Brayden and his friend have built a round concrete patio in Brayden's backyard.
The diameter of the patio is 14 feet.
Brayden wants to paint it and must calculate the area.
What is the area to the nearest square foot?
Use 3.14 for л.

A coffee's temperature changed by -54°F in =

\( = 22\frac{1}{2} \: minutes\)

The temperature change in the coffee each minute :-

\( = - 54 \div 22\frac{1}{2} \)

\( = - 54 \div \frac{(2 \times 22 + 1)}{2} \)

\( = - 54 \div \frac{45}{2} \)

\( = - 54 \times \frac{2}{45} \)

\( = \frac{ (- 54 \times 2)}{ \: \: 45} \)

\( = \frac{ - 108}{ \: \: \: 45} \)

\(\color{magenta} = - 2.4°F\)

Therefore , the temperature change in the coffee each minute was = -2.4°F .

Step-by-step explanation:

you can simply multiply things out.

4/9 × y = 8/3

4y = 9×8/3 = 3×8 = 24

y = 6

or you could have transformed the right hand side into a fraction of the same denominator (9) :

8/3 = 8/3 × 3/3 = (8×3)/(3×3) = 24/9

4/9 × y = 24/9

that means 4y = 24

y = 6

Step-by-step explanation:

something is missing here.

it is not clear, what exactly is 27 km. only the side of the orange triangle ? or the whole distance to the 90 degree angle ?

but in both cases that is not enough. we need some information about the split ratio of the orange side and the white side. it some angles in the graphic.

otherwise I can simply keep the given sides with their lengths but freely move the line between the orange and white triangles. there are infinite many solutions.

is it meant to be an isoceles triangle (2 equal sides) ? it certainly does not look like it, but that would be the only case where the given information can lead to a solution.

under that assumption the baseline of the white triangle is also 27 km.

the first side is 9km.

the second side we get via Pythagoras :

27² = 9² + x²

729 = 81 + x²

648 = x²

x = 25.46 km

now, since this is a right-angled triangle we can (especially to calculate the area) also consider the two sides enclosing the 90 degree angle as baseline and height.

the area of a triangle is baseline×height/2

area = 9×25.46/2 = 114.55 km²

Answer:

1-0.2=0.8

0.8*3300= 2640

Original price = 3300

sale = 20% = 3300×20/100 = 660

Selling price= 3300-660= 2640 rs

the sale price of the bicycle is 2640 Rs

Answer:

D. 49.314 ft²

Step-by-step explanation:

Area = 1/2 s² sinФ

= 1/2 * 15² * sin(26)

= 49.314 ft²

Neither of Nicole and Kiri are correct that evaluating the conditional If 15 is a prime number, then 20 is divisible by 4.

Nicole reasoning is incorrect because despite the fact that 20 is divisible by 4, it does not mean the conditional is true. The conditional states that “15 is a prime number”- this is incorrect. Because this is incorrect the validity of the conclusion does not justify the validity of the hypothesis. Kiri’s reasoning is inaccurate despite the fact that his explanation of the hypothesis is correct, the hypothesis has no direct implication on the conclusion.

Hence, their belief that the conditional is true are both wrong. A conditional is only true if the premise for that conditional is first true in itself and also directly affects the conclusion.

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Answer:

x=−2

y=7

Step-by-step explanation:

5x+2y=4

x−3y=−23

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

5x+2y=4,x−3y=−23

To make 5x and x equal, multiply all terms on each side of the first equation by 1 and all terms on each side of the second by 5.

5x+2y=4,5x+5(−3)y=5(−23)

Simplify.

5x+2y=4,5x−15y=−115

Subtract 5x−15y=−115 from 5x+2y=4 by subtracting like terms on each side of the equal sign.

5x−5x+2y+15y=4+115

Add 5x to −5x. Terms 5x and −5x cancel out, leaving an equation with only one variable that can be solved.

2y+15y=4+115

Add 2y to 15y.

17y=4+115

Add 4 to 115.

17y=119

Divide both sides by 17.

y=7

Substitute 7 for y in x−3y=−23. Because the resulting equation contains only one variable, you can solve for x directly.

x−3×7=−23

Multiply −3 times 7.

x−21=−23

Add 21 to both sides of the equation.

x=−2

The system is now solved.

x=−2,y=7

Graph if needed:

Answer:

I don;t know if you need the graph

Step-by-step explanation:

Now, we have 4 letters to arrange, with 2 \( y \)'s and 2 \( z \)'s. Using the same formula as before, the number of arrangements is \( \frac{4!}{2!2!} \).

To find all the anagrams of \( x^{2} y^{3} z^{2} \) that do not contain two consecutive \( y \)'s, we need to consider the different arrangements of the letters \( x, y, y, y, z, z \). First, let's find the total number of arrangements. We have a total of 6 letters, but the letter \( y \) appears three times and the letter \( z \) appears twice. Therefore, the total number of arrangements is given by the formula \( \frac{6!}{3!2!} \).

Next, we need to exclude the arrangements that have two consecutive \( y \)'s. To do this, we will consider the two \( y \)'s as a single unit. This reduces the problem to arranging the following letters:  \( x, yy, z, z \). Therefore, the number of anagrams of \( x^{2} y^{3} z^{2} \). that do not contain two consecutive \( y \)'s.

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There are two anagrams of \(\( x^{2} y^{3} z^{2} \)\)that do not contain two consecutive \(\( y \)'s.\)

To list all the anagrams of\(\( x^{2} y^{3} z^{2} \)\) that do not contain two consecutive \(\( y \)'s\), we can use the concept of permutations. An anagram is a rearrangement of the letters or variables in a given expression.

First, let's consider the arrangement of the variables:\(\( x^{2} y^{3} z^{2} \).\)We have two\(\( x \)'s, three \( y \)'s, and two \( z \)'s.\)

To avoid having two consecutive\(\( y \)'s\), we can start by fixing one \(\( y \)\)in the first position. Then, we have two remaining\(\( y \)'s\) to arrange in the remaining positions. Using permutations, we find that there are\(\( 2P2 = 2 \)\)ways to arrange the remaining two\(\( y \)'s.\)

Next, we have\(\( x^{2} \) and \( z^{2} \)\)to arrange. Since they are identical, there is only one way to arrange them.

Multiplying the results together, we find that there are \(e \( 2 \times 1 = 2 \)\) anagrams of \(\( x^{2} y^{3} z^{2} \)\)  that do not contain two consecutive \( y \)'s.

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Answer:

Option (C)

Step-by-step explanation:

In this question we will use the property " similarity of the triangles".

If DE and AC are parallel two triangles BED and BCA will be similar, corresponding sides of the triangles will be proportional.

\(\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}\)

Option (A).

\(\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}\)

\(\frac{22+12}{12}=\frac{14+26}{14}\)

\(\frac{34}{12}=\frac{40}{14}\)

\(\frac{17}{6}=\frac{20}{7}\)

But \(\frac{17}{6}\neq \frac{20}{7}\)

Therefore, given triangles are not similar.

AC and DE are not parallel.

Option (B).

\(\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}\)

\(\frac{25}{25-7}=\frac{21+9}{21}\)

\(\frac{25}{18}=\frac{30}{21}\)

\(\frac{25}{18}=\frac{10}{7}\)

But \(\frac{25}{18}\neq \frac{10}{7}\)

Therefore, AC and DE are not parallel.

Option (C).

\(\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}\)

\(\frac{22.5+15}{15}=\frac{40}{40-24}\)

\(\frac{37.5}{15}=\frac{40}{16}\)

2.5 = 2.5

Therefore, AC║DE.

Option (D).

\(\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}\)

\(\frac{17.5+5}{17.5}=\frac{20.4+6}{20.4}\)

\(\frac{22.5}{17.5}=\frac{26.4}{20.4}\)

\(\frac{9}{7}=\frac{22}{17}\)

But \(\frac{9}{7}\neq \frac{22}{17}\)

Therefore, AC and DE are not parallel.

Option (C) will be the answer.

Answer:

C

Step-by-step explanation:

Answer:

x + 6 = -6

Step-by-step explanation:

Assuming x = -6

\(x+6=0\)

Subtract 6

\(x+6-6=0-6\)

Simplify arithmetic

\(x=0-6\)

Simplify arithmetic(again)

\(x=-6\)

we technically solved the equation right at the beginning when we assumed x was equal to -6 in order to group the constants to the right.

Hope this helps, have a great day!

the rate at which water is being pumped into the tank in cubic centimeters per minute. is 1508527.582 cm³/min

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 8900 cm³/min,

dV/dt = k - 8900

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 11 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

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the answer will be thirty three cm.

The price of the stereo system after the markup was $691.20.

The original price of the stereo system was $720.

During the sale, the price was reduced by 20%, which is equivalent to multiplying by (1 - 0.2) = 0.8.

The discounted price was:

720 × 0.8 = $576

After the sale, the discounted price was marked up by 20%

It is equivalent to multiplying by (1 + 0.2) = 1.2.

So the final price was 576 × 1.2

= $691.20

Therefore, the price of the stereo system after the markup was $691.20.

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If the cost of one paperback book is less than $1, he would receive even more change.

To solve this problem, we need to know the cost of one paperback book. Unfortunately, that information is missing from the question. Without it, we cannot determine the total cost of the 5 paperback books and therefore cannot calculate Prakash's change.

However, we can make an educated guess based on the fact that the question mentions both paperback and hardcover books. Typically, hardcover books are more expensive than paperbacks, so we can assume that the cost of one paperback book is less than the cost of one hardcover book.

Assuming that each hardcover book costs $10, the total cost of 3 hardcover books would be $30. If Prakash gives the clerk $20 bills, he would pay $60 in total. If we subtract the cost of the 3 hardcover books ($30) from the total amount paid ($60), we are left with $30.

This is the maximum amount of change Prakash could receive if each paperback book costs $1.

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Answer:

-6

Chang the - to -1 cause that’s what is means multiple and get -6

The total amount that Jimmy has saved is $420.

Ratio shows the relationship between two or more numbers. It is the  number of times that one value is contained within other value.

Total amount saved = (sum of ratios x total value of R5 saved) / ratio that represents R5 saved

Sum of ratios = 2 + 5 + 7 = 14

Total value of R5 saved = 12 x 5 = R60

= (14 x 60) / 2 = $420

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Answer:

A

Step-by-step explanation:

slope is rise over run 4/1 so the slope is 4 and intercept is 3.

Answer:

Step-by-step explanation:

0.000000005% can be written as a fraction: 0.000000005 / 100

Answer: x = 20

5 x 1 - (3x/5) = -7

5 - (3x/5)= -7

5 + 7 = 3x/5

12 = 3x/5

12 x 5 = 3x

60 = 3x

60/3 = 3x/3

20 = x

Answer: 13:1

Step-by-step explanation:

convert 8 2/3 into a improper fraction: 26/3

now you have:  26/3: 4/6

find LCD (6)

52/6: 4/6

reduce further with the gcf ( GCF of 54 and 4 is 4)

divide by GCF

52 ÷ 4 = 13

4 ÷ 4 = 1

the ratio is 13:1

Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

Answer:

B

Step-by-step explanation:

NOTE:

it might be wrong since im in geometry, not algebra, i used to know this

A 45°-45°-90° right triangle is also called an isosceles right triangle.An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent.

The most important formula associated with any right triangle is the Pythagorean theorem. According to this theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of the right triangle. Now, in an isosceles right triangle, the other two sides are congruent. Therefore, they are of the same length “l”. Thus, the hypotenuse measures h, then the Pythagorean theorem for isosceles right triangle would be:

(Hypotenuse)2 = (Side)2 + (Side)2

h² = l² + l²

h² = 2l²

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The correct answer choice:

The student would be able to afford the in-state cost for one year at a public 2-year college.

The correct option is D.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

A student is planning to attend college in 5 years.

The student has saved $1,200 and plans to save another $50 per month over the next 60 months.

The total savings,

= 1200 + (50 x 60)

= $4200

That is equivalent to the cost of one year at a public 2-year college.

Therefore, the saving amount is equivalent to the cost of one year at a public 2-year college.

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The table shows the cost per year of attending different types of colleges.

A student is planning to attend college in 5 years. The student has saved $1,200 and plans to save another $50 per month over the next 60 months.

Based on this information about the student's plan, which statement about the possible choices for a college is true?

Answer choices

The student would be able to afford the cost for one year at a private 4-year college.

The student would be able to afford out-of-state cost for half a year at a 4-year public college.

The student would be able to afford in-state cost for half a year at a public 4-year college.

The student would be able to afford in-state cost for one year at a public 2-year college.

Given:

1 chocolate chip cookie recipe = 12 cup of chocolate chips per batch.

Alonzo wants to make 3 12 batches.

Lets's find the number of chocolate chips he will need.

Number of batches he wants to make is = 3 x 12 = 36 batches

SInce 1 chocolate chip cookie recipe calls for 12 cup of chocolate chips per batch, we have:

The formula that can be used to determine the value of motorcycle n years after it was purchased is given as follows:

\(a_n = 0.8a_{n - 1}, n \geq 1\)

The first step is obtaining the type of the function, which is exponential, as the rate of change is multiplicative, and not additive.

The rate of change of the exponential function is calculated as follows:

y = 4000/5000 = 3200/4000 = ... = 0.8.

Hence the recursive sequence that gives the value of the motorbike after n years is the first option, given as follows:

\(a_n = 0.8a_{n - 1}, n \geq 1\)

The problem is given by the image shown at the end of the answer.

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Answer:

the first option is the answer, r = √6

Step-by-step explanation:

\(hypotenuse = \sqrt{opposite {}^{2} + adjacent {}^{2} } \)

hypotenuse = q = √12

adjacent = p = √6

opposite = r

substitute the values into the hypotenuse formula

\(q = \sqrt{r {}^{2} + p {}^{2} } \)

\( \sqrt{12} = \sqrt{r {}^{2} + ( \sqrt{6} ) {}^{2} } \)

\(( \sqrt{12} ) {}^{2} = r {}^{2} +6\)

\(12 = r {}^{2} + 6\)

\(12 - 6 = r {}^{2} \)

\(6 = r {}^{2} \)

\( \sqrt{6} = r\)

\(r = \sqrt{6} \)