I donno where on Eart do you find those questions from.lol.
Step-by-step explanation:
The volume of the rectangular bale of hay can be calculated using the formula:
V = lwh
where l, w, and h are the length, width, and height of the bale, respectively.
Substituting the given values, we get:
V = (4)(2)(2) = 16 cubic feet
The volume of the cylindrical bale of hay can be calculated using the formula:
V = πr^2h
where r is the radius of the bale (half the diameter), and h is the height of the bale.
Substituting the given values, we get:
V = π(4)^2(6) = 301.59 cubic feet
To find out how many rectangular bales contain the same amount of hay as one cylindrical bale, we can divide the volume of the cylindrical bale by the volume of one rectangular bale:
301.59 cubic feet / 16 cubic feet ≈ 18.85
Therefore, approximately 18.85 rectangular bales are required to contain the same amount of hay as one cylindrical bale. Rounded to the nearest tenth, this is 18.9 rectangular bales.
Given cos=4/5 and 0 <0< 90 find sin 20.
a.-24/25 b. 24/25
c. -24/27 d.-27/25
It is given that cos(θ)=4/5 and 0 <0< 90, the value of sin(θ) would be 24/25. So, the correct answer is option b.
To find sin(2θ) in terms of cos(θ), we will use double angle formula for sin which states that:
sin(2θ) = 2 sin(θ) cos(θ)
It is given that cos(θ) = 4/5,
Using the Pythagorean identity to find sin(θ):
[tex]sin^2[/tex](θ) + [tex]cos^{2}[/tex](θ) = 1
[tex]sin^2[/tex](θ) = 1 - [tex]cos^{2}[/tex](θ)
sin(θ) = [tex]\sqrt{(1 - (4/5)^2)}[/tex]
sin(θ) = 3/5
Substituting these values into double angle formula for sin:
sin(2θ) = 2 sin(θ) cos(θ)
sin(2θ) = 2 (3/5) (4/5)
sin(2θ) = 24/25
Therefore, the answer is (b) 24/25.
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In Exercises 13 and 14, the solids are similar. Find the surface area of solid B. (See Example
Pyramid A
Pyramid B
14.
27 in.
S = 48 in.²
+
36 in.
●
I
The surface area of solid B is calculated as:
13. 144π ft² 14. 85.3 ft²
How to Find the Surface Area of Similar Solids?Recall that the ratio of the surface areas of similar solids is equal to the square of the ratio of their linear measures.
Thus, we have the following:
13. Let the surface area of solid B be represented as x, therefore:
36π / x = 4² / 8²
x * 4² = 36π * 8²
16x = 2,304π
16x/16 = 2,304π/16 [division property of equality]
x = 144π ft²
14. Let the surface area of solid B be represented as x, therefore:
48 / x = 27² / 36²
Cross multiply:
x * 27² = 48 * 36²
729x = 62,208
729x/729 = 62,208/729 [division property of equality]
x = 85.3 ft²
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A blacktop on a playground has the dimension
shown in the model.
10 m
8 m
24 m
8 m
What’s the area of the blacktop in square meters?
A 196 B 576 C 78 D 272
The area of the blacktop in square meters is: 272m²
How to find the area of the composite figure?The formula for the area of a rectangle is:
A = l * w
where:
l is length
w is width
Thus:
A = 10m * 8m
A = 80m²
That’s the area of the first rectangle.
A = l x w
A = 24m x 8m
A = 192m²
That’s the area of the second rectangle.
Total area of composite shape = 192m² + 80m² = 272m²
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For what value of n are the line y = 3x + 1 and y = nx - 4 perpendicular?
A -1
B 1/4
C 3
D -1/3
I’ll give brainly if you get the correct answer !!!
Answer:
D. -1/3
The slopes of perpendicular lines are negative reciprocals of each other. In other words, the product of the slopes of perpendicular lines is -1. So the slope of a line perpendicular to a line with a slope of 3 will have a slope of -1/3. D is correct.
4g to 3.5g write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator
4g to 3.5g written as a fraction in simplest form is equal to 8/7.
What is a ratio?In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this exercise, you are required to determine the ratio as a fraction in simplest form. Therefore, we would multiply both the numerator and denominator by 2 as follows;
Ratio = 4g/3.5g × 2/2
Ratio = 8g/7g
Ratio = 8/7
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What number is exactly halfway between 212,900 and 213,500?
Step-by-step explanation:
(212900 + 213500) ÷ 2
426400/2 = 213200
The number exactly halfway between 212,900 and 213,500 is 213,200.
Finding the number that is halfway between two given values is a fundamental concept in mathematics, and it involves a simple calculation using basic arithmetic.
To find the number that is exactly halfway between two values, you need to add the two values together and then divide the sum by 2.
In this case, 212,900 + 213,500 = 426,400.
Dividing 426,400 by 2 gives us 213,200, which is the number exactly halfway between the two given values.
Therefore, 213,200 is the answer to the question.
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A triangle has one angle that is 8 degrees more than twice another of its angles. The two smaller angles are equal in measure. Find the measure of all the angles.
Answer:
The measure of both of the smaller angles is 43°.
The measure of the larger angle is 94°.
Step-by-step explanation:
We can model the larger angle in relation to the smaller angle by representing each of the smaller angles (which are equal in measure) as a variable x and the larger angle as a variable y.
[tex]y = 2x + 8[/tex]
This shows that the larger angle is eight degrees more than twice (2 times) the smaller angles' measures.
We can now model the sum of all the triangle's angle measures because we know that a triangle's interior angle measures add to 180°.
[tex]2(\text{small}) + \text{large} = 180[/tex]
[tex]2x + y = 180[/tex]
What we have now is a system of equations which we can solve for using substitution. The first equation ([tex]y = 2x + 8[/tex]) is a definition of y in terms of x, so we can substitute that definition into the second equation and solve for x.
[tex]\begin{cases} y = 2x + 8 \\ 2x + y = 180\end{cases}[/tex]
[tex]2x + (2x + 8) = 180[/tex]
[tex]4x + 8 = 180[/tex]
[tex]4x = 172[/tex]
[tex]\boxed{x = 43\textdegree}[/tex]
So, the measure of each of the smaller angles is 43°.
Now, we can plug that x-value back into the first equation and solve for y.
[tex]y = 2(43) + 8[/tex]
[tex]y = 86 + 8[/tex]
[tex]\boxed{y = 94\°}[/tex]
So, the measure of the larger angle is 94°.
need help please if i dont do this i wont be able to play football
Answer:
3.5 litres.
Step-by-step explanation:
We can use the unit rate method to find how much tea Ben drinks per hour.
First, we can convert 2/3 of an hour to an hour by multiplying it by 3/2:
2/3 hour * 3/2 = 1 hour
This tells us that the rate of drinking tea is constant, and Ben drinks 3 and 1/2 liters of tea per hour.
Therefore, Ben drinks 3.5 liters of tea per hour.
The vertices of ∆MNO and ∆PQR are described in the table. ∆MNO ∆PQR M (3, 9) P (−1, −3) N (9, 9) Q (−3, −3) O (12, 3) R (−4, −1) How can ∆MNO ~ ∆PQR be justified using rigid and non-rigid transformations? ∆MNO was dilated by a scale factor of 3 from the origin, then rotated 90° clockwise about the origin to form ∆PQR.
∆MNO was dilated by a scale factor of 3 from the origin, then translated down 2 and left 5 units to form ∆PQR.
∆MNO was dilated by a scale factor of one third from the origin, then reflected over the x-axis to form ∆PQR.
∆MNO was dilated by a scale factor of one third from the origin, then rotated 180 degree clockwise about the origin to form ∆PQR.
The correct justification for the similarity between ∆MNO and ∆PQR is:
∆MNO was dilated by a scale factor of 3 from the origin, then rotated 90° clockwise about the origin to form ∆PQR.
To see why this is the case, we can apply the transformations to the vertices of ∆MNO and see if they match the vertices of ∆PQR.
First, we dilate ∆MNO by a scale factor of 3 from the origin:
M' = 3M = (3(3), 3(9)) = (9, 27)
N' = 3N = (3(9), 3(9)) = (27, 27)
O' = 3O = (3(12), 3(3)) = (36, 9)
Next, we rotate the dilated triangle 90° clockwise about the origin:
P' = (cos(90°)P - sin(90°)Q, sin(90°)P + cos(90°)Q)
= (0P - (-1)Q, 1P + 0Q) = (Qx + 1, Py)
Q' = (cos(90°)Q - sin(90°)P, sin(90°)Q + cos(90°)P)
= (0Q - (-3)P, 1Q + 0P) = (Px + 3, Qy)
R' = (cos(90°)R - sin(90°)S, sin(90°)R + cos(90°)S)
= (4R - 4S, -4R - 4S) = (4(R - S), -4(R + S))
Substituting the coordinates of the original vertices, we get:
P' = (-1 + 1, -3) = (0, -3)
Q' = (-3 + 1, -1) = (-2, -1)
R' = 4(-4 + 1, -1 + 3) = (-12, 8)
Comparing the coordinates of ∆PQR with those of the transformed ∆MNO, we can see that they match. Therefore, the similarity between ∆MNO and ∆PQR can be justified by dilating ∆MNO by a scale factor of 3 from the origin, then rotating it 90° clockwise about the origin to form ∆PQR.
how much is 3/4 times 16/9
Answer:4/3
Step-by-step explanation:48/36
1. (06.01 LC)
A person in the audience of a talk show has a 15% chance of winning free movie tickets. What is the chance that a person in the audience may not win free movie tickets? (5 points)
85%
70%
35%
30%
Pls answer
woth 28 points!!
Answer: 10.46 m
Step-by-step explanation:
C=[tex]\pi d[/tex]
=[tex]\pi (3.33)[/tex]
=10.46 m
Answer:
C = 10.45 m (round 10.5 m)
Step-by-step explanation:
we solve with the formula C=πd, where "c" is the circumference and "d" the diameter
C = π × 3.33
C = 3.14 × 3.33
C = 10.45 m (round 10.5 m)
Use the graph on the right to answer the questions.
f(x)= (1 row) x + 7, x less-than or equal to -3
(2 row) -x, -3 is less than x is less-than or equal to 0
(3 row) sqaure root of x, 0 is less than x is less than 4
What is the value of f(−3)?
f(−3) =
What are the domain and range of f(x)?
A: Domain: (Negative infinity, infinity), Range: (Negative infinity, infinity)
B: Domain: (Negative infinity, 4), Range: (Negative infinity, 4)
C: Domain: (Negative infinity, 4], Range: (Negative infinity, 4]
The domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.
What is function in math?Function is a process or a set of rules that take input values and produces an output. It is a mathematical expression that takes the inputs, performs an operation and produces an output. Functions are used to model real-world scenarios and to solve problems. It helps to simplify the code and makes it easier to understand and debug. Functions are also used to create reusable code that can be used in different applications.
A: Domain: (Negative infinity, infinity), Range: (Negative infinity, infinity)
B: Domain: (Negative infinity, 4), Range: (Negative infinity, 4)
C: Domain: (Negative infinity, 4], Range: (Negative infinity, 4]
D: Domain: [-3, 4], Range: [-7, 4]
Answer: D: Domain: [-3, 4], Range: [-7, 4]
The domain of f(x) is the set of all x-values for which the function is defined, which in this case is [-3, 4]. The range of f(x) is the set of all y-values for which the function is defined, which in this case is [-7, 4]. The value of f(-3) is -7, according to the graph.
To calculate the value of f(x) at any x-value, we can use the three equations given in the graph. For x ≤ -3, f(x) = x + 7. For -3 < x ≤ 0, f(x) = -x. For 0 < x < 4, f(x) =√x.
In conclusion, the domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.
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The domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.
What is function in math?
Function is a process or a set of rules that take input values and produces an output. It is a mathematical expression that takes the inputs, performs an operation and produces an output. Functions are used to model real-world scenarios and to solve problems. It helps to simplify the code and makes it easier to understand and debug. Functions are also used to create reusable code that can be used in different applications.
A: Domain: (Negative infinity, infinity), Range: (Negative infinity, infinity)
B: Domain: (Negative infinity, 4), Range: (Negative
infinity, 4)
C: Domain: (Negative infinity, 4], Range: (Negative infinity, 4]
D: Domain: [-3, 4], Range: [-7, 4]
Answer: D: Domain: [-3, 4], Range: [-7, 4]
The domain of f(x) is the set of all x-values for which the function is defined, which in this case is [-3, 4]. The range of f(x) is the set of all y-values for which the function is defined, which in this case is [-7, 4]. The value of f(-3) is -7, according to the graph.
To calculate the value of f(x) at any x-value, we can use the three equations given in the graph. For x ≤-3, f(x) = x+7. For -3 <x≤0, f(x)=-x. For O <x<4, f(x)=√x.
To calculate the value of f(x) at any x-value, we can use the three equations given in the graph. For x ≤-3, f(x) = x + 7. For -3 <x ≤ 0, f(x) = -x. For O <x<4, f(x)=√x.
In conclusion, the domain and range of the given function f(x) are [-3, 4] and [-7, 4] respectively. The value of f(-3) is -7.
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Use < , > , or = to compare the following numbers.
Answer:
-11<-1
-5>-8
11>-6
Step-by-step explanation:
In this case I'm assuming we're looking for the greater number. When it comes to negative number the number thats closest to zero would be greater than the one not. Positive numbers are always greater than negative numbers.
Answer: -11<-1, -5>-8, 11>-6.
Step-by-step explanation:
-1> -11 because -1 is closer to positive than -11
-5>-8 because -5 is closer to positive than -8
11>-6 because 11 is a positive number
Let f be the function given by f(x) = 2x +3x^2 Evaluate (1/3)
Answer: So, the value of the function f(x) = 2x + 3x^2 when x = 1/3 is 1.
Step-by-step explanation: To evaluate the function f(x) = 2x + 3x^2 at x = 1/3, we can substitute the value of x into the function. This gives us:
f(1/3) = 2(1/3) + 3(1/3)^2
Solving this expression following the order of operations, we first solve the exponent:
f(1/3) = 2(1/3) + 3(1/9)
Then we solve the multiplication:
f(1/3) = 2/3 + 3/9
= 6/9 + 3/9
= 9/9
= 1
So, the value of the function f(x) = 2x + 3x^2 when x = 1/3 is 1.
Solve the equation:
3x/5 - 4 = - 6 + x
Enter in your answer as x=
Answer:
x=5
Step-by-step explanation:
Add 4 to both sides to eliminate the constant term on the left side.
53x−4+4=−6+x+4
53x=−2+x
Multiply both sides by 5 to clear the fraction on the left side.
5×53x=5×(−2+x)
3x=−10+5x
Subtract 3x from both sides to collect the variable terms on the right side.
3x−3x=−10+5x−3x
0=−10+2x
Add 10 to both sides to eliminate the constant term on the right side.
0+10=−10+2x+10
10=2x
Divide both sides by 2 to get the value of x.
210=22x
5=x
Step-by-step explanation:
3/5 x -4 = -6 + x add 6 to both sides of the equation
3/5 x + 2 = x subtract 3/5 x from both sides
2 = 2/5 x multiply both sides by 5/2
5/2 * 2 = x = 5
Daniel works at an electronics store, and he claims that the popularity of a toaster (measured in number of sales) is inversely proportional to its cost. If 12 customers buy a toaster that costs $, according to Daniel's theory, how many customers would buy a toaster that costs $750?
According to Daniel's theory, 18 customers would buy a toaster that costs $750.
How to find how many customers would buy a toaster that costs $750If the popularity of a toaster is inversely proportional to its cost, we can set up a proportion as:
popularity of toaster 1 / cost of toaster 1 = popularity of toaster 2 / cost of toaster 2
Let's let x be the number of customers who would buy a toaster that costs $750.
We can write:
12 / 500 = x / 750
Simplifying:
12(750) = 500x
9000 = 500x
x = 18
Therefore, according to Daniel's theory, 18 customers would buy a toaster that costs $750.
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The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam. Passed exam Did not pass exam Row Totals Completed exam review 55% 10% 65% Did not complete exam review 20% 15% 35% Column Totals 75% 25% 100% Part A: What is the percentage of students who passed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points) Part B: What is the percentage of students who passed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points) Part C: Is there an association between passing the exam and completing the exam review? Justify your answer. (2 points)
A. The percentage of students who passed the exam and completed the exam review is given as 55%.
B. The percentage of students who did not complete the exam review and passed the exam is given as 20%.
C. There is most probably an association between completing the exam review and passing the exam.
Part A:
The percentage of students who passed the exam and completed the exam review is given as 55%.
Part B:
The percentage of students who did not complete the exam review and passed the exam is given as 20%.
Part C:
The percentage of students who passed the exam and completed the exam review is 55%, while the percentage of students who passed the exam and did not complete the exam review is 20%.
These percentages are significantly different from each other, indicating that there is likely an association between completing the exam review and passing the exam.
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Chicken that costs $2.29 is being marked up 12%. If Scott buys 4 lbs of chickens how much will he pay?
Scott will pay $10.26 for 4 lbs of chicken.
What is unitary method?
Simply put, the unitary method is used to find the value of one unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here. This method is mainly used for the concept of ratio and proportion.
Given,the chicken costs $2.29 and it's being marked up by 12%.
Then the new price of the chicken will be
[tex]2.29 + (2.29 \times 0.12) = 2.29 + 0.275 = 2.565[/tex]
So, the price of the chicken per pound will be $2.565 / 1 lb = $2.565.
By the concept of unitary method ,If Scott buys 4 lbs of chicken, then the total cost will be 4 lbs x $2.565/lb = $10.26
Therefore, Scott will pay $10.26 for 4 lbs of chicken.
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Consider the function f(x) = 5x² - 8x +7, 0≤ x ≤ 8.
The absolute maximum of f(x) (on the given interval) is at x =
and the absolute minimum of f(x) (on the given interval) is at x =
Answer:
maximum: x = 8minimum: x = 0.8Step-by-step explanation:
You want the x-coordinates of the absolute extrema of the function f(x) = 5x² -8x +7 on the interval [0, 8].
Absolute extremaThe absolute extrema of a function on an interval will lie at the ends of the interval or at a turning point within the interval.
For a quadratic ax²+bx+c, the turning point is at x=-b/(2a). For the given function, the turning point is at ...
x = -(-8)/(2·5) = 0.8
This lies within the interval, and represents the location of the absolute minimum of this function whose graph opens upward.
Interval endsThe graph of the function is symmetrical about the vertical line through the turning point. The function increases as x-values are farther from the turning point, so the end of the interval farthest from x = 0.8 will be the location of the absolute maximum. That is at x = 8.
The absolute minimum at x = 0.8; the absolute maximum is at x = 8.
Need help asap please!
Answer: with what?
Step-by-step explanation:
Explain what you need help with pls.
Simplify the expression:
-2(x + 3) + 4(x + y -2) + -y
Answer: -3 x y + x + 4.
Step-by-step explanation:
Hurry! With 2 pairs of jeans AB 4 shirts CDEF and 2 pairs of shoes GH how many different outfits are possible? Use a tree diagram show the possibilities
Answer:
Step-by-step explanation:
To calculate the total number of different outfits possible, we can use the multiplication principle of counting. We multiply the number of choices for each item together to get the total number of outfits.
Number of choices for jeans: 2 (pair of jeans AB)
Number of choices for shirts: 4 (shirts CDEF)
Number of choices for shoes: 2 (pair of shoes GH)
Total number of outfits: 2 x 4 x 2 = 16
Here's a tree diagram showing the possibilities:
modify it
Jeans Shirt Shoes
/\ /\ /\
/ \ / \ / \
A B C D G H
/ \ / \ / \
CDEF CDEF CDEF CDEF CDEF CDEF
/ \ / \ / \ / \ / \ / \
GHGH GHGH GHGH GHGH GHGH GHGH
The tree diagram shows that there are 2 choices for jeans (A or B), 4 choices for shirts (C, D, E, or F), and 2 choices for shoes (G or H). We can follow the branches of the tree to see all the possible outfit combinations, which total to 16.
Sue received $20,000 as an inheritance from her uncle. He stipulated that she save this money for her 2 children’s college education. She would like to have $50,000 saved up in 10 years. What annual interest must she earn in order to reach this goal (she will make no additional deposits to this account)?
Sue must earn an annual interest rate of 6.9% on the $20,000 in order to reach her goal of saving $50,000 in 10 years.
What is amount?Amount If you wish to make an additional deposit to this account, you must first provide the amount you wish to deposit. Once the amount has been provided, you will be able to make the deposit. Please note that all deposits must be made in accordance with applicable laws and regulations.
In order to reach her goal of saving $50,000 in 10 years, Sue must earn an annual interest rate of 6.9%. This rate is calculated by using the formula A = P (1 + r)ⁿ, where A is the future amount, P is the present amount, r is the rate of interest, and n is the number of years.
In this case, Sue has a present amount of $20,000 and a future amount of $50,000. Therefore, the formula becomes $50,000 = $20,000 (1 + r)^10. Solving for r, the rate of interest is 6.9%. This means that Sue must earn an annual interest rate of 6.9% on the $20,000 in order to reach her goal of saving $50,000 in 10 years.
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Help on questions 10 and 11
The margin of error, using a 95% confidence level is 0.026. The Option C.
What is the margin of error for this case?The margin of error can be calculated using the formula which is "Margin of Error = Critical Value * Standard Deviation"
Given:
Sample proportion is 26%
Sample size is 1100
We can then calculate the Standard Deviation as follows:
= sqrt((p * (1 - p)) / n)
Plugging in the values, we get:
= sqrt((0.26 * (1 - 0.26)) / 1100)
= sqrt (0.00017490909)
= 0.01322497637
≈ 0.013
We must find Critical Value for a 95% confidence level. For a normal distribution, the Critical Value is approximately 1.96. Now, we can calculate the Margin of Error which is
= Critical Value * Standard Deviation
= 1.96 * 0.013
≈ 0.026
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find the probability that a randomly selected point within the circle falls in the red shaded area 106
Answer:
0.29
Step-by-step explanation:
Knowing that the shaded angle is 106 degrees, and a circle's angle total is 360 degrees, we will know what fraction of the circle is shaded by dividing the shaded region's angle by the angle of an entire circle:
106/360 = 0.29
The fraction of the circle that is shaded is also the probability that a randomly selected point within the circle falls in the shaded region since we just divided the desired outcome by all of the possible outcomes.
Find the distance between the two points rounding to the nearest tenth (if necessary). (-3, -3) and (-6, 1)
The distance between the points (-3, -3) and (-6, 1) is 5 units
We know that the distance formula between two points (x₁, y₁) and (x₂, y₂) is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
We need to find the distance between the points (-3, -3) and (-6, 1)
Let us assume that (x₁, y₁) = (-3, -3)
and (x₂, y₂) = (-6, 1)
Using above distance formula, the distance between the points (-6,7) and (-1,1) would be,
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(1 - (-3))² + ((-6) - (-3))²]
d = √[(1 + 3)² + (-6 + 3)²]
d = √[(4)² + (-3)²]
d = √[16 + 9]
d = √(25)
d = 5 units
This is the required distance.
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Which choice shows 9 + (6 + 3) correctly rewritten using the associative property
and then correctly simplified?
O (9+6) + 3 = 9+9=18
O (9+6) + 3 = 15 + 3 = 18
O 3+ (9+6)= 3+15= 18
O 6+ (9 + 3) = 6 + 12 = 18
The associative property of 9 + (6 + 3) is 6+ (9 + 3) and it's simplified as 6+12 = 18.
What is associative property?The associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result.
For example, a+(b+c) is the same as b+(a+c). If a,b,c are real numbers.
This means that 9 + (6 + 3) can also be written as
6+ (9 + 3). The two expression must give thesame result.
6+ (9 + 3) = 6+ 12 = 18
Therefore the associative property of 9 + (6 + 3) is 6+ (9 + 3) and it's simplified as 6+12 = 18
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A doll sold for $228 in 1975 and was sold again in 1986 for $472. Assume that the growth in the value V of the collector's item was exponential.
a) Find the value k of the exponential growth rate. Assume V₁ = 228.
(Round to the nearest thousandth.)
The value k of the exponential growth rate will be 0.045.
Given that:
$228 in 1975
$472 in 1986
Let 'x' be the number of years and 'y' be the selling price. Then the equations are given as,
[tex]\rm 288 = P_o \times e^{k *1975} \ \ \ \ \ \ ...(1)\\\\\rm 472 = P_o \times e^{k *1986} \ \ \ \ \ \ ...(2)[/tex]
From equations (1) and (2), then
[tex]e^{k(1986 - 1975)} = \dfrac{472}{288}\\\\e^{k(1986 - 1975)} = 1.63889[/tex]
Take log on both sides, then
k x (11) = ln 1.63889
k = 0.494/11
k = 0.045
The value k of the exponential growth rate will be 0.045.
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Working with the Future Value of a Single-Payment Annuity
Use the formula to solve the following problems.
fv=P(1+r)n
where P is the principal, r is the periodic interest rate,
and n is the number of compounding periods.
1. After 10 years, what is the value of an annuity in which you invest $10,000 at
an APR of 4%? Assume interest is compounded annually.
Type answer here...
In the given problem, solving using the given formula, after ten years, the value of the annuity in which you put $10,000 at a 4% annual interest rate is roughly $14,802.42.
How to Solve the Problem?The given formula to solve the problem is fv=P(1+r)n.
Where:
P = $10,000 (the principal)
r = 0.04 (the annual interest rate)
n = 10 (the number of years)
Furthermore, plugging in the values into the formula, we have:
fv = P(1+r)^n
= $10,000(1+0.04)^10
= $14,802.42 (rounded to two decimal places)
In conclusion, the ten-year value of a annuity of $10,000 with a 4% annual interest rate will approximately be $14,802.42.
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