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3 years ago

Match a member of the letter column to a member in the number column

Mathematics

1 answer:

Lena [83]3 years ago

7 0

Answer:

$mark \: the \: following \: boxes \to \\ \boxed{box \: 3} \\ \boxed{box \: 4} \\ \boxed{box \: 1} \\\boxed{box \: 2}$

Step-by-step explanation:

$\boxed{ ({y}^{3})^{2} } = {y}^{6} \to \boxed{box \: 3} \\ \boxed{ {y}^{ - 2} } = \frac{1}{ {y}^{2}} \to \boxed{box \: 4} \\ \boxed{ {y}^{8} \div \: y^{3} } = {y}^{5} \to \boxed{box \: 1} \\ \boxed{ {y}^{4} \times y^{4} } = {y}^{8} \to \boxed{box \: 2}$

♨Rage♨

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Let

x------> the number of multiple choice question

y------> the number of free response question

we know that

$3x+8y=55$ -----> equation A

$x+y=15$

$x=15-y$ -----> equation B

Substitute equation B in equation A

$3[15-y]+8y=55$

$45-3y+8y=55$

$5y=55-45$

$5y=10$

$y=2$

Find the value of x

$x=15-y$

$x=15-2=13$

therefore

<u>the answer is</u>

the number of multiple choice question are $13$

the number of free response question are $2$

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genetic experiment with peas resulted in one sample of offspring that consisted of green peas and yellow peas. a. Construct a %

Andreas93 [3]

Complete Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

Answer:

The 95% confidence interval is $0.2392 < p < 0.3108$

No, the confidence interval includes 0.25, so the true percentage could easily equal 25%

Step-by-step explanation:

From the question we are told that

The total sample size is $n = 432 + 164 =596$

The number of offspring that is yellow peas is $y = 432$

The number of offspring that is green peas is $g = 164$

The sample proportion for offspring that are yellow peas is mathematically evaluated as

$\r p = \frac{ 164 }{596}$

$\r p = 0.275$

Given the the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = (100 - 95)\%$

$\alpha = 5\% = 0.0 5$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically evaluated as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1- \r p )}{n} }$

=> $E = 1.96 * \sqrt{\frac{0.275 (1- 0.275 )}{596} }$

=> $E = 0.0358$

The 95% confidence interval is mathematically represented as

$\r p - E < p < \r p + E$

=> $0.275 - 0.0358 < p < 0.275 + 0.0358$

=> $0.2392 < p < 0.3108$

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3 years ago

Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos

Tanya [424]

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$P_{1} = (- 1, 4)$

$P_{2} = (6, 2)$ and

$P_{3} = (4, - 5)$

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $(x_1, y_1)$ and $(x_2, y_2)$ is:

$\sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+} \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}}$