The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
As per the given,
Principle amount P = $2800
Rate of interest = 6% = 0.06
Compound quarterly n = 4
Time period T = 5 yeras
a)
Total amount = P(1 + R/n)^(nT)
Total amount = 2800(1 + 0.06/4)^(4 x 5)
Total amount = 2800(1.015)^20
Total amount = $3771.19
b)
Let's say the equivalent annual interest rate is r.
n = 1
3771.19 = 2800(1 + r/1)^(1 x 5)
3771.19 = 2800(1 + r)^5
1.061 = 1 + r
r = 0.06136 = 6.136%
Hence"The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%".
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Once an antibiotic is given, number of bacteria decreases at a rate of 15%/day. There were about 15,000 bacteria prior to the treatment. The graph models the number of bacteria after x days of treatment. What are the key features of the exponential function modeled in terms of this situation and how can they be interpreted? Select each correct answer. 30 The line y = 0 is an asymptote of the graph. The x-intercept is 30. The line x = 0 is an asymptote of the graph. The asymptote indicates that there will never be more than 15,000 bacteria. The y-intercept is 15,000. The y-intercept represents the number of bacteria when treatment began. The asymptote indicates that as time increases, the number of bacteria approaches 0.
Answer:
The line y = 0 is an asymptote of the graph.
The y-intercept is 15,000.
The y-intercept represents the number of bacteria when treatment began.
The asymptote indicates that as time increases, the number of bacteria approaches 0.
Step-by-step explanation:
Took the test
Four siblings have a dog walking business. The table shows the hours worked by each sibling. Each sibling earns $25.50 per hour and the total number of hours worked is represented by 10h+15 , where h represents the number of hours Michael worked.
The total amount of money the siblings earned is equal to $1504.5.
How to determine the total amount the siblings earned?From the information provided, the total number of hours worked is represented by this mathematical expression:
10h + 15
where:
h represents the number of hours Michael worked.
Next, we would determine the number of hours Michael worked by summing up all of the total number of hours worked by each of the four siblings and equating it to the total number of hours worked:
2.5(h + 3) + 4(h - 2) + 31 + h = 10h + 15
7.5h + 26 = 10h + 15
10h - 7.5h = 26 - 15
2.5h = 11
h = 4.4 hours.
For the total number of hours worked by each of the four siblings, we have:
Total hours = 10h + 15
Total hours = 10(4.4) + 15
Total hours = 44 + 15
Total hours = 59 hours.
At a rate of $25.50 per hour, the total amount the siblings earned is given by:
Total earnings = $25.50 × 59
Total earnings = $1504.5.
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Complete Question:
Four siblings have a dog walking business. The table shows the hours worked by each sibling. Each sibling earns $25.50 per hour and the total number of hours worked is represented by 10h + 15 , where h represents the number of hours Michael worked. What was the total amount the siblings earned?
The scale of a map is 1:20 000. What area does 8 cm² represent?
The 8 cm² area on a map represent the actual area = 3200000000 cm² .
Scale factor of a map
S = 1/20000
The scale factor for area is found by squaring the scale factor for length. Thus the scale factor for area is S^2
When applied to the area we consider S^2 as a scale factor.
The area on the map = 8 cm²
So The actual area = 8 × (20000)^2 = 8× 20000×20000
=3200000000 cm² = 320000 m² =32 hectare.
So the 8 cm² area on a map represent the actual area = 3200000000 cm² .
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You are solving a measurement problem where the numbers 4.5160 x 10−3, 2.09 x 107, and 5.8 x 103 are multiplied. How many significant digits should the product have?
2
1
5
3
The number of significant digits that the product should have is; 2
How to express numbers in Scientific notations?Scientific notation is defined as a way of expressing a number as a number between 1 and to multiplied by a power of 10. This is usually in the form A * 10ⁿ
Where;
A is any real number between 1 and 10
n is any integer
When multiplying scientific notations, the final product must be to the scientific notation that has the least decimal place.
Since the least decimal place in the given measurement is 2, hence the significant digits the product should have is 2
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Determine which statements are the converse, inverse, and contrapositive of the following statement.
If it is after midnight, Anissa is sleeping.
All rights reser
If Anissa is sleeping, it is not after midnight.
If Anissa is sleeping, it is after midnight.
If it is not after midnight, Anissa is sleeping.
If it is not after midnight, Anissa is not sleeping.
If Anissa is not sleeping, it is not after midnight.
Converse
Contrapositive
Inverca
The statements are characterized as converse, inverse, and contrapositive statements as follows:
A) If it is after midnight, Anissa is sleeping: Converse statements(B) If Anissa is sleeping, it is not after midnight: Inverse statements(C) If Anissa is sleeping, it is after midnight: Converse statements(D) If it is not after midnight, Anissa is sleeping: Inverse statements(E) If it is not after midnight, Anissa is not sleeping: Contrapositive statements(F) If Anissa is not sleeping, it is not after midnight: Contrapositive statementsConverse statements:
If anything, we would say the opposite: "If the grass is wet, it's pouring." "If it is NOT raining, then the grass is NOT wet," would be our inverse claim. If the grass is not wet, it is not raining, according to our contrapositive.Inverse statements:
Each of the original statements is presupposed to be false in an inverted statement. "If it is not snowing" would be the polar opposite of "If it is snowing." "Then it is not chilly" would be the polar opposite of "then it is cold."Contrapositive statements:
When you reverse the hypothesis and the conclusion in a statement and reject both of them, you have a contrapositive statement. When the hypothesis and the conclusion are switched in this example and both are negated, the outcome is: If it is not a triangle, then it is not a polygon.So, the given sentences are:
(A) If it is after midnight, Anissa is sleeping: Converse statements(B) If Anissa is sleeping, it is not after midnight: Inverse statements(C) If Anissa is sleeping, it is after midnight: Converse statements(D) If it is not after midnight, Anissa is sleeping: Inverse statements(E) If it is not after midnight, Anissa is not sleeping: Contrapositive statements(F) If Anissa is not sleeping, it is not after midnight: Contrapositive statementsTherefore, the statements are characterized as converse, inverse, and contrapositive statements as follows:
A) If it is after midnight, Anissa is sleeping: Converse statements(B) If Anissa is sleeping, it is not after midnight: Inverse statements(C) If Anissa is sleeping, it is after midnight: Converse statements(D) If it is not after midnight, Anissa is sleeping: Inverse statements(E) If it is not after midnight, Anissa is not sleeping: Contrapositive statements(F) If Anissa is not sleeping, it is not after midnight: Contrapositive statementsKnow more about converse statements here
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Answer:
1,2,4
Step-by-step explanation:
edem
the unite rate of the ratio 12/5/3/10 is 8/1. Yes or no
Yes, the unit rate of the ratio 12/5/3/10 is 8/1 as per given in the problem.
What does unit rate mean?A unit rate is the price for one unit of a given quantity. With one as the denominator, we express this as a ratio. You would run 7 yards on average every second if you ran 70 yards in 10 seconds, for instance. The 70 yards in 10 seconds and the 7 yards in 1 second ratios are both rates, however the 7 yards in 1 second ratio is a unit rate.
Here, given that the unit rate for the ratio given is 8/1
We have to check whether the ratio is correct or not
So, (12/5)/(3/10)
=(12/5)×(10/3)
=8/1
Therefore, the ratio 8/1 is correct as per given in the sum
So, the answer is yes
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f(x) = 2x; translate up 5 units, reflect in x-axis.
After f(x) = 2x translated up 5 units, then it reflect in x-axis is g(x) = f(2x)+5.
What does a graphing translation mean?
A graph can be vertically translated by moving the base graph up or down in the y-axis direction. Each point on a graph is moved k units vertically to translate the graph by that many units.The rules for transforming a function f(x) into g(x):
g(x) = a·f(b(x-c)) + d
a = vertical dilation (stretch); reflects across x-axis if negativeb = horizontal dilation (stretch); reflects across y-axis if negativec = horizontal translation (shift); shift right if c is positive, left if c is negatived = vertical translation; up if d is positive, down if d is negativeHence, After f(x) = 2x translated up 5 units, then it reflect in x-axis is g(x) = f(2x) + 5.
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The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of type i error if the new blood test is used?.
The probability of type I error if the new blood test is used is 0.05
Given data;
It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested who do not have the condition received an incorrectly positive response. Take into account the null hypothesis that "the person does not have the disease."
The probability that the blood test report will be positive if someone has the disease = 0.97 The probability that the blood test report will be positive if someone does not have the disease is = 0.05
The null hypothesis is: "The individual does not have the disease."
The type I error occurs when we reject the null hypothesis, but it was true in reality.
Therefore, the probability of type I error = The probability that the blood test report will be positive if someone does not have the disease.
⇒ 0.05
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A poster is to have an area of 200 square inches with 1 inch margins on the left and right sides, and 2 inch margins on the top and bottom. Varying the dimensions of the poster changes the area of the region inside the margins. What is the maximum area inside the margins?.
Using the Optimization problem solving strategy, the maximum area inside the margins is 108 inch².
Firstly , we can develope a function of two variables. let the length of poster be x inch and width be y inch.
total Area of poster (A ) = x × y = 200 inch² ---(1)
we have provided that bottom and top margin is 2 inch each and right -left margin is 1 inch each.
So, length of poster inside margin (l) = (x-4 ) inch
width of poster inside the margin (w) = (y-2) inch
Area inside the margins = l × w sq. inch
= (x-4)(y-2) sq.inch ---(2)
from (1) we can find out the value of one variable and put in equation (2) ,
from( 1), y = 200/x
Area inside margins= (x-4)(200/x - 2) = 2(x -4)( 100/x - 1) = 2( 100 - x - 400/x + 4)
Area inside margins = 2 ( -x - 400/x + 104)
To minimize the area inside the margins we take first order derivative of it
dA/ dx = d/dx[ 2( -x - 400/x + 104) ]
= 2 d/dx ( -x - 400/x +104) = 2 ( -1 + 400/x² )
critical points occurs when dA /dx = 0
2 ( -1 + 400/x² ) = 0 => 800/x² = 2
=> x² = 400 => x = 20
putting value of x in equation (1) we get ,
x×y = 200 = 20× y => y = 10
so, length of poster is 20 inch and width is 10 inch.
Now, length of poster inside margin (l) = 16 inch
width of poster inside margin (w) = 8 inch
maximum area inside margin is 108 inch².
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Factorise pm- pm + 3qm - 3qn
Answer:
3q(m-n)
Step-by-step explanation:
pm - pm + 3qm - 3qn
= 3qm - 3qn (pm-pm cancelled out such as 2x-2x=0)
= 3q(m-n)
a manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.1 years, and standard deviation of 0.5 years. the 10% of items with the shortest lifespan will last less than how many years? give your answer to one decimal place.
The shortest lifespan will last less than 2.5 years.
What is standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
First, we must utilize the conventional normal table to determine the value for z if 10% of the region (probability) to its left will be present. We can observe that about z = -1.282.
Now, we have to find the value of x, that corresponds to the value of z.
Since,
(x - μ) / σ = z
(x - 3.1) / 0.5 = -1.282
x = 2.459
Hence, the shortest lifespan will last less than 2.5 years.
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Evaluate (-3 1/3) ^2 ( Need this by tomorrow, but that depends on time :] )
Answer:
[tex]33\frac{1}{3}[/tex]
Step-by-step explanation:
square is just multiplying things twice
(-3 1/3)(-3 1/3)
(-10/3)(-10/3)
100/3
33 1/3
Hopes this helps
Answer: 1
Step-by-step explanation:
(-3 1/3)= (-1/3)+(-1/3)+(-1/3) = -1
(-3 1/3)^2 = (-1)^2 = (-1)(-1) = 1
Jessie uses 20 liters of gasoline to travel 200 kilometers, how many liters of gasoline will he use on a trip of 700 kilometers?.
Trip of 700 km required 70 liter gasoline
For go 200 km Distance total gasoline required = 20 liter
For go 1 km Distance total gasoline required = 20÷200
= 0.1 liter
Total trip distance =700 km
Total gasoline required for going 700 km = Total distance×Gasoline required for 1 km
Total gasoline required for going 700 km = 700×0.01
= 70 liters
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70 liters of gasoline will be used on a trip of 700 kilometers.
Given that,
200 kilometer is covered by 20 liters of gasoline.
For go 1 km Distance total gasoline required = 20÷200
= 0.1 liter
Now,
Let x be the liters of gasoline required for a 700-km trip.
⇒ 20/200 = x/700
⇒ (200) (x) = (20) (700)
⇒ 200x = 14,000
⇒ 200x/200 = 14,000/200
or, x = 70
Therefore, the answer is :
70 liters of gasoline will be needed for a 700 kilometer of trip.
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what is 3/5 times 6/7
Answer:
Step-by-step explanation:
Ok:
1. Straight out Multiplication. Denominator to denominator and numerator to numerator!
3/5*6/7=
18/35=
Answer: 18/35
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A fruit seller bought oranges at rs 48 per dozen. At what price should he sell 30 oranges so as make 10%profit
Answer:
132 rs
Step-by-step explanation:
Cost of one orange = 48 : 12 = 4 rs
cost of 30 orange = 4 * 30 = 120 rs
10 : 100 = x : 120
x = (120 * 10)/100
x = 12 rs
final price = 120 + 12 = 132 rs
One moving company charges $19.85 plus $0.20 per mile to rent a van. The company also rents truck for $24.95 plus $0.17 per mile. At how many miles is the price the same for renting vehicles?
answer:19.8 should be the answer?
Step-by-step explanation:
6. Erin leaves home at 11am. She cycles at a speed of 16 miles per hour for 90 minutes. She
stops for half an hour. Erin then cycles home and arrives at 3pm.
(a) Draw a distance-time graph to show Erin's journey.
(b) What is Erin's average speed on the return part of her cycle?
The average speed of Erin on the return part is 12 miles/hour
Given, Erin leaves home at 11am. She cycles at a speed of 16 miles per hour for 90 minutes. She stops for half an hour. Erin then cycles home and arrives at 3pm.
We have to find the average speed on the return part of her cycle.
Now, using distance formula, we get
Distance = Speed × Time
Distance = 16 miles per hour × 90 × 1/60 hours
Distance = 24 miles
As, average speed = Total distance/Total time
Average speed = 24 miles / 2 hours
Average speed = 12 miles per hour
Hence, the average speed of Erin on the return part is 12 miles/hour
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the 3 conditions for sampling distributions must be met in order to calculate p-hat. group of answer choices true false
The correct answer is False because, If the sample size is large enough (n greater than or equal to 30) the sampling distribution is approximately normal regardless of the shape of the population.
The sample fraction, often called the "p-hat", is the ratio of the number of sample successes to the size of the sample. The standard deviation of (p) decreases as the sample size n increases. This is because n is included in the denominator of the standard deviation formula. That is, (p has) has fewer variables for larger samples. The P-hat (must be a lowercase p with a caret (^) circumflex) indicates the percentage of the sample (this is the x-bar, the average of the samples).
A p-hat (proportion) sampling distribution is a collection of equal-sized repeated sample proportions drawn from the same population to represent it. According to the central limit theorem, the sampling distribution of p-hat is approximately normally distributed for large sample sizes.
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ASAP! exponent rules
Answer:
C: 9
Step-by-step explanation:
3^4/3^2
3*3*3*3/3*3 cancel out 2 threes from the bottom and top.
3*3=9
What is 1/3 divided by 4/5?
Answer:
[tex]\frac{5}{12}[/tex]
Step-by-step explanation:
Step 1: Set up the problem
There are two ways to set up this problem.[tex]\frac{1}{3}[/tex] ÷ [tex]\frac{4}{5}[/tex][tex]\frac{\frac{1}{3} }{\frac{4}{5} }[/tex]Step 2: Solve
To solve the first set up you can use the keep, change, flip methodKCF: keep the first term, change from division to multiplication, flip the second term[tex]\frac{1}{3}[/tex] ÷ [tex]\frac{4}{5}[/tex][tex]\frac{1}{3}[/tex] × [tex]\frac{5}{4}[/tex] = [tex]\frac{5}{12}[/tex]To solve the second set up you multiply by the denominator's reciprocal[tex]\frac{\frac{1}{3} }{\frac{4}{5} }[/tex][tex]\frac{1}{3}[/tex] × [tex]\frac{5}{4}[/tex] = [tex]\frac{5}{12}[/tex]Which of the following are integers?
a. 9
b. 7
c. 0
d. 4
Answer: All of them are integer
Step-by-step explanation:
They are all integer.
19) If each side of
an equilateral
triangle is 4x+6 long,
what is the
perimeter of the
triangle in terms of
x?
you can refer to the explanation I wrote for you on paper since it is much easier... look at the pic uploaded
Find the perimeter of the polygon with the vertices U-2, 4), (3, 4), and IP(3,-4). Round your answer to the nearest
hundredth. y’all please help
Perimeter of the polygon with given vertices is 22.43
Given:
Point 1 : (-2,4) ,
Point 2 : (3,4),
Point 3 :(3,-4)
Perimeter of a polygon = Sum of all the sides length of polygon
1. Length of Point 1 and point 2 = √[(x₂-x₁)²+(y₂-y₁)² ]
= √[(3+2)²+(4-4)² ]
= 5
2.Length of Point 1 and point 3 = √[(x₂-x₁)²+(y₂-y₁)² ]
= √[(3+2)²+(-4-4)² ]
= 9.43
3. Length of Point 2 and point 3 =√[(x₂-x₁)²+(y₂-y₁)² ]
= √[ (3-3)²+(-4-4)² ]
= 8
So, Perimeter of the polygon = 5+9.43+8
Perimeter of the polygon = 22.43
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In one day, the bakery made 719 bagels. The bagels were divided into 9 equal shipments. A few bagels
were left over and given to the baker. How many bagels did the baker get?
Answer:
8 bagels
Step-by-step explanation:
This is a remainder division problem. We need to divide 719 by 9 and find the remainder.
First off, 9 is bigger than 7, so we need to move to the next digit. How many times does 9 go into 71? 9 times 7 is 63! That's the closest smaller number we can get, so I will write a 7 in the long division problem above the 1. I will subtract 63 from 71 to get 8.
7
9 | 719
-63
8
Now, the 9 can be brought down, making our 8 into an 89. How many times does 9 go into 89? 9 times 9 is 81! That's the closest we can get! I will write a 9 by the 7 above the 9 in 719, and write 81 below the 89. Subtracting these leaves us with a remainder of 8.
79
9 | 719
-63 ↓
89
-81
8
This means that the bagels were sent in 9 equal shipments of 79 bagels each, and the baker was left with 8 bagels!
Figure I
A
12
11
10
9
8
5432
1
-12-11-10-9-876-5-4-3-2-1
--2
3
#8543456
-6
L
-8
9
-10
-11
-12
followed by a
Figure J
1 2 3 4 5 6 7 8 9 10 11 12
Answer:
need more clarification and need better picture
Step-by-step explanation:
plsssss
The graph of the function, f(x) = x2 - 5x - 7 opens
and has a
value.
The parabola has a positive leading coefficient, which means that it opens upwards.
The graph opens up or down?We want to find the leading coefficient and see how the parabola opens.
A general quadratic equation is written as:
y = A*X^2 +b*X+ c
Where a is the leading coefficient.
If a is positive, then the parabola opens upwards, and if a is negative, the parabola opens downwards.
In this case, the equation is:
y = x^2 - 5x - 7
The leading coefficient is a = 1, it is positive, so the parabola opens upwards.
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Please help pleaseee
Measure of angle M is 76°, angle N is 76° and side LN is 18 in.
According to figure,
LM = 18 in
∠NLM = 28°
In triangle LMN
LN = LM
= 18 in
Therefore, ∠LMN = ∠LNM = x (LN = LM)
∠LMN + ∠NLM + ∠LNM = 180°
x + 28 + x = 180
2x + 28 = 180
2x = 180 - 28
2x = 152
x = 152/2
x = 76
Hence, ∠M = ∠N = 76°.
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There is a bag filled with 3 blue and 4 red
marbles.
A marble is taken at random from the bag,
the colour is noted and then it is not
replaced.
Another marble is taken at random.
What is the probability of getting at least 1
red?
The probability of getting at least 1 red marbles is 3/7.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.Probability of getting at least one red = 1 − Probability of getting red marbles
Total number of marbles = 7
Probability of getting red marbles = 4/7
Probability of getting at least one red = 1 - Probability of getting red marbles
= (7-4)/7
= 3/7
Hence, The probability of getting at least 1 red marbles is 3/7.
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vera makes a table to help her find the area of the base of a rectangular box with a volume of 672 cubic inches and a height of 16 inches.
Answer:
Step-by-step explanation:
I am not sure
A student used the equation below to create a table.
y = 2.50x
The student used 15 as one of the values for the x. Which ordered pair could be taken from the table?
O a 17.50, 15)
Ob (15, 17.50)
Oc 37.50, 15)
Od (15,37.50)
The resulting ordered pair is (15, 37.50) when the value of x as 15.
Ordered pair
Ordered pair refers a set of numbers that tells us where to find a point on a coordinate grid. In the grid, the first number represents the value on the x-axis and the second number represents the value on the y-axis.
Given,
A student used the equation below to create a table.
y = 2.50x
The student used 15 as one of the values for the x.
Here we need to find the resulting ordered pair.
Through the given question we have identified that the given function is,
y = 2.50x.
Here x represents the number of students.
Now, we have to calculate the y value for 15 number of students,
So, here we have to apply the value x as 15, then we get,
y = 2.50 (15)
Now, we have to perform the multiplication on it,
y = 37.50
Therefore, the resulting ordered pair is (15, 37.50)
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