Answer:
(3) y+2=2(x-8)
Step-by-step explanation:
Substitute the point into the equation and see if it is true
(8,-2)
(1) y+2=2(x+8)
-2+2 = 2(8+8)
0 = 2(16)
False
(2) y-2=2(x-8)
-2-2 = 2(8-8)
-4 =2 (0)
False
(3) y+2=2(x-8)
-2+2 = 2( 8-8)
0 = 2(0)
True
(4) y-2=2(x+8)
-2-2 = 2(8+8)
-4 = 2(16)
False
Answer:
[tex]\boxed{y+2=2(x-8) }[/tex]
Step-by-step explanation:
[tex]x=8[/tex]
[tex]y=-2[/tex]
[tex]\sf Check \ the \ third \ option.[/tex]
[tex]-2+2=2(8-8)[/tex]
[tex]\sf Both \ sides \ must \ be \ equal.[/tex]
[tex]0=2(0)[/tex]
[tex]0=0[/tex]
Last month a factory produced 800 television sets. This month the same factory produced 1064 television sets. What percent did production increase?
Answer:
33%
Step-by-step explanation:
Increase is equal to (1064-800)
=264
So the percent = (264/800)×100
=33%
The factory's output went up by around 33% from last month to this month, reflecting a significant growth in television set production.
To calculate the percentage increase in production, we use the concept of percentage change.
The formula for percentage change is = [(new value - old value) / old value] × 100,
In this case, the old value is 800 (last month's production) and the new value is 1064 (this month's production).
The percentage increase in production can be calculated as follows:
[(1064 - 800) / 800] × 100 = (264 / 800) × 100 ≈ 33%.
Therefore, the production increased by approximately 33%.
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The length of each side of a cubical wooden block is 16 inches. What is the volume of
the block
Hey there! I'm happy to help!
To find the volume of a cube, you simply take whatever the side length is and multiply it by itself 3 times, which is also known as cubing the number!
16×16×16=4096
You can also write it as 16³=4096
This is because the length is 16, the width is 16, and the height is 16, so you multiply them all together!
I hope that this helps! Have a wonderful day!
The area of rectangle is 36 cm2 and breadth is one fourth of the length.Find length and breadth of rectangle.
We know
[tex]\boxed{\sf Area=Length\times Breadth}[/tex]
[tex]\\ \sf\longmapsto x(4x)=36[/tex]
[tex]\\ \sf\longmapsto 4x^2=36[/tex]
[tex]\\ \sf\longmapsto x^2=\dfrac{36}{4}[/tex]
[tex]\\ \sf\longmapsto x^2=9[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{9}[/tex]
[tex]\\ \sf\longmapsto x=3[/tex]
Breadth=3mLength=4(3)=12mA committee of 3 is to be chosen from 4 girls and 7 boys.Find the expected number of girls in a committe, if numbers are chosen at random
Answer: There is only 1 girl.
Step-by-step explanation:
As you can see the probability of choosing a girl is 4/11 out of the whole people which is 7 boys and 4 girls. And the same way the probability of choosing a boy is 7/11 which is almost doubled the amount of girls. So to think about it, there will be more boys than girls if there is a random selection because the boys chances of getting picked is high.
Simplify i^38 ????????
Answer:
i is defined as the square root of -1.
i^2 = -1
i^3 = -i
i^4 = 1
Following the pattern, we see that i^40 = 1, so i^38 is two above, or equal to -1.
So, i^38 = -1.
Let me know if this helps!
someone please help me
Answer:
3 mL
Step-by-step explanation:
The fluid level is called the concave meniscus. The adhesive force causes it to crawl up on the sides, but you should ignore that while reading the level.
Find the value of x.
Answer:
6x + 6 = 32
6x = 32 - 6
6x = 26
divide both sides by 6
6x/6 = 26/6
6x + 6 = 4.35
9x - 9 = 24
9x = 24 + 9
9x = 33
divide both sides by 9
9x/9 = 24/9
9x + 9 = 2.66
9x + 9 = 2.66
Answer: x=3
Step-by-step explanation:
[tex]\frac{32}{24} =\frac{4}{3} \\\\\frac{4}{3}=\frac{6x+6}{9x-9}\\ x=3[/tex]
If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is
Answer:
The percentage of variation in the dependent variable explained by the variation in the independent variable is 80 %.
Step-by-step explanation:
A coefficient of correlation of 0.8 means that dependent variable changes in 0.8 when independent variable changes in a unit. Hence, the percentage of such variation ([tex]\%R[/tex]) is:
[tex]\%R = \frac{\Delta y}{\Delta x}\times 100\,\%[/tex]
Where:
[tex]\Delta x[/tex] - Change in independent variable, dimensionless.
[tex]\Delta y[/tex] - Change in dependent variable, dimensionless.
If [tex]\Delta x = 1.0[/tex] and [tex]\Delta y = 0.8[/tex], then:
[tex]\%R = 80\,\%[/tex]
The percentage of variation in the dependent variable explained by the variation in the independent variable is 80 %.
the volume of a cube is 3375 cubic inches. what is the measure of each side of the cube
Answer:
The measure of each side of the cube is
15 inchesStep-by-step explanation:
Since it's a cube all it's sides are equal
To find the length of each side we use the formula
Volume of a cube = l³
where l is the measure of one side
From the question
Volume = 3375 cubic inches
Substitute this value into the formula and solve for l
That's
[tex] {l}^{3} = 3375[/tex]Find the cube root of both sides
That's
[tex] \sqrt[3]{ {l}^{3} } = \sqrt[3]{3375} [/tex]We have the final answer as
l = 15 inchesHope this helps you
You pay $16 to buy four pizzas, How much did each pizza cost?
Answer:
16 dollars = 4 pizzas
4 dollars = 1 pizza
Each pizza costs 4 dollars.
Let me know if this helps!
Answer: $4
Step-by-step explanation:
16 divided by 4, equals 4.
in the diagram, find the values of a and b.
Answer:
m∠a = 67° , m∠b = 42°Step-by-step explanation:
∠a is alternate interior angle to ∠ECD
∠b is alternate interior angle to ∠BCD
so:
If AB || CD then:
m∠a = m∠ECD = 25° + 42° = 67°
m∠b = 42°
complete explanation please
Which expression is equivalent to x12 + 5x6 – 14?
Your job in a company is to fill quart-size bottles of oil from a full 100-gallon oil tank. Then you are to pack 12 quarts of oil in a
case to ship to a store. How many full cases of oil can you get from a full 100-gallon tank of oil?
8 cases of oil
33 cases of oil
25 cases of oil
34 cases of oil
Answer:
33 cases of oil
Step-by-step explanation:
You start with 100 gallons of oil.
1 gallon = 4 quarts
100 gallons = 100 * 4 quarts
100 gallons = 400 quarts
You start with 400 quarts.
You place 12 quarts in each box.
400/12 = 33 1/3
You can pack 33 full cases plus 1/3 of another case.
The question only askes about full cases.
Answer: 33 cases of oil
The number of cases of oil will be 8 cases of oil. Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
It is your responsibility to fill quart-size oil bottles from a 100-gallon oil tank at work. The next step is to prepare a case to transport 12 quarts of oil to a retailer.
The number of cases of oil that you can get from a full 100-gallon tank of oil will be given as,
⇒ 100 / 12
⇒ 8.33
⇒ 8 cases of oil
Thus, the correct option is A.
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A controversial bill is being debated in the state legislature. Representative Williams wants to estimate within 2 percentage points and with 95% confidence the difference in the proportion of her male and female constituents who favor the bill. What sample size should she obtain?
Answer:
The sample size is [tex]n = 2401[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E= 2\% = 0.02[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 5\% = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Let assume that the sample proportion is [tex]\r p = 0.5[/tex]
Generally the sample size is evaluated as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p ( 1- \r p )[/tex]
[tex]n = [\frac{1.96}{0.02} ]^2 * 0.5 ( 1- 0.5 )[/tex]
[tex]n = 2401[/tex]
The Venn diagram shows 3 type numbers odd even in prime
What is the approximate area of a circle enclosed by a piece of rope 50.24 inches long? (Use the fact that π ≈ 3.14 to make your calculations.)
Answer:
the approximate area of this circle is 200.96 inches long.
Step-by-step explanation:
To answer this problem we need to remember that the area of a circle is given by the formula:
Area = π[tex]r^2[/tex] where r is the radius.
and the perimeter is:
Perimeter = 2πr
Now, the problem tells us that the circle is enclosed by a piece of rope that's 50.24 inches long. So the perimeter of the circle is 50.24 inches.
Since we have the value of the perimeter and the value of pi, we are going to substitute these values in the perimeter formula to find r.
Perimeter = 2πr
50.24=2(3.14)r
50.24= 6.28r
50.24/6.28= r
8= r
Thus, the radius of the circle is 8 inches long.
Now, we can use this value to find the area of the circle:
Area = π[tex]r^2[/tex]
Area = π[tex]8^2[/tex]
Area = 3.14 (64)
Area = 200.96
Therefore, the approximate area of this circle is 200.96 inches long.
The approximate area of a circle enclosed by a piece of rope is 200.96 square inch.
The length of rope by which a circle is made, is known as circumference of circle.
Circumference of circle = [tex]2\pi r[/tex] , where r is radius of circle.
Since, length of rope is 50.24 inches.
[tex]2\pi r=50.24\\\\r=\frac{50.24}{2*3.14}=8 inch[/tex]
Area of circle = [tex]\pi r^{2}[/tex]
= [tex]3.14 *(8)^{2}=200.96[/tex] square inch
Thus, the approximate area of a circle enclosed by a piece of rope is 200.96 square inch.
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Complete the table for the given rule.
Rule: y is 0.750.750, point, 75 greater than x
x y
0
3
9
Answer:
está inglês não dá para entende
Which of these numbers are greater than 24? Check all that apply.
O A. 12
B. 15
O C. 42
D. 41
E. 13
D F. 18
Answer:
A, B, E, F
Step-by-step explanation:
24>12, 24>15, 24>13, 24>18, 24<42, 24<41
PLEASE HELP !! (2/5) -50 POINTS-
Answer:
3 -1 -2
5 1 6
Step-by-step explanation:
An augmented system has the coefficients for the variables and then the solution going across
Rewriting the equations to get them in the form
ax + by = c
-3x+y =2
3x-y =-2
5x+y = 6
The matrix is
3 -1 -2
5 1 6
Please help!! 25 points!!
9514 1404 393
Answer:
(a) a^4/(4b^2)
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
__
Your expression simplifies as follows.
[tex]\dfrac{3a^2b^{-4}}{12a^{-2}b^{-2}}=\dfrac{3}{12}\cdot\dfrac{a^{2-(-2)}}{b^{-2-(-4)}}=\boxed{\dfrac{a^4}{4b^2}}[/tex]
The numbers 1,2,3,4,5,6,7,8,9. How would you put them in each of a square block to create the sum on each line to make the number 15. The sum of each diagonals should also be 15.
Answer:
Here's one way:
4 9 2
3 5 7
8 1 6
Step-by-step explanation:
The weights of a sample of college textbooks has a bell-shaped distribution with a mean of 8.1 p o u n d s ( l b s ) and a standard deviation of 2.1 l b s . According to the Empirical Rule, what percent of all college textbooks will weigh between 1.8 and 14.4 l b s ?
Answer:
The interval ( 1,8 ; 14,4 ) will contains 99,7 % of all values
Step-by-step explanation:
For Normal Distribution N ( μ ; σ ) the Empirical Rule establishes that in the intervals:
( μ ± σ ) we find 68,3 % of all values
( μ ± 2σ ) we find 95,4 % of all values
( μ ± 3σ ) we find 99,7 % of all values
Then we have a normal distribution N ( 8,1 ; 2,1 )
3*σ = 3* 2,1 = 6,3
And 8,1 - 6,3 = 1,8 8,1 + 6,3 = 14,4
Then the interval ( 1,8 ; 14,4 ) will contains 99,7 % of all values
The grade appeal process at a university requires that a jury be structured by selecting individuals randomly from a pool of students and faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of students and faculty
Correct question is ;
The grade appeal process at a university requires that a jury be structured by selecting eight individuals randomly from a pool of nine students and eleven faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of six students and two faculty?
Answer:
A) 7.144 × 10^(-5)
B) 0.00131
C) 0.0367
Step-by-step explanation:
We are given;
Number of students = 9
Number of faculty members = 11
A) Now, the number of ways we can select eight students from 9 =
C(9, 8) = 9!/(8! × 1!) = 9
Also, number of ways of selecting 8 individuals out of the total of 20 = C(20,8) = 20!/(8! × 12!) = 125970
Thus, probability of selecting a jury of all students = 9/125970 = 7.144 × 10^(-5)
B) P(selecting a jury of all faculty) = (number of ways to choose 8 faculty out of 11 faculty)/(Total number of ways to choose 8 individuals out of 20 individuals) = [C(11,8)]/[C(20,8)] = (11!/(8! × 3!))/125970 = 0.00131
C) P(selecting a jury of six students and two faculty) = ((number of ways to choose 6 students out of 9 students) × (number of ways to choose 2 faculty out of 11 faculty))/(Total number of ways to choose 8 individuals out of 20 individuals) = [(C(9,6) × C(11,2)]/125970
This gives;
(84 × 55)/125970 = 0.0367
[tex]Solve. Clear fraction first.6/5 + 2/5 x = 89/30 + 7/6 x + 1/6[/tex]
Step-by-step explanation:
we have denominators 5, 6 and 30.
the smallest number that is divisible by all 3 is clearly 30.
so, we have to multiply everything by 30 to eliminate the fractions.
180/5 + 60/5 x = 89 + 210/6 x + 30/6 =
36 + 12x = 89 + 35x + 5
-58 = 23x
x = -58/23
In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study. Carry answer to the nearest ten-thousandths. (Bonus Question)
a. What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178?
b. What is the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025?
Answer:
a
[tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]
b
[tex]P( X >0.025 ) = 0.99379[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.10[/tex]
The sample size is [tex]n = 100[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{\frac{ p (1 - p )}{n} }[/tex]
=> [tex]SE = \sqrt{\frac{ 0.10 (1 - 0.10 )}{100} }[/tex]
=> [tex]SE =0.03[/tex]
The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178
[tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} < \frac{ X - 0.10}{SE} < \frac{ 0.178 - 0.10}{0.03} )[/tex]
Generally [tex]\frac{ X - 0.10}{SE} = Z (The \ standardized \ value \ of X )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} <Z < \frac{ 0.178 - 0.10}{0.03} )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P (2.4 <Z < 2.6 )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P(Z < 2.6 ) - P (Z < 2.4 )[/tex]
From the z-table
[tex]P(Z < 2.6 ) = 0.99534[/tex]
[tex]P(Z < 2.4 ) = 0.9918[/tex]
[tex]P( 0.172 < X < 0.178 ) =0.99534 - 0.9918[/tex]
[tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]
the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as
[tex]P( X >0.025 ) = P (\frac{ X - 0.10}{SE} > \frac{ 0.0025- 0.10}{0.03} )[/tex]
[tex]P( X >0.025 ) = P (Z > -2.5 )[/tex]
From the z-table
[tex]P (Z > -2.5 ) = 0.99379[/tex]
Thus
[tex]P( X >0.025 ) = P (Z > -2.5 ) = 0.99379[/tex]
For each ordered pair, determine whether it is a solution to y=-9.
Is it a solution?
Yes or No
(1, -9)
(7,3)
(-9,4)
(0, -9)
Answer:
(1, -9) yes
(7,3) no
(-9,4) no
(0, -9) yes
Step-by-step explanation:
The y value must be -9
The x value can be any value to satisfy the equation y = -9
The angle between a chord and a targent is equal to the angle in the alternate segment
that's the diagram above
if <BAD =19°
find <ACB
Answer:
19
Step-by-step explanation:
The angle between a chord and a targent is equal to the angle in the alternate segment
if <BAD =19°
<ACB=19
A gas station sells regular gas for $2.30 per gallon and premium gas for $3.00 a gallon. At the end of a business day 320 gallons of gas had been sold, and receipts totaled $799. How many gallons of each type of gas had been sold
Answer:
90 gallons premium gas
230 gallons regular gas
Step-by-step explanation:
We can use the given information to form a system of equations.
First, let's set the variables:
Regular gas: r
Premium gas: p
Throughout the entire day, they sold 320 gallons of r and p combined.
r+p=320
Now, regular gas sells for 2.30 per gallon, which can be written as 2.30r
premium can be shown similarly as 3.00p. After all the gallons they sold, they got 799 in total.
2.30r + 3.00p = 799
As a system of equations, it can be written like this...
r+p=320
2.30r + 3.00p = 799
Now solve. (I won't explain much of the steps here but I'll show it. Comment questions if you have any, and I'll try to answer them.)
r=320-p
2.30r + 3.00p = 799
2.30(320-p)+3.00p=799
736+0.7p=799
0.7p=63
p=90 gallons of premium gas
Now we can solve for regular by just plugging in 90 gallons premium into the top equation.
r+p=320
r+90=320
r=230 gallons of regular gas
check work.
230(2.30)+90.0(3.00)=799
529+270=799
799=799
A region is bounded by x=y^2 and x=4 and y=0 and revolved about the line x=5. Find the volume using shell method.
If you draw the bounded region in the x,y-plane, you'll find it to be somewhat ambiguous, but since y = 0 cuts the area between the parabola x = y ² and x = 4 perfectly in half, you can use either the top or bottom half. I'll use the top one, i.e. assume y ≥ 0.
For every x taken from the interval [0, 4], we can get a shell with height √x. The distance from x to the axis of revolution, x = 5, is 5 - x, which corresponds to the radius of the shell. The area of this shell is
2π (radius) (height) = 2π (5 - x) √x
Then the volume of the solid is the sum of infinitely many such shells made at every 0 ≤ x ≤ 4, given by the integral
[tex]\displaystyle 2\pi \int_0^4 (5-x)\sqrt x\,\mathrm dx = 2\pi \int_0^4 \left(5x^{1/2}-x^{3/2}\right)\,\mathrm dx \\\\ = 2\pi \left(\frac{10}3x^{3/2}-\frac25x^{5/2}\right)\bigg|_0^4 \\\\ = \boxed{\frac{416\pi}{15}}[/tex]