Answer:
Z = (42-20)/4 = 5.5
Z = X-μ / σ
Step-by-step explanation:
The z-score for the data value of 42 is 5.5.
What is a z-score?A z-score is defined as the fractional representation of data point to the mean using standard deviations.
Formula of z-score = (X - μ) / σ
Given,
μ = 20
σ = 4
X = 42
z-score = (X - μ) / σ
Substitute the values,
z-score = (42-20)/4
z-score = 22/4
z-score = 5.5
Hence, the z-score for the data value of 42 is 5.5.
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a store sign reads "Take 75% of the original price when you take an additional 15% off the sale price, which is 60% off the original price." Is the stores sign accurate?
Answer:
The new price is 66% off the original not 75% off
Step-by-step explanation:
Let x be the original price
First take 60 percent off
x - x*60% = new price
x- .60x = .40x
The new price is .40x
Then take 15 % off
(.40x) - (.40x)*15%
.40x - .40x*.15
.40x - .06x
.34x
100 -.34 =.66
The new price is 66% off the original not 75% off
A superhero can fly from New York to Los Angeles in 30 minutes. The distance from New York to Los Angeles is approximately 2,450 miles.
How many miles per hour is the superhero flying?
Work Shown:
30 min = 30/60 = 0.5 hours
distance = rate*time
rate = distance/time
rate = (2450 miles)/(0.5 hours)
rate = (2450/0.5) mph
rate = 4900 mph
For the sake of comparison, a typical commercial passenger jet can reach max speeds of about 600 mph.
Consider this equation. √x - 1 - 5 = x - 8 The equation has(two valid solutions, one valid solution) and(one extraneous solution, no extraneous solutions) A valid solution for x is(0, 4, 2, 5)
The equation has 2 valid solutions; no extraneous solutions
The given equation is:
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
First, we determine the solutions
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
Add 5 to both sides
[tex]\sqrt{x - 1} = x - 8 + 5[/tex]
[tex]\sqrt{x - 1} = x - 3[/tex]
Square both sides
[tex]x - 1 = (x - 3)^2[/tex]
Expand
[tex]x - 1 = x^2- 3x - 3x + 9[/tex]
[tex]x - 1 = x^2- 6x + 9[/tex]
Collect like terms
[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]
[tex]x^2 - 7x + 10 = 0[/tex]
Expand again
[tex]x^2 - 2x-5x + 10 = 0[/tex]
Factorize
[tex]x(x - 2) -5(x -2)= 0[/tex]
Factor out x - 2
[tex](x - 5)(x -2)= 0[/tex]
Split
[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]
[tex]x= 5[/tex] or [tex]x = 2[/tex]
The above values are valid values of x.
Hence, the equation has 2 valid solutions; no extraneous solutions
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Answer:
That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.
Step-by-step explanation:
for plato users
What is the product of 2/5 × 3/4?
Answer:
3/10
Step-by-step explanation:
2/5*3*4
=6/20
=3/10
A circular fence is being placed to surround a tree. The diameter of the
fence is 4 feet. How much fencing is used? *
Answer:
12.6 ft
Step-by-step explanation:
If P is (-5, 4) and Q is (7, -5), what is 2/3 of that?
Answer: 10
Step-by-step explanation:
Sqrt (7- -5)^2+(-5-4)^2 =
Sqrt (12)^2+(-9)^2 =
Sqrt 225 = 15
2/3 * 15 = 30/3 = 10
10 times as much as 9
Answer:
90
Step-by-step explanation:
10 x 9
=> 90
10 times 9 is 90.
In an experiment, you choose to have two randomly assigned groups. In one, you take measurements both pretest and posttest; with the second, a posttest-only measure. This describes which task of conducting an experiment
Answer:
The answer is "Specific treatment levels".
Step-by-step explanation:
When we experimenting with 'level' which is related to the quantity or magnitude of treatment. For this part of an experiment or study, a group or individual is exposed to a specified set of circumstances. For example: If four categories are exposed to different doses of a given drug, then each dose reflects a level of a treatment factor in the model.
Nasa is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before the launch and has a diameter of 4.7 feet. What is the total weight in pounds?
Answer:
Step-by-step explanation:
Algebra 2, please help! thank you
The function y = 2 cos 3(x + 2π∕3) +1 has a phase shift (or horizontal shift) of
A) –2π∕3
B) 3
C) 1
D) 2
Answer:
-2pi/3
Step-by-step explanation:
y = 2 cos 3(x + 2π∕3) +1
y = A sin(B(x + C)) + D
amplitude is A
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
We have a shift to the left of 2 pi /3
Answer:
A
Step-by-step explanation:
The standard cosine function has the form:
[tex]\displaystyle y = a\cos (b(x-c)) + d[/tex]
Where |a| is the amplitude, 2π / b is the period, c is the phase shift, and d is the vertical shift.
We have the function:
[tex]\displaystyle y = 2 \cos 3\left(x + \frac{2\pi}{3}\right) + 1[/tex]
We can rewrite this as:
[tex]\displaystyle y = \left(2\right)\cos 3\left(x - \left(-\frac{2\pi}{3}\right)\right) + 1[/tex]
Therefore, a = 2, b = 3, c = -2π/3, and d = 1.
Our phase shift is represented by c. Thus, the phase shift is -2π/3.
Our answer is A.
If a=120° , find the measure of angles b, c and d.
Explain your reasoning.
Answer:
b=120°
c=60°
d=60°
SEE THE IMAGE FOR SOLUTION
Of the travelers arriving at a small airport, 60% fly on major airlines, 20% fly on privately owned planes, and the remainder fly on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 50% are traveling for business reasons, whereas 70% of those arriving on private planes and 80% of those arriving on other commercially owned planes are traveling for business reasons. Suppose that we randomly select one person arriving at this airport.
What is the probability that the person
a. is traveling on business?
b. is traveling for business on a privately owned plane?
c. arrived on a privately owned plane, given that the person is traveling for business reasons?
d. is traveling on business, given that the person is flying on a commercially owned plane?
Answer:
a) 0.55 = 55% probability that the person is traveling on business
b) 0.14 = 14% probability that the person is traveling for business on a privately owned plane.
c) 0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.
d) 0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
50% of 60%(major airlines)
70% of 20%(privately owned airplanes)
80% of 100 - (60+20) = 20%(comercially owned airplanes). So
[tex]p = 0.5*0.5 + 0.7*0.2 + 0.8*0.2 = 0.55[/tex]
0.55 = 55% probability that the person is traveling on business.
Question b:
70% of 20%, so:
[tex]p = 0.7*0.2 = 0.14[/tex]
0.14 = 14% probability that the person is traveling for business on a privately owned plane.
Question c:
Event A: Traveling for business reasons.
Event B: Privately owned plane.
0.55 = 55% probability that the person is traveling on business.
This means that [tex]P(A) = 0.55[/tex]
0.14 = 14% probability that the person is traveling for business on a privately owned plane.
This means that [tex]P(A \cap B) = 0.14[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.14}{0.55} = 0.2545[/tex]
0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.
Question d:
Event A: Commercially owned plane.
Event B: Business
80% of those arriving on other commercially owned planes are traveling for business reasons.
This means that:
[tex]P(B|A) = 0.2[/tex]
0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.
The acute angle of the right angle triangle are in the ratio of 4:5
Answer:
Since the triangle is a right angled triangle, one of the angles is 90°. In the right angled triangle, the acute angles are in the ratio 4:5. Let the measures of the acute angles of the triangle in degrees be 4k and 5k, where k is a constant.
Step-by-step explanation:
hope it helps.
Answer:
40and50
Step-by-step explanation:
let the acute angles be 4x and 5x then,
4x+5x+90=180 [sum of all angles of a right angled triangle]
or,9x=180-90
or,x=90/9
x=10
4x=4×10=40
5x=5×10=50
6x + 7y = 4x + 4y
Complete the missing value in the solution to the equation.
( ?,-4)
Hi there!
»»————- ★ ————-««
I believe your answer is:
(6, -4)
[tex]x = 6[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
We would need to solve for 'x'. We are already given the 'y' value of '-4', so we would need to substitute y for '-4', and then undo operations to isolate 'x'.⸻⸻⸻⸻
[tex]\rightarrow 6x + 7(-4) =4x + 4(-4)\\\\\rightarrow 6x - 28 = 4x - 16\\\\\rightarrow 6x - 28 + 28 = 4x - 16 + 28\\\\\rightarrow 6x = 4x + 12\\\\\rightarrow 6x - 4x = 4x - 4x + 12\\\\\rightarrow 2x = 12\\\\\rightarrow \frac{2x=12}{2}\\\\\rightarrow \boxed{x = 6}[/tex]
⸻⸻⸻⸻
The '6' would replace the question mark.
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
-1/5y+7=7
What is the value of y?
find the solution to the system of equations.
y= -7x + 3
y= -x - 3
Answer:
x = 1 y = -4
Step-by-step explanation:
-7x + 3 = -x - 3
-7x = -x - 6
-6x = -6
x = 1
y = - (1) - 3
y = -1 - 3
y = -4
Assume a researcher wants to compare the mean Alanine Aminotransferase (ALT) levels in two populations, individuals who drink alcohol and individuals who do not drink alcohol. The mean ALT levels for the individuals who do not drink alcohol is 32 with a standard deviation of 14, and 37 individuals were in the sample. The mean ALT levels for individuals who drink alcohol is 69 with a standard deviation of 19, and 38 individuals were in the sample. Construct and interpret a 95% confidence interval demonstrating the difference in means for those individuals who drink alcohol when compared to those who do not drink alcohol.
a. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.22 and 39.78.
b. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.33 and 39.67
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
d. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.41 and 39.59.
Answer:
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
Step-by-step explanation:
Given :
Groups:
x1 = 69 ; s1 = 19 ; n1 = 38
x2 = 32 ; s2 = 14 ; n2 = 37
1 - α = 1 - 0.95 = 0.05
Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :
The confidence interval obtained is :
(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between
(24.32 ; 39.68) .
A line is perpendicular to the line y = 4x - 3 and has x-intercept (2,0). Which of the following is an equation of the line?
Answer:
y = -1/4x+1/2
Step-by-step explanation:
y = 4x - 3
This is in slope intercept form, y = mx+b where the slope is m
The slope is 4
Perpendicular lines have slopes that are negative reciprocals
-1/4 is the slope of the perpendicular line
y = -1/4x+b
Using the point (2,0)
0 = -1/4(2)+b
0 = -1/2+b
b = 1/2
y = -1/4x+1/2
Yemi earns 8000naira a month and Bisi earns 6000naira a month. Find the ratio between their income.
Answer:
8:6
or
4:3
Step-by-step explanation:
How much state tax is withheld from $36,200 if the tax rate is 4%?
Answer:
$1448
Step-by-step explanation:
Tax=rate*amount=(4/100)*36200=1448
A survey is sent out to 500 people asking questions related to the link between religion and sexual behavior at a young age. The survey does not have any tracking device, and the results are sent to a database that gives no indication of who or where the results came from. However, the database is posted online for religion and human behavior researchers to freely conduct statistical analyses. The responses to this survey are
a. both confidential and anonymous.
b. confidential only.
c. anonymous only.
d. neither confidential nor anonymous.
Answer:
c
Step-by-step explanation:
Since the the identities of the survey takers were kept secret, it would be anonymous. If it wasn't anonymous, then people would know who took the survey.
Since the survey results were released online for analyses, it is not confidential. If it were to be confidential, then the survey distributors would have kept the results to themseles.
CHứng minh rằng trong hệ g - phân với 2
HELP ME OUT ASAPPP PLSSS
Answer:
https://linksharing.samsungcloud.com/ul5cX9oOmhzt
True or false? The polynomial 3xy + 4z - 8 is a trinomial.
Answer:
False is the answer.Step-by-step explanation:
answer is False.Answer:
True.
Step-by-step explanation:
A trinomial is an algebraic expression consisting of 3 terms. The terms in this instance are: 3xy, 4z, and -8.
what us 10 to the power of two
the answer is
10² ( ten square )
step by step :
10² = 10 × 10
= 100
Answer: 100
Step-by-step explanation: 10*10=100
Find the missing side round your answer to the nearest tenth
Answer:
x=13.2
Step-by-step explanation:
cos(43)=x/18
x=18×cos(43)
x=13.2
Answered by GAUTHMATH
2. Mandla spent one quarter of his pocket money on sweets. a. What fraction does he have left? b. If he had R40 pocket money, how much did he spend?
Answer:
a. 3/4 of pocket money left
b. R10
Step-by-step explanation:
a. 4/4 - 1/4 = 3/4
b. 40/4 = 10 = 1/4 of pocket money
(a). The fraction of pocket money left is 3/4
(b). If he had R40 pocket money, he spend R10.
What is the Ratio?The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
Operators which let do basic mathematical calculation
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
Mandla spent one-quarter of his pocket money on sweets
Let x be the total amount of pocket money Mandla had originally
Solution of (a).
⇒ x - (1/4)x
⇒ (3/4)x
The fraction of pocket money left = 3/4
Solution of (b).
1/4 of pocket money
⇒ (1/4)x
⇒ (1/4)40
⇒ 10
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The distribution of SAT scores is approximately normal with a mean of 1500.
If 1628 is the 90th percentile, what is the standard deviation?
Answer:
Hello,
Answer
[tex]\sigma=457,95...[/tex]
Step-by-step explanation:
p(z<a)=0.9
p(z<1.29)=0.9015
p(z<1.28)=0.8997
using linear interpolation: with 4 decimals
p(z<1.282)<0.9
[tex]\dfrac{1628-1500}{\sigma} =1.282\\\\\sigma =\dfrac{1628-1500}{1.282}\\\\\sigma=457,95...\\[/tex]
T
On Melissa's 6th birthday, she gets a $2000 CD that earns 5% interest, compounded semiannually. If the
CD matures on her 16th birthday, how much money will be available?
TE
$
(S
9514 1404 393
Answer:
$3277.23
Step-by-step explanation:
The future value of the CD with interest at rate r compounded semiannually for t years will be given by ...
A = P(1 +r/2)^(2t)
where P is the principal value.
For the given rate and time, this is ...
A = $2000(1 +0.05/2)^(2·10) = $2000(1.025^20) ≈ $3277.23
The value of the CD at maturity will be $3277.23.
1/10 + 3/5
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