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2 years ago

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Roger went shoe shopping with his cousins Derek and Kamal. Roger bought a pair of basketball shoes that cost $74.95. Derek spent

$24.55 more than Roger on a pair of running shoes. Kamal bought the same running shoes as Derek. Since he had a coupon, Kamal paid 4/ 5 as much as Derek for the shoes. How much money did Kamal spend on running shoes?

1 answer:

bezimeni [28]2 years ago

8 0

Answer:

I'm pretty sure its $19.65

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The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have originally contained 6 milli

anzhelika [568]

Answer:

$A(t)=6\cdot2^{-\frac{t}{5730 }$

Step-by-step explanation:

The general formula for exponential decay given a half-life $t_\frac{1}{2}$ is

$N(t)=N_{0}\cdot2^{\frac{-t}{t_{1/2} }$

where N(t) is the amount at time t, $N_0$ is the initial amount (at time t=0), and $t_\frac{1}{2}$ is the half life of the substance.

The half life of carbon-14, is approximately 5,730 years.

$t_\frac{1}{2}$ = 5730 years

$N_0$ = 6 milligrams

Therefore:

Amount of carbon-14 remaining in the bone fragment after t years is:

$A(t)=6\cdot2^{-\frac{t}{5730 }$

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2 years ago

There are 345 students at a college who have taken a course in calculus, 212 who have taken a course in discrete mathematics, an

ollegr [7]

Answer:

369 students have taken a course in either calculus or discrete mathematics

Step-by-step explanation:

I am going to build the Venn's diagram of these values.

I am going to say that:

A is the number of students who have taken a course in calculus.

B is the number of students who have taken a course in discrete mathematics.

We have that:

$A = a + (A \cap B)$

In which a is the number of students who have taken a course in calculus but not in discrete mathematics and $A \cap B$ is the number of students who have taken a course in both calculus and discrete mathematics.

By the same logic, we have that:

$B = b + (A \cap B)$

188 who have taken courses in both calculus and discrete mathematics.

This means that $A \cap B = 188$

212 who have taken a course in discrete mathematics

This means that $B = 212$

345 students at a college who have taken a course in calculus

This means that $A = 345$

How many students have taken a course in either calculus or discrete mathematics

$(A \cup B) = A + B - (A \cap B) = 345 + 212 - 188 = 369$

369 students have taken a course in either calculus or discrete mathematics

4 0

1 year ago

The picture below shows a box sliding down a ramp:

Gennadij [26K]

Answer:

$AC=15.1\ ft$

Step-by-step explanation:

we know that

In the right triangle ABC

The function sine of angle 68 degrees is equal to divide the opposite side SB by the hypotenuse AC

so

$sin(68\°)=\frac{AB}{AC}$

substitute the values and solve for AC

$sin(68\°)=\frac{14}{AC}$

$AC=\frac{14}{sin(68\°)}$

$AC=15.1\ ft$

4 0

2 years ago

Most US adults have social ties with a large number of people, including friends, family, co-workers, and other acquaintances. I

xxTIMURxx [149]

Answer:

$t=\frac{669-634}{\frac{732}{\sqrt{1700}}}=1.971$

$p_v =2*P(t_{(1699)}>1.971)=0.049$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 634 at 10% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=669$ represent the sample mean

$s=732$ represent the sample standard deviation

$n=1700$ sample size

$\mu_o =68$ represent the value that we want to test

$\alpha=0.$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different from 634, the system of hypothesis would be:

Null hypothesis: $\mu = 634$

Alternative hypothesis: $\mu \neq 634$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{669-634}{\frac{732}{\sqrt{1700}}}=1.971$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=1700-1=1699$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(1699)}>1.971)=0.049$

Conclusion

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 634 at 10% of signficance.

3 0

1 year ago

A dolphin is 42 feet underwater and ascends at a constant rate for 14 seconds until it reaches the surface. Identify and interpr

Cloud [144]

Ok so, based on the graph lets say that x = seconds and y = depth of dolphin. the interception in both points is when they are at 0 i.e when x is equals 0 and y equals 0. So At 0 seconds, the dolphin is 42 feet below the surface. So we say that x = 0, y = -42 and then the y intercepts = -42 so the point of interception is(0 (seconds),-42(depth of the dolphin)) When the clock says it's 14 seconds, the dolphin is even with the surface (0 below the surface this time). So we say that x = 14, y = 0. In this case The x intercept = 14 (14,0). But we need to calculate The slope with the formula= (y2 - y1)/(x2 - x1) = 42/14 = 3. Therefore, the formula for this line is y = 3x - 42.

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2 years ago