Robert has taken three classes so far. Each class has been a 3 credit hour class. In his classes, he has received two Bs (which calculates as a 3.0/class for purposes of his GPA) and one C (which calculates as a 2.0 for purposes of his GPA). Robert recently learned that there is a minimum GPA needed for him to remain in good standing. He asks you if you think he is in good standing, or if he should be worried.
a. What is Robert’s cumulative GPA? To calculate this, add his GPA for each of his classes and divide by the number of classes he has taken.
b. Should Robert be worried about meeting SAP?
c. Explain why or why not.
d. Which SAP criterion relates to this scenario?

Answer: The region that satisfies both inequalities is the shaded area that is above the line y = x and below the line y = -x + 1. One point that lies in this region is (0, 0), which satisfies both inequalities because 0 is greater than negative x (which is also 0) and less than x + 1 (which is 1). So the ordered pair (0, 0) makes both inequalities true.

Step-by-step explanation:

Answer: The circumference of the cutter is approximately 119.32 millimeters.

Step-by-step explanation: The formula for the circumference of a circle is C=2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

In this problem, the radius of the circular cutter is given as 19 millimeters, so we can substitute that value into the formula:

C = 2πr

C = 2 × 3.14 × 19

C = 119.32

Rounding to the nearest hundredth, we get:

C ≈ 119.32 millimeters

Therefore, the circumference of the cutter is approximately 119.32 millimeters.

The formula to calculate the circumference of a circle is C=2πr, where r is the radius of the circle and π (pi) is a constant approximately equal to 3.14.

Given that the radius of the cutter is 19 millimeters, we can calculate its circumference as follows:

C = 2πr

C = 2 x 3.14 x 19

C = 119.32

Therefore, the cutter's circumference is approximately 119.32 millimeters

Answer: $75.00 (rounded to the nearest dollar)

The fish tank has a capacity of 64 gallons, and Emily has already filled 13 gallons of salt water. So, the amount of space left for water is:

64 - 13 = 51 gallons

To fill the fish tank to 7/8 of its capacity, Emily needs to add:

(7/8) x 64 = 56 gallons

Since she has already added 13 gallons of salt water, Emily needs to add:

56 - 13 = 43 gallons

Therefore, Emily needs to add 43 gallons of water to fill the fish tank to 7/8 of its capacity.

The correct answer to the above question is option (a) The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 0.5 seconds is equal to the height of the cannonball at 2 seconds.

Symmetry refers to a property of an object or a function that remains unchanged when transformed by a specific operation.

For example, a geometric shape is symmetric if it can be divided into parts that are mirror images of each other.

The answer to the above question is The height of the cannonball over time is symmetric about the line x = 1.5 seconds, which indicates the height of the cannonball at 0.5 seconds is equal to the height of the cannonball at 2 seconds.

This is because the heights at 0.5 seconds and 2 seconds are equidistant from the line x=1.5 seconds, and they have the same magnitude but opposite signs. Therefore, the graph of the height of the cannonball over time is symmetric with respect to the vertical line x=1.5 seconds.

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the can in the case of cat food will be 12.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

There are 12 cans of cat food in total.

Since there are 2 layers and each layer has 6 cans, you can calculate the total number of cans by multiplying the number of cans in one layer by the number of layers:

6 cans/layer x 2 layers = 12 cans.

Hence the can in the case of cat food will be 12.

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Trigonometric functions such as cosine and sine are periodic functions with a repeating pattern. The cycle of the feature is 12, which means that the temperature pattern repeats every 12 months or years.

 Trigonometric identities are  equalities that involve trigonometric functions and are valid for all the values ​​of the variables given in the equation. There are several different trigonometric identities for the side length and angle of a triangle.

Yes you are right! Trigonometric functions such as cosine and sine are periodic functions with a repeating pattern. Because they repeat every 2π, they are often used to model and describe things that repeat periodically, such as temperature changes, sound waves, and the motion of objects. The formula you provided uses a cosine function  to model  temperature changes over a 12 month period. The maximum afternoon temperature is given by the formula t = 85 - 25cos(πx/6), where x is the number of months. The amplitude of the cosine function is 25, which represents the maximum temperature variation  from the mean of 85 degrees Fahrenheit. The cycle of the feature is 12, which means that the temperature pattern repeats every 12 months or years.

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there were 240 pages in the printing task.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Now we can use the last two equations to solve for "p". First, substitute "r" into the equation for Printer A's printing rate:

r + 4 = (p / t)

(p / 40) + 4 = (p / 24)

Multiplying both sides by 120 (the least common multiple of 40 and 24) to eliminate the fractions, we get:

3p + 480 = 5p

480 = 2p

p = 240

Therefore, there were 240 pages in the printing task.

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Answer: 2.8831036e+17

Step-by-step explanation:

Answer:

5,767,911,845,985,421,000

Step-by-step explanation:

20023555 X 119994 = 2,402,794,503,470T

To square this number, we can multiply it by itself:

2,402,794,503,470^2 =

5,767,911,845,985,421,000

Therefore, the result of 20023555 X 119994 squared is 5,767,911,845,985,421,000.

In a case whereby Another company is advertising 59$ for their service plan ,The customer bill using Percentages can be expressed as   $67.85.

In math, a percentage is a number or ratio expressed as a fraction of 100. It is denoted by the symbol %. Percentages are commonly used in many areas of math and science, such as statistics, finance, and physics. They are a useful way to express proportions, ratios, and rates in a standardized and easily understandable format.

The equation can be set up as ;

59 * (1+ 15%)

59 * (1.15)

=67.85

Therefore, the customer bill is $67.85

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The area of the shape with the given features is 34.625 square cm

From the question, we have the following parameters that can be used in our computation:

Composite figures

The area of the shape is the sum of the areas of individual shapes

So, we have

Area = triangle + quarter circle

This gives

Area = 1/2 * 6 * 5 + 1/4 * 3.14 * 5^2

Evaluate

Area = 34.625

Hence, the area is 34.625 square cm

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Answer:

a. f(x) = 5x + 12

Step-by-step explanation:

a. f(3) = 5(3) + 12 = 15 + 12 = 27

If you replace 3 into x of the other equations, the result will not be 27

Answer:

a. f(x) = 5x + 12

Step-by-step explanation:

a. f(3) = 5(3) + 12 = 15 + 12 = 27

If you replace 3 into x of the other equations, the result will not be 27

Answer:

192 ft³

Step-by-step explanation:

Formula for the volume of a square pyramid is V=s²h/3, where s=base edge length and h=height. Remember: Order of Operations!!

V=6²(16)/3

 =36(16)/3

 =12(16)

 =192

Answer:

yes

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Gwen gets the interest amount in two different ways, which depend on his choice. If he deposits in simple interest, the interest amount is 1400, and if in compound interest 1680.9.

Simple interest:

The cost of borrowing is represented by simple interest (SI). It represents the interest in the principal only expressed as a percentage of the principal. Because they only have to pay interest on loans they take out, borrowers will gain from simple interest. By multiplying the interest amount by the tenure and the principal amount, one may quickly calculate simple interest. Simple interest does not take prior interest into account. It is based just on the initial contribution sum.

 S.I = (Principal * Rate of interest * Time)/100

Compound interest:

Compound interest (CI), as opposed to simple interest (SI), which just earns interest on the principal, also earns interest on earlier interest payments. The principal amount is increased by the interest. Interest on Interest is referred to as CI. Compound interest, which is based on the primary power of compounding, causes investments to increase in value exponentially.

    C.I = (Principal(1 + (rate/100))^(time)) - Principal

Given:

Principal = 3500

Rate = 4%

Time = 10 years

Simple Interest = (Principal * Rate of interest * Time)/100

                        = (3500 * 4 * 10)/100

                        = 1400

Compound Interest = [tex](Principal(1 + (rate/100))^{(time)}) - Principal[/tex]

                               = (3500(1 + 0.04)¹⁰) -3500

                               = 5180.9 -3500 ⇒ 1680.9

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Answer:

102.19 cubic inches

Step-by-step explanation:volume =cross-section area * Length

cross-section area= (5.1 *4.6)+((13.6-4.6)*2.8)= 23.46 + 25.2= 48.66 square inches.

Length we take 2.1 in

volume = 46.66 * 2.1in = 102.19 cubic inches

Answer:

x = - 1

Step-by-step explanation:

Just by looking, we can tell that the axis of symmetry in this graph is going to be a vertical line. to make vertical lines, we start with:

x = ____

For a quadratic, the vertical line always hits the vertex. The x value of the vertex is - 1.

Therfore, the equation of the axis of symmetry is x = - 1

Square Area = side x side = 3x3 = 9

Rectangle Area = side x side= 7x3= 21

9 + 21 = 30 square inches

Answer:

30 square inches

Step-by-step explanation:

   [tex]\boxed{\text{\bf Area of rectangle = length *width}}[/tex]

Rectangle1:

     Area = 6 * 3

              = 18 square inches

Rectangle2:

Area = 4 * 3

          = 12 square inches

Area of the figure = area of rectangle1 + area of rectangle2

                             = 18 + 12

                             = 30 square inches

To solve this problem, we need to count the total number of ways that Umberto can remove two notes from his wallet, and then count the number of ways that he can remove two notes that add up to each of the given amounts.

There are a total of 4 possible notes that Umberto can choose from, so there are 4 choose 2 = 6 ways that he can remove two notes from his wallet.

To find the number of ways that he can remove two notes that add up to $11, we can observe that there is only one possible pair of notes: the $1 note and the $10 note. Therefore, the probability of getting a pair of notes that add up to $11 is 1/6.

To find the number of ways that he can remove two notes that add up to $70, we can observe that there is only one possible pair of notes: the $20 note and the $50 note. Therefore, the probability of getting a pair of notes that add up to $70 is 1/6.

To find the number of ways that he can remove two notes that add up to $80, we can observe that there is only one possible pair of notes: the $20 note and the $60 note (which is not in his wallet). Therefore, the probability of getting a pair of notes that add up to $80 is 0/6, which means it is impossible.

To find the number of ways that he can remove two notes that add up to at least $11, we can count the number of pairs of notes that add up to $11 or more. There are three such pairs: $1 and $10, $1 and $20, and $10 and $20. Therefore, the probability of getting a pair of notes that add up to at least $11 is 3/6, which simplifies to 1/2.

So, the probabilities for each part are:

A. $11: 1/6

B. $70: 1/6

C. $80: 0/6 (impossible)

D. at least $11: 1/2

For function [tex]f(x) = \left \{ {\frac{x+1}{x^{2} -1} ,\ {x\neq 1} \atop {1,\ x=1}} \right.[/tex] given in the problem, the limit [tex]\lim_{x \to 1} f(x)[/tex] doesn't exists.

A relation between a set of inputs and a set of allowable outputs is called a function, and it has the characteristic that every input is associated to precisely one output. When every element in set A has one end and only one image in set B, then the mapping from set A to set B is a function. Let A & B be any two non-empty sets.

Now for given function,

Limit exists, if LHL=RHL=f(a)

I.  [tex]f(x) = \frac{1-x^{2} }{x-1}=\frac{(1-x)(1+x)}{x-1} = \frac{-(x-1)(x+1)}{(x-1)} = -(x+1)[/tex]

applying limit,

[tex]\lim_{x \to 1} f(x)= -2[/tex], LHL= RHL= f(1) = -2. Hence, limit exists

II. [tex]f(x) = \frac{x^{2} -x^{3} }{x^{2} -1}=\frac{-x^{2} (x -1)}{(x-1)(x+1)} = \frac{-(x^{2} )}{(x+1)}[/tex]

applying limit,

[tex]\lim_{x \to 1} f(x)= \frac{-1}{2}[/tex] , also LHL= RHL= f(1) = -1/2. Hence, limit exists

III. [tex]f(x) = \left \{ {\frac{x+1}{x^{2} -1} ,\ {x\neq 1} \atop {1,\ x=1}} \right.[/tex]

[tex]for x\neq 1,\\f(x)=\frac{(x+1)}{x^{2} -1} = \frac{x+1}{(x-1)(x+1)} = \frac{1}{x-1}[/tex]

RHL= [tex]\lim_{x \to 1+h} f(x) = \lim_{h \to 0} f(1+h) =\lim_{h \to 0} \frac{1}{1+h-1}[/tex]

[tex]\lim_{h \to 0} \frac{1}{h} =[/tex] Undefined.

LHL = [tex]\lim_{x \to 1-h} f(x) = \lim_{h \to 0} f(1-h) =\lim_{h \to 0} \frac{1}{1-h-1}[/tex]

[tex]\lim_{h \to 0} \frac{1}{h} =[/tex] Undefined

and [tex]f(1)=1[/tex]

Hence,[tex]\lim_{x \to 1} f(x)[/tex] doesn't exists

IV. [tex]f(x) = \left \{ {\frac{x^{2} -3x+2}{x -1} ,\ {x\neq 1} \atop {-1,\ x=1}} \right.[/tex]

[tex]for x\neq 1,\\f(x)=\frac{(x^{2} -3x+2)}{x -1} = \frac{(x-1)(x-2)}{(x-1)} = {x-2}[/tex]

RHL= [tex]\lim_{x \to 1+h} f(x) = \lim_{h \to 0} f(1+h) =\lim_{h \to 0} (1+h-2)= -1[/tex]

LHL= [tex]\lim_{x \to 1-h} f(x) = \lim_{h \to 0} f(1-h) =\lim_{h \to 0} (1-h-2)= -1[/tex]

and f(1) = -1

Hence,[tex]\lim_{x \to 1} f(x)[/tex]  exists

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Answer:

First, we need to calculate the total cost of car insurance for six months:

Mr. Jones' insurance = $160

Mrs. Jones' insurance = $290

Total insurance cost for six months = $160 + $290 = $450

To find the monthly cost, we divide the total cost by 6:

$450 ÷ 6 = $75

Therefore, the answer is A. $75. They should budget $75 per month for car insurance.

The ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is 25:8.

The surface area of a cylinder is given by the formula:

SA = 2πr^2 + 2πrh

Assume the radius of the smaller cylinder is r, and the radius of the larger cylinder is R. Since the two cylinders are similar, we know that the ratios of corresponding lengths are equal:

R/15 = r/12

Solving for r, we get:

r = 12R/15 = 4R/5

Now we can calculate the surface area of each cylinder:

SA small = 2πr^2 + 2πrh = 2π(4R/5)^2 + 2π(4R/5)(12) = 96πR^2/25

SA large = 2πR^2 + 2πRh = 2πR^2 + 2πR(15) = 30πR^2

The ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is:

SA large/SA small = (30πR^2)/(96πR^2/25) = 25/8

Therefore, the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is 25:8.

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Answer:

NO ITS 25:16!!!!

Step-by-step explanation:

a. A U B = {1,2,3,5,7,10,11,12,13,14,16,17,19,20}

b. A n B = {5,10,13,14,16,19}

c. A' n B = {20}.

a. A U B (the union of sets A and B):

To find the union of sets A and B, we combine all elements from both sets without duplication and put them together in a single set.

A = {2,3,5,7,10,11,12,13,14,16,17,19}

B = {5,10,13,14,16,19,20}

Combining the elements from both sets, we get:

A U B = {1,2,3,5,7,10,11,12,13,14,16,17,19,20}

b. A n B (the intersection of sets A and B):

To find the intersection of sets A and B, we look for the elements that are common to both sets. In other words, we find the elements that are present in both A and B.

A = {2,3,5,7,10,11,12,13,14,16,17,19}

B = {5,10,13,14,16,19,20}

Comparing the elements in both sets, we find that the common elements are: A n B = {5,10,13,14,16,19}

c. A' n B (the complement of A intersection B):

To find the complement of A intersection B, we first find A intersection B, as determined in the previous step to be {5,10,13,14,16,19}.

Then, we find the elements that are in the universal set U but not in A intersection B:

U = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

A intersection B = {5,10,13,14,16,19}

Comparing the elements in the universal set U and A intersection B, we find that the complement of A intersection B is:

A' n B = {20}

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we can see that Kiran is farthest from home (6 blocks away) at time 5, when he reaches the bank. He spends the most time away from home (9 minutes) during his entire journey.

How to make graph?

To make a graph showing Kiran's distance from home over time, we can use the following steps:

Divide the journey into three parts: from home to store, from store to bank, and from bank to home.

Calculate the time taken for each part of the journey based on the distance and speed.

Use a coordinate system to plot Kiran's distance from home on the y-axis and time on the x-axis.

Plot the points corresponding to Kiran's position at different times for each part of the journey.

Connect the dots to form a continuous line.

Let's go through each part of the journey in more detail:

Home to store: Kiran is driving at a speed of 1 block per minute, and the distance is 3 blocks. Therefore, he reaches the store in 3 minutes.

Store to bank: After spending 2 minutes at the store, Kiran continues driving at a speed of 1 block per minute, and the distance is 3 blocks. Therefore, he reaches the bank in 5 minutes.

Bank to home: After spending 4 minutes at the bank, Kiran drives at a speed of 2 blocks per minute, and the distance is 6 blocks. Therefore, he reaches home in 9 minutes.

To plot the graph, we can use a coordinate system where the x-axis represents time in minutes and the y-axis represents Kiran's distance from home in blocks. We can label the points on the graph corresponding to Kiran's position at different times, as follows:

At time zero, Kiran is at home, which is 0 blocks away from home.

At time three, Kiran reaches the store, which is 3 blocks away from home.

At time five, Kiran reaches the bank, which is 6 blocks away from home (3 blocks from the store plus 3 blocks from home).

At time nine, Kiran reaches home again, which is 0 blocks away from home.

To create the graph, we can plot these points and connect them with a line, as shown in the attached image.

Graph showing Kiran's distance from home over time

From the graph, we can see that Kiran is farthest from home (6 blocks away) at time 5, when he reaches the bank. He spends the most time away from home (9 minutes) during his entire journey.

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The cost of the AMC A-List is $20.

A budget is a financial plan that outlines expected income and expenses over a specific period, usually a month, quarter, or year. It helps individuals, businesses, and governments to manage their finances effectively by providing a roadmap for spending and saving.

To solve this question, we can simply subtract the costs of the other two categories from the total budget:

Total budget - (Streaming services cost + Miscellaneous cost) = AMC A-List cost

$80 - ($40 + $20) = $80 - $60 = $20

Thus, the cost of the AMC A-List is $20.

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If the total monthly entertainment budget is $80, and it is distributed among three categories (AMC A-List, streaming services, and miscellaneous), what is the cost of AMC A-List if the streaming services cost $40 and miscellaneous expenses are $20?

Answer:

C

Step-by-step explanation:

y <= 2x - 2

the delimiter line is therefore

y = 2x - 2

that is true for all 4 answer options.

but the y-values must be smaller than the values in the line. so, the area right-down from the line is correct.

that leaves us with B and C.

dotted line or solid line - the difference is if the line values are included in the solution or excluded.

if the line is dotted, then the line is not included.

if the line is solid, then the line is included.

because the inequality uses "<=", the line is included.

so, the answer with the solid line is correct : C.

Answer: The the fossil is approximately 8,267 years old.

Step-by-step explanation: To solve this problem, we can use the formula for exponential decay:

N(t) = N₀ * (1/2)^(t/T)

where:

N(t) = the amount of carbon-14 remaining after time t

N₀ = the initial amount of carbon-14

T = the half-life of carbon-14

Let's assume that the fossilized leaf originally contained 100% of its normal amount of carbon-14. Since it now contains only 33% of its normal amount, we can say that:

N(t) = 0.33N₀

Substituting this into the formula above, we get:

0.33N₀ = N₀ * (1/2)^(t/5600)

Dividing both sides by N₀ and taking the logarithm base 2 of both sides, we get:

t/5600 = log₂(0.33)

t = 5600 * log₂(0.33)

t ≈ -14187 years

This result is negative, which doesn't make sense in the context of the problem. It means that the fossil must be older than our initial assumption of 100% carbon-14. Let's assume instead that the fossil originally contained 50% of its normal amount of carbon-14 (which is more realistic). Then, we can say that:

N(t) = 0.5N₀

Substituting this into the formula above, we get:

0.5N₀ = N₀ * (1/2)^(t/5600)

Dividing both sides by N₀ and taking the logarithm base 2 of both sides, we get:

t/5600 = log₂(0.5)

t = 5600 * log₂(0.5)

t ≈ 8267 years

Therefore, the fossil is approximately 8267 years old.

Graph 1 shows the solution to the system of linear inequalities.

When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical, or as a combination of the two.

When a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression. Several types of linear inequalities can be represented in a number of different ways.

For the given system of linear equalities, the solution of the inequality A is the shaded area above the dashed line .

Also, the solution of the inequality B is the shaded area below the dashed line.

Plotting the graph we see that, the graph is as follows:

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The complete question is: