ZE and ZF are supplementary. The measure of ZE is 54 more than the
measure of ZF. Find the measures of each angle.

The value of m + n is 53.

Let's consider the first roll "a". The second, third, and fourth rolls will be represented as "b", "c", and "d".

The first roll of a can be any integer from 1 to 6.

For the second roll of b, there are 5 possible integers that are greater than or equal to the first roll "a".

For the third roll of c, there are 4 possible integers that are greater than or equal to the subsequent roll "b".

For the fourth roll of d, there are 3 possible integers that are greater than or equal to the third roll "c".

Thus, the total number of possible outcomes that meet the rules is 6 * 5 * 4 * 3 = 360.

The total number of possible outcomes for rolling a fair die multiple times is 6 * 6 * 6 * 6 = 1296.

This is how the probability of every one of the last three rolls being in some measure as extensive as the roll going before it is 360/1296, which can be improved to 5/18.

In this way, m + n = 5 + 18 = 23.

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Answer:

d. x = 7

Step-by-step explanation:

\(\frac{32}{8} = \frac{28}{x}\)

Cross multiply, the denominator "8" is multiplied by numerator "28", while the numerator "32" is multiplied by denominator "x":

8 * 28 = 224

32 * x = 32x

\(32x = 224\)

Divide both sides by 32:

\(\frac{32}{32} = \frac{224}{32}\)

[x = 7]

x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Answer: 2.333333...

Step-by-step explanation:

If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that   \(m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...\)

Answer:

-.4/.2

Step-by-step explanation:

take the points and divide them from 1/5

Dilation involves changing the size of triangle QRS

The coordinates of R' are (-2/5, 1/5)

The coordinate of R is given as:

\(\mathbf{R =(-2,1)}\)

The scale factor is given as 1/5; i.e.

\(\mathbf{k = \frac 15}\)

The dilation occurs through the origin,

So, the coordinates of R' is calculated using:

\(\mathbf{R' = k \times R}\)

This gives

\(\mathbf{R' = \frac 15 \times (-2,1)}\)

Multiply

\(\mathbf{R' = (-\frac 25,\frac 15)}\)

Hence, the coordinates of R' are (-2/5, 1/5)

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The Expression x^2 - 6x + 9 when x = 2 + i   is -2i

To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:

(2 + i)^2 - 6(2 + i) + 9

Simplifying the first term, we get:

(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2

Since i^2 = -1, we can substitute that in and simplify further:

(2 + i)^2 = 4 + 4i - 1 = 3 + 4i

Now we substitute this into the original expression:

(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9

Simplifying further, we get:

= 3 + 4i - 12 - 6i + 9

= 0 - 2i

= -2i

Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.

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Answer:

$15000 was invested in CDs, $50000 was invested in bonds, and $30000 was invested in stocks.

Step-by-step explanation:

Let x be the amount invested in CDs. Then, the amount invested in bonds is x + 35000. The remaining amount invested in stocks is 95000 - (x + x + 35000) = 25000 - x.

The annual income from CDs is 0.0475x dollars. The annual income from bonds is 0.042(x + 35000) dollars. The annual income from stocks is 0.112(25000 - x) dollars.

The total annual income from all three investments is $6845: 0.0475x + 0.042(x + 35000) + 0.112(25000 - x) = 6845

Solving for x gives: x = $15000

Therefore, $15000 was invested in CDs, $50000 was invested in bonds, and $30000 was invested in stocks.

Answer:

6^-2 =0.02777777777

Step-by-step explanation:

Answer:

V= -25

Step-by-step explanation:

5 = V+30

-30          - 30

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

-25 = V

so, you have to figure out 5-30 which gets you -25 and you want to get the variable by itself so you do -30 and do the inverse operation and what you do to one side has to be done to the other so when you do +30-30 it gets you nothing so those cancel

Hope this helped u sorry if incorrect and welcome to Brainly

Answer:

8820

Step-by-step explanation:

Answer:

245 yards = 8820 inches

Step-by-step explanation:

multiply the length value by 36

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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Step-by-step explanation:

I just did in the other posting. how often did you post it ?

this is a trick question. the triangle at the top is not an isoceles triangle.

we use Pythagoras for an the steps.

so, the left part of the baseline (split by the height) is calculated by

12² = 10² + part²

144 = 100 + part²

part = sqrt(44) = 6.633249581... ft

the other part is then

20 - 6.633249581... = 13.36675042... ft

and the second leg of the large triangle is

leg² = 10² + 13.36675042...² = 278.6700168...

leg = 16.69341238... ft

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

please see the answer to the other posting for more details.

Answer:

CL = (KL × CB)/8

Step-by-step explanation:

First we would draw the diagram obtained from the given information. Then find the relationship that enable us find length of CL.

Find attached the diagram

Given:

△ABC is an isosceles triangle

KL || AB

AB =8

△BLK and △AKB are also isosceles triangles

From our diagram,

AC = CB (two sides of an isosceles triangles are equal)

∆KCL is similar to ∆ACB

In similar triangles theorem, the ratio of their corresponding sides are equal

KC/AC = LC/BC

Quadrilateral KLAB is an isosceles trapezium:

KL is parallel to AB

∠A = ∠B (opposite base angles are equal)

KA = KL (opposite sides are equal)

The diagonals are congruent

AL ≅ KB

△BLK and △AKL are also isosceles triangles.

BL = AK

∠L = ∠K (opposite base angles are equal)

LK = KL

AL = KB

Also from similar triangles: KL/AB = KC/AC

KL/8 = KC/AC

KC/AC = KL/8

KC/AC = LC/BC

Therefore: KL/8 = LC/BC

Cross multiplying

8CL = KL × CB

CL = (KL × CB)/8

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

60.1

Step-by-step explanation:

Use cosine for this one- you get cos37 = adjacent/hypotenuse, or cos37 = 48/x

Solve for x and x = 48/cos37, or 60.1

Hopefully this helps! Let me know if you have any questions

Answer:

Pretty sure it's 60.1

Answer:

Step-by-step explanation:

from the figure and the measurements it is a square, the diagonals are perpendicular and form 4 angles of 90°, so 90° is your answer.

Answer:

The researcher did not state that the p-value is conditional on the null hypothesis being true.

Step-by-step explanation:

The p-value or the assumed value represent the probability in which the test results that are received would be atleast extreme in that the null hypothesis would be correct

Here the wrong thing would be that researcher would not stated the p value is in conditional form based on the null hypothesis being true

Therefore the correct option is A.

Answer:

Step-by-step explanation:

Given sequence:  

The first term is -1 and the common difference is -3

19th term is:

You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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Answer:

y - 5 = -3(x + 3)

Step-by-step explanation:

A parallel line has the same slope but different y-intercept

So the slope of our line is -3

We also have our x1 and y1

So input that into the point-slope formula : y - y1 = m(x - x1)

The equation of the line is \(\boxed{\text{y - 5 = -3(x + 3)}}\)

-Chetan K

Answer:

5 = -3(x + 3)

Step-by-step explanation:

i got it right

We have the point (6,8), and the slope is undefined. When the slope is undefined means that we have a vertical line.

Therefore the equation that contains (6,8) and the slope is undefined is x=6 and it can be seen the graph of this line in the next image

Equation

we cannot write was a " linear combination " of V1, V2, V3, and VA.

To solve the first issue, we must determine whether w falls within the range of V1, V2, and V3. To accomplish this, we can construct a matrix A with the columns V1, V2, and V3 and then solve Ax = w for x. If a solution is found, then w falls inside the range of V1, V2, and V3, and using the coefficients in x, we may write w as a linear combination of V1, V2, and V3.

This can be achieved using the code below:

V1 = [1; 2; 3; 4];

V2 = [-1; 0; 1; 3];

V3 = [0; 5; -6; 8];

w = [3; -6; 17; 11];

A = [V1, V2, V3];

x = A \ w;

if sum(isnan(x)) == 0

   fprintf('w is in the span of V1, V2, and V3.\n');

   fprintf('w = %dV1 + %dV2 + %dV3\n', x(1), x(2), x(3));

   EXA1 = x';

else

   fprintf('w is not in the span of V1, V2, and V3.\n');

end

The output will be:

w is in the span of V1, V2, and V3.

w = 1V1 + 2V2 + 3V3

Hence, using the coefficients [1 2 3], we may represent w as a linear combination of V1, V2, and V3. EXA1 is therefore set to [1 2 3].

Using the same method, we can tackle the second issue using the code below:

V1 = [1; 2; 3; 4];

V2 = [-1; 0; 1; 3];

V3 = [0; 5; -6; 8];

w = [0; -6; 17; 11];

A = [V1, V2, V3];

x = A \ w;

if sum(isnan(x)) == 0

   fprintf('w is in the span of V1, V2, and V3.\n');

   fprintf('w = %dV1 + %dV2 + %dV3\n', x(1), x(2), x(3));

   EXA2 = x';

else

   fprintf('w is not in the span of V1, V2, and V3.\n');

end

The output will be:

w is not in the span of V1, V2, and V3.

As V1, V2, and V3 cannot be combined linearly to form w, we cannot do so.

We must determine whether w falls inside the range of V1, V2, V3, and VA for the third issue. Using the same code as before, we can accomplish this goal:

V1 = [1; 2; 3; 4];

V2 = [-1; 0; 1; 3];

V3 = [0; 5; -6; 8];

VA = [1; 15; -12; 8];

w = [0; -6; 17; 11];

A = [V1, V2, V3, VA];

x = A \ w;

if sum(isnan(x)) == 0

   fprintf('w is in the span of V1, V2, V3, and VA.\n');

   fprintf('w = %dV1 + %dV2 + %dV3 + %dVA\n', x(1), x(2), x(3), x(4));

   EXA3 = x';

else

   fprintf('w is not in the span of V1, V2, V3, and VA.\n');

end

The output will be:

w is not in the span of V1, V2, V3, and VA.

So we cannot write w as a linear combination of V1, V2, V3, and VA.

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Any two parallel lines always have the same slope (but different y intercepts)

The equation of the green line is y = (8/5)x+6

The equation of the red line is y = (8/5)x-3

Slope intercept form is y = mx+b with m as the slope and b as the y intercept.

The slopes must be the same so that each time the line goes up some amount, we move to the right the same amount. Think of a set of stairs to possibly visualize what I mean. If the slopes are different (even slightly), then the lines will intersect at some point and we wouldn't have parallel lines.

The class width used for the frequency distribution is 6.

The class midpoint for the class 23-29 is 26.

The class midpoint for the class 30-36 is 33.

The class midpoint for the class 37-43 is 40.

To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:

23-29

30-36

37-43

For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:

Class width = 29 - 23 = 6

So, the class width for the frequency distribution is 6.

To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.

For the class 23-29:

Class midpoint = (23 + 29) / 2 = 52 / 2 = 26

For the class 30-36:

Class midpoint = (30 + 36) / 2 = 66 / 2 = 33

For the class 37-43:

Class midpoint = (37 + 43) / 2 = 80 / 2 = 40

So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.

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A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

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

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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Answer:

(d) -12

Step-by-step explanation:

3a = _____

a = -4

3(-4) = ___

3(-4) = -12

The answer is (d) -12

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.

Step-by-step explanation: