From the standard normal table, the respective probabilities are; 0.908 and 0.841
How to find the probability from z-score?
Formula for calculating the standard score or z score is:
z = (x - μ)/σ
where:
z is the standard score
x is the raw score
μ is the population mean
σ is the population standard deviation
A) We are given;
x = 95
μ = 110
σ = 15
Thus;
z = (95 - 110)/15
z = 1.33
From the normal standard distribution table we can find the probability from the z-score as;
P(x > 95) = 1 - 0.091759.
P(x > 95) = 0.908
B) We are given;
x = 125
μ = 110
σ = 15
Thus;
z = (125 - 110)/15
z = 1
From the normal standard distribution table we can find the probability from the z-score as;
P(x > 95) = 1 - 0.158655.
P(x > 95) = 0.841
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A newspaper article reported that people spend a mean of 7 hours per day watching TV, with a standard deviation of 1.8 hours. A psychologist would like to conduct interviews with the 5% of the population who spend the most time watching TV. She assumes that the daily time people spend watching TV is normally distributed. At least how many hours of daily TV watching are necessary for a person to be eligible for the interview? Carry your intermediate
According to the confidence interval only persons who watch at least 9.9 hours TV per day are eligible.
According to the statement
we have given that the mean of 7 hours per day watching TV, and a standard deviation of 1.8 hours.
And we have to find that the At least how many hours of daily TV watching are necessary for a person to be eligible for the interview.
So, For this purpose,
The confidence interval is is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level.
Let us Assume x is the amount of hours that 5% of the persons exceeds.
Then P(z<(x-7)/1.8) = 0.95
From a standard normal table, we know that:
(x-7)/1.8 = 1.6449
x-7 = 2.9607
x = 9.9607
So, According to the confidence interval only persons who watch at least 9.9 hours TV per day are eligible.
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Which expression shows the factored form of 49x² - y²?
Step-by-step explanation:
49x^2-y^2=(7x)^2-(y)^2
=(7x+y) (7x-y)
Therefore, a^2-b^3
=(a+b) (a-b)
Research suggests that students could benefit from later school starting times. A school administrative team is considering a proposal to move the starting time of the local schools one hour later than the current start time. To measure interest in the proposal, members of the team randomly select subjects attending a large high school soccer tournament played on the high school grounds on a Saturday morning. The team finds that 58% of those surveyed support a later high school start time. Which type of bias is most likely to be present in the survey results?
This is undercoverage bias because adults with older children are more likely to be included in the sample.
This is question wording bias because the phrasing of the later start times question may be confusing to some subjects.
This is nonresponse bias because some of those selected may choose to not provide their opinion on later start times.
This is voluntary response bias because vocal supporters of later start times will be more likely to offer their opinion.
The type of bias which is most likely to be present in the survey results is undercoverage bias because adults with older children are more likely to be included in the sample.
ResearchThis is a diligent inquiry or examination to seek or revise facts, principles, theories,or applications. It is used to make an extensive investigation or search for truth in an experiment.
Bias
In statistics, bias is the difference between the expectation of the sample estimator and the true population value, which reduces the representativeness of the estimator by systematically distorting it
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Merger_Model_Evaluation_-_Question.xlsx 19 The implied enterprise value of Snap Inc., calculated using the assumptions and acquisition premium provided, is: $92,165 $30,498 $92,661
$91,669
The implied enterprise value of Snap Inc., calculated using the assumptions and acquisition premium provided, is $91,669
How to calculate the value?Share Price, P = 44.29
Premium on the acquisition, p = 20%
Therefore, effective share price for acquisition, P* = P x (1 + p) = 44.29 x (1 + 20%) = $ 53.15
Number of shares outstanding, N = 1,734 MM
Equity value, E = P* x N = 53 x 1,734
= $92,158.63 MM
Net Debt, D = - 496
Hence, the implied enterprise value:
= Equity value + net debt
= 92,158.63 + (- 496)
= $$91,669
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Which pair of functions are inverses of each other? O A. F(a) = I - 9 and g(2) = 2*9 O B. Ax) = 5x - 11 and g(a) = 2+11 O C. F(a) = V2m and g(2) = (3) ° O D. f(a) = ; + 8 and g(x) = 6x - 8 SUBMIT
The pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5
How to determine the function and the inverse?The complete question is added as an attachment
Function 1
f(x) = 5x - 11 and g(x) = (x + 11)/5
Represent 5x - 11 with y in f(x) = 5x - 11
y = 5x - 11
Swap x and y
x = 5y - 11
Add 11 to both sides
x + 11 = 5y
Divide by 5
y = (x + 11)/5
Express as a function
g(x) = (x + 11)/5
From the question, we have:
f(x) = 5x - 11 and g(x) = (x + 11)/5
This means that the function g(x) is an inverse of the function f(x)
Hence, the pair of functions that are inverses of each other is (a) f(x) = 5x - 11 and g(x) = (x + 11)/5
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Deion misses 4% of the free throws he attempts in a seaon. How many total free throws did he attempt if he missed 17
Answer: 425
Step-by-step explanation:
Think of this problem as 4% of a number equals 17
since in math, the word 'of' usually means multiplication, we can think of it that way.
Also, 4% = 0.04
[tex]x*0.04=17[/tex]
[tex]0.04x=17[/tex]
[tex]\frac{0.04x}{0.04} =\frac{17}{0.04}[/tex]
[tex]x=425[/tex]
Slope 0, ordered pair -8, 4
Answer:
Step-by-step explanation:
y-4=0(x+8)
y-4=0
y=4
Answer:
i
Step-by-step explanation:
y-4=0(x+8)
y-4=0
y=4
A poll was conducted by a home mortgage company regarding home ownership in the United States. The company polled 1,488 Americans and found that 69% of those polled own a home. What is the approximate margin of error, assuming a 99% confidence level?
If the sample size is 1488 and confidence interval of 99% then the margin of error is 0.03088.
Given sample size of 1488, percentage of those polled own a home be 69% and confidence level be 99%.
We are required to find the approximate margin of error.
Margin of error is the difference between calculated values and real values.
n=1488
p=0.69
Margin of error=z*[tex]\sqrt{p(1-p)/n}[/tex]
Z score when confidence level is 99%=2.576.
Margin of error=2.576*[tex]\sqrt{0.69(1-0.69)/1488}[/tex]
=2.576*[tex]\sqrt{(0.69*0.31)/1488}[/tex]
=2.576*[tex]\sqrt{0.2139/1488}[/tex]
=2.576*[tex]\sqrt{0.0001437}[/tex]
=2.576*0.01198
=0.03088
Hence if the sample size is 1488 and confidence interval of 99% then the margin of error is 0.03088.
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Answer:
0.031
Step-by-step explanation:
Plato/Edmentum
If Amn, Bpq are two matrices, state the conditions when they are conformable for (i) addition, (ii) multiplication (iii) addition and multiplication.
Answer:
matrices can be added together if both have the same order
Addition is both commutative and associative
matrices can be multiplied together if the number of column in the right hand matrix equals the number of row in the left hand matrix
Proofs and congruent triangles ( serious full answers only or 1 star and report )
Answer:
There are 5 ways to find if two triangles are congruent.
SSS- {Side Side Side Congruence.}
This law of congruence states that if we have two triangles, each with the same measures on each 3 sides it deems the triangles congruent.
SAS- {Side Angle Side Congruence.}
This law of congruence states that if we have two triangles, with 2 equal sides and one angle which is common among them; the triangles are congruent.
ASA- {Angle Side Angle Congruence.}
This law of congruence states that if we have two triangles, with 2 congruent angle measures and 1 congruent side; the triangles are indeed congruent.
AAS- {Angle Angle Side Congruence.}
You may be wondering how this law of congruence differs from the previous one. ASA refers to any two angles and the included side, whereas AAS refers to the two corresponding angles and the non-included side.
HL- {Hypotenuse Leg Congruence.}
This law of congruence states that if we have two triangles, with a common (congruent) leg and hypotenuse; the triangles are congruent.
I really hoped this helped, if it didn't leave a comment I am always open to feedback. If it did let me know, brainiest is always appreciated!
Hope you have a great rest of your day.
Answer:
Step-by-step explanation:
for completeness, here is the answer again:
1 Given is correct
2 Definition of right angle is correct
3 should be sum of interior angles in a triangle
4 is substitution
5 subtracting 90degree from left and right hand side
6 is definition of complementary angles
Enter the correct answer in the box. If z>0, what is the quotient of 20 square root of z^6 • square root of 16x^7 in simplest radical form? If necessary, rationalize the denominator
The correct answer which represents the quotient of 20√z⁶ ÷ √16z⁷ in simplest radical form is; (5√z)/z.
What is the quotient of the expression in its simplest radical form?The quotient given can be evaluated by means of the laws of indices as follows;
20√z⁶ ÷ √16z⁷
= 20√z⁶ ÷ 4√z⁷
= 5 √(z⁶/z⁷)
= 5 √z^(-1)
= 5 × z^(-1/2)
= 5/√z
Hence, by rationalisation; we have;
= (5√z)/z.
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The equation y equals 15 times 2 to the power of t shows the number of infected people from an outbreak of the measles. The variable y represents the number of infected people, and t represents time in weeks. In how many weeks will the number of infected people reach 1200?
It will take 6 weeks for the number of infected people to reach 1200
How to determine the number of weeks?The function is given as:
y equals 15 times 2 to the power of t
Rewrite the function properly as follows
y = 15 * 2^t
When the population is 1200, the equation becomes
15 * 2^t = 1200
Divide both sides by 15
2^t = 80
Take the logarithm of both sides
t * log(2) = log(80)
Divide both sides by log(2)
t = 6.3
Approximate
t = 6
Hence, it will take 6 weeks for the number of infected people to reach 1200
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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 16 mm halfway across a horizontal distance of 80 mm.
Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
Answer:
[tex]\textsf{A)} \quad (x-40)^2=-100(y-16)[/tex]
B) Focus = (40, -9)
Directrix: y = 41
Axis of symmetry: x = 40
Step-by-step explanation:
The x-intercepts of a parabola are the points at which the curve intercepts the x-axis (when y = 0).
The x-coordinate of the vertex of a parabola is halfway between the x-intercepts.
The y-coordinate of the vertex if the minimum or maximum height of the parabola.
Part AA jumping spider's movement is modeled by a parabola.
Define the variables:
x = horizontal distance of the spidery = height of the spiderFrom the information given:
x-intercepts = (0, 0) and (80, 0)vertex = (40, 16)Standard form of a parabola with a vertical axis of symmetry:
[tex](x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0[/tex]
Vertex: (h, k)Focus: (h, k+p)Directrix: y = (k-p)Axis of symmetry: x = hIf p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.
Substitute the vertex (40, 16) and one of the x-intercept points (0, 0) into the formula and solve for p:
[tex]\implies (0-40)^2=4p(0-16)[/tex]
[tex]\implies 1600=-64p[/tex]
[tex]\implies p=-25[/tex]
Substitute the vertex and the found value of p into the formula:
[tex]\implies (x-40)^2=4(-25)(y-16)[/tex]
[tex]\implies (x-40)^2=-100(y-16)[/tex]
Part BGiven:
Vertex = (40, 16) ⇒ h = 40 and k = 16p = -25Substitute the given values into the formulas for focus, directrix and axis of symmetry:
Focus
⇒ (h, k+p)
⇒ (40, 16 + (-25)))
⇒ (40, -9)
Directrix
⇒ y = (k-p)
⇒ y = (16 - (-25))
⇒ y = 41
Axis of symmetry
⇒ x = h
⇒ x = 40
Which expressions are equivalent to 2(4f + 2g)?
Answer:
For example, 8f + 4g is one of the most used expression
Another example is 4 (2f + g), is correct too
At a hockey game, a vender sold a combined total of 210 sodas and hot dogs. The number of sodas sold was 36 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
123 soda and 87 hot dogs
Step-by-step explanation:
Let s = # soda and h = # hot dogs
s + h = 210 s = h + 36 Substitute the h + 36 for s into the first equation
s + h = 210
(h + 36) + h = 210
h + 36 + h = 210 Combine the h's
2h + 36 = 210 Subtract 36 from both sides
2h = 174 Divide both sides by 2
h = 87 This is the number of hot dogs. Substitute this into either equation above to find the sodas.
s + h = 210
s + 87 = 210
s = 123
OR
s = h + 36
s = 87 + 36
s = 123
11. Use the following information for problems a-b. The table shows the results of a school lunch survey. In the
survey, students were asked whether they have chores and a curfew
Using it's concept, the probabilities are given as follows:
a) C. 7/20.
b) D. 15/22.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For item a, we have that there are 60 students with no curfew, and of those, 21 have no chores, hence the probability is given by:
p = 21/60 = 7/20
Which means that option C is correct.
For item b, we have that there are 66 students with no shores, and of those, 45 have a curfew, hence the probability is given by:
p = 45/66 = 15/22
Which means that option D is correct.
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A golf lesson lasts from 10:00 a.m. - 11:15 a.m. and includes a 15 minute break with equal lengths of time before and after the break. At what time should the break start?
The time at which the break started is 10 : 30 am.
What time did the break start?The first step is to convert the time between 10:00 a.m. - 11:15 a.m. to minutes.
The time between 10:00 a.m. - 11:15 a.m. is 1 hour 15 minutes
In order to convert hours to minutes, multiply hour by 60
1 x 60 = 60 minutes
60 minutes + 15 minutes = 75 minutes
The second step is to subtract the time from the break from the duration of the golf lesson
75 minutes - 15 minutes = 60 minutes
The third step is to divide 60 minutes into equal halves by dividing 60 by 2
60 / 2 = 30 minutes
The last step is to add 30 minutes to the time the lesson started : 10 : 00 am + 30 minutes = 10 : 30 am
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what’s the approximate value of tan 1
Answer: tan 1 radians = 1.557, tan 1 degrees = 0.017
What is the length of the transverse axis (y-2)^2/16 - (x+1)^2/144= 1
The length of the transverse axis is 8.
What is transverse axis length?The transverse axis of the hyperbola is the straight line connecting vertices A and A'. The line segment connecting the vertices of a hyperbola is referred to as the transverse axis or AA'.The hyperbola's equation is expressed as (yk)2b2(xh)2a2=1). The center is (h,k), b defines the transverse axis, and a defines the conjugate axis. The section of a line where a hyperbola's vertices form.Given the equation of hyperbola:[tex]\frac{(y-2)^{2} }{16}[/tex][tex]-\frac{(x+1)^{2} }{144 }[/tex][tex]=1[/tex]
Rewrite this equation as [tex]\frac{(y-2)^{2} }{4^{2} }[/tex][tex]-\frac{(x+1)^{2} }{12^{2} }[/tex][tex]=1[/tex]
When comparing this equation to the common hyperbola equation with a vertical transverse axis is [tex]\frac{(y-k)^{2} }{a^{2} }[/tex][tex]-\frac{(x+h)^{2} }{b^{2} }[/tex][tex]=1[/tex]
[tex]h = -1[/tex]
[tex]k= -2[/tex]
[tex]a = 4[/tex]
[tex]b = 12[/tex]
The length of the transverse axis is[tex]2a = 2*4[/tex]
[tex]=8.[/tex]
The length of the transverse axis is 8.
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Your Turn
Solve the equation by using Properties of Equality.
3. 5x − 10 = 20
4.
+9=21
Answer: for number 3, x= 6
Step-by-step explanation:
Because of stormy weather a pilot flying at 35,000 ft descends 8,000 ft.
What is his new altitude
Answer:
35,000 - 8000=27,000 altitude
If a square root parent function is vertically stretched by a factor of 6, what is
the equation of the new function, G(x)?
OA. G(x) = -6√√x
O B. G(x)=√x
OC. G(x) = √6x
O D. G(x) = 6-√x
Parent function = √x
On stretching vertically by factor of 6
New function G(x) = 6√x
1. How many fifties are there in one hundred thousand?
pls I need the ans as quickly as possible
The guy wire is approximately blank feet long
Answer: The guy wire = 393.4 ft
Step-by-step explanation:
Given images:
Refer to the attachment below (I apologize for the bad writing on the computer)
Given information:
Height of the tower = 175 ft
Height of the wire = 15 ft from the top (Opposite)
Angle with the ground = 24°
Length of wire = Unknown (Hypotenuse)
Determine the trigonometric function:
The primary choice will be the Sine function because the angle is opposite to the height and the wire is the hypotenuse of the system.
Determine the equation:
sin θ = (Opposite) / (Hypotenuse)
sin (24°) = (175 - 15) / (Length)
Simplify value in parenthesis
sin (24°) = (160) / (Length)
Multiply the Length of wire on both sides
sin (24°) * (Length) = (160) / (Length) * (Length)
sin (24°) * (Length) = (160)
Divide sin (24°) on both sides
sin (24°) * (Length) / sin (24°) = (160) / sin (24°)
Length = 160 / sin (24°)
[tex]\Large\boxed{Length~=~393.4~ft}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Suppose that 5 workers can complete a certain task in 12 days. If there are 4 workers, how many days would it take for them to finish the same task
Answer:
15 days
Step-by-step explanation:
5 workers times 12 days is 60 days per worker which gets reduced based on how many workers there are. 60 divide by 4 workers now brings down to 15 days. 5 workers, 12 days. 10 workers 6 days etc.
Please help 50 points
Answer:
m∠RQS = 109°
Step-by-step explanation:
Angles on a straight line sum to 180°.
Therefore:
⇒ m∠RQS + m∠SQT = 180°
⇒ (15x + 4) + (10x + 1) = 180
⇒ 15x + 4 + 10x + 1 = 180
⇒ 15x + 10x + 4 + 1 = 180
⇒ 25x + 5 = 180
⇒ 25x + 5 - 5 = 180 - 5
⇒ 25x = 175
⇒ 25x ÷ 25 = 175 ÷ 25
⇒ x = 7
Now that we have found the value of x, substitute this into the expression for m∠RQS:
⇒ m∠RQS = 15(7) + 4
= 105 + 4
= 109°
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Interpreting Slope in a Line of Best Fit
Use the scatterplot and equation to answer the question.
AY
180+
160+
140+
120+
100+
80+
Number of Customers Served
2
60+
40+ y= 17.9x+6.67
20+
3 4 5 6 7 8 9
Number of Hours
x
The data reflects the number of hours an employee
spends working a checkout line (x), paired with the
number of customers served (y). How can the slope of
the line be interpreted?
With each additional hour, between 6 and 7
customers are served.
With each additional hour, nearly 18 customers are
served.
Each additional customer requires 17.9 minutes to
check out.
O Each additional customer requires 6.67 minutes to
check out.
Done
Answer:
b
Step-by-step explanation:
b
A poster is 15 inches wide by 24 inches tall. A smaller version of the same poster is created using a scale factor of 2/3. What is the area of the smaller poster
The area of the small poster is 160 inches square
How to determine the area
From the information given, we have the poster to take the form of a rectangle
The formula for area of a rectangle is;
Area = length × width
For the smaller poster created using a scale of factor 2/3
Length = 2/ 3 × 24
Length = 16 inches
Width = 2/ 3 × 15
Width = 10 inches
Substitute into the formula
Area = 16 × 10
Area = 160 inches square
Thus, the area of the small poster is 160 inches square
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SOMEONE PLEASE HELP ASAPP I NEED HELP
Answer:
11
Step-by-step explanation:
NO LINKS!! Please help me with this problem
Information : The given hyperbola is a horizontal hylerbola with its centre (3 , -5) and one of its focus at (9 , -5) and vertex at (7 , -5) and as we can see that the focus and vertex have same y - coordinates, it must have its Transverse axis on line y = - 5.
Now,
it's vertex is given, I.e (7 , -5)
so, length of semi transverse axis will be equal to distance of vertex from centre, i.e
a = 7 - 3 = 4 unitsNow, it's focus can be represented as ;
[tex]\qquad \sf \dashrightarrow \: (3 + ae, - 5 )[/tex]
so,
ae + 3 = 9and we know, a = 4
[tex]\qquad \sf \dashrightarrow \: 4e + 3 = 9[/tex]
[tex]\qquad \sf \dashrightarrow \: 4e = 6[/tex]
[tex]\qquad \sf \dashrightarrow \: e = \cfrac{3}{2} [/tex]
Now, let's find the measure of semi - conjugate axis (b)
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = {a}^{2} ( {e}^{2} - 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{9}{4} - 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{9 - 4}{4} )[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{5}{4} )[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 20[/tex]
[tex]\qquad \sf \dashrightarrow \: b = \sqrt{20} [/tex]
So, it's time to write the equation of hyperbola, as we already have the values of a and b ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {(x - h)}^{2} }{ {a}^{2} } - \cfrac{( {y - k)}^{2} }{ {b}^{2} } = 1[/tex]
[ plug in the values, and h = x - coordinate of centre, and k = y - coordinate of centre ]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ ({x-3)}^{2} }{ {16}^{} } - \dfrac{ {(y+5)}^{2} }{ { {20} }^{} } = 1[/tex]
Hello and Good Morning/Afternoon:
Let's solve this problem step-by-step:
Let's find the format of the standard form of hyperbole:
[tex]\hookrightarrow \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} =1[/tex]
(h,k): hyperbole center ⇒(3,-5)Let's find the value of a, b:
value of a: distance between vertex (7, -5) and center (3, -5)[tex]a = \sqrt{(7-3)^2+(-5--5)^2} =\sqrt{16} =4[/tex]
value of b: [tex]\sqrt{c^2-a^2}[/tex]⇒value of c: distance between focus (9, -5) and center (3, -5)
[tex]c = \sqrt{(3-9)^2+(-5--5)^2}=\sqrt{36} =6[/tex]
⇒ therefore:
[tex]b = \sqrt{c^2-a^2} =\sqrt{6^2-4^2}=\sqrt{20}[/tex]
Let's plug everything into our standard form of the equation:
[tex]\frac{(x-3)^2}{4^2} -\frac{(y--5)^2}{(\sqrt{20})^2 } =1\\\frac{(x-3)^2}{16} -\frac{(y+5)^2}{20 } =1[/tex] <== Answer
Hope that helps!
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