Based on the given parameters, the value of the money to invest initially is $994.8
How to determine the amount of investment?The given parameters about the compound interest are
Principal Amount, P = $2130
Interest Rate, R = 6.4%
Time, t = 12
Number of times, n = 12 i.e. monthly
To calculate the amount, we have:
A = P + CI
Where
C = P(1 + R)^t
So, we have
A = P(1 + R)^t
This can be rewritten as
A = P(1 + R/n)^nt
Substitute the known values in the above equation
2130 = A * (1 + 6.4%/12)^(12*12)
So, we have
A = 2130/[(1 + 6.4%/12)^(12*12)]
Evaluate the expression
A = 994.8
Hence, the amount of the investment is $994.8
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A new computer game costs $160,000 to research and develop. Once completed, individual games can be produced for just $.20 each. If the first 275 are given away as samples, how many games must be sold for the average price to be $2?
Answer: The correct answer is (d) 89,200 games.
To find the number of games that must be sold, we need to set up an equation to represent the total revenue from the game sales and solve for the number of games sold.
The total revenue from the game sales is equal to the number of games sold multiplied by the price per game, minus the cost of research and development.
Let X be the number of games sold
Total revenue = X * $2 - $160,000
We also know that the total cost of producing the games is equal to the number of games produced multiplied by the cost per game.
Total cost = X * $0.20
We can set the total revenue equal to the total cost and solve for X:
X * $2 - $160,000 = X * $0.20
X = 89,195
Since we gave away the first 275 games for free, we need to add 275 to the number of games sold to find the total number of games that must be sold.
Total number of games sold = X + 275 = 89,195 + 275 = 89,470
Therefore, the correct answer is (d) 89,200 games.
An observer whose eye level is 5 ft is observing the top of an object with a mirror on the
ground. The mirror is 3 feet from the observer and 12 feet from the object. Calculate the
height of the object.
The height of the object is 20 feet.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
An observer whose eye level is 5 ft is observing the top of an object with a mirror on the ground.
The mirror is 3 feet from the observer and 12 feet from the object.
Using proportion
5/ 3= x/ 12
60= 3x
x = 20 feet
hence, the height of the object is 20 feet.
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f(x) = 2(x²-7)
Find f(2).
Question 12 of 25
Anthony surveys a group of students at his school about whether they play a
sport. This table shows the results broken down by gender.
Boys
Girls
Total
Play a sport
95
76
171
Do not play a
sport
45
59
104
Total
overe pot independent because Nair) 0.10
140
135
275
Are being a girl and playing a sport independent events? Why or why not?
Being a female and participating in sports are independent events for the provided data because P(girl) = P(girl participates in sports)
What are independent events?These are the occurrences that are independent of other occurrences.
Occurrences A and B are independent events when the likelihood of one occurring is unaffected by the occurrence of the other.
Probability of independent events formula:
"P(A∩B) = if A and B are independent occurrences P(A).P(B)
What exactly is probability?Finding the chance that an event will occur is the focus of this area of mathematics."
P(A) = n(A)/n(S), where n(A) is the number of positive outcomes and n(S) is the total number of possible outcomes for an event A.
For given question,
We have been given a table that shows the results broken down by gender.
Play sports Do not play sports Total
Boy 95 45 140
Girl 76 59 135
Total 171 104 275
Using the definition of probability:
⇒ P(girl) = Number of girls/ Number of students
⇒ P(girl) = 135/275
⇒ P(girl) = 0.49 ....................(1)
Now we find the probability of girls that play a sport.
Using the definition of probability:
P(girl plays a sport)
= Number of girls who plays a sport/ number of students who plays a sport
= 76/ 171
= 0.44 ......................(2)
From (1) and (2),
P(girl) = P(girl plays a sport)
Thus, being a girl and playing a sport are Independent events.
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ABDE is an isosceles trapezoid. Select all parts that are marked congruent.
Side AB and Side AE
Angle E and Angle D
Angle E and Angle B
Angle A and Angle B
Angle A and Angle D
Side AE and Side BD
Side AB and Side ED
The concurrent parts in the given ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD.
Concurrent triangles:Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size. These triangles may be moved, flipped, twisted, and turned to get a similar effect. When relocated, they are parallel to one another. The concurrence sign is '≅'.
Here we have,
ABDE is an isosceles trapezoid.
Draw 2 diagonals in a given trapezoid
Then the 2 diagonal will divide the trapezoid into 4 triangles
Here ΔAOB, ΔBOD, ΔEOD, and AOE
From the formed triangles
ΔAOB and ΔEOD will be two concurrent triangles
Then Side AB ≅ Side ED
ΔBOD and AOE will be two concurrent triangles
Side AE ≅ Side BD
Therefore,
The concurrent parts in the given ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD.
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Suppose that you’d like to retire in 40 years and you want to have a future value of $ 500000 in a savings account. Also suppose that your employer makes regular monthly payments into your retirement account.
If you can expect an APR of 7% for your account, how much do you need your employer to deposit each month?
Employer Contribution =
The formulas we have been using assume that the interest rate is constant over the period in question. Over a period of 40 years, though, interest rates can vary widely. To see what difference the interest rate can make, let’s assume a constant APR of 4% for your retirement account. How much do you need your employer to deposit each month under this assumption?
Employer Contribution =
a) If only your employer makes the monthly deposits into your retirement account for the future value of $500,000 in 40 years at 7% APR, your employer contributions should be $190.49.
b) If only your employer makes the monthly deposits into your retirement account for the future value of $500,000 in 40 years at 4% APR, your employer contributions should be $423.03.
What is the future value?The future value represents the amount expected to be the balance in the investment account after a period.
The future value can be used to determine the periodic payments required to meet the target balance, using an online finance calculator.
Periodic Deposits at 7%:N (# of periods) = 480 months (40 years x 12)
I/Y (Interest per year) = 7%
PV (Present Value) = $0
FV (Future Value) = $500,000
Results:
PMT (Periodic deposits) = $190.49
Sum of all periodic payments = $91,435.07
Total Interest = $408,564.93
Periodic Deposits at 4%:N (# of periods) = 480 (40 years x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $0
FV (Future Value) = $500,000
Results:
PMT (Periodic deposits) = $423.03
Sum of all periodic payments = $203,052.33
Total Interest = $296,947.67
Thus, the periodic deposits to meet the future value will depend on the interest rate.
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if you form a triangle from three given side lengths, will you always get one triangle or more than one triangle?
If the three side lengths are all different then you will only get one triangle. However, if two or more of the side lengths are the same then you can get more than one triangle.
What is known as a triangle?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total
How is a triangle made?Three diagonals must meet at three different locations to form a triangle. There are five possible arrangements of three diagonals. We categorize them according on how many different diagonal endpoints there are. The quantity of triangles with 3, 4, and 5 endpoints will be counted directly.
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Equation that passes through 4,-3 and -4,7
Determine if the events are independent or dependent.
P(A) = 0.65 P(B) = 0.25, P(A and B)0.40
P(A) = 0.22 P(B) = 0.45, P(A and B) .0.099
P(A) = 0.42 P(B) = 0.62, P(A| B) =
0.2604
You roll a pair of dice at the same time.
You choose two marbles from a bag, without replacement.
The events P(A) = 0.22 P(B) = 0.45, P(A and B) = 0.099 and rolling a pair of dice at the same time are independent events. Others are dependent events.
What is Independent and Dependent Events?Independent events are events for which the occurrence of this event does not depend on any other events.
Dependent events are those events for which it's occurrence depends on other events.
Two events A and B are independent, if
P(A | B) = P(A)
P(A and B) = P(A) × P(B)
P(A) = 0.65, P(B) = 0.25 and P(A and B) = 0.40
P(A) × P(B) = 0.65 × 0.25 = 0.1625 ≠ P(A and B)
∴ A and B are dependent events.
P(A) = 0.22 P(B) = 0.45 and P(A and B) = 0.099
P(A) × P(B) = 0.22 × 0.45 = 0.099 = P(A and B)
∴ A and B are independent events.
P(A) = 0.42 P(B) = 0.62 and P(A| B) = 0.2604
P(A| B) = 0.2604 ≠ P(A)
∴ A and B are dependent events.
If you roll a pair of dice at the same time, probability for any number to occur on dice 1 does not affect the probability of any number to occur on dice 2.
∴ A and B are independent events.
If you choose two marbles from a bag, when the first marble is chosen, then the second marble you choose will not be the first marble in any case. So second event depends on the first event.
∴ A and B are dependent events.
Hence, as P(A and B) = P(A) × P(B) satisfies for the events P(A) = 0.22 P(B) = 0.45, P(A and B) = 0.099, is is independent events. Also rolling a pair of dice at the same time is also independent events. The rest of the events are dependent events as it does not satisfies the condition for independent events.
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Mario makes 6 throw shots out of his first 10 attempts
Ok⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Answer: 4
Step-by-step explanation: If you are trying to see how many Mario missed that would be 4
A store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing 18$ is displayed by the store manager at a selling price of 2$. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
if the markup is 11%, well, we simply add that to the cost of the item, in this case 18.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{11\% of 18}}{\left( \cfrac{11}{100} \right)18}\implies 1.98~\hfill \underset{selling~price}{\stackrel{18 ~~ + ~~1.98}{\text{\LARGE 19.98}}}[/tex]
Two machines produce sound pressure levels of approximately 80 dB(A) each. What is their approximate combined sound pressure level?
83.01dB is approximate combined sound pressure level.
What is sound pressure level?
The result of the pressure changes in the air caused by sound waves is sound pressure, often known as sound pressure level. The hearing threshold is the lowest sound pressure that a human can hear, and the pain threshold is the maximum sound pressure that a person can tolerate.
The difference between sound pressure at the pain threshold and the hearing threshold is a million times higher.
We have sound pressure level denoted as (Lp) of each machine
i.e 80 dB,(given).
Therefore, we can calulate sound pressure level from both machines combined by given formula,
SPL = 10 * Log(10^(SPL(1) /10) + 10^(SPL(2) /10) +10^(SPL(3) /10) + ............)
where,
SPL= sound pressure level(dB)
=> SPL = 10 * Log(10^(80 /10) + 10^(80 /10))
=> SPL = 10 * Log(10^8 + 10^8)
=> SPL = 10 * 8.301
=> SPL = 83.01dB
Hence, 83.01dB is approximate combined sound pressure level.
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A waterproof speaker sells for $179, which is marked up by 30% of the selling price. What is the cost of the speaker? A. $152.30 B. $132.50 C. $123.50 D. $125.30
The original cost of the speaker will be equal to $125.3. The correct option is D.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that a waterproof speaker sells for $179, which is marked up by 30% of the selling price.
The cost price of the speaker will be calculated as,
Cost price = 179 x 0.7
Cost price = $125.3
Therefore, the original cost of the speaker will be equal to $125.3. The correct option is D.
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B OA) A Which statements are necessary to prove the two triangles are congruent by SSS? O B) D =CD, AB = C, mzBDA = 90° AD, BD = CD, mzBDA = 90° O a OD) AD AD, BD = CD, AB = AC BD = CD, AB= AC
The statements that are necessary to prove the two triangles are congruent by SSS are AD≅ AD, BD ≅ CD, and AB ≅ AC.
What is congruence?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Here,
To prove that two triangles are congruent using the SSS Congruence criterion, we must establish that all three sides of one triangle are equal to all the corresponding sides of the other.
Thus,
Side AD in ∆ADB is congruent to side AD in ∆ADC.
Side BD in ∆ADB is congruent to side CD in ∆ADC.
Side AB in ∆ADB is congruent to side AC in ∆ADC.
Hence, based on the SSS congruence criterion, it is concluded that both triangles are congruent. i.e AD≅ AD, BD ≅ CD, AB ≅ AC.
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Answer:
D
Step-by-step explanation:
To prove that two triangles are congruent using the SSS Congruence criterion, we must establish that all three sides of one triangle are equal to all the corresponding sides of the other.Thus,Side AD in ∆ADB is congruent to side AD in ∆ADC.Side BD in ∆ADB is congruent to side CD in ∆ADC.Side AB in ∆ADB is congruent to side AC in ∆ADC.Therefore, based on the SSS congruence criterion, it is concluded that both triangles are congruent.The statements necessary to prove that they are congruent by SSS is: D
Determine whether the expressions are equivalent.
0.4(k+3) is to 0.4 k+1.2
Equivalent. 0.4(k+3)=0.4 k+1.2
Not equivalent. 0.4(k+3)=0.4 k+0.8
Equivalent. 0.4(k+3)=0.4 k+0.4
Not equivalent. 0.4(k+3)=0.4 k+0.4
Both the expressions are equivalent to each other.
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Given expression:
LHS
0.4(k+3)
= 0.4k + 0.4 × 3
= 0.4k + 1.2
RHS
0.4 k+1.2
LHS = RHS
Therefore, both the expressions are equivalent to each other.
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Does it make sense to discuss the similitude between 2 rombii, 2 squares, 2 rectangles, 2 parralelegrams, and 2 conguent polygons
Yes, it makes sense to discuss the similarity between these shapes.
How to determine if it make sense to discuss the similitude between 2 rombii, 2 squares?Two shapes are considered similar if they have the same shape, but possibly different sizes. This means that the angles of the shapes are the same and the sides of the shapes are in the same ratio.
Two rhombi are similar if they have the same angle measures and the lengths of their sides are in the same ratio.
Two squares are similar if they have the same angle measures and the lengths of their sides are in the same ratio.
Two rectangles are similar if they have the same angle measures and the lengths of their sides are in the same ratio.
Two parallelograms are similar if they have the same angle measures and the lengths of their sides are in the same ratio.
Two congruent polygons are similar by definition, since congruent shapes are identical in size and shape.
It is important to note that similarity is different from congruence. Congruent shapes are identical in size and shape, whereas similar shapes have the same shape but possibly different sizes.
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Need an answer pls will mark Brainliest
Answer:
4 m^3 - 38 m^2 + 57 m - 72 = (4 m^2 - 6 m + 9)(m - 8) + 0
Step-by-step explanation:
Compute (4 m^3 - 38 m^2 + 57 m - 72) ÷ (m - 8) using polynomial long division:
m - 8 | 4 m^3 | - | 38 m^2 | + | 57 m | - | 72
To eliminate the leading term of the numerator, 4 m^3, multiply m - 8 by 4 m^2 to get 4 m^3 - 32 m^2. Write 4 m^2 on top of the division bracket and subtract 4 m^3 - 32 m^2 from 4 m^3 - 38 m^2 + 57 m - 72 to get -6 m^2 + 57 m - 72:
| | | 4 m^2 | | | |
m - 8 | 4 m^3 | - | 38 m^2 | + | 57 m | - | 72
| -(4 m^3 | - | 32 m^2) | | | |
| | | -6 m^2 | + | 57 m | - | 72
To eliminate the leading term of the remainder of the previous step, -6 m^2, multiply m - 8 by -6 m to get -6 m^2 + 48 m. Write -6 m on top of the division bracket and subtract -6 m^2 + 48 m from -6 m^2 + 57 m - 72 to get 9 m - 72:
| | | 4 m^2 | - | 6 m | |
m - 8 | 4 m^3 | - | 38 m^2 | + | 57 m | - | 72
| -(4 m^3 | - | 32 m^2) | | | |
| | | -6 m^2 | + | 57 m | - | 72
| | | -(-6 m^2 | + | 48 m) | |
| | | | | 9 m | - | 72
To eliminate the leading term of the remainder of the previous step, 9 m, multiply m - 8 by 9 to get 9 m - 72. Write 9 on top of the division bracket and subtract 9 m - 72 from 9 m - 72 to get 0:
| | | 4 m^2 | - | 6 m | + | 9
m - 8 | 4 m^3 | - | 38 m^2 | + | 57 m | - | 72
| -(4 m^3 | - | 32 m^2) | | | |
| | | -6 m^2 | + | 57 m | - | 72
| | | -(-6 m^2 | + | 48 m) | |
| | | | | 9 m | - | 72
| | | | | -(9 m | - | 72)
| | | | | | | 0
The quotient of (4 m^3 - 38 m^2 + 57 m - 72)/(m - 8) is the sum of the terms on top of the division bracket. Since the final subtraction step resulted in zero, m - 8 exactly divides 4 m^3 - 38 m^2 + 57 m - 72, and there is no remainder.
| | | 4 m^2 | - | 6 m | + | 9 | (quotient)
m - 8 | 4 m^3 | - | 38 m^2 | + | 57 m | - | 72 |
| -(4 m^3 | - | 32 m^2) | | | | |
| | | -6 m^2 | + | 57 m | - | 72 |
| | | -(-6 m^2 | + | 48 m) | | |
| | | | | 9 m | - | 72 |
| | | | | -(9 m | - | 72) |
| | | | | | | 0 | (remainder) invisible comma
(4 m^3 - 38 m^2 + 57 m - 72)/(m - 8) = (4 m^2 - 6 m + 9) + 0
Write the result in quotient and remainder form:
Answer: 4 m^3 - 38 m^2 + 57 m - 72 = (4 m^2 - 6 m + 9)(m - 8) + 0
3. For the graph above, what is the approximate y-value of the point of intersection?
0-1
04
03
02
Answer: 02
Step-by-step explanation: w
Multiply by using the Distributive Property. (x2 + 3)(x − 4) =
The expression is obtained by simplifying it by the distributive Property is x³-4x²+3x-12.
What is distributive property?The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example, we can write a(c+b) in the form of (ac+bc).
It is given that, the expression is (x² + 3)(x − 4)
The expression is simplified using the distributive property as,
=(x² + 3)(x − 4)
=x²(x − 4)+3(x − 4)
=x³-4x²+3x-12
Thus, the expression is obtained by simplifying it by the distributive Property is x³-4x²+3x-12.
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The multiplication of the term (x² + 3)(x - 4) using distributive property is x³ - 4x² + 3x - 12.
Distributive property explains to us how to solve expressions in the form of a(b + c).
After apply distributive property, this term converts as ab+ac
The given expression is,
(x² + 3)(x - 4)
Solve by using distributive property formula (a+b)(c+d)= a(c+d) + b(c+d),
x²(x - 4) + 3(x - 4)
Now further simplify by using formula a(b+c) = ab+ac,
x³ - 4x² + 3x - 12.
The required multiplication of the given terms is x³ - 4x² + 3x - 12.
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Which diagram shows a pair of angle measures that prove lines a and b are parallel?
Answer:
c
...................
Answer:
the answer is the option C
Help me with geometry
Answer:
34
Step-by-step explanation:
This is somewhat hard to explain for me. I attached a picture/diagram to help.
They are congruent angles.
Angle N, inside the MNP triangle is 34. Which means the adjacent angle is 56.
The interior angles of a triangle add up to 180.
So to find angle M in triangle LNM, we can do 180 - 90 - 56.
Therefore the m<LMN = 34
What is the solution to 9|x – 8| < 36?
4 < x < 12
x < –4 or x > 12
x > –12 or x < 8
–4 < x < 8
Answer:
4 < x < 12
Step-by-step explanation:
x - 8 ≥ 0
x ≥ 8
If x ≥ 8
9(x-8) < 36
9x - 72 < 36
9x < 36 + 72
9x < 108
9/9 x < 108/9
x < 12
8 ≤ x < 12
if x < 8
9(-x+8) < 36
-9x + 72 < 36
-9x < 36 - 72
-9x < -36
-9/-9 x > -36/-9
x > 4
4 < x < 8
4<x<12
NEED HELP NOW Convert 110 kilograms to pounds. (1 kilogram = 2.204 pounds)
The required answer in the given problem, given weight of 5 kilograms and convert it to 11.02 pounds. By multiplying the given weight by the conversion factor of 2.204 pounds/kilogram, obtain the weight in pounds.
Conversion from kilograms to pounds:
To convert a weight value from kilograms to pounds, we use the conversion factor of 1 kilogram equals 2.204 pounds. This means that for every 1 kilogram, there are 2.204 pounds. To convert a weight from kilograms to pounds, we multiply the given value in kilograms by the conversion factor.
To convert 110 kilograms to pounds, we can use the conversion factor that states 1 kilogram is equal to 2.204 pounds. Here's the step-by-step process:
Step 1: Write down the given weight in kilograms, which is 110 kilograms.
Step 2: Multiply the given weight by the conversion factor:
110 kilograms x 2.204 pounds/kilogram
Step 3: Perform the multiplication:
110 x 2.204 = 242.44 pounds
Therefore, 110 kilograms is equal to 242.44 pounds.
In the given problem, given weight of 5 kilograms and convert it to 11.02 pounds. By multiplying the given weight by the conversion factor of 2.204 pounds/kilogram, obtain the weight in pounds.
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Valentino's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what she found. Type of Crust Number Sold Thin crust 293 Thick crust 216 Stuffed crust 174 Pan style 195 Based on this information, of the next 3000 pizzas she sells, how many should she expect to be thin crust? Round your answer to the nearest whole number. Do not round any intermediate calculations. pizzas X
Answer:
1120
Step-by-step explanation:
Given the information below:
The Relative Frequency of selling a pan style pizza =
Therefore, if Valentino's Pizzeria were to sell 4000 pizzas, the expected number of Pan style pizza sold will be:
Number of Pan Style Pizza Sold = Relative Frequency of pan Style Pizza Purchase X Total Number of Sales
They should expect to sell 1120 pan Style pizzas.
Write a quadratic function to model the graph to the right.
f(x)=____
f(x) = x² + 2x + 2
Solution:
Given vertex (1,1)
a = 1
Formula of quadratic equation is :
y = a(x + b)² + c
where, a =1, x=x, b = x1, c = y1
Substituting the values in the equation, we get
y = x² + 2x + 2
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A quadratic function to model the graph to the right is f(x) = x² + 2x + 2
What is a quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Solution:
Given vertex (1,1)
a = 1
Formula of quadratic equation is :
y = a(x + b)² + c
where, a =1, x=x, b = x1, c = y1
Substituting the values in the equation, we get
y = x² + 2x + 2
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The doubling period of a bacterial population is 15 minutes. At time t=120 minutes, the bacterial population was 90000.
What was the initial population at time t=0 ?
Find the size of the bacterial population after 3 hours.
The doubling period of a bacterial population is 15 minutes. the initial population at time t=0 is 351.56. the size of the bacterial population after 3 hours is:359,997.44.
How to find the initial population?y = total amount of bacteria
a = initial bacterial at time 0
b = growth factor
t=120 minutes =15 minutes 8 times
So,
t=8
90000 = a (2)^8
90000 = a (256)
90000/256 = a
351.56 = a (initial population)
Equation:
y = 351.56 (2)t
After 3 hours (15 minutes 10 times), or at t = 10
y = 351.56 (2)^10
y= 359,997.44
Therefore the initial population at time t=0 is 351.56. the size of the bacterial population after 3 hours is:359,997.44.
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Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years.
Answer:
11.6 years
Step-by-step explanation:
1800 = 900 x (1 + 0.06/12)^ 12t
1800 = 900 x (1 + 0.005)^12t
1800 = 900 x (1.005)^12t
1800 = 900 x 1.061678^t
1800/900 = (900 x 1.061678^t)/ 900
2 = 1.061678^t
log(1.061678) 2 = t
t = 11.5813
t = 11.6
5.6.8 let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e). show that this need not be true if f is continuous but not uniformly continuous.
Proof. (1): To prove {f(xn)} is a Cauchy sequence just need to prove ∀ > 0, ∃N, s.t.,∀n, m > N,
have |f(xn) − f(xm)| < . Since f is uniformly continuous on set E, thus ∀ > 0, ∃δ > 0, s.t.,
∀x, y ∈ E, if |x − y| < δ,then |f(x) − f(y)| < .as {xn} is a Cauchy sequence, then ∃N, s.t.,
∀n, m > N, |xn − xm| < δ, thus |f(xn) − f(xm)| < which proves {f(xn)} is a Cauchy sequence.
(2): for example f(x) = 1
x
, x ∈ (0, 2) which is continuous but not uniformly continuous. {
1
n
} is
a Cauchy sequence, however, {f(xn)} does not converge which proves that it is not a Cauchy
sequence.
Showing that this need not be true if f is continuous but not uniformly continuous.
Given :
let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e).
( 1 )
If f is uniformly continuous on E, then given ε > 0 there is δ > 0 such that if x, y are in E and |x−y| < δ,
then |f(x) − f(y)| < ε. Let (xn) be a Cauchy sequence in E. Then given δ > 0 there is N such that if p, q > N,
then |xp − xq| < δ, and thus |f(xp) − f(xq)| < ε, implying that (f(xn)) is a Cauchy sequence.
( 2 )
Let E = {1, 1/2, 1/3, · · } and f(1/n) = 1 is n is odd, f(1/n) = −1 if
n is even. Then f is continuous but not uniformly continuous. The sequence (xn) = (1/n) in E is Cauchy but the
sequence (f(xn)) = (1, −1, 1, −1, · · ·) is not Cauchy.
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Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.
A sample of 72 stocks traded on the NYSE that day showed that 29 went up.
You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of a = 0.02.
What is the test statistic for this sample?
Use p rounded to 4 decimal places. (Report answer accurate to 4
decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to 4 decimal places.)
p-value =
The p-value is either less than (or equal to) or
greater than?
This p-value leads to a decision to...
reject the null or accept the null or fail to reject the null?
As such, the final conclusion is that... (select a letter)
A) There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went
up is is more than 0.3.
B) There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that
went up is is more than 0.3.
C) There is sufficient evidence to support the claim that the proportion of stocks that went up is is more
than 0.3.
D) There is not sufficient sample evidence to support the claim that the proportion of stocks that went up
is is more than 0.3.
The test statistic and the p-value of the research are respectively z = 1.9072 and p-value = 0.0283 and the conclusion is that; D) There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is more than 0.3.
How to find the p-value from the research?Let us first of all define the hypotheses;
Null Hypothesis; H₀: p ≤ 0.3
Alternative Hypothesis; Hₐ: p > 0.3
Sample proportion is;
p^ = 29/72 = 0.403
The formula for the test statistic is;
z = (p^ - p)/(√(p(1 - p)/n))
Plugging in the relevant values gives;
z = (0.403 - 0.3)/(√(0.3(1 - 0.3)/72))
z = 1.9072
From p-value from z-score calculator, we have that;
p-value = 0.0283
p-value is greater than the significance value and as such we fail to reject the null hypothesis and conclude that There is not sufficient sample evidence to support the claim that the proportion of stocks that went up
is is more than 0.3.
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Target charges $4.40 for 8 sodas. Walmart charges $7.08 for 12 sodas. Which store has
the best unit price? How much cheaper is it?
Answer:
Target
Step-by-step explanation:
$4.40/8 is 0.55 and $7.08/12 is 0.59