How to solve this problem

Polygon abc is dilated, rotated and translated to form polygon a’b’c’d. The endpoint of ab at (0,-7) and (8,8), and the endpoint

Yanka [14]

Answer:

Step-by-step explanation:

3 0

3 years ago

Name all the radii. Please help me.

rosijanka [135]

Answer:

Step-by-step explanation:

we know,

radius is the distance from center of a circle to the circumference.

Here, from the figure we get,

There are three radius marked in this circle.

These measurements are-

OU , OR and OT

So, the radii are-

OR , OU , OT

7 0

4 years ago

For the real-valued functions, find the composition and specify its domain using interval notation.

Helen [10]

Answer:

Composition: $f(x)\,^o\,h(x)=4\,\sqrt{x+4} -1$

Domain = { $x\,/\,x\geq \,-4$ }

Step-by-step explanation:

Given

$f(x)=4\,x-1\,\,\, and \,\,\, h(x)=\sqrt{x+4}$

The requested composition becomes:

$f(x)\,^o\,h(x)=f(h(x))\\f(x)\,^o\,h(x)=f(\sqrt{x+4} )\\f(x)\,^o\,h(x)=4\,\sqrt{x+4} -1$

Then the Domain consists of all Real x-values for which the function is defined. In this case, the function is defined for all x-values for which the square root is defined, that is all x values for which:

$x+4\geq \,0$ (so the square root is defined in the Real number system)

This means $x\geq \,-4$

The Domain is then all the Real x-values such that $x\geq \,-4$

6 0

3 years ago

When I sit and watch my students take exams, I often think to myself "I wonder if students with bright calculators are impacted

hodyreva [135]

Answer:

There is a difference between the two means.

Step-by-step explanation:

The hypothesis can be defined as:

H₀: The mean exam scores of my SAT 215 students with colorful calculators are same as the mean scores of my STA 215 students with plain black calculators, i.e. μ₁ - μ₂ = 0.

Hₐ: The mean exam scores of my SAT 215 students with colorful calculators are different than the mean scores of my STA 215 students with plain black calculators, i.e. μ₁ - μ₂ ≠ 0.

Assume that the significance level of the test is, α = 0.05. Also assuming that the population variances are equal.

The decision rule:

A 95% confidence interval for mean difference can be used to determine the result of the hypothesis test. If the 95% confidence interval contains the null hypothesis value, i.e. 0 then the null hypothesis will not be rejected.

The 95% confidence interval for mean difference is:

$CI=\bar x_{1}-\bar x_{2}\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\times S_{p}\times \sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}$

Compute the pooled standard deviation as follows:

$S_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}} {n_{1}+n_{2}-2}}}=\sqrt{\frac{(49-1)(4.7)^{2}+(38-1)(5.7)^{2}}{49+38-2}}=5.16$

The critical value of t is:

$t_{\alpha/2, (n_{1}+n_{2}-2)}=t_{0.05/2, (49+38-2)}=t_{0.025, 85}=1.984$

*Use a t-table.

Compute the 95% confidence interval for mean difference as follows:

$CI=\bar x_{1}-\bar x_{2}\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\times S_{p}\times \sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}$

$=(84-87)\pm 1.984\times 5.16\times \sqrt{\frac{1}{49}+\frac{1}{38}}$

$=-3\pm 2.133\\=(-5.133, -0.867)\\\approx(-5.13, -0.87)$

The 95% confidence interval for mean difference is (-5.13, -0.87).

The confidence interval does not contains the value 0. This implies that the null hypothesis will be rejected at 5% level of significance.

Hence, concluding that the mean exam scores of my STA 215 students with colorful calculators are different than the mean scores of my STA 215 students with plain black calculators.

7 0

3 years ago

HELP ASAP Expand the expression: 3(n+4)

Studentka2010 [4]

Multiply 3 and n, and 3 and 4.

3n+12

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hope it helps

4 0

3 years ago