All categories

13 days ago

Which equation represents the function graphed on the coordinate plane?

Mathematics

2 answers:

zzz [11.9K]13 days ago

5 0

The answer is B. g(x) = |x + 4| – 10. The second choice accurately reflects the function depicted in the graph provided. The graph represents an absolute value function characterized by its "V" shape. The fundamental form of this type of function is presented, from which we can derive the correct answer by applying all given transformations. The graph displays that the function was lowered by 10 units and shifted 4 units leftward. This leads to the function featuring "-10" and "+4", where the negative denotes downward movement and the positive signifies leftward movement. It’s crucial to note that for horizontal movements, addition indicates leftward displacement, while subtraction indicates rightward. By implementing these changes on the fundamental function, we arrive at the conclusion that option B is indeed correct.

PIT_PIT [11.9K]13 days ago

4 0

The intersection of the two lines occurs at (-4,-10). Thus, you would add 4 to x and subsequently subtract 10 from the equation. Therefore, the answer is: B. g(x) = |x + 4| – 10.

You might be interested in

A new weight-watching company, Weight Reducers International, advertises that those who join will lose an average of 10 pounds a

Inessa [12221]

Answer:

The value calculated is Z = 2.53, which exceeds 1.96 at a significance level of 0.05

This leads to the rejection of the null hypothesis H₀

Thus, we accept the alternative hypothesis

This implies that individuals participating in Weight Reducers will lose more than 10 pounds

Step-by-step explanation:

Step(i):-

The size of the random sample 'n' = 50

The new weight-loss program, Weight Reducers International, claims that members will shed an average of 10 pounds within the initial two weeks, with a standard deviation of 2.8 pounds.

Population mean 'μ' = 10 pounds

Population standard deviation 'σ' = 2.8 pounds

Sample mean 'x⁻' = 9

Significance level ∝ = 0.05

Step(ii):-

Null hypothesis: H₀: μ < 10

Alternative hypothesis: H₁: μ > 10

Test statistic calculation

$z= \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }$

$z= \frac{9 - 10}{\frac{2.8}{\sqrt{50} } } = \frac{-1}{0.395} = 2.53$

The determined Z value is 2.53

In this case, the critical value Z is 1.96 at the 0.05 significance level

Step(iii):-

Calculated Z value of 2.53 is greater than 1.96 at a significance level of 0.05

Consequently, we reject the null hypothesis H₀

We accept the alternative hypothesis

Conclusion:-

We determine that individuals who sign up for Weight Reducers will experience a weight loss exceeding 10 pounds

6 0

1 month ago

Suppose that the weights of airline passenger bags are normally distributed with a mean of 47.88 pounds and a standard deviation

Zina [12044]

Answer:

There is a probability of 24.51% that the weight of a bag exceeds the maximum permitted weight of 50 pounds.

Step-by-step explanation:

Problems dealing with normally distributed samples can be addressed using the z-score formula.

For a set with the mean $\mu$ and a standard deviation $\sigma$ , the z-score for a measure X is calculated by

$Z = \frac{X - \mu}{\sigma}$

Once the Z-score is determined, we consult the z-score table to find the related p-value for this score. The p-value signifies the likelihood that the measured value is less than X. Since all probabilities total 1, calculating 1 minus the p-value gives us the probability that the measure exceeds X.

For this case

Imagine the weights of passenger bags are normally distributed with a mean of 47.88 pounds and a standard deviation of 3.09 pounds, thus $\mu = 47.88, \sigma = 3.09$

What probability exists that a bag’s weight will surpass the maximum allowable of 50 pounds?

That translates to $P(X > 50)$

Thus

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{50 - 47.88}{3.09}$

$Z = 0.69$

$Z = 0.69$ has a p-value of 0.7549.

<pthis indicates="" that="" src="https://tex.z-dn.net/?f=P%28X%20%5Cleq%2050%29%20%3D%200.7549" id="TexFormula10" title="P(X \leq 50) = 0.7549" alt="P(X \leq 50) = 0.7549" align="absmiddle" class="latex-formula">.

Additionally, we have that

$P(X \leq 50) + P(X > 50) = 1$

$P(X > 50) = 1 - 0.7549 = 0.2451$

There is a probability of 24.51% that the weight of a bag will exceed the maximum allowable weight of 50 pounds.

</pthis>

6 0

1 month ago

555 grams of wool were needed to knit a sweater, a hat, and a scarf. The hat required 5 times less wool than the sweater and 5 g

Zina [12044]

Answer:

The amount of wool required for a sweater was 400 grams.

A hat needed 80 grams of wool.

A scarf required 75 grams of wool.

Step-by-step explanation:

Let

x ------> grams of wool necessary for a sweater

y -----> grams of wool necessary for a hat

z -----> grams of wool necessary for a scarf

From the information given

x+y+z=555 -----> equation A

y=x/5 ----> x=5y -----> equation B

y=z+5 ---> z=y-5 ----> equation C

By substituting equations B and C into equation A, we can solve for y:

(5y)+y+(y-5)=555

7y=560

y=80 grams

Now, find x

x=5(80)=400 grams

Next, determine z

z=80-5=75 grams

In conclusion,

400 grams of wool was required for the sweater,

the hat needed 80 grams of wool, and

the scarf required 75 grams of wool.

4 0

1 month ago

Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In

Zina [12044]

Answer:

In approximately 81 days, it is likely that the teacher on bus duty will be certified in CPR

Step-by-step explanation:

The probability of a teacher obtaining certification in Cardio-Pulmonary Resuscitation (CPR) is as follows:

36 out of 80

Hence

$p = \frac{36}{80} = 0.45$

In a school year lasting 180 days, how many days can we anticipate that the teacher on bus duty will likely have CPR certification?

45% of the time

0.45 multiplied by 180 results in 81 days

In approximately 81 days, it is likely that the teacher on bus duty will be certified in CPR

7 0

26 days ago

You decide to make milk a loss leader. You drop the price from its cost of $2.59 per gallon to $1.99 per gallon. What is the per

Zina [12044]

Answer: The loss percentage per gallon is 23.17%

Step-by-step explanation:Original price per gallon is $ 2.59

Discounted price per gallon is $ 1.99

Now, we will calculate the percentage loss per gallon, using the Direct Rule of Three as follows:

Price Percentage

2.59 100

1.99 x*****************************

2.59 * x = 1.99 * 100

2.59x = 199

x = 199/2.59

x = 76.83

So the percentage loss = 100 - 76.83

The percentage loss is 23.17%

4 0

8 days ago

Read 2 more answers