the formula for the compound interest is given as follows,
[tex]A=P(1+\frac{R}{100})^t[/tex]here P = 2000 , R = 8 % , t = t.
so the value(V) is
[tex]\begin{gathered} V=2000(1+\frac{8}{100})^t \\ V=2000(1+0.08)^t \end{gathered}[/tex][tex]V=2000(1.08)^t[/tex]so the answer is option C
Which normal distribution has a wider spread: distribution A with a mean of one and a standard deviation of two, or distribution B with a mean of two and a standard deviation of one?
The normal distribution with mean of one and standard deviation of two has the wider spread.
Normal distribution:
Normal distribution defines a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.
Given,
Here we have the distributions,
Distribution A with a mean of one and a standard deviation of two, or Distribution B with a mean of two and a standard deviation of one
Now, we have to identify the normal distribution has a wider spread.
Here the normal distribution with a mean of 1 and standard deviation of 2 will be wider than a distribution with a mean of 2 and standard deviation of 2.
Because, the distributions with greater standard deviations indicate greater variability/spread of its variables around the mean.
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Find the area of the triangle below.9.9 m5.6 m4.4 m7.8 m
the Answer
Step by Step Explanation
The area of the triangle formula is
[tex]A=\frac{h_b\cdot b}{2}[/tex]where
[tex]\begin{gathered} h_b=4.4m \\ b=9.9m \end{gathered}[/tex]Subs, the value in above equation
[tex]\begin{gathered} A=\frac{h_b\cdot b}{2} \\ A=\frac{4.4_{}\cdot21.78}{2} \\ A=21.78 \end{gathered}[/tex]The area of the triangle is 21.78 cm^2
describe the reflection (s) that carry the regular pentagon onto itself.
EXPLANATION:
The reflection that is made on a figure,reverses its position with respect to a line called the axis of reflection.
IMPORTANT NOTE:
To make the reflection of the geometric figure shown in the exercise, we need to know the vertices and coordinates of the figure that allow us to make the corresponding reflection in the Cartesian plane of the pentagon
Suppose your bank charges a $7 monthly fee and $0.11 per check. If you write 62 checks in a year, how much money in fees would you expect to pay for the year? Type out acalculations and make sure your final answer is clear.
The cost has a monthly fee and a per check fee.
We can write the bank fee as:
[tex]C(m,c)=7m+0.11c[/tex]m: months, c: number of checks.
If, in a year (m=12 months), you write 62 checks (c=62), the total fee is:
[tex]C(12,62)=7\cdot12+0.11\cdot62=84+6.82=90.82[/tex]You expect to pay a yearly fee of $90.82.
an item is regular priced at $60. Linda bought it on sale for 30% off the regular price. how much did Linda pay?
Given data
*An item is regular priced at $60
*Linda bought is on sale on discount is 30%
Linda pay the price on the item is calculated as
[tex]\begin{gathered} p=60\times30\text{ PERCENT} \\ =60\times0.3 \\ =18 \end{gathered}[/tex]Thus, the charged amount on an item is $18
The graph of a quadratic function with vertex (0, -1) is shown in the figure below.Find the range and the domain in interval notation please include paranthese or brackets within your answer.
The domain is all the values that the function can take on the x axis, in this case it would be all the real numbers:
[tex]domain\to(-\infty,\infty)[/tex]The range is all the values that the function can take on the y-axis. For this function it will grow from vertex to infinity:
[tex]range\to\lbrack-1,\infty)[/tex]Remember that when intervals are written, parentheses are used for open values and square brackets for exact values.
20. Damilola wrote the equation h = 2d + 1 to represent the height of hisplant, h, after a certain number of days. In this relationship, he identified has the dependent variable, and d as the independent variable. Do youagree? Why or why not?*
As we can see we have the next equation
[tex]h=2d+1[/tex]where h is the dependent variable and d is the independent variable
So we agree, because d does not depend on the height, but the height depends on the days
In order words
An independent variable is a variable that represents a quantity that is modified in an experiment. In this case d
A dependent variable represents a quantity whose value depends on how the independent variable is modified. In this case h
independent vs dependent equation5х – Зу = 10 бу = kx - 42
We will assume that we want to know if the system of equations is independent or dependent:
[tex]\begin{cases}5x-3y=10\text{ (1)} \\ 6y=kx-42\text{ (2)}\end{cases}[/tex]where k is a real number. We will try to find the solutions to the system, and we will try to give values to k for which the system becomes independent or dependent.
We will use substitution, we solve for the variable x on the first equation to obtain:
[tex]\begin{gathered} 5x-3y=10 \\ 5x=10+3y \\ x=\frac{10+3y}{5} \end{gathered}[/tex]And now we replace it onto the second equation:
[tex]\begin{gathered} 6y=k(\frac{10+3y}{5})-42 \\ 6y=\frac{10k+3ky}{5}-42 \\ 6y=\frac{10k+3ky-210}{5} \\ 30y=10k+3ky-210 \\ 30y-3ky=10k-210 \\ y(30-3k)=10k-210 \\ y=\frac{10k-210}{30-3k} \end{gathered}[/tex]And the value of x will be:
[tex]\begin{gathered} x=\frac{10+3(\frac{10k-210}{30-3k})}{5}=\frac{10+\frac{10k-210}{10-k}}{5} \\ =\frac{10(10-k)+10k-210}{5(10-k)} \\ =\frac{100-10k+10k-210}{50-5k} \\ =-\frac{110}{50-5k} \\ =-\frac{22}{10-k} \end{gathered}[/tex]This means that a solution of the system will be:
[tex]\begin{cases}x=-\frac{55}{10-k} \\ y=\frac{10k-210}{30-3k}\end{cases}[/tex]Now, for finding the values which make the system dependent. This happens when the lines have the same slope, this is, when:
[tex]\begin{gathered} \frac{-5}{-3}=\frac{k}{6} \\ \frac{5}{3}=\frac{k}{6} \\ 30=3k \\ 10=k \end{gathered}[/tex]We did the division of the opposite of the coefficient of x, over the coefficient of y. This means that the system will be independent for each value of k different than 10, and will be dependent for k=10.
Tickets to a show cost $5.50 for adults and $4.25 for students. A family is purchasing 2 adult tickets and 3 student tickets.
Estimate the total cost.
What is the exact cost?
If the family pays $25, what is the exact amount of change they should receive?
The exact cost is $23.75 for the show, and the exact change they should get is $1.25.
An adult ticket to the show costs $5.50
A student ticket to the show costs $4.25.
A family buys two adult tickets and three student tickets. This would imply that the total cost of two adult tickets would be
⇒ 2 × 5.5 = $11
It also implies that the total cost of three student tickets is
3 × 4.25 = $12.75
The total cost of two adult tickets and three student tickets is
⇒ 11 + 12.75 = $23.75
If the family pays $25, the exact change they should get is
⇒ 25 - 23.75 = $1.25
Thus, the exact cost is $23.75 for the show, and the exact change they should get is $1.25.
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Trey has bought 10 pounds of dog food. He feeds his dog2/5pounds for each meal. For how many meals will the food last?Write your answer in simplest form
ANSWER
25 meals
EXPLANATION
Trey has 10 pounds of food to give to his dog. To know for how many meals the food will last we have to divide the total amount of food by the amount of food he gives the dog in each meal,
[tex]10\colon\frac{2}{5}[/tex]To divide this we can use the KCF rule:
• K,eep the first fraction. In this case the first number is a whole number, which we can think of as a fraction with denominator 1.
,• C,hange the division sign into a multiplication sign.
,• F,lip the second fraction.
[tex]10\colon\frac{2}{5}=10\times\frac{5}{2}[/tex]And to multiply we just multiply the numerators and the denominators,
[tex]10\times\frac{5}{2}=\frac{10\times5}{1\times2}=\frac{50}{2}[/tex]To write it in simplest form we have to simplify the fraction. Note that 50 is an even number, so it is divisible by 2. 50 divided by 2 is,
[tex]\frac{50}{2}=25[/tex]Hence, the food will last 25 meals
The function 1 (2) = 4x is used to calculate the litter of piglets born on the farm; x represents the number of female pigs on the farm. Each female pig births 4 piglets. The
farmer will need pens to house all the piglets. One pen can house 8. The number of pens required is written as p(x)=+1, where x is the number of piglets. The farmer
always builds one extra pen. Which of the following functions represents the number of pens as a function of the female pigs?
p(p(x))
p(l(z))
1(p(x))
1 (1 (x))
A function which represents the number of pens as a function of the female pigs is: p(l(z)).
How to determine the function that represents the number of pens?From the information provided, we have the following the following functions:
Function, l(z) = 4x
Where:
l(z) represents the litter of piglets born on the farm.x represents the number of female pigs on the farm.Function, p(x) = x/8 + 1
Where:
p(x) represents the number of pens required.x represents the number of piglets.Next, we would substitute the the litter of piglets born on the farm l(x) into the number of pens required as follows;
p(x) = x/8 + 1
p(l(z)) = 4x/8 + 1
p(l(z)) = 0.5x + 1
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Complete Question:
Function l(z) = 4x is used to calculate the litter of piglets born on the farm; x represents the number of female pigs on the farm. Each female pig births 4 piglets. The farmer will need pens to house all the piglets. One pen can house 8. The number of pens required is written as p(x) = x/8 + 1, where x is the number of piglets. The farmer always builds one extra pen. Which of the following functions represents the number of pens as a function of the female pigs?
p(p(x))
p(l(z))
1(p(x))
1 (1 (x))
a family walked 240 miles in 4 hours yesterday at this rate how many hours will it take to walk another 150 miles
A family walked 240 miles in 4 hours yesterday at this rate how many hours will it take to walk another 150 miles ?
_____________________________________________________
Rate
240 miles / 4 hours = 60 miles / hour
_______________________
Can you see the updates?
_____________________
150 miles ÷ rate = time ( 150 miles)
150 miles ÷ 60 miles/hour = 150/ 60 = 2.5 hours
___________________________________
Total time = 4 h + 2.5 h = 6.5 h
_________________________________
Answer
It will take 2.5 h to walk another 150 miles (in total 240 + 150, 6.5 h )
Johanna just returned from a trip to South Africa. She has 7342 rands, the currency of South Africa. She looks up the exchange rate and finds that 1 South African rand = 0.1125 U.S. dollars. What is the value of her money in U.S. dollars
Johanna has 7,342 Rands.
The exchange rate is 1 Rand = 0.1125
To find the value of the money in US dollars, multiply the amount in Rands by 0.1125
[tex]7,342\times0.1125=\$825.975[/tex]Therefore, the value of the money in US dollars is $825.975
Use the two-way table on left and right-handed people to create a two-way table that shows the joint and marginal relative frequencies. Drag and drop the numbers to complete the table. Dominant Hand left. right. totalfemale 11. 104. 115Male. 24. 92. 116total. 35. 196. 231 Dominante hand left. rigth. totalfemale maletotalBank:0.0480.1520.1670.3760.3980.4500.4980.5020.5260.84810.104
1st Row (Female)
[tex]\begin{gathered} \frac{11}{231}=0.048 \\ \frac{104}{231}=0.450 \\ \frac{115}{231}=0.498 \end{gathered}[/tex]2nd Row (Male)
[tex]\begin{gathered} \frac{24}{231}=0.104 \\ \frac{92}{231}=0.398 \\ \frac{116}{231}=0.502 \end{gathered}[/tex]Third Row (Total)
[tex]\begin{gathered} \frac{35}{231}=0.156 \\ \frac{196}{231}=0.848 \\ \frac{231}{231}=1 \end{gathered}[/tex]The completed table is given below:
The minute hand of a clock extends out to the edge of the clock's face, which is a circle of radius 4 inches. What area does the minute hand sweep out between 9:15 and9:35? Round your answer to the nearest hundredth.
To solve the question, we have to make use of the fact that
A minute hand travels 360 degrees in 60 min
From the question given, we are told that the minute hand sweep out between 9:15 and
9:35, thus
There are 20 minutes in between 9:15 and 9:35
Thus
We can get the area using the formula
[tex]\begin{gathered} Area=\frac{\text{minutes turned}}{60}\times\pi r^2 \\ \text{where} \\ r=4\text{ inches} \end{gathered}[/tex]Area will be
[tex]\begin{gathered} \text{Area}=\frac{20}{60}\times\pi\times4^2 \\ \text{Area}=\frac{1}{3}\times\pi\times16 \\ \text{Area}=16.755 \end{gathered}[/tex]Thus, the area will be 16.76 in²
3. Select all the expressions that will have a remainder. 377 644 74 – 3 96 = 5 56 – 2
To obtain the term that will give a remainder, we will have to check if the dividend is a multiple of the divisor
Dividends and divisors are the two key ingredients that yield the quotient. The dividend is the number being divided, while the divisor is the number by which the dividend is divided. In other words, given a÷b, a is the dividend and b is the divisor
Looking at
37 ÷ 3 = (12 remainder 1), 37 is not a multiple of 3, so this will give a remainder of 1
64 ÷ 4 = (16 remainder 0), 64 is a multiple of 4, so this will not give a remainder
74 ÷ 3 = (24 remainder 2), 74 is not a multiple of 3, so this will give a remainder of 2
96 ÷ 5 = (19 remainder 1), 95 is not a multiple of 5, so this will give a remainder of 1
56 ÷ 2 = (28 remainder 0), 56 is a multiple of 2, so this will not give a remainder
What is the mixed number answer 4 4/9 + 8 7/9
Hello there. To solve this question, we'll have to remember some properties about mixed numbers.
Given the mixed number a b/c, we can write it as and it is the same as
Therefore in the expression:
[tex]4\frac{4}{9}+8\frac{7}{9}[/tex]We rewrite it as
[tex]4+\frac{4}{9}+8+\frac{7}{9}[/tex]Adding the fractions, we have:
[tex]12+\frac{11}{9}=\frac{119}{9}[/tex]And we have to write the answer in mixed fraction form, therefore we perform
[tex]\frac{119}{9}=\frac{117+2}{9}=13\frac{2}{9}[/tex]This is the answer we're looking for.
find each unit rate. round to the nearest hundredth if necessary 325 meters in 25 seconds
325 meters in 25 seconds
To find out the unit rate divide the total meters by the total seconds
so
325/25=13 m/sec
therefore
the answer is
13 m/secor 13 m per one secondIdentify the local extrema on the graph below. Type your answer as a coordinate (x,y). If there is not a local maximum/minimum then type "none".positive (opening up) absolute value graph with vertex at (1,-3)Local minimum is at the coordinate AnswerLocal maximum is at the coordinate Answer
The graph is given and local minima from the graph is
[tex](1,-3)[/tex]And the local maxima is none.
Hi, can you help me answer this question please, thank you!
The number of sick days an employee takes per year is believed to be about 12.
The mean purpose of null hypothesis is to verify or disprove the proposed statistical assumptions, also is usually associated with just ‘equals to’ sign as a null hypothesis can either be accepted or rejected.
If you wish to test the claim that mean number of sick days an employee takes per year is not equal to 12 days, then the null hypothesis is "the mean number of sick days an employee takes per year is equal to 12 days".
Then, the correct null hypothesis is:
[tex]H_0\colon\mu=12\text{ days}[/tex]The alternative hypothesis is an alternative to the null hypothesis, then if you want to check the claim that mean number of sick days an employee takes per year is not equal to 12 days, then the alternative hypothesis is "mean number of sick days an employee takes per year is not equal to 12 days".
Then, the correct alternative hypothesis is:
[tex]H_a\colon\mu\ne12\text{ days}[/tex]yson does 75 sit-ups during his work out. He wants to increase his sit-ups by 15%. Which represents the new amount of sit-up
Answer:
he does 86 sit ups instead of 75 to increase by 15 percent
Step-by-step explanation:
Answer: The correct answer is 86.25 sit-ups (or round-up to 87 whole sit-ups).
Step-by-step explanation:
S = current amount of sit-ups (75)
S2 = Increased amount of sit-ups by 15%
The equation:
S2 = S + (S x .15)
S2 = 75 + (75 x .15)
S2 = 75 + 11.25
S2 = 86.25 sit-ups
Draw the given angles in standard position. 110 degrees, - 80 degrees
Standard Position of Angles
An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis.
The ray on the x-axis is called the initial side and the other ray is called the terminal side.
Positive angles are measured counterclockwise, negative angles are measured clockwise.
The angle of 110 degrees is positive so it must be measured counterclockwise. The angle -80 will be drawn clockwise.
The following image shows the required angles:
Seniors at a high school are allowed to go off campus for lunch if they have a grade of A in all their classes or perfect attendance. An assistant principal in charge of academics knows that the probability of a randomly selected senior having A's in all their classes is 0.1. An assistant principal in charge of attendance knows that the probability of a randomly selected senior having perfect attendance is 0.16. The cafeteria staff know that the probability of a randomly selected senior being allowed to go off campus for lunch is 0.18. Use the addition rule of probability to find the probability that a randomly selected senior has all As and perfect attendance.
Given:
Probability a randomly selected senior has A = 0.1
Probability a randomly selected senior has a perfect attendance = 0.16
Probability a randomly selected senior is being allowed to go offf campus: P(A or B) = 0.18
Let's find the probability that a randomly selected senior has all As and a perfect attendance using addition rule for probability.
Apply the formula below:
P(A or B) = P(A) + P(B) - P(A and B)
Rewrite for P(A and B):
P(A and B) = P(A) + P(B) - P(A or B)
P(A and B) = 0.1 + 0.16 - 0.18
Therefore, the probability that a randomly selected senior has all As and perfect attendance is
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y = -16x2 + 261x + 130
Answer
The highest height attained by the rocket = 1194.4 feet
Explanation
The height of the rocket, y, in feet as a function of the time, x in seconds as
y = -16x² + 261x + 130
We are then asked to find the maximum height reached by the rocket
To do this, we would use the differentiation analysis to obtain the maximum of this function.
At maximum point for any function,
The first derivative = (dy/dx) = 0
The second derivative = (d²y/dx²) < 0
y = -16x² + 261x + 130
First derivative
(dy/dx) = -32x + 261 = 0
32x = 261
Divide both sides by 32
(32x/32) = (261/32)
x = 8.15625 s
We can then substitute this value of x (time) into the equation to get the maximum height (y)
y = -16x² + 261x + 130
At x = 8.15625 s,
y = -16 (8.15625)² + 261 (8.15625) + 130
= -1064.39 + 2128.78 + 130
= 1194.39
= 1194.4 feet to the nearest tenth.
Hope this Helps!!!
Write the function whose graph is the graph of y=x^3, but is shifted to the right 3 units.y=
The Solution:
Given the function below:
[tex]y=x^3[/tex]When the function is shifted to the right by 3 units, the new function becomes:
[tex]y=(x-3)^3[/tex]Therefore, the correct answer is
[tex]y=(x-3)^3[/tex]The ratio of the number of oranges to the number of apples is 1 : 3.21 oranges were added and the ratio became 4 : 5. How many fruitswere there initially?
Answer
There were 15 oranges initially.
There were 45 apples initially.
Hence, there were (15 + 45) = 60 fruits there initially.
Explanation
Let the number of oranges be x
Let the number of apples be y
The ratio of the number of oranges to the number of apples is 1 : 3 implies:
[tex]\begin{gathered} x\colon y=1\colon3 \\ \frac{x}{y}=\frac{1}{3} \\ \text{Cross multiply} \\ y\times1=x\times3 \\ y=3x----i \end{gathered}[/tex]If 21 oranges were added and the ratio became 4 : 5, this implies:
[tex]\begin{gathered} (x+21)\colon y=4\colon5 \\ \frac{x+21}{y}=\frac{4}{5} \\ \text{Cross multiply} \\ 5(x+21)=4\times y \\ 5x+105=4y----ii \end{gathered}[/tex]To know how many fruits were there initially, solve the system of the equations:
[tex]\begin{gathered} \text{Substitute }y=3x\text{ into }ii \\ 5x+105=4(3x) \\ 5x+105=12x \\ \text{Combine the like terms} \\ 12x-5x=105 \\ 7x=105 \\ \text{Divide both sides by 7} \\ \frac{7x}{7}=\frac{105}{7} \\ x=15 \end{gathered}[/tex]x = 15 implies there were 15 oranges initially.
To get y, substitute x = 15 into equation (i):
[tex]\begin{gathered} y=3x----i \\ y=3\times15 \\ y=45 \end{gathered}[/tex]y = 45 implies there were 45 apples initially.
Hence, there were (15 + 45) = 60 fruits there initially.
There are 3 consecutive odd integers that sum to –9. What is the least of these integers?
let the three consecutive numbers are,
a , a+ 1 , a+2
sum of the numbers = -9
a + a +1 + a + 2 = -9
3a + 3 = -9
3a = -9 - 3
3a = -12
a = -12/3
a = -4
so the least number is a = -4
thus the answer is -4.
1. In the function f(x) = 2x +3, what does the x represent?2. In the function f(x) = 2x + 3, what does the f(x) represent?
a. h(-4) = -13
b. h(t) = 23 , t = 14
c. h(13) = 21
d. h(t) = -33 , t = -14
Can I Plss get help on this homework number 1
1.
given the equation
[tex]y=0.32x-20.53[/tex]where
x= number of times at bat
y=number of hits
y=? when x=175
then
[tex]y=0.32(175)-20.53[/tex][tex]y=56-20.53[/tex][tex]y=35.49[/tex]then
Correct answer is option A
A player who is at bat 175 times should expect 35 hits
What is the area of the circle below, in terms of ?90 metersO 457O 907O 1807O 81007134
Step 1: Write out the formula
[tex]\begin{gathered} \text{Area of a circle = }\pi r^2 \\ \text{where } \\ r=\text{ the radius of the circle} \end{gathered}[/tex]Step 2: Write out the given values and substitute them into the formula
[tex]r=90m[/tex]Therefore,
[tex]\text{ the area of the circle = }\pi(90)^2=\pi\times8100=8100\pi m^2[/tex]Hence, the area in terms of pi is
[tex]8100\pi[/tex]The last choice is the correct answer