Answer:
0.40905 - 0.10204 = .30701 = 30.7 %
Step-by-step explanation:
0.23 0.40905
1.27 0.10204
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.
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What is the slope of the line shown below?
A.
B.
C.
-
D.
3
Answer:
D
Step-by-step explanation:
Option D is correct. Slope of the line shown in the graph is 3.
The slope of the line is the ratio of the rise to the run, or rise divided by the run.
It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=(y₂-y₁)/(x₂-x₁)
The line is passing through point (2, 2) and (4, 8).
Lets find the corresponding point values y₂= 8, y₁ = 2, x₂= 4 and x₁ =2.
Plug in the values in slope formula:
Slope = (8-2)/(4-2)
=6/2
=3
Hence, slope of the line shown in the graph is 3. Option D is correct.
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Question
Find the sample variance of the following set of data:
12, 7, 6, 4, 11.
Select the correct answer below:
Answer:
Variance is 256
Step-by-step explanation:
Variance:
[tex]var = \frac{ ({ \sum x})^{2} }{n} - {( \frac{ \sum x}{n} })^{2} [/tex]
x is the number or item in the data
n is the number of terms
[tex]{ \tt{ \sum x = (12 + 7 + 6 + 4 + 11)}} \\ { \tt{ \sum x = 40}}[/tex]
Therefore:
[tex]variance = \frac{ {40}^{2} }{5} - { (\frac{40}{5}) }^{2} \\ \\ = 320 - 64 \\ variance = 256[/tex]
Simplify the following expression. (4x − 8)(4x + 8)
Answer:
16x^2 - 64
Step-by-step explanation:
(4x − 8)(4x + 8)
We recognize that this is the difference of squares
(a-b) (a+b) = a^2 - b^2
=(4x)^2 - 8^2
=16x^2 - 64
Please help. I’ll mark you as brainliest if correct
Answer:
(a)
dependent
(b)
x = -3t - 12
y = -5t - 16
z = t
Step-by-step explanation:
2x - 3y - 9z = 24 Eq. 1
x + 3z = -12 Eq. 2
-3x + y - 4z = 20 Eq. 3
2x - 3y - 9z = 24
(+) -9x + 3y - 12x = 60 3 * Eq. 3
--------------------------------
-7x -21z = 84 Eq. 4
7x + 21z = -84 7 * Eq. 2
(+) -7x - 21z = 84 Eq. 4
-----------------------------
0 = 0
(a) The system is dependent.
(b)
z = t
x + 3z = -12 Eq. 2
x + 3t = -12
x = -3t - 12
2x - 3y - 9z = 24 Eq. 1
2(-3t - 12) - 3y - 9t = 24
-6t - 24 - 3y - 9t = 24
-3y - 15t = 48
-y - 5t = 16
-y = 5t + 16
y = -5t - 16
x = -3t - 12
y = -5t - 16
z = t
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
What is 12 1/2% as a fraction
3/25
1/8
6/25
1/4
9514 1404 393
Answer:
1/8
Step-by-step explanation:
The percent symbol % can be thought of as being fully equivalent to /100.
12 1/2% = (12 1/2)/100 = (25/2)/100 = 25/200 = 1/8
_____
Additional comment
It can be useful to memorize the decimal equivalents of the reciprocals of the numbers up to 12.
1/12 = 0.0833...(repeating 3)
1/11 = 0.0909...(repeating 09)
1/10 = 0.1
1/9 = 0.111...(repeating 1)
1/8 = 0.125
1/7 = 0.142857...(repeating the same 6 digits)
1/6 = 0.1666...(repeating 6)
1/5 = 0.2
1/4 = 0.25
1/3 = 0.333...(repeating 3)
1/2 = 0.5
Of course, any of these is expressed as a percentage by multiplying by 100%. 1/8 = 12.5%, 1/6 = 16.6...% (repeating 6)
Mrs. Simpson’s calculus class has an exam with an average score of 80 and standard deviation of 15. Assume that exam scores are normally distributed. If Mrs. Simpson decides to give an A grade to students who score in the top 20% of the class, what exam score is needed in order to get the A grade? (3pts)
Answer:
93 is the exam score needed in order to get the A grade in Mrs Simpson’s test
Step-by-step explanation:
Let x be the score that gives an A grade
Mathematically from the z-score formula, we know that;
z-score = x-mean/SD
From the question, x = ? , mean = 80 and SD = 15
Thus;
z-score = x-80/15
But in this question, we have the probability but we do not have the z-score
So we need the z-score that is equivalent to 20%
20% is same as 0.2
Using the standard normal distribution table, a probability of 0.2 corresponds to a z-score of 0.84
Thus, mathematically;
0.84 = x-80/15
x-80 = 15(0.84)
x-80 = 12.6
x = 80 + 12.6
x = 92.6 which is approximately 93
Given the trinomial, what is the value of the coefficient B in the factored form?
2x2 + 4xy − 48y2 = 2(x + By)(x − 4y)
Answer:
B = 6
Step-by-step explanation:
2x^2 + 4xy − 48y^2
Factor out 2
2(x^2 + 2xy − 24y^2)
What 2 numbers multiply to -24 and add to 2
-4 *6 = -24
-4+6 = 2
2 ( x+6y)( x-4y)
Answer:
[tex]\huge\boxed{B=6}[/tex]
Step-by-step explanation:
They are two way to solution.
METHOD 1:Factor the polynomial on the left side of the equation:
[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]
Therefore:
[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]
METHOD 2:Multiply everything on the right side of the equation using the distributive property and FOIL:
[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]
Compare polynomials:
[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]
From here we have two equations:
[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]
[tex]1)\\2B-8=4[/tex] add 8 to both sides
[tex]2B=12[/tex] divide both sides by 2
[tex]B=6[/tex]
[tex]2)\\-8B=-48[/tex] divide both sides by (-8)
[tex]B=6[/tex]
The results are the same. Therefore B = 6.
Examining and Interpreting a Statistical Report
To help make his case to potential investors in his invention, Martin found a poll conducted by Gallup, a well-known research organization. Take some time to read the report, and then answer the questions to analyze the merits and limitations of this survey.
Part A
The poll report includes a table titled, “Americans Using Cash Now Versus Five Years Ago, by Age.” The age intervals are not equal. Why do you think the Gallup organization chose the age intervals of 23–34, 35–54, and 55+ to display these results?
The Gallup organization chose the age intervals of 23–34, 35–54, and 55+ to display these results due to they wanted to identify the habits about the use of cash in the different stages of a person's life, differentiated by ranges of unequal age.
Application of statistics in the collection of information.
Although the most common case when preparing a frequency table is to develop equal ranges that allow the behavior of the respondents to be identified every certain number of possible values.
Example:
0.1 - 10 10.1 - 20 20.1 - 30
On some occasions, irregular or uneven ranges are used that refer to a specific market stage or niche.
In part A of the exercise, you can clearly identify the three stages of adult life that could change your money-use habits:
23 - 34: Group that could be called "young adults", possibly made up of university students, and people who recently started their work stage. 35 - 54: Group of "middle-aged people", made up of people who have been working and managing their finances for a long time, even those who are even close to retirement. 55 or more: People of the "third age" or close to said category, made up of pre-pensioners and pensioners or people who are no longer active in employment.
As you can see, each of these groups present great differences that, from the point of view of a person interested in investing in their invention, a poll report like this is more attractive to select the niche of potential investors based on the work stage of said person.
By this reason, The Gallup organization chose the age intervals due to their money-habits, depending on the stage of his/her life.
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Which graph shows the polar coordinates (-3,-) plotted
If c o v (x comma space y )space equals space 1260, s subscript x squared equals 1600, and s subscript y squared equals 1225 , then the coefficient of determination is:
Complete Question
The complete question is shown on the first uploaded image
Answer:
The coefficient is [tex]r =0.81[/tex]
Step-by-step explanation:
From the question we are told that
[tex]cov(x, y )= 1260[/tex]
[tex]s_x^2 = 1600[/tex]
[tex]s_y^2 = 1225[/tex]
Generally the coefficient of determination is mathematically represented as
[tex]r = [ \frac{cov(x,y)}{ \sqrt{s_x^2} * \sqrt{s_y^2} } ]^2[/tex]
substituting values
[tex]r = [ \frac{ 1260}{ \sqrt{1600} * \sqrt{1225} } ]^2[/tex]
[tex]r =0.81[/tex]
Georgianna claims that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons. We have a random sample of 20 children from the city, with a mean of 4.6 years of piano lessons and a standard deviation of 2.2 years. Required:Explicitly state and check all conditions necessary for inference on these data.
Answer:
The condition are
The Null hypothesis is [tex]H_o : \mu = 5[/tex]
The Alternative hypothesis is [tex]H_a : \mu < 5[/tex]
The check revealed that
There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 5 \ year[/tex]
The sample size is n = 20
The sample mean is [tex]\= x = 4.6 \ years[/tex]
The standard deviation is [tex]\sigma = 2.2 \ years[/tex]
The Null hypothesis is [tex]H_o : \mu = 5[/tex]
The Alternative hypothesis is [tex]H_a : \mu < 5[/tex]
So i will be making use of [tex]\alpha = 0.05[/tex] level of significance to test this claim
The critical value of [tex]\alpha[/tex] from the normal distribution table is [tex]Z_\alpha = 1.645[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 4.6 - 5}{ \frac{2.2}{\sqrt{20} } }[/tex]
[tex]t = -0.8131[/tex]
Looking at the value of t and [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis
This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.
Find the area of the shape shown below.
2
2
4
Hurry and answer plz!!!!
1
Answer:
7 square units
Step-by-step explanation:
We can break down this complex shape into smaller shapes.
I've broken it down into a rectangle, a square, and a triangle (See attached picture)
Let's first find the area of the triangle. To do this we use the formula [tex]\frac{bh}{2}[/tex]. The base is 1 (because the top is 2, and 1 is already used on the triangle - 2-1 = 1.) and the height is 2 (because 4 is already used on the left, and 2 was used on the right so 4-2=2).
[tex]\frac{2\cdot1}{2} = \frac{2}{2} = 1[/tex].
Now let's find the area of the top square - we can just square 2 which is 4.
To find the area of the bottom rectangle, we can multiply it's two side lengths of 2 and 1 = 2.
Adding these all together gets us 4+2+1 = 7.
Hope this helped!
A triangle has two sides of lengths 8 and 10. What value could the length of
the third side be? Check all that apply.
Answer:
8, 10, 4, 7
Step-by-step explanation:
Missing side = x
Rules for x:
It should be less than the sum of the other two sides
It should be greater than the difference of the other two sides
8 + 10 = 18
10 - 8 = 2
2<x<18
8, 10, 4, 7
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Brief and easy(if possible) explanation on how to do these?
Answer:
linear pairs are supplement which means it always equals to 180°
Read image for instructions
The last part answers the first part for you, just look at the y-values.
In other words:
A' (-8, 2)
B' (-4, 3)
C' (-2, 8)
D' (-10, 6)
Explanation:
When you reflect any point over the x-axis, the y-value of the ordered pair is going to change.
This makes sense especially considering that the x-axis is horizontal, so the only way you could cross is to move up or down. If you were to move left or right, you'd only be able to cross the y-axis, since it's vertical.
Now for the last part, as I mentioned above, if you are reflecting across the y-axis, the x-values of the ordered pair is going to change.
A'' (8, 2)
B'' (4, 3)
C'' (2, 8)
D'' (10, 6)
Take note that the only thing that changes for the respective value is its sign, while the number itself stays the same.
Uche is a cartographer. He picks a scale to fit a map of India onto a page of an atlas. The page is 121212 by 121212 inches, with 0.750.750, point, 75 inch margins on all 444 sides. India measures 3{,}2143,2143, comma, 214 kilometers from north to south and 2{,}9332,9332, comma, 933 kilometers from west to east. Uche wants the longest dimension of India to fit exactly in between the margins of the page. If kkk is the number of kilometers per inch in Uche's scale, which equation best models the situation
The scale ratio of a point A to another point B is the division of the length of B by the length of A. The best equation that models the situation is: [tex]10.5k= 3214[/tex]
The page dimension is:
[tex]Length = 12[/tex]
[tex]Width = 12[/tex]
The length and the width of Uche's book are equal; this means the pages of Uche's book have the shape of a square
The margin of 0.75 on either sided means the usable dimension is:
[tex]Length = 12 - 2 * 0.75 =10.5[/tex]
The dimension of India is:
[tex]Length = 3214[/tex]
[tex]Width =2933[/tex]
The longest side in India's dimension is:
[tex]Longest = 3214[/tex]
From Uche's book, the longest dimension is:
[tex]Longest = 10.5[/tex]
So, the scale equation is:
k * longest length of Uche's book = longest side of India
This gives:
[tex]k * 10.5 =3214[/tex]
[tex]10.5k =3214[/tex]
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Find the common ratio for the following sequence. Type a numerical answer in the space provided. If necessary, use the
/ key to represent a fraction bar. Do not type spaces in your answer.
2,-2, 2, -2, ...
Answer:
-1
Step-by-step explanation:
the common ratio in this geometric series is -1
HURRY plSSSSSSSSSSSSSSSSSSSSSS
What is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is eighty degrees and the other is unknown.
Answer:
The unknown is 100
Step-by-step explanation:
A straight line is 180 degrees
We have two angles x, and 80
x+80 = 180
x = 180-80
x= 100
Find the slope of a line perpendicular to the line defined by the equation 3x-5y=12
Answer:
-5/3
Step-by-step explanation:
Note the slope intercept form: y = mx + b
Note that:
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
Isolate the variable, y. First, Subtract 3x from both sides:
3x (-3x) - 5y = 12 (-3x)
-5y = -3x + 12
Next, divide -5 from both sides. Remember to divide from all terms within the equation:
(-5y)/-5 = (-3x + 12)/-5
y = (-3x/-5) + (-12/5)
Simplify.
y = (3x/5) - 12/5
y = (3/5)x - 12/5
You are trying to find the perpendicular slope to this line. To do so, simply flip the slope (m) as well as the sign:
Original m = 3/5
Flipped m = -5/3
-5/3 is your perpendicular slope.
Answer:
5
m = - ---- perpendicular slope
3
Step-by-step explanation:
3x - 5y = 12 -------->> convert to y = mx + b
- 5y = - 3x + 12
- 5y = - (3x + 12) --- eliminate the negative
5y = 3x + 12
3x + 12
y = -------------
5
3 12
y = -----x + -----
5 5
the above equation is the form of y = mx + b
where m is the slope and b is the intercept
5
therefore, m = - ---- perpendicular slope
3
hat is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is ninety seven degrees and the other is unknown
pls
Let on of the angle be x
ATQ
97 + x = 180
x = 180 - 97 (Angles on same line adds upto 180°) (Linear pair cuz 2 angles)
x = 83
The unknown angle is 83°
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Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
There are [tex]10[/tex] divisions between $3.2$ and $3.3$
so that means each division is $\frac{3.3-3.2}{10}=0.01$
A is the 3rd division after $3.2$, So A is $3.2+3\times0.01=3.23$
similarly, C is 3 division behind $3.2$ so it will be $3.17$
and B is $3.34$
A represents the decimal 3.23
B represents the decimal 3.34
C represents the decimal 3.17
Calculating the decimal values:We can see that there are 10 divisions between 3.2 and 3.3.
The difference between the two points for 10 divisions is 3.3 -3.2 = 0.1 unit.
Therefore, one division will be equal to 0.1/10 = 0.01 unit
So, point A is 3 divisions after 3.2, thus
A = 3.2 + 0.01×3
A = 3.23
Similarly,
B = 3.3 + 0.01×4
B = 3.34
And,
C = 3.2 - 0.01×3
C = 3.17
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How do write 841, 620 in three different ways?
Answer:
1) 841,620
2) 800,000+40,000+1,000+600+20
3) Eight hundred forty-one thousand, six hundred twenty
Hope this helps!
Which graph represents a linear function that has a slope of 0.5 and a y-intercept of 2?
On a coordinate plane, a line goes through points (negative 2, 0) and (0, 1).
On a coordinate plane, a line goes through points (0, 2) and (4, 0).
On a coordinate plane, a line goes through points (0, 2) and (2, 3).
On a coordinate plane, a line goes through points (negative 4, 0) and (0, 2).
Answer:
f(x)=1/2x+2
Step-by-step explanation:
Using formula y=mx+b.
m is 0.5 or 1/2 as stated above
f(x)= 1/2x+b
If it were y=1/2x, it would intersect at 0,0 and we want 0,2
so b should be 2
therefore
Y=1/2x+2
or
f(x)=1/2x+2
Answer:
D
Step-by-step explanation:
Write the polar form of a complex number in standard form for [tex]25[cos(\frac{5\pi }{6}) + isin(\frac{5\pi }{6})][/tex]
Answer:
Standard Complex Form : [tex]-\frac{25\sqrt{3}}{2}+\frac{25}{2}i[/tex]
Step-by-step explanation:
We want to rewrite this expression in standard complex form. Let's first evaluate cos(5π / 6). Remember that cos(x) = sin(π / 2 - x). Therefore,
cos(5π / 6) = sin(π / 2 - 5π / 6),
π / 2 - 5π / 6 = - π / 3,
sin(- π / 3) = - sin(π / 3)
And we also know that sin(π / 3) = √3 / 2. So - sin(π / 3) = - √3 / 2 = cos(5π / 6).
Now let's evaluate the sin(5π / 6). Similar to cos(x) = sin(π / 2 - x), sin(x) = cos(π / 2 - x). So, sin(5π / 6) = cos(- π / 3). Now let's further simplify from here,
cos(- π / 3) = cos(π / 3)
We know that cos(π / 3) = 1 / 2. So, sin(5π / 6) = 1 / 2
Through substitution we receive the expression 25( - √3 / 2 + i(1 / 2) ). Further simplification results in the following expression. As you can see your solution is option a.
[tex]-\frac{25\sqrt{3}}{2}+\frac{25}{2}i[/tex]
help please i need this now step by step
Answer:
40 mi ^2
Step-by-step explanation:
SA = 2(lw+wh+lh) where l is the length, w is the width, h is the height
SA = 2( 2*2 + 2*4 * 2*4)
= 2( 4+8+8)
= 2(20)
= 40 mi ^2
$17,818 is invested, part at 11% and the rest at 6%. If the interest earned from the amount invested at 11% exceeds the interest earned from the amount invested at 6% by $490.33, how much is invested at each rate? (Round to two decimal places if necessary.)
Answer:We know the total amount of money invested. $17818
x+y=17818,
We know that the difference in interest earned by the two accounts is $490.33
0.11*x-0.06*y=490.33
x=17818-y
We substitute for x
0.11*(17818-y)-0.06*y=490.33
We multiply out
1959.98-0.11y-0.06*y=490.33
We combine like terms.
1469.65=0.17*y
Isolate y
y=1469.65/0.17
y=8645 at 6%
Calculate x
x=17818-8645
x=9173 at 11%
Check
0.11*9173-0.06*8645=490.33
interest earned at 11%=1009.03
interest earned at 6%=518.70
1009.03-518.7=490.33
490.33=490.33
Since this statement is TRUE and neither amount is negative then all is well.We know the total amount of money invested. $17818
x+y=17818,
We know that the difference in interest earned by the two accounts is $490.33
0.11*x-0.06*y=490.33
x=17818-y
We substitute for x
0.11*(17818-y)-0.06*y=490.33
We multiply out
1959.98-0.11y-0.06*y=490.33
We combine like terms.
1469.65=0.17*y
Isolate y
y=1469.65/0.17
y=8645 at 6%
Calculate x
x=17818-8645
x=9173 at 11%
Check
0.11*9173-0.06*8645=490.33
interest earned at 11%=1009.03
interest earned at 6%=518.70
1009.03-518.7=490.33
490.33=490.33
Since this statement is TRUE and neither amount is negative then all is well.
Amira has 3/4 of a bag of cat food her cat eats 1/10 of a bag per week how many weeks will the food last
What is the value of n
Answer:
9 + 18 = 27
27 + n + 1
= n = 27 - 1 = 26.
n = 26
9 + 18 + 26 + n + 7 =
53 + n + 7
53 + 7 + n
60 + n = 360
n = 360 - 60 = 300
so, n 300
so = 9, 18, 300, 26