A publisher sells 10⁶ copies of a new book. Each book sells 10² pages. How many pages total are there in all of the books sold? Write the answer using exponents.
1 point

Answer:

13) The ratio is not equivalent

14) The ratio is equivalent

15) The ratio is not equivalent

16) The ratio is equivalent

17) The ratio is equivalent

18) The ratio is not equivalent

I hope this helps

Answer:

Subtracting \(3x^2+4x-5\) from \(7x^2+x+9\) results in a polynomial. After subtracting \(4x^2-3x\) from this polynomial the difference is 14

Step-by-step explanation:

The question given is:

Subtracting \(3x^2+4x-5\) from \(7x^2+x+9\) results in a polynomial. After subtracting \(4x^2-3x\) from this polynomial the difference is?

First we will Subtracting \(3x^2+4x-5\) from \(7x^2+x+9\)

\(7x^2+x+9-(3x^2+4x-5)\\=7x^2+x+9-3x^2-4x+5\\Combining\:like\:terms\\=7x^2-3x^2+x-4x+9+5\\=4x^2-3x+14\)

So, the polynomial we get is: \(4x^2-3x+14\)

Now, subtracting \(4x^2-3x\: from\: 4x^2-3x+14\)

\(4x^2-3x+14-(4x^2-3x) \\=4x^2-3x+14-4x^2+3x\\Combining\:like\:terms\\=4x^2-4x^2-3x+3x+14\\=14\)

The difference is 14

So, Subtracting \(3x^2+4x-5\) from \(7x^2+x+9\) results in a polynomial. After subtracting \(4x^2-3x\) from this polynomial the difference is 14

Using it's concept, it is found that the average rate of change of the function during the interval from 0 to 2 seconds is given by:

B. -32 ft/s; the average change in altitude of the ball each second over that interval.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

\(r = \frac{f(b) - f(a)}{b - a}\)

In this problem, the function is given by:

f(t) = -16t² + 100.

The outputs are given as follows:

Hence the average rate of change is given by:

r = (36 - 100)/(2 - 0) = -32 ft/s.

And the correct option is:

B. -32 ft/s; the average change in altitude of the ball each second over that interval.

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Answer:

Step-by-step explanation:

14

Answer:

12

Step-by-step explanation:

The average rate of change in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ 2, 4 ]

f(b) = f)4) = 32 ← from table

f(a) = f(2) = 8 ← from table

Then average rate of change is

\(\frac{32-8}{4-2}\) = \(\frac{24}{2}\) = 12

Answer:

x = 8

Step-by-step explanation:

the average is calculated as

average = \(\frac{sum}{count}\)

given that the average of both sets of data are equal then

\(\frac{4+x}{2}\) = \(\frac{2+8+x}{3}\) ( cross- multiply )

3(4 + x) = 2(10 + x) ← distribute parenthesis on both sides

12 + 3x = 20 + 2x ( subtract 2x from both sides )

12 + x = 20 ( subtract 12 from both sides )

x = 8

Using probability, we can find that the probability of getting the outcome 10 is = 3/16.

The likelihood that an event will occur is described by the concept of probability. In real life, making future predictions is a common task. Whether we know how an event will turn out is up to us. When this occurs, we say there's a chance the event will happen. In conclusion, probability offers a wide variety of wonderful applications in industries like games, business, and this quickly developing area of artificial intelligence.

Here in the question,

Total number of outcomes when the spinners are spined, and the sum is 10 is = 16.

Now, the number of times the sum of both the spinners is 10 is = 3.

Therefore, the probability that the outcome is 10 = 3/16.

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The exponential functions are: f(x) = 2^(3x+1), ƒ(x) = -4^x, and f(x) = 0.8^x+2.

Exponential functions are the type of functions where the variable is in an exponent. The general form of the exponential function is given by y = ab^x, where a and b are constants and b is the base.

Using this information, let us check which of the given functions are exponential functions.1. f(x) = −(4)* = -4

This is a constant function. It is not an exponential function.2. f(x) = x^6

This is a polynomial function. It is not an exponential function.3. f(x) = 1/x

This is a rational function. It is not an exponential function.4. f(x) = π6x

This is a periodic function. It is not an exponential function.5. f(x) = 23x+1= (2^3) * 2^x

This is an exponential function.6. ƒ(x) = (-4)* = -4x

This is an exponential function.7. f(x) = 0.8x+2

This is an exponential function.8. f(x) = 8 - x

This is a linear function. It is not an exponential function.

Thus, the exponential functions are: f(x) = 2^(3x+1), ƒ(x) = -4^x, and f(x) = 0.8^x+2.

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The random number generation by the device is not appropriate for generating values according to the Binomial distribution with n=5 and p=0.45.

To test whether the generated values follow the expected Binomial distribution, we can use the Chi-squared goodness-of-fit test. The steps to perform this test are as follows

Define the null hypothesis and alternative hypothesis. In this case, the null hypothesis is that the generated values follow the expected Binomial distribution with n=5 and p=0.45. The alternative hypothesis is that the generated values do not follow this distribution.

Choose a significance level. In this case, the significance level is 0.05.

Calculate the expected frequencies for each category of the Binomial distribution with n=5 and p=0.45. We can use the formula for the Binomial distribution to calculate the probabilities, and then multiply them by the total number of observations to get the expected frequencies.

Expected frequency for each category = P(category) x total number of observations

Expected frequency for category 0 = P(0) x 1200 = 0.0176 x 1200 = 21.12

Expected frequency for category 1 = P(1) x 1200 = 0.1284 x 1200 = 154.08

Expected frequency for category 2 = P(2) x 1200 = 0.3574 x 1200 = 428.88

Expected frequency for category 3 = P(3) x 1200 = 0.4162 x 1200 = 499.44

Expected frequency for category 4 = P(4) x 1200 = 0.1949 x 1200 = 233.88

Expected frequency for category 5 = P(5) x 1200 = 0.0055 x 1200 = 6.6

Calculate the Chi-squared test statistic. The formula for the Chi-squared test statistic is:

Chi-squared = Σ ( (observed frequency - expected frequency)^2 / expected frequency )

where Σ is the sum over all categories. Using the expected frequencies and the observed frequencies from the table, we can calculate the Chi-squared test statistic

Chi-squared = ( (28-21.12)^2 / 21.12 ) + ( (168-154.08)^2 / 154.08 ) + ( (423-428.88)^2 / 428.88 ) + ( (459-499.44)^2 / 499.44 ) + ( (105-233.88)^2 / 233.88 ) + ( (17-6.6)^2 / 6.6 ) = 94.67

Calculate the degrees of freedom. The degrees of freedom for the Chi-squared test are equal to the number of categories minus 1. In this case, there are 6 categories, so the degrees of freedom are 5.

Calculate the P-value of the test. We can use a Chi-squared distribution table or a calculator to find the P-value for the Chi-squared test with 5 degrees of freedom and a test statistic of 94.67. The P-value is less than 0.01 (about 0.000000000000000000000000000000000000000001), so we reject the null hypothesis that the generated values follow the expected Binomial distribution with n=5 and p=0.45.

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The given question is incomplete, the complete question is:

A random number generation device is expected to generate random values according to the Binomial distribution with n=5 and p=0.45. To ensure that the device's random number generation is appropriate, 1200 recently generated random values by this device have been organized in the following table. If the Chi-squared goodness-of-fit test is used with a significance of 0.05 to test whether random values have been appropriately generated by the device, what is the P-value of the test rounded to two places after the decimal, and the decision made?

Answer: 1 1/2

Step-by-step explanation:

1 4/5 = 9/5

1 1/5 = 6/5

\(\frac{9}{5} / \frac{6}{5}\\ \\\frac{9}{5} * \frac{5}{6}\\ \\\frac{45}{30} \\ \\1\frac{1}{2}\)

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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Donald paid the wager to Bill after losing the bet, he may not be able to recover the funds from Bill.

Given that Donald had willingly fulfilled his part of the bet by paying the wager to Bill, it would be difficult for him to recover the funds. Generally, once a payment is made and received, it is considered a final transaction, and the payer loses any legal entitlement to demand a refund. This principle is known as the "doctrine of consideration" or "consideration of contract."

In this case, Donald voluntarily transferred the funds to Bill, acknowledging his loss and fulfilling his obligation under the bet. Consequently, Donald may not have a legal basis to recover the funds from Bill, as he has already relinquished his claim to them.

However, it is important to note that legal outcomes can vary based on jurisdiction and specific circumstances. Laws and regulations governing bets and contracts can differ, so consulting with a legal professional would provide the most accurate guidance for this particular situation.

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The required coordinates of the vertices of △ABC after it has been rotated 90 degrees, reflected across the line y=0, and then translated according to the rule (x+3,y-3) are A''' = [8, 1], B''' = [-3, -6], and C''' = [-5, -4].

To determine the coordinates of the vertices of △ABC after it has been rotated 90 degrees, reflected across the line y=0, and then translated according to the rule (x+3,y-3), we need to apply these transformations to the coordinates of the original vertices in the order given.

First, we rotate the triangle 90 degrees counterclockwise around the origin. This transformation can be represented by the matrix:[cos(90) -sin(90)][sin(90) cos(90)]

Applying this matrix to the coordinates of the vertices of △ABC, we get:A' = [-5, 4]B' = [6, -3]C' = [8, -1]

Next, we reflect the triangle across the line y=0.

This transformation can be represented by the matrix:[-1 0][0 1]

Applying this matrix to the coordinates of the vertices of △ABC', we get:A'' = [5, 4]B'' = [-6, -3]C'' = [-8, -1]

Finally, we translate the triangle according to the rule (x+3,y-3).

This transformation can be represented by the matrix:[1 0][0 1]

Applying this matrix to the coordinates of the vertices of △ABC'', we get:A''' = [8, 1]B''' = [-3, -6]C''' = [-5, -4]

Therefore, the coordinates of the vertices of △ABC after given transformations are A''' = [8, 1], B''' = [-3, -6], and C''' = [-5, -4].

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Answer:

The frame is not a rectangle.

Step-by-step explanation:

11^2 + 14^2 = 17.8

because he measured 19, the angles are not 90°

Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

The answer would be A. -4

Step-by-step explanation:

If you right it out like x-6=5(x+2), then you distribute the 5, you get: x-6=5x+10. Then subtract x from both sides, you get: -6=4x+10. Subtract 10 from both sides, you get: -16=4x. The all you have to do is divide both sides by 4, and you get: -4=x

Answer:B = 18,  A = B + 23 = 18+23 = 41.

Step-by-step explanation:Last year . . .  

   A = 2B + 5     (1)

The number . . .  

   A = B + 23.    (2)

Equations (1) and (2) have the same left sides --- hence, their right sides are equal :

   2B + 5 = B + 23.

It implies

   2B - B = 23 - 5

    B     = 18.

ANSWER.  B = 18,  A = B + 23 = 18+23 = 41.

Given

The vectors u and v as,

To find the vector representing u+v.

Explanation:

It is given that,

Two vectors u and v are represented as,

Then, the vector representing u+v is given by,

The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.

The formula for the continuous exponential growth is given by the formula:

P = Pe^(rt)

where,P is the population in the future.

P0 is the initial population.

t is the time.

r is the continuous interest rate expressed as a decimal.

e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.

Therefore, t = 25.We will now use the formula:

P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.

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Answer: I got 97,042.7

Step-by-step explanation:

Using the volume of the rectangular prism and the cube we know that it is (D) impossible that cubes will fit the rectangular prism as its volume is greater.

The space occupied within an object's borders in three dimensions is referred to as its volume.

It is sometimes referred to as the object's capacity.

The capacity of an object is measured by its volume.

For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.

The quantity of space occupied by a three-dimensional object can also be used to describe volume.

Rectangular prism volume:
V = whl

V = 2*212*4

V = 1,696 in³

Cube's Volume:

V = a³

V = 12³

V = 1728

Then, cubes are needed to fill the rectangular prism:
1696/1728 = 0.98

Hence, not possible.

Therefore, using the volume of the rectangular prism and the cube we know that it is (D) impossible that cubes will fit the rectangular prism as its volume is greater.

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Correct question:

A rectangular prism has a length of 4 in., a width of 2 in., and a height of 212 in.

The prism is filled with cubes that have edge lengths of 12 in.

How many cubes are needed to fill the rectangular prism?

A. 2

B. 4
C. 6

D. Not possible

Answer:

x = 48

Step-by-step explanation:

log⁡〖 (2x+4)〗=2

Raise each side to the base of 10

10 ^log⁡〖 (2x+4)〗=10^2

The 10 ^log cancels

2x+4 = 100

Subtract 4 from each side

2x+4-4 = 100-4

2x = 96

Divide by 2

2x/2 = 96/2

x =48

Answer:

x=35

Step-by-step explanation:

We know that sum of angles in a triangle=180

120

o

+25

o

+x=180

145

o

+x=180

o

x=35

o

x=60°, y=15°, angle C is 45°, angle DBC is 105° and angle CBA is 75°.

In the given figure, ∠DBC=7y°, ∠CBA=5y°, ∠C=3y° and ∠D=x°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Here,

∠DBC+∠CBA=180° (Sum of adjacent angles is 180°)

⇒ 7y°+5y°=180°

⇒ 12y°=180°

⇒ y°=15°

∠DBC=7y°=105°, ∠CBA=5y°=75° and ∠C=3y°=45°

Now, ∠DBC=∠C+∠A

⇒ 105°=45°+∠A

⇒ ∠A=60°

Therefore, x=60°, y=15°, angle C is 45°, angle DBC is 105° and angle CBA is 75°.

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Answer:

15.3

Step-by-step explanation:

the 8 in the hundredths place is greater so the 2 in the tenths place has to go up one to be 3 so 15.3

Answer

Area of the real dining hall = 72 m²

Explanation

The area of any rectangular shape is given as

Area = L × W

where

L = Length of the rectangle

W = Width of the rectangle

For this question, we have been given the dimensions of the dining hall in the drawing and told that

5 cm in the drawing = 6 m in reality

So, if the real length of the dining is L

5 cm = 6 m

10 cm = L

We can write a mathematical relationship by cross multiplying

(5) (L) = (10) (6)

5L = 60

Divide both sides by 5

(5L/5) = (60/5)

L = 12 m

If the real width of the dining hall is W

5 cm = 6 m

5 cm = W

We can write a mathematical relationship by cross multiplying

(5) (W) = (5) (6)

5W = 30

Divide both sides by 5

(5W/5) = (30/5)

W = 6 m

So, for the real dining hall,

Length = 12 m

Width = 6 m

Area = Length × Width

Area = 12 × 6

Area = 72 m²

Hope this Helps!!!

The  percent of students who chose each website is as follows:

Website A: 29.17%

Website B: 10.83%

Website C: 18.33%

Website D: 8.33%

To find the percent of students who chose each website, you can calculate the percentage for each website by dividing the number of students who chose that website by the total number of students and then multiplying by 100.

Let's calculate the percentages:

For Website A: (35/120) x 100 = 29.17%

For Website B: (13/120) x 100 = 10.83%

For Website C: (22/120) x 100 = 18.33%

For Website D: (10/120) x 100 = 8.33%

So, the percent of students who chose each website is as follows:

Website A: 29.17%

Website B: 10.83%

Website C: 18.33%

Website D: 8.33%

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Answer:

w=24, I hope this helps

Step-by-step explanation:

17=41-w w=24,

Answer:

The fourth one

Step-by-step explanation:

41 - 17 = 24

How to check your answer

24 + 17 = 41

Answer:

None of the Above

Step-by-step explanation:

Key Skills required are: One Variable Equations, Supplementary Angle Pairs, Substitution, and Triangles.

1) To find the measure of Angle C, we first need to find the measure of angle DBC and Angle D.

2) We are given that Angle EBA is x and Angle EBD is 4x+13 and Angle D is 3x + 9 (we will use Angle D later in the problem)

3) Now, we need to use the fact that Angle EBA and Angle EBD are supplementary (they form a linear pair, so they are supplementary).

A pair of supplementary angles add up to  180 degrees (as they form a straight angle).

4) x + 4x + 13 = 180

5) Combine like terms --> 5x + 13 = 180

6) Move 13 to the other side --> 5x = 167

7) Divide by 5 and solve for x: x= 33.4

8) Now we got that x is 33.4, we can get the measure of angle DBC and Angle D.

9) Angle DBC is congruent to Angle EBA. So to find the measure of DBC we need to find the measure of Angle EBA. EBA is just x, so it is 33.4 degrees

10) Therefore, Angle DBC also measures 33.4 degrees.

11) To find angle D, we substitute x into 3x + 9 (We are given angle D is 3x + 9 based on the problem)

12) 3(33.4) + 9 = 100.2 + 9 = 109.2

13) Now we use the interior angles sum of a triangle to find Angle C.

The interior angles of a triangle sum up to 180 degrees.

14) With the statement above we can make this equation: 109.2 + 33.4 + Angle C = 180

15) Simplify by combining like terms: 142.6 + Angle C = 180

16) 37.4 degrees would be the measure of C, so I feel it would be none of the above.

Hope you understood and have a nice day!! :D

Answer:

Question 5 is positive 8

Step-by-step explanation:

I need to see the number line for question 4