Each of these numbers represents the weight of a student in kilograms. What is the median of this data set?

39, 48, 45, 48, 51, 46, 52, 51, 43, 41

If you have 1 nickle, how many quarters do you have? (3)

If you have 4 nickles, you have 3 times as many quarters (3)(4) = 12

If you have n nickles, then you have 3n quarters so 3n = q, you have  a slightly different equation.

If you fix this equation and use substitution like you did, you can get the right answer; you can also try to work in the other information that you have - converting all coin values to cents

    5n + 10d + 25q = 460

This problem can be solved by setting up and solving a system of linear equations. After setting up the equations n+d+q=30, 5n+10d+25q=460, and d=q+2, you substitute and simplify to find that there are 10 nickels, 12 dimes, and 8 quarters.

Let's denote the number of nickels as n, dimes as d, and quarters as q. We have the following three equations based on the information given:

Solving these equations simultaneously will give you the numbers of each coin. If you substitute the third equation into the first and second equation, you get:

Simplify these equations to determine the values of n, q, and d. You would find that n=10, d=12, and q=8. So you have 10 nickels, 12 dimes, and 8 quarters.

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Answer:

2.50

Step-by-step explanation:

The average rate of change over the interval −2≤x≤2 is:

(f(2) − f(-2)) / (2 − -2)

From the table, we see that f(2) = 14 and f(-2) = 4.

(14 − 4) / (2 − -2)

10 / 4

2.50

Answer:

2.50

Step-by-step explanation:

Answer: 1 Triangle weighs as much as 2 marbles.

Step-by-step explanation: Since we know there balanced, we can figure out using equations whatever we do to the first side so to the other.

Answer:

5x+y=-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = 5x - 3   it's a slope-intercept form

y = 5x - 3         subtract 5x from both sides

-5x + y = -3          change the signs

5x - y = 3     it's a standard form

5x - y = 3          subtract 3 from both sides

5x - y - 3 = 0         it's a general form

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

r: It is the radius of the cylinder

h: It is the height of the cylinder

We have as data, observing the figure, that they give us the radio. Then, the height is missing.

Answer:

Option B

Answer:

The correct answer is -

2. the height of the cylinder  

Step-by-step explanation:

The volume of the cylinder is given as :

[tex]V= \pi r^{2} h[/tex]

In the given figure, we have the radius. So, we need the height in order to calculate the volume.

So, the correct answer is -

2. the height of the cylinder  

Answer:

45°

Step-by-step explanation:

Each corner of a square is a right angle. That is 90° which divided by 2 equals 45°

Look at the image below :)

In case you didn't know, corresponding angles are equal to each other and are on the same side of the traversal

Therefore the answer is angle CGH

Hope this helped!  

Answer:

Step-by-step explanation:

When two lines are crossed by another line, the angles in matching corners are called corresponding angles.

When the two lines are parallel Corresponding Angles are equal.

∠AFG and ∠CGH are corresponding angles.

The lines AB and CD are parallel, therefore m∠AFG = m∠CGH.

∠CGH and ∠DGH are supplementary angles.

Therefore m∠CGH + m∠DGH = 180°

Substitute m∠DGH = 54°:

m∠CGH + 54° = 180°          subtract 54° from both sides

m∠CGH = 126°

Therefore m∠AFG = 126°.

Answer:

S=546 [tex]ft^{2}[/tex]

Step-by-step explanation:

The equation for the volume of a sphere and the surface area of a sphere are as follows

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

[tex]S=4\pi r^{2}[/tex]

As we know that V=1200 we can use the volume equation to solve for r

[tex]1200=\frac{4}{3} \pi r^{3}\\900=\pi r^{3} \\[/tex]

Now we can plug r into the surface area equation

[tex]S=4\pi (\sqrt[3]{\frac{900}{\pi } })^{2} \\\\S=546.09\\S=546 ft^2[/tex] }

ANSWER

9.7 units

EXPLANATION

According to the Pythagoras Theorem, the square of the hypotenuse is equal to the sum of the squares of the two shorter legs

[tex] {x}^{2} + {7}^{2} = {12}^{2} [/tex]

This implies that,

[tex] {x}^{2} + 49= 144[/tex]

Group similar terms,

[tex] {x}^{2} = 144 - 49[/tex]

[tex] {x}^{2} = 95[/tex]

[tex]x = \sqrt{95} [/tex]

[tex]x = 9.7 \: units[/tex]

to the nearest tenth.

Answer:

Option D.) 28 Pa

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

In this problem

[tex]P*V=k[/tex]

step 1

Find the value of k

For [tex]P=84\ Pa,V=51\ L[/tex]

substitute and solve for k

[tex]k=84*51=4,284[/tex]

step 2

If the volume is expanded to 153 L, what will the new pressure be?

we have

The equation is equal to

[tex]P*V=4,284[/tex]

For  [tex]V=153\ L[/tex]

substitute

[tex]P*153=4,284[/tex]

[tex]P=4,284/153[/tex]

[tex]P=28\ Pa[/tex]

Answer:

The answer is 15/52. (Please make me as brainliest (: )

The probability that he will get a blue pen, and he will not get a yellow highlighter is 15/52 option fourth is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

We have:

Eli has 8 black pens and 5 in his desk drawer. He also has 3 yellow highlighters, 4 green highlighters, and 5 pink highlighters in his pencil case.

Total pens = 8+5 = 13

The probability of choosing the blue pen = 5/13

Total highlighter = 3+4+5 = 12

The probability of choosing yellow highlighter = 3/12 = 1/4

The probability of not choosing yellow highlighter = 1 - (1/4) = 3/4

The probability that he will get a blue pen, and he will not get a yellow highlighter:

= (5/13)(3/4)

= 15/52

Thus, the probability that he will get a blue pen, and he will not get a yellow highlighter is 15/52 option fourth is correct.

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Answer:

Final answer is [tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex].

Step-by-step explanation:

Given problem is [tex]\sqrt[3]{x}\cdot\sqrt[3]{x^2}[/tex].

Now we need to simplify this problem.

[tex]\sqrt[3]{x}\cdot\sqrt[3]{x^2}[/tex]

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}[/tex]

Apply formula

[tex]\sqrt[n]{x^p}\cdot\sqrt[n]{x^q}=\sqrt[n]{x^{p+q}}[/tex]

so we get:

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{1+2}}[/tex]

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{3}}[/tex]

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex]

Hence final answer is [tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex].

The original expression ∛x * ∛[tex]x^2[/tex] simplifies to x.

This means that the cube root of x times the cube root of [tex]x^2[/tex] is equal to x.

To simplify the expression ∛x * ∛[tex]x^2[/tex], we can apply the rules of exponents and radicals.

The cube root of x is equivalent to raising x to the power of 1/3.

Similarly, the cube root of [tex]x^2[/tex]  is equivalent to raising [tex]x^2[/tex] to the power of 1/3.

So, we have:

∛x = [tex]x^{(1/3)[/tex]

∛[tex]x^2 = (x^2)^{(1/3)} = x^{(2/3)[/tex]

Now, let's multiply these two expressions:

[tex]x^{(1/3)}\times x^{(2/3)[/tex]

To simplify, we add the exponents when multiplying like bases:

[tex]x^{(1/3 + 2/3)} = x^{(3/3)} = x^1[/tex]

So, the simplified expression is just x.  

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Answer:

option D

Lines a and b are parallel and lines c and d are parallel.

Step-by-step explanation:

Given in the question four lines a , b, c, d.

If two parallel lines (a,b) are cut by a transversal(d), then corresponding angles m<7 and m<15 are congruent.

They are know as corresponding angles.

Hence lines a and b are parallel.

If two parallel lines (c,d) are cut by a transversal(d), then corresponding angles m<13 and m<15 are congruent.

They are know as corresponding angles

Hence lines c and d are parallel

Final answer:

The number of 4-letter passwords using the letters A-Z with repetition allowed is 456,976, while without repetition it's 358,800.

Explanation:

When calculating the number of 4-letter passwords that can be made using the letters A through Z, two scenarios are considered: one where repetition of letters is allowed, and one where it is not allowed.

Scenario a) Repetition of letters is allowed

For each position in the 4-letter password, there are 26 possibilities (since there are 26 letters in the alphabet). Because repetition is permitted, each of the four positions can be filled by any of the 26 letters. Thus, the total number of possible passwords can be found by multiplying the number of choices for each position: 26 x 26 x 26 x 26 = 456,976.

Scenario b) Repetition of letters is not allowed

When repetition of letters is not allowed, the number of choices decreases for each subsequent position in the password. The first position can be filled by any of the 26 letters, the second can be filled by 25 remaining letters (since one letter has been used), the third position by the 24 remaining letters, and the fourth by 23 remaining letters. Thus, the calculation would be: 26 x 25 x 24 x 23 = 358,800.

Answer:

1) vertex = (-2,4)

2) Focus = (-0.5,4)

3) x= -3.5

   y= 4

4)  y=4

Step-by-step explanation:

General equation of parabola that is parallel to a-axis and vertex at (h,k) is given as

(y - k)^2 = 4p (x - h)

where

vertex of parabola is at (h,k)

focus of parabola is given at (h + p, k)

the directrix of parabola is given as x = h - p.

Now

1)

finding vertex of parabola:

Given equation of parabola

(y-4)^2=6(x+2)

Comparing with the general form, we get

h=-2 ,k=4 and 4p=6

hence vertex = (-2,4)

2)

Finding focus

Comparing with the above standard form we get

k=4, h=-2, p=3/2

Since the given parabola is parallel to x-axis and also p is positive hence it will opens to the right.

As focus is inside the parabola and it is p units to the right of the vertex:

hence

focus of parabola (h + p, k)=(-2+3/2 , 4)

                                            =(-0.5,4)

3)

Comparing with the above standard form we get

k=4, h=-2, p=3/2

Since the given parabola is parallel to x-axis and also p is positive hence it will opens to the right.

As directrix is outside the parabola and it is p units to the left of the vertex:

hence

directrix x=h-p

                = -2-3/2

                =-7/2

                = -3.5

             y= 4

4)

Finding Axis of symmetry:

as the vertex is (-2,4) also the given parabola is parallel to x-axis so

the axis of symmetry is a horizontal straight line passing through the vertex  at y=4 !

ANSWER

Brayden should have expanded the parenthesis first.

EXPLANATION

The expression Brayden is trying to simplify is

[tex]4n - {( n - 2)}^{2} [/tex]

To simplify this expression, the first thing to do is to expand the perfect square to obtain:

[tex]4n - {( n}^{2} - 4n + 4)[/tex]

We can now distribute the negative to the terms in the parenthesis.

[tex]4n - { n}^{2} + 4n - 4[/tex]

Answer:

He should have simplified [tex](n-3)^2[/tex] first then distribute the negative sign.

Step-by-step explanation:

Given that Brayden is simplifying the expression [tex]4n-(n-3)^2[/tex]. He begins by distributing the negative to the terms inside the parentheses. Which is basically the wrong step for the given problem.

Now we need to find about what should he have done instead.

According to order of operations, we should begin with exponent first.

So that means he should have simplified [tex](n-3)^2[/tex] first then distribute the negative sign.

Answer:

the answer to that is the very first response.

Step-by-step explanation:

you see, 6(4x+5) is equal to saying (6•4x) + (6•5). hope this helped!

It’s the first answer choice, the second answer choice, and the forth one.

Answer:

41.7 % to the nearest tenth.

Step-by-step explanation:

5 out of did not arrive on time.

As a percentage this is 5*100 / 12

= 41.7 % .

Answer:

Jim is 5, Dad is 20

Step-by-step explanation:

Since dad is 4 times as old as Jim that means 5 x 4=20 and in ten years Jim will be 15 and Dad will be 30 and 15 x 2 is 30.

Hope this helps!

Answer:

15 yards, 45 feet and 540 inches are equal.

Step-by-step explanation:

To know if the measurements are equal, we first need to convert all the measures to the same unit. In this case, I will convert them all to feet.

a.6 feet

b.15 yards ≈ 45 feet

c.45 feet

d.600 inches ≈ 50 feet

e. 12 feet

f. 540 inches  ≈ 45 feet

Therefore, b, c and f are equal.

Answer:

The sequence of transformation is reflected across the y-axis and translated 2 units down

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) translate h units to the right

∴ Its image is (x + h , y)

- If point (x , y) translate h units to the left

∴ Its image is (x - h , y)

- If point (x , y) translate k units up

∴ Its image is (x , y + k)

- If point (x , y) translate k units down

∴ Its image is (x , y - k)

* Now lets solve the problem

∵ The vertices of figure ABCD are:

  A (-1 , 3) , B (1 , 0) , C (2 , 3) , D (1 , 4)

∵ The vertices of figure A"B"C"D" are:

  A" (1 , 1) , B" (-1 , -2) , C" (-2 , 1) , D" (-1 , 2)

* Lets compare between ABCD and A"B"C"D"

∵ All x-coordinates has opposite signs

  -1 ⇒ 1 , 1 ⇒ -1 , 2 ⇒ -2 , 1 ⇒ -1

∴ The ABCD is reflected across the y-axis

∵ All y-coordinates subtracted by 2

 3 ⇒ 1 , 0 ⇒ -2 , 3 ⇒ 1 , 4 ⇒ 2

∴ The ABCD is translated 2 units down

* The sequence of transformation is reflected across the y-axis

  and translated 2 units down

Answer:

Summation: [tex]\sum_{n=1}^4(3n+12)[/tex]

Explicit formula: [tex]a_n=3n+12[/tex]

Step-by-step explanation:

The given series is 15 + 18 + 21 + 24.

The first term of this series is [tex]a_1=15[/tex].

The common difference is [tex]d=18-15=3[/tex]

The explicit formula is given by: [tex]a_n=a_1+d(n-1)[/tex].

We plug in the known values to get:

[tex]a_n=15+3(n-1)[/tex]

[tex]a_n=15+3n-3[/tex]

The explicit formula is [tex]a_n=3n+12[/tex]

The summation that represents the series is: [tex]\sum_{n=1}^4(3n+12)[/tex]

Answer:

3 12

Step-by-step explanation:

Answer:

I think it's B.

Step-by-step explanation:

Because the equation is 1 - 0.144/24 should represent the amount of emails to be answered after one day.

Answer:

D. The decay rate, which reveals the hourly rate of change in the number of customers whose subscriptions are due to be renewed.

Step-by-step explanation:

An exponential decay function is,

[tex]f(x)=a(1-r)^x[/tex]

Where, a is initial value,

r is rate of change per period,

x is the number of periods,

(1-r) is decay factor that shows the periodic rate of change in the initial value.

Given expression that represents the number of such customers after n days is,

[tex]15,000(1-\frac{0.144}{24})^{24n}[/tex]

By comparing,

15,000 is the initial number of customers who are due to be renewed,

[tex]\frac{0.144}{24}[/tex] is the change per hour in the number of customers,

24n is the total number of hours,

[tex](1-\frac{0.144}{24})[/tex] is the decay factor or decay rate that reveals the hourly rate of change in the number of customers,

Hence, option 'D' is correct.

Answer:

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.

Step-by-step explanation:

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).

[tex]\frac{530-260}{30-9} =\frac{270}{21} =12.857[/tex]

6.  Write the equation of the line.  

[tex]y-y_{1} m(x-x_{1} )\\y-260=12.857(x-9)\\y=12.857(x-9)+260[/tex]

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.

y=12.857(22-9)+260

y=12.857(13)+260

y=427.141

ANS: 427.141 calories

The equation for the line of best fit is written as ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope determined by minimizing the sum of squared errors (SSE). You substitute various x-values to calculate the resulting y-values, then plot these points to visualize the line of best fit. The correlation coefficient 'r' and coefficient of determination 'r²' are used to measure the goodness of fit.

To write an equation for the line of best fit, or the least-squares regression line, you would use the formula ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope of the line. Generally, 'b' is determined by minimizing the sum of the squared differences between the observed (actual) and predicted values of y, also known as the sum of squared errors (SSE). To do this, you would typically use statistical techniques or software that perform these calculations. Let's consider an example, the equation of the best-fit line is ŷ = -173.51 + 4.83x. Here, -173.51 is the value of 'a', and 4.83 is the value of 'b'.

While working with any specific equation, you can create a table of values by substituting different values for 'x' and calculating the resulting values for 'y'. You then plot these points and draw a line through them to visualize the line of best fit. The correlation coefficient 'r' and coefficient of determination 'r²' are also used to measure the goodness of fit of the regression line.

Remember, while your sample data might give you a best-fit line for your sample, testing the significance of the correlation coefficient is needed to confirm the suitability of this line for the overall population.

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Answer:

(a) Option 3

(b) Option 1

(c) Option 2

Step-by-step explanation:

Given information: m∠ABC = m∠CBD

Prove: BC bisects ∠ABD.

Proof:

[tex]m\angle ABC=m\angle CBD[/tex]             (Given)

Definition of congruent: Two angles are congruent if their measures are equal.

[tex]\angle ABC\cong \angle CBD[/tex]         (Definition of bisect)

Definition of bisect: If a line divides an angle in two equal parts, then the line is called angle bisector.

BC bisects ∠ABD                    (Definition of bisect)

Hence proved.

An angle bisector divides the angle into two equal parts. The justification of each step of the flowchart is as follows

From the question, we are given that:

[tex]\angle ABC =\angle CBD[/tex]

This represents the first step of the flowchart.

So, the justification is (3) Given

From the figure, we have that:

[tex]\angle ABC \cong \angle CBD[/tex]

This represents the second step of the flowchart.

[tex]\cong[/tex] mean congruent

So, the justification is (1) Definition of congruent

Lastly:

Line BC bisects [tex]\angle ABC[/tex].

This represents the third step of the flowchart.

So, the justification is (2) Definition of bisect

Because line BC divides [tex]\angle ABC[/tex] into two equal halves.

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Answer:

124.7 in²

Step-by-step explanation:

A hexagon consists of six equilateral triangles, each of side a, and we can divide each of them into two right triangles.

So, we can calculate the area of one right triangle and multiply by 12.

The formula for the area of one triangle is

A = ½bh

Step 1. Calculate the length of the side a

Per the Pythagorean Theorem,

[tex]\begin{array}{rcl}h^{2} + \left(\dfrac{a}{2}\right)^{2} & = & a^{2} \\\\6^{2} + \dfrac{a^{2}}{4} & = & a^{2}\\\\36 & = &\dfrac{3a^{2}}{4}\\\\144 & = & 3a^{2}\\\\\end{array}\\\\[/tex]

[tex]\begin{array}{rcl}a^{2} & = & \dfrac{144}{3}\\\\a & = & \dfrac{12}{\sqrt{3}}\\\\a & = & \dfrac{12\sqrt{3}}{3}\\\\a & = & 4\sqrt{3}\\\\\end{array}[/tex]

2.Calculate the area of a small triangle

The base of a small triangle is  

b = ½a = ½ × 4√3 = 2√3

The area of one small triangle is

A = ½ bh = ½× 2√3 × 6 = 6√3 in²

3. Calculate the area of the hexagon

A = 12 × 6√3 = 72√3 = 124.7 in²

To find the area of a regular hexagon, use the formula A = (1/2) x Perimeter x Apothem, find the side length with the apothem, calculate the perimeter, and then apply the values to the formula.

To find the area of a regular hexagon with an apothem of 6 inches, you can use the formula for the area of a regular polygon, which is A = (1/2) x Perimeter x Apothem. A regular hexagon can be split into six equilateral triangles, which means each side of the hexagon is equal in length. Since the apothem corresponds to the height of each of these triangle components, you can use the fact that in an equilateral triangle, the ratio of the side to the apothem is √3:1 to find the side length. Once the side length (s) is known, you can find the perimeter (P) of the hexagon by multiplying the side length by six. Then, plug the perimeter and the apothem into the formula to calculate the area.

Step 1: Calculate the side length (s).

Step 2: Calculate the Perimeter (P).

Step 3: Calculate the area (A).

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the "y" axis

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

Then, we have the points:

[tex](x1, y1): (- 6, -3)\\(x2, y2) :( 6, -7)[/tex]

Substituting:

[tex]m = \frac {-7 - (- 3)} {6 - (- 6)}\\m = \frac {-7 + 3} {6 + 6}\\m = \frac {-4} {12}\\m = - \frac {1} {3}[/tex]

Thus, the equation is:

[tex]y = - \frac {1} {3} x + b[/tex]

We substitute a point to find the cut point:

[tex]-7 = - \frac {1} {3} (6) + b\\-7 = -2 + b\\b = -7 + 2\\b = -5[/tex]

Finally the equation is:

[tex]y = - \frac {1} {3} x-5[/tex]

ANswer:

[tex]y = - \frac {1} {3} x-5[/tex]

Answer:

[tex]\large\boxed{\{x\ |\ x>2\}}[/tex]

Step-by-step explanation:

[tex]5x+7>17\qquad\text{subtract 7 from both sides}\\\\5x+7-7>17-7\\\\5x>10\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}>\dfrac{10}{5}\\\\x>2[/tex]

Answer:

7.7%

Step-by-step explanation:

To find the percent error, take the absolute value of (actual amount - estimate) and divide it by the actual amount).  Then multiply it by 100 %

percent error = | actual - estimate|

                          -------------------------- * 100%

                             actual          

                      = | 2.6 -2.4|

                        ----------------- * 100%

                                  2.6

                      = .2 * 100%

                         -----------

                            2.6

                       =7.69230769%

To the nearest tenth percent

                      =7.7%

Answer:

distribution of numerical data. It is an estimate of the probability distribution of a continuous variable it is different then a bar graph

Step-by-step explanation: