An Olympic-sized pool, which holds 660,000 gallons of water,
is only 63% full. The pool maintenance company adds more
water, filling the pool to 90% full. How many gallons of water
did they add?
P
7.AR 3.1
a
244 200
178 200
B) 594 000
415.800
134

The price of the car after 5 years will be ₱1,500,000

Price of car = ₱2 000 000

Depreciation percentage = 5%

Depreciation = 5% × ₱2 000 000 = 0.05 × ₱2 000 000 = ₱100 000

The equation to solve the question will be:

= 2000000 - 100000x

where, x = number of years

= 2,000,000 - 100000(5)

= 2,000,000 - 500,000

= ₱1 500 000

The price of the car after 5 years will be ₱1,500,000

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The area of the circular portion of the yard is 225π feet squared

The area they want to enclose has a 30π fencing.

Therefore,

perimeter or circumference of a circle = 2πr

where

Therefore,

circumference of a circle = 2πr

30π = 2πr

divide both sides by 2π

30π / 2π = 2πr / 2π

r = 15 ft

Therefore,

area of the circular portion = πr²

area of the circular portion =  π × 15²

area of the circular portion = 225π

Therefore, the area of the circular portion of the yard is 225π feet squared

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hello

101.7 * 5.45 =

if you observe you'll see a decimal point after the third number. this tells us that the answer has a three significant figure

None of the provided options is correct. The simplified value of the expression [(23)4]2 is 65536.

To simplify the expression [(23)4]2, we start by evaluating the exponent inside the inner parentheses:

(23)4 = 23 * 23 * 23 * 23

This results in 256. Now, we substitute this value back into the expression:

[(23)4]2 = 2562

Squaring 256 gives us 65536. Therefore, the simplified value of the expression [(23)4]2 is 65536.

So, the correct answer is not listed among the options provided. None of the given options (a) 17666216, b) 12222617, c) 17222167, d) 16777216) match the simplified value of 65536.

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The statement "f(x) <= g(x) for all x > 0" does not necessarily imply that f(x) is always less than or equal to g(x) for all x > 0. This statement is false.

To demonstrate this, consider the following counterexample:

Let's assume f(x) = x and g(x) = x^2. Both f(x) and g(x) are continuous functions for all x > 0.

Now, if we examine the interval (0, 1), for any value of x within this interval, f(x) = x will always be less than g(x) = x^2. However, if we consider values of x greater than 1, f(x) = x will become greater than g(x) = x^2.

In this counterexample, we have f(x) <= g(x) for all x > 0 within the interval (0, 1), but the inequality is reversed for x > 1. Therefore, the statement "f(x) <= g(x) for all x > 0" is false.

It's important to note that the validity of the statement depends on the specific functions f(x) and g(x). There may be cases where f(x) <= g(x) holds true for all x > 0, but it cannot be generalized without further information about the functions.

In general, comparing the behavior of two continuous functions requires a more comprehensive analysis, taking into account the specific properties and characteristics of the functions involved.

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Total height of the ball is 13.25.

A curved line. part of a circle is known as arc.

Given that,

Speed of the ball is 15m/s

Height above the ground from where it is released is 2m

Equation of motion is v2 is u2+2as

When the ball reaches its maximum height v is 0

Since, acceleration due to gravity g is acting downwards  will be negative.

So, 15^2=2×10×s

S=11.25m

So, height from projection is 11.25 and

Total maximum height reached by ball is s+2 is 11.25 +2 = 13.25

There fore ,total height of the ball is 13.25.

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The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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Answer:

Circle

Step-by-step explanation:

\(x dx=-y dy \\ \\ \int x \text{ } dx=\int -y \text{ } dy \\ \\ \frac{x^2}{2}=-\frac{y^2}{2}+C \\ \\ x^2=-y^2+C \\ \\ x^2+y^2=C\)

Which is the equation of a circle.

The probabilities for all values of k (18 to 25), and then sum them up to find the exact probability of getting 18 or more heads in 25 tosses of a coin.

To find the exact probability of getting 18 or more heads in 25 tosses of a coin, we can use the binomial probability formula. The formula is:

P(X=k) = (n choose k) * \(p^{k} *(1-p)^{n-k}\)

where P(X=k) is the probability of getting k successes, n is the total number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which is the number of ways to choose k successes out of n trials.

In this case, we want to find the probability of getting 18 or more heads in 25 tosses of a coin. The probability of getting a head on any one toss of a fair coin is 1/2, so p = 1/2. The total number of trials is 25, so n = 25. Therefore, we can calculate the probability as follows:

P(X ≥ 18) = Σ P(X=k) from k=18 to 25

= Σ (25 choose k) * \((\frac{1}{2} )^{25} *(\frac{1}{2} )^{25-k}\) from k=18 to 25

Using a calculator or software, we can calculate each term of the sum and add them up. The exact probability of getting 18 or more heads in 25 tosses of a coin is approximately 0.035.

This means that out of all possible sequences of 25 coin tosses, only about 3.5% of them will have 18 or more heads.

In summary, to find the exact probability of getting 18 or more heads in 25 tosses of a coin, we can use the binomial probability formula.

The calculation involves finding the sum of several terms, which can be done using a calculator or software. The resulting probability is relatively low, indicating that getting 18 or more heads in 25 tosses of a coin is not a common occurrence.

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Answer:

1. It means he was smiling really happily.

2. It means everything was happening really slow, and it seemed like time stopped for a moment.

3. It means the boy wanted his little sister to stop annoying him.

4. It means they heard it directly from someone who has personal knowledge of it.

5. It means to dismiss or fire someone, in this case the boss fired him from his job.

The answer is c. Two.

When a researcher controls for gender, it means that the data is analyzed separately for each gender category. This approach allows the researcher to examine the relationship between variables while accounting for the potential differences between genders. By creating two separate groups based on gender (male and female), the researcher can analyze and compare the data within each group.

Therefore, controlling for gender will result in two partial tables, one for each gender category. Each partial table will contain the data specific to that gender, allowing for gender-specific analysis and comparisons. This approach enables the researcher to understand any variations or patterns that may exist within each gender group.

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Answer:

Yes, the probability distribution for the number of years of experience can be modelled by a binomial probability distribution

Step-by-step explanation:

We are told that on a recent sample, the paper claims that 45% of all employees believe their company president possesses low ethical standards.

This means the chance of success is p = 45% = 0.45

Now, 20 of the company's employees are randomly and independently sampled. This means that for any amount of success within this sample number can be represented by;

P(X = x) = C(n, x) × p^(x) × (1 - p)^(n - x)

Where;

x is the number of possible successes

n is the number of trials

p is the chance or probability of success

C(n, x) is the number of possible combinations that could occur

This formula represents the binomial probability distribution formula.

So yes, the probability distribution for the number of years of experience can be modelled by a binomial probability distribution

Answer:

x = 18

Step-by-step explanation:

Both angles together make 180, they are essentially supplementary angles thou not on the same line.

Set your formula up as

81 + 5x + 9 = 180

5x = 180 - 81 - 9

5x = 90

x = 90/5

x = 18

The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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Answer:

First choice

-∞ < y< ∞

Step-by-step explanation:

In this function,we need to use graph in order to find out the range.

Graph is attached.

To answer this question, we need to first calculate the cost of each orange. We can do this by dividing the total cost by the number of oranges purchased and the man can sell 52 oranges for 260 units and still make a profit of 30%.

To answer this question, we need to first calculate the cost of each orange. We can do this by dividing the total cost by the number of oranges purchased  , 2000 / 400 = 5

So each orange costs the man 5 units.

To make a profit of 30%, the man needs to sell the oranges for 1.3 times the cost.

1.3 x 5 = 6.5

Therefore, he needs to sell each orange for 6.5 units.

To determine how many oranges he can sell for 260 units, we can set up a proportion:

400 oranges / 2000 units = x oranges / 260 units

Solving for x, we get:

x = (260 x 400) / 2000 = 52

So the man can sell 52 oranges for 260 units and still make a profit of 30%.
The man buys 400 oranges for 2000, so the cost per orange is 2000/400 = 5. To achieve a 30% profit, he needs to sell each orange at 5 + (0.30 * 5) = 6.5. Now, if he wants to sell the oranges for 260, we need to find out how many oranges can be sold at 6.5 each. Simply divide 260 by the selling price per orange: 260/6.5 = 40 oranges. So, he can sell 40 oranges for 260 to get a profit of 30%.

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Answer:

t=2

Step-by-step explanation:

t>o and t² - 4 = 0

\(t^2=4\)

\(t=\sqrt{4}\)

\(t=+2/-2\)

As t>0

Therefore, t=+2

Thus, if t>o and t² - 4 = 0, the value of t=+2

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Answer:

Step-by-step explanation:

shortest-7

middle-24

longest-25

The data does not suggest that the true average total body bone mineral content during postweaning exceeds that during breastfeeding by more than 25g.

1. Hypotheses:

  - Null hypothesis (H0): The true average total body bone mineral content during postweaning is not more than 25g higher than during breastfeeding.

  - Alternative hypothesis (H1): The true average total body bone mineral content during postweaning exceeds that during breastfeeding by more than 25g.

2. Test statistic and significance level:

  - We will use a t-test to compare the means of the two groups.

  - The significance level is given as 0.05.

3. Calculate the test statistic:

  - Subtract the bone mineral content during breastfeeding (B) from the bone mineral content during postweaning (P) for each subject.

  - Calculate the mean difference and standard deviation of the differences.

  - Compute the t-test statistic using the formula: t = (mean difference - 25) / (standard deviation / √n), where n is the number of observations.

4. Degrees of freedom (df):

  - The degrees of freedom for this test is equal to the number of observations minus 1.

5. P-value:

  - Use a statistical computer package to calculate the P-value associated with the obtained test statistic and degrees of freedom.

6. Decision:

  - Compare the P-value to the significance level.

  - If the P-value is less than the significance level (0.05), reject the null hypothesis.

  - If the P-value is greater than or equal to the significance level, fail to reject the null hypothesis.

In this case, the conclusion is based on the calculated P-value. If the P-value is less than 0.05, we would reject the null hypothesis, indicating that the true average total body bone mineral content during postweaning does exceed that during breastfeeding by more than 25g. If the P-value is greater than or equal to 0.05, we would fail to reject the null hypothesis, suggesting that there is not enough evidence to conclude that the average bone mineral content during postweaning is significantly higher than during breastfeeding by more than 25g.

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Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)

Now we calculate the partial derivatives as follows,

∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...

and,

∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0

Therefore,

∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j

The curl of F is given by:

(cos(xy) - xy sin(xy)) i - sin(z)j.

To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:

r(t) = n* i + t}j + tcos atk, 15t52.

The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t

= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt

= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1

= sin(a) sin(n) - (a/2) cos(2a)

The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).

The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).

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Answer: it’s the second one

Step-by-step explanation:

Gerard concluded that triangle with given sides cannot be used as  building-frame support because it is not right triangle, he come to this conclusion because the Pythagoras-theorem is not satisfied.

In order to check if a triangle is "right-triangle", Gerard used the Pythagorean theorem. According to this theorem, in right triangle, the square of length of hypotenuse (the side opposite the right angle) is equal to sum of squares of other two sides,

So, the squares of the given sides are :

Square of √95 feet = (√95)² = 95 feet

Square of 8 feet = 8² = 64 feet

Square of √150 feet = (√150)² = 150 feet

We see that, 95 feet + 64 feet = 159 feet ≠ 150 feet,

Since the square of the longest side (√150) is not equal to the sum of the squares of the other two sides (√95 and 8), the Pythagorean-theorem is not satisfied.

Therefore, Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 feet is not a right triangle.

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The given question is incomplete, the complete question is

Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 cannot be used as a building frame support on the house because it is not a right triangle. How did Gerard come to that conclusion? explain.

Answer:

\(image = (0 \: \: 2)\)

The angle measure that corresponds to angle S is angle H.

Given information:

Figure 1 and Figure 3 are congruent figures.

That means, they have the same type of shape but have different sizes.

Therefore, as per the diagram,

PT ≅ GF

TR ≅ FD

RS ≅ DH

SQ ≅ HE

QP ≅ EG.

PTRSQ ≅ GFDHE.

Now, for angle measures,

Angle P is congruent to the angle G.

Angle T is congruent to the angle F.

Angle R is congruent to the angle D.

Angle S is congruent to the angle H.

Angle Q is congruent to the angle E.

As per the congruency of the figures,

∠S ≅ ∠H.

Therefore, ∠S ≅ ∠H.

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Answer:

reffrents a number

Step-by-step explanation:

Answer:

It's 1

Step-by-step explanation:

10 to the power 1 gives you 10

Answer:

Θ ≈ 28.07°

Step-by-step explanation:

using the sine ratio in the right triangle

sinΘ = \(\frac{opposite}{hypotenuse}\) = \(\frac{8}{17}\) , then

Θ = \(sin^{-1}\) ( \(\frac{8}{17}\) ) ≈ 28.07° ( to the nearest hundredth )

The solution of this inequality are x ≤ 2 and x ≥ 4 which is shown in the graph below.

In Mathematics and Geometry, an inequality is a relation that compares two (2) or more numerical data, number, and variables in an algebraic equation based on any of the inequality symbols;

In this scenario and exercise, we would solve and graph the given inequalities for x in parts as follows;

(x – 2)(x – 4) ≥ 0

(x – 2) ≥ 0

(x – 2) + 2 ≥ 0 + 2

x - 2 ≥ 0

x ≤ 2 (solid dot with an arrow that points to the left on a number line).

(x – 4) ≥ 0

(x – 4) + 4 ≥ 0 + 4

x - 4 ≥ 0

x ≥ 4 (solid dot with an arrow that points to the right on a number line).

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Answer:

3/5

Step-by-step explanation:

3 and 4 and 5 are more than 2 so they are 3 quantities and the total of the quantities are 5 so the answer should be 3/5

The fraction of crayons that are blue triangle is 1/5.

The ratio of blue rounds to non-blue crayons is

The fraction of footballs that are brown rubber footballs is 8/15 and here are 4 times as many rubber footballs as non-rubber footballs

A fraction represents a part of a whole.

1. Let's say Alexa had a total of 5x crayons in the bag.

the number of blue crayons in the bag is 2x,

There is one triangle for every two round crayons,

(1/2) × 2x = x (By condition)

So, the fraction of crayons that are blue triangle is x / 5x = 1/5.

The number of blue round crayons is 2x.

The number of non-blue crayons is 5x - 2x = 3x,

The ratio of blue rounds to non-blue crayons is 2x / 3x = 2/3.

2.

4 out of 5 wall footballs are rubber, 4/5 of the footballs in the bag are rubber.

The fraction of rubber footballs that are brown is 2/3.

The fraction of footballs that are brown rubber footballs is (4/5) × (2/3) = 8/15.

The fraction of non-brown rubber footballs is (4/5) - (8/15) = 4/15.

The ratio of rubber footballs to non-rubber footballs is (4/5) / (1/5) = 4.

So there are 4 times as many rubber footballs as non-rubber footballs

Hence,  the fraction of crayons that are blue triangle is 1/5.

The ratio of blue rounds to non-blue crayons is

The fraction of footballs that are brown rubber footballs is 8/15 and here are 4 times as many rubber footballs as non-rubber footballs

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