Evaluate. Write your answer as a whole number or as a simplified fraction.
8 to the power of 9
8 to the power of 7

Answer:

a=6, b=4.

Step-by-step explanation:

6+4=10, and 6-4=2.

Answer:

See below

Step-by-step explanation:

a+b =10

a-b = 2    add the two equations

2a = 12     then a = 6      a+b=10 so b = 4

The length of the shortest path that the gecko can take to reach the fly is \($2 \sqrt{29}$\) feet.

Here's how to solve the problem: We can start by sketching out a diagram of the room and labeling the positions of the gecko and the fly. We'll use the corner where the gecko is as the origin, and label the coordinates of the gecko as (0,1,1) and the coordinates of the fly as (12,1,7). The distance between these two points is the shortest path that the gecko can take to reach the fly.

Now we can use the distance formula to calculate this distance:

\($$\sqrt{(12-0)^2 + (1-1)^2 + (7-1)^2}=\sqrt{144+36}=2\sqrt{29}$$\)

Therefore, the length of the shortest path the gecko can take to reach the fly is \($2\sqrt{29}$\) feet.

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Answer:

9 feet

Step-by-step explanation:

this is asking for one length of the sides of the garden. using key words, such as ~squared~ we can conclude that the shape of the garden is in fact a square, therefore, all sides will be equal. 9x9 would be the equation used, and even then the number is too large. all of the other options are larger therefore I don't think they are your answer.

Answer:

what's the math problem

Step-by-step explanation:

The total volume of juice that Deeva has left after serving his freinds is 2240ml.

Total volume of the juice that Deeva has is 6720ml.

He is going to serve in 12 identical cups.

So, using unitary method,

Total volume of 12cups juice = 6720ml

Total volume in one cup juice = 6720/12ml

Total volume in one glass juice = 560ml.

Deeva served 8 cups of juices to his friends.

So, volume of juice served = Volume of one cup juice x volume of one cup juice

Volume of juice served = 560 x 8

Volume of juice served = 4480 ml.

The juice he had left = Initial amount of juice - juice served

the juice left = 6720 - 4480

The juice left = 2240ml.

Hence, the juice that has left after serving is 2240 ml.

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The volume of prism L is 750 cm³

A prism is a three-dimensional solid, that has two identical bases, rectangular or parallelogram-shaped faces, and the same cross-section.

The formula for the volume of a prism is V=Bh,

where B = base area and h = height.

We have,

Two similar prism

Prism L:

Length = 8 cm

Prism M:

Length = 20 cm

Volume = 1875 cm³

Applying the volume formula:

V = Bh

Base area = Length x width

1875 = Length x width x height

1875 = 20 x width x height

Width x height = 1875 / 20 = 93.75 _______(1)

Since prisms are similar we can use (1) in finding the Volume of prism L.

The volume of prism L:

= Length x width x height

= 8 x 93.75

= 750

Thus the volume of prism L is 750 cm³

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The complete question is:

L and M are two mathematically similar prisms.

Prism L has a length 8 cm.

Prism M has a length 20 cm.

Prism M has a volume of 1875 cm3

Work out the volume of prism L.

Answer:

150 is 100% of 150

Steps to solve "150 is 100 percent of what number?"

We have, 100% × x = 150

or,

100

100

× x = 150

Multiplying both sides by 100 and dividing both sides by 100,

we have x = 150 ×

100

100

x = 150

If you are using a calculator, simply enter 150×100÷100, which will give you the answer.

Answer:

56 meters

Step-by-step explanation:

5+5+5+11+7+16+7 = 56

Answer:

Should be 56 m

Step-by-step explanation:

5+7+16+7+11+5+5 = 56 m

1] (a) The probability that both chosen students are women is 0.3025 or 30.25%.

To find the probability, we can use a probability tree. Let's represent the first student as A and the second student as B.

(a) To find the probability that both chosen students are women, we start with the probability of selecting a woman as the first student, which is 55%. This probability is represented by P(A=W) = 0.55. Then, for the second student, given that the first student is a woman, the probability of selecting another woman is 54% (since there is one less woman in the remaining sample). This probability is represented by P(B=W|A=W) = 0.54.

To find the probability of both events occurring, we multiply the probabilities:

P(A=W and B=W) = P(A=W) * P(B=W|A=W) = 0.55 * 0.54 = 0.297.

Therefore, the probability that both chosen students are women is 0.297 or 29.7%.

(b) To find the probability that at least one of the two students is a woman, we can calculate the complement of the probability that both students are men.

The probability that both students are men is found by multiplying the probabilities of selecting a man for each student:

P(A=M and B=M) = P(A=M) * P(B=M|A=M) = 0.45 * 0.46 = 0.207.

Then, the probability that at least one of the two students is a woman is the complement of this probability:

P(at least one woman) = 1 - P(both men) = 1 - 0.207 = 0.793.

Therefore, the probability that at least one of the two students is a woman is 0.793 or 79.3%.

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The approximate probability of getting a z-score between +1 standard deviation and +2.5 standard deviations in a standard normal distribution is 0.1525.

To find the area under the standard normal curve between +1 standard deviation and +2.5 standard deviations, we can use a standard normal distribution table or calculator. Here are the steps:

Therefore, the area under the standard normal curve between +1 standard deviation and +2.5 standard deviations is approximately 0.1525.

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Answer:

ight so combine the 14x and the 4x thats 18x then divide by 18 90 divided by 18 is 5 so x is 5

Step-by-step explanation:

Answer:3,2,3 and 2

Step-by-step explanation: too much to explain but those are the answers

Answer:

25:26,28,30

26:-4,-2,0

27:W=V/LH

28:(A-PH)/2

Step-by-step explanation:

25: The first thing you need to do is 84/3=28, which is in the middle. On the  left side, it should be 28-2, which is 26, and on the right side, it should 28+2, which is 30, so the answer is 26,28,30.

26: The first thing you need to do is -6/3 = -2, which is in the middle. On the left side, it should be -2-2, which is -4, and on the right side, it should be -2+2 which is 0, so the answer is -4,-2,0.

27: V=LWH, W=V/LH.

28: A - PH = PH + 2B - PH, A - PH = 2B, (A - PH)/2 = 2B/2, B = (A - PH)/2.

Multi-step equations are those that must be solved over the course of two or more steps.

An equation that needs to be solved in two or more steps is known as a multi-step equation. There may be a combination of addition, subtraction, multiplication, and division in these questions. For proper equation solving, we could additionally need to combine like terms or apply the distributive property.

Similar to multi-step equations, multi-step inequalities might require combining like terms, the distributive property, and variables on both sides. Again, the only distinction when resolving inequalities is that when multiplying or dividing by a negative number, the sign must be reversed.

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The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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Answer:

i think its 2nd one and 3rd one

Step-by-step explanation:

a. the equation for the object's velocity is v(t) = -6 cos(t) - 1. b. the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

a) To find the equation for the object's velocity, we need to integrate the acceleration function with respect to time.

The integral of a(t) = 6 sin(t) with respect to t gives us the velocity function v(t):

v(t) = ∫(6 sin(t)) dt

Integrating sin(t) gives us -6 cos(t), so the equation for the object's velocity is:

v(t) = -6 cos(t) + C

To find the constant C, we use the initial velocity v(0) = -7 m/s:

-7 = -6 cos(0) + C

-7 = -6 + C

C = -1

Therefore, the equation for the object's velocity is:

v(t) = -6 cos(t) - 1

b) To find the object's displacement from time 0 to time 3, we need to integrate the velocity function over the interval [0, 3]:

Displacement = ∫[0,3] (-6 cos(t) - 1) dt

Integrating -6 cos(t) gives us -6 sin(t), and integrating -1 gives us -t. Applying the limits of integration, we have:

Displacement = [-6 sin(t) - t] from 0 to 3

Plugging in the upper and lower limits:

Displacement = [-6 sin(3) - 3] - [-6 sin(0) - 0]

Displacement ≈ -6 sin(3) + 3

Therefore, the object's displacement from time 0 to time 3 is approximately -6 sin(3) + 3 meters.

c) To find the total distance traveled by the object from time 0 to time t, we need to integrate the absolute value of the velocity function over the interval [0, t]:

Total Distance = ∫[0,t] |(-6 cos(t) - 1)| dt

Since the absolute value function makes the negative part positive, we can rewrite the equation as:

Total Distance = ∫[0,t] (6 cos(t) + 1) dt

Integrating 6 cos(t) gives us 6 sin(t), and integrating 1 gives us t. Applying the limits of integration, we have:

Total Distance = [6 sin(t) + t] from 0 to t

Plugging in the upper and lower limits:

Total Distance = [6 sin(t) + t] - [6 sin(0) + 0]

Total Distance = 6 sin(t) + t

Therefore, the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

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Answer:

Yes L is parallel to M because they are going the same direction on the graph.

The expected return on James's portfolio is 18%.

The expected return on Siebling Manufacturing Company's common stock is 8.4%.

To calculate the expected return on James's portfolio, we need to take the weighted average of the expected returns of MSFT and AAPL based on their respective investments.

Let's assume James invests x% in MSFT and (100 - x)% in AAPL.

The expected return on James's portfolio can be calculated as:

Expected Return = (x * Expected Return of MSFT) + ((100 - x) * Expected Return of AAPL)

Substituting the given values:

Expected Return = (x * 12%) + ((100 - x) * 24%)

To find the value of x that makes James's investments equal, we set the weights equal:

x = 100 - x

Solving this equation gives us x = 50.

Now we can substitute this value back into the expected return equation:

Expected Return = (50% * 12%) + (50% * 24%)

Expected Return = 6% + 12%

Expected Return = 18%

Therefore, the expected return on James's portfolio is 18%.

To calculate the expected return on Siebling Manufacturing Company's common stock, we can use the Capital Asset Pricing Model (CAPM).

The CAPM formula is:

Expected Return = Risk-Free Rate + Beta * Market Premium

Risk-Free Rate = 2%

Market Premium = 8%

Beta = 0.8

Expected Return = 2% + 0.8 * 8%

Expected Return = 2% + 6.4%

Expected Return = 8.4%

Therefore, the expected return on Siebling Manufacturing Company's common stock is 8.4%.

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Answer:

Part A:

The sequence of transformation that maps triangle DEF to triangle GHI are;

1) A reflection across the y-axis (x, y) →(-x, y) and

2) A translation 6 units down, (-x, y - 6)

Part B:

1) Yes

2) The points of the triangle GHI obtained from the mapping of triangle DEF using the given transformation are corresponding therefore, the mapping proves that the two triangles are congruent

Step-by-step explanation:

Part A:

The given coordinates of the vertices of triangle DEF are;

F(-1, 5), D(-5, 2), and E(-3, 1)

The given coordinates of the vertices of triangle IHG are;

I(1, -1), H(3, -5), and G(5, -4)

Therefore, the transformation that maps ΔDEF to ΔGHI are

1) A reflection across the y-axis (x, y) →(-x, y) and

2) A translation 6 units down, (-x, y - 6)

Reflection of point F(-1, 5) across the y-axis gives → (1, 5)

Followed by a translation 6 units down gives;

(1, 5) →T(y - 6) → I(1, -1)

Reflection of point D(-5, 2) across the y-axis gives → (5, 2)

Followed by a translation 6 units down gives;

(5, 2) →T(y - 6) → G(5, -4)

Reflection of point E(-3, 1) across the y-axis gives → (3, 1)

Followed by a translation 6 units down gives;

(3, 1) →T(y - 6) → H(3, -5)

Part B:

1) Yes mapping triangle DEF onto triangle GHI proves that the two triangles are congruent

2) The points of the triangle GHI obtained from the mapping of triangle DEF are the same, therefore, the mapping proves that the two triangles are congruent

Answer:

Step-by-step explanation:

Given f(x) = ln and g(x) = e^x + 1 to get  f(g(2))-g(f(e)), we need to first find the composite function f(g(x)) and g(f(x)).

For f(g(x));

f(g(x)) = f(e^x + 1)

substitute x for e^x + 1 in f(x)

f(g(x)) = ln (e^x + 1)

f(g(2)) = ln (e^2 + 1)

For g(f(x));

g(f(x)) = g(ln x)

substitute x for ln x in g(x)

g(f(x)) =  e^lnx + 1

g(f(x)) = x+1

g(f(e)) = e+1

f(g(2))-g(f(e)) = ln (e^2 + 1) - (e+ 1)

Fewer than 15% of coins were quarters. Exactly 80% of the coins were nickels, dimes, and quarters. Nickels, dimes, and quarters account for 95% of the total number of coins.

Quarters are coins that are used in many countries as a form of currency. Quarters are generally made of metal and are round in shape. They are typically smaller than other coins, such as dimes and nickels, and have a value of 25 cents (or one-fourth of a dollar). Quarters are often used in everyday transactions, such as buying candy or a newspaper, or to pay for parking. In the United States, there are five different designs of quarters in circulation, each representing a different state or territory.

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Answer:

The pattern is that each time, 8 is added. The next 2 numbers are 47, 55.

Step-by-step explanation:

7+8=15

15+8=23

23+8=31

31+8=39

39+8=47

47+8=55

Answer:

5 boys to 9 girls

Step-by-step explanation:

Let x = the number of boys

Boys = x

Girls = x + 4

x + (x + 4) = 14

2x + 4 = 14

2x = 10

x = 5

This means that there are 5 boys. Since girls = x + 4, 5 + 4 = 9. There are 5 boys and 9 girls.

I hope this helped and please mark me as brainliest!

Answer:

5:9

Step-by-step explanation:

One Simple Method:

We can plug in values that are reasonable, such as 5 and 9. 5 represents the amount of boys and 9 represents the amount of girls. There's four more girls than boys, adding up both terms there's a sum of 14 grandchildren.

Another Method:

using and creating an equation.

x represents boys

y represents girls

Our equation for boys:

x(x+4)=14

2x+4=14

Subtract 4 from both sides

2x=10

x=5

x=5 represents 5 boys.

Use x=5 in our equation for girls.

5+y=14

Subtract 5 from both sides

y=9

y=9 represents 9 girls.

live to be 80 years old and sleep 8 hours a day, How many years have I slept

Solution

A day has 24 hours

24 = 8 + 8 + 8

So you spent 1/3 of your time sleeping.

You can get the same answer if you do 8/24

8/24 = (8 ÷ 8) / ( 24 ÷ 8) = 1/3

All you need to do now is to find 1/3 of 80

1/3 of 80 = 1/3 × 80 = 80/3

80 / 3 = (78 + 2) / 3 = 78 / 3 + 2 / 3 = 26 + 2/3

So that is 26 years + ( 2/3 of a year)

What is 2 / 3 of a year?

Since 2 /3 of a year is a fraction of a year, the answer for 2 / 3 of a year will be in months.

1 year = 12 months.

Just find out what 2/3 of 12 is

2/3 of 12 is 2/3 times 12

2/3 times 12 = (2 times 12) / 3 = 24 / 3 = 8 months

Putting everything together, you slept for 26 years and 8 months during your lifetime.

Hope it helped!

Answer:

\(\Longrightarrow: \boxed{\sf{x=-\dfrac{11}{30} }}\)

Step-by-step explanation:

Isolate the term of x from one side of the equation.

First, add by 3/4 from both sides.

\(\sf{-\dfrac{3}{2}x-\dfrac{3}{4}+\dfrac{3}{4}=-\dfrac{1}{5}+\dfrac{3}{4} }\)

Solve.

⇒ = -3/2x=11/20

Then, you multiply by 2 from both sides.

2(-3/2x)=11*2/20

Solve.

11*2/20

11*2=22

22/20

Common factor of 2.

11/10

-3x=11/10

Divide by -3 from both sides.

\(\sf{\dfrac{-3x}{-3}=\dfrac{\dfrac{11}{10}}{-3}}\)

Solve.

\(\Longrightarrow:\boxed{\sf{x=-\dfrac{11}{30} }}\)

I hope this helps! Let me know if you have any questions.

The product of a rational and an irrational number can be either rational or irrational, depending on the specific numbers involved.

To illustrate this, let's consider an example:

Let's say we have the rational number 2/3 and the irrational number √2.

Their product would be (2/3) * √2.

In this case, the product is irrational.

The square root of 2 is an irrational number, and when multiplied by a rational number, the result remains irrational.

However, it's also possible to have a product of a rational and an irrational number that is rational. For example, if we consider the rational number 1/2 and the irrational number √4, their product would be (1/2) * 2, which equals 1. In this case, the product is a rational number.

Therefore, we cannot make a definitive statement that the product of a rational and an irrational number is always rational or always irrational. It depends on the specific numbers involved in the multiplication.

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Answer:

2 3/4 > 2 4/6

Step-by-step explanation:

Answer:

2 3/4 < 2 4/6

Step-by-step explanation:

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