The U.S. federal budget debt was $8612 billion in 2006 and $15,041 billion in 2011. Find the average rate at which the debt was increasing. Show all work

Answer:

8/27

Step-by-step explanation:

2/3 × 2/3 × 2/3

= 8/27

Answer: 0.4444 in decimal form

Step-by-step explanation:

Answer:

6.8

Step-by-step explanation:

The number is already rounded to the nearest tenth and hundredth.

The ounces of shaving cream will be 230 ounces.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:

= 56 ÷ 7/15

= 56 × 15/7

= 120

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Answer:

Step-by-step explanation:

80.000

The value of x in the triangle is 20 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Using triangle proportional theorem, If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Hence,

11 / 121 = 10 / 5x + 10

cross multiply

11(5x + 10) = 1210

55x + 110 = 1210

55x = 1210 - 110

55x = 1100

divide both sides of the equation by 55

x = 1100 / 55

x = 20

Therefore,

x = 20

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Answer: 30

Step-by-step explanation:

Plug in x for the expression

6^2 + x - x^2

36 + (3) - (3)^2

36 + 3 - 9

39 - 9

= 30

Answer:

Answer ≈ 0.022

Step-by-step explanation:

For these types of questions with sin cos or tan, you will need to use a calculator. There is no other way as far as I have seen on the internet to solve this type of problem. Anyways, what you have to do is take your calculator and put in:

sin

sin(2/3+3/5)  exactly like that

and the calculator will give this to you:

0.022105703 which you can then round up.

I hope this answer helped you out. If it did I would greatly appreciate it if you could check out my channel The Game Rater(or Nitro Studios the name might change). I would really appreciate that. Thanks.

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

C)

Step-by-step explanation:

The number of playes can only be 8, 9, 10 ,11 , 12

Answer:

x = 6

Step-by-step explanation:

x² - 12x + 36 ≤ 0

(x - 6)(x - 6) ≤ 0

(x - 6)² ≤ 0

x - 6 = 0

x = 6

es el único valor que cumple la condición, cualquier otro sera mayor que 0

To solve the question, we will apply the principle

If the sides are not equal, the sum of the two shortest sides must be greater than the longest sides

For option A

3 cm, 3cm, 3cm

All sides are equal so it satisfies the condition for a triangle

For option B

The sum of the two shorter sides (4cm and 8cm) = 12cm

while the longest side is 12cm

Since the sum of 12cm is not more than the longest side, then

the sides are NOT suitable for a triangle

For option C

5cm + 9cm = 14 cm

The longest side = 14cm

Since the sum 14cm is not greater than the longest side, then

the sides are NOT suitable for a triangle

For option D

Sum of the shorter sides = 6cm + 7cm = 13cm

longest side = 8cm

Since the sum of 13cm is greater than 8cm, then it is suitable for a triangle

For option E

Sum of shorter sides = 7cm + 7cm = 14cm

longer side = 10cm

Since the sum of 14cm is greater than 10cm, then it is suitable for a triangle

The answer in exponent form is 147x^29.

A scientific notation is a method of expressing very large numbers in the form of exponent.

In the given question, we have;

(7x^9)^2*3x^11

applying the law of indices,

(7x^9)^2*3x^11 = (7^2)*x^(9*2)*3x^11

                        = 49x^18*3x^11

                        = (49*3)*x^(18+11)

                        = 147x^29

Thus, the expression can be simplified as: 147x^29.

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It is important to note that sharing or requesting specific keys or answers to educational materials, including guided notes, would be considered unethical and potentially a violation of academic integrity.

Guided notes are intended to assist students in actively engaging with course material and enhancing their learning experience. It is recommended that you approach your teacher or instructor for any clarification or additional resources you may need to fully understand the content.

They are in the best position to provide you with the necessary guidance and support.

Instead of seeking shortcuts or unauthorized access to answers, it is more beneficial to invest time and effort in studying, asking questions, and actively participating in your educational journey.

This approach will not only help you grasp the subject matter more effectively but also promote personal growth and knowledge development.

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Answer:

4 units right, 2 units up

Step-by-step explanation:

For \(g(x)=(x-4)^2+2\), the graph of \(f(x)=x^2\) would need to move 4 units to the right and 2 units up. Hence, the vertex would be \((4,2)\) if we compare the function g(x) with the form \(y=a(x-h)^2+k\).

Answer:

0.065 units ³

Step-by-step explanation:

Volume of sphere = 4/3 π r³

=> 4/3 × 22/7 × 1/4 × 1/4 × 1/4

=> 0.065 units³

Answer:

\(\frac{1}{48}\) π units³

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = \(\frac{4}{3}\) πr³ ( r is the radius ) , then

V = \(\frac{4}{3}\) π × ( \(\frac{1}{4}\) )³

  = \(\frac{4}{3}\) π × \(\frac{1}{64}\) ( cancel 4 and 64 on numerator/ denominator by 4 )

  = \(\frac{1}{3}\) π × \(\frac{1}{16}\)

  = \(\frac{1}{48}\) π units³

Answer:

y^3 - 9y^2 + 26y - 29

Step-by-step explanation:

y - 4[y - 3(y - 2)] - 5

I'm going to separate it into parts

(y - 3)(y - 2)

y^2 - 5y + 6

(y - 4)(y^2 - 5y + 6)

y^3 - 5y^2 + 6y - 4y^2 + 20y - 24

y^3 - 9y^2 + 26y - 24

y^3 - 9y^2 + 26y - 24 - 5

y^3 - 9y^2 + 26y - 29

Answer: A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true.

Step-by-step explanation:

The null hypothesis\((H_0)\) and alternative hypothesis\((H_a)\) both are statements as per the researcher's claim that involves population parameter .

Null hypothesis has  ≤,≥ ,= signs

Alternative hypotheses has < , > , ≠ signs.

A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true.

To simplify the expression 3(sin⁸ - cos⁸) + 4(cos⁶ - 2sin⁶), we'll use the identity for the difference of squares and the identity for the square of a binomial.

First, let's focus on the expression sin⁸ - cos⁸. We can rewrite this using the identity for the difference of squares as follows: sin⁸ - cos⁸ = (sin⁴)² - (cos⁴)² = (sin⁴ + cos⁴)(sin⁴ - cos⁴) Next, we can use the identity for the square of a binomial, which states that

(a + b)² = a² + 2ab + b²,

to expand

(sin⁴ + cos⁴)² as follows:

(sin⁴ + cos⁴)² = sin⁸ + 2sin⁴cos⁴ + cos⁸

Now we can substitute

sin⁸ - cos⁸ with (sin⁴ + cos⁴)(sin⁴ - cos⁴)

and simplify:

sin⁸ - cos⁸ = (sin⁴ + cos⁴)(sin⁴ - cos⁴) = (sin⁴ + cos⁴)(sin⁴ + cos⁴)(sin² - cos²)

= (sin⁴ + cos⁴)(sin² - cos²)² = (sin² + cos² - 2sin²cos²)(sin² - cos²)² = (1 - 2sin²cos²)(sin² - cos²)²

Now we can substitute this expression into our original equation:

3(sin⁸ - cos⁸) + 4(cos⁶ - 2sin⁶) = 3(1 - 2sin²cos²)(sin² - cos²)² + 4(cos⁶ - 2sin⁶)

We can further simplify by factoring out 2sin² from the second term:

3(1 - 2sin²cos²)(sin² - cos²)² + 4(cos⁶ - 2sin⁶) = 3(1 - 2sin²cos²)(sin² - cos²)² + 4(2sin²cos²cos⁴ - 2sin⁶) = 3(1 - 2sin²cos²)(sin² - cos²)² + 8sin²(cos⁴ - sin⁴)

This is the final simplified form of the expression.

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Answer:34

Step-by-step explanation:

32+2=34

Answer:

= 34

Step-by-step explanation:

8t + 2 = (4) + 2 = 32 + 2 = 34

that's my answer , i wish my answer helps you

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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Answer:

Mason reads the fastest

Answer:

c

Step-by-step explanation:

try to see how much every person reads every one or two minutes.

Charlie: 350 in two min

Mason :400 in two min

Sarah: 450 in two min (the middle of 300-600 is 450)

so between the three Sarah wins.

now Reilly is a bit more difficult but you can see that she read 4000 in 20 min. so if we divide it by 10 we can see she reads 400 in 2 min. and therefore Sarah os the winner.

Based on their given probabilities, e would expect the color blue or green to be spun approximately 75 times in this experiment.

To find the expected number of times the color blue or green will be spun, we first need to add their probabilities:

0.25 + 0.125 = 0.375

This means that, on average, we would expect to see blue or green spun 0.375 times for every spin. To find the expected number of times this will happen over 200 spins, we can multiply the probability by the number of spins:

0.375 x 200 = 75

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Answer:

There will be lots

Step-by-step explanation:

It is actually infinite.

Answer:

False, the first percentile is less than 22 hours.

Step-by-step explanation:

xth percentile:

If a measure is said to be in the xth percentile, it means that x% of the measures are smaller than it, and (100-x)% are larger.

Twenty four of the families in the sample watched TV for less than 22 hrs per week. In the sample, there are 150 families.

This means that 22 is the:

24*100%/150 = 16th percentile.

The first percentile is greater than or equal to 22 hours: True or False?

The first percentile is less than the 16th percentile, which is 22. This means that this is false, the first percentile is less than 22 hours.

Answer:

8

Step-by-step explanation:

3/4 cup leaves 1/4 cup from each cup

1/4+1/4+1/4=3/4

so it would be 3/4+3/4+3/4+3/4+3/4+3/4+3/4+3/4=8 cups

Answer:

\( \boxed{f(x) = 2 {x}^{9} - 4 {x}^{2} + 4}\)

Option B is the correct option

Step-by-step explanation:

By looking at the end behavior , we can say that the degree of the polynomial must be odd and leading coefficient will be positive.

Thus , the correct choice is B.

Hope I helped!

Best regards!

The polynomial function that could have created the given curve on the xy-plane is \(f(x)= 2x^9-4x^2+4\)

Polynomial functions aree function having a leading degrees of 3 and greater.

The nature of the curve on the xy-plane depends on its end behaviour. From the given graph, the end behaviour shows that the equivalnt function has a positive leading coefficient and an odd degree.

From the listed option, the function that satisfies both criteria is \(f(x)=2x^9-4x^2+4\).

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