Answer :48 km.
Explanation:
Let the speed of Belinda be x km/h. Then, the speed of Alice is (x + 2) km/h.
When they meet in 3 hours, the distance between the towns is given by:
Distance = speed * time Distance = (x + 2) * 3 + x * 3 Distance = 6x + 6
When they meet in 4 hours, with Belinda's speed reduced by 1 km/h and Alice's speed two-thirds of her previous speed, the distance between the towns is given by:
Distance = speed * time Distance = (x - 1) * 4 + (2/3)(x + 2) * 4 Distance = 4x - 4 + (8/3)x + (16/3) Distance = (20/3)x + (4/3)
Since the distance between the two towns is the same in both cases, we can set the two expressions for distance equal to each other:
6x + 6 = (20/3)x + (4/3)
Multiplying both sides by 3, we get:
18x + 18 = 20x + 4
Solving for x, we get:
x = 7
Therefore, the speed of Belinda is 7 km/h, and the speed of Alice is 9 km/h.
To find the distance between the two towns, we can use either of the expressions for distance we obtained earlier:
Distance = 6x + 6 = 6(7) + 6 = 48
Therefore, the distance between the two towns is 48 km.
PLEASE HELP THIS IS DUE TODAY
In conclusion the value that correctly fills in the blank in the table is 0.69.
Why it is?
To find the relative frequency of boys, we need to use the information given in the frequency table. We know that the total number of boys is 120 - 37 = 83, since the total number of students is 120 and the number of girls is 37.
We can then calculate the relative frequency for boys by dividing the number of boys who prefer math or social studies (40 + 43 = 83) by the total number of students (120):
Relative frequency for boys = (40 + 43) / 120 ≈ 0.69
Rounding to the nearest hundredth, we get:
Relative frequency for boys ≈ 0.69
Therefore, the value that correctly fills in the blank in the table is 0.69.
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In March 2011, a California newspaper predicted that the price of gasoline in two years would be $4.10. The newspaper claimed that the prediction would be within 2% of the actual price of gasoline in March 2013. Given the data in the table, determine the percent error of the prediction. Was the newspapers claim correct or incorrect. Provide work or an explanation to justify your answer.
The newspaper's claim was incorrect, as the percent error of the prediction was 0.76%, which is greater than 2%.
What is percent error?It is the difference between the observed value and the true value, expressed as in percentage. It is used to quantify how accurately a given measurement, prediction or other value matches the true value.
The percent error of the prediction can be calculated using the following formula:
[(Predicted Price - Actual Price) / Actual Price] × 100.
For this problem, the percent error
= [(4.10 - 4.069) / 4.069] × 100
= 0.76%.
Therefore, the newspaper's claim was incorrect since the percent error did not fall within the specified 2%.
In this case, the newspaper's prediction of the price of gasoline in two years did not match the true value as closely as expected, since the percent error was 0.76%.
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45 points, need answers ASAP!!! Match each definition with the correct vocabulary word. The variable whose values result from counting or measuring something. The variable (often x) that does not depend on that of another. The variable (often y) whose value depends on that of another. The variable that has two or more groups, but there is no intrinsic ordering to the groups.
Answer:
Step-by-step explanation:
The matches are:
The variable whose values result from counting or measuring something: quantitative variableThe variable (often x) that does not depend on that of another: independent variableThe variable (often y) whose value depends on that of another: dependent variableThe variable that has two or more groups, but there is no intrinsic ordering to the groups: nominal variableYou have a 1
-gallon paint can in the shape of a cylinder. One gallon is 231
cubic inches. The radius of the can is 3
inches. What is the approximate height of the paint can? Use 3.14
for pi.
Answer:
Step-by-step explanation:
A bond is worth $100 and grows in value by 4 percent each year. Explain why the value of the bond after t years is given by 100•1.04^t
The value of the bond is multiplied by the factor [tex](1 + 0.04)[/tex], which is the same as multiplying by 1.04. After t years, the value of the bond will be multiplied by this factor t times, giving the formula:
[tex]100(1.04)t[/tex].
So, the value of the bond after t years is given by 100 • 1.04t.
What is a factor?A factor in mathematics is an expression or number that divides another expression or number without producing a residue. In other terms, a factor is a unit of measurement that may be multiplied by another unit of measurement to yield a specific outcome.
For example, 2 and 3 are factors of 6, because 2 multiplied by 3 equals 6. Similarly, (x + 1) and (x - 3) are factors of the expression [tex]x^2 - 2x - 3[/tex], because when these factors are multiplied together, they produce the expression:
[tex](x + 1) \times (x - 3) = x^2 - 2x - 3[/tex]
The bond is worth $100 initially, and it grows in value by 4% each year. This means that after one year, the value of the bond will be:
[tex]100 + 0.04(100) = 100(1 + 0.04) = 100(1.04)[/tex]
In other words, the value of the bond after one year is the initial value (100) multiplied by a factor of 1.04.
Similarly, after two years, the value of the bond will be:
[tex]100(1.04) + 0.04(100)(1.04) = 100(1.04)^2[/tex]
After three years, the value of the bond will be:
[tex]100(1.04)^2 + 0.04(100)(1.04)^2 = 100(1.04)^3[/tex]
In general, after t years, the value of the bond will be:
[tex]100(1.04)t[/tex]
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Riley is dividing a batch of 7 1/2 cups of salsa into equal servings that are 3/4 cup each. Select all of the expressions that can be used to find the number of servings Riley will have.
Thus, from the all given expressions, the number of servings Riley will ve using is 15/2 ÷ 3/4.
Explain about the mixed fraction?Once kids have a firm grasp on proper fractions, they are introduced to mixed numbers and incorrect fractions. A mixed number combines an integer (whole number) and a fraction. It is also sometimes referred to as a mixed fraction (part of a whole number).
The composite number's fractional component needs to be a legal fraction (less than one whole). The numerator (top number) of a correct fraction is less than its denominator (bottom number),
Given data:
Total batch of cup of salsa = 7 1/2Serving cup size = 3/4 each cupConvert the mixed fraction 7 1/2 in the proper fraction:
= 7 1/2
= (7*2 + 1)/2
= 15/2
Number of serving cups = Total amount of salsa / Serving cup size
Number of serving cups = 15/2 ÷ 3/4
Thus, from the all given expressions, the number of servings Riley will ve using is 15/2 ÷ 3/4.
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Complete question:
Riley is dividing a batch of 7 1/2 cups of salsa into equal servings that are 3/4 cup each. Select all of the expressions that can be used to find the number of servings Riley will have.
2/15 ÷ 3/415/2 ÷ 3/42/15 ÷ 4/515/2 ÷ 4/315/2 ÷ 3/4Jayden has 8 5/6 cups of rice. He uses 3 1/4 cups to make dinner. How many cups of rice does Jayden have left
Answer: 5 [tex]\frac{7}{12}[/tex] cups
Step-by-step explanation:
Subtract whole number values:
8 - 3 = 5 cups
Subtract fractions:
* Get common denominators
5/6 ➜ 10/12
1/4 ➜ 3/12
* Subtract
10/12 - 3/12 = 7/12
Answer:
5 7/12 cups
Answer:
67/12 cups of rice
Step-by-step explanation:
We Know
Jayden has 8 5/6 cups of rice.
8 5/6 = 53/6
He uses 3 1/4 cups to make dinner.
3 1/4 = 13/4
How many cups of rice does Jayden have left?
We Take
53/6 - 13/4 = 212/24 - 78/24 = 134/24 = 67/12
So, Jayden has 67/12 cups of rice left.
Find the exact value of b
help pls show ur work
The polygons are similar, therefore the missing lengths are: 12) 4; 13) 24
13. The triangles are similar by the SAS similarity theorem; 14. They are not.
How to Find the Sides of Similar Triangles?Recall that every pair of corresponding sides of similar triangles are always proportional to each other.
11. Let the missing side be x.
x/24 = 6/36
x/24 = 1/6
Cross multiply
6x = 24
x = 24/6
x = 4
12. x/20 = 36/30
x/20 = 6/5
Cross multiply:
5x = 120
x = 120/5
x = 24
13. m<VWU ≅ m<SWR based on vertical angles theorem [one pair of congruent included angles]
WV/WS = 40/5 = 8
WU/WR = 40/5 = 8 [two pair of proportional sides]
Therefore, both triangles are similar by the SAS similarity theorem.
14. The triangles are not similar because:
56/24 ≠ 28/13
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Use the Distributive Property to write an equivalent expression for -5(4+7y)
= -5( + )
Answer:
y = -3/7
Step-by-step explanation:
In a recent year and author wrote 191 check, use the poisson distribution to find the probability that on a random select today he wrote at least one check
The probability that on a random select today he wrote at least one check is 0.407
How to solveLet X be the no.of checks the author wrote in a day
Average,
u = 191 checks per year
191/365
= 0.5233/ day
X~Poisson ( u- 0.5233)
The p.m.f of X is given by
P(X=x) =
The probability that, on a randomly selected day, he wrote at least one check = P(
= 1 - P( X < 1)
= 1 - P(X=0)
= 1 - e^-0.5233 x 0.5233^0/0!
= 1 - e^-0.5233 x 1/
= 1 - 0.59256
= 0.407
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I need help with this please
Finding the total volume of a composite figure requires breaking it down into simpler shapes and then adding up their volumes.
How to find the volume of a composite figure>To find the total volume of a composite figure, you'll need to break it down into simpler shapes and calculate their individual volumes.
Then, you can add up these volumes to get the total volume of the composite figure.
Here are the general steps you can follow:
Identify the simpler shapes: Look for the individual shapes that make up the composite figure, such as cubes, rectangular prisms, pyramids, cylinders, or spheres.
Calculate the volume of each shape: Use the appropriate formula for each shape to find its volume. For example, the volume of a cube is calculated by multiplying the length, width, and height of the cube.
Add up the volumes of all the simpler shapes: Once you have found the volume of each simpler shape, add them up to get the total volume of the composite figure.
Adjust for overlapping shapes: If there are any overlapping shapes, subtract the volume of the overlapped portion to avoid double-counting.
Check your work: Double-check your calculations and make sure your final answer makes sense based on the dimensions of the composite figure.
Overall, finding the total volume of a composite figure requires breaking it down into simpler shapes and then adding up their volumes.
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The acceleration, in feet per second per second, of an object is given by the acceleration function a(t)=2sint+1. The initial velocity is v(0)=0 and the initial position is s(0)=3. Find the equation of the velocity function. Find the position function and the average value of the position function from time t = 2 seconds to t = 5 seconds. Show all your work.
Help pls
Using the derivative of the velocity, the average value of the position function from t = 2 seconds to t = 5 seconds is 14.5.
What is the position and average value of the position function from t = 2 to t = 5?Given:
Acceleration function, a(t) = 2sin(t) + 1
Initial velocity, v(0) = 0
Initial position, s(0) = 3
To find:
Velocity function, v(t)
Position function, s(t)
Average value of the position function from t = 2 seconds to t = 5 seconds
Solution:
We know that acceleration is the derivative of velocity, and velocity is the derivative of position. So we can find the velocity and position functions by integrating the acceleration function.
Velocity function:
[tex]v(t) = \int a(t) dt\\v(t) = \int (2sin(t) + 1) dt\\v(t) = -2cos(t) + t + C1[/tex]
We know that the initial velocity, v(0) = 0. Substituting this value in the above equation, we get:
[tex]0 = -2cos(0) + 0 + C1\\C1 = 2[/tex]
Therefore, the velocity function is:
[tex]v(t) = -2cos(t) + t + 2[/tex]
Position function:
[tex]s(t) = \int v(t) dt\\s(t) = \int (-2cos(t) + t + 2) dt\\s(t) = 2sin(t) + \frac{1}{2} t^2 + 2t + C2[/tex]
We know that the initial position, s(0) = 3. Substituting this value in the above equation, we get:
[tex]3 = 2sin(0) + 0 + 0 + C2\\C2 = 3\\[/tex]
Therefore, the position function is:
[tex]s(t) = 2sin(t) + \frac{1}{2} t^2 + 2t + 3[/tex]
Average value of the position function from t = 2 seconds to t = 5 seconds:
We can find the average value of the position function using the following formula:
[tex]Avg = (1/(b-a)) * \int(a,b) f(t) dt[/tex]
Here, a = 2 and b = 5. So, substituting the values in the above formula, we get:
[tex]Avg = (1/(5-2)) * \int(2,5) (2sin(t) + \frac{1}{2} t^2 + 2t + 3) dt\\Avg = \frac{1}{3} * [ -2cos(t) + 1/6 t^3 + t^2 + 2t ] \eval(2,5)\\[/tex]
[tex]Avg = \frac{1}{3} * [ (-2cos(5) + 1/6 (5^3) + 5^2 + 25) - (-2cos(2) + 1/6 (2^3) + 2^2 + 22) ]\\Avg = 14.5[/tex]
Therefore, the average value of the position function from t = 2 seconds to t = 5 seconds is 14.5.
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Find the arithmetic mean of 4 and 18
Answer:
The arithmetic mean of two numbers is found by adding them together and dividing the sum by 2.
So, the arithmetic mean of 4 and 18 is:
(4 + 18) / 2 = 22 / 2 = 11
Therefore, the arithmetic mean of 4 and 18 is 11.
Step-by-step explanation:
Answer:
STEP 1:let the arithmetic mean be p, q, r hence 4,p, q, r, 18
STEP 2:U5=18=a+4d
a+4d=18
we're a=4 therefore
4+4d=18
STEP 3:4d/4=(18-4)÷4=14/4
d=14/4=3.5
p=U2=a+d=4+3.5=7.5
q=U3=a+2d=4+(2×7.5)
=
Which of these would you expect to have a positive correlation? Check all that apply. HINT: There are two correct selections. Question 1 options: The number of TV shows you watch and the age of your car The shoe size of that adult and the salary they earn The value of a car and the age of the car The pages of a book you read and the time you spend reading that book A person's years of experience at a job and their salary A person's grade on a test and the number of missed homework assignments leading up to that test
A train moves southward at 400 km/hr. How long will it take to make a 1,200 km trip?
Answer:
3 hours
Step-by-step explanation:
1200/400=3
simplify 300/25 fraction with steps
Following the basic principles and theory of simplifying fraction it is visible that this question follows the, the basic calculations involving the basic mathematics
Therefore the , let us take the given numerator that is 300 and then divide it using the denominator that is 25 ,
so, when we divide 300 /25 we get, the answer as12
because, when we divide both the numerator and denominator with 5 (because 25 and 300 are a divisible by 5 and are also multiples of )
we clearly see that 300 is divisible by 5 and the answer comes out to be 12.
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Please help to solve b
a. The probability that a randomly selected American who moved in 2004 was an owner is 0.31. b. 0.38 c. 0.03 .
Describe probability ?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a fair coin and getting heads is 0.5, because there are two equally likely outcomes (heads or tails).
a. Probability that a randomly selected American who moved in 2004 was an owner:
Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million
Number of Americans who moved in 2004 and were owners = 11.7 million
Therefore, the probability that a randomly selected American who moved in 2004 was an owner is:
11.7 million / 38 million = 0.31 (rounded to the nearest hundredth)
b. Probability that a randomly selected American who moved in 2004 moved within the same state:
Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million
Number of Americans who moved in 2004 and moved within the same state = 11.7 million + 2.8 million
Therefore, the probability that a randomly selected American who moved in 2004 moved within the same state is:
(11.7 million + 2.8 million) / 38 million = 0.38 (rounded to the nearest hundredth)
c. Probability that a randomly selected American who moved in 2004 was a renter who moved to a different country:
Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million
Number of Americans who moved in 2004 and were renters who moved to a different country = 1.0 million
Therefore, the probability that a randomly selected American who moved in 2004 was a renter who moved to a different country is:
1.0 million / 38 million = 0.03 (rounded to the nearest hundredth)
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The attendance at Longwood middle school his first football game of the season is 437 people eat it at the second game is 4 to 76 people determine the approximate percent increase in attendance between the first and second game round your answer to the nearest 10th%
Approximate percent increase in attendance between the first and second game is 8.9%.
What is the approx. percentage increase in attendance between the first and second football games?
To calculate the percent increase in attendance between the first and second game, we can use the formula:
percent increase =
[(new value - old value) / old value] x 100%
where the old value is the attendance at the first game and the new value is the attendance at the second game.
Substituting the given values, we get:
percent increase = [(476 - 437) / 437] x 100%
percent increase = (39 / 437) x 100%
percent increase ≈ 8.92%
Rounding to the nearest tenth percent, we get the approximate percent increase in attendance between the first and second game as 8.9%.
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does anyone know how to find the particular solution for this nonhomogeneous equation:
y"+3y'-3y=3xe^-1
Using the equations, the particular solution is y_p(x)=-3x+1+2e⁻ˣ.
What are non-homogeneous differential equations?As we already know, homogeneous equations have zero on the right side of the equation. Thus, it is said that non-homogenous differential equations are those with a function on the right side of their equation.
We are given a non-homogeneous differential equation in the form:
y′′+3y′-3y=3xe^-1
The differential equation is called non-homogeneous because it is known to have a non-zero right-hand side.
To solve this differential equation, we first need to find the complementary function, which is the solution to the corresponding homogeneous differential equation y′′+3y′-3y=0.
We then take the first and second derivatives of y_p(x) and substitute them into the differential equation, y′′+3y′-3y=3xe^-1 and simplify.
This leads to the system of equations:
a + 3c = 3
a + 3b - 3c = 0
a + b + 3c = 1
Solving this system of equations, we find that a=-3, b=1, and c=2. Therefore, the particular solution is y_p(x)=-3x+1+2e⁻ˣ.
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This set of equations can be solved, and the results show that a=-3, b=1, and c=2. As a result, the specific answer is [tex]y_{p(x)} =-3x+1+2e^{-x}[/tex].
What are non-homogeneous differential equations?Homogeneous equations, as we already know, have "0" on the right side of the equation. Therefore, it is said that differential equations with a function on the right side of the equation are non-homogenous differential equations.
A non-homogeneous differential equation of the following shape is provided to us:
[tex]y^{''} +3y^{'} -3y=3xe^{-1}[/tex]
Since the right-hand side of the differential equation is known to be non-zero, it is referred to as non-homogeneous.
Finding the complementary function, which is the answer to the related homogeneous differential equation [tex]y^{''} +3y^{'} -3y=0[/tex], is the first step in solving this differential equation.
The differential equation [tex]y^{''} +3y^{'} -3y=3xe^{-1}[/tex] is then simplified by taking the first and second derivatives of [tex]y_{p(x)}[/tex] and substituting them into
the equation.
This results in the formulae system:
a + 3c = 3
a + 3b - 3c = 0
a + b + 3c = 1
This set of equations can be solved, and the results show that a=-3, b=1, and c=2. As a result, the specific answer is [tex]y_{p(x)} =-3x+1+2e^{-x}[/tex].
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find the sum of money that amounts to Rs- 3450 in 4 monts at the rate of 4½ %. per annam.
Answer:
To find the sum of money that amounts to Rs- 3450 in 4 months at the rate of 4.5% per annum, we can use the formula for simple interest:
Simple Interest = (Principal * Rate * Time) / 100
Where,
Principal = the sum of money borrowed or invested
Rate = the rate of interest per annum
Time = the time period in years
Since the time period given is 4 months, we need to convert it to years by dividing it by 12:
Time = 4/12 years = 1/3 years
Now, we can plug in the given values and solve for Principal:
Simple Interest = (Principal * Rate * Time) / 100
3450 = (Principal * 4.5 * 1/3) / 100
3450 * 100 = Principal * 4.5 * 1/3
11500 = Principal * 1.5
Principal = 11500 / 1.5
Principal = 7666.67 (rounded off to two decimal places)
Therefore, the sum of money that amounts to Rs- 3450 in 4 months at the rate of 4.5% per annum is Rs- 7666.67.
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Is 2 x5/8 the same of 10 x1/8
Answer:
Step-by-step explanation:
[tex]2\times \frac{5}{8} = \frac{2}{1} \times\frac{5}{8}= \frac{10}{8}[/tex]
[tex]10\times \frac{1}{8} =\frac{10}{1} \times \frac{1}{8}= \frac{10}{8}[/tex]
So yes they are the same.
Daisy and Oscar make £90 at a car boot sale. The split the money in the ratio 5:4. How much money did each of them make?
Answer:
Daisy made 50 and Oscar made 40.
Step-by-step explanation:
Daisy: Oscar: total
5 4 5+4 = 9
Taking the total made and dividing by 9.
90/9 = 10
Multiply each term in the ratio by 10.
Daisy: Oscar: total
5*10 4*10 9*10
50 40 90
Daisy made 50 and Oscar made 40.
Mary takes a sightseeing tour on a helicopter that can fly 378 miles against a 35 mph headwind in the same amount of time it can travel 630 miles with a 35 mph tailwind. Find the speed, in miles per hour, of the helicopter.
Answer:
The speed of the helicopter is 160mph.
Step-by-step explanation:
The speed of the helicopter is 160mph.
Speed
Speed =Distance/Time
450miles/s-35mph = 702miles/s+35
450×s+35 = 702×s-35
450s+15,750 = 702s-24,570
Collect like terms
702s-450s = 15,750 + 24,570
252s= 40,320
Divide both side by 252s
s= 40,320/252
s= 160mph
Inconclusion the speed of the helicopter is 160mph.
which of the statements is true for the two division problems below? A: (x^2-3x-18)÷(x-6) or B: (x^3-x^2-5x-3)÷(x^2+2x+1)
A equals (x+3) and b equals (x-3)
A and b both equal (x+3)
a and b both equal (x-3)
a equals (x-3) and b equals (x+3)
A equals (x+3) and b equals (x-3) the statement that is true for the two division problems is that a equals factor (x+3) and b equals (x-3).
For the first division problem, [tex](x^2-3x-18)[/tex]÷(x-6), the quotient is (x+3). To solve for the quotient, you first need to factor the numerator, which is (x-6)(x+3). Then, you need to divide the numerator by the denominator, which is (x-6). The quotient is (x+3). For the second division problem, [tex](x^3-x^2-5x-3)/(x^2+2x+1)[/tex], the quotient is (x-3). To solve for the quotient, you first need to factor the numerator, which is (x+1)(x-3). Then, you need to divide the numerator by the denominator, which is [tex](x^2+2x+1)[/tex]. The quotient is (x-3). Therefore, the statement that is true for the two division problems is that a equals (x+3) and b equals (x-3).
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Find the composition of transformations that
map ABCD to EHGF.
Reflect over the [? ]-axis, then translate
(x+[],y+[]).
Note: Enter x or y for axis.
4
7.
B C
o
Y
D
-1
3
2
0
2
3
H
4
Help
the composition of transformations that map ABCD to EHGF is a reflection over the y-axis followed by a translation by (4,7).
What is axis reflection ?
An axis reflection is a transformation in geometry that involves reflecting a point, a line, or an object across a given axis. In two dimensions, there are two axes of reflection: the x-axis and the y-axis.
When reflecting over the x-axis, all points stay in the same horizontal position but change their vertical position, so a point (x,y) is reflected to (x,-y).
When reflecting over the y-axis, all points stay in the same vertical position but change their horizontal position, so a point (x,y) is reflected to (-x,y).
Axis reflections can be used to transform geometric shapes such as polygons, circles, or lines. These transformations have important applications in various fields, including physics, engineering, computer graphics, and art.
To find the composition of transformations that map ABCD to EHGF, we first need to determine the individual transformations that are needed.
Reflecting over the y-axis will change the x-coordinates of the points, but leave the y-coordinates unchanged. So, to reflect over the y-axis, we negate the x-coordinates of the points.
The translation (x+4, y+7) will move each point 4 units to the right and 7 units up.
Therefore, the composition of transformations is:
Reflect over the y-axis by negating the x-coordinates:
A'(-2, 3), B'(-4, 2), C'(-4, 0), D'(-2, -1)
Translate by (4,7):
A''(2, 10), B''(0, 9), C''(0, 7), D''(2, 6)
Therefore, the composition of transformations that map ABCD to EHGF is a reflection over the y-axis followed by a translation by (4,7).
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Please see the attached
A restaurant borrows $15,700 for two months from a nearby bank. For this loan, the neighbourhood bank charges simple interest at a yearly rate of 10%. Suppose a month is one-twelfth of a year.
a) $218.06 in interest will be due after two months.
b) In the event that the restaurant doesn't pay, the balance due after two months is $15,918.06.
a) To find the interest that will be owed after 2 months, we first need to calculate the monthly interest rate:
r = (10%)/12 = 0.00833333...
We can use the formula for simple interest to find the interest owed:
I = Prt
where P is the principal (the amount borrowed), r is the interest rate per period, and t is the time in periods. Since the loan is for 2 months, we have t = 2/12 = 1/6 years.
Substituting the values, we get:
I = 15700 * 0.00833333... * (1/6) = 218.0555...
Rounding to the nearest cent, the interest owed after 2 months is $218.06.
b) The total amount owed after 2 months is the sum of the principal and the interest. Using the same values as above, we have:
The total amount owed = Principal + Interest
= 15700 + 218.0555...
= 15918.0555...
Rounding to the nearest cent, the amount owed after 2 months is $15,918.06.
The complete question is:-
A restaurant borrows $15700 from a local bank for 2 months. the local bank charges simple interest at an annual rate of 10% for this loan. assume each month is 1/12 of a year. answer each below. do not round any intermediate computations, and round your final answers to the nearest cent, if necessary, refer to the lists of financial formulas.
a) find the interest that will be owed after 2 months.
b) assuming the restaurant doesn't make any payments, find the amount owed after 2 months.
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Three students need to produce a prime factorization of
48. Donna states that the first factors in the tree should
be 6 and 8. Larry states that the first factors in the tree
should be 4 and 12. Trish states that the initial factors of
48 do not affect the prime factorization. Explain why Trish
is correct.
Answer:
students need to produce a prime factorization of 48. Donna states that the first factors in the tree should be 6 and 8. Larry states that the first factors in the tree should be 4 and 12. Trish states that the initial factors of 48 do not affect the prime factorization. Explain why Trish is correct.Trish is correct because the initial factors of 48 do not affect the prime factorization. Prime factorization is the process of breaking down a composite number into its prime factors. The prime factors of a number are those factors that are prime numbers. The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, which means that 48 can be expressed as a product of these prime factors. The order in which we choose the initial factors to start the prime factorization does not affect the result, as long as we continue to break down the resulting factors into their prime factors until we cannot break them down any further. Therefore, Trish is correct that the initial factors of 48 do not affect the prime factorization.
Trish is correct because the prime factorization of 48 will be the same regardless of which factors are chosen as the initial factors in the tree.
To see why, let's look at the prime factorization of 48:
48 = 2 × 2 × 2 × 2 × 3
No matter which factors are chosen as the initial factors, the same prime factors will eventually be found.
For example, if Donna's method is used, we could start with 6 and 8:
6 = 2 × 3
8 = 2 × 2 × 2
Then we could continue to factor each of these numbers until we reach prime factors:
6 = 2 × 3
8 = 2 × 2 × 2
= 2 × 2 × 2 × 3
= 2³ × 3
Now we have found all of the prime factors of 6 and 8, and we can combine them to get the prime factorization of 48:
48 = 2 × 2 × 2 × 2 × 3
If Larry's method is used, we could start with 4 and 12:
4 = 2 × 2
12 = 2 × 2 × 3
Then we could continue to factor each of these numbers until we reach prime factors:
4 = 2 × 2
12 = 2 × 2 × 3
= 2² × 3
Now we have found all of the prime factors of 4 and 12, and we can combine them to get the prime factorization of 48:
48 = 2 × 2 × 2 × 2 × 3
As we can see, the same prime factors are found regardless of which factors are chosen as the initial factors in the tree. Therefore, Trish is correct that the initial factors of 48 do not affect the prime factorization.
An algebraic expression is described as 14 more than the product of
3 and the difference of z and 9. What is the value of this expression
when z = 17?
The value of the expression is 38 when z = 17.
What is the value of this expression when z = 17?Given that, an algebraic expression is described as 14 more than the product of 3 and the difference of z and 9.
First, we write the expression:
The difference of z and 9 means we subtract 9 from z. We then take this result and multiply it by 3.
Finally, we add 14 to the product of 3 and the difference of z and 9.
3(z - 9) + 14
Where z represents the value that we want to substitute into the expression.
Substituting z = 17, we get:
3(z - 9) + 14
3(17 - 9) + 14
3(8) + 14
24 + 14
38
Therefore, the value of the expression is 38.
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Find the vertex and the
�
x- and
�
y-intercepts of the equation
�
=
�
2
−
2
�
−
8
y=x
2
−2x−8
Then, use the points to graph the parabola.
a) What is the vertex of the parabola? Enter your answer as an ordered pair.
Vertex
Preview
b) Identify the
�
x-intercept(s) of the parabola. Enter your answers as ordered pairs. Use a comma to separate answers as needed. If there are none, enter
None
None.
�
x-intercept
Preview
c) Identify the
�
y-intercept of the parabola. Enter your answer as an ordered pair.
�
y-intercept
Preview
d) Use the points you found to graph the parabola.
Answer:
Step-by-step explanation:
As seen in earlier sections, the process of completing the square is a useful tool in finding noninteger values of quadratic equations, especially intercepts. When a quadratic equation of the
form f (x) = ax2
+ bx + c is put through the process of completing the square it yields an
equation of the form f (x) = a(x – h)2
+ k . The conversion of the equation to this form will
yield critical information about the equation’s characteristics before you begin to graph it.
1.) The value of h is the distance left (if negative) or right (if positive) the graph
translates from the standard position.
2.) The value of k is the distance up (if positive) or down (if negative) the graph
translates from the standard position.
3.) The values of h and k, when put together as an ordered pair, give the vertex i.e.
(h, k).
4.) The equation x = h is the formula for the axis of symmetry.
The following example demonstrates how to find the following critical information of the
equation:
a.) vertex
b.) axis of symmetry
c.) y intercept (if any)
d.) x intercepts (if any)
Example 1: Find the vertex, axis of symmetry, x-intercept(s), and y-intercept and gr