Which inequality best represents the domain of the part shown
​

The domain of the graph of the exponential function is (d) all real numbers

From the question, we have the following parameters that can be used in our computation:

The graph of the exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

From the graph, the constant term is 0

So, the range is y > 0

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Answer:

14, 4pi, 9, sqrt 18

Step-by-step explanation:

Answer:

√18, 9, 4π, 14

Step-by-step explanation:

4π = 12.56637...

√18 = 4.24264...

14 = 14

9 = 9

From least to greatest:

4.24264..., 9, 12.56637..., 14

Answer:

√18, 9, 4π, 14

Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

To write a quadratic function to represent the height h of the acrobat t seconds after the jump, we can use the following formula:

\(h(t) = -16t^2 + vt + h0\)

Where h0 is the initial height of the acrobat, which is 25 feet, and v is the initial vertical velocity, which is 4 ft/s. Plugging in these values, we get:

\(h(t) = -16t^2 + 4t + 25\)

To find how long it will take for her to land safely on the net, we need to find the time at which h(t) = 5. In other words, we need to solve the equation:

\(-16t^2 + 4t + 25 = 5\)

Simplifying this equation, we get:

\(-16t^2 + 4t + 20 = 0\)

Dividing both sides by -4, we get:

\(4t^2 - t - 5 = 0\)

Now we can use the quadratic formula to solve for t:

\(t = (-b ± \sqrt(b^2 - 4ac)) / 2a\)

Where a = 4, b = -1, and c = -5. Plugging in these values, we get:

\(t = (1 ± \sqrt(1 + 4(4)(5))) / 8\)

Simplifying this equation, we get:

\(t = (1 ± 9) / 8\)

So, the two solutions are:

\(t = 1 and t = -5/4\)

Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

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Answer:

-10

Step-by-step explanation:

-5b + 35 = 85

-5b = 50

-5b/-5 = 50/-5

b = -10

Answer:

B = -10

Step-by-step explanation:

-5b + 35 = 85

work is shown in picture

Answer:

Step-by-step explanation:

time = 7 hours 30 minutes = 7.5 hours because 30 minutes is 1/2 hour

distance = 375 miles

rate = 375 / 7.5

rate = 50 miles per hour is the average.

Answer:

0.45x−0.125

Step-by-step explanation:

0.45x-1/4

0.45x - 0.25 ÷ 2

0.45x−0.125

Answer:

We conclude that the average number of pages that Sarah reads per hour will be: 10.75 page per hour

Step-by-step explanation:

Given

The average number of pages per hour can be calculated by simply dividing the total number of pages i.e. 64.5 pages by the number of hours spent on reading i.e. 6 hours.

Thus,

Average number of pages per hour = 64.5 pages / 6 hours

                                                            = 10.75 page per hour

Therefore, we conclude that the average number of pages that Sarah reads per hour will be: 10.75 page per hour

Answer:

First one is infinitely many solutions. Second one is One solution. The third one is No solution.

Step-by-step explanation:

First line both equations have the same line. second one are two completely different equations while the third one are parallel lines which never intersect.

The linear equation that shows how the wind power would need to grow to make this goal is y = 25x + 15

From the question, we have the following parameters that can be used in our computation:

(x, y) = (0, 15) and (5, 90)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 15

Using the other point, we have

5m + 15 = 90

So, we have

5m = 75

Divide by 5

m = 25

So, the equation becomes

y = 25x + 15

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Complete question

Using the two data points from Exercises 1 and 2, write a linear equation that shows how the wind power would need to grow to make this goal. Use years for the independent variable and terawatt hours for the dependent variable. Let year 0 represent year 2012, (0, 15) and (5, 90)

The amount of dry ingredients used in the cake recipe is approximately 7 cups.

To find the total amount of dry ingredients used in the cake recipe, we need to add up the amounts of flour, sugar, and cocoa.

3 ½ cups of flour is equal to 3 cups plus 0.5 cups, or 3 cups and 8 ounces.

2 ⅔ cups of sugar is equal to 2 cups plus 0.67 cups, or 2 cups and 10.72 ounces.

1 ¾ cups of cocoa is equal to 1 cup plus 0.75 cups, or 1 cup and 12 ounces.

Adding these amounts together, we get:

3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

To the nearest cup, this is equal to 7 cups.

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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Answer:

A and D are correct. This is a parallelogram, which is a quadrilateral. B is not correct because not all the sides are congruent. C is not correct. E and F are not correct because this parallelogram does not have any right angles.

We were told from the question that a sphere and a cube has identical volume of

3375 cm³.

We are to determine if they have identical surface area.

Let's use the cube to determine it.

let the edge of the cube be a cm

Volume of cube = 3375 cm³

recall that the formulas for volume of a cube is:

Volume = a³

So,

a³ = 3375 cm³

let's take square of both sides

a = 3√3375

a = 15 cm

Surface Area of cube = 6a²

= 6(15)²

= 6 * 225

Surface area of cube = 1350 cm²

They won't have identical surface area.

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

Step-by-step explanation:

ture

Answer:

false

Step-by-step explanation:

-7 is not greater than POSITIVE 6

a negative is no greater than a positive .

to make it a solution

flip the sign : -7 < 6

Answer:

x < -8.5

Step-by-step explanation:

-46 - 8x > 22

-8x > 68 -- when you divide by a negative number in an inequality, you flip the inequality sign

Therefore, x < -8.5

Answer:

Step-by-step explanation : devise ----> divide496 = 2*2*2*2*31The 2's can be used in 5 ways, that is, not take anytake 1take 2take 3take all 4the 31 can be used in 2 ways, either take or not take itnumber of factors = 5*2 = 10but that includes taking all or noneif we correspond to none as the factor 1 and if we take all we would get 496the factors would be1, 2, 4, 8, 16, 31, 62, 124, 248, and 496

Answer:

1260.04

Step-by-step explanation:

The formula for compound interest is:

A = P(1+\(\frac{r}{n}\)\()^{nt}\) where A is the final amount, P is the initial principal balance, r is the interest rate, n is the number of times interest applied per time period and t is the number of time periods elapsed. Since the deposit was compounded annually, just like the interest, we can omit the n in the equation.

Applying the formula to question:

800(1+\(\frac{2.88}{100}\)\()^{16}\) = 1260.04 (rounded off to nearest cent since it's money)

The rate of return for the entire portfolio, given the amount allocated to each of the four securities is

The rate of return would be the expected return of the proportion of the amounts invested into the various investment vehicles and their rates of return.

The rate of return for the portfolio is therefore :

= ∑ ( proportion invested x rate of return )

= ( 25 % x 12 % ) + ( 10 % x 7 % ) + ( 35 % x 22 % ) + ( 30 % x  - 12 % )

= 7. 8 %

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Ending Inventory Cost and Cost of Goods Sold using different inventory methods:

FIFO Method:

Ending Inventory Cost: $11,920

Cost of Goods Sold: $15,068

LIFO Method:

Ending Inventory Cost: $11,996

Cost of Goods Sold: $15,123

Weighted Average Cost Method:

Ending Inventory Cost: $11,974

Cost of Goods Sold: $15,087

Using the FIFO (First-In, First-Out) method, the cost of the ending inventory is determined by assuming that the oldest units (those acquired first) are sold last. In this case, the cost of the ending inventory is calculated by taking the cost of the most recent purchases (70 units at $142 per unit) plus the cost of the remaining 10 units from the March 10 purchase.

This totals to $11,920. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory at $124 per unit, 60 units from the March 10 purchase at $132 per unit, and 20 units from the August 30 purchase at $138 per unit), which totals to $15,068.

Using the LIFO (Last-In, First-Out) method, the cost of the ending inventory is determined by assuming that the most recent units (those acquired last) are sold first. In this case, the cost of the ending inventory is calculated by taking the cost of the remaining 10 units from the December 12 purchase, which amounts to $1,420, plus the cost of the 70 units from the August 30 purchase, which amounts to $10,576.

This totals to $11,996. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,123.

Using the Weighted Average Cost method, the cost of the ending inventory is determined by calculating the weighted average cost per unit based on all the purchases. In this case, the total cost of all the purchases is $46,360, and the total number of units is 200.

Therefore, the weighted average cost per unit is $231.80. Multiplying this by the 80 units in the physical inventory at December 31 gives a total cost of $11,974 for the ending inventory. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,087.

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The mean age will increase, and the median age will remain the same.

Option B is the correct answer.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Ages:

14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18

The mean of the ages.

= (14 + 15 + 15 + 16 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 17 + 18) / 13

= 211/13

= 16.23

The median of the ages.

= 16

Now,

18 becomes 19.

14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 19.

Mean = 212/13 = 16.3

Median = 16

Thus,

The mean age is increased.

The median is the same.

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The simplified sum is 191/30.In mixed number form, this is 6 and 11/30.3 2/3 + 2 7/10 equals 6 and 11/30.

To add the mixed numbers 3 2/3 and 2 7/10, we can follow these steps:First, convert both mixed numbers into improper fractions.

3 2/3 = (3 * 3 + 2)/3 = 11/3

2 7/10 = (2 * 10 + 7)/10 = 27/10

Now, we have 11/3 + 27/10.

To find a common denominator, we multiply the denominators: 3 * 10 = 30.Rewriting the fractions with the common denominator, we have 110/30 + 81/30.

Adding the numerators, we get 110 + 81 = 191.

The sum is 191/30.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 1.

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Answer:

C

Step-by-step explanation:

For these types of problems, its important that we focus on the base as well as the lengths of the base and any other given lengths.

Here, the net has a base that forms a square with side lengths of 8mm.

So automatically, we can eliminate choices a and d as both have a base that is a triangle rather than a square.

We've also noticed that the base has a length of 8mm

If we look at B and C closely, we can tell that B has base lengths of 10mm while C has base lengths of 8mm.

So C is the correct answer choice.

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a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.

Answer:

the answer is 17x+20

Step-by-step explanation:

7x+10x+20

17x+20

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Answer:

17x+20

Step-by-step explanation:

like terms= 7x and 10x so add= 17x

unlike term 20 it remains as it is.

so 17x+20 further cannot be simplified as both are unlike terms

Answer:

Let X be the age of the oldest employee.

Given that the youngest employee is 30.

We also know that the range of ages is 40 years.

Therefore, we can write:

X - 30 = 40

Adding 30 to both sides, we get:

X = 70

Therefore, the oldest employee is 70 years old.

Answer:

The age of the oldest employee is 70 years.

Step-by-step explanation:

The range of a data set is the difference between its maximum and minimum values.

\(\boxed{\sf Range=Maximum\;value-Minimum\;value}\)

Given the range is 40 years and the minimum value is 30 years, substitute these values into the formula and solve for maximum value:

\(\implies \sf 40=Maximum\;value-30\)

\(\implies \sf 40+30=Maximum\;value-30+30\)

\(\implies \sf Maximum\;value=70\)

Therefore, the age of the oldest employee is 70 years.

The person whose fruit salad will taste more melony is Genesis. The Option B is correct.

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.

We need to compute the melon percentage to determine whose fruit salad will taste more melony:

1. Ownen mixes 14 cups of melon and 3 cups of apple. The percentage for melon will be:

= 14/(3+14) × 100

= 82.3529411765

= 82.35%

2. Genesis mixes 6 cups of melon and 1 cups of apple. The percentage for melon will be:

= 6/7 × 100

= 85.7142857143

= 85.71%

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The formula for the area of a trapezoid is (a+b)*h/2, where a and b are the lengths of the bases and h is the height.

To estimate the total area between the curve and the x-axis using trapezoids, we can divide the region between the curve and the x-axis into a number of trapezoids, and calculate the area of each trapezoid. The sum of the areas of all the trapezoids will estimate the total area.

For example, consider the curve y = x^2 and the x-axis between x = 1 and x = 2. We can divide this region into 3 trapezoids with bases at x = 1, x = 1.5, x = 2, and heights of 0.25, 0.5625, and 1 respectively.

The area of the first trapezoid is (1 + 1.5) * 0.25 / 2 = 0.1875

The area of the second trapezoid is (1.5 + 2) * 0.5625 / 2 = 0.40625

The area of the third trapezoid is (2 + 2) * 1 / 2 = 1

The sum of the areas of all the trapezoids is 0.1875 + 0.40625 + 1 = 1.60625. This estimates the total area between the curve y = x^2 and the x-axis between x = 1 and x = 2.

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Using proportions, it is found that out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching this problem on the internet, it is found that out of 150 couples initially surveyed, 26 + 25 + 12 + 22 + 13 = 98 couples had at least one spouse preferring action movies, hence the proportion is:

p = 98/150 = 0.6533.

Out of the next 75 couples, the amount is:

A = 0.6533 x 75 = 49

Hence, out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.

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Answer:

I had a great quantity of apples and used 18 to make a large apple pie for my family and I, then I only had 24 left over.

Step-by-step explanation:

X in the equation represents the amount of apples I have at the beginning of the apple pie making process. Minus 18 represents the apples that are being used for the apple pie, so they are not there anymore. 24 represents the apples left over.