Viviana is tracking the number of calories she burns working out. Her watch
tracker says she burned 596 calories in 1 hour. Approximately how many calories
did she burn per minute? Round to the nearest tenth.

Using the normal distribution, the probability that a worker selected at random makes between $500 and $550 is: 2.15%.

The z-score of a measure X of a normally distributed variable with mean mu and standard deviation sigma is given by:

Z = (X - mu)/sigma

The mean and the standard deviation are given as follows:

mu = 400, sigma = 50

The probability is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 500, hence:

X = 550:

Z = (X - mu)/sigma

Z = (550 - 400)/50

Z = 3

Z = 3 has a p-value of 0.9987.

X = 500:

Z = (X - mu)/sigma

Z = (500 - 400)/50

Z = 2

Z = 2 has a p-value of 0.9772.

0.9987 - 0.9772 = 0.0215 = 2.15% probability.

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Step-by-step explanation:

g(x) is also called y. the functional result value for an input value x is shown in the y direction above or below that x value on the x axis.

so, when it says g(x) = c, the solution is to find the values of x for which b the function g delivers c as result.

now, we look at the graphic.

for example, g(x) = 0 (c = 0) has actually 3 solutions, as the function crosses the x-axis (and that means y or g(x) = 0) 3 times. so, there are 3 different values of x that create g(x) = 0.

but we are looking for a c that has only one solution (one value of x to create that result).

c = 1 ?

let's imagine a horizontal line through y = 1.

we see, it cuts the function also 3 times. 3 solutions.

c = -1 ?

a similar horizontal line through y = -1 cuts the function also 3 times. 3 solutions

but c = 3 !

a horizontal line through y = 3 stays above all the waves of the function and then cuts the function only one time at the very right. 1 solution !

and that is therefore our answer.

By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.

Herein we find the case of a rectangular tank being filled with water at constant flow are, which is dimensionally speaking, volume by time. We know that dimensions of the tank are described in centimeters, whereas flow rate is described in liters per minute. Please notice that a liter is equal to 1000 cubic centimeters:

t = [(80 cm) · (60 cm) · (50 cm) · (1 L / 1000 cm³)] / (24 L / min)

t = 10 min

By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.

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The distance from Sang to Jazmin is 101 yards.

From the discussion in the question, we can see that the positions of Sang and Jazmin can be construed to give a rectangle. We know that the rectangle is a four sided figure.

The diagonal is a line that is drawn from one side of the four sided figure to another. Hence we can be able to apply the Pythagoras theorem to obtain the distance from Sang to Jazmin.

From;

c^2 = a^2 + b^2

c = √a^2 + b^2

c = √(20)^2 + (99)^2

c = 101 yards.

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(3x² - 7x + 14) + (5x² + 4x - 6)

Match 3x² and 5x² to get 8x².

Combine −7x and 4x to get −3x.

Subtract 6 from 14 to get 8.

Therefore, the expression (3x² - 7x + 14) + (5x² + 4x - 6), is equivalent to the expression "B".

(2x² - 5x -3) + (-10x² + 2x + 7)

Combine 2x² and -10x² to get −8x².

Combine −5x and 2x to get −3x.

Add −3 and 7 to get 4.

Therefore, the expression (2x² - 5x -3) + (-10x² + 2x + 7), is equivalent to the expression "A".

(12x² - 2x - 13) + (-4x² + 5x +9)

Combine 12x² and -4x² to get 8x².

Combine −2x and 5x to get 3x.

Add −13 and 9 to get −4.

Therefore, the expression (12x² - 2x - 13) + (-4x² + 5x +9), is equivalent to the expression "C".

Considering the given box plots, we have that:

It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.

Hence, for class A, we have that:

Then:

Hence, for class B, we have that:

Then:

Hence the correct options are given as follows:

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The height is changing by 0.5 units per minute as evident in the given table.

It follows from the task content that the table given indicates that at, 0min, the height was 150.

While at 1 min, the height is 150.5. On this note, it follows that the height increases by 0.5 units for after every minute.

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To estimate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.

In mathematics, a cylinder exists as a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases exist normally circular (like a circle) and the center of the two bases exists joined by a line segment, which exists named the axis.

A cylinder exists as a closed solid that contains two parallel circular bases joined by a curved surface.

To calculate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.

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Solving the quadratic equation we conclude that:

The height of the rocket is defined by the quadratic equation:

[tex]d = 90t - 5t^2[/tex]

The maximum height is what we get in the vertex of the quadratic equation, such that for this quadratic equation, the vertex is at:

[tex]t = -90/(2*-5) = 9[/tex]

So the maximum height is what we get when we evaluate in t = 9:

[tex]d = 90*9 - 5*9^2 = 45[/tex]

The maximum height is 45ft.

Now we need to solve the equation for the largest value of t:

[tex]d = 90*t - 5t^2 = 0[/tex]

Rewriting it, we get:

[tex]0 = 90*t - 5*t^2\\\\0 = t*(90 - t*5)[/tex]

The maximum solution is what we get when:

0 = 90 - t*5

t = 90/5 = 18

The rocket is 18 seconds in the air.

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The correct  option (D).

There are infinitely many intersection points.

a two-variable equation that, when plotted on a graph, results in a straight line.

The term "point of intersection" refers to the intersection of two lines.

Russ is attempting to solve an equation whose two sides are both linear expressions.

He graphs the system and finds that they are on the same line after setting the expressions to y.

Since both lines are the same, there are an endless number of junction places.

Russ should therefore consider the outcome to be option (D) There are a limitless number of intersections.

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I understand that the question you are looking for is:

Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome? There are no intersection points. There is exactly one intersection point. There are exactly two intersection points. There are infinitely many intersection points.Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome?

A. There are no intersection points.

B. There is exactly one intersection point.

C. There are exactly two intersection points.

D. There are infinitely many intersection points

The y-intercept of the linear equation that models the data indicates that:

There was 1 inch of water on the tub when the water was turned on.

A linear function is modeled by:

y = mx + b

In which:

In this problem, when x changes by 1, y changes by 2, hence the slope is of 2. Hence, since when x = 1, y = 3, when x = 0, y = 3 - 2 = 1, which means that the y-intercept is of 1, and the correct interpretation is:

There was 1 inch of water on the tub when the water was turned on.

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Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces. This can be obtained by multiplying the fractions given with the total number.

From the question it is given that,

Carries family broke a package of graham crackers into 32 pieces.

Therefore total number of pieces will be 32 pieces.

carries two brothers each ate 1/8 of the pieces

This means that out of 32, 1/8 of the pieces were ate by the two brothers.

1/8 of 32 = 1/8 × 32 = 4 pieces

⇒ Carries two brothers each ate 4 pieces

the rest of the family ate 7/16 of the pieces

This means that out of 32, 7/16 of the pieces were ate by the rest of the family

7/16 of 32 = 7/16 × 32 = 14 pieces

⇒ the rest of carries family ate 14 pieces

remaining pieces = 32 - (4 + 14) = 32 - 18 = 14 pieces

⇒ there were 14 pieces remaining

Hence Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces.

carries two brothers each ate ____ pieces

the rest of carries family ate ____ pieces

there were ____ pieces remaining

Answer:

83in²

Step-by-step explanation:

This can also be expressed as;

Area of polygon=Area of ∆ABF +Area of rectangle BCDF + Area 0f ∆DEF

For ∆ABF;

Area of ∆ABO=∆AOF

Area of ∆ABF=2×Area of ∆ABO

Area of ∆ABO=1/2×Length×height

=1×4×7/2=28/2=14in

But area of ∆ABF=2×Area of ∆ABO

Area=2×14in=28in.

Area of rectangle;

Area=length×breadth

Area=5in×8in=40in.

Area of ∆DEF=2×Area of ∆EFG

Area=1/2× base× height

Area=1×2.5×6/2

Area=15/2=7.5in.

But area of ∆EFG=2×7.5in

=15in.

Area of polygon=28in+40in+15in=83in

He has thrown 425 free throws if he missed 17

The given parameters are:

Proportion of free throw missed, p = 4%

Number of free throw missed, n = 17

Let the total number of throws be N.

So we have

n = p * N

Substitute the known values in the above equation

17 = 4% * N

Divide both sides by 4%

N = 425

Hence, he has thrown 425 free throws if he missed 17

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Answer:

Is there more information?  There is not enough to find the slope of a line.  I'll answer with an equation that works, but I suspect it won't be correct.

Step-by-step explanation:

If the only requirement is to have a line that goes through (4,3).  Then one could simply say:

y = 4

This is a horizonal line that goes through (3,4), and will always produce a y value of 4 regardless of x.  No, it will not pass through (4,3) since y is aleways 4, regardless of x.

If you wanted to get fancier, we could write a needlessly more complex equation:

y = (4/3)x

When x = 3, y = 4, so (3,4) is on this line.  But (4,3) is not.  y = (4/3)(4) means y = (16/3), not 4.

The resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

Quadratic equation are equations that has a leading degree of 2. Most quadratic equations have 3 terms.

Given the quadratic equation x^2-19x-39 = 0

Add 39 to both sides to have:

x^2 - 19x - 39 + 39 = 0 + 39

x^2 -19x = 39

Complete the square of the resulting

x^2-19x+(19/2)^2 = 39 + (19/2)^2
(x+19/2)^2 = 39 + (19/2)^2

x + 19/2 = ±√39 + (19/2)^2

x = ±√39 + (19/2)^2 - 19/2

Hence the resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

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The solution to the system and the solution that fills the blank space is (6, 1)

This are also known as a set of simultaneous equations, also known as a system of equations which is a finite set of equations for which common solutions

Given the following system of equations

2y − x = 8, and

y − 2x = −5.

From equation 2;

y = -5 + 2x ............. 3

Substitute equation 2 into equation 1 to have:

2(-5+2x) - x = 8

Expand to have:

-10 +4x -x = 8

-10 + 3x = 8

3x = 8 + 10

3x = 18

Divide both sides

by 3

3x/3 = 18/3

x = 6

Substitute x = 6 into equation 3

y = -5 + 2x

y = -5 + 2(3)

y = -5 + 6

y = 1

Hence the solution to the system and the solution that fills the blank space is (6, 1)

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Answer:

Its D (6,7)

Step-by-step explanation:

We know that there are (3 + 1/2) groups, such that each group fill one bus.

2/5 of the students are boys, then the number of groups that we can make only with boys is:

(2/5)*(3 + 1/2) = 6/5 + 1/5 = 7/5 = 5/5 + 2/5 = 1 + 2/5

Then you can make one and a little less than a half of a group, which means that you need 1 and 2/5 of a buss to transport the boys, rounding that to the a whole number, you will need 2 busses to only transport the boys.

The original distance is:

D = (2 + 3/4) miles.

But Mark only covers 2/3 of that distance, then we have:

d = (2/3)*D = (2/3)*(2 + 3/4) miles = (4/3 + 2/4) miles

d = (4/3 + 1/2) miles = (8/6 + 3/6) miles = (1 + 5/6) miles

Mark is at (1 + 5/6) miles of his house.

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Answer:

Step-by-step explanation:

A system of equations for the problem can be written using the two given relationships between quantities of brass alloys.

Let x and y represent the quantities in grams of the 65% and 90% alloys used, respectively. There are two relations given in the problem statement.

  x + y = 500 . . . . . . quantity of new alloy needed

  0.65x +0.90y = 0.75(500) . . . . . quantity of copper in the new alloy

These are the desired system of equations.

This problem does not ask for the solution, but it is easily found using substitution for x.

  x = 500 -y

  0.65(500 -y) +0.90y = 0.75(500)

  (0.90 -0.65)y = 500(0.75 -0.65) . . . . . . subtract 0.65(500)

  y = 500(0.10/0.25) = 200

  x = 500 -200 = 300

300 grams of 65% copper and 200 grams of 90% copper are needed.

The correct option is A.

When the data are nominal or ordinal.

There are three types of correlation:

1. Positive and negative correlation

2. Linear and non-linear correlation

3. Simple, multiple, and partial correlation

There are different types of correlation one can use based on the types of variables being examined.

Spearman’s rho is a superb choice when you have nominal or ordinal data because Pearson’s isn't appropriate. Ordinal data have a minimum of three categories and the categories have a natural order. for instance , first, second, and third during a race are ordinal data.

Two variables can have some quite relationship, i.e., change in one may cause a change within the other.

If a change within the value of one variable causes a simultaneous change in the other variable in the same or opposite direction, then it’s termed as correlation, or these variables are said to be correlated. Keeping these in mind the answer to this question is When the data are nominal or ordinal

When the data are nominal or ordinal.

So the option no A is correct.

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I understand that the question you are looking for is:

There are different types of correlation one can use based on the types of variables being examined. When conducting an analysis, when do you need to use spearman’s rho instead of Pearson's r ?

A. When the data are nominal or ordinal.

B. When the data are ratio or interval.

C. When the data are random.

D. Spearman's rho should never be used for correlations.

Answer:

The frame will be 4 inches in width

Step-by-step explanation:

The length of the outside is 24+2x

The width of the outside is 20+2x

(24+2x)(20+2x) - 20(24) = 416

480 + 40x + 48x + 4x2 - 480 = 416

4x2 + 88x - 416 = 0

x2 + 22x - 104 = 0

(x+26)(x-4) = 0

x = -26 or x=4

The frame will be 4 inches in width

Answer:

x = 12

Step-by-step explanation:

sqrt(x+4) - 3 = 1

First get the sqrt all by itself on one side of the equation. Add 3 to both sides of the equation.

sqrt(x+4) = 1 + 3

sqrt(x+4) = 4

To "fix" the sqrt, that is, "undo it" and get rid of it, you have to SQUARE both sides of the equation.

(sqrt(x+4))^2 = 4^2

x + 4 = 16

subtract 4 to finish up.

x = 12

Check:

sqrt(12 + 4) - 3 = 1

sqrt16 - 3 = 1

4 - 3 = 1

1 = 1 Check!

The P(B|A) expressed in the simplest form will be (B) 2/7.

To find the P(B|A) expressed in the simplest form:

Given -

Total possible numbers = 2,3,4,5,6,7,8,9

Let the value of the number be AB.

Therefore, the P(B|A) expressed in the simplest form will be (B) 2/7.

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The complete question is given below:
A locker combination consists of two non-zero digits. The digits in a combination are not repeated and range from 2 through 9.

Event a = a first digit is an odd number

Event b = the second digit is an odd number

If a combination is picked at random with each possible locker combination being equally likely, what is P(B/A) expressed in the simplest form?

A.1/4

B.2/7

C.4/9

D.1/2

Answer:

  -3√11

Step-by-step explanation:

If the coefficients of a polynomial are rational, any irrational root will have a conjugate that is also a root.

The root 3√11 is irrational, so its conjugate, -3√11, will also be a root.

__

Additional comments

The conjugate of a root of the form a+√b or a+bi will be the same form with the sign changed: a-√b or a-bi.

The conjugate of 3√11 = 0 +√99 will be 0 -√99 = -3√11.

__

A quadratic with rational coefficients can only have irrational roots of the form a±√b, where 'a' and 'b' may be any rational number.

3 - √11  also be a root of f(x).

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Get the conjugate of any irrational zero if you want rational coefficients.

The conjugate of 3 + √11  is  3 - √11

x = 3 +√ 11

Subtract 3 on both sides

x minus 3 = 3 + √11 - 3

x - 3 = √11

By squaring on both sides

(x - 3)² =√ 11

Now subtract 11 on both sides

(x - 3)² - 11 = 0

To factor use the difference of squares

u² minus v² = (u minus v) (u plus v)

[(x - 3) - 11][(x - 3) + 11] = 0

We get,

(x - 3) - 1 = 0 or (x - 3) + 11 = 0

Solve for x - 3 and x

Add √11 on both sides of first equation and subtract √11 on both sides of second equation

x minus 3 = √11 or x minus 3 = - √11

By adding 3 on both sides

x = 3 + √11 or x = 3 - √11

As a result,

the root of 3 - √11 must likewise be f(x).

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When one organism gains a benefit at the expense of a second organism and causes them harm is called:

A. Parasitism

B. Mutualism

C. Commensalism

D. Predation

Answer:

Step-by-step explanation:

a

[tex]-16=r^3\implies \sqrt[3]{-16}=\sqrt[3]{r^3}\implies \sqrt[3]{-16}=r\implies \sqrt[3]{-2^4}=r \\\\\\ \sqrt[3]{(-2)^3\cdot 2^1}=r\implies -2\sqrt[3]{2^1}=r\implies -2\sqrt[3]{2}=r[/tex]

Applying the same-side interior angles theorem,

7. m∠4 = 50°; m∠5 = 130°

8. m∠2 = 15°; m∠8 = 15°.

The same-side interior angles theorem holds that, two interior angles on a side of a transversal are supplementary, that is they add up to 180 degrees.

According to the alternate exterior angles theorem, exterior angles that alternate each other along a transversal are congruent, that is they have equal measures.

7. m∠4 + m∠5 = 180 [same-side interior angles theorem]

Substitute

y + 2y + 30 = 180

3y + 30 = 180

3y = 180 - 30

3y = 150

y = 50

m∠4 = y = 50°

m∠5 = 2y + 30 = 2(50) + 30

m∠5 = 130°

8. m∠2 = m∠8 [alternate exterior angles theorem]

Substitute

x - 30 = 3x - 120

x - 3x = 30 - 120

-2x = -90

x = 45

m∠2 = x - 30 = 45 - 30 = 15°

m∠8 = 3x - 120 = 3(45) - 120 = 15°

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This would be the least common multiple of 3, 4, 5, and 9. We can start by listing the multiples of the biggest number, 9, and seeing if each of the numbers can be divisible by the smaller numbers.

9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180

180 would be the answer because it is the first number in our list that is divisible by 3, 4, 5, and 9.

Answer:

  triangle angle sum theorem

Step-by-step explanation:

The missing statement is one that justifies the sum of the angles in a triangle being 180°.

That justification is provided by the ...

  triangle angle sum theorem

Using a linear function, we have that:

a) The costs are:

i. C(x) < $1.3.

ii. C(x) > $2.3.

b) The times are:

i. Less than 9 minutes.

ii. At least 16 minutes.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the y-intercept is of 0.3, while the slope is of 0.2, hence the cost for a call of x minutes is:

C(x) = 0.3 + 0.2x.

For calls shorter than 5 minutes, the costs are:

C(x) < 0.3 + 0.2 x 5

C(x) < $1.3.

For calls longer than 10 minutes, the costs are:

C(x) > 0.3 + 0.2 x 10

C(x) > $2.3.

The cost is less than $2.10 for calls of less than x minutes, found as follows:

0.3 + 0.2x < 2.1

0.2x < 1.8

x < 9.

The cost is greater or equal to $3.50 for calls of at least x minutes, found as follows:

0.3 + 0.2x >= 3.5

0.2x >= 3.2

x >= 16.

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