Gasoline recently cost 82.5¢/ L. If Tonya’s car holds 58.5 L, how much should it cost to fill the tank?

its c

Step-by-step explanation:

rational because when you divide both values you get 1, it's a rational number

hope it helps!

Answer:

the first person gets €80, the second person gets €40, the third person gets €20 and the fourth person gets €10.

Step-by-step explanation:

Let’s call the amount of money that the first person gets “x”. Then, the second person gets half of x, which is x/2. The third person gets half of x/2, which is x/4. The fourth person gets half of x/4, which is x/8.

The sum of these amounts should be equal to 150€.

x + x/2 + x/4 + x/8 = 150

Multiplying both sides by 8 gives:

8x + 4x + 2x + x = 1200

15x = 1200

x = 80

Therefore, the first person gets €80, the second person gets €40, the third person gets €20 and the fourth person gets €10.

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I hope this helps! Let me know if you have any other questions.

Answer:

Approximately 16%

Step-by-step explanation:

To solve this problem using the empirical rule, we need to first standardize the value of 170 pages using the mean and standard deviation provided:

z = (x - k) / o

where x is the value we want to find the probability for (170 pages), k is the mean (195 pages), and o is the standard deviation (25 pages).

So,

z = (170 - 195) / 25 = -1

Now, we can use the empirical rule, which states that for a normal distribution:

- About 68% of the data falls within 1 standard deviation of the mean

- About 95% of the data falls within 2 standard deviations of the mean

- About 99.7% of the data falls within 3 standard deviations of the mean

Since we know that the distribution is normal, and we want to find the probability that a randomly selected book has fewer than 170 pages (which is one standard deviation below the mean), we can use the empirical rule to estimate this probability as follows:

- From the empirical rule, we know that about 68% of the data falls within 1 standard deviation of the mean.

- Since the value of 170 pages is one standard deviation below the mean, we can estimate that the probability of randomly selecting a book with fewer than 170 pages is approximately 16% (which is half of the remaining 32% outside of one standard deviation below the mean).

Therefore, the probability that a randomly selected book has fewer than 170 pages is approximately 16%.

Given: A water bottle cost 4 dollars and a hat cost 6 dollars.

Let x = Number of water bottles

y = Number of hats

The club wants to raise $1200.

i.e. Required equation : 4x+6y=1200

At x=0,

\(0+6y=1200\Rightarrow\ y=\dfrac{1200}{6}\Rightarrow\ y=200\)

At x= 300

\(4(300)+6y=1200\\\Rightarrow\ 1200+6y=1200\Rightarrow\ 6y=0\Rightarrow y=0\)

At x= 240

\(4(240)+6y=1200\\\Rightarrow\ 960+6y=1200\Rightarrow\ 6y=240\Rightarrow y=40\)

So,three ordered pairs(x,y) that exist on the line : (0,200), (300,0) and (240,40)

Plot these point on graph and join them.

Answer: the other guy is correct. Got it right on my test. Have a nice day. :|

Step-by-step explanation:

The differential equation that models the rate of change of the sum S(t) with respect to time t is given by dS/dt = k * e^(0.05t).  The formula for the sum S(t) is S(t) = (k/0.05) * e^(0.05t) + C. It is not possible to determine the exact value of k that will result in $3,500,000 in 41 years.

(a) The differential equation that models the rate of change of the sum S(t) with respect to time t is given by dS/dt = k * e^(0.05t), where k represents the annual investment amount and e^(0.05t) represents the continuous compounding growth factor.

(b) To determine a formula for the sum S(t), we need to integrate the rate of change equation from part (a). Integrating both sides with respect to t, we have ∫dS = ∫k * e^(0.05t) dt. Integrating the left side gives S(t), and integrating the right side gives (k/0.05) * e^(0.05t) + C, where C is the constant of integration. Thus, the formula for the sum S(t) is S(t) = (k/0.05) * e^(0.05t) + C.

(c) In order to find the value of k that will provide $3,500,000 in 41 years, we can use the formula derived in part (b) and substitute the given values. The equation becomes 3500000 = (k/0.05) * e^(0.05*41) + C. To determine the value of k, we need to know the constant of integration C or have additional information about the initial conditions. Without this information, it is not possible to determine the exact value of k that will result in $3,500,000 in 41 years. However, with the given equation, you can solve for the value of k by rearranging the equation and solving numerically using methods such as iteration or numerical approximation techniques.

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The mean amount of snow per day is equal to 19 cm snow per day.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The area of the polygon is 13.28in²

A polygon is any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.

The area of a polygon is expressed as;

A = 1/2 ap, where a is the apothem and p is the perimeter.

The apothem = side length × ( 2× tan(180/n) where n is the no of sides

side length = 16/8 = 2 in

apothem = 2 × ( 2 × tan(180/8)

= 2 × 2 × tan22.5

= 1.66 in

Therefore , area = 1/2 × 1.66 × 16

= 1.66 × 8

= 13.28 in²

therefore the area of the polygon is 13.28 in²

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The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.

To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.

The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.

For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.

To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,

where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.

Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.

Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.

However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.

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As per the mathematical operation both Jillian and Samuel are correct.

Given expression = 30+40+70,

The methodology by Jillian = added 30 and 40 and then 70

The methodology by Samuel = added 30 and 70 and then 40.

Determining the result of the given equation:

30 + 40 + 70

= 140

Reviewing the operations of both Jillian and Samuel

Jillian

He added 30 and 40 and then 70:

30 + 40 = 70

70 + 70 = 140

Samuel

He added 30 and 70 and then 40

30 + 70 = 100

100 + 40 = 140

The result of both mathematical operations is 140. Thus, it can be stated that both are correct.

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There are two correct statements regarding a 5 by 5 matrix with three eigenvalues, one of which has a three-dimensional eigenspace.

First, there must be at least two linearly independent eigenvectors associated with the eigenvalue that has a three-dimensional eigenspace. Second, the sum of the dimensions of the eigenspaces must be equal to the size of the matrix, which is 5 in this case.

To understand the first statement, recall that the dimension of an eigenspace is equal to the multiplicity of the associated eigenvalue, which is the number of times it appears as a root of the characteristic equation. Since one of the eigenvalues has a three-dimensional eigenspace, its multiplicity must be at least 3. This means there are at least 3 linearly independent eigenvectors associated with this eigenvalue, which is necessary to span a three-dimensional space. However, the sum of the multiplicities of all eigenvalues cannot exceed the size of the matrix, which is 5. Therefore, the remaining two eigenvalues must have a combined multiplicity of 2 at most, which implies that there are at most 2 linearly independent eigenvectors associated with each of them.

To understand the second statement, note that the sum of the dimensions of the eigenspaces is equal to the sum of the multiplicities of all eigenvalues. This follows from the fact that the eigenspaces associated with distinct eigenvalues are linearly independent. Since there are three distinct eigenvalues in this case, the sum of their multiplicities is at most 5, which means the sum of the dimensions of their eigenspaces is also at most 5. Since one of the eigenspaces has dimension 3, the sum of the dimensions of the other two eigenspaces must be at least 2, which means each of them has at least one linearly independent eigenvector.

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Answer:

Alternate interior angles theorem

Step-by-step explanation:

Hope it helps you in your learning process.

The probability of all four women being on the search committee as members in it is 1/273.

We have 15 people in total out of which there are 10 men and 5 women. We need four people on the committee out of these 15.

The probability of that happening can be calculated using the formula -

= Probability of all four women getting selected/Probability of all getting selected

= (5!/4!.1!) / (15!/4!11!)

= (5!/4!1!) * (4!11!/15!)

= (5*4*3*2*1) / (15*14*13*12)

= 1/273

From this, we know that if we need to have all four women as members of the search committee, the probability of that happening is 1/273.

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Answer:

3, 50 and 70

Step-by-step explanation:

Using exterior angle property, we have 15x+5+22x+4=120, 37x+9=120. x=3

B=15x+5=50

C=22x+4=70

Using the given values and a calculator, it is found that x = 60, x^2 = 990, y = 650, y^2 = 95,298, and xy = 9,402. The computed value of r indicates that y should tend to decrease as x increases.

By computing the correlation coefficient r, we can determine the relationship between variables x and y. With the given values, we find that x = 60, y = 650, and xy = 9,402. Plugging these values into the formula for r, we can solve for the correlation coefficient. Based on the computed value of r, which implies a negative correlation between x and y, we can conclude that as x increases from 3 to 24 months, the value of y should tend to decrease.

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Answer:

9

Step-by-step explanation:

1. Just input the x value with -180:

24 (+) -180 / 12 = answer

2. Follow PEMDAS to solve, which in this case division comes before addition:

24 + (-180 / 12)

24 + (-15)

3. Addition

24 + (-15) or 24 - 15

= 9

Therefore, 24 (+) -180 / 12 equals 9.

P(X)= R(X) - C(X)

Substituing the functions on the P(X) functions:

P(X)=25x-(1500+10x)

P(X)=25x-1500-10x

Solving:

P(x)=15x-1500, The answer would be the third option!

Answer:

- 9 + 12x

Step-by-step explanation:

- 3(3 - 4x) ← multiply each term in the parenthesis by - 3

= - 9 + 12x

(a) P(0) = 132,911, P(10) = 139,336, P(15) = 141,464.75, P(20) = 142,000, P(25) = 143,554.75 (all values are in thousands)

(b) The population growth rate is given by dp/dt, which is equal to 787

(c) The values of dp/dt remain constant at 787, indicating a constant population growth rate of 787,000 people per year, implying that the population is growing steadily over time, but the rate of growth is not changing.

(a) To evaluate P for t = 0, 10, 15, 20, and 25, we substitute these values into the given function:

P(0) = -14.452(0) + 787(0) + 132,911 = 132,911 (in thousands)

P(10) = -14.452(10) + 787(10) + 132,911 = 139,336 (in thousands)

P(15) = -14.452(15) + 787(15) + 132,911 = 141,464.75 (in thousands)

P(20) = -14.452(20) + 787(20) + 132,911 = 142,000 (in thousands)

P(25) = -14.452(25) + 787(25) + 132,911 = 143,554.75 (in thousands)

These values represent the estimated population of the country in thousands for the corresponding years.

(b) To determine the population growth rate, we need to find P'(t), which represents the derivative of P with respect to t:

P'(t) = dP/dt = 0 - 14.452 + 787 = 787 - 14.452

The population growth rate is given by dp/dt, which is equal to 787.

(c) Evaluating dp/dt for the same values as in part (a):

P'(0) = 787 - 14.452 = 787 (in thousands per year)

P'(10) = 787 - 14.452 = 787 (in thousands per year)

P'(15) = 787 - 14.452 = 787 (in thousands per year)

P'(20) = 787 - 14.452 = 787 (in thousands per year)

P'(25) = 787 - 14.452 = 787 (in thousands per year)

The values of dp/dt remain constant at 787, indicating a constant population growth rate of 787,000 people per year. This means that the population is growing steadily over time, but the rate of growth is not changing.

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Given that a population proportion represents the proportion of successes within a population and that there must be two outcomes (categories), success and failure, a confidence interval about a population proportion only makes sense for qualitative variables.

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.

The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level. For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.

The sample size, sample variability, and confidence level are all variables that have an impact on the CI's width

Assuming all other factors remained constant, a larger sample would result in a narrower confidence range. Additionally, more sample variability results in a wider range of.

Hence,  a population proportion represents the proportion of successes within a population and that there must be two outcomes (categories), success and failure, a confidence interval about a population proportion only makes sense for qualitative variables.

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Answer:

17

Step-by-step explanation:

f(x) is the same as y=. "What is f(5)" is the same as saying what is y=3x + 2 when x is 5.

Either way, you are going to replace x with is numerical value, which is 5, and then solve.

y = 3(5) + 2

y = 15 +2

y = 17

f(5) = 17

Answer:

118 feet.

Step-by-step explanation:

have a great day:)

Answer:

618

Step-by-step explanation:

Answer:

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Class 9

>>Maths

>>Surface Areas and Volumes

>>Surface Area of Cubes and Cuboids

>>The length, breadth and height of a room

Question

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The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost white washing the walls of the room and ceiling at the rate of Rs. 7.50 per m

2

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Medium

Solution

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Given:

L=5 m, B=4 m, H=3m

⇒Area to be white-washed = Area of cuboid − Area of base.

=2lh+2bh+2lb−lb

=2lh+2bh+lb

=[2×5×3+2×4×3+5×4]m

2

=74m

2

Cost of white washing per m

2

area = Rs.7.50

Cost of white washing 74m

2

area=74×7.50

= Rs.555

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y=\stackrel{\stackrel{m}{\downarrow }}{2}x+1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{2\implies \cfrac{2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{2}}}\)

so we're really looking for the equation of a line with a slope of -1/2 and that it passes through (4 , 6)

\((\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y-6=- \cfrac{1}{2}x+2\implies {\Large \begin{array}{llll} y=- \cfrac{1}{2}x+8 \end{array}}\)

The number you are is 2.

Let's break down the information provided:

You are a factor of 40 when paired with 15.

Your least common multiple (LCM) with 15 is not equal to 1.

To find the number that satisfies these conditions, let's examine the factors of 40. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. Now, we need to find a number from this list that is a factor of 40 when paired with 15.

To find the LCM of 15 and each factor of 40, we can compare their multiples:

For 15 and 1: LCM = 15

For 15 and 2: LCM = 30

For 15 and 4: LCM = 60

For 15 and 5: LCM = 15 (already the smaller number)

For 15 and 8: LCM = 120

For 15 and 10: LCM = 30 (already the smaller number)

For 15 and 20: LCM = 60 (already the smaller number)

For 15 and 40: LCM = 120 (already the smaller number)

From the list, we can see that the LCM of 15 with 5, 10, 20, and 40 is equal to 15. However, the problem states that the LCM of 15 with the number is not equal to 1. Thus, the number that satisfies both conditions is 2, as the LCM of 15 and 2 is 30, and it is not equal to 1. Therefore, the number you are is 2.

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Answer:

0.25 gallons

Step-by-step explanation:

Figure out how many fluid ounces make one gallon (128) Then start by dividing 128 by 32.. You should get 4. Make 4 a decimal and get 0.25

Answer: -7, -2, 2, 7

Step-by-step explanation:

750 people go on a coach trip each coach can hold 55 people How many coaches are needed?

750/55 = 13.636 coaches are needed.

Because you cannot have a partial coach, you round up to needing 14 coaches.