4
Hope this helps! :)
______________
Given that y varies directly as x when y = 2 and x = -12, find x when y = 5.
Answer:
x = -30
Step-by-step explanation:
Use the direct variation equation, y = kx
Plug in 2 as y and -12 as x, and solve for k:
y = kx
2 = k(-12)
-1/6 = k
So, the equation is y = -1/6x
Plug in 5 as y and solve for x:
y = -1/6x
5 = -1/6x
-30 = x
So, when y = 5, x = -30
The measure of the angle of depression from the top of a 270-meter building to a park bench on the ground is 36°45′. How far away is the park bench from the building? Round to the nearest whole number.
Answer:
202 m
Step-by-step explanation:
Given :
Angle of depression, θ = 36°45' ; 45/60 = 0.75 = 36 + 0.75 = 36.75°
The height, h = 270
The distance of park bench from the building, d is given by :
Tan θ = opposite / Adjacent
Tan 36.75 = d / 270
d = 270 * Tan 36.75
d = 201.61856
d, distance of Park bench from building is 202 m
In a sample of 400 students, 60% of them prefer eBooks.
A.Find 98% Confidence Interval for the proportion of all students that prefer ebooksb.
b. Find the margin of erro
Answer:
a) The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).
b) The margin of error is of 0.05.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In a sample of 400 students, 60% of them prefer eBooks.
This means that [tex]n = 400, \pi = 0.6[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.054[/tex].
Margin of error -> Question b:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 2.054\sqrt{0.6*0.4}{400}}[/tex]
[tex]M = 0.05[/tex]
The margin of error is of 0.05.
A.Find 98% Confidence Interval for the proportion of all students that prefer ebooksb.
Sample proportion plus/minus the margin of error.
0.6 - 0.05 = 0.55
0.6 + 0.05 = 0.65
The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
To buy a car, you borrow $28,000 with a term of five years at an APR of 5%. What is your monthly payment? (Round your answer to the nearest cent.)
$
How much total interest is paid? (Round your answer to the nearest cent.)
$
9514 1404 393
Answer:
monthly payment: $528.39interest paid: $3,703.40Step-by-step explanation:
The monthly payment is given by the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where the annual interest rate is r for t years on loan value P.
Filling in the given information, we find the monthly payment to be ...
A = $28000(0.05/12)/(1 -(1 +0.05/12)^(-12·5)) ≈ $528.39
The monthly payment is $528.39.
__
The total amount repaid is ...
($528.39/mo)(60 mo) = $31,703.40
The interest paid is the difference between this and the loan amount:
interest paid = $31,703.40 -28,000 = $3,703.40
The total interest paid is $3,703.40.
Jeremy read 243 pages on Saturday. He read 53 fewer pages on Sunday.
How many pages did he read in all?
243 = the pages read on Saturday
243 - 53 = 190 = the pages read on Sunday
190 + 243 = 433 = total pages read
Answer = 433
Help me ASAP plzzz……
Answer:20, 40, 40,100
Step-by-step explanation:
5x+2x+2x=180 9x=180 x=20
Sherri chose 1 marble at a time from a bag of 50 marbles, recorded its color, and returned it to the bag. She repeated this experiment 20 times.
how many blue marbles are in the bag?
Select one:
6
30
15
20
Answer:
20 is it's right answer I think ok
Please help me it is due soon, please no links
Answer:
The length of the three sides [tex]5, \sqrt{58} , \sqrt{65}[/tex]
The triangle is not a right triangle
Step-by-step explanation:
A = (3, 2) , B = ( 6, 9) , C = (10, 6)
Find the lengths using distance formula.
[tex]distance = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]AB = \sqrt{(6-3)^2 + (9-2)^2} = \sqrt{9 + 49 } = \sqrt{58}[/tex]
[tex]BC = \sqrt{(10-6)^2 + (6-9)^2} = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]
[tex]AC = \sqrt{(3-10)^2+(2-6)^2} = \sqrt{49 + 16} = \sqrt{65}[/tex]
Using Pythagoras theorem :
[tex](Longer \ side)^2 = sum \ of \ square \ of \ two \ other \ sides[/tex]
Longest side is AC . So we will check if it satisfies Pythagoras theorem :
[tex]\sqrt{65} = \sqrt{58} + 5^2\\65 = 58 + 25\\[/tex]
65 ≠ 58 + 25
So the sides does not satisfy Pythagoras theorem. Hence the triangle is not a right triangle.
MULTIPLE CHOICE LaShawn designs websites for local
businesses. He charges $25 an hour to build a website, and
charges $15 an hour to update websites once he builds them.
He wants to earn at least $100 every week, but he does not
want to work more than 6 hours each week. What is a possible
solution to describe how many hours LaShawn can spend
building a website (x) and updating a website (y) in a week?
A (1,4)
B (1,6)
C (2,3)
D (3, 3)
he graph shows the total number of participants in a town's recreation program at the end of every year since the year 2000.
The line of best fit for the data is given by the equation y=13x+50, where y is the total number of participants x years after the beginning of the year 2000.
Which statement correctly interprets the slope of the line of best fit?
The rate of change is 1 new participant every 13 years.
The rate of change is 13 new participants every 13 years.
The rate of change is 13 new participants every year.
The rate of change is 50 new participants every year.
Answer:
The rate of change is 13 new participants every year.
Step-by-step explanation:
y=13x+50
This is in the form y = mx+b where m is the slope and b is the y intercept
x is the number of years so for every year increase we gain 13 new participants
in a rectangle how many opposite sides are equal
Answer and Step-by-step explanation:
This is for your other question in case you don't see it.
1. 2 pairs (aka 4 sides) of Opposite Sides are equal
2. AB and DC are parallel, and AD and BC are parallel
3. Angles BDC and ACD are equal, angles DAC and DBC are equal, the angles ADB and BCD are equal, angles CAB and DBA are equal
4. 4 right angles
5. AB and DC are equal, and AD and BC are equal
6. 4 Triangles
7. False
8. Diagonals of a rectangle.
#teamtrees #PAW (Plant And Water)
Three consecutive integers have a sum of 30. Which equation can be used to find x, the value of the smallest of the three numbers? (x + 1) + (x + 2) = 30 x + (x + 1) + (x + 2) = 30 x (x + 1) (x + 2) = 30 3 x (x + 1) (x + 2) = 30
Answer:
X+(X+1)+X+2)=30
Step-by-step explanation:
A=1/2h(B+b);A=81,B=8,b=1 what is h
Answer:
81=1/2h×9,
81=1/18h
1458h=1
h=1/1458
Answer:
h=1/ 1458
hope it is helpful to you
Nicole works in a sporting goods store
and earns $324 a week and 5% of her
sales. One week Nicole earned $432.
What were her sales that week? Write
and equation and solve.
Answer:
2,160
Step-by-step explanation:
432-324=108 earnings based on sales
sales x 5%=108
sales=108/.05
sales=2,160
Does anyone know the answer to this?
Use a double integral to find the area of the following regions. The region bounded by all leaves of the rose r=2cos3θ
Answer:
Hence the area of the region bounded by all leaves of the rose is [tex]\pi[/tex].
Step-by-step explanation:
Here,
[tex]2 cos (3\Theta )=0\\\Rightarrow cos(3\Theta)=0\\\Rightarrow cos(3\Theta )=cos\left (\frac{\pi }{2} \right )\\\Rightarrow \Theta =\left (\frac{\pi }{6},-\frac{\pi }{6} \right )[/tex]
Now consider for one leaf of rose:-
[tex]Area = 3\int_{-\frac{\pi }{6}}^{\frac{\pi }{6}}\frac{r^{2}}{2}d\Theta \\\\ = \frac{3}{2}\int_{-\frac{\pi }{6}}^{\frac{\pi }{6}}4 cos^{2}\left ( 3\Theta \right ) d\Theta \\\\ = \frac{12}{2}\int_{-\frac{\pi }{6}}^{\frac{\pi }{6}} \frac{cos(6\Theta +1)}{2}d\Theta\\\\ =\frac{6}{2}\left [ \frac{sin(6\Theta +\Theta )}{6} \right ]_{-\frac{\pi }{6}}^{\frac{\pi }{6}}\\\\ =3\times \left [ \frac{\pi }{6}+\frac{\pi }{6} \right ]\\\\ =3\times \frac{2\pi }{6}\\\\ = \pi[/tex]
Which number is rational?
Answer:
D. Square root of 16
Step-by-step explanation:
Rational numbers are numbers that have simple answers. It is also considered as fractions, Integers, and possible square roots.
- If you chose the square root of 2 = 1.41
- Pi has a value of 3.14, It's not a fraction nor an integer so it's an Irrational number
- Square root of 10 is 3.16
- So Square root of 16 is 4 which is a regular number and a possible square root.
Thank you!
Answer:
last option- square root of 16 is a rational number
Based on past experience, a bank believes that 8.9 % of the people who receive loans will not make payments on time. The bank has recently approved 220 loans. What must be true to be able to approximate the sampling distribution with a normal model
Answer:
To be able to approximate the sampling distribution with a normal model, it is needed that [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], and both conditions are satisfied in this problem.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they will make payments on time, or they won't. The probability of a person making the payment on time is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The sampling distribution can be approximated to a normal model if:
[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
Based on past experience, a bank believes that 8.9 % of the people who receive loans will not make payments on time.
This means that [tex]p = 0.089[/tex]
The bank has recently approved 220 loans.
This means that [tex]n = 220[/tex]
What must be true to be able to approximate the sampling distribution with a normal model?
[tex]np = 220*0.089 = 19.58 \geq 10[/tex]
[tex]n(1-p) = 220*0.911 = 200.42 \geq 10[/tex]
To be able to approximate the sampling distribution with a normal model, it is needed that [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], and both conditions are satisfied in this problem.
Solve for x in the equation x squared + 14 x + 17 = negative 96.
look at pic 10 pts will mark brainilest
The population of a city is increasing at a rate of 4% each year. In 2000, there were 236,000npeople in the city. Let t represent the number of years since 2000 and P represent the population. Write an exponential growth function to model
The exponential growth function to model represents as P = 236,000 (1+ 0.04)⁹ and 335,902 people in 2009.
What is the exponential growth function?The exponential growth function is given by:-
y = A(1 +r)ⁿ
where r is the rate of growth and A is the initial amount and n is the time period.
Let t represent the number of years since 2000 and P represent the population.
The population of a city is increasing at a rate of 4% each year. In 2000, there were 236,000 people in the city.
Put A = 236,000 , r = 0.04 and t = 9, we get
P = 236,000 (1+ 0.04)⁹
P = 335,902
Hence, the exponential growth function to model represents P = 236,000 (1+ 0.04)⁹ and 335,902 people in 2009.
Learn more about exponential growth and decay here:
brainly.com/question/2193820
#SPJ6
Find the area of a regular
polygon with 5 sides that has a
side length of 6 inches and an
apothem of 9 inches.
Answer:
area of polygon : 120in²
What is the value of k?
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Answer:
k = 10
Step-by-step explanation:
The exterior angle is equal to the sum of the remote interior angles.
115° = (4k +5)° +(6k +10)°
115 = 10k +15 . . . . . . . . . . . divide by °, simplify
100 = 10k . . . . . . . . . . . . subtract 15
10 = k . . . . . . . . . . . . . . divide by 10
can anyone prove this:
1+1=3
Answer:
indeed
Step-by-step explanation:
just carry the one when adding
Step-by-step explanation:
1 = 1
41 – 40 = 61 – 60
16 + 25 – 40 = 36 + 25 – 60
4² + 5² – 2 * 4 * 5 = 6² + 5² – 2 * 6 * 5
(4 – 5)² = (6 – 5)²
4 – 5 = 6 – 5
4 = 6
2 = 3
1 + 1 = 3…proved
What is the true solution to In 20+ In 5= 2 In x?
x=5. A
X= 10 b
X=50 c
X= 100 d
ln(20) + ln(5) = 2 ln(x)
ln(20×5) = ln(x ²)
ln(100) = ln(x ²)
100 = x ²
x = 10
plz help i dont know what to do
ANSWER QUICK
Answer:
the last one is correct.............
A random sample of 10 observations was selected from a normal population distribution. The sample mean and sample standard deviations were 20 and 3.2, respectively. A 95% prediction interval for a single observation selected from the same population is
Answer:
18.0167≤x≤21.9833
Step-by-step explanation:
Given the following
sample size n = 10
standard deviation s = 3.2
Sample mean = 20
z-score at 95% = 1.96
Confidence Interval = x ± z×s/√n
Confidence Interval = 20 ± 1.96×3.2/√10
Confidence Interval = 20 ± (1.96×3.2/3.16)
Confidence Interval = 20 ± (1.96×1.0119)
Confidence Interval = 20 ± 1.9833
CI = {20-1.9833, 20+1.9833}
CI = {18.0167, 21.9833}
Hence the required confidence interval is 18.0167≤x≤21.9833
hii please help me :)
Answer:
1.) A = (1/2bh) 4 + lxw
= 1/2 x 7 x 13 x 4 + 7 x 7
182 + 49 = 231cm2
l think u can use the formula to find the area of the other pyramids
Can y’all help me? :)
Answer:
Option A: [tex]5\frac{1}{4} *4\frac{1}{5}[/tex]
Step-by-step explanation:
Area of a parallelogram is base times height so in this case it would be 5 1/4 times 4 1/5. 5 1/4 being the base and 4 1/5 being the height.
A student is running a 3-kilometer race. He runs 1kilometer every 2minutes. Select the function that describes the distance from the finish line after xminutes
Answer:
(0.5X) - 3 = Distance from the finish line
Step-by-step explanation:
Given that a student is running a 3-kilometer race, and runs 1 kilometer every 2 minutes, to determine the function that describes the distance from the finish line after X minutes, the following calculation must be performed:
1 = kilometers for every 2 minutes
X = every number of minutes
1/2 = 0.5 = kilometers per minute
(0.5X) - 3 = Distance from the finish line
Thus, if the student runs for 4 minutes, the equation would operate as follows:
0.5 x 4 - 3 = X
2 - 3 = X
-1 = X