Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

Answers

Answer 1

Two equations that have the same solution as the given equation are;

2.3p – 10.1 =  6.49p – 4

230p – 1010 = 650p – 400 – p

What is Multiplication property of equality?

Both sides of an equation will remain equal, when both sides are

multiplied by the same amount.

The given equation: 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

Simplifying the above equation by collecting like terms gives;

2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4

2.3·p - 10.1 = 6.49·p - 4

Multiplying both sides of the original equation by 100 gives

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

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Related Questions

Identify the sequence that lists sides of STU in order from shortest to longest

ST, UT, SU

UT, SU, ST

SU, ST, UT

SU, UT, ST

Answers

On soloing the provided question we can say that - Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area. A = 210-123 = 87 sq unit

what is triangle?

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

the sum of the areas of the circle, the triangle, and the square.

Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area.

A = 210-123 = 87 sq unit

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Find the 8th term of the geometric sequence whose common ratio is 3/2 and whose first term is 6.

Answers

Answer:

A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is always the same. This ratio is called the common ratio of the sequence.

In this case, the common ratio is 3/2 and the first term is 6. The nth term of a geometric sequence can be found using the formula:

a_n = a_1 * r^(n-1)

where a_n is the nth term, a_1 is the first term, and r is the common ratio.

Substituting the given values, we have:

a_8 = 6 * (3/2)^(8-1) = 6 * (3/2)^7

Calculating, we find that the 8th term is:

a_8 = 6 * (3/2)^7 = 6 * (9/2) = 27

Therefore, the 8th term is 27.

Step-by-step explanation:

A prescription indicates that 1.25 grams of a given drug should be taken

Twice a day. If the drug is available in 500 milligram tablets, how many tablets does it Will the patient take every 12 hours?

Answers

Ans=5 tablets.
Solutions
Convert grams to milligrams: 1.25g*1000=1250mg
1250mg/500mg*1 tab=2.5 tabs
How many tablets will the patient take every 12 hours: 24 hours/12 hours = 2
Therefore, every 12 hours the patient will take: 2.5*2= 5 tablets.

Itzel purchased 18 pounds of oranges.
How many ounces of oranges did she
purchase?

Answers

Answer:

288

Step-by-step explanation:

1 pound is equal to 16 ounces

if Itzel purchases 18 pounds, to convert to ounces simply multiply 18 by 16.

Answer:

288

I wish you luck in your assignments.

(I just noticed someone got here in before me and answered WAY better. So I edited this to tell you to give them brainliest.)

100 points Pls help me with the red ones

Answers

Answers:
For 36 people with peanuts = 9 cups
For 4 people with peanuts = 1 cup
For 6 people with peanuts = 1.5 cups
For 4 people with M & MS = 8/12 cups or 0.67 cups
For 6 people with M & MS = 1 cup
For 36 people with raisins = 1.5 cups
For 4 people with raisins = 2/12 cups or 0.17 cups
For 6 people with raisins = 0.25 cups
For 36 people with candy corn = 3.9 cups
For 4 people with candy corn = 0.43 cups
For 6 people with candy corn = 0.65 cups

Step-by-step explanation:
1. Set up a proportion to find how many cups it takes to feed 36 people peanuts given that it takes 3 cups to feed 12 people. This means that the proportion would be 3/12 = x/36. Cross multiply. This would give you 12x = 108. Divide 12 on both sides. Now, the equation is solved since you found out x = 9 cups.

2. Set up a proportion to find how many cups it takes to feed 4 people peanuts given that it takes 3 cups to feed 12 people. This means that the proportion would be 3/12 = x/4. Cross multiply. This would give you 12x = 12. Divide 12 on both sides. Now, the equation is solved since you found out x = 1 cup.

3. Set up a proportion to find how many cups it takes to feed 6 people peanuts given that it takes 3 cups to feed 12 people. This means that the proportion would be 3/12 = x/6. Cross multiply. This would give you 12x = 18. Divide 12 on both sides. Now, the equation is solved since you found out x = 1.5 cups.

4. Set up a proportion to find how many cups it takes to feed 4 people M & Ms given that it takes 2 cups to feed 12 people. This means that the proportion would be 2/12 = x/4. Cross multiply. This would give you 12x = 8. Divide 12 on both sides. Now, the equation is solved since you found out x = 0.67 cups.

5. Set up a proportion to find how many cups it takes to feed 6 people M & Ms given that it takes 2 cups to feed 12 people. This means that the proportion would be 2/12 = x/6. Cross multiply. This would give you 12x = 12. Divide 12 on both sides. Now, the equation is solved since you found out x = 1 cup.

5. Set up a proportion to find how many cups it takes to feed 36 people raisings given that it takes 0.5 cups to feed 12 people. This means that the proportion would be 0.5/12 = x/36. Cross multiply. This would give you 12x = 46.8. Divide 12 on both sides. Now, the equation is solved since you found out x = 3.9 cups.

6. Set up a proportion to find how many cups it takes to feed 4 people raisins given that it takes 0.5 cups to feed 12 people. This means that the proportion would be 0.5/12 = x/4. Cross multiply. This would give you 12x = 2. Divide 12 on both sides. Now, the equation is solved since you found out x = 0.17 cups.

7. Set up a proportion to find how many cups it takes to feed 6 people raisins given that it takes 0.5 cups to feed 12 people. This means that the proportion would be 0.5/12 = x/6. Cross multiply. This would give you 12x = 3. Divide 12 on both sides. Now, the equation is solved since you found out x = 0.25 cups.

8. Set up a proportion to find how many cups it takes to feed 36 people candy corn given that it takes 1 1/3 cups to feed 12 people. Simplify 1 1/3 to 1.3. This means that the proportion would be 1.3/12 = x/36. Cross multiply. This would give you 12x = 46.8. Divide 12 on both sides. Now, the equation is solved since you found out x = 3.9 cups.

9. Set up a proportion to find how many cups it takes to feed 4 people candy corn given that it takes 1 1/3 cups to feed 12 people. Simplify 1 1/3 to 1.3. This means that the proportion would be 1.3/12 = x/4. Cross multiply. This would give you 12x = 5.2. Divide 12 on both sides. Now, the equation is solved since you found out x = 0.43 cups.

10. Set up a proportion to find how many cups it takes to feed 6 people candy corn given that it takes 1 1/3 cups to feed 12 people. Simplify 1 1/3 to 1.3. This means that the proportion would be 1.3/12 = x/6. Cross multiply. This would give you 12x = 7.8. Divide 12 on both sides. Now, the equation is solved since you found out x = 0.65 cups.


Barrett is comparing the membership fees for two museums. The art museum charges a one-time fee of $8.25 plus $2.25 per month. The science museum charges a one-time fee of $10.75 plus $3.50 per month. How much does Barrett save by joining the art museum instead of the science museum? Enter your answers in the boxes.

(blank) $ + (blank) $ m put answers in blanks

Answers

Barrett saves by joining the art museum instead of science museum is $2.50 plus $1.25 per month.

What is concept of savings?

Saving money is one of the essential aspects of building wealth and having a secure financial future. Saving money gives you a way out of the uncertainties of life and provides you with an opportunity to enjoy a quality life.Savings represents an individual's unspent earnings. It is the amount that remains after meeting the household expenses.

What are benefits of membership?

Member benefits are the perks, services, and access that members receive as part of their membership. In other words they are what members get in exchange for joining the organization and if applicable, paying member dues.

Now we have

Fee charged by science museum= $10.75

Fee charged by art  museum         =$8.25

Now by subtracting he saves       =$2.50

Again

he saves =amount charged by science - amount charged by arts

              = $3.50 -$2.25

              = $1.25

In the results he saves $2.50 +$1.25 per month.

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Identify two segments that are marked congruent to each other on the
diagram below. (Diagram is not to scale.)

Answers

LJ and LI are the figure's two congruent portions. Congruency means that the segments' sizes and shapes will be comparable.

What is congruency?

Two triangles are said to be congruent to one another according to the Side-Angle-Side Congruence Theorem (SAS) if the included angle and corresponding two sides of one triangle match those of the other. Two sides that are being considered are determined to have an included angle. Therefore, using the SAS Congruence Theorem to prove that two triangles are congruent based on the fact that they have two pairs of corresponding sides and one pair of corresponding angles is insufficient.

given

The two segments LI and LJ that are marked in the illustration are congruent to one another.

Congruency means that the segments will have the same size and shape.

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What is 507 less than 607

Answers

Yes 607 is a greater number which makes 507 LESS! Please mark brainliest

Ratio is equivalent to the ratio of 120 to 36

Answers

Answer:10/3

Explanation
120/36 = 6 x 20/6x6

=20/6

=2x10/2x3

=10/3

120:36 is equivalent to 10:3

What is a ratio?

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"The trick with ratios is to always multiply or divide the numbers by the same value.

Given here the ratio is 120:36≡10:3

 Hence,  120:36 is equivalent to 10:3                                

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X 1 3 5 7
у -9 -17 -25 -33
find the equation of the linear function represented by the table in slope intercept form

Answers

The equation of the linear function represented by the table in slope intercept form is y = -4x - 5.

What is slope-intercept form?

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

Given two points (x,y), the slope is the change in y divided by the change in x.

The points are (1,-9) and (3,-17) -

m = (y2-y1)/(x2-x1)

m = [-17-(-9)]/(3-1)

m = -8/2

m = -4

Then the slope equation will be -

y = -4x + b

Taking points (1,-9) and substituting in the equation to get the value of b -

-9 = -4(1) + b

-9 = -4 + b

-9 + 4 = b

b = -5

Therefore, the slope intercept form of equation is y = -4x - 5.

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SOMEONE HELP! I don’t understand

Answers

Answer:

Step-by-step explanation:

That is not possible.

Find the slope (-7,4) and (-7,-8)

Answers

Answer: The slope for this line is not defined.

Step-by-step explanation: We can find the slope of a line using the formula m = y2 -y1/x2 - x1

here, (x1,y1) = (-7,4)

and, (x2,y2) = (-7,-8)

now, m= -8-4/-7+7

        m = -12/0

        So, the slope for this line is not defined as we are getting zero in the denominator.

HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

D.

Step-by-step explanation:

4/5 ÷ 3 = 4/5 * 1/3

This is 1/3 of 4/5.

Select the correct answer from each drop-down menu. Let d(t) be the total number of miles Joanna has cycled, and let t represent the number of hours after stopping for a break during her ride. So, d(4) = 68 . This means that after a 4 hour break , Joanna cycled 68 miles total .

Answers

The numeric value of the function d(t) = 12t + 20 at t = 4 is given as follows:

d(4) = 48.

The interpretation of this numeric value is that after a time of 4 hours, Joanna has cycled 68 miles.

How to interpret the function?

The function for this problem is defined as follows:

d(t) = 12t + 20.

The meaning of each variable is given as follows:

t: time in hours after the break.d(t): distance cycled after t hours.

The numeric value at t = 4 is obtained replacing the lone instance of t in the function by 4, as follows:

d(4) = 12(4) + 20

d(4) = 48 + 20

d(4) = 68 miles.

Meaning that after a time of 4 hours, the distance cycled by Joanna was of 68 miles.

Missing Information

The function for this problem is defined as follows:

d(t) = 12t + 20.

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James bought a movie ticket
and popcorn for $12.20. The movie ticket cost $8.45.
Use the equation c + $8.45 = $12.20 to find which size
popcorn James bought. How much change did James get
if he paid with a $20 bill?

Answers

If James paid with a $20 bill, he would get $7.25 in change ($20 - $12.20 = $7.25).

What is change?

Change is a natural part of life. It is the process of making or becoming different, and can happen in an instant or over a long period of time. Change may refer to a transformation in a person’s life, such as a career switch, a change in lifestyle, or growth in maturity. It can also refer to a shift in the environment, such as a change in the weather, a demographic shift, or a dramatic event.

The equation c + $8.45 = $12.20 can be rewritten as c = $12.20 - $8.45. Solving this equation yields c = $3.75. This means James bought a popcorn for $3.75.
If James paid with a $20 bill, he would get $7.25 in change ($20 - $12.20 = $7.25).

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It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed, estimate how much longer I will be driving for. this is my questions its muliple choice, the answer ive come to is 1h 25m but thats not one of the answers to chose from what do i do?

Answers

If the total length of the journey is 146 km and he maintain the same  speed, the longer time he will be using for driving  will be 65m.

How can the time be calculated?

The  total length of my journey is 146 km.

Then the remain of the journry to reach 146 km = 146- 48 = 98

Then the if the same speed is maintained the estimate of  longer time he will be using for driving  will be calculated as :

(32 * 98)/48

Then get the productor quotient = 196/3 = 65 minutes

Therefore, option E is correct.

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MISSING OPTIONS:

A. 32

B.40

C. 52

D. 60

E.65

The angle bisectors of triangle ABC are , , and . They meet at a single point . (In other words, is the incenter of .) Suppose , , , and .

Answers

To solve this we must be knowing each and every concept related to triangle. Therefore, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.

What is triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The denotes a triangle having vertex A, B, and C. In Euclidean geometry, every three non-collinear points define a unique triangle and, by extension, a unique plane.

In geometry, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.

Therefore, the angle bisector is indeed the ray, line, or fragment that splits a particular angle in two equal pieces.

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Anna wants to buy 4 sweaters. The sweater come at a discount rate. If you buy one sweater regular price the other sweater is 40% off. How much percent is off of each sweater?

Answers

Answer:

20%

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

If you buy a sweater, the second one is at 40% discount.

Divide the discount between the two to get:

40%/2 = 20%

You get a discount of 20% for each sweater.

Answer:

Discount percentage = 20%

Step-by-step explanation:

Discount of the sweaters,

→ first sweater = 0%

→ other sweater = 40%

The average discount percent is,

→ (first sweater + other sweater)/2

→ (0% + 40%) ÷ 2

→ (0 + 40)/2

→ 40/2

→ 20% off

Hence, the answer is 20% off.

which of the following best describes the graph below

Answers

Option A) In the graph for each value of x there is exactly one value of y

So the function is  a One to One function.

What is a function?

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|

A function f is said to be injective if it maps different items in its domain to other elements; for example, f = f implies x1 = x2. Alternatively, every element of the function's codomain is at most one of its domain's elements.

If some function output value corresponds to more than one input value, the function is said to be many-to-one (sometimes written as "many-one"). If the domain of f contains two different values a and b such that f(a)=f, the function f is many-to-one in symbols (b).

In the graph for each value of x there is exactly one value of y

So the function is  a One to One function.

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Just before a referendum on a school​ budget, a local newspaper polls 417 voters to predict whether the budget will pass. Suppose the budget has the support of ​54% of the voters. What is the probability that the​ newspaper's sample will lead it to predict​ defeat?

Answers

Answer:

The probability here is 62%

The probability that the newspaper's sample will lead it to predict defeat is approximately 0.0495, or about 5%.

What is probability?

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Let X be the number of voters in the sample who do not support the budget (i.e., who will vote against it). Then X follows a binomial distribution with parameters n = 417 (the sample size) and p = 1 - 0.54 = 0.46 (the probability that a voter does not support the budget).

The probability that the sample will lead the newspaper to predict defeat is the probability that X is greater than half the sample size (since the budget will be defeated if more than half of the voters in the population vote against it). In other words, we need to calculate:

P(X > 0.5n) = P(X > 0.5 × 417) = P(X > 208.5)

We can use a normal approximation to the binomial distribution to estimate this probability. The mean of the binomial distribution is np = 417 × 0.46 = 191.82, and the standard deviation is √(np(1-p)) = √(417 × 0.46 × 0.54) = 10.04.

To apply the normal approximation, we standardize the random variable X as follows:

Z = (X - np) / √(np(1-p))

Then we can use a standard normal distribution table or calculator to find the probability:

P(X > 208.5) = P(Z > (208.5 - 191.82) / 10.04) = P(Z > 1.65) ≈ 0.0495

Therefore, the probability that the newspaper's sample will lead it to predict defeat is approximately 0.0495, or about 5%.

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Which of the following would not be an example of a compound event?
(1) having a coin land on heads three consecutive times
(2) pulling a king out of a deck of cards
(3) missing two free throws in a row
(4) answering four true/false questions correctly by guessing

Answers

The only option that is not a compound event is; (2) pulling a king out of a deck of cards

How to identify a compound event?

Compound probability is defined as a mathematical term that relates to the likeliness of two independent events occurring.

Thus, a simple event has only one outcome while  a compound event involves the probability of more than one outcome

1) For a coin to land on heads three consecutive times means that there can only be three possible independent outcome  and so this is a compound event.

2) Pulling a king out of a deck of cards is a simple event and not compound because it has only one outcome.

3) This is a compound event because we are dealing with two independent probabilities.

4) This is a compound event because we are dealing with two independent events which are true or false answers.

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Marcus makes the statement "15 more than twice a number is equal to 5” What number makes Marcus's statement true?
O-5
O 7.5
O -2.5
O 10

Answers

So we know that we need to add 15 to the double of this number. We know we need to add 15 since it says "15 more than" and we know we need to double/multiply the number by two since it says "twice a number"! We also know that this mystery number equals 5.

Therefore, we can set up our equation and solve! The variable x is used to represent the number we're looking for!

2x + 15 = 5

2x = -10

x = -5

So, your answer should be -5!

Please help will mark Brainly

Answers

The graph of the given inequality y < 4x - 5 is attached below.

What is graph of inequality?

Treat the <, ≤, >, ≥ or sign as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either < or >. Graph the equation as a solid line if the inequality is either or .

A region on one side of a line can be used to graphically represent an inequality. For the purpose of indicating that a line is not a part of the region, inequality plots that use the < or > symbols have a dashed line. Plotting a solid line indicates that an inequality that uses the symbol

" or " is included in the region.

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Help!! Like what even is this

Answers

The new transformation coordinates are B""(6, 15), C""(-3, 12), and Dilate k=3 by multiplying both x and y by 3.

what is coordinates ?

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

given

For point B,

B(1,2) → B'(1 , -2) → B"( 2, -5) → B""( 6 ,-15)

For point C,

C(-2,1) → C'( -2 , -1) → C"( -1 , -4 )→ C"" ( -3 , -12)

In order to reflect a point across the x-axis, keep the x coordinate constant while changing the y coordinate to its opposite.

<1, -3> the following translations: Add 1 to x, take 3 away from y.

Add 3 to both x and y to dilate k=3.

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What is this expression in simplified form?
(√22) (5√2)
O A. 10√11
O B.
12√11
O c.
20v/11
OD. 24√/11

Answers

General Formulas and ConceptsPre-Algebra

Radicals

Simplifying radicals

ApplicationStep 1: Define

Let's organize what the problem gives us.

We are given an expression to simplify:  [tex]\displaystyle (\sqrt{22})(5 \sqrt{2})[/tex]

Step 2: Work

Recall the specific rules to simplify radicals. We will apply those rules here to help us answer the question:

[tex]\displaystyle\begin{aligned}(\sqrt{22})(5 \sqrt{2}) & = 5 \sqrt{44} \\& = 5 \sqrt{4 \cdot 11} \\& = (5 \sqrt{4})(\sqrt{11}) \\& = (5 \cdot 2)(\sqrt{11}) \\& = \boxed{ 10 \sqrt{11} }\end{aligned}[/tex]

∴ the expression (√22)(5√2) simplifies down to 10√11.

Answer

∴ the expression in simplified form is equal to A. 10√11.

___

Topic: Pre-Algebra

Unit: Radicals

40% of an hour?

(I've tried 24 minutes...it's not the answer)

Answers

40% of an hour is 24 minutes.

Given there are 60 minutes in an hour, we can multiply this by 0.4 to find that 24 minutes constitutes 40% of an hour. I assume the system is not working properly for you, but 40% of an hour is 24 minutes.

40% of an hour is 24 minutes = 2/5 hours.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Given that,

there are 60 minutes in an hour,

we can multiply this by 0.4 to find that 24 minutes constitutes 40% of an hour.

i.e. 60*40%= 24 minutes

Hence, 40% of an hour is 24 minutes = 2/5 hours.

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There was a sample of 700 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 9.4% each year.
Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams.
Write an exponential function showing the relationship between y and t.

Answers

The exponential function  can be written as y = 700e^-0.094t.

What is the exponential function?

We know that the term function would have to do with a mathematical rule that we can use to be able to obtain specific values. Now we have to know that there was a sample of 700 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 9.4% each year.

We can use;

N = Noe^-rt

N = amount at time t

No = Amount at the beginning

r = decay rate

t = time taken

Thus we have; y = 700e^-0.094t

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You get to spin the wheel one time. What's the probability that you will
land on bankrupt?

Answers

The likelihood of the word "BANKRUPT" appearing on the Wheel of Fortune is 1/9 = 11.1%.

How many bankrupts are on the Wheel of Fortune?

The ratio of the number of "1s" to all the other numbers on the spinner determines this probability. The spinner has a total of 8 numbers on it. The spinner has three ones on it. A "1" spinning is 3 out of 8 likely.

Select a direction, get a matrix, locate an eigenvector, normalize it, take its adjoint, multiply by your vector, determine the magnitude of the result, then square that. Finished, that's the likelihood.

Two Bankrupt wedges and one Lose a Turn wedge are also included on the wheel. The contestant's turn is forfeited if they land on either, and the Bankrupt wedge also gets rid of whatever money or rewards they have acquired during the round.

The likelihood of spinning "BANKRUPT" on any given spin of the Wheel of Fortune is 1/9 = 11.1%.

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Write and solve a system of equations for each of the following problems. You must write two questions for each problem, thank you

1. Ella is a landscape photographer. She sells small prints for $50 each, and large prints for $75
each. One weekend she sold a total of 52 prints for a total of $2975. How many of each size print did
Ella sell?
2. At a hot air balloon festival, Georges's balloon is at an altitude of 40 meters and rises at a rate of
10 meters per minute. William's balloon is at an altitude of 165 meters and descends at a rate of 15
meters per minute. In how many minutes will both balloons be at the same altitude? What is that
altitude?

Answers

The system of equations that satisfy the given problems is x + y = 52 and 50x + 75y = 2975, and the value of x = 15 and y= 37.

What is system of equations?

A system of linear equations consists of two or more equations and looks for common answers.

1. Let us suppose small prints = x

Large prints = y

Total prints sold can be written as follows:

x + y = 52

The total cost of the prints can be written as follows:

50x + 75y = 2975

The system of equations is:

x + y = 52   . . . equation 1

50x + 75y = 2975 . . .equation 2

Using equation 1 we have:

x = 52 - y

Substituting the value of x in equation 2 we have:

50(52 - y) + 75y = 2975

2600 - 50y + 75y = 2975

25y = 2975 - 2600

25y = 375

y = 15

Now, substituting the value of y in equation 1 we have:

x + 15 = 52

x = 52 - 15

x = 37

Hence, the solution of the system of equations is y = 15 and x = 37.

2. Let us suppose the altitude = x.

The rising balloon can be thus written as:

40 +10x

The descending balloon can be written as:

165 - 15x

Solving the system of equations by substituting the value of x we get x= 5.

Hence, the altitude at which both the balloons are at the same height is 5m.

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The ratio of the measure of an exterior angle of a triangle to the measure of the adjacent interior angle is 1:4. Is the
triangle acute or obtuse?

Justify your answer.

A.) Acute; the measure of the interior angle must be 144º.

B.)Acute; the measure of the interior angle must be 36°.

C.)Obtuse; the measure of the interior angle must be 144º

D.)The triangle could be acute or obtuse, depending on the measures of the other two angles.

Answers

The correct answer is B
D. The triangle could be acute or obtuse, depending on the measures of the other two angles.

The ratio of the measure of an exterior angle of a triangle to the measure of the adjacent interior angle is 1:4, which means that for every 1 degree of the exterior angle, there are 4 degrees of the interior angle. However, this does not provide enough information to determine the overall shape of the triangle.

The triangle could be acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (one angle greater than 90 degrees) depending on the measures of the other two angles. For example, if the interior angle measure is 36 degrees, the exterior angle would be 9 degrees, and the triangle could be acute. On the other hand, if the interior angle measure is 144 degrees, the exterior angle would be 36 degrees, and the triangle could be obtuse.
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