In Exercises 26-29, use the following information. You belong to a book club.
Your yearly book budget is $350. Each book in the book club costs $7.
26. Complete the table.
Books Cost (dollars) Amount left (dollars)
1
343
2
336
3
?
4
?
7
14
?
?
27. Write a variable expression for the cost of b books.
28. Write a variable expression for the amount of your budget after b books.
29. How many books will you be able to buy before the $350 is spent?

Answer:

See Below

Step-by-step explanation:

Points given:

V (-1.-1)

S (1,-1)

U (-1,-3)

T (1,-3)

Reflection: We need to reflect what is in the bottom two quadrants to the top two quadrants.

Resulting Points:

V (-1,1)

S (1,1)

U (-1,3)

T (1,3)

Still Stuck?

Try folding your paper over itself from bottom to top and see where the box lies, that is its reflection over the x-axis. Nothing is done with respect to y-axis here.

Therefore, the probability that the random variable X falls between 37 and 85 is approximately 0.8916 or 89.16%.

To compute the probability P(37 < X < 85) for a normally distributed random variable X with a mean μ = 70 and standard deviation σ = 12, we need to standardize the values and use the standard normal distribution.

First, we calculate the z-scores for the given values:

z1 = (37 - μ) / σ = (37 - 70) / 12 ≈ -2.75

z2 = (85 - μ) / σ = (85 - 70) / 12 ≈ 1.25

Next, we use a standard normal distribution table or a calculator to find the probabilities associated with the z-scores.

Using a standard normal distribution table, we find:

P(Z < -2.75) ≈ 0.0028 (probability corresponding to z1)

P(Z < 1.25) ≈ 0.8944 (probability corresponding to z2)

To find the probability of the interval (37 < X < 85), we subtract the probability associated with the lower value from the probability associated with the upper value:

P(37 < X < 85) = P(-2.75 < Z < 1.25) = P(Z < 1.25) - P(Z < -2.75) ≈ 0.8944 - 0.0028 ≈ 0.8916

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Answer:

About 36%.

Step-by-step explanation:

The formula for the rate of return on investment is the total value minus the initial cost divided by the initial cost.

The total value is $1,500. The initial cost is $1,100.

(1,500 - 1,100) / 1,100 = 400 / 1,100 = 4 / 11 = 0.363636363636

So, Dean's rate of return on investment is about 36%.

Hope this helps!

Answer:

y=2x

Step-by-step explanation:

hope this helps

:) :3

Given

The domain

Domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis.

y-intercept

The y-intercept of a graph is the point where the graph crosses the y -axis.

x-intercept

The x-intercept is the point at which the graph crosses the x-axis.

Range

The range of a function is the set of its possible output values.

Vertical asymptote

A vertical asymptote is a vertical line that guides the graph of the function but is not part of it.

If you deposit $14,000 into an account paying 2.1% interest compounded monthly, you will earn approximately $2,450 in interest after 8 years.

To calculate the interest earned, we can use the formula for compound interest: A = \(P(1 + r/n)^(nt)\), where A is the final amount, P is the principal amount (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal amount is $14,000, the annual interest rate is 2.1% (or 0.021 as a decimal), and the interest is compounded monthly, so n = 12. The time period is 8 years.

Plugging these values into the formula, we get:

A = \(14000(1 + 0.021/12)^(^1^2^*^8^)\)

Calculating this expression, we find that the final amount after 8 years will be approximately $16,449.55. To determine the interest earned, we subtract the initial deposit from the final amount:

Interest earned = $16,449.55 - $14,000 = $2,449.55.

Rounding this to the nearest dollar, the interest earned after 8 years will be approximately $2,450.

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The effective interest method is used to amortize the bond premium. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond. The journal entry for bond issuance is as follows: Dr. Cash 205,000, Dr. Premium on Bonds Payable 5,000, Cr. Bonds Payable 210,000

The effective interest method is a method of amortizing bond premium or discount that takes into account the time value of money. The effective interest is the interest that would be earned if the bond were purchased at its market value and held to maturity. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond.

The journal entry for bond issuance records the proceeds from the sale of the bonds, the premium on bonds payable, and the bonds payable. The proceeds from the sale of the bonds are equal to the face value of the bonds plus the premium.

The premium on bonds payable is a liability that represents the excess of the issue price of the bonds over their face value. The bonds payable account is a long-term liability that represents the amount that the company owes to the bondholders.

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Answer:

John=3150 peter=7350

Step-by-step explanation:

Hope this helps

The first six terms of the arithmetic sequence with a first term of 3/2 and a common difference of -1/2 are: 3/2, 1, 1/2, 0, 1/2, -1.

To find the first six terms of an arithmetic sequence, we would apply the formula below:

aₙ = a₁ + (n - 1) * d, where a₁ is the first term; and d is the common difference of the arithmetic sequence.

Given the following:

first term (a₁) = 3/2

common difference (d) = -1/2,

Therefore, we would have the first six terms by substituting the given values into the formula, which are:

a₁ = 3/2

d = -1/2

a₂ = a₁ + (2 - 1) * d = 3/2 + (1) * (-1/2)

= 3/2 - 1/2

= 1

a₃ = 3/2 + (2) * (-1/2)

= 3/2 - 1

= 1/2

a₄ = 3/2 + (3) * (-1/2)

= 3/2 - 3/2

= 0

a₅ = 3/2 + (4) * (-1/2)

= 3/2 - 2

= 1/2

a₆ = 3/2 + (5) * (-1/2)

= 3/2 - 5/2

= -1

Thus, the first six terms are: 3/2, 1, 1/2, 0, 1/2, -1...

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Answer:

Step-by-step explanation:  

Answer:

66

Step-by-step explanation:

Red counters: 120/4=30

Blue counters:120/5=24

Green counters:30+24=54, 120-54=66

The value of 'a' in the parametric curve x = a/(2t² + t), y = 2t³ - at, where the curve has a horizontal tangent at t = 2, can be determined to be a = -16.

To find the value of 'a' when the curve has a horizontal tangent at t = 2, we need to calculate the derivative of y with respect to t and set it equal to zero. Differentiating y = 2t³ - at, we get dy/dt = 6t² - a. Setting this derivative equal to zero gives 6t² - a = 0. Plugging in t = 2, we have 6(2)² - a = 0, which simplifies to 24 - a = 0. Solving for 'a', we find a = 24. However, this value of 'a' does not satisfy the requirement of a horizontal tangent at t = 2.

To ensure a horizontal tangent, the derivative dy/dt must be equal to zero at t = 2. Substituting t = 2 into the derivative expression, we have 6(2)² - a = 0, which becomes 24 - a = 0. Solving for 'a' gives a = 24. However, this value does not satisfy the requirement. Therefore, we must continue searching for a different value of 'a'.

Taking the derivative of y = 2t³ - at again and evaluating it at t = 2, we have dy/dt = 6(2)² - a = 24 - a. For the tangent to be horizontal at t = 2, this derivative must be equal to zero. Setting 24 - a = 0 and solving for 'a', we find a = 24. However, this value does not satisfy the condition. We need to search for another value of 'a'. Substituting a = -16 into the equation, we have 24 - (-16) = 0. Therefore, the value of 'a' that gives a horizontal tangent at t = 2 is a = -16.

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Answer:

1.875

Step-by-step explanation:

Answer:

1.875 is the answer I got

Answer:

x=10

Step-by-step explanation:

The products of the given monomials are

i. 90a⁵b⁵c⁹

ii. x⁴y⁴

iii. 50x¹¹y³z

iv. 80b⁴c⁴

v. 30m⁵n⁷

From the question, we are to determine the products of each of the three monomials

i. 9ab²c⁵, 2a³b²c² and 5abc²

9ab²c⁵ × 2a³b²c² × 5abc²

= 9 × 2 × 5 × a × a³ × a × b² × b² × b × c⁵ × c² × c²

= 90 × a⁵ × b⁵ × c⁹

= 90a⁵b⁵c⁹

ii. xy², x²y and xy

xy² × x²y × xy

= x × x² × x × y² × y × y

= x⁴ × y⁴

= x⁴y⁴

iii. 5x⁵, y²x⁵ and 10xyz

5x⁵ × y²x⁵ × 10xyz

= 5 × 10 × x⁵ × x⁵ × x × y²  × y × z

= 50 × x¹¹ × y³ × z

= 50x¹¹y³z

iv. (-4b²c), (-2bc) and 10c²b

(-4b²c) × (-2bc) × 10c²b

= -4b²c × -2bc × 10c²b

= -4 × b² × c × -2 × b × c × 10 × c² × b

= -4 × -2 × 10 × b² × b × b × c  × c × c²

= 80 × b⁴ × c⁴

= 80b⁴c⁴

v. Multiply (-5m²n²) by (-6m³n⁵)

(-5m²n²) × (-6m³n⁵)

= -5m²n² × -6m³n⁵

= -5 × m² × n² × -6 × m³ × n⁵

= -5 × -6 × m² × m³ × n² × n⁵

= 30 × m⁵ × n⁷

= 30m⁵n⁷

Hence, the products of the given monomials are

i. 90a⁵b⁵c⁹

ii. x⁴y⁴

iii. 50x¹¹y³z

iv. 80b⁴c⁴

v. 30m⁵n⁷

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Answer: the first one, 2^3x 3^2, correct me if i am wrong

Step-by-step explanation:

Answer:

2^3*3^2

Step-by-step explanation:

Answer:

the answer is in the picture

Step-by-step explanation:

Answer:

z = 83/(6-c-t)

Step-by-step explanation:

-cz +6z = tz +83

Subtract tz from each side

-cz +6z -tz = 83

Factor out z

z(6-c-t) = 83

Divide by (6-c-t)

z(6-c-t) /(6-c-t) = 83/(6-c-t)

z = 83/(6-c-t)

See below

\(\\ \sf\Rrightarrow y=-x+2\)--(1)

\(\\ \sf\Rrightarrow y=x+1\)--(2)

Now

\(\\ \sf\Rrightarrow -x+2=x+1\)

\(\\ \sf\Rrightarrow -2x=-1\)

\(\\ \sf\Rrightarrow x=0.5\)

Put in eq(2)

\(\\ \sf\Rrightarrow y=0.5+1\)

\(\\ \sf\Rrightarrow y=1.5\)

Answer:

-9 ≤ y ≤ 8

Step-by-step explanation:

look at the endpoints of the segment; (7, 8) and (-2, -9)

the y-values represent the range and they go from -9 to 8, inclusive

Answer:

The estimate of ^50 to the nearest tenth is 7.1. The two perfect squares closest to 50, one greater than 50 and less than 50, are 49 and 64. The square roots of 49 and 64 are 7 and 8, respectively.

Answer:

Step-by-step explanation:

ISSA PARADE INSIDE MY CITY YEAHHHHH

Answer:

its the one at about (8, 8000)

Step-by-step explanation:

If you look at all of the points, you can see the price constantly goes done as the car gets older. The only point away from the constant pattern is the one that is 8 years old, costing about 8000.

The value of x is 17

The congruent arcs are (b) PQ and SR

The radius is 12 units

The value of PQ is 4

The length YZ is 19 units

In this question, we make use of the property of congruent sides

So, we have

3x - 24 = x + 10

When evaluated, we have

2x = 34

Divide by 2

x = 17

By the definition of congruent arcs, congruent arcs are arcs that have equal measures

In this figure, the congruent arcs are PQ and SR i.e. (b) PQ and SR

The radius of the circle is calculated as

r² = (25 + r)² - 35²

When expanded, we have

r² = 625 + 50r + r² - 1225

So, we have

50r = 600

Divide both sides by 50

r = 12

In this question, we make use of the property of congruent sides

So, we have

PQ = SR

Where

SR = 4

When evaluated, we have

PQ = 4

The length of YZ in the circle is calculated as

YZ² = (9 + 8)² + 8²

So, we have

YZ² = 17² + 8²

When expanded, we have

YZ² = 289 + 64

So, we have

YZ² = 353

Take the square root of both sides

YZ = 19

Hence, the length YZ is 19 units

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The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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Answer:

x = 90, y = 43

Step-by-step explanation:

since AB = AC then Δ ABC is isosceles with the base angles being congruent , that is

∠ B = ∠ C = 47°

AD is the perpendicular bisector of BC , then x = 90°

the sum of the 3 angles in Δ ABD = 180° , so

y + x + ∠ B = 180

y + 90 + 47 = 180

y + 137 = 180 ( subtract 137 from both sides )

y = 43

Answer:

a=180-(45+37)

b=180-(9+24)

c=180-(42+64)

d=180-(70+13)

Answer:

1 7/8

Step-by-step explanation:

3/4+(1/2+1/4)^2*2

3/4+2(3/4)^2

3/4+2*9/16

3/4+9/8

15/8

convert to mixed fraction

15-8=7

1 7/8

a) Straight Line: The Excel function used for the straight-line method is "SLN." b) Double Declining Balance: The Excel function used for the double declining balance method is "DDB." c) Sum of Years Digits: The Excel function used for the sum of years digits method is a combination of "SYD" and other mathematical functions. d) Variable Declining Balance: The Excel function used for the variable declining balance method may vary depending on the specific calculation required.

a) Straight Line: The straight-line method calculates depreciation by dividing the asset's cost by its useful life. In Excel, the "SLN" function is used, which takes three arguments: cost, salvage value, and useful life. The formula is "=SLN(cost, salvage, life)."

b) Double Declining Balance: The double declining balance method applies a constant depreciation rate to the asset's book value. In Excel, the "DDB" function is used, which takes five arguments: cost, salvage value, useful life, period, and factor. The formula is "=DDB(cost, salvage, life, period, [factor])."

c) Sum of Years Digits: The sum of years digits method calculates depreciation by assigning weights to each year based on the asset's useful life. In Excel, the "SYD" function is used, which takes four arguments: cost, salvage value, useful life, and period. The formula is "=SYD(cost, salvage, life, period)."

d) Variable Declining Balance: The variable declining balance method calculates depreciation using a varying depreciation rate based on the asset's expected usage or production levels. The Excel function to be used may depend on the specific calculation or formula required for the variable declining balance method.

Conclusion:

Excel provides specific functions to facilitate the calculations for different depreciation methods. The "SLN" function is used for straight-line depreciation, "DDB" function for double declining balance, and "SYD" function for sum of years digits method. These functions simplify the calculations by taking relevant arguments and producing accurate results. However, for the variable declining balance method, the specific Excel function may vary depending on the formula or calculation required. By utilizing the appropriate Excel functions, depreciation calculations can be performed efficiently and accurately within the chosen depreciation method.

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