The final amount with interest earned at a rate of 3.4% compounded semi-annually would be approximately $7,758.
HOW CAN WE CALCULATE INTEREST?Let's calculate the values based on the given information.
Given:
Initial deposit (P) = $7,500
Interest rate (r) = 3.4% or 0.034 (decimal)
Compounding frequency (n) = 2 (semi-annually)
We can use the compound interest formula to calculate the values:
A = P[tex](1 + r/n)^(nt)[/tex]
Where:
A = the final amount (including interest)
P = the principal amount (initial deposit)
r = the interest rate (in decimal)
n = the number of times interest is compounded per time period
t = the number of time periods
Let's calculate the final amount (A) after one year (2 semi-annual periods):
A =[tex]$7,500(1 + 0.034/2)^(2*1)[/tex]
A =[tex]$7,500(1.017)^2[/tex]
A = $7,500(1.034344) [rounded to 6 decimal places]
A ≈ $7,758 [rounded to the nearest dollar]
So, after one year, the final amount with interest earned at a rate of 3.4% compounded semi-annually would be approximately $7,758.
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Lauren works at a reception hall and is setting tables for a retirement party. She takes a basket of 98 soup spoons, and she places 8 soup spoons on every table she sets.
Write an equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x.
y=
The equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x, is:
y = 98 - 8x
The initial number of soup spoons, 98, is reduced by 8 for each table Lauren sets. Therefore, the number of soup spoons remaining after x tables have been set is 98 - 8x.
Evander Holyfield (the champion boxer who had part of his ear bitten off by Mike Tyson) made $290 million during his boxing career but declared bankruptcy because of poor financial choices. His July interest at 18% was $248. What was Evander’s principal at the beginning of July? (Use 360 days a year. Do not round intermediate calculations. Round your final answer to the nearest whole dollar.)
Evander's principal at the beginning of July was approximately $16,533. Rounded to the nearest whole dollar, this is $16,533.
How do we calculate?Applying the formula for simple interest:
Interest = Principal x Rate x Time
Here, we know the interest ($248), the rate (18%), and the time (1/12 of a year for one month, since we're using a 360-day year).
Let the principal = "P":
$248 = P x 0.18 x (1/12)
$248 = P x 0.015
P = $248 / 0.015
P ≈ $16,533.33
Simple interest is described as an interest charge that borrowers pay lenders for a loan.
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What is the opposite of 12 written in simplest terms?
Answer:
Step-by-step explanation:
It is -12.
The opposite of a positive number would be its negative.
A recipe for sugar cookies requires 2 cups of flour for every 2/3 cups of sugar. At this rate, how many cups of sugar should be used if 5 cups of flour included?
According to the given information, if 5 cups of flour are used in the recipe, we should use 5/3 cups of sugar.
What is multiplication?Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. It is a way of repeatedly adding a number to itself a certain number of times. The number being multiplied is called the multiplicand, while the number of times it is being multiplied is called the multiplier. The result of the multiplication operation is called the product
According to the given information:If the recipe requires 2 cups of flour for every 2/3 cups of sugar, we can write this relationship as:
2 cups of flour : 2/3 cups of sugar
To find out how many cups of sugar should be used if 5 cups of flour are included, we can set up a proportion:
2 cups of flour / 2/3 cups of sugar = 5 cups of flour / x cups of sugar
where x is the number of cups of sugar we want to find.
To solve for x, we can cross-multiply:
2 cups of flour * x cups of sugar = 2/3 cups of sugar * 5 cups of flour
2x = (2/3) * 5
2x = 10/3
x = 5/3
Therefore, According to the given information, if 5 cups of flour are used in the recipe, we should use 5/3 cups of sugar.
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1. The relationship between distance
measured on a map and the actual
distance on the ground
A. A sketch
B. A statement
C. Layout
D. Scale
What if the correct answer
Answer: A Map Scale.
Step-by-step explanation:
A Map Scale is the relationship with the ground.
PLEASE HELP! An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1200, determine the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. The probability is what?
(Round to three decimal places as needed.) Thanks!
The probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is: 0.305.
The interpretation and how to arrive at the propabilityThe interpretation of the statement that the probability of the sample mean being within $80 of the population mean is 0.305 is that if we take multiple samples of 400 ethanol railroad-car shipments, about 30.5% of the time, the sample mean tariff rate will be within $80 of the population mean tariff rate.
To arrive at the propability, we will first list the data as follows:
Standard deviation of tariff rates, σ = $1200
Sample size, n = 400
Margin of error, E = $80
Standard deviation of sample mean = σ/√n = 1200/√400 = 60
To find the probability, we need to calculate the z-score for the margin of error.
z = E / standard deviation of sample mean = 80 / 60 = 4/3.
When we use the standard normal distribution table, we will arrive at the probability of a z-score between -1.33 and 1.33. This probability is approximately 0.305.
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Work backwards, using the Distributive Property, to check the factors and identify the original polynomial of this factored function: (2 + 5)( + 7)
NO LINKS!! URGENT HELP PLEASE!!!
Find a formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector "l" of segment AB.
A(-6, 4), B(14, -12)
Answer:
The perpendicular bisector of a line segment AB is the line that passes through the midpoint of AB and is perpendicular to AB.
To find the equation of the perpendicular bisector of segment AB, we can follow these steps:
Find the midpoint M of AB. The coordinates of M are:M = ( (x1 + x2)/2, (y1 + y2)/2 )
where A = (x1, y1) and B = (x2, y2).
In this case, A = (-6, 4) and B = (14, -12), so the coordinates of M are:M = ( (-6 + 14)/2, (4 - 12)/2 ) = (4, -4)
Find the slope m of AB. The slope of AB is:m = (y2 - y1) / (x2 - x1)
In this case, the slope of AB is:m = (-12 - 4) / (14 - (-6)) = -16/20 = -4/5
Find the slope of the line that is perpendicular to AB. The slope of a line perpendicular to AB is the negative reciprocal of the slope of AB. So, the slope of the line that is perpendicular to AB is:m_perp = -1/m
In this case, the slope of the line that is perpendicular to AB is:m_perp = -1/(-4/5) = 5/4
Use the point-slope form of the equation of a line to find the equation of the perpendicular bisector. The point-slope form of the equation of a line is:y - y1 = m(x - x1)
We can use the midpoint M as the point (x1, y1) and the slope m_perp as the slope m:y - (-4) = (5/4)(x - 4)
Simplifying, we get:
y + 4 = (5/4)x - 5
Moving terms around, we get:(5/4)x - y - 9 = 0
So, the formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector of segment AB is:
(5/4)x - y - 9 = 0
Select all the expressions that have the same value. a \large 3^3 b \large 3^4 c \large 6^2 d \large 6^3 e \large 9^2 f \large 9^3
The expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
Selecting all expressions that have the same value.To compare the expressions, we can simplify them using the rules of exponents:
a) 3^3 = 27
b) 3^4 = 81
c) 6^2 = 36
d) 6^3 = 216
e) 9^2 = 81
f) 9^3 = 729
Using the above as a guide, we have the following:
Therefore, the expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
So, options b and e have the same value.
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If the point (1,5) lies on a circle with center (0,0), determine which point in quadrant 2 that also lies on the circle.
Answer:
If the point (1,5) lies on a circle with center (0,0), then the radius of the circle is the distance from the center to the point (1,5), which is:
r = sqrt((1-0)^2 + (5-0)^2) = sqrt(26)
So the equation of the circle is:
x^2 + y^2 = 26
To find a point in quadrant 2 that lies on the circle, we need to find a point with a negative x-coordinate and a positive y-coordinate that satisfies this equation.
Among the given options, only (a) (-5,1) and (e) (-2,3) have a negative x-coordinate. Let's check if they satisfy the equation of the circle:
For point (a) (-5,1):
x^2 + y^2 = 26
(-5)^2 + 1^2 = 26
25 + 1 = 26
This point does not lie on the circle.
For point (e) (-2,3):
x^2 + y^2 = 26
(-2)^2 + 3^2 = 26
4 + 9 = 26
This point also does not lie on the circle.
Therefore, among the given options, there is no point in quadrant 2 that lies on the circle.
Step-by-step explanation:
since the center of the circle is at the origin, that means that the circle is evenly going through all four quadrants - one quarter arc after the other.
the point (1, 5) is in the first quadrant (upper right one, positive x, positive y).
the circle arc in the second quadrant (upper left one, negative x, positive y) is the mirrored image of the arc in the first quadrant across the y-axis.
so, the point on it gets mirrored too.
that means, it's coordinates are then the same y and the x is converted to its negative value :
(-1, 5)
that is the easily identifiable point in the second quadrant that has to be on the circle.
Choose the tool or tools you can use to
measure the object. Then measure the length.
string and straws
art.
non
7. straws
about
Company LLC. All Rights Reserved.
straws
00
Topic 12 Reteaching
The tools you can use to measure the object is Ruler
What is the technique to determine the size of a string using ruler?First you need to Indicate the starting and ending points of the curved line on the string. To determine the distance between the two markings on the string, lay the string flat on a ruler, or a stretched-out measuring tape if the line is curved, and measure the length in between.
Commonly found in bars and restaurants, disposable straws intended for one-time use have a common size of 8.5 inches in length and width. The typical size of a drinking straw is one that is having a width of 24 inches. At times, you may need a lengthier or broader straw to suit yourself.
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Is the figure line symmetric?
If yes, how many lines of symmetry does the figure have?
a picture of a snow flake
Answer:
Yes, the figure is line symmetric.
A snowflake has six lines of symmetry. Therefore, the correct answer is: 6.
The value of y is directly proportional to the value
of x. If x = 8, then y = 12. What is the value of x when y = 30?
Answer:
If the value of y is directly proportional to the value of x, we can use the formula for direct variation to find the value of x when y = 30. The formula for direct variation is:
y = kx
where k is the constant of proportionality.
To find the value of k, we can use the values given in the problem:
y = kx
12 = k(8)
Solving for k, we get:
k = 12/8 = 3/2
Now that we know k, we can use the formula for direct variation to find the value of x when y = 30:
y = kx
30 = (3/2)x
Solving for x, we get:
x = (30)/(3/2) = 20
Therefore, when y = 30, x = 20
. The formula 9x - 5y = -160 relates the
temperature in degrees Fahrenheit y to
the temperature in degrees Celsius x.
Tell whether the relationship is a direct
variation. Explain your answer.
The given formula 9x - 5y = -160 is not in the form of direct variation.
Calculating the type of variationThe given formula 9x - 5y = -160 relates the temperature in degrees Fahrenheit y to the temperature in degrees Celsius x.
To determine whether the relationship is a direct variation or not, we need to consider the definition of direct variation.
A relationship is said to be a direct variation if one variable is a constant multiple of the other variable, i.e., y = kx or x = ky, where k is a constant of proportionality.
However, the given formula is not in the form of direct variation. It is a linear equation in two variables, and there is no constant of proportionality present.
Hence, we can conclude that the given relationship is not a direct variation.
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What expression is equivalent to 4- 1/3-7/8+1/6?
A. 6/24-8/24-21/24+4/24?
Answer for brainliest. Don't care if its wrong.
The simplified form of the expression is 71/24.
What is the simplified form?
To simplify the expression 4 - 1/3 - 7/8 + 1/6, we can follow the order of operations, which dictates that we perform multiplication and division before addition and subtraction.
Here's the step-by-step solution:
Find a common denominator for the fractions involved. In this case, the least common denominator (LCD) is 24, which is the least common multiple of 3, 8, and 6.
Convert the fractions to have the same denominator, which is 24:
4 - 1/3 - 7/8 + 1/6
= 4 * 24/24 - 1/3 * 8/8 - 7/8 * 3/3 + 1/6 * 4/4 (Multiplying each fraction by the appropriate form of 1 to get the common denominator)
= 96/24 - 8/24 - 21/24 + 4/24 (Performing the multiplication)
Combine the numerators over the common denominator:
= (96 - 8 - 21 + 4)/24 (Combining numerators)
= 71/24 (Performing the subtraction)
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a recipe for sugar cookies calls for 3 cups of sugar and 6 cups of flour so how many cups of sugar are there for each cup of flour?
The number of cups of sugar that are there for each cup of flour would be = 1/2 cup of sugar.
How to calculate the number of cups of sugar for each cup of flour?The recipe contains sugar of = 3 cups
The recipe contains flour of = 6 cups
If 3cups sugar = 6 cups of flour
X cups sugar = 1 cup of flour
make X the subject of formula;
X = 3×1/6
X = 3/6 = 1/2
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A car is purchased for $19,500. After each year, the resale value decreases by 20%. What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.
The resale value of the car after 3 years is $9,984.
How to find the resale value after 3 years?Since the resale value decreases by 20%. Thus, the resale value of the car will be 80% of its original value.
After the first year, the resale value of the car will be 80% of its original value:
Resale value after 1 year = 80/100 * $19,500 = $15,600
After the second year, the resale value of the car will be 80% of its value after the first year:
Resale value after 2 years = 80/100 * $15,600 = $12,480
After the third year, the resale value of the car will be 80% of its value after the second year:
Resale value after 3 years = 80/100 * $12,480 = $9,984
Therefore, the resale value of the car after 3 years will be $9,984.
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LESSON 19 SESSION 5
✪ Which solutions, if any, do the inequalities -2(c-4) ≤-4 and d-6>-4
have in common? Show your work.
The solutions the inequalities -2(c-4) ≤-4 and d-6>-4 have in common are values greater than 2
Calculating the solutions the inequalities have in commonFrom the question, we have the following parameters that can be used in our computation:
-2(c-4) ≤-4 and d-6>-4
Using the above as a guide, we have the following:
-2(c - 4) ≤ -4
Divide by -2
c - 4 ≥ 4
So, we have
c ≥ 0
Next, we have
d - 6 > -4
Add 6 to both sides
So, we have
d > 2
This means that the solutions are c ≥ 0 and d > 2
So, the solutions the inequalities have in common are values greater than 2
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what is the answer (x+80)(x-20)
Answer:
Using the FOIL method to multiply (x + 80)(x - 20), we get:
(x + 80)(x - 20) = x^2 - 20x + 80x - 1600
Simplifying the expression, we get:
(x + 80)(x - 20) = x^2 + 60x - 1600
Therefore, the answer is x^2 + 60x - 1600.
A carpenter has two different-sized circular saws. The smaller saw has the radius shown. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.
How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π
.
If the radius of smaller-saw is 1.25 in, and radius of larger-saw is 2 inches, then larger-saw is 4.71 inches greater the smaller-saw.
The "Circumference" of a circle is defined as the distance around the boundary of a circle, it is also called perimeter of circle;
The diameter of the smaller saw can be calculated as:
⇒ diameter = 2 × radius = 2 × 1.25 inches = 2.5 inches;
The diameter of the larger saw is 1.5 inches greater than the diameter of the smaller saw, which means,
⇒ diameter of larger saw = diameter of smaller saw + 1.5 inches,
⇒ diameter of larger saw = 2.5 inches + 1.5 inches = 4 inches;
So, Circumference of circle is = 2 × π × radius;
The Circumference of "smaller-saw" = 2 × 3.14 × 1.25 inches,
⇒ circumference of smaller saw = 7.85 inches;
circumference of "larger-saw" = 2 × 3.14 × 2 inches
⇒ circumference of larger saw = 12.56 inches;
The difference in circumference between the two saws is:
⇒ circumference of larger saw - circumference of smaller saw
⇒ 12.56 inches - 7.85 inches = 4.71 inches;
Therefore, the circumference of the larger saw is 4.71 inches greater than the circumference of the smaller saw.
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The given question is incomplete, the complete question is
A carpenter has two different-sized circular saws. The smaller saw has the radius as 1.25 inch. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.
How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π
100 Points! Multiple choice algebra questions. For questions 3 and 4, use f(x)=x+5 and g(x)=2x.
Find (f+g) (x).
Find (f·g) (x).
Photo attached. Thank you!
3. The value of the function (f+g)(x) is option A: 3x+5. 4. The value of: (f·g)(x) is Option C: 2x² + 10x.
What is sum and product of function?The function that results from summing the results of the two functions for a specific input value x is known as the sum of two functions (f+g)(x). To put it another way, we just add the function values at each x-axis point. The function that results from multiplying the outputs of the two functions for an input value x is known as the product of two functions (fg)(x). In other words, we multiply the values of the function at each x-axis position. Two functions can be combined or multiplied to create new functions, each of which has a unique set of attributes.
Given that, f(x)=x+5 and g(x)=2x.
3. The value of (f+g)(x) is:
f(x + g) (x)= f(x) + g(x) = (x+5) + 2x = 3x+5
4. The value of:
(f·g)(x) = f(x) · g(x) = (x+5) · 2x = 2x² + 10x
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Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
The equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
How to solveWe can observe from the table that the number of books collected increases by 10 for each week.
Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:
b = mw + c
where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).
The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):
10 = 10 * 1 + c
c = 0
Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).
Weeks (w) Books Collected (b)
1 10
2 20
3 30
4 40
Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
Help please i dont remeber how to do this
Answer:
-20
Step-by-step explanation:
[tex]\frac{5}{3}x +\frac{1}{3} x=13\frac{1}{3}+\frac{8}{3}x\\\\\frac{6}{3} x = 13 \frac{1}{3} +\frac{8}{3} x\\\\\frac{-40}{3} =\frac{2}{3} x\\\\\frac{3}{2} *(\frac{-40}{3} )\\\\\frac{3}{2} *\frac{2}{3} x\\\\-20 = x[/tex]
Write an equation of the line below.
Find the slope of the line that contains these points.
(1, -3) (2, -5)
use slope equation -5 - (-3)/(2-1) then solve
The distance of 15 miles on a map is represented by 2 inches.
If the distance between two cities on the map is 8 inches, what is the actual distance
between them?
A 60 miles
B 75 miles
C 90 miles
D 120 miles
awing of an airplane. The airplane has a 100-foot wings
Answer:
A. 60 miles
Step-by-step explanation:
2 in. = 15mi or like 2in+2in+2in+2in = 8in
15mi+15mi+15mi+15mi = 60mi
2×4 =8
/
/
v
4 × 15mi = 60mi
Description of the circumscribed angle
A circumscribed angle is an angle that has its vertex on the circumference of a circle and whose sides are chords of the circle. The measure of a circumscribed angle is equal to half the measure of the intercepted arc. Circumscribed angles are important in geometry because they are used to prove theorems about angles, chords, and arcs in circles. The opposite angles of a cyclic quadrilateral are always supplementary, and the sum of the angles in a cyclic polygon is always equal to (n-2)180 degrees, where n is the number of sides of the polygon.
Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A
co
5
H
The mapping diagram above|
Set B
✓in
-2
3
O
7
શ function since
where there
Answer:
It is not a function
Step-by-step explanation:
A function is a rule from x to y that applies to all elements of x. Every element of x should have one image only.
Here, element "1" has two images 3 and 7. Therefore it's not a function.
50 points! Multiple choice algebra question. Gilda used the formula f(x) = x/144 to convert square inches to square feet. Find the inverse of f(x). Photo attached. Thank you,
I really need help with this to find x value and need reasons
Answer:
x = 45 degrees
Step-by-step explanation:
All angles in a triangle will add up to 180 degrees. So far we have 57 degree of 180. We also see a supplementary angle, with one side being 102 degrees, so the other is 78 degrees, because it must add up to 180. We see that the arrows in the bases show that the corners are even, so now we know two corners: one with 57 degrees and the other with 78.
Now, follow this equation to find x:
57 + 78 + x = 180
135 + x = 180
-135 -135
x = 45