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Amiraneli [1.4K]

2 years ago

4

If a first experiment can be performed in 5 distinct ways and a second experiment can be performed in 9 distinct ways, the two

experiments together can be performed in how many distinct ways?

1 answer:

tatuchka [14]2 years ago

6 0

Answer:

45

Step-by-step explanation:

5 × 9 = 45

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Find the simplified product b-5/2b x b^2+3b/b-5

White raven [17]

Answer:

The product $\frac{b-5}{2b}\times\frac{b^2+3b}{b-5}=\frac{b+3}{2}$

Step-by-step explanation:

Given expression $\frac{b-5}{2b}$ and $\frac{b^2+3b}{b-5}$

We have to find the product of $\frac{b-5}{2b}\times\frac{b^2+3b}{b-5}$

Consider the given expression $\frac{b-5}{2b}\times\frac{b^2+3b}{b-5}$

Multiply fractions, we have,

$\frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}$

$=\frac{\left(b-5\right)\left(b^2+3b\right)}{2b\left(b-5\right)}$

Cancel common factor ( b - 5 )

we have, $=\frac{b^2+3b}{2b}$

Apply exponent rule,

$\:a^{b+c}=a^ba^c$

$b^2=bb$

$=bb+3b=b(b+3)$

$=\frac{b\left(b+3\right)}{2b}$

Cancel common factor b , we have,

$=\frac{b+3}{2}$

Thus, the product $\frac{b-5}{2b}\times\frac{b^2+3b}{b-5}=\frac{b+3}{2}$

8 0

2 years ago

Read 2 more answers

An increased number of colleges have been using online resources to research applicants. According to a study from last year, 3

Aneli [31]

Answer:

D. H0: p ≤0.36 H1: p>0.36

$$$(Right tail test) Z_{\alpha}=Z_{0.1}=1.28155$

$Z_p=-0.25516$

D. Reject H0. There is sufficient evidence to support the hypothesis that the proportion of admissions officers who visit an applying students' social networking page has increased in the past year

Step-by-step explanation:

To solve this problem, we run a hypothesis test about the population proportion.

$$$Sample proportion: $\bar P=0.47\\Sample size n=100$\\Significance level \alpha=0.10$\\(Left tail test) Z_{1-\alpha}=Z_{0.90}=-1.28155$\\(Right tail test) Z_{\alpha}=Z_{0.1}=1.28155$\\(Two-tailed test) $Z_{1-\alpha/2}=Z_{0.95}=-1.64485$ and $ Z_{\alpha/2}=Z_{0.05}=1.64485\\\\$

The appropriate hypothesis system for this situation is:

$H_0:\pi_0=0.35\\H_a:\pi_0 > 0.35\\\\$Proportion in the null hypothesis is:\\\pi_0=0.35\\\\$

$$$The test statistic is $Z=\frac{(\bar P-\pi_0)\sqrt{n}}{\sqrt{\pi_0(1-\pi_0)}}\\$The calculated statistic is Z_c=\frac{(0.47-0.35)\sqrt{100}}{\sqrt{0.35(1-0.35)}}=-0.25516\\p-value = P(Z \geq Z_c)=0.01620\\\\$

Since, the calculated statistic $Z_c$ is greater than critical $Z_{\alpha}$ , the null hypothesis should be rejected. There is enough statistical evidence to state that the proportion of admissions officers who visit an applying students' social networking page has increased in the past year.

5 0

2 years ago

The triangles are congruent by SSS or HL. The diagram shows the sequence of three rigid transformations used to map ABC onto A"B

Pani-rosa [81]

Answer:

The sequence of transformation used to map ABC onto A"B"C" is reflection, then rotation, then translation.

Step-by-step explanation:

To map ABC onto A"B"C" steps are:

step 1: Reflection of ABC

step 2: rotation of A'BC by some angle to obtain A'B'C'.

step 3: translation of A'B'C' by some units to the right to obtain the given transformation A"B"C".

7 0

2 years ago

Read 2 more answers

James has established the following monthly budget for himself: Rent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8090 [49]

Answer:

James's monthly income is $1250.

Step-by-step explanation:

If the budget accounts for James's entire monthly income, the sum of the cost of all the items on the budget is his total monthly income.

Income = 300 + 175 + 125 + 200 + 250 + 50 + 25 + 125 = $1250

6 0

2 years ago

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A golden rectangle is 32cm long.The ratio of length to width is (1 + square root of 5) :2. What is the width of the rectangle in

zhannawk [14.2K]

Answer:

Width = 16(√5) - 1

Step-by-step explanation:

We are told that the golden rectangle is 32 cm long.

Thus, length = 32 cm

We are also told that the ratio of the length to the width is; (1 + √5):2

Thus;

If a length of (1 + √5) yields a width of 2

Then, a length of 32 cm would yield a width of; (32 x 2)/(1 + √5)

So corresponding width = 64/(1 + √5)

We want to reduce this width to it's simplest radical form which means the denominator should have no square root.

Thus, let's multiply top and bottom by (1 - √5);

Width = 64 x (1 - √5)/[(1 + √5) x (1 - √5)]

Width = 64(1 - √5)/(1 - 5)

Width = 64(1 - √5)/(-4)

Width = -16(1 - √5)

Width = 16(√5 - 1)

Width = 16√5 - 1

8 0

2 years ago