Answers
Answer:
y=54 degrees
Step-by-step explanation:
2y+72=180
2y=108
y=54
Answer:
B
Step-by-step explanation:
72 + y + y = 180
72 + 2y = 180
2y = 108
2y/2 = 108/2
y = 54
Hope this helps ^-^
Related Questions
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is the following.
y 0 1 2 3
p(y) 0.50 0.25 0.20 0.05
A) Compute E(Y).
B) Suppose an individual with Y violations incurs a surcharge of $110Y2. Calculate the expected amount of the surcharg.
Answers
Answer:
A. The E(Y) is 0.80
B. The expected amount of the surcharges is $165
Step-by-step explanation:
A. In order to calculate the E(Y), we would have to calculate the following formula:
E(Y)=∑yp(y)
E(Y)=(0*0.5)+(1*0.25)+(2*0.20)+(3*0.05)
E(Y)=0+0.25+0.40+0.15
E(Y)=0.80
B. In order to calculate the expected amount of the surcharges we would have to calculate the following formula:
E($110Y∧2)=110E(Y∧2)
=110∑y∧2p(y)
=110((0∧2*0.5)+(1∧2*0.25)+(2∧2*0.20)+(3∧2*0.05))
110(0+0.25+0.80+0.45)
=$165
What is the common difference of the sequence 20, 17, 14, 11, 8.... ?
Answers
Answer:
-3
Step-by-step explanation:
every sequence goes down by -3
Answer:
take away 3. the common difference is 3
Step-by-step explanation:
take away 3
Which are true of the function f(x)=49(1/7)?select three options. A)The domain is the set of all real numbers. B) the range is the set of all real numbers. C) the domain is x >0. D)the range is y>0. E)as increases by 1, each y value is one -seventh of the previous y-value.
Answers
Answer:
A,D and E
Step-by-step explanation:
We are given that a function
[tex]f(x)=49(\frac{1}{7})^x[/tex]
The given function is exponential function .
The exponential function is defined for all real values of x.
Therefore, domain of f=Set of all real numbers
Substitute x=0
[tex]y=f(0)=49>0[/tex]
Range of f is greater than 0.
x=1
[tex]y(1)=\frac{49}{7}[/tex]
x=2
[tex]y=49(\frac{1}{7})^2=\frac{1}{7}y(1)[/tex]
As x increases by 1, each value of y is one-seventh of the previous y-value.
Therefore, option A,D and E are true.
Answer:
A D E
Step-by-step explanation:
Edge2020 quiz
Solve the following and
make sure to write your
answer in scientific
notation.
(1.5 x 105)(5 x 103)
Answers
Answer:
7.5* 10^8
Step-by-step explanation:
(1.5 x 10^5)(5 x 10^3)
Multiply the numbers
1.5*5=7.5
Add the exponents
10 ^(5+3) = 10^8
Put back together
7.5* 10^8
This is in scientific notation
Suppose that we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2. Consider the following procedure for accomplishing our task:
1. Flip the coin.
2. Flip the coin again.
3. If both flips land on heads or both land on tails, return to step 1. 4. Let the result of the last flip be the result of the experiment.
(a) Show that the result is equally likely to be either heads or tails.
(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?
Answers
Answer:
Step-by-step explanation:
Given that;
the following procedure for accomplishing our task are:
1. Flip the coin.
2. Flip the coin again.
From here will know that the coin is first flipped twice
3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails
But if the outcomes of the two flip are different i.e they did not land on both heads or both did not land on tails , then we will consider such an outcome.
Let the probability of head = p
so P(head) = p
the probability of tail be = (1 - p)
This kind of probability follows a conditional distribution and the probability of getting heads is :
[tex]P( \{Tails, Heads\})|\{Tails, Heads,( Heads ,Tails)\})[/tex]
[tex]= \dfrac{P( \{Tails, Heads\}) \cap \{Tails, Heads,( Heads ,Tails)\})}{ {P( \{Tails, Heads,( Heads ,Tails)\}}}[/tex]
[tex]= \dfrac{P( \{Tails, Heads\}) }{ {P( \{Tails, Heads,( Heads ,Tails)\}}}[/tex]
[tex]= \dfrac{P( \{Tails, Heads\}) } { {P( Tails, Heads) +P( Heads ,Tails)}}[/tex]
[tex]=\dfrac{(1-p)*p}{(1-p)*p+p*(1-p)}[/tex]
[tex]=\dfrac{(1-p)*p}{2(1-p)*p}[/tex]
[tex]=\dfrac{1}{2}[/tex]
Thus; the probability of getting heads is [tex]\dfrac{1}{2}[/tex] which typically implies that the coin is fair
(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?
For a fair coin (0<p<1) , it's certain that both heads and tails at the end of the flip.
The procedure that is talked about in (b) illustrates that the procedure gives head if and only if the first flip comes out tail with probability 1 - p.
Likewise , the procedure gives tail if and and only if the first flip comes out head with probability of p.
In essence, NO, procedure (b) does not give a fair coin flip outcome.
The percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14 defectives. Determine a 88% confidence interval for the proportion defective for the process today. Place your LOWER limit, rounded to 3 decimal places, in the first blank. For example, 0.123 would be a legitimate answer. Place your UPPER limit, rounded to 3 decimal places, in the second blank. For example, 0.345 would be a legitimate entry.
Answers
Answer:
The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)
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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 160, \pi = \frac{14}{160} = 0.088[/tex]
88% confidence level
So [tex]\alpha = 0.12[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.12}{2} = 0.94[/tex], so [tex]Z = 1.555[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 - 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.053[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 + 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.123[/tex]
The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)
For the dilation, DO, K = (10, 0) → (5, 0), the scale factor is equal to _____.
Answers
Answer:
[tex] \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]scale \: factor = \frac{5}{10} = \frac{1}{2} \\ [/tex]
Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain plant has a standard beta distribution with α = 4 and β = 3.(a) Compute E(X) and V(X). (Round your answers to four decimal places.)E(X) = Correct: Your answer is correct.V(X) = Correct: Your answer is correct.(b) Compute P(X ≤ 0.5). (Round your answer to four decimal places.)
Answers
Answer:
(a) The value of E (X) is 4/7.
The value of V (X) is 3/98.
(b) The value of P (X ≤ 0.5) is 0.3438.
Step-by-step explanation:
The random variable X is defined as the proportion of surface area in a randomly selected quadrant that is covered by a certain plant.
The random variable X follows a standard beta distribution with parameters α = 4 and β = 3.
The probability density function of X is as follows:
[tex]f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} ; \hspace{.3in}0 \le x \le 1;\ \alpha, \beta > 0[/tex]
Here, B (α, β) is:
[tex]B(\alpha,\beta)=\frac{(\alpha-1)!\cdot\ (\beta-1)!}{((\alpha+\beta)-1)!}[/tex]
[tex]=\frac{(4-1)!\cdot\ (3-1)!}{((4+3)-1)!}\\\\=\frac{6\times 2}{720}\\\\=\frac{1}{60}[/tex]
So, the pdf of X is:
[tex]f(x) = \frac{x^{4-1}(1-x)^{3-1}}{1/60}=60\cdot\ [x^{3}(1-x)^{2}];\ 0\leq x\leq 1[/tex]
(a)
Compute the value of E (X) as follows:
[tex]E (X)=\frac{\alpha }{\alpha +\beta }[/tex]
[tex]=\frac{4}{4+3}\\\\=\frac{4}{7}[/tex]
The value of E (X) is 4/7.
Compute the value of V (X) as follows:
[tex]V (X)=\frac{\alpha\ \cdot\ \beta}{(\alpha+\beta)^{2}\ \cdot\ (\alpha+\beta+1)}[/tex]
[tex]=\frac{4\cdot\ 3}{(4+3)^{2}\cdot\ (4+3+1)}\\\\=\frac{12}{49\times 8}\\\\=\frac{3}{98}[/tex]
The value of V (X) is 3/98.
(b)
Compute the value of P (X ≤ 0.5) as follows:
[tex]P(X\leq 0.50) = \int\limits^{0.50}_{0}{60\cdot\ [x^{3}(1-x)^{2}]} \, dx[/tex]
[tex]=60\int\limits^{0.50}_{0}{[x^{3}(1+x^{2}-2x)]} \, dx \\\\=60\int\limits^{0.50}_{0}{[x^{3}+x^{5}-2x^{4}]} \, dx \\\\=60\times [\dfrac{x^4}{4}+\dfrac{x^6}{6}-\dfrac{2x^5}{5}]\limits^{0.50}_{0}\\\\=60\times [\dfrac{x^4\left(10x^2-24x+15\right)}{60}]\limits^{0.50}_{0}\\\\=[x^4\left(10x^2-24x+15\right)]\limits^{0.50}_{0}\\\\=0.34375\\\\\approx 0.3438[/tex]
Thus, the value of P (X ≤ 0.5) is 0.3438.
Tasha wants to take money out of the ATM for a taxi fare. She wants to do a quick estimate to see if taking $120 out of her bank account will overdraw it. She knows she had $325 in the account this morning when she checked her balance. Today she bought lunch for $19, a dress for $76, a pair of shoes for $53, and a necklace for $23. She also saw a movie with a friend for $12. Rounding each of her expenses to the nearest tens place, estimate how much money Tasha has left in her account before she goes to the ATM. Do not include the $ in your answer.
Answers
Answer:145
Step-by-step explanation: $19=20 76=80 53=50 23=20 12=10 total = 180 325-180 =145
Which of the x-values are solutions to the following inequality? 17 > x Choose all answers that apply: (A) x = 7 (B) x = 12 (C) x = 17
Answers
Answer:
7 and 12
Step-by-step explanation:
7 and 12 are ok
17 is not
hope this helps
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The inequality is given below.
x < 17
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ2
A financial advisor is analyzing a family's estate plan. The amount of money that the family has invested in different real estate properties is normally distributed with a mean of $225,000 and a standard deviation of $50,000. Use a calculator to find how much money separates the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings.
Answers
Answer:
The amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.
Step-by-step explanation:
Let the random variable X represent the amount of money that the family has invested in different real estate properties.
The random variable X follows a Normal distribution with parameters μ = $225,000 and σ = $50,000.
It is provided that the family has invested in n = 10 different real estate properties.
Then the mean and standard deviation of amount of money that the family has invested in these 10 different real estate properties is:
[tex]\mu_{\bar x}=\mu=\$225,000\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{50000}{\sqrt{10}}=15811.39[/tex]
Now the lowest 80% of the amount invested can be represented as follows:
[tex]P(\bar X<\bar x)=0.80\\\\\Rightarrow P(Z<z)=0.80[/tex]
The value of z is 0.84.
*Use a z-table.
Compute the value of the mean amount invested as follows:
[tex]\bar x=\mu_{\bar x}+z\cdot \sigma_{\bar x}[/tex]
[tex]=225000+(0.84\times 15811.39)\\\\=225000+13281.5676\\\\=238281.5676\\\\\approx 238281.57[/tex]
Thus, the amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.
Subtract -6 4/9-3 2/9-8 2/9
Answers
Answer:
[tex]-\frac{161}{9}=\\or\\-16\frac{8}{9}[/tex]
Step-by-step explanation:
[tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}=\\\\-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=\\\\-\frac{161}{9}=\\\\-16\frac{8}{9}[/tex]
Teresa's parents are getting phones that each and 64 GB of storage how many bits of storage come with each phone answer both in scientific in standard notation
Answers
Answer:
5.12 x 10¹¹ bit
Step-by-step explanation:
1GB = 8 x 10⁹ bits
so 64gb = 64 x 8 x 10⁹
= 512 x 10⁹
= 5.12 x 10¹¹ bits
scientific notation = 5.12 x 10¹¹ bits
standard Notation = 512 ,000,000,000 bits.
what 826,497 in standard form answer
Answers
Answer:8.2 x 10^5
Step-by-step explanation:
Which is the better buy? Store A: $250 of 20% off Or Store B $280 at 25% off
Show your work
Answers
Answer:
Store A
Step-by-step explanation:
So. What we are going to want to do here is start off by having two stores obviously. And we have the sales that they have. If the discount is 20% rhat means the new price will be 80% of 250. So we take 250 x .8 = 200
If the discount is 25%, that means the new price will be 75% of what it was before hand. So we take 280 x .75 = 210. So the better price is at Store a
A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola yequals25minusxsquared. What are the dimensions of the rectangle with the maximum area? What is the area?
Answers
Answer:
The answer is "[tex]\bold{\frac{32}{3}}\\[/tex]"
Step-by-step explanation:
The rectangle should also be symmetrical to it because of the symmetry to the y-axis The pole of the y-axis. Its lower two vertices are (-x,0). it means that
and (-x,0), and (x,0). Therefore the base measurement of the rectangle is 2x. The top vertices on the parabola are as follows:
The calculation of the height of the rectangle also is clearly 16-x^2, (-x,16,-x^2) and (x,16,-x^2).
The area of the rectangle:
[tex]A(x)=(2x)(16-x^2)\\\\A(x)=32x-2x^3[/tex]
The local extremes of this function are where the first derivative is 0:
[tex]A'(x)=32-6x^2\\\\32-6x^2=0\\\\x= \pm\sqrt{\frac{32}{6}}\\\\x= \pm\frac{4\sqrt{3}}{3}\\\\[/tex]
Simply ignore the negative root because we need a positive length calculation
It wants a maximum, this we want to see if the second derivative's profit at the end is negative.
[tex]A''\frac{4\sqrt{3}}{3} = -12\frac{4\sqrt{3}}{3}<0\\\\2.\frac{4\sqrt{3}}{3}= \frac{8\sqrt{3}}{3}\\\\\vertical \ dimension\\\\16-(\frac{4\sqrt{3}}{3})^2= \frac{32}{3}[/tex]
Write the expression in simplest form 3(5x) + 8(2x)
Answers
Answer:
31x[tex]solution \\ 3(5x) + 8(2x) \\ = 3 \times 5x + 8 \times 2x \\ = 15x + 16x \\ = 31x[/tex]
hope this helps...
Good luck on your assignment...
The expression [tex]3(5x) + 8(2x)[/tex] in simplest form is 31x.
To simplify the expression [tex]3(5x) + 8(2x)[/tex], we can apply the distributive property:
[tex]3(5x) + 8(2x)[/tex]
[tex]= 15x + 16x[/tex]
Combining like terms, we have:
[tex]15x + 16x = 31x[/tex]
Therefore, the expression [tex]3(5x) + 8(2x)[/tex] simplifies to [tex]31x.[/tex]
To learn more on Expressions click:
https://brainly.com/question/14083225
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if rectangle ABCD was reflected over the y-axis, reflected over x axis, and rotated 180°, where would point A' lie?
Answers
Answer:
Option C (-4,-1) (In Quadrant III)
Step-by-step explanation:
Coordinate = (-4,1)
=> Reflecting over y-axis will make the coordinate (4,1)
=> Reflecting across x-axis will make the coordinate (4,-1)
=> Rotating 180 will make it (-4,-1)
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97%, how many citizens should be included in your sample
Answers
Question:
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97% , how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 18 years.
Answer:
61.03
Step-by-step explanation:
Given:
Standard deviation = 18
Sample estimate = 5
Confidence level = 97%
Required:
Find sample size, n.
First find the Z value. Using zscore table
Z-value at a confidence level of 97% = 2.17
To find the sample size, use the formula below:
[tex] n = (Z * \frac{\sigma}{E})^2[/tex]
[tex] n = ( 2.17 * \frac{18}{5})^2 [/tex]
[tex] n = (2.17 * 3.6)^2 [/tex]
[tex] n = (7.812)^2 [/tex]
[tex] n = 61.03 [/tex]
Sample size = 61.03
You are given an n×n board, where n is an even integer and 2≤n≤30. For how many such boards is it possible to cover the board with T-shaped tiles like the one shown? Each cell of the shape is congruent to one cell on the board.
Answers
Answer:
7
Step-by-step explanation:
The number of cells in a tile is 4. If colored alternately, there are 3 of one color and 1 of the alternate color. To balance the coloring, an even number of tiles is needed. Hence the board dimensions must be multiples of 4.
In the given range, there are 7 such boards:
4×4, 8×8, 12×12, 16×16, 20×20, 24×24, and 28×28
The graphs below have the same shape. What is the equation of the blue
graph?
Answers
Answer: b
Explanation:
The -2 outside of the parentheses means it’s at y=-2 and the -4 inside the parentheses means it’s at x= 4 because it’s always the opposite
Given a normal distribution with (mean) μ= 50 and (standard deviation) σ = 4, what is the probability that:__________.
a) x>43
b) x<42
c) x>57.5
d) 42
e) x<40 or x>55
f) 5% of the values are less than what X value?
g) 60% of the values are between what two X values (symmetrically distributed around the mean)?
h) 85% of the values will be above what X value?
Answers
Answer:
a) P(x > 43) = 0.9599
b) P(x < 42) = 0.0228
c) P(x > 57.5) = 0.03
d) P(x = 42) = 0.
e) P(x<40 or x>55) = 0.1118
f) 43.42
g) Between 46.64 and 53.36.
h) Above 45.852.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 50, \sigma = 4[/tex]
a) x>43
This is 1 subtracted by the pvalue of Z when X = 43. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{43 - 50}{4}[/tex]
[tex]Z = -1.75[/tex]
[tex]Z = -1.75[/tex] has a pvalue of 0.0401
1 - 0.0401 = 0.9599
P(x > 43) = 0.9599
b) x<42
This is the pvalue of Z when X = 42.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{42 - 50}{4}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
P(x < 42) = 0.0228
c) x>57.5
This is 1 subtracted by the pvalue of Z when X = 57.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{57.5 - 50}{4}[/tex]
[tex]Z = 1.88[/tex]
[tex]Z = 1.88[/tex] has a pvalue of 0.97
1 - 0.97 = 0.03
P(x > 57.5) = 0.03
d) P(x = 42)
In the normal distribution, the probability of an exact value is 0. So
P(x = 42) = 0.
e) x<40 or x>55
x < 40 is the pvalue of Z when X = 40. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40 - 50}{4}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
x > 55 is 1 subtracted by the pvalue of Z when X = 55. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 50}{4}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944
1 - 0.8944 = 0.1056
0.0062 + 0.1056 = 0.1118
P(x<40 or x>55) = 0.1118
f) 5% of the values are less than what X value?
X is the 5th percentile, which is X when Z has a pvalue of 0.05, so X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = -1.645*4[/tex]
[tex]X = 43.42[/tex]
43.42 is the answer.
g) 60% of the values are between what two X values (symmetrically distributed around the mean)?
Between the 50 - (60/2) = 20th percentile and the 50 + (60/2) = 80th percentile.
20th percentile:
X when Z has a pvalue of 0.2. So X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = -0.84*4[/tex]
[tex]X = 46.64[/tex]
80th percentile:
X when Z has a pvalue of 0.8. So X when Z = 0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.84 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = 0.84*4[/tex]
[tex]X = 53.36[/tex]
Between 46.64 and 53.36.
h) 85% of the values will be above what X value?
Above the 100 - 85 = 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.037 = \frac{X - 50}{4}[/tex]
[tex]X - 50 = -1.037*4[/tex]
[tex]X = 45.852[/tex]
Above 45.852.
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.
A. 91.68
C. 92.95 D. 91.69 < μ < 98.31
Answers
Answer:
B) 92.03 < μ < 97.97
99% confidence interval for the mean score of all students.
92.03 < μ < 97.97
Step-by-step explanation:
Step(i):-
Given sample mean (x⁻) = 95
standard deviation of the sample (s) = 6.6
Random sample size 'n' = 30
99% confidence interval for the mean score of all students.
[tex]((x^{-} - Z_{0.01} \frac{S}{\sqrt{n} } , (x^{-} + Z_{0.01} \frac{S}{\sqrt{n} })[/tex]
step(ii):-
Degrees of freedom
ν = n-1 = 30-1 =29
[tex]t_{0.01} = 2.462[/tex]
99% confidence interval for the mean score of all students.
[tex]((95 - 2.462 \frac{6.6}{\sqrt{30} } , 95 + 2.462\frac{6.6}{\sqrt{30} } )[/tex]
( 95 - 2.966 , 95 + 2.966)
(92.03 , 97.97)
Final answer:-
99% confidence interval for the mean score of all students.
92.03 < μ < 97.97
Please help me find Jebel dhanna in UAE map.
Answers
Answer:
The full name of the place is the "Danat Jebel Dhanna". The Jebel Dhanna is currently located in the Abu Dhabi. It is said that it is one of the most best beach in the UAE, they also say that it is the biggest resort, of course, with a bunch of hotels.
hope this helps ;)
best regards,
`FL°°F~` (floof)
What is the solution of √1-3x = x+3 ?
Answers
Answer:
{-1, -8}
Step-by-step explanation:
Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".
Squaring both sides of the given equation, we get:
1 - 3x = x^2 + 6x + 9, or x^2 + 6x + 8 + 3x, or
x^2 + 9x + 8 = 0. Factoring, we get: (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.
Answer:
I hope the given equation is :
{-1, -8}
First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,
1 - 3x = (x + 3)²
1 - 3x = (x + 3)*(x + 3) Since a² = a * a
1 - 3x = x² + 3x + 3x + 3² By multiplication.
1 - 3x = x² + 6x + 9 Combine the like terms.
x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation
x² + 9x + 8 = 0 Combine the like terms.
Next step is to factor the trinomial to solve the above equation for x.
For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.
So, 8 = 1 * 8
Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,
x² + 1x + 8x + 8 = 0
(x² + 1x) + (8x + 8) = 0 Group the terms.
x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.
(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).
So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.
Hence, x = -1 and - 8.
Next step is to plug in -1 and -8 in the original equation to cross check the solutions.
For x = -1,
Simplify each sides separately.
2 = 2
2 = 2 is correct. So, x = -1 satisfy the equation.
Hence, x = -1 is the real solution of the given equation.
Similarly let's plug in x = -8 now. So,
Simplify each sides separately.
5 = 2
5 = 2 is not true. So, x = -8 is the extraneous solution.
Therefore, the only solution is x = -1.
Hence, the correct choice is C.
Hope this helps you!
Step-by-step explanation:
mark brainlies plssssssssss
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С
Micaela tried to rotate the square 180° about the origin.
Is her rotation correct? If not, explain why.
O No, she translated the figure instead of rotating it.
O No, she reflected the figure instead of rotating it.
O No, the vertices of the image and pre-image do not
correspond.
Yes, the rotation is correct.
cu
Answers
Answer:
it’s C
Step-by-step explanation:
No, the vertices of the image and pre-image do not correspond
No, the vertices of the image and pre-image do not correspond, Micaela tried to rotate the square 180° about the origin. Hence, option C is correct.
What is rotation about the origin?A figure can be rotated by 90 degrees clockwise by rotating each vertex of the figure 90 degrees clockwise about the origin.
Let's take the vertices of a square with points at (+1,+1), (-1,+1), (-1,-1), and (+1,-1), centered at the origin, can be found in the following positions after rotation:
The vertex (+1,+1) would be rotated to the point (-1,-1).The vertex (-1,+1) would be rotated to the point (+1,-1).The vertex (-1,-1) would be rotated to the point (+1,+1).The vertex (+1,-1) would be rotated to the point (-1,+1).Micaela's rotation must be accurate if it led to the same points. Her rotation is incorrect if the points are different, though.
It is impossible to tell if Micaela's rotation is accurate without more details or a diagram.
Thus, option C is correct.
For more information about rotation about the origin, click here:
https://brainly.com/question/30198965
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The volume of a trianglular prism is 54 cubic units. What is the value of x?
3
5
7
9
Answers
Answer:
X is 3 units.
Step-by-step explanation:
Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.
If log 5 = p and log 2=q then log 200 can be written in terms of p and q as?
Answers
Work Shown:
log(200) = log(2^3*5^2)
log(200) = log(2^3) + log(5^2)
log(200) = 3*log(2) + 2*log(5)
log(200) = 3*q + 2*p
log(200) = 2p + 3q
The log rules I used were
log(A*B) = log(A)+log(B)
log(A^B) = B*log(A)
The equivalent expression of log(200) is 2p + 3q
The logarithmic expression is given as:
[tex]\mathbf{log 200}[/tex]
Rewrite as:
[tex]\mathbf{log(200) = log (25 \times 8)}[/tex]
Express as exponents
[tex]\mathbf{log(200) = log (5^2 \times 2^3)}[/tex]
Split
[tex]\mathbf{log(200) = log (5^2) +log(2^3)}[/tex]
Apply law of logarithms
[tex]\mathbf{log(200) = 2log (5) +3log(2)}[/tex]
From the question;
log(5) = p and log(2) = q
So, we have:
[tex]\mathbf{log(200) = 2p +3q}[/tex]
Hence, the equivalent expression of log(200) is 2p + 3q
Read more about logarithmic expressions at:
https://brainly.com/question/9665281
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 409 gram setting. It is believed that the machine is underfilling the bags. A 42 bag sample had a mean of 404 grams. Assume the population standard deviation is known to be 24. A level of significance of 0.01 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answers
Answer:
[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-1.35)=0.0885[/tex]
For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409
Step-by-step explanation:
Information given
[tex]\bar X=404[/tex] represent the sample mean
[tex]\sigma=24[/tex] represent the population standard deviation
[tex]n=42[/tex] sample size
[tex]\mu_o =409[/tex] represent the value to verify
[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean is less than 409, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 409[/tex]
Alternative hypothesis:[tex]\mu < 409[/tex]
The statistic for this case is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-1.35)=0.0885[/tex]
For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409
Any help would be greatly appreciated
Answers
Answer:
[tex]\boxed{\sf \ \ \ 49a^8b^6c^2 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex](-7a^4b^3c)^2=(-1)^27^2a^{4*2}b^{3*2}c^2=49a^8b^6c^2[/tex]
as
[tex](-1)^2=1[/tex]