Answer:
B is the correct answer.
Step-by-step explanation:
-2x+3y+z=-6
z=6
-2x+3y+6=-6
-2x+3y=-12
-2(3)+3(2)
-6+6=0 A is incorrect
-2(3)+3(-2)=-12
-6-6=-12
B is the correct answer.
I am not going to show C or D, because you have the right answer. Hope this helps you. Thank you.
Find the area of the shape shown below.
3.5
2
2
Answer:
26.75 units²
Step-by-step explanation:
Cube Area: A = l²
Triangle Area: A = 1/2bh
Step 1: Find area of biggest triangle
A = 1/2(3.5)(2 + 2 + 5)
A = 1.75(9)
A = 15.75
Step 2: Find area of 2nd biggest triangle
A = 1/2(5)(2)
A = 1/2(10)
A = 5
Step 3: Find area of smallest triangle
A = 1/2(2)(2)
A = 1/2(4)
A = 2
Step 4: Find area of cube
A = 2²
A = 4
Step 5: Add all the values together
A = 15.75 + 5 + 2 + 4
A = 20.75 + 2 + 4
A = 22.75 + 4
A = 26.75
Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x) =20x^2+40x+600 dollars.
Required:
a. At what rate was the property tax increasing with respect to time in 2008?
b. By how much did the tax change between the years 2008 and 2012?
Answer:
a) 40 dollars
b) 480 dollars
Step-by-step explanation:
Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0
T'(x) = 2(20)x¹ + 40x° + 0
T'(x) = 40x+40
At x = 0,
T'(0) = 40(0)+40
T'(0) = 40
Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).
b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)
Given T(x) =20x²+40x+600
T(4) =20(4)²+40(4)+600
T(4) = 320+160+600
T(4) = 1080 dollars
Also T(0) =20(0)²+40(0)+600
T(0) = 0+0+600
T(0)= 600 dollars
T(4) - T(0) = 1080 - 600
T(4) - T(0) = 480 dollars
Hence, the tax has changed by $480 between 2008 and 2012
The function fix) = (x - 4)(x - 2) is shown.
What is the range of the function?
8
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
all real numbers greater than or equal to - 1
6
2
16
2
14
COL
40
8
G D
Answer:
The range of the function f(x)= (x-4)(x-2) is all real numbers greater than or equal to -1
Step-by-step explanation:
On a coordinate plane, a line goes through (negative 3, 3) and (negative 2, 1). A point is at (4, 1). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)? y − 1 = −2(x − 4) y – 1 = Negative one-half(x – 4) y – 1 = One-half(x – 4) y − 1 = 2(x − 4)
Answer:
y - 1 = -2(x - 4).
Step-by-step explanation:
First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).
(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.
The line will be parallel to the given line, so the slope is the same.
Now that we have a point and the slope, we can construct an equation in point-slope form.
y1 = 1, x1 = 4, and m = -2.
y - 1 = -2(x - 4).
Hope this helps!
The slope of the line passing parallel to the given line and passes through the point (4, 1) is y = -2x + 9
The equation of a straight line is given by:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
The slope of the line passing through the points (-3,3) and (-2,1) is:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]
Since both lines are parallel, hence they have the same slope (-2). The line passes through (4,1). The equation is:
[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]
Find out more at: https://brainly.com/question/18880408
Question on Statistics and Confidence Intervals
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation. (10 points)
The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)
The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80
This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%
We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.
The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)
=========================================
In summary, we have these answers
confidence level = 90%margin of error = 5% = 0.05confidence interval = (0.70, 0.80)interpretation = We're 90% confident that the average exam score is between 0.70 and 0.80Can somebody explain how trigonometric form polar equations are divided/multiplied?
Answer:
Attachment 1 : Option C
Attachment 2 : Option A
Step-by-step explanation:
( 1 ) Expressing the product of z1 and z2 would be as follows,
[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]
Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,
cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],
sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]
cos(3π / 2) = 0,
sin(3π / 2) = - 1
Let's substitute those values in our expression,
[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]
And now simplify the expression,
[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]
The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.
( 2 ) Here we will apply the following trivial identities,
cos(π / 3) = [tex]\frac{1}{2}[/tex],
sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],
cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],
sin(- π / 6) = [tex]-\frac{1}{2}[/tex]
Substitute into the following expression, representing the quotient of the given values of z1 and z2,
[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒
[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]
The simplified expression will be the following,
[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]
The solution will be option a, as you can see.
Identify whether the sampling method is simple random, systematic, stratified, cluster, or convenience. Explain.
In a nationwide study of registered voters conducted by The New York Times, 390 people are randomly selected out of those registered as Republicans, 430 people are randomly selected out of those registered as Democrats, and 180 people are randomly selected out of those registered as Independents.
Answer: stratified
Step-by-step explanation:
In stratified sampling, you divide the population into subgroups, or strata, with similar characteristics, like here we have divided the population into subgroups that depend on their political alignment. This is used when you can expect that the results have a noticeable variation between the different subgroups. Usually, you want to have the same number of population for eac subgroup, but sometimes it is hard for different reasons (not enough people in one subgroup, for example)
In cluster sampling we also use subgroups, but the subgroup itself is the unit of the sampling, while in this case, we are randomly selecting individuals of the given subgroups.
So this would be a "stratified sampling".
Which choice is equivalent to the expression below? √-12
A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i
PLEASE DON’T GUESS
Answer:
D. 2i√3
Step-by-step explanation:
You have the expression √-12. You can divide the number in the radical sign into the numbers that make up the expression. After you do this, you will be able to take numbers out of the radical sign
√(-12)
√(-1 × 4 × 3)
√-1 = i
√4 = 2
√3 = √3
2i√3
The answer is D.
the length of a mathematical text book the is approximately 18.34cm and its width is 11.75 calculate ?
the approximate perimeter of the front cover?
the approximate area of the front cover of the book?
Answer:
Perimeter=60.18cm
Area=215.495cm^2
Step-by-step explanation:
Given:
Length of book=18.34cm
Breadth=11.75cm
Solution:
Perimeter=2(l +b)
P=2(18.34+11.75)
P=2 x 30.09
P=60.18cm
Area=l x b
A=18.34 x 11.75
A=215.495 cm^2
Thank you!
Quick! Andrew has to play 15 games in a chess tournament. At some point during the tournament he has won half of the games he has played, he has lost one-third of the games he has played and two have ended in a draw. How many games has Andrew still to play?
[tex]x[/tex] - the number of the games he played
[tex]\dfrac{x}{2}[/tex] - the number of the games he won
[tex]\dfrac{x}{3}[/tex] - the number of the games he lost
[tex]x=\dfrac{x}{2}+\dfrac{x}{3}+2\Big|\cdot6\\6x=3x+2x+12\\x=12[/tex]
[tex]15-12=3[/tex]
so, he has still 3 games to play
Find the volume of the cylinder. Round your answer to the nearest tenth.
Answer:
716.75 m^3
Step-by-step explanation:
Volume of a cylinder:
=> PI x R^2 x H
H = Height
R = Radius
=> PI x 3.9^2 x 15
=> PI x 15.21 x 15
=> PI x 228.15
=> 228.15 PI
or
=> 228.15 x 3.14159
=> 716.75 m^3
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
If “n” is a positive integer divisible by 3 and n is less than or equal to 44, then what is the highest possible value of n?
Answer:
Step-by-step explanation:
positive integer divisible by 3 includes
3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...
less than highest possible value is 42
a vegetable garden and he's around the path of seemed like a square that together are 10 ft wide. The path is 2 feet wide. Find the total area of the vegetable garden and path
Answer:
Garden: 36 square feet
Path: 64 square feet
Step-by-step explanation:
Let's first find the total area. The total area will be 100 square feet since the side length is 10. Since the path is 2 feet wide and on all sides, that means that the inside square will have a side length of 6. That means that the vegetable garden is 36 square feet. The path will be 100 - (the garden), and the garden is 36 square feet, which means the outer path will be 64.
The base of a triangle is 4 cm greater than the
height. The area is 30 cm. Find the height and
the length of the base
h
The height of the triangle is
The base of the triangle is
Answer:
Step-by-step explanation:
Formula for area of a triangle:
Height x Base /2
Base (b) = h +4
Height = h
h + 4 x h /2 = 30cm
=> h +4 x h = 60
=> h+4h =60
=> 5h = 60
=> h = 12
Height = 12
Base = 12 +4 = 16
) A random sample of size 36 is selected from a normally distributed population with a mean of 16 and a standard deviation of 3. What is the probability that the sample mean is somewhere between 15.8 and 16.2
Answer:
The probability is 0.31084
Step-by-step explanation:
We can calculate this probability using the z-score route.
Mathematically;
z = (x-mean)/SD/√n
Where the mean = 16, SD = 3 and n = 36
For 15.8, we have;
z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4
For 16.2, we have
z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4
So the probability we want to calculate is;
P(-0.4<z<0.4)
We can get this using the standard normal distribution table;
So we have;
P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)
= 0.31084
Question 36 of 40
The distance of a line bound by two points is defined as
L?
O A. a line segment
B. a ray
O
c. a plane
O D. a vertex
SUBMI
Answer:
A. a line segment
Step-by-step explanation:
a ray is directing in one dxn, and has no end pointa plane is a closed, so more than 2 points a vertex is a single point itselfWhat is the solution to X+9 = 24?
A. x = 33
B. x= 15
C. x= 18
D. x= 9
Answer:
X+9=24
Or,x=24-9
:.x=15
Step-by-step explanation:
Answer:
B. x=15
Step-by-step explanation:
To find the solution to the equation, we must get x by itself on one side of the equation.
[tex]x+9=24[/tex]
9 is being added to x. The inverse of addition is subtraction. Subtract 9 from both sides of the equation.
[tex]x+9-9=24-9[/tex]
[tex]x=24-9[/tex]
[tex]x=15[/tex]
Let's check our solution. Plug 15 in for x.
[tex]x+9=24 (x=15)[/tex]
[tex]15+9=24[/tex]
[tex]24=24[/tex]
This checks out, so we know our solution is correct. The answer is B. x=15
Try to get to every number from 1 to 10 using four 4's and any number of arithmetic operations (+, −, ×, ÷). You may also you parentheses.
Answer:
Step-by-step explanation:
1. 4/4+4-4=1
2. 4/4+4/4=2
3. 4+4/4-4=3
4. 4 × (4 − 4) + 4=4
5. (4 × 4 + 4) / 4=5
6. 44 / 4 − 4=6
7. 4+4-4/4=7
8. 4+4+4-4=8
9. 4+4+4/9=9
10. 44 / 4.4=10
Answer:
1 = (4 x 4)/(4 x 4) or (4 + 4)/(4 + 4) or (4 / 4) x (4 / 4) or (4 / 4)/(4 / 4)
2= (4 x 4)/(4 + 4) or 4 / ((4+4)/4)
3= (4 + 4 + 4)/4 or (4 x 4 - 4)/4
4 = 4 - (4 - 4)/4
5 = (4 x 4 + 4)/4
6 = 4 + (4 + 4)/4
7 = 4 - (4/4) + 4
8 = 4 + (4 x 4)/4
9 = 4 + 4 + (4/4)
10 - I tried the best. You might need ! or sqrt operator to get 4.
Updated:
I forgot we could use 4, 44, 444, or 4444, so that 10 could be expressed as:
10 = (44 - 4)/4
Which expression is equal to 7 times the sum of a number and 4
Answer:
7(n + 4)
Step-by-step explanation:
Represent the number by n. Then the verbal expression becomes
7(n + 4).
point estimate A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean
Answer:
The 95 percent Confidence Interval is for the population is (38.911 , 41.089)
Step-by-step explanation:
To solve the above question, we would be making use of the confidence interval formula:
Confidence Interval = Mean ± z score × σ/√n
In the above question,
Mean = 40
σ = Standard deviation = 5
n = number of samples = 81
Confidence Interval = 95%
The z score for a 95% confidence interval = 1.96
Therefore, the confidence interval =
= 40 ± 1.96 (5/√81)
= 40 ± 1.96(5/9)
= 40 ± 1.0888888889
Confidence Interval
a)40 + 1.0888888889
= 41.0888888889
Approximately = 41.089
b ) 40 - 1.0888888889
= 38.911111111
Approximately = 38.911
Therefore, the 95 percent Confidence Interval is for the population is (38.911 , 41.089)
How to graph the line y=4/3x
Answer:
make a table of values
Step-by-step explanation:
then plot using those values
The required graph has been attached which represents the line y = 4/3x
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
We have been given the equation of a line below as:
y = 4/3x
Rewrite in slope-intercept form.
y = (4/3)x
Use the slope-intercept form to discover the slope and y-intercept.
Here the slope is 4/3 and y-intercept = (0, 0)
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
When substitute the value of x = 0, then the value of y = 0, and When substitute the value of x = 3, then the value of y = -4,
Hence, the graph represents the line y = 4/3x
Therefore, the required graph of the line y=4/3x will be shown in the as attached file.
Learn more about the graphs here:
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#SPJ2
Which quadratic equation would be used to solve for the unknown dimensions?
0 = 2w2
512 = w2
512 = 2w2
512 = 2l + 2w
Answer:
C
Step-by-step explanation:
Answer:
C: 512 = 2w2
Step-by-step explanation:
on edge
What is the solution to this system of linear equations?
y-x = 6
y + x = -10
(-2,-8)
(-8.-2)
(6.-10)
(-10.6)
Answer:
The correct answer is A
Step-by-step explanation:
Answer:
(-8, -2)
Step-by-step explanation:
y-x = 6
y + x = -10
Add the two equations together to eliminate x
y-x = 6
y + x = -10
--------------------
2y = -4
Divide by 2
2y/2 = -4/2
y = -2
Now find x
y+x = -10
-2+x = -10
x = -8
If Company X has 1600 employees and 80% of those employees have attended the warehouse training course how many employees have yet to attend?
Answer:
320
Step-by-step explanation:
Total no of employees = 1600
% of employees attended the training = 80%
no. of employee who attended the training = 80/100* 1600 = 1280
No. of employees who are yet to attend the training = Total no of employees - no. of employee who attended the training = 1600-1280 = 320
Thus, 320 employees have yet to attend the training
Tessa’s employee benefits include family health care coverage. She contributes 18% of the cost. Tessa gets paid biweekly and $108.00 is taken out of each paycheck for family health care coverage. How much does her employer contribute annually for the family coverage? Clearly show your work.
The answer is $12792
Explanation:
It is known Tessa pays $108.00 to contribute to family coverage every two weeks and this represents 18% of the total payment. This implies the employer pays the 82% missing (100% - 18% = 82%). Additionally, with this information, it is possible to know the amount the employer has to pay every two weeks that represents 82%. The process is shown below:
1. Write the values you know and use x to represent the value you need to find
108 = 18
x = 82
3. Cross multiply
x 18 = 8856
4. Find the value of x by solving this simple equation
x = 8856 ÷ 18
x = 492 - Amount the employer pays every two weeks for Tessa's family coverage
Now that we know the money the employer pays every two weeks, it is possible to calculate the annual amount of money. Follow the process below.
1. Consider one year has a total of 52 weeks and divide this number of weeks by 2 because the payment for the family coverage occurs every 2 weeks
52 ÷ 2 = 26
2. Finally, multiply the money paid by the employer every two weeks by 26
26 weeks x $492 = $12792- This is the total the employer pays annually
the product of two consecutive positive integer is 306
Answer:
[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]
Step-by-step explanation:
The product means multiplication.
There are two positive consecutive integers.
Let the first positive consecutive integer be x.
Let the second positive consecutive integer be x+1.
[tex](x) \times (x+1) =306[/tex]
Solve for x.
Expand brackets.
[tex]x^2 +x =306[/tex]
Subtract 306 from both sides.
[tex]x^2 +x -306=306-306[/tex]
[tex]x^2 +x -306=0[/tex]
Factor left side of the equation.
[tex](x-17)(x+18)=0[/tex]
Set factors equal to 0.
[tex]x-17=0[/tex]
[tex]x=17[/tex]
[tex]x+18=0[/tex]
[tex]x=-18[/tex]
The value of x cannot be negative.
Substitute x=17 for the second consecutive positive integer.
[tex](17)+1[/tex]
[tex]18[/tex]
The two integers are 17 and 18.
The product of two consecutive positive integers is 306.
We need to find the integers
solution : Let two consecutive numbers are x and (x + 1)
A/C to question,
product of x and (x + 1) = 306
⇒x(x + 1) = 306
⇒x² + x - 306 = 0
⇒ x² + 18x - 17x - 306 = 0
⇒x(x + 18) - 17(x + 18) = 0
⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18
so x = 17 and (x +1) = 18
Therefore the numbers are 17 and 18.
Hope it helped u if yes mark me BRAINLIEST
TYSM!
Please help with this
Answer:
A
Step-by-step explanation:
● first one:
The diagonals of a rhombus are perpendicular to each others wich means that they form four right angles.
STP is one of them so this statement is true.
● second one:
If ST and PT were equal this would be a square not a rhombus.
● third one:
If SPQ was a right angle, this woukd be a square.
● fourth one:
Again if the diagonals SQ and PR were equal, this would be a square.
please help
-3(-4x+4)=15+3x
Answer:
x=3
Step-by-step explanation:
● -3 (-4x+4) = 15 + 3x
Multiply -3 by (-4x+4) first
● (-3) × (-4x) + (-3)×(4) = 15 + 3x
● 12 x - 12 = 15 +3x
Add 12 to both sides
● 12x - 12 + 12 = 15 + 3x +12
● 12 x = 27 + 3x
Substract 3x from both sides
● 12x -3x = 27 + 3x - 3x
● 9x = 27
Dividr both sides by 9
● 9x/9 = 27/9
● x = 3
A speedboat moves at a rate of 25 km/hr in still water. How long will it take
someone to ride the boat 87 km downstream if the river's current moves at a rate of
4 km/hr?
Answer:
3 hours
Step-by-step explanation:
Downstream, the speeds add up:
25 + 4 = 29 km/hIt will take:
87/29= 3 hrsTo ride 87 km.