Answer:
True
Step-by-step explanation:
Given that:
M = 27, sample of n = 36 scores, µ = 30 and σ = 18.
The z score is used in statistics to determine by how many standard deviations the raw score is above or below the mean. If the z score is positive, the raw score is greater than the mean and if the z score is negative the raw score is less than the mean. The z score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that M = 27, this means that x = 27. Therefore:
[tex]z=\frac{x-\mu}{\sigma}\\\\for \ a\ sample\ size(n):z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\z=\frac{27-30}{18/\sqrt{36} } =\frac{-3}{3}=-1[/tex]
This sample mean corresponds to a z-score of z = –1.00.
25 point please help I would really appreciate it :)))
Answer:
(a) 40
(b) 15% per week, to the nearest percent.
Step-by-step explanation:
Given:
old production,
P(w) = 230(1.1^w)
(a) At week 0, w=0, so
P(0) = 230(1.1^0) = 230
Difference (old - new) = 230-190 = 40
(b) about 15% per week
(c) from the 4th week on
approximate growth rate of new factory
N(w) = 190(R^w)
we know
w=0, N(0) = 190
w=7, N(7) = 505
so R=(505/190)^(1/7) = 1.1499 = 1.15 approx.
(c)
The old production tabulated:
w P(w) New
0 230 190
1 253 220
2 278 252
3 306 290
4 337 337
5 370 380
6 407 440
7 448 505
So we see that at the end of the 4th week, the two productions match, and new factory begins to exceed old production.
PLEASE HELP ME !!!!!!!!!!!!!!!!!
Answer:
2
Step-by-step explanation:
The series is a geometric series with a common ratio (r) of 1/2 and a first term (a1) of 1/2^0 = 1. The sum of such a series is given by ...
S = a1/(1 -r) 1/(1 -1/2) = 2
The sum of the series is 2.
When writting a equation how do you know where to put the equal sign?
Type the correct answer in the box. Use numerals instead of words.
Find the area of this shape.
4 cm
2 cm
4 cm
4 cm
5.75 cm
The area of the shape is
square centimeters.
Answer:
35 cm squared
Step-by-step explanation:
Triangle area = bxh 2 = 5.75 x 8 / 2 = 23
Trapezium Area = a+b /2 x h = 8 + 4 /2 x 2 = 12
23 + 12 = 35
Hope that helped!!! k
(2.05 MC) Triangle PQR is transformed to Triangle P'Q'R'. Triangle PQR has vertices P(4,0), Q(0,-4) and R(-8,-4). Triangle P'Q'R' has vertices P'(1,0), Q'(0,-1), and R'(-2,-1). Part A: What is the scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' Part B: Write The Coords of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis Part C: Are the two Triangles PQR and P"Q"R" congruent?
Answer:
Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4
Part B:
P''(-1, 0)
Q''(0, -1)
R''(2, -1)
Part C:
The two Triangles PQR and P''Q''R'' are not congruent
Step-by-step explanation:
The coordinates of triangle PQR are;
P(4, 0)
Q(0, 4)
R(-8, -4)
The coordinates of triangle P'Q'R' are;
P'(1, 0)
Q'(0, -1)
R'(-2, -1)
Part A:
The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' can be found from the ratio of the respective coordinates as follows;
The ratio of the x, and y coordinates of the points are;
P'/P = x'/x = 1/4, y'/y =0/0
R'/R = x'/x = -2/-8 = 1/4, y'/y =-1/-4 = 1/4
Therefore, the scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' = 1/4
Part B: For reflection across the y-axis, we have;
Pre-image (x, y) becomes the image, (-x, y)
Therefore, we have;
Reflection of P'(1, 0) about the y-xis becomes P''(-1, 0)
Reflection of Q'(0, -1) about the y-xis becomes Q''(0, -1)
Reflection of R'(-2, -1) about the y-xis becomes R''(2, -1)
Part C:
The two Triangles PQR and P''Q''R'' are similar but they are not congruent as the dimensions of PQR are larger than the dimensions of the sides of triangle P''Q''R''.
(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4
(B) Coordinates of Δ P"Q"R"
P" (-1,0)
Q"(0,-1)
R"(2,-1)
(C) Triangles PQR and P"Q"R" are not congruent.
Given
ΔPQR is transformed into ΔP'Q'R'
Coordinates of P, Q, R are
P (4,0),
Q(0,-4)
R(-8,-4)
Coordinates of P'Q'R' are
P'(1,0)
Q'(0,-1)
R'(-2,-1)
(A) By Distance formula we can find the distance between P Q and P'Q'
Distance formula = [tex]D= \sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2 }[/tex]
Where D = Distance between two points [tex](X_1.Y_1) \; and\; (X_2.Y_2)[/tex]
from distance formula we can write that
[tex]PQ = \sqrt{(0-4)^2+ (-4-0)^2} }\\[/tex]
PQ = [tex]4\sqrt{2}[/tex]
Similarly
P'Q'= [tex]\sqrt{2}[/tex]
PQ /P'Q' = 4
hence the scale factor of dilation is 1/4 (Compression)
(B )The Coordinates of Reflection about y axis can be written for a point
[tex](x,y ) \; as \; (-x,y)[/tex]
So the Coordinated of Δ P"Q"R" can be written as
P" (-1,0)
Q"(0,-1)
R"(2,-1)
(C) ΔPQR and ΔP"Q"R" are similar triangles but they are not congruent because their sides are not equal in size.
For more information please refer to the link below
https://brainly.com/question/12413243
A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 40 dumpster loads of waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week. A f(x) = −2x + 40. B f(x) = 2x + 40 C f(x) = −2x + 50 D f(x) = 2x + 50
Answer:
The answer is A f(x) = -2x + 40
Step-by-step explanation:
it has a negative 2 because the dumps are decreasing by 2 every week and x is the amount of weeks and + 40 because that is the amount you started with.
Simplify the expression so there is only one positive power for each base. (5^-2 x 4^-4)^-2
Answer:
Step-by-step explanation:
[tex](5^{-2}[/tex] × [tex]4^{-4}[/tex] [tex])^{-2}[/tex]
=[tex](5^{-2}[/tex][tex])^{-2}[/tex] x [tex](4^{-4})^{-2}[/tex] ∴[tex](a.b)^{n} =a^{n} .b^{n}[/tex]
=[tex]5^{-2.-2}[/tex] x [tex]4^{-4 . -2}[/tex] ∴[tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex] // here m is an exponent of [tex]a^{n}[/tex].
=[tex]5^{4}[/tex] x [tex]4^{8}[/tex]
WILL GIVE BRAINLIEST!!!!!! Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown: Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. Part B: The length of rod PR is adjusted to 17 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work.
A) Here, We'll use "Pythagoras Theorem" which tells:
a² + b² = c²
So, PR² = PQ² + QR²
PR² = 14² + 9²
PR² = 196 + 81
PR = √277
In short, Your Answer would be 16.64 Feet
B) Again, Use the Pythagoras Theorem,
c² - a² = b²
18² - 14² = b²
b² = 324 - 196
b = √128
b = 11.31
In short, Your Answer would be 11.31 Feet
Part A: Using the Pythagorean Theorem. a^2 + b^2 = c^2
PQ^2 + QR^2 = PR^2 (The rods make a right triangle, where PR would be the hypotenuse, and QR and PQ would be legs a and b.)
14^2 + 9^2 = PR^2
196 + 81 = PR^2
Square root of 277 = PR
16.64 = PR
So, the hypotenuse would be equal to 16.64 ft.
Part B: Using the Pythagorean Theorem. a^2 + b^2 = c^2
PR^2 - PQ^2 = QR^2 (Trying to find the height of QR this time, not the hypotenuse, since we know what it is already. Subtracting the value of leg a from the hypotenuse will give us the value of leg b, QR.)
18^2 - 14^2 = QR^2
324 - 196 = QR^2
Square root of 128 = QR
So, the new height of QR would be 11.31 ft.
one day shahed was playing with numbers.He wrote 15 fractions using all natural numbers from 1 to 30 exactly once-either as numerator or as denominator.How many of these fractions are most is integers.
Answer:
15
Step-by-step explanation:
half of 30 is 15
he used all the numbers upto 30 once
all the numbers in between arent integers but decimals
Write an equation to model the distance between the point (2,4) and any point along the curve
y=4x3 + 1.
Answer:
Distance D = √ [(2 - x)^2 + (3 - 4x^3)^2].
Step-by-step explanation:
Use the distance formula:
D = √[(x2 - x1)^2 + (y2 - y1)^2].
So here it is
D = √[(2 - x)^2 + (4 - y)^2] where x,y is any point on the curve.
D = √[2 - x)^2 + (4 - (4x^3 + 1))^2]
D = √ [(2 - x)^2 + (3 - 4x^3)^2]
Check whether 301 is a term of the list of numbers 5, 11, 17, 23, . . .
Answer:
not a term
Step-by-step explanation:
There is a common difference between consecutive terms in the sequence, that is
d = 11- 5 = 17 - 11 = 23 - 17 = 6
This indicate 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 = 5 and d = 6, thus
[tex]a_{n}[/tex] = 5 + 6(n - 1) = 5 + 6n - 6 = 6n - 1
Equate this to 301 and solve for n
6n - 1 = 301 ( add 1 to both sides )
6n = 302 ( divide both sides by 6 )
n = 50.333....
Since n is not an integer value then 301 is not a term in this sequence.
A man traveled to his country home, a distance of 150 miles and then back. His average rate of speed going was 50 miles an hour and his average return speed was 30 miles per hour. His average rate of speed for the entire trip was Need help will mark brainlist
Answer:
37.5 mi/h
Step-by-step explanation:
time = distance / speed
On the trip 'going', the time was (150 mi)/(50 mi/h) = 3 h.
On the return trip, the time was (150 mi)/(30 mi/h) = 5 h.
__
speed = distance / time
The average speed for the whole trip was ...
speed = (150 mi +150 mi)/(3 h +5 h) = (300 mi)/(8 h) = 37.5 mi/h
His average rate of speed was 37.5 miles per hour.
How do you graph y=2/3x-4
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▹ Answer
You can use a graphing calculator.
▹ Step-by-Step Explanation
Attached is a screenshot.
Hope this helps!
CloutAnswers ❁
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Answer:
See explanation and picture attached
Step-by-step explanation:
We can break down this expression into it's core components:
Since the constant here is -4, the y intercept is -4.
Since the value we are multiplying x by is [tex]\frac{2}{3}[/tex], the slope is [tex]\frac{2}{3}[/tex]. This means for every time we go horizontal 3 units, the line increases by 2.
The graph is attached.
Hope this helped!
A company makes nylon and canvas backpacks. The profit on a nylon backpack is $3 and the profit on a canvas backpack is $10. How many backpacks must the company sell to make a profit of more than $250? Write a linear inequality that describes the situation.
Answer:
3x +10y is greater than or equal to 250.
Step-by-step explanation:
The question asks us to write an inequality which shows that both nylon and canvas added should be greater than or equal to 250.
Since we don't know the number of nylon backpacks and canvas backpacks the company makes, we used the variables "x" and "y" to represent the number of backpacks they made from each style.
Answer:
3n + 10c > 250
Step-by-step explanation:
I confirmed it in grandpoint
Angles L and M are supplementary. What is the sum of
their measures?
The sum of the measures of angles L and M is
180 degree
Step-by-step explanation:
supplementary means anhke havinv sum of 180 degree
so sum to two supplemrntary angles is 180 drgree
Supplementary angles always add to 180.
One way I think of it is "supplementary angles form a straight angle", and both the words "supplementary" and "straight" start with the letter "S".
In contrast, complementary angles form a corner. Both "complementary" and "corner" start with "co". By "corner", I mean a 90 degree corner.
Use the following prompt to answer the next 6 questions. Suppose we want to test the color distribution claim on the M&M’s website that a bag of plain M&M’s is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown. We select a sample of 400 plain M&M’s and found the following: Color Blue Orange Green Red Yellow Brown Frequency 30 48 55 66 70 131 Is there evidence to doubt the color distribution claimed by the website? Use ????=0.05
Answer:
The claim on the M&M’s website is not true.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]
Here,
[tex]O_{i}[/tex] = Observed frequencies
[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.
The chi-square test statistic value is, 14.433.
The degrees of freedom is:
df = k - 1 = 6 - 1 = 5
Compute the p-value as follows:
[tex]p-value=P(\chi^{2}_{k-1} >14.433) =P(\chi^{2}_{5} >14.433) =0.013[/tex]
*Use a Chi-square table.
The significance level is, α = 0.05.
p-value = 0.013 < α = 0.05.
So, the null hypothesis will be rejected at 5% significance level.
Thus, concluding that the claim on the M&M’s website is not true.
The formula for the remaining volume of fuel in a car's tank is I-E\cdot DI−E⋅DI, minus, E, dot, D, where III is the initial volume of fuel, EEE is the fuel efficiency, and DDD is the distance traveled. Carson drove a distance of 120120120 kilometers. He initially had 303030 liters of fuel, and his car's fuel efficiency is 100100100 cubic centimeters per kilometer. What calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters? Choose 1 answer: Choose 1 answer: (Choice A) A 30-\dfrac{100}{1000}\cdot 12030− 1000 100 ⋅12030, minus, start fraction, 100, divided by, 1000, end fraction, dot, 120 (Choice B) B 30\cdot 1000-100\cdot 12030⋅1000−100⋅12030, dot, 1000, minus, 100, dot, 120 (Choice C) C \dfrac{30}{1000}-100\cdot 120 1000 30 −100⋅120start fraction, 30, divided by, 1000, end fraction, minus, 100, dot, 120 (Choice D) D 30-100\cdot 1000\cdot 12030−100⋅1000⋅120
Answer:
30-100/1000*120
Step-by-step explanation:
Source: Khan Academy
Answer:
30 - 100/1000 x 120
Step-by-step explanation:
Parabolic microphones are used for field audio during sports events. The microphones are manufactured such that the equation of their cross section is x=1/34y^2, in inches. The feedhorn part of the microphone is located at the focus
a. How far is the feedhorn from the edge of the parabolic surface of the microphone?
b. What is the diameter of the microphone? Explain your reasoning
c. If the diameter is increased by 5 inches, what is the new equation of the cross section of the microphone?
Answer:
a. 8.5 in.
b. 34 in
c. x = 1/39 x^2.
Step-by-step explanation:
Part a.
x = 1/34 y^2
y^2 = 34x
Comparing with y^2 = 4px where p is the focus:
4p = 34
p = 8.5 in.
Part b.
The diameter = 4p = 34 in.
Part c.
Diameter = 4p = 34 + 5 = 39 in
The new equation is x = 1/39 x^2.
Alex has a block of wood that is in the shape of a prism with the dimensions shown. He cuts a 10-cm square hole through the center of the prism. What is the volume of the remaining solid?
Answer:
1,120
Step-by-step explanation:
Find the volume of the larger figure. This can be represented using the formula for volume.
V = lwh
V = 5*18*18
V = 1620
Now, find the volume of the cut out piece of the wood. We will subtract this from the larger block.
V = lwh
V = 5*10*10
V = 500
Subtract, and you will have your answer.
1620 - 500 = 1,120
The tens digit is 2 less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 154. Find the original number.
Answer:
68
Step-by-step explanation:
Hello, the number is 'ab' meaning that we can write it as 10a +b
For instance 42 = 10*4 + 2
So, a = b - 2
and 10a + b + 10b + a = 154
11(a+b)=154
a+b = 154/11 = 14
We replace a by b - 2
b+b-2 = 14
2b = 14 + 2 = 16
b = 8 and then a = 6
the original number is 68.
Thanks
What is the simplified form of 4x−2(3y)−3?
Answer:
4x - 6y -3
Step-by-step explanation:
4x−2(3y)−3
Distribute
4x - 6y -3
Answer:
4x−6y−3
Step-by-step explanation:
All you really have to do is multiply -2 time 3y and thats it.
please solve this equation using quadratic formula
Step-by-step explanation:
x+3/x-2-1-x/x=17/4find the LCM of the denominators (x-2)x=x^2-2x
(x^2-2x)4=4x^2-8x divide the denominator by the LCM and then multiply x to the numerator
(x+3)4=4×+3
(1-x)(4x-8)
1(4x-8)-x(4x-8)
4x-8-4x^2-8x=4x
What is the value of the 6 in 13.76?
Answer:
0.06
Step-by-step explanation:
This is because the 6 is in the hundredths place.
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▹ Answer
0.06 (Hundreths)
▹ Step-by-Step Explanation
The '6' is in the hundreths place. This is written as 0.06. As a fraction, it is written as 6/100.
Hope this helps!
CloutAnswers ❁
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also being timed help!
Answer: 4
Step-by-step explanation:
Shelly and Terrence completed x tasks in a game. Terrence's total points were 20 less than Shelly's total. The expression below shows Terrence's total points in the game: 90x − 20
What does the first term of the expression represent?
A. The total points Shelly earned
B. The number of tasks Terrence completed
C.The sum of Shelly's and Terrence's total points
D. The number of tasks Shelly completed
Answer:
The correct option is;
A. The total points Shelly earned
Step-by-step explanation:
The given details are;
The number of tasks completed by Shelly and Terrence in the game = x
The total points scored by Terrence = 20 less than the total point scored by Shelly
The expression for Terrence's total point is 90·x - 20
Let the total points Shelly earned = Y
Therefore since the total points scored by Terrence = 20 less than the total point scored by Shelly, we have;
The total points scored by Terrence = Y - 20
Comparing the two expressions for the total points scored by Terrence which are;
90·x - 20 and Y - 20 we have;
90·x - 20 = Y - 20
Adding 20 to both sides of the equation gives;
90·x - 20 + 20= Y - 20 + 20
Which gives;
90·x = Y
Therefore, the first term of the expression 90·x - 20, which is 90·x is equal to Y, which is the total points Shelly earned
The correct option is therefore the total points Shelly earned.
Answer:
A. The total points Shelly earned
Step-by-step explanation:
Hope this helps!
Have a great day! :)
plz help asap i only have limited time i will give brainliest
Answer:
The answer is none.
Step-by-step explanation:
BecauseSide of the square is greater than breadth of rectangle. Answer: How can this be possible? Side of any square cannot be more than breadth of rectangle unless and until the square is bigger than the rectangle.Side of the square can be greater than length of triangle: Answer: Not at all possible. How can the length of a square be greater than the length of a rectangle? then the square would no longer have the same sides. And as i said before, squares cant be long unless and until they are bigger than the rectangle.Hope this helps....
Have a nice day!!!!
SIMPLIFY (i)35 + 25 x 72 – 51 ÷(10 + 7) (ii)-6 x 9 + 7 – 12 ÷ 3 – 5 Pls give me the correct answer
Answer:
i.1832 ii.-56
Step-by-step explanation:
using BODMAS for the first question we solve for what's in the bracket after we go with the division and after multiplication next addition and subtract in doing all that we get
35+25*72-51/17
35+25*72-3
35+1800-3
1835-3
1832
you can also use your calculator to verify answer
ii.-6*9+7-4-5
-54+7-4-5
-47-4-5
-56
Solve for x: -2x - 4 > 8
x<-6
X > -6
x<-2
x>-2
Answer:
x < -6
Step-by-step explanation:
-2x - 4 > 8
-2x > 12
x < -6, you have to flip the inequality when you multiply or divide by a negative
Answer:
a
Step-by-step explanation:
Can somebody please tell me if it’s right? i’ll mark u the brainliest
Answer:
Yes, you are correct.
Step-by-step explanation:
You are substituting the measure of angle x as the measure of angle a since they are congruent to each other.
solve for b in the mathematical formula A=1/2(a+b)h
Answer:
[tex]b = \frac{2A}{h} - a[/tex]Step-by-step explanation:
[tex]A = \frac{1}{2} (a + b)h[/tex]Multiply both sides by 2
We have
2A = (a + b)h
Divide both sides of the equation by h
That's
[tex] \frac{(a + b)h}{h} = \frac{2A}{h} [/tex]We have
[tex]a + b = \frac{2A}{h} [/tex]Move a to the right side of the equation to make b stand alone
We have the final answer as
[tex]b = \frac{2A}{h} - a[/tex]Hope this helps you
