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3 years ago

The law of cosines is used to find the measure of Z.

Mathematics

2 answers:

TEA [102]3 years ago

7 0

Answer:

C. 51º

Step-by-step explanation:

Shtirlitz [24]3 years ago

6 0

Answer:

C. $Z=51^{\circ}$

Step-by-step explanation:

We have been given a triangle. We are asked to find the measure of angle Z using Law of cosines.

Law of cosines: $c^2=a^2+b^2-2ab\cdot \text{cos}(C)$ , where, a, b and c are sides opposite to angles A, B and C respectively.

Upon substituting our given values in law of cosines, we will get:

$16^2=19^2+18^2-2(19)(18)\cdot \text{cos}(Z)$

$256=361+324-684\cdot \text{cos}(Z)$

$256=685-684\cdot \text{cos}(Z)$

$256-685=685-685-684\cdot \text{cos}(Z)$

$-429=-684\cdot \text{cos}(Z)$

$\frac{-429}{-684}=\frac{-684\cdot \text{cos}(Z)}{-684}$

$0.627192982456=\text{cos}(Z)$

$\text{cos}(Z)=0.627192982456$

Now, we will use inverse cosine or arc-cos to solve for angle Z as:

$Z=\text{cos}^{-1}(0.627192982456)$

$Z=51.1566718^{\circ}$

$Z\approx 51^{\circ}$

Therefore, the measure of angle Z is approximately 51 degrees.

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Which fraction has a terminating decimal?<br> - 11/19<br> - 4/7<br> - 1/3<br> - 3/150

babunello [35]

<h3>Answer: D) 3/150</h3>

==========================================================

Explanation:

With the use of a calculator, we see that,

11/19 = 0.57894736842106...., the decimals eventually repeat; but unfortunately my calculator ran out of room to show the repeating portion
4/7 = 0.5714285714285714..., the block "571428" repeats forever
1/3 = 0.333333.... the 3s go on forever
3/150 = 0.02

So 3/150 converts to the terminating decimal 0.02

The word "terminate" means "stop". In the other decimal values, the decimal digits go on forever repeating the patterns mentioned.

----------------------

A non-calculator approach will have us simplify 3/150 into 1/50 after dividing both parts by the GCF 3. Then notice how 50 has the prime factorization of 2*5*5. The fact that the denominator 50 can be factored in terms of only 2's and 5's is enough evidence to conclude that the fraction converts to a terminating decimal.

If the denominator factors into some other primes, other than 2s and 5s, then we don't have a terminating decimal. So that's why 11/19, 4/7 and 1/3 convert to non-terminating decimals.

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3 years ago

What is the greatest common factor (gcf) of the numerator and denominator in the rational expression below? 7x+14/2x^2+x-6

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The answer is C. The numerator 7x+14 can be factored as 7(x+2). The denominator 2x^2+2x-6 can be factored as (x+2)(2x-3). The greatest common divisor of 7(x+2) and (x+2)(2x-3) is obviously x+2, which is contained in both of the two expressions.

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3 years ago

1/3 of a cup of flour is used to make 6 cinnamon rolls. How much fliur is needed to make 1 cinnamon roll?

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3 years ago

According to a 2018 survey by Bankrate, 20% of adults in the United States save nothing for retirement (CNBC website). Suppose t

nalin [4]

Answer:

0.5981 = 59.81% probability that three or less of the selected adults have saved nothing for retirement

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they save nothing for retirement, or they save something. The probability of an adult saving nothing for retirement is independent of any other adult. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

20% of adults in the United States save nothing for retirement (CNBC website).

This means that $p = 0.2$

Suppose that sixteen adults in the United States are selected randomly.

This means that $n = 16$

What is the probability that three or less of the selected adults have saved nothing for retirement?

This is:

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{16,0}.(0.2)^{0}.(0.8)^{16} = 0.0281$

$P(X = 1) = C_{16,1}.(0.2)^{1}.(0.8)^{15} = 0.1126$

$P(X = 2) = C_{16,2}.(0.2)^{2}.(0.8)^{14} = 0.2111$

$P(X = 3) = C_{16,3}.(0.2)^{3}.(0.8)^{13} = 0.2463$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0281 + 0.1126 + 0.2111 + 0.2463 = 0.5981$

0.5981 = 59.81% probability that three or less of the selected adults have saved nothing for retirement

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3 years ago

The prices of consumer goods do not always exactly follow the CPI. The following chart shows several consumer items, along with

zloy xaker [14]

The reasonable estimate of the current customer price index is 195. The option B is the correct option.

<h3>Customer price index</h3>

Customer price index is the price index which measures the weight average of price of basket of customers goods or services.

It can be given as,

$\rm CPI_t=\dfrac{C_t}{C_0}\times 100$

Here $\rm C_t$ is the cost of market basket in current period and $\rm C_0$ is the cost of market basket in the base period.

Cost of market basket in current period is

$\rm C_t=15.66+119.75+23.99+37.50\\\\C_t=196.9$

Cost of market basket in 1983 is,

$\rm C_0=8.85+71.25+13.95+22.7\\\\C_0=116.8$

Substitute all the values in the formula

$\rm CPI_t=\dfrac{C_t}{C_0}\times 100\\\\\rm CPI_t=\dfrac{196.9}{116.8}\times 100\\\\\rm CPI_t=1.685\times 100 \\\\ CPI_t=168.5\\\\\rm CPI_t= 170 \ \rm approx$

Thus the value of current CPI is 168.5 which is near about the 170.

Hence, the reasonable estimate of the current customer price index is 195. The option B is the correct option.

Learn more about the customer price index here;

brainly.com/question/25495502

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2 years ago