A diamond is purchased for $ 2500 . Suppose its value increases 5 % each year.
a. What is the value of diamond after 8 years?

There are 126 ways a student can select 5 questions from an exam containing 9 questions

The given parameters are

Total questions, n = 9

Selected question, r = 5

The number of ways is calculated as

Ways = nCr

This gives

Ways = 9C5

Apply the combination formula

Ways = 9!/5!4!

Evaluate

Ways = 126

Hence, there are 126 ways a student can select 5 questions from an exam containing 9 questions

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9:28 would be the time the movie ends

Answer:

9:28

Step-by-step explanation:

First, add an hour to 7:45. Then, find how much time there is until you reach the next hour. After that, take the remaining time and add it on. 7:45 plus one hour is 8:45. There is fifteen minutes until the next hour, so subtract that from the forty three minutes. Add that fifteen minutes on and you are at nine o'clock. There is twenty eight minutes left. Add it in to nine o'clock. You now have the time the movie will end

Hope this helps! :)

Answer:

answer is 502.91

Step-by-step explanation:

answer is 502.91

Answer:

502.91

Step-by-step explanation:

Answer:

Step-by-step explanation:

an area of a rectangle is

A= LW

A=51/2 (3)

A= 153/2

A= 76.5 ft

The inequality given by 4x - 2 > 1/2 has the solution x > 5/8 or (5/8 , +∞).

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.

Given the inequality 4x - 2 > 1/2, add 2 to both sides.

4x - 2 + 2 > 1/2 + 2

4x > 5/2

Multiply both sides by 1/4.

1/4(4x) > 1/4(5/2)

x > 5/8

To check, let x = 3/4

x = 3/4 ≥ 5/8

Substitute this value to the inequality.

4x - 2 > 1/2

4(3/4) - 2 > 1/2

3 - 2 > 1/2

1 > 1/2

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The equation in slope-intercept form is y = 4x + 1

Given,

Points (x, y) = (-1, 5)

Parallel to y = 4x - 5

Now,

Recall that a parallel line to the one given has to have the same slope. The slope of the line given is "4" (the coefficient that accompanies "x").

Therefore the equation of a parallel line has to be of the form:

y = 4x - b

5 = 4(-1) - b

5 = -4 - b

b = -4 - (-5)

b = -4 + 5

b = 1

So the equation now becomes:

y = 4x + 1

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Answer:

68 degrees higher.

Step-by-step explanation:

You have to start at negative ( -11 to 0 ) which is already 11 degrees and then you need to count how much degrees from 0 to 57.

Answer: 68°F warmer was the temperature in Los Angeles

Step-by-step explanation:

[tex]57^0F-(-11^0F)=\\\\57^0F+11^0F=\\\\68^0F[/tex]

Answer:6.25

Step-by-step explanation:25/4=6.25 hope this helps

Answer:

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When two straight lines or rays intersect at a shared endpoint, an angle is generated. The measure of ∠3 is 31°.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

Given that ∠2 and ∠3 are supplementary angles. Therefore, the sum of the two angles will be 180°. Thus, we can write the sum of the two angles as,

∠2 + ∠3 = 180°

Also, it is mentioned in the question that the measure of ∠2 is 149°. Therefore, substitute the value of ∠2 in the above equation.

149° + ∠3 = 180°

∠3 = 180° - 149°

∠3 = 31°

Hence, the measure of ∠3 is 31°.

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Using the segment addition postulate, the values are:

a. y = 6

b. RS = 50

ST = 29

Based on the segment addition postulate, the following equation is true which we can use in finding the missing measures:

RS + ST = RT.

Given:

RS = 8y + 2,

ST = 4y + 5,

RT = 79.

a. Plug in the given values into RS + ST = RT:

8y + 2 + 4y + 5 = 79

12y + 7 = 79

12y = 79 - 7

12y = 72

y = 6

b. RS = 8y + 2 = 8(6) + 2

RS = 50

ST = 4y + 5 = 4(6) + 5

ST = 29

Thus, using the segment addition postulate, the values are:

a. y = 6

b. RS = 50

ST = 29

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The slope of the line that contains the given points A(0,6), B(4,0) is -3/2.

It is given in the question that the line contains the points A(0,6) and B(4,0).

We know that:-

The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-

m = (d-b)/(c-a)

Here, we have

m = slope of the line

(a,b) = (0,6)

(c,d) = (4,0)

Hence, putting the values of (a,b) and (c,d) , we get

Slope of the line that contains the given points A(0,6), F(4,0) is given by:-

(0-6)/(4-0) = -6/4 = -3/2

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The given situation presents a word problem and can be solved by converting the word problem into an equation.

Word problem is a few sentences representing a real-life scenario where a problem needs to be solved by method of a mathematical calculation.

According to the given situation:

Total number of bags – number of bags emptied=number of bags left

Total number of bags filled= b

Number of bags emptied=4

Number of bags left=6

Hence,

b-4=6

Solving the equation,

b=6+4

b=10

Note: The provided question does not include the options of equation. Possible options are:

4b=6; b+4=6; b/4=6; b-4=6

Hence, the equation used to determine the numbers of bags initially filled is b-4=6 and number of bags are 10 bags.

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Considering that the surface area and the volume of the cylinders are equal, the surface areas are given as follows:

14. 108π ft².

15. 250π ft².

For a cylinder of radius r and height h, the surface area is given by:

S = 2πr(h + r).

The volume is given by:

V = πr²h.

For item 14, the parameters are given as follows:

r = 6 ft, h = x ft.

Hence we solve for x equaling the surface area and the volume as follows:

V = S

36πx = 12π(x + 6)

3x = x + 6

2x = 6.

x = 3.

Hence the surface area is:

S = 12π(3 + 6) = 108π ft².

For item 15, the parameters are given as follows:

r = 10 ft, h = x ft.

Hence we solve for x equaling the surface area and the volume as follows:

V = S

100πx = 20π(x + 10)

5x = x + 10

4x = 10.

x = 2.5.

Hence the surface area is:

S = 20π(2.5 + 10) = 250π ft².

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Answer: 2.223 billion years old

Step-by-step explanation:

since 71 percent of the rock is remaining, the half life hasn't been reached yet. Hence, we know uranium isn't 4.5 billion years old yet. However, every-time 4.5 billions years pass, the rock get smaller by 2 times(a scale factor of 1/2). Hence, you can express that in a log equation:

[tex]\log_{2}(100/(percent of rock remaining))=[/tex] Fraction of 4.5 billions years of time passed

[tex]\log_{2}(100/50)=1[/tex]   ==> 100% of 4.5 billion years passed. When 50% of rock remains, 4.5 billion years have passed.

[tex]\log_{2}(100/100)[/tex] =

[tex]\log_{2}(1)=0[/tex]   ==> 0% of 4.5 billion years passed. When the rock hasn't decayed at all yet, that means that it is 0 years old.

[tex]\log_{2}(100/71)=0.494[/tex]   ==> 49.4 % of 4.5 billion years passed

0.494*4.5 billion =2.223 billion years passed

2.223 billion years old

Answer:

False

Step-by-step explanation:

Let's just analyze it.

x=2 if and only if |x|=2

That can be rewritten as:

if x = 2 then |x| = 2

AND

if |x| = 2 then x = 2

Let's solve each one separately:

we have x = 2

we can simply get |x| by removing the sign, if any. There is none, so |x| = 2.

The first part checks out.

we have |x| = 2

As with absolute values, this means that either x = 2 or x = -2

So we know from |x| that x is either 2 or -2, but the logical statement said "if |x| = 2 then x = 2", which is too specific - it forgets about -2.

The second part is false.

Overall, we now know that "X=2 if and only if |x| = 2" is false because x = -2 is a counterexample. We get: "False if and only if True" which itself is false.

Answer:

f = 1

Step-by-step explanation:

-9 + 8f = -6 + 5f

move variables

-9 + 6 = -3

-3 + 8f = 5f

5f - 8f = -3f

-3 = -3f

divide by -3

f = 1

Step-by-step explanation:

[tex]n = \frac{ - 5}{3} [/tex]

ATTACHED IS THE SOLUTION!!

If-then form of the given statement : an acute angle measures less than 90 will be : If an angle is an acute angle, then the angle measures less than 90 degrees.

We can understand this problem by using  the above statement as an example like :

If an angle is an acute angle, then the angle measures less than 90 degrees. The part after if : an angle is an acute angle is called a hypotheses and the part after then : the angle measures less than 90 degrees is called a conclusion.

Hypotheses followed by a conclusion is called an If-then statement or a conditional statement.

This is noted as :

p → q

This is read - if p then q.

A conditional statement is false if hypothesis is true and the conclusion is false. The example above would be false if it said  "If an angle is an acute angle, then the angle does not measure less than 90 degrees."

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Answers

1.1) So, we're given that 6cm is 15 ft to scale. That means that every 2cm = 5ft. So, the dimensions of her room are 5ft x 10ft.

1.2) In square feet that makes 15 (length*width)

1.3) We want a 3-foot wide couch (1/5 of 15) which means it will be 1/5 of 6cm, which equals 1.2 cm wide.

The value of the number is 9

From the question, we are to determine the number

From the given information,

"3 times a number is increased by 22"

Let the number be x

Thus,

3x + 22

"the result is 14 less than 7 times the number"

That is,

3x + 22 = 7x - 14

Now, solve the equation

3x + 22 = 7x - 14

22 + 14 = 7x - 3x

36 = 4x

x = 36/4

x = 9

Hence, the value of the number is 9

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The equation of a line with slope = 3 and y-intercept = (0,2) is: y = 3x + 2

Now,

Given:

To find: Equation of the line

Finding:

=> y = 3x + 2, which the required equation of the line.

Hence, The equation of a line with slope = 3 and y-intercept = (0,2) is: y = 3x + 2.

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If point D is located on the line MV, then the ratio that relates MD to DV is 3 : 1

The given parameters are

Calculate the distance between point D and point M using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have

MD = √(-6 - 0)^2 + (3 + 3/4)^2

Calculate the distance between point D and point V using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have

DV = √(2 - 0)^2 + (-2 + 3/4)^2

The ratio that relates MD to DV is represented as

Ratio = MD : DV

So, we have

MD : DV = √(-6 - 0)^2 + (3 + 3/4)^2 : √(2 - 0)^2 + (-2 + 3/4)^2

This gives

MD : DV = √(-6)^2 + (3 3/4)^2 : √(2)^2 + (-1 1/4)^2

Evaluate the exponents

MD : DV = √[36 + 225/16] : √[4 + 25/16]

Evaluate the sum

MD : DV = √[801/16] : √[89/16]

Divide ratios by √[89/16]

MD : DV = √9 : √1

Evaluate the exponent

MD : DV = 3 : 1

Hence, the ratio that relates MD to DV is 3 : 1

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The correct option is (B) 9/13.

The probability that it will not snow on Tuesday is 9/13.

The ratio of the quantity of favorable outputs to the overall number of possibilities of an event is defined as probability.

The number of favorable results for an experiment with 'n' outcomes is denoted by x.

The following formula is used to determine the probability of an event.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n.

Some properties of the probability are mentioned below-

Now, for the stated question;

The probability that it will snow on Tuesday is 4/13.

Use property 1;

Then, the probability that it will not snow on Tuesday is;

= 1 - 4/13

= (13 - 4)/13

= 9/13

Therefore, the probability that it will not snow on Tuesday is 9/13.

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Answer:

There is nothing to refer to

Step-by-step explanation:

The inequality that shows the number of visits she needs to make in order to get a free movie ticket is 7.5v + 70 ≥ 175

An equation is an expression that shows the relationship between two or more numbers and variables.

Let v represent the number of visits she needs to make in order to get a free movie ticket.

She needs at least 175 points for a free movie ticket. Hence:

7.5v + 70 ≥ 175

The inequality that shows the number of visits she needs to make in order to get a free movie ticket is 7.5v + 70 ≥ 175

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