Find the missing angle.
92° 78°

The value of x in the triangle is 12.285.

We have,

We use cosine identities.

So,

Cos Ф = Base / Hypotenuse

Now,

Cos 35= x/15

0.819 = x/15

x = 0.819 x 15

x = 12.285

Thus,

The value of x is 12.285.

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Answer:

0.1 oz

Step-by-step explanation:

1000=10 oz

10 drops

1000/100=10

10/100=O.1 oz

I'm sorry, but I cannot answer this question without additional information about the dimensions of the capsule. Please provide me with the necessary information so that I can assist you.

The decision meets each of the criteria by: Buying 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each enables the purchase of 700 frozen delights within the $400 budget and satisfies the objective of producing at least $800 in profit.

I have made the decision to buy 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each in order to fulfil the requirement of buying 700 frozen delights at a price of no more than $400.

Cost of purchasing 500 popsicles = (500 * $0.50)

Cost of purchasing 500 popsicles = $250

Cost of purchasing 200 ice cream sandwiches =(200 * $1.50)

Cost of purchasing 200 ice cream sandwiches  = $300

So, Total cost of purchasing all 700 frozen treats is $550 ($250 + $300) which is within the budget of $400.

I intend to sell the popsicles for $1.50 each and the ice cream sandwiches for $3.00 each in order to meet the requirement of turning a profit of at least $800. This would bring in $1350 in income for the ice cream sandwiches and $750 for the popsicles (500 * $1.50 and 200 * $3.00 respectively).

The objective of producing a profit of at least $800 is met after deducting the expense of buying the frozen treats from the overall income.

Net profit =($1350 - $550)

Net profit = $800

Therefore purchasing  500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each satisfies the objective of producing at least $800 in profit.

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Answer:

  2035.8 ft³

Step-by-step explanation:

You want to know the volume of a cylinder with radius 6 ft and height 18 ft.

The volume of a cylinder is given by the formula ...

  V = πr²h

For the given dimensions, the volume is ...

  V = π(6 ft)²(18 ft) ≈ 2035.8 ft³

The volume of the cylinder is about 2035.8 cubic feet.

__

Additional comment

If you use 3.14 for π, you get 2034.7 cubic feet.

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Answer:

The answer is A.

A graph passes through a point if its equation is equal to the coordinate of this point. In this exemple:

5x+4y=8

we replace the variables with 4 and -3 (x with 4 and y with -3):

5(4)+4(-3)=8

20-12=8

8=8 so it passes.

NOW , for the slope:

slope = - 5/4 ( the equation is 5x+4y=8 , the cartesian equation is 5x+4y-8=0. THE cartesian equation with variables is ax+by+c=0) NOW this is linked with the slope bcz the slope is linked to the director vector (-b;a) that gives (-4;5), this is the director vector's formula that we're going to call U. THEN with this formula you get the slope: Y of U / X of U = 5/-4 = - 5/4 (bcz you dont leave the denominator with a negative sign).

THAT'S it thats the answer.

the answer to your math problem is 2000

The result of 1/11 in the base 10 system is given as is 0.09.

To visualize the long division of 1 ÷ 11 in a base ten system:

Set up the long division: 11 outside and 1.00 inside the division bracket.

Place the decimal point in the quotient above the dividend's decimal point.

Bring down the first digit (0) and divide 11 into 10; it goes 0 times.

Subtract the product (0) from 10, leaving 10.

Bring down the next digit (0) and divide 11 into 100; it goes 9 times.

Subtract 99 from 100, leaving a remainder of 1.

The result is 0.09.

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Answer:

there are no choices given but...

Step-by-step explanation:

this simplifies to 8/3, or 2 2/3

find the choice that isn't either of those ( is also 2.66666 repeating)

Answer:

check attachment

Step-by-step explanation:

First write in point-slope form:

y-y1=m(x-x1)

Now substitute:

y-(-1)=3/4(x-(-4))

And then just solve. You should get a y-intercept of 2.

The required Mark has completed 38.46% of the race.

To calculate the percentage of the race completed by Mark, we can divide the number of miles he has run by the total length of the race and then multiply by 100 to convert the result to a percentage.

So, Mark has run 5 miles out of a total of 13 miles:

Percentage of race completed = (5/13) x 100%

Calculating this expression, we get:

Percentage of race completed = 38.46%

Therefore, Mark has completed 38.46% of the race.

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The equation 2x² - 7x - 30 = 0 has two solutions: x = -5/2 and x = 6 and both solutions are real.

Given the equation in the question:

2x² - 7x - 30 = 0

We can use the quadratic formula to to determine the number and type of solutions :

x = (-b±√(b² - 4ac)) / (2a)

2x² - 7x - 30 = 0

a = 2

b = -7

c = -30

Plugging in these values, we get:

x = (-b±√(b² - 4ac)) / (2a)

x = (-(-7) ± √((-7)² - ( 4 × 2 × -30))) / (2×2)

x = (7 ± √( 49 - ( -240))) / (4)

x = (7 ± √( 49 + 240)) / (4)

x = (7 ± √( 289)) / (4)

x = (7 ± 17) / 4

x = (7 - 17) / 4 and x = (7 + 17) / 4

x = -5/2 and x = 6

Therefore, the two solutions are x = -5/2 and x = 6.

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The minimum height the second beaker must be so it does not overflow is 9.55 inches.

Given that a beaker has a radius of 1.8 inches and height of 4.6 inches. we need to find the height of another beaker which has the radius of 1.25 in and has same volume,

Volume of a cylinder = π × radius² × height

= 3.14 × 1.8² × 4.6

= 46.8 in³

Now, the second beaker =

46.8 = 3.14 × 1.25² × h

h = 46.8 / 3.14 × 1.25²

h = 9.55

Hence, the minimum height the second beaker must be so it does not overflow is 9.55 inches.

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Answer:

Step-by-step explanation:

4. A. Im not sure but that seems like the most logical.

5. D.

6. B.

7. B.

8. I think it's A. maybe-

9.- id-k sorry-

10. i--dk..]

11. C

12. D

13. B.

15. C.

16. C

17. A.

18. D

19. C.

21. D.

22. -(x+1)/(x-1)(x+2) x does not equal -3, -2, 1, and 6

23. i d-ksorry

24.i-d-k sorry

25. D.

Hope this helped sorry i culdn't get them all-

The answers to all parts are shown below.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

1. x⁴ + 5x³ + 7x² -3x - 10 = 0

= (x-1)(x+2)(x² + 4x + 5)

Thus, the rational roots are 1 and -2.

2. 3x² -4 = - x⁴

x⁴ + 3x² -4 = 0

(x-1)(x+1)(x² + 4) =0

Thus, the zeroes are 1, -1, -2i, +2i.

3. We can write the zeroes as

p(x)=(x-1)(x-2)(x+2)(x+3).

So, p(x) = x⁴ + 2x³ -7x² -8x +12

4. x³ -3x² +4x- 12=0

(x-3)(x²+4) =0

x= 3, -2i, 3i

5.  x= 1,2,4,6,8,10,11

y= 0,-1,0,4,8,9,8

So, equation of line

(y- 0) = (-1-0)/(2-1)(x-1)

y = -1(x-1)

y + x +1=0

6. x= 2,5,12,20 and y= 30,12,5,3

k = 30/2

k = 15

So, the relationship is y= 15x.

7. cn = constant(k)

n= 44

then, c= 30/44 = 0.68

and, k = 44 x 0.68

k = 30

So, c = 1.5 dollars per person.

8. 125¹/³

= (5³)¹/³

= 5

9. y = 293(1.06)⁴ = 370

10. log₃ 2187

= log₃ 3⁷

= 7

11. log₄ 22

= 2.29

12 . y= 4/x

The new equation is  y = 4/(x - 7) + 6.

13. (6-x)/ (x² + 2x - 3) / (x² -4x- 12)/ (²x² + 4x + 3)

= - (x+1)/ (x+1)(x+2)

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Answer:

100

Step-by-step explanation:

the room is square this means each wall equal 25 .4 walls *25 =100 square feet

Answer:120

Step-by-step explanation:

Answer:

y = 3/4x + 15

Step-by-step explanation:

Given;

A line passes through the point (-8, 9) and has a slope of 3/4

Question:

Write an equation in slope-intercept form for this line.​

Solve:

Slope-intercept form ⇒ y=mx+b

Which-

Based on the given;

Using slope intercept form to find y-intercept;

y=mx+b

9 = 3/4(-8) + b

9 = -6 + b

9+6 = -6+6 + b

b = 15

Therefore now we can write an equation.

y = 3/4x + 15

RevyBreeze

The area of the trapezoid with parallel sides of 8 meters and 7 meters, and a height of 4 meters, is 30 square meters.

To find the area of a trapezoid, we use the formula:

Area = (a + b)h/2

where "a" and "b" are the lengths of the parallel sides of the trapezoid, and "h" is the height of the trapezoid.

In this case, we are given that the parallel sides are 8 meters and 7 meters, and the height is 4 meters.

Substituting these values into the formula, we get:

Area = (8 + 7) x 4 / 2

= 15 x 4 / 2

= 60 / 2

= 30 square meters

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The correct option is A.

The interquartile range for Data Set A is 15 and the interquartile range for Data Set B is 10.

Given that, the box plots display the scores that two different groups of students got on their last math quiz.

We need to find the interquartile range of each data set.

So, the interquartile range of data set A = 80-65 = 15

the interquartile range of data set B = 90-80 = 10

Hence, the interquartile range for Data Set A is 15 and the interquartile range for Data Set B is 10.

The correct option A.

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Answer:

Answer:Radians = Degrees × 3.14/180

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174135×0.0174

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174135×0.0174 = 2.355

Answer:

-7≤y≤2

Step-by-step explanation:

The range measures the highest and lowest numbers up and down on the y-axis for a line. In order to determine range, start with the smallest number (the farthest place the line touches going down) then write less than or equal to. This is because the two dots are closed, meaning they include what the line touches. Afterward, add another less than or equal to, and then add the biggest number (the highest place the line touches going up). The range basically gives you your boundaries, and tells you how high or low the line you are describing is. And after that, you're done!

I hope this helps :)

The point after a dilation by a scale factor of 2 with the origin as the center of dilation, and a translation over the y-axis is (-16, 2).

Given is a point, (8, 1) we need to find the coordinates of a point which is dilated from the origin by the scale factor of 2 and translation over the y-axis,

So, the coordinates of after dilation by k scale factor =

(x, y) = (kx, ky)

So, (8, 1) = (16, 2)

Now, the translation over the y-axis gives,

(x, y) = (-x, y)

Therefore, (16, 2) = (-16, 2)

Hence, the point after a dilation by a scale factor of 2 with the origin as the center of dilation, and a translation over the y-axis is (-16, 2).

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Using chi-squared goodness-of-fit test with Benford's Law, observed check frequencies were found to be significantly different, indicating possible fraud. The test statistic was 756.153, exceeding the critical value of 15.51.

Using chi-squared goodness-of-fit test with Benford's Law, observed check frequencies were found to be significantly different, indicating possible fraud. The test statistic was 756.153, exceeding the critical value of 15.51.

To test for goodness-of-fit with Benford's Law, we can use the chi-squared goodness-of-fit test. The null hypothesis is that the observed frequencies follow Benford's Law, while the alternative hypothesis is that they do not.

We can start by calculating the expected frequencies for each leading digit based on Benford's Law. According to Benford's Law, the expected proportion of leading digits is

P(d) = log10(1 + 1/d), where d is the leading digit (1, 2, ..., 9).

Then, we can calculate the expected frequencies by multiplying the proportion by the sample size

Expected frequency for digit d = P(d) * sample size.

Using this formula, we can calculate the expected frequencies for each digit

Expected frequencies: 3.542, 2.019, 1.518, 1.221, 1.028, 0.886, 0.778, 0.697, and 0.643.

We can use these expected frequencies and the observed frequencies to calculate the chi-squared statistic

chi-squared = Σ (observed frequency - expected frequency)² / expected frequency

We can then compare this value to the chi-squared distribution with 8 degrees of freedom (since there are 9 digits and one constraint, which is that the frequencies must add up to the sample size). Using a significance level of 0.05 and a chi-squared distribution table or calculator, the critical value is 15.51.

Plugging in the observed and expected frequencies, we get

chi-squared = (0 - 3.542)²/3.542 + (12 - 2.019)²/2.019 + (0 - 1.518)²/1.518 + (73 - 1.221)²/1.221 + (482 - 1.028)²/1.028 + (186 - 0.886)²/0.886 + (8 - 0.778)²/0.778 + (23 - 0.697)²/0.697 + (0 - 0.643)²/0.643

chi-squared = 756.153

Since the calculated chi-squared statistic (756.153) is greater than the critical value (15.51), we reject the null hypothesis and conclude that the observed frequencies are not consistent with Benford's Law. This suggests that the check amounts are the result of fraud.

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Corellian Engineer used the Bottom up (Micro) approach to estimate the total cost of developing a new navigation system for its YT-1300 Freighter. The total cost estimate of $17,500. So, the correct option is C).

The process that Corellian used for this estimate is the Bottom up (Micro) approach, which involves estimating costs for each component or task in the project and then summing them up to get the total cost estimate.

In this case, they estimated the costs for programming, beta testing, installation, and final shake down, and then added them up to get the total cost estimate of $17,500.

So, the correct answer is C).

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The interest on the loan using the Banker's Rule is $139.20.

The formula for calculating interest using the Banker's Rule is:

Interest = Principal x Rate x Time / 360

where:

Principal is the amount of the loan

Rate is the interest rate as a decimal

Time is the time period in days

Using this formula, we can calculate the interest on the loan as:

Interest = 4800 x 0.088 x 105 / 360

Interest = 139.20

Therefore, the interest on the loan using the Banker's Rule is $139.20.

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a) The proportion of the investments had a return of between 10% and 30% is given as follows: 0.68 = 68%.

b) The proportion of the investments had a return of between -10% and 50% is given as follows: 0.997 = 99.7%.

c) The proportion of the investments had a return either less than 10% or more than 30% is given as follows: 0.32 = 32%.

d) The proportion of the investments had a positive return is given as follows: 0.9985 = 99.85%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

Hence the percentages for this problem are given as follows:

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The value of length of AG is,

AG = 157.02

We have to given that;

AD = 31 cm

DC = 22 cm

Hence, We get;

AC = √31² + 22²

AC = √961 + 484

AC = √1445

AC = 38

Thus, We get;

cos 76° = AC / AG

0.242 = 38 / AG

AG = 38/0.242

AG = 157.02

Therefore, The value of length of AG is,

AG = 157.02

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∠ AFE is supplementary to ∠ AFB and the measure of ∠ AFE = 102⁰.

option A.

Supplementary angles are the two angles that sum up to 180 degrees.

That is, if the sum of two angles is equal to 180 degrees, then the two angles are supplementary.

From the given diagram we can form the following equation;

∠ AFE + ∠ AFB = 180 (sum of angles on a straight line is equal to 180⁰ )

∠ AFE = 180 - ∠ AFB

∠ AFE = 180 - 78

∠ AFE = 102⁰.

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