Answer:
Step-by-step explanation:
The effective tax rate is the amount of tax paid as a percentage of the total purchase price. To calculate the effective tax rate, you can divide the amount of tax by the total purchase price and multiply the result by 100 to get the answer as a percentage.
In this case, the effective tax rate would be:
(1200 / 24000) * 100 = 5%
So Chris's effective tax rate on the purchase of his car is 5%.
Match each polynomial on the left with its two factors on the right.
x³-27
x² +27
x+3
x-3
x² + 3x +9
x² + 3x-9
x²-3x+9
x²-3x-9
Answer:
hi
Step-by-step explanation:
[tex]x {}^{3} - 27 = {x}^{3} - {3}^{3} \\ = (x - 3)( {x}^{2} + 3x + 9) \\ {x}^{3} + 27 = {x}^{3} + {3}^{3} \\ = (x + 3)( {x}^{2} - 3x + 9)[/tex]
Marvin was 1.55m tall a year ago. now,he is 1.62m tall. find the percentage increase in Marvin's height correct to 2 decimal places
Answer:
4.52 %
Step-by-step explanation:
the percentage increase in height is calculated as
[tex]\frac{increase}{original}[/tex] × 100%
increase in height = 1.62 - 1.55 = 0.07 ,
then
% increase = [tex]\frac{0.07}{1.55}[/tex] × 100% = 0.045.. × 100% ≈ 4.52% ( to 2 decimal places )
write the sentence as an equation
n and 328 more is the same as 13
The equation which correctly represents the sentence in discuss as required is; n + 328 = 13.
Which sentence correctly represents the equation?It follows from the task content that the equation which correctly represents the sentence given in the task content is to be determined.
The word phrase; n and 328 more can be represented as; n + 328.
Therefore, n and 328 more is the same as 13 can be represented as; n + 328 = 13.
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1. The equation 24x² + 2x = 15 has 2 solutions. What is
the greater of the 2 solutions?
A. 3/
B.
M + NO
C.
D. 1/1
E.
Answer:
Step-by-step explanation:
To find the solutions of the equation 24x² + 2x - 15 = 0, you can use the quadratic formula.
The quadratic formula states that given a quadratic equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0, the solutions are given by:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 24, b = 2, and c = -15, so:
x = (-2 ± √(2² - 4 * 24 * -15)) / 2 * 24
x = (-2 ± √(4 + 1440)) / 48
x = (-2 ± √(1444)) / 48
Taking the square root of both sides, we have:
x = (-2 ± 38.2) / 48
Therefore, the solutions are:
x = (-2 + 38.2) / 48 = 36.2 / 48 = 0.75
x = (-2 - 38.2) / 48 = -40.2 / 48 = -0.84
Since 0.75 > -0.84, the greater of the two solutions is 0.75.
Answer:
the answers are: 36/48
-40/48
PLS HELPP
louise has planted 96 shrubs. the garden centre guaranteed her that at least 7/8 of the shrubs would survive. What is the minimum number od shrubs that should survive?
Answer:
84
What is a fraction?A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
We can first convert 96 into a fraction.
96 = [tex]\frac{96}{1}[/tex]Now that we know this, we can solve for the number of shrubs. If we know that at least [tex]\frac{7}{8}[/tex] of the shrubs should survive, we can use an equation that looks like this:
([tex]\frac{7}{8}[/tex]) × ([tex]\frac{96}{1}[/tex]) =?Solving the equation:
([tex]\frac{7}{8}[/tex]) × ([tex]\frac{96}{1}[/tex]) = 84Therefore, the minimum number of shrubs that should survive is 84.
someone help me please and thank you
Ordinal data can be ordered, as the naming implies. Both have "ord" to help remember the connection. An example of this would be something like small, medium, large. The items do not have to be numeric in nature.
Nominal data is any category or name. Order isn't present here. For example, if a survey asked about a person's favorite color, then there isn't any inherent order here.
The inside diameter of a randomly selected piston ring is a random variable with mean value 11 cm and standard deviation 0.02 cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.)
(a) Calculate P(10.99 ? X ? 11.01) when n = 16.
(b) How likely is it that the sample mean diameter exceeds 11.01 when n = 25?
a) P(10.99 ≤ X ≤ 11.01) = 0.9544
b) Probability that the sample mean diameter exceeds 11.01 when n = 25 is 0.0062.
We are given the following in the question:
Mean, μ = 11 cm
Standard Deviation, σ = 0.02 cm
We are given that the distribution of diameter is a bell-shaped distribution that is a normal distribution.
Formula: z = (x - μ)/σ
a) P(10.99 ≤ X ≤ 11.01 when n = 16)
Standard error due to sampling = σ/n = 0.02/√16 = 0.005
P(10.99 ≤ X ≤ 11.01) = P((10.99 - 11)/0.005 ≤ z ≤ (11.01 - 11)/0.005)
= P(-2 ≤ z ≤ 2) = 0.9772-0.0228
= 0.9544 = 95.44%
b) P(sample mean diameter exceeds 11.01 when n = 25)
Standard error due to sampling = σ/n = 0.02/√25 = 0.004
P(x > 11.01) = P(z > (11.01 - 11)/0.004) = P(z > 2.5)
= 1 - P(z ≤ 1) = 1 - 0.9938 = 0.0062 = 0.62%
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Color the rational numbers blue
Leave the irrational numbers alone
Answer:
The answer is provided in the image below.
Given one form of a sequence, write the other form an= an-1 -4
In the algebra on of the form of sequence is arithmetic progression or sequence which is described below.
What is an arithmetic sequence?In the arithmetic sequence the common difference between any two consecutive terms remains constant .
In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).
Formula for any nth term in AP,
T = a + nd
d = T₂-T₁
Where, a is first term , n is nth term and d is common difference
If aₙ = aₙ₋₁ -4
where aₙ is a nth term and aₙ₋₁ is a (n-1)th term
Now,
a + nd = a + (n-1-1)d - 4
nd = (n - 2)d - 4
nd = nd -2d - 4
2d = -4
d = -2
So, aₙ = a -2n
aₙ₋₁ = a -2(n - 2)
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Solve x - 5 = 8 - 4x
Answer:
Step-by-step explanation:
x - 5 = 8 - 4x
rearrange
x - 5 = -4x + 8
x + 4x - 5 = -4x + 4x + 8
5x - 5 = 8
5x - 5 + 5 = 8 + 5
5x = 13
Divide by 5
5x/5 = 13/5
x = 13/5 or 2 [tex]\frac{3}{5}[/tex]
or 2.6 as a decimal
The area of Rhode Island is about 1000
square miles. The area of Alaska is about
5.7 x 105 square miles.
Complete the statement based on the
information above:
Alaska's area is ___ times the area of rhode island
Answer:
57
Step-by-step explanation:
To find the ratio of the area of Alaska to the area of Rhode Island, we need to divide the area of Alaska by the area of Rhode Island.
The area of Rhode Island is 1000 square miles and the area of Alaska is 5.7 x 10^5 square miles.
So, the ratio is: 5.7 x 10^5 / 1000 = 57
Therefore, Alaska's area is 57 times the area of Rhode Island.
5.7 x 10^5 divided by 1000 = 57.
PLEASE HELP MISSING
WORK
Jonathan wants to save up enough money so that he can buy a new sports equipment set that includes a
football, baseball, soccer ball, and basketball. This complete boxed set costs $85.50. Jonathan has $22.00 he
saved from his birthday. In order to make more money, he plans to wash neighbors' windows. He plans to
charge $4 for each window he washes
Part A
Write and solve an inequality that represents the number of windows Jonathan can wash in order to save at
least the minimum amount he needs to buy the boxed set.
Inequality:_______
PART B
GRAPH THE SOLUTION ON A NUMBER LINE
Explain the meaning of your inequality from Part A based on the context of the problem
The inequality that shows the least amount he needs is 4x + 22 ≥ 85.50 which shows he needs at least $15.875
What is the inequality that show the least amount he needs to buy boxed setThe Inequality that will represent this problem is 4x + 22 ≥ 85.50, where x is the number of windows Jonathan washes.
To solve the inequality, we'll start by subtracting 22 from both sides:
4x ≥ 63.50
And finally, dividing both sides by 4:
x ≥ 15.875
So, Jonathan needs to wash at least 15 windows in order to save up enough money to buy the boxed set.
b.
The graph on the number line showing x ≥ 15.875 is attached below
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6. Application Juanita, who is 1.82 meters tall, wants to
find the height of a tree in her backyard. From the
tree's base, she walks 12.20 meters along the tree's
shadow to a position where the end of her shadow
exactly overlaps the end of the tree's shadow. She is
now 6.10 meters from the end of the shadows. How
tall is the tree?
The height of tree is 9.9372.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
ΔABC ~ ΔDEF only if ratio of two sides of ΔABC and corresponding two sides of ΔDEF is equal and the angle included in both sides are congruent.
Given;
Juanita is 1.82 meters tall
From the tree's base, she walks 12.20 meters along the tree's shadow to a position where the end of her shadow.
She is now 6.10 meters from the end of the shadows.
Now,
Let, h be the height of the tree;
Here, ΔABC ~ ΔADE,
So, DE/BC = AD/AB
h/1.82 = (6.10 + 12.20)/6.10
h/1.82= 18.30/6.10
h=33.306/6.10
h=5.46
h = 1.82*5.46
= 9.9372
Therefore, by congruency of triangle the answer will be 9.9372.
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Data analysts pay attention to sample size in order to achieve what goals? select all that apply.
The practise of extracting information from data to guide better business decisions is known as data analysis. Five iterative phases typically comprise the data analysis process:
Choose the data you want to examine.
gather the data
Clean up the data before analysis.
Study the information
Interpret the analysis' findings
It is common knowledge that data analysts focus on the sample size in order to
To prevent a few outlier responses from distorting the results
ensuring that the data reflects a variety of viewpoints
to prevent making erroneous conclusions due to a tiny sample size
An analyst of data is who?
An individual involved in the handling of data is referred to by this phrase.
Such a person aids in the analysis, retrieval, and drawing of conclusions from the information at hand.
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The perimeter of a triangle is 39 inches. If the length of the shortest side is 1/2 the length of the longest side, and the length of the third side is 1 less than the length of the longest side, what is the length of each side?
.. who. staple. food of the Vedic Aryan was ?
A) Barley and rice. B) MMilk
Answer: b
Step-by-step explanation: ias chinadu
B because that's the VA which would be intellectually specialist.
For time 0≤t≤10 , water is flowing into a small tub at a rate given by the function F defined by F(t)=arctan(π/2−t/10). For time 5≤t≤10 , water is leaking from the tub at a rate given by the function L defined by L(t)=0. 03(20t−t^2−75). Both F(t) and L(t) are measured in cubic feet per minute, and t is measured in minutes. The volume of water in the tub, in cubic feet, at time t minutes is given by W(t).
(a) At time t=3 , there are 2. 5 cubic feet of water in the tub. Write an equation for the locally linear approximation of W at t=3 , and use it to approximate the volume of water in the tub at time t=3. 5.
(b) Find W′′(8). Using correct units, interpret the meaning of W′′(8) in the context of the problem.
(c) Is there a time t , for 5
(d) The tub is in the shape of a rectangular box that is 0. 5 foot wide, 4 feet long, and 3 feet deep. What is the rate of change of the depth of the water in the tub at time t=6 ?
(a) W(3.5) ≈ 2.5 + 0.483(0.5) ≈ 2.7625 cubic feet.
(b) W''(8) ≈ -0.0397 - (-0.6) ≈ 0.5603 cubic feet per minute per minute.
(c) We can solve for t numerically using a graphing calculator or other numerical method. One possible solution is t ≈ 5
What is the quadratic equation?
The quadratic equation is a formula used to solve quadratic equations of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable.
(a) To find the locally linear approximation of W at t=3, we first need to find W(3) and W'(3).
We know that at time t=3, the volume of water in the tub is 2.5 cubic feet. Therefore, W(3) = 2.5.
To find W'(3), we need to use the fact that the rate of change of the volume of water in the tub is equal to the rate of water flowing in minus the rate of water leaking out.
So, W'(t) = F(t) - L(t).
At time t=3, we have F(3) = arctan(π/2 - 3/10) ≈ 1.383 cubic feet per minute, and L(3) = 0.03(20*3 - 3² - 75) = 0.9 cubic feet per minute. Therefore, W'(3) = 1.383 - 0.9 = 0.483 cubic feet per minute.
The locally linear approximation of W at t=3 is given by:
W(t) ≈ W(3) + W'(3)(t-3)
W(t) ≈ 2.5 + 0.483(t-3)
To approximate the volume of water in the tub at time t=3.5, we plug in t=3.5 into the above equation:
W(3.5) ≈ 2.5 + 0.483(0.5) ≈ 2.7625 cubic feet.
(b) To find W''(8), we first need to find an expression for W'(t). We know that:
W'(t) = F(t) - L(t)
Taking the derivative with respect to t:
W''(t) = F'(t) - L'(t)
We know that F(t) = arctan(π/2 - t/10), so F'(t) = -1/(10π/4 - t²/100 + t/5²) * (1/5), where we used the chain rule and the derivative of arctan(x) = 1/(1+x²). Evaluating this expression at t=8, we get F'(8) ≈ -0.0397 cubic feet per minute.
We also know that L(t) = 0.03(20t - t²- 75), so L'(t) = 0.03(20 - 2t). Evaluating this expression at t=8, we get L'(8) = -0.6 cubic feet per minute.
Therefore, W''(8) ≈ -0.0397 - (-0.6) ≈ 0.5603 cubic feet per minute per minute.
Interpreting the meaning of W''(8), we see that it represents the rate of change of the rate of change of the volume of water in the tub at time t=8. Specifically, W''(8) tells us how quickly the volume of water in the tub is changing with respect to time at time t=8 is changing.
(c) Yes, there is a time t for which the volume of water in the tub is neither increasing nor decreasing. This occurs when the rate of water flowing into the tub is equal to the rate of water leaking out. That is, we need to find a value of t such that F(t) = L(t).
We can solve for t numerically using a graphing calculator or other numerical method. One possible solution is t ≈ 5
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The PTO has 1,932 tickets to sell for the school carnival. They want to split the tickets equally into at least 3, but less than 10 ticket booths. How many ticket booths could they split them into without having any left over? Please explain your answer.
The PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths, without having any tickets left over.
How many ticket booths could they split?We need to find a number that is divisible by at least 3, but less than 10.
We can start by listing out the multiples of 3 and see which one is closest to 1,932:
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12
3 × 5 = 15
3 × 6 = 18
3 × 7 = 21
3 × 8 = 24
3 × 9 = 27
We can see that the closest multiple of 3 to 1,932 is 1,932 ÷ 3 = 644. This means that if the PTO split the tickets into 644-ticket batches, they would have 3 equal booths of 644 tickets each.
We can check whether 644 is also divisible by 4, 5, 6, 7, 8, or 9, as those numbers are less than 10. We can see that 644 is not divisible by 4 or 5, but it is divisible by 6, 7, 8, and 9. This means that the PTO could also split the tickets into 6, 7, 8, or 9 ticket booths, with each booth having an equal number of tickets.
Therefore, the PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths.
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Sherri saves nickels and dimes in a coin purse for her daughter. The total value of the coins in the purse is $0.95. The
number of nickels is 2 less than 5 times the number of dimes. How many nickels and how many dimes are in the coin
purse?
Let's represent the number of dimes in the coin purse as d. Then, the number of nickels in the coin purse can be represented as 5d - 2.
The total value of the coins can be expressed as:
0.05 * (5d - 2) + 0.10 * d = 0.95
Expanding and simplifying the equation, we get:
0.05 * 5d - 0.05 * 2 + 0.10 * d = 0.95
0.50d - 0.10 = 0.95
0.50d = 1.05
d = 2.10
Since the number of dimes must be a whole number, we round d down to 2. So, there are 2 dimes in the coin purse and 5 * 2 - 2 = 6 nickels in the coin purse.
Jesus believes in looking his best when searching for a job. He wants to save $435 for a new suit for his interviews. He currently has $65.00 and he can save $18.00 per week from his work.
How many weeks in total will it take him to save for the suit, assuming he puts the $65.00 into an account on week 1 and starts saving each week thereafter?
Answer:
6.7 weeks.
Step-by-step explanation:
65.00 x 6.7 = 435.50
Answer:
Step-by-step explanation:
He has $65 on the first week. He’s missing $370. If he can save $18 a week. 370/18 = 20.5. But they’re asking for the total weeks it’ll take. So add the first week. 20.5 + 1 = 21.5
not mine but he did he get it right
Find GI, AGI, TI...
Given:
Wages : $145,000
Interest : $2500,
Contribution towards the retirement: $3000
Exemptions: $4100
Deductions: $2800
-Thanks!
The GI (Gross Income) is $147,500, AGI (Adjusted Gross Income) is $144,500, and TI (Taxable Income) is $137,600.
What is Interest?
Interest is the income that is returned to the holder of capital. Different kinds of interest include gross interest and net interest.
To find GI (Gross Income), we add wages and interest:
GI = Wages + Interest = $145,000 + $2500 = $147,500
To find AGI (Adjusted Gross Income), we subtract the contributions towards retirement from GI:
AGI = GI - Contributions towards Retirement = $147,500 - $3000 = $144,500
To find TI (Taxable Income), we subtract exemptions and deductions from AGI:
TI = AGI - Exemptions - Deductions = $144,500 - $4100 - $2800 = $137,600.
Therefore, the taxable income is $137,600.
Hence, GI (Gross Income) is $147,500, AGI (Adjusted Gross Income) is $144,500, and TI (Taxable Income) is $137,600.
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Can someone pls help me?
What is the initial value of the function?
The initial value of the function is 1.
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.
A relationship in which one input value exactly equals one output value is known as a function. A function's initial value is a crucial component. A starting value or starting point is exactly what it sounds like: It is an initial value.
The line intersects the y-axis at (0,1).
The initial value of the function is 1.
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Find the equation of the line with slope 7 which goes through the point (−2,−9).
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-9})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{ 7}(x-\stackrel{x_1}{(-2)}) \implies y +9= 7 (x +2) \\\\\\ y+9=7x+14\implies {\Large \begin{array}{llll} y=7x+5 \end{array}}[/tex]
Graph the linear inequality.
x < 2
The ratio of horizontal distance to height of the ramp is 15:1. A builder has a roll of nonslip rubber mat that is 15 feet long. Does he have enough forever to cover the Ramp completely?
Answer:
No. The length of the ramp is [tex]\sqrt{226[/tex] The rubber mat will be too short
Step-by-step explanation:
The American flag has 50 stars, 7 red stripes, and 6 white stripes. Write a ratio to represent the ratio of stars to red stripes.
The ratio of stars to red stripes is 50 to 7
How to write a ratio to represent the ratio of stars to red stripes.from the question, we have the following parameters that can be used in our computation:
Number of stars = 50
Red stripes = 7
White stripes = 6
Using the above as a guide, we have the following:
Ratio = Stars : Red stripes
substitute the known values in the above equation, so, we have the following representation
Stars : Red stripes = 50 : 7
Hence, the ratio is 50 : 7
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How do you solve this equation 4(x+3)= -8
Answer:
x= -5
Step-by-step explanation:
4(x + 3) = -8
4x + 12 = -8
4x = -20
x = -5
Out of 1000 students who appeared for C.A. Intermediate Examination, 750 failed in Math, 600 failed in Accounts and 600 failed in Costing, 450 failed in both Math & Accounts, 400 failed in both Math & Costing, 150 failed in both Accounts & Costing. The Students who failed in all the three Subjects were 75. Prove that the above data is not correct.
Yes, the data provided is not correct. This can be proven using the principle of inclusion-exclusion.
According to the given data, the total number of students who failed in Math is 750, the total number of students who failed in Accounts is 600, and the total number of students who failed in Costing is 600.
However, if we apply the principle of inclusion-exclusion, the total number of students who failed in at least one of the three subjects should be equal to the sum of the number of students who failed in each subject, minus the number of students who failed in two subjects, plus the number of students who failed in all three subjects.
Therefore, using this principle, we have:
750 + 600 + 600 - 450 - 400 + 75 = 975
This result shows that the number of students who failed in at least one of the three subjects is 975, which is greater than the total number of students who appeared for the examination (1000), which is not possible.
Therefore, the given data is not correct.
The value of a machine, V , at the end of t years
The value of machine after 2 years is $346.4.3
What is Rate of Depreciation?Subtract the asset's cost from its salvage value (what you anticipate it to be worth at the end of its useful life) to determine depreciation using the straight-line technique. The amount that can be depreciated, or the depreciable basis, is the outcome. Subtract this sum from the asset's useful life, which is measured in years.
Given:
C = $707 (the original cost),
r = 0.3 (the rate of depreciation),
and t = 2 (years that have gone by)
Using the Formula
V = C [tex](1-r)^t[/tex]
V = (707)(1 - 0.3)²
V = (707)(0.7)²
V = (707)(0.49)
V = 346.43
Thus, the value of machine is $346.43
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Isosceles trapezoid KRWT is shown
Given KRWT is an isosceles trapezoid with KR and TW
Prove: WK = TR
An incomplete two-column proof is shown
Answer Choices:
-
-
-
-
What is the missing statement in step 3
More info is in the picture
Thank you for any help!
The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In isosceles trapezoid KRWT, the trianngles are ΔKTW and ΔRWT are formed.
In trianngles ΔKTW and ΔRWT, then we have
KW = TR {Given}
∠W = ∠T {Isosceles angles}
WT = WT {Common side}
Then the trianngles ΔKTW and ΔRWT are congruent to each other.
The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.
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