Which is a quadratic function?
f(x) = 2x + x + 3
f(x) = 0x2 – 4x + 7
f(x) = 5x2 – 4x + 5
f(x) = 3x3 + 2x + 2

Answer:

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 ...

_____

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.

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:

Answer: 15 lines of symmetry.

Step-by-step explanation:

There are 15 lines of symmetry does a 15 sided polygon have.

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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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:

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

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 :

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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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.

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

Answer:

  C, B, A

Step-by-step explanation:

From smallest to largest, the side lengths are ...

The shortest side is opposite the smallest angle, so the angles, smallest to largest, are C, B, A.

___

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:

Answer:

complementary angles

Step-by-step explanation:

∠1 and ∠2 form a right angle and are complementary, that is they sum to 90°

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]

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).

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

[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.

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.

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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[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).

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.

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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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

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.

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

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

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)

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.

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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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.

_____

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

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.

The mean retirement age is 59.7

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

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.

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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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

Answer:

Step-by-step explanation:

Look at the picture.

1. How much more iced tea did Pablo have than Rosa?

Pablo 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

      Pablo iced tea

      Rosa iced tea

Pablo has 3 7/9 quarts of iced tea and Rosa has 4 1/12 quarts.