\( \frac{9}{27} \)

\( \frac{2}{6} \)

\( \frac{5}{18} \)

\( \frac{15}{45} \)


(one of those fraction is not equivalent to
\( \frac{1}{3} \) )

​

Answer:

Step-by-step explanation:

x-intercept (x,0) , y intercept (0,y)

10: -3x-4y=12

x=0 , -3(0)-4y=12

-4y=12 , ⇒ y=12/-4 ⇒ y=-3

y=0 : -3x-4(0)=12

-3x=12 ⇒ x=12/-3 ⇒ x=-4

-9x+4y=-36

x=0 , 4y=-36 , y=-36/4 , y=-9  

y=0 , -9x=-36 , x=-36/-9 , x=4

5x-3y=-15

x=0 , -3y=-15 , y=-15/-3 , y=5

y=0 , 5x=-15 , x=-15/5 , x=-3

Answer:

O \(\sf y = 20000(1 - 08) ^5\)

O $13181.63

explanation:

\(\sf compound \ interest = P(1 + \dfrac{r}{100})^{n}\)

insert the following given values

\(\sf \hookrightarrow 20000(1 - \frac{8}{100} )^5\)

\(\sf \hookrightarrow 20000(1 - 0.08)^5\)

\(\sf \hookrightarrow 13181.63\)

Answer:

A.21

Step-by-step explanation:

We can use trigonometry to slove for sides in this triangle...

Using the 60 degree angle...we can solve for x.

We are dealing with adjacent and opposite sides, so we use the tangent function in the calculator.

And since we're using tangent, we have to use opposite/adjacent

We have tan60=x/7sqrt3-multiply the adjacent side(7qrt3) to the other side,

and we have 7sqrt3tan60=x--enter this in to you're calculator, and you should

get an answer of 21

1. After 32 minutes the two pools will have the same amount of water.
2. 2,280 liters of water will be in each pool when they have the same amount.

Let's call the time in minutes when the two pools have the same amount of water "t". Getting into variables here.

At time t, the first pool will have 1272 + 31.5t liters of water, and the second pool will have 1600 + 21.25t liters of water.

For the two pools to have the same amount of water, we need:

1272 + 31.5t = 1600 + 21.25t

10.25t = 328

t = 32 minutes

I underlined all the answers if you don't want to read the entire thing, lol.

Question 1: So, 32 minutes after starting, the two pools will have the same amount of water.
Question 2: The amount of water in each pool will be:

1272 + 31.5 * 32 = 1600 + 21.25 * 32 = 1600 + 680 = 2,280 liters.

If a > 3, then a, a + 2, and a + 4 cannot all be primes, and they can't all be powers of primes either.


1. Let's first analyze the numbers a, a + 2, and a + 4. Notice that at least one of these numbers must be divisible by 3 since they are consecutive even numbers.
2. If a is divisible by 3, then it cannot be prime as a > 3.
3. If a is not divisible by 3, then either a + 2 or a + 4 must be divisible by 3.
4. Since a + 2 and a + 4 are consecutive even numbers, one of them is divisible by 2, and thus, not prime.
5. Now, let's consider the possibility of them being powers of primes.
6. If a is a power of a prime, then it must be divisible by the prime it's raised to. Since a > 3, it cannot be a power of 3 or a power of 2, as it would then be divisible by 2 or 3.
7. If a + 2 or a + 4 are powers of primes, they must also be divisible by their respective prime bases, which contradicts the fact that they are consecutive even numbers and not prime themselves.

Therefore, if a > 3, it is impossible for a, a + 2, and a + 4 to all be primes or powers of primes.

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Answer:

\( \frac{1}{5} \)

Step-by-step explanation:

\( \frac{2}{5} = y \: \\ x \ = 2 \\ \frac{ \frac{2}{5} }{2} = \frac{2}{2} \: \\ \frac{1}{5} = y \: when \: \: 1= x\)

Answer:

the third option

Step-by-step explanation:

when X is negative f(x) is positive. and when f(x) is negative x is positive

Answer:

88 won and 66 lost

Step-by-step explanation:

Won = \(\frac{154}{4+3}\)×4 = 88 games

Lost = 154 - 88 = 66 games

It is true that the existence of two local maxima does not guarantee the presence of a local minimum. It is possible for a function to have multiple local maxima and no local minimum.

For example, consider the function f(x,y) = x^4 - 4x^2 + y^2. This function has two local maxima at (2,0) and (-2,0), but no local minimum. Therefore, the statement "if f(x,y) has two local maximal, then f must have a local minimum" is false. The presence or absence of local maxima and minima depends on the behavior of the function in the immediate vicinity of a point, and cannot be determined solely based on the number of local maxima. It is possible for a function to have an infinite number of local maxima and minima, or none at all. Therefore, it is important to carefully analyze the behavior of a function in order to determine the presence or absence of local extrema.

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Given the cost and demand functions:

we can find the revenue with the following expression:

then, the profit can be calculated with the difference between the revenue and C(x):

to find the max profit, we can find the derivative of P(x) and find its root to get the value of x that maximizes the function P(x):

therefore, the production level that results in the maximum profit is x = 1350.

Finally, to find the price, we can evaluate x = 1350 on p(x):

therefore, the price that the company should charge for each drill to maximize profit is $115

The value of 5 - 4x is 7/3, which is equivalent to option (d) d. 17

If 7x³ = 24, we can solve for x by taking the cube root of both sides:

\((7x^3)^{1/3} = (24)^{1/3} \\x = (24)^{1/3} \div7^{1/3}\)

To find the value of 5 - 4x, we can substitute the expression for x into the second equation:

5 - 4x = \(5 - 4(24)^{1/3} \div 7^{1/3\)

Simplifying, we get

5 - 4x = 5 - 4(2/3)

5 - 4x = 5 - (8/3)

5 - 4x = (15/3) - (8/3)

5 - 4x = 7/3

So the value of 5 - 4x is 7/3, which is equivalent to option (d) d. 17

The cube root of a number is a value that when multiplied by itself twice, produces the original number.

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The formula that will help eli determine how much money he will earn in one week is a = 9h + nb

Let

a = (9 × h) + (n × b)

a = 9h + nb

Complete question:

Eli works in an electronics repair shop. he earns 9 dollars an hour plus a bonus for each item her repairs.

write a formula that will help eli determine how much money he will earn in one week

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The Weighted Average Cost of Capital (WACC) for Snuggly Baby Corp. is calculated based on the company's capital structure, including common equity, preferred equity, and bonds. The WACC is influenced by the expected returns and prices of these securities.

To calculate the WACC, we need to determine the proportion of each component in the capital structure and multiply it by its respective cost of capital.

For Snuggly Baby Corp., the capital structure consists of 6,130,000 shares of common equity, 1,006,000 shares of preferred equity, and 81,400 bonds.

The cost of common equity is calculated using the expected return and the price of the shares. Similarly, the cost of preferred equity is calculated using the expected return and the price of the preferred shares. The cost of debt, represented by the bonds, is calculated using the yield-to-maturity.

Once we have the costs of each component, we multiply them by their respective proportions in the capital structure and sum them up to determine the overall WACC. Please note that to provide an accurate calculation of the WACC, additional information is required, such as the market value of each component and the weights assigned to them in the capital structure. Without this information, it is not possible to provide an exact WACC calculation.

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Answer:

$15

Step-by-step explanation:

For every $13 he earns he saves $5

so 13×3 is 39 and then multiply 5 times 3 and you get 15

your answer is $15

According to the histogram, about 6% of the students did more than 40 push-ups in a minute during the APE class of 35 students.

The given histogram shows the number of push-ups done by the 35 students in the APE class. The horizontal axis represents the number of push-ups, while the vertical axis represents the number of students. According to the histogram, the majority of the students did between 20 to 30 push-ups, with only a few doing more than 40 push-ups. Specifically, about 6% of the students did more than 40 push-ups in a minute. This means that the students who did more than 40 push-ups are in the top 6% of the class in terms of performance.

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Answer:

hj cfffdsybb dth. anf. then just coerdubj a

Step-by-step explanation:

yyoaoanba. buinbd. onvtshsjfsushvsvswyyw

Answer:

(-3, -8)

Step-by-step explanation:

When we rotate a point 180 degrees around the origin, its ordered pair changes from (x, y) to (-x, -y). So all we have to do to figure out the point's coordinates after being rotated 180 degrees is to make both the x- and y-coordinates negative.

That gives us (-(3), -(8)) or (-3, -8). Hopefully that makes sense! :)

Answer:

80kg

Step-by-step explanation:

Given:

W = 80 + 5.4t

Where,

W = the wrestler's weight (in kilograms

t = number of months

What was the wrestler's weight before his special diet?

W = 80 + 5.4t

When t = 0 (that is before the weight gain)

W = 80 + 5.4t

= 80 + 5.4(0)

= 80kg

When t = 1 ( first month of the weight gain)

W = 80 + 5.4t

= 80 + 5.4(1)

= 80 + 5.4

= 85.4 kg

The wrestler's weight before his special diet is 80kg

ALTERNATIVELY

W = 80 + 5.4t

80 = the fixed weight

5.4 = weight gained per month

t = number of months

Therefore,

The fixed weight which is 80kg is the weight of the wrestler before the special diet.

Answer:

10.8

Step-by-step explanation:

This is correct on khan academy.

The number 3 107/125 is greater than  3.151.

A number that is stated as bοth a whοle number and a fractiοn, such 3 1/2, is referred tο as a mixed number. A fractiοn, such as 7/2, that has the numeratοr higher than οr equal tο the denοminatοr is referred tο as an imprοper fractiοn. Yοu must multiply the whοle number by the denοminatοr, add the numeratοr, and then place it οver the οriginal   denοminatοr in οrder tο cοnvert a  mixed number tο an imprοper fractiοn.

Divide the numeratοr by the denοminatοr and then write the residue as a fractiοn with the same denοminatοr tο turn an imprοper fractiοn intο a mixed number.

The given numbers are: 3.515 οr 3 107/125.

Cοnvert 3 107/125 tο a decimal.

3 107/125 = (3 * 125 + 107)/125 = 482/125 = 3.856

Cοmparing the twο 3.515 and 3.856 we οbserve that 3.856 is greater than 3.515.

Hence, the number 3 107/125 is greater than 3.151.

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The maximum amount of water that the pool can hold is 1000 cubic feet.

To find the maximum amount of water that the rectangular prism swimming pool can hold, we need to calculate its volume.

The volume of a rectangular prism is given by:

V = l x w x h

where l is the length, w is the width, and h is the height of the prism.

Given the dimensions of the swimming pool, we have:

l = 16 feet

w = 12.5 feet

h = 5 feet

Therefore, the volume of the swimming pool is:

V = l x w x h

V = 16 feet x 12.5 feet x 5 feet

V = 1000 cubic feet

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Answer:

C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I had that same answer. I did it with my teacher and he said it was b

Answer:

The equation of the parabola is (x-2)^2 = 48(y-5)

Step-by-step explanation:

Mathematically, we can obtain the equation of a parabola from its focal point and the directrix given.

Firstly, we need to find the distance between the director and the vertex

That would be ;

|-7-(5)| = 12

We should kindly note that the directrix is below the vertex and thus it is a right-side parabola with a positive value of p = 12

Thus, the equation needed would be;

(x-h)^2 = 4p(y-k)

From the question, h = 2

p = 12 ( calculated) and k = 5

So the equation would be;

(x-2)^2 = 4(12)(y-5)

= (x-2)^2 = 48(y-5)

Answer:

A

Step-by-step explanation:

Answer:

It is Choice C 71%.

I got this on the unit test

Step-by-step explanation:

Answer:

69-43= 26

therefore "U" is worth 26 U=26

Step-by-step explanation:

Answer:

its 26, because whaen u subtract 43 from 69 u will get 26

Step-by-step explanation:

We are given 4x+y=6x-1 to graph. The easiest way to graph is to turn this equation into slope-intercept form, which is y=mx+b.

First, we are going to subtract 4x from both sides to isolate the y variable which gets us y=2x-1, and now we have slope-intercept form. Now we're going to use what we know about the form to graph.

In such form, m is the slope and b is the y-intercept. Our b in our equation is -1, so you're going to put a dot at (0,-1) on the y-axis. Then for our slope, it is 2, but it's easier to envision as rise over run where 2 is how much we rise and 1 is how much we run (or move to the right). So from our starting point from the y-axis, we're going to move up 2 units and then to the right one unit. And with two dots on the graph, we can run a line through it which will give us our graphed line.

For safe measures, you can continue the pattern of rising 2 and running 1, or you can go down 2 and left 1, which is the opposite and yet still confines to the line.

If you don't understand this explanation, I also recommend checking out desmos! It's a graphing calculator online in which you can plug this equation in and it graphs it for you! The file I have attached to this is from desmos to help you see the graph, I hope you do well!

To solve this problem we will have to convert 4x + y = 6x - 1 to point - slope form, for simplicity --- ( 1 )

4x + y = 6x - 1,

- 2x + y = - 1,

Point - Slope Form : y = 2x - 1

Now let's graph this equation. Consider the x - intercept and y - intercept of this graph --- ( 2 )

0 = 2x - 1

2x = 1

x = 1 / 2 = 0.5 ( x - intercept ),

y = 2(0) - 1 = 0 - 1 = - 1 ( y - intercept )

We know that the x - intercept is 0.5, so we can plot the point (0, 0.5). Similarly we can plot the point ( - 1,0 ) given the y - intercept is - 1. After plotting these points we can run a line through them, creating our graph.

The rate of change of the angle of elevation is -2π/3 radians/second.

We can use the tangent ratio to solve this problem. Since the rope is attached to the boat, we can draw a right triangle with the rope as the hypotenuse. The angle of elevation is the angle formed by the rope and the horizon.

The pulley is 5 feet above the water level, so the length of the opposite side (the side adjacent to the angle) is 5 feet. The length of the hypotenuse is 12 feet, since the boat is 12 feet from the dock.

Using the tangent ratio, we can calculate the angle of elevation:

tan(θ) = opp/hyp = 5/12

θ = arctan(5/12) = 0.927 rad

Now, since the rope is being pulled in at 3 ft/sec, the length of the hypotenuse is decreasing at a rate of 3 ft/sec. Therefore, the rate of change of the angle of elevation is:

rate of change of θ = -(3 ft/sec) / (12 ft) = -2π/3 radians/second

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Any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

Within 2 standard deviations of the mean refers to the range that includes data points within two units of standard deviation from the mean. In this case, the mean is 180 and the standard deviation is 35.

To find the range within 2 standard deviations of the mean, we need to calculate the upper and lower bounds.

The upper bound can be found by adding 2 standard deviations (2 * 35 = 70) to the mean: 180 + 70 = 250.

The lower bound can be found by subtracting 2 standard deviations (2 * 35 = 70) from the mean: 180 - 70 = 110.

Therefore, any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

It's important to note that this answer is specific to the given mean and standard deviation. If the mean and standard deviation were different, the range within 2 standard deviations would also be different.

Always calculate the upper and lower bounds based on the provided mean and standard deviation to determine the range within 2 standard deviations accurately.

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For the mutual fund investment, the chosen options are a starting amount of $900 and a rate of annual return of 7%.
To calculate Khalid's weekly profits based on the number of weeks, a function is determined using the given data. The graph of Khalid's profits is plotted alongside Harper's profits.
The solution to the system of equations is found by determining the point where Harper's and Khalid's profit functions intersect. This represents the week when their profits are equal.
The average rate of change of Khalid's profits from week 3 to week 6 is calculated, representing the rate at which his profits are changing over that period.

The chosen options for the mutual fund investment are a starting amount of $900 and a rate of annual return of 7%. To calculate the future value of the investment after 30 years, we can use the compound interest formula: FV = PV * (1 + r)^n. Plugging in the values, we get FV = 900 * (1 + 0.07)^30 = $6,084.38.
To calculate Khalid's weekly profits based on the number of weeks, we can observe the given table and identify the pattern. The function for Khalid's profits can be determined by fitting a curve to the given data points. Plotting Khalid's profits on the same graph as Harper's profits allows for a visual comparison.
The solution to the equation h(x) = k(x) represents the point where Harper's and Khalid's profit functions intersect. It indicates the week when.
their profits are equal. By finding the x-coordinate of this point, the specific week can be determined.
The average rate of change of Khalid's profits from week 3 to week 6 can be calculated by finding the slope of the line passing through those two points. It represents the average rate at which Khalid's profits are changing over that specific period, indicating the growth or decline in his business during that time.

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Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

To calculate the future value of a three-year uneven cash flow given below, using an 11% discount rate, we need to use the formula;

Future value of uneven cash flow = cash flow at year 1/(1+discount rate)¹ + cash flow at year 2/(1+discount rate)² + cash flow at year 3/(1+discount rate)³ + cash flow at year 4/(1+discount rate)⁴

Given the cash flows;

Year 0: $0

Year 1: $600

Year 2: $500

Year 3: $400

Then the Future value of uneven cash flow

= $600/(1+0.11)¹ + $500/(1+0.11)² + $400/(1+0.11)³

= $600/1.11 + $500/1.23 + $400/1.36

=$540.54 + $405.28 + $293.00

=$1,238.82

Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

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