Answer:
[tex]P(X\geq 9)=P(X=9)+P(X=10)[/tex]
And using the probability mass function we got:
[tex]P(X=9)=(10C9)(0.913)^9 (1-0.913)^{10-9}=0.383[/tex]
[tex]P(X=10)=(10C10)(0.913)^{10} (1-0.913)^{10-10}=0.402[/tex]
And replacing we got:
[tex] P(X \geq 9) = 0.383 +0.402= 0.785[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of students graduated", on this case we now that:
[tex]X \sim Binom(n=10, p=0.913)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find the following probability:
[tex]P(X\geq 9)=P(X=9)+P(X=10)[/tex]
And using the probability mass function we got:
[tex]P(X=9)=(10C9)(0.913)^9 (1-0.913)^{10-9}=0.383[/tex]
[tex]P(X=10)=(10C10)(0.913)^{10} (1-0.913)^{10-10}=0.402[/tex]
And replacing we got:
[tex] P(X \geq 9) = 0.383 +0.402= 0.785[/tex]
D
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
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.
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The graphs below have the same shape. What is the equation of the blue
graph?
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
Simplify 8x + 10y + 9x - 3y by identifying and combining like terms. A. 17x + 13y B.24y C.17x+7 D.17x + 7y
Answer:
17x +7y
Step-by-step explanation:
8x + 10y + 9x - 3y
Combine like terms
8x+ 9x + 10y - 3y
17x +7y
8x+9x are like terms and 10y -3y are like terms
Answer:
17x + 7y
Step-by-step explanation:
8x + 10y + 9x - 3y
Rearrange.
8x + 9x + 10y - 3y
Factor out x and y.
x (8 + 9) + y (10 - 3)
Add or subtract.
x (17) + y (7)
17x + 7y
Which is the better buy? Store A: $250 of 20% off Or Store B $280 at 25% off
Show your work
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
what 826,497 in standard form answer
Answer:8.2 x 10^5
Step-by-step explanation:
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
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
Any help would be greatly appreciated
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]
>
3. Express or-a-7
80X-9=7
Answer:
x = 1/5
Step-by-step explanation:
Step 1: Add 9 to both sides
80x = 16
Step 2: Divide both sides by 80
x = 16/80
Step 3: Simplify by dividing top and bottom by 16
x = 1/5
And we have our final answer!
Answer:
x = 1/5
Step-by-step explanation:
80x - 9 = 7
Add 9 into both sides.
80x = 7 + 9
80x = 16
Divide 80 into both sides.
x = 16/80
Simplify.
x = 1/5
Point P is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of P A is 2 and the length of P B is 3. The Length of A A prime is 4 and the length of B B prime is 5. Is triangle A'B'C' a dilation of triangle ABC? Explain. Yes, it is an enlargement with a scale factor of 3. Yes, it is an enlargement with a scale factor of Eight-thirds. No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally. No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.
Answer:
C. No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
Step-by-step explanation:
Dilation is the process in which the size i.e dimensions of a given figure is either increased or decreased by a scale factor, without changing the shape of the figure.
Given that: PA = 2, PB = 3, A[tex]A^{I}[/tex] = 4, B[tex]B^{I}[/tex] = 5.
So that: P[tex]A^{I}[/tex] = 6, P[tex]B^{I}[/tex] = 8.
Therefore, triangle A'B'C' is not an exact dilation of triangle ABC. So that the correct option is; No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
Answer:
the answer is c
Step-by-step explanation:
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
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.
A rectangle or pyramid has a volume of 1296 in.³, a height of 24 inches, and a base length of 6 inches. What is the width of its base?
Answer: base width = 27 in
Step-by-step explanation:
Base width = 3 x (V / hl)
3 x (1296 / 24 x 6)
3 x (1296 / 144)
3 x 9 = 27
How many solutions does the system have?
You can use the interactive graph below to find the answer.
y=x+1
y = 2x – 5
Choose 1 answer:
The answer has one solution:
_______________________________
→ x = 6 ; y = 7 ; or, write as: [6, 7].
_______________________________
Step-by-step explanation:
_______________________________
Given:
y = x + 1;
y = 2x – 5 ;
_______________________________
2x – 5 = x + 1 ; Solve for "x" ;
Subtract "x" ; and Subtract "1" ; from Each Side of the equation:
2x – x – 5 – 1 = x – x + 1 – 1 ;
to get:
x – 6 = 0 ;
Now, add "6" to Each Side of the equation;
to isolate "x" on one side of the equation;
and to solve for "x" :
x – 6 + 6 = 0 + 6 ;
to get:
x = 6 .
_______________________________
Now, let us solve for "y" ;
We are given:
y = x + 1 ;
Substitute our solved value for "x" ; which is: "6" ; for "x" ; into this given equation; to obtain the value for "y" :
y = x + 1 ;
= 6 + 1 ;
y = 7 .
_______________________________
Let us check our answers by plugging the values for "x" and "y" ;
("6" ; and "7"; respectively); into the second given equation; to see if these values for "x" and "y" ; hold true:
Given: y = 2x – 5 ;
→ 7 =? 2(6) – 5 ?? ;
→ 7 =? 2(6) – 5 ?? ;
→ 7 =? 12 – 5 ?? ;
→ 7 =? 7 ?? ;
→ Yes!
_______________________________
The answer has one solution:
→ x = 6 ; y = 7 ; or, write as: [6, 7].
_______________________________
Hope this is helpful! Best wishes!
_______________________________
For the dilation, DO, K = (10, 0) → (5, 0), the scale factor is equal to _____.
Answer:
[tex] \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]scale \: factor = \frac{5}{10} = \frac{1}{2} \\ [/tex]
Solve this system using substitution then write your answer as an ordered pair (x,y) X-5y=4 and Y=2x+14
Answer:
(74/9,274/9)
Step-by-step explanation:
You have
x-5y=4 and
y=2x+14
so we subsitute y in the first equation
x-5(2x+14)=4
x-10x-70=4
-9x=74
x=74/9
so y=2(74/9)+14
y=148/9+14
y=274/9
so the oredered pair is
(74/9,274/9)
The solution of the system of equations given is (-74/9, -22/9).
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given linear equations are,
x - 5y = 4
y = 2x + 14
We have to solve this by substitution.
Substituting the value of y as y = 2x + 14 in the first equation x - 5y = 4,
x - 5 (2x + 14) = 4
By the distributive property,
x - 10x - 70 = 4
-9x = 74
x = -74/9
y = 2x + 14 = (2 × -74/9) + 14 = -22/9
Hence the solution of the system of equations as the ordered pair is (-74/9, -22/9).
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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
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
How would plot y=1/4x-4 on graph
Answer:
________________________
MAN IF U ANSWER THIS QUESTION U ENDED 2020 Which of the following is equal to the square root of the cube root of 6? 6 to the power of one sixth 6 to the power of one third 6 to the power of two thirds 6 to the power of three halves
Answer:
6 to the power of 1/6
Step-by-step explanation:
In general, a root is the same as a fractional power. That is, ...
[tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]
So, the square root of a cube root is ...
(6^(1/3))^(1/2)
According to the rules of exponents, a power of a power is ...
(a^b)^c = a^(bc)
so, the above root of a root is ...
(6^(1/3))^(1/2) = 6^((1/3)(1/2)) = 6^(1/6)
The square root of the cube root of 6 is 6 to the power of 1/6.
Answer:
A) 6^1/6 or 6 to the power of 1 sixth
A researcher used the technique with 9 students and observed that they had a mean of 10.8 hours with a standard deviation of 1.5. A level of significance of 0.05 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{10.8-11}{\frac{1.5}{\sqrt{9}}}=-0.4[/tex]
The degrees of freedom are given by:
[tex]df=n-1=9-1=8[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(8)}<-0.4)=0.350[/tex]
Since the p value is higher than the the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from the traditional methods.
Step-by-step explanation:
Assuming this first part of the problem obtained from the web: "Using traditional methods, it takes 11.0 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed"
Information given
[tex]\bar X=10.8[/tex] represent the mean height for the sample
[tex]s=1.5[/tex] represent the sample standard deviation
[tex]n=9[/tex] sample size
[tex]\mu_o =11[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to check if the true mean for this case is equal to 11 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 11[/tex]
Alternative hypothesis:[tex]\mu \neq 11[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{10.8-11}{\frac{1.5}{\sqrt{9}}}=-0.4[/tex]
The degrees of freedom are given by:
[tex]df=n-1=9-1=8[/tex]
And the p value would be given by:
[tex]p_v =P(t_{(8)}<-0.4)=0.350[/tex]
Since the p value is higher than the the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from the traditional methods.
Suppose the expected returns on equity of two firms, Macrosoft and Microsoft, that operate in the same business are 10.50% and 13.00%, respectively. What is the return on assets in this business if Macrosoft has no debt?
Answer:
The return on assets in this business for Macrosoft is
ROA = 10.50%
Step-by-step explanation:
Return on Equity:
ROE represents how much a firm is generating profits by using the shareholder's money.
ROE is calculated as
[tex]$ {ROE = \frac{Annual \:\: net\: \: income}{Average \:\: shareholder's \:\: equity} $[/tex]
Return on Assets:
ROA represents how much a firm is generating profits for every dollar of its assets.
ROA is calculated as
[tex]$ {ROA = \frac{Annual \:\: net\: \: income}{Total \:\: assests} $[/tex]
What is the return on assets in this business if Macrosoft has no debt?
Debt plays an important role in the calculations of return on assets.
We know that
Assets = Liabilities + Equity
Since the Macrosoft has no debt, its return on assets will be same as return on equity.
Assets = Equity
ROA = ROE
ROA = 10.50%
Help me with answer B
Thank you
Answer:
193.77 < p < 1806.23
Step-by-step explanation:
You want R(p) > 2,100,000, so ...
-6p^2 +12000p > 2100000
p^2 -2000p < -350000 . . . . divide by -6
Adding (2000/2)^2 = 1000000 will "complete the square".
p^2 -2000p +1000000 < 650000 . . . . complete the square
(p -1000)^2 < 650000
-√650000 < p -1000 < √650000 . . . . take the square root
1000 -806.23 < p < 1000 +806.23 . . . .add 1000
193.77 < p < 1806.23 . . . . range of prices for desired revenue
Please help me....I need it
Answer:
Volume: 3x2x4=24 so the volume is 24 Meter3
Surface area:
52 Square meter
f(x) = 2x – 1 g(x) = 7x – 12 What is h(x) = f(x) + g(x)?
After a 4% reduction, you purchase a new suit for $288. What was the original price of the suit?
Answer:
$300
Step-by-step explanation:
Let [tex]x[/tex] be the original price.
[tex]x \times (1-0.04)=288[/tex]
[tex]0.96x=288[/tex]
[tex]x=\frac{288}{0.96}[/tex]
[tex]x=300[/tex]
Answer:
$300
Step-by-step explanation:
If it was a 4% reduction then we get:
[tex]x*0.96=288\\[/tex]
Divide both sides by 0.96
[tex]x=300[/tex]
The original suit price was $300
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?
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]
What is the common difference of the sequence 20, 17, 14, 11, 8.... ?
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
what is the answer to the equation -(-(-(-2)))
Answer:
2
Step-by-step explanation:
Since there are four negative signs, we have -1 multiplying each other 4 times, multiplying by positive 2. This is then 1 * 2, which is 2.
Answer:
+2
Step-by-step explanation:
=> -(-(-(-2))))
=> -(-(+2))
=> -(-2)
=> +2
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.
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
Please answer this correctly
Answer:
80-119 ⇒ 5
Because
80-99 ⇒ 3
100-119 ⇒ 2
So 2+3 = 5
Answer:
80-119: 5
Step-by-step explanation:
If you just added up, you can find all the values.
Area of trapezoid 5 inch h=5 inch 15 inch
Answer:
50 in²
Step-by-step explanation:
If we assume that 5 inch and 15 inch are the base dimensions, the area formula tells us the area is ...
A = (1/2)(b1 +b2)h
A = (1/2)(5 in +15 in)(5 in) = 50 in²
The area of the trapezoid is 50 square inches.
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.
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