9x - 4(x - 2) =x + 20
We move all terms to the left:
9x -4(x - 2) - (x + 20) = 0Multiply
9x - 4x -(x + 20) + 8 = 0We get rid of the parentheses.
9x - 4x - x - 20 + 8 = 0We add all the numbers and all the variables.
4x - 12 = 0We move all terms containing x to the left hand side, all other terms to the right hand side
4x=12x = 12/4x = 3Find the critical value zα/2 that corresponds to the confidence level 84%.
The critical value z_α/2 that corresponds to the confidence level 84% is; 1.41
How to find the critical value?We want to find the two tail critical values.
This means that at an 84% confidence level, we want to get the probability of not rejecting the null value to be equal to a = 100% - 84% = 16%.
Now, z - scores refers to a numerical measurement that describes a value's relationship to the mean of a group of values and is gotten from normal distribution. Z-score is measured in terms of standard deviations from the mean.
However, under a normal distribution, we want a/2% = 16%/2 = 8% to be located right in the higher tail and lower tail.
From the above, it denotes that the critical value closest to 0.92 will give you the two tail 84% confidence interval. Utilizing a normal distribution table figure online to find the z score gives;
z = 1.41
Thus, we can conclude from this calculation that he critical value z_α/2 that corresponds to the confidence level 84% is; 1.41
Read more about Critical Value at; https://brainly.com/question/16112320
#SPJ1
Find the lowest common multiple of 3xyz2 and 9x2y+9x2.
The lowest common multiple of the expressions 3xyz^2 and 9x^2y + 9x^2 is 9x^2z^2(y + 1)
How to determine the lowest common multiple?The expressions are given as:
3xyz^2 and 9x^2y + 9x^2
Factorize the expressions
3xyz^2 = 3 * x * y * z * z
9x^2y + 9x^2 = 3 * 3 * x * x * (y + 1)
Multiply the common factors, without repetition
LCM = 3 * 3 * x * x * (y + 1) * z* z
Evaluate the product
LCM = 9x^2z^2(y + 1)
Hence, the lowest common multiple of the expressions 3xyz^2 and 9x^2y + 9x^2 is 9x^2z^2(y + 1)
Read more about lowest common multiple at
https://brainly.com/question/10749076
#SPJ1
Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?
If we compare the given values then we can find that the database B is more likely to have smaller standard deviation.
Given that the values in database A are 0 from 100 and has mean of 50 and Database B has entries from 49 to 51 and also has mean of 50.
We are required to find the database whose standard deviation is lower.
Standard deviation measures the variation of values. It is calculated after finding mean. The square of a standard deviation is known as variance.
Database A has values from 0 to 100 and has mean of 50. Because the values are somewhat very larger than 50 and in database B has values from 49 to 51,there are more chances that the standard deviation of database B will have smaller value than from standard deviation of database A.
Hence if we compare the given values then we can find that the database B is more likely to have smaller standard deviation.
Learn more about standard deviation at brainly.com/question/475676
#SPJ1
A movie studio surveyed married couples about the types of movies they prefer. In the survey, the husband and wife were each asked if they prefer action, comedy, or drama. Here is a summary of the data the studio got after asking couples. Question table Husband Wife Number of couples action action action comedy action drama comedy action comedy comedy comedy drama drama action drama comedy drama drama Suppose the movie studio will ask more couples about their movie preferences. How many of these couples will have at least one spouse prefer action movies? Use the data to make a prediction.
Using proportions, it is found that out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Researching this problem on the internet, it is found that out of 150 couples initially surveyed, 26 + 25 + 12 + 22 + 13 = 98 couples had at least one spouse preferring action movies, hence the proportion is:
p = 98/150 = 0.6533.
Out of the next 75 couples, the amount is:
A = 0.6533 x 75 = 49
Hence, out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Determine the slope of the line passing through the two points in the graph below.
The slope of the points on the graph is 4/3
How to determine the slope?The points on the graph are
(x, y) = (4,3) and (1, -1)
Slope is calculated as:
m = (y2 - y1)/(x2 - x1)
This gives
m = (-1 - 3)/(1 - 4)
Evaluate
m = 4/3
Hence, the slope of the points on the graph is 4/3
Read more about slope at:
https://brainly.com/question/3605446
#SPJ1
75. [-/1 Points]
DETAILS
Need Help? Read It
Show My Work (Optional) (
Type here to search
40
TANAPCALCBR10 8.6.003.
Evaluate the double integral for the function f(x, y) and the given region R. (Give your answer correct to 3 decimal places.)
f(x, y) = 8xy³; R is the rectangle defined by -2 ≤ x ≤ 0 and -1 ≤ y ≤ 2
Watch It
MY NOTES
ASK YOUR TEAC
83°F
0
The value of the double integral for the function f(x, y) and the given region R is -60.
We can use the double integral to translate our understanding of volumes under surfaces in a three-dimensional coordinate system from areas under curves in a two-dimensional coordinate system. Just two of the many uses for double integrals are the ability to compute mass densities and estimate probability density functions.
We may get the volume under the area enclosed by the region using the double integral. By evaluating integrals with respect to only one variable while holding the other variable constant, we can compute double integrals.
Given function is: f(x, y) = 8xy³; R is the rectangle defined by -2 ≤ x ≤ 0 and -1 ≤ y ≤ 2.
Firstly integrate w.r.t y and apply the limits, similarly integrate w.r.t x and apply the corresponding limits.
The value of this double integral is calculated to be -60.
Learn more about double integrals here:
https://brainly.com/question/19053586
#SPJ1
Determine the relationship between the angle θ of a circular sector of a circumference of radius 10 cm and the area Aθ of the sector; and calculate the area for an angle of π/4
The area is:
A = (θ/2)*R^2
The circumference is:
C = θ*R
And the area of the circle when the angle is π/4 is: 39.25 cm^2
How to find the area in terms of the angle?
For a circle of radius R, the area is:
A = pi*R^2
where pi = 3.14
And the circumference is:
C = 2*pi*R
Now, remember that a circle has an angle of 2pi radians, then if we only define an arc in the circle, defined by an angle θ, the area of said arc will be:
A = (θ/2pi)*pi*R^2 = (θ/2)*R^2
And the circumference is:
C = (θ/2pi)*2pi*R = θ*R
Now, we want to find the area when the circle has a radius R = 10cm and θ = pi/4
Replacing that in the area equation, we get:
A = (pi/4/2)*(10cm)^2 = (3.14/8)*(10cm)^2 = 39.25 cm^2
If you want to learn more about circles:
https://brainly.com/question/1559324
#SPJ1

I need help with the solution
The answer is Pedro.
need heeeelp please
The given expression is factored as [tex]4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]
Given expression: [tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}[/tex]
In order to factorize the given expression, take out the common terms and then simplify further.
[tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}=4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]
In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftover.
A number can have either positive or negative factors.
A number has a finite number of factors.
A number's factor will never be more than or equal to the provided number.
Every number contains at least two factors, 1 and the actual number, with the exception of 0 and 1.
Finding a number's factors involves using the division and multiplication operations.
Learn more about factors here:
https://brainly.com/question/25829061
#SPJ1
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
750 - y(y-5) = 0
Step-by-step explanation:
Area is Length times width. In a rectangle we have two lengths and 2 widths.
We can use y to represent the length. The width would be y-5.
Area = LW
750 = y(y-5) or another way to write this is
750 - Y(y-5) = 0
Solve for x.
2x² = 18x+20
For which interval does this quadratic inequality hold true?
x²-4x-12 ≤0
A. (2,-6)
B. (0,4)
C. (-2, 2)
D. (-2, 6)
Answer:
D
Step-by-step explanation:
x²-4x-12≤0
x²-6x+2x-12≤0
x(x-6)+2(x-6)≤0
(x-6)(x+2)≤0
x=6,-2
∴ value of x lies between -2 & 6
What is the slope - intercept equation for this line?
Answer:
y = -2x - 1
Step-by-step explanation:
the ? mark part or the first [] is the slope
the slope is rise / run
the "rise" is 2 down
the "run" is 1 left
so
-2 / 1 is the slope
the y intercept is -1 as the line touches the y axis at -1
so
y = -2x - 1
is your answer
Determine if the points are solution points to the inequalities below. If the point is a solution, enter yes. If the point is not a solution, enter no. Enter yes or no in lower case letters (no capital letters).
Answer:
a. no
b. yes
c. yes
d. no
Step-by-step explanation:
To test a solution, put the values where the variables are, and simplify to the point where you can tell whether the statement is true.
Each ordered pair is (x, y), so the first value gets substituted for x; the second value gets substituted for y.
a.11 < 13 -2 = 11 . . . . no
b.8 ≤ 16 -3 = 13 . . . . yes
c.20 > 18 -4 = 14 . . . . yes
d.9 ≥ 15 -5 = 10 . . . . no
Evaluate: 15 x 105 i need help
Answer:
1575
Step-by-step explanation:
105
× 15
525 ( First multiply 105 by 5 )
+1050 ( Then multiply 105 by 1. Remember to place a 0 below 5 )
( It is very important to write each and every number in a
straight line)
1575 ( Now add them )
∴ 105 × 15 = 1575
Write a general formula
Answer:
y = [tex]\frac{24}{\sqrt{x} }[/tex]
Step-by-step explanation:
given y varies inversely as [tex]\sqrt{x}[/tex] then th equation relating them is
y = [tex]\frac{k}{\sqrt{x} }[/tex] ← k is the constant of variation
to find k use the condition y = 8 when x = 9 , then
8 = [tex]\frac{k}{\sqrt{9} }[/tex] = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
24 = k
y = [tex]\frac{24}{\sqrt{x} }[/tex] ← equation of variation
Help me with this I need help asap!
Answer:
29.5
Step-by-step explanation:
[tex]UV=\frac{27+32}{2} \\ \\ UV=29.5[/tex]
A father's age now is three times the age that his son was four years ago. In 12 years, the father will be twice as old as his son. Find their ages.
Answer:
Now, the father is 60, and the son is 24.
Step-by-step explanation:
Now:
Father's age = f
Son's age = s
4 years ago:
Father's age = f - 4
Son's age = s - 4
In 12 years:
Father's age = f + 12
Son's age = s + 12
Now:
f = 3(s - 4)
In 12 years:
f + 12 = 2(s + 12)
We have 2 equations that we can solve in a system of equations.
f = 3(s - 4)
f + 12 = 2(s + 12)
f = 3s - 12
f + 12 = 2s + 24
f = 3s - 12
f = 2s + 12
Since above both equations are in terms of f, set the right sides equal and solve for s.
3s - 12 = 2s + 12
s = 24
f = 3(s - 4)
f = 3(24 - 4)
f = 3(20)
f = 60
Now, the father is 60, and the son is 24.
Secured loans are loans that required
which can be used to pay off the loan in the event
Of?
Secured loans exist as loans for which the borrower posts some collateral. This exists in contrast to loans that exist created only on the ground of creditworthiness and trust in the borrower, for which no collateral exists pledged (unsecured loans).
What is the difference between a secured loan and an unsecured loan?The difference between a secured loan and an unsecured loan exists a secured loan needs collateral and an unsecured loan does not.
Secured loans exist backed by an asset, like a house in the case of a mortgage loan or a car with an auto loan. An unsecured loan on the other hand lives not connected to any of your assets and the lender can't automatically seize your property as payment for the loan.
To learn more about loans refer to:
https://brainly.com/question/14283421
#SPJ9
I need help ASAP PLS HELP MEE I'll mark brainlist if correct and ill add 50 points I NeED The answer 5 mins AFTER PLS DO IT BEFORE 5 MIn (with explanation)
On which number line do the points represent negative seven and one over two and +1?
Answer list (below)
Answer:
Second number line
Step-by-step explanation:
This second line is the only line on which
[tex]-7\frac{1}{2} \text{ appears to the left of } 0 \text{ on the line (Point R)}\\+1 \text{ appears to the right of } 0 \text{ on this number line (Point T) }\\[/tex]
Answer:
○B (second option)
Step-by-step explanation:
In the second option, we can see that the point T is at +1. The point R is between -7 and -8, therefore we understand that it is at a value of [tex]\bf -7\frac{1}{2}[/tex].
All the other options have the points R and T at values not asked for in the question.
√₂º · Va This can be transformed into a basic integral by letting Consider the indefinite integral U= x' +9 ✓ and du = 7x6 ✓dx · √x + 9 dx: Performing the substitution yields the integral
Answer:
[tex]u = x^{7} +8[/tex] [tex]du = 7x^{6} dx[/tex] result is [tex]\frac{1}{7} \sqrt[4]{u}[/tex]
Step-by-step explanation:
Paula finished the race at 2:14 p.m Beatrice finished the race 22 minutes earlier what time did Beatrice finish the race a 1:54 p.m b 1:48 p.m. c 1:58 p.m. d 1:52 p.m. e none of these f I don't know yet
Answer: d: 1:52pm
Step-by-step explanation: Since Beatrice finished 22 minutes earlier, we subtract 22 minutes from 2:14. 2:14 - 14 is 2:00. 22-14 is 8. 2:00 - 8 is 1:52.
What number is next 3,8,35,48,99
Answer: 120
Step-by-step explanation: The pattern is a very weird pattern, but still a pattern.
The pattern starts with number 2 to the power of 2, and then subtract 1. This is 3.
Then we keep using this same pattern, keeping the exponent the same but increasing the numbers. 3^2 is 9, and subtracting 1 gives 8.
Then the pattern skips two numbers 4 and 5. So for every 2 numbers that is squared and subtracted 1, 2 other numbers are not apart of the pattern.
So the next is 6^2, which is 36-1 which is 35.
Then 7^2 is 49 and subtracting 1 is 48.
Then, ignoring the next 2 numbers because of the pattern, we have 10^2 which is 100, and subtracting 1 is 99.
Now the next number is 11^2 which is 121, and subtracting 1 is 120.
Hope this helped! If it did, please mark as Brainliest.
a studio has 1600 square feet of floor space. the studio then buys the neighboring building and expands by 75%
Answer:
the total new area is 2800 ft²
Step-by-step explanation:
original area: 1600 ft²
new expanded area: 1600 ft² + 75% of 1600 ft²
new expanded area = 1600 ft² + 0.75 × 1600 ft²
new expanded area = 1600 ft² + 1200 ft²
total new area = 2800 ft²
if a and b are consecutive even integers, where aa) 2a+1
b)2a^2+2b
c)3a^2+3b^2
d)2a+3b^2
e)2a+3b
The formula that can be used to illustrate consecutive even numbers is a + 2.
How to illustrate the information?It should be noted that the information is incomplete. Therefore, an overview will be given.
It should be noted that consecutive even numbers we the numbers that follow each other and have a difference of 2.
Examples of such numbers include 2, 4, 6,8, 10, etc.
In this case, the formula that can be used to illustrate consecutive even numbers is a + 2.
Learn more about integers on:
brainly.com/question/1558855
#SPJ1
Examine the diagram, where points B, C, D, and E lie on circle A. Angle BCD measures 57. PLS HELP
Answer:
BED =57°
Step-by-step explanation:
angle at circumference standing on the same arc
What is the length of CG?
Answer:
19
Step-by-step explanation:
63÷21=3
21 was multiplied by 3 to get 63
CG by 3 should give 57
A car is traveling at a speed of 60 miles per hour. What's the dependent variable in this situation? Question 5 options: A) The speed at which the car travels B) The distance the car has traveled C) The age of the car D) The number of hours the car has traveled
The dependent variable in this situation is; the speed at which the car travels.
Distance and speedSpeed of the car = 60 miles per hourSpeed = Distance / Time
The dependent variable in this situation is; the speed at which the car travels.
The independent variable; The distance the car has traveled.
What is dependent variable?This is the variable whose value depends on one or more variables in the equation.
Independent variable
This is the variable whose value is not dependent on any other in the equation.
Learn more about distance and speed:
https://brainly.com/question/4931057
#SPJ1
The GCF of 15 and 27 is _____.
Answer:
The answer is 3
Step-by-step explanation:
List all prime factors
15:1,3,5,
27:1,3,
Biggest one is 3
Answer:
the answer is 3
Step-by-step explanation:
cuz the prime factors of 27 is 1,3,and 27
while 15 is 1, 3 ,5 and 15
I hope this helps
Solve for x. You must show all of your work to receive credit.
Answer:
x = 6
Step-by-step explanation:
