A water tank is built in the form of a right rectangular prism, with dimensions that measure 13.4 ft by 8.7 ft by 7.5 ft. How many cubic feet of water would it hold when it is full? Round your answer to the nearest tenth if necessary.

The solution for system of equation provided as per the given question will be x = -19 and y = 55 or (-19,55).

It is given that the equations are:

y = –3x – 2

Simplifying it further, we get:

y + 3x = -2 (equation 1)

5x + 2y = 15 (equation 2)

Multiplying y + 3x = -2 by 2 and subtracting from 5x + 2y = 15, we get:

2y - 2y + 5x -6x = 15 + 4

-x = 19

x = -19

Plugging the value of x in the equation y + 3x = -2, we get:

y + 3 × - 19 = -2

y - 57 = -2

y = -2 + 57

y = 55

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Answer:

neither one of those are a dot plot

Step-by-step explanation:

Answer:

height of kids in class is the dot plot

Step-by-step explanation:

If A and B are independent events, it means that the occurrence of one event does not affect the probability of the occurrence of the other event. In other words, the probability of event A happening is the same whether or not event B happens and vice versa.

To illustrate this, let's consider an example. Say we have two events: flipping a coin and rolling a dice. The probability of getting heads on the coin is 1/2 and the probability of rolling a 3 on the dice is 1/6.

These events are independent because the outcome of one event does not affect the outcome of the other event. So, the probability of getting heads on the coin AND rolling a 3 on the dice is (1/2) x (1/6) = 1/12.

Another way to check if two events are independent is to use the formula P(A and B) = P(A) x P(B). If the result of this equation is true, then the events are independent. If not, they are dependent.

Overall, understanding the concept of independent events is important in probability theory because it helps us calculate the probability of multiple events happening simultaneously.

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Answer:

12/13

Step-by-step explanation:

The probability of not drawing an ace is =

1 minus the probability of drawing an ace.

there are 4 aces in a deck

hence the probability of not drawing an ace =

1 - \(\frac{4}{52}\)

= 48/52 = 12/13

The required probability of not drawing an ace would be 12/13.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

You draw a card from a standard deck of 52 playing cards.

The probability of not drawing an ace is P(E)

There are 4 aces in a deck

So the number of favorable outcomes n(E)= 4

And the total number of outcomes n(S) = 52

Thus, the probability of drawing an ace = n(E)/n(S) = 4 / 52

The probability of not drawing an ace will be:

⇒ P(E) = 1 - n(E)/n(S)

⇒ P(E) = 1 - 4 / 52

⇒ P(E) = 48/52

⇒ P(E) = 12/13

Therefore, the required probability of not drawing an ace would be 12/13.

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Answer:

CPCTC

Step-by-step explanation:

BD is perpendicular to AC, forming two right triangles. The hypotenuses are congruent, as is our leg that we will call b. If we use Law of Sines to find our angles a and c (no matter the values), we would find that because b is the same leg in both triangles and the hypotenuses are congruent, angles a and c are congruent, so therefore your missing angle in both triangles is congruent, and using a trig function will find that AD and CD are congruent, making all of both triangles congruent.

Answer:

the product of negative five times a number and the quantity four plus three times the number

Step-by-step explanation:

Answer:

The second one

Step-by-step explanation:

Answer:

417 $

b h h h h h h h h h h h h

Answer:5868<9845<91387<969156

Step-by-step explanation:

The formula for the circumference of a circle is "c = 2 pi r", where "c" represents the circumference, "pi" represents the mathematical constant pi (approximately equal to 3.14159), and "r" represents the radius of the circle.

This formula relates the distance around a circle to its size, and is useful for calculating various measurements related to circles, such as arc length and sector area. It is important to note that the formula for the circumference of a circle assumes the circle is a perfect, unbroken curve, and thus may not be accurate for circles that are not perfectly round.

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The 4 questions to answer the problem are:

The question that will be used to answer this question will be a new question as follows:

In 1997, there were 85,000 Netflix subscribers. The number of subscribers increased at a rate of 13.4% each year.

From the question above, we have the following:

Inital subscribers, a = 85 thousand

Rate of increase, r = 13.4%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 + r)ˣ

So, we have the following representation

f(x) = 85 * (1 + 13.4%)ˣ

This gives

(a) f(x) = 85 * (1.134)ˣ

(b) The graph is attached

(c) The initial value is 85

(d) The rate of change is 13.4%

Hence, the function is f(x) = 857000 * (1.134)ˣ

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There is a 45.22% chance that a randomly selected sample proportion of 100 purchases will be 0.48 or less.

To find the probability of a sample proportion of 0.48 or less if the true population proportion is 0.60, we can use the sampling distribution of the sample proportion and the z-score.

Given:

Sample size (n) = 100

Observed sample proportion ) = 0.48

True population proportion (p) = 0.60

To find the probability, we need to standardize the observed sample proportion using the z-score formula:

z = ( - p) / √(p * (1 - p) / n)

Substituting the values:

z = (0.48 - 0.60) / √(0.60 * (1 - 0.60) / 100)

= -0.12 / √(0.24 / 100)

= -0.12 / √0.0024

= -0.12 / 0.049

Using a standard normal distribution table or a statistical calculator, we can find the probability associated with the z-score.

The probability of a sample proportion of 0.48 or less, given a true population proportion of 0.60, is the probability to the left of the z-score obtained.

P ≤ 0.48) = P(z ≤ -0.12)

Using a standard normal distribution table, we find that the probability of z ≤ -0.12 is approximately 0.4522.

Therefore, the probability of a sample proportion of 0.48 or less, given a true population proportion of 0.60, is approximately 0.4522 or 45.22%.

This means that there is a 45.22% chance that a randomly selected sample proportion of 100 purchases will be 0.48 or less, if the true population proportion is 0.60.

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Answer:

yes I know the answer to your answer that is the answer. your welcome. hope this helps.

Step-by-step explanation:

24x - 19 = 16x + 13

24x = 16x + 32

8x = 32

x = 4

Answer:

14

Step-by-step explanation:

4 hits/8 games = 1 hit per 2 games =1/2

14 hits per 28 games = 14/28 =1/2

Answer:

The annual percentage yield (APY) is a measure of the return on an investment that takes into account the effect of compounding interest. To calculate the APY for an investment of $8000 at an interest rate of 4.75% compounded daily, you can use the formula:

APY = (1 + r/n)^(n*t) - 1

where r is the annual interest rate as a decimal (0.0475 in this case), n is the number of times the interest is compounded per year (365 for daily compounding), and t is the number of years (1 in this case).

Plugging these values into the formula gives:

APY = (1 + 0.0475/365)^(365*1) - 1 APY ≈ 0.0486

So, the APY for this investment is approximately 4.86%.

Step-by-step explanation:

The expression equal to (x² + 36)² is (x⁴ + 72x² + 1296).

The expression equal to (x² + 36)² is (x⁴ + 72x² + 1296). To arrive at the answer, the following steps can be followed:Step 1: Rewrite the given expression (x² + 36)² as(x² + 36) (x² + 36)

Step 2: Expand the expression by multiplying each term in the first expression by each term in the second expression(x²)(x²) + (x²)(36) + (36)(x²) + (36)(36) Simplifying the above expression gives x⁴ + 36x² + 36x² + 1296Grouping like terms gives x⁴ + 72x² + 1296

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The given parametric equations are given as:x = 3t², y = 2t³The surface generated by revolving the curve x = 3t², y = 2t³ about the y-axis can be obtained by using the formula for the surface area of revolution.Surf. area =  ∫2πy √(1+(dy/dx)²)dx, where y is a function of x and x lies between the limits of rotation.The limits of rotation of the curve are 0 and 1.Therefore, the surface area of revolution is given as:Surf. area = ∫₂π 2t³ √(1+(dy/dx)²)dxWhere, x = 3t² and y = 2t³∴ dy/dx = (dy/dt)/(dx/dt) = 6t/2t² = 3/tSurface area of revolution, Surf. area = ∫₂π 2t³ √(1+(dy/dx)²)dx= ∫₂π 2t³ √(1+(3/t)²)dx= ∫₂π 2t³ √(t²+9)/t²dx= ∫₂π 2t² √(t²+9)dt= [2/3 (t²+9)³/2]₂π = (2/3)[(1²+9)³/2 - (0²+9)³/2]×(2π)Therefore, Surf. area = (2/3)[(10³/2) - (3³/2)]×(2π)= (2/3)[(100√10 - 27√2)]×(2π)≈ 560.50 sq units.Orientation of the curve is shown in the figure below:The curve is oriented in such a way that the y-axis is towards the observer and the x-axis is perpendicular to the plane of the paper.

The ideal travel angle for manual cutting operations is a push angle of 30-45 degrees.

Explanation: When performing manual cutting operations, it is important to consider the travel angle, which refers to the direction in which the cutting tool moves in relation to the workpiece. The recommended travel angle for most cutting operations is a push angle of 30-45 degrees. This means that the cutting tool should be positioned at an angle, pushing forward against the workpiece as it cuts. This angle allows for optimal cutting efficiency and control.

A push angle within this range ensures that the cutting force is distributed evenly, minimizing the risk of tool slippage or workpiece damage. It also helps to maintain good visibility of the cutting path, reducing the chances of errors or accidents. Additionally, the push angle allows the operator to exert sufficient downward pressure on the cutting tool, aiding in effective material removal. Overall, a push angle of 30-45 degrees is considered the most effective for achieving accurate and efficient manual cutting operations.

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Answer:

about 11%

Step-by-step explanation:

70-63=7

7/63= 0.111111= 11%

Answer: 11.1...%

Your tip is 7, and you want 7/63 as a percentage, which would be 11.111111...%. The answer should be 11/1...%.

I hope this helped!

To find the equation of the tangent line to the curve y = 5ex cos(x) at the point (0, 5), we need to find the slope of the tangent line at that point.

First, we find the derivative of y with respect to x:

dy/dx = 5ex (-sin(x)) + 5ex cos(x)

Next, we evaluate the derivative at x = 0:

dy/dx |x=0 = 5e0 (-sin(0)) + 5e0 cos(0) = 5

So the slope of the tangent line at (0, 5) is 5.

Now we use the point-slope form of the equation of a line to find the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is the given point.

Plugging in the values we have:

y - 5 = 5(x - 0)

Simplifying, we get:

y = 5x + 5

So the equation of the tangent line to the curve y = 5ex cos(x) at the point (0, 5) is y = 5x + 5.

Step 1: Find the derivative of the function y.
Given function y = 5e^x cos(x), we will differentiate it with respect to x using the product rule.

Product rule: (uv)' = u'v + uv'
Let u = 5e^x and v = cos(x).

Step 2: Find u' and v'.
u' = d(5e^x)/dx = 5e^x
v' = d(cos(x))/dx = -sin(x)

Step 3: Apply the product rule.
y' = u'v + uv'
y' = (5e^x)(cos(x)) + (5e^x)(-sin(x))
y' = 5e^x(cos(x) - sin(x))

Step 4: Find the slope of the tangent line at the given point (0, 5).
Substitute x = 0 in the derived equation.
y'(0) = 5e^0(cos(0) - sin(0)) = 5(1)(1 - 0) = 5

Step 5: Use the point-slope form to find the equation of the tangent line.
Point-slope form: y - y1 = m(x - x1)
Given point: (0, 5) => x1 = 0 and y1 = 5
Slope (m) = 5

Step 6: Plug the values into the point-slope form.
y - 5 = 5(x - 0)
y - 5 = 5x

Step 7: Rewrite the equation in slope-intercept form (y = mx + b).
y = 5x + 5

The equation of the tangent line to the curve y = 5e^x cos(x) at the point (0, 5) is y = 5x + 5.

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The width (w) of the river is 148.3 feet. The distance between point A to point C on the opposite banks of the river.

Width is the measure of something from one side to  other side.

Given that,

Point A, the biologist walks upstream 100 feet and sights to point C.

From this sighting, it is determined that θ = 56°.

We have to determine the width of the river.

According to the question,

This forms a right-angled triangle with the adjacent side to the 56-degree angle and the opposite side = width of the river.

So,  tan56 = opposite side / adjacent side.

Therefore,

tan 56 = x/100

Where x = the width of the river.

x = 100 x tan56

x = 100 x 1.48

x= 148.3

Thus, the width w of the river is 148.3 feet.

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Answer:

Center: at the point (-3, 2)

Radius: 3 units

Answer: Slope intercept form

Step-by-step explanation:

m=slope

b=y-intercept

Answer:

12

Step-by-step explanation:

Each friend has 2 arms, right? So 6 friends with 2 arms would be 6 x 2. 6 x 2 = 12

each arm. well ever person had two arms. so one for each arm. so 1 x 2 x 6 would be 12. so 12 bracelet

Answer:

it rise over run so put 2y on graph count down 4 and move right 1

Step-by-step explanation:

The 44th term of the arithmetic sequence with a first term of 3510 and a common difference of -15 is 2850.

To find the term of the arithmetic sequence that corresponds to the value 2850, we can use the formula for the nth term of an arithmetic sequence:

nth term = first term + (n - 1) * common difference

In this case, the first term is 3510 and the common difference is -15. Let's substitute these values into the formula and solve for n:

2850 = 3510 + (n - 1) * (-15)

Now we can simplify the equation:

2850 = 3510 - 15n + 15

Subtract 3510 from both sides:

-660 = -15n

To solve for n, divide both sides of the equation by -15:

n = -660 / -15

Simplifying further:

n = 44

Therefore, the 44th term of the arithmetic sequence with a first term of 3510 and a common difference of -15 is 2850.

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Answer:

Is there an option of 45

Step-by-step explanation:

x-15=30

so +15

x=45