Answer:
Let (x+1) = the larger number
Step-by-step explanation:
Two consecutive numbers differ by 1. The larger is 1 more than the smaller. The expression for 1 more than x is (x+1).
please help asap urgent
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Answer:
6 unit cubesStep-by-step explanation:
Look at the picture.
Ms. Walker used a coordinate plane to plot her students' scores on a recent quiz. She let x represent the number of correct answers they had on their quiz and y represent the number of points earned. She then plotted the ordered pairs (17, 68), (20, 80), and (24, 96) to represent the data from three students.
What is the slope of the graph in points per question?
Answer:
Slope = 4
Step-by-step explanation:
The x-axis values to represent the number of correct answers.
The y-axis values to represent the number of points earned.
The points on the graph are: (17,68) , (20,80) and (24,96)
The slope(m) of the graph = change in y ÷ change in x
i.e [tex]\frac{80 - 68}{20 - 17}[/tex] = [tex]\frac{96 - 80}{24 - 20}[/tex] = 4
The equation of the straight line graph is;
y=4x
The slope of the graph, representing points earned per correct answer on the quiz, is 4. This is found by dividing the change in points earned by the change in correct answers between any two points on the graph.
Explanation:The slope of a graph in the coordinate plane is the ratio of the change in y (the vertical difference) to the change in x (the horizontal difference) between any two points on the line. In this case, the difference in y (points earned) for the pairs given by Ms. Walker, for example between (20, 80) and (24, 96), is 16. The difference in x (number of correct answers) in the same pairs is 4. Therefore, the slope of the graph, which represents the points per question, is 16 divided by 4: 4 points per question. This means that for each correct answer (each increase in 1 on the x-axis), the number of points earned (y) increases by 4.
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The original price of a mountain bike was reduced $125 if p = the mountain bike's original price in dollars, which algebraic expression represents the reduce price?
Answer:
The answer to this question is p-125, because P is the cost of the bike, and reduce = subtract. YW :)
If p is the mountain bike's initial price in dollars, the (P- $ 125 is an algebraic equation indicates the lowered price.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
If p is the initial price of the mountain bike in dollars, the algebraic equation (P- $ 125) reflects the reduced price.
Hence, (P- $ 125) is the correct expression.
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PLEASE HELP ASAP 40 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer: The answer is D
Step-by-step explanation:
Factor and set each set equal to zero to get x=0,2,-1,1
Answer:
D
Step-by-step explanation:
x¹³ - 2x¹² - x¹¹ + 2x¹⁰ = 0
x¹⁰(x³ - 2x² - x + 2) = 0
x¹⁰ [x²(x - 2) - (x - 2)] = 0
x¹⁰(x² - 1)(x - 2) = 0
x = 0 (multiplicity 10)
x = 1
x = -1
x = 2
You are choosing between two health clubs. Club A offers membership for a fee of $ 17 plus a monthly fee of $22. Club B offers membership for a fee of $13 plus a monthly fee of 24. After how many months will the total cost of each health club be the same ? What will be the total cost for each club?
Answer:
2 months$61 (for two months)Step-by-step explanation:
Club B's savings of $17 - 13 = $4 in fee is eaten up at the rate of $24 -22 = $2 per month in monthly fees. It will take $4/($2/mo) = 2 mo for the total costs to be equal.
After 2 months, the amount at each club will be ...
$17 + 22×2 = $61$13 + 24×2 = $61_____
If you want to write equations, the club costs (a and b) in terms of months (m) of membership are ...
a = 17 +22m
b = 13 +24m
The difference is zero when ...
a - b = 0
(17 +22m) -(13 +24m) = 0
4 -2m = 0 . . . . . . . simplify
4 = 2m . . . . . . . . . add 2m . . . Note that 4 is 17-13; 2 is 24-22, as above.
4/2 = m = 2 . . . . . . divide by the coefficient of m
The difference in total cost will be zero after 2 months.
Julian needs to spend at least seven hours each week practicing the drums. He has already practiced five and one third hours this week. He wants to split the remaining practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours he needs to practice on each of the two days.
Final answer:
Julian needs to practice at least 8 and 1/6 hours on each of the last two days of the week.
Explanation:
To determine the minimum number of hours Julian needs to practice on each of the last two days of the week, we can use an inequality. Julian needs to spend at least seven hours each week practicing the drums, and he has already practiced five and one-third hours this week. Let's represent the minimum number of hours he needs to practice on each of the remaining two days as 'x'. The inequality can be written as:
5 1/3 + 2x ≥ 7
Now let's solve the inequality:
So, the minimum number of hours Julian needs to practice on each of the last two days of the week is 8 and 1/6 hours (or approximately 8.17 hours).
Find the inverse of the function. f(x) = the cube root of quantity x divided by six. - 7
Answer:
[tex]f^{-1}(x)=6(x+7)^{3}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\sqrt[3]{\frac{x}{6}}-7[/tex]
Let
[tex]y=f(x)\\ y=\sqrt[3]{\frac{x}{6}}-7[/tex]
Exchanges the variable x for y and y for x
[tex]x=\sqrt[3]{\frac{y}{6}}-7[/tex]
Isolate the variable y
[tex]x+7=\sqrt[3]{\frac{y}{6}}[/tex]
elevates to the cube both members
[tex](x+7)^{3}=\frac{y}{6} \\ \\y=6(x+7)^{3}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=6(x+7)^{3}[/tex] ------> inverse function
Select the correct answer
What is the 10th term of the geometric sequence 3,6, 12, 24,48 ...?
A. 512
B. 3,072
C. 768
D. 1,536
Answer:
hey mate.
Step-by-step explanation:
Select the correct answer
What is the 10th term of the geometric sequence 3,6, 12, 24,48 ...?
A. 512
B. 3,072
C. 768
D. 1,536
is ... 768
Answer:
D
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r is the common ratio
r = 6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2
Using a₁ = 3 and r = 2, then
[tex]a_{10}[/tex] = 3 × [tex]2^{9}[/tex] = 3 × 512 = 1536 → D
Suppose you had been in charge of designing the study. what sample size would be needed to construct a margin of error of 2% with 95% confidence? use the prior point estimate of p* = 0.15 for this calculation. round up to the nearest whole number. (for example, 144.1 would round to 145)
Answer:
1225
Step-by-step explanation:
hihi. So the equation for MoE is (z*) * SE. The z* for a 95% Confidence is one you should have memorized but for repeatability sake you can always just do an inverse Norm to find the z* for these types of applications. To do so, you can always type this command into your calculator: invNorm(conf + (1-conf)/2, 0, 1).
(When I say conf here I am referring to the confidence level as a decimal).
All that's left is the Standard Error or SE to be short. Since you gave a p* estimate then we can use the equation for SE when dealing with proportions/percents which is sqrt(p(1-p) / n) where p is the proportion and n is the sample size, which we are solving for. Once you have this established it's a basic multi-step solve for n which comes out to be 1225 after rounding.
A side note, the included picture is a bit messy due to my refusal to round when doing these kinds of problems. Rounding errors are more common than you think
The sample size would be 1225 needed to construct a margin of error of 2% with 95% confidence and this can be determined by using the formula of margin of error.
Given :
A margin of error of 2% with 95% confidence.The prior point estimate of p* = 0.15.The following calculation can be used to determine the sample size needed to construct a margin of error of 2% with 95% confidence.
[tex]\rm MOE = z \times \sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]0.02=1.96\times \sqrt{\dfrac{0.15\times 0.85}{n}}[/tex]
[tex]\left(\dfrac{0.02}{1.96}\right)^2= \dfrac{0.15\times 0.85}{n}[/tex]
[tex]n = \dfrac{(1.96)^2\times 0.15 \times 0.85}{(0.02)^2}[/tex]
[tex]n = 1224.51[/tex]
n = 1225 (round off)
The sample size would be 1225 needed to construct a margin of error of 2% with 95% confidence.
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please help:Find the coordinates of the midpoint of a segment having the given endpoints.
Q(0.3, 1.8), R(2.7, 3.9)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{0.3}~,~\stackrel{y_1}{1.8})\qquad R(\stackrel{x_2}{2.7}~,~\stackrel{y_2}{3.9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{2.7+0.3}{2}~~,~~\cfrac{3.9+1.8}{2} \right)\implies \left(\cfrac{3}{2}~,~\cfrac{5.7}{2} \right)\implies (1.5~,~2.85)[/tex]
Final answer:
The coordinates of the midpoint are (1.35, 2.85).
Explanation:
The coordinates of the midpoint of a segment can be found by averaging the x-coordinates of the endpoints and averaging the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (0 + 2.7) / 2 = 1.35, and the y-coordinate of the midpoint is (1.8 + 3.9) / 2 = 2.85. Therefore, the midpoint of the segment with endpoints Q(0.3, 1.8) and R(2.7, 3.9) is (1.35, 2.85).
How many cans of paint are needed to cover an area of 2200 square units if one can of paint covers in area 400 square units
The cans of paints and areas are illustrations of equivalent ratios.
5.5 cans are needed to paint an area of 2200 units square
The given parameter is:
[tex]\mathbf{Cans : Area = 1 : 400}[/tex]
Express as fraction
[tex]\mathbf{\frac{Cans }{ Area }= \frac{1 }{ 400}}[/tex]
Multiply both sides by Area
[tex]\mathbf{Cans= \frac{1 }{ 400} \times Area}[/tex]
When the area is 2200, we have:
[tex]\mathbf{Cans= \frac{1 }{ 400} \times 2200}[/tex]
[tex]\mathbf{Cans= 5.5}[/tex]
Hence, 5.5 cans are needed to paint an area of 2200 units square
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5.5 cans of paint are required to cover an area of 2200 square units, but since you can't have half a can, you would actually need 6 cans of paint.
Explanation:This problem can be solved using simple division, which is a common concept in Mathematics. Given that one can of paint covers 400 square units, to find out how many cans of paint are needed to cover an area of 2200 square units, we need to divide the total area by the area that one can covers. So, 2200 ÷ 400 = 5.5.
However, you cannot have half a paint can, so you would need 6 cans of paint to fully cover the area. Here, we apply the mathematical principle of rounding up because you can't use half a can of paint.
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Yesterday, Pablo had 4 4/9 quarts of iced tea, and Rosa had 3 5/12 quarts of iced tea.
How much more iced tea did Pablo have than Rosa?
Pablo gave Rosa 15% of his iced tea today. How much iced tea do each of them have now? Write your answer in fraction form.
1. How much more iced tea did Pablo have than Rosa?
= 4 4/9 - 3 5/12 = 40/9 - 41/12 = 40/9 - 41/12 = (40 × 4)/(9 × 4) - (41 × 3)/(12 × 3) = 160/36 - 123/36= 37/36= 37/36 = 1 1/36Pablo has 1 1/36 quarts of ice tea more than Rosa.
2. Pablo gave Rosa 15% of his iced tea today. How much iced tea do each of them have now? Write your answer in fraction form.
Iced tea given
= 15% × 4 4/9= 15/100 × 40/9 = 600/900= 2/3Pablo iced tea
= 40/9 - 2/3 = 40/9 - (2 × 3)/(3×3) = 40/9 - 6/9= 34/9= 3 7/9Rosa iced tea
= 41/12 + 2/3 = 41/12 + (2 × 4)/(3 × 4) = 41/12 + 8/12= 49/12= 4 1/12Pablo has 3 7/9 quarts of iced tea and Rosa has 4 1/12 quarts.
Let f(x)=14/7+2e^−0.6x . What is f(3) ? Enter your answer, rounded to the nearest tenth, in the box.
Answer:
[tex]f(3)=1.9[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\frac{14}{7+2e^{-0.6x}}[/tex]
we know that
f(3) is the value of the function for the value of x equal to 3
so
substitute the value of x=3 in the function
[tex]f(3)=\frac{14}{7+2e^{-0.6(3)}}=1.9[/tex]
Answer:
1.9
Step-by-step explanation:
fX)=14/7=2e^-0.6x = 1.9
Which of the following statements is true concerning triangle XYZ below?
Answer:
The correct answer to this problem is the second option: YZ is the longest side.
Step-by-step explanation:
In order to solve this problem, we need to understand the relationship between angle measure and side lengths in a triangle.
In a triangle, the longest side is located across from the largest angle measure, the smallest side is located across from the smallest angle, and the middle length side is located across from the medium sized angle.
Using this knowledge, we can conclude that since XYZ is the smallest angle, XZ must be the smallest side. We can also state that since YXZ is the largest angle, YZ is the longest side.
Looking at the answer options, the only choice that aligns with this information is the second option: YZ is the longest side, and thus we can conclude that this is the correct answer.
Hope this helps!
YZ is the longest side
Step-by-step explanation:
You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How much money will be in the account after 10 years? Round your answer to the nearest whole number.
Answer:
A=Pe^rt
P= princible (1300)
e= (2.71828)- function on a graphing calculator
r = interest rate (.05 or 5%)
t = time (10 years)
A = 1300e^.05(10)
A = 1300e^.5
A = 2143.337652
A = 2143
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1300\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]\bf A=1300\left(1+\frac{0.05}{1}\right)^{1\cdot 10}\implies A=1300(1.05)^{10}\implies \stackrel{\textit{rounded up}}{A=2118}[/tex]
Which set of points contains the solutions to the inequality y ≥ 1⁄4x + 5?
A. {(–3,–17), (4,11), (7,19)}
B. {(4,6), (8,8), (–3,6)}
C. {(3,4), (2,3), (8,27)}
D. {(–2,–1), (4,–7), (5,1)}
Answer:
B. {(4,6), (8,8), (–3,6)}
Step-by-step explanation:
You can graph the equation and plot the points, or you can try the points algebraically. For the latter, it is convenient to rearrange the inequality a bit.
y ≥ 1/4x + 5 . . . . . given
4y ≥ x + 20 . . . . . multiply by 4
You can use this form, or you can subtract x to get ...
4y -x ≥ 20
Trying the offered points, we want 4y-x to be at least 20. We get ...
A: 4(-17) -(-3) = -65 . . . . less than 20
B: 4(6)-4 = 20 . . . a solution
4(8) -8 = 24 . . . a solution
4(6)-(-3) = 27 . . . a solution . . . . set B contains solutions to the inequality
C: 4(4)+3 = 19 . . . . less than 20
D: 4(-1)-(-2) = -2 . . . . less than 20
Sara had some candy in her pocket. She first kept 2 pieces herself and then gave her 5 children 3 pieces each. If she didn't have any candy left over, how many pieces of candy did she start with
17 pieces. She had two and she had to have 15 to give to the children. If each child got 3 and there is 5. This turns into 3*5=15. Then you would add 15+2 to get 17
Sara initially had 17 candies. This computation is based on the 2 pieces she kept for herself and the three pieces of candy each of her five children received.
Explanation:The subject of this question is mathematics, specifically it deals with basic arithmetic and problem solving. According to the problem, Sara kept 2 pieces of candy for herself and then gave each of her 5 children 3 pieces. In mathematical terms, this can be represented as an equation: 2 (pieces Sara kept) + 5 (children) * 3 (pieces each child received) = Total pieces of candy Sara had initially.
To solve this equation, first multiply the number of children by the pieces each received: 5 * 3 = 15. Then add the pieces Sara kept: 2 + 15 = 17. Therefore, Sara initially had 17 pieces of candy.
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How many lines of symmetry does a 15 sided polygon have?
Answer: 15 lines of symmetry.
Step-by-step explanation:
There are 15 lines of symmetry does a 15 sided polygon have.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
Number of lines of symmetry does a 15 sided polygon have
Since, We know that;
Number or line of symmetry is equal to number of sides of polygon.
Here, Number of side = 15
Hence, There are 15 lines of symmetry does a 15 sided polygon have.
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Patty deposited $650 in a savings account with two percent simple interest. If she keeps it in the account for one year, how much interest will she earn?
$15
$18
$12
$13
Answer:
$13
Step-by-step explanation:
Depost of 650.00 into a bank account paying 2% simple interest per year. You left the money in for 1 year. Find the interest earned and the amount earned in 1 year.
The interest is $13, and the amount is 663.00.
Answer:
13
Step-by-step explanation:
Please help me with this proof
5. Next time include the entire page in the photo. I'm guessing it's U at the top right and O at the bottom right.
First box.
SE ≅ SU
Given
Second box
angle 1 ≅ angle 2
Those are vertical angles, which are always congruent
Third box
angle E = angle U
Given
Next box, three arrows in.
triangle MES ≅ triangle OUS
Angle - Side - Angle
Last box:
MS ≅ SO
Corresponding parts of congruent triangles.
-----------
6.
First box:
angle E ≅ angle U
Given
Second box:
NS ≅ NS
reflexivity (aka it's the same segment)
Third box:
angle 1 = angle 2
Definition of angle bisector
Next box:
triangle WNS ≅ triangle ENS
Angle - Side - Angle
Next:
WN ≅ EN
Corresponding parts of congruent triangles.
Answer:
5. Next time include the entire page in the photo. I'm guessing it's U at the top right and O at the bottom right.First box. SE ≅ SUGivenSecond boxangle 1 ≅ angle 2Those are vertical angles, which are always congruentThird boxangle E = angle UGivenNext box, three arrows in.triangle MES ≅ triangle OUSAngle - Side - AngleLast box:MS ≅ SOCorresponding parts of congruent triangles.-----------6.First box:angle E ≅ angle UGivenSecond box:NS ≅ NSreflexivity (aka it's the same segment)Third box:angle 1 = angle 2 Definition of angle bisectorNext box:triangle WNS ≅ triangle ENSAngle - Side - AngleNext: WN ≅ ENCorresponding parts of congruent triangles
I did this problem and I was told I did it wrong how do I fix it??
Answer:
(1/8)(cos(4x) -4cos(2x) +3)
Step-by-step explanation:
Your answer is correct as far as it goes. You now need to use a power-reducing identity on the cos(2x)² term in your answer. The appropriate one is ...
cos(x)² = (1/2)(1 +cos(2x))
In the context of this problem, using this formula gives you ...
sin(x)⁴ = (1/4)(1 -2cos(2x) +(1/2)(1 +cos(4x))
sin(x)⁴ = (1/8)(cos(4x) -4cos(2x) +3)
Raymond took out a 25-year loan for $135,000 at an APR of 3.6% compounded monthly. If his bank charges a prepayment fee of 6 months' interest on 80 % of the balance, what prepayment fee would he be charged for paying off the loan 5 years early?
A. 683.10
B 546.08
C. 695.49
D. 543.46
Answer:
D. 543.46
Step-by-step explanation:
The formula for the remaining balance on the loan is ...
A = P(1 +r)^n +p((1 -(1 +r)^n)/r)
where P is the principal, p is the monthly payment, r is the monthly interest rate, and n is the number of months.
We have P=135,000, p = TBD, r = 3.6%/12 = .003, n = 20×12 = 240.
___
The monthly payment is given by the same formula by setting A=0. In this case, n is 25 years, or 300 payments. Solving for p, we get, ...
p = Pr(1 +r)^n/((1 +r)^n -1) = Pr/(1 -(1 +r)^-n)
So, the monthly payment is ...
p = 135,000×0.003/(1 -1.003^-300) = 683.10
Using this value in the formula for remaining balance, we get ...
A = 135000(1.003^240) +683.10((1 -1.003^240)/0.003) = 37,459.20
___
80% of this balance is 29,967.36. The answer choices only make sense if we assume the interest penalty is equivalent to the interest being compounded monthly:
$29,967.36 × (1.003^6 -1) = $543.47
The closest match among answer choices is ...
D. 543.46
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. Last year, 9 employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age.
The mean retirement age is 59.7
What is mean for the given sample data?The sample mean is a statistic obtained by calculating the arithmetic average of the values of a variable in a sample.
To calculate the arithmetic mean of a set of data we must first add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed (see Sigma Notation) we obtain the following formula for the mean (M):
M=∑ x/n
Given, the sample data of ages of 9 employees respectively are
52, 63, 67, 50, 59, 58, 65, 51, 56.
Mean of sample data
M=∑ x/n
M=(52+63+67+50+59+58+65+51+56)/9
M=537/9
M=59.667
Hence, the mean for the given sample data round to one more decimal place than is present in the original data values is 59.7
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Note- The complete question is mentioned below
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age.
52, 63, 67, 50, 59, 58, 65, 51, 56.
Final answer:
To find the mean retirement age for the 9 employees, add up all ages, divide by the number of employees, yielding a mean retirement age of 71.6 years.
Explanation:
Mean Retirement Age Calculation:
Add up all the ages: 65 + 67 + 68 + 70 + 72 + 74 + 75 + 76 + 77 = 644
Count the number of ages, which is 9
Divide the total sum of ages by the number of employees to find the mean: 644 / 9 = 71.6 years
given T(-5,8,3) and M(-2,-1,-6) find the ordered triple that represents TM. Then find the magnitude of TM.
Answer:
TM = (3,-9,-9)
The magnitude of TM = 3√19
Step-by-step explanation:
Given T=(-5,8,3) and M = (-2,-1,-6)
TM is the difference between the vector M and the vector T
So,
TM = M - T = (-2,-1,-6) - (-5,8,3) = (-2+5 , -1-8 , -6-3) = (3,-9,-9)
The magnitude of TM = The distance of TM = [tex]\sqrt{3^2+(-9)^2+(-9)^2}=\sqrt{9+81+81}=\sqrt{171} = \sqrt{9*19} =3\sqrt{19}[/tex]
So, TM = (3,-9,-9) and |TM| = 3√19
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Q1: What is an outlier? What is a cluster?
Q2: How do you determine the equation of a line of best fit for data?
Q3: Explain the difference between frequency and relative frequency.
Answer:
Ans1.
Outlier
A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data.
Cluster
When data seems to be "gathered" around a particular value.
For example: for the values 2, 6, 7, 8, 8.5, 10, 15, there is a cluster around the value 8.
Ans.2
A line of best fit (or "trend" line) is a straight line that best represents the data on a scatter plot.
This line may pass through some of the points, none of the points, or all of the points.
i will explain through an example
1. Prepare a scatter plot of the data on graph paper.
2. Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible.
3. Find two points that you think will be on the "best-fit" line.
4. We are choosing the points (9, 260) and (30, 530).
You may choose different points.
5. Calculate the slope of the line through your two points (rounded to three decimal places).
6. Write the equation of the line.
7. This equation can now be used to predict information that was not plotted in the scatter plot.
Question: Predict the total calories based upon 22 grams of fat. ANS: 427.141 calories
Ans.3
1.Frequency is the number of times a result occurs, while “relative frequency” is the number of times the result occurs divided by the number of times the experiment is repeated.
2.Frequency can easily be determined by conducting a simple experiment and noting how many times the event in question occurs; no calculations are needed. On the other hand, relative frequency is determined by using simple division.
Francine Flicka found a bargain when she bought a lawn mower. She paid the store's clerk three $20 bills and received him $7.45 in change. If the sales tax is 7.3%, what was the selling price of the mower before taxes?
$56.39
$53.55
$52.55
$48.97
Answer:
$48.97
Step-by-step explanation:
Let p represent the marked price of the mower. Then the price with tax is ...
with tax = p + 7.3%×p = 1.073p
The amount Flicka paid is the amount tendered less the change she received, so is ...
3×$20 - 7.45 = with tax = 1.073p
To find p, we can divide by its coefficient:
(3 × $20 - 7.45)/1.073 = p ≈ $48.97
The selling price before taxes was $48.97.
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Comment on the problem
If you check the answer, you find the amount with tax is ...
$48.97 × 1.073 ≈ $52.54481 ≈ $52.54
so the change Flicka would have received would have been $7.46, not $7.45. If the price were $48.98, then the change would have been $7.44. There is no price at which the mower can be marked that will make the total with tax come to $52.55. There is no solution to this problem.
Answer:
$48.97
Step-by-step explanation:
She paid three $20 bills
3 × 20 = $60
She received $7.45 change
60 - 7.45 = $52.55
The mower was for $52.55 with sales tax.
The sales tax is 7.3%.
Before the sales tax (reduce tax).
52.55 × (1-7.3%)
= $48.97
please help Find the area of the figure.
Answer:
69.09 yd^2
Step-by-step explanation:
14.1*9.8=138.18
138.18*0.5=69.09
Answer:
69.09 square yd.
Step-by-step explanation:
Area of a triangle is
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
From the given figure it is clear that height of the triangle is 9.8 yd and base of the triangle is 14.1 yd.
Substitute the given values in he above formula, to find the area of triangle.
[tex]A=\dfrac{1}{2}\times 14.1\times 9.8[/tex]
[tex]A=69.09[/tex]
Hence, the area of triangle is 69.09 square yd.
Ribbon costs $0.45 per foot . A sewing project calls for 20. 5 feet of ribbon to the nearest cent that will be the cost of the ribbon for the project
To find the total cost of the ribbon, multiply the length needed (20.5 feet) by the cost per foot ($0.45), which equals $9.225. Round this to the nearest cent to get $9.23.
To calculate the cost of the ribbon needed for a sewing project, you multiply the length of the ribbon required by the cost per foot. In this case, the project calls for 20.5 feet of ribbon and the ribbon costs $0.45 per foot. The formula to use is: Total Cost = Length in Feet x Cost Per Foot. Now, let's do the math:
Total Cost = 20.5 feet x $0.45/foot = $9.225.
To round to the nearest cent, the total cost would be $9.23.
Elizabeth attempts a field goal by kicking a football from the ground with an initial vertical
velocity of 64 ft/s. How long will the football be in the air?
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{64}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{0\qquad \textit{from the ground}}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf h(t)=-16t^2+64t+0\implies h(t)=-16t^2+64t\implies \stackrel{\textit{hits the ground}~\hfill }{0=-16t^2+64t} \\\\\\ 0=-16t(t-4)\implies t= \begin{cases} 0\\ \boxed{4} \end{cases}[/tex]
Check the picture below, it hits the ground at 0 feet, where it came from, the ground, and when it came back down.
The lengths of the sides of triangle ABC are represented in terms of the variable m, where m>6 AB = m - 2 BC = m + 4 AC = m list the angles from smallest to largest.
Answer:
C, B, A
Step-by-step explanation:
From smallest to largest, the side lengths are ...
AB = c = m -2AC = b = mBC = a = m +4The shortest side is opposite the smallest angle, so the angles, smallest to largest, are C, B, A.
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Comment on side naming
Side c is opposite vertex (and angle) C, so is between vertices A and B. Thus the names AB and c are both names for the side of the triangle opposite angle C.
Answer:
C, B, A
Step-by-step explanation: