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2 years ago

What is the product mentally of (ab + 3)(ab - 3)

Mathematics

2 answers:

AleksAgata [21]2 years ago

3 0

Answer:

ab² - 9

Step-by-step explanation:

Given in the question an expression

(ab + 3)(ab - 3)

To product mentally we will use polynomial identity called

Difference of squares

here a = ab

b = 3

(ab + 3)(ab - 3) = ab² - 3² = ab² - 9

xxTIMURxx [149]2 years ago

3 0

Answer:

$a^2b^2 - 9$

Step-by-step explanation:

We are given the following expression and we are to determine its product mentally:

$( a b + 3 ) ( a b - 3 )$

For this, we can use the FOIL method, which stands for First, Outer, Inner, Last.

First means multiply the terms which come first in each of the binomial, Outer means multiply the outermost terms in the product. Inner means multiply the innermost two terms. Last means multiply the terms which occur last in each binomial.

So we get:

$ab*ab +3*(-3)=a^2b^2 - 9$

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the diagram, JG = 5 cm and GE = 10 cm. Based on this information, can G be a centroid of triangle HJK?

SIZIF [17.4K]

Point G cannot be a centroid because GE is wider that JG or JG is shorter than GE. So in this diagram GE is wider than JG with 10 cm and 5 cm respectively based on this information Point G cannot be a centroid of triangle HJK. So the answer is point G cannot be a centroid because JG is shorter than GE.

4 0

2 years ago

Read 2 more answers

Suppose that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage

Zigmanuir [339]

Answer:

We conclude that the percentage of blue candies is equal to 29%.

Step-by-step explanation:

We are given that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%.

Let p = population percentage of blue candies

So, Null Hypothesis, $H_0$ : p = 29% {means that the percentage of blue candies is equal to 29%}

Alternate Hypothesis, $H_A$ : p $\neq$ 29% {means that the percentage of blue candies is different from 29%}

The test statistics that will be used here is One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of blue coloured candies = 28%

n = sample of colored candies = 100

So, the test statistics = $\frac{0.28-0.29}{\sqrt{\frac{0.29(1-0.29)}{100} } }$

= -0.22

The value of the z-test statistics is -0.22.

Also, the P-value of the test statistics is given by;

P-value = P(Z < -0.22) = 1 - P(Z $\leq$ 0.22)

= 1 - 0.5871 = 0.4129

Now, at a 0.10 level of significance, the z table gives a critical value of -1.645 and 1.645 for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of z, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the percentage of blue candies is equal to 29%.

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3 years ago

What is y - 8 = -1/2 (x + 4) in standard form (8th grade math)

Natalija [7]

Y-8=-1/2x + (-2)
+8 +8
y=-1/2x +6
I just used a 2 step equation for it. I first used Distributive Property. Then Subtracted 8 from each side

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2 years ago

1. A number minus 6 is – 22. Find the number,

Savatey [412]

Answer:

-16

Step-by-step explanation:

X-6= -22

X = -22+6

X = - 16

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1 year ago

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Ricardo and Tammy practice putting golf balls. Ricardo makes 47% of his putts and Tammy makes 51% of her putts. Suppose that Ric

yaroslaw [1]

Answer:

0.3821 = 38.21% probability that Ricardo makes a higher proportion of putts than Tammy.

Step-by-step explanation:

To solve this question, we need to understand the normal distribution, the central limit theorem, and subtraction of normal variables.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction of normal variables:

When we subtract normal variables, the mean of the subtraction will be the subtraction of the means, while the standard deviation will be the square root of the sum of the variances.

Ricardo makes 47% of his putts, and attempts 25 putts.

By the Central Limit Theorem, we have that:

$\mu_R = 0.47, s_R = \sqrt{\frac{0.47*0.53}{25}} = 0.0998$