Answer:
127
Step-by-step explanation:
by............doing this .
At the beginning of the year, the odometer on an SUV read 37,532 miles. At the end
of the year, it read 52,412 miles. If the car averaged 24 miles per gallon, how many
gallons of gasoline did it use during the year?
He used 620 gallons of gas
Pablo deposits $5000 into an account that pays simple interest at a rate of 3% per year. How much interest will he be paid in the first 6years?
Answer:
$5900
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Simple Interest Rate Formula: A = P(1 + rt)
P is principle amountr is ratet is time (in years)Step-by-step explanation:
Step 1: Define
Identify variables
P = 5000
r = 3% = 0.03
t = 6
Step 2: Find Interest
Substitute in variables [Simple Interest Rate Formula]: A = 5000(1 + 0.03 · 6)(Parenthesis) Multiply: A = 5000(1 + 0.18)(Parenthesis) Add: A = 5000(1.18)Multiply: A = 5900Evan invested $800 in an account that pays 3.25% interest compounded annually.
Assuming no deposits or withdrawals are made, find how much money Evan would
have in the account 12 years after his initial investment. Round to the nearest tenth
(if necessary).
Answer:
Evans would have $852.8
Step-by-step explanation:
Given
[tex]PV = \$800[/tex]
[tex]r = 3.25\%[/tex]
[tex]t = 2[/tex]
[tex]n = 1[/tex] --- annually'
Required
The future value
This is calculated using:
[tex]FV = PV*(1 + \frac{r}{n})^{nt[/tex]
So, we have:
[tex]FV = 800 * (1 + 3.25\%/1)^{2*1}[/tex]
[tex]FV = 800 * (1 + 3.25\%)^{2}[/tex]
[tex]FV = 800 * (1 + 0.0325)^{2}[/tex]
[tex]FV = 800 * (1 .0325)^2[/tex]
[tex]FV = 852.845[/tex]
[tex]FV = 852.8[/tex]
FV =
HELP PLEASE giving out brainilest
9514 1404 393
Answer:
160 cm³
Step-by-step explanation:
The ratio of the linear dimensions is the square root of the ratio of areas:
scale factor B/A= √(64/144) = 8/12 = 2/3
The ratio of volumes is the cube of the scale factor:
(volume B)/(volume A) = (2/3)³ = 8/27
Then the volume of pyramid B is ...
volume B = (volume A) × (volume B)/(volume A)
= (540 cm³) × (8/27) = 160 cm³ . . . . volume of pyramid B
_____
Equivalently, the ratio of volumes is the 3/2 power of the ratio of areas.
Vb = Va(64/144)^(3/2) = (540 cm³)(4/9)^(3/2) = (540)(8/27) cm³ = 160 cm³
Select the true statement about the relationship between sample size and the standard deviation of distribution of sample means, also known as the standard error.
a. As sample size increases, standard error increases.
b. Sample size does not have an impact on standard error.
c. As sample size increases, standard error decreases.
d. As sample size decreases, standard error decreases.
Answer:
c. As sample size increases, standard error decreases.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
Thus:
The standard error is inversely proportional to the square root of the sample size, that is, as the sample size increases, the standard error decreases, and the correct answer is given by option c.
10. (10.04 MC)
What are the period and phase shift for f(x) = -4 tan(x − n)? (1 point)
T
Period: n; phase shift: x =
2
Period: n; phase shift: x = n
TT
Period: 2n; phase shift: x =
2
Period: 2n; phase shift: x = 0
Answer:
Period: [tex]\pi[/tex]
Phase shift: n
Step-by-step explanation:
Tangent function:
Has the following format:
[tex]f(x) = \tan{ax - n}[/tex]
In which the period is [tex]\frac{\pi}{x}[/tex] and the phase shift is n.
In this question:
[tex]f(x) = -4\tan{(x-n)}[/tex]
[tex]a = 1[/tex], and thus, the period is [tex]\pi[/tex], with a phase shift of n.
ou want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99% confident that you esimate is within 0.1% of the true population proportion. How large of a sample size is required
Answer: the required sample size =1658944
Step-by-step explanation:
When the prior population proportion for the study is unknown , then the formula for sample size is [tex]Sample \ size = 0.25(\dfrac{z^*}{Margin\ of \ error})^2[/tex]
z-value for 99% confidence = 2.576
[tex]Sample \ size = 0.25(\dfrac{2.576}{0.001})^2\\\\=0.25(2576)^2\\\\=1658944[/tex]
Hence, the required sample size =1658944
A person takes a multiple-choice exam in which each question has five possible answers. Suppose that the person has no idea about the answers to three of the questions and simply chooses randomly for each one.
Required:
a. What is the probability that the person will answer all three questions correctly?
b. What is the probability that the person will answer exactly two questions correctly?
c. What is the probability that the person will answer exactly one question correctly?
d. What is the probability that the person will answer no questions correctly?
e. Suppose that the person gets one point of credit for each correct answer and that 1/3 point is deducted for each incorrect answer. What is the expected value of the person’s score for the three questions?
Answer:
a. 0.008 = 0.8% probability that the person will answer all three questions correctly.
b. 0.096 = 9.6% probability that the person will answer exactly two questions correctly.
c. 0.384 = 38.4% probability that the person will answer exactly one question correctly.
d. 0.512 = 51.2% probability that the person will answer no questions correctly.
e. The expected value of the person’s score for the three questions is -0.2.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the person answers it correctly, or they do not. The probability of a person answering a question correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Each question has five possible answers.
Person has no idea which option is correct, so the probability of answering correctly is:
[tex]p = \frac{1}{5} = 0.2[/tex]
Three questions:
This means that [tex]n = 3[/tex]
a. What is the probability that the person will answer all three questions correctly?
This is [tex]P(X = 3)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.2)^{3}.(0.8)^{0} = 0.008[/tex]
0.008 = 0.8% probability that the person will answer all three questions correctly.
b. What is the probability that the person will answer exactly two questions correctly?
This is [tex]P(X = 2)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{3,2}.(0.2)^{2}.(0.8)^{1} = 0.096[/tex]
0.096 = 9.6% probability that the person will answer exactly two questions correctly.
c. What is the probability that the person will answer exactly one question correctly?
This is [tex]P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.2)^{1}.(0.8)^{2} = 0.384[/tex]
0.384 = 38.4% probability that the person will answer exactly one question correctly.
d. What is the probability that the person will answer no questions correctly?
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.2)^{0}.(0.8)^{3} = 0.512[/tex]
0.512 = 51.2% probability that the person will answer no questions correctly.
e. Suppose that the person gets one point of credit for each correct answer and that 1/3 point is deducted for each incorrect answer. What is the expected value of the person’s score for the three questions?
The expected number of correct answer is:
[tex]E(X) = np = 3*0.2 = 0.6[/tex]
And the expected number of wrong answers is 3 - 0.6 = 2.4. So, the expected score is:
[tex]S(x) = 0.6 - \frac{2.4}{3} = 0.6 - 0.8 = -0.2[/tex]
The expected value of the person’s score for the three questions is -0.2.
Zahara frosted eleven cupcakes today. Dania frosted seven times as many. How many cupcakes did Dania frost?
How much of a radioactive kind of rhodium will be left after 120 seconds if the half-life is 30 seconds and you start with 480 grams?
9514 1404 393
Answer:
30 grams
Step-by-step explanation:
The time 120 seconds is 4 times the half-life of 30 seconds. That means (1/2)^4 = 1/16 of the original amount will remain. That is (480 g)(1/16) = 30 g.
30 g of the radioactive rhodium will be left
Determine the value of x.
1) 14.75
2)15.25
3)11.92
4)18.56
where is EF to the nearest tenth??
Answer:
37.7
Step-by-step explanation:
EF and ED define the Tangent of D
Tan(37) = side opposite D / side adjacent to D
Opposite means a line (FE) that is not connected to the angle. It is never the longest line (hypotenuse) in a Right Triangle
Adjacent means the leg that is connected to the angle, but is not the hypotenuse.
Tan(D) = opposite over adjacent
Opposite = x
Adjacent = 50
Tan(37) = 0.7536 rounded to 4 places, but I've kept the exact value in my calculator.
0.7536 = x / 50 Multiply both sides by 50
0.7536*50 = x
x = 37.6777
The nearest 1/10 is 37.7
The time it takes to build a house (T), varies directly with the floor area (A), and inversely with the number of workers (W). What is the equation that models this situation?
Answer:
T = k * (A/W)
Step-by-step explanation:
Which of the following correctly names a side of the triangle below?
A. ZC
B. B
С. АВ
D. AABC
Answer:
C. [tex]\frac{}{AB}[/tex]
Step-by-step explanation:
You can solve this in two ways, firstly by eliminating all the wrong answers, and secondly by just knowing that the horizontal line in [tex]_[/tex][tex]\frac{}{AB}[/tex] means that we are talking about a line.
This is how we solve this question by using the eliminating process.
(A. ∠C) is not the right answer because the ∠ sign lets us know that this answer represents an angle, not a line
(B. B) is not the right answer because it represent a point, not a line (in math we use a singular capital letter to represent points)
(D. ΔABC) is not the right answer because the Δ sign lets us know that the answer represents a triangle, not a line.
Therefore, the only option left is C. [tex]\frac{}{AB}[/tex]
Linear function please help it’s due in 30 mins
What is the solution of StartRoot x + 2 EndRoot minus 15 = negative 3?
9514 1404 393
Answer:
x = 142
Step-by-step explanation:
You want to find x such that ...
[tex]\sqrt{x+2} -15=-3\qquad\text{given}\\\\\sqrt{x+2} =12\qquad\text{add 15}\\\\x+2=144\qquad\text{square both sides}\\\\\boxed{x=142}\qquad\text{subtract 2 to get x by itself}[/tex]
Answer:
a
Step-by-step explanation:
how can i solve the following
2(x + 3) = x - 4
Answer:
x=-10
Step-by-step explanation:
2(x+3)=x-4
2*x+2*3=x-4
2x+6=x-4
2x-x=-4-6
x=-10
Answer:
[tex]x = - 10[/tex]
Step-by-step explanation:
Let's solve:
[tex]2(x+3)=x−4[/tex]
Step 1: Simplify both sides of the equation.
[tex]2(x+3)=x−4 \\ (2)(x)+(2)(3)=x+−4(Distribute) \\ 2x+6=x+−4 \\ 2x+6=x−4[/tex]
Step 2: Subtract x from both sides.
[tex]2x+6−x=x−4−x \\ x+6=−4[/tex]
Step 3: Subtract 6 from both sides.
[tex]x+6−6=−4−6 \\ x=−10[/tex]
14.
Find the domain of
x ¹ -2 / x + 1
Answer:
?????????????????????????
PLEASE HELP ASAP I NEED THIS LIKE RIGHT NOW NO LINKS OR WILL BE REPORTED! SHOW ALL OF YOUR WORK! 3. The area of the square rug is 484 feet squared. (a) What is the length of one side? Write it as a square root. SHOW ALL OF YOUR WORK. (Hint: How do you find the area of a square? What is the equation?) (b) write the area as a number squared SHOW ALL OF YOUR WORK
Answer:
well,
it's more than (20ft)²
bc 20*20 =400
21² = 21 * 21 = 441
getting closer...
22² = 22 * 22 = 484
[tex] \sqrt{484} = {22}^{2} [/tex]
yet, we arrived, short trip tough, pls leave the bus in an orderly manner
Donte simplified the expression below.
4(1+3i)-(8-5i)
4+3i-8+5i
-4+8i
What mistake did he make?
Answer:
A. He did not apply the distributive property correctly for 4(1+3i)
Step-by-step explanation:
Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 15 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Kyle, Carol, and Adam are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.
Answer:
1 / 1365
Step-by-step explanation:
Given that :
Number of employees to choose from = 15
Number of employees to be chosen = 4
Probability of choosing You, Kyle, Carol and Adam
Recall ;
P(A) = number of required outcome / Total possible outcomes
Number of required outcome = 4C4
Total possible outcomes = 15C4
nCr = n! ÷ (n-r)!r!
Using calculator to save computation time :
15C4 = 1365
4C4 = 1
P(choosing you, Kyle, Carol and Adam) :
1 / 1365
plz help i dont know what to do
ANSWER QUICK
Answer:
the last one is correct.............
What is the area of the triangle
Answer:
60m^2 is the answer im pretty sure
Step-by-step explanation:
yeah man thats it
Which is a stretch of an exponential decay function?
f(x)=4/5(5/4)x
f(x)=4/5(4/5)x
f(x)=5/4(4/5)x
f(x)=5/4(5/4)x
NEED HELP ON THIS ASAP PLZ!!
Answer:
cos0 = 6.8556546i/23 or sqrt-47/23
Step-by-step explanation:
hypotenuse is 23, opposite is 24
we have to find the adjacent using the pythagorean theorem
24^2 + b^2 = 23^2
576+b^2=529
subtract
b^2=-47
b=sqrt-47
sqrt of -47 is 6.8556546i, there is an i since it is the square root of a negative
cos = adjacent/hypotenuse
The table shows the results of an experiment in which the spinner shown above was spun 50 times. Find the experimental probability of each outcome.
not shaded
Answer:
[tex]P(x < 4) = \frac{9}{50}[/tex]
Step-by-step explanation:
Given
[tex]n(S) = 50[/tex]
See attachment for distribution
Required
[tex]P(x < 4)[/tex]
This is calculated as:
[tex]P(x < 4) = \frac{n(1) + n(2) + n(3)}{n(S)}[/tex]
Using the data on the frequency distribution table, we have:
[tex]P(x < 4) = \frac{4 + 2 + 3}{50}[/tex]
[tex]P(x < 4) = \frac{9}{50}[/tex]
NO LINKS!!!
Change the standard form equation to vertex form and compare the function to the parent function y = x^2.
1. y = x^2 - 2x - 2
Completing the square gives
[tex]x^2-2x-2=(x-1)^2-3[/tex]
and comparing to [tex]y=x^2[/tex], the graph of [tex]y=x^2-2x-2[/tex] would be a horizontal shift to the right by 1 unit, and a vertical shift down by 3 units.
Hope this help!!!
Have a nice day!!!
Christian Robbie are construction arytenoids stained glass window whose length is 7.3 inches longer than its width if the area of the window is 596.9 in.² find the width and the length
Answer:
w ≈ 21.053 inches
l ≈ 28.353 inches
Step-by-step explanation:
44%adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
Answer:
.101501615
.84982392
.901244701
Step-by-step explanation:
For this question use a binomial distribtuion
a.
12C3*.44³*(1-.44)⁹= .101501615
b.
to find at least 4 find the probability of less than 4 and take its compliment
12C0*(1-.44)¹²+12C1*.44*(1-.44)¹¹+12C2*.44²*(1-.44)¹⁰+12C3*.44³*(1-.44)⁹= .15017608
1-.15017608=.84982392
c.
To find less than eight's probability find the proability of at least 8 and take its compliment
12C8*.44⁸(1-.44)⁴+12C9*.44⁹(1-.44)³+12C10*.44¹⁰(1-.44)²+12C11*.44¹¹*(1-.44)+12C12*.44¹²= .098755299
1-.098755299= .901244701
please help me this is due today!! it’s number 6
what is the length of AB
