A triangular box of sticky notes is shown. The volume of the box of sticky notes is 54.6 cubic inches. What is the height of the box of sticky notes?

Answer:

a = 10

b = 5

Step-by-step explanation:

A 30-60-90 triangle is a right triangle where the interior angles measure 30°, 60° and 90° and the sides are in the ratio 1 : √3 : 2.

The formula for the ratio of the sides is x : x√3 : 2x where:

From inspection of the given triangle, the measure of the side opposite the 30° angle is "b", the side opposite the 60° angle is 5√3, and the hypotenuse is "a". Therefore:

If x√3 = 5√3, then x = 5. Therefore:

The number of each type of basket made is as follows:

2-point basket = 19

3-point basket = 9

The team made 28 baskets and scored 65 points. Some baskets were 2-point baskets, and some baskets were 3-point baskets.

let

x = number of 2-point basket

y = number of 3-point basket

Therefore, using equation

x + y = 28

2x + 3y = 65

multiply equation(i) by 2

2x + 2y = 56

2x + 3y = 65

subtract he equation

y = 9

Therefore,

x = 28 - 9

x = 19

Therefore, the team made 19 2-point basket and 9 3-point basket.

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According to the banker's rule, Amber can afford to borrow a maximum of $96,900.

The banker's rule is a guideline used by some lenders to determine the maximum amount that an individual can borrow based on their annual income.

According to the banker's rule, the maximum amount that can be borrowed is typically a multiple of the borrower's annual income.

The exact multiple used in the banker's rule may vary depending on the lender and the borrower's financial situation, but a common multiple used is 3.

Therefore, to calculate the amount that Amber can afford to borrow using the banker's rule, we can multiply her annual income by 3.

Given that Amber makes $32,300 annually, we can calculate the amount that can be borrowed using the banker's rule as follows:

Maximum amount that can be borrowed = Annual income * Banker's rule multiple

Maximum amount that can be borrowed = $32,300 * 3

Maximum amount that can be borrowed = $96,900

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Thus, the value of x for the given bottom isosceles triangle is found to be x = 88°.

Additional angles are two angles that add up to 180 degrees. The situation when they happen to be on the identical side of a straight line is a typical one.

For the top isosceles triangle:

Base angle = ?

Using the property of supplementary angles:

base angle + 113 = 180

base angle = 180 - 113

base angle = 67

Now, using the Triangle sum Theorem:

Vertex angle = ?

Vertex angle + 67 + 67 = 180

Vertex angle = 180 - 134

Vertex angle = 46

For the bottom isosceles triangle:

base angle  = Vertex angle of top triangle (vertically opposite angles)

base angle  = 46

Now,

For the values of x, use Triangle sum Theorem:

x + 46 + 46 = 180

x = 180 - 92

x = 88

Thus, the value of x for the given bottom isosceles triangle is found to be x = 88°.

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The percentage profit on the car is 12% if a car was bought for 5600 and sold for 6272.

To calculate the percentage profit, we need to find the profit first.

Profit = Selling price - Cost price

Profit = 6272 - 5600 = 672

The profit on the car is $672.

Now, we can calculate the percentage profit using the formula

Percentage profit = (Profit / Cost price) x 100%

Percentage profit = (672 / 5600) x 100%

Percentage profit = 0.12 x 100%

Percentage profit = 12%

Therefore, the percentage profit on the car is 12%.

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The length of the diagonal from L to N is approximately 60.8, and the length of the diagonal from M to O is approximately 47.0.

To find the lengths of the diagonals of rectangle LMNO, we first need to find the length of MN and LO.

Since LMNO is a rectangle, we know that opposite sides are congruent, so LN = MO and LO = MN.

Given that LN = 4x - 17 and MO = 2x + 13, we can set them equal to each other and solve for x:

4x - 17 = 2x + 13

2x = 30

x = 15

Now that we know x, we can find LN and MO:

LN = 4x - 17 = 4(15) - 17 = 43

MO = 2x + 13 = 2(15) + 13 = 43

Therefore, MN = LO = 43.

To find the length of the diagonals, we can use the Pythagorean theorem. Let's call the diagonal from L to N d1, and the diagonal from M to O d2:

d1^2 = LM^2 + LN^2

d1^2 = MN^2 + LN^2

d1^2 = 43^2 + 43^2

d1^2 = 3698

d1 ≈ 60.8

d2^2 = MO^2 + LM^2

d2^2 = MN^2 + LM^2

d2^2 = 43^2 + 18^2

d2^2 = 2209

d2 ≈ 47.0

Therefore, the length of the diagonal from L to N is approximately 60.8, and the length of the diagonal from M to O is approximately 47.0.

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Answer:

Step-by-step explanation:

720

Answer:

Step-by-step explanation:

The total number are 12+14+16=42

and the movie was not a comedy are adventure and drama which stands for 12 and 16. The total of them is 28.

So the movie was not a comedy is 28/42 = 2/3

Answer:

D.

Step-by-step explanation:

If you want to know the chance that the movie you watched was not a comedy, you have to do some math. Don't worry, it's not hard. You just need to use this formula:

P(not funny) = 1 - P(funny)

This means that the probability of not laughing is one minus the probability of laughing. How do we find the probability of laughing? Well, we look at how many movies are comedies and how many movies are total. In this case, there are 14 comedies and 42 movies in total. So we divide 14 by 42 and get:

P(funny) = 14 / 42

This fraction can be simplified to:

P(funny) = 1 / 3

Now we plug this into the formula and get:

P(not funny) = 1 - (1 / 3)

This can be simplified to:

P(not funny) = 2 / 3

So there you have it. The probability that the movie was not a comedy is 2 / 3. That means you have a higher chance of watching a boring movie than a funny one. Maybe you should pick a different genre next time.

The right answer is d. 2/3.

Answer:

It'd be 4300 mililiters

Step-by-step explanation:

3.8× 100= 3800

3800+500=4300

The equation of a circle with center (a, b) and radius r is:

(x - a)^2 + (y - b)^2 = r^2

(x, y) represents any point on the circle

A circle is described as a shape consisting of all points in a plane that are at a given distance from a given point, the center.

The properties of the circle are as follows:

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According to the information, We can continue drawing more triangles by varying the angles in different ways.

Since the given triangle has one side with a fixed length of 4 cm, we can draw an infinite number of triangles by varying the other two angles.

To draw the second triangle, we can keep the 50 degree angle fixed and change the 40 degree angle. For example, we could draw a triangle with a 50 degree angle, a 60 degree angle, and a side of length 4 cm.

To draw the third triangle, we can keep the 40 degree angle fixed and change the 50 degree angle. For example, we could draw a triangle with a 30 degree angle, a 40 degree angle, and a side of length 4 cm.

We can continue drawing more triangles by varying the angles in different ways.

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Step-by-step explanation:

oh you have to do is that you have to see 15 / 18 ft * 15 / 1

The value of cos (2theta) will be; 161/289

We are given that tan(A) = -8/15, therefore opposite is 8 and adj is 15

hyp = √8²+15²

= √ 64+225

= √ 289

= 17

Thus, cos (theta) = 8/17 and since theta is in second quadrant, cos tetha will be negative

cos (theta) = -15/17

cos²(theta) = 225/289

sin(theta) = 8/17

sin²(theta) = 64/289

cos(2theta) = cos²(theta) -sin²(theta)

= 225/289 - 64/289

= 161/289

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The kite's vertical distance from the ground, with an angel of elevation 39° from the line of sight of Jennifer is equal to 7.4 feet.

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

The kite's vertical distance from the ground is the sum of its vertical height from Jennifer's hand and the distance from the ground to the hand

we shall represent the vertical height of the kite from Jennifer's hand with the letter x so that;

x = 36 inches × sin 39°

x = 3 feet × sin 39° {36 inches = 3 feet}

x = 1.8880 feet

kite's vertical distance from the ground = 1.9 ft + 5.5 ft = 7.4 feet

Therefore, the kite's vertical distance from the ground, with an angel of elevation 39° from the line of sight of Jennifer is equal to 7.4 feet.

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5.) The measure of angle D of the given triangle would be = 59.5°

To calculate the missing angles, sine rule is used which is ;

Sine rule = a/sin A = b/sin B

Where a = 23

A = 56°

b = 24

B = X

That is;

23/sin56° = 24/sinx

Make sin X the subject formula;

Sin X = sin56×24/23

= 0.829037572×24/23

= 19.89690174/23

= 0.865082684

X = Sin-1 (0.865082684)

= 59.89214806

= 59.9° (approximately)

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The test statistic (3.46) is greater than the critical value (2.05), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.02 level to support the company's claim that above 61% of the chips do not fail in the first 1000 hours of their use.

The null hypothesis for this scenario is that the proportion of computer chips that do not fail in the first 1000 hours of their use is equal to or less than 61%, while the alternative hypothesis is that the proportion is greater than 61%. Mathematically:

H0: p ≤ 0.61

Ha: p > 0.61

where p is the true proportion of computer chips that do not fail in the first 1000 hours of their use.

To test this hypothesis, we can use a one-tailed z-test for proportions. Using the given sample information, we can calculate the test statistic as:

z = (0.64 - 0.61) / sqrt((0.61 * 0.39) / 1600) = 3.46

where 0.39 is the complement of 0.61, and sqrt denotes the square root. The critical value for a one-tailed test at the 0.02 level of significance is 2.05.

Since the test statistic (3.46) is greater than the critical value (2.05), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.02 level to support the company's claim that above 61% of the chips do not fail in the first 1000 hours of their use.

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For a loan of $24,000 at 6% interest over 60 months, the monthly payment is $466.47.

A monthly payment is the sum of money that is made towards a debt or loan on a regular basis; it normally consists of both the main and interest. It is a set sum that the borrower must consistently pay until the debt is repaid in full. Mortgages, auto loans, student loans, and personal loans all frequently include monthly installments. The loan amount, the interest rate, and the term of the loan all affect how much will be paid each month.

We can use the following calculation to determine a loan's monthly payment:

M = P * (r * (1 + r)ⁿ) / ((1 + r)ⁿ⁻¹)

where:

M = payment each month

P = Principal (the loaned amount)

r = (Divide the annual interest rate by 12 to get the monthly interest rate)

n = total payments (12 divided by the number of years)

By entering the specified values, we obtain:

P = 24000

r = 6% / 12 = 0.005

n = 60

M = 24000 * (0.005 * (1 + 0.005)⁶⁰) / ((1 + 0.005)^60 - 1)

M = $466.47 (rounded to the nearest cent)

So, $466.47 is the monthly payment for a $24,000 loan with a 6% interest rate over 60 months.

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Hannah needs to earn an annual interest rate of approximately 5.88% to reach $1,000,000 in 25 years.

To determine the rate Hannah needs to earn to reach $1,000,000 in 25 years, we can use the future value formula for an annuity:

[tex]FV = Pmt * [(1 + r)^n - 1] / r[/tex]

where:

FV = future value (in this case, $1,000,000)

Pmt = periodic payment (in this case, Hannah's annual contribution)

r = annual interest rate

n = number of periods (in this case, 25 years)

Hannah will deposit $3,000 this year and increase her deposits by $750 each following year. So her annual contributions will be:

Year 1: $3,000

Year 2: $3,750

Year 3: $4,500

...

Year 25: $21,750

To simplify the calculation, we can use the average annual contribution over the 25-year period, which is:

[tex][(3,000 + 21,750) / 2] = $12,375[/tex]

Now we can plug in the values into the formula and solve for r:

[tex]1,000,000 = 12,375 * [(1 + r)^25 - 1] / r[/tex]

Multiplying both sides by r and dividing both sides by 12,375, we get:

[tex]r x (1 + r)^25 = 120.75[/tex]

We can solve for r using trial and error, or using a financial calculator or spreadsheet. Using trial and error, we can try different interest rates until we find the one that makes the equation true. One possible method is to start with a reasonable guess, such as 6%, and adjust up or down until we get close to 120.75. After a few iterations, we find that:

r = 5.88%

Therefore, Hannah needs to earn an annual interest rate of approximately 5.88% to reach $1,000,000 in 25 years, assuming she deposits $3,000 this year and increases those deposits by $750 each following year.

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Step-by-step explanation:

h o g   =   6 ( x^2 + x - 2)   + 1

             = 6x^2 + 6x -12 + 1

             = 6x^2 + 6x -11              put in -7 for 'x'

                  6 (-7^2) + 6 (-7) - 11

               = 241

* * * edited * * *

The exterior angle at K in triangle HJK is 139°, whereas the exterior angle at J is 53°. Shortest side is JK.

We know that the sum of exterior angles of a triangle is 360°. So,

Exterior angle at K + exterior angle at J + exterior angle at H = 360°

139 + 53 + exterior angle at H = 360

exterior angle at H + 192 = 360

exterior angle at H = 360 - 192

exterior angle at H = 168°

Now, we will calculate the interior angles of triangle HJK. We know that exterior and interior angles are supplementary and makes a sum of 180 degree.

Interior angle K + exterior angle K = 180

Interior angle K + 139 = 180

Interior angle K = 180 - 139 = 41°

Interior angle H + exterior angle H = 180

Interior angle H + 168 = 180

Interior angle H = 180 - 168 = 12°

Interior angle J + exterior angle J = 180

Interior angle J + 53 = 180

Interior angle J = 180 - 53 = 127°

A triangle's shortest side is always opposite the smallest angle. So, in this question the smallest angle is ∠H and the side opposite to it is KJ, hence KJ is the shortest side.

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Answer:

Step-by-step explanation:

You want to compare the average rates of change on the interval [-6, -3] of the functions f(x) = 4x² and g(x) = 8x².

The average rate of change of p(x) on the interval [a, b] is given by ...

  ARC = (p(b) -p(a))/(b -a)

The average rate of change is ...

  ARC = (f(-3) -f(-6))/(-3 -(-6))

  ARC = (36 -144)/3 = -108/3 = -36

The average rate of change of f(x) on [-6, -3] is -36.

The average rate of change is ...

  ARC = (72 -288)/3 = -216/3 = -72

The average rate of change of g(x) on [-6, -3] is -72.

The ratio of the rates of change is ...

  ARC(g(x))/ARC(f(x)) = -72/-36 = 2

The average rate of change of g(x) is 2 times that of f(x).

__

Additional comment

We hope you noticed that g(x) is f(x) scaled vertically by a factor of 2. That scale factor is the ratio of the rates of change of the two functions.

The weight of the tallest dog which is of height 20 inches on this scatter-plot showing dog heights and their weights is 30 pounds.

The graphs, scatter plots, or scatter charts show the relationship between two variables in a data set that has been analysed.  Both a two-dimensional plane and the Cartesian-system are used to represent the data points. Observing and illuminating correlations between two numerical variables is the main purpose of scatter plots. When the data are viewed as a whole, the dots in a scatter plot show patterns in addition to the values of the individual data points. The Y-axis is used to plot the dependent variable, while the X-axis is used to represent the independent variable or attribute. Using a scatter plot, you may see what happens to one variable when another variable is altered. To determine whether the two variables are connected, a scatter plot is utilised.

The scatter plot shows the dog weights & their heights surveyed.

Data represented on X-axis(independent variable) : heights of dogs

Data represented on Y-axis(dependent variable) : weights of dogs

Lowest weight of dog=5 pounds(approx)

Greatest weight of the dog surveyed=41 pounds(approx)

Lowest height of surveyed dog=5 inches.

Greatest height of surveyed dog=20 inches.

∴The weight of tallest dog with 20 inches if height=30 pounds

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The correct list of functions ordered from 0 ≤ x ≤ 3 is:

h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x

Line connecting the interval's endpoints in order to compute the average rate of change for each function over range 0 x 3.

For f(x) = x^2, the slope between x = 0 and x = 3 is:

[tex](f(3) - f(0)) / (3 - 0) = (9 - 0) / 3 = 3[/tex]

For g(x) = 2x + 1:

[tex](g(3) - g(0)) / (3 - 0) = (7 - 1) / 3 = 2[/tex]

For h(x) = sin(x):

[tex](h(3) - h(0)) / (3 - 0) = (sin(3) - sin(0)) / 3[/tex] ≈ 0.279

For k(x) = e^x, the slope between x = 0 and x = 3 is:

[tex](k(3) - k(0)) / (3 - 0) = (e^3 - 1) / 3[/tex] ≈ 6.076

Therefore, correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3 is:

[tex]h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x[/tex]

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--The complete Question is, Consider the following four functions:

f(x) = x^2

g(x) = 2x + 1

h(x) = sin(x)

k(x) = e^x

What is the correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3? --

Answer:

Step-by-step explanation:

Evaluate the expression

Divide 18 by 3 = 6

Then add the 6 to the 8

then subtract 7 from 14

answer=7

The value of x is given as follows:

x = 9.40 cm.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The parameters for this problem are given as follows:

Applying the cosine, the value of x is obtained as follows:

cos(20º) = x/10

x = 10 x cosine of 20 degrees

x = 9.40 cm.

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The probability of hitting the black circle inside the target is approximately 0.0314.

The probability of hitting the white portion of the target is approximately 0.686.

Part A:

The black circle has a diameter of 2 units, which means it has a radius of 1 unit. The area of the circle is πr^2, which is π(1)^2 or π square units. The area of the white square is 10 x 10 or 100 square units.

The probability of hitting the black circle inside the target is the ratio of the area of the circle to the area of the square, which is π/100 or approximately 0.0314. This probability is closer to 0 because the circle is much smaller than the square, and the likelihood of hitting the exact center of the circle is low.

Part B:

The white portion of the target is the area of the square minus the area of the black circle, which is 100 - π square units.

The probability of hitting the white portion of the target is the ratio of the area of the white portion to the area of the square, which is (100-π)/100 or approximately 0.686.

This probability is closer to 1 because the white portion of the target is much larger than the black circle, and there are many possible areas of the square that could be hit.

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The branch of mathematics that analyzes situations in which players must make decisions and then receive payoffs most often used by economists is "game theory". So, option C is the correct answeer.

Game theory is a branch of mathematics that studies how people or organizations interact in situations where there are choices to be made and where the outcome of each choice depends on the choices made by others. It is often used in economics to model the behavior of firms and consumers in markets, and to analyze strategic interactions between competitors in oligopolistic industries.

One of the most famous examples of game theory is the prisoner's dilemma, which is a simple model that illustrates how two individuals might not cooperate, even if it appears that it is in their best interest to do so.

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The volume of the sphere with a diameter of 28 millimeters is 4398.23 cubic millimeters.

To find the volume of a sphere with a diameter of 28 millimeters, we can use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.

Step 1: Calculate the radius.

Since the diameter is 28 millimeters, the radius is half of that, which is 14 millimeters (28/2).

Step 2: Use the volume formula.

V = (4/3)πr³

V = (4/3)π(14³)

Step 3: Calculate the volume.

V = (4/3)π(2744)

V ≈ 4398.23 cubic millimeters

So, the volume of the sphere with a diameter of 28 millimeters is approximately 4398.23 cubic millimeters.

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A completely randomized model in a single factor study means that the assignment of treatments is completely random, with no underlying pattern or bias.

When analyzing the difference in means between treatments in a single factor, a completely randomized model means that each individual or unit in the study has an equal chance of being assigned to any of the treatment groups.

In other words, the assignment of treatments is completely random, with no underlying pattern or bias.

This type of experimental design is important because it helps to minimize the effects of confounding variables and other sources of bias.

By randomly assigning treatments to study participants, researchers can be confident that any observed differences in the outcome variable are due to the treatment itself, rather than to other factors that may vary between the groups.

In statistical analysis, a completely randomized model can be used to test whether there are significant differences in the means between the different treatment groups.

This can be done using methods such as analysis of variance (ANOVA) or t-tests, depending on the number of treatment groups and the type of outcome variable being measured.

Overall, the completely randomized model is an important tool for ensuring that the assignment of treatments in a single factor study is unbiased and that the resulting data are suitable for statistical analysis.

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The solution of the system of equations in this problem is given as follows:

(4,0).

The equations that compose the system in this problem are given as follows:

We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.

From the graph given by the image presented at the end of the answer, the solution to the system is given as follows:

(4,0).

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