Answer:
[tex]f(x) = -14x + 14[/tex]
Step-by-step explanation:
Given
[tex]Initial\ Value = 14[/tex]
[tex]Rate = -14[/tex]
Required:
Write as a function
Let x be the quantity that changes:
A function is of the form:
[tex]f(x) = mx + b[/tex]
Where
m = slope or rate
b = y intercept or initial value.
So, we can say that:
[tex]m = -14[/tex]
[tex]b = 14[/tex]
Substitute values for b and m in [tex]f(x) = mx + b[/tex]
[tex]f(x) = -14x + 14[/tex]
A meat inspector has randomly selected 30 packs of 95% lean beef. The sample resulted in a mean of 96.2% with a sample standard deviation of 0.8%. Calculate an upper prediction bound for the leanness of a new pack using a prediction level of 99%. Assume normality. The contents of seven similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8,10.0, 10.2, and 9.6 liters. Find a 95% confidence interval for the mean contents of all such containers, assuming an approximately normal distribution.
Answer:
a
The upper bound of the 99% prediction level is [tex] 98.2 [/tex]
b
The 95% confidence interval is [tex]9.7383 < \mu < 10.2617 [/tex]
Step-by-step explanation:
Considering first question
From the question we are told that
The sample size is n = 30
The sample mean is [tex]\= x = 96.2\%[/tex]
The standard deviation is [tex]s = 0.8\%[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
=> [tex]df = 30 - 1[/tex]
=> [tex]df = 29[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the t distribution table the critical value of at a degree of freedom of is
[tex]t_{\alpha , 29} = 2.462[/tex]
Generally the 99% prediction level is mathematically represented as
[tex]\= x \pm [(t_{\alpha , df }) * s * (\sqrt{1 + \frac{1}{ n} } )}] [/tex]
Generally the upper bound of the 99% prediction level is mathematically represented as
[tex]\= x + [(t_{\alpha , df }) * s * (\sqrt{1 + \frac{1}{ n} } )}] [/tex]
=> [tex] 96.2 + (2.462 ) * 0.8 * (\sqrt{1 + \frac{1}{ 30} } )}] [/tex]
=> [tex] 98.2 [/tex]
Considering second question
Generally the sample is mathematically represented as
[tex]\= x = \frac{\sum x_i}{n}[/tex]
=> [tex]\= x = \frac{ 9.8 + 10.2 + \cdots +9.6 }{7}[/tex]
=> [tex]\= x = 10[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ \frac{ \sum ( x_ i - \= x)}{n-1} }[/tex]
=> [tex]\sigma = \sqrt{ \frac{ ( 9.8 -10)^2 + ( 10.2 -10)^2 + \cdots + ( 9.6 -10)^2 }{7-1} }[/tex]
=> [tex]\sigma = 0.283[/tex]
Generally the degree of freedom is mathematically represented as
[tex] df = n- 1 [/tex]
=> [tex] df = 7- 1 [/tex]
=> [tex] df = 6 [/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the t distribution table the critical value of at a degree of freedom of is
[tex]t_{\frac{\alpha }{2} , 6 } = 2.447[/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , 6 } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E =2.447* \frac{0.283 }{\sqrt{7} }[/tex]
=> [tex]E =0.2617[/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]10 -0.2617 < \mu < 10 + 0.2617[/tex]
=> [tex]9.7383 < \mu < 10.2617 [/tex]
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CHAPTER 22
Statistics and Central Tendencies
results are shown in the table below.
Number of visits
Number of people
1
6
2 3
119
5
7.
8
6
S
7.
4
(a) Find the median number of visits per person.
(b) Calculate the mean number of visits per person.
[ Jan., paper 1, No. 21
ling between two cities, 3/8 of the passengers ar
Fifty people visiting a museum were asked how many times they had visited the museum
Answer:
p
Step-by-step explanation:
Solve the equation formed when f ( x ) = g ( x ).
f ( x ) = 4 x − 4
g ( x ) = 1 2 x + 3
Group of answer choices
A. x = -4
B. x = 4
C. x = 2
D. x = -2
Answer:
The answer should be x = -7/8 but it doesn't say that for any of the choices
Step-by-step explanation:
The legs of a right triangle measure 8 inches and 12 inches. What is the area
of the triangle?
A. 192 sq. inches
B. 24 sq. inches
C. 48 sq. inches
D. 96 sq. inches
Answer:48 sq. Inches
Step-by-step explanation:
An african elephant in rhe wils will eat for as long as 16 hours each day. For how many hours does an elephant eat in one year? There are 365 days in one year.
Answer:
5840
Step-by-step explanation:
16 x 365 is 5840
Answer:
5,840
Step-by-step explanation:
16x365=?
16x365=5,840
A population grows exponentially at the rate of 1.35%. How long (in years) will it take the population to double?
Answer: Approximately 51 years.
Step-by-step explanation: A population grows by changing exponentially over time, which can be mathematically demonstrated as:
[tex]P=P_{0}e^{rt}[/tex]
where
P is the population after time
P₀ is initial population, when time = 0
r is a percentage rate of growth
t is time passed
In this case, we have to calculate the amount of time it has passed for a population to double, so [tex]P=2P_{0}[/tex]:
[tex]2P_{0}=P_{0}e^{0.0135t}[/tex]
[tex]e^{0.0135t}=2[/tex]
[tex]ln(e^{0.0135t})=ln2[/tex]
Using Logarithm Rule [tex]ln(e^{k})=k[/tex]:
[tex]0.0135t=0.693[/tex]
t = 51.34
For a population with rate of 1.35%, it will take approximately 51 years to double.
The midpoint of AB is M(6,-3). If the coordinates of A are (4, - 7), what are the
coordinates of B?
Answer:
(8,1)
Step-by-step explanation:
(8,1) you have to add do to the same to B
Pont B is located at coordinates at the line AB (8, 1)
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, The midpoint of AB is M(6,-3). If the coordinates of A are (4, - 7)
From the general formula of midpoints of a line
coordinates of midpoint = ((x₂ + x₁)/2, (y₂ + y₁)/2)
where,
(x₁, y₁) are the coordinates of A
(x₂, y₂) are the coordinates of B
And in our case Coordinates of the midpoint are (6, -3)
Thus,
6 = (4 + x₂)/2
x₂ = 8
-3 = (-7 + y₂)/2
y₂ = 1
therefore, the coordinates of Pont B at line AB are (8, 1)
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Given that 3x – tan y = 4, what is dy/dx in terms of y?
Answer:
[tex]\frac{dy}{dx}[/tex] = 3 cos² y ⇒ B
Step-by-step explanation:
∵ 3x - tan(y) = 4
∵ The differentiation of tan(y) with respect to x is sec² y · dy/dx
∵ The differentiation of 3x with respect to x is 3
∵ the differentiation to 4 with respect to x is 0
∴ d/dx [3x - tan(y) = 4] is 3 - sec² y · dy/dx = 0
∵ 3 - sec²(y) · dy/dx = 0
→ Subtract 3 from both sides
∴ - sec² y · dy/dx = -3
→ Divide both sides by -1
∴ sec² y · dy/dx = 3
→ Divide both sides by sec²(x)
∴ [tex]\frac{dy}{dx}=\frac{3}{sec^{2}y}[/tex]
→ Remember [tex]\frac{1}{secy}[/tex] = cos y
∵ [tex]\frac{1}{sec^{2}y}[/tex] = cos² y
∴ [tex]\frac{3}{sec^{2}y}[/tex] = 3 cos² y
∴ [tex]\frac{dy}{dx}[/tex] = 3 cos² y
dy/dx of 3x – tan y = 4 in terms of y is;
dy/dx = 3cos²y
We are given;
3x - tan y = 4
Let's differentiate in terms of y to get;
3 - sec²y(dy/dx) = 0
This is because the derivative of tan y in terms of y is sec²y(dy/dx).
Thus, using addition property of equality, we have;
3 = sec²y(dy/dx)
Now, in trigonometric ratios;
sec y = 1/cos y
Thus;
sec²y = 1/cos²y
Therefore;
3 = (1/cos²y) (dy/dx)
Thus;
dy/dx = 3cos²y
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A researcher wishes to estimate within $5 the average repair cost of for a refrigerator. If she wishes to be 90% confident, how large of a sample would be necessary if the population standard deviation is $15.50?
Answer:
The sample size 'n' = 26
Step-by-step explanation:
Explanation:-
Given a researcher wishes to estimate within $5 the average repair cost of for a refrigerator
Given estimate "E" = $5
The estimate within the average is determined by
[tex]E = \frac{Z_{0.10}S.D }{\sqrt{n} }[/tex]
Level of significance ∝ = 90 % or 10%
= 0.90 or o.10
Z₀.₁₀ = 1.645
[tex]E = \frac{Z_{0.10}S.D }{\sqrt{n} }[/tex]
[tex]5 = \frac{1.645 X15.50 }{\sqrt{n} }[/tex]
√n = [tex]\frac{25.49}{5} = 5.099[/tex]
Squaring on both sides , we get
n = 26
Conclusion:-
The sample size 'n' = 26
The weight of eggs from a local farm are Normally distributed with mean of 2.1 ounces and a standard deviation of 0.25 ounces.
A graph titled Weight of Eggs has ounces on the x-axis going from 1.35 to 2.85 in increments of 0.25. The highest point of the curve is at 2.1. Everything to the left of that point and under the curve is labeled average, everything to the right is large.
An egg that weighs 2.0 ounces or more is labeled large and anything below is labeled average.
What percent of eggs from this farm are labeled as large? Round to the nearest tenth.
⇒ 65.5 IS THE ANSWER
Answer:
65.5
Step-by-step explanation:
Answer:
65.5
Step-by-step explanation:
For the following quadratic equation, find the discriminant.
-x^2 + 20x -126 =5
i need help please
Answer:
d=-124
Step-by-step explanation:
To find the discriminant use the equation b^2-4ac
So, 20^2-4(-131)(-1)
400-524= -124
d=-124
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Answer:
lol
Step-by-step explanation:
A password contains eight digits. How many different passwords can be formed?
Now lets assume you use a stronger password with a mix of lowercase and uppercase characters, such as "blUeFisH", then the character set is 52. In this case, there are 52^8 possible combinations of 8 character passwords. So, to break an 8 character password, it will take (1.7*10^-6 * 52^8) seconds / 2, or 1.44 years.
A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 35 minutes.
Answer:
Step-by-step explanation:
From the given information:
[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]
Given that the solution is pumped at a slower rate of 4gal/min
Then:
[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]
[tex]R_{out}= \dfrac{2A}{50+t}[/tex]
The differential equation can be expressed as:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]
Integrating the linear differential equation; we have::
[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]
[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]
multiplying above integrating factor fields; we have:
[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]
[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]
[tex](50 + t)^2 A = (50 + t)^3+c[/tex]
A = (50 + t) + c(50 + t)²
Using the given conditions:
A(0) = 20
⇒ 20 = 50 + c (50)⁻²
-30 = c(50) ⁻²
c = -30 × 2500
c = -75000
A = (50+t) - 75000(50 + t)⁻²
The no. of pounds of salt in the tank after 35 minutes is:
A(35) = (50 + 35) - 75000(50 + 35)⁻²
A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]
A(35) =69.6193 pounds
A(35) [tex]\simeq[/tex] 70 pounds
Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.
For a sample, the 95% confidence interval is (0.202, 0.482). What is the point estimate, \hat{p}, of this sample?
Answer:
The Point estimate p = 0.342
Step-by-step explanation:
For the sample, 95% confidence interval (0.202,0.482) . The Confidence interval width = (0.482 - 0.202) = 0.28
The margin of error = 0.28/2
The margin of error = 0.14
So, Point estimate p = Lower bound + Margin of error
Point estimate p = 0.202 + 0.14
Point estimate p = 0.342
Therefore, the Point estimate p = 0.342
How do I solve problems like
5 + 2y = 1
Answer:
y=-2
Step-by-step explanation:
its like in the paper sorry it if crops out
Which of the following is equivalent to 3/8
0.0025
3.75
25/100
375/1,000
Answer:
375/1,000
Step-by-step explanation:
3/8=0.375
375/1,000 =0.375
Your classmate tells you the details of the great deal he got on his mortgage: 30-year 1.1% fixed rate with a 20% down payment
If his new home costs $136,000, what is his down payment?
Answer:
27200
Step-by-step explanation:
Which statement about residual plots is NOT true?
A. The vertical axis shows residuals.
B. If there is an obvious pattern, the model is probably reasonable.
C. The x-axis appears in the middle of the graph.
D. The sum of the residuals is 0.
Answer:
A is the correct answer
Step-by-step explanation:
The not correct statement about residual plot is If there is an obvious pattern, the model is probably reasonable.
What is a residual plot?A residual plot shows the difference between the observed response and the fitted response values.
Given that, Which statement about residual plots is not true
In the given options,
If there is an obvious pattern, the model is probably reasonable, this option is not correct because, The pattern in the residual plot suggests that predictions based on the linear regression line will result in greater error as we move from left to right through the range of the explanatory variable.
So, it is not needed if there is an obvious pattern, then the model is probably reasonable,
Hence, the not correct statement about residual plot is If there is an obvious pattern, the model is probably reasonable.
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Write the letters of the expressions that are equivalent to the given expression.
5(2x + 3)
a. 10x + 15
b. 5x + 15x + 5x
c. 10x + 8
Answer: A.) 10x + 15
Step-by-step explanation:
You would distribute (multiply) the 5 to the 2x which would then make it 10x and you would distribute (multiply) the 5 to the 3 which would then make it 15. Because the 5 is a positive number the sign stays the same.
Therefore, 10x + 15 is your answer.
It is assumed that the test results for a class follow a normal distribution with a mean of 78 and a standard deviation of 36. If you know that a student's grade is greater than 72, what is the probability that it is greater than 84? What do I know? What do I want to find out? What do we expect the answer to be? How do I go from what I know to what I want to find? Does this answer seem reasonable?
Answer:
0.7143
- You know the minimum possible grade of the student
- You want to find out the probability that that grade which is greater than 72 is also greater than 84
- Expect the answer to be 0.7143
- The explanation/steps is given below
- The answer seems (and is) reasonable. You only created a new lower limit.
Step-by-step explanation:
Distribution Type: Normal
Mean: 78
Standard deviation: 36
Range of marks: [78 - 36], [78 + 36] = [42 to 114]
If you know that a student's grade is greater than 72, what is the probability that it's greater than 84?
In this case, the full probability level is between 72 and the upper limit of 114 (instead of between 42 and 114). First, find the fraction of this probability.
[114 - 72] ÷ [114 - 42] = 42/72 = 0.5833
So, the probability of a student's mark falling between 72 and 114 is 0.5833.
Now making this a whole interval, 114 - 72 = 42
What fraction of this interval of 42 will bear marks between 84 and 114?
[114 - 84] = 30
30/42 = 0.7143
Because of the first part of the question "If you know (are sure) that a student's grade is greater than 72...", your answer stops at 0.7143, since 72 was used as the lower limit.
What number group is 45/5 in
Answer:
Its in rational
Step-by-step explanation:
Answer:
45/5 is a rational number
Step-by-step explanation:
45/5 is equal to 9.
9 is a rational number.
A cake recipe called for using 6 ¼ cups of sugar before baking and another 5 ¾ cups after baking. What is the total amount of sugar needed in the recipe?
Answer:12 cups of sugar are needed in the recipe
Step-by-step explanation:
6 ¼ + 5 ¾ =11 4/4=12
The total amount of sugar needed for the cake recipe is 12 cups.
Given that, A cake recipe called for using 6¼ cups of sugar before baking and another 5¾ cups after baking.
What is addition of two fractions?To add fractions there are three simple steps:
Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator.
Step 3: Simplify the fraction (if possible)
Now, the total amount of sugar needed
6¼ + 5¾
= 25/4 + 23/4
= (25+23)/4
= 48/4
= 12
Hence, the total amount of sugar needed for the cake recipe is 12 cups.
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HELPPPPPPP PLEASEEEEEEEEWEEE
Answer:C
Step-by-step explanation: slope of 0 will always be horizontal
V = 4 + at, solve for A
Answer:
a=v-4
Step-by-step explanation:
HELP PLEASE!! NUMBER 6!!
You will get the brainiest if you can tell me how you did it, so I can finish doing them myself lol. If It comes back right, I will give it you instantly. Thank you very much.
Answer:
hey it's not clear....
What is the answer I’m dumb
Answer:
9units
Step-by-step explanation:
what is 13x144 i don't know what it it im 2nd grade
Answer:
Step-by-step explanation: 1,872
Answer: 1,872
Step-by-step explanation:
Brainliest be good peeps Calculate the missing term in each
proportion.
2/11= /55
36/42= /
9/ = 21/28
6/9= /15
Answer:
1) 10
2) (not enough info) I got 6/7
3) 12
4) 10
Step-by-step explanation:
Find a GCF and find the numerator.
an electrician has a 16-foot spool of wire and he needs to cut an 11-foot, 4-inch piece from the spool to make a repair. how many inches of wire will he have left on the spool after he makes the repair
The electrician will have 56 inches of wire left on the spool after he makes the repair.
First, we need to convert the length of the wire that the electrician needs to cut into inches. 11 feet is equal to 11 * 12 = 132 inches, and 4 inches is equal to 4, so the total length of the wire that the electrician needs to cut is 132 + 4 = 136 inches.
The electrician started with a spool of wire that was 16 feet long, or 16 * 12 = 192 inches long. If he needs to cut 136 inches of wire, he will have 192 - 136 = 56 inches of wire left on the spool.
Therefore, the electrician will have 56 inches of wire left on the spool after he makes the repair.
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