In the figure BD||EG and the measure of angleACB=35 degree. What is the measure of angle GFH
A 35. B 55. C 135. D 145

Answer:

x=-2

y=5

Step-by-step explanation:

x+2y=8   equation-1  

-x+3y=17 equation-2

5y=25

Both side divided 5,

y=5

Equation-1, y=5

x+2(5)=8

x+10=8

Both side -10

x+10-10=8-10

x=-2

Equation-2, y=5

-x+3(5)=17

-x+15=17

Both side -15

-x+15-15=17-15

-x=2

x=-2

Step-by-step explanation:

here is the answer Step-by-step for you

I hope you understand...

The symbolic representation of the conditional probability

\(P(G'|O) = \frac{P(G'nO)}{P(O)}\)

This is a conditional probability problem ; which can be expressed explicitly as ;

Probability of A given B is defined as ;

\(P(A|B) = \frac{P(AnB)}{P(B)} \)

Let :

Probability that a player is an outfielders = P(O)

Probability that a player is a Great hitter = P(G)

Therefore, we have :

\(P(G'|O) = \frac{P(G'nO)}{P(O)}\)

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a. The conditions for a valid sampling distribution for p are:

Randomization Condition: The sample of 1785 adults must be selected randomly from the population of all U.S. adults.

10% Condition: The sample size, 1785, must be less than 10% of the population of all U.S. adults.

Success/Failure Condition: The number of successes (people who attended church) and failures (people who did not attend church) in the sample must both be at least 10.

b. The sampling distribution of p is approximately normal with mean equal to the true proportion of U.S. adults who attended church last week, which is given as 0.40 in the newspaper report. The standard deviation of the sampling distribution can be calculated using the formula:

sqrt[(p*(1-p))/n]

where p is the true proportion and n is the sample size. Substituting p=0.40 and n=1785, we get:

sqrt[(0.40*(1-0.40))/1785] = 0.014

Therefore, the sampling distribution of p has mean 0.40 and standard deviation 0.014.

c. To find the probability of obtaining a sample of 1785 adults in which 44% or more say they attended church last week, assuming the newspaper report's claim is true, we need to calculate the z-score and use a standard normal table or calculator to find the corresponding probability.

The z-score can be calculated using the formula:

z = (x - mu) / sigma

where x is the sample proportion, mu is the population proportion (given as 0.40), and sigma is the standard deviation of the sampling distribution (calculated as 0.014 above). Substituting x=0.44, mu=0.40, and sigma=0.014, we get:

z = (0.44 - 0.40) / 0.014 = 2.857

Using a standard normal table or calculator, we find that the probability of obtaining a z-score of 2.857 or higher is approximately 0.0021.

Therefore, the probability of obtaining a sample of 1785 adults in which 44% or more say they attended church last week, assuming the newspaper report's claim is true, is approximately 0.0021.

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Answer:

j + 3 ≤ 12

Hope this helps :)

Solution, Explanation, & Check part below

Step-by-step explanation:

1. Isolate variable by doing the inverse operation which is subtracting 3 on both sides of the equation.

j + 3 ≤ 12

- 3 - 3

j ≤ 9

j can be any number that is less than 9 or equal to 9.

Check:

9 + 3 ≤ 12

12 ≤ 12

12 is equal to 12 ✓

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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The type of transformation represented is rotation

Transformation techniques is the process of changing the position of an object on the xy-plane.

The transformation technique that we have include;

From the diagram, you can see that the vertices ABC rotates clockwisely to generate the position A'B'C'. Hence the type of transformation represented is rotation

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Answer:

yes, but there is a better way

Step-by-step explanation:

instead of multiplying x+3 on both sides, I would instead subtract 2 on both sides. If you do this, it would be easier to write this equation in standard form and find the intervals.

In summary, to solve the inequality (x - 2)/(x + 3) ≥ 2, we can multiply both sides of the inequality by x + 3 only when x > -3 to preserve the direction of the inequality.

To solve the inequality (x - 2)/(x + 3) ≥ 2, we need to consider the impact of multiplying both sides of the inequality by x + 3.

When multiplying both sides of an inequality by a positive number, the direction of the inequality remains the same. However, if we multiply both sides by a negative number, the direction of the inequality is reversed.

In this case, the expression x + 3 is in the denominator of the left side of the inequality. If we multiply both sides of the inequality by x + 3, we need to consider two scenarios:

If x + 3 is positive: In this case, we can multiply both sides of the inequality by x + 3 without changing the direction of the inequality.

If x + 3 is negative: Multiplying both sides of the inequality by x + 3 would require flipping the direction of the inequality.

Therefore, we need to ensure that x + 3 is positive before multiplying both sides by x + 3 to preserve the direction of the inequality.

To determine when x + 3 is positive, we set the denominator equal to zero and solve for x:

x + 3 = 0

x = -3

So, if x > -3, then x + 3 is positive.

In summary, to solve the inequality (x - 2)/(x + 3) ≥ 2, we can multiply both sides of the inequality by x + 3 only when x > -3 to preserve the direction of the inequality.

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The mean of this distribution is 0.55

The standard error of this distribution is 0.0384

We have the following:

p=0.55

sample size, n=168

Mean of distribution:

Mean=true proportion of voters who support a restaurant

Mean=p=0.55

Hence, the mean of distribution is 0.55

Standard error of the distribution:

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

\(=\sqrt{\frac{0.55(1-0.55)}{168} }\)

=0.0384

Hence, the standard error is 0.0384

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The questions was incomplete, the complete question is given below:

Suppose the true proportion of voters in the county who support a restaurant tax is 0.55. Consider the sampling distribution for the proportion of supporters with sample size n = 168.

What is the mean of this distribution?

What is the standard error of this distribution?

Answer:

y12111097

Step-by-step explanation:

because I know the answer

The given expression is $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ and we need to rewrite this expression without any denominator in it. Step-by-step explanation: We can use the concept of the Least Common Multiple (LCM) of the denominators to remove the fractions in the expression. By taking the LCM of the denominators of the given expression, we have,$LCM\text{ of }t, u, v = t \cdot u \cdot v$ Now, multiplying each term of the given expression with the LCM $t \cdot u \cdot v$, we get,$\frac{6}{t}\cdot t \cdot u \cdot v+\frac{8}{u}\cdot t \cdot u \cdot v-\frac{9}{v}\cdot t \cdot u \cdot v$$6uv + 8tv - 9tu$$\therefore \text{The given expression without any denominator is } 6uv + 8tv - 9tu.$Thus, we can rewrite the given expression $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ without any denominator in it as $6uv + 8tv - 9tu$.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM. Take the positive integers 4 and 6 as an illustration.

There are four multiples: 4,8,12,16,20,24.

6, 12, 18, and 24 are multiples of 6.

12, 24, 36, 48, and so on are frequent multiples for the numbers 4 and 6. In that lot, 12 would be the least frequent number. Now let's attempt to get the LCM of 24 and 15.

LCM of 24 and 15 is equal to 222235 = 120.

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Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Lucy's dog needs to gain 6 pounds.

Lucy's dog lost 6 pounds so the dog will have to gain 6 pounds.

Answer:

C. \(1.18b\)

Step-by-step explanation:

Hi! Ace here!

In order to do this, we have to convert 18% into a decimal.

The decimal form of it is .18.

So we have to do

\(b+.18b\)

Combine like terms:

\(1.18b\)

I hope this helped

Answer:

1.18b

Step-by-step explanation:

Remember: percentage = decimal × 100

total = b + 18% x b

Factor out b:

total = b x (1 + 18%) = b x (1 + 0.18)

total = b x 1.18 = 1.18b

The values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

We can use the following formulas to find the variance of X:

Var(X) = E[X^2] - (E[X])^2

E[X] = p1 + 2p2 + 3p3

E[X^2] = p1 + 4p2 + 9p3

Substituting these expressions into the formula for the variance, we get:

Var(X) = p1 + 4p2 + 9p3 - (p1 + 2p2 + 3p3)^2

Simplifying this expression, we get:

Var(X) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\)

To maximize Var(X), we want to maximize this expression subject to the constraint p1 + p2 + p3 = 1. We can use Lagrange multipliers to find the maximum. Let:

L(p1, p2, p3, λ) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3 + λ(1 - p1 - p2 - p3)\)

Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 2/7, p2 = 3/7, p3 = 2/7, λ = 4/7

Therefore, the values of p1, p2, p3 that maximize Var(X) are p1 = 2/7, p2 = 3/7, and p3 = 2/7.

To minimize Var(X), we want to minimize the expression \(-(p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\) subject to the constraint p1 + p2 + p3 = 1. We can use the same Lagrange multiplier method to find the minimum. Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 0, p2 = 1/3, p3 = 2/3, λ = 2/3

Therefore, the values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

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Answer:

625 cm³ and 64000 cm³

Step-by-step explanation:

Given

x = \(\sqrt[3]{V}\) ( cube both sides )

x³ = V

(a)

x = 25 cm , then

V = 25³ = 625 cm³

(b)

x = 40 cm , then

V = 40³ = 64 000 cm³

Wouldnt the answer be anything above 12? Because if Y is unknown, and you're taking 2 away from it, and it still has to be greater than 10, then it should be anything above 12. Unless it's saying that the number is greater than 10, and you are just taking away 2 from a number and it doesn't have to be greater than 10.

Answer:

John is verey not smart

Step-by-step explanation:

Because he has fat

The answer is (A) (11, 4).

Step-by-step explanation:  Given that two vertices of a right-angled triangle are A(5, 12) and B(11, 12).

We can plot the given points on the co-ordinate plane as shown in the attached figure.

We will then see that only the point C(11, 4) will lie exactly below the point B(11, 12). Also, the segment AB and BC are the legs of the triangle, AC is the hypotenuse.

The lengths of the three sides are

\(AB = 11 - 5 = 6\\\\BC = 12 - 4 = 8\\\\AC = \sqrt{AB^{2} +BC^{2} } = \sqrt{6x^{2}+8^{2} } = \sqrt{100} = 10\)

Thus, the correct option is (A).

Answer:

Step-by-step explanation:

(7 - y)/(5 + 4) = 1/3

(7 - y)/9 = 1/3

21 - 3y = 9

-3y = -12

y = 4

To calculate the standard deviation of the sampling distribution of p-hat, the answer will be 59 students.

By calculating,

600/10=60 and 59 students which is less than 10% of the population.

A sampling distribution, also known as a finite-sample distribution, in statistics is the probability distribution of a given random-sample-based statistic. The sampling distribution is the probability distribution of the values that the statistic takes on if an arbitrarily large number of samples, each involving multiple observations (data points), were used separately to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample. Although only one sample is frequently observed, the theoretical sampling distribution can be determined.

Because they offer a significant simplification before drawing conclusions using statistics, sampling distributions are crucial in the field. They enable analytical decisions to be made based on the probability distribution of a statistic rather than the combined probability distribution of all the individual sample values

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Answer:

Step-by-step explanation:

Remark

You have an isosceles triangle. That means that the angles opposite the marked sides are equal. So mark the angle on the lower left of the triangle as 50 degrees.

The solution to problem depends on the fact that the sum of the two inside angles of the triangle (each of which is marked as 50 degrees) not supplementary to the exterior angle, are still equal to the exterior angle.

Givens

<1 = 50 degrees

<2 = 50 degrees

Exterior angle = 15x + 25   Substitute the givens into the equation

Equation

<1 + <2 = 15x + 25

Solution

50 + 50  = 15x + 25                       Combine the left side

100 = 15x + 25                               Subtract 25 from both sides

100 - 25 = 15x + 25 - 25                Combine

75 = 15x                                          Divide both sides by 15

75/15 = 15x/15                      

5 = x

Answer

<1 = 50 degrees

<2 = 50 degrees

15x + 25 = 75 + 25 = 100

Answer:

The value is \(v_b = 9.89 \ miles /hour\)

Step-by-step explanation:

From the question we are told that

The velocity of the wind southward is \(v = 5 j \ miles / hour\)

The resultant velocity of the bird with the with wind is \(V= \sqrt{53}\)

Generally for an object moving in the northwest direction the angle with the horizontal is 45°

Generally the velocity of the bird in the along the x -axis is

\(V_x= v_b cos 45^o i\)

Generally the velocity of the bird in the along the y -axis is

\( V_y=(v_b sin 45^o - 5)j\)

Here \(v_b\) is the velocity of the bird without the wind

Generally the resultant velocity of the bird with the with wind is mathematically represented as

\(V = \sqrt{V_x^2 + V_y^2 }\)

=> \( \sqrt{53} = \sqrt{(v_b cos 45^o)^2 + (v_b sin 45^o - 5)^2 }\)

Generally

\(sin 45^o = \frac{1}{\sqrt{2} }\)

and

\(cos 45^o = \frac{1}{\sqrt{2} }\)

So

\( \sqrt{53} = \sqrt{(v_b* (\frac{1}{\sqrt{2} ))^2 + ([v_b * (\frac{1}{\sqrt{2} ) ]- 5)^2 }\)

=> \(53 = \frac{1}{2} v_b^2 + \frac{1}{2} v_b^2 + 5^2 -2*5 * \frac{1}{\sqrt{2} } v_b\)

=> \( 53 = v_b^2 + 25 - 5 \sqrt{2} v_b\)

=> \( v_b^2 - 5 \sqrt{2} v_b -28 = 0\)

Solving the above quadratic equation using quadratic formula we obtain that

\(v_b = 9.89 \ miles /hour\)

The other value is negative so we do not make use of it because we know that the bird is moving in the positive x and y axis

two angles that add up to 90 degrees are called complementary angles.

Answer:

HCF × LCM = product of two numbers

product = 120 × 4 = 480

possible pairs of number

(4,120),(8,60),(12,40),(20,24)

Answer:

The number of skateboards of each color is 11 and 4

Step-by-step explanation:

Let x represent blue skateboards and

y represent red skateboards.

From the question, the total number of skateboards is 15, that is,

x + y = 15 ...... (1)

and their product is 44, that is,

xy = 44 ...... (2)

From equation (1),

x + y = 15

We can write that

x = 15 - y ...... (3)

Substitute this into equation (2)

xy = 44

(15-y)y = 44

15y -y² = 44

Then,

y² - 15y + 44 = 0

Solve quadratically

y² -4y -11y + 44 = 0

y(y-4) -11(y-4) = 0

(y-11)(y-4) = 0

y-11 = 0 OR y-4 = 0

y = 11 OR y = 4

Put the values of y into equation (3) for x

x = 15 - y

When y = 11

x = 15 - 11

x = 4

and when y = 4

x = 15 -4

x = 11

(4,11) and (11,4)

It is either 4 blue and 11 red skateboards OR 11 blue and 4 red skateboards.

Hence, the number of skateboards of each color is 11 and 4.

Answer:

(-308, -352)

Step-by-step explanation:

For a dilation from the origin, you multiply the x and y by the scale factor.

-7 * 44 = -308

-8 * 44 = -352

(-308, -352)