A cylindrical swimming pool has a diameter of 12 feet and a height of 4 feet. How many gallons of water can the pool contain? Round your answer to the nearest whole number. (1 ft3 ≈ 7. 5 gal)

Answer:

x = 9

Step-by-step explanation:

\(2x + 3 = 3x - 6\)

\(3 = x - 6\)

\(x = 9\)

Let p be the proportion of defectives in the shipment. Since p = 0.10 and we have a sample of n = 10 components drawn from the shipment, then from the binomial distribution we get:

Let p be the proportion of defectives in the shipment.

Thus, the probability that the distributor will return the shipment if the proportion of defectives in the batch is in fact 10% is 0.2639.

Summary:In summary, we are given that the proportion of defectives in the shipment is 10% and we are asked to find the probability that the distributor will return the shipment if 10 components are sampled and more than 1 of the 10 is defective. We can calculate this probability using the binomial distribution, which yields a probability of 0.2639.

Learn more about probability click here:

https://brainly.com/question/13604758

#SPJ11

Answer:

25 black and 11 white

Step-by-step explanation:

lets say black marbles are x and white marbles are y

x+y=36

y+14=x

So: y+14+y=36

2y=22

y=11

Hence, x=25

Hope that helps!

Answer:

addition

Step-by-step explanation:

as x=23+5

x=28.

I think so this is the ans.

Answer:

\(14 tan\theta = -48\)

Step-by-step explanation:

\(cos \theta = \frac{-7}{25}\\\\cos^2 \theta = \frac{49}{625}\\\\sin^2 \theta = 1 - cos^2 \theta\\\\\)

        \(=1 - \frac{49}{625}\\\\=\frac{625-49}{625}\\\\=\frac{576}{625}\\\\\)

\(sin \theta = \sqrt{\frac{576}{625}} = \frac{24}{25}\)

\(tan \theta = \frac{sin \theta}{cos \theta}\)

          \(=\frac{\frac{24}{25}}{\frac{-7}{25}}\\\\=\frac{24}{25} \times \frac{25}{-7}\\\\=\frac{-24}{7}\)

\(14 tan \theta = 14 \times \frac{-24}{7} = 2 \times -24 = -48\)

Answer:

19/3 (6 1/3)

Step-by-step explanation:

To write an exponential function in the form y = ab^x that passes through the points (0, 9) and (10, 9216), we need to find the values of a and b.

The exponential function that satisfies the given conditions is y = 9 * (2^(x/5)).

Let's start by substituting the coordinates of the first point (0, 9) into the equation y = ab^x:

9 = ab^0

Since any number raised to the power of 0 is 1, we have:

9 = a * 1

This simplifies to:

a = 9

Now, substitute the coordinates of the second point (10, 9216) into the equation:

9216 = 9 * b^10

To solve for b, we can take the 10th root of both sides of the equation:

b^10 = 9216/9

b^10 = 1024

Taking the 10th root, we have:

b = 2

Now we have the values of a and b, so the exponential function that goes through the given points is:

y = 9 * (2^(x/5))

Learn more about exponential here: brainly.com/question/29160729

#SPJ11

Martha's claim that the 25% of the learners are girls, is correct.

In this question,

There are 900 boys and 300 girls at Eqinisweni secondary school.

Martha claims that 25% of the learners are girls.

We need to verify her claim by means of calculations.

Based on the given conditions, we formulate:

300 / (900 + 300)

We simplify above expression.

= 300 / 1200

= 1/4               ..................(Cross out the common factor)

Now multiply a number 25 to both the numerator and the denominator:

= (1 × 25)/(4 × 25)

= 25/200

Now we rewrite a fraction with denominator equals 100 to a percentage: 25%

This means, Martha's claim that the 25% of the learners are girls, is correct.

Learn more about the fraction here:

https://brainly.com/question/8969674

#SPJ4

Answer:

the midpoint of the point A and B is P( 5,-3)

Step-by-step explanation:

A(8,-7)= ( x1,y1)

B(2,1)= (x2,y2)

P(x,y)= ?

now,

P( x,y) = ( x1+x2/2 , y1+y2/2)

= ( 8+2/2 ,-7+1/2)

=( 10/2 ,-6/2)

=(5 ,-3)

x = 1 , y = -3 , z = -6

Step-by-step explanation:

Solution file attached

im pretty sure its 8.94

One polygon has 6 sides and the other has 7 sides.

Polygons are closed 2D shapes made up of straight lines. Regular polygons have sides of equal length and angles of equal measure. In this problem, we are given information about two regular polygons.

We are told that the total number of sides in both polygons is 13. Let's call the number of sides in one polygon "n" and the number of sides in the other polygon "m". Then, we know that:

n + m = 13

Next, we are given the total number of diagonals in both polygons, which we can calculate using the formula:

d = (n(n-3) + m(m-3))/2

where "d" is the total number of diagonals. We are told that d = 25. Substituting this value and the equation for n + m into the diagonal formula, we get:

25 = (n(n-3) + m(m-3))/2

25 = (n² - 3n + m² - 3m)/2

50 = n² - 3n + m² - 3m

We can use the equation n + m = 13 to solve for one variable in terms of the other. For example, we can solve for "m" by subtracting "n" from both sides:

m = 13 - n

Substituting this into the previous equation, we get:

50 = n² - 3n + (13-n)² - 3(13-n)

50 = n² - 3n + 169 - 26n + n² - 36 + 3n

Simplifying this equation, we get:

2n² - 26n + 45 = 0

We can use the quadratic formula to solve for "n":

n = (26 ± √376)/4

n ≈ 5.61 or n ≈ 8.39

Since we are dealing with whole numbers of sides, "n" must be either 6 or 8. Plugging each value into the equation n + m = 13, we find that the other polygon must have the opposite value.

To know more about polygon here

https://brainly.com/question/24464711

#SPJ4

Answer:

The signs of each monomial in the second polynomial are changed.

When subtracting two polynomials, the subtraction affects each monomial in the second polynomial by inverting the sign of each coefficient. That is, every coefficient in the second polynomial is multiplied by -1.

Polynomials are mathematical expressions that contain one or more terms. These terms are made up of coefficients and variables raised to powers, like x^2, y, or z^3.

When subtracting two polynomials, we need to keep in mind that each term within the polynomial is affected.

Example: Consider the following polynomial:

2x^2 + 3xy + 4y^2

When we subtract the polynomial 3x^2 - 2xy - 5y^2 from the above polynomial, we need to invert the sign of each coefficient in the second polynomial. That is, we have:

2x^2 + 3xy + 4y^2 - (3x^2 - 2xy - 5y^2)

Now, inverting the sign of each coefficient in the second polynomial, we get:

-3x^2 + 2xy + 5y^2

So the final result is:

2x^2 + 3xy + 4y^2 - (3x^2 - 2xy - 5y^2)

= 2x^2 + 3xy + 4y^2 - 3x^2 + 2xy + 5y^2

= -x^2 + 5xy + 9y^2

To know more about the "polynomial":https://brainly.com/question/4142886

#SPJ11

The coordinates of B when it is given that A(5,-2) and M(12,6) is (29, 14).

If M is the mid-point of line segment AB, and the coordinates of A = (5,-2) while the coordinates of B = (12,6), then the coordinates of M = (8.5,2), which is what you stated that you got.

You are provided with M = (12,6) so you need to identify the coordinates of B. So, just ask yourself how did I get from A to M ? The answer is move 7 right and 8 up since 5 + 7 = 12 while -2 + 8 = 6. All you have to do is add 7 more to the x-value and 8 more to the y-value to obtain the correct answer of (19,14).

Learn more about coordinate on;

https://brainly.com/question/17206319

#SPJ1

Find the coordinates of B when it is given that A(5,-2) and M(12,6),

The probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.9476

To determine the probability

The given parameters are:

True proportion and the mean (p) = 0.06

The samples size (n) = 235

Start by calculating the standard deviation using

\(\sigma = \sqrt{\frac{p(1-p)}{n} }\)

This gives

\(\sigma = \sqrt{\frac{0.06\;*\;(1-0.06)}{235} }\)

\(\sigma = \sqrt{\frac{0.06\;*\;(0.94)}{235} }\)

\(\sigma = \sqrt{\frac{0.0564}{235} }\)

\(\sigma = \sqrt{0.00024 }\)

\(\sigma = 0.01549\)

Next, we calculate the x values

\(x = x_{1} \pm x_{2}\)

where x₁ = 0.06 and x₂ = 0.03

x = x₁ + x₂ , x₁ - x₂

x = 0.06 + 0.03, 0.06 - 0.03

x = 0.09, 0.03

Calculate the z score for both x values

\(z = \frac{x\; - \; \mu}{\sigma}\)

\(z = \frac{0.09\; - \; 0.06}{0.01549}, \frac{0.03\; - \; 0.06}{0.01549}\)

\(z = \frac{0.03}{0.01549}, \frac{-0.03}{0.01549}\)

\(z = 1.94, -1.94\)

The p values at the z scores are:

p = 0.9738, 0.0262

Note: refer to z tables to find the p values

Calculate the difference

p = 0.9738 - 0.0262

p = 0.9476

Hence, the probability that the sample proportion will differ from the population proportion by less than 0.03 is 0.9476

Visit the link below to learn more about probabilities:

brainly.com/question/25870256

#SPJ4

The statement, if function, (x,y) = f(x) ·f(y) for all (x,y) such that f(x,y) > 0, then x ⊥⊥y is true.

By definition, two random variables x and y are said to be independent (denoted as x ⊥⊥ y) if the joint probability distribution function f(x, y) can be expressed as the product of the marginal probability distribution functions f(x) and f(y) for all values of x and y.

In this case, if we have f(x, y) = f(x) · f(y) for all (x, y) such that f(x, y) > 0, it implies that the joint probability distribution function can be factorized into the product of the marginal probability distribution functions. Therefore, x and y are independent, and we can conclude that x ⊥⊥ y.

To learn more about random variable: https://brainly.com/question/17217746

#SPJ11

Part A) Your profit in this market for beans will depend on the market equilibrium price and your production costs. The specific profit amount cannot be determined without knowing the market price and your production costs.

Part B) To earn positive profits under price competition, you need to have production costs lower than the market price. By reducing your production costs through various strategies, you can increase your chances of earning positive profits in the duopoly market for beans.

Let us discuss in a detailed way:

Part A) Your profit in this market for beans will depend on the market equilibrium price and your production costs. As a duopoly, you and the other farmer will compete on price, aiming to maximize your individual profits.

In a competitive market, price tends to be driven down to the marginal cost of production. If both you and the other farmer have identical production costs, and the market is perfectly competitive, the price of the beans will likely settle at the marginal cost of production. In this case, since you share the land equally, your 50% share of the 20 square mile plot would be 10 square miles.

To determine your profit, you need to consider your production costs and the price at which you can sell your beans. If the market price equals your production cost, your profit would be zero. If the market price is higher than your production cost, you will earn positive profits, and if it is lower, you will incur losses.

Part B) In order to earn positive profits under price competition, a firm must have a production cost that is lower than the market price. Applying this to the situation above, you can earn positive profits by growing these beans on your land if your production cost is lower than the market price.

To achieve this, you could focus on reducing your production costs through various means such as improving farming techniques, using more efficient equipment, or negotiating better deals for inputs like fertilizers and pesticides. By lowering your production costs, you can maintain a competitive advantage and potentially earn positive profits even if the market price is relatively low.

In summary, your profit in this market for beans will depend on the market equilibrium price and your production costs. To earn positive profits, you need to ensure that your production costs are lower than the market price. By focusing on cost reduction strategies, you can increase your chances of earning positive profits in the duopoly market for beans.

To know more about duopoly and its impact on market competition, refer here:

https://brainly.com/question/33139765#

#SPJ11

At an angle of 270 degrees (or 3π/2 radians) on a circle with a radius of 2 and center at (0, 0), the x-coordinate is 0 and the y-coordinate is -2.

To find the x and y coordinates at an angle of 270 degrees (or 3π/2 in radian measure) on a circle of radius 2 with center (0, 0), we can use the trigonometric definitions of sine and cosine.

The x-coordinate (x-value) represents the horizontal position on the circle, while the y-coordinate (y-value) represents the vertical position.

For a point on the unit circle (circle with radius 1) at a given angle θ, the x-coordinate is given by cos(θ) and the y-coordinate is given by sin(θ).

In this case, the circle has a radius of 2, so we need to multiply the cosine and sine values by 2 to get the x and y coordinates, respectively.

Using the angle 270 degrees (or 3π/2 in radian measure):

x-coordinate = 2 * cos(3π/2)

y-coordinate = 2 * sin(3π/2)

Evaluating these expressions:

x-coordinate = 2 * cos(3π/2) = 2 * 0 = 0

y-coordinate = 2 * sin(3π/2) = 2 * (-1) = -2

Therefore, at an angle of 270 degrees (or 3π/2 radians) on the circle of radius 2 with center (0, 0), the x-coordinate is 0 and the y-coordinate is -2.

To learn more about circles visit : https://brainly.com/question/24375372

#SPJ11

Answer:

5 more cubes

Step-by-step explanation:

you just keep on adding the cubes. So i am in honors math and the easiest way to do math like this just use paper so start with the number of cubes and the just keep on adding till you get to the number you need in this case that number is 11.

Answer:

y = -2/5x - 3

Step-by-step explanation:

y= -2/5x + b

-3 = -2/5(0)  + b

-3 = 0 + b

-3 = b

Answer:

Step-by-step explanation:

The standard form of this exponential function is

\(y=a(b)^x\) where a is the initial value and b is the growth rate. Our initial value is 490 and our growth rate is .2 so the equation is

\(y=490(.2)^x\)

Answer:

im not entirely sure what you're asking so here are some example answers

half of (1/3 + 1/4)

= half of (7/12) = 7/24

half of 1/3 = 1/6

half of 1/4 = 1/8

Answer:

17:14 or 17 to 14

Step-by-step explanation:

since you know there are 14 girls, subtract 14 from 31 and then you'll get 17. since its asking for a ratio of boys to girls not girls to boys, you put boys first, then girls. so your answer will be 17:14

f(x) = Area = (length)(width)

width = x

The length is 16 yards greater than 3 times x

length = 3x+16

f(x) = (3x+16)(x) = 3x^2 + 16x

Answer:

Step-by-step explanation:

We have been given that -- The length of a rectangular parking lot is 16 yards greater than 3 times its width, x, in yards

Length of parking lot is 16 + 3x

Width of parking lot is x

We have to write the function f(x) that describes the area, in square yards, as a function of the width, x

Area of rectangle is Length × width

\( \sf Area = f(x) \)

put value of length and width here,

\( \sf f(x) = (16 + 3x)(x )\)

\( \sf f(x) = 3x^2 + 16x \)

Therefore, f(x) = 3x² + 16x

Some of the metrics that I would look at to determine whether or not a new feature will be successful are as follows:

It should be noted that metrics are the measures of quantitative assessment used for comparing, and tracking performance or production.

Metrics are heavily relied on in the financial analysis of companies to make decisions.

Learn more about metrics on:

brainly.com/question/1837503

#SPJ1

The given series 1/n² is convergent, and its sum is π²/6.

The terms of the series are given by 1/n², where n is the index of the term. To find the partial sums of the series, we can add up the first n terms of the series. The partial sum S_n can be expressed as:

S_n = 1/1² + 1/2² + 1/3² + … + 1/n²

We can now calculate the first few partial sums to graph them:

S_1 = 1/1² = 1

S_2 = 1/1² + 1/2² = 1 + 1/4 = 5/4

S_3 = 1/1² + 1/2² + 1/3² = 5/4 + 1/9 ≈ 1.3611

S_4 = 1/1² + 1/2² + 1/3² + 1/4² ≈ 1.4236

Continuing this pattern, we can calculate more partial sums. Now, let's graph both the sequence of terms and the sequence of partial sums on the same screen.

Based on the graph, we can see that as n increases, the partial sums S_n approach a finite value, and they do not diverge to infinity. This suggests that the series 1/n² is convergent.

To find the sum of the series, we can take the limit of the partial sums as n approaches infinity:

lim(n->∞) S_n = lim(n->∞) (1/1² + 1/2² + 1/3² + … + 1/n²)

Using the formula for the sum of the squares of reciprocals, which is π²/6, we can conclude that:

lim(n->∞) S_n = π²/6

Therefore, the given series 1/n² is convergent, and its sum is π²/6.

To learn more about convergent here:

brainly.com/question/15415793#

#SPJ11

Answer:

6a + 2

Step-by-step explanation:

2 ×3a = 6a 2×2 = 4

it gives 6a + 4

(If this is wrong, it would be better to attach an image)

To determine a formula for the n-th term of an arithmetic sequence, we need to find the common difference (d) first.

The common difference is the constant value that is added or subtracted to each term to get to the next term.

In this case, we can find the common difference by subtracting the fourth term from the seventh term:

d = a₇ - a₄

d = 31 - 19

d = 12

Now that we have the common difference, we can use it to find the formula for the n-th term of the arithmetic sequence. The formula is given by:

aₙ = a₁ + (n - 1)d

In this formula, aₙ represents the n-th term, a₁ represents the first term, n represents the position of the term, and d represents the common difference.

Since we don't have the first term (a₁) given in the problem, we can find it by substituting the known values for a₄ and d:

a₄ = a₁ + (4 - 1)d

19 = a₁ + 3(12)

19 = a₁ + 36

a₁ = 19 - 36

a₁ = -17

Now we can substitute the values of a₁ and d into the formula to get the final formula for the n-th term:

aₙ = -17 + (n - 1)(12)

Therefore, the formula for the n-th term (aₙ) of the given arithmetic sequence is aₙ = -17 + 12(n - 1).

Learn more about Arithmetic sequence here -: brainly.com/question/30194025

#SPJ11

The equation of the line are :

(a) y = x + 1, (b) 4y = 3x - 1, (c) y = -x + 1, (d)  y = -2x + 1 and (e) y = 2x.

Slope intercept form of the line is y = mx + c, where m is the gradient and c is the y intercept.

Point slope of the line is (y - y') = m (x - x'), where m is the gradient and (x', y') is a point.

(a) Equation of the line through (2, 3) and gradient 1.

Substituting in point slope form,

y - 3 = 1 (x - 2)

y - 3 = x - 2

y = x + 1

(b) Equation of the line through (-1, -1) and gradient 3/4.

y - -1 = 3/4 (x - -1)

y + 1 = 3/4 x + 3/4

y = 3/4 x - 1/4

4y = 3x - 1

(c) Equation of the line through (1, 0) and (-2, 3).

Slope, m = (3 - 0) / (-2 - 1) = -1

y intercept = 1

y = -x + 1

(d) Equation of the line through (0, 1) and (-1, 3).

Slope, m = (3 - 1) / (-1 - 0) = -2

y - 1 = -2 (x - 0)

y = -2x + 1

(e) Equation of the line through (1, 2) and parallel to the line with gradient 2.

Two parallel lines have the same slope.

y - 2 = 2 (x - 1)

y = 2x

Learn more about Equation of Lines here :

https://brainly.com/question/21511618

#SPJ1