Answer:
d= -3
Step-by-step explanation:
Rearrange variables to the left side of the equation: -4.3x 10d= -0.0043
Divide both sides of the equation by the coefficient of variable
Reduce the fraction
Convert fraction into negative exponential form
Convert both sides of the equation into terms with the same with same base
Simplify using exponent power rule
Based on the given conditions, corresponding exponents are equal
A contractor is building a new house and wants to determine the size of its foundation. The length of the
foundation is 6 feet more than 2 times its width. The value of the area of the foundation (in square feet)
is 1046 more than the value of the perimeter of the foundation (in feet). Which of the following values
are correct? Show work.
A. Area: 1196 sq ft
B. Worth: 23 ft
C. Perimeter: 150 ft
D. Length 29 ft
Answer:
A, B, C
Step-by-step explanation:
You want to find the dimensions, perimeter, and area of a foundation such that the length is 6 feet more than twice the width, and the area is 1046 more that the value of the perimeter.
SetupWe can let x and y represent the length and width, respectively. Then the given relations translate to the equation ...
A = LW . . . . . . . area formula
P = 2(L +W) . . . . perimeter formula
y = 2x +6 . . . . . relation between dimensions
xy = 2(x +y) +1046 . . . . . relation between perimeter and area
SolutionUsing the first equation to substitute for y, we have ...
x(2x +6) = 2(x +(2x +6)) +1046
2x² +6x = 6x +1058 . . . . . . . . . . . . eliminate parentheses
x² = 529 . . . . . . . . . . . . . subtract 6x and divide by 2
x = √529 = 23 . . . . . . . . . width; matches B
y = 2(23) +6 = 52 . . . . length
area = (23)(52) = 1196 . . . area; matches A
perimeter = 2(23 +52) = 2(75) = 150 . . . . matches C
The area is 1196 square feet. (A)
The width is 23 feet. (B)
The perimeter is 150 feet. (C)
Calculate the difference and enter below. -9-(-10)
Answer: 1
Step-by-step explanation: So, since this is a subtraction problem of negative numbers, we will make this an inverse operation, and make this an addition problem (It's easier to solve) So, now it will be written as -9 + 10. This is the same as 10-9, which would give us our answer; 1. I hoped this helped.
1/a+1/b=1/c, what is the average (arithmetic mean) of a and b?
The arithmetic mean of a and b in the expression 1/a + 1/b = 1/c is 2c.
What is the arithmetic mean or average?Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.
Given, An expression of the form 1/a + 1/b = 1/c.
We know average of two numbers is sum of those numbers divided by 2.
So, {(1/a) + (a/b)}/2 = 1/c.
Now to keep the equality we also have to divide the RHS by 2.
Therefore, {(1/a) + (a/b)}/2 = (1/c)/2.
{(1/a) + (a/b)}/2 = (1/c)×((1/2).
{(1/a) + (a/b)}/2 = 1/2c.
So, The arithmetic mean of 1/a + 1/b is 1/2c.
Now taking the reciprocal of 1/a and 1/b which is a and b the arithmetic mean is
2c.
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Right Answers Only! thank you
Answer:
D
Step-by-step explanation:
The equation is like this :
Popcorn + 5(Price of each juice bottle) = total cost
1.59 + 5j = 13.34
Subtract both sides with 1.59
5j = 11.75
A and C are obviously wrong
B is wrong because there is only one of the juice bottle in the diagram
The answer is D
Question 14 of 50
In a transformation, the preimage is the original figure and the image is the figure in the new location.
False
True
Answer:
True
Step-by-step explanation:
Is the exponential representation below increasing or decreasing?
y=200(0.75)x
The exponential representation is a decreasing function
How to determine if the exponential representation is increasing or decreasing?From the question, we have the following parameters that can be used in our computation:
y = 200(0.75)x
Rewrite properly
So, we have the following representation
y = 200(0.75)ˣ
An exponential function is represented as
y = abˣ
Where
b = rate
This means that
b = 0.75
Since b is less than 1, then the function is a decreasing function
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Give a proof showing that the following formula is a theorem. Be sure to submit your answer by clicking the submit button. V.2 3 pts TE (A → (B − C)) → (B → (A → C)) 11
We can prove the formula given in the question as a theorem using the truth table method.
A Truth Table is referred to as a logic table that can be used to perform logic functions with some formulas. The logic functions that can be performed include Boolean algebra.
Let A, B, and C represent propositions. We construct a truth table as follows:
A B C (A → (B − C)) (B → (A → C))
T T T T T
T T F T F
T F T T T
T F F T T
F T T T T
F T F T T
F F T T T
F F F T T
From the truth table, we can see that the formula holds for all possible truth values of A, B, and C. Therefore, the formula is a theorem.
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if the 90% confidence limits for the population mean are 57 and 63, which of the following could be the 97% confidence limits A. [56, 64] b. [58, 65] c. [56. 61] d. [59, 63] e. [60, 60] f. None of the above
f 57 and 63 are the 90% confidence limits for the population mean, then [60, 60] might be the 97% confidence limit.
What are the definitions and categories of population?A population is a discrete collection of things having observable traits, such humans or animals, for the purpose of analysis and data collection. It is made up of a comparable collection of species that live in a specific area and have the ability to interbreed.
What does the term "population mean" mean?The average calculated from the whole population, distribution, or group is known as the population mean. It is calculated by dividing the total number of population variables by the sum of all population variables. The population mean can be found here as. Observations in the population are added together to form X.
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To kick off the summer, Leah is planning a "School's Out!" party for all her friends. She and
her mom pick up a giant sub and a vat of root beer from Subs & Suds. When they get to the
park, they cut the sub into 18 equal sections. Each section is 1/3
of a foot long.
Which equation can you use to find the length g of the giant sub?
Answer:
g = 18(1/3)
Step-by-step explanation:
The sub is made of 18 sections of 1/3, so it is 18(1/3) feet long (or 6ft when simplified)
2, 7, 4, 2, 3, 6, 11
MEAN:
MEDIAN:
MODE:
RANGE:
answer: Mean:5
median:4
range: 9
mode: 2
Step-by-step explanation:
decide, without calculation, if each of the integrals below are positive, negative, or zero. let d be the region inside the unit circle centered at the origin. let t, b, r, and l denote the regions enclosed by the top half, the bottom half, the right half, and the left half of unit circle, respectively. positive 1. positive 2. negative 3. negative 4. zero 5.
The region inside the unit circle centered at the origin is 1. positive 2. positive 3. positive 4. positive 5. negative
Without calculation we need to state if the each of the integrals below are positive, negative, or zero. let d be the region inside the unit circle centered at the origin
xeˣ is positive for positive , and negative for negative , but the exponential factor makes the positive part dominating, so that the integral over D is positive overall.
The integrals over B and T are identical by symmetry, and both are equal to half the value of the integral over D, so they are both positive as well.
The integral over L is negative because it takes strictly non-positive values of x .
Similarly, the integral over R is positive because it considers non-negative values of x.
Therefore, the region inside the unit circle centered at the origin is 1. positive 2. positive 3. positive 4. positive 5. negative
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what is the value of the estimated standard error for the following set of d (differneces) scroes 4, 8, 4 ,4
The value of the estimated standard error is 1.
The set of d (differneces) scroes: 4, 8, 4 ,4
Consider,
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Mean of the D-score is [tex]$$\begin{aligned}\bar{d} & =\frac{1}{n} \sum d_i \end$[/tex]
[tex]=\frac{1}{4}[/tex](4+8+4+4)
=5
Standard deviation of D-score is given by [tex]$$\begin{aligned}\hat{\sigma} & =\sqrt{\frac{1}{n-1} \sum_{i=1}^n\left(d_i-\bar{d}\right)^2} \\& =\sqrt{\frac{1}{4-1}\left\{(4-5)^2+(8-5)^2+(4-5)^2+(4-5)^2\right\}} \end[/tex]
The value of the estimated standard error for the following set D scores is
[tex]$$\begin{aligned}\widehat{\mathrm{SE}(d)} & =\frac{\hat{\sigma}}{\sqrt{n}} \\& =\frac{2}{\sqrt{4}}\end{aligned}$$[/tex]
[tex]=\frac{2}{2}=1[/tex]
Therefore, the value of the estimated standard error for the following set of d scroes is 1.
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Write the function in terms of its
cofunction. Assume that any angle in
which an unknown appears is an
acute angle.
CSC 23°
-
The choices:
-sin 67°
-sec 23°
-CSC 157°
-sec 67°
CSC 23° can be written as sec 67° in as its cofunction.
Trigonometric Ratios:A branch of mathematics called trigonometry in geometry focuses on the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to angles and sides.
The six trigonometric ratios are sin, cos, tan, cot, cosec, and sec.
From Trigonometrical Ratios of (90° - θ)
=> sin (90° - θ) = cos θ
=> cos (90° - θ) = sin θ
=> tan (90° - θ) = cot θ
=> csc (90° - θ) = sec θ
=> sec (90° - θ) = csc θ
=> cot (90° - θ) = tan θ
Here we have CSC 23°
Here we need to write csc 23° into its cofunction
From Trigonometrical Ratios of (90° - θ)
csc (90° - θ) = sec θ
23° can be taken as (90 - 67)°
=> csc 23° = csc (90 - 67)° = sec 67°
Therefore,
CSC 23° can be written as sec 67° in as its cofunction.
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What are the vertex and range of y = |2x + 6| + 2? 1 (0, 2); 2 < y < ∞ 2 (0, 2); −∞ ≤ y < ∞ 3 (−3, 2); 2 < y < ∞ 4 (−3, 2); −∞ ≤ y < ∞
Answer:
(−3, 2); 2 < y < ∞
Step-by-step explanation:
It's either (−3, 2); 2 < y < ∞ or (−3, 2); −∞ ≤ y < ∞ but I'm pretty sure its (−3, 2); 2 < y < ∞
an ice cream company is going to open new stores in los angeles, chicago, and new orleans. the monthly cost for a square foot .find the total monthyl rent for all three stores.find the total monthyl rent for of rental space in each city was follows. los angeles $5.25, chicago $6.95 and new orleans $4.25. the store in los angels will be 560 square , chicago will be 330 square feet and new orleans will be 495 square feet.
The total monthly rent for these three stores is $8,786.25.
What is total ?
Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.
The outcome of adding two or more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding two or more numbers together results in a new result or total.
The monthly cost for a square foot of rental space in each city is as follows:
Place Monthly Cost for a Square Foot
Los Angeles $5.75
San Francisco $6.95
Seattle $4.25
It is also provided that the store in Los Angeles will be 580 square feet, the store in San Francisco will be 500 square feet, and the store in Seattle will be 465 square feet.
Compute the total monthly rent for these three stores as follows:
Total Monthly Rent = Monthly Cost for a Square Foot × Area
= (5.75 * 580) +(6.95 * 500) +(4.25 * 465)
= 3335 + 3475 + 1976.25
= 8786.25
Thus, the total monthly rent for these three stores is $8,786.25.
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The SAT and ACT are the two major standardized tests that colleges use to evaluate applicants. Most students take just one of these tests. However, some students take both. This Excel file gives the scores of 60 students who took both tests. Can we relate the two tests? Plot the data with SAT on the x axis and ACT on the y axis and answer the questions below.
Student SAT ACT
1 1000 24
2 870 21
3 1090 25
4 800 21
5 1010 24
6 880 21
7 860 19
8 1040 24
9 920 17
10 850 22
11 740 16
12 840 17
13 840 19
14 780 22
15 500 10
16 1060 25
17 830 19
18 830 20
19 780 12
20 870 21
21 1440 32
22 1190 30
23 1120 27
24 1120 25
25 490 7
26 800 16
27 590 12
28 800 18
29 1050 23
30 830 16
31 990 24
32 960 27
33 870 18
34 890 23
35 700 16
36 880 21
37 970 21
38 880 24
39 930 22
40 1020 24
41 920 22
42 980 27
43 860 23
44 790 14
45 810 19
46 1030 23
47 420 21
48 620 18
49 1080 23
50 1220 30
51 800 20
52 1150 28
52 1000 19
54 1080 22
55 1140 24
56 970 20
57 1030 25
58 970 20
59 920 21
60 1060 24
Question 1. Find the slope and intercept of the least squares regression line (draw the least squares line on your plot).
intercept (use 4 decimal places)
1.6263
slope (use 4 decimal places)
.0214
Question 2. Give the value of the test statistic for a test of H0: ß1 = 0.
(use 4 decimal places)
Question 3. If the alternative hypothesis is Ha: ß1 ? 0, what is the rejection region if the significance level of the test is a = .05? Use this t-table to determine your answer.
t =
t =
Question 4. What is the correct conclusion for this hypothesis test?
Do not reject the null hypothesis H0; the SAT score is not useful for predicting the ACT score.
Reject the null hypothesis H0 and conclude that in a linear model SAT score is useful for predicting the ACT score.
Question 5. Determine a 95% confidence interval for the slope ß1 of the least squares line (use 3 decimal places in your answers; use this t-table to determine the correct t-value).
lower endpoint of confidence interval
upper endpoint of confidence interval
the linear relationship between the SAT and ACT scores 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted
Given that many high school students take either the SAT or the ACT.
However, some students take both.
Data were collected from 60 students who took both college entrance exams.
SAT score ACT score with a of 180.
Average 912 21
standard deviation 180 5
Correlation between the two variables r = 0.817
WE have for two variables if we have correlation coefficient then the square of correlation coefficient gives the fraction of variation in the values of the SAT scores is accounted for by the linear relationship between the SAT and ACT scores
So we find square of r
i.e. r by the linear relationship between the SAT and ACT scores 0.6675 or 66.75% of the variation in the values of the SAT scores is accounted
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Answer:
j
Step-by-step explanation:
pecan theatre inc. owns and operates movie theaters throughout florida and georgia. pecan theatre has declared the following annual dividends over a six-year period: year 1, $80,000; year 2, $90,000; year 3, $150,000; year 4, $150,000; year 5, $160,000; and year 6, $180,000. during the entire period ended december 31 of each year, the outstanding stock of the company was composed of 250,000 shares of cumulative, preferred 2% stock, $20 par, and 500,000 shares of common stock, $15 par
Preferred shares = 0.40/25.00 = 1.60%
Common shares = 0.07/17.50 = 0.40%
What is stock market?
The phrase "stock market" describes a number of marketplaces where shares of publicly traded firms can be purchased and sold. Such financial transactions take place on official exchanges and in over-the-counter (OTC) markets that adhere to a predetermined set of rules.
Year Total Preference Common Dividend per
dividend dividend dividend common share
1 80000 80000 0 0.32 0.00
2 90000 90000 0 0.36 0.00
3 150000 130000 20000 0.52 0.04
4 150000 100000 50000 0.40 0.10
5 160000 100000 60000 0.40 0.12
6 180000 100000 80000 0.40 0.16
Note: 2.40 0.42
Preference dividend per year = 250000*$20*2%= 100000
Preference dividend for the 3rd year includes arrear dividend of $20000 for the 1st year
and $10000 for the second year, in addition to the $100000 dividend of that year.
Average annual dividend per share:
Preferred shares = 2.40/6 = $0.40
Common shares = 0.42/6 = $0.07
Average annual percentage return:
Preferred shares = 0.40/25.00 = 1.60%
Common shares = 0.07/17.50 = 0.40%
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A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. The volume of each small box is 8 cubic feet
and the volume of each large box is 21 cubic feet. A total of 20 boxes of paper were
shipped with a combined volume of 264 cubic feet. Determine the number of small
boxes shipped and the number of large boxes shipped.
4
x = number of small boxes
y = number of large boxes
well, we know a total of 20 boxes, large and small were shipped, that means that whatever "x" and "y" may be, we know that x + y = 20.
so the volume of one small box is 8 ft³, so sticking to ft³, we can say that the volume of 1 box is 8(1) ft³, and the volume of 2 boxes will then be 8(2) and three is 8(3) ft³ and the volume of "x" boxes will then just be 8(x) ft³.
now, we can say the same thing about large boxes, volume of 1 is 21(1) ft³, for two is 21(2) ft³, for three 21(3) ft³, and for "y" boxes that'll just be 21(y) ft³.
that said, well hell their volume combined must be 8x + 21y, and we happen to know that's 264 ft³, namely 8x + 21y = 264.
[tex]\begin{cases} x+y=20\\\\ 8x+21y=264 \end{cases}\hspace{5em}\stackrel{\textit{using the 1st equation}}{x+y=20\implies }y=20-x \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{8x+21(\underset{y}{20-x})=264}\implies 8x+420-21x=264 \\\\\\ 8x+420=264+21x\implies 8x+156=21x\implies 156=13x \\\\\\ \cfrac{156}{13}=x\implies \boxed{12=x}\hspace{13em}\stackrel{20~~ - ~~12}{\boxed{y=8}}[/tex]
Find the degree measure of each angle in the triangle.
Answer:
∠N° = 19°
∠M° = 35°
∠L° = 126°
Step-by-step explanation:
Total angle in a triangle: 180°
∠N° = x°
∠M° = ( 2x - 3 )°
∠L° = ( 7x - 7 )°
180 = N + M + L
180 = x + 2x - 3 + 7x - 7
180 = 10x - 10
10x = 180 + 10
10x = 190
Divide both side by 10
x = 19
∠N° = x° = 19°
∠M° = ( 2x - 3 )° = ( 2(19) - 3 )° = 35°
∠L° = ( 7x - 7 )° = ( 7(19) - 7 )° = 126°
Graph the following inequality. 8x+y>-4
Answer:
8x + y > 4
y > -8x + 4
this isn’t mine but can someone correct this if it’s wrong right quick?
Answer:
That looks correct to me!
Given that lines PQ and RS are parallel and t is a transversal, use a two column proof to prove <4=<6.
∠4=∠6 because each pair of alternate interior angles is equal ( The two column proof is attached ).
what is the two-column proof?Every two-column proof has exactly two columns. One column represents our statements or conclusions and the other lists our reasons. In other words, the left-hand side represents our “if-then” statements, and the right-hand side explains why we know what we know.
We can clearly observe here that ∠1=∠5 , ∠2=6, ∠3=∠7, ∠4=∠8 as Corresponding angles are equal.
∠4 + ∠3 = 180°……..(1) PQ is the straight line
∠6 + ∠7 = 180°……..(2) t is the straight line
therefore from the two equations we get
∠4 =∠6
Hence, ∠4 ≅∠6 ( The two column proof is attached )
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Emilio buys liter bottles of shampoo when the store has the promotion shown. Write an expression in two different ways to represent the total cost 0f 3 liters of shampoo. Let L be the regular price of a liter bottle.
The expressions for the total costs are 2L + 0.7L and 2.7L
How to determine the expression for the total cost?From the question, we have the following parameters that can be used in our computation:
Number of litres = 3
Regular price = L
Discount = 30%
This means that there is a discount on the third item
So, we have the following expression
Total amount = 2 * L + L * (1 - discount)
Substitute the known values in the above equation, so, we have the following representation
Total amount = 2 * L + L * (1 - 30%)
Total amount = 2 * L + L * 0.7
This gives
Total amount = 2L + 0.7L
Evaluate the sum
Total amount = 2.7L
Hence, the expression is 2.7L
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The expression for the total cost of 3 liters of shampoo is written as
2.7 L2L + 7L/10How to write the expressionLet L be the regular price of a liter bottle
The expression is written in decimal and in fraction
For the promotion buy 2 liters get 30% of 3rd liter
30% off = 0.3 off
= (1 - 0.3)
= 0.7
The total cost will be
= 2 * L + 0.7 * L
= 2L + 0.7L
= 2.7 L
The cost of three bottles of shampoo is 2.7L
In another way
= 2L + (1 - 0.3)L
= 2L + 0.7L
using fractions
= 2L + 7L/10
= 27L/10
the other way is writing in fraction
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Why is [sin(2x)] / sin(x) = 2cos(x)?
we want to set up a christmas tree and put some lights on it. let's design and implement the light switches. we want to control the lights by two switches. one of the switches is in the living room and one at the entrance hallway. you should design the associated circuit, so that the lights are on if the switches mismatch.
By using logic gate, it can be concluded-
XOR table is used in this case?
What is logic gate?
Logic gate is a device which is used to build digital circuit.
Logic gate can make passage for a system to pass through when some logical conditions are fulfilled.
Different types of logic gates are-
AND gate, OR gate, NAND gate, XOR gate, NOR gate etc.
Here one switch is in the entrance hallway and other is in the living room.
The lights are on if the switches mismatch.
For this case, XOR table is used
A B Result
0 1 1
1 0 1
0 0 0
1 1 0
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Consider the experiment of rolling a pair of fair dice until a sum of 7 is obtained. Let X denote the number of trials needed to obtain a sum of 7.
a) Notice that X is discrete. What is the distribution of X?
b)What is the theoretical average value (mu) of X?
c)What is the theoretical variance of X?
d) Consider the random variable Y, the average number of trials needed to roll a sum of 7 based on 25 trials. What is E[Y] and Var (Y)?
a) The distribution of X is a discrete geometric distribution with pmf p(x) = (5/36)(1/6)^(x-1).b) The theoretical mean (mu) of X is 6.c) The theoretical variance of X is 35.d) The expected value of Y is 6 and the variance of Y is 3.875.
The distribution of X is a discrete geometric distribution, which means that the probability of X taking on any particular value is given by the formula p(x) = (5/36)(1/6)^(x-1). The theoretical mean (mu) of X is 6, which means that on average it should take 6 trials to obtain a sum of 7. The theoretical variance of X is 35, which means that there is a considerable amount of variability in the number of trials needed to obtain a sum of 7. If we consider the random variable Y, the average number of trials needed to roll a sum of 7 based on 25 trials, then the expected value of Y is 6 and the variance of Y is 3.875. This indicates that the average number of trials needed to obtain a sum of 7 is 6 and that the variability decreases as more trials are taken.
a) p(x) = (5/36)(1/6)^(x-1)
b) theoretical mean (mu) of X mu = 6
c) Var(X) = (5/36)*∑x=1∞(1/6)^(x-1)^2 - mu^2
= (5/36)*(1-1/36^2) - 6^2
= 35
d) The expected value of Y , E(Y) = 6
Var(Y) = Var(X/6)
= Var(X)/6^2
= 35/6^2
= 3.875
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enter the number to complete the linear combination.after substitution:gcd(85, 51) yields sequence: 85 51 34 17 0
The Greatest Common Divisor (GCD) of 85 and 51 is 17.
Greatest Common Divisor(GCD)The greatest common factor that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).
Explanation
Step 1: Divide 85 by 51. The quotient is 1 and the remainder is 34.
Step 2: Divide 51 by 34. The quotient is 1 and the remainder is 17.
Step 3: Divide 34 by 17. The quotient is 2 and the remainder is 0.
Step 4: Since the remainder is 0, the Greatest Common Divisor (GCD) of 85 and 51 is 17.
The GCD of 85 and 51 is 17.
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Please help will mark Brainly
Answer:
C.
Step-by-step explanation:
Since Y is confirmed to cost 18
It will cancel out Answer "A" and "D"
It says River Z costs 2 dollars per hours plus a 10 dollar deposit
So that would cancel Answer "B" because you're not removing 10 dollars from the 2 dollars per hour.
So it would be...
Y= c = 18
X= c = 2n + 10
After I ate some pizza, there was 5/8 of the original pizza still left. My son at 1/3 of that. What fraction of the original pizza did he eat?
Answer:1/4 (I think)
What is tan(sin^-1(x/2))
with steps pls
Answer:
[tex]\dfrac{x\sqrt{4-x^2}}{4-x^2}[/tex]
Step-by-step explanation:
Given:
[tex]\tan \left(\sin^{-1}\left(\dfrac{x}{2}\right)\right)[/tex]
[tex]\boxed{\begin{minipage}{5cm}\underline{Trigonometric Identity}\\\\$\tan(\arcsin(x))=\dfrac{x}{\sqrt{1-x^2}}$\\ \end{minipage}}[/tex]
Use the tan(arcsin(x)) trigonometric identity and replace x for (x/2):
[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\left(\dfrac{x}{2}\right)^2}}[/tex]
Simplify the denominator:
[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\dfrac{x^2}{4}}}[/tex]
[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{\dfrac{4-x^2}{4}}}[/tex]
[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{\sqrt{4}}}}[/tex]
[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{2}}}[/tex]
[tex]\textsf{Apply the fraction rule}: \quad \dfrac{\frac{a}{c}}{\frac{b}{c}}=\dfrac{a}{b}[/tex]
[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}}[/tex]
Multiply the numerator and denominator by the denominator to eliminate the radical from the denominator:
[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}} \cdot \dfrac{\sqrt{4-x^2}}{\sqrt{4-x^2}}[/tex]
Simplify:
[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x\sqrt{4-x^2}}{4-x^2}[/tex]