One number is twice another number. If the larger is diminished by 10, the result is 2 more than the smaller. Find the numbers.

So think of it like this she starts off $32 negative and subtract 3 from each box of cards she makes . So each box of cards she will make $8 that being said

32/8 =4 (it will take 4 box of cards to pay off her booth expense).

Sales would be 11x 4 =44

Expenditures would be 3x4 =32 (the amount used to make cards ) +32(the amount paid for the booth)

Which in total would be $64

Sidney needs to sell [tex]\( \boxed{4} \)[/tex] boxes of cards to cover her expenditures, totaling [tex]\( \$44 \)[/tex] in sales and expenditures.

To determine when Sidney's sales will cover her expenditures, we set up the following equations:

1. Cost equation:

  Total cost C consists of booth cost [tex]\( \$32 \)[/tex] plus material cost [tex]\( \$3 \)[/tex] per box:

  [tex]\[ C = 32 + 3n \][/tex]

  where n is the number of boxes of cards sold.

2. Revenue equation:

  Total revenue [tex]\( R \)[/tex] is obtained from selling each box for [tex]\( \$11 \)[/tex] :

  [tex]\[ R = 11n \][/tex]

3. Break-even point:

  To find when sales cover expenditures, set [tex]\( R = C \)[/tex]:

  [tex]\[ 11n = 32 + 3n \][/tex]

  Simplify and solve for n :

  [tex]\[ 11n - 3n = 32 \][/tex]

  [tex]\[ 8n = 32 \][/tex]

  [tex]\[ n = \frac{32}{8} = 4 \][/tex]

4. Calculation:

  - Number of cards: Sidney needs to sell 4 boxes of cards.

  - Sales: Total revenue [tex]\( R \)[/tex] at break-even point:

    [tex]\[ R = 11 \cdot 4 = \$44 \][/tex]

  - Expenditures: Total cost C at break-even point:

    [tex]\[ C = 32 + 3 \cdot 4 = \$44 \][/tex]

Sidney will cover her expenditures after selling 4 boxes of cards, where her total revenue from sales equals her total costs, including booth fees and material costs. This ensures she breaks even in terms of financial outlay versus income from sales.

Sidney needs to sell 4 boxes of cards to cover her expenditures, resulting in total sales of [tex]\( \$44 \)[/tex] and total expenditures of [tex]\( \$44 \)[/tex].

Answer: 6 x 7 = 42

Step-by-step explanation: I believe this is because there are 6 different ways from the school to the park and seven routes from the park to his grandmother's house. To find the total you multiply 6 and 7.

Answer:

Step-by-step explanation:

The formula of a volume of a cube:

[tex]V=a^3[/tex]

a - length of an edge

We have V = 27 in³. Substitute:

[tex]a^3=27\to a=\sqrt[3]{27}\\\\a=3\ in[/tex]

The expressions A (4x + 2), B (2(1 + 2x)), D (2x + 1 + 2x + 1), and E (x + x + x + x +1+1) are equivalent to the given expression 2(2x + 1).

The expressions equivalent to 2(2x + 1) are the ones that, when simplified, result in equivalent algebraic outputs. Let's verify this step-by-step:

Hence, the expressions that are equivalent to 2(2x + 1) are A, B, D, and E.

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The expressions that are equivalent to 2(2x + 1) are A. 4x + 2 and B. 2(1 + 2x).

The expression 2(2x + 1) can be simplified by distributing the 2 to both terms in the parentheses. This gives us 2 * 2x + 2 * 1, which simplifies to 4x + 2. Therefore, option A (4x + 2) is equivalent to 2(2x + 1).

We can also distribute the 2 to the terms inside the parentheses in option B (2(1 + 2x)). This gives us 2 * 1 + 2 * 2x, which simplifies to 2 + 4x, also equivalent to 2(2x + 1).

Option C (2(2x) + 1) is not equivalent because it simplifies to 4x + 1, not 2(2x + 1).

Option D (2x + 1 + 2x + 1) is not equivalent because it simplifies to 4x + 2, not 2(2x + 1).

Option E (x + x + x + x + 1 + 1) is not equivalent because it simplifies to 4x + 2, not 2(2x + 1).

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Answer:

P = 95%

Step-by-step explanation:

The average is:

[tex]\mu = 3\ minutes[/tex]

The standard deviation is:

[tex]\sigma = 0.25\ minutes[/tex].

We want the probability that the red light lasts between 2.5 minutes and 3.5 minutes

This is:

[tex]P(2.5 <X <3.5)[/tex]

Now we must transform these values to those of a standard normal distribution to facilitate calculation by using the probability tables.

[tex]P(2.5-3 <X- \mu<3.5-3)\\\\P(\frac{2.5-3}{0.25} <\frac{X- \mu}{\sigma}<\frac{3.5-3}{0.25})\\\\P(-2<Z<2)[/tex]

This is:

[tex]P(-2 <Z <2) = P(Z <2) - P(Z <-2)[/tex] ---------- (By the symmetry of the standard normal distribution)

When you search for the normal standard table, you get the following value:

[tex]P(Z <2) = 0.9772\\\\P(Z <-2) = 0.0228\\\\P(-2 <Z <2) = 0.9772 - 0.0228\\\\P(-2 <Z <2) = 0.9544[/tex]

Answer:

m<ALO=35°

Step-by-step explanation:

we know that

The right triangle AOL is congruent with the right triangle BOL

because

OA=OB=radius of the circle

OL is a common side

LA=LB ---> by applying the Pythagoras theorem

therefore

m<AOL=m<AOB/2

m<AOL=110°/2

m<AOL=55°

Remember that

m<AOL+m<ALO=90° ------> by complementary angles

m<ALO=90°-55°=35°

Answer:

11

Step-by-step explanation:

5.5 x 4= 22 divided by 2= 11

Final answer:

To compare the area of two squares, calculate each area by squaring the length of a side, then form a ratio. A square with a side length twice that of another has four times the area.

Explanation:

Calculating the Area of a Square and Comparing to Another Square

To calculate the area of a square, you need to multiply the length of one side by itself since all sides of a square are equal in length. If we have a square with a side length of 4 inches, its area would be 4 inches × 4 inches = 16 square inches. Now, if we take another square with dimensions that are twice the first square, its side length would be 8 inches.

The area of this larger square is 8 inches × 8 inches = 64 square inches. When we compare the area of the larger square to the smaller one, we create a ratio. The ratio of their areas is 64 to 16, or simplified, 4 to 1. This means the larger square has an area that is four times as big as the area of the smaller square.

Answer:

the correct answer is C). 3,600

Step-by-step explanation:

divide 36,000 by 10 and you get your answer hope this helps

p.s. you,re pretty

The correct answer is:

y = -4x + 3

Answer:

The equation "y = -4 x + 3" represents a line parallel to the line shown on the graph.

Step-by-step explanation:

The line shown on the graph corresponds to the equation "y = -4 x + 8".

All linear functions with the same slope are represented by parallel lines.

The slope of the function of the graph is -4 and the slope function of the answer is -4, too. Therefore both of them represents parallel lines.

The function "y = 4 x - 1" has got different slope, so it represents a different line.

Answer:

1/3(3.14)2^2(24)

Step-by-step explanation:

The volume of a cone is given by the formula;

1/3πr³

Considering the radius is 2 cm and the height is 24 cm (4 times the diameter).

Therefore;

Volume = 1/2(3.14)2²(24)

            This can be used to calculate the volume.

Answer:

A. 72 in^2.

Step-by-step explanation:

What you do is you have to use the formula for a surface area of a rectangular prism which is:

A=2(wl+hl+hw).

Your height is 3 inches.

Your width is 2 inches.

Your length is 6 inches.

You will plug that into the formula.

A=2(2*6+3*6+3*2).

A=2(12+18+6)

A=2(36)

A=72 in^2 is your answer.

Answer:

The Surface Area is 72 square inches

Step-by-step explanation:

2*3=6 and 6*2=12

2*6=12 and 12*2=24

6*3=18 and 18*2=36

36+24+12=72

Answer:96 km/h

Step-by-step explanation:

Answer:

he did a full circle turn around

Step-by-step explanation:

Answer:

The answer is D. 245

Step-by-step explanation:

I got it right on the quiz

Hope this help :)

Answer:

D

Step-by-step explanation:

To find the equation of the line, substitute the point (-5,1) and the slope 3/2 into the point slope form [tex]y - y_1 =m(x-x_1)[/tex].

The equation is [tex]y - 1 = \frac{3}{2}(x --5)\\y - 1 = \frac{3}{2}(x+5)[/tex]

Answer: 1. x>0

2. all real numbers

3. x>2

4. x<2

5. x>-2

6. x<0

Step-by-step explanation:

Answer:

Step-by-step explanation:

To have all the function are defined, all the values in the square root must be ≥ 0 and the value in the cubic can be all real number

1. s(x) = [tex]\sqrt{x}[/tex] <=> x ≥ 0

2. n(x) = [tex]\sqrt[3]{2-x}[/tex] <=> x belongs to all real number

3. z(x) = [tex]\sqrt{x-2}[/tex] <=> x-2 ≥ 0 <=> x ≥ 2

4. q(x) =  [tex]\sqrt{2-x}[/tex] <=> 2 -x ≥ 0 <=> x ≤ 2

5. h(x) = [tex]\sqrt{2+x}[/tex] <=> 2+x ≥ 0  <=> x ≥  -2

6. v(x) = [tex]\sqrt{-x}[/tex] <=> = -x ≥ 0 <=> x ≤ 0

Hope it will find you well.

A quadrilateral is a polygon with four sides. The area of the quadrilateral is 37.5 units².

A quadrilateral is a polygon with four sides.

The area of the quadrilateral is the sum of all the areas of triangles A, B, C, and rectangle D.

1.  Area of triangle A

[tex]\rm Area\ \triangle A=\dfrac{1}{2} \times Perpendicular \times Base[/tex]

                [tex]\rm =\dfrac{1}{2} \times 8\times 4\\\\=16\ units^2[/tex]

2. Area of triangle B

[tex]\rm Area\ \triangle B=\dfrac{1}{2} \times Perpendicular \times Base[/tex]

                [tex]\rm =\dfrac{1}{2} \times 5\times 5\\\\=12.5\ units^2[/tex]

3.  Area of triangle C

[tex]\rm Area\ \triangle C=\dfrac{1}{2} \times Perpendicular \times Base[/tex]

                [tex]\rm =\dfrac{1}{2} \times 4\times 3\\\\=6\ units^2[/tex]

4. Area of rectangle D,

[tex]\rm Area\ Rectangle\ D= Perpendicular \times Base[/tex]

                            [tex]\rm =1\times 3\\\\=3\ units^2[/tex]

[tex]\text{The area of the quadrilateral} = \triangle A+\triangle B+\triangle C+\rm Rectangle\ D[/tex]

                                             [tex]=16+12.5+6+3\\\\=37.5\rm\ units^2[/tex]

Hence, the area of the quadrilateral is 37.5 units².

Learn more about Quadrilateral:

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The line segment that’s hitting the y-axis at (0,4) will not change its position after being reflected.

Answer:

Step-by-step explanation:

The first graph will not change at all if reflected over the y-axis.  the other graphs will change.

Final answer:

The value that is two standard deviations above the mean for the depth of snow at Yellowstone's lower geyser basin is calculated to be 4.94 inches.

Explanation:

To find the value that is two standard deviations above the mean in a normally distributed set of data, you simply add two times the standard deviation to the mean. Given that the mean depth of snow at Yellowstone's lower geyser basin is 3.9 inches with a standard deviation of 0.52 inches, we perform the following calculation:

Value = Mean + (2 × Standard Deviation)

Value = 3.9 + (2 × 0.52)

Value = 3.9 + 1.04

Value = 4.94 inches

Therefore, two standard deviations above the mean is 4.94 inches of snow.

The value that is two standard deviations above the mean depth of the snow at Yellowstone National Park in April at the lower geyser basin is 4.94 inches.

The value that is two standard deviations above the mean is calculated as follows:

- Mean= 3.9 inches

- Standard deviation = 0.52 inches

To find the value that is two standard deviations above the mean, we multiply the standard deviation by 2 and then add this to the mean:

- Value = Mean + (2 × Standard deviation)

- Value = 3.9 + (2 × 0.52)

- Value = 3.9 + 1.04

- Value = 4.94 inches

The scale factor of triangle ABC to triangle DEF is 1/6.

Compare corresponding side lengths:

I observed that a side length of triangle ABC (2 units) is 6 times smaller than the corresponding side length of triangle DEF (12 units).

This initial comparison hinted at a scale factor of 1/6.

Checked other side lengths:

To confirm, I verified that the other side lengths also have a ratio of 1/6.

AB = 2 units, DE = 12 units (2/12 = 1/6)

AC = 4 units, DF = 24 units (4/24 = 1/6)

BC = 2 units, EF = 12 units (2/12 = 1/6)

Since all corresponding side lengths have a ratio of 1/6, this confirms that triangle ABC is a scaled-down version of triangle DEF with a scale factor of 1/6.

Complete question:

Answer:

Step-by-step explanation:

60 mph hope that helps

Answer:

the answer is 8

Step-by-step explanation:

if its wrong, blame math..way : )

Answer:

The greatest common factor of these two numbers is 8. :)

Step-by-step explanation:

The factors 64 and 88 have in common are 1,2,4 and 8. And the greatest of the preceding is 8, thus you get your answer. :)

Answer:

i think b but its probably wrong knowing my luck

Step-by-step explanation:

m∠KPF = 29°, m∠H = 129°. Using angle properties, we found m∠KPF by subtracting known angles from 360° and m∠H by alternate interior angles.

To solve this problem, we'll use several properties of angles in circles, particularly those formed by chords, secants, and tangents intersecting inside or outside a circle.

Given:

- PKHE is an inscribed quadrilateral.

- ∠E = 120°.

- ∠EPK = 51°.

- PF is parallel to EH.

We need to find:

- m∠KPF

- m∠H

Let's start by drawing the situation:

        P

       / \

      /   \

     /     \

    /_______\

   E         H

      K

Step 1: Determine m∠KPE

Since PF is parallel to EH, we have alternate interior angles:

m∠KPE = m∠EPK = 51°

Step 2: Find m∠KEH

Inscribed angle ∠KEH is half the measure of its intercepted arc, ∠E. So:

m∠KEH = 1/2× m∠E = 1/2× 120° = 60°

Step 3: Find m∠KPH

∠KPH is an exterior angle to triangle KPE:

m∠KPH = m∠KPE + m∠KEH

        = 51° + 60°

        = 111°

Step 4: Find m∠KPF

In quadrilateral KPFH, the sum of angles is 360°. So:

m∠KPF + m∠KPH + m∠E + m∠H = 360°

m∠KPF + 111° + 120° + m∠H = 360°

m∠KPF + m∠H = 360° - 111° - 120°

m∠KPF + m∠H = 129°

We'll use this relationship in the next step.

Step 5: Find m∠H

Using the fact that PF is parallel to EH, we have alternate interior angles:

m∠H = m∠KPF = 129°

Step 6: Find m∠KPF

From step 4:

m∠KPF + m∠H = 129°

m∠KPF + 129° = 129°

m∠KPF = 0°

So, the final answers are:

- m∠KPF = 0°

- m∠H = 129°

Answer:

98,470.4 cubic cm

Step-by-step explanation

Answer:   25x⁴ - 49

Step-by-step explanation:

  (5x² - 7)(5x² + 7)

= 5x²(5x² + 7)  - 7(5x² + 7)

= 25x⁴ + 35x² - 35x² - 49

= 25x⁴ + (       0      )  - 49

= 25x⁴ - 49

Answer:

The perimeter of rectangle is [tex]18\ cm[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

[tex]x=y+5[/tex] ----> equation A

[tex]120=xy+2x^{2}+2y^{2}[/tex]  ---> equation B (area of the constructed figure)

substitute the equation A in equation B

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}[/tex]

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]

using a graphing calculator -----> solve the quadratic equation

The solution is

[tex]y=2\ cm[/tex]

Find the value of x

[tex]x=y+5 ----> x=2+5=7\ cm[/tex]

Find the perimeter of rectangle

[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]

Answer:

The perimeter of the rectangle = 18 cm

Step-by-step explanation:

* The figure consists of one rectangle and four squares

* Lets put the dimensions of the rectangle and the four squares

- The width of the rectangle is x

∵ The length of the rectangle is 5 cm longer than the width

∴ The length of the rectangle is x + 5

∵ Area the rectangle = L × W

∴ Area rectangle = x(x + 5) = x² + 5x ⇒ (1)

* There are four squares constructed each in one side

  of the rectangle

- Two squares constructed on the length of the rectangle

∴ The length of the sides of the squares = x + 5

∵ Area the square = S²

∴ Its area = (x + 5)² ⇒ use the foil method

∴ Its area = x² + 10x + 25

∵ They are two squares

∴ Its area = 2x² + 20x + 50 ⇒ (2)

- Two squares constructed on the width of the rectangle

∴ The length of the sides of the squares = x

∴ Its area = x²

∵ They are two squares

∴ Its area = 2x² ⇒ (3)

- Area rectangle = x(x + 5) = x² + 5x ⇒ (3)

* Now lets make the equation of the area of the figure by

 adding (1) , (2) and (3)

∴ The area of the figure = 2x² + 20x + 50 + 2x² + x² + 5x  

                                         = 5x² + 25x + 50⇒ (4)

∵ The area of the figure = 120 cm² ⇒ (5)

* Put (4) = (5)

∴ 5x² + 25x + 50 = 120 ⇒subtract 120 from both sides

∴ 5x² + 25x +50 - 120 = 0 ⇒ add the like term

∴ 5x² + 25x -70 = 0 ⇒ divide both sides by 5

∴ x² + 5x - 14 = 0 ⇒ factorize it to find the value of x

∴ (x - 2)(x + 7) = 0

* Lets equate each bracket by 0

∴ (x - 2) = 0 ⇒ x = 2

∴ (x + 7) = 0 ⇒ x = -7 ⇒ rejected no -ve side length

∴ x = 2

* Now lets find the dimensions of the rectangle

∵ Length rectangle = x + 5

∴ Length rectangle = 2 + 5 = 7 cm

∴ Width rectangle = 2

∵ The perimeter of the rectangle = 2(L + W)

∴ The perimeter of the rectangle = 2(2 + 7) = 18 cm

* The perimeter of the rectangle = 18 cm

Answer:

-5 and 1

Step-by-step explanation:

Ask yourself these questions:

Where does the graph cross the X axis?  Or,

At what x's is y=0?

Answer:

It's C. 1/8 ÷ 2

Step-by-step explanation:

7. There is no tree diagram, sticking it as impossible to solve at the moment.

8.  The temperature went down 5 degrees and then goes up 7 degrees. The low temperature is -5.

9. The formula is [tex]\frac {3}{4} * \frac {1}{6}[/tex], or 1/8