A low standard deviation implies that the data exists grouped around the mean, whereas a large standard deviation indicates that the data exists more dispersed.
What is meant by standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data exists grouped around the mean, whereas a large standard deviation indicates that the data exists more dispersed.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Because it aids in comprehending measurements when the data is scattered, standard deviation is significant. The standard deviation of the data will be higher the more evenly dispersed the data is.
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Identify the range of the function.
A [-4,0]
B (-4,0)
C [-3,1]
D (-3,1)
Answer: [-4, 0] which is choice A
=====================================================
Reason:
lowest point is when y = -4
highest point is when y = 0
The range is any value of y between these values, including the endpoints themselves. We say the range is [tex]-4 \le y \le 0[/tex] which condenses to the interval notation [-4, 0]
Use square brackets to include the endpoints.
If there were open holes at the highest and lowest points, then we would use curved parenthesis instead.
Is the following statements true or false?
Answer: False
Step-by-step explanation: The two lines do not overlap so they do not intercept.
The amount of money an engineer receives from a bank if he invests $50,000 for 7 years at 11.5% per annum compound interest.
Answer:
$107125.80
working out:
50000x1.115^7=107125.8 (rounded)
-The polynomial function p(x) = x² + 4x³ - 7x² - 22x + 24 has known factors of (x + 4) and (x - 1).
a. Rewrite p(x) as the product of linear factors.
b. Draw a rough sketch of the graph of the function.
Answer:
p(x) = (x +4)(x +3)(x -1)(x -2)see the first attachment for a graphStep-by-step explanation:
Given p(x) = x⁴ + 4x³ - 7x² - 22x + 24 with known factors (x +4) and (x -1), you want the function written as a product of linear factors, and a sketch of the graph.
A graphing calculator can help with both parts of this. It can show you the remaining zeros are -3 and 2, so the remaining linear factors are (x +3) and (x -2). At the same time, it produces a graph of the function. This is shown in the first attachment.
a. RewriteSynthetic division is a convenient way to find the remaining factors of the polynomial. Dividing by (x+4) gives ...
p(x) = (x +4)(x^3 -7x +6) . . . . . . shown in the second attachment
And dividing the cubic by (x -1) gives ...
p(x) = (x +4)(x -1)(x^2 +x -6) . . . . . . shown in the second attachment
The quadratic will have linear terms with constants that sum to 1 and have a product of -6. These constants are 3 and -2.
The rewrite of p(x) is ...
p(x) = (x +4)(x +3)(x -1)(x -2)
b. Graph
The 4th degree polynomial has a positive leading coefficient, so is above the x-axis at both the left and right ends of the graph. The graph crosses the x-axis at x = -4, -3, 1, and 2.
We note these roots are symmetrical about x=-1, so there will be a maximum at that point. That maximum is p(-1) = (-1 +4)(-1 +3)(-1 -1)(-1 -2) = 3·2·(-2)(-3) = 36. The minimum values will be found approximately halfway between -4 and -3, and again between -1 and -2. Those minima will be approximately p(-3.5) = (-.5)(.5)(-4.5)(-5.5) ≈ -6.2
The y-intercept is +24, the constant in the polynomial.
With the zero crossings, line of symmetry, local maximum, approximate local minima, and the y-intercept, we can make a passable sketch of the graph.
A graph is seen in the first attachment.
Salesman A gets paid $300 a month plus $8 for every sale he makes. Salesman B gets paid $1500 a mont. Write and equation and solve to see how many salesman a must make in order to make the same amount of salesman b
The salesman A must make 150 order to make the same amount of salesman B .
In the question ,
it is given that ,
Salesman A gets paid $300 per month
for every sale salesman A get $8 .
let the number of sales made by salesman A be "x" .
So, amount made by salesman A = 300 + 8x
Salesman B earns per month = $1500 .
To make the amount earned by both the salesman same ,
300 + 8x = 1500
8x = 1500 - 300
8x = 1200
x = 1200/8
x = 150
Therefore , The salesman A must make 150 order to make the same amount of salesman B .
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Zach submitted the work shown below when trying to simplify the expression 3 + 2(2x - 4) what mistake did he make and what is the correct simplified expression with correct steps
Answer:
The number “2” that is a outside the brackets multiplies both of the numbers inside the brackets.
Step-by-step explanation:
3+2(2x-4)
3+4x-8
4x-5
Suppose the commute times for employees of a large company follow anormal distribution. If the mean time is 24 minutes and the standarddeviation is 5 minutes, 95% of the employees will have a travel time within which range?
The empirical rule state that, for normally distributed data, almost all of the data fall within three standard deviations either side of the mean. Specifically,
-68% of data within 1 standard deviation.
-95% of data within 2 standard deviation
-99.7 of data within 3 standard deviation.
In our case the mean is
[tex]\mu=24[/tex]and the standard deviation is
[tex]\sigma=5[/tex]then, the empirical formula imply that
[tex]\begin{gathered} \mu-2\sigma=24-2\cdot5 \\ \mu-2\sigma=24-10 \\ \mu-2\sigma=14 \end{gathered}[/tex]and
[tex]\begin{gathered} \mu+2\sigma=24+2\cdot10 \\ \mu+2\sigma=24+10 \\ \mu+2\sigma=34 \end{gathered}[/tex]then, the answer is 14 minutes to 34 minutes
Answer:
D
Step-by-step explanation:
Select the correct answer.
Which of the following represents a function?
B. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}
C. x -5 -1 9 8 -1
y 1 7 23 17 1
The relation which represents a function is the mapping diagram.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value).
In this scenario, the same x-value of the given ordered pairs (3, 2) and (3, 4) have the different output variable (y-value) and as such does not represent a function. Similarly, the table of values has the same x-value (-1) which outputs different numerical values.
Based on the ordered pairs and table shown above, we can reasonably and logically deduce that it is only the mapping diagram that represents a function.
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hellp please ?????????????
Answer:
see explanation
Step-by-step explanation:
since the dilatation is centred at the origin , then multiply each of the original coordinates by the scale factor of 2
Q (2, 2 ) → Q' (2(2), 2(2) ) → Q' (4, 4 )
P (0, 0 ) → P' (2(0), 2(0) ) → P' (0, 0 )
R (- 2, - 4 ) → R' (2(- 2), 2(- 4) ) → R' (- 4, - 8 )
S (4, - 2 ) → S' (2(4), 2(- 2) ) → S' (8, - 4 )
Last winter it snowed 5 inches in December 17 inches in January 13 inches in February and 2 inches in March how much snow fell during the entire winter 
37 inches total, but 35 with just December, January, and February (depending on the definition of winter)
Given m || n, find the value of x and y.
119°
to
yº
E
x+119°=180°(Co-interior angles are supplementary m || n)
[tex]x = 180 - 119 \\ x = 61[/tex]
y=119°(alternate angles are equal m ||n)
GOODLUCK.
Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other.
BRO HELP ITS DUE TMRW WILL GIVE BRAINLIEST AND POINTS
Considering the given figure, the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other is: In parallelogram EFGH show EK is congruent to KG and F.K is congruent to KH
How to determine the correct rephrase of the proof about parallelogram diagonalsThe diagonals refer to the lines running between the two opposite ends of the parallelogram
Bisecting means sharing into two equal parts
congruent means a copy that is equal in dimension hence can be used in place of the other image
The diagonals of a parallelogram bisect each other means that the diagonals cut each other to form two equal parts such that each part is congruent to each other.
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change from radical form to exponential expression in fractional form. No need to evaluate just be put in simplest form
To convert from radical form to exponential in fractional form, we can follow:
[tex]\sqrt[m]{b^n}=b^{\frac{n}{m}}[/tex]Firstly, notice that 9 is the same as 3 squared:
[tex]\sqrt[4x+2]{9}=\sqrt[4x+2]{3^2}[/tex]Now, we can apply the change:
[tex]\sqrt[4x+2]{3^2}=3^{\frac{2}{4x+2}}[/tex]Also, notice that we can factor out the 2 on the denominator to cancel with the two on the numerator:
[tex]3^{\frac{2}{4x+2}}=3^{\frac{2}{2(2x+1)}}=3^{\frac{1}{2x+1}}[/tex]So, the expression in the simples form and fractional exponent is:
[tex]3^{\frac{1}{2x+1}}[/tex]Carter wants to use the model above to solve 273 ÷ 13. Explain how he would find parts A, B, and C of the model.
Using the model Carter will find parts A, B and C b to be
Part A = 26 tens
Part B = 13
Part C = 13 ones
What is a model?A model is a representation in form of shape used for to achieve a desired aim. Models are choose with respect to the importance
How to determine parts A. part B, and part C using the modelThe given model is a rectangle
Subtracting 13 from 273 to give 260. This can be arranged in tens by doing
= 260 / 10
= 26
Hence, A is 26 tens
Representing the C part in place value we have 13 ones
Since B = C, we have B = 13
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2x + 3y = 13
Step 2 of 2: Determine the missing coordinate in the ordered pair (?, 3/2) so that it will satisfy the given equation
Answer:
[tex]\frac{17}{4}[/tex]
Step-by-step explanation:
Replace y with 3/2 and solve for x
2x + 3(3/2) = 13
2x + 9/2 = 13 Subtract 9/2 from both sides
2x = [tex]\frac{13}{1}[/tex] - [tex]\frac{9}{2}[/tex]
2x = [tex]\frac{26}{2}[/tex] - [tex]\frac{9}{2}[/tex]
2x = [tex]\frac{17}{2}[/tex] Divide both sides by 2
x = [tex]\frac{17}{2}[/tex] ÷ [tex]\frac{2}{1}[/tex]
x = [tex]\frac{17}{2}[/tex] x [tex]\frac{1}{2}[/tex]
x = [tex]\frac{17}{4}[/tex] o r4 [tex]\frac{1}{4}[/tex] or 4.25
Sally can paint a room in 4 hours while it takes Steve 3 hours to paint the same room. How long would it take them to paint the room if they worked together?
Hi,Hope you could help me with the attached question. Thanks!A random sample of 380 married couples found that 298 had two or more personality preferences in common. In another random sample of 574 married couples, it was found that only 36 had no preferences in common. Let p1 be the population proportion of all married couples who have two or more personality preferences in common. Let p2 be the population proportion of all married couples who have no personality preferences in common.
We were given that:
For P
Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P = {2, 4, 6, 8}. What is P' ?
{2, 4, 6, 8}
{1, 2, 3, 4, 5, 6, 7, 8}
{1, 3, 5, 7}
{1, 3, 5, 7, 8}
Answer:
{1, 3, 5, 7}
Step-by-step explanation:
U = {1, 2, 3, 4, 5, 6, 7, 8}
P = {2, 4, 6, 8}
P'= {1, 3, 5, 7}
Just answer what the ss says
The scatterplot of the data is attached accordingly. The Linear Regression equation for Y is ŷ = 0.82X + 2.31. Note that there is a positive correlation. This is because the y variable tends to increase as the x variable increases.
What is linear regression?Linear regression is a statistical method for modeling the connection between a scalar output and one or more explanatory factors. When there is only one independent factor, simple linear regression is employed; when there are more than one, multiple linear regression is utilized.
Note that the regression equation is usually given as:
ŷ = bX + a; where
y = dependent variable
b = Slope/coefficient
X = Independent Variable
a = Constant/ Intercept.
Notice that the regression line splits evenly between the data points exhibiting a linear relationship that is positively correlated.
From the graphing calculation, we have:
The sum of X = 21
The sum of Y = 33.39
Mean X = 3
Mean Y = 4.77
Sum of squares (SSₓ) = 28
Sum of products (SP) = 22.96
Recall that the regression equation is given as:
ŷ = bX + a;
Where;
b = SP/SSₓ and
a = [tex]M_{y}[/tex] -[tex]bM_{x}[/tex]
Hence,
b = 22.96/28
= 0.82
a = [tex]M_{y}[/tex] - bMₓ = 4.77 - (0.82*3) = 2.31
hence,
ŷ = 0.82X + 2.31.
Lets find Y if x = 10
y = 0.82 (10) + 2.31 [plugging in the value]
= 8.2 +2.31
= 10.51
Let's find X where Y = 10
10 = 0.82X + 2.31. [Plugging in the value]
collect like terms over the equation sign
10-2.31 = 0.82X
⇒ 7.69 = 0.82X [Divide both sides by 0.82
7.69/0.82 = X
X = 9.37804878049
X [tex]\approx[/tex] 9.38
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when 9 times a number is increased by 30, the answer is the same as when 140 is decreased by the number. Find this number
Answer: 11
Step-by-step explanation:
Let the number be x.
[tex]9x+30=140-x\\\\10x=110\\\\x=11[/tex]
Adriel is going to invest in an account paying an interest rate of 2.4% compounded monthly. How much would Adriel need to invest, to the nearest ten dollars, for the value of the account to reach $120,000 in 8 years?
The principal amount is $99,055.82.
What is Compound interest?When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits. Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.
Given:
Amount = 120,000
r = R/100
r = 2.4/100
r = 0.024 per year,
Then, solve the equation for P
P = A / [tex](1 + r/n)^{nt}[/tex]
P = 120,000.00 /[tex](1 + 0.024/12)^{(12)(8)[/tex]
P = 120,000.00 / [tex](1 + 0.002)^{(96)[/tex]
P = $99,055.82
Hence, the principal amount is $99,055.82.
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Hi I just need Part A. I’m in high school calculus 1 and this is a homework. thank you !
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define what happens when a function is shrunk vertically
When the factor is greater than 1, the condition that satisfies the function is to multiply by 1.4
When the graph is verticcally shrunk, this means that the function is multiplied by 1.4
Hence, the function becomes:
[tex]1.4\times f(x)=1.4\cdot f(x)[/tex]STEP 2: Define what happens when the graph is shifted left by 3 units.
If the function is shifted left by 3 units, this implies that we add 3 units to the x of the function.
This gives:
[tex]1.4.f(x+3)[/tex]Use the Exemption amounts in Figure 2.2 on page 132 to find the
(a) amount for exemptions and (b) annual state income taxes.
11. Jeff Falls, a heating system
salesman, is single with 3
dependents. He earns $57,900
annually, and his state's tax rate
is 3%.
13. Rick Delgado earns $43,500
annually as an automobile
mechanic. He is married but
has no dependents. The state
tax rate is 4.6%.
12. Sara Moon is a video editor
who earns $63,840 annually.
She is married, has 2 dependents,
and her state tax rate is 4%.
14. Julie Bookwalter is single,
claims 1 dependent, and
earns $32,300 annually. The
state tax rate is 2.5%.
11. The amount he pays in annual state income tax is $1,497.
13. The amount that will be paid for tax will be $2000.
14. The amount he pays in annual state income tax is $707.50.
How to estimate the annual state income tax?11. Given;
Annual earnings = $57,900
State tax rate = 3%
Amount earned in exemption = $8,000
Taxable Income = Annual Income - Exemptions
Igor's taxable income = $57,900 - $8,000 = $49,900
Taxable Income × Tax rate = Amount paid as tax
The amount he pays is therefore; $49,900 × 3% = $1,497
13. The amount that will be paid as tax will be:
= 4.6% × $43500
= $2000
Therefore, the amount is $2000.
12. a) We can see that the exemptions for a married person are $4000 and $2000 per dependent. Since there are 2 dependents, therefore:
Amount for exemptions = $4000 + (2 dependents × $2000 per dependent)
Amount for exemptions = $4000 + $4000 = $8000
Amount for exemptions = $8000
b) Taxable wages = Annual gross pay - Exemptions
Taxable wages = $63840 - $8000 = $55840
Annual state income taxes = Taxable wages × State tax rate
Annual state income taxes = $55840 × 4% = $2233.6
14. The amount he pays in annual state income tax is $707.50.
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462 people get on an empty train at a station. At the first stop, 234 more people get on the train, and 95 people get off. There are no more stops until the train reaches it final destination, where everybody gets off the train. How many people get off the train at the final destination?
Answer:
wow your so goood
Step-by-step explanation:
How many square mega meters are in 9,000,000 square kilometers?
Answer:
9 square megameters
Explanation:
Given:
[tex]\begin{gathered} 1.0\times10^6\text{ square kilometers}=1\text{ square megameter} \\ \implies1\text{ square kilometers}=\frac{1}{1.0\times10^6}\text{ square megameter} \end{gathered}[/tex]We want to find out how many square megameters are in 9,000,000 square kilometers.
Multiply both sides of the equation by 9,000,000.
[tex]\begin{gathered} 1\times9,000,000\text{ square km}=\frac{9,000,000}{1.0\times10^6}\text{ square megameter} \\ \implies9,000,000\text{ square km}=9\text{ square megameter} \end{gathered}[/tex]There are 9 square megameters in 9,000,000 square kilometers.
214 ÷ 9 = ___.
Twenty-three and two-ninths
Twenty-three and five-ninths
Twenty-three and seven-ninths
24
Answer:
Twenty-three and seven-ninths
Step-by-step explanation:
Might not be correct I don't really remember how to do this
Find the volume of this cylinder. Use 3 for a.14 ftV = 7r2h=9 ftVV ~ [?]ft3
The formula for the Volume(V) of the cylinder is given as,
[tex]V=\pi r^2h[/tex]Given:
[tex]\begin{gathered} \pi=3 \\ r=14ft \\ h=9ft \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} V=3\times14^2\times9=3\times196\times9=5292ft^3 \\ \therefore V=5292ft^3 \end{gathered}[/tex]Hence, the volume of the cylinder is
[tex]5292ft^3[/tex]help on both problems
Answer:
114 cm^2; x = 6: it is not possible because the lengths of the sides when solved are not the right size. x - 1 is bigger than 2x - 4 in the picture but in reality it is not. it doesnt make sense
Step-by-step explanation:
for the first one the area of a trapezoid is [tex]\frac{1}{2} h(b_{1} +b_{2})[/tex]
so
first find the height of the triangle
8^2 + h^2 = 10^2
64 + h^2 = 100
h^2 = 36
h = 6
so
the height is 6
now plug it in
[tex]\frac{1}{2} * 6 (25 + 13)[/tex]
[tex]\frac{1}{2} * 6(38)[/tex]
114 cm is the first answer
for the second one you can add all of them together and set them equal to 27
x - 1 + 2x - 4 + 3x - 4 = 27
6x - 9 = 27
6x = 36
x = 6
that is the second answer
it is not possible because the lengths of the sides when solved are not the right size. x - 1 is bigger than 2x - 4 in the picture but in reality it is not. it doesnt make sense
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
Well your answer is down below
Step-by-step explanation:
First as a Inequality −3(2x−5)<5(2−x)
Step 1: Simplify both sides of the inequality.
−6x+15<−5x+10
Step 2: Add 5x to both sides.
−6x+15+5x<−5x+10+5x
−x+15<10
Step 3: Subtract 15 from both sides.
−x+15−15<10−15
−x<−5
Step 4: Divide both sides by -1.
−x−1<−5−1 x>5
So your answer is x>5
hope this helps
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teresa earned 425 dollars for working 25 hours last week what is her hourly rate
Answer: $17
Step-by-step explanation:
$425 divided by 25
Answer:
Her hourly rate is $17/hr.
Step-by-step explanation:
We can figure this out by taking the total dollars ($425) and dividing it by how many hours she spent working (25). 425 divided by 25= 17. Therefore, her hourly rate is 17$/hr.