All categories

2 years ago

You are in a bike race. When you get to the first checkpoint, you are $\frac{2}{5}$

Mathematics

1 answer:

Black_prince [1.1K]2 years ago

6 0

Answer:

The distance from the star to the second checkpoint is 4 miles

Step-by-step explanation:

The complete question in the attached figure

we know that

When you get to the second checkpoint, you are 1/4 of the distance to the finish

The distance from the star to the second checkpoint is equal to the total distance multiplied by 1/4

The total distance is 40 miles ( see the attached figure)

The distance from the star to the second checkpoint is

$\frac{1}{4}(40)=10\ miles$

<em>Find out the distance from the start to the first checkpoint</em>

Multiply the distance from the star to the second checkpoint by 2/5

$\frac{2}{5}(10)=4\ miles$

You might be interested in

A tank can contain 40 gallons of gas, but it is not completely full. How much gas is in the tank if 6.5% of the tank is empty?

Katena32 [7]

37.4 Gallons of gas should be your answer! Hope i helped!

6 0

2 years ago

Read 2 more answers

In addition to the facts in the diagram, which other statements are necessary to prove that ∆ABC is congruent to ∆EFG by the ASA

insens350 [35]

It should be B because you have to have 2 angles to know for sure.

8 0

2 years ago

Read 2 more answers

If a hurricane was headed your way, would you evacuate? The headline of a press release states, "Thirty-four Percent of People o

IgorC [24]

Answer:

The 98% confidence interval would be given by (0.326;0.354)

Step-by-step explanation:

1) Notation and definitions

$X=63$ number of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

$n=6138$ random sample taken

$\hat p=0.34$ estimated proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

$p$ true population proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

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".

The population proportion have the following distribution

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

2) Confidence interval

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 98% of confidence, our significance level would be given by $\alpha=1-0.98=0.02$ and $\alpha/2 =0.01$ . And the critical value would be given by:

$z_{\alpha/2}=-2.33, z_{1-\alpha/2}=2.33$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.34 - 2.33\sqrt{\frac{0.34(1-0.34)}{6138}}=0.326$

$0.34 + 2.33\sqrt{\frac{0.34(1-0.34)}{6138}}=0.354$

The 98% confidence interval would be given by (0.326;0.354)

8 0

2 years ago

shanti wrote the predicted values for a data set using the line of best fit y = 2.55x – 3.15. she computed two of the residual v

Delvig [45]

<span>The question asks us to determine the values for a and b in the linear equation. Linear equation in the slope-intercept form is : y = a x + b. This equation is: y = 2.25 x - 3.15. The slope: a = 2.25 and the y-intercept is: b = -3.15. Answer: a = 2.25 and b = - 3.15.</span>

8 0

2 years ago

Read 2 more answers

One month julia collected 8.4 gallons of rainwater. That month she used 5.2 gallons of rainwater to water her garden and 6.5 gal

Andru [333]

Given

One month julia collected 8.4 gallons of rainwater.

she used 5.2 gallons of rainwater to water her garden

6.5 gallons of rainwater to water flowers

Find out how much was the supply of rainwater increased or decreased by the end of the month.

To proof

As given in the question

One month julia collected 8.4 gallons of rainwater

she used 5.2 gallons of rainwater to water her garden and 6.5 gallons of rainwater to water flowers

Total water she used in the month = 5.2 gallons + 6.5gallons

= 11.7 gallons

Let the supply of rainwater increased or decreased by the end of the month

be x .

Than the equation become in the form

x + 8.4 = 11.7

x = 3.3 gallons

Therefore the supply of rainwater increased or decreased by the end of the month is 3.3 gallons.

Hence proved

8 0

2 years ago

Read 2 more answers