Consider the polynomial function T(x)=2x(x-3)(x+1). What are the zeros of T(x)

algerbra. com The ninth graders at a high school are raising money by selling T-shirts and baseball caps. The number of T-shirts

My name is Ann [436]

Answer:

$36$ T-shirts and $12$ Baseball Caps

Step-by-step explanation:

GIVEN: The ninth graders at a high school are raising money by selling T-shirts and baseball caps. The number of T-shirts sold was three times the number of caps. The profit they received for each T-shirt sold was $\$5.00$ , and the profit on each cap was $\$2.50$ .

TO FIND: If the students made a total profit of $\$210$ , how many T-shirts and how many caps were sold.

SOLUTION:

Let the total number of T-shirts sold are $=\text{t}$

Let the total number of Baseball Caps sold are $=\text{b}$

Profit received on each T-shirt $=\$5.00$

Profit received on each Baseball Caps $=\$2.50$

Total profit received on T-shirts $=\$5.00\text{t}$

Total profit received on Baseball Caps $=\$2.50\text{b}$

$5\text{t}+2.5\text{b}=210$

Also,

The number of T-shirts sold was three times the number of caps.

$\text{t}=3\text{b}$

putting in equation,

$5\times\text{3b}+2.5\text{b}=210$

$17.5\text{b}=210$

$\text{b}=12$

$\text{t}=3\times12$

$\text{t}=36$

Hence total $36$ t-shirts and $12$ baseball Caps were sold.

6 0

3 years ago

X - 7 greater than or equal to 12.8

vladimir1956 [14]

Im pretty sure is equal to 12.8

6 0

3 years ago

Read 2 more answers

The parabola y=x^2 is reflected across the x-axis and then scaled vertically by the factor of 1/8. What is the equation of the n

poizon [28]

Answer:

y = (-1/8)x^2

Step-by-step explanation:

Start with y = x^2. When the original parabola has been reflected across the x-axis, the pertinent equation becomes y = -x^2.

Now if this is scaled vertically by a factor of 1/8, we get:

y = (-1/8)x^2

8 0

3 years ago

If your annual salary is 47,980 what is your biweekly pay

bogdanovich [222]

Annual salary = 47,980
If you are paid biweekly, you are paid 26 times per year, so

biweekly pay = 47,980 / 26 = 1,845.38

5 0

3 years ago

In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and de

Naily [24]

Answer:

$z=\frac{0.0156-0.0114}{\sqrt{0.01554(1-0.01554)(\frac{1}{32601}+\frac{1}{88})}}=0.318$

$p_v =P(Z>0.318)=0.375$

So the p value is a very high value and using the significance level provided $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in arizona is not significantly higher than the national incident rate at 1% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=507$ represent the number of children diagnosed with Autism Spectrum Disorder (ASD) in Arizona

$n_{1}=32601$ sample elected from arizona

$\hat p_{1}=\frac{507}{32601} =0.0156$ represent the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in arizona

$p_{2}=\frac{1}{88}= 0.0114$ represent the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in the nation

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if that the incident of ASD is more in Arizona than nationally, the system of hypothesis are:

Null hypothesis: $p_{1} \leq p_{2}$

Alternative hypothesis: $p_{1} > p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{507+1}{32601 +88}=0.01554$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.0156-0.0114}{\sqrt{0.01554(1-0.01554)(\frac{1}{32601}+\frac{1}{88})}}=0.318$

Statistical decision

The significance level provided is $\alpha=0.01$ , and we can calculate the p value for this test.

Since is a one right sided test the p value would be:

$p_v =P(Z>0.318)=0.375$

So the p value is a very high value and using the significance level provided $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in arizona is not significantly higher than the national incident rate at 1% of significance.

5 0

3 years ago