Find the area of the triangle

The statement that describes when the plans are based on the same number of aerobic exercise sessions is:

The number of strength-training exercises and aerobic exercises per week is calculated as follows:

Let a be the number of strength-training exercises and b be the number of aerobic exercises per week respectively.

For the beginner plan:

15a + 20b = 90  eqn. (1)

For the advanced plan:

20a + 30b = 130 eqn. (2)

Solving the simultaneous equation by elimination method:

Multiply eqn. (1) by 3 and eqn. (2) by 2

45a + 60b = 270 eqn. (3)

40a + 60b = 260 eqn. (4)

Subtract eqn. (4) from eqn. (3)

5a = 10

a = 2

Substitute a = 2 in eqn (2)

b = 3

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Complete question:

A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week.

Which statement describes when the plans are based on the same number of aerobic exercise sessions?

Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.

Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.

Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.

Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.

Answer:

0.0001

Step-by-step explanation:

Debra needs 13.875 cups of fertilizer.

First, let's convert the garden's length and width to square yards:

9 (1/3) yards * 12 yards = 111 square yards

Now we can find out how many cups of fertilizer Debra needs:

111 square yards * (1/8 cup) = 13.875 cups

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer. The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier. It is used for combining groups of identical size.

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The number is 21.

"Information available from the question"

I am a two digit odd number I am a factor of 84 and also a multiple of 7.

Now,  The factors of 84 are:

1 × 84

2 × 42

3 × 28

4 × 21

6 × 14

7 × 12

The positive multiples of 7 are:

7,14,21,28,35,42,49,56,63,70,77,84

The factors of 84 that are also multiples of 7 are:

84,42,28,21,14,7

You are given that the number is odd.

The odd ones are 7 and 21.

It could be either.

7 is a factor of 84.

7 is a multiple of 7.

7 is odd.

21 is a factor of 84.

21 is a multiple of 7.

21 is odd.

Then the number has to be 21.

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Answer:

a) 38.40 yd  (2 dp)

b) 211.18 yd²  (2 dp)

Step-by-step explanation:

Formula

\(\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)\)

\(\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2\)

\(\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}\)

Calculation

Given:

\(\begin{aligned}\implies \textsf{Arc length} &=2 \pi (11)\left(\dfrac{200^{\circ}}{360^{\circ}}\right)\\ & = 22 \pi \left(\dfrac{5}{9}\right)\\ & = \dfrac{110}{9} \pi \\ & = 38.40\: \sf yd \:(2\:dp)\end{aligned}\)

\(\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{200^{\circ}}{360^{\circ}}\right) \pi (11)^2\\& = \left(\dfrac{5}{9}\right)\pi \cdot 121\\& = \dfrac{605}{9} \pi\\& = 211.18\: \sf yd^2 \:(2\:dp)\end{aligned}\)

Please note:  As you have not specified if π should be approximated, I have not used an approximation for π.

Answer:

76 unit

Step-by-step explanation:

because added the rectangle size and added the 60 with 16

Answer

Part 1

Step-by-step explanation:

T2=3(5)-12=3

T3=-3

T4=-21

T5=-75

Given the right triangle:

Where a is the short side. Then, using the definition of the sine function:

But we know that:

Finally:

Answer:

\(white \: socks \: number = 6 \\ brown \: socks \: number = 5 \\ \frac{w \: s \: n}{b \: s \: n} = \frac{6}{5} = 1.2 \)

The ratio of white socks to brown socks is 6:5.

Given that,

Based on the above information, the calculation is as follows:

= 6:5

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Answer:

8/5

Step-by-step explanation:

Clay soil = 1/5 pounds

Bale of strraw = 1/8

How much clay soil will he need to use the whole bale of straw

Let

Clay soil needed = x

Bale of straw needed = 1

Clay soil : Bale of straw

1/5 : 1/8 = x : 1

1/5 ÷ 1/8 = x / 1

1/5 × 8/1 = x / 1

8/5 = x / 1

Cross product

8 * 1 = 5 * x

8 = 5x

Divide both sides by 5

x = 8/5

= 1 3/5

8/5 pounds of clay soil is needed to make the whole bale of straw

Regarding the exponential function y = 3(2)^x, we have that:

An exponential function is defined as follows:

y = ab^(x/n).

In which the parameters are defined as follows:

The function for this problem is given as follows:

y = 3(2)^x.

Hence the parameters are given as follows:

At x = 3, the numeric value of the function is obtained as follows:

y = 3 x 2^3

y = 3 x 8

y = 24.

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Dang, I'm only 12 I don't knowwwww

Answer:

hey buddy sorry i dont know the answer hope this help

Step-by-step explanation:

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly can be calculated as follows:

Given, Principal = Rs 1200Time = 1.5 yearsInterest rate = 40% per annum, compounded quarterly

Let r be the quarterly rate of interest. Then we can convert the annual interest rate to quarterly interest rate using the following formula: \text{Annual interest rate} = (1 + \text{Quarterly rate})^4 - 1$$

Substituting the values, we get:0.40 = (1 + r)^4 - 1 Solving for r, we get:r = 0.095 or 9.5% per quarter

Now, we can use the formula for the amount of money after time t, compounded quarterly: $A = P \left( 1 + \frac{r}{4} \right)^{4t}

Substituting the values, we get:A = Rs 1200 x $\left(1 + \frac{0.095}{4} \right)^{4 \times 1.5}= Rs 1893.09

Therefore, the amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

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Let x equal the number of tiny book boxes and y equal the number of large book boxes.

Because John must pack at least 35 boxes:

(number of tiny book boxes) + (number of large book boxes) = (at least) 35

x + y ≥ 35

Since John needs to pack at least 350 books:

(number of small books packed) + (number of large books packed) (is at least) 350

(number of small books per box)(number of boxes of small books) + (number of large books per box)(number of boxes of small books) ≥ 350

15x + 8y ≥ 350

Your system of inequalities is:

x + y ≥ 35

15x + 8y ≥ 350

The number of bacteria  After 3 hours, in the petri dish would be approximately 823,542,481.

To calculate the number of bacteria in the petri dish after a certain number of hours, you can use the formula:

Number of bacteria = Initial number of bacteria × (growth factor)^(number of hours)

In this case, the initial number of bacteria is 500,500,500 and the growth factor is 1.21.21, point, 2.

Let's calculate the number of bacteria after 1 hour:

Number of bacteria after 1 hour = 500,500,500 × (1.21.21, point, 2)^1

Number of bacteria after 1 hour ≈ 500,500,500 × 1.21.21, point, 2 ≈ 605,662,605

After 1 hour, the number of bacteria in the petri dish would be approximately 605,662,605.

If you want to calculate the number of bacteria after multiple hours, you can simply raise the growth factor to the power of the number of hours. For example, to calculate the number of bacteria after 3 hours:

Number of bacteria after 3 hours = 500,500,500 × (1.21.21, point, 2)^3 ≈ 500,500,500 × 1.21.21, point, 2 × 1.21.21, point, 2 × 1.21.21, point, 2 ≈ 500,500,500 × 1.64642042 ≈ 823,542,481

After 3 hours, the number of bacteria in the petri dish would be approximately 823,542,481.

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Your answer would be 230,000

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given points

STEP 2: Plot these points

STEP 3: Get the new points from the given function

STEP 4: Plot these new points also

Hence, the type of mapping here is One-to-One

The correct solution to the quadratic equation x^2 + 7x + 12 = 0 is x = -3 or x = -4.

To solve the quadratic equation x^2 + 7x + 12 = 0 numerically, we can use the quadratic formula or factorization. In this case, let's use factorization.

The given equation can be factored as (x + 3)(x + 4) = 0. By setting each factor equal to zero, we can find the possible values for x:

x + 3 = 0    ->    x = -3

x + 4 = 0    ->    x = -4

Therefore, the correct solution to the quadratic equation x^2 + 7x + 12 = 0 is x = -3 or x = -4.

Option (a) x = -1 or x = -1, option (c) x = -3 or x = -3, and option (d) x = 2 or x = -1 are not correct solutions to the equation. Option (b) x = -4 or x = -3 matches the correct solutions derived through factorization.

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Answer:

2%

Step-by-step explanation:

Answer:

2% is the answer of this question

When meters are longer and more complex, we use the term "kilometer."

A kilometer is a unit of length in the metric system, and it is equal to 1,000 meters. The prefix "kilo-" denotes a factor of 1,000, so when we use the term "kilometer," we are referring to a measurement that is 1,000 times longer than a meter.

The use of kilometers is common in various contexts where longer distances are involved.

For example, when measuring the distance between cities or countries, or when discussing the length of roads, highways, or large-scale projects, kilometers are often used as the preferred unit of measurement.

Kilometers provide a convenient way to express distances that would be cumbersome to represent in meters. They allow for easier visualization and comprehension of larger distances, as they condense the number of digits required to express the measurement.

Additionally, the use of kilometers aligns with the decimal-based nature of the metric system, facilitating conversions and calculations.

In summary, the term "kilometer" is employed when meters become longer and more complex, representing a unit of measurement that is 1,000 times greater than a meter and facilitating the expression of larger distances in a more manageable and efficient manner.

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The polynomial function f(x)=5 (2x+3)(x+4) (x − 2) has exactly 3 zeros. So statement A is correct.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is f(x)=5(2x+3)(x+4) (x − 2)

The roots we can find by using 2x+3=0, x+4=0 and x-2=0

x=-3/2

x+4=0

x=-4

and x=2 are the roots of function.

Roots are nothing but zeros of the polynomial.

The function has exactly 3 zeros.

Hence, the polynomial function f(x)=5 (2x+3)(x+4) (x − 2) has exactly 3 zeros. So statement A is correct.

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The quadratic equation, x(2) + 2 =420 can be used to find x.

you can use trial and error

x(2) + 2 =420

210(2)=420 but we need to add the two so lower the \(120\)

209(2)=418+2 = 420

so, the x value must less than 21.

A quadratic equation with variable x is written in standard form as \(ax2 + bx + c = 0\), where a, b, and c are constants such that the value of an is non-zero but the values of b and c can both be zeros.

Let's change \(ax2 + bx + c = 0\) from its standard form to its vertex form, which is \(a (x - h)2 + k = 0\), where (h, k) is the vertex of the quadratic function \(f(x) = a (x - h)2 + k\). Keep in mind that 'a' has the same value in both equations. Just set them equal so we can determine how the variables relate to one another.

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Answer:

Step-by-step explanation:

5x-2(3x+7)=-10

5x-6x-14=-10

-x=4

x=-4

y=3(-4)+7

y=-5

Let x be the total number of student tickets sold.

Then, x - 25 is the number of adult tickets sold.

660 = 3x + 6(x - 25)

660 = 3x + 6x - 150

9x = 810

x = 90

Thus, 90 student tickets were sold.

To calculate the probabilities, we need to use the concept of binomial probability.

For a fair coin being tossed 5 times:

(a) Probability of getting five heads:

The probability of getting a head in a single toss is 1/2.

Since each toss is independent, we multiply the probabilities together.

P(Head) = 1/2

P(Tails) = 1/2

P(Five Heads) = P(Head) * P(Head) * P(Head) * P(Head) * P(Head) = \((1/2)^5\) = 1/32 ≈ 0.03125

So, the probability of obtaining five heads is approximately 0.03125 or 3.125%.

(b) Probability of getting four heads:

There are five possible positions for the four heads.

P(Four Heads) = (5C4) * P(Head) * P(Head) * P(Head) * P(Head) * P(Tails) = 5 * \((1/2)^4\) * (1/2) = 5/32 ≈ 0.15625

So, the probability of obtaining four heads is approximately 0.15625 or 15.625%.

(c) Probability of getting one head:

There are five possible positions for the one head.

P(One Head) = (5C1) * P(Head) * P(Tails) * P(Tails) * P(Tails) * P(Tails) = 5 * (1/2) * \((1/2)^4\) = 5/32 ≈ 0.15625

So, the probability of obtaining one head is approximately 0.15625 or 15.625%.

For a fair die being thrown eight times:

(a) Probability of a 6 occurring six times:

The probability of rolling a 6 on a fair die is 1/6.

Since each roll is independent, we multiply the probabilities together.

P(6) = 1/6

P(Not 6) = 1 - P(6) = 5/6

P(Six 6s) = P(6) * P(6) * P(6) * P(6) * P(6) * P(6) * P(Not 6) * P(Not 6) = \((1/6)^6 * (5/6)^2\) ≈ 0.000021433

So, the probability of rolling a 6 six times is approximately 0.000021433 or 0.0021433%.

(b) Probability of a 6 never happening:

P(No 6) = P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) = \((5/6)^8\) ≈ 0.23256

So, the probability of not rolling a 6 at all is approximately 0.23256 or 23.256%.

(c) Probability of an odd number of 6s:

To have an odd number of 6s, we can either have 1, 3, 5, or 7 6s.

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

\(P(One 6) = (8C1) * P(6) * P(Not 6)^7 = 8 * (1/6) * (5/6)^7P(Three 6s) = (8C3) * P(6)^3 * P(Not 6)^5 = 56 * (1/6)^3 * (5/6)^5P(Five 6s) = (8C5) * P(6)^5 * P(Not 6)^3 = 56 * (1/6)^5 * (5/6)^3P(Seven 6s) = (8C7) * P(6)^7 * P(Not 6) = 8 * (1/6)^7 * (5/6)\)

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

Calculate each term and sum them up to find the final probability.

After performing the calculations, we find that P(Odd 6s) is approximately 0.28806 or 28.806%.

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Answer:

answer is 27 trust me. I can't explain step by step so please trust ma ans is27

Simplify the integrands by polynomial division.

\(\dfrac{t^2}{1 - 3t} = -\dfrac19 \left(3t + 1 - \dfrac1{1 - 3t}\right)\)

\(\dfrac t{1 + 4t} = \dfrac14 \left(1 - \dfrac1{1 + 4t}\right)\)

Now computing the integrals is trivial.

5.

\(\displaystyle \int \frac{t^2}{1 - 3t} \, dt = -\frac19 \int \left(3t + 1 - \frac1{1-3t}\right) \, dt \\\\ = -\frac19 \left(\frac32 t^2 + t + \frac13 \ln|1 - 3t|\right) + C \\\\ = \boxed{-\frac{t^2}6 - \frac t9 - \frac{\ln|1-3t|}{27} + C}\)

where we use the power rule,

\(\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C ~~~~ (n\neq-1)\)

and a substitution to integrate the last term,

\(\displaystyle \int \frac{dt}{1-3t} = -\frac13 \int \frac{du}u \\\\ = -\frac13 \ln|u| + C \\\\ = -\frac13 \ln|1-3t| + C ~~~ (u=1-3t \text{ and } du = -3\,dt)\)

8.

\(\displaystyle \int \frac t{1+4t} \, dt = \frac14 \int \left(1 - \frac1{1+4t}\right) \, dt \\\\ = \frac14 \left(t - \frac14 \ln|1 + 4t|\right) + C \\\\ = \boxed{\frac t4 - \frac{\ln|1+4t|}{16} + C}\)

using the same approach as above.