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3 years ago

5

Your class is taking a trip to a museum that is 190 miles away. The bus can travel at 55 miles per hour. At least how many hours

should your class plan for the trip to the museum?

1 answer:

Fofino [41]3 years ago

8 0

Answer:

3 hours and 45 minutes

Step-by-step explanation:

190/55=3.4545

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The exponential function y= a(b)^x passes through the points (3,25) and (8,10). Which of the following is closest to the value o

Yuki888 [10]

If the exponential function $y=ab^x$ passes through the points (3,25) and (8,10), the value of b is 0.833

The given exponential equation is:

$y=ab^x$

The function passes through the points (3, 25) and (8, 10)

Substitute x = 3 and y = 25 into the function $y=ab^x$

$25=ab^3$ ............................(1)

Substitute x = 8 and y = 10 into the function $y=ab^x$

$10=ab^8$ .............................(2)

Divide equation (2) by equation (1)

$\frac{10}{25}=\frac{ab^8}{ab^3} \\\\0.4=b^5\\\\b=0.4^\frac{1}{5} \\\\b=0.4^{0.2}\\\\b=0.833$

Therefore, if the exponential function $y=ab^x$ passes through the points (3,25) and (8,10), the value of b is 0.833

Learn more on exponential functions here: brainly.com/question/12940982

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3 years ago

What is the greatest common factor of x^3 and x?

Lapatulllka [165]

I dont completely know but it might be 3

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3 years ago

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The book rack sold 24 paperbacks on Saturday, 17 of them mysteries. What percent of the books were mysteries?

igomit [66]

Answer:

About 71% of the books were mystery books

Step-by-step explanation:

To find the percentage of something you simply divide the amounts. 17 of the 24 books were mystery so to find the percentage of mystery books you do 17 divided by 24

17/24= 0.70833333333

and round it to 71

8 0

3 years ago

the polynomial 3x+5 is divided by x+2 what is the quotient, pls be quick im taking a algebra progress check due in 25 min

il63 [147K]

Answer:

The quotient of the rational function is $3 -\frac{1}{x+2}$ .

Step-by-step explanation:

We proceed to solve the expression by solely algebraic means below:

1) $\frac{3\cdot x + 5}{x+2}$ Given

2) $\frac{(3\cdot x + 5) + 0}{x + 2}$ Modulative property

3) $\frac{(3\cdot x +5) + [1+(-1)]}{x+2}$ Existence of additive inverse/Associative property

4) $\frac{(3\cdot x + 6)+(-1)}{x+2}$ Definition of addition/Commutative and associative properties

5) $\frac{3\cdot (x+2)}{x+2} + \left(-\frac{1}{x+2} \right)$ $\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$ / $\frac{-a}{b} = \frac{a}{-b} = -\frac{a}{b}$ /Distributive property

6) $3 -\frac{1}{x+2}$ Definition of division/Existence of multiplicative inverse/Modulative property/Definition of subtraction/Result

The quotient of the rational function is $3 -\frac{1}{x+2}$ .

5 0

3 years ago

In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525 likely voters living in California. This is the 14

lbvjy [14]

Answer:

We are confident at 99% that the difference between the two proportions is between $0.380 \leq p_{Republicans} -p_{Democrats} \leq 0.420$

Step-by-step explanation:

Part a

Data given and notation

$X_{D}=3266$ represent the number people registered as Democrats

$X_{R}=2137$ represent the number of people registered as Republicans

$n=7525$ sampleselcted

$\hat p_{D}=\frac{3266}{7525}=0.434$ represent the proportion of people registered as Democrats

$\hat p_{R}=\frac{2137}{7525}=0.284$ represent the proportion of people registered as Republicans

The standard error is given by this formula:

$SE=\sqrt{\frac{\hat p_D (1-\hat p_D)}{n_{D}}+\frac{\hat p_R (1-\hat p_R)}{n_{R}}}$

And the standard error estimated given by the problem is 0.008

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion of Democrats that approve of the way the California Legislature is handling its job

$\hat p_A =\frac{1894}{3266}=0.580$ represent the estimated proportion of Democrats that approve of the way the California Legislature is handling its job

$n_A=3266$ is the sample size for Democrats

$p_B$ represent the real population proportion of Republicans that approve of the way the California Legislature is handling its job

$\hat p_B =\frac{385}{2137}=0.180$ represent the estimated proportion of Republicans that approve of the way the California Legislature is handling its job

$n_B=2137$ is the sample for Republicans

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.64$

And replacing into the confidence interval formula we got:

$(0.580-0.180) - 1.64 \sqrt{\frac{0.580(1-0.580)}{3266} +\frac{0.180(1-0.180)}{2137}}=0.380$

$(0.580-0.180) + 1.64 \sqrt{\frac{0.580(1-0.580)}{3266} +\frac{0.180(1-0.180)}{2137}}=0.420$

And the 99% confidence interval would be given (0.380;0.420).

We are confident at 99% that the difference between the two proportions is between $0.380 \leq p_{Republicans} -p_{Democrats} \leq 0.420$

5 0

3 years ago