Convert into log form
a^b = c

The measure of angle C is obtained as 35 degrees

Give that;

b^2 = a^2 + c^2 - 2ac Cos B

a = 29

c = 24

B = 101 degrees

b^2 = (29)^2 + (24)^2 - [2 * 29 * 24 cos 101]

b^2 = 841 + 576 + 266

b = 41 cm

Now;

b/sinB = c/sinC

bsinC = csinB

sinC = csinB/b

sinC =  24 * sin 101/41

C = sin-1(24 * sin 101/41)

C = 35 degrees

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Answer:

Θ ≈ 58°

Step-by-step explanation:

using the Cosine Rule in the triangle

cosΘ = [tex]\frac{80^2+60^2-70^2}{2(80)(60)}[/tex] = [tex]\frac{64000+3600-4900}{9600}[/tex] = [tex]\frac{5100}{9600}[/tex] = [tex]\frac{51}{96}[/tex] , then

Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{51}{96}[/tex] ) ≈ 58° ( to the nearest degree )

the PERT weighted average is 9 days

PERT can be defined as an estimating technique that uses a weighted average of three numbers to get a final estimate.

The formula for finding the PERT weighted average is given as;

PERT weighted average = (Optimistic + (4 X Most Likely) + Pessimistic)/6

We have;

Substitute the values into the formula

PERT weighted average  = [tex]\frac{6 + 4(8) + 16 }{6}[/tex]

PERT weighted average  = [tex]\frac{54}{6}[/tex]

PERT weighted average  = 9 days

Thus, the PERT weighted average is 9 days

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A cross-section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base square, triangle, and, trapezoid.

A cross-section parallel to the base will be a square.

One perpendicular to the base will be a trapezoid, or if it passes through the vertex of the pyramid, a triangle.

Hence, a cross-section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base square, triangle, and, trapezoid.

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A parallelogram is a quadrilateral in which opposite sides are equal, and the opposite angles sum up [tex]180^{o}[/tex]. Thus, the measures of the two different angles in the question are 70° and 110° i.e option D.

A parallelogram is a quadrilateral in which opposite sides are equal, and the opposite angles sum up [tex]180^{o}[/tex]. It has four straight sides and can be classified as a quadrilateral.

Thus from the given question, we have:

(6n − 70)° + (2n + 10)° =  [tex]180^{o}[/tex]

8n - 60 =  [tex]180^{o}[/tex]

8n =  [tex]180^{o}[/tex] + 60

8n = 240

n = [tex]\frac{240}{8}[/tex]

  = [tex]30^{o}[/tex]

n = [tex]30^{o}[/tex]

So that,

i. (6n − 70)° = (6[30] − 70)°

                = 180 - 70

                = [tex]110^{o}[/tex]

ii. (2n + 10)° = (2[30] + 10)°

                  = 60 + 10

                  = [tex]70^{o}[/tex]

Therefore, the measures of the two different angles are 70° and 110°. Option D.

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Answer:

b, 50° and 130°

Step-by-step explanation:

edge 2023 :)

^ that shi sucks btw we needa boycott the program or smt

Answer:

28.5 ft²

Step-by-step explanation:

shaded area = area of triangle minus area of rectangle

shaded area = (1/2)bh - LW

base of triangle = 5 ft + 4 ft = 9 ft

height of triangle = 3 ft + 6 ft = 9 ft

shaded area = (1/2)(9 ft)(9 ft) - (4 ft)(3 ft)

shaded area = 40.5 ft² - 12 ft²

shaded area = 28.5 ft²

The measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.

A triangle with two sides and angles of equal length and degrees is an isosceles triangle.

Acute Triangle:-

A triangle whose all angels are greater than and less than 90° i.e., all angels are acute is called an acute triangle.

Therefore, all the three angles are less than 90 degrees and two angles are equal.

If one angle is 36 degrees, the other two angles will be 72 degrees each.

If the two angles are 36 degrees each, the last angle will be 108 degrees. 108 degrees is greater than 90 degrees..

Therefore, the angles will be 36°, 36° and 72°.

Hence, the measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.

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Percentage for lakeside is 38%

Percentage for Jungle is 26%

Percentage for Desert is 18%

Percentage for Coast is 12%

Percentage for Prairie is 6%

To determine the percentage, divide the given value by the total number and multiply by 100

Total  = 24000

Percentage for lakeside = [tex]\frac{9120}{24000}[/tex] × 100

% of lakeside = [tex]0. 38[/tex] × 100 = 38%

Percentage for Jungle = [tex]\frac{6240}{24000}[/tex] × 100

% of Jungle = [tex]0. 26[/tex] × 100 = 26%

Percentage for Desert = [tex]\frac{4320}{24000}[/tex] × 100

% of Desert = [tex]0. 18[/tex] × 100 = 18%

Percentage for Coast = [tex]\frac{2880}{24000}[/tex] × 100

% of coast = [tex]0. 12[/tex] × 100 = 12%

Percentage for Prairie = [tex]\frac{1440}{24000}[/tex] × 100

% of Prairie = [tex]0. 06[/tex] × 100 = 6%

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Answer:

(x + 3)^2 + (y - 2)^2 = 25 .

Step-by-step explanation:

The center is at (-3, 2) and the radius is 5.

General form is

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

So here we have:

(x  - (-3)^2 + (y - 2)^2 = 5^2

(x + 3)^2 + (y - 2)^2 = 25

The graph of the exponential function f(x) = 5(2)ˣ is as shown in the attached file.

We want to draw the graph of the exponential function;

f(x) = 5(2)ˣ

At input of x = 0, we have;

f(x) = 5(2)⁰ = 5

At input of x = 1, we have;

f(x) = 5(2)¹ = 10

At x = -1, we have;

f(x) = 5(2)⁻¹ = 2.5

At x = -2, we have;

f(x) = 5(2)⁻² = 1.25

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The data is significant at a significance level of 0.01 indicating that the average mass of apples in a farmer's orchard differs from 100g to a level of 0.01. Option C is correct.

Given as the farmer states that the average mass of an apple grown in his orchard is 100g, he measures the mass of 150 apples grown in his orchard and finds that the average mass per apple is 98g and the results are calculated as statistically significant at the 0.01 level.

The null hypothesis is:

H₀ = 100

Because of the farmer's claim.

The alternative hypothesis is:

H₁ ≠ 100

The alternative hypothesis tests the farmer's claim at a level of significance. Results are calculated as statistically significant at the 0.01 level.

This means that at the 0.01 level, the null hypothesis is rejected, i.e. H the average mass of the farmer's orchard differs from 100. Since it is significant at the 0.01 level, it will be significant at the 0.05, 0.1 and increasing levels.

Thus, at the significance level of 0.01, the average mass of apples grown in the farmer's orchard differs by 100 g. The correct answer is therefore given by option C.

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The display that would best show the measures of variation of the given prices is; B: Box and Whisker Plot

We are given the prices of Phone chargers in a store as;

$19, $18, $15, $17, $19, $12, $19, and $15.

Now, since we want to determine the display that would best show the measures of variation, the best display would be a box and whisker plot. This is because Box and Whisker plots are a great chart to use when showing the distribution of data points across a selected measure. These  box and whisker plots display ranges within variables measured.

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Answer:

Yes,

Common ratio = 5.

Step-by-step explanation:

If its geometric it will have a common ratio.

5/1 = 5

25/5 = 5

125/25 = 5

So its geometric with commo ratio 5.

See

The point D is

3 units left from origin

1 units up from origin

The point is

Direct variation

Multiply k=2

Option A

n/3n - 2.

The denominator of the given simplified expression is

The given expression is ( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 )

To find the denominator of the simplified expression :

First, simplify the given expression as below ;

( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 )

( 2n/2₍₃ₙ ₊ ₂₎ ( 3n + 2/ 3n - 2 )  ( here by taking the common term 2 outside the factor )

= (n/1) ( 1/ 3n - 2 ) ( here by simplifying the factors )

= n/3n - 2.

Therefore, ( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 ) = n/3n - 2

Therefore the result of the given simplified expression is = n/3n - 2.

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Based on the given inequality; x < 9 or x ≥ 14, the possible values of x are $8 and $14

x < 9 or x ≥ 14

From the options

All values less than 9 are

$8

All values greater than or equal to 14 are

$14

Therefore, based on the options given, the possible values of x are $8 and $14

Complete question:

The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Check all that apply. $8 $9 $11 $13 $14 $15

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Answer:

15.7 square feet

Step-by-step explanation:

To find the area of the garden we find the area of the rectangle and the area of the semicircle.

The area of the rectangle:

A=bh

A=(29)(20)

A=580ft^2

As shown in the picture, the width of the rectangle is 20 ft wide, which means that the diameter of the semicircle is also 20ft wide. The diameter is two times the radius, which means the radius of the semicircle is 10ft.

The area of a circle is represented by the equation: [tex]A=\pi r^{2}[/tex]

A semicircle is half of a circle, therefore the equation to find the area of a semicircle is: [tex]A=\frac{1}{2}\pi r^{2}[/tex]

Plugging our radius of 10ft in we get:

[tex]A=\frac{1}{2}\pi (10)\\ A=5\pi[/tex]

We use 3.14 for our value of [tex]\pi[/tex] to get:

[tex]A=5(3.14)\\A=15.7ft^{2}[/tex]

Therefore, the area of the rose garden is 15.7 square feet.

Answer:

x-3

Step-by-step explanation:

Laura's age goes first. You don't know what it is, so you have to leave it as x. You know Jeri is 3 years younger, so you subtract from x.

1) [tex]\overline{WX} \cong \overline{UY}[/tex], [tex]\angle YXZ \cong \angle XYZ[/tex] (given)

2) [tex]\overline{XY} \perp \overline{XY}[/tex] (reflexive property)

3) [tex]\triangle WXY \cong \triangle UYX[/tex] (SAS)

4) [tex]\overline{WY} \perp\overline{ UX}[/tex] (CPCTC)

Answer:

x/8 gallons.

Step-by-step explanation:

The 8 containers have the larger capacity as the 2 totals are x and the other containers are 16 in total.

Capacity of each of the large containers = x/8 gallons.

Answer:

[tex]140in {}^{3} [/tex]

Step-by-step explanation:

Substituting values of B and h into the Formular.

[tex]v = \frac{bh}{3} \\ v = \frac{15 \times 28}{3} = 140in {}^{3} [/tex]

Answer:

a = -1

Step-by-step explanation:

1. Subtract [tex]\frac{2}{3}[/tex] from both sides.

[tex]6a=-\frac{16}{3} - \frac{2}{3}[/tex]

2. Solve the side after the equal sign.

[tex]6a=-6[/tex]

3. Divide 6 from both sides.

[tex]a=-1[/tex]

4. Hope this helped!

[tex]:)[/tex]

The value of a + b + c based on the product formula is 8.

From the information given, the product of the proper divisor is illustrated.

Based on the information, the addition of the symbols will be:

= a + b + c

= 3 + 3 + 2

= 8

In conclusion, the correct option is 8.

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Answer:

Bet $100 and remove all non-face cards.

Step-by-step explanation:

Each option may be answered on the basis of the ratio of face cards to non-face cards, which we'll say is R.

a. removing all of the black cards  No.  The vale of R does not change.  R is the same for both black and red cards, so removing one color does not change R.

b. removing all non-face cards  Yes.  The only cards left are face cards.  The odds of drawing 2 face cards in a row from this modified deck is 100%

c. removing all kings  No.  Face cards are being removed and will thus lower the probability of picking one.

d. removing all of the red cards  No.  Same reasoning as in (a.).

The translation that represents T–4, 6(x, y) is (b) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up

The translation rule is given as:

T–4, 6(x, y)

This can be rewritten as

T(x- 4, y + 6)

The above represents a translation 4 units left and 6 units up

Hence, the translation that represents T–4, 6(x, y) is (b) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up

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The steps that can be used to increase the ball is:

Scale factor = [tex]\frac{Scale diagram}{Original}[/tex]

This refers to the measure for similar figures that is used to show the scale through which a figure is bigger or smaller than another.

Hence, we can see that from the given image, one can increase the size of the ball by making use of the scale factor which measures the scale diagram and then divides it from the original and this would retain the dimension but would make it larger.

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Answer:

39

Step-by-step explanation:

I assume the father's age is a 2-digit number. He is not 9 years old or younger, and he is not 100 years old or older.

The sum of the digits of a two-digit number goes up by 1 from one number to the next unless the number ends in 9.

For example, from 17 to 18, the sum of the digits goes from 8 to 9.

If the number ends in 9, for example, 29, the digits add to 11. Then the next number is 30, and now the sum of the digits is 3, which is less than 11.

The father's age now is a number whose sum of digits is not only greater than the sum of the digits next year, but it is 3 times greater.

Let's look at 2-digit number and the next number and the sum of their digits.

19, 20; sums: 10, 2; 10/2 = 5, not 3

29, 30; sums: 11, 3; 11/3 ≠ 3

39, 40; sums: 12, 4; 12/4 = 3

Answer: The father is 39 years old.

Answer: 39 years

Step-by-step explanation:

The father says that adding both of the digits in his age will be 3 times greater than adding both digits one year later. Before we even start answering the problem, this tells us that the father's age has 2 digits in it.

Let's represent the 10's digit with x, and the 1's digit with y. If the father's age was 45, for example, x would be 4 and y would be 5.

Let's first make an equation to represent this situation:

The sum of the digits of the father's age would be represented by x + y, as x and y are the 10's digit and 1's digit respectively.

The father's age next year would be one greater than the current year, which makes y become y + 1. Then, the sum of the digits would be x + y + 1.

Now, we must make the first equation 3 times larger than the second and solve for the sum.

[tex]x + y = 3(x+y+1)\\ x+y=3(x+y)+3\\ 1(x+y)-3(x+y)=3\\ -2(x+y)=3\\ x+y=\frac{3}{-2}=-\frac{3}{2}[/tex]

However, we can neither have a fraction or a negative as a sum of two digits in an age, as digits are always positive integers from 0 to 9.

This flaw came from the assumption that after 1 year, the sum of the digits will be x + y + 1. This isn't always true, as any number with its 1's digit of 9 turns into 0 the next year, and not 10. Instead, the x value increases by 1.

For example, someone the age 69 becomes 70 the next year, x increases by 1 and y becomes 0.

Let's make a new equation to try and see this.

We know that his current age has to have y = 9 for his new age to be y = 0. Therefore, the current sum of digits is x + 9.

The next year, we know that the 10's place will increase by 1 and the 1's place becomes 0. Therefore the sum of digits is x + 1 + 0, or x + 1.

Since the current sum of digits is 3 times greater than the sum next year, let's multiply the second equation by 3 to get equality. We just need to calculate the 10's digit, as the 1's digit is already 9.

[tex]x+9 = 3(x+1)\\ x+9=3x+3\\ 9=2x+3\\ 6=2x\\ x=3[/tex]

Since the 10's digit (or x) is 3 and the 1's digit (or y) is 9, the father's age is 39, and he will turn 40 next year.

New mean is 2.53% larger than the original mean.

What is mean?

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.

We can find the percentage larger is the mean of the new list in comparison with the original as shown below:

Given, set of number 55, 70, 81, 83, 88, 91

Median= (81+83)/2

= 164/2

= 82

Mean = (55+70+81+83+88+91)/6

= 468/6

= 78

New value which is added = 82*1.12

= 91.84

New Mean = (55+70+81+83+88+91+91.84)/7

= 559.84/7

= 79.97

Increase in mean = 79.97-78

=1.97

increase percentage (1.97/78) *100

= 2.53%

Hence, new mean is 2.53% larger than the original mean.

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