jaci runs cross country for her high school. on average she runs 6 minutes per mile

The price paid by Jason for the gallons of gas he used for the trip is $2.15per gallon of gas.

As given in the question,

Reading of odometer in the starting of trip = 42,876.1

Reading of odometer in the end of trip = 43,156.1

Total distance covered by Jason on his trip = 43,156.1 - 42,876.1

                                                                         = 280 miles

Average miles per gallon of Jason's car = 35 miles per gallon

Gallons of gas used by Jason on his trip = 280 / 35

                                                                   = 8 gallons

Amount of money used to fill gas = $17.20

Price of the gas per gallon = 17.20 / 8

                                            = $2.15 per gallon of gas.

Therefore, the price paid by Jason for the per gallon of gas is equal to $2.15 per gallon of gas.

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The solution for the given inequality is 1 < m ≤ 4. The graph for the obtained solution set is shown below.

Two expressions are related by comparative operations like 'less than or 'greater than or 'less than or equal or 'greater than or equal. Then that equation is said to be an "inequality equation".

For example, a < k ≥ b, etc.

The given inequality equation is

-2 < 3m - 5 ≤ 7

On adding 5 to the inequality, we get

-2 + 5 < 3m - 5 + 5 ≤ 7 + 5

⇒ 3 < 3m ≤ 12

On dividing by 3, we get

⇒ 3/3 < 3m/3 ≤ 12/3

⇒ 1 < m ≤ 4

Therefore, the solution set for the given inequality is (1, 4].

The obtained solution set is shown on the number line here.

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Mrs. Gilmore and Brianna are 17 feet apart.

Pythagoras theorem is one of the mathematical principles that can be applied to determine the value of the unknown side of a right angled triangle. Where a right angled triangle is one with one of its angles to equal [tex]90^{o}[/tex].

In the given question, sketching the distance apart of each person, it would form a right angled triangle.

Let the distance in feet between Mrs. Gilmore and Brianna be represented by d.

Then;

[tex]/Hyp/^{2}[/tex] = [tex]Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]d^{2}[/tex] = [tex]15^{2}[/tex] + [tex]8^{2}[/tex]

   = 225 + 64

   = 289

d = 17

Therefore, Mrs. Gilmore and Brianna are 17 feet apart.

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The 350 percent is less than the cube root of 50.

Here given two numbers,

∛50 and 350%

To compare the numbers we have to make to to simplest fraction,

∛50

The radical form of the cube root of 50 is ∛50, and the exponent form is (50)⅓ . The prime factorization of 50 is 2 x 5 x 5,

so the cube root of 50 in its simplest radical form is ∛50 .

50 cube root : 3.684031499

350%

The number 350% can be expressed as ,

350 / 100

350/100 = 3.5

So by comparing 3.684031499 and 3.5, 3.684031499 is larger

So ∛50 is larger than 350%

Therefore 350% is < ∛50.

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Answer:

350 percent is less than the cube root of 50

Step-by-step explanation:

The Volume of the Cylindrical Silo is 88000 cubic feet

What is Volume?

Volume is a measurement of three-dimensional space that is occupied. It is frequently mathematically quantified using SI-derived units or different imperial or US customary units. The concept of length is linked to the definition of volume.

Solution:

Given:

Height of the Container = 70 feet

Circumference of the Base = 125.7 feet

To Find: Volume of the Container

Volume = πr²h

Circumference = 2πr

125.7 = 2 * 3.14 * r

r = 20.01

Volume = 3.14 * 20.01 * 20.01 * 70

Volume = 88007.94 cubic feet

Volume = 88000 cubic feet (approx)

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Answer: y = 3x + 2

Step-by-step explanation:

Let's start with what we know. To calculate the slope, we do:
(y1 - y2)/(x1 - x2)

So, for this equation we get:

(5 - 2)/(3-0)

We get 3/3, so the slope = 1. So far, we have:

y = 3x + b

Let's use one of our coordinates to plug this in:

2 = 0 + b

So b = 2.

So our final equation is:
y = 3x + 2

The linear function in this problem is defined as follows:

y = -328.275x + 3142.5.

The number of CD's sold by year decreases by about 328 million per year. About 3143 million of CD's were sold in 2010.

The estimate for the year of 2019 is of: 188 million CD's.

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients of the function are defined as follows:

Two points of the linear function in this problem are given as follows:

(2, 2485.6), (6, 1172.5)

The slope is given by the change in y divided by the change in x, hence:

m = (1172.5 - 2485.6)/4 = -328.275.

Then:

y = -328.275x + b.

When x = 2, y = 2485.6, hence the intercept b is obtained as follows:

2485.6 = -328.275(2) + b.

b = 2485.6 + 328.275(2)

b = 3142.5.

Hence the function is:

y = -328.275x + 3142.5.

2019 is nine years after 2010, hence the estimate is obtained as follows:

y = -328.275(9) + 3142.5 = 188 million CD's.

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With the help of time -distance formula we can calculate travel time in km for any given problem or situation.

We know the formula we relate to distance and  time that which  is called time -distance formula is :

t= d/s, where d is the distance and s is the speed of the object.To calculate travel time in km, first, we need to divide the total distance in km by the average speed of travel in terms of km/hour, later multiplying the result by 60 to get the travel time in minutes.

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Assuming that Nathalie's weight is still measured in pounds and ounces and that she has not lost or gained any weight since her birth, we can calculate her current weight as follows:

A) Nathalie weighs 7 pounds and 9 ounces at birth, which is equal to 7.5625 pounds. If she now weighs 12 times as much, she weighs 7.5625 * 12 = 90.75 pounds. In ounces, this is equal to 90.75 * 16 = 1452 ounces.

B) To calculate the percentage increase in Nathalie's weight, we need to first calculate the increase in her weight, which is equal to 90.75 - 7.5625 = 83.1875 pounds. We can then divide this increase by her original weight of 7.5625 pounds and multiply by 100% to express the result as a percentage: (83.1875 / 7.5625) * 100% = 1103.9%. This means that Nathalie's weight has increased by more than 1100% since she was born.

If the heights of five dogs are 400 mm, 370 mm, 470 mm, 330 mm and 500 mm. Then the standard deviation of the heights of the dogs is:

c) 70 mm

Given:

five friends were comparing the height of their dogs.

the heights at the shoulders were 400mm, 370mm, 470mm, 330mm and 500mm.

we are asked to find out the standard deviation of the heights of these dogs = ?

First find mean :

(400+ 370+470 + 330 + 500)/5

Mean = 2070/5

Mean = 414

standard deviation = √∑(xi - mean)²/N-1

= √(400-414)²+(370-414)²+(470-414)²+(330-414)²+(500-414)²/4

= √(14)²+(-44)²+(56)²+(-84)²+(86)²/4

= √196+1936+3136+7056+7396/4

= √19720/4

= √4930

= 70.21

rounding it to the nearest integer.

= 70 mm

Hence we get the required standard deviation as 70 mm.

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Answer:

Step-by-step explanation:

To put in slope intercept form, isolate y.

4y = -2x +4

Further divide by 4 to isolate y.  What you do on one side of an equation, you also do on the other side.

4y/4 = -2x/4 +4/4

y = -1/2x +1

the probability that alex and jose end up on the same team is 44.4%

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

there are two kids in the group, Alex and his best friend Jose.

alex and Jose end up on the same team

Since the order of students in the team is not important so the combination will be used.

The number of ways of selecting 5 students out of 10 is

C(10,5) = 252

Rest of 5 students will go into team B. Therefore, the number of elements in the sample space is 252.

P(Alex and Jose are in one team) = 112 / 252 = 0.4444

Hence the probability that Alex and Jose end up on the same team is 44.4%

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Step-by-step explanation:

To find the values of the trigonometric functions, we need to know the angle whose cosine, sine, etc. we are trying to find. In this case, we are given that the cosine of the angle is 3/5, but we are not told the measure of the angle itself. We can find the values of the other trigonometric functions using the given value of the cosine, but we must first express the value in radians.

Since the cosine of an angle is equal to the x-coordinate of the point on the unit circle that is located on the terminal side of the angle, we can find the value of the angle in radians by finding the inverse cosine (cos^-1) of 3/5. In other words, we want to find the angle such that the cosine of the angle is 3/5.

The inverse cosine function is denoted by cos^-1, so we can write:

$\cos^{-1}(3/5) = \theta$

where $\theta$ is the measure of the angle in radians.

To find the value of the other trigonometric functions, we can use the following relationships:

$\cos^2\theta = 1 - \sin^2\theta$

$\tan^2\theta = \frac{\sin^2\theta}{\cos^2\theta} = \frac{1 - \cos^2\theta}{\cos^2\theta}$

$\csc^2\theta = \frac{1}{\sin^2\theta}$

$\sec^2\theta = \frac{1}{\cos^2\theta}$

$\cot^2\theta = \frac{\cos^2\theta}{\sin^2\theta} = \frac{\cos^2\theta}{1 - \cos^2\theta}$

We can now plug in the value of $\theta$ that we found earlier and use these relationships to find the values of the other trigonometric functions:

a. $\cos\theta = \cos(\cos^{-1}(3/5)) = \frac{3}{5}$

b. $\sin^2\theta = 1 - \cos^2\theta = 1 - (\frac{3}{5})^2 = \frac{4}{25}$

c. $\cos^2\theta = (\frac{3}{5})^2 = \frac{9}{25}$

d. $\tan^2\theta = \frac{\sin^2\theta}{\cos^2\theta} = \frac{\frac{4}{25}}{\frac{9}{25}} = \frac{4}{9}$

e. $\csc^2\theta = \frac{1}{\sin^2\theta} = \frac{1}{\frac{4}{25}} = \frac{25}{4}$

f. $\sec^2\theta = \frac{1}{\cos^2\theta} = \frac{1}{\frac{9}{25}} = \frac{25}{9}$

g. $\cot^2\theta = \frac{\cos^2\theta}{\sin^2\theta} = \frac{\frac{9}{25}}{\frac

As per the daily mean, the peak power load when max is possible to calculate with a computer or calculator.

The highest outdoor temperature and the mean daily peak power load for a sample of 6 days are provided in the table. However, it is impossible to estimate the peak power load when the highest temperature is 84 without more details. The presented data only reflects a sample of 6 days, which may not be typical of the full population, and the connection between peak power load and maximum temperature may not be linear. Furthermore, using the provided data to conduct any calculations is impossible without access to a computer or calculator.

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The quadratic equation 7 · x · (2 ·x + 5) = 0 have the points x₁ = 0 and x₂ = - 5 / 2 as its x-intercepts.

In this problem we must determine the the x-intecerpts of a quadratic equation, that is, the values of x such that A · x² + B · x + C = 0. This question can be resolved by means of algebra properties. First, write the quadratic equation:

7 · x · (2 ·x + 5) = 0

Second, expand the expression and simplify until standard form is found:

7 · x · (2 ·x + 5) = 0

14 · x² + 35 · x = 0

Third, complete the square:

x² + (35 / 14) · x + 25 / 16 = 25 / 16

(x + 35 / 28)² = 25 / 16

Fourth, clear the variable x:

x + 35 / 28 = ± 5 / 4

x = - 35 / 28 ± 5 / 4

x = - 5 / 4 ± 5 / 4

The points x₁ = 0 and x₂ = - 5 / 2 are the x-intercepts of the quadratic equation 7 · x · (2 ·x + 5) = 0.

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For straight lines l1 and l2 to be parallel, the value of x will be 4/3

Given that:

A machine is set to make parallel cuts on stone tiles.

Line l2 has equation y = 3/4

Line l1 has gradient -(3x-4)/8

Since y = 3/4. It is a horizontal line and the gradient of a horizontal line is 0. Also, if the straight lines l1 and l2 are parallel, then their will be the same. Thus:

-(3x-4)/8 = 0

-(3x-4) = 0

3x - 4 = 0

3x = 4

x = 4/3

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The function A is a linear function.

The function B is not a linear function.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Function A.

The coordinates:

(0, 1), (1, 0), (2, -1), (3, -2), (4, -1)

The rate of change of a linear function between any two points is the same.

Rate of change:

= (0 - 1) / (1 - 0) = -1/1 = -1

= (-1 - 0) / (2 - 1) = -1/1 = -1

= (-2 + 1) / (3 - 2) = -1/1 = -1

The function A is a linear function.

Function B.

The linear function graph is a straight line.

Function B graph is not a straight line.

Thus,

Function A is a linear function but function B is not a linear function.

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The area of the shaded sector is 9π unts²

The term "turn" also refers to a 360° rotation. Angles between 0° and 360° are calculated. We require a circle's circumference, which is equal to 2 r r, where r is the circle's radius.

In any circle of radius r, the ratio of the arc length ℓ to the circumference equals the ratio of the angle θ subtended by the arc at the center and the angle in one revolution. Thus, measuring the angles in radians, ℓ2πr=θ2π⟹ ℓ=rθ.

Find the diagram attached

Given the following

Radius = 6

Theta = pi/2 = 90°

Area of the sector = theta/360×πr²

Area if the sector = 90/360 × π(6)²

Area of the Sector = 1/4 × 36π

Area of the sector = 9π unts²

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A strong negative linear association between two variables is scatter plot 4.

What is standard normal random?
We shall read probabilities out rather than directly working with Z's density function to compute probabilities for Z. The elements in the tables are probabilities of the kind P(Zz), and they are tables of cumulative probabilities. Following are a number of examples that will help to clarify how to use the tables.The standard normal random.

Very dispersed and lacking in association is scatter plot 1.

Positive correlation may be seen in scatter plots 2 and 3.

Scatter figure #4 clearly illustrates a strong inverse relationship between the variables.

Hence the Correct answer is scatter plot 4.

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At 99%, the confidence level will be (26.03,33.97)

given that

random sample n = 20

mean = 30

standard deviation = 6.2

the degree of freedom

df = n-1

   = 20-1

   =19

"t" at confidence level 99%, will be:

[tex]\alpha[/tex] = 1 - 0.99

  =0.01

[tex]\alpha[/tex]/2 = 0.01/2

     =0.005

t×[tex]\alpha[/tex]×df = t× 0.005 × 19

   By using the student table, we get

 = 2.861

The margin of error will be:

E = t[tex]\alpha[/tex]/2df× ([tex]\frac{s}{\sqrt{n} }[/tex])

   = 2.861 ×[tex]\frac{6.2}{\sqrt{20} }[/tex]

  = 3.97

At 99%, confidence interval will be:

=x - E < μ < x + E

=30 - 3.97 < μ < 30 + 3.97

=(26.03,33.97)

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Answer:

20:3 ratio

Step-by-step explanation:

Answer:20 horses to 3 cows or 20:3

Step-by-step explanation:

The answer would be 20:3. If you notice that Both 40 and 6 can be divided by 2 so you would divide 40 by 2 and get 20 as your answer. And for the next you would divide 6 by 2 getting 3. So your ratio would be 20 horses to 3 cows or 20:3. I hope you were able to understand and I hope this helps you! I'm so sorry I didn't see your question earlier!

The value of the correlation coefficient between exam 1 score and exam 2 score is -1.

Given:

suppose that every student in this class earns exactly twice as many points on exam 2 as on the exam 1.

what would be the value of the correlation coefficient between exam 1 score and exam 2 score = ?

1. the coefficient will be exactly one since it measures linear dependence and these are perfectly linear dependent.

2. the coefficient will be exactly one since it measures linear dependence and these are perfectly linear dependent.

3. the coefficient will be exactly one, it doesn't matter which score is higher.

4. the expected value will be 0 since there won't be any correlation between random values.

5. the coefficient will be -1 every high score is matched by a low score on the other test.

Hence we get the required answer.

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The standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16

Given, the chance that a certain type of thumbtack lands point up when you toss it in the air is 80%.

we have to find the standard deviation of the proportion of the given data that it lands point up out of 100 tosses.

Number of trials be, 100

probability of success be, 80/100 = 0.8

On using the formula of Standard deviation, we get

standard deviation = n×p×(1 - p)

standard deviation = 100×0.8×(1 - 0.8)

standard deviation = 100×0.8×0.2

standard deviation = 16

So, the standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16

Hence, the standard deviation of the proportion of times that it lands point up out of 100 tosses be, 16

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The radius of a circle having the equation x² + y² + 8x - 6y + 21 = 0 is 2  units .

In the question ,

it is given that ,

the circle is having the equation ⇒ x² + y² + 8x - 6y + 21 = 0 ,

we know that ,

general equation of circle is written as x² + y² + 2fx + 2gy + c = 0 ;

so , radius of circle is calculated using the below formula ,

radius = √(f² + g² - c)

On comparing,  given equation of circle with general equation of circle ,

we get , the values of f = 4 and g = -3 .

So after substituting the values of f , g and c in the radius formula ,

we get ,

radius = √(16 [tex]+[/tex] 9 - 21)

= √(16 [tex]+[/tex] 9 - 21)

= √(25 - 21) = √4 = 2 .

Therefore , the given circle has radius = 2 units .

The given question is incomplete , the complete question is

What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0  ?

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Answer:

It's a good idea to make a savings plan for all of your regular expenses, as well as any unexpected expenses that may come up. This can include things like housing costs, groceries, utilities, transportation costs, insurance premiums, and debt payments. It can also be helpful to save for larger expenses that you know are coming up, such as a vacation or a home repair. By making a plan for your savings, you can ensure that you have the funds available to cover all of your expenses, both expected and unexpected.

Answer:

1. FY and FT

Step-by-step explanation:

1. Which sides form angle F?

Answer: FY and FT

Sides FY and FT form the sides of ΔFYT for which ∠F is the included angle.

A triangle is a polygon having three vertices and three edges. Sum of the interior angles of a triangle is 180°.

There are three sides and three angles for the triangle.

For ΔFYT given here, FY, YT and FT are the edges or sides of the triangle. ∠F, ∠Y and ∠T are the angles of this triangle formed at vertices F, Y and T respectively.

∠F is formed by the edges FT and FY

∠Y is formed by the edges FY and YT

∠T is formed by the edges YT and FT

Hence, sides of the triangle FYT for which angle F is the included angle are FT and FY.

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Answer:

Yes, 11/81 is an irrational number.

Step-by-step explanation:

Because it is a fraction with a non-terminating, non-repeating decimal expansion.