Use the following formulas to answer the questions below: T(M, R) R + 0.6(M R) M(z) 220-z where R- resting heart rate, M- maximum heart rate, and -age Recall our discussion of heart rate and composition of functions from the end of the section. Find the training heart rate function, T(M) for a person with a resting heart rate of 62 beats per minute, then find the following. a. Find the maximum heart rate function, M() for a person a years of age. M(x)

Answer:

1/9

Step-by-step explanation:

5a=45

divide it by 5 and a will =9

9b=1

divide 1 by 9

you get 1/9=b

therefore 9x1/9=1

True. The general solution to a third-order differential equation typically contains three arbitrary constants.

The general solution to a third-order differential equation must contain three constants. This is because the order of a differential equation refers to the highest derivative present in the equation. A third-order differential equation involves the third derivative of the unknown function.

When solving a differential equation, we typically find a general solution that encompasses all possible solutions to the equation. This general solution includes an arbitrary number of constants, depending on the order of the differential equation.

For a third-order differential equation, the general solution will contain three arbitrary constants. This is because each constant represents a degree of freedom in the solution, allowing us to accommodate a wide range of functions that satisfy the given differential equation.These constants can be determined by applying initial conditions or boundary conditions to the differential equation, which narrows down the solution to a particular function.

Therefore, when dealing with a third-order differential equation, it is expected that the general solution will contain three constants to account for the necessary degrees of freedom in constructing the solution.

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True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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The marginal benefit from studying one extra hour is 5 percent.

Now,

Given:

To find: Marginal benefit on studying one hour extra.

Finding:

Now, marks scored on studying 4 hours is 80 percent and 5 hours is 85 percent.

Thus, the extra percentage that is scored is because of the 1 hour of extra studying.

The extra percentage = marginal benefit of studying extra = 85 - 80 = 5 percent.

Hence, the marginal benefit from studying one extra hour is 5 percent.

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Divide the lengths to find the scale :

35/7 = 5

Now divide the width by the scale to get the scaled width:

30/5 = 6 inches

the scaled drawing is 7 x 6

area of scaled drawing = 7 x 6 = 42 square inches

Answer:

270kg!

Step-by-step explanation:

2.3 : 2.2

3x : 5y and 7 : 11

3x : 5y

7 : 11

To find x:

3x = 7

x = 7/3 (Bring 3 over to 7 to divide)

x = 2.3 OR 2/1/3

To find y:

5y = 11

y = 11/5 (Bring 5 over to 11 to divide)

y = 2.2 OR 2/1/5

So,

x = 2.3

y = 2.2

Therefore, the answer is:

x : y = 2.3 : 2.2

The mean absolute deviation of the given list of numbers is 7.75. Hence, the correct answer is option A: 7.75.

To calculate the mean absolute deviation (MAD) of a set of numbers, follow these steps:

For the given set of numbers, determine the mean (average).

Mean = (22 + 14 + 24 + 20 + 36 + 28 + 43 + 35) / 8 = 222 / 8 = 27.75

Calculate the absolute deviation for each number by subtracting the mean from each individual number and taking the absolute value.

Absolute Deviation: |22 - 27.75| = 5.75

|14 - 27.75| = 13.75

|24 - 27.75| = 3.75

|20 - 27.75| = 7.75

|36 - 27.75| = 8.25

|28 - 27.75| = 0.25

|43 - 27.75| = 15.25

|35 - 27.75| = 7.25

Find the average of the absolute deviations by summing them up and dividing by the total count (which is 8 in this case).

(5.75 + 13.75 + 3.75 + 7.75 + 8.25 + 0.25 + 15.25 + 7.25) / 8 = 62 / 8 = 7.75

Therefore, the mean absolute deviation of the given list of numbers is 7.75. Hence, the correct answer is option A: 7.75.

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Answer:

\(\boxed{\textsf{The value of x is \textbf{7}.}}\)

Step-by-step explanation:

Given that 9213x5 is a multiple of 9 and we need to find out the value of x .So the rule for divisibility for 9 is :-

Test for Divisibility by 9 :-

A number is divisible by 9 if the sum of the digits is divisible by 9 .

Here the sum of the digits is :-

\(\sf\implies Sum_{(digits)}= 9+2+1+3+x+5=\pink{20+x}\)

Now here to make 20 +x divisible by 9 is should be equal to 27 since 27 is the nearest smallest multiple of 9 .

\(\sf\implies 20 + x = 27 \\\\\sf\implies x = 27-20 \\\\\sf\implies\boxed{\pink{\sf x = 7 }}\)

Answer:

(-12,8)

Step-by-step explanation:

Answer:

P= ( 18s + 12 ) + ( 2s + 2 ) or just P = 20s + 14

Step-by-step explanation:

9s + 6 is said twice just add both together and it is. 18s + 12.

Same with s + 1 so it would be 2s + 2.

You can add it all together and its 20s + 14.

P = Perimeter.

156.52 - x = 56.29

just flip x with 56.29

156.52 - 56.29 = x

x = 100.23

Answer: 212.81

Step-by-step explanation: You would, in this case, carry the 156.52 across the equal sign and then swap out the subtraction sign with an addition sign. You would then flip the equation around so it would like this: 156.52+56.29=??. All you would have to do now, is add the numbers and you have you answer. Good luck on your test!

Correction: Keep the subtraction sign and then you should get your answer.

So it would look like this: 156.52-56.29=??

                                           Answer=100

Thanks to someone who corrected me

Answer:

\(10x^2 (10x^2 -3)\)

Step-by-step explanation:

\(100x^4 -30x^2 \\ 10x^2 \cdot \frac{100x^4 -30x^2}{10x^2} \\ 10x^2 (10x^2 -3)\)

An annual payment is found approximately $617.34. The correct option is e.. $617.34.

To find the size of your payments, you can use the formula for calculating the equal installments on a loan.

First, calculate the annual payment by dividing the borrowed amount ($2,000) by the present value factor of an annuity due with 4 periods at a 9% interest rate.

Using a financial calculator or spreadsheet, the present value factor of an annuity due with 4 periods at 9% interest rate is 3.2403.

Dividing $2,000 by 3.2403 gives us an annual payment of approximately $617.34.
Therefore, the correct answer is e. $617.34.

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Answer:

there is an economic principle that states that 1 dollar today is worth more than 1 dollar in the future, since an invested dollar could earn interests and gain value.

For example, we can assume a 6% interest rate (0.5% monthly interest rate), and using the present value formula we can determine the present value of $100:

In order to calculate the value of $100 given to us tomorrow, we would need to determine a daily interest rate = 6% / 360 = 0.00017

since the amount of money is not that large and the interest rate is rather low, the difference in value is not that large. But imagine if you used a 24% interest rate instead of 6% (monthly interest rate = 2%)

as the interest rate increases, the present value decreases.

Answer:

17%

Step-by-step explanation:

90-75 = 15 (the amount of apple decreased by 15)

15/90 = 16/67%

16.67% rounded to the nearest percent, is 17%.

Hope that helps!

The simplified expression of |(1/4-1/5)+(-3/4+1/8)| is |-0.57|.

In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD). As an illustration, LCM (4, 5) = 20. In this case, the LCM 20 may be divided by both 4 and 5, hence these two numbers are referred to as the divisors of 20.

When the fractions' denominators differ, LCM can also be used to add or subtract any two fractions. LCM is used to make the denominators common when doing any arithmetic operations using fractions, such as addition and subtraction.

The given expression is:

|(1/4-1/5)+(-3/4+1/8)|

Take the LCM:

|(5 - 4)/ 20 + (-24 + 4)  32|

|1/20 - 20/32|

Take the LCM:

|(32 - 400) / 640|

|-368 / 640|

|-0.57|

Hence, the simplified expression of |(1/4-1/5)+(-3/4+1/8)| is |-0.57|.

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Answer:

Yes and no solution :)

Step-by-step explanation:

No explanation needed for the first part.

2 as a fraction is 2/1

So rewrite as 2/1 + 2/1

We can multiply the whole equation by lets say.... 428

Now we have 856/428 + 856/428

Now we can put 0 at the other side of the equation... because... yes

856/428+856/428 = 0

Now lets just move one of these to the other side of the equation :)

856/428 = -856/428

Now I dont know, how about we cancel out the denominators.

856=-856

now if we move the right side back to the left... we get

1712=0

This equation is not true therefor 2+2 has no solution

Answer:

Box A: 2 × 4.5 × 6 = 54 cubic inches

Box B: 6 × 2.5 × 3 = 45 cubic inches

Box C: 5 × 4.5 × 2.25 =

50.625 cubic inches

Box D: 2.5 × 2.25 × 3 = 16.875 cubic inches

From least to greatest, the order of the boxes' volumes is D, B, C, A.

Answer:

8

Step-by-step explanation:

Answer: 567

Step-by-step explanation: 9*9=81  then you take 81 and times it by however many days there is in the week (aka 7) 81*7=567

34% of the data in a normal distribution is more than 1 standard deviation above the mean.

In a normal distribution, about 68% of the data falls within one standard deviation above or below the mean. This means that roughly 34% of the data falls one standard deviation above the mean.

To be more precise, we can use the empirical rule or the 68-95-99.7 rule, which states that:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Therefore, if we assume that the normal distribution is perfectly symmetrical, we can estimate that roughly 34% of the data falls more than one standard deviation above the mean.

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The equation of the line tangent to the function y = x^3 + 3x^2 + 2 at its point of inflection is: y = -3x - 6.

To find the equation of the line tangent to the function y = x^3 + 3x^2 + 2 at its point of inflection, we need to determine the derivative of the function and evaluate it at the point of inflection. First, let's find the derivative of y with respect to x: dy/dx = 3x^2 + 6x. The point of inflection occurs where the second derivative of the function changes sign. Taking the derivative of dy/dx, we have: d^2y/dx^2 = 6x + 6. Setting d^2y/dx^2 equal to zero and solving for x, we find: 6x + 6 = 0; x = -1.  At x = -1, the point of inflection is (-1, y) on the original function. To find the slope of the tangent line at this point, we substitute x = -1 into the derivative: dy/dx = 3(-1)^2 + 6(-1) = -3. So, the equation of the line tangent to the function at its point of inflection is: y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values, we have: y = -3x + b

To find b, we substitute the coordinates of the point of inflection (-1, y):y = -3(-1) + b; y = 3 + b. Since the point of inflection lies on the line, we can substitute the y-value and solve for b: 3 + b = x^3 + 3x^2 + 2; b = -6. Therefore, the equation of the line tangent to the function y = x^3 + 3x^2 + 2 at its point of inflection is: y = -3x - 6.

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The expected value for this game is $0.80.

The expected value for this game is calculated using  the formula below:

Data given:

If you pull a green candy you will have to pay them $1.00 and there is a 0.4 probability that you pull a green candy

If you pull a red candy you will have to pay them $2.00 and there is a 0.6 probability that you pull a red candy.

Expected value = (0.6 * $2.00) + (0.4 * -$1.00)

Expected value  = $1.20 - $0.40

Expected value = $0.80

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Answer:

48 is 8 times as many as 6.

4 times as many as 12 is 48.

1.75 is 14 times as many as 8.

Step-by-step explanation:

Step-by-step explanation:

that simply stands for

48 = 8×6

4×12 = 48

112 = 14×8

Answer:

2.16350 people did not cast vote.

Answer:

1700 people did not vote

Step-by-step explanation:

2. 15000+23650=38650-350=1700 people.

The image of (5, 8) after a reflection over the line y = - x is (-5, -8 ).

To see the graph.

Given,

In the question:

What is the image of (5,8) after the reflection over the line y= -x?

Now, According to the question:

The image of (-5,8) after a reflection over the y-axis

When a point is reflected over y axis, then the value of x changes to -x.

the value of y remains the same.

But, It is given that  the reflection over the line y= -x

Hence, The image of (5, 8) after a reflection over the line y = - x is

(-5, -8 ).

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Answer:

7.03, 6.75, 6.72, 6.08, 6.4

Step-by-step explanation:

Given:

\(\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)\)

To prove:

The given statement.

Proof:

We have,

\(\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)\)

\(LHS=\cos^4 \alpha+\sin^4\alpha\)

\(LHS=(\cos^2 \alpha)^2+(\sin^2 \alpha)^2\)

\(LHS=(\cos^2 \alpha+\sin^2\alpha)^2-2\sin ^2\alpha\cos^2 \alpha\)     \([\because a^2+b^2=(a+b)^2-2ab]\)

\(LHS=(1)^2-2(1-\cos^2 \alpha)\cos^2 \alpha \)      \([\because \cos^2 \alpha+\sin^2\alpha=1]\)

\(LHS=1-2\cos^2 \alpha+2\cos^4 \alpha \)

Now,

\(RHS=\dfrac{1}{4}(3+\cos 4 \alpha)\)

\(RHS=\dfrac{1}{4}[3+(2\cos^2 2\alpha-1)]\)        \([\because \cos 2\theta=2\cos^2\theta -1]\)

\(RHS=\dfrac{1}{4}[2+2\cos^2 2\alpha]\)

\(RHS=\dfrac{1}{4}[2+2(2\cos^2 \alpha-1)^2]\)        \([\because \cos 2\theta=2\cos^2\theta -1]\)

\(RHS=\dfrac{1}{4}[2+2(4\cos^4 \alpha-4\cos \alpha+1)]\)        \([\because (a-b)^2=a^2-2ab+b^2]\)

\(RHS=\dfrac{1}{4}[2+8\cos^4 \alpha-8\cos \alpha+2]\)

\(RHS=\dfrac{1}{4}[4+8\cos^4 \alpha-8\cos \alpha]\)

\(RHS=1+2\cos^4 \alpha-2\cos \alpha\)

\(RHS=1-2\cos^2 \alpha+2\cos^4 \alpha \)

\(LHS=RHS\)

Hence proved.