Erica earned a total of $67,250 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than three times the amount she earned from her job at the college. How much did she earn (in dollars) from her job at the college?

By using the midpoint approach, the price elasticity of demand between each of the given prices are:

The price elasticity of demand measures the responsiveness of the quantity demanded by a consumer with respect to a specific change in price of the product, all things being equal (ceteris paribus).

By using the midpoint approach, the price elasticity of demand between each of the given prices is given by:

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (15 - 5)/[(15 + 5)/2]/(25 - 30)/[(25 + 30)/2]

Price elasticity of demand = 1/-0.1818

Price elasticity of demand = 5.50.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (25 - 15)/[(25 + 15)/2]/(20 - 25)/[(20 + 25)/2]

Price elasticity of demand = 0.5/-0.2222

Price elasticity of demand = 2.25.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (35 - 25)/[(35 + 25)/2]/(15 - 20)/[(15 + 20)/2]

Price elasticity of demand = 0.33/-0.2857

Price elasticity of demand = 1.17.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (45 - 35)/[(45 + 35)/2]/(10 - 15)/[(10 + 15)/2]

Price elasticity of demand = 0.25/-0.4

Price elasticity of demand = 0.63.

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AnswEr :

Let's assume , three Consecutive integers be x , ( x +1 ) & ( x+2 ) , such that , x < ( x +1 ) < ( x +2 ) .

⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\: According \: to \: the \: Given \: Question \::}}\\[/tex]

⠀⠀⠀⠀⠀— The product of three consecutive integers is 30 times the smallest of the three integers.

[tex] \sf \dashrightarrow \:30\: \bigg\{ \: Smallest_{(\:integer\:)}\:\bigg\}\:\:=\: \:\bigg\{ \: I^{st} \:Integer\:\bigg\}\: \:\bigg\{\: II^{nd}\:Integer\:\bigg\}\: \:\bigg\{ \: III^{rd} \:Integer\:\bigg\}\:\:\: \\\\\sf \dashrightarrow \:30\: \bigg\{ \:x\:\bigg\}\:\:=\: \:\bigg\{ \: x\:\bigg\}\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:x^2 + 3x + 2 \:\:\: \\\\ \sf \dashrightarrow \:x^2 + 3x - 28 \:= \:0\: \\\\ \sf \dashrightarrow \:\:\bigg\{ \: x - 2 \:\bigg\}\:\:\bigg\{ \: x + 7 \:\bigg\}\: \:= \:0\: \\\\ \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:-7\: \&\:2\:}}}}}\:\bigstar \: \\\\\\[/tex]

Therefore ,

When , x = 2 ,

When , x = –7 ,

Answer:

Hi,

Step-by-step explanation:

If the "is" means is equal to

Let's say a-1, a, a+1 the 3 consecutive integers.

[tex](a-1)*a*(a+1)=30*(a-1)\\\\(a-1)*(a*(a+1)-30)=0\\\\(a-1)(a^2+a-30)=0\\\\(a-1)(a^2+6a-5a-30)=0\\\\(a-1)(a(a+6)-5(a+6))=0\\\\(a-1)(a+6)(a-5)=0\\\\a=1\ or\ a=-6\ or\ a=5\\[/tex]

[tex]\begin{array}{|c|c|c|c|c|}a&a-1&a+1&Prod&30*(a-1)\\---&----&----&----&--------\\1&0&2&0&30*0=0\\5&4&6&120&4*30=120\\-6&-7&-5&-210&30*(-6)=-180\end{array}\\[/tex]

The two sets are : (0,1,2) and (4,5,6).

Answer:

Yes

Step-by-step explanation:

The sum must be greater than 8 it can't be 7 anyway. Sums can be 9, 10 or 12. P = (4+3+1)/36 = 3/36

Answer:

8x

Step-by-step explanation:

(3x+1)+(3x-1), the 1's cross out, so it is 3x+3x=6x. 6x+2x=8x.

Answer:

8x

Step-by-step explanation:

got it right!!!

Answer:

a. D. f⁻¹(x) = x - 21, for all x

b. f(f ⁻¹(x)) = f(x - 21) = x and f ⁻¹(f(x)) = f ⁻¹(x + 21) = x

Step-by-step explanation:

See attached picture.

The required answers are:

a. The inverse of the function is f1(x) = x - 21

b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

a. To find the inverse function of f(x) = x + 21, we can interchange x and y and solve for y:

x = y + 21

Now, let's solve for y:

y = x - 21

Therefore, the equation for f1(x), the inverse function, is f1(x) = x - 21.

b. To verify that the equation is correct, we need to show that f(f(x)) = x and f¯¹ (f(x)) = x.

First, let's calculate f(f(x)):

f(f(x)) = f(x + 21) = (x + 21) + 21 = x + 42

Since f(f(x)) = x + 42, we can see that f(f(x)) is not equal to x. Therefore, f(f(x)) ≠ x.

Now, let's calculate f¯¹(f(x)):

f¯¹(f(x)) = f¯¹(x + 21) = (x + 21) - 21 = x

Since f¯¹(f(x)) = x, we can see that f¯¹(f(x)) is equal to x.

Thus, we have verified that the equation for the inverse function, f1(x) = x - 21, is correct by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

Therefore, the required answers are:

a. The inverse of the function is f1(x) = x - 21

b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

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Answer:

2.66666666667

Step-by-step explanation:

(1/8)^-1/3 means 1/8 to the -1/3 power, which equals 2.66666666667. So the answer is 2.66666666667.

The new sample size based on the information will be B-M, B-C, B-R, 8.

Sample size is the number of participants or observations that are included in a study. This is usually represented by n.

When the boys and girls are to be chosen, the new sample size based on the information will be B-M, B-C, B-R, 8.

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Answer:

Step-by-step explanation:

B-M, B-C, B-R, 8.

Step-by-step explanation:

an open (empty) point means the point itself is not included.

a closed (filled) point means the point itself is included.

the x values going from -3 (not included) to -1 (included) means

-3 < x <= -1

so, the second answer is correct.

Answer:

9: 50

10: 90

11: 60

12: 25 and 115

13: 130 and 40

Thats all i can do, im sorry but i hope this helps ^^

The correct function shown in the graph is,

⇒ log₁₀ (ax) = 1

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:

⇒ log₁₀ (ax) = 1

or , ax = 10¹ = 10

Thus, x  = 10/a

So, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option D, that is, when a = 3. That will make x = 3.33 and thus, .

⇒ log (3 × 3.33) = 0.99 ≈ 1

Thus, out of the given options only Option D seems to be the most probable answer.

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The interval which the function is negative is (-∞, -6)

The equation of the function is given as:

[tex]g(x) = \sqrt[3]{x + 6}[/tex]

When the function is negative.

It means that g(x) is less than 0

i.e. g(x) < 0

So, we have:

[tex]\sqrt[3]{x + 6} < 0[/tex]

Take the cube of both sides

x + 6 < 0

Subtract 6 from both sides

x < -6

The above represents a value from negative infinity to -6

i.e.  (-∞, -6)

Hence, the interval which the function is negative is (-∞, -6)

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The original height  of the water in a pool is 5 ft , Option B is the correct answer.

An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.

It is given in the question that

A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.

the height of the water is 4.75 feet.

The equation

4.75 = x + (negative 0.25)

can be used to find x, the original height of the water in a pool.

4.75 = x - 0.25

x = 5

Therefore the original height  of the water in a pool is 5 ft , Option B is the correct answer.

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Answer:

B

Step-by-step explanation:

The area of the figure is 51.4 unit²

Figure ABCDEF is shown. A is located at 5, negative 8. B is located at 11, negative 8. C is located at 11, 0. D is located at 6

See attachment for the figure

The figure can be divided into the following shapes:

The area of the trapezoid is:

Area = 0.5 * (Sum of opposite sides) * height

So, we have:

Trapezoid 1 = 0.5 * (8 + 5) * 5 = 32.5

Trapezoid 2 = 0.5 * (5 + 4.8) * 2 = 9.8

The area of the triangle is:

Area = 0.5 * Base * Height

This gives

Triangle = 0.5 * 4.8 * 4 = 9.6

Add the individual areas

Area = 32 + 9.8 + 9.6

Evaluate the sum

Area = 51.4

Hence, the area of the figure is 51.4 unit²

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Answer: None

Step-by-step explanation:

There is only one pair of angles and one pair of sides, which is not sufficient to prove triangle congruence.

Answer:

Angle1 and Angle2 are supplementary.

Step-by-step explanation:

There are at least 8 pairs and I want to say up to maybe 16 pairs if angles that are supplementary.

Supplementary angles add up to 180°. So any pair that is lying together on a straight line (that's 180°) are supplementary:

1&2

2&4

3&4

1&3

5&6

6&8

7&8

5&7

Since angles don't have to touch in order to be supplementary there are many more pairs.

Answer:

4,186.67 in³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(10 in)³

V = (4/3)(3.14)(1,000 in³)

V = 4,186.666667 in³

Answer:

A=l*w

Step-by-step explanation:

so We Derive Their Formula

L=A/w

105600

Significant figures are used in scientific fields to show precision.

Multiplication

When rounding to significant figures you need to first do the operation shown. So, before we round we need to multiply 573.06 * 184.25.

This is an important step whenever you are rounding to significant figures. If you preround, you will be left with the wrong answer.

Significant Figures

Now that we have the answer before rounding, we need to know how to determine significant figures. If there is a decimal point present, then start counting significant figures at the first non-zero digit from the left.

For example:

If the decimal point is not present, then start counting significant figures from the first non-zero digit from the right.

For example:

Rounding

Finally, we can round our answer. Firstly, there are more than 4 digits before the decimal point. This means that our rounded answer will not have a decimal point, so when counting sig figs we will start from the right. Remember, even when rounding, a number should always have the same number of digits before the decimal point, even if they are not all significant.

Since we are rounding to 4 sig figs, we need to look at the 5th digit from the left, which is 8. This means we will round up.

So, write the first 4 digits of the number, but round the last one up. Then, write the remaining digits before the decimal point as 0.

The value of x for each radical equation is 243 , 125,8,256 respectively.

The correct question is attached as an image with the answer.

When in an equation the variable is under a radical it is called a Radical Equation.

It is given in the question that

which radical matches to the solution

[tex]\rm \sqrt[5]{x^4} = 81 \\\\\sqrt[3]{x^4} = 625\\\\\sqrt[3]{x^5} = 32\\\\ \sqrt[4]{x^3}=64[/tex]

[tex]\rm x^4 = 81^5\\x = 243[/tex]

[tex]\rm x^4 = 625^3\\x = 125\\[/tex]

[tex]x^5 = 32^3\\x = 8\\[/tex]

[tex]\rm x ^3 = 64^4\\x = 256[/tex]

Therefore for each radical the value of x is determined.

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Answer:

Step-by-step explanation:

First, label it out:

Then, we add up 12 twice (Since the length is on 2 sides):

Now, we write down a 6 in the ?:

Width = 6.

We are not done!

Now, we have to solve for area.

The amount of Rita deposit is $2556.

The interest calculated on the principal amount or the initial investment.

It is given in the question

If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days.

P = ?

S.I. =  $63.90

Interest = 6%

T = 150days

S.I. = (P *R*T)/100

63.90 = P * 6 * 150*100 /360

63.90 * 360*100 /( 150 *6) = P

P = $2556

Therefore the amount of Rita deposit is $2556.

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The rise from the ground by the skateboard is 5.5 inches

The length of the skateboard is given as:

Length (l) = 18 inches

The angle of elevation (x) is

x = 17∘

Represent the height with h.

The value of h is calculated using the following tangent ratio:

tan(x) = h/l

Make h the subject

h = l * tan(x)

Substitute known values

h = 18 * tan(17)

Evaluate

h = 5.5

Hence, the rise from the ground by the skateboard is 5.5 inches

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Answer: 5.3

Step-by-step explanation:

S​OH-CAH-TOAsin 17=oppositehypotenuse=x18sin 17=hypotenuseopposite​=18x​sin 17=sin 17=  x1818x​sin 171=1sin 17​=  x1818x​18 sin 17=18 sin 17=  xxx=5.262690...≈5.3x=5.262690...≈5.3

The arithmetic sequence that has a common difference of -5 from the options given is: A. 8, 3, -2, -7...

The common difference of an arithmetic sequence is determined as: a term - previous term.

For the sequence, 8, 3, -2, -7,.. the common difference is:

-7 - 2 = -2 - 3 = 3 - 8 = -5.

Therefore, the arithmetic sequence with a common difference of -5 is: A. 8, 3, -2, -7...

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Answer:

When -3v = -18 is solved, the result is:

21v

The result of this mathematical sentence is v=6

First degree equation is a mathematical sentence - having at least one unknown. Its representation is given by ax + b = 0. To calculate an equation, as it is in the expression in the statement, simply: isolate x and divide the second to the first member.

*Note: Equal signs, the result will be equated as positive.

-3v = -18

v = -18/-3

v = 6

Therefore, the correct value of this equation is v = 6.

The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The question is: Consider the function f(x) = (-2/3)x - 24  Which conclusions can be drawn about f⁻¹(x) Select two options:

f⁻¹(x) has a slope of -2/3

f⁻¹(x) has a restricted domain.

f⁻¹(x) has a y-intercept of (0, –36).

f⁻¹(x) has an x-intercept of (–36, 0).

f⁻¹(x) has a range of all real numbers.

f(x) = (-2/3)x - 24

To find the inverse of a function:

interchange the x and y

x = (-2/3)y - 24

y = (-3/2)(x + 24)

y = (-3/2)x - 36

The slope of a function f⁻¹(x) is -3/2

From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.

Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

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Answer:

D and  E

Step-by-step explanation:

did the test

Answer:

3/4 cups

Step-by-step explanation:

3 1/2 divided by 2

A second-degree polynomial takes the form

[tex]f(x) = ax^2 + bx + c[/tex]

for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.

Differentiating f(x) with respect to x gives

[tex]\dfrac{df}{dx} = 2ax + b[/tex]

We're told that

• f(x) is increasing on [0, 8]

• f(x) is decreasing on ]-10, 0]

and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write

[tex]f(x) = ax^2 + c[/tex]

We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint

[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]

Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so

[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]

This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.

Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,

a = 1, c = -60   ⇒   f(x) = x² - 60   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}

a = 2, c = -124   ⇒   f(x) = 2x² - 124   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}

etc.