Answer:
$854.90
Step-by-step explanation:
List Price Before Tax = $778.95
Sales Tax Rate = 9.75% = 0.0975
Total Cost of the Camera = ?
Sales Tax = List Price Before Tax x Sales Tax Rate
Sales Tax = $778.95 x 9.75%
Sales Tax = $75.9476
or
Sales Tax = $75.95
Now add the Sales Tax in List Price Before Tax, to compute the Total Cost of the Camera, as follows;
Total Cost of the Camera = Sales Tax + List Price Before Tax
Total Cost of the Camera = $75.95 + $778.95
Total Cost of the Camera = $854.90
A car is traveling at a speed of 120 kilometers per hour. What is the car's speed in miles per hour? How many miles will the car travel in 4 hours?
Answer:
The car's speed is 74.5444 mi/hr. It travels 298.2576 miles in 4 hours.
Step-by-step explanation:
If we want to know the speed in mi/hr, we must convert the km to mi. We can convert from kilometers to miles as follows.
mi = km * 0.62137
Then, if the car is moving at 120 km / hr, we have that the car is moving at
120*0.62137 mi /hr, which is 74.5644 mi/hr. If we want to know how many miles the car travels in four hours, we multiply the speed times the total time. Hence
total distance = 74.5444 mi/hr * 4 hr = 298.2576 miles.
lists the amount of U.S. cash per capita in circulation as of June 30 in the given year. Use linear approximation to estimate the amount, C(2010), of cash per capita in circulation in the year 2010.
Answer:
C(2010) = $1312 using linear approximation.
Step-by-step explanation:
The full complete question is attached to this solution.
The full table is given as
Year | 1970 | 1980 | 1990 | 2000
Cash |$180 |$262 |$564 | $938
we are told to use linear approximation to obtain C(2010)
Linear approximation, Mathematically, results in
C(2010) = C(2000) + C'(t) [t]
where t = years since 2010 = (Year - 2000)
Linear approximation gives C'(t) as the rate of change of C with time
C'(t) = (ΔC/Δt)
We will be using the latest year for this approximation.
ΔC = C(2000) - C(1990) = 938 - 564 = $374
Δt = 2000 - 1990 = 10
C'(t) = (374/10) = $37.4 per year.
C(2010) = C(2000) + C'(t) [t]
t = 2010 - 2000 = 10
C(2000) = $938
C'(t) = $37.4 per year
C(2010) = 938 + (37.4)(10) = $1312
Hope this Helps!!!
The amount, C(2010), of cash per capita in circulation in the year 2010 = $1312.
The full table is given as
Year | 1970 | 1980 | 1990 | 2000
Cash |$180 |$262 |$564 | $938
we are told to use linear approximation to obtain C(2010)
Linear approximation, Mathematically, results in
C(2010) = C(2000) + C'(t) [t]
where t = years since 2010 = (Year - 2000)
Linear approximation gives C'(t) as the rate of change of C with time
C'(t) = (ΔC/Δt)
We will be using the latest year for this approximation.
ΔC = C(2000) - C(1990) = 938 - 564 = $374
Δt = 2000 - 1990 = 10
C'(t) = (374/10) = $37.4 per year.
C(2010) = C(2000) + C'(t) [t]
t = 2010 - 2000 = 10
C(2000) = $938
C'(t) = $37.4 per year
C(2010) = 938 + (37.4)(10) = $1312.
Complete question:
Find the quadratic equation of the form y=ax^ 2 +bx+c, whose graph passes through the points (2, 3) ( -2,7)and (1, - 2) .
Answer:
y = 2x^2 -x -3
Step-by-step explanation:
It can be convenient to use the quadratic regression capability of a graphing calculator or spreadsheet. That's what we did in the attachment.
__
Fill in the given points in the equation to find three linear equations in a, b, c.
3 = a(2^2) +b(2) +c
7 = a(-2)^2 +b(-2) +c
-2 = a(1^2) +b(1) +c
Subtracting the last equation from the first two gives ...
(3) -(-2) = (4a +2b +c) -(a +b +c) ⇒ 5 = 3a +b
(7) -(-2) = (4a -2b +c) -(a +b +c) ⇒ 9 = 3a -3b . . . . . [eq5]
Subtracting the second of these equations from the first gives ...
(5) -(9) = (3a +b) -(3a -3b) ⇒ -4 = 4b
b = -1
Dividing [eq5] by 3 gives ...
3 = a - b
3 = a -(-1)
2 = a
Using the original 3rd equation, we have ...
-2 = a +b +c
-2 = 2 +(-1) + c
-3 = c . . . . . . . . subtract 1
The desired quadratic is ...
y = 2x^2 -x -3
A rectangle has an area of K + 19k + 60 square inches. If the value of k and the dimensions of the rectangle are all natural
numbers, which statement about the rectangle could be true?
The length of the rectangle is k-5 inches.
The width of the rectangle is k + 4 inches.
The length of the rectangle is k-20 inches.
The width of the rectangle is k + 10 inches.
Step-by-step explanation:
By definition, the area of a rectangle is given by:
A = w * lA=w∗l
Where,
w: width of the rectangle
l: length of the rectangle
We then have the following expression for the area:
A = k ^ 2 + 19k + 60A=k
2
+19k+60
What we must do is factorize the expression following the following steps:
1) Find two numbers that are equal to 19
2) Find two multiplied numbers equal to 60
We have then:
A = (k + 15) (k + 4)A=(k+15)(k+4)
Therefore, the width of the rectangle is:
w = (k + 4)w=(k+4)
Answer:
Thats correct! The answer is B. (2nd option.) I took edge.
Step-by-step explanation:
five rock songs and six hip-hop songs on a disk jockeys playlist for a radio show. If the disc jockey shuffle the songs randomly, what is the possibility that all hip-hop song are played consecutively
Answer 39916800
Step-by-step explanation:
The probability that all hip-hop songs are played consecutively is 0.18%.
To calculate the probability that all hip-hop songs are played consecutively, to consider the total number of possible song arrangements and the number of arrangements where all hip-hop songs are consecutive.
The total number of song arrangements calculated using the concept of permutations. Since there are a total of 11 songs on the playlist, the number of possible arrangements is 11!.
Now, let's calculate the number of arrangements where all hip-hop songs are played consecutively treat the 6 hip-hop songs as a single unit or block. This means 6! ways to arrange the hip-hop songs within that block.
Since we have 5 rock songs remaining, we can arrange them in 5! ways.
Therefore, the total number of arrangements where all hip-hop songs are played consecutively is 6! ×5!.
To calculate the probability, we divide the number of favorable outcomes (where all hip-hop songs are played consecutively) by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = (6! × 5!) / 11!
Calculating the numerical value:
Probability = (720 × 120) / 39,916,800
Probability ≈ 0.00180
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Men’s heights are normally distributed with mean 69.5 inches and a standard deviation of 2.4 inches.
Women’s heights are normally distributed with mean 63.8 inches and a standard deviation of 2.6 inches
The Gulfstream 100 is an executive jet that seats six and it has a doorway height of 51.6 inches.
a. What percentage of adult men can fit through the door without bending?
b. what percentage of adult women can fit through the door without bending?
c. Does the door design with a height of 51.6 inches appear to be adequate? Why didn’t engineers design a larger door?
d. What doorway height would allow 60% of men to fit without bending?
Answer:
a. The percentage of adult men that will fit through the door without bending is 0.
b. The percentage of adult women that will fit through the door without bending is 0.
c. No, it is not adequate. There must be another technical reasons to not use a larger door.
d. The doorway height that would allow 60% of men to fit without bending is 70.1 inches.
Step-by-step explanation:
a. To fit throught the door, the height has to be under 51.6. To calculate this proportion, we have to calculate the z-score for X=51.6 for the distribution of men's height N(μ=69.5, σ=2.4).
We can calculate the z-score as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{51.6-69.5}{2.4}=\dfrac{-17.9}{2.4}=-7.4583[/tex]
[tex]P(X<51.6)=P(z<-7.4583)=0[/tex]
The percentage of adult men that will fit through the door without bending is 0.
b. To fit throught the door, the height has to be under 51.6. To calculate this proportion, we have to calculate the z-score for X=51.6 for the distribution of women's height N(μ=63.8, σ=2.6).
We can calculate the z-score as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{51.6-63.8}{2.6}=\dfrac{-12.2}{2.6}=-4.6923[/tex]
[tex]P(X<51.6)=P(z<-4.6923)=0[/tex]
The percentage of adult women that will fit through the door without bending is 0.
c. No, it is not adequate. There must be another technical reasons to not use a larger door.
d. We can calculate this finding a z-value z1 for which P(z<z1)=0.60.
Looking in a standard normal distribution table, the value for z1 is z1=0.25335.
Then, transforming to our adult men's height distribution, we have:
[tex]X=\mu+z\sigma=69.5+0.25335*2.4=69.5+0.6=70.1[/tex]
The doorway height that would allow 60% of men to fit without bending is 70.1 inches.
Imagine you are studying a population of finches on one of the Galåpagos Islands. You have been recording many of the birds' physical traits, including the length of both wings. You observe that for 80% of individuals measured, the length of the left wing is not significantly different from the length of the right wing (in other words, they are symmetrical). But for about 20% of birds measured, the wing lengths are asymmetrical. This distribution is true from generation to generation. Suddenly, a rare 5-day windstorm takes over the island. After the storm, you spend the next several days netting each bird on the island that survived the storm. You discover that 85% of the birds with symmetrical wings survived the storm, whereas only 5% of the birds with asymmetrical wings did. Propose a hypothesis to explain this observation.
Answer:
The distribution of symmetrical to asymmetrical will change so that close to 100% of birds will have symmetrical wingspans.
Answer:
Refer below.
Step-by-step explanation:
The appropriation of symmetrical to asymmetrical will change so near 100% of flying creatures will have symmetrical wingspans.
The segments shown below could form a triangle.
A. True
B. False
Final answer:
The answer to whether the segments with lengths of 1, 8, and 8 can form a triangle is True.
Explanation:
Can Segments Form a Triangle?
To determine if the segments with lengths of 1 and 8 can form a triangle, we need to apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we have two sides that are each 8 units long, and one side that is 1 unit long.
Let's add the lengths of the two shorter segments: 1 + 8 = 9.
This sum is greater than the length of the other segment, which is 8. Now, we will check the sum of the other two possible pairs:
8 + 8 = 16, which is greater than 1.8 + 1 = 9, which is also greater than 8.Since all combinations of the sums of two sides are greater than the third side, these segments can indeed form a triangle.
Thus, the answer to whether the segments with lengths of 1, 8, and 8 can form a triangle is True.
Match each
Match each investment characteristic to the level of risk involved.
growth
savings
speculation
high risk because returns are not guaranteed, but time frames are set
moderate risk because expectations of returns are reasonable and average
low risk because of steady interest without fluctuation in value
High Risk because returns are not guaranteed, but time frames are set
—Speculation
Moderate Disk because expectations of returns are reasonable and average
—Growth
Low Risk because of steady Interest without fluctuation in value
—Savings
In investment terms, growth corresponds to high risk as returns aren't guaranteed, savings relate to low risk due to steady interest income, and speculation signifies moderate risk as it has reasonable return expectations.
Explanation:The types of investment can be associated with different levels of risk as follows:
Growth is correlated with high risk because the returns are not guaranteed, but time frames are set. For example, investing in a start-up tech firm may have great potential for growth, but also carries a significant risk if the company does not succeed. Savings are associated with low risk due to steady interest without fluctuation in value. This might be a savings account or a fixed-rate bond, where the earnings are steady and dependable, and there is little risk of losing your initial investment. Speculation presents a moderate risk because expectations of returns are reasonable and average. This could be investments in commodities, real estate or foreign exchange, where there is some risk involved but also the potential for significant gains. Learn more about Investment Risk here:
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Distribute 5000 among three friends in ratio of 1:2:3.What will be the greatest share?
Answer:
2500
Step-by-step explanation:
Find out how much 1 part is. Add all the parts together
1+2+3=6
find how much of 5000 is 1 part
5000/6=833.3 recurring
833.3 is 1 part
then multiple the parts
8.333.3 x 1
8.333.3 x 2
8.333.3 x 3
8.333.3 r : 1.666.6 r : 2500
The value of the greatest share is 2500.
Important information:
Total amount = 5000Given ratio = 1:2:3We need to find the greatest share.
Ratio:Let 5000 is divided in three shares whose values are [tex]x, 2x[/tex] and [tex]3x[/tex].
[tex]x+2x+3x=5000[/tex]
[tex]6x=5000[/tex]
[tex]x=\dfrac{5000}{6}[/tex]
[tex]x=\dfrac{2500}{3}[/tex]
The value of greatest share is [tex]3x[/tex].
[tex]3x=3\times \dfrac{2500}{3}[/tex]
[tex]3x=2500[/tex]
Therefore, the value of greatest share is 2500.
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3 tenths plus 17 hundredths=
Answer: [tex].47[/tex]
3 tenths is written as
Decimal: [tex].3[/tex]
Fraction: [tex]\frac{3}{10}[/tex]
17 hundredths is written as
Decimal: [tex].17[/tex]
Fraction: [tex]\frac{17}{100}[/tex]
Add
[tex]3/10+17/100[/tex]
[tex]=.47[/tex]
Fraction Form
[tex].47=\frac{47}{100}[/tex]
One quart is approximately equal to 0.95 liter. To convert quarts to liters, which operation should you use? Why?
A..Addition; there is about 0.95 liter in 1 quart. Add when converting smaller units to larger units.
B...Division; there is about 0.95 liter in 1 quart. Divide when converting smaller units to larger units.
c...Multiplication; there is about 0.95 liter in 1 quart. Multiply when converting larger units to smaller units.
D......Subtraction; there is about 0.95 liter in 1 quart. Subtract when converting larger units to smaller units.
Answer:
c...Multiplication; there is about 0.95 liter in 1 quart. Multiply when converting larger units to smaller units.
Step-by-step explanation:
1 quart : 0.95 litre
X quarts : ?
X/1 = ?/0.95
? = 0.95 × X
A triangular prism was sliced parallel to its base. What is the shape of the cross section shown in the figure?
Answer:
it would be a triangle
Step-by-step explanation:
Typing errors in a text are either nonword errors (as when "the" is typed as "teh") or word errors that result in a real but incorrect word. Spell‑checking software will catch nonword errors but not word errors. Human proofreaders catch 70 % of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 10 word errors. (a) If X is the number of word errors missed, what is the distribution of X ? Select an answer choice. X is binomial with n = 10 and p = 0.7 X is binomial with n = 10 and p = 0.3 X is approximately Normal with μ = 3 and σ = 1.45 X is Normal with μ = 7 and σ = 1.45 If Y is the number of word errors caught, what is the distribution of Y ? Select an answer choice. Y is Normal with μ = 7 and σ = 1.45 Y is approximately Normal with μ = 3 and σ = 1.45 Y is binomial with n = 10 and p = 0.3 Y is binomial with n = 10 and p = 0.7 (b) What is the mean number of errors caught? (Enter your answer as a whole number.) mean of errors caught = What is the mean number of errors missed? (Enter your answer as a whole number.) mean of errors missed = (c) What is the standard deviation of the number of errors caught? (Enter your answer rounded to four decimal places.) standard deviation of the number of errors caught = What is the standard deviation of the number of errors missed? (Enter your answer rounded to four decimal places.) standard deviation of the number of errors missed =
Answer:
a) X is binomial with n = 10 and p = 0.3
Y is binomial with n = 10 and p = 0.7
b) The mean number of errors caught is 7.
The mean number of errors missed is 3.
c) The standard deviation of the number of errors caught is 1.4491.
The standard deviation of the number of errors missed is 1.4491.
Step-by-step explanation:
For each typing error, there are only two possible outcomes. Either it is caught, or it is not. The probability of a typing error being caught is independent of other errors. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
10 word errors.
This means that [tex]n = 10[/tex]
(a) If X is the number of word errors missed, what is the distribution of X ?
Human proofreaders catch 70 % of word errors. This means that they miss 30% of errors.
So for X, p = 0.3.
The answer is:
X is binomial with n = 10 and p = 0.3.
If Y is the number of word errors caught, what is the distribution of Y ?
Human proofreaders catch 70 % of word errors.
So for Y, p = 0.7.
The answer is:
Y is binomial with n = 10 and p = 0.7
(b) What is the mean number of errors caught?
[tex]E(Y) = np = 10*0.7 = 7[/tex]
The mean number of errors caught is 7.
What is the mean number of errors missed?
[tex]E(X) = np = 10*0.3 = 3[/tex]
The mean number of errors missed is 3.
(c) What is the standard deviation of the number of errors caught?
[tex]\sqrt{V(Y)} = \sqrt{np(1-p)} = \sqrt{10*0.7*0.3} = 1.4491[/tex]
The standard deviation of the number of errors caught is 1.4491.
What is the standard deviation of the number of errors missed?
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.3*0.7} = 1.4491[/tex]
The standard deviation of the number of errors missed is 1.4491.
(a). X follows a binomial distribution with n = 10 and p = 0.3, while Y follows a binomial distribution with n = 10 and p = 0.7.
(b) The mean number of errors caught is 7 and the mean number of errors missed is 3,
(c) Both with a standard deviation of approximately 1.4491.
Let's analyze the given problem step by step.
Part (a): Distribution of X and Y
X represents the number of word errors missed.
Since 70% of word errors are caught, 30% of word errors are missed.
Therefore, X follows a binomial distribution with n = 10 (total errors) and p = 0.3 (probability of missing an error).
Thus, X is binomial with n = 10 and p = 0.3.Y represents the number of word errors caught.
Since 70% of word errors are caught, Y follows a binomial distribution with n = 10 and p = 0.7 (probability of catching an error).
Thus, Y is binomial with n = 10 and p = 0.7.Part (b): Mean Number of Errors Caught and Missed
Mean of errors caught: The mean of a binomial distribution is given by µ = np. For Y (caught errors), µ = 10 × 0.7 = 7. Thus, the mean number of errors caught is 7.Mean of errors missed: For X (missed errors), µ = 10 × 0.3 = 3. Thus, the mean number of errors missed is 3.Part (c): Standard Deviation of the Number of Errors Caught and Missed
Standard deviation of errors caught:
The standard deviation of a binomial distribution is given by σ = √(np(1-p)). For Y (caught errors), σ = √(10 × 0.7 × 0.3) ≈ 1.4491.Thus, the standard deviation of the number of errors caught is approximately 1.4491.
Standard deviation of errors missed: For X (missed errors), σ = √(10 × 0.3 × 0.7) ≈ 1.4491. Thus, the standard deviation of the number of errors missed is approximately 1.4491.
A study conducted by the Pew Research Center reported that 58% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 15 cell phone owners is studied. What is the probability that 10 or more of them used their phones for guidance on purchasing decisions? Round your answer to 2 decimal places
Final answer:
The student is asked to calculate the probability that 10 or more out of 15 cell phone owners use their phones for help with purchasing decisions, with a 58% chance each. The calculation is done using the binomial probability formula and the answer is rounded to two decimal places.
Explanation:
The student seeks to determine the probability that 10 or more cell phone owners out of a sample of 15 use their phones for guidance on purchasing decisions, given that 58% of cell phone owners do so. This question can be addressed using the binomial probability formula:
[tex]P(X ≥ k) = Σ (nCk * p^k * (1-p)^(n-k))[/tex]
n is the sample size (15 in this case),k is the number of successes (10, 11, 12, 13, 14, or 15 in this case),p is the probability of success on a single trial (0.58), andnCk is the combination of n items taken k at a time.To find the total probability of 10 or more successes, we sum the probabilities of having 10, 11, 12, 13, 14, or 15 successes. Each of these probabilities is found by plugging the appropriate numbers into the binomial formula. In practice, to simplify the calculation, one might use statistical software or a binomial probability calculator.
After calculating these probabilities and summing them up, we round the answer to two decimal places as per the instruction given in the question.
If the height and base of the parallelogram shown are each decreased by 2 cm, what is the area of the new parallelogram?
complete question:
If the height and base of the parallelogram shown are each decreased by 2 cm, what is the area of the new parallelogram?
A parallelogram with a base of 10 centimetres and a height of 8 centimetres.
Answer:
area = 48 cm²
Step-by-step explanation:
A parallelogram is quadrilateral with 4 sides formed by 2 pair of parallel lines. The area of a parallelogram is represented as follows :
area of parallelogram = B × H
where
B = breadth
H = height
According to the question the height and the base each reduced by 2 cm.
The new base = 10 - 2 = 8 cm
The new height = 8 - 2 = 6 cm
area = B × H
area = 8 × 6
area = 48 cm²
The following definitions are used: a relation on a set A is defined to be irreflexive if, and only if, for every x A, x R x; asymmetric if, and only if, for every x, y A if x R y then y R x; intransitive if, and only if, for every x, y, z A, if x R y and y R z then x R z. The following relation is defined on the set A = {0, 1, 2, 3}. Determine whether the relation is irreflexive, asymmetric, intransitive, or none of these. (Select all that apply.) R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)}
The relation R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} is not irreflexive, asymmetric, or intransitive.
Explanation:To determine whether the relation R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} is irreflexive, asymmetric, or intransitive, we will analyze each property.
Irreflexive: Since every element in the relation has the form (x, x) where x is an element of A, and all such pairs exist in R2, the relation is not irreflexive.Asymmetric: Since the relation contains (x, y) and (y, x) pairs for some x, y in A, it violates the definition of an asymmetric relation. Therefore, R2 is not asymmetric.Intransitive: The relation R2 does not violate the transitive property. For example, (0,1) and (1,2) are in R2, and it also contains (0,2), satisfying the transitive property. Therefore, R2 is not intransitive.Therefore, the relation R2 is none of the given properties (irreflexive, asymmetric, or intransitive).
A triangular prism has a height of 9 meters. The area of the triangular base measures 16 square meters. What is the volume of the triangular prism?
A. 15 cubic meters
B. 60 cubic meters
C. 72 cubic meters
D. 144 cubic meters
Answer:
D. 144 cubic meters
Step-by-step explanation:
Volume of triangular prism(V)= Area of a triangle(A)×height of the prism(H)
That is,
V=AH
Where,
A=Area of a triangle
H=Height of the prism
Given,
A=1/2× base×height=16 square meters
Height=9 meters
Therefore,
Volume of triangular prism=16 square meters×9 meters
=144 cubic meters
Answer: D. 144 cubic meters
Step-by-step explanation:
A triangular prism consists of 2 triangular faces(base) and 3 rectangular faces.
The formula for determining the volume of a triangular prism is expressed as
Volume = area of the triangular base × height of the prism
Area of triangular base = 1/2 base × height
From the information given,
Height of prism = 9 meters
Area of triangular base = 16 square meters
Volume of the triangular prism = 16 × 9 = 144 cubic meters
On the morning of November 9, 1994-the day after the electoral landslide that had returned Republicans to power in both branches of Congress-several key races were still in doubt. The most prominent was the Washington contest involving Democrat Tom Foley, the reigning speaker of the house. An Associated Press story showed how narrow the margin had become (120): With 99 percent of precincts reporting, Foley trailed Republican challenger George Nethercutt by just 2,174 votes, or 50.6 percent to 49.4 percent. About 14,000 absentee ballots remained uncounted, making the race too close to call. Let p = P(Absentee voter prefers Foley). How small could p have been and still have given Foley a 20% chance of overcoming Nethercutt's lead and winning the election?
Answer:
p = 0.574197
Step-by-step explanation:
There are 14000 ballots left.
The lead is 2174, so he needs to lead at least 2175 in these 14000 ballots.
He does so if he gets at least 8088 votes.
If P(x >= 8088) = 0.20, then the corresponding z score to this is, by table/technology,
z = 0.841621234
Now, as
z = (x - u) / s
and
u= n p
s = sqrt(n p(1-p))
Then
0.841621234 = (8088 - 14000*p) / sqrt(14000p(1-p))
Solving for p here,
p = 0.574197
The mean of the sample is 24.444 squares with a standard deviation of 2.45 squares. Single-ply toilet paper requires 26 squares to absorb one-quarter cup of water. Josh would like to carry out a test to determine if there is convincing evidence that the mean number of squares of Fluffy that are needed to absorb one-quarter cup of water is fewer than 26 squares. What is the appropriate test statistic and P-value of this test?
Answer:
t = -2.69 , p = 0.0078
Step-by-step explanation:
We have the following data:
Sample Mean = x = 24.444
Sample Standard Deviation = s = 2.45
Sample size = n = 18
Josh wants to test that mean number is lesser than 26. So our test value is 26 i.e.
u = 26
Since Josh wants to test that mean would be fewer than 26, so this would be a left tailed test with a less than sign in Alternate Hypothesis. Therefore, the hypothesis would be:
[tex]H_{o}: u\geq 26\\H_{a}: u<26[/tex]
Since, we do not know the value of Population standard deviation, and we have the value of sample standard deviation, we will use One-Sample t-test for the population mean.
The formula to calculate the test-statistic would be:
[tex]t=\frac{x-u}{\frac{s}{\sqrt{n}}}[/tex]
Substituting the values in this formula gives us:
[tex]t=\frac{24.444-26}{\frac{2.45}{\sqrt{18}}}\\t=-2.69[/tex]
This means, the test statistic would be -2.69
Since, the sample size is 18, the degrees of freedom would be:
Degrees of freedom = df = n - 1 = 17
To find the p-value we need to check the p-value against test statistic of 2.69, with 17 degrees of freedom and One-tailed test. This value comes out to be:
p-value = 0.0078
Therefore, the correct answer would be:
t = -2.69 , p = 0.0078
A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases?
Answer: a) 15, b) 1.
Step-by-step explanation:
A researcher studying public opinion of proposed social security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more Americans does the researcher need to sample in the following cases?
(a) 10% of all adult Americans support the changes
Here, [tex]np>5\ and\ n(1-p)>5[/tex]
And , [tex]p=0.10[/tex]
So, consider the equality, to find the value of 'n'.
[tex]np=5\\\\n\times 0.10=5\\\\n=\dfrac{5}{0.10}\\\\n=50[/tex]
So, there are [tex]50-35=15[/tex] more adult Americans needed.
(b) 15% of all adult Americans supports the changes
Here, [tex]p=0.15[/tex]
So, again we get that
[tex]np=5\\\\n\times 0.15=5\\\\n=\dfrac{5}{0.15}\\\\n=33.33\\\\n\approx 34[/tex]
So, there are [tex]35-34=1[/tex] more adult Americans needed.
Hence, a) 15, b) 1.
The length of a rectangle is five less than its width. The area of the rectangle is 84 square feet. Write a quadratic equation in standard form, ax^2+bx+c=0
Given:
The length of a rectangle is 5 less than its width.
The area of the rectangle is 84 square feet.
We need to determine the quadratic equation in standard form that represents the area of the rectangle.
Dimensions of the rectangle:
Let l denote the length of the rectangle.
Let w denote the width of the rectangle.
Since, it is given that the length is 5 less than its width, it can be written as,
[tex]l=5-w[/tex] and [tex]w=w[/tex]
Area of the rectangle:
The area of the rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting A = 84, [tex]l=5-w[/tex] and [tex]w=w[/tex], we get
[tex]84=(5-w)\times w[/tex]
[tex]84=5w-w^2[/tex]
Adding both sides of the equation by w², we have;
[tex]w^2+84=5w[/tex]
Subtracting by 5w on both sides, we get;
[tex]w^2-5w+84=0[/tex]
Thus, the quadratic equation in standard form for the area of the rectangle is [tex]w^2-5w+84=0[/tex]
the composition of the senate of the 107th congress is 53 republicans, 42 democrats, and 5 independents. a new committee is being formed to study ways to benefit the arts in education. if 3 senators are selected at random to head the committee, find the probability
Answer:
The correct answer is 161700.
Step-by-step explanation:
Total number of members of the senate of 107th congress is 100 in which there are 53 republicans, 42 democrats and 5 independents.
A new committee is to be formed from these 100 congressmen to study the benefits of arts in education.
Number of senators required to head the new committee is 3.
Therefore total number of ways 3 members are selected in the population of 100 congressmen is given by [tex]\left[\begin{array}{ccc}100\\3\end{array}\right][/tex] = 161700.
Thus there are 161700 ways one can select 3 senators to head a committee.
solve for y 6=2(y+2)
Answer:
y=1
Step-by-step explanation:
6=2(y+2)
Divide each side by 2
6/2=2/2(y+2)
3 = y+2
Subtract 2 from each side
3-2 = y+2-2
1 = y
Answer:
y = 1
Step-by-step explanation:
6 = 2 ( y + 2 )
6 = 2y + 4
subtract four from both sides
2 = 2y
divide by 2 on both sides
y = 1
A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 215.
Answer:
[tex]P(\bar X>215)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we apply this formula to our probability we got this: for the value of 215
[tex] z = \frac{215-200}{\frac{50}{\sqrt{40}}}= 1.897[/tex]
And we can find this probability using the complement rule and with the normal standard distribution or excel we got:
[tex] P(z >1.897) = 1-P(z<1.897) =1- 0.971= 0.029[/tex]
Step-by-step explanation:
Let X the random variable that represent the ratings of applicants from a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(200,50)[/tex]
Where [tex]\mu=200[/tex] and [tex]\sigma=50[/tex]
We select a sample size of n =40. We are interested on this probability
[tex]P(\bar X>215)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we apply this formula to our probability we got this: for the value of 215
[tex] z = \frac{215-200}{\frac{50}{\sqrt{40}}}= 1.897[/tex]
And we can find this probability using the complement rule and with the normal standard distribution or excel we got:
[tex] P(z >1.897) = 1-P(z<1.897) =1- 0.971= 0.029[/tex]
PLEASE HELP ASAP!!!
When would you use a line graph?
A. if the data is given as data pairs
B. if the data is numerical
C. to compare categories
D. to compare change over time
You can also choose more than one
Answer:
d AND C
Step-by-step explanation:
The school held there talent quest and this year they had 1,204 people in attendance. Last year the attendance was only 860. What was the percentage increase from last year?
Answer:
28.57℅
Step-by-step explanation:
If last year attendance was 860 and the attendance increases to 1204:
Attendance increment = 1204-860
= 344
%increase = increment/current attendance × 100%
% increase = 344/1204 × 100
℅ increase = 34400/1204
% increase = 28.57%
Therefore the percentage increase from last year is 28.57℅
The ratio of forks to knives in Isabella’s kitchen drawer is 4 to 5. There are
16 forks in the drawer. How many knives are there?
Answer:
20 knives
Step-by-step explanation:
the ratio of fork to knives is [tex]\frac{4}{5}[/tex] and their are 16 forks, so we put the ratio of fork and knives equal to number of fork and knives so its:
[tex]\frac{4}{5}[/tex] = [tex]\frac{16}{x}[/tex] We cross multiply
80 = 4x Divide both side by 4
x = 20
we can check too
16/20 if we simplify, its give us 4/5
There are 20 knives in Isabella's kitchen.
The ratio of forks to knives in Isabella’s kitchen drawer is 4 to 5.
Given that there are 16 forks in the drawer, we can set up a proportion to find the number of knives:
4/5 = 16/X
Cross multiply to get: 4X = 80
Divide by 4 to find X = 20
Therefore, there are 20 knives in Isabella's kitchen drawer.
An experiment consists of selecting a letter at random from the letters in the word IRRESISTIBLE and observing the outcomes. What is the appropriate sample space for this experiment
Sample space for the experiment is {B, E, I, L , R , S, T } .
Hence option D is correct.
Given, that the word IRRESISTIBLE .
An experiment consist of selecting a letter at random from the letters in the given word.
The number of distinct letters in the word is 7 i.e I is 3 times in the word but consider it as single letter.
Therefore the appropriate sample space for the experiment is {B, E, I, L , R , S, T } .
Thus the option D is correct.
Know more about sample space,
https://brainly.com/question/30206035
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The sample space for an experiment consists of all possible outcomes or events that can occur. In this case, the experiment involves selecting a letter at random from the letters in the word "IRRESISTIBLE."
The appropriate sample space for this experiment would be the set of all individual letters that can be selected from the word. Therefore, the sample space is:
Sample space = {I, R, E, S, T, I, B, L}
Each element of the sample space represents a possible outcome of the experiment, which is selecting a specific letter from the word "IRRESISTIBLE."
It is important to note that the sample space only includes the individual letters as outcomes, and it does not consider the order or repetition of the letters in the word.
for such more question on sample space
https://brainly.com/question/2117233
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What is the median of the data set?
87, 98, 106, 82, 111, 120
Answer:
The median is 102
Step-by-step explanation:
Median = a measure of central tendency. It represents the value for which 50% of observations a lower and 50% are higher. Put simply, it is the value at the center of the sorted observations.
Therefore, the answer 102 is correct.
(I need to be granted one more brainliest to level up so if my answer helped, it would be very much appreciated to award that to me, no obligations though!)