Evaluate the expression. If necessary, round to the nearest hundredth.

Mathematics

1 answer:

Nat2105 [25]3 years ago

6 0

Answer:

B. 23.

Step-by-step explanation:

In the expression

$7^{log_7 23 }$

the logarithm $log_7(23)$ in the exponent is asking us the following question:

<em>"to what power should I raise 7 to as to get 23?"</em>

Let us call that number $x$ , then we have

$log_7(23)=x$ , which means

$7^x=23$

$\boxed{7^{log_7(23)}=23}$

which is Choice B.

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Jade wants to buy a $200,000 term life insurance policy. She is 34 years old. Using the premium table, what is her annual premiu

AnnZ [28]

Premium rates are usually for premium per fixed face value. Jade's annual premium for a 10 year policy is given by Option b: $1,202

<h3>How to calculate the total annual premium for $x ?</h3>

If its given that the annual premium is $p per $y face value, then we can calculate the annual premium for $1 face value and then use it to calculate annual premium for $x.

Using proportions, we get:

$\rm \$y \: face \: value : \$p \: annual \: premiun\\\\\rm \$1 \: face \: value : \$\dfrac{p}{y} \: annual \: premiun\\\\\rm \$x\:face\: value : \$\dfrac{p \times x}{y} \: annual \: premiun\\$

For given case, from the tables, we see that for age 34, and 10 year life insurance for female gender , there is annual premium of 6.01 per $1000 face value.
Thus, we have p = 6.01, y = 1000

Since Jade wants to buy Life insurance for $200,000, thus, x = $200,000

Putting it in the above derived formula, we get:

$\rm \$x\:face\: value : \$\dfrac{p \times x}{y} \: annual \: premium\\\\\rm \$200000\:face\: value : \$\dfrac{6.01 \times 200000}{1000} \: annual \: premium\\ = \$1202 \: annual \: premiun$