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Oxana [17]
3 years ago
10

(04.06 MC) In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area

where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. One line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded above the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded in below the line. The graph represents which system of inequalities? y ≤ −3x − 1 y ≤ −x − 4 y ≥ −3x + 1 y ≤ −x − 4 y ≤ 3x − 1 y ≤ −x + 4 y ≤ 3x − 1 y ≥ −x + 4

Mathematics
1 answer:
KonstantinChe [14]3 years ago
6 0

Answer:

(D)y ≤ 3x − 1 y ≥ −x + 4

Step-by-step explanation:

The line f(x) is solid and goes through the points (0, 4) and (4, 0) and is shaded above the line.

The line that satisfies the point (0,4) and (4,0) is y=-x+4

Since it is shaded above the line, we have the inequality sign  ≥.

Therefore, one of the lines is y≥-x+4

In the equation of the line y=3x-1

When x=0, y=3(0)-1=-1

When x=2, y=3(2)-1=5

Since it is shaded below the line, we have the inequality sign ≤ .

Therefore, the other line is y≤3x-1.

The correct option is D.

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A college counselor is interested in estimating how many credits a student typically enrolls in each semester. The counselor dec
Ket [755]

Answer:

(a) The usual load is not 13 credits.

(b) The probability that a a student at this college takes 16 or more credits is 0.1093.

Step-by-step explanation:

According to the Central limit theorem, if a large sample (<em>n</em> ≥ 30) is selected from an unknown population then the sampling distribution of sample mean follows a Normal distribution.

The information provided is:

Min.=8\\Q_{1}=13\\Median=14\\Mean=13.65\\SD=1.91\\Q_{3}=15\\Max.=18

The sample size is, <em>n</em> = 100.

The sample size is large enough for estimating the population mean from the sample mean and the population standard deviation from the sample standard deviation.

So,

\mu_{\bar x}=\bar x=13.65\\SE=\frac{s}{\sqrt{n}}=\frac{1.91}{\sqrt{100}}=0.191

(a)

The null hypothesis is:

<em>H</em>₀: The usual load is 13 credits, i.e. <em>μ</em> = 13.

Assume that the significance level of the test is, <em>α</em> = 0.05.

Construct a (1 - <em>α</em>) % confidence interval for population mean to check the claim.

The (1 - <em>α</em>) % confidence interval for population mean is given by:

CI=\bar x\pm z_{\alpha/2}\times SE

For 5% level of significance the two tailed critical value of <em>z</em> is:

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

Construct the 95% confidence interval as follows:

CI=\bar x\pm z_{\alpha/2}\times SE\\=13.65\pm (1.96\times0.191)\\=13.65\pm0.3744\\=(13.2756, 14.0244)\\=(13.28, 14.02)

As the null value, <em>μ</em> = 13 is not included in the 95% confidence interval the null hypothesis will be rejected.

Thus, it can be concluded that the usual load is not 13 credits.

(b)

Compute the probability that a a student at this college takes 16 or more credits as follows:

P(X\geq 16)=P(\frac{X-\mu}{\sigma}\geq \frac{16-13.65}{1.91})\\=P(Z>1.23)\\=1-P(Z

Thus, the probability that a a student at this college takes 16 or more credits is 0.1093.

3 0
2 years ago
Read 2 more answers
Please help!!!! Sine and cosine ratios
Kipish [7]

Answer: 40.9

Step-by-step explanation:

Given

angle given is 23^{\circ}

RC=16

Using trigonometry

\Rightarrow \sin 23^{\circ}=\dfrac{RC}{PC}\\\\\Rightarrow \sin 23^{\circ}=\dfrac{16}{X}\\\\\Rightarrow X=\dfrac{16}{\sin 23^{\circ}}\\\\\Rightarrow X=40.948\approx 40.9

Using cosine formula

\Rightarrow \cos 23^{\circ}=\dfrac{PR}{X}\\\\\Rightarrow PR=40.9\times \cos 23^{\circ}\\\Rightarrow PR=37.69\approx 37.7

8 0
3 years ago
Please urgent! will give brainliest<br><br> Solve for x in simplest form.<br> 7=1/6(8x=24)
nlexa [21]

Answer:

Step-by-step explanation:

dived 24 by 8 and you get 3

8 0
2 years ago
I need this answered ASAP
Lady bird [3.3K]

Answer:

23x^{2}

Step-by-step explanation:

This can be simplified by combing like terms.

8x^2 and 15x^2 are like terms. Since both numbers are positive, we add them together.

The sum of 8x^2 and 15x^2 is 23x^2

I hope this helps.

6 0
3 years ago
Jorge scored 18 out of 45 free throws. What decimal
katen-ka-za [31]

Answer:

0.4 (not rounded)

Step-by-step explanation

You can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 18 and 45 using

GCF(18,45) = 9

18÷945÷9=25

We know that

25

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2÷5

Then using

Long Division for 2 divided by 5

gives us

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6 0
3 years ago
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