The 20% rate the bank borrowed Oliver the loan for 3 months gives an interest of $125.
How can the simple interest be calculated?The amount Oliver borrowed = $2,500
The interest rate applied to the loan = 20%
Required: To calculate the simple interest using the formula, I = P•R•T
Where;
I = The simple interest
P = The principal borrowed = $2,500
T = The time or loan duration = 3 months = 1/4 year
R = The rate at which the loan is applied = 20% = 0.2
Therefore;
I = $2,500 × 0.2/year × 3/12 year = $125
The correct option for the interest paid on the loan is therefore;
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Answer:
125
Step-by-step explanation:
Find the distance traveled in 25 seconds by an object traveling at a velocity of v(t) = 20 + 5cos(t) feet per second
Answer:
499.338 feet
Step-by-step explanation:
You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.
DistanceThe distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...
\(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)
The distance traveled in 25 seconds is 499.33 feet.
It is required to find the distance traveled in 25 seconds.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
We have to find the distance , we will integrate v(t) from 0 to 25 second.
Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.
Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is
1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.
According to given question we have
Given a velocity function v, the distance s is figured by taking the integral. In this case,
v = 20 + 5 cos(t)
s = 20t + 5 sin(t) from 0 to 25
= s(45)-s(0)
s(0) = 0
so, the distance is
s(25) = 20*25 + 5sin(25)
= 500 -0.661
=499.33 feet.
Therefore, the distance traveled in 25 seconds is 499.33 feet.
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triangle ABC: A(2,-3), B(-4,5), C(-5,0).
dilate triangle ABC by a scale factor of 4.
PLEADR HELP
The coordinates of the vertices of the new triangle are A'(8,-12), B'(-16,20), C'(-20,0). The area of the new triangle will be 4 times the original triangle.
What is the scale factor?The scale factor is defined as the ratio of the new image's size to the old image's size. The dilation center is a fixed point in the plane. The dilation transformation is defined based on the scale factor and the center of dilation. If the scale factor is greater than one, the image will stretch.
Given that ABC is a triangle. The vertices of the triangle are A(2,-3), B(-4,5), C(-5,0).
The triangle is dilated by a scale factor of 4.
To find the coordinate of the new triangle multiply 4 with x-coordiante and y-coordiante of the vertices of the triangle ABC.
The new coordinate of A is (2×4,-3×4) → A'(8,-12).
The new coordinate of B is (-4×4,5×4) → B'(-16,20).
The new coordinate of C is (-5×4,0×4) → B'(-20,0).
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Find A − B and B − A. (Enter your answers in list form. Enter EMPTY or ∅ for the empty set.)
The main answer is that without specific values or elements for sets A and B, we cannot determine the result of A - B and B - A.
To find A - B, we need to subtract the elements in set B from set A. Similarly, to find B - A, we need to subtract the elements in set A from set B.
However, I need the specific values or elements of sets A and B to perform the calculations. Could you please provide the values or elements of the sets?In order to perform set subtraction, we need the specific elements or values of sets A and B. Set subtraction involves removing the common elements between the sets.
Let's say set A is {1, 2, 3} and set B is {2, 3, 4}. To find A - B, we remove the elements in set B from set A. Thus, A - B would be {1}.
To find B - A, we remove the elements in set A from set B. Therefore, B - A would be {4}.
Please provide the values or elements of sets A and B, and I will be able to calculate A - B and B - A accordingly.
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Write an expression to represent: 9 more than the quotient of 2 and x
Expression for given numerical is: 9+ (2/x)
Given that we have an word equation that is 9 more than the quotient of 2 and x
A quotient is a quantity produced by the division of two numbers.
Quotient of 2 and x is \(\frac{2}{x}\).
Nine(9) more than 2/x is = 9+ (2/x)
So we have an expression that is:
9+ (2/x)
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PLEASE HELP ILL GIVE THANKS, 5.0, AND BRAINLIEST TO WHOEVER ANSWERS CORRECTLY PLEASE HELP AND ILL GIVE A HIGH POINT COUNT
Sophie bikes at a
speed of s miles per hour. Her friend Rana is slower, her biking
speed 1S only r miles per hour.
Today the girls went for 20 miles trip, each girl was biking at her usual speed. How
long did Sophie wait for Rana after her own arrival to the finish?
Answer:
if Rama road 1 mph Sophie waited (20-4) = 16 hours
Step-by-step explanation:
Sophie road 5 mph for 20 miles
distance = rate of speed times time traveled
d = st
20 =5t
t = 20/5 = 4 hours
Rana road r mph for 20 mile
d=rt
20=rt
t =20/r
Sophie waited 20/r - 4 hours
20/r -4 = (20-4r)/r
if Rana road at 4 mph, Sophie waited (20-4(4))/r = 4/4 = 1 hour
If Rana road at 3 mph, Sophie waited (20-4(3))/3 = 8/3 = 2 hours 40 minutes
if Rama road at 2 mph Sophie waited (20-4(2))/2 = 12/2 = 6 hours
if Rama road 1 mph Sophie waited (20-4) = 16 hours
Complete this sentence: The shortest side of a triangle is always opposite the _____
A. second-longest side
B. longest side
C. angle with the smallest measure
D. angle with the greatest measure
By answering the above question, we may state that angle with the smallest measure, the smallest-measured angle
what are angles?An angle is a form in Euclidean geometry made composed of two rays, referred to as the angle's sides, that converge at a centre point known as the angle's vertex. In the plane where they are positioned, two rays may come together to make an angle. A planar collision produces an angle as well. Dihedral angles are what these are known as. A potential arrangement of two rays or lines that share a termination is called an angle in plane geometry. The Latin word "angulus," which means "horn," is where the English word "angle" originates. The intersection of the two rays, often referred to as the angles' sides, is known as the vertex.
angle with the smallest measure
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Find the sizes of unknow angles of this triangle
To determine to measure of the unknown angle, be sure to use the total sum of 180°. If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2.
A function of random variables used to estimate a parameter of a distribution is a/an _____.
Answer:
an unbiased estimator
Step-by-step explanation:
Find the surface area of each solid figure
Answer:
Step-by-step explanation:
Clark's Country Pet Resort is fencing a new play area for dogs. The manager has purchased 260yd of fence to enclose a rectangular pen. The area of the pen must be 3784yd^2. What are the dimensions of the pen?The length(longer side) is __ yd.The width(shorter side) is __yd.
The manager purchased 260 yd of fence for the pen, this tells us that the perimeter of the pen is 260 yd.
Step 1. Let's call the length of the pen "l" and the width of the pen "w".
Since the pen is rectangular, the formula to calculate the perimeter is:
\(2l+2w\)And since we already know the value of the perimeter, we have the following equation:
\(2l+2w=260\)Step 2. We can also find an expression for the area of the pen.
The formula for the area of a rectangle is:
\(l\times w\)And since in this case, the area of the pen is 3784 yd^2:
\(l\times w=3784\)Step 3. So far we have two equations:
\(\begin{gathered} 2l+2w=260 \\ l\times w=3784 \end{gathered}\)Step 4. The next step is to solve for l in the first equation:
\(\begin{gathered} 2l+2w=260 \\ 2l=260-2w \\ l=130-w \end{gathered}\)And substitute that into the second equation:
\(\begin{gathered} l\times w=3784 \\ (130-w)\times w=3784 \end{gathered}\)We have found an equation that only depends on w.
Step 5. Apply the distributive property on the previous equation:
\(130w-w^2=3784\)Step 6. Re-arrange the equation so that is equal to 0:
\(-w^2+130w-3784=0\)We have a quadratic equation that we will solve using the general quadratic formula.
First, we define our variables a, b and c as the coefficients of w^2, w, and the independent term:
\(\begin{gathered} a=-1 \\ b=130 \\ c=-3784 \end{gathered}\)Step 7. The general quadratic formula is:
\(w=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)Substituting a, b, and c:
\(w=\frac{-130\pm\sqrt[]{(130)^2-4(-1)(-3784)}}{2(-1)}\)And we start solving what is inside the square root:
\(w=\frac{-130\pm\sqrt[]{16900-15136}}{-2}\)Solving the subtraction:
\(\begin{gathered} w=\frac{-130\pm\sqrt[]{1764}}{-2} \\ \end{gathered}\)Solving the square root:
\(w=\frac{-130\pm42}{-2}\)And there will be two solutions for w, one using the + sign and the other using the - sign.
First, using the - sign we get:
\(w=\frac{-130-42}{-2}=\frac{-172}{-2}=86\)And the using the + sign:
\(\begin{gathered} w=\frac{-130+42}{-2} \\ w=\frac{-88}{-2} \\ w=44 \end{gathered}\)We have two answers for w, but we keep the smaller because the width is the shorter side.
\(w=44\)The width is 44 yd.
Step 7. Now we substitute this value of w into the equation from step 1:
\(\begin{gathered} 2l+2w=260 \\ 2l+2(44)=260 \\ \text{And solve for l:} \\ 2l+88=260 \\ 2l=260-88 \\ 2l=172 \\ l=\frac{172}{2} \\ l=86 \end{gathered}\)The length is 86 yd.
Answer:
length: 86 yd
width: 44yd
Select the correct answer.
Use a graphing tool to solve the equation for x.
-4x-1= 5x + 4
As per the system of linear equations concept, the solution of x is -1.282
Linear equations:
Linear equation is referred as the algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.
Given,
Here we have the equations -4x - 1 = 5ˣ + 4
Now, we need to find the value of x by using the graph.
In order to plot the graph for the given linear equation,
First, we have to split the equation into two,
Like the following:
y = -4x - 1
y = 5ˣ + 4
Now, we plot the graph of both equations
Then we get the graph like the following.
Where the red line represents the equation y = -4x - 1 and the green line represents the equation y = 5ˣ + 4.
While we looking into the graph, we have identified the solution is,
x = -1.282
Therefore, the solution of x is -1.282
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Enter the equation of a circle that is congruent to circle C and is centered at point P
The equation of a circle that is congruent to circle C and is centered at point P is (x - 5)² + (y - 1)² = 5².
What is the equation of a circle?In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.Based on the information provided, we have the following parameters for the equation of this circle:
Center (h, k) of P = (1, 5)Radius (r) of P = 5 units.By substituting the given parameters, we have:
(x - h)² + (y - k)² = r²
(x - 5)² + (y - 1)² = 5²
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Larry read a 400-page book. He read at a rate of 10 pages per day for d days.
Answer:
It took him 40 days to complete the book.
Step-by-step explanation:
Divide 400 by 10 and you should get 40 as an answer.
Answer:
d=400/10
Hope this helps
Exponential Data
In this activity, you will graph and write exponential functions to model population data presented in tables. Then you’ll use your models to make predictions and draw a conclusion.
Question 1
A town’s population has been exponentially increasing for the past 10 years. The town council initially recorded the town’s population at 6,000 people and tracked it each year after that. The table represents their data.
Years Town Population
(in thousands)
0 6
1 6.9
2 9
3 10.5
4 13
5 14.2
6 18
7 20.8
8 26
9 31.3
Use the graphing tool to plot the population data and determine the curve of best fit.
Part A
Question
What is the equation of the curve of best fit for the population data?
Enter the correct answer in the box by replacing a and b with the values from the graphing tool. Do not round the values of a and b.
Part B
Question
If the town continues to grow at the same rate, approximately what will be the population, to the nearest 100 people, 25 years after the town council started tracking the population data?
341,100 people
180,000 people
271,200 people
572,400 people
Question 2
Because of the growth in the town’s population, the agricultural department kept track of the town’s native bee population during the same time period. They feared with the increase of people in the town, the bee population would start to decrease, affecting the ecosystem. Their data is shown in the table.
Years Bee Population
(in thousands)
0 320
1 225
2 152.6
3 111.2
4 75
5 56.8
6 36.7
7 26.9
8 17.5
9 13.2
Use the graphing tool to plot the population data and determine the curve of best fit.
Part A
Question
What is the equation of the curve of best fit for the population data?
Enter the correct answer in the box by replacing a and b with the values from the graphing tool. Do not round the values of a and b.
Part B
After several years of recording the data, the agricultural committee requested help from the town council for a grant to boost the bee population. The council denied the request, saying it wouldn’t take any action until the population dropped below 5,000 bees.
In the 12th year after initially recording the bee population, the agricultural committee plans to speak with the board again. Will the committee have a good chance of convincing the board to help support bees this time around? Justify your conclusion using mathematical reasoning.
Answer:
1.The equation of best fit is ŷ = 2.69152X + 3.45818.
Step-by-step explanation:
hi my name is Shila and I'm trying to explain how to solve this problem to my daughter but a but confused can you direct me please?
As given by the question
There are given that the point
\(\frac{8}{6}\)Now,
First, break the point
So,
\(\frac{8}{6}=\frac{4}{3}\)According to the above point, there are showing 3 in the denominator
So, between 0 and 1 divide 3 parts in the number line
Then,
Please help!
Triangle ABC has angle measures as shown. Show work. Complete sentence.
(a) What is the value of x?
(b) What is the measure of angle CBA?
(c) What is the measure of angle CAB?
(d) When these 3 interior angles of a triangle are added together, what does it equal?
9514 1404 393
Answer:
(a) x = 22
(b) 46°
(c) 44°
(d) 180°
Step-by-step explanation:
Because the sum of the interior angles of a triangle is 180°, we know that the sum of the acute angles in a right triangle is 90°.
(a)The sum of the marked acute angles is 90°.
2x +(3x -20) = 90
5x = 110 . . . . . . . . . . add 20, collect terms
x = 22 . . . . . . . . . divide by 5
__
(b)∠CBA = (3x -20)° = (3·22 -20)° = 46°
__
(c)∠CAB = 2x° = 2(22)° = 44°
__
(d)The sum of a triangle's interior angles is 180°.
Factor the polynomial.
2x²10x + 12 =
Answer: 2(x+3)(x+2)
Step-by-step explanation:
Two trains leave towns 566 kilometers apart at the same time and travel toward each other. One train travels 11 km/h slower than the other. If they meet in 2 hours, what is the rate of each train?
Answer:
The speeds are 74 mph and 87 mph.
Step-by-step explanation:
Let x = speed of slower train
x + 13 = speed of faster train
The trains meet when the sum of the distances = 483
3x + 3(x+13) = 483
6x + 39 = 483
6x = 444
x = 74 mph
The speeds are 74 mph and 87 mph.
On October 12, 2020, the number of new cases of Covid 19 in Milwaukee was 235. On Oct. 22, 2020, the number of new cases in Milwaukee was 395.
a. Create an exponential model for new cases in terms of days.
b. Based on your model, what would be the number of new cases on Oct. 31, 2020?
c. The actual number of new cases on Oct. 31, 2020, was 1043. How well does this fit your model?
a. To create an exponential model for new cases in terms of days, we can use the formula: y = a * b ^ x, where y is the number of new cases, x is the number of days since the first observation, and a and b are constants that we need to determine. Using the two data points given, we can set up a system of equations:
235 = a * b ^ 0
395 = a * b ^ 10
Solving for a and b, we get:
a = 235
b = (395/235)^(1/10) = 1.067
Therefore, the exponential model for new cases in Milwaukee is:
y = 235 * 1.067 ^ x
b. To find the number of new cases on Oct. 31, 2020, we need to plug in x = 19 (since Oct. 31 is 19 days after Oct. 12) into the model:
y = 235 * 1.067 ^ 19 = 1018.5
Therefore, based on the exponential model, we would expect around 1019 new cases on Oct. 31, 2020.
c. The actual number of new cases on Oct. 31, 2020, was 1043. This is higher than the predicted value of 1019, but not by a huge margin. Overall, the model seems to fit the data reasonably well, especially considering that there are many factors that can affect the number of new cases in a given area, and that the model is based on only two data points. However, it is worth noting that the exponential model assumes that the growth rate of new cases remains constant over time, which may not be a realistic assumption in the long run.
Funke, Adamu, Shehu, Kwame and Tanko play a game of cards. Funke says to Adamu, "If you give me 5 cards, you will have as many as Tanko has and if I give you 4 cards, you will have as many as Kwame has."Funke and Adamu together have 13 cards more than what Kwame and Tanko together have. If Adamu has 2 cards more than what Shehu has and the total number of cards be 133, how many cards does Adamu have?
This involves basic arithmetic calculations and simultaneous equations.
Adamu has 25 Cards
Let the following letters represent the number of cards each has;
A: ADAMU
F: FUNKE
S: SHEHU
K: KWAME
T: TANKO
If adamu gives funke 5 cards, he will have as many as tanko. Thus;A - 5 = T --- eq 1
If funke gives adamu 4 cards, he will have as many as kwame. Thus;A + 4 = K --- eq 2
Funke and adamu have a total of 13 more cards than the total that kwame and tanko have. Thus;A + F = K + T + 13 --- eq 3
Adamu has 2 cards more than what Shehu has. Thus;A - 2 = S --- eq 4
From online research, the Total Number of cards is 134 and not 133. Thus;
A + F + K + S + T = 134 --- eq 5
Let's put A - 5 = T and A + 4 = K in eq 3 to get;
A + F = (A + 4) + (A - 5) + 13
A + F = 2A + 12
F = 2A - A + 12
F = A + 12
Let's put A - 2 = S ; F = A + 12 ; A - 5 = T and A + 4 = K into eq 5 to get;
A + A + 12 + A + 4 + A - 2 + A - 5 = 134
Simplifying gives;
5A + 9 = 134
5A = 134 - 9
5A = 125
A = 125/5
A = 25
Adamu has 25 Cards
Find the minimum or maximum value of f(x)= -.25x^2+4x-18
Answer:
=0.5+4
Step-by-step explanation:
hopefully im right:) have a nice day!
15. Jonas played 9 holes of golf
and received the following
scores. Positive scores indi-
cate that Jonas was above
par. Negative scores indicate
that he was below par. Find
Jonas's total after 9 holes. Is
his score above or below par?
+2, +1,-1, 0, 0, -1, +3,
+4, -1
Answer:
Step-by-step explanation:
To find Jonas's total score after 9 holes of golf, we add up all the individual scores:
+2 + 1 - 1 + 0 + 0 - 1 + 3 + 4 - 1 = 7
Jonas's total score after 9 holes is 7.
Since the total score is positive (above zero), Jonas's score is above par.
What is the length of BD?
Answer:
D stays for 1 and as B is -6
the length of BD should be 7
good luck <3!
please can anyone help
51x51
pleasee
Answer:
51 x 51 = 2601
Step-by-step explanation:
Answer:
2601
Step-by-step explanation:
hope it helps
A sample of bacteria is growing at a continuously compounding rate. The sample triples in 10 days.
Find the formula for the daily rate. Type your answer as a fraction.
Answer:
r=ln3/10
Step-by-step explanation:
The daily rate is given by 3 to the power x divided by 10.
We have given that a sample of bacteria is growing at a continuously compounding rate.
The sample triples in 10 days.
What is the formula for the daily rate?The daily rate of the bacteria growth is. exponential growth is in the form
y = abˣ
where y, x are variables.
a is the initial value
Sample triples, in 10 days. therefore the value of b=3.
Therefore we get,
\(y=3a^{\frac{x}{10}\)
\(y=a3^{\frac{x}{10}\)
Therefore the daily rate is given by \(3^{\frac{x}{10}\).
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Explain your answer to the question in the picture with steps please, thank you.
Part (a)
Answer: Constant of proportionality = 5/8
Reason:
The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.
The direct proportion line must pass through the origin. In other words, the y intercept must be zero.
=====================================
Part (b)
Answer: Not Proportional
Reason:
The y intercept isn't zero.
Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.
A number increased by sixteen is equal to thirty-seven
Answer:
21
Step-by-step explanation:
It would have to be twenty one because thirty seven minus sixteen is twenty one it's simple math-
What is the equation for the line in slope intercept form
Answer:
The equation is y = -4x + 5Step-by-step explanation:
Looking at the graph, we can say that the y-intercept is 5. All we need to do now is to find the slope. I took two points (0, 5) and (3, -7)
We know that:
Slope formula = Rise/RunFormula = y = mx + b (m = slope; b = y-intercept)Work
=> -12/3=> Slope = -4Since the slope is -4, the value of 'm' must be -4.
Our equation = y = -4x + 5Hence, the equation is y = -4x + 5
Hoped this helped.
\(BrainiacUser1357\)
*
Between 10 A.M. and 11 A.M., 48 people came into Brad's store.40 of them
made a purchase. What is the number of favorable outcomes of people
who made a purchase?
Answer: The answer is 40 there are 40 favorable outcomes of people who made a purchase.
Step-by-step explanation:
PLEASE ANYONE definition of a percent increase?
Answer:
In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared. The comparison is expressed as a ratio and is a unitless number.
Step-by-step explanation:
I hope it helps