100) = +8 what is) when x = 102

The numeric value of the exponential expression in this problem is given by the following option:

A. 2^12.

The exponential expression for this problem is defined as follows:

8^x/2^y.

8 is the third power of 2, hence:

8 = 2^3.

When a term is elevated to two of it's powers, the powers are multiplied, hence:

(2^3)^x = 2^(3x).

Meaning that the exponential expression is then written as follows:

8^x/2^y = 2^(3x)/2^y.

When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:

2^(3x)/2^y = 2^(3x - y).

As stated in the problem, the numeric value of the expression 3x - y is given as follows:

3x - y = 12.

Hence the entire expression is simplified as follows:

2^(3x - y) = 2^12.

Meaning that the correct option is given by option A.

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Answer:A. 2^12.

Step-by-step explanation:i did it and got it right

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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Answer:

1 11/12 cups of water

Answer:

  a) Megan's total so far is 3 km more than necessary for an average of 15 km

  b) 22 km

Step-by-step explanation:

a) The total of differences from 15 is ...

  -1 + 8 + (-2) +(-2) = 3

Since this is more than 0, Megan's average is more than 15.

__

b) The total of differences from 17 is ...

  -3 +6 -4 -4 = -5

To increase her average to 17 km, Megan must walk 17+5 = 22 km on Friday.

_____

Comment on the approach

In general, I find it easier mentally to deal with small numbers than with larger ones. So adding small differences can be easier than computing larger sums.

a) By computing the difference from the supposed average, we have effectively found the difference of the sum of values from the total necessary to give the required average. That is, Megan's average would be 15 if her total distance were 4·15 = 60. Her total distance is (4·15 +3) = 63, so her average is more than 15.

b) By finding out how much the total is below that necessary for the desired average, we determine the amount above that average the final number needs to be.

  (14 -17) +(23 -17) +(13 -17) +(13 -17) +(Friday -17) = 0 . . . . the Friday value to make an average of 17

  14 +23 +13 +13 +Friday = 5·17 . . . . . . . add 5·17

  (14 +23 +13 +13 +Friday)/5 = 17 . . . . . . shows the Friday amount gives the required average

  Friday = 17 -((14 -17) +(23 -17) +(13 -17) +(13 -17)) . . . . first equation rearranged to show how we computed Friday

  Friday = 17 -(-5) = 17 +5 = 22

The quadrant is First Quadrant

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the study of angles, triangles, and the relationships between the sides and angles of triangles. It is used in a wide range of applications, including navigation, engineering, physics, and astronomy.

Solution:

If sin(theta) > 0 and cos(theta) > 0, this means that the sine of theta is positive and the cosine of theta is positive. In the Cartesian plane, this condition is satisfied in the first quadrant, where both the x and y coordinates are positive.

In other words, if a point (x, y) represents the values of cos(theta) and sin(theta), respectively, then x and y are both positive. This point lies in the first quadrant, which is the region above the x-axis and to the right of the y-axis.

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Answer:

14. 90%

15. 9%

16. 166%

17. 189%

18. 10%

19. 266%

20. 40%

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

C

Step-by-step explanation:

it gets steeper. Hope this helps!

When the value of the slope gets bigger, the graph of a line gets steeper. The correct answer is C.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The slope of a line is a measure of how steep the line is.

It is defined as the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line.

If the slope of a line is large, it means that the line rises or falls rapidly as we move along it.

Conversely, if the slope is small, the line rises or falls more gradually.

When the value of the slope gets bigger, it means that the rise or fall of the line per unit of horizontal distance (run) increases.

This causes the line to become steeper, i.e., the angle it makes with the x-axis increases.

On the other hand, when the slope gets smaller, the line becomes less steep, i.e., the angle it makes with the x-axis decreases.

Thus,

When the value of the slope gets bigger, the graph of a line gets steeper.

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The percentage change in the price is 15.78% decrease.

What is the percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. Per 100 is what the term percent signifies. The sign "%" represents it.

Here are some percentage examples:

Now,

Initial price=4.1

Final price=3.5

Change=3.5-4.1= -0.6 , minus means decrease in price

final value + initial value=7.6

then

percentage change by midpoint approach = (final value-initial value) / ((final value + initial value)/2) *100

=0.6/3.8*100

=0.1578*100

=15.78%

hence,

         The percentage change in the price is 15.78% decrease.

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Answer:

366.6is your answer right answer right

The 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list is (0.28, 0.38).

Let's calculate the sample proportion;

Sample proportion = 93 / 283 = 0.33

The margin of error of the data can be calculated by;

Margin of error = Z * √(p(1-p) / n)

where:

Margin of error = 1.96 * sqrt(0.33 * (1-0.33) / 283) = 0.05

The confidence interval can be calculated as

Confidence interval = 0.33 ± 0.05 = (0.28, 0.38)

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Answer:

V = l x w x h

V = 2m x 1.5m x  1m

V = 3 cubic meter

The image is attached of the graph of the inequality y < 4x - 5.

What is the inequality equation?

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

To graph the inequality y < 4x - 5 using the slope-intercept form, follow these steps:

Rewrite the inequality in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

y = 4x - 5

Plot the y-intercept on the y-axis.

The y-intercept is -5, so plot the point (0, -5).

Use the slope to find a second point on the line.

The slope is 4, so start at the y-intercept and move up 4 units and to the right 1 unit to find the point (1, -1).

Draw a dashed line through the two points.

Since the inequality is y < 4x - 5, use a dashed line to indicate that the line itself is not part of the solution.

Shade the region that satisfies the inequality.

To do this, pick a test point that is not on the line and plug its coordinates into the inequality. If the inequality is true for that point, shade the region that contains the test point. If the inequality is false for that point, shade the region that does not contain the test point.

Let's use the test point (0, 0). Plug its coordinates into the inequality to get:

0 < 4(0) - 5

This simplifies to 5 < 0, which is false. Therefore, we need to shade the region that does not contain the test point.

Since the inequality is y < 4x - 5, we need to shade the region below the dashed line.

Label the shaded region with the inequality symbol.

The inequality is y < 4x - 5, so label the shaded region below the dashed line with the symbol "<".

hence, The image is attached of the graph of the inequality y < 4x - 5.

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The values of tht missing part of the triangle are;

A= 20.9°

a = 13.06

c = 33.6

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side c

sinB/b = sinC/c

sin45.9/26.30 = sin113.2/c

csin 45.9 = 26.30 × sin113.2

0.718c = 23.90

c = 23.90/0.718

c = 33.6

Angle A = 180-(113.2+ 45.9)

angle A = 20.9°

sinA/a = sinB/b

sin20.9/a = 0.718/26.30

0.357 × 26.30 = 0.718a

a = 9.389/0.718

a = 13.06

Therefore A = 20.9°

a = 13.06

c = 33.6

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The expression value of 3x^2 - 2x+3 is 6x^2 - 13x + 6

Value of an Expression The value of the expression is the result of the calculation described by this expression when the variables and constants in it are assigned values. Letters can be used to represent numbers in an algebraic expression.

Apply the distributive property:

→ 3x (2 - 3) - 2 (2x - 3)

Apply the distributive property:

→ 3x (2x) + 3x ⋅ -3 - 2 (2x - 3)

Apply the distributive property:

→ 3x (2x) + 3x ⋅ -3 - 2 (2x) - 2 ⋅ -3

Simplify each term:

→ 6x^2 - 9x - 4x  + 6x

Subtract 4x from -9x

→ 6x^ - 13x + 6

Therefore, the expression value of 3x^2 - 2x+3 is 6x^2 - 13x + 6

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The value of the expression given is 136.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expression is,

3x² - 2x + 3

We have to find the value of the expression when x = 7.

Substitute x = 7.

(3 × 7²) - (2 × 7) + 3 = (3 × 49) - 14 + 3

                               = 147 - 14 + 3

                               = 136

Hence the value of the expression is 136.

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Answer:

x ≥ 1.5

Step-by-step explanation:

2x - 3 ≥ 0 ( add 3 to both sides )

2x ≥ 3 ( divide both sides by 2 )

x ≥ 1.5

The sale price of coat is $180 and the sale price of boot is $284 when 20% off a coat and a pair of boots are now  on sale.

Given that,

20% off a coat and a pair of boots are now  on sale. The coat normally sells for $225. The boots cost $130 on the open market.

We have to find the coat's sale price and what is the cost of the boots on sale.
We know that,

The formula for the sales price is S = P - PD

Where, S is sales price, P is the original price and D is the discount percent.

P = 225 and D = 20%

S = 225 - 225 × 20%

S = 225 - 45

S = $180 is the sale price of coat.

Now,

Total regular price = 225 + 130 = 355

S = 355 - 355 × 20%

S = $284 is the sale price of boots.

Therefore, The sale price of coat is $180 and the sale price of boot is $284.

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a) The mean rainfall from seeded clouds exceeds 25 acre-feet is 1.99

b) As per the normal distribution, with the significance level 0.05 the rainfall is normally distributed.

c) The power of the test if the true mean rainfall is 27 acre-feet is 23.5%

d) The sample size would be required to detect a true mean rainfall of 27.5 acre-feet if we wanted the power of the test to be at least 0.9 is 28 clouds

e) The upper bound is greater than 25 acre-feet, we can support the claim that the mean rainfall from seeded clouds exceeds 25 acre-feet with a level of confidence of 99%.

a) To support a claim that mean rainfall from seeded clouds exceeds 25 acre-feet, we can perform a one-tailed hypothesis test with a significance level of α = 0.01.

Substituting the values, we get:

t = (25.96 - 25) / (4.48 / √20) = 1.99

b) To test if the rainfall is normally distributed, we can perform a normal probability plot and a Shapiro-Wilk test.

Using software, we can create a normal probability plot and perform the Shapiro-Wilk test.

The Shapiro-Wilk test also does not reject the null hypothesis that the data is normally distributed at a significance level of α = 0.05, we can assume that the rainfall data is normally distributed.

c) To compute the power of the test if the true mean rainfall is 27 acre-feet, we can perform a one-tailed hypothesis test with a significance level of α = 0.01. The null hypothesis H0 is that the mean rainfall is less than or equal to 25 acre-feet, and the alternative hypothesis Ha is that the mean rainfall is greater than 25 acre-feet.

Substituting the values, we get:

t = (25.96 - 27) / (4.48 / √20) = -1.43

Using software or a t-distribution table, we find that the probability of rejecting the null hypothesis when the true mean is 27 acre-feet is 0.235. Therefore, the power of the test is 0.235 or 23.5%.

d) To determine the sample size required to detect a true mean rainfall of 27.5 acre-feet with a power of at least 0.9, we can use power analysis.

Substituting the values, we get:

d = (27.5 - 25) / 4.48 = 0.56

Therefore, a sample size of at least 28 clouds would be required to detect a true mean rainfall of 27.5 acre-feet with a power of at least 0.9.

e) To answer the question in part (a) by constructing a one-sided confidence bound on the mean diameter, we can use a one-sided confidence interval with a level of confidence of 99%.

Substituting the values, we get:

x + tα,df * (s / √n) = 25.96 + 2.861 * (4.48 / √20) = 27.23

This means that we can be 99% confident that the true population mean rainfall from seeded clouds is greater than 27.23 acre-feet.

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Answer:a

Step-by-step explanation:

The value x represents a reference point on a motion map.

Option (A) is correct.

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

A point used to find or describe the location of something. Reference point that is moving is when you look out the window of a car and notice that you are moving faster than the car next to you.

The relationship between motion and reference point is that an object is in motion when its position with respect to a reference point varies over time. This indicates that they have a similar relationship.

Therefore, the value x represents a reference point on a motion map.

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Answer:

$3

Step-by-step explanation:

Answer:

3$

Step-by-step explanation:

The degree of each expression is the highest power to which the variable, x is raised. Looking at the polynomial expressions, the degrees of the original expressions and that of the simplified expressions are the same.

For the first, second and third polynomial expressions, the degree is 1

For the fourth and fifth polynomial expressions, the degree is 2

There is no change in the degree of the original expression and the degree of the combined expression. Change would only occur if original the expressions were multiplied instead of being added.

Answer:

A The mean for waiter B is higher than the mean for waiter A.

Answer:

The mean for waiter B is higher than the mean for waiter A.

Step-by-step explanation:

Test approved

A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:

(x, y)                                              →                 (-x, y).

\(f(x) = \frac{3}{8} (4)^x\)                               →              \(g(x) = \frac{3}{8} (4)^{-x}\)

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Amount to be repaid for Bank A is $2,696.625 and Amount to be repaid for Bank B is $2,741.25. However, I will choose Bank B because it offers a lower interest rate.

The formula to calculate the simple interest is;

I = PRT

Where;

P is principal

R is rate

T is time

Now, we are given that;

Bank A;

Principal amount; P = $2550

Interest rate; R = 11.5% = 0.115

Time; t = 6 months = 0.5 years

Thus;

I = (2550 * 0.115 * 0.5)

I = $146.625

Amount to be repaid = 2550 + 146.625

Amount to be repaid = $2,696.625

Bank B;

Principal amount; P = $2550

Interest rate; R = 7.5% = 0.075

Time; t = 12 months = 1 year

Thus;

I = (2550 * 0.075 * 1)

I = $191.25

Amount to be repaid = 2550 + 191.25 = $2,741.25

Thus, bank B offers a more favorable interest rate and as such would be the preferred bank.

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Answer:

rectangle

Step-by-step explanation:

a kite and a rhombus both have acute angles

The value of a + b is given as follows:

a + b = 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For function f(x), we have that when x increases by 3 from x = 1 to x = 4, f(x) increases by 6 from f(x) = 3 to f(x) = 9, hence the slope m is given as follows:

m = 6/3

m = 2.

Hence:

f(x) = 2x + b.

When x = 1, f(x) = 3, hence the intercept b is given as follows:

3 = 2 + b

b = 1.

Hence:

f(x) = 2x + 1.

For function g(x), we have that when x increases by 3 from x = 1 to x = 4, f(x) increases by 15 from f(x) = 5 to f(x) = 20, hence the slope m is given as follows:

m = 15/3

m = 5.

Hence:

g(x) = 5x + b.

When x = 1, g(x) = 5, hence the intercept b is given as follows:

5 = 5 + b

b = 0.

Hence:

g(x) = 5x.

The value of a, representing the x-coordinate of the intersection point, is obtained as follows:

5x = 2x + 1

3x = 1

x = 1/3.

Hence the value of b is of:

b = 5/3.

Meaning that the sum is of:

a + b = 1/3 + 5/3 = 6/3 = 2.

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Answer: There are 5 choices for the book to put on the first slot and 4 choices for the book to put on the second slot, since we have to pick a math book each time. Then, there are 6 choices for the book to put on the third slot, 5 choices for the book to put on the fourth slot, and 4 choices for the book to put on the fifth slot, since we have to pick a history book each time.

Therefore, the total number of ways to put the books on the shelf is:

5 × 4 × 6 × 5 × 4 = 2,400

So there are 2,400 ways to arrange the 5 math books and 6 history books on the shelf such that the first two slots are filled with math books and the next three with history books.

Step-by-step explanation:

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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