Angles ABC and DEF are complementary angles. If m/ABC = 72°, what is m/DEF?

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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Answer:

Step-by-step explanation:

Based on the information provided, the residual plot makes sense based on the scatter plot.

In the given scatter plot, the points are plotted with horsepower on the x-axis and observed MPG (miles per gallon) on the y-axis. The scatter plot shows the relationship between horsepower and MPG for the motorcycles.

The residual plot, on the other hand, shows the differences between the observed MPG values and the predicted MPG values based on the regression line or model. Residuals represent the vertical distances between the observed data points and the regression line.

Looking at the residual plot, we can see that the residuals are scattered randomly around the zero line. Some residuals are positive, while others are negative, indicating that the observed MPG values deviate both above and below the predicted MPG values.

Given this information, option A is the correct answer: "The random residual plot makes sense because the scatter plot appears to have a linear relationship." The scatter plot does not necessarily suggest a positive or negative relationship between horsepower and MPG. It simply shows the general trend or pattern. The random distribution of residuals in the residual plot indicates that the regression model is capturing the relationship adequately, and the variations or deviations from the regression line are random, which is expected in a good regression model.

The residual plot created by Jorge does make sense as it reflects the negative relationship between horsepower and miles per gallon present in the original scatter plot. As the horsepower increases, the miles per gallon decreases which is depicted accurately in the residual plot made.

The best answer for this is B. The random residual plot makes sense because the scatter plot appears to have a negative relationship. A residual plot is a graph that is used to examine the goodness of fit in regression and ANOVA analysis. It is the differences between the observed and predicted values of data. The points in a residual plot are randomly dispersed around a horizontal axis if the corresponding regression model is appropriate for the data.

In this case, the scatter plot demonstrates a negative relationship between the horsepower of motorcycles and miles per gallon. As the horsepower increases, the miles per gallon decrease. This negative relationship is reflected in the pattern of residuals, which fluctuates around the zero line on the y-axis of the residual plot. Consequently, the random distribution of residuals on Jorge's plot does make sense given the scatter plot data.

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Answer:

Problem: 0.5(5-7x)=8-(4x+6)

Answer: x= -1

Answer:

96

Step-by-step explanation:

3 x (4 + 2) x 5 + 6

3 x 6 x 5 + 6

18 x 5 + 6

90 + 6

96

Answer:

3.1x x+12.04zx-1.2z.....

Answer:

\( s = \sqrt{30} - 2\sqrt{5} m \)

Step-by-step explanation:

Given:

Formula for side length of cube, \( s = \sqrt{\frac{SA}{6} \)

Where, S.A = surface area of a cube, and s = side length.

Required:

Difference in side length between a cube with S.A of 180 m² and a cube with S.A of 120 m²

Solution:

Difference = (side length of cube with 180 m² S.A) - (side length of cube with 120 m² S.A)

\(s = (\sqrt{\frac{180}{6}}) - (\sqrt{\frac{120}{6}})\)

\( s = (\sqrt{30}) - (\sqrt{20}) \)

\( s = \sqrt{30} - \sqrt{4*5} \)

\( s = \sqrt{30} - 2\sqrt{5} m \)

Answer:

B, E, D

Step-by-step explanation:

You just look for the ones that have the same factors as 5:2

Answer:

A

C

D

Step-by-step explanation:

if I'm not wrong, I'm sure is that

Answer:

A = 1547.52

Step-by-step explanation:

Area of Circle Formula: A = πr²

Simply find r and plug it in:

d = 44.4

r = d/2 = 44.4/2 = 22.2

A = π(22.2)²

A = 1547.52

Answer:

-64

Step-by-step explanation:

The first step would be the parentheses. 80 divided by -10 is -8. Square that and it's 64. But there's a negative in front of the parentheses, so it's -64.

-19.99; The line of best fit underpredicts the student's science test score.

So correct option is A.

A prediction is an estimation or forecast about future events or conditions, based on past data and trends, current information, and/or mathematical models. Predictions can be made in various fields, such as finance, weather, sports, social sciences, and natural sciences. The accuracy of predictions depends on many factors, including the quality of the data used, the assumptions made, the complexity of the system being analyzed, and the reliability of the methods used. Predictions are not always accurate and are often subject to revision as new information becomes available.

The predicted science score for the student with IQ 100 can be calculated using the line of best fit:

ŷ = −20.3 + 0.7489 * 100 = 71.59

The residual is the difference between the actual science test score and the predicted science score:

residual = actual score - predicted score = 52.6 - 71.59 = -19.99

So the line of best fit underpredicts the student's science test score by 19.99 points.

Therefore, the residual is:

-19.99; The line of best fit underpredicts the student's science test score.

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Measuring to fit a cabinet opening includes a few extra steps to get the doors made in the right sizes for your remodel or renovation:  

Measure the inside edges: When measuring the width, measure from left to right, starting with the inside edge of the left stile (vertical part of the face frame) to the inside edge of the right stile. When measuring height, measure from the inside edge of the bottom rail (horizontal part of the face frame) to the inside edge of the top rail. We build to 1/16 inch increments, so be precise.

Add space for door overlay: Cabinet doors for framed cabinets must be larger than the cabinet opening to look right and close properly. We refer to this as an "overlay". The industry standard for most cabinet doors is a 1/2 inch overlay around the cabinet door. To create a 1/2 inch door overlay on all four sides, add 1 inch to your total height, and 1 inch to your total width

Explanation:

How many surface has a pyramid?

5 Faces

It has 5 Faces. The 4 Side Faces are Triangles. The Base is a Square.

The zeros of the polynomial x⁴ - 6x³ - 21x² - 150x - 100  are 0.6511 and 8.262 respectively

Zeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively.

The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0. All such domain values of the function, for which the range is equal to zero, are called the zeros of the polynomial.

To find the zeros of this polynomial function, we have to write the function appropriately.

x⁴ - 6x³ - 21x² = 150x - 100

x⁴ - 6x³ - 21x² - 150x - 100 = 0

The roots of this function is 0.6511 and 8.262 respectively

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Answer: $1.25

Step-by-step explanation: (6*3) = 18 + (2*3.50)= 7

18+7=25

25*.25= 6.25

25-6.25= 18.75

20-18.75 = 1.25

Answer:

Step-by-step explanation:

The first thing we need to focus on is the fact the large bag (30 cups) is 2.5 larger than the small bag. So, the first we need to do is divided 30 by 2.5, which is 12. (300/25 = 30/2.5 = 12, in case you're confused.) So the small bag has 12 cups of sugar.

What that down, we need to focus how many cakes the small bag can make, which was 9. 3/4 of a cup is left over. We can create an equation from that info, that being 9x + 0.75 = 12. Now let's solve for x.

9x + 0.75 = 12

First, subtract 0.75 from both sides. With that, we can solve for x directly.

9x = 12 - 0.75

9x = 11.25

Now, divide both sides by 9.

x = 11.25/9

x = 1.25

With that, we now know that each cake needs 1.25 cups of sugar.

With that, the last thing we need to is divide 30 by 1.25. Again, I can use powers of ten, to quickly divide 3000 by 125 (10²) to get 24 cakes.

With that done, we have our answer. 24 cakes can be made with a large bag of sugar.

I hope this helps!  (⌒ω⌒)

Answer:

see the list below

Step-by-step explanation:

did all the formulas for each and I believe the order is from (smallest to biggest)

1. The half sphere or hemisphere (3rd in the pic)

2.The pyramid

3.slanted cone

4.cone

5.slanted cylinder

6.and finally the cylinder

Volume of cylinder II< Volume of cylinder I< Volume of Cone II< Volume of pyramid <Volume of Cone I

The amount of space occupied by a three-dimensional figure as measured in cubic units.

                            = 1/3*22/7*5*5*7

                            =25 cm³

                               = 22/7*4*4*5

                               = 251.42 cm³

                               = 2/3*22/7*3.5*3.5*3.5

                               = 89.833 cm³

                               = 10*5*6

                               = 100 cm³

                               = 22/7*6*6*8

                               = 905.14 cm³

                            = 1/3*22/7*4.5*4.5*7.5

                            =159.107 cm³

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Answer:

11/12

Step-by-step explanation:

no of sample space=12

number of 7 to occur is 1/12

number of not 7:

since the total probability is 1

so 1-1/12=11/12

Answer:

?

Step-by-step explanation:

What did you Ssayyy? Umm yeah so the text kinda cut off at the end, looks like you were clicking the middle button on ur keyboard

Answer:

−1.518108

Step-by-step explanation:

pretty sure this is it, if not just message me and ill be more than happy to help you out :)

Answer:

29

Step-by-step explanation:

(4+[8=4x(2)]x3)+1

(4+[8=8]x3)+1

(4+[8x3])+1

(4+24)+1

28+1

29

The coordinates of the y-intercepts is -24

The point where a line crosses the y-axis, or where the value of x equals 0, is known as the y-intercept. By setting x=0 in the line's equation and calculating y, you can determine the y-intercept of a line. Typically, the y-intercept is shown as (0,b), where b is the point's y-coordinate.

To find the coordinates of the y-intercept of the function

f(x) = x² - 10x - 24,

we need to find the value of the function when x = 0,

because the y-intercept occurs at the point where the graph of the function crosses the y-axis,

which is the point where x = 0.

So, we can substitute x = 0 into the function:

f(0) = 0² - 10(0) - 24

     = -24

Therefore, the y-intercept has coordinates (0, -24).

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Answer:

20%

Step-by-step explanation:

1/5 = 0.20 → multiply by 100 = 20%

Answer:

20 percent

Step-by-step explanation:

All percentages have a denominator of 100, and 100 divided by 5 is 20.

Answer:

4n²(7n-10)(n+2)

Step-by-step explanation:

The first step is to factor out a 4n² or take common from each term:

The next step is to factor 7n² + 4n - 20. We can do this by grouping:

Therefore, the complete factorization is:

The number of pints that Lin will have is given as follows:

38 pints.

The number of pints is obtained applying the proportions in the context of the problem.

The proportion is applied as it is a unit conversion problem, hence we must use the unit conversion rate from gallons to pints.

The unit conversion rate from gallons to pints is given as follows:

1 gallon = 8 pints.

The number of gallons is given as follows:

4 and 3/4 = 4 + 0.75 = 4.75.

Hence the number of pints is given as follows:

8 x 4.75 = 38 pints.

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In this case for a)

Check point 4 is located at -213ft above the sea level

So we need to add 124 to the checkpoint 4 altitude

for the b)

ANSWER

a)-89ft

b)1972 ft lower

Step-by-step explanation:

98 - 3 * 2 * 4 equal to 9 - 2 * 840 + 9 - 6 equal to -7

The evaluation of 14(7) -d 2f when d = 2 and f = 4 is 82.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

An expression,

14(7) -d 2f.

To find the value of the expression:

Substitute the given value of d and f.

When d = 2 and f = 4,

the equation is,

14(7) -(2)2(4)

= (14 x 7) - ( 2 x 2 x 4)

= 98 - 16

= 82

The evaluation of the equation when d = 2 and f = 4 is 82.

Therefore, the solution is 82.

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