Answer:
Explained below.
Step-by-step explanation:
The z-test statistic is given as follows:
[tex]Z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}[/tex]
Here,
[tex]\bar X=\text{Sample Mean}\\\\\mu=\text{Population Mean}\\\\\sigma=\text{Population standard deviation}\\\\n=\text{Sample size}[/tex]
The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or greater than what was the truly observed value of the test statistic.
(i)
The difference between the sample mean and the original population mean are directly proportional to the z-test statistic.
So, increasing the difference between [tex]\bar X[/tex] and [tex]\mu[/tex] will lead to an increase in the z-score.
And as the Z-score increases the p-value of the test decreases.
Thus, the complete statement is:
"Increasing the difference between the sample mean and the original population mean will result in an increase in the absolute value of z, and a decrease in the probability of obtaining a sample with that mean."
(ii)
The population standard deviation is inversely proportional to the z-test statistic.
So, increasing the population standard deviation will lead to a decrease in the z-score.
And as the Z-score decreases the p-value of the test increases.
Thus, the complete statement is:
"Increasing the population standard deviation will result in a decrease in the absolute value of z, and an increase in the probability of obtaining a sample with that mean"
(iii)
The number of scores in the sample is directly proportional to the z-test statistic.
So, increasing the number of scores in the sample will lead to an increase in the z-score.
And as the Z-score increases the p-value of the test decreases.
Thus, the complete statement is:
"Increasing the number of scores in the sample will result in an increase in the absolute value of z, and an decrease in the probability of obtaining a sample with that mean."
FIRST CORRECT ANSWER GETS BRAINLIEST 50 PTS [tex](2x-5)^{2} +3(2x-5)-18[/tex]
Answer:
4x² -14x - 8
Step-by-step explanation:
(2x - 5)² + 3(2x-5) - 18
Expand brackets.
(2x-5)(2x-5) + 6x -15 - 18
2x(2x-5)-5(2x-5) + 6x - 33
4x² - 10x - 10x + 25 + 6x - 33
Combine like terms.
4x² -14x - 8
Answer:
4x^2 -14x -8
Step-by-step explanation:
( 2x-5)^2 + 3( 2x-5) -18
Foil
(2x-5)(2x-5) = 4x^2 -10x-10x +25 = 4x^2 -20x+25
Distribute
3( 2x-5) = 6x -15
( 2x-5)^2 + 3( 2x-5) -18
Replace with the foil and distribute
4x^2 -20x+25 +6x -15 - 18
Combine like terms
4x^2 -14x -8
Eric completed 1/3 of his homework before dinner and then 2/7 after dinner. How much homework did Eric complete?
The homework completed by Eric will be equal to 13/21.
What is the fraction?
The fraction is defined as the division of the whole part into an equal number of parts.
To add fractions, you first have to set the denominators equal to each other. To do this, you find the LCD (least common denominator) of the two fractions until you find a shared number.
To do this, list out the multiples of each number (3x1=3,3x2=6,3x3=9, and so on. Do this also with 7) The LCD for 3 and 7 is 21. 3x7=21, and 7x3=21. You want to set each fraction’s denominator equal to 21.
You want to multiply each side of 1/3 by 7. 1/3 would become 7/21. You’d do this because 3x7=21, and if you multiply the bottom by you need to multiply the top by. 7x3=21 so you multiply both sides by 3 to get 6/21.
Now you have 7/21 and 6/21 and can add them. Now that they are equal, you can ignore the denominator and just add the numerators. 7+6=13 so Eric completed 13/21 of his homework.
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3x - 5y+5=0
4x+ 7y+8=0
Please help
Answer:
Y= -4. X=5
Step-by-step explanation:
This is a simultaneous equation
3x+5y= -5 ------------(1)
4x+5y= -8 ------------(2)
Using elimination method
Eliminate x
×4. 3x+5y= -5
×3. 4x+7y= -8
12x+20y= -20
-(12x+21y= -24) Minus
-y=4 therefore y= -4
Substitute x into equation 1
3x+5(-4)= -5
3x-20= -5
3x= -5+20
3x= 15
x=5
99 students choose to attend one of three after school activities: football, tennis or running.
There are 61 boys.
19 students choose football, of which 5 are girls.
31 students choose tennis.
28 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
Answer: [tex]\dfrac{49}{99}[/tex]
Step-by-step explanation:
There are 61 boys --> 38 girls
A) 19 chose football: 5 are girls --> 14 are boys
B) 38 girls: 28 chose running, 5 chose football --> 5 girls chose tennis
C) 31 students chose tennis: 5 are girls --> 26 are boys.
D) 61 boys: 14 chose football, 26 chose tennis --> 21 boys chose running.
[tex]\large\boxed{\begin{array}{l|cc||c}&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&14&5&19\\Tennis&26&5&31\\\underline{Running}&\underline{\quad 21\quad}&\underline{\quad 28\quad}&\underline{\quad 29\quad}\\Total&61&38&99\end{array}}[/tex]
Total running = 21 boys + 28 girls = 49
Total students = 99
[tex]\dfrac{\text{Total running}}{\text{Total students}}=\large\boxed{\dfrac{49}{99}}[/tex]
What is the height of the prism if there is 30 square centimeters and the volume is 90 cubic centimeters
Answer:
60
Step-by-step explanation:
If two digit number, the digit at unit place is
2 more the digit at tens place. If three times
the sum of digits is added to the number, the
number will be reversed. Find the number.
Answer:
24
Step-by-step explanation:
let the 2 digit number be ab then digit in unit place is 2 more than ten place
2 digit number is a a + 2 where b = a + 2.
Thus sum of digits = a + a + 2 = 2a + 2, then
ab + 3(2a + 2) = ba ← using place value of digits
10a + b + 6a + 6 = 10b + a, that is
16a + 6 + b = 10b + a ( subtract 10b + a from both sides
15a - 9b + 6 = 0 ← substitute b = a + 2
15a - 9(a + 2) + 6 = 0
15a - 9a - 18 + 6 = 0
6a - 12 = 0 ( add 12 to both sides )
6a = 12 ( divide both sides by 6 )
a = 2
Thus the number is 24
Please answer this question now
Answer:
[tex] r = 17.5 [/tex]
Step-by-step explanation:
Given ∆TRS,
Where,
m < R = 105°
TR = s = 15
RS = t = 6
ST = r = ?
Find r using the Law of Cosines.
[tex] r^2 = s^2 + t^2 - 2*s*t*cos(R) [/tex]
Plug in the values stated above into the formula
[tex] r^2 = 15^2 + 6^2 - 2*15*6*cos(105) [/tex]
[tex] r^2 = 225 + 36 - 180*(-0.2588)[/tex]
[tex] r^2 = 261 + 46.584 [/tex]
[tex] r^2 = 307.584 [/tex]
[tex] r = \sqrt{307.584} [/tex]
[tex] r = 17.5 [/tex] (to the nearest tenth)
What is the value of f(-1) ?
Answer:
f(-1) = 12
Step-by-step explanation:
Using the graph for f(x) let x=-1
Find the y value when x= -1
f(-1) = 12
6) Which expressions are equivalent to 12x + 36y? Choose ALL that apply.
12(x + 3y)
9(3x + 4y)
6(2x + 6y)
4(3x + 9y)
2(6x + 24y)
3(4x + 12y)
the 1st one
third one
fourth one
the last one
each of the equation has one of the common factor out
12(x + 3y), 6(2x + 6y), 4(3x + 9y) and 3(4x + 12y) are the equivalent expressions of 12x + 36y.
What is Expression?An expression is combination of variables, numbers and operators.
Equivalent expressions are expressions that work the same even though they look different.
The given expression is 12x + 36y.
Twelve times of x plus thirty six times of y.
When we solve each expression we have to get 12x + 36y.
1. 12(x + 3y)- Equivalent expression
By distributive property
=12x+36y
2. 9(3x + 4y)- Not Equivalent expression.
27x+36y
3. 6(2x + 6y)- Equivalent expression
12x+36y
4. 4(3x + 9y)-Equivalent expression
5. 2(6x + 24y)- Not Equivalent expression.
12x+48y
6. 3(4x + 12y)-Equivalent expression
12x+36y
Hence, 12(x + 3y), 6(2x + 6y), 4(3x + 9y) and 3(4x + 12y) are the equivalent expressions of 12x + 36y.
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the point slope form of the equation of the line that passes through (-5,1 ) and (10,-7) is y +7= - 1/2 (x-10) what is the standard form of the equation for this line ?
Answer:
The standard form of the equation is y = -x/2 -2
Step-by-step explanation:
The standard form of equation of this line is expressing the line in the form;
y = mx + c
So let’s make a rearrangement to what we have at hand;
y + 7 = -1/2(x-10)
2(y + 7) = -1(x-10)
2y + 14 = -x + 10
2y = -x + 10 -14
2y = -x -4
divide through by 2
y = -x/2 -2
pleaseeeeee hellppp me pleadeee
Answer:
Mode: 100
Mean: 46.94444...
Median: 29.5
Range: 150
Step-by-step explanation:
Mode: most occurring number: 100
Mean: Plus everything and divide by how many number there is: 845/18=46.94....
Median: The middle number, but you need to line it from smallest to greatest.
0, 0, 0, 1, 3, 4, 5, 12, 29, 30, 40, 50, 100, 100, 100, 100, 121, 150
29 and 30 is in the middle. In this case, you plus 29+30 and divide by 2. =29.5
Range: Largest number-Smallest number. You also need to line it from smallest to largest: 150-0=150
Hope this helps, BRAINLIEST would really help me:)
Can someone help me ok this question
Answer:
the answer is 2/5 or 0.4
.
What is the vertex of y=-3x^2+6x+15? Help is much appreciated.
Answer:
(1, 18)
Step-by-step explanation:
Rewrite the equation in vertex form by completing the square for -3x^2 + 6x + 15. This = -3(x - 1)^2 + 18.
Set y equal to the new right side.
y = -3(x - 1)
Use the vertex form, y = a(x - h)^2 + k, to determine the values of a, h, and k.
a = -3
h = 1
k = 18
Vertex = (h, k) / (1, 18)
John lent 2,550 to Mohan at 7.5 per cent
per annum. If Mohan discharges the debt after
8 months by giving an old black and white
television and 1,422.50. Find the price of
the television.
Answer: $1,077.50 or $1,078.06 (see below)
Step-by-step explanation:
Since the interest is applied after 1 year and the debt was repaid in 8 months, no interest was accrued on the $2,550 loan.
Thus, the price of the tv is: $2,550 - $1,422.50 = $1,077.50
Note: If interest is charged for the 8 months (3/4 of a year), then the interest added to the loan amount is: 0.75(3/4) = $0.56
⇒ the the price of the tv is: $1,077.50 + $0.56 = $1,078.06
help me out??? first pic is the graph second is the answer choices
Answer: Choice D. 2x^2+2y^2 = 32
=================================================
Explanation:
The highest point of this circle is (0,4). The lowest point is (0,-4). The midpoint between the two mentioned points is (0,0). This is the center of the circle. You'll find that (0,0) is also the midpoint of the left-most and right-most points on this circle.
(h,k) = (0,0) is the center
r = 4 is the radius as it is the distance from the center to the edge of the circle
(x-h)^2 + (y-k)^2 = r^2
(x-0)^2 + (y-0)^2 = 4^2
x^2+y^2 = 16 is one way to express the equation of the circle
For some reason, your teacher has decided to multiply both sides by 2. I'm not exactly sure why. But doing so leads to...
x^2+y^2 = 16
2(x^2+y^2) = 2*16
2x^2+2y^2 = 32
This matches up with choice D.
Answer:
D.
Step-by-step explanation:
According to the graph, the circle has a center of (0, 0) and a radius of 4. That means that the equation of the circle will be (x - 0)^2 + (y + 0)^2 = 4^2.
x^2 + y^2 = 16
A. If you divided all terms by 20, the radius would become 16 / 20 = 8 / 10 = 0.8. That is not 1, so choice A is incorrect.
B. If you multiplied all terms by 6, the radius would be 16 * 6 = 96, which is not 144. Choice B is incorrect.
C. This choice is obviously incorrect, since it should be + y instead of - y.
D. This choice is correct. All terms are multiplied by 2.
Hope this helps!
What is the slope of the line?
O slope = 1/3
O slope = -3
O slope = 3
Answer:
Slope = 3
Step-by-step explanation:
Slope is rise (vertical distance) over run (horizontal distance).
Our rise is equal to 3
Our run is equal to 1
So, slope = 3/1 = 3
PLZ HELP WILL GIVE BRAINLIEST
Answer:
Hey there!
We have the slope is equal to -2.5, and the y intercept is 3.
Thus, the equation is y=-2.5x+3
Hope this helps :)
what is angle and how would you know
Answer:
Angle:
When two lines/rays intersect at a point, they form an angle.
=> Angles may be in radians and degrees.
See the attached file in which two rays intersect to form an angle.
Answer:
[tex]\boxed{\mathrm{view \: explanation \: and \: attachment}}[/tex]
Step-by-step explanation:
Two lines (arms/rays) intersect at one point (vertex) creating an angle.
Factor the polynomial.
X2-13x+30
Answer:
[tex] \ \boxed{(x - 3)(x - 10)}[/tex]Step-by-step explanation:
[tex] {x}^{2} - 13x + 30[/tex]
Write -13x as a difference
[tex] {x}^{2} - 3x - 10x + 30[/tex]
Factor out x from the expression
[tex]x(x - 3) - 10x + 30[/tex]
Factor out -10 from the expression
[tex]x(x - 3) - 10(x - 3)[/tex]
Factor out x-3 from the expression
[tex](x - 3)(x - 10)[/tex]
Hope I helped!
Best regards!!
A man invested $800 at a 5.5% annual interest rate. How long will it take for his
money to earn $132 in interest?
Answer:
3 years
Step-by-step explanation:
I assume it's simple interest.
I = Prt
132 = 800 * 0.055 * t
t = 132/(800 * 0.055)
t = 132/44
t = 3
Answer: 3 years
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
B.
Step-by-step explanation:
First, it must be in descending order (i.e. largest to smallest). Thus, we can eliminate C and D since they go from smallest to largest.
Next, we need to find the degree of A and B. The degree of a polynomial is simply the highest exponent value of all the variables in a single term. If this is confusing, let's use A as an example.
In A, we have four terms: x^3y^3, xy^2, 5xy, and -4. This is a sixth degree polynomial. This is because for the first and largest term, x^3 and y^3, the total value of their exponents is 6. Because of this, A is not our answer.
For B, the biggest term is xy^2, and the degree is 1+2=3. Therefore, our answer is B since it is a third degree polynomial and it's in descending order.
Note that C is also a third-degree polynomial, but it's not written in descending order.
PLSSSSS HELLLLLLP!!!!!
Answer:
[tex]\frac{3n^2-7n+15}{(n+3)(n-4)}[/tex] will be the answer.
Step-by-step explanation:
The given expression is,
[tex]\frac{3n}{(n+3)}+\frac{5}{(n-4)}[/tex]
By solving this expression,
[tex]\frac{3n}{(n+3)}+\frac{5}{(n-4)}[/tex]
= [tex]\frac{3n(n-4)}{(n+3)(n-4)}+\frac{5(n+3)}{(n+3)(n-4)}[/tex]
= [tex]\frac{3n(n-4)+5(n+3)}{(n+3)(n-4)}[/tex]
= [tex]\frac{3n^2-12n+5n+15}{(n+3)(n-4)}[/tex]
= [tex]\frac{3n^2-7n+15}{(n+3)(n-4)}[/tex]
Therefore, fraction given in option (2) will be the answer.
US
Find the value of x.
80
93
112
y
Z
x = [?]
Answer:
x = 74°
Step-by-step explanation:
The diagram shown in this question, is a Quadrilateral inscribed in a circle
It is important to note that
The sum of opposite angles in a Quadrilateral = 180°
93° + z = 180°
z = 180° - 93°
z = 87°
In a cyclic quadrilateral,
Intercepted angle = 1/2(Intercepted arc)
Intercepted angle = 93°
Intercepted arc = x + 112°
Hence,
93° = 1/2(x + 112)°
93° × 2 = x + 112°
186° = x + 112°
x = 186° - 112°
x = 74°
Answer:
It’s 87° for mine
Step-by-step explanation:
PLEASE HELP ASAP IM REALLY TRING TO FINISH A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
__♥__♥_____♥__♥___ Put This
_♥_____♥_♥_____♥__ Heart
_♥______♥______♥__ On Your
__♥_____/______♥__ Page If
___♥____\_____♥___ You Had
____♥___/___♥_____ Your Heart
______♥_\_♥_______ Broken
________♥_________…………….
In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown.
Tell whether each statement is True or False.
a. True.
b. False.
c. True.
d. True.
e. True.
Step-by-step explanation:a. This statement is true because angles 6 and 8 are vertical angles. That means they are congruent.
b. This statement is false because Elm Street is a straight line, which means that angles 1 and 2 are supplementary angles and their measures will add up to be 180 degrees. 65 + 125 = 190, which is not equal to 180.
c. This statement is true because angles 5 and 1 correspond to each other.
d. This statement is true because angles 7 and 8 form a straight line.
e. This statement is true because they are interior angles that are alternate.
Hope this helps!John has 9 boxes of apples. Each box holds 16 apples. If 7 boxes are full, and 2 of the boxes are half full, how many apples does john have?
Answer:
128 Apples
Step-by-step explanation:
Answer:
128 apples
Elaborated:
Your first multiple 16 and 7 which is 112. Your than multiply 2 and 8 since the remaining boxes are half full which is 16. 112+16 is 128. Hope this helps!
Find the value of sin(θ) for an angle theta in standard position with a terminal ray that passes through the point (4,-3)
Answer:
[tex]\dfrac{-3}{5}[/tex]
Step-by-step explanation:
It is given that a terminal ray that passes through the point (4,-3).
x = 4
y = -3
Using Pythagoras theorem, the value of hypotenuse is
[tex]r=\sqrt{x^2+y^2}[/tex]
[tex]r=\sqrt{(-3)^2+(4)^2}[/tex]
[tex]r=\sqrt{9+16}[/tex]
[tex]r=\sqrt{25}[/tex]
[tex]r=5[/tex]
We, know that
[tex]\sin \theta = \dfrac{y}{r}[/tex]
[tex]\sin \theta = \dfrac{-3}{5}[/tex]
Therefore, the value of [tex]\sin \theta[/tex] is [tex]\dfrac{-3}{5}[/tex].
Answer:
Step-by-step explanation:
Sarah serves at a restaurant and makes 20% of what she sells as tips. Her base salary is $10.20an hour. Each hour she sells an average of $60 of food and drinks. She also makes time and a half when she works over 8 hours during a single shift. Her work week contains three 10-hour shifts, one 5-hour shift, and one 11-hour shift. Using the same income deductions as stated in the previous question, what is Sarah’s annual gross income and annual net income.
Sara works 46 hours per week
9 hours are overtime and 37 hours are regular time
pay rate at time and a half: 10.20∗1.5=15.30
regular hours plus overtime pay
37∗10.20=377.40
9∗15.30=137.70
Income due to tips
Total hours worked∗60per hour∗20%
46∗60∗.20=552
Weekly Income=Hourly income + tips
Weekly Income=377.40+137.70+552.00
Weekly Income=1067.10
Annual income=Weekly income∗52
Annual income=55489.20
BRAINLIEST! ASAP! A boat travelling at top speed upstream moves at 15km/hr. When it travels downstream, again at top speed< it moves at 25km/hr. What is the boat's top speed in still water?
Answer:
20 km/hr
Step-by-step explanation:
The boat's still-water speed is the average of its speeds against and with the current:
(15 +25)/2 = 20 . . . km/hr
__
If you want to write equations, you can let b and c represent the speeds of the boat and current in km/hr.
b - c = 15 . . . . upstream speed
b + c = 25 . . . . downstream speed
Add these two equations, and you get ...
(b -c) +(b +c) = (15) +(25)
2b = 40
b = 20 . . . . divide by 2
The speed of the boat in still water is 20 km/hr.
Answer:
20 km/hr
Step-by-step explanation:
To solve this, you have to find the average speed it is going. To find this, you just add up all of the speeds mentioned and divide it by the number of speeds you added.
15 +25=40
40/2=20
20km/hr!!!
Good luck on what you are doing I hope you do well! Brainliest would be great :)
Which of the following is the concept illustrated with the misentered data? A. The procedure for constructing the confidence interval is not robust. The smaller the sample size, the less resistant the mean. Therefore, the confidence interval is more robust.
Answer:
B. Te procedure for constructing the confidence interval is robust. The larger the sample size, the more resistance the mean. Therefore, the confidence interval is more robust.
Step-by-step explanation:
Misentered data illustrates the concept that if the sample size is larger it will be more resistance to mean. This means confidence interval is more robust. In statistics, robust is a modification of confidence interval. It refers to strength of statistical model. Robust statistics is resistant to errors in statistical model.