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3 years ago

For each situation, give an example that includes the original price and final price after markup or markdown.

Mathematics

2 answers:

Over [174]3 years ago

8 0

Answer:

Step-by-step explanation:

its correct mark pls i really need

il63 [147K]3 years ago

4 0

Answer:

go to your book read it or ask your sir or ma'am

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Which of the following pairs of terms are like terms?

swat32

Answer:

Step-by-step explanation:

they have the same variable

3 0

3 years ago

Prove that 17^16+17^14 is divisible by 5

fredd [130]

We'll use the exponent rule that a^(b+c) = a^b*a^c

to break up 17^16 into 17^(14+2) = 17^14*17^2

That allows us to factor like so

17^16+17^14

17^14*17^2+17^14*1

17^14(17^2 + 1)

Computing 17^14 is a lot more difficult compared to computing 17^2 + 1, assuming you only could use paper and pencil.

Note that 17^2 = 17*17 = 289, so 17^2 + 1 = 289+1 = 290

Because 290 ends in a 0, this means that 5 is a factor

290 = 5*58

This makes 5 to be a factor of the original expression.

----------------

So overall,

17^16+17^14 = 17^14(17^2 + 1) = 17^14*290 = 17^14*5*58 = 5*17^14*58

The stuff "17^14*58" doesn't matter. All we care about is that factor of 5.

Since 5 is a factor, this means that 17^16+17^14 is a multiple of 5, or 17^16+17^14 is divisible by 5.

Phrased another way, 17^16+17^14 all divided over 5 leads to some integer. In this case, the integer would be the result of 17^14*58.

6 0

3 years ago

Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions th

trasher [3.6K]

Answer:

(a) 100 fishes

(b) t = 10: 483 fishes

t = 20: 999 fishes

t = 30: 1168 fishes

(c)

$P(\infty) = 1200$

Step-by-step explanation:

Given

$P(t) =\frac{d}{1+ke^-{ct}}$

$d = 1200\\k = 11\\c=0.2$

Solving (a): Fishes at t = 0

This gives:

$P(0) =\frac{1200}{1+11*e^-{0.2*0}}$

$P(0) =\frac{1200}{1+11*e^-{0}}$

$P(0) =\frac{1200}{1+11*1}$

$P(0) =\frac{1200}{1+11}$

$P(0) =\frac{1200}{12}$

$P(0) = 100$

Solving (a): Fishes at t = 10, 20, 30

$t = 10$

$P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483$

$t = 20$

$P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999$

$t = 30$

$P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168$

Solving (c): $\lim_{t \to \infty} P(t)$

In (b) above.

Notice that as t increases from 10 to 20 to 30, the values of $e^{-ct}$ decreases

This implies that:

${t \to \infty} = {e^{-ct} \to 0}$

So:

The value of P(t) for large values is:

$P(\infty) = \frac{1200}{1 + 11 * 0}$

$P(\infty) = \frac{1200}{1 + 0}$

$P(\infty) = \frac{1200}{1}$

$P(\infty) = 1200$

5 0

3 years ago

In exercises 5-10, use your new conjectures to calculate the measure of each lettered angle.

Viktor [21]

Answer:

Step-by-step explanation:

I can barely see enough to do 5 and 6. 7 the diagram is unclear and 9 I can't tell where the letters are. I suggest you darken the lines and make sure the letters for the unknowns are clear. Don't hold the paper: just as the picture was taken the image moved slightly. I don't know what to suggest.

Five

The ray defining a is pointing right at the five. That's my first assumption.

You need to find the interior angle connected to a.

Pentagon exterior angles

The total number of degrees for the exterior angles of a pentagon is 360

Supplement of 140 degrees

140 + x = 180 because the exterior and interior angles are supplementary

x = 180 - 140

x = 40

Find a

a + 40 + 60 + 84 + 68 = 360

a + 252 = 360

a = 360 - 252

a = 108

Six

This is really hard to read. Including b, there are three angles that are marked the same

Supplement to 68

180 - 68 = 112

Find b

112 + 43 + x + 89 + x +x = 360

244 + 3x = 360

3x = 116

x = 116/3

x = 38.67

Since b is marked as equal to 1 of the 3 exterior angles that are equal, b = 38.67

That is all I can read.

4 0

4 years ago

A pedestal for a statue is made with 405 cubic feet of concrete. a rectangular prism with a height of 9 feet. what is the area o

enyata [817]

45 square feet is the area of the base of the pedestal.

what is rectangular prism?

A rectangular prism is a 3D figure with 6 rectangular faces.
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

we know that

The volume of the pedestal (rectangular prism) is given by the formula

V = B × h

where

B is the area of the rectangular base of pedestal

V = 405 ft³

h = 9 ft

put the given values in the formula and solve for B

405 = B × 9

B = 405/9

B = 45 ft²

Therefore, 45 square feet is the area of the base of the pedestal.

Learn more about rectangular prism

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3 0

2 years ago