The painting shown at the right has an area of 440in^2. What is the values of x?

Total capacity the tower holds 1.034 x 10^5  gallons of water

One tower holds 8.4 x 10^3 gallons of water

Other tower holds 9.5 x 10^4 gallons of water

The combined water capacity of the two towers in scientific notation is,

Total capacity the tower holds = 9.5 x 10^4 + 8.4 x 10^3

    = 9.5 x 10^4 + 0.84 x 10^4

    = 10.34 x 10^4

    = 1.034 x 10^5

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The probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.

Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.

When events A and B are independent, the probability of them occurring together is the product of their individual probabilities.

P(A and B) = P(A) * P(B) = 0.31 * 0.76 = 0.2356

P(A|B) = P(A and B) / P(B) = 0.2356 / 0.76 = 0.31 (It is same as P(A) because events A and B are independent)

P(B|A) = P(A and B) / P(A) = 0.2356 / 0.31 = 0.76 (It is same as P(B) because events A and B are independent)

P(A or B) = P(A) + P(B) - P(A and B) = 0.31 + 0.76 - 0.2356 = 0.8144

Therefore, the probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.

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Answer:

5 cm

Step-by-step explanation:

Let the shorter side be a, longer side be b, hypotenuse be c

By Pythagorean theorem:

a² + b² = c²

a² + (a + 7)² = (a + 8)²

a² + a² + 14a + 49 = a² + 16a + 64

a² - 2a - 15 = 0

a² + 3a - 5a - 15 = 0

a(a + 3) - 5(a + 3) = 0

(a + 3)(a - 5) = 0

a = -3 or a = 5

Because a is a side length and is a positive number

a = 5

Answer:

By deciding to make the width 8 feet wide, this meant that the figure was to be a rectangule of length X feet by width 8 feet.

A = Lx W

200sq feet = X *8

X = 25 feet.

thus, the patio should be 25 feet long

Answer:

19/8

Step-by-step explanation:

8x-7=-12

8x=19

x=19/8

Answer:

8-7n=-12

Step-by-step explanation:

The average speed that would allow arriving at school on time is equal to 24.32 miles per hour if school starts in 37 minutes.

The speed that is required to arrive on time can be determined by the following formula;

s = d ÷ t

Here d represents the distance and t represents the time

As the school starts in 37 minutes and the distance is 15 miles, substituting these values in the equation;

s = (15/37) miles per minute

As 1 hour = 60 minutes; multiply by 60 to find the speed in miles per hour as follows;

s = 15/37 × 60

s = 900/37

s = 24.32 miles per hour

Therefore, the average speed that would allow arriving at school on time is calculated to be 24.32 miles per hour.

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The present worth of the tuition cost for a student planning to enroll at the university for 9 years, with the first 4 years costing $7,200 per year and a 5% annual increase for the next 5 years, can be calculated at an interest rate of 8% per year. The present worth is $23,455.297.

To calculate the present worth of the tuition cost, we need to consider the time value of money, which accounts for the fact that money in the future is worth less than money in the present. We can use the concept of present value to determine the worth of future cash flows in today's dollars.

For the first 4 years, the tuition cost is constant at $7,200 per year. To find the present value of these cash flows, we can use the formula for the present value of a fixed cash flow series. Applying this formula, we find that the present value of the first 4 years' tuition cost is

\(7,200 + 7,200/(1+0.08) + 7,200/(1+0.08)^2 + 7,200/(1+0.08)^3.\)

For the next 5 years, the tuition cost increases by 5% per year. We can use the concept of future value to calculate the value of these cash flows in the last year of the 9-year period. Applying the formula for future value, we find that the tuition cost in the last year is \($7,200*(1+0.05)^5.\)

Finally, we can sum up the present value of the first 4 years' tuition cost and the future value of the tuition cost in the last year to obtain the total present worth of the tuition cost for the 9-year period.

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The given bounded region is the set

\(R = \left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^4 \le y \le x^{1/4} \right\}\)

assuming the curves are \(y=x^4\) and \(x=y^4\implies y=x^{1/4}\) (since \(x>0\) in the first quadrant).

The coordinates of the centroid are \((\bar x, \bar y)\) where \(\bar x\) and \(\bar y\) are the average values of \(x\) and \(y\), respectively, over the region \(R\). These are given by the ratios

\(\bar x = \dfrac{\displaystyle \iint_R x \, dA}{\displaystyle \iint_R dA} \text{ and } \bar y = \dfrac{\displaystyle \iint_R y\,dA}{\displaystyle \iint_R dA}\)

Compute the area of \(R\).

\(\displaystyle \iint_R dA = \int_0^1 \int_{x^4}^{x^{1/4}} dy \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \frac45 - \frac15 = \frac35\)

Integrate \(x\) and \(y\) over \(R\).

\(\displaystyle \iint_R x \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} x \, dy \, dx \\\\ ~~~~~~~~ = \int_0^1 x \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{5/4} - x^5\right) \, dx \\\\ ~~~~~~~~ = \frac49 - \frac16 = \frac5{18}\)

\(\displaystyle \iint_R y \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} y \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left((x^{1/4})^2 - (x^4)^2\right) \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left(x^{1/2} - x^8\right) \, dx \\\\ ~~~~~~~~ = \frac12 \left(\frac23 - \frac19\right) = \frac5{18}\)

Then the centroid's coordinates are

\(\bar x = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}} \approx 0.463\)

\(\bar y = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}}\)

Answer:

0.8

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."

It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.

One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.

Complete and correct Question:

Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.

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Answer:

It should be 3 to 8

Step-by-step explanation:

Answer:

3:8

Step-by-step explanation:

because there are 3 cups of drink mix and 8 cups of water

Answer:

You will get 13$ and 50 Cents

Answer: $56

Step-by-step explanation:

Let the original price of the jacket be x.

Since Kevin went to a store that offers a 20% discount and bought a jacket and saved $11.20 after using the coupon.

The original price of the jacket goes thus:

20% × x = $11.20

0.2 × x = 11.20

0.2x = 11.20

x = 11.20 / 0.2

x = 56

The original price of the jacket will then be $56

The surface area will decrease at the rate of 50.2 when the height is 10 feet and the radius is 8 feet.

First, let's understand what is right circular cylinder.

A right circular cylinder has parts that are perpendicular to its base and a closed circular surface with two parallel bases on both ends. Another name for it is a right cylinder.

What is the formula for the surface area of right circular cylinder?\(A=2\pi rh+2\pi r^2\).

Also we don't need to remember this we can get this we have 2 parallel bases that is circular so the area of circular part is 2*pi* r^2. For the Perpendicular part if we cut the cylinder then it will make a rectangle.

Volume is always constant whatever we change in radius and height.

dA/dt  =  2*pi *(r*dh/dt+h*dr/dt) + 4*pi*r

Given is that dh/dt = 2

dr/dt = -4

we have to change the surface area when r = 8 feet.

h= 10 feet.

dA/dt = 2* pi* (8*2 + 10*(-4)) + 4*pi*8

        = 2* pi*(16-40) + 32* pi

       = -48*pi+ 32*pi

       = -16*pi

       = -50.2

The surface area will decrease at the rate of 50.2.

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Answer:

$ 7800

Step-by-step explanation:

P'(t) = 3t² + 10t + 6

\(P(t) = \int\limits^a_b {P'(t)} \, dt\)

For the 4th year, the limits are [3,4]

\(P(t) = \int\limits^4_3 {3t^2 + 10t + 6} \, dt\\\\= [\frac{3t^3}{3} + \frac{10t^2}{2} + 6t]^{^4}__{3}\\\\\)

\(=[\frac{3(4)^3}{3} + \frac{10(4)^2}{2} + 6(4)]-[\frac{3(3)^3}{3} + \frac{10(3)^2}{2} + 6(3)]\\\\=[\frac{3(64)}{3} + \frac{10(16)}{2} + 24]-[\frac{3(27)}{3} + \frac{10(9)}{2} + 18]\\\\= [64 + 5(16) + 24]-[27+5(9) + 18]\\\\= 168-90\\\\= 78\)

= $ 7800

Answer:

n = -15         and          m = -3

Step-by-step explanation:

To solve the given system of equation, we will follow the steps below:

n = 5m ----------------------------------------------------------------------------(1)

n = \(\frac{2}{3} m -13\) ---------------------------------------------------------------------(2)

substitute for n= 5m in equation (2)

5m =  \(\frac{2}{3} m -13\)

subtract \(\frac{2}{3} m\) from both-side of the equation

5m -  \(\frac{2}{3} m\)  = \(\frac{2}{3} m\) -  \(\frac{2}{3} m -13\)

At the right-hand side of the equation  \(\frac{2}{3} m\)  will cancel-out leaving us with just -13

5m -  \(\frac{2}{3} m\)  = -13

\(\frac{15m - 2m }{3}\) = -13

\(\frac{13m}{3}\) = -13

multiply both-side of the equation by 3

3 ×  \(\frac{13m}{3}\) = -13 ×  3

At the left-hand side of the equation 3 will cancel-out 3 leaving is with just 13m

13m = -39

Divide both-side of the equation by 13

13m/13  = -39/13

m = -3

substitute m = -3 in  equation (1)

n = 5m

n = 5 (-3)

n = -15

Therefore, n = -15         and          m = -3

The leading coefficient determines the shape of the graphs, such as how

the characteristic of a function are directed.

Correct response:

The graphs that represents functions that have a negative leading

coefficient are;

Graph A:

The function in graph A is x³

When the coefficient of x³ is negative, the value of the function rises as x decreases from 0 to -∞, and decreases as x increases from 0 to ∞

Therefore;

Graph B:

The value of the graph decreases as the magnitude of x increases

therefore, the graph is similar to a quadratic function, such that the leading

coefficient is negative, which inverts the function to give increasing output

with negative value as the value of x increases.

Therefore;

Graph C:

The given function in graph C is a linear function having a negative slope,

therefore;

Graph D:

The function of the graph in Graph D, that have y values that increases

exponentially as x increases is a quadratic function.

Given that y increases as the value of x increases, the leading coefficient

(coefficient of x²) is positive.

Therefore;

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The processes used to determine if a function is a state or path function include integration/differentiation and examining the differential form of the function. Integrating a function with respect to a variable yields a state function, while differentiating a function with respect to a variable yields a path function.

If the differential form of a function involves only state variables, it is a state function. If it involves both state and path variables, it is a path function.

To determine whether a function is a state or path function, we can examine the properties of the function and the variables involved. A state function depends only on the current state of the system and is independent of the path taken to reach that state. In contrast, a path function depends on the path taken to reach a particular state.

One common process used to determine the nature of a function is integration or differentiation. Integrating a function with respect to a variable yields a state function, whereas differentiating a function with respect to a variable yields a path function. For example, integrating the pressure (P) with respect to volume (V) yields a state function called the internal energy (U). On the other hand, differentiating the work (W) with respect to volume (V) yields a path function known as pressure (P).

Another process used is the examination of the differential form of the function. If the differential form of a function involves only state variables, then the function is a state function. For instance, the differential form of the enthalpy (H) involves only state variables (dH = dU + PdV), making it a state function. However, if the differential form involves both state and path variables, the function is a path function. An example is the differential form of heat (Q), which involves both state and path variables (dQ = dU + PdV), indicating that it is a path function.

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Answer:

C

Step-by-step explanation:

\(\frac{35}{100}*1800\\35*18\\\)

630

The portion of protein will be 630.

The “pie chart” is also known as a “circle chart”, dividing the circular statistical graphic into sectors or sections to illustrate the numerical problems.

Given that a pie chart showing the distribution of the calories of 1800 in different nutrients, we need to find the portion of protein,

Here the portion of protein = 35%

So,

35 / 100 × 1800 = 630

Hence the portion of protein will be 630.

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Answer:

y= -x to the power of 2

so the answer is the first one!

Hope this helps!!

For a given set of side lengths to create a triangle, the sum of any two sides must be greater than the length of the third side.

4 in, 7 in, 12 in = Not Possible

4 + 7 = 11 > 12 = False

4 + 12 = 16 > 7 = True

7 + 12 = 19 > 4 = True

6 mm, 6 mm, 10 mm = Possible

6 + 6 = 12 > 10 = True

6 + 10 = 16 > 6 = True

5 ft, 8 ft, 12 ft = Possible

5 + 8 = 13 > 12 = True

5 + 12 = 17 > 8 = True

8 + 12 = 20 > 5 = True

7 cm, 9 cm, 16 cm = Not Possible

7 + 9 = 16 > 16 = False

7 + 16 = 23 > 9 = True

9 + 16 = 25 > 7 = True

Hope this helps!

Answer:

Step-by-step explanation:

The length of XN is 6

Calculation

By angle bisector theorem

\(\frac{AX}{NX} =\frac{AY}{NY}\)

\(\frac{18}{NX} =\frac{12}{4}\)

\(NX=\frac{18*4}{12} =6\)

Therefore, the length of side NX in the given triangle is 6.

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The length of side NX in the given triangle is 6.

By angle bisector theorem

According to the angle bisector theorem, PQ/PR = QS/RS or a/b = x/y. An angle bisector is a line or ray that divides an angle in a triangle into two equal measures

Therefore, the length of side NX in the given triangle is 6.

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Answer:

No

Step-by-step explanation:

Total cups of the mixture = 40 c water + 70 c milk = 110 c

40/110 x 100 = 36.4% water

She is not correct.

Answer:

4.73

Step-by-step explanation:

10% is 10

so, you have to multiple 3×.10=.30

3-.30=2.70

2.70×.75 because 7.5% is .75

that is 2.0250 and then you have to add 2.0250 with 2.70 that is 4.7250 and if you round it. It is 4.73

Hope that works