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2 years ago

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In which of the following stores would you pay the least amount for an item that is priced $360? Store A: Sale of 10% off and a

successive discount of 10% off. Store B: Sale of 15% with no additional discount. Store C: Sale of $35 off and a successive discount of 10% off.

1 answer:

Crazy boy [7]2 years ago

3 0

The right answer for the question that is being asked and shown above is that: "A: Sale of 10% off and a successive discount of 10% <span>off." The </span><span>store that would let you pay the least amount for an item that is priced $360 is the Store A.</span>

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6. Two observers, 7220 feet apart, observe a balloonist flying overhead between them. Their measures of the

MaRussiya [10]

Answer:

The ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

Step-by-step explanation:

Let's call:

h the height of the ballonist above the ground,

a the distance between the two observers,

$a_1$ the horizontal distance between the first observer and the ballonist

$a_2$ the horizontal distance between the second observer and the ballonist

$\alpha _1$ and $\alpha _2$ the angles of elevation meassured by each observer

S the area of the triangle formed with the observers and the ballonist

So, the area of a triangle is the length of its base times its height.

$S=a*h$ (equation 1)

but we can divide the triangle in two right triangles using the height line. So the total area will be equal to the addition of each individual area.

$S=S_1+S_2$ (equation 2)

$S_1=a_1*h$

But we can write $S_1$ in terms of $\alpha _1$ , like this:

$\tan(\alpha _1)=\frac{h}{a_1} \\a_1=\frac{h}{\tan(\alpha _1)} \\S_1=\frac{h^{2} }{\tan(\alpha _1)}$

And for $S_2$ will be the same:

$S_2=\frac{h^{2} }{\tan(\alpha _2)}$

Replacing in the equation 2:

$S=\frac{h^{2} }{\tan(\alpha _1)}+\frac{h^{2} }{\tan(\alpha _2)}\\S=h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})$

And replacing in the equation 1:

$h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})=a*h\\h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}$

So, we can replace all the known data in the last equation:

$h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}\\h=\frac{7220 ft}{(\frac{1 }{\tan(35.6)}+\frac{1}{\tan(58.2)})}\\h=3579,91 ft$

Then, the ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

6 0

2 years ago

The number of species n found on islands typically increases with the area of the island A. Suppose that this relationship is su

Crazy boy [7]

Answer:

$n(A) = n_1A^k$

Step-by-step explanation:

Taking into account that the growth rate of the number of species on the island is proportional to the density of species (number of species between area of the island), a model based on a differential equation is proposed:

$\frac{dn}{dA} = k\frac{n}{A}$

This differential equation can be solved by the method of separable variables like this:

$\frac{dn}{n} = k\frac{dA}{A}$ with what you get:

$\int\ {\frac{dn}{n}}\ = k\int\ {\frac{dA}{A}}$

$ln|n| = kln|A|+C$ . Taking exponentials on both sides of the equation:

$e^{ln|n|} = e^{ln|A|^{k}+C}$

$n(A) = e^{C}A^{k}$

how do you have to $n (1) = n_1$ , then

$n(A) = n_1A^k$

8 0

2 years ago

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and

Alex787 [66]

One <u>possible inequality</u> is:

299m+261j ≥ 1000.

Explanation:

m is the number of cups of milk and j is the number of cups of juice.

Each cup of milk contains 299 mg of calcium. This gives us 299m mg of calcium for m cups of milk drank.

Each cup of juice contains 261 mg of calcium. This gives us 261j mg of calcium for j cups of juice drank.

Together, this would be a total of 299m+261j mg of calcium.

We want to meet or exceed 1000 mg of calcium. This means we could have more than 1000 or equal to 1000; this gives us the inequality symbol "greater than or equal to":

299m+261j ≥ 1000

5 0

2 years ago

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

In the roof truss, line BG bisects ∠ABC and ∠DEF, m∠ABC= 112°, and ∠ABC≅∠DEF.

Dennis_Churaev [7]

In the given diagram, line BG bisects ∠ABC and ∠DEF, m∠ABC= 112°, and ∠ABC≅∠DEF. So the measure of angles are :

1. m∠DEF= 112° because ∠ABC≅∠DEF

2. m∠ABG= 56° because a straight line BG is bisecting ∠ABC in two equal parts. So, $\frac{112}{2} = 56$

3. m∠CBG= 56° because ∠ABG and ∠CBG are equal.

4. m∠DEG= 56° because ∠ABG ≅ ∠DEG

7 0

2 years ago

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