Look at the stem-and-leaf plot. What is the range in scores? Key 6l4 = 64 A. 36 B. 83.5 C. 84.45 D. 100

The vertex of the parabola is at approximately (15, 2,350) which means that the maximum daily profit occurs when the price of each solar panel is increased by $5 fifteen times.

The function P(x) = −6x² + 180x + 1,000 models the daily profit of a company

where;

x = number of $5 price increases for each solar panel.

The vertex form of the quadratic function is P(x) = a(x-h)² + k

where;

(h,k) = vertex of the parabola.

To find the vertex, we can use the formula h = -b/2a and substitute the values of a, b, and c from the given function.

In this case, a = -6, b = 180, and c = 1000.

h = -b ÷ 2a

h = -180 ÷ (2 × (-6))

h = 15

So the x-coordinate of the vertex is 15.

To find the y-coordinate, we can substitute x=15 into the original function:

P(15) = -6(15)² + 180(15) + 1,000

P(15) = 2,350

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Answer:

This question is not fully filled out.

Answer:

Step-by-step explanation:

Hello! 12+60 does not need to be factored because it is not division. 12 + 60 = 72.

If you meant 12/60, then I can help you.

The factors of 12 are: 1, 2, 3, 4, 6, 12.
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

From this, we can see the greatest common factor they share is 12.

12/12 is 1, and 60/12 = 5. So, 12/60 = 1/5.

Answer:

8%: $295

10% : $6005

15%: $595

Step-by-step explanation:

Let's break this down:

Let's call the amounts invested at 8% and 10% combined = x
Then call the amount invested at 15% = x + $300
8% of x = 0.08x
10% of (6300 - x) = 0.1(6300 - x)
15% of (x + $300) = 0.15(x + $300)
0.08x + 0.1(6300 - x) + 0.15(x + $300) = $773
0.18x = $53
x = $53/0.18 = $295

a = amount invested at 8%

how much is 8% of "a"? (8/100) * "a", namely 0.08a.

b = amount invested at 10%

how much is 10% of "b"? (10/100) * "b", namely 0.10b.

c = amount invested at 15%

how much is 15% of "c"? (15/100) * "c", namely 0.15c.

we know the total amount invested is 6300, so whatever "a", "b" and "c" might be, we know that a + b + c = 6300.

we also know that the yielded amount in interest is 773, so if we simply add their interest, that'd be 0.08a + 0.10b + 0.15c = 773.

we also know that the combined amounts of "a + b" plus 300 bucks is "c", so really c = a + b + 300.

[tex]c = a + b + 300 \\\\[-0.35em] ~\dotfill\\\\ a+b+c=6300\implies c=6300-a-b\implies \stackrel{\textit{substituting from the equation above}}{a+b+300=6300-a-b} \\\\\\ 2a+2b+300=6300\implies 2a+2b=6000\implies 2(a+b)=6000[/tex]

[tex]a+b=\cfrac{6000}{2}\implies a+b=3000\implies \boxed{b=3000-a} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{c = a + b + 300}\implies \stackrel{\textit{substituting from above}}{c=a+(3000-a)+300}\implies {\Large \begin{array}{llll} c=3300 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{we also know that} }{0.08a+0.10b+0.15c=773}\implies \stackrel{\textit{now, substituting "b" and "c"}}{0.08a+0.10(3000-a)+0.15(3300)=773}[/tex]

[tex]0.08a+300-0.10a+495=773\implies -0.02a+300+495=773 \\\\\\ -0.02a+795=773\implies -0.02a=-22\implies a=\cfrac{-22}{-0.02}\implies {\Large \begin{array}{llll} a=1100 \end{array}} \\\\\\ \stackrel{\textit{now, we know that}}{b=3000-a}\implies {\Large \begin{array}{llll} b=1900 \end{array}}[/tex]

The measure of the arc angle DE is derived to be 46.5055° using the arc length of the sector.

The arc measure DE and the angle it subtends at the center of the circle are directly proportional.

so arc DE = m∠DQE {central angle}

Arc length of the sector = (central angle / 360) x (2 x π x radius)

8.73 in = (m∠DQE / 360) x (2 x 22/7 x 10 in)

m∠DQE = (8.13 in × 360 × 7)/(2 × 22 × 10) {cross multiplication}

m∠DQE = 46.5055° = arc DE

Therefore, the measure of the arc angle DE is derived to be 46.5055° using the arc length of the sector.

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You would have $1.75 left before tax after purchasing all the vitamins.

Let's calculate the total cost of the vitamins first.

From the question, we can deduce the following:1 bottle of multivitamins = $3.751 bottle of vitamin D = $4.851 bottle of vitamin C = $2.95

Now, let's calculate the cost of what you got:2 bottles of multivitamins = 2 x $3.75 = $7.501 bottle of vitamin D = 1 x $4.85 = $4.852 bottles of vitamin C = 2 x $2.95 = $5.90

Total cost of the vitamins is = $7.50 + $4.85 + $5.90 = $18.25

If you have $20 (total amount) to spend on this purchase, after spending, you would have: balance = total amount - total cost balance = $20 - $18.25 balance = $1.75

So you would have $1.75 left before tax after purchasing all the vitamins.

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[tex]\dfrac{x}{19.48} =0.189[/tex]

[tex]x=0189\times19.48[/tex]

[tex]\boxed{\bold{x=3.68172}}[/tex]

The approximate number of people who will receive a small prize at this year's fair is 12,000.

What is number?

A number is a mathematical concept used to represent a quantity or value. It can be represented by numerals, symbols, or words.

To estimate the number of people who will attend this year's fair, we can calculate the average attendance of the last 5 years:

Average attendance = (270,000 + 280,000 + 300,000 + 320,000 + 330,000) / 5

= 300,000

Therefore, a reasonable estimate of the number of people who will attend this year's fair is 300,000.

To find the approximate number of people who will receive a small prize at this year's fair, we need to multiply the number of people who receive raffle tickets by the proportion of those who will receive a small prize:

Number of people who will receive a small prize = 60,000 x 0.2

= 12,000

Therefore, the approximate number of people who will receive a small prize at this year's fair is 12,000.

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Answer:

62500

Step-by-step explanation:

To multiply 250 and 25, we can first multiply the two numbers ignoring their zeroes and then add the zeroes back in the product.

250 multiplied by 25 is:

25 × 25 = 625 (ignoring the zeroes)

250 × 25 = 62500 (adding the zeroes back in)

Therefore, 250 multiplied by 25 is equal to 62500.

The circular is around 305 cm in circumeference.

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle.

Substituting d = 97 cm and using the value of π to be 3.14159, we get:

C = πd

C = 3.14159 × 97 cm

C ≈ 304.731 cm

Rounding this to 3 significant figures, we get:

C ≈ 305 cm

Therefore, the circumference of the circle is approximately 305 cm.

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The probability that both officers will be seniors is 0.29 or 29%.

There are a total of 22 council members.

To find the probability that both officers are seniors, we need to find the probability of selecting a senior for the first officer and then a senior for the second officer.

The probability of selecting a senior for the first officer is 12/22 since there are 12 seniors out of 22 total members.

After one senior has been selected, there are only 11 seniors left out of a total of 21 remaining members.

Therefore, the probability of selecting another senior for the second officer is 11/21.

To find the probability of both events occurring together, we multiply the probabilities:

P(selecting 2 senior officers) = (12/22) x (11/21) = 0.287 or 0.29 (rounded to two decimal places).

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The additional number of pennies needed to complete 1 dime is 3

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

Pennies = 7

As a general rule

Ten pennies have the same value as 1 dime.

This means that

7 pennies + x = 1 dimes

So, we have

7 pennies + x = 10 pennies

Where x is the additional pennies needed

When evaluated. we have

x = 3

Hence, the additional number of pennies needed is 3

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In brains, we want a balance between excitatory and inhibitory signals to maintain proper neural functioning.

Since, We know that;

In brains, we want a balance between excitatory and inhibitory signals to maintain proper neural functioning.

This balance is important because too much excitatory signaling can cause overstimulation and potential harm, while too much inhibitory signaling can lead to neural suppression and lack of responsiveness.

Hence, The proper balance between the two types of signals is necessary for healthy neuronal activity, and maintaining that balance is a key aspect of neural health.

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Answer:

(x, y) = (-10, 0) and (x, y) = (-2, 0)

Step-by-step explanation:

To find the points on the x-axis that are a distance 5 from P(-6,3), we can use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Since we want to find the points that are a distance of 5 from P(-6,3) on the x-axis, we know that y = 0 for these points. So we can simplify the distance formula to:

d = √((x - (-6))^2 + (0 - 3)^2)

d = √((x + 6)^2 + 9)

We want to find the values of x that make d = 5. So we can set up the equation:

5 = √((x + 6)^2 + 9)

Squaring both sides, we get:

25 = (x + 6)^2 + 9

Subtracting 9 from both sides, we get:

16 = (x + 6)^2

Taking the square root of both sides (remembering to include both the positive and negative square root), we get:

x + 6 = ±4

Subtracting 6 from both sides, we get:

x = -10 or x = -2

So the two points on the x-axis that are a distance of 5 from P(-6,3) are (-10, 0) and (-2, 0).

Therefore, the two answers are:

(x, y) = (-10, 0) and (x, y) = (-2, 0)

Answer:

(x, y) = (-10, 0)   (smaller x-value)

(x, y) = (-2, 0)     (larger x-value)

Step-by-step explanation:

To find the all the points on the x-axis that are a distance of 5 from P(-6, 3), we can use the distance formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

As the distance is 5,  d = 5.

Let (x₁, y₁) = (-6, 3).

As the points to be found are on the x-axis, their y-coordinates are zero.

Therefore, let (x₂, y₂) = (a, 0).

Substitute these values into the distance formula:

[tex]\implies \sqrt{(a-(-6))^2+(0-3)^2}=5[/tex]

Simplify and solve for a:

[tex]\implies \left(\sqrt{(a+6)^2+(-3)^2}\right)^2=5^2[/tex]

[tex]\implies (a+6)^2+9=25[/tex]

[tex]\implies (a+6)^2+9-9=25-9[/tex]

[tex]\implies (a+6)^2=16[/tex]

[tex]\implies \sqrt{(a+6)^2}=\sqrt{16}[/tex]

[tex]\implies a+6=\pm 4[/tex]

[tex]\implies a+6-6=-6\pm 4[/tex]

[tex]\implies a=-10, -2[/tex]

Therefore, the points on the x-axis that are a distance of 5 units from P(-6, 3) are:

The compound amount after 3 years is $2275.22.

In this case, you are given:

Principle = $2,000

rate = 0.0353

time = 3

You need to find A, the compound amount after 3 years.

To do this, you need to plug in the values of P, r and t into the formula and use a calculator:

A=P×e^rt

A=2000×(e)^0.0353×3

A≈2275.22

Therefore, by the compound interest the answer will be $2275.22.

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The graph of [tex]g(x) = 10^{(x+2)} +3[/tex] will be the graph of [tex]f(x) = 10^x[/tex] shifted left by 2 units and up by 3 units. It will still be an increasing exponential function that passes through the point (-2,4) instead of (0,1).

What is graph?

In mathematics, a graph is a visual representation of the relationships between objects. A graph consists of vertices, which are points or nodes, and edges, which are lines or arcs connecting the vertices.

To understand the transformation of the graph of [tex]g(x) = 10^{(x+2)} +3[/tex], we can first examine the basic graph of [tex]f(x) = 10^x[/tex]. This graph is an increasing exponential function that passes through the point (0,1), and as x gets larger, the y-values grow at an increasingly rapid pace.

Now let's consider the transformations applied to f(x) to obtain g(x):

The "+2" inside the exponent of [tex]10^{(x+2)[/tex] shifts the graph of f(x) to the left by 2 units. This means that the point (0,1) on the graph of f(x) will be moved to the left to the point (-2,1) on the graph of g(x).

The "+3" added outside the exponent of [tex]10^{(x+2)[/tex] shifts the entire graph of f(x) upwards by 3 units. This means that every point on the graph of f(x) will be shifted up by 3 units to obtain the corresponding point on the graph of g(x).

Therefore, the graph of [tex]g(x) = 10^{(x+2)} +3[/tex] will be the graph of [tex]f(x) = 10^x[/tex] shifted left by 2 units and up by 3 units. It will still be an increasing exponential function that passes through the point (-2,4) instead of (0,1).

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The account balance after 7 years = $1,547.48

We know that the formula for the compound interest is:

[tex]A = P(1 + r/n)^{nt}[/tex]

where,

A = amount (principal + interest)

P = Principal amount

R = interest rate as a percent

r = interest rate as a decimal

n = number of compounding periods

and t = time in years

Here, P = $700, t = 7 and R = 12%

First, convert R as a percent to r as a decimal

r = R/100

r = 12/100

r = 0.12 rate per year,

Using above formula, the amount after 7 years would be,

[tex]A = P(1 + r/n)^{nt}[/tex]

[tex]A = 700.00(1 + \frac{0.12}{1} )^{1\times 7}[/tex]

A = 700.00 × (1 + 0.12)⁷

A = $1,547.48

Therefore, the total amount accrued on a principal of $700.00 at a rate of 12% per year compounded 1 times per year over 7 years is $1,547.48.

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The total number of books in all the piles is 4 x  72 = 288.

For one to be able to create the equal stacks of books in all  of the four styles, one need to look at the greatest common divisor (GCD) .

Hence the GCD of 300, 90, 6, and 180:

300 = 2² x  3  x  5²

90 = 2 x  3²  x  5

6 = 2 x  3

180 = 2²  * 3²  *x 5

The GCD is 2²  x 3²  = 36.

In terms of the number of piles, we have to divide the total number of books in all of the style by the GCD: Hence:

300 ÷  36 = 8.33...

90  ÷ 36 = 2.5

6  ÷ 36 = 0.17...

180 / ÷ 36 = 5

For one to be able to find the total number of books in all of pile, we need to multiply the GCD by the number of piles:

36 x  2 = 72

Hence, each pile will need to contain 72 books. The total number of books in all the piles is 4 x  72 = 288.

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The areas of the composite figures are:

Case 1: 21 m²

Case 2: 217.5 m²

Case 3: 42 m²

Case 4: 168 cm²

Case 5: 252 m²

Case 6: 27 in²

Case 7: 39 cm²

Case 8: 44 cm²

Case 9: 558

Case 10: 70

Case 11: 78 cm²

Case 12: 21 ft²

In this problem we need to determine the areas of triangles, rectangles and composite figures formed by adding triangles and rectangles. The area formulas are introduced below:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

The areas are now determined below:

Case 1:

A = 0.5 · (7 m) · (6 m)

A = 21 m²

Case 2:

A = (9 m) · (15 m) + 0.5 · (11 m) · (15 m)

A = 217.5 m²

Case 3:

A = 0.5 · (7 m) · (12 m)

A = 42 m²

Case 4:

A = 2 · 0.5 · (6 cm) · (8 cm) + 2 · 0.5 · (15 cm) · (8 cm)

A = 168 cm²

Case 5:

A = 2 · 0.5 · (7 m) · (9 m) + 2 · 0.5 · (21 m) · (9 m)

A = 252 m²

Case 6:

A = (9 in) · (2 in) + (3 in)²

A = 27 in²

Case 7:

A = (9 cm) · (3 cm) + (6 cm) · (2 cm)

A = 39 cm²

Case 8:

A = (4 cm) · (5 cm) + (2 cm) · (3 cm) + (3 cm) · (6 cm)

A = 44 cm²

Case 9:

A = 2 · 0.5 · 10 · 18 + 18 · 21

A = 558

Case 10:

A = 14 · 5

A = 70

Case 11:

A = (12 cm) · (6.5 cm)

A = 78 cm²

Case 12:

A = (3 ft) · (5 ft) + (3 ft) · (2 ft)

A = 21 ft²

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Answer:  B, D, A

Step-by-step explanation:

1. In order to be greater than 0 when multiplying 2 numbers they must be the same sign so that happens in quadrant 1 an 3.   B

2. y is negative in quadrant 3 and 4 which are below the x-axis.  D

3.  since x=0 is a line that goes up and down.  It' along the y-axis. A

Answer:

(d)  Option 2 - The set of all points in quadrants I and III {x and y have the same sign}.

(e)  Option 4 - The set of all points below the x-axis.

(f)  Option 1 - The set of all points on the y-axis.

Step-by-step explanation:

xy > 0 means that the product of x and y is positive.

This is true if both x and y have the same sign (either both positive or both negative).

In quadrant I all points have both a positive x and y coordinate.

In quadrant III all points have both a negative x and y coordinate.

Therefore, the correct answer is:

[tex]\hrulefill[/tex]

y < 0 means that y is negative.

All points above the x-axis have a positive y-coordinate.

All points below the x-axis have a negative y-coordinate.

The y-coordinate of all points on the x-axis is equal to zero.

Therefore, the correct answer is:

[tex]\hrulefill[/tex]

x = 0 means that x is equal to zero.

All points on the x-axis have:

All points on the y-axis have:

The coordinates of the origin are (0, 0).

Therefore, the correct answer is:

Answer:

slope = - 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 5 ) and (x₂, y₂ ) = (3, - 5 )

m = [tex]\frac{-5-5}{3-(-2)}[/tex] = [tex]\frac{-10}{3+2}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2

The equation of the line in slope-intercept form is; y = 6x - 5

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.

The slope (m) represents the rate of change of the line, which is the amount by which y changes when x increases by 1. The y-intercept (b) represents the point at which the line intersects the y-axis.

By using the slope-intercept form of a line, we can easily graph a line by plotting the y-intercept and then using the slope to find additional points on the line.

For the given line, the slope is 6 and the y-intercept is -5.

Therefore, the equation of line in slope-intercept form is;

y = 6x - 5

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Answer:

72 such cuboids are required to make a perfect cube.

Step-by-step explanation:

V = l x w x h

V = 12 cm x 9 cm x 8 cm = 864 cm^3

edge length = V^(1/3) = (864 cm^3)^(1/3) = 12 cm

V_cube = edge length^3 = 12 cm^3

number of cubes = V_cuboid / V_cube = 864 cm^3 / 12 cm^3 = 72

Therefore, 72 such cuboids are required to make a perfect cube.

The answer of the given question based on the equation is , the unknown number is 6.

An equation is the  mathematical statement that asserts equality of the two expressions. It typically consists of the two expressions separated by equal sign " = ". The expressions can include variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation. Solving an equation involves finding the value(s) of the variable(s) that make the equation true.

The statement can be translated into an equation as follows:

2(y - 2) = 8

Simplifying the equation, we can distribute the 2 on the left-hand side:

2y - 4 = 8

Then, we can add 4 to both sides to isolate the variable:

2y = 12

Finally, we divide both sides by 2 to solve for y:

y = 6

Therefore, the unknown number is 6.

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The expression in the form (x +a)² + b is shown below.

We have to expression given expression in the form (x +a)² + b.

1. x² + 12x

x² + 12x + 36 - 36

= (x +6)² - 36

2. x² + 3x - 2

x² + 2 . 3x /2 - 9/4 + 9/4 -2

(x+ 3/2)² - 17/4

3. x²+ 1/2 x

x² + 2 . 1/4 x + (1/2)² - (1/2)²

= (x+ 1/2)² - 1/4

4. x² - 2/9 x

=  x² + 2 . 2/20 x + 4/400 - 4/400

= (x+ 2/200)² - 1/100

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Answer:

This is the formula:

1 degree = π/180 radians

To convert 70 degrees to radians, we can multiply by the conversion factor:

70 degrees × π/180 = 7π/18 radians

So 70 degrees is equal to 7π/18 radians.:)

The total 'x' number of cups of trail mix  Orly uses c cups of raisins, she will make 10c / 3 cups of trail mix.

Orly uses 3 cups of raisins for every 10 cups of trail mix,

Which means that the ratio of cups of raisins to cups of trail mix is 3:10.

let us consider x be the number of cups of trail mix

and c be the number of cups of raisins.

We can set up a proportion to solve for the number of cups of trail mix,

⇒ 3/10 = c/x

To solve for x, we can cross-multiply and simplify,

⇒ 3x = 10c

⇒ x = 10c / 3

Therefore, if Orly uses c cups of raisins, she will make 10c / 3 cups of trail mix.

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The first circle have the values of x = 89° and y = 8.49. The second circle have values of x = 132° and y = 15.72. And the third circle have the value of a = 8.67.

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the first circle:

28° = x - 61° {secant tangent angle}

x = 28° + 61°

x = 89°

y² = 4 × 18

y = √72

y = 8.4853

For the second circle:

triangles formed by intersecting tangents are congruent so;

x = 2 × [180 - (24 + 90)]

x = 2 × 66°

x = 132°

tan 24 = 7/y {opposite/adjacent}

y = 7/tan 24

y = 15. 7223

For the third circle:

9(9 + a) = 21 × 8 {secant secant}

81 + 9a = 168

9a = 168 - 81

9a = 87

a = 87/9

a = 9.6667.

Therefore, the first circle have the values of x = 89° and y = 8.49. The second circle have values of x = 132° and y = 15.72. And the third circle have the value of a = 8.67.

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Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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The solution is :

The length of the rectangle is L=18cm

The width of the rectangle is W=10cm

We have,

Given data

let the length be x

L=x

Width= x-8

W= x-8

Perimeter= 56cm

But we know that the perimeter is expressed as

P=2L+2W

substitute our data

56=2(x)+2(x-8)

56=2x+2x-16

56+16=4x

72=4x

divide both sides by 4

x= 72/4

x=18cm

Hence the Length is 18cm

L=18cm

The width= 18-8

W=10cm

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complete question:

Arectangle has a width that is 8 centimeters less than its length. The perimeter of the rectangle is 56 centimeters. Find both the width and length of the rectangle. Show your work.