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valentina_108 [34]
3 years ago
11

Find the product. (4m^2 – 5)(4m^2 + 5)

Mathematics
1 answer:
aliya0001 [1]3 years ago
3 0

Answer: 16m^4−25


Step-by-step explanation:

(4m^2−5)(4m^2+5)

=(4m^2+−5)(4m^2+5)

=(4m^2)(4m^2)+(4m^2)(5)+(−5)(4m^2)+(−5)(5)

=16m^4+20m^2−20m^2−25

=16m^4−25

You might be interested in
5. (9r 3 + 5r 2 + 11r) + (-2r 3 + 9r - 8r 2)
ad-work [718]

Answer:

7r³ - 3r² + 20r

Step-by-step explanation:

(9r³ + 5r² + 11r) + (-2r³ + 9r - 8r²)

You can get rid of the parentheses since there is nothing to distribute.

9r³ + 5r² + 11r - 2r³ + 9r - 8r²

Combine like factors.

7r³ - 3r² + 20r

3 0
2 years ago
A national survey of companies included a question that asked whether the company had at least one bilingual telephone operator.
nirvana33 [79]

Answer:

The first option is correct. Option A is correct.

LCL = 0.270, and UCL = 0.397

80% Confidence interval = (0.270, 0.397)

Step-by-step explanation:

The data for Y and N for the 90 companies is attached to this solution provided.

Y represents companies with at least 1 bilingual operator and N represents companies with no bilingual operator.

The number of Y in the data = 30

Hence, sample proportion of companies with at least one bilingual operator = (30/90) = 0.3333

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = 0.3333

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 80% confidence level for sample size of 90 is obtained from the z-tables.

Critical value = 1.280

Standard error of the mean = σₓ = √[p(1-p)/n]

p = sample proportion

n = sample size = 90

σₓ = √[0.3333×0.6667)/90] = 0.0496891568 = 0.04969

80% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.3333 ± (1.28 × 0.04969)

CI = 0.3333 ± 0.0636021207

80% CI = (0.2696978793, 0.3969021207)

80% Confidence interval = (0.270, 0.397)

Hope this Helps!!!

3 0
3 years ago
A restaurant chain has two locations in a medium-sized town and, believing that it has oversaturated the market for its food, is
scoray [572]

Answer:

Yes, since the test statistic value is greater than the critical value.

Step-by-step explanation:

Data given and notation

\bar X_{1}=360000 represent the mean for the downtown restaurant

\bar X_{2}=340000 represent the mean for the freeway restaurant

s_{1}=50000 represent the sample standard deviation for downtown

s_{2}=40000 represent the sample standard deviation for the freeway

n_{1}=36 sample size for the downtown restaurant

n_{2}=36 sample size for the freeway restaurant

t would represent the statistic (variable of interest)

\alpha=0.05 significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the true mean of revenue for downtown is higher than for freeway restaurant, the system of hypothesis would be:

Null hypothesis:\mu_{1}\leq \mu_{2}

Alternative hypothesis:\mu_{1} > \mu_{2}

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}} (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Determine the critical value.

Based on the significance level\alpha=0.05 and \alpha/2=0.025 we can find the critical values from the t distribution dith degrees of freedom df=36+36-2=55+88-2=70, we are looking for values that accumulates 0.025 of the area on the right tail on the t distribution.

For this case the value is t_{1-\alpha/2}=1.66

Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

t=\frac{360000-340000}{\sqrt{\frac{50000^2}{36}+\frac{40000^2}{36}}}}=1.874

What is the p-value for this hypothesis test?

Since is a right tailed test the p value would be:

p_v =P(t_{70}>1.874)=0.033

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given \alpha=0.05 we see that p_v so we can conclude that we reject the null hypothesis, and the true mean for the downtown revenue restaurant seems higher than the true mean revenue for the freeway restaurant.

The best option would be:

Yes, since the test statistic value is greater than the critical value.

5 0
2 years ago
WILL GIVE BRAINLIEST<br>What is the value of x in the figure? 1042 (3x – 19)​
Anna11 [10]

Answer:

x = 41

Step-by-step explanation:

We know these angles will be equal to each other (they are across from each other, I honestly forget the term ) so we can set up an equation

Our equation from given: 104 = 3x - 19

Adding 19 to both sides 123 = 3x

Dividing both sides by 3: 41 = x

Answer: x = 41

5 0
3 years ago
If f(x) =1/x and g(x) = x - 2 what is f(g(x)) when X = 1​
Fed [463]

Answer:

f(g(x)) = -1

Step-by-step explanation:

f(x) =  \frac{1}{x}  \\  \\ g(x) = x - 2 \\  \\  \implies \: f(g(x)) =  \frac{1}{x - 2}  \\  \\  \implies \: f(g(1)) =  \frac{1}{1 - 2} \\  \\  \implies \: f(g(1)) =  \frac{1}{ - 1} \\  \\  \implies \: f(g(1)) =   - 1

8 0
2 years ago
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