Based on the calculations, the interest rate on the stock in four (4) years is equal to 7.1%.
Given the following data:
Amount borrowed (Principal) = $22,000.
Simple interest, I = $78.40.
Time = 4 year.
To determine the interest rate on the stock in four (4) years:
How to calculate simple interest?Mathematically, simple interest can be calculated by using this formula:
I = PRT
Where:
S.I is the simple interest.P is the principal or starting amount.R is the interest rate.T is the time measured in years.Making R the subject of formula, we have:
R = I/PT
Substituting the given parameters into the formula, we have;
R = 6260/(22,000 × 4)
R = 6260/(88,000)
Interest rate = 0.071 = 7.1%.
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At Roxas Middle School, every student studies Spanish, Chinese, or both Spanish and Chinese. There are $374$ students enrolled at the school, and $100$ of these students study both Spanish and Chinese. Also, the number of students studying Spanish is twice the number studying Chinese. How many students at Roxas Middle School study Spanish?
Based on the number of students at Roxas Middle School and the number of students studying Chinese and Spanish, the number of students who study Spanish is 182 students.
What number of students study Spanish?The first thing to do is to find out the number of students who are studying either Spanish or Chinese:
= Total number of students - Students studying both Spanish and Chinese
= 374 - 100
= 274 students
Then, assuming the number of students studying Chinese alone is x, the expression to find them would be:
274 = 2x + x
Solving gives:
2x + x = 274
3x = 274
x = 274 / 3
x = 91 students
The number studying Spanish is twice this number so will be:
= 91 x 2
= 182 students
In conclusion, there are 182 student studying Spanish.
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PLEASE HELP, TIMED
University students in an Iowa town have a mean hourly wage of $11.75, with a standard deviation of $1.25. The distribution of hourly wages is not assumed to be symmetric.
Between what two-hourly wages does Chebyshev's Theorem guarantee that we will find at least 75% of the people?
Round your answers to the nearest hundredth.
The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages between $9.25 and $14.25.
What does Chebyshev’s Theorem state?When the distribution is not normal, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages within 2 standard deviations of the mean, hence the bounds are:
11.75 - 2 x 1.25 = $9.25.11.75 + 2 x 1.25 = $14.25.More can be learned about the Chebyshev Theorem at https://brainly.com/question/25303620
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A lawn-mowing company is trying to grow its business. It had 30 clients when they started its business and wants to increase by 6 new clients each week. Use an
arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data.
Of(x)=6x +30,0 ≤ y ≤4
Of(x)=6x+24; 0 < y < 4
Of(x)=6x +30, 30 ≤ y ≤ 48
Of(x)=6x+24; 30 ≤ y ≤ 48
Answer:
Step-by-step explanation:
Option C.
Step-by-step explanation:
Initial number of clients = 18
Number of Increase per week = 4
We need to use an arithmetic sequence to write a function.
So, the required arithmetic sequence for four weeks is
18, 22, 26, 30
Here, first term is 18 and common difference is 4. The range is [18,30].
The explicit formula of n arithmetic sequence is
where, a is first term and d is common difference.
Substitute a=18 and d=4 in the above formula.
The function notation is
The function is f(x)=4x+14 and the range is 18 ≤ y ≤ 30.
Therefore, the correct option is C.
Question 3 of 10
If a circle has a diameter of 24 inches, which expression gives its area in
square inches?
OA. 12. T
OB. 242. T
O C. 122. T
OD. 24. T
SUBMIT
Answer:
OB:.242.T gives it's area in square inches
Determine a solution to system of linear inequalities graphed and justify your answer.
just for fun cuz I've heard of different answers.. what's:
6÷2(1+2) = ??
Answer:9
Step-by-step explanation:1+2=3 6/2=3
3x3=9
a wooden cube has 6 sides. The sides are labeled A, B, C, D, E, and F. What is the probability of rolling a B? Write your answer as a fraction.
Answer:
1/6
Step-by-step explanation:
You have six choices and you want to pick only 1 of those choices.
1/6
[tex]\displaystyle\frac{1}{6}[/tex]
Step-by-step explanation:Probability explains the likelihood of an event occurring. The outcome you are finding the probability for is the successful outcome. The sample size is the total number of possible outcomes.
Simple Probability
Simple probability is when there is only one single event. In this situation, the cube is only being rolled once, so it's a simple probability question. To solve this question as a fraction, the numerator should be the number of successful outcomes and the denominator should be the sample size.
Solving for P(B)
Since there are 6 sides with 6 letters, the sample size is 6. So, 6 should be the denominator. We are finding the probability of "B", which means there is 1 successful outcome. Thus, the numerator should be 1.
This means as a fraction the probability is [tex]\frac{1}{6}[/tex].
How many numbers are in the list 433, 429, 425, ... -103, -107?
Answer:
135
Step-by-step explanation:
The number is in descending order by 4.Then add the first and last number i.e.
433+107===> 540
divide 540 by 4
540/4
= 135
Answer:
134
Step-by-step explanation:
-107/4 = -26.75
429/4 = 107.25
107.25 - (-26.75)
107.25 + 26.75 = 134
832 x156 show your work
Answer:
129792
Step-by-step explanation:
156
× 832
----------
312
468
+ 1248
---------------
129792
What is the following quotient?
√120 divided by √30
02
4
O 2√10
O 3√10
Step-by-step explanation:
sqrt(120) / sqrt(30) = sqrt(120/30) = sqrt(4) = 2
The quotient of √120 divided by √30 is 2.
What is Square Root?Square root of a number is the value such that the value when multiplied to itself two times gives the original number.
It is denoted by the symbol √.
For example, square root of 16 is 4 since 4 × 4 = 16
The given numbers are √120 and √30.
We have to find the quotient when √120 is divided by √30.
Try to write each of the number as a product of perfect squares if possible.
√120 = √(4 × 30)
We know that √(ab) = √a √b
So, √120 = √4 × √30 = 2√30 (∵√4 =2)
√120 /√30 = 2√30 / √30 = 2
Hence the required quotient is 2.
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You can now sell 50 cups of lemonade per week at 39¢ per cup , but demand is dropping at a rate of 5 cups per week each week. Assuming that raising the price does not affect demand , how fast do you have to raise your price if you want to keep your weekly revenue constant.
Answer:
3.9¢ per cup per week
Step-by-step explanation:
Revenue is the product of price and quantity sold. The rate of change in any of these quantities can be found by solving the derivative equation at using the given values.
Relation of rates of changeRevenue (r) is the product of price (p) and quantity sold (q):
r = pq
Differentiating with respect to time, we have ...
r' = p'q +pq'
Given valuesThe values given for the problem are ...
r' = 0p' = rate to be foundp = 39 (cents per cup)q' = -5 (cups per week)q = 50Using the above derivative relation, we have ...
0 = p'(50) +39(-5) . . . . . . fill in given values
Solutionp' = 195/50 = 3.9 . . . . . . add 195, divide by 50
The price must be raised at the rate of 3.9 cents per week to maintain unchanging revenue.
A backyard pool has a concrete walkway around it that is 5' wide on all sides the total area of the pool and the walkway is 950' at the length of the pool is 8' longer than the width find the dimensions of the pool
The dimensions of the pool would give a quadratic equation x² + 28x - 770 = 0
How to determine the dimension
For the pool, we have that;
Let the width = x feet
Length = (x+8) feet
The pool alongside the walkway gives;
Width = x + 5 + 5 = (x + 10) feet
Length = x + 8 + 5 + 5 = (x + 18) feet
Total area of the pool with walkway = 950 square feet
Note that formula for area is given as
Area = length * width = 950
Equate the length and width
(x+18) × (x + 10) = 950
Using the FOIL method, we have;
(x × x )+ (x × 10) + (18 × x) + (18 × 10) = 950
x² + 10x + 18x + 180 -950 = 0
collect like terms
x² + 28x - 770 = 0
Thus, the dimensions of the pool would give a quadratic equation x² + 28x - 770 = 0
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on a recent trip, the smiths drove at an average speed of 55 miles per hour. if the trip took 5 1/2 hours, how many miles did they drive?
Answer:
302.5
Step-by-step explanation:
5 1/2 = 5.5
55 miles per hour * 5.5 hours
55*5.5
302.5
Composition of two functions:Basic
The functions, q(x) and r(x) are defined as 2•x + 1, and -5•x - 3, respectively, therefore;
[tex] \: (q \: \circ \: r) (1)= - 15[/tex]
[tex] \: (r \: \circ \: q) (1)= -18[/tex]
Which method can be used to evaluate the given composite functions?The given functions are;
q(x) = 2•x + 1
r(x) = -5•x - 3
The evaluation of the composite functions can be presented as follows;
[tex](q \: \circ \: r) (x)= q(r(x))[/tex]
Therefore;
[tex](q \: \circ \: r) (1)= q(r(1))[/tex]
r(1) = -5×1 - 3 = -8Which gives;
[tex](q \: \circ \: r) (1)= q( - 8)[/tex]
q(-8) = 2×(-8) + 1 = -15
Therefore;
[tex](q \: \circ \: r) (1)= - 15[/tex]
Similarly, we have;
[tex](r \: \circ \: q) (1)= r(q(1))[/tex]
q(1) = 2×1 + 1 = 3
r(3) = -5×3 - 3 = -18
Which gives;
[tex](r \: \circ \: q) (1)= -18[/tex]
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STATISTICS:
Using the research question, "Do certain musical genres impact the task performance of those high in neuroticism?" determine the:
1. Dependent and Independent Variable:
2. Moderator OR Mediator:
The dependent variable here is task performance. The independent variable in the question is musical genres.
What is a dependent variable?This is the term that is used to refer tp the variable that is of interest. It is the variable that one is trying to determine.
The independent variable is the x variable. It is the variable that helps us check the impact that it has on the dependent variable.
The task performance is what we want to know here. To do so we want to use the genre of music.
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Heyy I just need some help with question 13,17,19 if anyone could help me and show the work that would be amazing thank you!!
Answer:
13. Answer: 0
17. Answer: 3
19. Answer: 2
Step-by-step explanation:
13. f(g(3))
First find g(3) on the right graph.
We see that at x = 3, g(x) = 4
So g(3) = 4
Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer
17.f(f(5))
f(5) = 1
f(f(5)) = f(1) = 3 answer
19. g(g(2))
g(2) = 0
g(g(2)) = g(0) = 2 answer
Given two independent random samples with the following results:
n1=13
x‾1=141
s1=13
n2=9
x‾2=161
s2=12
Use this data to find the 98% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.
Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval.
Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 3 of 3: Construct the 98% confidence interval. Round your answers to the nearest whole number.
please explain
The point estimate of difference of the sample his will be -20.
How to illustrate the information?Based on the information given, the. following can be depicted:
n1 = 13
x1 = 141
s1 = 13
n2 = 9
x2 = 161
s2 = 12
The point estimate of difference will be:
= 141 - 161
= -20
The margin of error to be used in constructing the confidence interval will be calculated by multiplying the standard error which is 5.467 and the critical value. This will be:
= 5.467 × 2.528
= 13.822
The margin of error is 13.822.
The confidence interval will now be:
= (-20 + 13.822) and (-20 - 13.822)
= -6.178 and -33.822
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Can someone please help me with this ty
Answer:
92 degrees
Step-by-step explanation:
The sum of the exterior angles will be 360.
67 x 4 = 268. That means that the last angles must be 92 (360 - 268)
Explain why organization was important in your thought process and calculation for an accurate solution. You should also reflect on how correct organization of a problem can help you in everyday life. Include real-world examples to support your response.
It should be noted that organization was important in the thought process and calculation for an accurate solution.
What is problem solving?It should be noted that problem-solving enables us to identify and exploit opportunities in the environment and exert control over the future.
In this case, problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations
Also, good problem solving activities provide an entry point that allows all students to be working on the same problem.
In this case, the open-ended nature of problem solving allows high achieving students to extend the ideas involved to challenge their greater knowledge and understanding and problem solving develops mathematical power.
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g. Exactly 14 proper subsets h. Exactly 15 proper subsets How many elements does A contain if it h a. 64 subsets? b. 31 proper subsets? c. No proper subset? d. 255 proper subsets?
I don't know what you mean by g. and h., so I'll just skip that part.
I'm assuming you're asking about some arbitrary finite set [tex]A[/tex].
a. If [tex]A[/tex] has 64 subsets, then [tex]A[/tex] has [tex]\log_2(64) = \boxed{6}[/tex] elements. This is because a set of [tex]n[/tex] elements has [tex]2^n[/tex] subsets/elements in its power set.
b. A proper subset is a subset that doesn't contain all the elements of the parent set. This means we exclude the set [tex]A[/tex] from its power set. The power set itself would have 32 elements, so [tex]A[/tex] would have [tex]\log_2(32) = \boxed{5}[/tex] elements.
c. The empty set is a proper subset of any non-empty set. However, if [tex]A=\emptyset[/tex], then it has no proper subsets. So [tex]A[/tex] must be the empty set and have [tex]\boxed{0}[/tex] elements.
d. By the same reasoning as in part (b), if [tex]A[/tex] has 255 proper subsets, then it has a total of 256 subsets, and [tex]\log_2(256) = \boxed{8}[/tex].
1. How many fifties are there in one hundred thousand?
pls I need the ans as quickly as possible
The graph shows the side view of a water slide
Step-by-step explanation: Given that the graph shows the side view of a water slide with dimensions in feet.
We are to find the rate of change between the points (0, ?) and (?, 40).
From the graph, we note that
the y co-ordinate for the x co-ordinate 0 is 80 and the x co-ordinate for the y co-ordinate 40 is 5.
So, the given two points are (0, 80) and (5, 40).
The rate of change for a function f(x) between the points (a, b) and (c, d) is given by
Therefore, the rate of change for the given function between the points (0, 80) and (5, 40) is
Thus, the required rate of change is -8.
Find the total area of the shaded region.
The two curves intersect when [tex]y=0[/tex] and [tex]y=1[/tex]. Over the range [tex]0\le y\le1[/tex], the curve [tex]x=12y^2[/tex] lies above [tex]x=12y^3[/tex]. Hence the area of the shaded region is
[tex]\displaystyle \int_0^1 (12y^2 - 12y^3) \, dy = 4y^3 - 3y^4\bigg|_0^1 = (4-3)-(0-0) = \boxed{1}[/tex]
1. You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.
2.What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?
The techniques that can be used to best explain for each equation that I have created are:
What are the techniques?A) For graphing - This is often used in checking if your answer is correct, if the math is known to be a little tedious, graphing is recommended
(b) For factoring: x^2 -3x +4 '
Where: (x-4)(x+1)=0
Then x=-1, 4
(c) For square root method: x^2 = 64
Therefore x = + or - [tex]-\sqrt{64}[/tex] = + or - 8
(d) For completing the square: x^2 + 4x = 11 and x^2 +4x + 4
Note that: x^2 +4x + 4
= x^2 + 4x = -4
= x^2 +4x + 4 = -4 + 4
= (x+2)^2 = 0
So, x = -2
(e) For quadratic formula: 6x² + 7x -19 =0
x= [-b + or - sqr(b² - 4ac)]/2a
Note that b=7
a=6
c=-19
Therefore
x= [-7+ or - sqr(49+4(6)(9)]/2
2. if the discriminant is said to be negative, then the equation is one that is made up of two imaginary or complex solutions.
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See full question below
You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.
a. graphing
b. factoring
c. square root method
d. completing the square
e. quadratic formula
2. What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?
what is the midpoint of a segment with endpoints (-3, 2) and (7, -5)?
Answer:
[tex](2,-1.5)[/tex]
Step-by-step explanation:
The midpoint formula goes as follows:
[tex](x,y)=(\frac{x1+x2}{2} , \frac{y1+y2}{2})[/tex]
Lets plug in our values, let x1 be -3, x2 be 7, y1 be 2, y2 be -5.
[tex](\frac{-3+7}{2} , \frac{2+-5}{2})[/tex]
Solve numerators
[tex](\frac{4}{2} , \frac{-3}{2})[/tex]
Solve
[tex](2 , -1.5)[/tex]
Therefore the midpoint must be at [tex](2,-1.5)[/tex]
i need help with these 2
Answer:
Step-by-step explanation: Hey for the second one I got y = -3/4x -0.5 I'm not sure if its correct though sorry if not
ill try my best to explain my solution though
1. From the parallel equation (3x + 4y = 12) all we need to do is find the slope
So the easiest way to do so is to put the said equation in y-intercept form
y=mx +b
m= slope
b= y intercept
so 1. 3x + 4y = 12
=
4y = 12-3x
divide that by 4 to get only y
y=3-3/4x
-3/4 is our slope
y=-3/4x+b
than we have a point -2, -2
if we put -2 for y
-2=-3/4x+b
and then we put our -2 for x
-2 = -3/4 * -2 + b
=
-2 = -1.5 +b
b=-0.5
Answer : y=-3/4x-0.5
Una química tiene 3 soluciones acidas de varias concentraciones. La primera es 10% acida; la segunda 20% y la tercera 40%. ¿Cuántos mililitros de cada una debe ella usar para hacer 100ml de una solución al 18%, si tiene que usar cuatro veces mas de la solución al 10% que de la solución al 40%?
Based on the percentage of the first, second, and third acids, the milliliters of each acid that should be used to make 100 ml of 18% are:
10% acid = 40 ml20% acid = 50 ml40% acid = 10 mlWhat concentrations are needed to make the solution?Assuming the concentration of the 40% acid is denoted as x, the other acid concentrations would be:
10% acid = 4x
20% = 100 - 5x
The target solution is 100ml of 18%.
Solving gives:
(10% × 4x) + (20% × (100 - 5x)) + (40% × x) = 18% x 100
(80% × x) + 20 - x = 18
(80x - 100x) / 100 = 18 - 20
-20x / 100 = -2
20x = 200
x = 200 / 20
x = 10 ml
The 10% solution:
= 10 x 4
= 40 ml
20% acid:
= 100 - (5 x 10)
= 50 ml
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Any helppppppp??????
First find volume of both the cylinders:
Cylinder Volume Formula: πr²h
(r => radius, h => height)
*Container A:
r = 8
h = 15
πr²h = π(8)²(15) = 960π³
*Container B:
r = 11
h = 13
πr²h = π(11)²(13) = 1573π³
What % of container B is empty after the pumping is complete?
The water pumped from A to B, and we want to know remaining that is empty: A < B: 1573π³- 960π³ = 613π³. Now to find %:
[tex]\frac{613\pi^{3} }{1573\pi ^{3}} * 100 = 0.39 * 100 =[/tex] 39% or 40% (Nearest Tenth)
Hope it helps!
The intersection point of an angle bisectors of a triangle
Answer: The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter . The incircle touches each side of the triangle
Find the mean and standard deviation for the set of data. {25,16,28,6,30,7,26,20,22}
Answer: 8.7 the mean is 20
Step-by-step explanation: