what is the area of the circle?​

Answer: 12.5

Step-by-step explanation:

Answer:

The area of this shape is \(50cm^2\).

Step-by-step explanation:

To find the area of this figure, you only need to know the area of the rectangle and the area of the triangle. The area of the rectangle would be 5 * 6 = \(30cm^2\). Since the length of the rectangle plus the base of the triangle is equivalent to 14, that means the base of the triangle is equal to 14 - 6 = 8 cm. The formula for the area of a triangle is \(\frac{1}{2} bh\), the base you now know is 8 cm, and the height is 5 cm, which means the area of the triangle would be \(\frac{1}{2} *5*8\) = \(\frac{1}{2} * 40\) = \(20cm^2\). Add the area of the rectangle to the area of the triangle and you'll get the area of the entire shape, which is 30 + 20 = \(50cm^2\).

Answer:

84 years

Step-by-step explanation:

Given :

At present :

Let :

daughter's age = x

Woman's age = 2x

21 years ago :

Woman's age = 3 times daughter's age

2x - 21 = 3(x - 21)

2x - 21 = 3x - 63

-21 + 63 = 3x - 2x

42 = x

Daughter's age = 42

Woman's age = 2x = 84

Hence, woman's present age is 42 years

The approximate probability that no more than 30 items out of the random sample of 600 are defective is approximately 0.9983 or 99.83%.

To calculate the approximate probability that no more than 30 items out of a random sample of 600 are defective, we can use the binomial distribution formula. The binomial distribution is used to model the probability of a certain number of successes (in this case, the number of defective items) in a fixed number of independent Bernoulli trials (evaluating each item).

Given:

Probability of an item being defective (p) = 3% = 0.03

Number of trials (n) = 600

Number of defective items (k) we want to calculate the probability for is no more than 30.

Using the binomial distribution formula:

P(X ≤ 30) = Σ(k=0 to 30) [(nCk) * p^k * (1-p)^(n-k)]

Where nCk represents the number of combinations of choosing k items out of n.

However, calculating this sum directly can be tedious. Instead, we can use an approximation for the binomial distribution when n is large (n ≥ 30) and p is not too close to 0 or 1. This approximation uses the normal distribution:

Approximately, the binomial distribution can be approximated by a normal distribution with mean (μ) = n * p and standard deviation (σ) = √(n * p * (1-p)).

So, in our case:

μ = 600 * 0.03 = 18

σ = √(600 * 0.03 * 0.97) ≈ 4.1589

Now, to find the probability of no more than 30 defective items, we calculate the z-score:

z = (30 - μ) / σ

z = (30 - 18) / 4.1589 ≈ 2.89

Using the standard normal distribution table or a calculator, we can find the corresponding probability for a z-score of 2.89, which is approximately 0.9983.

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750 mL is equivalent to 25.36 oz.

When measuring liquids, the metric system and the US customary system are commonly used. In the metric system, the standard unit of measurement for liquids is milliliters (mL) and in the US customary system, it's ounces (oz).

To convert between these units, you can use a conversion factor.

One way to convert mL to oz is to use the conversion factor of 1 oz = 29.5735 mL. To find the number of ounces in 750 mL, you can use this conversion factor to set up an equation:

750 mL = x oz

Where x is the number of ounces you want to find. To solve for x, you can divide both sides of the equation by the conversion factor:

x = 750 mL / 29.5735 mL/oz

x = 25.36 oz

It's important to note that this is an approximation and for more accurate measurements, you should use an online calculator or consult a chart.

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Answer: the value of x is 9 and the value of y is 9 there you have your answer

Step-by-step explanation:

The kinetic energy of the Mars Climate Orbiter spacecraft is approx    3.31 x 10^7 joules.

To determine the kinetic energy of the Mars Climate Orbiter spacecraft, we can use the formula:

Kinetic energy = (1/2) * mass * velocity^2

Given:

Mass of the spacecraft (m) = 629 kg

Velocity of the spacecraft (v) = 1.20 x 10^4 km/h

First, we need to convert the velocity from km/h to m/s:

1 km = 1000 m

1 h = 3600 s

Velocity in m/s = (1.20 x 10^4 km/h) * (1000 m/km) / (3600 s/h) ≈ 333.33 m/s

Now, we can calculate the kinetic energy:

Kinetic energy = (1/2) * (629 kg) * (333.33 m/s)^2

Kinetic energy ≈ 3.31 x 10^7 joules

Therefore, the kinetic energy of the Mars Climate Orbiter spacecraft is approximately 3.31 x 10^7 joules.

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Answer:3

Step-by-step explanation: the closest multiple of for is 16 then reminder 3

Answer:

9

Step-by-step explanation:

one side of a triangle =x

the other two sides measure = (x-4) each

perimeter = 19

therefore :

perimeter of a triangle = x + (x-4) + (x-4)

I.e = x+x+x-4-4=19

= 3x -8=19

= 3x = 19+8

3x=27

divide both sides by 3

x=9

The correct answer is option is option d) not exact but having an integrating factor x c e.

Integrating factor is defined as the function which is selected in order to solve the given differential equation. It is most commonly used in ordinary linear differential equations of the first order. When the given differential equation is of the form; dy/dx + P(x) y = Q(x)

We have, (x2+y2)dy= -xydx

⇒dxdy= -(x2+y2xy)

Substitute y=vx

⇒ - dxdy=v+xdxdv

⇒v+xdxdv= -(1+v2v)

⇒ xdxdv= -(1+v2v−v)

            = -(−1+v2v3)

⇒v31+v2dv =xdx

Integrating both sides we get, −2v21+logv= logx-logc, where c is constant

⇒−2v21+log(cvx)=0

⇒y=cex2/2y2

Now using y(1)=1⇒c=e−1/2

Also y(x0)=e

⇒e=e−1/2+x02/2e2⇒1=−1/2+x02/2e2

⇒x02=3e2

⇒x0=\(\sqrt{3}\)e

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Answer:

52%

Step-by-step explanation:

Since there are 25 numbers in 1-25, you need to divide 100/25 which is 4.

There are 13 odd numbers in 1-25 so you need to multiply 13x4.

13x4=52

There is a 52% chance she will pick an odd number.

To find the absolute maximum value of h(x) = -2x^2 + x over the interval [-3, 3], we need to identify critical points and evaluate the function at those points as well as the interval's endpoints.

First, find the critical points by taking the derivative of h(x) and setting it to 0:

h'(x) = -4x + 1

-4x + 1 = 0
4x = 1
x = 1/4

Now, evaluate h(x) at the critical point and the endpoints of the interval:

h(-3) = -2(-3)^2 + (-3) = -18
h(1/4) = -2(1/4)^2 + (1/4) = -1/8 + 1/4 = 1/8
h(3) = -2(3)^2 + 3 = -15

Comparing the values, we can see that the absolute maximum value is h(1/4) = 1/8.

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The amount of money he paid monthly is   £503.75.

Andy is buying a car he negotiated 7% decrease on a £6500 car he will pay the full balance in 12 equal monthly payments.

Therefore, the amount paid monthly can be calculated as follows:

amount he bough the car = 6500 - 7% of 6500

amount he bough the car = 6500 - 7 / 100 × 6500

amount he bough the car =  6500 - 455

amount he bough the car = 6045

Therefore,

amount paid each month = 6045 / 12

amount paid each month =  £503.75

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Given

A chemist wishes to mix a solution that is 8% acid.

She has on hand 8 liters of a 2% acid solution and wishes to add some 12% acid solution to obtain the desired 8% acid solution.

To find: How much 12% acid solution should she add?

Explanation:

It is given that,

A chemist wishes to mix a solution that is 8% acid.

She has on hand 8 liters of a 2% acid solution and wishes to add some 12% acid solution to obtain the desired 8% acid solution.

Now, Let x be the liters of acid added to obtain the desired 8% acid solution.

Then,

Hence, 12liters of acid is added to 12% acid solution.

The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.

The realization of the stochastic process implies that the values of the stochastic process are observed at particular points in time. It is denoted by x(t) and takes the form of a function of time t.

If the process is discrete, then the function is a sequence of values at discrete points in time.

A stochastic process is one that evolves over time and the outcomes are uncertain.

The given expression P(X5=3|X4=3,X3=3,X2=1,X1=4, X0=1) gives the probability of X5 being equal to 3 given that X4 is equal to 3, X3 is equal to 3, X2 is equal to 1, X1 is equal to 4, and X0 is equal to 1.

To understand the above expression, suppose we have a stochastic process with values X0, X1, X2, X3, X4, and X5.

The given expression provides the conditional probability of the value of X5 being equal to 3 given that X0, X1, X2, X3, and X4 take specific values.

The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.

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Answer:

c; y = 2x

Step-by-step explanation:

if it was without the coupon the fee would be the $2 per mile (2x) with the $35 which would be

y = 2x + 35

but with the coupon the $35 reservation is removed so only 2x is left

y = 2x

If you draw a tiny circle with a 90-degree sector, it is not a dilation of the original circle because a dilation is a transformation that changes the size of an object while preserving its shape.

In a dilation, all corresponding points in the original and the transformed shapes lie on a line passing through the center of dilation, and the scale factor of the dilation determines the ratio of the corresponding lengths of any two segments that join corresponding points.

In the case of the tiny circle with a 90-degree sector, the sector has a different shape than the original circle, and the sector has a larger perimeter than the corresponding arc of the original circle. Therefore, the sector is not a dilation of the original circle.

Furthermore, a 90-degree sector of a circle can be obtained by cutting a part of the original circle and thus cannot be obtained by dilation alone.

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The solution to the given differential equation, subject to the initial condition y(1) = 40, is |x|^y = e^(-5x^2 + 5). To solve the differential equation xy' = y - 10x^3 we use integrating factors.

Step 1: Rewrite the equation in standard form

Divide both sides of the equation by x:

y' - (1/x)y = -10x^2

Step 2: Identify the integrating factor (IF)

The integrating factor is given by:

IF = e^(∫(-1/x)dx)

  = e^(-ln|x|)

  = 1/x

Step 3: Multiply both sides of the equation by the integrating factor

1/x * (xy' - y) = 1/x * (-10x^2)

Simplifying, we have:

y' - y/x = -10x

Step 4: Integrate both sides of the equation

∫(y' - y/x)dx = ∫(-10x)dx

Integrating, we get:

y ln|x| = -5x^2 + C

Step 5: Solve for y by exponentiating both sides

e^(y ln|x|) = e^(-5x^2 + C)

Taking the exponential, we have:

|x|^y = e^(-5x^2 + C)

Step 6: Apply the initial condition

When x = 1, y = 40. Substituting these values, we get:

1^40 = e^(-5(1)^2 + C)

1 = e^(-5 + C)

Simplifying, we find:

C = 5 - ln(1)

Therefore, the equation becomes |x|^y = e^(-5x^2 + 5).

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An equation of the line through the points (-6, 5) and (-3, -3) is y = -8x/3 - 11.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (-6, 5) and (-3, -3) by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 5 = (-3 - 5)/(-3 + 6)(x + 6)

y - 5 = -8/3(x + 6)

y - 5 = -8x/3 - 16

y = -8x/3 - 16 + 5

y = -8x/3 - 11

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The approximate probability that the total score is at least 375 when a fair six-sided die is rolled 100 times is (d) 0.4420.

When a fair six-sided die is rolled, the random variable X represents the outcome. The mean (μX) of X is 3.5, and the standard deviation (σX) is 1.71.

To find the probability that the total score is at least 375 when the die is rolled 100 times, we can use the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approximates a normal distribution.

In this case, the sum of the outcomes of 100 rolls of the die follows a normal distribution with a mean of μX multiplied by the number of rolls (100) and a standard deviation of σX multiplied by the square root of the number of rolls (10). Therefore, the approximate probability can be calculated by finding the probability that the sum is greater than or equal to 375.

Using a normal distribution table or a calculator, we can find that the approximate probability is 0.4420, which corresponds to answer (d). This means that there is a 44.20% chance that the total score will be at least 375 when the die is rolled 100 times.

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Hi there!

\(\large\boxed{A = 1200in^{2}}\)

To solve, we can divide the figure into a rectangle and triangle:

The rectangle has dimensions 20in and 30in. The formula A = l × w will be used to find the area.

The triangle has dimensions 40 (10 + 20 + 10) in and 30 in. The formula A = 1/2(b· h) can be used to find the area.

Find the area of each shape:

A = 20 × 30 = 600in²

A = 1/2(40 × 30) = 600in²

Find the sum of both to find the area of the total figure:

600 + 600 = 1200in²

Part a: The value of x such that the both lines are parallel to each other is (x = 12).

Part : The value of y such that the both lines are parallel to each other is (y = 108).

In the given figure;

Part a: For making the lines w and t parallel to each other; their corresponding angles must be equal.

Thus,

4x + 60 = 9x

Solving;

9x - 4x = 60

5x = 60

x = 12

Thus, the value of x for which both lines w and t are parallel is 12.

Part b: For making the lines u and v parallel to each other; their corresponding angles must be equal.

Thus, 9x = y

Put x = 12.

y = 9×12

y = 108.

Thus, the value of y for which both lines u and v are parallel is 108.

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In question 27, the price elasticity of supply for shampoo is given as 20, and the price of shampoo increases by 0.7%. The expected change in the quantity of shampoo supplied can be determined using the concept of price elasticity of supply. However, the specific percentage change in quantity supplied is not provided, so a precise answer cannot be given based on the given information.

In question 20, an inferior good in which the income effect dominates the substitution effect is referred to as a Giffen good. It is not classified as a normal good, luxury good, mass-produced good, or favored good.

In question 30, the cross elasticity of demand measures the responsiveness of the quantity demanded of a particular good to changes in the prices of its substitutes and complements. The correct answer is that the cross elasticity of demand measures the responsiveness to changes in both substitutes and complements.

In question 27, without the specific percentage change in quantity supplied, we cannot determine the exact outcome based on the given information. The price elasticity of supply of 20 suggests that the quantity supplied is highly responsive to changes in price, but the specific percentage change in quantity supplied cannot be calculated without additional data.

In question 28, the relationship between pasta being a Giffen good and other characteristics is not specified. While pasta being a Giffen good indicates that the quantity demanded increases as the price increases, it does not imply whether pasta is a normal good, luxury good, or how price changes affect quantity demanded.

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Answer: n = 0 and -2

Step-by-step explanation:

Equate the expressions to zero

n(n+2) = 0

n = 0 and n+2 = 0

n = 0 and n = -2

Answer:

I thank it would be 10 and 5

Step-by-step explanation:

I hope this helps

Answer: x = \(\frac{25}{6}\)

Step-by-step explanation:

     We will cross-multiply the two fractions given to help us solve.

  Given:

\(\displaystyle \frac{6}{5} =\frac{5}{x}\)

  Cross-multiply:

6 * x = 5 * 5

6x = 25

  Divide both sides of the equation by 6:

x = \(\frac{25}{6}\)

Answer:

x = 25/6

Step-by-step explanation:

6/5 = 5/x

Cross multiply.

6x = 25

Divide by 6.

x = 25/6

Answer:

The maximum a person can weigh to go on the ride safely is 100.5 kg

Step-by-step explanation:

The specification for the maximum weight of each person that goes on the ride = 100 kg

Therefore, given that the maximum possible error of a measurement is equal to 1/2 multiplied by the unit of measurement, we have that the specified maximum weight, \(W_{max}\), can be written as follows;

\(W_{max}\) = (100 ± 0.5) kg, which gives the maximum a person can weigh to go on the ride safely as 100 kg + 0.5 kg = 100.5 kg