Answer:
x=-1
Step-by-step explanation:
Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.
Find the percent of her laps that are completed in less than 134 seconds. (Round your answer to two decimal places.)
The fastest 5% of her laps are under how many seconds? (Round your answer to two decimal places.)
sec
Answer:
97% of her laps are completed in less than 134 seconds.
The fastest 5% of her laps are under 125.96 seconds.
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 = 129.71, \sigma = 2.28[/tex]
Find the percent of her laps that are completed in less than 134 seconds.
We have to find the pvalue of Z when X = 134. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{134 - 129.71}{2.28}[/tex]
[tex]Z = 1.88[/tex]
[tex]Z = 1.88[/tex] has a pvalue of 0.9699, so 97% of her laps are completed in less than 134 seconds.
The fastest 5% of her laps are under how many seconds?
This is the 5th percentile of times, which is X when Z has a pvalue of 0.05, that is, X when Z = -1.645. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 129.71}{2.28}[/tex]
[tex]X - 129.71 = -1.645*2.28[/tex]
[tex]X = 125.96[/tex]
The fastest 5% of her laps are under 125.96 seconds.
A student used f(x)=5.00(1.012)^x to show how the balance in a savings account will increase over time. What does the 5.00 represent?
Answer:
x=0, which represents the savings at the beginning of the savings plan
Step-by-step explanation:
Intercept, when x (the number of years/months) is zero. which represents the savings at the beginning of the savings plan
Laura is saving money to buy a game. The game cost $36, and so far she has saved three- fourths of this cost. How much money has Laura saved
Answer:
27
Step-by-step explanation:
3/4*36=27
therefore the answer is
27
Find the area of the following shape. You must show all work to receive credit A (-4, 0), B(0, 4), C(2, 2), D(1,0)
9514 1404 393
Answer:
13 square units
Step-by-step explanation:
See the attached figure.
The horizontal dashed line divides the figure into two pieces:
a triangle 4 wide and 2 higha trapezoid 2 high with bases 5 and 4The appropriate area formulas can be used to find the areas of these. The figure's area will be their sum.
A = (1/2)bh = (1/2)(4)(2) = 4 . . . . square units
A = (1/2)(b1 +b2)h = (1/2)(5 +4)(2) = 9 . . . . square units
The area of the shape is ...
(4 +9) square units = 13 square units
Simplify 42/56 i am gonna need to show work so i dont fail
Answer:
42/56 = 3/4
Step-by-step explanation:
Answer:
The simplified fraction is [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Simplifying Fractions
A given fraction [tex]\frac{a}{b}[/tex] can be simplified if a and b have common factors, i.e. if they can be evenly divided by at least one equal number.
The fraction is:
[tex]\frac{42}{56}[/tex]
We'll simplify it by 2 since both numbers are even:
[tex]\frac{42}{56}=\frac{21}{28}[/tex]
The next prime common factor is 7. Dividing by 7:
[tex]\frac{42}{56}=\frac{21}{28}=\frac{3}{4}[/tex]
Thus, the simplified fraction is [tex]\frac{3}{4}[/tex]
what is 49/100 as a decimal?
Answer:
0.49
Step-by-step explanation:
49/100 = 0.49
I uh apparently need to explain more
Express in simplest radical form
Answer:
gg
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
2 x 2 =4
What is the value of the angle on the top left of this quadrilateral
112°
88°
90°
70°
Can anyone help me pls
Answer:0.125
Step-by-step explanation:
There is only 1/8 that is whistle so convert into percent and get 0.125. Hope this helps
Answer:
0.125
Step-by-step explanation:
There are 8 possibilities.
Only 1 whistle.
1/8 = 0.125
HELP I'M BEING TIMED I WILL GIVE 5 points... a thankyou...5 stars... and a brainliast if correct.
Geoffrey is evaluating the expression StartFraction (negative 3) cubed (2 Superscript 6 Baseline) Over (Negative 3) Superscript 5 Baseline (2 squared) EndFraction as shown below.
StartFraction (negative 3) cubed (2 Superscript 6 Baseline) Over (Negative 3) Superscript 5 Baseline (2 squared) EndFraction = StartFraction (2) Superscript a Baseline Over (negative 3) Superscript b Baseline EndFraction = StartFraction c Over d EndFraction
What are the values of a, b, c, and d?
A. a = 4, b = 2, c = 16, d = 9
B. a = 4, b = negative 2, c = 16, d = 9
C. a = 8, b = 8, c = 256, d = 6,561
D. a = 8, b = 8, c = 256, d = negative 6,561
Answer:
i think its a or d but im hoorible at math so if its wrong im sorry
Step-by-step explanation:
Answer:
a = 4, b = 2, c = 16, d = 9
Step-by-step explanation:
Solving the first part of the question by indices,
Comparing the rightmost term with the second term in the question,
a = 4, b = 2
Solving on,
Comparing with the final term in the question,
c = 16 and d = 9
Therefore,
a = 4, b = 2, c = 16, d = 9
Step-by-step explanation:
Chase is making a cake for his daughter's birthday. The normal recipe calls for 8 ounces of butter and 16 ounces of sugar. Chase then decides to make a slightly smaller cake and only use 6 ounces of butter. How many ounces of sugar will he need in his smaller cake?
Answer:
A lot
Step-by-step explanation:
Why am I baking cakes. I SUCK.
There are 12 ounces of sugar will he need in his smaller cake.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The normal recipe calls for 8 ounces of butter and 16 ounces of sugar.
Let the amount of sugar will he need in his smaller cake = x
So, By definition of proportion, we get;
⇒ Amount of Butter / Amount of Sugar
⇒ 8 / 16 = 6 / x
⇒ x = 6 × 16 / 8
⇒ x = 12 ounces
Learn more about the proportion visit:
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x^2+24x+c
I need help
Answer: c=144
Step-by-step explanation:
Which is bigger 57.8% or 0.578 ?
Answer:
They are the same
Step-by-step explanation:
When you convert 0.578 into a percentage you get 57.8%
When you convert 57.8% into a decimal you get 0.578
Stella is going to invest in an account paying an interest rate of 7% compounded
continuously. How much would Stella need to invest, to the nearest ten dollars, for
the value of the account to reach $1,650 in 9 years?
Answer:
$901.64
Step-by-step explanation:
Given data
rate= 7%
Final amount = $1650
time= 9 years
Let us apply the compound interest formula to solve for the Principal amount P
A=P(1+r)^t
substitute
1650=P(1+0.07)^9
1650=P(1.07)^9
1650=P1.84
Divide both sides by 1.84
P=1650/1.83
P=901.64
Hence she needs to invest $901.64
Answer:
880
Step-by-step explanation:
Find all values of X,where |x| = 11.
Answer:
X = 11 or -11
Step-by-step explanation:
Amelia pays $24 to rent a boat at the lake for up to six hours she constructs the inequality and number line below to represent the number of hours X she can use the boat?
how many HOURS are in d days and h hours?!
Answer:
24
Step-by-step explanation:
because its 24 gkrjkkmn lol
PLEASE HELP I NEED HELP WITH AN ALGEBRA 2 QUESTION ILL GIVE BRAINLEST
Answer:
the zeros of the function are those that result, when plugged into the equation, in zero; the zeros are -3, 1, and 1/2
Step-by-step explanation:
all possible factors:
±3/2, ±1/2, ±3, ±1
2x³ + 3x² - 8x + 3
let '2' = p and let '3' = q
factors of 'p' are 1 and 2
let '3' = q
factors of 'q' are 1 and 3
possible factors are q/p
Question 3 of 5
Is either x = 5 or x= 15 a solution to 25 – x= 5?
A. x= 15 is a solution, but x = 5 is not.
B. Neither is a solution.
C. They are both solutions.
O D. x = 5 is a solution, but x = 15 is not.
Answer:
B
Step-by-step explanation:
Neither is a solution because when you subtract 5 from 25 you get 20.
The number of transistors per IC in 1972 seems to be about 4,000 (a rough estimate by eye). Using this estimate and Moore's Law, what would you predict the number of transistors per IC to be 20 years later, in 1992?
From the Moore's Law, the predicted number of transistors per IC in 1992 would be approximately 4,096,000.
Given data:
Based on this exponential growth pattern, use the estimate of 4,000 transistors per IC in 1972 to predict the number of transistors per IC in 1992.
To predict the number of transistors per IC in 1992, determine how many doublings occurred during the 20-year period from 1972 to 1992.
Since each doubling represents a multiplication by 2, calculate the number of doublings as follows:
Number of doublings = (1992 - 1972) / 2
Number of doublings = 20 / 2
Number of doublings = 10
Now, use this number of doublings to predict the number of transistors per IC in 1992:
Predicted number of transistors per IC in 1992 = 4,000 * (2^10)
Predicted number of transistors per IC in 1992 = 4,000 * 1,024
Predicted number of transistors per IC in 1992 ≈ 4,096,000
Hence, based on Moore's Law and the estimate of 4,000 transistors per IC in 1972, the predicted number of transistors per IC in 1992 would be approximately 4,096,000.
To learn more about Moore's Law, refer:
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If Angela's $98,760 home appreciates three percent a year, what is the appreciated
value in 5 years?
Answer:
2962.8
Step-by-step explanation:
you wants to divide how much percent into the house in three years then the answer would be
Which statement is represented by the equation 3x +0.6 = 7?
A.The product of 3 and x added to 0.6 is equal to 7
B. The sum of x and 0.6 multiplied by 3 is equal to 7
C.The product of 3 times the sum of x and 0.6 is equal to 7
D.The sum of 3 and x multiplied by 0.6 is equal to 7
Answer:the right answer is a
Step-by-step explanation:
ive done this question
hope it helps
HELP ME PLEASE, IF I DONT GET THIS DONE I'M GOING TO FAIL
Answer:
2.7 mpg less than Evan's
Step-by-step explanation:
Riley gets 430.1 / 11 = 39.1 mpg
Evan gets 418 / 10 = 41.8 mpg
41.8 - 39.1 = 2.7
9514 1404 393
Answer:
2.7, less
Step-by-step explanation:
To find miles per gallon (MPG), divide miles by gallons.
Riley's car:
(430.1 mi)/(11 gal) = 39.1 mi/gal
Evan's car:
(418 mi)/(10 gal) = 41.8 mi/gal
__
Then the difference is ...
41.8 -39.1 = 2.7 . . . miles per gallon
We note that Riley's MPG is less than Evan's, so we can write ...
Riley's car gets 2.7 miles per gallon less than Evan's car.
Is either x = 6 or x = 8 a solution to 12 + x = 20? O A. Neither is.a solution. B. X = 6 is a solution, but x = 8 is not. C. X= 8 is a solution, but x = 6 is not D. They are both solutions. SUBMIT
Answer:
C. x = 8 is a solution, but x = 6 is not
Step-by-step explanation:
12 + 6 = 18
12 + 8 = 20
20 - 12 = 8
The price of an item has been reduced by 60%. The original price was $52
Four friends are training for long races.
Eduardo ran 5.123 miles, Kandis ran 6.34 miles, Khaliyah ran 7.1 miles, and Moises ran 8 miles.
Khaliyah ran how much further than Eduardo?
Answer:
1.977
Step-by-step explanation:
line up your decimal points
7.100
- 5.123 (borrow from 1 to make it 0 and make the 0 to the right of it a 10)
(now borrow from the 10 to make it 9 and make the other zero a 10)
7.100
- 5.123 (now borrow from 7 to make it 6 and make the 0 to the right of it a 10)
7 (now borrow from the 10 to make it 9 and subtract the 2)
7.100
- 5.123 (now subtract 1 from 10 and then subtract 5 from 6)
1.977
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 y 0 1 2 3 4 p(y) 0.50 0.20 0.15 0.10 0.05 Suppose an individual with Y violations incurs a surcharge of 100Y 2 . Calculate the expected amount of the surcharge
Answer:
1) The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1
2) The expected amount of surcharges is $250
Step-by-step explanation:
Given that;
Y 0 1 2 3 4
p(y) 0.50 0.20 0.15 0.10 0.05
1)
Value of E(Y)
E(Y) = (0×0.50) + ( 1×0.20) + ( 2×0.15) + (3×0.10) + (4×0.05)
= 0 + 0.20 + 0.3 + 0.3 + 0.2
E(Y) = 1
Therefore, The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1
b)
Suppose an individual with Y violations incurs a surcharge of $100Y² , the expected amount of the surcharge is given by,
E($100Y²) = 100E(Y)²
= 100∑Y²P(y)
= 100(0²×0.50) + ( 1²×0.20) + ( 2²×0.15) + (3²×0.10) + (4²×0.05)
= 100( 0 + 0.2 + 0.6 + 0.9 + 0.8 )
= 100(2.5)
= $250
Therefore; The expected amount of surcharges is $250
a vendor had 200 balloons for sale .If he sold 125 of them,what percent remains unsold?
Answer: 37.5%
Step-by-step explanation:
200-125=75
75 divided by 200 is 0.357
since we need percent so were gonna move the decimal point 2 places so the final answer is 37.5% remain unsold
Part 2: Free Response 11. The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is Normal with mean 8.1 ounces and standard deviation 0.1 ounces. Company managers do not want the weight of a chocolate bar to fall below 8 ounces, for fear that consumers will complain. (a) Find the probability that the weight of a randomly selected candy bar is less than 8 ounces.
Answer:
0.1587 = 15.87% probability that the weight of a randomly selected candy bar is less than 8 ounces.
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.
The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is Normal with mean 8.1 ounces and standard deviation 0.1 ounces.
This means that [tex]\mu = 8.1, \sigma = 0.1[/tex].
(a) Find the probability that the weight of a randomly selected candy bar is less than 8 ounces
This is the pvalue of Z when X = 8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 8.1}{0.1}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.1587 = 15.87% probability that the weight of a randomly selected candy bar is less than 8 ounces.
The equation of line q is 5y - 4x = 10. Write an equation of the line that is perpendicular to q and passes through the point (-15, 8).
a.5x + 4y + 43 = 0
c.-15x + 8y = 0
b.8x + -15y = 0
d.5x + 4y = 0