x = [tex]\frac{y}{3}[/tex] - [tex]\frac{2}{3}[/tex]
2a<-4+a need some help with the answer?
Answer: there is the answer, number line, and graph answers
Step-by-step explanation:
A lumber company is making boards that are 2857.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 16 is made, and it is found that they have a mean of 2858.7 millimeters with a variance of 100.00. A level of significance of 0.05 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the boards are either too long or too short
Answer:
The test statistic 't' = 0.68 < 2.1314 at 0.05 level of significance
Null Hypothesis is accepted
There is no sufficient evidence to support the claim that the boards are either too long or too short
Step-by-step explanation:
Step(i):-
Mean of the Population (μ) = 2857.0 millimetres
size of the sample 'n' = 16
Mean of the sample (x⁻) = 2858.7 millimetres
The Variance of the sample (S²)= 100.00
Standard deviation of the sample (S) = √100 =10
Degrees of freedom = n-1 =16-1 =15
Level of significance =0.05
Tabulated value = [tex]t_{\frac{0.05}{2} , 15} = t_{0.025,15} = 2.1314[/tex]
Step(ii):-
Null Hypothesis :H₀ : There is no sufficient evidence to support the claim that the boards are either too long or too short
Alternative Hypothesis: H₁:There is sufficient evidence to support the claim that the boards are either too long or too short
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{2858.7 -2857}{\frac{10}{\sqrt{16} } }[/tex]
t = 0.68
The calculated value = 0.68 < 2.1314 at 0.05 level of significance
Null Hypothesis is accepted
Final answer:-
There is no sufficient evidence to support the claim that the boards are either too long or too short
We choose a number from the set 1, 2, 3,..., 100 uniformly at random and denote this number by X. For each of the following choices decide whether the two events in question are independent or not.
a. A = {X is even), B-(X is divisible by 5}
b. C= (X has two digits), D = {X is divisible by 31}
c. E= {X is a prime), F = {X has a digit 5}
Answer:
(a) A and B are dependent.
(b) C and D are dependent.
(c) E and F are dependent.
Step-by-step explanation:
Two sets are said to be independent if the intersection of the two set is empty. That is the sets are disjoint.
Let's examine the situations to determine if they are independent or not.
(a) A = {2, 4, 6, . . . , 10, . . . , 20, . . .} and B = {5, 10, 15, . . . , 20, . . .}. Since A n B = {10, 20, . . .}, then the sets are dependent
(b) C = {10, 11, 12, . . . , 31, . . . , 62, . . . , 93, . . .} and D = {31, 62, 93}. Since C n D = {31, 62, 93}, then the sets are dependent.
(c) E = {5, 7, 11, . . .} and F = {5, 15, . . .}. Since E n F = {5}, then the set are dependent.
Thus
(a) A and B are dependent.
(b) C and D are dependent.
(c) E and F are dependent.
10. Wnte an equation in point-slope form for the lne through the given point with the given slope.
(-3,-5);m=-2/5
A. Y+5=-2/5(x+3)
B. Y+5=(-2/5)x-3
C. Y-5=-2/5(x+3)
D. Y-5=-2/5(x-3
Answer:
We conclude that an equation in the point-slope form will be:
y+5 = -2/5 (x+3)
Hence, option A is true.
Step-by-step explanation:
We know that the point-slope form of the line equation is
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
Given
point (-3, -5)slope m = -2/5substituting the values m = -2/5 and the point (-3, -5) in the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
y - (-5) = -2/5 (x-(-3))
y+5 = -2/5 (x+3)
Therefore, we conclude that an equation in the point-slope form will be:
y+5 = -2/5 (x+3)
Hence, option A is true.
The value of your father’s car when bought was $30,000. If it loses 10% of its value every year, how long until the vehicle is only worth $20,000?
Answer:
6.7
Step-by-step explanation:
10% of 30000
10/100 x 30000
0.10 x 30000
=3000
In order to find how long you have to divide 20k with 3k
20000/3000 = 6.66666667
Round it up and you get 6.7
plz answer i will thank you and brainliest u
Answer:
15
Step-by-step explanation:
The amount of water displacement would be equivalent to the volume of the rock, which is 1800. We find this by doing 10 x 12 which is 120. Now we can divide 1800 by 120, which is 15. Giving us the dimensions 10 x 12 x 15.
What is the rate of change of the function described in the table?
Answer:
It’s 5
Step-by-step explanation:
-2/3 divided by -4/9
Answer: 1.5
Step-by-step explanation:
If you only have a 1/4 measuring cup and a recipe calls for 3 1/4cups of flour, how many 1/4 cups would you need to use?
Answer:
17 cups i believe. lemme check. naw its 13
Step-by-step explanation:
Answer:
in total 3 cups of 1/4 of flour.
Step-by-step explanation:
WILL MARK YOU BRAINLIEST
Reflect (-5, -3) over the X-axis.
Then translate the result down 2 units.
What are the coordinates of the final point?
Answer:
_____________the answer is (-7,-3)______________
the middle school choir concert was 1 1/4 hours long. each song was 1/,8 of an hour how many songs did the audience hear during the choir concert
A.9 songs
B.10 songs
C.12 songs
D.32 songs
Answer:
b
Step-by-step explanation:
2) What is 18th term in this sequence: 45, 49, 53, 57,
Answer:
a₁₈ = 113
Step-by-step explanation:
There is a common difference d between consecutive terms
d = 49 - 45 = 53 - 49 = 57 - 53 = 4
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 45 and d = 4, then
a₁₈ = 45 + (17 × 4) = 45 + 68 = 113
Find the slope of the line that is perpendicular
Y=3x+5
Answer:
y = -1/3 + 5
Step-by-step explanation:
you get the reciprocal of the slope in order to make a perpendicular copy
Please help me answer this with the correct answer :)
Explain your answer
I will give braisnlt :)
Answer: b
Step-by-step explanation:
n(n+1)+2n+1
expand and simplicity
Answer:
n² + 3n +1
Step-by-step explanation:
n(n+1) + 2n + 1
i) distribute n into the parantheses= (n×n) + (n×1) + 2n + 1
= n² + n + 2n + 1
ii) collect like terms= n² + 3n +1
Adam can paint 38 feet of fence per hour. How many yards of fence can he paint per hour?
Answer:
12
Step-by-step explanation:
Answer:
12 yards per hour
Step-by-step explanation:
What is the slope of the line segment?
A graph is shown. The values on the x axis are 0, 1, 2, 3, 4, and 5. The values on the y axis are 0, 5, 10, 15, 20, and 25. A straight line joining the ordered pairs 0, 0 and 1, 5 and 2, 10 and 3, 15
5
1 over 5
negative 1 over 5
−5
Answer:
The slope is 5
Step-by-step explanation:
divide the change in y by the change in y
you can use two different points for example 1,5 and 3,15
the change in y between these points is 10, the change in x is 2
10/2=5
also since the values of x increase constantly by 1 and it's a continuous line (meaning the domain could be any number between 1 and 3 in this graph) you can calculate only the change in y and that will give you the slope
Solve for x.
log₈(3x+1)+16=18
What is the slope of the line
(Picture below)
I know there is a very similar question already out there
but my version is requesting different functions
Cami is comparing the growth rates in the value of two items in a collection. the value of a necklace increases by 3.2% per year. the value of a ring increases by 0.33% per month.
1a) Write a function to represent the value of A of the necklace after t years, assuming the initial value of $1
1b) then write an equivalent function with a power of 12t
2a) Write a function to represent the value of B of the ring after t years with the power of 12t , assuming the initial value of $1
2b) then write an equivalent function with a power of t
so
1a) A= 1 (1+3.2/100)^t
A= $1.032
1b) ????? please help
2a) B=1 (1+0.33/100)^12t
B= $1.04
2b) ???????? please help
ty ty ty this momma is trying to help her kids and is a bit lost !
Problem 1, part (a)
t = number of years
A = value of the necklace after t years
3.2% = 3.2/100 = 0.032
If the necklace starts off being $1, then after t years, it will have this value
A = 1*(1 + 0.032)^t
A = 1.032^t
You were close, but forgot about the exponent t
------------------------------------
Problem 1, part (b)
Since t represents the number of years, this means 12t represents the number of months, because there are 12 months in a year.
The annual growth rate is 3.2%, which converts to 0.032
Divide this over 12 and we get the approximate value 0.032/12 = 0.00267
So we get this new equivalent function
A = 1*(1+0.00267)^(12t)
A = 1.00267^(12t)
=========================================================
Problem 2, part (a)
t = number of years
12t = number of months
The ring's value goes at a rate of 0.33% per month, which converts to the decimal form 0.0033
The value of the ring is
B = 1*(1 + 0.0033)^(12t)
B = 1.0033^(12t)
------------------------------------
Problem 2, part (b)
We'll take the reverse approach in what we did with part (b) of the previous problem. There we divided by 12 to go from an annual rate to a monthly rate.
We'll multiply by 12 to go from the monthly growth rate to the annual growth rate.
The monthly growth rate of 0.33% turns into the annual growth rate of 12*0.33% = 3.96%, and that turns into the decimal form 0.0396
So,
B = 1*(1+0.0396)^t
B = 1.0396^t
represents the value of the ring after t years.
Craig has £13.40
He sees this offer in a restaurant:
Main courses £8.90 each. Buy one main course and get the 2nd HALF PRICE!
Can he afford to buy two main courses? Show your working.
Caroline took a math test and got 19 out of 25 questions correct. What percent of the questions did she answer correctly?
Answer:
76%
Step-by-step explanation:
do the amount of correct answers divided by the total of questions asked.
An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an estimate at the 85% level of confidence. For a sample of 295 third graders, the mean words per minute read was 26.9. Assume a population standard deviation of 2.7. Construct the confidence interval for the mean number of words a third grader can read per minute. Round your answers to one decimal place
Answer:
85% level of the confidence interval is
(26.337, 26.662)
Step-by-step explanation:
Explanation:-
Given the size of the sample 'n' = 295
Mean of the sample x⁻ = 26.5
The Standard deviation of the Population = 2.7
85% level of the confidence interval is determined by
[tex](x^{-} - Z_{0.15} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.15} \frac{S.D}{\sqrt{n} })[/tex]
Critical value Z₀.₁₅ = 1.036
85% level of the confidence interval is determined by
[tex](x^{-} - Z_{0.15} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.15} \frac{S.D}{\sqrt{n} })[/tex]
[tex](26.9 -1.036 \frac{2.7}{\sqrt{295} } , 26.5 + 1.036 \frac{2.7}{\sqrt{295} })[/tex]
( 26.5 - 0.1628 , 26.5+0.1628)
(26.3372,26.6628)
what is 300x21444444
Answer:
6433333200
Step-by-step explanation:
quick math
I need help, pls !!!
Answer:
D) 11.2 Orange
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (-8, -1)
Point (-3, 9)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute [DF]: [tex]\displaystyle d = \sqrt{(-3+8)^2+(9+1)^2}[/tex]Add: [tex]\displaystyle d = \sqrt{(5)^2+(10)^2}[/tex]Exponents: [tex]\displaystyle d = \sqrt{25+100}[/tex]Add: [tex]\displaystyle d = \sqrt{125}[/tex]Simplify: [tex]\displaystyle d = 5\sqrt{5}[/tex]Evaluate: [tex]\displaystyle d = 11.1803[/tex]Round: [tex]\displaystyle d = 11.2[/tex]help please jejedjjdnfndnf
Answer:
x = 24 degrees
Step-by-step explanation:
A line is 180 degrees. If we are given that angle BOC is 156 degrees, we can subtract that from 180. 180 - 156 = 24.
Pls mark brainliest.
through: (-9, 0), perpendicular to
y = 3x - 2
In slope intercept form
Answer:
The equation perpendicular to y = 3x - 2 and passing through (-9, 0) in the slope-intercept form will be:
[tex]\:\:y\:=-\frac{1}{3}x-3[/tex]Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptGiven the line
y = 3x - 2
comparing with the slope-intercept form of the line equation
The slope of the line y = 3x - 2 is: m = 3
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = 3
Thus, the slope of the the new perpendicular line = – 1/m = -1/3 = -1/3
The point-slope form of the line equation is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
m is the slope of the line(x₁, y₁) is the pointIn our case:
m = -1/3(x₁, y₁) = (-9, 0)now substituting the perpendicular slope m = -1/3 and (-9, 0) in the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-0=-\frac{1}{3}\left(x-\left(-9\right)\right)[/tex]
[tex]y=-\frac{1}{3}\left(x-\left(-9\right)\right)[/tex]
[tex]y=-\frac{1}{3}\left(x+9\right)[/tex]
[tex]\:\:y\:=-\frac{1}{3}x-3[/tex]
Therefore, the equation perpendicular to y = 3x - 2 and passing through (-9, 0) in the slope-intercept form will be:
[tex]\:\:y\:=-\frac{1}{3}x-3[/tex]Watch help video
Anthony is going to invest in an account paying an interest rate of 2.7% compounded
quarterly. How much would Anthony need to invest, to the nearest hundred dollars,
for the value of the account to reach $130 in 10 years?
Answer:
Submit Answer
attempt 2 out of
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Answer:
Anthony needs to invest $99.33.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Interest rate of 2.7% compounded quarterly.
This means that [tex]r = 0.027, n = 4[/tex].
How much would Anthony need to invest, to the nearest hundred dollars, for the value of the account to reach $130 in 10 years?
We have to find P for which: [tex]A = 130, t = 10[/tex]. So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]130 = P(1 + \frac{0.027}{4})^{4*10}[/tex]
[tex]P = \frac{130}{(1 + \frac{0.027}{4})^{4*10}}[/tex]
[tex]P = 99.33[/tex]
Anthony needs to invest $99.33.
The sum of the measures of the angle in any triangle is 180 degrees. In triangle ABC, angles A and B have the same measure, while angle C is 42 degrees larger than each of the other two angles. Find the measure of angle C.
Answer:
88°
Step-by-step explanation:
we can say the two base angles are each x°
the vertex angle (∡C) is (42 + x)°
add them all and set equal to 180°
x + x + x + 42 = 180
3x + 42 = 180
3x = 138
x = 46
∡C = 46 + 42 = 88°
If angle C is 42 degrees larger than each of the other two angles. then measure of angle c is 88 degrees.
What is Angle Sum property?The sum of angles of a triangle are 180 degrees.
Given that,
The sum of the measures of the angle in any triangle is 180 degrees. In triangle ABC, angles A and B have the same measure, while angle C is 42 degrees larger than each of the other two angles. we can say the two base angles are each x°
the vertex angle (∡C) is (42 + x)°
add them all and set equal to 180°
x + x + x + 42 = 180(By angle sum property)
3x + 42 = 180
Shift 42 to RHS
3x = 180-42
3x = 138
Divide both sides by 3.
x = 46
∡C = 46 + 42 = 88°
Therefore angle C is 88°.
To learn more on Angle sum property click:
https://brainly.com/question/4316040
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A local pizza restaurant delivery time has a uniform distribution over 10 to 75 minutes. What is the probability that the pizza delivery time is more than 30 minutes on a given day
Answer:
The probability that the pizza delivery takes more than 30 minutes is 61.53%.
Step-by-step explanation:
To determine the percentage of probability that the pizza will take more than 30 minutes to be delivered, knowing that the delivery delay time is evenly distributed between 10 and 75 minutes, the following calculation must be performed:
75 - 10 = 65
100/65 = 1.53
30 - 10 = 20
65 - 20 = 40
40 x 1.53 = 61.53
Therefore, the probability that the pizza delivery takes more than 30 minutes is 61.53%.
Answer:
0.6923
Step-by-step explanation:
we have to find P(X>45)
uniform distribution formula is P(X>A) = (b-A)/(b-a)
we have A = 30, a = 10 and b =75
P(X>45) = (75-30)/(75-10) = 45/65
P(X>45) = 0.6923
