Find the greatest common factor (reverse of distributing)

The required value of the x in the expression of angle is 19.

An expression of angle is given as 7x + 2 = 135°, the value of the x is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
7x + 2 = 135
Simplifying,
7x = 135 - 2
7x = 133
x = 133 / 7
x = 19

Thus, the required value of the x in the expression of angle is 19.

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Answer:

1,875$ in intrest

Step-by-step explanation:

10000x.0375x5=1875

The probability that all adjacent points differ in color is given as follows:

1/10. (second option).

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the total outcomes, we have an arrangement of 6 elements, due to the six points, with 3 and 3 repetitions, as 3 are green and 3 are red, hence the number of total outcomes is calculated as follows:

\(T = A_6^{3,3} = \frac{6!}{3!3!} = 20\)

For the desired outcomes, there are two, given as follows:

This means that the probability that all adjacent points differ in color is calculated as follows:

p = 2/20 = 1/10.

Hence the second option is the correct option.

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Answer: i think its B

Step-by-step explanation:

Answer:

it's 82

Step-by-step explanation:

26+72=98

180-98=82

The probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

The standard deviation of the age of people who suffered heart attacks soon after using cocaine was 10 years. In a random sample of size 49, what is the probability the mean age at heart attack after using cocaine is greater than 42?We are given the following details:

The mean age of people in the study who suffered heart attacks soon after using cocaine was only 44.

Standard deviation = 10

Sample size = 49

Now we need to find the z-score using the formula:

z = (x - μ) / (σ / √n)

wherez is the z-score

x is the value to be standardized

μ is the mean

σ is the standard deviation

n is the sample size.

Substitute the values in the formula as given,

z = (42 - 44) / (10 / √49)z = -2 / (10/7)

z = -1.4

Probability of z > -1.4 can be found using the standard normal distribution table or calculator.

P(z > -1.4) = 0.9192

Therefore, the probability the mean age at heart attack after using cocaine is greater than 42 is 0.9192. Hence, the correct option is D. 0.9192.

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The volume V of the solid obtained by rotating the region bounded by the given curves about the specified line is 16π/3 cubic units.

The volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis is given by the formula:

V = 2π/3 ∫12 [(6 - 3/2x)2 - 02] dx

The integral can be evaluated using integration by parts. First, we let u = 6 - 3/2x and dv = dx. Then, du = -3/2dx and v = x. We then have:

V = 2π/3 [x2(6 - 3/2x) - 2/3∫12 x dx]

The integral is evaluated easily as:

V = 2π/3 [x2(6 - 3/2x) - 2/3(x2/2)12]

Substituting the limits and solving, we get the volume V as:

V = 2π/3 [(6 - 3)2 - (12/2)]

Therefore, the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis is 2π/3(8 - 1/2) ≈ 16π/3 cubic units.

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The value of the expression below when x=5x=5?

8x+9 is equal to \(7^{2}\) (or) 49.

Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)

The expression,

y = 8x + 9

If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:

So, we can substitute x = 5,

Then, y = 8 * 5 + 9

Calculate the product or quotient,

y = 40 + 9

Calculate the sum or difference,

y = 49

We can write alternative form,

y = \(7^{2}\)

Therefore,

Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.

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Answer:

We shall need to pick at least 4 balls to be sure that we are getting balls with the same color

Step-by-step explanation:

Here, we want to know the least number of balls to be taken out of the box to be sure that we have all the three colors represented.

We know there are 12 identical balls, with the least numbers of balls being 1 and 2. Hence, to be able to know we have all the colors of balls represented, we will need to have taken all the less represented ones i.e the 1 and 2 , and this means that the next number of ball which would be taken will confidently confirm that we have taken all the colors since we would have exhausted picking other balls at this point.

So we shall be needing at least 4 balls picked to ensure that we have all the colors represented

Answer:

25

Step-by-step explanation:

Distance (d) = √(11 - -13)2 + (2 - 9)2

= √(24)2 + (-7)2

= √625

= 25

Answer: 25 is the answer

Step-by-step explanation:

When a thesis test is being performed for a population mean, the probability of a type II error isn't dependent on the sample mean. Option B is the right answer.

A type II error occurs when a null thesis isn't rejected despite it being incorrect. It's worth noting that the threat of making a type II error is affected by several factors, including the sample size, the true population mean, the position of significance, and the variability of the data.

As a result, the larger the sample size, the lower the threat of making a type IIerror.The true population mean also has an impact on the liability of a type II error. As the difference between the true mean and the hypothecated mean grows, the threat of a type II error decreases.

The position of significance is also pivotal in determining the threat of a type II error. As the significance position increases, the threat of a type II error decreases.

So, the correct answer is B

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Answer:

M expression:

3x^2/2

D expression:

3, 3/4 x^2, 2/3

Answer:

16404.2 feet

Step-by-step explanation:

1 in = 2.54 cm

1 km = 100000 cm

5 km = 100000*5 = 500000

1 feet = 12 in

500000 cm = 500000/2.54 = 196850.39 in  

196850.39 in = 196850.36 / 12 = 16404.2 feet

1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water

Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.

From the information given, we have that;

Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water

So, we have that there is 1 liter of water in the tub

In order to displace, you need to put something in that is the same amount

Now, let's convert the units

1 liter = 1000 cubic cm

Hence, you need 1000 cubic cm to displace 1 liter

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Answer:

Step-by-step explanation:

To find a second solution y2 for the differential equation (DE) y'' - 4y = 0 using the reduction of order method, we assume y2(x) takes the form y2(x) = v(x) * y1(x), where y1(x) = e^(-2x) is the known first solution.

Let's start by finding the derivatives of y2:

y2'(x) = v'(x) * y1(x) + v(x) * y1'(x)

y2''(x) = v''(x) * y1(x) + 2 * v'(x) * y1'(x) + v(x) * y1''(x)

Substituting these expressions into the original DE, we get:

v''(x) * y1(x) + 2 * v'(x) * y1'(x) + v(x) * y1''(x) - 4 * v(x) * y1(x) = 0

Since y1(x) = e^(-2x), y1''(x) = 4e^(-2x) and y1'(x) = -2e^(-2x), the equation becomes:

v''(x) * e^(-2x) - 4v(x) * e^(-2x) + 2v'(x) * e^(-2x) + 4v(x) * e^(-2x) = 0

Simplifying the equation further:

v''(x) * e^(-2x) + 2v'(x) * e^(-2x) = 0

Next, let's make a substitution u(x) = v'(x) * e^(-2x):

u'(x) = v''(x) * e^(-2x) - 2v'(x) * e^(-2x)

Plugging this into the equation, we get:

u'(x) + 2u(x) = 0

This is now a first-order linear homogeneous differential equation, which we can solve easily. Separating variables and integrating, we have:

∫(1/u) du = -2 ∫dx

ln|u| = -2x + C1

Solving for u, we get:

u(x) = C2e^(-2x)

Now, we can find v(x) by integrating u(x):

v(x) = ∫(u(x) / e^(-2x)) dx = ∫(C2e^(-2x) / e^(-2x)) dx = ∫C2 dx = C2x + C3

Finally, the second solution y2(x) is given by:

y2(x) = v(x) * y1(x) = (C2x + C3) * e^(-2x)

Therefore, the second solution to the DE y'' - 4y = 0 using the reduction of order method is y2(x) = (C2x + C3) * e^(-2x).

To solve the initial value problem (IVP) y'' - 5y' + 6y = 0, y(0) = 0, y'(0) = 1, we can use the method of characteristic equation.

First, let's find the characteristic equation by assuming a solution of the form y(x) = e^(rx):

r^2 - 5r + 6 = 0

Factoring the quadratic equation, we have:

(r - 2)(r - 3) = 0

So the roots are r1 = 2 and r2 = 3.

Since we have distinct real roots, the general solution for the homogeneous equation is given by:

y(x) = C1e^(2x) + C2e^(3x)

To find the particular solution for the IVP, we differentiate y(x) to find y'(x):

y'(x) = 2C1e^(2x) + 3C2e^(3x)

Now we substitute the initial conditions y(0) = 0 and y'(0) = 1 into the general solution and its derivative.

For y(0):

0 = C1e^(20) + C2e^(30)

0 = C1 + C2

For y'(0):

1 = 2C1e^(20) + 3C2e^(30)

1 = 2C1 + 3C2

We now have a system of equations:

C1 + C2 = 0

2C1 + 3C2 = 1

Solving this system of equations, we find C1 = 1 and C2 = -1.

Therefore, the particular solution for the IVP is:

y(x) = e^(2x) - e^(3x)

So the solution to the IVP y'' - 5y' + 6y = 0, y(0) = 0, y'(0) = 1 is y(x) = e^(2x) - e^(3x).

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The distance from the center of the valve to the line of action of the force is approximately d = 63.97 lb. and the angle between the line of action of the force and the x-axis is approximately  φ=-39.31°

To solve this problem, we can use the equations of equilibrium for a rigid body in two dimensions, which state that the sum of forces and the sum of moments acting on the body must be equal to zero.

First, let's draw a free body diagram of the valve and label the forces and moments acting on it:

       F

       |

       |

       |

--------o--------

    Mx   Mz

where F is the applied force, Mx and Mz are the moments, and o represents the center of the valve.

Next, we can write the equations of equilibrium for the valve:

ΣFx = 0: d + Fcosθ = 0

ΣFy = 0: -Fsinθ = 0

ΣMz = 0: Mz + Fdcosθ - Fdsinθ = 0

ΣMx = 0: Mx + Fdsinθ + Fdcosθ = 0

where d is the distance from the center of the valve to the line of action of the force, and φ is the angle between the line of action of the force and the x-axis.

Solving for d and φ, we get:

d = -Fcosθ = -70cos25° ≈ -63.97 lb

φ = arctan(Mx/(F + Mz)) = arctan(-61/(70 - 43)) ≈ -39.31°

Therefore, the distance from the center of the valve to the line of action of the force is approximately 63.97 lb, and the angle between the line of action of the force and the x-axis is approximately -39.31°.

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Answer: 40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

The sum of the lengths of the two longest altitudes in a triangle with sides 8, 12, and 14 would be \(12 + 14 = 26\) units.

In a triangle, the lengths of the two longest altitudes are equal to the lengths of the corresponding sides.

The sides in two different forms or polygons that are in the same position are said to have corresponding sides.

The two polygons have the same size and shape if they are congruent.

Congruence exists between the corresponding sides and angles.

So, the sum of the lengths of the two longest altitudes in a triangle with sides 8, 12, and 14 would be \(12 + 14 = 26\) units.

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The sum of the lengths of the two longest altitudes in the triangle with sides 8, 12, and 14 is 17 units.

The sum of the lengths of the two longest altitudes in a triangle can be found using the formula:

Sum of altitudes = (a + b + c) / 2

In this case, the sides of the triangle are given as 8, 12, and 14 units.

The longest altitude in a triangle is the altitude drawn from the longest side. So, we need to find the longest side in the given triangle.

To do that, we can arrange the sides in descending order: 14, 12, 8.

Now, we can use the formula to find the sum of the lengths of the two longest altitudes:

Sum of altitudes = (14 + 12 + 8) / 2 = 34 / 2 = 17 units

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To obtain the graph of g(x) = 4^(x+3) from the graph of f(x) = 4^x, several transformations can be applied.

First, there is a horizontal shift of 3 units to the left in the graph of g compared to f. This means that the entire graph of g is shifted to the left by three units.

Secondly, there is a vertical stretch in the graph of g compared to f. The base value of 4 remains the same, but the exponent (x+3) causes the function to be stretched vertically. This results in the graph of g being steeper than the graph of f.

The graph of g(x) = 4^(x+3) is obtained from the graph of f(x) = 4^x by shifting the graph three units to the left and vertically stretching it. These transformations alter the position and shape of the original graph to create the new graph.

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a) The value of z corresponding to an area of 0.1210 can be found using statistical tables or a statistical calculator.

b) Similarly, the value of z corresponding to an area of 0.9898 can be obtained using statistical tables or a statistical calculator.

c) To find the value of z at the 45th percentile, we can use the standard normal distribution table or a statistical calculator.

a) To find the value of z corresponding to an area of 0.1210, you can use a standard normal distribution table or a statistical calculator. By looking up the area of 0.1210 in the table, you can determine the corresponding z-value. For example, if you find that the z-value for an area of 0.1210 is -1.15, then -1.15 is the value of z corresponding to the given area.

b) Similarly, to find the value of z corresponding to an area of 0.9898, you can refer to a standard normal distribution table or use a statistical calculator. Find the z-value that corresponds to the area of 0.9898. For instance, if the z-value for an area of 0.9898 is 2.32, then 2.32 is the value of z corresponding to the given area.

c) To find the value of z at the 45th percentile, you can use a standard normal distribution table or a statistical calculator. The 45th percentile corresponds to an area of 0.4500. By finding the z-value for an area of 0.4500, you can determine the value of z at the 45th percentile. For example, if the z-value for an area of 0.4500 is 0.125, then 0.125 is the value of z at the 45th percentile.

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Based on the given graph, the following describes the polynomial function.

The function has an odd degree. (Option B)

The function has one turning point. (Option C)

The function does not have a negative leading coefficient since its leading coefficient is positive. It also has x-intercepts at x=-6, x=-2, x=4, and x=6, so the statement "the function has zero x-intercepts" is incorrect.

A polynomial function is a mathematical function that consists of one or more terms, where each term is a constant, a variable, or a product of a constant and a variable raised to a non-negative integer power.

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Answer:

7 days (counting the first day)

Step-by-step explanation:

1st you need to count the first day.

500 - 200 = 300.

300 divided by 50 is 6.

6 + 1 = 7

Answer:

63.0769230769

Step-by-step explanation:

Answer:

469 this was correct on Delta Math!!!

Step-by-step explanation:

The equation of the parabola is y = -3(x + 2)^2 + 6

How to determine the parabola equation?

From the graph, we have:

Vertex, (h,k) = (-2,6)

Point (x,y) = (-1,3)

A parabola is represented as:

y = a(x - h)^2 + k

Substitute (h,k) = (-2,6)

y = a(x + 2)^2 + 6

Substitute (x,y) = (-1,3)

3 = a(-1 + 2)^2 + 6

Evaluate

3 = a + 6

Subtract 6 from both sides

a = -3

Substitute a = -3 in y = a(x + 2)^2 + 6

y = -3(x + 2)^2 + 6

Hence, the equation of the parabola is y = -3(x + 2)^2 + 6

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Disclaimer: The question provided by you is incomplete, the above sloution is done as per a similar question which is attached as a image

Question : Write an equation of the parabola in vertex form. (-2, 6) (-1, 3)

An equation of the parabola is y=​

Answer:

----------------------------

The probability of rolling an even number on a single die is 3/6 or 1/2.

Consider the possible outcomes of rolling the two dice:

So, the only way to not have an even product is if both dice are odd.

The probability of rolling an odd number on a single die is also 1/2, so the probability of rolling two odd numbers is (1/2) x (1/2) = 1/4.

Therefore, the probability of rolling an even product is:

Answer:

66.6

Step-by-step explanation:

If 7 teachers for 252 student

We divide 468÷7= 66.6

66.6 teacher

Here you are

We have found a value of b that makes y(t) = \(e^2t\) [1; 4; -1/2] a solution of y′ = [4 1 3; 2 3 3; −2 −1 −1]y. To check if y(t) is a solution of y′ = Ay, we need to substitute it into the differential equation and see if it holds.

Let's start by finding y′:

y′(t) = [\(2e^2t, 8e^2t, 4be^2t\)]

Now, let's find Ay:

Ay = [4 1 3; 2 3 3; −2 −1 −1] [1; 4; b] = [4+4b; 14; -5-b]

We want y(t) = e^2t [1; 4; b] to satisfy y′ = Ay, so we set them equal:

y′ = Ay

[\(2e^2t; 8e^2t; 4be^2t] = [4+4b; 14; -5-b] e^2t\) [1; 4; b]

Expanding this equation, we get:

\(2e^2t\)= (4+4b)\(e^2t\)

\(8e^2t\) = 14 \(e^2t\)

\(4be^2t\)= (-5-b) \(e^2t\)

The second equation is always true, so we can ignore it. For the first equation, we can cancel out \(e^2t\) on both sides to get:

2 = 4+4b

Solving for b, we get:

b = -1/2

Finally, we can substitute b = -1/2 back into the third equation to check if it holds:

4be^2t = (-5-b) \(e^2t\)

-2e^2t = (-5 + 1/2)\(e^2t\)

This equation is true, so we have found a value of b that makes y(t) = \(e^2t\) [1; 4; -1/2] a solution of y′ = [4 1 3; 2 3 3; −2 −1 −1]y.

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