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3 years ago

Factor the following trinomial.

Mathematics

2 answers:

MA_775_DIABLO [31]3 years ago

6 0

Answer:

Final answer is D. $(y-7)(y-8)$

Step-by-step explanation:

We need to factor the given trinomial $y^2-15y+56$

$=y^2-7y-8y+56$

Make two groups of first two and last two term then find GCF

$=y(y-7)-8(y-7)$

$=(y-8)(y-7)$

$=(y-7)(y-8)$

Which correctly matches with choice D)

Hence final answer is D. $(y-7)(y-8)$

horsena [70]3 years ago

4 0

Step-by-step explanation: This trinomial is in a special form that can be factored as the product of two binomials.

The first position in each binomial will be a factor of the y² term

and since y² breaks down into y · y, we use those as our factors.

The second term in each binomial will be factors of the

constant term that add to the coefficient of the middle term.

Since the middle term is negative, we use

negative factors of the constant term .

The factors that give us a product of 56 and add to -15 are -8 and -7.

So our answer is (y - 8)(y - 7).

This is the same as (y - 7)(y -8).

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In a class of 100 students, 25 students have hardcover and 75 students have paperback textbooks for the course. If you randomly

galina1969 [7]

h = prob of hardcover = .25

p = prob of paperback = .75

Prob(2 hardcover of 10) = (10 choose 2) (.25)^2 (.75)^8

= ( 10(9)/2 ) (1/4^10) (1^2 3^8)

= 295245/1048576

≈ 28.15%

I think I just did the binomial distribution. We can approximate it as a normal distribution. The mean and variance in this case are computed thus:

N=10, n=2

μ = Np = 2.5

σ² = Npq = 1.875

σ = 1.3693

P(n) = 1/(σ√2π)e^-(n-μ)/(2σ²)

P(2) = 1/(1.3693√2π)e^-(2 - 2.5)/(2 (1.875))

P(2) = 33.3%

Pretty good, not great.

6 0

3 years ago

A sample of 200 observations from the first population indicated that X1 is 170. A sam- ple of 150 observations from the second

nikitadnepr [17]

Answer:

a. If the P-value is smaller than the significance level, the null hypothesis is rejected.

b. Pooled proportion = 0.8

c. z = 2.7

d. As the P-value (0.0072) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

We will use the P-value approach, so the decision rule is that if the P-value is lower than the significance level, the null hypothesis is rejected.

The claim is that the proportions differ significantly.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

The significance level is 0.05.

The sample 1, of size n1=200 has a proportion of p1=0.85.

$p_1=X_1/n_1=170/200=0.85$

The sample 2, of size n2=150 has a proportion of p2=0.7333.

$p_2=X_2/n_2=110/150=0.7333$

The difference between proportions is (p1-p2)=0.1167.

$p_d=p_1-p_2=0.85-0.7333=0.1167$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{170+110}{200+150}=\dfrac{280}{350}=0.8$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.8*0.2}{200}+\dfrac{0.8*0.2}{150}}\\\\\\s_{p1-p2}=\sqrt{0.0008+0.00107}=\sqrt{0.00187}=0.0432$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.1167-0}{0.0432}=\dfrac{0.1167}{0.0432}=2.7$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=2\cdot P(z>2.7)=0.0072$

As the P-value (0.0072) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

6 0

3 years ago

Jennifer is 4 years older than Harvey. Harvey is twice as old as Gwen. If Gwen is g years old, which expression represents Jenni

Dafna11 [192]

Answer:

2g+4

Step-by-step explanation:

Harvey is twice as old as Gwen. The equation for this is 2g.

If we need to find Jennifer's age, which is 4 years older than Harvey, then we need to add 4 to Harvey's age.

2g+4

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4 years ago

Which Which is the simplified form of the expression ?

Stells [14]

Answer:

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3 years ago

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H ( x ) { − 2 + 3 , i f x < 1 1 /2 x + 1 if x ≥ 1 }

hoa [83]

Answer:????

Step-by-step explanation:

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3 years ago