Find the range of given data. 12, 35, 10, 16, 22, 40, 36, 50
Answer:
[tex]40[/tex].
Step-by-step explanation:
The range of a set of numbers is the difference between the maximum and minimum numbers.
In this set of number, [tex]50[/tex] is the maximum while [tex]10[/tex] is the minimum. Hence, the range would be [tex]50 -10= 40[/tex].
A high school has found over the years that out of all the students who are offered admission, the proportion who accept is 70%.
After the administration has made some changes to the school, they want to check if the proportion of students accepting
has changed significantly. Suppose they offer admission to 210 students and 156 accept. Is this evidence of a change from
the status quo?
Answer:
The p-value of the test is 0.1738, which means that for a level of significance above this, there is evidence of a change from the status quo.
Step-by-step explanation:
A high school has found over the years that out of all the students who are offered admission, the proportion who accept is 70%. Test if there is a change from status quo.
At the null hypothesis, we test if the proportion is 70%, that is:
[tex]H_0: p = 0.7[/tex]
At the alternate hypothesis, we test if there is a change from status quo, that is, the proportion is different from 70%. So
[tex]H_a: p \neq 0.7[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
70% is tested at the null hypothesis:
This means that [tex]\mu = 0.7, \sigma = \sqrt{0.7*0.3}[/tex]
Suppose they offer admission to 210 students and 156 accept.
This means that [tex]n = 210, X = \frac{156}{210} = 0.7429[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.7429 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{210}}}[/tex]
[tex]z = 1.36[/tex]
P-value of the test and decision:
The p-value of the test is the probability that the sample proportion differs from 0.7 by at least 0.7429 - 0.7 = 0.0429, which is P(|z| > 1.36), which is 2 multiplied by the p-value of z = -1.36.
Looking at the z-table, z = -1.36 has a p-value of 0.0869
2*0.0869 = 0.1738
The p-value of the test is 0.1738, which means that for a level of significance above this, there is evidence of a change from the status quo.
Instructions: Find BD, given that line AB is the angle bisector of
CAD...please help
Answer:
BD = 2
Step-by-step explanation:
here's your solution
==> in ∆ABC and ∆ ABD
==> angle C = angle D. [ = to 90° ]
==> AB is common side
==> angle BAC = angle BAD. [ BA is angle bisector]
==> hence both traingle are congruent
==> so, BD = BC. [ by C.P.C.T ]
==> BC = 2. [ Given ]
==> BD = 2
hope it helps
100 POINTS!!! Please help.
Answer:
[tex]\dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]
Step-by-step explanation:
Given expression:
[tex](a^{10}b^{0}cde^{3})^{-2}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{1}{(a^{10}b^{0}cde^{3})^{2}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \dfrac{1}{a^{(10 \times 2)}b^{(0 \times 2)}c^2d^2e^{(3 \times 2)}}[/tex]
Simplify:
[tex]\implies \dfrac{1}{a^{20}b^{0}c^2d^2e^{6}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^0=1:[/tex]
[tex]\implies \dfrac{1}{a^{20}(1)c^2d^2e^{6}}[/tex]
[tex]\implies \dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]
Pls help me i need to fill in the boxes that dont have anything in them but i aldo need to fill in the one that says "A="
Step-by-step explanation:
[tex] \bf \red { Area: \; \boxed{ 24 } units^2} [/tex]
Formula of area of a parallelogram is :
Area of parallelogram = b × h○ b denotes base
○ h denotes height
Here,
Base of the parallelogram is 6 units and height is 4 units.→ Area of the parallelogram = 6 units × 4 units
→ Area of the parallelogram = 24 units²
[tex] \therefore [/tex] Area of the parallelogram is 24 units².
[tex] \bf \purple { Perimeter: \; \boxed{ 22 } units} [/tex]
Perimeter of parallelogram = Sum of all sidesSince, opposite sides of a parallelogram are equal. So,
○ First side = 6 units
○ Second side = 5 units
○ Third side = 6 units
○ Fourth side = 5 units
→ Perimeter = ( 6 + 5 + 6 + 5 ) units
→ Perimeter = ( 12 + 10 ) units
→ Perimeter = 22 units
[tex] \therefore [/tex] Perimeter of the parallelogram is 22 units.
[tex]\boxed{ \sf { AREA \; FORMULA }} [/tex]
[tex]\boxed { \sf { A = Base \times Height }} [/tex]
Which value satisfies the following inequality?
Solve: 47-4x<7
Answer:
D
Step-by-step explanation:
if x=11, -4(11)=-44. 47-44=3 and 3<7 which is true.
One number is three more than twice another number. If the sum of the two numbers is 30 , find the numbers
Answer:
9 = 1st number
21 = 2nd number
Step-by-step explanation:
given that :
1st number = x __eq_i
2nd number (in terms of the first number) = 2x + 3 __eq_ii
1st number + 2nd number = 30 __eq_iii
input eq_i and eq_ii in eq_iii
x + 2x + 3 = 30
3x + 3 = 30
3x = 30 - 3
x = 27 ÷ 3
x = 9
9 = 1st number
input the value of x in eq_ii
2x + 3
2(9) + 3
18 + 3
21 = 2nd number
hope that helps.
Nina needs to make an array to solve this division problem: 142 3. How should she do it?
She should make rows of 3 until she has 140 rows. She will have 1 left over.
She should make rows of 3 until she has 142 rows. She will have o left over.
She should make rows of 3 until she has 47 rows. She will have 0 left over.
She should make rows of 3 until she has 47 rows. She will have 1 left over.
Answer: D
Step-by-step explanation: She should make rows of 3 until she has 47 rows. She will have 1 left over. Because 47*3 = 141 plus the left over 142
Which property can be used to solve the equation?
10-12
Ο Ο Ο Ο
addition property of equality
O subtraction property of equality
multiplication property of equality
division property of equality
Plz help I’ll give Brainlyest
Answer:
Subtraction property of equality
Step-by-step explanation:
HELP PLEASE THIS IS DUE T O D A Y!!!
9. The table below includes information about the vertices of a triangle. Which of the following best represents the missing information?
A. (3,2)
B. (3, -2)
C. (-3, 2)
D. (-3, -2)
Answer:
your answer would be A
Step-by-step explanation:
it is kinda confusing but if you are reflecting off the x axis, you change the y, and if you are reflecting off the y axis, you would change the x
hope this helps and have a nice day!
You want to buy a $135,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan at
6.1% interest for the rest.
How much is the loan amount going to be?
What will your monthly payments be?
How much total interest do you pay?
Suppose you want to pay off the loan in 15 years rather than 30. What will your monthly payment be?
On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
total is 500
obtained is 400
so, percentage - 400/500 X 100 = 80%
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Zoran graphed the line shown below. Which of the following represents the
equation and slope of the line?
A. y = -7; slope = -7
B. x = -7; slope = 0
C. x = -7; slope is undefined
D. y = -7; slope = 0
20 Points!
Answer:
option d is correct answer
Step-by-step explanation:
equation y=-7 and slope zero
as equation of staight line y= MX+c
The we can say that the slope of the line is undefined and the {y} - intercept is -7.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is that Zoran graphed the line shown in the image.
The line is parallel to the {x} axis. So, it has no slope. Or, we can say that the slope of the line is undefined. It intersects the line at y = -7, at the {y} - axis. So, the {y} - intercept will be {y} = -7.
Therefore, the we can say that the slope of the line is undefined and the {y} - intercept is -7.
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Refer to the diagram shown.
I need help with this please help me
Using the paths shown, how long is the shortest route from Lexington to Somerville?
Answer:
1 [tex]\frac{1}{4}[/tex] miles
Step-by-step explanation:
the routes from Lexington to Somerville are
Lexington → Brookfield → Somerville with distance
[tex]\frac{3}{8}[/tex] + [tex]\frac{7}{8}[/tex] = [tex]\frac{3+7}{8}[/tex] = [tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{1}{4}[/tex] miles
the other route is
Lexington → Brookfield → Yardley → Somerville with distance
[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{3+4+4}{8}[/tex] = [tex]\frac{11}{8}[/tex] = 1 [tex]\frac{3}{8}[/tex] miles
the shortest distance is
Lexington → Brookfield → Somerville , a distance of 1 [tex]\frac{1}{4}[/tex] miles
find the solution to the system of equations y=1/2x +1 y=-x+1
Answer:
x=0, y=1
Step-by-step explanation:
10. The amount of people using a certain product can be modeled by P = 85(1.2) where t is the
number of years since the product was first released. What is the growth rate?
A) 2%
B) 20%
C) 120%
D) 12%
Answer:
B) 20%
Step-by-step explanation:
Exponential equation:
An exponential equation is given by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial amount and r is the growth rate, as a decimal.
In this question:
[tex]P(t) = 85(1.2)^t[/tex]
Growth rate:
We want to find r, so:
[tex]1 + r = 1.2[/tex]
[tex]r = 1.2 - 1 = 0.2[/tex]
The growth rate is of 0.2 = 2%, and the correct answer is given by option B.
Can someone help me
Can y’all help me on question 34?!
Write the augmented matrix for each system of equations.
-2x - 2y + 5z = 1
-5x - 5y + 7z = 4
9x - 2y + 2z = -1
Answer: it D :)
Step-by-step explanation:
say something and i give brainlyest
Answer:
Its always ily, but never stwywimc
Step-by-step explanation:
Write the nth term of the following sequence in terms of the first term of the sequence.
1, 8, 15, 22, ...
Answer:
a(n) = 1 + 7(n-1)
Step-by-step explanation:
You just rolled two standard 6-sided number cubes. What is the probability the first cube shows a 3 or the sum of the two cubes is 4 or 9?
Select the correct answer.
Rewrite the following
equation as a function of x.
25.34 – 6257 – 500 = 0
OA f(x) = 1 1 1 1 2 4 - 2
B. f(1) = -25r4 +
C. f(x) = 2534 -
D. f(1) = 2*4 +
Іст
Answer:
C
Step-by-step explanation:
Hey there come here and help
Answer:
Its between A and B
Step-by-step explanation:
I think its B Tho
Find the slope of the line shown on each graph below
The slope of the lines that passes trough the points (-2,-1) and (-4,-7) is m = 3 , (2,-3) and (6,-13) is m = -2.5 , (-3,4) and (-3,-8) is m = undefined , (-5,7) and (3,-1) is m = -1 .
What is slope ?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b).
(-2,-1) and (-4,-7)
m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−7−−1)/(−4−−2)
m=−6/−2
m = 3
(2,-3) and (6,-13)m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−13−−3)/(6−2)
m=−10/4
m=−5/2
m = -2.5
(-3,4) and (-3,-8)m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−8−4)/(−3−−3)
m=−12/0
m is undefined
(-5,7) and (3,-1)m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−1−7)/(3−−5)
m=−8/8
m = -1
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Samantha was driving down a road and after 4 hours she had traveled 70 miles. At this speed, how many hours would it take Samantha to drive 105 miles?
Answer:
6 hours
Step-by-step explanation:
70miles divided by 4 hours equals 17.5mph
106miles divided by 17.5 mph = 6 hours
Answer:
6 hours
Step-by-step explanation:
105miles ÷ 70miles=1.5
4×1.5= 6
Evaluate the ex’s press ion when a=2 and c= -6. 2a+c
Step-by-step explanation:
2a+c
=2( 2+(-6) )
=2( -4 )
= -8
The pairs of polygons below are similar. Give the sale factor of figure A to figure B
Answer:
Given that Figure A and Figure B are similar polygons, the scale factor of Figure A to Figure B = 5/2.
Recall:
Similar Polygons have corresponding side lengths whose ratio are equal. That is, their pairs of corresponding sides are proportional.
The ratio of any of their corresponding side length = scale factor
Given the two pairs of similar polygons, the scale factor of figure A to figure B will be calculated as follows:
A side length of Figure A = 10
Corresponding side length of Figure B = 4
Scale factor of Figure A to Figure B = 10/4 = 5/2
Step-by-step explanation:
Which could NOT be the shape of the graph of a quadratic function?
Answer:
the bottom right could NOT
the fourth option is the answer (. ^ ᴗ ^.)
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
What is the equation of C(t)?
C(t) = −(x − 5)2
C(t) = (x − 5)2
C(t) = −x2 + 5
C(t) = x2 + 5
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,
C(t) = a(t - 0)² + 5
C(t) = at² + 5
The equation is passing through the point (1, 4), then we have
4 = a (1²) + 5
4 = a + 5
a = - 1
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
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