Point F is on line segment EG. Given FG = 3x - 5, EF = 2, and
EG = 5x – 8, determine the numerical length of FG.

Answer:

1÷y/-x

Step-by-step explanation:

1÷y/-x

1×-x/y

-x/y

The root diameter, also known as the minor diameter, is the smallest diameter of a thread. It is an important dimension in thread design and influences the fit and functionality of threaded connections.

In thread terminology, the root diameter refers to the smallest diameter of a threaded object. It is also known as the minor diameter or the base diameter. The root diameter is measured at the bottom of the thread grooves or valleys, where the threads meet the unthreaded portion of the object.

The minor diameter is an essential parameter in thread design and measurement. It determines the size of the internal thread or the mating external thread that will fit into it. It plays a crucial role in ensuring proper engagement and functionality of threaded connections. The root diameter is typically smaller than the major diameter, which is the largest diameter of the thread. The difference between the major diameter and the minor diameter determines the depth of the thread.

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Answer:

cos(A + B) = [tex]\frac{-3\sqrt{5}+1}{8}[/tex]

Step-by-step explanation:

Let us revise some rule of trigonometry

The sign of the trigonometry functions in the four quadrants

In the given question

→ Angle A is in the 4th quadrant

∵ sin(A) = -1/2

→ Use the 1st rule above to find cos(A)

∵ (-1/2)² + cos²(A) = 1

∴ 1/4 + cos²(A) = 1

→ Subtract 1/4 from both sides

∴ cos²(A) = 3/4

→ Take square root for both sides

∴ cos(A) = ±√(3/4)

→ In the 4th quadrant cos is a positive value

∴ cos(A) = (√3)/2

→ Angle B is in the 2nd quadrant

∵ sin(B) = 1/4

→ Use the 1st rule above to find cos(B)

∵ (1/4)² + cos²(B) = 1

∴ 1/16 + cos²(B) = 1

→ Subtract 1/16 from both sides

∴ cos²(B) = 15/16

→ Take square root for both sides

∴ cos(B) = ±√(15/16)

→ In the 2nd quadrant cos is a negative value

∴ cos(B) = (-√15)/4

Let us find the exact value of cos(A + B)

→ By using the 2nd rule above

∵ cos(A + B) = cos(A) cos(B) - sin(A) sin(B)

∴ cos(A + B) = [tex](\frac{\sqrt{3}}{2})(-\frac{\sqrt{15}}{4})-(-\frac{1}{2})(\frac{1}{4}) =-\frac{3\sqrt{5}}{8}+\frac{1}{8}[/tex]

∴ cos(A + B) = [tex]\frac{-3\sqrt{5}+1}{8}[/tex]

a.  The probability that she will pass all three tests is 0.2925.

b.  The probability that she will pass at least two of the three tests is 0.8150 (rounded to four decimal places).

To calculate the probability of passing all three tests, we need to multiply the probabilities of passing each individual test since the events are independent.

(a) Probability of passing all three tests:

P(passing test I) = 90% = 0.9

P(passing test II) = 65% = 0.65

P(passing test III) = 50% = 0.5

P(passing all three tests) = P(passing test I) * P(passing test II) * P(passing test III)

= 0.9 * 0.65 * 0.5

= 0.2925

Therefore, the probability that she will pass all three tests is 0.2925.

(b) To calculate the probability of passing at least two of the three tests, we can sum up the probabilities of passing exactly two tests and passing all three tests.

Probability of passing exactly two tests:

P(passing two tests) = [P(passing test I) * P(passing test II) * (1 - P(passing test III))] +

[P(passing test I) * (1 - P(passing test II)) * P(passing test III)] +

[(1 - P(passing test I)) * P(passing test II) * P(passing test III)]

P(passing two tests) = [0.9 * 0.65 * (1 - 0.5)] + [0.9 * (1 - 0.65) * 0.5] + [(1 - 0.9) * 0.65 * 0.5]

= 0.2925 + 0.1575 + 0.0725

= 0.5225

Probability of passing all three tests: 0.2925 (calculated in part (a))

P(passing at least two tests) = P(passing two tests) + P(passing all three tests)

= 0.5225 + 0.2925

= 0.8150

Therefore, the probability that she will pass at least two of the three tests is 0.8150 (rounded to four decimal places).

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Answer:

A and C

Step-by-step explanation:

A) Two squares with the same side lengths are always congruent

C) Two rhombuses with the same side lengths are always congruent.

Two geometric shapes are called congruent if they have the same size and the same shape.

Therefore the true statements are A and C.

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Answer:

<10

Step-by-step explanation:

The value of x is approximately 2.8462° and the value of maN is 37°.

To find the value of x and maN, we need to use the given information. According to the question, maN is equal to (13x)°.
To solve for x, we can set up an equation:
maN = (13x)°
Now, since we know that maN is equal to 37°, we can substitute this value into the equation:
37° = (13x)°
To isolate x, we divide both sides of the equation by 13:
37° / 13 = (13x)° / 13
This simplifies to:
2.8462° ≈ x°
Therefore, the value of x is approximately 2.8462°.
Now, let's find the value of maN. We already know that maN is equal to (13x)°. Substituting the value of x that we just found, we get:
maN = (13 * 2.8462)°
Simplifying the multiplication:
maN = 37°
So, the value of maN is 37°.
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The calculated values of w are w = -3 + 4i and w = 3 - 4i

From the question, we have the following parameters that can be used in our computation:

w = a + bi

Also, we have

[tex]\sqrt{-7 - 24i}[/tex]

This means that

[tex]a + bi = \sqrt{-7 - 24i}[/tex]

Square both sides

So, we have

(a + bi)² = -7 - 24i

Expand the exponent

a² + 2abi - b² = -7 - 24i

When both sides of the equation are compared, we have

a² - b² = -7

2ab = -24

When solved for a and b, we have

a = -3 and b = 4 or a = 3 and b = -4

Recall that

w = a + bi

So, we have

w = -3 + 4i and w = 3 - 4i

Hence, the values of w are w = -3 + 4i and w = 3 - 4i

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Solution

The two straightaway sections of the track are each 84.39 meters. The two semi-circular sections can be joined to form a circle whose radius is 36.5 meters and so the diameter of this circle is 2×36.5=73 meters. The circumference of this circle will be π×73 meters and so the total perimeter of the track is

2×84.39+π×73≈398.12.

So the perimeter of the track is less than 400 meters.

For the first lane on the track, the straightaway sections are each 84.39 meters long. However, the curved sections form a circle whose radius is now 36.5+1.22=37.72 meters. The diameter of the circle will be 2×37.72=75.44 meters. So the perimeter of lane 1 is

2×84.39+π×75.44≈405.78.

So the perimeter of lane 1 on the track is more than 400 meters and is almost 8 meters more than the perimeter of the inside of the track.

Suppose we let x denote the distance from the inside of lane 1 which gives a perimeter of 400 meters. This perimeter will be consist of the two straight sections which contribute 2×84.39 meters to the perimeter. In addition, there will be two semi-circular sections of radius 36.5+x meters. Combining these gives a circle whose diameter is 2×(36.5+x) meters. So we want

2×84.39+π×2×(36.5+x)=400.

Rewriting this we find

2π×x=400−2×84.39−2π×36.5

Solving for x we find

x≈0.30.

Note that this value for x is not exact but approximate. It is accurate to within about two ten thousandths of a meter or a fraction of a millimeter. So approximately 30 centimeters from the inside of lane 1 the perimeter of the track is 400 meters.

Approximately 30 meters from the inside border will someone run to make one lap equal exactly 400 meters .

Given,

Track length = 400 meters.

The two straightaway sections of the track are each 84.39 meters. The two semi-circular sections can be joined to form a circle whose radius is 36.5 meters and so the diameter of this circle is 2×36.5=73 meters. The circumference of this circle will be π×73 meters and so the total perimeter of the track is:

2×84.39+π×73≈398.12.

So the perimeter of the track is less than 400 meters.

For the first lane on the track, the straightaway sections are each 84.39 meters long. However, the curved sections form a circle whose radius is now 36.5+1.22=37.72 meters. The diameter of the circle will be 2×37.72=75.44 meters. So the perimeter of lane 1 is

2×84.39+π×75.44≈405.78.

So the perimeter of lane 1 on the track is more than 400 meters and is almost 8 meters more than the perimeter of the inside of the track.

Suppose we let x denote the distance from the inside of lane 1 which gives a perimeter of 400 meters. This perimeter will be consist of the two straight sections which contribute 2×84.39 meters to the perimeter. In addition, there will be two semi-circular sections of radius 36.5+x meters. Combining these gives a circle whose diameter is 2×(36.5+x) meters. So we want

2×84.39+π×2×(36.5+x)=400.

Rewriting this we find

2π×x=400−2×84.39−2π×36.5

Solving for x we find

x≈0.30.

So approximately 30 centimeters from the inside of lane 1 the perimeter of the track is 400 meters.

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Answer:

C)

The roots are 0,6, 3, and -11

Answer:

The answer is 66/3

Step-by-step explanation: I got it from khan academy

Answer:

37/18 pie in total, for individual see below

Step-by-step explanation:

kyle has 8/9 apple pie left

bobby has 1/6 of peach pie left

joanie has 2/3 of blueberry pie left

evie has 1/3 of cherry pie left

so in total: 8/9+1/6+2/3+1/3=19/18+1=37/18

Answer: V=pi*r^2

Step-by-step explanation:

Step-by-step explanation:

The following formula's can be used to find the volume, surface area, and lateral area of a cylinder.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Volume of a Cylinder}}\\\\V=\pi r^2 h\end{array}\right}[/tex]

Where:

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Surface Area of a Cylinder}}\\\\SA=2\pi rh+2 \pi r^2\end{array}\right}[/tex]

Where:

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Lateral Area of a Cylinder}}\\\\LA=2\pi rh\end{array}\right}[/tex]

Where:

The lateral area refers to the surface area excluding the top and bottom circular bases of the cylinder.

Answer:

$0.21 per year

Step-by-step explanation:

$0.21 times 5 years equals $1.05

So its $0.21

The annual rate of change is $0.21 per year

Cost of lunch in 2004 = $2.20

Cost of lunch in 2009 = $3.25

Difference in cost = $3.25 - $2.20 = $1.05

Number of years = 2009 - 2004 = 5 years

The annual rate of change will be:

= Difference in cost / Years taken

= $1.05/5

= $0.21 per year.

Therefore, the annual rate of change is $0.21 per year.

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Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

this is because

[tex]2=\frac{2}{1}[/tex]

and the reciprocal of this is [tex]\frac{1}{2}[/tex]

[tex]\frac{2}{1}[/tex] → [tex]\frac{1}{2}[/tex]

Answer:

a=6, b=3, c=pi

Step-by-step explanation:

Got it right on edge

Using sine function concepts, it is found that possible values for a, b and c are given by:

The standard sine function is given by:

[tex]y = a\sin{(bx + c)}[/tex]

In which:

In this problem:

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Answer:

C. 16

Step-by-step explanation:

y^2-z^2

(-5)^2-(-3)^2

25-9

16

Answer:

Step-by-step explanation:

y = - 5

y^2 = (-5)^2

y^2 = 25

z = - 3

z^2 = (-3)^2

z^2 = 9

y^2 - z^2 = 25 - 9 = 16

Answer:

The correct answer is that the slope is 32.

Step-by-step explanation:

Using the slope-intercept form, the slope is 32 .

a) E = UΣV^T, b) Generate a vector of independent standard normal random variables, z = (z1, z2)^T, c) x1 = μ + E^(1/2)z1, x2 = μ + E^(1/2)z2, d) the factor loading is the square root of 1.586 multiplied by the vector (0.924, -0.383), e) 1 - (0.924^2 * 1.586), f) X1 = μ1 + (factor loading for X1) * F1, X2 = μ2 + (factor loading for X2) * F2.

(a) The singular value decomposition (SVD) expression for the covariance matrix E can be written as: E = UΣV^T, where U is an orthogonal matrix consisting of the eigenvectors of E, Σ is a diagonal matrix with the square roots of the eigenvalues of E on the diagonal, and V^T denotes the transpose of the matrix V.

(b) To generate random vectors from the multivariate normal distribution N(0, E), where a = (0, 0)^T and E is given, you can follow these steps:

1. Compute the matrix square root of E, denoted as E^(1/2), by performing the eigenvalue decomposition of E: E = QΛQ^T, where Q is a matrix of the eigenvectors of E and Λ is a diagonal matrix with the eigenvalues of E on the diagonal.

2. Generate a vector of independent standard normal random variables, z = (z1, z2)^T.

3. Compute the random vector x = μ + E^(1/2)z, where μ is the mean vector (0, 0)^T.

(c) Using the provided N(0, 1) random numbers (-0.626, 0.184, -0.836, 1.5), and assuming these correspond to z1, z2, z3, and z4 respectively:

1. Take the first two values (-0.626 and 0.184) as z1 and z2, and compute the random vector x1 = μ + E^(1/2)z1.

2. Take the next two values (-0.836 and 1.5) as z3 and z4, and compute the random vector x2 = μ + E^(1/2)z2.

(d) When using only the second eigenvalue and eigenvector (A2 and e2) for factor analysis, the factor loadings can be calculated as the square root of the eigenvalue multiplied by the corresponding eigenvector. In this case, the factor loading is the square root of 1.586 multiplied by the vector (0.924, -0.383).

(e) The specific variances for the two random variables can be obtained by subtracting the squared factor loadings from their respective eigenvalues. For the first random variable (X1), the specific variance is 4 - (0.383^2 * 1.586). For the second random variable (X2), the specific variance is 1 - (0.924^2 * 1.586).

(f) The random variables X1 and X2 can be expressed in terms of the obtained factor loadings as:

X1 = μ1 + (factor loading for X1) * F1,

X2 = μ2 + (factor loading for X2) * F2,

where μ1 and μ2 are the means of X1 and X2 respectively, and F1 and F2 are the latent factors associated with X1 and X2, respectively.

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The geometric average of -17%, 30%, and 35% is option c) 13.36%.

To find the geometric average, we multiply the values together and then take the nth root, where n is the number of values.

For the given percentages -17%, 30%, and 35%, we calculate the geometric average as follows:

Geometric Average = (1 + (-0.17))(1 + 0.30)(1 + 0.35)^(1/3) - 1

Simplifying the expression:

Geometric Average = (0.83)(1.30)(1.35)^(1/3) - 1

Calculating further:

Geometric Average ≈ 1.1336 - 1 ≈ 0.1336

Converting to percentage:

Geometric Average ≈ 0.1336 * 100 ≈ 13.36%

Therefore, the geometric average of -17%, 30%, and 35% is approximately 13.36%, corresponding to option c).

The geometric average is useful for calculating the average rate of change over multiple periods. It takes into account the compounding effect of successive percentage changes. It is important to note that the geometric average is different from the arithmetic average, which is calculated by summing the values and dividing by the number of values.

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Answer:

0

Step-by-step explanation:

The probability that at least one child will inherit the hereditary disease is approximately 16.9%.

To calculate the probability that at least one child will inherit the hereditary disease, we can use the concept of complementary probabilities.

The probability of the event "at least one child inherits the disease" is equal to 1 minus the probability that none of the children inherit the disease.

The probability that a child does not inherit the disease is 1 minus the probability that they do inherit the disease, which means it is 1 - 0.06 = 0.94.

Since the couple plans to have three children, we multiply the probability of not inheriting the disease for each child:

Probability of none of the children inheriting the disease = 0.94^3 = 0.830584.

Finally, we subtract this value from 1 to get the probability of at least one child inheriting the disease:

Probability of at least one child inheriting the disease = 1 - 0.830584 = 0.169416 or 16.9% (rounded to one decimal place).

Therefore, the probability that at least one child will inherit the hereditary disease is approximately 16.9%.

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Answer:

m = -1

y-int (0, 5)

General Formulas and Concepts:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

The y-intercept is the y value when x = 0.

Another way to reword that is when the graph crosses the y-axis.

Step-by-step explanation:

Step 1: Define equation

y = -x + 5

Step 2: Define parts

Slope m = -1

y-intercept = 5

Answer:

Step-by-step explanation:

Find the required figure in the attachment. From the figure, <A = <B (alternate interior angle)

Given

∠A=6x+5

∠B=4x+45

Since <A = <B hence;

6x+5 = 4x+45

Collect the like terms

6x-4x = 45-5

2x = 40

Divide both sides by 2;

2x/2 = 40/2

x = 20

Hence the value of x is 20°

Next is to get the measure of <A

Since <A = 6x+5

Substitute x = 20° into the expression

<A = 6(20)+6

<A = 120+6

<A = 126°

Hence the measure of <A is 126°

Answer:

125

Step-by-step explanation:

It's right on khan

Answer:

[tex]\huge{\bold{\boxed{\sf{x = 8 }}}}[/tex]

Step-by-step explanation:

[tex]6.5x - 10 = 4.5x + 6[/tex]

Move 4.5x to left hand side and change its sign.

Similarly, move 10 to right hand side and change its sign.

⇒[tex]6.5x - 4.5x = 6 + 10[/tex]

Subtract 4.5x from 6.5x

⇒[tex]2x = 6 + 10[/tex]

Add the numbers: 6 and 10

⇒[tex]2x = 16[/tex]

Divide both sides by 2

⇒[tex]\frac{2x}{2} = \frac{16}{2}[/tex]

Calculate

⇒[tex]\boxed{\sf{ x = 8 }}[/tex]

Hope I helped!

Best regards!

~[tex]\sf{TheAnimeGirl}[/tex]

Answer:

m < -(1/4)

Step-by-step explanation:

4(2m + 3)-7 < 3

8m + 12 - 7 < 3

8m + 5 < 3

8m < -2

m < -(1/4)

The correct solution is m < -1/4, which is not among the provided options.

To find the solution to the inequality 4(2m + 3) - 7 < 3, let's solve it step by step.

First, we simplify the left side of the inequality:

4(2m + 3) - 7 < 3

8m + 12 - 7 < 3

8m + 5 < 3

Next, we isolate the variable term by subtracting 5 from both sides:

8m + 5 - 5 < 3 - 5

8m < -2

To solve for m, we divide both sides of the inequality by 8:

(8m)/8 < (-2)/8

m < -1/4

So, the correct solution to the inequality is m < -1/4.

Comparing the options provided:

A. m > -1: This option is not correct because the solution to the inequality is m < -1/4, not m > -1.

B. m < 1: This option is not correct because the solution is m < -1/4, not m < 1.

C. m > 8: This option is not correct because the solution is m < -1/4, not m > 8.

D. m < 8: This option is not correct because the correct solution is m < -1/4, not m < 8.

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Step-by-step explanation:

it may help you to understand.

Answer:

the last one is -4 the first one -2 I think

Step-by-step explanation:

im at this level of math

Answer:

X=16

Step-by-step explanation:

Solving for variable 'x'.

Add '-6x' to each side of the equation.

20 + 4x + -6x = -12 + 6x + -6x

Combine like terms: 4x + -6x = -2x

20 + -2x = -12 + 6x + -6x

Combine like terms: 6x + -6x = 0

20 + -2x = -12 + 0

20 + -2x = -12

Add '-20' to each side of the equation.

20 + -20 + -2x = -12 + -20

Combine like terms: 20 + -20 = 0

0 + -2x = -12 + -20

-2x = -12 + -20

Combine like terms: -12 + -20 = -32

-2x = -32

Divide each side by '-2'.

x = 16

Simplifying

x = 16

Answer:

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]

From the question the points are

(1, -3) and (3, -5)

The slope is

[tex]m = \frac{ - 5 - - 3}{3 - 1} = \frac{ - 5 + 3}{2} = - \frac{2}{2} = - 1 \\ [/tex]

We have the final answer as

Hope this helps you

Answer:

3 and negative 5

Step-by-step explanation: