Answer:
x = 4
Step-by-step explanation:
To find x, plug in 14 into the function
f(x) = 3x + 2
14 = 3x + 2
Solve for x
14 = 3x + 2
12 = 3x
4 = x
So, the answer is x = 4
The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 325 grams and a standard deviation of
10 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final
answers to 2 decimal places.)
3378
318.26
to
33174
a. Highest 10 percent
b. Middle 50 percent
c. Highest 80 percent
d. Lowest 10 percent
Answer:
a. Above 337.8 grams.
b. Between 318.25 grams and 331.75 grams.
c. Above 316.59 grams.
d. Below 312.2 grams
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 325 grams and a standard deviation of 10 grams.
This means that [tex]\mu = 325, \sigma = 10[/tex]
a. Highest 10 percent
This is X when Z has a pvalue of 1 - 0.1 = 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 325}{10}[/tex]
[tex]X - 325 = 10*1.28[/tex]
[tex]X = 337.8[/tex]
So 337.8 grams.
b. Middle 50 percent
Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.
25th percentile:
X when Z has a pvalue of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 325}{10}[/tex]
[tex]X - 325 = -0.675*10[/tex]
[tex]X = 318.25[/tex]
75th percentile:
X when Z has a pvalue of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 325}{10}[/tex]
[tex]X - 325 = 0.675*10[/tex]
[tex]X = 331.75[/tex]
Between 318.25 grams and 331.75 grams.
c. Highest 80 percent
Above the 100 - 80 = 20th percentile, which is X when Z has a pvalue of 0.2. So X when Z = -0.841.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.841 = \frac{X - 325}{10}[/tex]
[tex]X - 325 = -0.841*10[/tex]
[tex]X = 316.59[/tex]
Above 316.59 grams.
d. Lowest 10 percent
Below the 10th percentile, which is X when Z has a pvalue of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 325}{10}[/tex]
[tex]X - 325 = -1.28*10[/tex]
[tex]X = 312.2[/tex]
Below 312.2 grams
Compute the exact value of the function for the given x-value without using a calculator. (2 points) f(x) = 5x for x = -1
Answer:
The exact value of the function for the given x-value is of -5.
Step-by-step explanation:
In this question, we compute the numeric value of the function f(x) for x = -1, that is, we replace every instance of x in the function by -1.
f(x) = 5x for x = -1
[tex]f(-1) = 5(-1) = -5[/tex]
The exact value of the function for the given x-value is of -5.
hi could anyone please help me with this
Work out the perimeter of this semicircle.
Take it to be 3.142 and write down all of the digits given by your calculator.
18 cm give your answer in cm
Answer:
46.278cm
Step-by-step explanation:
(π+2)r
=πr+d
=9π+18=46.278cm
A restaurant bill is $21. You leave a 15% tip. Which of the following represents the amount a customer pays including the tip of 15% if the bill was dollars?
a. 0.15b
b. 15b
c. b + 0.15b
d. 1.15b
e. 1.015b
f. b + 15/100b
g. b + 0.15
Can someone help me pls
Answer:
x = 10 units
Step-by-step explanation:
By theorem,
Perpendicular drawn from the center to the chord of a circle, bisects the chord.
AB = BC = 6
In right triangle ΔCBD,
By applying Pythagoras theorem,
CD² = BC² + BD²
= 6² + 8²
CD = [tex]\sqrt{36+64}[/tex]
= 10
Since, CD and the side measuring x are the radii of the circle D.
x = CD = 10 units
Suppose a caravan (5 cars) travels 100 km, beginning in front of one tollbooth, passing through a second tollbooth, and nishing just after a third tollbooth. The distance between two tollbooths is 50 km. Each car takes 12 sec to serve. The tollbooth starts to serve the caravan when the entire caravan is lined up. The caravan can only dispatch a tollbooth after all cars in the caravan are served. What is the end-to-end delay (from when the caravan is lined up before 1st tollbooth till the caravan is served by the 3rd tollbooth)
Answer:
1 hr 2 min 30 secs
Step-by-step explanation:
Assume Propagation speed = 100 km/hr
number of cars = 5
distance between booths = 50 km
Total distance = 100 km
take taken to serve each car = 12 secs
Determine the end to end delay
first calculate the propagation delay = Total distance / propagation speed
= 100 / 100 = 1 hr
next calculate : Time taken to serve 5 cars in each Tollbooth
= 5 * 12 secs = 60 secs
Next calculate : transmission delay ( time taken by three tollbooth to reach 5 cars )
= 60 secs * 3 = 180 secs = 2 min 30 secs
therefore end-end delay
= propagation delay + transmission delay
= 1 hr 2 min 30 secs
If a Play Station was bought for $558 after a 10%
discount, what was the original price of the Play
Station?
The original price of the play station is $620.
Given that, the cost of the play station=$558 and discount=10%.
We need to find the original price of the play station.
What is a discount?The definition of discount is reduced prices or something being sold at a price lower than that item is normally sold for.
Let the original price be x.
Now, x-10% of x=558
⇒x-0.1x=558
⇒0.9x=558
⇒x=$620
Therefore, the original price of the play station is $620.
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Round 5,278 to the nearest thousand.
PLS HELP!!!!
7x=28
x/9=3
5x=125
14=x÷2
8x=40
Answer:
7x=28
x = 4
x/9=3
x = 27
5x=125
x = 25
14=x÷2
x = 28
8x=40
x = 5
ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE
Answer:
300 inches cubed
Step-by-step explanation:
Attached is an image of the explanation. Sorry about the handwriting I was trying to write fast.
Create an inequality, 5 less than a number is less than -2
Answer:
x - 5 < -2
Answer is there
which of the following shows the correct solution steps and solution to
3x - 2 = -11
A young couple just purchased a home for $180,000 in a nice area. The realtor suggested they can expect the value of their home to
Increase by 6% each year.
A function model that describes the value of the house is:
h(x) = 180000(1.06)*
where x is the number of years they have owned their home.
Using the model, how much should the house be worth after they have owned it for 5 years? (round to the nearest dollar)
A $954,000
B. $240,881
C. $190,800
D. $234,000
ILL GIVE BRAINLYIEST
Answer:
D. $234,000
Step-by-step explanation:
6% of $180,000 is $10,800
Multiply that times 5 years
$10,800x5=$54,000
add that value to the base price
$180,000+$54,000=$234,000
Just need the answer
Answer:
It seems no one can eat just one potato ship
Step-by-step explanation:
How many miles are in 506,880 inches
Answer:
8 miles
Step-by-step explanation:
Answer:
8 miles
Step-by-step explanation:
1 mile:63360 inches
506880 divided by 63360 = 8
If each edge of a cube is 5 cm, what is the volume of the cube?
Answer:
Volume =[tex]5^{3}[/tex] = [tex]125 cm^{3}[/tex]
Explain why the t-distribution has less spread as the number of degrees of freedom increases. Choose the correct answer below. A. The t-distribution has less spread as the degrees of freedom increase because the variability introduced into the t-statistic becomes greater as n increases. B. The t-distribution has less spread as the degrees of freedom increase because, as n increases, s becomes closer to by the law of large numbers. C. The t-distribution has less spread as the degrees of freedom increase because, as n increases, less information is known about by the law of large numbers. D. The t-distribution has less spread as the degrees of freedom increase because, for large values of n, n30, the t-distribution and the normal distribution are the same.
Answer:
B. The t-distribution has less spread as the degrees of freedom increase because, as n increases, s becomes closer to sigma by the law of large numbers.
Step-by-step explanation:
The sample standard deviation, s gets considerably closer to the population standard deviation, σ, this trend follows the proposition of the law of large numbers whereby the mean or average value changes as the sample size, n increases. According to the law of large numbers, as the sample size increases, the sample mean gets continously closer to the population mean, sample standard deviation follows this same trend and thus variability or spread decreases as sample size increases.
The plausible reason that explains why the t-distribution will have a less spread as the number of degrees of freedom increases is because: as n increases, s becomes closer to by the law of large numbers. (Option B)
Note the following:
Based on the theorem of large number, the population mean and sample mean will get closer as the sample size increases.By implication, the sample standard deviation, s, and the population standard deviation, σ becomes closer too, thus, the spread will reduce as the sample size increases.Therefore, the plausible reason that explains why the t-distribution will have a less spread as the number of degrees of freedom increases is because: as n increases, s becomes closer to by the law of large numbers. (Option B)
Learn more here:
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Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x^2-8x-3
Answer:
x = 1 and vertex = (1, - 7 )
Step-by-step explanation:
Given a quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 )
The the equation of the axis of symmetry which is also the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 4x² - 8x - 3 ← is in standard form
with a = 4, b = - 8 , then
x = - [tex]\frac{-8}{8}[/tex] = 1
That is equation of axis of symmetry is x = 1
Substitute x = 1 into the function for y- coordinate of vertex
y = 4(1)² - 8(1) - 3 = 4 - 8 - 3 = - 7
vertex = (1, - 7 )
michelle has four credit cards with the balances and interest rates listed below. She wants to pay off her credit cards one at a time, based on the interest rate. In which order should Michelle pay off her credit cards
Answer:
3,2,1,4
Step-by-step explanation:
what is the solution set of the equation (x -2) (x-a) = 0 ?
Answer:
x=2, x=a
Step-by-step explanation:
(x -2) (x-a) = 0
(x-2)(x-a) = 0
x-2=0
x-2+2=0+2
x=2
x-a=0
x-a+a=0+a
x=a
You need to make 8 servings of fried fish.
Each serving takes 7.5 ounces of flour.
How many ounces of flour do you need?
Answer: 60 ounces of flour
Step-by-step explanation:
8•7.5=60
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator
0.30 cm to 0.42 cm
Answer:
[tex]\dfrac{5}{7}[/tex]
Step-by-step explanation:
Given numbers are :
0.30 cm and 0.42 cm
We need to find the ratio of the above whole numbers.
Taking 0.3 cm on the numerator and 0.42 cm on the denominator. So,
[tex]\dfrac{0.3}{0.42}=\dfrac{\dfrac{3}{10}}{\dfrac{42}{100}}\\\\=\dfrac{3}{10}\times \dfrac{100}{42}\\\\=\dfrac{10\times 3}{42}\\\\=\dfrac{10}{14}\\\\=\dfrac{5}{7}[/tex]
So, the required fraction is equal to [tex]\dfrac{5}{7}[/tex].
Name the postulate or theorem you can use to prove the triangles congruent.
Answer:
You can use the ASA Postulate to prove the Angle-Angle-Side Congruence Theorem. A flow proof is shown below. If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.
Step-by-step explanation:
Hope it helps! Correct me if I am wrong!
I'm sure about my answer!
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Its ok if you don't want to!
Given g(x) = -2x – 4, find g(6).
Answer:
x= -16
Step-by-step explanation:
g(x) =-2x-4
g(6)=-2(6)-4
g(6) = -12-4
g(6)=-16
The value of g(6) for the given function g(x) = -2x – 4 will be -16.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
Given the function,
g(x) = -2x – 4
Now,
g(6) means value of g(x) at x = 6
So,
g(6) = -2(6) - 4
g(6) = -12 - 4 = -16
Hence "The value of g(6) for the given function g(x) = -2x – 4 will be -16".
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b)Given 0º < x < 360° , solve for x in:
2 sin (2x - 30°) = √3.
Answer:
180°
because x is the mid pf 0° and 360°
I don’t know it help me pls
Answer:
its the yellow one hope this helps
Step-by-step explanation:
i did the math and checked !!!
plz help me ill give brainly
Answer:
3.6 divided by 3 = 1.2 so 1.2 yards of material can be used on each skirt.
Step-by-step explanation:
Question Help
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question
Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. What do the results tell us?
97 71 334 93 85 59 6 77 39 51
a. Find the mean
Answer:
(a) Mean = 55.9
(b) Median = 59
(c) Mode = No mode
(d) Midrange = 93
Step-by-step explanation:
(a) Mean
The formula for finding mean of an ungrouped data = Σx/n
Where
Σ is the sum of all the data
n is the number of data in the set
Therefore,
Σx=615
n = 11
Mean = 615/11
=55.9
(b) Median
Median is the middle number after arranging the set of data in either ascending or descending order.
By arranging the numbers, the middle is 59 which is the Median
(c) mode
Mode is the number that occurs most in a set of data.
From the given set of numbers, all the numbers appear once. Therefore, there is no mode
(d) Midrange
This is the difference between the biggest and the smallest number in a set of data.
Therefore,
the midrange = 97-4
=93
Task 1
Nonlinear Systems of Equations
Create a system of equations that includes one linear equation and one quadratic equation.
Part 1. Show all work in solving your system of equations algebraically.
Part 2. Graph your system of equations and show the solution graphically to verify your solution.
Task 2
Polynomial Identities
Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.
Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a3 + b3 = (a + b)(a2 − ab + b2) to calculate the sum of the cubes of your numbers without using a calculator.
Answer:
part 1 : y = x^2 + 3x + 5
y = x + 13
solution:
x^2 + 3x + 5 = x + 13
x^2 + 2x -8 = 0
(x+4)(x-2) = 0
x = -4 or x = 2
if x = -4, y = 9
if x = 2 , y = 15
part 2 : x^2 + 2x + 1 = 0
(x + 1)^2 = 0
x = -1
y = 1
task 2
part 1 : Let our two digit number be 26
Next, we rewrite it as a difference of two numbers
26=32-6
We want to square 26 using the identity:
In this case,
x=32
y=6
Substituting into the identity
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