the following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes). quarter-mile times: 0.92 0.96 1.04 0.93 1.00 mile times: 4.52 4.35 4.60 4.71 4.51 after viewing this sample of running times, one of the coaches commented that the quarter-milers turned in the more consistent times. use the standard deviation and the coefficient of variation to summarize the variability in the data. quarter-milers standard deviation (to decimals) coefficient of variation (to decimal) % milers standard deviation (to decimals) coefficient of variation (to decimal) % does the use of the coefficient of variation indicate that the coach's statement should be qualified? (i) yes; the coefficient shows that as a percentage of the mean, the quarter-milers' times show less variability. (ii) no; the coefficient shows that as a percentage of the mean, the quarter-milers' times show more variability. choose the correct answer. - select your answer -

Answer:

60 + 5x = 125 - 10x

Step-by-step explanation:

Jeter- 60 + 5x

Callie- 125 - 10x

Set them equal to each other to find out when they will equal the same amount

Answer:

The answer can be expressed in multiple forms

[tex]4.\overline3\overline3[/tex] weeks

[tex]4\frac{1}{3}[/tex] weeks

Step-by-step explanation:

Lets write down what we are given

Jeter Initial Amount = $60.00

Callie Initial Amount = $125.00

Deposit/Withdrawal Per Week

Jeter + $5.00

Callie - $10.00

We can set up an expression for Jeter's money

[tex]60+5w[/tex]

We can set up an expression for Callie's money

[tex]125-10w[/tex]

[tex]w[/tex] represents the number of weeks

We can set each expression equal to each other to find out when they will have the same amount of money.

[tex]60+6w=125-10w[/tex]

Lets solve for [tex]w[/tex].

Add [tex]10w[/tex] to both sides of the equation.

[tex]60+5w+10w=125-10w+10w[/tex]

Combine like terms and simplify.

[tex]60+15w=125[/tex]

Subtract 60 from both sides of the equation.

[tex]60+15w-60=125-60[/tex]

Evaluate the subtraction and simplify..

[tex]15w=65[/tex]

Divide both sides of the equation by 15.

[tex]\frac{15w}{15}=\frac{65}{15}[/tex]

Simplify the left side by cancelling the common factor of 15.

[tex]w=\frac{65}{15}[/tex]

[tex]w=\frac{13}{3}[/tex]

[tex]w=4.3333[/tex]

[tex]w=4\frac{1}{3}[/tex]

For the function, the x-intercept of g(x) is at (5,0).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Given f(x) = ln(x)

and g(x) = -f(x - 4)

the function is

g(x) = -ln(x - 4)

when x = 5

g(x) = -ln(5 - 4)

g(x) = -ln1

g(x) = 0

the coordinates are (5, 0)

Hence the x-intercept is (5, 0).

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Answer:

Step-by-step explanation:

∠ EGF=180-∠FGH

          = 180-(180-112)

          = 112°

∠LKM= 90= 8X -6

           2(4X-3)=90

             4X-3=45°

3)

22=4X-10

 X=8

NR= 3(8) +6

     = 30

The scale factor to produce figure {2} from figure {1} is -

{K} = 4/3.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller. Mathematically, we can write -

{K} = A/B

Given are two right triangles as figure {1} and {2}.

We can write the scale factor as the ration of the lengths of the legs as -

{K} = 4/3

Therefore, the scale factor to produce figure {2} from figure {1} is -

{K} = 4/3.

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Answer:

x ≈ - 2.70 or x ≈ 2.03

Step-by-step explanation:

Given:

[tex]1.5x^2+x-8.2=0[/tex]

Solve:

Multiply both sides by 10:

[tex]1.5x^2\cdot \:10+x\cdot \:10-8.2\cdot \:10=0\cdot \:10[/tex]

[tex]15x^2+10x-82=0[/tex]

Quadratic Formula: [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Using the Quadratic formula:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Knowing that;

quadratic equation of the form: [tex]ax^2+bx+c=0[/tex]

a = 15

b = 10

c = -82

Plug it in:

[tex]=\frac{-10\pm \sqrt{10^2-4\cdot \:15\left(-82\right)}}{2\cdot \:15}[/tex]

[tex]=\frac{-10\pm \:2\sqrt{1255}}{2\cdot \:15}[/tex]

Separate the solutions since there are two:

[tex]x_1=\frac{-10+2\sqrt{1255}}{2\cdot \:15},\:x_2=\frac{-10-2\sqrt{1255}}{2\cdot \:15}[/tex]

[tex]=\frac{-10+2\sqrt{1255}}{30}[/tex]

[tex]=\frac{-5+\sqrt{1255}}{15}[/tex]

[tex]x=\frac{-5+\sqrt{1255}}{15},\:x=-\frac{5+\sqrt{1255}}{15}[/tex]

Which as a decimal is:

[tex]x=-\frac{5+\sqrt{1255}}{15}[/tex] ⇒ [tex]\left\mathrm Decimal}:\quad x=-2.69506\dots \right[/tex]

[tex]x=\frac{-5+\sqrt{1255}}{15}[/tex]    ⇒   [tex]\left\mathrm{Decimal}:\quad x=2.02839\dots \right[/tex]

Rounding:

-2.69506.. ≈ -2.70

2.02839..  ≈ 2.03

Hence, x ≈ - 2.70 or x ≈ 2.03.

RevyBreeze

The required simplified value of the measure of the multiplication factor x in the circle is 2.25.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Arc VW = 12x + 25 °
∠VXW = 52°

According to the question,
Arc VW = ∠VXW
12x + 25 = 52
x = 52 - 25 / 12
x = 2.25

Thus, the required simplified value of the measure of the multiplication factor x in the circle is 2.25.

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The equation of the line that passes through the point (6, -3) and has a slope of {m} = - k is →

y = - kx + (6k - 3).

The general equation of a straight line is -

y = mx + c

where -

{m} → slope

{c} → y - intercept

Given is the line that passes through the point (6, -3) and has a slope of {m} = - k.

We can write the general equation as -

y = mx + c

Now -

{m} = - k                     .... Eq { 1 }

We can write -

y = - kx + c

For the point (6, - 3), we can write -

- 3 = - 6k + c

{c} = 6k - 3                           .... Eq { 2 }

We can write the equation of the line as -

y = - kx + (6k - 3)

Therefore, the equation of the line that passes through the point (6, -3) and has a slope of {m} = - k is →

y = - kx + (6k - 3).

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Answer:

After several hours of observation, he determined the lab dish had 1953125 bacteria.

A number system is defined as a system of writing to express numbers.

Given that A lab technician observed 5 bacteria growing in a lab dish.

One hour later he observed 25 bacteria.

Every hour he notice about 5 times as many as the hour before.

After several hours of observation, he determined the lab dish had 5 to the power of 9 bacteria.

5⁹

Five to the power of nine

1953125

Hence, After several hours of observation, he determined the lab dish had 1953125 bacteria.

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of 298000}}{\left( \cfrac{16}{100} \right)298000}\implies 47680[/tex]

Answer:

57 degrees

Step-by-step explanation:

The radian measure of angle A is -13π/18.

The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the shape of the angle can also be used to represent the angle, with the middle letter indicating the location of the angle (i.e.its vertex).

Given an angle A = -130°

to find the radian measure,

we know that,

1° = π/180 radians

-130° = -130(π/180)

-130° = -13π/18

Hence the value in radian is -13π/18.

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Answer:

[tex]\sf 1. \quad \dfrac{3}{8}[/tex]

[tex]\sf 2. \quad \dfrac{7}{24}[/tex]

Step-by-step explanation:

Spinner 1 is divided into 6 congruent sections.

There are 3 red sections, 2 blue sections and 1 yellow section.

Therefore, the probability of spinning each of the three colors is:

    [tex]\bullet \quad \sf P(R_1)=\dfrac{3}{6}=\dfrac{1}{2}[/tex]

    [tex]\bullet \quad \sf P(B_1)=\dfrac{2}{6}=\dfrac{1}{3}[/tex]

    [tex]\bullet \quad \sf P(Y_1)=\dfrac{1}{6}[/tex]

Spinner 2 is divided into 3 sections of differing sizes.

The red section is half of the spinner. The blue and yellow sections are quarters of the spinner.

Therefore, the probability of spinning each of the three colors is:

    [tex]\bullet \quad \sf P(R_2)=\dfrac{1}{2}[/tex]

    [tex]\bullet \quad \sf P(B_2)=\dfrac{1}{4}[/tex]

    [tex]\bullet \quad \sf P(Y_2)=\dfrac{1}{4}[/tex]

If each spinner is spun once, then:

The probability that both spinners both show red is:

[tex]\sf P(R_1)\;and\;P(R_2)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}[/tex]

The probability that both spinners both show blue is:

[tex]\sf P(B_1)\;and\;P(B_2)=\dfrac{1}{3} \times \dfrac{1}{4}=\dfrac{1}{12}[/tex]

The probability that both spinners both show yellow is:

[tex]\sf P(Y_1)\;and\;P(Y_2)=\dfrac{1}{6} \times \dfrac{1}{4}=\dfrac{1}{24}[/tex]

Therefore, the probability that both spinners show the same colour is:

[tex]\sf P(R_1\;\&\;R_2)\;or\;P(B_1\;\&\;B_2)\;or\;P(Y_1\;\&\;Y_2)=\dfrac{1}{4}+\dfrac{1}{12}+\dfrac{1}{24}=\dfrac{9}{24}=\dfrac{3}{8}[/tex]

If each spinner is spun once, the probability of getting a red from spinner 1 and a blue from spinner 2 is:

[tex]\sf P(R_1)\;and\;P(B_2)=\dfrac{1}{2} \times \dfrac{1}{4}=\dfrac{1}{8}[/tex]

The probability of getting a blue from spinner 1 and a red from spinner 2 is:

[tex]\sf P(B_1)\;and\;P(R_2)=\dfrac{1}{3} \times \dfrac{1}{2}=\dfrac{1}{6}[/tex]

Therefore, the probability of getting a red-blue combination is:

[tex]\sf P(R_1\;\&\;B_2)\;or\;P(B_1\;\&\;R_2)=\dfrac{1}{8}+\dfrac{1}{6}=\dfrac{7}{24}[/tex]

Answer:

-0.05 per share  (loss)

Step-by-step explanation:

2 years net loss = 1 mm

so EPS (earnings per share) = -1/20 = -0.05 per share loss

The solution set of the inequality is (-7.5, 1), and the correct graph is the one in option A.

Here we want to solve the inequality below:

-10 < 2x + 5 < 7

To solve this, we need to isolate the variable x, then we will get:

-10 < 2x + 5 < 7

-10 - 5 < 2x < 7 - 5

-15 < 2x < 2

-15/2 < x < 2/2

-7.5 < x < 1

So the solution set is (-7.5, 1)

So the graph of this will be a number line that starts at -7.5 and ends at 1, that would be the one in option a.

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The concentration of 1 mg/mL can be described as: 103 ug/mL and [tex]10^{9}[/tex] ppm.

The concentration of a solution can be expressed as the amount of solute in a given volume of the solution. The expression for concentration can be in terms of mass per volume, such as milligrams per milliliter (mg/mL) or grams per liter (g/L), or in terms of moles per volume, such as moles per liter (mol/L).

A concentration of 1 mg/mL means that there is 1 milligram of solute in every milliliter of the solution. This can be converted to micrograms per milliliter (ug/mL) by multiplying by 1000, giving us

[tex]1mg/mL=1000ug/mL=10^{6} ug/mL[/tex].

Parts per million (ppm) is another expression of concentration. To convert mg/mL to ppm, we need to know the density of the solution, which is given as 1.00 g/mL. We can use this density to convert the mass of solute to volume and then find the ratio of solute to solution volume.

[tex]1mg/mL=1mg/1mL=1g/1000mL=1/1000 g/mL= 10^{-3}g/mL\\[/tex]

So, [tex]1mg/mL=10^{-3}g/mL=10^{-3} *10^{6} mg/mL=10^{9} ppm[/tex].

Therefore, the concentration of 1 mg/mL can be expressed as: 103 ug/mL and [tex]10^{9}[/tex] ppm.

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The percentage rate of change per hour to the nearest hundredth is 3%.

Function to represent decay is A(t)= 150×([tex].97^{t}[/tex]).

Percentage means out of hundred. If we want to calculate percentage the we have to make the fraction out of hundred.

It means that if same thing is distributed among 100 people how much a single person would get.

Now for the given question:

For radioactive decay the mathematical equation is

      A(t) = A(0)[tex](1-r)^{t}[/tex]

where A(0) is the initial quantity = 150 gm. and r is the rate of decay = 51%

For hourly decay,

     A(24)= A(0)(1-0.51) as 1 day has 24 hour and each day substance decay by 51%.

     A(24)= A(0)×0.49

but,

   A(24)= A(0)[tex](1-r)^{24}[/tex]

0.49A(0)=A(0)[tex](1-r)^{24}[/tex]       (we do this to calculate r)

.049= [tex](1-r)^{24}[/tex]

1-r = [tex]\sqrt[24]{.49}[/tex]

1-r= 0.97

r = 1- 0.97

r= 0.03

r = 3%

Function for hourly decay,

A(t) = 150 ×[tex](1-r)^{t}[/tex]

A(t) = 150 ×[tex](1-0.03)^{t}[/tex]

A(t)= 150×([tex].97^{t}[/tex])

Hence, Hourly rate of decay is 3% and the equation for hourly rate o decay is A(t)=150×[tex].97^{t}[/tex].

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a. Qualitative    b. Quantitative discrete    c. Quantitative discrete   d. Qualitative

Question a is qualitative because it does not ask for a numerical answer but rather for a yes or no response. Question b is quantitative discrete because it requires a numerical answer from the respondent, but the answer is limited to a range of possible values (0-30 days). Question c is quantitative discrete because it requires a numerical answer from the respondent, but the answer is limited to a range of possible values (0-7 days). Question d is qualitative because it does not ask for a numerical answer but rather for a yes or no response. All of these questions are part of the Gallup-Healthways Well-Being Index survey, which is used to track trends in U.S. residents' health and wellbeing on a regular basis. The survey covers six areas of health and wellness, and the questions used to measure the Index provide both qualitative and quantitative data.

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Box plot is the use of a rectangle to represent data where the vertical sides of the rectangle represents the lower and upper quartile.

From the box plot,

The minimum is 153 cm

The first quartile is 168.4 cm

The second quartile is 174.2 cm

The third quartile is 183.9

The maximum is 195 cm

See attachment for the missing box plot.

There are 5 vertical lines in a box plot

The first represents the minimum value

The second represents the first quartile

The third represents the second quartile i.e. the median

The fourth represents the third quartile

The last represents the maximum quartile

From the attached box plot.

The first vertical line is 153 cm

The second vertical line is 168.4 cm

The third vertical line is 174.2 cm

The fourth vertical line is 183.9 cm

The firth vertical line is 195 cm

Hence:

The minimum is 153 cm

The first quartile is 168.4 cm

The second quartile is 174.2 cm

The third quartile is 183.9

The maximum is 195 cm

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The total cost of either plan is, 42

The number of DVD's rented is, 31

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Plan 1- membership fee of $11 and charges $1 for every DVD

Plan 2- $42 per month for unlimited DVD rentals

The two plans cost the same amount

The total cost of either plan = ?

The number of DVD's rented = ?

Suppose, the number of DVD's is n

So, cost in plan 1,

=  membership fee  +  n x (charges $1 for every DVD)

=   11 + n x 1

=   11 + n

And, cost in plan 2,

=  42

According to given condition,

cost is equal in both cases,

11 + n = 42

n = 31

Hence, the total cost and number of DVD's are respectively,  45 & 31

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The system of equations has its solution to be (4, 0)

From the question, we have the following parameters that can be used in our computation:

. 3x + 4y = 12

2x + y = 8

Make y the subject

y = 8 - 2x

So, the second equation becomes

3x + 4(8 - 2x) = 12

Open the brackets

This gives

3x + 32 - 8x = 12

So, we have

-5x = -20

Divide

x = 4

Recall that

y = 8 - 2x

So, we have

y = 8 - 2(4)

y = 0

Hence, the solution is (4, 0)

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Check the picture below.

since we know the triangle EBD is an isosceles, that means that BE = BD, and twin sides will yield twin angles, so the ∡EBD is simply the difference of 180 - 57 - 57, as far as ∡ABC, well, that's just 19 + 66 + 19.  ∡DBC is 19° because both triangles on left and right are congruent.

For the first scenario (choosing 3 balls from 1 to 9):

[tex]_{9}C_{3} = \frac{9!}{3!(9 - 3)!} [/tex]

For the second scenario (choosing 5 potato chips from 20):

[tex]_{20}C_{5} = \frac{20!}{5!(20 - 5)!} [/tex]

For the third scenario (choosing 2 team members as captain and co-captain from 24):

[tex]_{24}P_{2} = \frac{24!}{(24 - 2)!} [/tex]

The first situation is a combination. In a combination, the order of the items does not matter. In this game, it does not matter what order the 3 balls are in, as long as you have the correct numbers in a row. If you choose balls 1, 2, and 3, it's the same as if you choose 3, 2, and 1. A permutation, on the other hand, would require the order of the items to be specific. In this game, the order of the numbers doesn't matter, making it a combination.

The second situation is a combination. In this scenario, you are choosing 5 out of 20 different potato chips, and the order in which you choose them doesn't matter. Whether you choose chips 1, 2, 3, 4, and 5, or chips 5, 4, 3, 2, and 1, the combination is still the same.

The third situation is a permutation. In a permutation, the order of the items matters, meaning the first chosen person will be the captain and the second chosen person will be the co-captain. In this scenario, there are 24 people to choose from, and the order in which they are chosen determines their role as captain or co-captain. A combination, on the other hand, only cares about the items themselves, not the order in which they are chosen. In this scenario, the order matters, making it a permutation.

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Answer:
The inverse of a function is the reflection of a function over the line y=x. Therefore, this will reflect the function over the line of symmetry.

As the line of symmetry in this case is the x-axis, the inverse function can be found by switching the x and y values.

So we have f(x) = 1.5x + 100, and the inverse function is therefore y=1.5x+100

Please let me know if this helps. :)

The possible sequences of rolls are [tex]6^7[/tex].

It is the total number of possible outcomes from a given set.

We have,

Standard six-sided die:

The number of times the dice are rolled = 7 times.

Now,

Number of sides in a dice = 6

So,

The total possible outcomes.

= [tex]6^7[/tex]

Thus,

The possible sequences of rolls are [tex]6^7[/tex].

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Answer:

105

Step-by-step explanation:

First off, please don't simply copy this for your homework, as the only person that is harmed is you.

(7)        (3)

(4)   x   (2)    = 35 * 3 = 105

^

Is the ways to choose the positions of the 4

------------^

Is the way to choose the positions of the 1s and 2s.

Answer:

a + c = 1250

$7.00a + $5.50c = $7979

Step-by-step explanation:

Making the system of equations for the number of tickets involved how many attended and who attended

It's showing 1250 attended and children and adults showed up. Let's a = adults and c = children

a + c = 1250 <--- that's saying adults + children equal 1250

For $ earned, it involves how much each ticket was and the total cost

Looks like we have prices for a and c and the total cost which was 7979. Since adults were 7.00, we'll call that 7.00a. And for children it was 5.50, we'll call that 5.50c

Putting it together 7.00a + 5.50c = 7979 because all the $7.00 tickets plus all the $5.50 tickets cost $7979

The value of 1+1 in base 10 is 2 and its value in base 2 is 10

Addition in math is a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.

For example if there 20 apples, 30mangoes and 40 cashews in a basket. The total number of fruits in the basket is obtained by adding all the fruits together.

This is means the total number of of fruit = 20+30+40 = 90 fruits.

Therefore 90 fruits are in the basket.

Similarly, the addition of 1 and 1 will give

1+1 = 2. This answer is in base 10.

1+1 can also be in base two and 1+1 in base 2 = 10

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The third bit of output, Y[2], can be implemented using AND, OR, and NOT gates to calculate the sum of the product of the first bits of both inputs, A[1] and B[1], plus the product of the second bits of both inputs, A[0] and B[0].

The maximum value that can be represented in 2 bits for A(A[1:0]) is 3, and the maximum value that can be represented in 2 bits for B[1:0] is also 3. The maximum possible value of Y is 9, which requires 4 bits to represent. The truth table for the multiplier is shown below:

A[1] A[0] B[1] B[0] Y[3] Y[2] Y[1] Y[0]

0    0    0    0    0     0     0     0

0    0    0    1    0     0     0     1

0    0    1    0    0     0     1     0

0    0    1    1    0     0     1     1

0    1    0    0    0     0     0     0

0    1    0    1    0     0     0     1

0    1    1    0    0     0     1     0

0    1    1    1    0     0     1     1

1    0    0    0    0     0     0     0

1    0    0    1    0     0     0     1

1    0    1    0    0     0     1     0

1    0    1    1    0     0     1     1

1    1    0    0    0     1     0     0

1    1    0    1    0     1     0     1

1    1    1    0    0     1     1     0

1    1    1    1    1     1     1     1

The third bit of output, Y[2], can be implemented using AND, OR, and NOT gates as follows:

Y[2] = A[1] * B[1] + (A[1] + B[1]) * (A[0] * B[0])

This can be simplified to Y[2] = A[1] * B[1] + A[0] * B[0]. That is, the third bit of output Y[2] is equal to the product of the first bits of both inputs, A[1] and B[1], plus the product of the second bits of both inputs, A[0] and B[0].

The third bit of output, Y[2], can be implemented using AND, OR, and NOT gates to calculate the sum of the product of the first bits of both inputs, A[1] and B[1], plus the product of the second bits of both inputs, A[0] and B[0].

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The value of n/p = 5n/3p.

It is a branch of mathematics that deals with the occurrence of a random event.

Let's assume that the total number of numbers in the list is T. Therefore, p + n = T.

The probability of picking a positive number is 3/5.

So p/T = 3/5.

Ratio of the number of negative numbers to the number of positive numbers is n/p.

Divide the two equations we get

n/p = (n/T) / (p/T) = (n/T) / (3/5) = (5/3) * (n/T) = 5n/3p

Hence, the value of n/p = 5n/3p.

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