The following dot plots compare the height of the members of the basketball team and the swimming team.



Determine the mean, median, mode and range for the dot plot. Show your work.


(2pts) Mean:

(2pts) Median:

(1pt) Mode:

(2pts) Range/Spread:

Answer:

5. x = -1 or x = -3

6. b = -2 or b = 6

7. n = 5 or n = 4

Step-by-step explanation:

5. x² + 4x + 3 = 0

Factorize

x² + 3x + x + 3 = 0

x(x + 3) +1(x + 3) = 0

(x + 1)(x + 3) = 0

Set each of the factors equal to zero and solve for x

x + 1 = 0 or x + 3 = 0

x = -1 or x = -3

6. b² - 4b - 14 = -2

Put all terms on one side of the equation leaving zero on one side

b² - 4b - 14 + 2 = 0

b² - 4b - 12 = 0

Factorize

b² - 6b + 2b - 12 = 0

b(b - 6) +2(b - 6) = 0

(b + 2)(b - 6) = 0

Set each of the factors equal to zero and solve for b

b + 2 = 0 or b - 6 = 0

b = -2 or b = 6

7. n² = 9n - 20

Put all terms on one side of the equation leaving zero on one side

n² - 9n + 20 = 0

n² - 5n - 4n + 20 = 0

n(n - 5) -4(n - 5) = 0

(n - 5)(n - 4) = 0

Set each of the factors equal to zero and solve for b

n - 5 = 0 or n - 4 = 0

n = 5 or n = 4

Answer:

Step-by-step explanation:

Given that:

a)

[tex]f(x,y) = e^{3x} + y^3 - 3ye^x \\ \\ \implies \dfrac{\partial f}{\partial x} = 0 = 3e^{3x} -3y e^x = 0 \\ \\ e^{2x}= y \\ \\ \\ \implies \dfrac{\partial f}{\partial y } = 0 = 3y^2 -3e^x = 0 \\ \\ y^2 = e^x[/tex]

[tex]\text{Now; to determine the critical point:}[/tex]- [tex]f_x = 0 ; \ \ \ \ \ f_y =0[/tex]

[tex]\implies e^{2x} = y^4 = y \\ \\ \implies y = 0 \& y =1 \\ \\ since y \ne 0 , \ \ y = 1, \ \ x= 0\\\text{Hence, the only possible critical point= }(0,1)[/tex]

b)

[tex]\delta = f_xx, s = f_{xy}, t = f_{yy} \\ \\ . \ \ \ \ \ \ \ \ D = rt-s^2 \\ \\ i) Suppose D >0 ,\ \ \ r> 0 \ \text{then f is minima} \\ \\ ii) Suppose \ D >0 ,\ \ \ r< 0 \ \text{then f is mixima} \\ \\ iii) \text{Suppose D} < 0 \text{, then f is a saddle point} \\ \\ iv) Suppose \ D = 0 \ \ No \ conclusion[/tex]

[tex]Thus \ at (0,1) \\ \\ \delta = f_{xx} = ge^{3x}\implies \delta (0,1) = 6 \\ \\ S = f_{xy} = -3e^x \\ \\ \implies S_{(0,1)} = -3 \\ \\ t = f_{yy} = 6y \\ \\[/tex]

[tex]\implies t_{0,1} = 6[/tex]

[tex]Now; D = rt - s^2 \\ \\ = (6)(6) -(-3)^2[/tex]

[tex]= 36 - 9 \\ \\ = 27 > 0 \\ \\ r>0[/tex]

[tex]\text{Hence, the critical point} \ (0,1) \ \text{appears to be the local minima}[/tex]

c)

[tex]\text{Suppose we chose x = 0 and y = -3.4} \\ \\ \text{Then, we have:} \\ \\ f(0,-3.4) = 1+ (-3.4)^3 + 3(3.4) \\ \\ = -28.104 < -1[/tex]

[tex]\text{However, if f (0,1) = 1 +1 -3 = -1 \\ \\ f(0,-3.4) = -28.104} < -1} \\ \\ \text{This explains that} -1 \text{is not an absolute minimum value of f(x,y)}[/tex]

Answer:

12:45

Step-by-step explanation:

Step One: An hour after 11:20 is 12:20, plus 15 minutes is 12: 35.

Step Two: Just add 10 minutes, because it doesn't matter when you add the ten minutes.

Answer:

-18

Step-by-step explanation:

2x²-7xy+3y²

2(3²)-7(3)(4)+3(4²)

2(9)-84+3(16)

18-84+48

18+48-84

-18

Answer:

No.

Step-by-step explanation:

Well at first glance it might seem so but there are two points particularly that can tell you that these points cannot be within a function.

The points (3,2) and (3,-2) will yield an undefined slope (a straight vertical line). There is no possibility that the other points can be in this line (as their y - values are different) and there is no possibilty that this is a function at all according to the vertical line test (the test is that if you draw a vertical line that there shouldn't be more than one point on it).

Answer: 123.05

Use annuity formula

Answer:

Step-by-step explanation:

Since we're talking about making a deposit of a certain amount every month rather than just one big deposit, we are talking about an annuity. The formula for the value of an annuity is A(t)=d[(1+rn)nt−1](rn) where A(t) is the value of the annuity, d is the amount of each deposit, n is the number of deposits per year, t is the number of years, and r is the rate of interest. In this case we know we want the value of the annuity to be A(t)=$150,000, we want to make deposits every month, or 12 times a year, so n=12, we want to reach our desired value in 30 years, so t=30, and our account earns 7% interest, so r=0.07. We can plug in all of these values and solve for d to find the amount we need to deposit each month:

A(t)150,000150,000150,000d=d[(1+rn)nt−1](rn)=d[(1+0.0712)12⋅30−1]0.0712≈d[(1.00583)360−1]0.00583≈1,219.97d≈122.95

The amount you need to deposit each month is approximately $122.95.

Answer:

Average of Gilbert in last 5 test = 86.6

Step-by-step explanation:

Given:

Score earned by Gilbert in last 5 test = 94, 72, 83, 94, 90

Find:

Average of Gilbert in last 5 test

Computation:

Average value = Sum of all events / Total number of events

Average of Gilbert in last 5 test = Sum of all last results / Number of results

Average of Gilbert in last 5 test = [94 + 72 + 83 + 94 + 90] / 5

Average of Gilbert in last 5 test = [433] / 5

Average of Gilbert in last 5 test = 86.6

Answer:

The 99% confidence interval for the mean consumption of meat among males over age 43 is between 2.9 pounds and 3.1 pounds.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{1.3}{\sqrt{1384}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 3 - 0.1 = 2.9 pounds

The upper end of the interval is the sample mean added to M. So it is 3 + 0.01 = 3.1 pounds

The 99% confidence interval for the mean consumption of meat among males over age 43 is between 2.9 pounds and 3.1 pounds.

Answer:

4th one its negative,linear association

Step-by-step explanation:

The option that best describes the relationship between the variables on the scatter plot is negative, linear association.

Variables have a negative association when the line of best fit is downward sloping. Variables have a linear association when the line of best fit is a straight line. Variables have a positive association when the line of best fit is upward sloping.

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Answer:

15 hours

so, 8 x y = 120

Step-by-step explanation:

[tex]8\sqrt{120} =[/tex] 15

Answer:

12 students

Step-by-step explanation:

CLEAN THAT IPAD FOR HIM

Answer:

12 students went to the beach fewer than 2 times.

Step-by-step explanation:

Just count the total number of dots that come before 2.

Answer:

Exact form: p= 3/2

Decimal form: p= 1.5

Mixed Number: p=1 [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:

[tex]t \approx 2.639[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccc}{} & {USA\ 1} & {Japan\ 2} & {\bar x} & {64.6} & {67.5} &{n} & {30} & {30} & {\sigma} & {4.0} & {4.5} \ \end{array}[/tex]

See attachment for data

Required

Determine the test statistic

The test statistic is calculated using:

[tex]t = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}[/tex]

So, we have:

[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{4.0^2}{30} + \frac{4.5^2}{30}}}[/tex]

[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{16.00}{30} + \frac{20.25}{30}}}[/tex]

[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{16.00+20.25}{30}}}[/tex]

[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{36.25}{30}}}[/tex]

[tex]t = \frac{-2.9}{\sqrt{1.2083}}[/tex]

[tex]t = \frac{-2.9}{1.099}[/tex]

[tex]t \approx -2.639[/tex]

The absolute value is:

[tex]t \approx 2.639[/tex]

Answer:

20

Step-by-step explanation:

Answer:

697.5 ft squared

Step-by-step explanation:

Divide into top two squares and rectangle on bottom so...

(10×7.5)+(8×7.5)×(12.5×45)=area

75+60+562.5=697.5 ft squared

Answer:

214 seconds

Step-by-step explanation:

3 times 60 is 180. 180 plus 34 is 214.

Answer:

85.80

Step-by-step explanation:

85.82 is closet to 85.80 snice 2 is a low number

Answer:

$43.20

Step-by-step explanation:

20% of $50.00 is $10.00. $50 - $10 is $40. 8% of $40 is $3.20. Since this is tax, you must add it. $40+$3.20 = $43.20

Answer:

LN = 4 units

Step-by-step explanation:

Since M is on LN , then

LN = LM + MN , that is

4x = 3 + x ( subtract x from both sides )

3x = 3 ( divide both sides by 3 )

x = 1

Then

LN = 3 + x = 3 + 1 = 4

The required length of the line LN = 4.

Given that,
Point M is on the line segment LN. Given LN=4x, MN= x, and LM=3,  to determine the numerical length of LN.

The line is a curve showing the shortest distance between 2 points.

LN = LM + MN
4x = 3 + x
4x - x = 3
3x = 3
x = 3 / 3
x = 1

Length of LN
LN = 4x
     = 4 * (1)
     = 4

Thus the required length of the line LN = 4.

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Answer:

i think its 3 in all the boxes but trying is better than not ig wait no nvm

Answer256pi

Step-by-step explanation:

Area=pi*r^2

=pi*16^2

256pi

Answer:

Equivalent fraction of a given fraction is got by multiplying or dividing its numerator and denominator by the same whole number. For example, if we multiply the numerator and denominator of 2/3 by 4 we get. 2/3 = 2×4 / 3×4 = 8/12 which is an equivalent fraction of 2/3.

Step-by-step explanation:

Answer:

Equate the divisor to 0

2x-1=0

2×=1

×=1/2

Putting onto the polynomial

f(1/2) = (1/2)³-1/2)²+3(1/2)-2

=-5/8

Answer:

x=5, y=3

Step-by-step explanation:

7x-11=24: 7x=35: x=5

3(5)+9=8x: 24=8x: x=3