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3 years ago

A graph of average resting heart rates is shown below. The average resting heart rate for adults is 72 beats per

Mathematics

1 answer:

Fed [463]3 years ago

3 0

Answer:

Option (1)

Step-by-step explanation:

Characteristics of the graph attached,

1). Heart rates of the teenagers (0 to 20 years) varies from 112 beats per minute to 72 beats per minute.

2). Heart rates of the adults (20 years to 50 years) remains constant (72 beats per minute)

Option 1). Since average resting heart rate of the teenagers decreases from 0 to 10 years, so at the 20 years of age heart rate will be less than a teenager of 20 years.

Therefore, statement is not supported by the graph.

Option (2). A 20-year-old has the same average resting heart as at 30-year-old. [True]

Therefore, this option is supported by the graph.

Option (3). A 40-year-old may have the same average resting heart rate for 10 years.

[True]

Therefore, this statement is supported by the graph.

Option (4). The average resting heart rate for teenagers steadily decreases.

[True]. There is a linear decrease in the teenagers heart rate shown in the graph.

Therefore, the given statement is true and supported by the graph.

Option (1) will be the answer.

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amm1812

Answer:

Step-by-step explanation:

The blue graph, g(x), is shifted down 8 units.

So the answer is f(x)-8 which is A

5 0

3 years ago

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Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

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2 years ago

The boxes are shaped as right rectangular prisms. The larger box has a length of 24cm a width of 10 cm, and height of 30cm. The

irina1246 [14]

Answer:

900cm^2

Step-by-step explanation:

24, 10, 30 in half= 12, 5, 15 so, 12*5*15=900cm^2

5 0

3 years ago

Which statement is true?

love history [14]

<h2>Hello!</h2>

The answer is:

The second option,

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

Discarding each given option in order to find the correct one, we have:

<h2>First option,</h2>

$\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}$

The statement is false, the correct form of the statement (according to the property of roots) is:

$\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}$

<h2>Second option,</h2>

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

The statement is true, we can prove it by using the following properties of exponents:

$(a^{b})^{c}=a^{bc}$

$\sqrt[n]{x^{m} }=x^{\frac{m}{n} }$

We are given the expression:

$(\sqrt[m]{x^{a} } )^{b}$

So, applying the properties, we have:

$(\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }$

Hence,

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

<h2>Third option,</h2>

$a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}$

The statement is false, the correct form of the statement (according to the property of roots) is:

$a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}$

<h2>Fourth option,</h2>

$\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}$

The statement is false, the correct form of the statement (according to the property of roots) is:

$\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }$

Hence, the answer is, the statement that is true is the second statement:

$(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }$

Have a nice day!

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3 years ago

If one ml. Equals one gram how much does a liter of water weigh

stich3 [128]

It will equal 1 Kg because 1ml = 1 gram

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3 years ago

Read 2 more answers