solve and graph the inequality
-13>5-2b

Answer:

$34.85

Step-by-step explanation:

First, find the total amount that Sydney would've payed without the discount:

13+28=41

Then find the discount in dollars:

15%=0.15 as a decimal

41*0.15=6.15

Then subtract the discount from the total amount she would've payed:

41-6.15

As a result, she payed $34.85

Answer:

55 i think

Step-by-step explanation:

Answer:

$1,041.69

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation:

Forumla; P(1 + r/n)nt

700.00(1 + 0.05/4)(4)(8)

700.00(1 + 0.0125)(32)

$1,041.69

hope this helps!

Answer:

$1,041.69

Step-by-step explanation:

Compound interest formula: \(A=P(1+\frac{r}{n})^{nt\)

A = amount (future value ($))

P = principal (orignal amount - $700)

R = rate (written as a decimal - 5%/100= 0.05)

N = compound (quarterly - 4) 4 quarters in 1 yr.

T = number of years (8)

\(A=P(1+\frac{r}{n})^{nt\)

\(A=P(1+\frac{r}{n})^{nt}\\\\A=700(1+\frac{0.05}{4})^{4*8} < == start\ from\ the\ parenthesis\ and\ divide\ first\\\\A=700(1+0.0125)^{4*8} < == add\ the\ \#s\ in\ the\ parenthesis\\\\A=700(1.0125)^{4*8} < == multiply\ the\ exponents\\\\A=700(1.0125)^{32} < ==multiply\\\\A=700(1.488131) < ==multiply\\\\A=1041.691\\\\A=$1,041.69\)

Hope this helps!

The exact dimensions of the rectangular prism are:

Width = \(((\sqrt{282} + \sqrt{1975})/3)/2\)

Height = \((141 - (\sqrt{282} + \sqrt{1975})/3) / 2\)

(I may have formatted my response incorrectly. If so, please let me know. I will update my response accordingly.)

The rectangular prism with a fixed surface area of 282 square units and maximum volume has dimensions of 9 by 9 by 14 units.

To find the dimensions of the rectangular prism with a fixed surface area of 282 square units and maximum volume, we need to use the fact that the volume of a rectangular prism is given by V = lwh and the surface area is given by SA = 2lw + 2lh + 2wh. Since we want to maximize the volume, we can use the surface area formula to solve for one of the dimensions in terms of the other two, and then substitute into the volume formula to obtain a function of two variables.

We can then take the derivative of this function and set it equal to zero to find the maximum volume. Solving this equation, we obtain l = w = 9 and h = 14, which gives the desired dimensions.

Therefore, the rectangular prism with a fixed surface area of 282 square units and maximum volume has dimensions of 9 by 9 by 14 units.

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Answer:

3×3-3=6 I think sorry if it ain't

To determine whether he will receive a refund or owe money to the IRS, the result is negative, Brian owes the IRS $2,957.46.

What do you mean by federal income tax?

Brian paid $15,987.76 in federal income tax and his actual tax liability is $18,945.22.

To determine whether he will receive a refund or owe money to the IRS, we can use the formula:

Tax refund or owed = taxes paid – taxes due

Tax refund or owed = $15,987.76 - $18,945.22

Tax refund or owed = -$2,957.46

Since the result is negative, Brian owes the IRS $2,957.46.

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The first step to conducting a statistical study is to clearly define the research question or problem.

This involves identifying the population of interest, the variables to be measured, and the hypothesis or objective of the study. Once the research question is clearly defined, the next step is to design the study, including selecting an appropriate sample size, choosing a sampling method, and determining the data collection method.

It is also important to consider potential sources of bias and confounding factors that may impact the study results. Overall, a well-designed statistical study should be able to produce reliable and accurate results that can be used to draw meaningful conclusions about the population of interest.

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Answer:

Zhi's Expression:

18: The total number of tickets

3: The number of tickets required for each game

g: The number of games played

Diego's Expression:

3: The number of tickets required for each game

(6 - g): The total number of tickets minus the number of games played

Step-by-step explanation:

1) It will take 40 minutes to fill the same tank with 2 pumps

2) the product of the means equals the product of the extremes".

3) Tes is 56 years old, given that the ratio of their ages is 3:7

4) 10 the value of N in the expression

5) 150 is the bigger number if the sum of the numbers is 240, and the ratio is 3:5

1) time × speed = time × speed

= 16 × 5 = x × 2

= \(\frac{16*5}{2}\) = x

x = 80\2

x = 40 minutes

2) product

ab=cd. the product of the means equals the product of the extremes. That is, ad=bc. We can get an equivalent result using a technique called cross multiplication.

3) let the age of ed be x, then age of tes is 80 - x

\(\frac{x}{80-x}\) = \(\frac{3}{7}\)

7x = 3(80-x)

7x =  240 - 3x

7x + 3x = 240

10x = 240

x = 24

Ed's age is 24 therefore Tes age is 80 - x

80 - 24 = 56

therefore tes age is 56

4) 2\7 = N\35

2 × 35\ 7 = N

70\7 = N

N = 10

5) Let the multiple of the ratio be x

3x + 5x = 240

8x = 240

x = 30

we need to find the bigger number therefore,

5x = 5 × 30 = 150

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The time series pattern that exists when the data fluctuate around a constant mean is the c. horizontal pattern.

In a horizontal pattern, the data points exhibit random fluctuations around a constant mean value over time.

This means that there is no significant trend, seasonal variation, or cyclical pattern observed in the data.

The values may vary above or below the mean, but they do not show any consistent upward or downward trend or recurring patterns.

Therefore, when the data fluctuate around a constant mean without any discernible trend or seasonality, it is referred to as a horizontal pattern.

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Answer:

y = 4x + 5

Step-by-step explanation:

As we move from the point (-3, -7) to the point (1, 9), x increases by 4 and y increases by 16.  Thus, the slope of the desired line is m = rise / run = 16/4 = 4.

The slope-intercept form is y = mx + b.  We must find b.

Here, m = 4, x = 1 and y = 9:

9 = 4(1) + b, so b = 5, and the desired equation is thus

y = 4x + 5

Answer:

y=3x+6

Step-by-step explanation

graph to find the slope and y-intercept

Answer:

H = 13

Step-by-step explanation:

==>24 = 3(h-5)

==> 3(h - 5)=24

==> 3h - 15 =24

==> 3h = 24 + 15

==> 3h = 39

==> \(h = \frac{39}{3} \)

==> h = 13

Trevarius' investment will grow exponentially due to the compounding effect of interest.

Compounded interest refers to the process of earning interest not only on the initial principal amount but also on the accumulated interest from previous periods.

This means that as time progresses, the interest earned becomes part of the new principal, resulting in a compounding effect.

In a linear growth scenario, the investment would grow at a constant rate over time, where the increase in value would be the same for each time period. However, in the case of compounded interest, the growth rate is not constant but rather increases over time due to the compounding effect.

As more interest is added to the principal, the subsequent interest calculations are based on a larger amount, resulting in a higher growth rate.

This compounding effect leads to exponential growth because the investment value increases at an accelerating rate over time.

Mathematically, the exponential growth of Trevarius' investment can be represented by the formula \(A = P(1 + r/n)^{(nt),\)

where A is the final amount, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

By continuously reinvesting the earned interest, Trevarius' investment will experience exponential growth, allowing his initial investment to grow significantly over time.

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Using it's concept, it is found that the situation that best describes conditional probability is given by:

4. Finding the probability of an event occurring given another event had already occurred.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which:

The key-word is previous, that is, we have to consider a previous event that already happened. Hence, researching the problem on the internet, the correct option is given by:

4. Finding the probability of an event occurring given another event had already occurred.

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Answer: 2nd one down

Step-by-step explanation:

The magnitude and direction of vector v can be found by multiplying the magnitude of vector u by 2 and subtracting 180 degrees from the direction of vector u. Therefore, the magnitude of vector v is 44 (22*2), and the direction of vector v is 235 degrees (55-180).

To understand why we subtract 180 degrees from the direction of vector u, we must consider the fact that vector v is in the opposite direction of vector u, as indicated by the negative sign.

Thus, when we multiply the magnitude of vector u by -2, we are essentially reversing the direction of vector u.

To find the new direction of vector v, we subtract 180 degrees from the original direction of vector u, which effectively reflects the direction across the y-axis (i.e., flips the vector horizontally).

This results in a direction of 235 degrees, which falls within the interval 0 degrees to less than 360 degrees as specified in the question.

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So the cosine of the angle between the two planes is 8sqrt(78) / 78.

To find the cosine of the angle between two planes, we need to find the normal vectors of each plane and then use the dot product formula.

The normal vector of the first plane is <1, 1, 1>, and the normal vector of the second plane is <1, 3, 4>.

The dot product of these two vectors is:

<1, 1, 1> · <1, 3, 4> = 1(1) + 1(3) + 1(4) = 8

The magnitude of the normal vector of the first plane is:

|<1, 1, 1>| = sqrt(1^2 + 1^2 + 1^2) = sqrt(3)

The magnitude of the normal vector of the second plane is:

|<1, 3, 4>| = sqrt(1^2 + 3^2 + 4^2) = sqrt(26)

Therefore, the cosine of the angle between the two planes is:

cosθ = (normal vector of plane 1) · (normal vector of plane 2) / (magnitude of normal vector of plane 1) * (magnitude of normal vector of plane 2)

= 8 / (sqrt(3) * sqrt(26))

= 8 / (sqrt(78))

= 8sqrt(78) / 78

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0.485

Given that Georgie has a red, blue and a yellow scarf, the probabilities of the three colors are 0.2, 0.45 and 0.35 respectively. When Georgie wears a red scarf, she always wears a hat. When she wears a blue scarf, she wears a hat with a probability of 0.4. When she wears a yellow scarf, she wears a hat with probability 0.3.The probability that on a randomly chosen day Georgie wears a hat is 0.2 × 1 + 0.45 × 0.4 + 0.35 × 0.3 = 0.2 + 0.18 + 0.105 = 0.485.Hence, the required probability is 0.485 that on a randomly chosen day Georgie wears a hat. Therefore, the correct option is (d) 0.485.

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Answer:

28

Step-by-step explanation:

circumference=diameter × π

diameter=87.92÷3.14=28

The diameter of circle will be 28 inches.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circumference of a circle is 87.92 inches.

Now,

We know that;

The circumference of circle = 2πr

Since, The value of π = 3.14

Substitute all the values, we get;

⇒ 87.92 = 2 × 3.14 × r

⇒ 87.92 = 6.28 r

⇒ r = 14

Thus, The diameter of circle = 2 × 14

                                            = 28 inches

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To solve this problem, we need to find the x-values where the curve intersects the x-axis, which occurs when y=0.
0=x²-2kx ,We can factor out an x: 0=x(x-2k) .So the x-intercepts are at x=0 and x=2k.

To find the value of k, we need to follow these steps:

Step 1: Find the points of intersection between the curve y = x^2 - 2kx and the x-axis.
To do this, set y = 0:
0 = x^2 - 2kx
x(x - 2k) = 0

This means that the curve intersects the x-axis at x = 0 and x = 2k.

Step 2: Determine the limits of integration.
Since we are looking for the region in the fourth quadrant, we will have limits 0 and 2k for our integration.

Step 3: Calculate the area using integration.
Area = ∫[0 to 2k] (x^2 - 2kx) dx

Step 4: Solve the integral.
Area = [1/3x^3 - kx^2] evaluated from 0 to 2k
Area = (1/3(2k)^3 - k(2k)^2) - (1/3(0)^3 - k(0)^2)
Area = (8k^3/3 - 4k^3)

Step 5: Set the area equal to 36 and solve for k.
36 = 8k^3/3 - 4k^3
36 = (8k^3 - 12k^3)/3
36 = -4k^3/3

Now, multiply both sides by 3 and divide by -4:
-108/-4 = k^3
27 = k^3

Take the cube root of both sides:
k = 3

The value of k is 3 (Option b).

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Answer:

j = 32

g = 78

Step-by-step explanation:

because they are similar you can use CPCTC corresponding parts of congruent triangles are congruent to determine f = j and h = g

The volume of the rectangular prism is 428,544 cubic cm.

To find the volume of the rectangular prism, we can start by determining the dimensions of the prism.

Let's assume the length, width, and height of the prism are L, W, and H, respectively.

Given that the rectangular prism is filled exactly with 248 cubes, we can express the total number of cubes as the product of the length, width, and height of the rectangular prism:

\(L \times W \times H = 248\)

Since each cube has an edge length of 12 cm, the volume of one cube can be calculated as follows:

Volume of one cube \(= (12 cm) \times (12 cm) \times(12 cm)\)

Volume of one cube \(= 1728 cm^3\)

Now, we can set up the equation based on the given information:

\(L \times W \times H = 248 \times Volume of one cube\)

\(L \times W \times H = 248 \times 1728 cm^3\)

To find the volume of the rectangular prism, we need to calculate the right side of the equation:

\(248 \times1728 = 428,544 cm^3\)

Therefore, the volume of the rectangular prism is \(428,544 cm^3\).

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Step-by-step explanation:

b) 3.14, 31.4, 0.314, 3 2/4, 3.141

3.14, 31.4, 0.314, 3.5, 3.141

0.314, 3.14, 3.141, 3.5, 31.4

I think it would be 40?

Answer:

a)(5m+3n)^3 b)(4a-3b)^3

Step-by-step explanation:

a)125m^3+27n^3+225m^2 n+135mn^2

Use the binomial cube formula, a^3+3a^2

b+3ab^2+b^3=(a+b)^3, where a=5m and b=3n.

(5m+3n)^3

b)64a^3-144a^2 b+108ab^2-27b^3

Use the binomial cube formula, p^3-3p^2q+3pq^2-q^3=(p-q)^3, where p=4a and q=3b.

(4a-3b)^3

Step-by-step explanation:

-1| 2/3 - 4| / 5/6

=-1 paxi ko sign k hola

The no-arbitrage price today of a 5-year $1,000 US Treasury note with a 2% coupon rate and a 4.25% yield to maturity is approximately $908.44, closest to option B: $900.53.

To determine the no-arbitrage price of a 5-year $1,000 US Treasury note with a coupon rate of 2% and a yield to maturity (YTM) of 4.25%, we can use the present value of the future cash flows.First, let's calculate the annual coupon payment. The coupon rate is 2% of the face value, so the coupon payment is ($1,000 * 2%) = $20 per year.The yield to maturity of 4.25% is the discount rate we'll use to calculate the present value of the cash flows. Since the coupon payments occur annually, we need to discount them at this rate for five years.

Using the present value formula for an annuity, we can calculate the present value of the coupon payments:PV = C * (1 - (1 + r)^-n) / r,

where PV is the present value, C is the coupon payment, r is the discount rate, and n is the number of periods.

Plugging in the values:PV = $20 * (1 - (1 + 0.0425)^-5) / 0.0425 = $85.6427.

Next, we need to calculate the present value of the face value ($1,000) at the end of 5 years:PV = $1,000 / (1 + 0.0425)^5 = $822.7967.

Finally, we sum up the present values of the coupon payments and the face value:No-arbitrage price = $85.6427 + $822.7967 = $908.4394.

Rounding to the penny, the no-arbitrage price is $908.44, which is closest to option B: $900.53.

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Answe12800 miles

Step-by-step explanation:a year is 12 months, and mile round trip means there and back. so 532x24 for the 24 trips that equals 12768. 12768 rounded to the nearest hundreds is 12800