A water tower holds 26400 gallons of water. The water company can fill the tower at a rate of 20 gallons per minute,
How many hours would it take the water company to all the tower if it is completely empty?
o 22 hours
24 hours
220 hours
0 440 hours

Answer:

x+6=y

Step-by-step explanation:

Answer:

a)

slope = (-4 cm) / (650 cm)

slope ≈ -0.00615

b)  the section of the road measured horizontally is approximately 3983.74 cm long.

Step-by-step explanation:

change in horizontal distance = (change in vertical distance) / slope

change in horizontal distance = (-24.5 cm) / (-0.00615)

change in horizontal distance ≈ 3983.74 cm

Step-by-step explanation:

2.25

6.4

4

1.333

Hope is will help you

Answer:

18

Step-by-step explanation:

\(\frac{6}{1/3} =\frac{6*3}{1} \\=18\)

Answer:

x = -25

Step-by-step explanation:

Hi there!

In order to solve this, add 50 to both sides to isolate x.

x = -25

Hope this helps!

Thomas' installment payment that he pays in one fortnight is approximately k523.08.

To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).

First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:

Interest = Principal × Interest Rate

= k10,000 × 0.36

= k3,600

The total amount to be repaid is the sum of the principal and the interest:

Total Amount = Principal + Interest

= k10,000 + k3,600

= k13,600

Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:

Number of Fortnights = 52 weeks / 2

= 26 fortnights

To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:

Installment Payment = Total Amount / Number of Fortnights

= k13,600 / 26

≈ k523.08

Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.

It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.

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Answer:

See step by step.

Step-by-step explanation:

lets define the events:
A: cuban festival        C: tropical Garden
B: street art show      D: african festival

a) theoretically the probability is

\(P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\\)
This is 25% (for each one, equally)

b) The experimental probability is given by:

\(P(A)= \frac{32}{150} =0.2133\)

\(P(B)= \frac{38}{150} =0.2533\)

\(P(C)= \frac{35}{150} =0.2333\)
\(P(D)= \frac{45}{150} =0.3000\)

c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.  

Answer: The fraction of an hour that Jessica was with an instructor was 5/12....

Step-by-step explanation:

1/2 X 5/6= 5/12

Answer:

(5,3)

Step-by-step explanation:

Answer:

(5, 3)

Step-by-step explanation:

(x, y)----> (x + 3, y + 4)

(2,  -1)----> (2 + 3, -1 + 4)

(5, 3)

Question:

1. Find the magnitude and the positive direction angle for u.

u = (-12, 5)

For theta degree, round to the nearest tenth as needed.

2. For the vector r = (-9, -10), find -9r.

Answer:

(1)

The magnitude of vector u is 13.

The positive direction of vector u is 157.4° (to the nearest tenth)

(2)

-9r = (81, 90)

Step-by-step explanation:

(1) For a given vector u = (a, b), the magnitude of u is given by;

\(|u| = \sqrt{a^2 + b^2}\)            --------------------(i)

The direction of such vector is given by;

θ = tan ⁻¹ (\(\frac{b}{a}\))                    -------------(ii)

Where;

a and b are the x and y components of the vector.

Now,

From the question,

u = (-12, 5)

(a) From equation (i), the magnitude of u is therefore;

\(|u| = \sqrt{(-12)^2 + (5)^2}\)

\(|u| = \sqrt{144 + 25}\)

\(|u| = \sqrt{169}\)

\(|u| = 14\)

Therefore, the magnitude of vector u is 13.

(b) From equation (ii) the direction of vector u is therefore;

θ = tan ⁻¹ (\(\frac{5}{-12}\))

θ = tan ⁻¹ (-0.41667)

θ = -22.62°

The direction here is negative, but we have been told to find the positive direction.

From the given x and y components of the vector, it can be deduced that the the vector lies in the negative x direction and the positive y direction.

Therefore, the vector lies in the second quadrant. This is shown in the diagram attached to this response.

To get the positive direction, m, we need to add 180° to the result of θ = -22.62° i.e

m = 180° + (-22.62)°

m = 157.38°

Therefore, the positive direction of vector u is 157.4° (to the nearest tenth)

(2) For the vector r = (-9, -10), we are asked to calculate -9r.

Since;

r = (-9, -10)

-9r = -9(-9, -10)    [Multiply by -9]

-9r = (81, 90)

Therefore, -9r = (81, 90)

The measure of the print is 2 inches.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1' = 1/8''

This means,

12 inch = 1/8 inch

Now,

16 feet = 12 x 16 inch = 192 inch

So,

12 inch = 1/8 inch

Multiply 16 on both sides.

16 x 12 inch = 16/8 inch

192 inch = 2 inch

Thus,

2 inches is the measure of the print.

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Answer:

  (-20x -25)/(x^2-x-30)

Step-by-step explanation:

You want to simplify the rational expression (3x²)/(x²-x-30) -(3x+5)/(x-6).

Usually these problems are constructed so that the higher-degree polynomial denominator has the lower degree denominator as a factor. That is the case here.

  \(\dfrac{3x^2}{x^2-x-30}-\dfrac{3x+5}{x-6}=\dfrac{3x^2}{(x+5)(x-6)}-\dfrac{(x+5)(3x+5)}{(x+5)(x-6)}\\\\=\dfrac{3x^2-(3x^2+20x+25)}{x^2-x-30}\)

  \(=\boxed{\dfrac{-20x-25}{x^2-x-30}}\)

Answer:

The sum is -3

Step-by-step explanation:

6(sum+8)=30

=6sum+48=30

=6sum=-18

=Sum=-3

For a sample of study time in beginning and ending of semester of gvsu students.

95% confidence interval is ( 4.078, 4.602 ) and Upper bound is 4.602 and Lower bound is 4.078..

We have given that,

Sample size, n = 86

Standard deviations, sd = 1.24

Samle mean, X-bar = 4.34

Formula for confidence interval is

X-bar +- Z (sd/√n)

where, Z ---> test statistic value

Also, we have 95% confidence interval

Using the Z-table , we can get the value of z-statistic for 95% of confidence interval is 1.96 ..

Plugging all known values in above formula.

Confidence interval is

4.34± 1.96(1.24/√86)

=> 4.34 ± 1.96(0.1337)

=> 4.34 ± 0.2620

Upper bound of confidence interval is

4.34 + 0.2620 = 4.602

Lower bound of confidence interval is

4.34 - 0.2620 = 4.078

Hence, the upper and lower bounds of confidence interval are 4.602 and 4.078 respectively.

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Complete question:

Towards the end of the semester students are busy. Of all of the GVSU students, a sample of 86 students was taken. Study time per week at the beginning of the semester and study time at the end of the semester was recorded. The differences were then calculated End - Beginning. A sample mean difference of 4.34 hours/week with a corresponding standard deviation of 1.24 hours per week were found. Calculate a 95% confidence interval. (Remember to go to the hundredths place for both the upper and lower bounds.) Upper bond=? and

Lower bond=

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

840

Step-by-step explanation:

You can divide by 5 and get 168

840/6 = 140

840/21 = 40

Answer:

The largest 3 digit number divisible by 5, 6, & 21 is 840.

Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A proportional relationship is an equation that passes through the origin (0,0).

For A, the equation is y=2x+1

For B, the equation is y=2x-1

For C, the equation is y=2x

For D the equation is y=3x-3

Only C passes through the origin

Hope this helps!

Answer:

4500 miles

Step-by-step explanation:

Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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Answer:

\(f(x) = \left \{ {{x + 3} \quad \text{if} \ -3 \leq x < -1\atop {5} \quad \text{if} \ -1 \leq x \leq1} \right.\)

Step-by-step explanation:

You can find the first function if you know the general form of a line:

\(y = mx + b\)

where \(m\) is the slope and \(b\) the intercept point with the \(y\)-axis.

So in the first case the slope is 1 because the next formula

\(m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2-0}{-1+3} = 1\)

And you can find the interception point if extend the line, then in our case is  3.

So the function is:

\(f(x) = x + 5\)

In the other case is constant function that's mean that the function has the next form

\(f(x) = k\)

Where \(k\) is a constant.

So you only have to observe what is the value for each point in the interval, in this occasion is 5.

So the final answer is:

\(f(x) = \left \{ {{x + 3} \quad \text{if} \ -3 \leq x < -1\atop {5} \quad \text{if} \ -1 \leq x \leq1} \right.\)

Answer:

2x

Step-by-step explanation:

5, 10, 20, 40, 80

each step is multiplying by 2, therefore the sequence is 2x

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The reflection across y=-x swaps the coordinates and negates both of them. The first-quadrant figure becomes a third-quadrant figure.

  (x, y) ⇒ (-y, -x)

Answer: 21:9 and 42:18

Step-by-step explanation:

14:6 at its most basic form is 7:3, so find anything that could be equal to this if a number is multiplied on both sides.

21:9 is our simplified ratio multiplied by 3 on both sides.

42:18 is our simplified ratio multiplied by 6 on both sides.

But, the final ratio doesn't work, because 7 and 3 respectively cannot multiply to 13 and 8 with the same value.

The equivalent fraction for the given fraction is 1/5.

Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.

The given fraction is 3/15.

The equivalent fraction is 3/15 =1/5

Therefore, the equivalent fraction for the given fraction is 1/5.

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The volume of a cylinder is given by

where r is the radius of the base and h is the height of the cylinder.

Now, in our case, r = 6 in and h = 10 in ; therefore,

The surface area of a cylinder is given by

putting in the values of h and r gives

which is our answer!

Answer:

a) 1600 cm³ = 97.63799 pulgadas cúbicas or 97.63799in³

b) 88 mm = 3.30709 pulgadas or 3.30709 in

Step-by-step explanation:

En la pregunta anterior, se nos pide que expresemos las medidas de la pregunta anterior en pulgadas cúbicas y pulgadas respetuosamente.

Por lo tanto

a) El volumen del motor Nissan = 1600 cm³ a ​​pulgadas cúbicas (in³)

1 cm³ = 0.0610237 pulg³

1600 cm³ =

Cruz multiplicar

1600cm³ × 0.0610237 pulg³ / 1 cm³

= 97.63799 pulgadas cúbicas o 97.63799in³

b) El diámetro del motor Nissan = 84 mm a pulgadas

1 mm = 0.0393701 pulgadas

84 mm =

Cruz multiplicar

= 84 mm × 0.0393701 pulgadas / 1 mm

= 3.30709 pulgadas

To determine whether the furnace will be adequate for a 1,400 square foot house with a 9-foot ceiling, we need to calculate the volume of the house and compare it to the volume the furnace is designed to heat.

The volume of the house can be found by multiplying the square footage by the ceiling height:

1,400 sq ft x 9 ft = 12,600 cubic feet

Since the furnace is designed to heat 10,000 cubic feet, and the house has a volume of 12,600 cubic feet, the furnace may not be adequate for heating the house. The furnace is not capable to heat the entire house.