Answer:
Step-by-step explanation:
3/4x + 5 = 5 -2( x + 7 )
First, use Distributive Property.
-2 ( x + 7 ) --> -2x - 14
3/4x + 5 = 5 -2x - 14
Next, you can get rid of the fraction by multiplying EVERYTHING by 4...
3x + 20 = 20 - 8x - 56
Then, move x by subtracting 3x on BOTH sides...
20 = 20 - 11x - 56
Combine like terms...
20 = - 11x - 36
Add 36 on BOTH sides...
56 = - 11x
Divide -11 on BOTH sides...
56/11 = 5.09 repeating
x = 5.0909090909090909...
Correct me if I'm wrong, but there you go!
What is the equation of the line that passes through the point (4,-2)(4,−2) and has a slope of \frac{5}{4}
4
5
The equation of the line that passes through the point (4, -2) and has a slope of 5/4, in point-slope form is: y + 2 = 5/4(x - 4).
How to Find the Equation of a Line? Goes through a Point?If we are given a point (a, b), that a line goes through and we also know the slope (m) of the line, the equation of the line can be written as y - b = m(x - a) in point-slope form
Given that the line has the following:
A point (a, b) = (4, -2)
The slope of the line (m) = 5/4
To write the equation of the line, substitute m = 5/4, a = 4, and b = -2 into y - b = m(x - a):
y - (-2) = 5/4(x - 4)
y + 2 = 5/4(x - 4)
The answer is: y + 2 = 5/4(x - 4).
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I need help with this please help me
Answer: 45
Step-by-step explanation:
Mr and Mrs Jones received their heating bill the details follows
Present meter reading: 2410
Previous meter reading: 2090
Charge per unit: 12p per unit
Service charge: 20p per day for 14 days.
VAT: 5%
Find the total increase of the heating bill.
Answer:
Previous meter reading: 2090
Charge per unit: 12p per unit
Step-by-step explanation:
Answer:
£43.26
Step-by-step explanation:
Given readings:
Present meter reading: 2410Previous meter reading: 2090Calculate the number of units used:
[tex]\begin{aligned} \textsf{Number of units used} &= \textsf{Present meter reading} - \textsf{Previous meter reading}\\&= \sf 2410 - 2090\\&= \sf 320\; units \end{aligned}[/tex]
Given charges:
Charge per unit: 12p per unit.Service charge: 20p per day for 14 days.Calculate the cost excluding VAT:
[tex]\begin{aligned}\textsf{Cost (exc. VAT)}&=\textsf{(\# of units $\times$ charge per unit)}+\textsf{(\# of days $\times$ service charge per day)}\\ & = \sf 320 \times \£0.12 + 14 \times \£0.20\\&= \sf \£38.4+\£2.8\\&= \sf \£41.20\end{aligned}[/tex]
To find the total cost including VAT at 5%, multiply the cost (exc. VAT) by 1.05:
[tex]\begin{aligned}\textsf{Cost (inc. VAT at 5\%)}&= \sf \£41.20 \times 1.05\\&= \sf \£43.26\end{aligned}[/tex]
If a and b are positive numbers, find the maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5.
The maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5 is 0 ≤ x ≤ 5 is 5^b.
What is the maximum value?Generally, To find the maximum value of a function on a given interval, it is generally helpful to find the critical points (points, where the derivative is equal to zero or the function, is undefined) and the endpoints of the interval, and then evaluate the function at these points to find the maximum value.
The d/dx f(x) is given by:
f'(x) = ax^(a-1)(5-x)^b - bx^a(5-x)^(b-1)
Setting this equal to zero and solving for x, we find that the critical points are x = 0, x = 5, and x = (5b)/(a+b).
We can then evaluate the function at these points to find the maximum value. At x = 0, f(x) = 0^a*(5-0)^b = 5^b.
At x = 5, f(x) = 5^a*(5-5)^b = 0.
At x = (5b)/(a+b),
f(x) = [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b.
Since a and b are positive, the maximum value must occur at either x = 0 or
x = (5b)/(a+b).
To determine which of these points gives the larger value of f(x), we can compare the values of
5^b and [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b.
The expression [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b is equal to [(5b)/(a+b)]^a*[(a+b-5b)/(a+b)]^b.
Since a and b are positive, [(5b)/(a+b)]^a and [(a+b-5b)/(a+b)]^b are both greater than or equal to 1, so the expression [(5b)/(a+b)]^a*[(a+b-5b)/(a+b)]^b is greater than or equal to 1.
Therefore, the maximum value of f(x) is 5^b, which occurs at x = 0.
Thus, the maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5 is 5^b.
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(9^x-4)(9^3x+2)=9^10
Answer: x=3
Step-by-step explanation:
[tex]\displaystyle\\(9^{x-4})(9^{3x+2})=9^{10}\\\\9^{x-4+3x+2}=9^{10}\\\\9^{4x-2}=9^{10}\\\\4x-2=10\\\\4x-2+2=10+2\\\\4x=12[/tex]
Divide both parts of the equation by 4:
[tex]x=3[/tex]
Kala swam 4 kilometers against the current in the same amount of time it took her to swim 12 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Kala swim if there were no current?
Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Distance = Rate x Time
Let Kala's swimming speed = X
4 km = (X-2)×Time
12 km = (X+2) × Time
4/x-2 = 12/x+2
Apply cross multiplication
4(x+2)=12(x-2)
4x+8=12x-24
Take all variables on one side
4x-12x=-24-8
-8x=-32
Divide both sides by 8
x=4
Kala swims 4 km/hour
With the current he swims 6 km/hour
Hence, Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.
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A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.Hours of Sleep Age Group39 or younger 40 or older Fewer than 6 38 366 to 6.9 60 577 to 7.9 79 778 or more 63 90(a) Conduct a test of independence to determine whether hours of sleep are independent of age.State the null and alternative hypotheses.H0: Hours of sleep per night is not independent of age.Ha: Hours of sleep per night is independent of age.H0: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups.Ha: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups. H0: Hours of sleep per night is independent of age.Ha: Hours of sleep per night is not independent of age.H0: Hours of sleep per night is mutually exclusive from age.Ha: Hours of sleep per night is not mutually exclusive from age.Find the value of the test statistic. (Round your answer to three decimal places.)What is the p-value? (Round your answer to four decimal places.)p-value =Using a 0.05 level of significance, what is your conclusion?Reject H0. We conclude that hours of sleep per night and age are not independent.Do not reject H0. We cannot conclude that hours of sleep per night and age are not independent. Do not reject H0. We conclude that hours of sleep per night and age are independent.Reject H0. We cannot conclude that hours of sleep per night and age are independent.(b) What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?Fewer than 6 % 6 to 6.9 % 7 to 7.9 % 8 or more %
Sleep hours per night is independent.
Given the data:
Hours of Sleep 39 or younger 40 or older
> 6 _____38 36
6 to 6.9 _ 61 58
7 to 7.9 __76 74
8 or more 65 92
The analysis will be conducted using the Chisquare statistic:
The supposition
H0: The amount of sleep each night is independent
H1: The amount of sleep each night is not independent
χ² = (observed - Expected) (observed - Expected)2 / Predicted
to speed up computation. To conduct the analysis, we might utilize a Chisquare calculator:
The evaluation statistic is 4.0061.
Row - 1 * The degree of freedom (column - 1)
Degree of freedom is equal to (4-1)*(2-1)=3*1=3.
Pvalue is 0.261.
Since Pvalue >, we are unable to reject the hypothesis that sleep duration is independent total %
> 6 _____38 36_ 74 _ 14.8
6 to 6.9 61 58 _ 119 23.8
7 to 7.9 __76 74 150 30
8 or higher 65 92 157 31.4
_______240 260 500 100
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Mr. Brooks spent one over two of an hour making gingerbread cookies and one over fourths of an hour breaking the cookies. She then spent 45 minutes decorating the cookie. How many total minutes did she spend on her gingerbread cookies
90 minutes
Step-by-step explanation:
1/2 an hour = 30 minutes
1/4 an hour = 15 minutes
45+15=60
60+30=90
Statement
1. 3x + 10 = 8x - 15
2. 10 = 5x - 15
3. 25 = 5x
4. 5 = x
5. x = 5
What are the reason for these
Answer:
1. Given
2. Subtraction P.O.E
3. Addition P.O.E
4. Division P.O.E
5. Symmetric P.O.E
Step-by-step explanation:
P.O.E stands for Property of Equality
PLEASE HURRY WILL GIVE BRAINLIEST
Answer:
1.d
2.a
3.e
4.g
5.f
6.c
7.b
Step-by-step explanation:
did it already
if you played this game 559 times how much would you expect to win or lose? round your answer to two decimal places. losses must be expressed as negative values.
The probability of winning or loosing the game is x/559
The term probability is known as the occurrence of a random event and it can be written between zero to one.
Here we need to find how much would you expect to win or lose, if you played this game 559 times.
While we looking into the given question, we have known that there is no proper number of time that the coin has tossed so let us consider x be the amount of time the coin has been tossed.
AS we know that the formula to find the probability is written as
P(E) = n(E)/n(S)
here the value of n(S) is 559 and the value of n(E) is x.
So, the probability is written as,
=> P = x/559
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40 minus 8 divided by -4 + 6 x -7
Answer: 40 minus 8 divided by -4 + 6 x -7 = 0
Step-by-step explanation: i literally just used a calculator -_-
Find the dimensions of a rectangle with perimeter 76 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.)
The dimensions of a rectangle are 19m.
Here we have to find the dimensions of a rectangle.
Data given:
Perimeter = 76m
The formula for the perimeter of the rectangle:
perimeter = 2( length + breadth)
So,
76 = 2 ( l+b)
l + b = 38
l = 38 -b
The formula for the area of the rectangle:
Area = length × breadth
A =( 38-b)×b
= 38b - b²
At maximum point:
dA/ dw = 38 - 2b
38 - 2b = 0
b = 19
Therefore the dimension is 19m.
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Determine whether the sequence is arithmetic or not .if it is,find the common difference and the next three terms given
2,5,8,11,...
2,-4,6,8,10,...
-6,-10,-14,-18,...
40,42,44,46,...
1.2,1.8,2.4,...
1,5,9,13,.
Therefore the common difference in this AP series is 4 and the next 3 terms are 1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.
Arithmetic sequences are what?Rows with a defined pattern, in which the difference between two consecutive terms is equal and fixed, are referred to as arithmetic sequences and series, also known as rows and counting series. In other words, by adding a fixed integer to the previous term, each term in the arithmetic arrangement is obtained from the previous term. To put it another way, every term in the arithmetic series (except from the first term) is obtained by adding a specific integer to the term that comes before it.
Here,
This mathematical sequence can be written as follows:
A, A+D, A+2D, A+3D, A+4D, etc. , a+(n-1)d or
where:
First term: a
d stands for common variation.
It is stated that the arithmetic sequence formula is
a = a + (n-1)d
where
First term: a
n = the number of terms
d stands for common variation.
Common Difference
In mathematical terminology, the common difference is the difference between two words.
2, 5, 8, 11, and more problems
Answer: To determine if a row is an arithmetic sequence or not, first identify the similarities between the rows.
d = 5 - 2 d = 8 - 5 d = 11-8
d = 3.
Each of them differs by 3 points.
The following three words are then 2, 5, 8, 11, 11+3, 11+6, 11+9 or 2, 5, 8, 11, 14, 17, and 20.
Issues 2, 4, 6, 8, and 10 exist.
Answer:
d = -4 - 2 = -6
d = 6 - (-4) = 10
It does not contain arithmetic sequences because there is no common difference.
Challenge: -6, -10, -14, -18,...
Answer:
d = -10 - (-6) = -4
d= -14 - (-10) = -4
d= -18 - (-14) = -4
There is a -4 difference between them all.
The following three terms are then 6, 10, 14, 18, -18, -18 + (-4), -18 + (-8), -18 + (-12), or 6, 10, 14, 18, -18, -22, -26, -30.
Issues 40, 42, 44, 46,...
Answer:
d = 42 - 40 = 2
d = 44 - 42 = 2
d = 46 - 44 = 2
All of them differ by 2 points.
The subsequent three words are either 40, 42, 44, 46, 48, 50, 52 or 40, 42, 44, 46, 46 + 2, 46 + 4, 46 + 6.
Issues: 1.2, 1.8, 2.4,...
Answer:
d = 1.8 - 1.2 = 0.6
d = 2.4 - 1.8 = 0.6
They are all separated by 0.6.
1.2, 1.8, 2.4, 2.4 + 0.6, 2.4 + 1.2, 2.4 + 1.8 or 1.2, 1.8, 2.4, 3.0, 3.6, 4.2 are the following three words.
Issues 1, 5, and 9,13
Answer:
d = 5 - 1 = 4
d = 9 - 5 = 4
d = 13 - 9 = 4
They are all divided by 4 in common.
The subsequent three terms are either 1, 5, 9, 13, 17, 21, or 25. These are 1, 5, 9, 13, 13 + 4, 13, 8, 13, and 12.
Therefore the common difference in this AP series is 4 and the next 3 terms are 1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.
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Anything helps. Thank you for the help.
Answer: Attached to the post.
Step-by-step explanation:
First, label points A and B--given as (3, -3) and (3, 1) respectively. Now connect the points to form line segment AB.
We need to reflect this line segment over the line y = x. To visualize this easier, let's draw line y = x. Two coordinates on this line is (1, 1) and (0, 0). Plot these points and connect them to form line y = x.
Finally, we need to reflect line segment AB over y = x. Imagine the line y = x is a mirror and reflect the line segment AB over it. In my diagram, line segment A'B' is the answer.
find the sum by adding each term together. use the summation capabilities of a graphing utility to verify your result. (round your answer to four decimal places.) 5 1 k2 4 k
The result of the following summation is 114.
We are given the following summation, i = 1 to 6 ∑(4i + 5)
To determine the sum by adding the values, we will substitute the values of i, starting from i = 1 to i = 6, in the expression.
= 4(1) + 5 + 4(2) + 5 + 4(3) + 5 + 4(4) + 5 + 4(5) + 5 + 4(6) + 5
= 4(1) + 4(2) + 4(3) + 4(4) + 4(5) + 4(6) + 30
= 4 + 8 + 12 + 16 + 20 + 24 + 30
= 114
Thus, the result of the sum is 114.
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What is 150% of 32?
Answer: 48
Step-by-step explanation:
[tex]\displaystyle\\\frac{32(150\%)}{100\%} =\\\\\frac{4800}{100}= \\\\48[/tex]
Answer:
48
Step-by-step explanation:
150% = 150/100 = 1.5
Then:
32 * 1.5 = 48
question 3.
Graph the line for y+1=−35(x−4) on the coordinate plane.
Answer:
(0, 139) and (139/35, 0)
Step-by-step explanation:
1. Given: Cos θ = (3/5), Find: Csc θ
2. Given: Sin θ = (5/6), Find: Cot θ
3. Given: tan θ = (3/4), Find: Cot θ
4. Given: Sec θ = (7/2), Find: Cos θ
5. Given: Sin θ = (2/3), Find: Cosec θ
6. Given: Sin θ = (2/3), Find: Cos θ
7. Given: Cos θ = (3/4), Find: Tan θ
8. Given: Tan θ = (6/4), Find: Sin θ
9. Given: Tan θ = (7/5), Find: Cos θ
10. Given: Tan θ = (7/5), Find: Sec θ
Help please.
the trigonometric function of all the given question is obtained.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
Given: Cos θ = (3/5), Find: Csc θ = 5/4
Given: Sin θ = (5/6), Find: Cot θ = 11/5
Given: tan θ = (3/4), Find: Cot θ= 4/3
Given: Sec θ = (7/2), Find: Cos θ= 2/7
Given: Sin θ = (2/3), Find: Cosec θ=3/2
Given: Sin θ = (2/3), Find: Cos θ=5/3
Given: Tan θ = (6/4), Find: Sin θ=6/7.21
Given: Tan θ = (7/5), Find: Cos θ=5/8.6
Given: Tan θ = (7/5), Find: Sec θ= 8.6/5
Hence the above trigonometric function of all the given question is obtained.
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Mrs. Conrad's art class was painting murals. She had 4 bottles of red paint, 5 bottles of green paint, 4 bottles of yellow paint, 6 bottles of blue paint, and 5 bottles of orange paint. Use the bar diagram to write and evaluate two numerical expressions to represent the total number of bottles of paint.
Answer:
24
Step-by-step explanation:
4+5+6+4+5=24
simple
no big deal
what angle is half of its supplement; the measure of one angle is 15 less than half the measurement of its supplement; complement angle; complementary angles add up to; what are supplementary angles; two angles that add up to 90
So one angle is of measurement 130 degree and the other angle is of measurement 50 degree.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "pening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
According to our question-
One angle's measurement is 15 less than its supplement's measurement.
Let's say that the supplement angle is measured in degrees.
So the measurement of the other angle is
And the sum of the measurement of supplementary angles is 180.
Multiplying both sides by 2
Therefore, one angle is 130 degrees in length and the other is 50 degrees.
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A library is holding a special five-day event honoring successful local writers. One writer will be invited to be a guest speaker for each night from Monday through Friday, and no writer will be asked to participate twice. The writers have each written books in only one of four different genres—science fiction, mystery, historical fiction, and non-fiction. A, J, and X are all science fiction writers. B and Y are both mystery writers. C and Z are both historical fiction writers. L is a non-fiction writer. The following conditions apply without exception:
At least one writer from each genre will be invited to speak on at least one night.
No two authors from the same genre will be invited to speak on the following night.
If C is invited to speak, then X is invited to speak on the following night.
If Y is invited to speak, then neither C nor A are invited to speak.
If X and J are both invited to speak, then neither will speak on either the first or last night.
If L and B are both invited to speak, then neither will speak on either the first or last night.
If L is invited to speak on Friday, then on what days MUST a science fiction writer be invited? Possible Answers:Monday and Wednesday
Monday and Tuesday
Tuesday and Thursday
Only Wednesday
Monday and Thursday
As per the concept of probability, If L is invited to speak on Friday, then the science fiction writer be invited on Monday and Wednesday
Probability:
In statistics, probability refers the possible and favorable outcome of the particular event.
Given,
Here we need to find if L is invited to speak on Friday, then on what days MUST a science fiction writer be invited.
Here we know that the writers of the same genre may not speak on consecutive nights.
And here we have the only five slots to fill, two of the three science fiction writers must speak on Monday and Friday
So, If both X and J are invited, then at least one will be forced to speak on Monday or Friday, which is not allowed.
Then, modification of the rules is actually just a bit of a red herring, since all of the answer choices except for the one regarding science fiction writers is true regardless.
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find the value of x if triangle abs is an equillateral triangle. pick any two sides and set them equal to eachother
If the triangle ABC is an equilateral triangle having the length as (4x - 3) , and perimeter as 63 in , then the value of x is 6 .
The triangle having all the sides of equal measure is termed as Equilateral triangle.
The triangle ABC is equilateral triangle,
The measure of length of side of triangle ABC is = 4x - 3 ;
The perimeter of the triangle is = 63
So, According to the question,
(4x - 3) + (4x - 3) + (4x - 3) = 63
12x - 9 = 63
12x = 63 + 9
12x = 72
x = 72/12
x = 6
Therefore, the value of x in the given triangle is 6.
-- The given question is incomplete, the complete question is
"Find the value of x, if the triangle ABC is an equilateral triangle with length of each side as (4x - 3), and the perimeter of the equilateral triangle ABC is 63 inches." --
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Reconsider the data from Medicine and Science in Sports and Exercise described in Exercise 8-32. The sample size was seven and the sample mean and sample standard devi ation were 315 watts and 16 watts, respectively. (a) Is there evidence that leg strength exceeds 300 watts at significance level 0.05? Find the P-value.
Using the t-distribution, it is found that the 95% confidence interval for the mean peak power after training is (301.2, 328.8).
We have the standard deviation for the sample, thus, the t-distribution is used.
The sample mean is 315.
The sample standard deviation is s = 16.
The sample size is n = 7.
The interval is:
mean ± t s/√n
To build the interval, we need to find the critical value, which looking at the t-table for a 95% confidence interval with 8 - 1 = 7 df is t = 2.4469.
Then, replacing the values:
315 - 2.4469 16/√8 = 301.2
315 + 2.4469 16/√8 = 328.8
The 95% confidence interval for the mean peak power after training is (301.2, 328.8).
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8.22. Let S be the set of all polynomials of degree at most 3. An element s(x) of S can then be expressed as
s(x) = ax3 + bx2 + cx + d, where a, b, c, d ? R. A relation R is defined on S by p(x) R q(x) if p(x) and
q(x) have a real root in common. (For example, p = (x ? 1)^2 and q = x^2 ? 1 have the root 1 in common so
that p R q.) Determine which of the properties reflexive, symmetric, and transitive are possessed by R.
R possess Symmetric property.
Let S be the set of all polynomials of degree at most 3.
s(x) = ax³ + bx² + cx + d
we know that polynomial is a mathematical expression of one or more algebraic terms each of which consist of a constant multiplied by one or more variables raised to a non negative power.
The reflexive property states that every element of the set is related to itself.
The symmetric property is defined as if one element in a set is related to the other, then we can say that the second element is also related to the first element.
The transitive property states that if a, b, c are three quantities, and if a is related to b and b is related to c then a and c are related to each other.
So here we observe that R will posses symmetric property.
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A television station claims that the amount of advertising per hour of broadcast time has an average of 15 minutes and a standard deviation equal to 1.2 minutes. You watch the station for 1â hour, at a randomly selectedâ time, and carefully observe that the amount of advertising time is equal to 17 minutes. Calculate theâ z-score for this amount of advertising time. A. zequalsnegative 1.05 B. zequals1.05 C. zequals1.67 D. zequalsnegative 1.67
The z-score for the time spent on advertisement as calculated is 1.666 .
According to a television station, there is 15 minutes on average of advertising every hour of broadcast time, with a standard deviation of 1.2 minutes.
i.e.
mean = 15
SD =1.2
Per hour's worth of advertising is represented by the random variable x.
z = x - mean / SD
Since x=17 , we have
z = ( 17 - 15 ) / 1.2
= 2 / 1.2
= 1.666
Consequently, this amount of advertising time has a z-score of -1.666.
A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
A standard normal table is a mathematical table for the values of, displaying the values of the cumulative distribution function of the normal distribution. It is also known as the unit normal table or the z-score table. The Z-score, commonly referred to as the standard score, expresses how far away from the mean an object is.
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A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let μ1 and μ2 represent the average amount of nitrogen per batch for fertilizer's A and B, respectively. Which of the following is the approptiate conclusion at the 5% significance level?a. Reject H 0; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor Bb. Reject H 0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.c.Fail to reject H 0; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor Bd. Fail to reject H 0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B
The appropriate conclusion at the 5% significance level is b. Reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.
How to calculate test statistic?[tex]\bar{x_1}[/tex] = pounds per batch distributor A = 23
[tex]\bar{x_2}[/tex] = pounds per batch distributor B = 18
[tex]\sigma_{1}[/tex] = standard deviation distributor A = 4
[tex]\sigma_{2}[/tex] = standard deviation distributor B = 5
n = sample size = 4
α = significance level = 5% = 0.05
Test statistic is using z test to find the z value from two population, after that we can search p-value and then comparing the p-value with significance level.
If p-value is lower than significance level, the null hypothesis (H0) is accepted. But, if p-value is higher than significance level, the H0 is rejected.
Calculate test statistic by this formula,
Z = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1 + \sigma^2_2}{n}}}[/tex]
= [tex]\frac{23-18}{\sqrt{\frac{4^2 + 5^2}{4}}}[/tex]
= [tex]\frac{5}{\sqrt{\frac{16 + 25}{4}}}[/tex]
= 1.56
Using z table for 1.56, we get 0.9406. Since is right tailed test. So, p value is
p-value = 1 - 0.9406
= 0.0594
Then, p-value is 0.0594 is higher than significance level 0.05. So, H0 is rejected.
Thus, the conclusion is reject H0, we cannot conclude the mean amount of fertilizer per batch distributor A is greater than distributor B.
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Hi can someone please help me Im struggling with this!!!
The measures of the angles formed by the parallel lines and their common transversal are;
Part A; B. c is equal to b
Part B; c = 60°
Second part; Angle P is 80°
Third part; The missing reason in step 3 is the option D.
Fourth part; Angle B is 72°
What are parallel lines?Parallel lines are lines in the same plane that have the same slope. The perpendicular distance between parallel is constant, such that they do not meet.
D. Vertical angles are congruent
Fourth part; Angle B is
Part A; JK is parallel to LM
Angle ∠c and angle ∠b are corresponding angles, therefore;
∠c and ∠b are congruent
∠c = ∠b
Therefore;
B. c is equal to b
Part B
Angle ∠b and 2·∠b are linear pair angles
Linear pair angles are supplementary, therefore
∠b + 2·∠b = 180°
3·∠b = 180°
∠b = 180°/3 = 60°
∠b = 60°
∠c = ∠b = 60°
B. c = 60°
Second part;
Angle P and the vertical angle to the 100° angle are same side interior angles.
Vertical angles are congruent, therefore;
Angle P and 100° are same side interior angles
Same side interior angles are supplementary, therefore;
m∠P + 100° = 180°
m∠P = 180° - 100° = 80°
Third part;
Angle ∠2 and angle ∠3 are formed by the transversal t and w, therefore, they are vertical angles
Vertical angles theorem states that two sets of linear pair angles, that have congruent angles are formed from the intersection of two lines.
Therefore:
∠2 ≅ ∠3, reason: D. Vertical angles are congruent
Fourth part;
Line A is parallel to line B
The angles, 4·m -24, and 3·m are corresponding angles
Corresponding lines formed by the transversal and two parallel lines are congruent, therefore;
4·m - 24 = 3·m
4·m - 3·m = 24
m = 24 degrees
Taking angle ∠B as the angle formed at the intersection of line B and the transversal, 4·m - 24 we get;
∠B = 4·m - 24
∠B = 4 × 24 = 72°
Angle ∠B = 72°
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7. At a point on the ground 20 m from the wall of a house, the elevation of the bottom of the window was 12°. From the same point, the elevation of the top of the window was 14°. Calculate the height of the window.
Answer:
d = h(cot1 - cot2)
d = 100(cot30 - cot45))
d = 100* (1.732 - 1)
d = 100*0.732
d = 73.2 m
15. Two leaky containers are filling with water. Water enters container A at a rate of 2 cup per 1 • minute and leaks out at 3 2 , 1 3 a rate of 4 cup per a minute. Water enters container B at a rate of 3 cup per 1 5 minute and leaks out at a rate of 1 2 cup per 3 _ minute. Which container needs to be filled faster in order for both containers to gain the same amount of water per minute? By how much more water per minute? Explain.
Container B needs to be filled faster in order for both containers to gain the same amount of water per minute , and by 1/6 water per minute .
What is the rate at which water is filled?Since water enters container A at a rate of 2/3 cup per 1/2 minute, then we can say that;
Rate of Filling container A = (2/3)/(1/2) = 4/3 cups per minute
We are also told that in container A, water leaks out at a rate of 1/4 cup per 3/4 minute. Thus;
Rate of leaking container A = (1/4)/(3/4) = 1/3 cups per minute
Amount of water in Container A in one minute = (4/3) - (1/3)
= 1
Similarly;
Since water enters container B at a rate of 3/4 cup per 1/2 minute, then we can say that;
Rate of Filling container B = (3/4)/(1/2) = 3/2 cups per minute
We are also told that in container B, water leaks out at a rate of 1/2 cup per 3/4 minute. Thus;
Rate of leaking container B = (1/2)/(3/4) = 2/3 cups per minute
Amount of water in Container B in one minute = (3/2) - (2/3) = 5/6
Since amount of water per minute in container A is 1 and the amount of water per minute in container B is 5/6 , then it means that container A fills faster by container B by; 1 - 5/6 = 1/6
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Complete question is;
two leaky containers are filling with water. water enters container a at a rate of 2/3 cup per 1/2 minute and leaks out at a rate of 1/4 cup per 3/4 minute. water enters container b at a rate of 3/4 cup per 1/2 minute and leaks out at a rate of 1/2 cup per 3/4 minute. which container needs to be filled faster in order for both containers to gain the same amount of water per minute? by how much more water per minute? explain
