Answer: (8^{12})^3=8^{12\times 3}=8^{36}
Step-by-step explanation:
Given : the expression (8^{12})^3
We have to simplify the given expression and choose the correct from the given options.
Consider the expression (8^{12})^3
Using property of exponents,
\left(a^b\right)^c=a^{b\times c}
We have,
(8^{12})^3=8^{12\times 3}=8^{36}
graph the function f(x)=3/8(×-1)(x-9)
What is the total surface area if the composite figure below?
(8cm×5cm)+(1/2×5×5)cm^2
=40cm^2+12.5cm^2
=52.5cm^2
Answer:
b
Step-by-step explanation:
AHH!! IM STUCK PLEASE HELP! :(
Think about this. If we were to align the coefficients with their solutions to form this matrix, it would be the following -
[tex]\begin{bmatrix}2&-6&-2&|&1\\ 0&3&-2&|&-5\\ 0&2&2&|&-3\end{bmatrix}[/tex]
Now this is one way to assign the coefficients. As you can see, 2, - 6, - 2 are present as the coefficients for the first row. Similarly 0, 3, - 2 are present as the coefficients for the second row - ( as one term is missing from this row, it is replaced with a " 0 " ). The same applies for the third row. The end values of the system of equation is present as the last column.
The options are assigned in a manner with which the coefficients and variables are present in two columns, while the end values of the system of equation given, is present as the last column. Knowing the arrangement of both the coefficients and the end values of the system of equation, all we have to do is add these " variables " as one column -
Solution = Option B
Obesity is a risk factor for many health problems such as type 2 diabetes, high blood pressure, joint problems, and gallstones. Using data collected in 2018 through the National Health and Nutrition Examination Survey, the National Institute of Diabetes and Digestive and Kidney Diseases estimates that 37.7% of all adults in the United States have a body mass index (BMI) in excess of 30 and so are categorized as obese. The data in the file Obesity are consistent with these findings.
BMI:
16.2 46.8 39 13.6 31.3
31.1 36.7 29 34.2 7.4
24.8 32.4 41 34.8 30.8
23.8 38 16 21.2 14
8 26.1 320 31 37.8
24 39.2 26 31.3 32
38.8 23.8 524 35 20.4
51.5 23.4 17 27.5 19.8
28 27.9 33 422 45.7
26.5 44.6 30 37.8 56.3
43.1 27.5 23 49.5 22.9
18.7 35.3 19 31.2
28.2 34.5 24 29
17.9 25.6 11 26.1
33.1 27.3 11 26.5
25.6 28 29 25.5
Requried:
a. Use the Obesity data set to develop a point estimate of the BMI for adults in the United States. (Round your answer to two decimal places.) Are adults in the United States obese on average?
b. What is the sample standard deviation? (Round your answer to four decimal places.)
c. Develop a 95% confidence interval for the BMI of adults in the United States. (Round your answers to two decimal places.)
Answer:
a. A point estimate of the BMI for adults in the United States can be calculated from the sample mean, which has a value M=44.57.
b. The sample standard deviation is s=79.9507.
c. The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).
Step-by-step explanation:
We start by calculating the sample mean and standard deviation of the BMI data:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{75}(16.2+31.1+24.8+. . .+22.9)\\\\\\M=\dfrac{3343}{75}\\\\\\M=44.57\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{74}((16.2-44.57)^2+(31.1-44.57)^2+(24.8-44.57)^2+. . . +(22.9-44.57)^2)}\\\\\\s=\sqrt{\dfrac{473016.8667}{74}}\\\\\\s=\sqrt{6392.1198}=79.9507\\\\\\[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=44.57.
The sample size is N=75.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{79.9507}{\sqrt{75}}=\dfrac{79.9507}{8.66}=9.232[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=75-1=74[/tex]
The t-value for a 95% confidence interval and 74 degrees of freedom is t=1.993.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.993 \cdot 9.232=18.39[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 44.57-18.39=26.18\\\\UL=M+t \cdot s_M = 44.57+18.39=62.96[/tex]
The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).
Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?
This question is incomplete, here is the complete question:
Suppose in the next year, 2007, College D's expenses and enrollment remain about the same, but in addition to their current revenues, they receive an additional $50,000,000 grant. This would allow them to reduce average tuition by how much?
A) $1388.89
B) $3571.43
C) $5555.56
D) $9500.00
E) $25888.89
number of students = 36,000
Answer: A) $
1388.89
Step-by-step explanation:
the college received additional grant which is $50,000,000
and the number of students is 36,000,
and we also know that expenses and enrollment remained the same.
So if we have more money (grants) and nothing changed (expenses remain the same)
dividing the grant by the number of students will show just how much the average tuition fee would be reduced
therefore R = G/n
R = 50,000,000 / 36000
R = 1,388.888 ≈ $1388.89
Problem of the Day
The tortoise and the hare were arguing: who's the fastest? The tortoise boasted he
could swim 220 miles in 10 hours. The hare bragged he could hop 90 miles in 2 hours.
But who is faster? How can you tell?
Answer:
hare
Step-by-step explanation:
Their average rates are ...
tortoise: (220 mi)/(10 h) = 22 mi/h
hare: (90 mi)/(2 h) = 45 mi/h
The hare has a faster speed than the tortoise.
During a football game, a team lost 12 yards on the first play and then gained 5 yards on each of the next 3 plays. Which method finds the total yards at the end of the first four plays?
A) add –12 to 3 times 5
B) add 12 to 3 times 5
C) add –12, 5, and 3
D) add 12, 5, and 3
They got 5 yards on 3 plays. For total yards multiply the 3 plays by 5 yards. The first play was negative, so add the negative value. The answer is A.
Answer:
A
Step-by-step explanation:
Suppose that a tunnel is dug through the center of the earth. You stand on a tower 100 m tall and drop a 3-kg rock into the tunnel. What is the frequency of the resulting harmonic motion?
Answer:
The frequency of the resulting harmonic motion is 0.000219 Hz
Step-by-step explanation:
We are going to calculate the time it takes for one single wave ocillation.
Frequency and the time taken to finish a single wave oscillation are inversely proportional. The formula for calculating frequency when given the time taken to complete a wave cycle is written as: f = 1 / T
In this formula, f represents frequency and T represents the time period or amount of time required to complete a single wave oscillation.
I consider the initial speed to be zero, because it is of no significance compared with the free fall into the earth, through the earth and back again.
Given from Wikipedia:
The diameter of the earth is 1.2742 * 10⁴ km which is 1.27 * 10⁷ m
2 times the radius = diameter, so the radius of the earth = (1.27 * 10⁷ m) /2 = 6.4 * 10⁶ m
radius earth = r
r = 6.4 * 10⁶ m
Now imagine the tunnel and the free fall.
1. Initially the rock has no speed.
2. Due to the gravitational accelleration, the rock will increase it's speed every second by a factor of 9.8.
3. The Rock gains speed untill it reached the centre of the earth. By then it will have reached it's maximum speed and it has travelled the distance r !
4. After this moment, the Rock will be slowed down because of the negative accelleration...
After it has travelled from the centre of the earth to the other end of the earth, it will have stopped completely, and again passing the distance r.
5. Now at the other end of the earth there is the same initial situation as described at point 1, only the Rock has travelled the distance equal to the diameter of the earth, (exactly 2 times r).
So basically, the samething happens once more, only this time it starts exactly from the other end of the earth...
6. Initially the rock has no speed.
7. Due to the gravitational accelleration, the rock will increase it's speed every second by a factor of 9.8.
8. The Rock gains speed untill it reached the centre of the earth. By then it will have reached it's maximum speed.
9. By now the Rock will be slowed down because of the negative accelleration... It is moving towards the initial starting point...
After it has travelled from the centre of the earth to the other end of the earth, it will have stopped completely.
10. Now finally the Rock is exactly at the starting position.
In reality there will have been some loss of speed due to friction, so the Rock will be slightly lower then the 100 m above the ground.
let's calculate the time it takes to free fall for the distance r.
initial speed =0 and after 6.4 * 10⁶ m it's speed will be maximum. We need to find out how much time passes before that distance is passed.
r = v*t + 0.5*a*t²
r = 0 + 0.5*a*t²
0.5*a*t² = r
t² = r / ( 0.5 * a )
t² = 6.4 *10⁶ / ( 0.5 * 9.8 )
t² = 1.306 * 10 ⁶
t = 1142.86 s
Now please confirm that in order for the Rock to move back to the initial starting point it has to travel 4 times as much time. It has to travel r to centre of the earth then another r to travel to to the other side of the earth, and back again. So indeed 4 times r.
The time it will take must be the same as 4 * 1142.86 s
now this is the time of one single wave ocillation.
Since T = 4571.43 s
f = 1 / 4571.43
f = 0.00021874993164 Hz
The frequency of the resulting harmonic motion is 2.19 *10-4
The frequency of the resulting harmonic motion is 0.000219 Hz
hurry helpppppppppp please guys
Answer: The box with three shaded squares and one non-shaded square
Step-by-step explanation:
You are trying to find the representation of the shaded region.
The scale shows point A at 0.75, and the scale can range from 0 to 1.
0.75 is equal to 3/4 of 1
3 of the 4 squares are shaded
So, the common ratio is 3:4 or 3/4
Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as well as in your final answer. 360 units2 586 units2 456 units2 552 units2
Answer:
Option (4)
Step-by-step explanation:
Surface area of a prism = 2B + P×h
where B = Area of the triangular base
P = perimeter of the triangular base
h = height of the prism
B = [tex]\frac{1}{2}(\text{leg 1})(\text{leg 2})[/tex]
Since, (Hypotenuse)² + (Leg 1)² + (Leg 2)² [Pythagoras theorem]
(20)² = (12)² + (Leg 2)²
Leg 2 = [tex]\sqrt{400-144}[/tex]
= 16 units
Therefore, B = [tex]\frac{1}{2}\times 12\times 16[/tex]
= 96 units²
P = 12 + 16 + 20
P = 48 units
h = 7.5 units
Surface area of the prism = 2(96) + (48×7.5)
= 192 + 360
= 552 units²
Therefore, surface area of the given triangular prism = 552 units²
Option (4) will be the answer.
What is the value of the expression? 8 and one-half minus 2 + 4 and three-fourths
Answer:
11 and one fourth.
or
[tex]11\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given the expression to be solved:
8 and one-half minus 2 + 4 and three-fourths
Let us solve them step by step:
8 and one-half can be represented as:
[tex]8\dfrac{1}{2}[/tex]
Method to solve a mixed fraction of the form [tex]p\frac{q}{r}[/tex] is:
[tex]p\dfrac{q}{r} = \dfrac{p\times r+q}{r}[/tex]
[tex]8\dfrac{1}{2}= \dfrac{8 \times 2+1}{2} = \dfrac{17}{2}[/tex]
Similarly, solving 4 and three-fourths:
[tex]4\dfrac{3}{4} = \dfrac{4 \times 4+3}{4} = \dfrac{19}{3}[/tex]
Now, the given expression:
[tex]8\dfrac{1}{2}-2+4\dfrac{3}{4}[/tex]
[tex]\Rightarrow \dfrac{17}{2} -2+\dfrac{19}{4}\\\Rightarrow \dfrac{17 \times 2-2 \times 4+19\times 1}{4}\\\Rightarrow \dfrac{34-8+19}{4}\\\Rightarrow \dfrac{45}{4}\\\Rightarrow 11\dfrac{1}{4}[/tex]
So, the answer is 11 and one fourth.
Answer:
11 and 1/4 on edge or B
Step-by-step explanation:
What is the first step when solving the equation below for x?
4x – 0.2 =
1.9
Add 1.9 to both sides of the equation.
Divide each side of the equation by 4.
Add 0.2 to both sides of the equation.
o
Subtract 0.2 from both sides of the equation.
Answer:
The answer is option 3.
Step-by-step explanation:
In order to solve the equation, you have to add 0.2 to both sides to eliminate -0.2 on the left side and make x the subject :
[tex]4x - 0.2 = 1.9[/tex]
[tex]4x - 0.2 + 0.2 = 1.9 + 0.2[/tex]
[tex]4x = 2.1[/tex]
Answer:
Add 0.2 to both sides of the equation
Step-by-step explanation:
4x-0.2=1.9
+0.2 + 0.2
4x=2.1
:4 :4
x=2.1/4
Suppose your boss wants you to obtain a sample to estimate a population mean. Based on previous analyses, you estimate that 49 is the approximate value of the population standard deviation. You would like to be 99% confident that your estimate is within 38 of the true population mean. What is the minimum sample size required
Answer:
the minimum sample size n = 11.03
Step-by-step explanation:
Given that:
approximate value of the population standard deviation [tex]\sigma[/tex] = 49
level of significance ∝ = 0.01
population mean = 38
the minimum sample size n = ?
The minimum sample size required can be determined by calculating the margin of error which can be re[resented by the equation ;
Margin of error = [tex]Z_{ \alpha /2}} \times \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]38 = \dfrac{2.576 \times 49}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = \dfrac{2.576 \times 49}{38}[/tex]
[tex]\sqrt{n} = \dfrac{126.224}{38}[/tex]
[tex]\sqrt{n} = 3.321684211[/tex]
[tex]n= (3.321684211)^2[/tex]
n ≅ 11.03
Thus; the minimum sample size n = 11.03
answer of this please
Answer: 205 and 1/7
Step-by-step explanation:
Hope this helped!
<!> Brainliest is appreciated! <!>
5) BRAINLIEST + 10+ POINTS! A 60 foot tall radio tower r feet from an observer subtends an angle of 3.25°. Use the arc length formula to estimate r (the distance between the observer and the radio tower) to the nearest foot. r≈ ___ feet
Answer:
1057
Step-by-step explanation:
tower is 60 feet high.
angle of 3.25 degrees.
3.25/360 * 2 * pi * r = the arc length of this angle.
that would be equal to 0.0567232007* r
if we assume the arc length and the height of the tower are approximately equal, then 0.0567232007 * r = 60
solving for r, we get r = 60/0.0567232007 = 1057.768237 feet.
that's about how far the tower is from the observer.
since the arc length is going to be a little longer than the length of the chord formed by the flagpole, this means that the distance of 1057.768237 meters is going to be a little less than the actual distance.
Answer:
≈ 1058 ft
Step-by-step explanation:
Use of arc formula: s=rθ
Given:
s= 60 ftθ= 3.25°= 3.25*π/180°= 0.0567 radr= s/θ= 60/0.0567 ≈ 1058 ft
A questionnaire about study habits was given to a random sample of students taking a large introductory stats class. The sample of 35 students reported that they spent an average of 115 minutes per week studying stats. Assume that the standard deviation is 40 minutes.A) Give a 95% confidence interval for the mean time spent studying stats by students in this class.B) Is it true that 95% of the students in the class have weekly studying times that lie in the interval you found in (A)? Explain
Answer:
(a) The 95% confidence interval for the mean time spent studying stats is (101.75, 128.25).
(b) TRUE.
Step-by-step explanation:
Let the random variable X represent the time spent per week studying stats.
The information provided is:
[tex]\bar x=115\\\sigma=40\\n=35\\\alpha=0.05[/tex]
(a)
The (1 - α)% confidence interval for the population mean is:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}[/tex]
The critical value of z for 95% confidence level is, z = 1.96.
Compute the 95% confidence interval for the mean time spent studying stats as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}[/tex]
[tex]=115\pm 1.96\cdot \frac{40}{\sqrt{35}}\\\\=115\pm13.252\\\\=(101.748, 128.252)\\\\\approx (101.75, 128.25)[/tex]
Thus, the 95% confidence interval for the mean time spent studying stats is (101.75, 128.25).
(b)
The true mean time spent studying stats by students in this class is contained in the 95% confidence interval, (101.75, 128.25) with a probability of 0.95.
The sample mean time spent studying stats is, [tex]\bar x=115\ \text{minutes}[/tex].
The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample ([tex]\bar x[/tex]) approaches the whole population mean (µ).
The sample size selected here is (n = 35 > 30) quite large.
So according to the law of large numbers the population mean is approximately 115 minutes.
And since the population mean is contained in the interval, it can be said that 95% of the students in the class have weekly studying times that lie in the interval (101.75, 128.25).
Estimate √50. Round your answer to the nearest Whole Number. *
Answer:
7
Step-by-step explanation:
√50 is close to √49
49 is a perfect square, 50 is close to 49.
√49 = 7
√50 ≈ 7.071068
Answer:
V50≈7
Step-by-step explanation:
V50=V5^2*2=V5^2*V2=5V2=5*1.41=7.05
V49<V50<V64
V50≈7
Please help I would be very greatful. On a coordinate plane, a solid straight line has a positive slope and goes through (0, 0.2) and (3, 2.2). Everything to the right of the line is shaded. Which linear inequality is represented by the graph? y > Two-thirdsx – One-fifth y ≥ Three-halvesx + One-fifth y ≤ Two-thirdsx + One-fifth y < Three-halvesx – One-fifth
Answer: C. y ≤ 2/3x + 1/5
Step-by-step explanation: From 1/5 on the y coordinate plane go up 2 and right 3 and it perfectly matches, so it would be C. 100% on Edge2020.
Answer:
C
Step-by-step explanation:
just did the test.
Imagine that a researcher develops a new cancer drug that shrinks tumors, which she measures using an MRI. The researcher needs to determine if the new drug performs differently from, or the same as, the current gold-standard drug therapy which shrinks tumor diameter by an average of 0.1 mm. After performing an experiment to test the new drug on a group of 6399 cancer patients, the researcher analyzes the measurements of tumor shrinkage by using a one-sample z-test for a mean at the significance level of α = 0.05, with power of 0.94. Assume that the researcher knows the standard deviation of tumor reduction is Ï = 2.5 mm. perhaps from, previous studies with similar populations. Assuming that in fact the null hypothesis is true and that the new cancer drug shrinks tumors by the same amount as the gold-standard drug, what is the probability that the test will lead the researcher to this decision? Give the probability as a percentage to the nearest whole number. _________%
Answer:
Assuming that the null hypothesis is true and that the new cancer drug shrinks tumors by the same amount as the gold-standard drug, the probability that the test will lead the researcher to this decision = 95%
Step-by-step explanation:
The nulll hypothesis is correct and we are not rejecting it, which means we are making the correct decision.
P(not rejecting the null | null hypothesis is true)
= 1 - P(rejecting null hypothesis | null hypothesis is true)
= 1 - P(type I error)
P(type I error) = significance level of the test = 0.05
P(not rejecting the null | null hypothesis is true)
= 1 - 0.05
= 0.95
= 95%
Hope this Helps!!!
Three populations have proportions 0.1, 0.3, and 0.5. We select random samples of the size n from these populations. Only two of the distributions of the sample proportions are normally distributed. Choose all possible values of n.
a. 10
b. 100
c. 50
d. 40
e. 20
Answer:
(1) A Normal approximation to binomial can be applied for population 1, if n = 100.
(2) A Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.
(3) A Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.
Step-by-step explanation:
Consider a random variable X following a Binomial distribution with parameters n and p.
If the sample selected is too large and the probability of success is close to 0.50 a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
np ≥ 10 n(1 - p) ≥ 10The three populations has the following proportions:
p₁ = 0.10
p₂ = 0.30
p₃ = 0.50
(1)
Check the Normal approximation conditions for population 1, for all the provided n as follows:
[tex]n_{a}p_{1}=10\times 0.10=1<10\\\\n_{b}p_{1}=100\times 0.10=10=10\\\\n_{c}p_{1}=50\times 0.10=5<10\\\\n_{d}p_{1}=40\times 0.10=4<10\\\\n_{e}p_{1}=20\times 0.10=2<10[/tex]
Thus, a Normal approximation to binomial can be applied for population 1, if n = 100.
(2)
Check the Normal approximation conditions for population 2, for all the provided n as follows:
[tex]n_{a}p_{1}=10\times 0.30=3<10\\\\n_{b}p_{1}=100\times 0.30=30>10\\\\n_{c}p_{1}=50\times 0.30=15>10\\\\n_{d}p_{1}=40\times 0.10=12>10\\\\n_{e}p_{1}=20\times 0.10=6<10[/tex]
Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50 and 40.
(3)
Check the Normal approximation conditions for population 3, for all the provided n as follows:
[tex]n_{a}p_{1}=10\times 0.50=5<10\\\\n_{b}p_{1}=100\times 0.50=50>10\\\\n_{c}p_{1}=50\times 0.50=25>10\\\\n_{d}p_{1}=40\times 0.50=20>10\\\\n_{e}p_{1}=20\times 0.10=10=10[/tex]
Thus, a Normal approximation to binomial can be applied for population 2, if n = 100, 50, 40 and 20.
Use a(t) = −9.8 meters per second per second as the acceleration due to gravity. (Neglect air resistance.) A canyon is 1300 meters deep at its deepest point. A rock is dropped from the rim above this point. How long will it take the rock to hit the canyon floor? (Round your answer to one decimal place.)
Answer:
t = 16.3 s
Step-by-step explanation:
The equation to determine the time it will take to get to the canyon floor is.
H = ut - 1/2(gt²)
In this case
U = initial velocity= 0
H = 1300 metres
g = -9.8 ms^-2
1300= 0 - 1/2(-9.8t²)
1300= 9.8t²/2
1300*2= 9.8t²
2600= 9.8t²
2600/9.8= t²
265.306= t²
√265.306 = t
16.288 =t
To one decimal place
t = 16.3 s
What amount invested at 10% compounded semiannually will be worth $6380.00 after 38 months? Calculate the result to the nearest cent.
Given Information:
Annual interest rate = r = 10%
Accumulated amount = A = $6380.00
Semi-annual compounding = n = 2
Number of years = t = 38/12 = 19/6
Required Information
Principle amount= P = ?
Answer:
Principle amount= P = $4,684.05
Step-by-step explanation:
The principal amounts in terms of compound interest is given by
[tex]$ P = \frac{A}{(1 + i)^N} $[/tex]
Where
i = r/n
i = 0.10/2
i = 0.05
N = n*t
N = 2*19/6
N = 19/3
So, the principal amount is
[tex]P = \frac{6380.00}{(1 + 0.05)^{19/3}} \\\\P= \$4,684.05 \\\\[/tex]
Therefore, you need to invest $4,684.05 at 10% compounded semiannually for 38 months to get $6380.00 in savings.
Which product will result in a sum or difference of cubes?
A (x + 7)(x2 – 7x + 14)
B (x + 8)(x2 + 8x + 64)
C (x – 9)(x2 + 9x + 81)
D (x – 10)(x2 – 10x + 100)
Answer:
C. (x - 9)(x^2 + 9x + 81).
Step-by-step explanation:
The cube identities are
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Checking against the list the one that fits is the difference formula:
x^2 - 9^2 = (x - 9)(x^2 + 9x + 81).
a=1, b = 9, ab = 1 *9 = 9.
The life of an electric component has an exponential distribution with a mean of 8 years. What is the probability that a randomly selected one such component has a life less than 5 years? Answer: (round to 4 decimal places)
Answer:
The probability is 0.4647
Step-by-step explanation:
The variable X is the life of an electric component in years.
X follows a exponential distribution, it means that the probability that the life of an electric component is less than x years is calculated as:
[tex]P(X<x)=1-e^{\frac{-x}{\beta } }[/tex]
Where [tex]x\geq0[/tex] and [tex]\beta[/tex] is the mean life of the electric component.
So, replacing x by 5 and [tex]\beta[/tex] by 8, we get that the probability that a randomly selected component has a life less than 5 years is:
[tex]P(X<5)=1-e^{\frac{-5}{8 } }=0.4647[/tex]
3(x + 2) = 12 solve for x
Answer:
x = 2.
Step-by-step explanation:
3(x + 2) = 12
3x + 6 = 12
3x = 6
x = 2
Hope this helps!
Answer:
4
Step-by-step explanation:
Solve for X. Assume that lines which appear tangent are tangent
Answer:
E
Step-by-step explanation:
(x+8)×8=12²=144
x+8=144/8=18
x=18-8=10
The value of x is 10.
Tangent-secant TheoremWhen a tangent and secant share a common endpoint outside the circle the product of the secant and the external part of the secant is equal to the square of the tangent.
Given to usinternal part of the secant = (x+8),
external part of the secant = 8,
tangent = 12,
According to Tangent-secant Theorem[tex](x+8)\times 8 = 12^2\\8x+64 = 144\\8x = 144-64\\8x = 80\\x = \dfrac{80}{8}\\x=10[/tex]
Hence, the value of x is 10.
Learn more about tangent-secant theorem:
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Which of the following is the rule for rotating the point with coordinates (x,y), 180° clockwise about
the origin?
Answer:
A. (x, y) ⇒ (-x, -y)
Step-by-step explanation:
Rotation 180° in either direction is equivalent to reflection across the origin, and/or reflection across both axes (in either order). It negates both coordinates.
(x, y) ⇒ (-x, -y) . . . . rotation 180°
find the missing side length in the image ?= _____
Answer:
72
Step-by-step explanation:
45/35=x/56
9/7=x/56
7x=9*56
:7. :7
x=9*8
x=72
If tan A=2/3 and tan B= -3/5 what is the exact value of cot(A-B)?
Answer:
cot(A-B) = 3/19
Step-by-step explanation:
The formula for cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A)
we know that cot A = 1/ Tan A
Given
tan A=2/3
therefore cot A = 1/ tan A = 1/2/3 = 3/2
tan B= -3/5
cot B = 1/ tan B = 1/-3/5 = -5/3
Thus,
(Cot A Cot B + 1 ) = (3/2)*(-5/3 )+ 1 = -5/2 +1 = (-5+2)/2 = -3/2
(Cot B - Cot A) = -5/3 -3/2 = (-5*2) + (-3*3) / 2 = -10 -9/2 = -19/2
Thus,
cot(A-B) = (Cot A Cot B + 1 ) / (Cot B - Cot A) = -3/2 / -19/2 = 3/19
Thus,
cot(A-B) = 3/19
when the sun is ay certain angles in the sky a 50 foot building casts a 20 foot shadow, what is the length of the shadow in feet cast by a flag pole 20 feet at the same time?
[tex]50/20=20/x\implies50x=400\implies\boxed{x=8\mathrm{ft}}[/tex]
Hope this helps.
The length of the shadow cast by the flag pole is 6.4 feet.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that;
Height of building= 50 foot
Shadow= 20foot
Now,
Let x be the length of the shadow cast by the flag pole. Then we have:
2050=x20
Cross-multiplying, we get:
50x=20×20
Dividing both sides by 50, we get:
x=5020×20
Simplifying, we get:
x=58×4
Multiplying, we get:
x=6.4
Therefore, by the proportion the answer will be 6.4 feet.
More can be learned about proportions at;
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