of 0.75 feet.

∫(47-15)dt from t=1 to t=2 = [47t-15t] from t=1 to t=2 = 0.922

So the total increase in height from t=1 to t=2 is 0.922 feet. Adding this to the starting height of 0.75 feet, we get the height of the water at t=2:

0.75 + 0.922 = 1.672 feet

Therefore, the correct option is (C).

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Answer:

35

Step-by-step explanation:

Change the percent to decimal form and of means multiply.

25% of 140

.25 * 140

35

Answer:

35

Step-by-step explanation:

The correct option for the given graph is option 1 and option 3. The equation matches the intersection point (1,1).

For option 1: intersection point (1,1)

substitute the values of x & y in the given equation.

1 = 3 (1) - 2

1 = 1

LHS = RHS

For option 2: point (1,1)

substitute the values of x & y in the given equation.

1 = 2 (1) + 3

1 = 5

LHS ≠ RHS

For option 3: point (1,1)

substitute the values of x & y in the given equation.

1 = -2 (1) + 3

1 = 1

LHS = RHS

For option 4: point (1,1)

substitute the values of x & y in the given equation.

1 = - [tex]\frac{1}{2}[/tex] (1) + 3

1 = [tex]\frac{5}{2}[/tex]

LHS ≠ RHS

For option 5: point (1,1)

substitute the values of x & y in the given equation.

1 = - [tex]\frac{1}{3}[/tex] (1) + 3

1 = [tex]\frac{8}{9}[/tex]

LHS ≠ RHS

Therefore, correct option for the given graph is option 1 and option 3.

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Step-by-step explanation:

For Part A, use the function f(x) to find the average of tests taken.

X is number of test taken

f(x) is the average score given said num of tests taken,x,

We want after test number 3 so using the function,

[tex]f(x) = 0.2x + 79[/tex]

Plug in. 3 for x, and we will get our answer.

[tex]f(3) = 0.2(3) + 79 = 79.6[/tex]

Part B: Use the table for the answer.

When 2 test are taken, the average test score is

84

So part B is 84.

Part C:

[tex]f(2) = 0.2(2) + 79 = 79.4[/tex]

[tex]g(2) = 84[/tex]

Since

[tex]g(2) > f(2)[/tex]

The science class had a higher average after 2 tests

Answer:

you shoulda payed attention in class

Step-by-step explanation:

also u know it's bad when the test is so hard you can't even cheat on it

Answer:

Firm 2's structure is in the form of a cylinder, so the formula to get the enclosed space or volume of the cylinder will be,

Volume = πr²h

where r = radius of the structure

h = height of the Firm

By substituting the values of 'r' and 'h' in the given formula,

V =

�

(

70

2

)

2

(

60

)

π(

2

70

)

2

(60)

=

�

(

35

)

×

60

π(35)×60

= 6597.345

≈ 6597.35 cubic feet

Total enclosed space of Firm 2 is 6597.35 cubic feet.

Answer:

8, 8.001, 8.01, 8.1, 9, 11, 13, 16

Step-by-step explanation:

From the instructions given, we know that variable u [tex]\geq[/tex] 8. the  [tex]\geq[/tex]  sign means that the number is greater than or is equal to the number, which is in this case, 8. In the numbers given, (0, 7, 7.999, 8.01, 11, 3, 7.9, 8, 8.1, 13, 5, 7.99, 8.001, 9, 16) we name the numbers greater than or equal to 8 that are stated in the list.

Noah sold 10 small avocados and 20 large avocados.

Let's assume that Noah sold "x" small avocados and "y" large avocados.

From the given information, we can write two equations:

x + y = 30 (since Noah sold a total of 30 avocados)

0.35x + 0.50y = 13.50 (since Noah made $13.50)

Now, we can use any method to solve these equations, such as substitution or elimination. Here, we will use the substitution method:

From the first equation, we can write:

x = 30 - y

Substituting this value of x in the second equation, we get:

0.35(30 - y) + 0.50y = 13.50

Simplifying this equation, we get:

10.50 - 0.35y + 0.50y = 13.50

0.15y = 3

y = 20

Substituting this value of y in the equation x = 30 - y, we get:

x = 30 - 20 = 10

Therefore, Noah sold 10 small avocados and 20 large avocados.

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The probability that a randomly selected baby will weigh more than 9.75 pounds at birth is 0.0062, or about 0.62%. This means that the vast majority of babies will weigh less than 9.75 pounds at birth, as this value is more than two standard deviations above the mean.

We can use the standard normal distribution to solve this problem by first standardizing the value of 9.75 pounds using the formula:

z = (x - mu) / sigma

where x is the value of 9.75 pounds, mu is the mean of 7.25 pounds, and sigma is the standard deviation of 1.0 pound.

Substituting the values, we get:

z = (9.75 - 7.25) / 1.0 = 2.5

We can then use a standard normal distribution table or calculator to find the probability of a z-score greater than 2.5. From the table or calculator, we find that this probability is approximately 0.0062.

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The intersection of two evens a and b is the event that both a and b occur that is option A is correct.

The intersection of two events A and B is defined as the event that occurs when both A and B occur simultaneously. It is denoted by A ∩ B, where the symbol ∩ represents intersection.

For example, if event A is "getting a head when flipping a coin" and event B is "rolling a 6 on a fair die", then the intersection of A and B would be the event "getting a head when flipping a coin and rolling a 6 on a fair die".

For example, suppose A represents the event "rolling an even number on a dice" and B represents the event "rolling a number greater than 3 on a dice". The intersection of A and B is the event that "rolling a number that is both even and greater than 3 on a dice", which consists of the outcomes {4, 6}.

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Complete Question:

the intersection of two events a and b is the event that:

a) both a and b occur.

b) the union of ac and bc occurs.

c) the union of a and b does not occur.

d) either a or b or both occur.

e) either a or b, but not both.

f) none of the above.

The larger number if the difference of the numbers is 52 is 65.

A number is five times a smaller number. Let's find the larger number when their difference is 52.

Therefore,

let

x = smaller number

larger number = 5x

There difference is 52. Hence,

5x - x = 52

4x = 52

divide both sides of the equation by 4

x = 52 / 4

x = 13

Therefore,

larger number = 5(13) = 65

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Answer:

y = 22 - x2  or x = 12 - x2

Step-by-step explanation:

Answer:

2072

Step-by-step explanation:

Multiply 14 x 37

518 x 4

2072

Answer: $2,072 a month

Step-by-step explanation:

multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply  518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072

The value of x is 5

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. All diameters are chord and but all chords are not diameter.

Since the value of the chords are thesame, the arc length RS and PQ are thesame.

Therefore ;

x+17 = 4x+2

collect like terms

4x -x = 17-2

3x = 15

divide both sides by 3

x = 15/3

x = 5

therefore the value of x is 5

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The probability of rolling a number 10 or less is 1, and the probability of rolling a number greater than 10 is 0.

The 10-sided die has 10 faces, each marked with a unique number from 1 to 10. When we talk about the probability of rolling a particular number, we're asking what the chances are of that number coming up when the die is rolled.

In this case, the question asks for the probability of rolling a number 10 or less, which means we're interested in the probability of rolling any number from 1 to 10. Since all the possible outcomes are numbers from 1 to 10, the probability of rolling a number 10 or less is certain, or 1.

This is because the sum of probabilities of all possible outcomes of an experiment is always 1.

Similarly, the probability of rolling a number greater than 10 is impossible, or 0. This is because there are no possible outcomes greater than 10 on the 10-sided die. In general, the probability of an event that cannot occur is always 0.

So, the probability of rolling a number 10 or less is 1, and the probability of rolling a number greater than 10 is 0.

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As per the given statement, the quadratic equation is to be used to find the exact solutions to this equation, and the quadratic equation is given by [tex]ax² + bx + c = 0[/tex].

To solve the quadratic equation, we can use the quadratic formula given by[tex]x = (-b ± sqrt(b² - 4ac)) / 2a[/tex] Where x is the variable, a, b, and c are coefficients with a ≠ 0, and sqrt is the square root symbol.To find the exact solutions to this equation, we can use the quadratic formula with a = 2, b = 6, and c = 12.

Substituting these values in the quadratic formula, we get

[tex]x = (-6 ± sqrt(6² - 4 × 2 × 12)) / 2 × 2= (-6 ± sqrt(36 - 96)) / 4= (-6 ± sqrt(-60)) / 4= (-6 ± i√60) / 4= (-3 ± i√15) / 2[/tex]

Hence, the exact solutions to the given equation are [tex](-3 + i√15) / 2 and (-3 - i√15) / 2.[/tex]

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Boys are taller than girls on average, with a larger center of data and larger range in height;

the dot plots are not shown.

Answer:

1/12 or 0.0833

Step-by-step explanation:

P(Coin) = 1/2

P(Dice) = 1/6

1/2 × 1/6 = 1/12

The equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].

Given,

x+2y=2

y = 1 - [tex]\frac{x}{2}[/tex]

Slope = -1/2 = [tex]m_{1}[/tex]

Let Slope of line perpendicular to line x+2y=2 is [tex]m_{2}[/tex]

⇒  [tex]m_{1}[/tex] *    [tex]m_{2}[/tex] = -1

Then [tex]m_{2}[/tex] = 1/2

Equation of line perpendicular is given by

[tex]y = \frac{1}{2}x + c[/tex]

Since it contains point (5,6)

6 = [tex]\frac{1}{2} (5) + c[/tex]

c= [tex]\frac{7}{2}[/tex]

Then the equation of line is:

[tex]y = \frac{1}{2}x+ \frac{7}{2}[/tex].

Therefore, the equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].

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