Beth needs to fertilize her flowerbed, which is in the shape of a regular pentagon. A bag of fertilizer states that it can fertilize up to 150 square feet, but Beth is not sure how many bags of fertilizer she should buy. Each side of the pentagon is 15 feet long

Answer:

Sue's percentage profit = 9% on each tin of green paint she sells.

Step-by-step explanation:

Litres of green paints mixed = 50 litres

Ratio of litres of yellow paint and litres of blue paint = 1:4.

To determine the litres of yellow paint, we say:

[tex]yellow \: paint = \frac{1}{4} \times 50 = 10 \: litres[/tex]

To determine the litres of blue paint, we say:

[tex]blue \: paint = \frac{4}{5} \times 50 = 40 \: litres[/tex]

Since yellow paint is sold in 5 litres per tin and each tin cost £38; she has 10 litres of yellow paint in all. That implies that she has 10/5 = 2 tin of yellow paint. If one tin cost £38; 2 tin cost 2 × £38 = £76

Similarly,

Since blue paint is sold in 10 litres per tin and each tin cost £58; she has 40 litres of blue paint in all. That implies that she has 40/10 = 4 tin of blue paint. If one tin cost £58; 4 tin cost 4 × £58 = £232

Total cost of yellow and blue paints = £232 + £76

= £308

Since Sue sells all the green paint she makes in 10 litre tins at £89.32 per tin and she has 50 litres in all; we say: 50/10 litres = 5 tins = 5 × £89.32 = £446.60.

Thus, selling price of the green paint = £446.60

[tex]profit \: \% = \frac{selling \: price - cost \: price}{cost \: price} \times \frac{100}{1} [/tex]

[tex]profit \: \% = \frac{446.60 - 308}{308} \times \frac{100}{1} [/tex]

[tex]profit \: \% = \frac{138.60}{308} \times \frac{100}{1} [/tex]

[tex]profit \: \% = 0.45 \times 100[/tex]

[tex]profit \: \% = 45\%[/tex]

Sue's percentage profit for selling all the tins of green paint is 45%, having sold 5 tins. Therefore, Sue's percentage profit for selling each of the paint will be:

[tex]profit \: \% \: on \: each \: green \: tin = \frac{45}{5} = 9\%[/tex]

Hence, Sue's percentage profit for selling each tin of green paint is 9%.

Proof

9% × 5 tins of green paint = 45%

Final answer:

Sue's percentage profit on each tin of green paint she sells is approximately 44.94%. This is calculated by finding the total cost of inputs, subtracting from the total sales revenue, and then finding the profit ratio to the cost.

Explanation:

To calculate Sue's percentage profit on each tin of green paint she sells, we need to first determine the cost of producing the green paint and then subtract that cost from the selling price. The green paint is produced in a ratio of 1:4 yellow to blue paint, making 50 litres total. Therefore, Sue uses 10 litres of yellow paint and 40 litres of blue paint to make 50 litres of green paint.

Yellow paint costs £38 for a 5-litre tin, so two tins are needed (costing £76 total) to get the required 10 litres. Blue paint costs £58 for a 10-litre tin, so four tins are needed (costing £232 total) to get 40 litres. This brings the total cost to £308 for 50 litres of green paint.

Sue sells her green paint at £89.32 per 10-litre tin. Therefore, for 50 litres, she gets 5 tins x £89.32 = £446.60.

The profit Sue makes is the selling price minus the cost price, which is £446.60 - £308 = £138.60. To find the percentage profit per tin, divide the profit by the cost and multiply by 100:

(£138.60 / £308) x 100 = 44.94%

Therefore, Sue's percentage profit on each tin of green paint she sells is approximately 44.94%.

To solve the system of equations y=x^2-3x+2 and y=-9x-3, set them equal and solve the resulting quadratic equation using the quadratic formula to obtain the solutions for x; then substitute back to find y.

To solve the system of equations given by y = x2 - 3x + 2 and y = -9x - 3, we must find the values of x and y that satisfy both equations simultaneously. Since both expressions are equal to y, we can set them equal to each other to find the x-values that satisfy both equations:

x2 - 3x + 2 = -9x - 3

Rearrange the equation by adding 9x and 3 to both sides:

x2 + 6x - 1 = 0

This is a quadratic equation, which we can solve by factoring, completing the square, or using the quadratic formula. In this case, factoring is not straightforward, so we may opt for the quadratic formula:

x = (-b ± √(b2 - 4ac)) / (2a)

Here, a = 1, b = 6, and c = -1. Plugging these into the quadratic formula gives us:

x = (-6 ± √(36 + 4)) / 2

x = (-6 ± √(40)) / 2

x = (-6 ± 2√(10)) / 2

x = -3 ± √(10)

So the solutions for x are x = -3 + √(10) and x = -3 - √(10). To find the corresponding y-values, substitute these x-values back into either of the original equations.

The solution to the system of equations is:
(x, y) = (-1, 6) and (-5, 42)

To solve the system of equations:

1. Substitute the expression for y from the second equation into the first equation. This gives us:

x^2 - 3x + 2 = -9x - 3

2. Rearrange the equation to bring all terms to one side, setting the equation equal to zero:

x^2 - 3x + 9x + 2 + 3 = 0

x^2 + 6x + 5 = 0

3. Factor the quadratic equation:

(x + 1)(x + 5) = 0

4. Apply the zero product property to find the values of x that satisfy the equation:

x + 1 = 0 or x + 5 = 0

x = -1 or x = -5

5. Substitute these values of x back into either equation to find the corresponding values of y. Let's use the second equation:

For x = -1:
y = -9(-1) - 3 = 9 - 3 = 6

For x = -5:
y = -9(-5) - 3 = 45 - 3 = 42

Therefore, the solution to the system of equations is:
(x, y) = (-1, 6) and (-5, 42)

The dependent variable is muscle mass.

The dependent variable in this relationship is muscle mass.

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Given:

AB is the diameter of a circle.

m∠CAB = 26°

To find:

The measure of m∠CBA.

Solution:

Angle formed in the diameter of a circle is always 90°.

⇒ m∠ACB = 90°

In triangle ACB,

Sum of the angles in the triangle = 180°

m∠CAB + m∠ACB + m∠CBA = 180°

26° + 90° + m∠CBA = 180°

116° + m∠CBA = 180°

Subtract 116° from both sides.

116° + m∠CBA - 116° = 180° - 116°

m∠CBA = 64°

The measure of m∠CBA is 64°.

The size of angle CBA is 128 degrees.

To find the size of CBA, we can use the fact that angles in a triangle add up to 180 degrees. Since AB is a diameter, it divides the circle into two semicircles, and angle CAB is an inscribed angle that is half the measure of the central angle.

Therefore, m(CAB) = 26 degrees, and m(CBO) = 2 * 26 = 52 degrees. Since angle CBA is an exterior angle of triangle CBO, it is equal to the sum of the remote interior angles, which is 180 - 52 = 128 degrees.

So, the size of CBA is 128 degrees. The answer is option D. 74.

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Answer:

Shapes 1 and 3 are congruent

Step-by-step explanation:

The only thing different between them is that the first one is tilted to look different.

Answer:

the 1st and 3rd one.

Step-by-step explanation:

the first 3 are similar in shape but, the 1st and 3rd one are congruent because they have the same size and shape.

Answer:

11

Step-by-step explanation:

Formula for finding a circumference = [tex]2\pi r[/tex]

You are given the circumference which is [tex]22\pi[/tex]

[tex]22\pi =2\pi r[/tex]

So you divide both sides by [tex]2\pi[/tex] and [tex]\pi[/tex] cancels out

[tex]\frac{22\pi }{2\pi } =\frac{2\pi }{2\pi } *r[/tex]

r=11

Answer:

11

Step-by-step explanation:

To calculate the area of Spencer's 7x7 quilt, each square patch measuring 1 3/4 inches is calculated for area (3.0625 sq. in.) and then multiplied by the total number of patches (49), resulting in a total quilt area of 150.0625 square inches.

Spencer made a quilt for his cousin's doll with a 7x7 array of square patches. To find the area of the whole quilt, we need to calculate the area of one patch and then multiply by the total number of patches. The length of each patch is 1 3/4 inches, which can also be represented as 1.75 inches.

First, we find the area of one patch:

Since there are 49 patches in total (7 patches per row × 7 rows), we then find the total area:

Therefore, the area of Spencer's quilt is 150.0625 square inches.

Final answer:

The area of Spencer's quilt is 150.0625 square inches.

Explanation:

Spencer made a quilt for his cousin's doll that had a 7x7 array of square patches, each measuring 1 3/4 inches in length. To find the area of the quilt, you would calculate the area of one patch and then multiply it by the total number of patches in the quilt.

First, convert the inches to a decimal to make the calculation easier:

Area of one square patch = length × width

Since the patches are square, the length and width are the same:

Area of one patch = 1.75 inches × 1.75 inches = 3.0625 square inches

To find the total area of the quilt:

Total area of quilt = area of one patch × number of patches

There are 7 rows and 7 columns in the quilt:

Total patches = 7 × 7 = 49

Total area of quilt = 3.0625 square inches × 49 = 150.0625 square inches

Therefore, the area of the whole quilt is 150.0625 square inches.

Answer:

7

Step-by-step explanation:

To find the slop, use (rise/run)

The y goes from 0 to 7/3

The x goes from 0 to 1/3

This means it would be (7/3)/(1/3)

This equals 7 as when you divide fractions, the second fraction goes to its reciprocal and you multiply

7/3 * 3/1

You can eliminate both 3 leaving you with 7/1 which is 7

Answer:

0

Step-by-step explanation:

1/3(21)-1-1/2(12)

7-1-6=6-6=0

Answer:

Step-by-step explanation:

$

1050

Explanation:

To calculate interest the formula is :  

P

r

t

=

i

where P= Principle, r=rate as a decimal, t+ time in years.

(assuming simple interest)

P

r

t

=

i

5000

⋅

0.07

⋅

3

=

i

i

=

$

1050

Answer:

1050

Step-by-step explanation:

Answer:

This is true because negative and positive is positive that why there is a addition sign in the middle and positive 40 becomes negative

Step-by-step explanation:

Answer: 205 buttons

Step-by-step explanation:

Garcia has 2 button collections. One has 321 buttons in it. The other has 704 buttons. The total button collection will be:

= 321 + 704 = 1025

Since she wants to divide it equally among 5 friends, we divide 1025 by 5. This will be:

= 1025 ÷ 5

= 205

Each friend will get 205 buttons.

Answer:

Each friend will receive 205 buttons

Step-by-step explanation:

In this question, we are tasked with calculating the number of buttons each of 5 Garcia's friend will receive

Firstly, we will need to find the total number of buttons available

That would be 321 + 704 = 1025 buttons

Now to find the distribution per friend, we simply divider the total by 5

That would be 1025 buttons ÷ 5 = 205 buttons

This means that each of the five friends will receive 205 buttons each

Answer:

it is many triangles

Step-by-step explanation:

Answer:

They can be chosen in 6,840 different ways

Step-by-step explanation:

In this question, we are tasked with calculating the number of ways in which the 1st, 2nd and 3rd students can be chosen.

For the first position, we have 20 people vying for the position and we are to select only one for the position.

The number of ways this is achievable is 20C1 ways = 20 ways

For the second position, we are left with 19 students vying for the position and we are to select only one for the position. The number of ways this is possible is 19C1 ways = 19 ways

For the third position, we are left with 18 students vying for the position. The number of ways this is possible is 18C1 ways = 18 ways

Thus, the total number of ways this cane be done is; 20 ×19 ×18 = 6,840 ways

Answer:

2/7

Step-by-step explanation:

Each time you play, you get 1 number. Since 8/28 numbers win, you have a 8/28 chance to win if you buy one ticket. 8/28 = 2/7

Answer:

a) 0.0156

b) 0.4219

c) 0.1406

Step-by-step explanation:

We are given the following information:

We treat adult having type O+ blood as a success.

P(Adult have type O+ blood) = 0.25

Then the number of adults follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 3

a) All three are type O+

[tex]P(x =3)\\= \binom{3}{3}(0.25)^3(1-0.25)^0\\= 0.0156[/tex]

b) None of them is type O+

[tex]P(x =0)\\= \binom{3}{0}(0.25)^0(1-0.25)^3\\= 0.4219[/tex]

c) Two out of the three are type O

[tex]P(x =2)\\= \binom{3}{2}(0.25)^2(1-0.25)^1\\= 0.1406[/tex]

Using the principle of binomial probability, the probability o the required events are :

Recall :

A.) Probability that all 3 are O+ :

x = 3

P(x = 3) = 3C3 × 0.25³ × 1 = 0.0156

B.) Probability that none 3 are O+

x = 0

P(x = 3) = 3C0 × 1 × 0.75³= 0.4219

C.) Probability that 2 out of the three are O+

x = 2

P(x = 2) = 3C2 × 0.25² × 0.75¹ = 0.1406

Therefore, the required probabilities are : 0.0156, 0.4219 and 0.1406 respectively.

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Answer:

Step-by-step explanation:

This is an increase of 9

Or, as a percentage (rounded to two decimal places):

an increase of 50%

Answer:

1. 26.6

2. 12.3

3. 23.3

4. 10.9

Step-by-step explanation:

1. tan(31) = 16/x

x = 16/tan(31)

x = 26.62847172

2. sin(43) = x/18

x = 18sin(43)

x = 12.27597048

3. cos(53) = 14/x

x = 14/cos(53)

x = 23.26296198

4. cos(33) = x/13

x = 13cos(33)

x = 10.90271738

Answer:

1. 26.6 units

2. 12.3 units

3. 23.3 units

4. 10.9 units

Step-by-step explanation:

1. We have the opposite and adjacent sides here for angle 31 degrees. So we need to use tangent, which is opposite / adjacent:

[tex]tan(31)=16/x[/tex]

[tex]x=16/(tan(31))[/tex] ≈ 26.6 units

2. We have the opposite and hypotenuse sides here for angle 43 degrees. So we need to use sine, which is opposite / hypotenuse:

[tex]sin(43)=x/18[/tex]

[tex]x=18*sin(43)[/tex] ≈ 12.3 units

3. We have the adjacent and hypotenuse sides here for angle 53 degrees. So we need to use cosine, which is adjacent / hypotenuse:

[tex]cos(53)=14/x[/tex]

[tex]x=14/(cos(53))[/tex] ≈ 23.3 units

4. We have the adjacent and hypotenuse sides here for angle 33 degrees. So we need to use cosine, which is adjacent / hypotenuse:

[tex]cos(33)=x/13[/tex]

[tex]x=13*cos(33)[/tex] ≈ 10.9 units

Hope this helps!

Answer:

27Pi cm2

Step-by-step explanation:

took the test

27π square centimeters(Volume) of metal was used to make the holder.

The amount of space within a cylinder is its volume. You can find it by dividing the base area by the height.

Given that, a candle holder of metal whose radius is 3 cm and height is also 3 cm. Since the given object is a cylinder. Hence,

volume of candle holder = Area of base * height

the volume of candle holder = π 3² * 3 = 27π

Therefore, the metal used in the candle holder is 27π square centimeters (Volume).

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Answer:

option A is the correct one

Step-by-step explanation:

The product of the expression negative 9 x (5 minus 2x) is 18x² - 45x.

The correct option is c) negative 18 x minus 45 x.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given expression:

Negative 9 x (5 minus 2x).

To find the product:

First, we simplify the expression,

-9x (5 - 2x)

Solving the parenthesis,

-9 (5 - 2x)

= -45x + 18x².

= 18x² - 45x.

= 18 x squared minus 45 x

Therefore, 18x² - 45x is the required expression.

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An expression for the profit of the company is 26x - 0.0002x^2 - 120,000.

To find the expression for the profit of a company, we need to subtract the cost from the revenue.

The cost of the company is given by the expression 14x + 120,000, where x represents the quantity of the product being produced or sold.

The revenue of the company is given by the expression 40x - 0.0002x^2, where x represents the quantity of the product being produced or sold.

To find the profit, we subtract the cost from the revenue:

Profit = Revenue - Cost

Profit = (40x - 0.0002x^2) - (14x + 120,000)

To simplify the expression, we distribute the negative sign:

Profit = 40x - 0.0002x^2 - 14x - 120,000

Combining like terms:

Profit = (40x - 14x) - 0.0002x^2 - 120,000

Simplifying further:

Profit = 26x - 0.0002x^2 - 120,000

Therefore, an expression for the profit of the company is 26x - 0.0002x^2 - 120,000.

Final answer:

The profit of a company is the difference between its total revenue and costs, and can be calculated using the formula P = R - (14x - 0.0002x²), where P is profit, R is revenue, and x is the number of units.

Explanation:

To calculate the expression for the profit of the company, we need to find the difference between the total revenue and the total cost.

Given the cost can be modeled by 14x - 0.0002x2, and assuming the revenue is R, the profit P can be represented as:

P = R - (14x - 0.0002x²)

If we are given a specific value for the revenue, we would substitute it in place of R to find an explicit expression for P. For instance, if the revenue is $200,000, the profit formula would be:

P = $200,000 - (14x - 0.0002x²)

It's important to note that the profit decreases as the cost increases, and when costs exceed revenue, the company experiences a loss.

FOLLOW ME FOR CLEARING YOUR NEXT DOUBT

Hey there!

The Distributive Property states that

a(b+c)=ab+ac

Now simplify this expression:

6.3(m+7)+m+2

Distribute 6.3:

6.3m+44.1+m+2

Combine Like terms:

6.4m+m+44.1+2

7.4m+46.1

With this we're done!

Hope everything is clear.

Let me know if you have any questions!

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[tex]\boxed{An~Emotional~Helper}[/tex]

Answer:

the base length of the triangle is 4 units, u can count that. and the height of triangle is 2 units, thats the dotted line one. and the equation of triangle area is (length x height) divided by 2so in this case it'll be (4x2) /2=4 square units.

Step-by-step explanation:

Answer:

The base is 7 and the height is 9

Step-by-step explanation:

vertices Q(-1,1), R(6, 1), S(6-8), and T(-1,-8)

If you look at the coordinates, you will notice that Q and R lie on line y = 1

and S and T lie on the line y = -8

so  line QR || line ST

that means the height of this rectangle is  |1 - -8| = 9

the  length must be  from point Q to R

length = |-1 - 6| = 7

dimension is  7 by 9

Answer: 2m+5=15

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

2x+5=15 can represent this situation. 15-5=10... 10/2= 5

Answer:

hunter

Step-by-step explanation:

Final answer:

Hunter is correct that the hypotenuse of a right triangle acts as the diameter of its circumcircle, with the circumcenter located at the midpoint of the hypotenuse.

Explanation:

When constructing a circumcircle of a right triangle, Hunter's assertion is correct. According to a well-known theorem, the hypotenuse of a right triangle will be the diameter of the circumcircle that can be drawn around the triangle. This is because the center of the circumcircle, known as the circumcenter, is equidistant from all vertices of the triangle, and for a right triangle, this point is the midpoint of the hypotenuse.

Since the circumcenter is the midpoint of the hypotenuse, and the hypotenuse is the longest side of a right triangle, it will also serve as the diameter of the circumcircle. The radius of the circle, therefore, extends from this midpoint to any of the triangle’s vertices. Daniel's statement that the circumcenter would be located inside the triangle is incorrect for a right triangle, though it might be true for acute or obtuse triangles.

Answer: Four is the exterior angle.

Step-by-step explanation:

Answer: The height of the tank is 9.02 feet

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Volume of a cylinder = π radius² x height

Replacing with values given:

7252 = 3.14 ( 16 )² h

Solving for h (height)

7252 / 3.14(16)² =h

7252 /3.14 (256) =h

7252 / 803.84 = h

9.02 =h

The height of the tank is 9.02 feet

Feel free to ask for more if needed or if you did not understand something.

Answer:

9.02

Step-by-step explanation:

Answer:

Therefore I would earn $532,761 more on the first investment than in the second investment.

Step-by-step explanation:

The formula of compound interest

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

Compound interest [tex]I=A-P[/tex]

A= Amount after n years

P= Principal

r=Rate of interest

n= Number of years

First investment,

P₁=$22,000, r=12%=0.12 and n=30 years

[tex]A_1= 22,000(1+0.12)^{30}[/tex]

    =659,118.28

   ≈$659,118

[tex]I_1[/tex]= [tex]A_1[/tex]-P₁

  =$(659,118-22,000)

 =$637,118

Second investment,

P₂=$22,000, r=6%=0.06 and n=30 years

[tex]A_1= 22,000(1+0.06)^{30}[/tex]

    =126,356.81

   ≈$126,357

[tex]I_2[/tex]= [tex]A_2[/tex]-P₂

  =$(126,357-22,000)

  =$104357

[tex]I_1-I_2[/tex]

=$(637,118-104,357)

=$532,761

Therefore I would earn $532,761 more on the first investment than in the second investment.

Answer:

113.1

Step-by-step explanation:

V=[tex]\frac{4}{3}[/tex]πr³

Answer:

the answer is 1,555.2

Step-by-step explanation:

Answer:1.5552x10 cubed

Step-by-step explanation: