The ratio of their radii is 8/2 = 4.
What is ratio?Ratio is a comparison of two or more quantities expressed in terms of their relative sizes. It is a way to express one number as a fraction of another number. For example, if a person has three apples and two oranges, the ratio of apples to oranges can be expressed as 3:2. Ratios can also be expressed as fractions or percentages.
To show that Circle D and Circle E are similar, we need to determine if the ratio of their radii is equal to the ratio of their distances from the origin. The ratio of their radii is 8/2 = 4. The distance from the origin for Circle D is sqrt((8)²+ (-2)²) = sqrt(64 + 4) = sqrt(68) = 8.24. For Circle E, the distance from the origin is sqrt((5)² + (1)²) = sqrt(26) = 5.1. The ratio of their distances from the origin is 8.24/5.1 = 1.61. Since the ratio of their radii (4) is equal to the ratio of their distances from the origin (1.61), we can conclude that Circle D and Circle E are similar.
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Solve by using elimination. Express your answer as an ordered pair.
(7x+2y=5
(3x + 2y = -15
Answer:
x=5, y=-15
Step-by-step explanation:
7x+2y=5
3x+2y=-15
4x=20
x=5
7(5)+2y=5
2y=-30
y=-15
lify (x3y3)31(32x13y18)312xy32xy2xy32x2x3y534xy2x3y534x
The simplified expression is x^(454)y^(584) * 2^(109).
To simplify the given expression, we need to use the laws of exponents. The laws of exponents are:
- (a^m)^n = a^(mn)
- a^m * a^n = a^(m+n)
- a^m / a^n = a^(m-n)
Using these laws, we can simplify the given expression as follows:
(x^3y^3)^31 * (32x^13y^18)^31 / (2xy^3)^2 * (2xy^3)^2 * (2x)^2 * (2x^3y^5)^3 * (4xy)^5 * (2x^3y^5)^3 * (4x)^5
= x^(3*31)y^(3*31) * 32^31x^(13*31)y^(18*31) / 2^2x^2y^(3*2) * 2^2x^2y^(3*2) * 2^2x^2 * 2^(3*2)x^(3*3)y^(5*3) * 4^5x^5y^(5*5) * 2^(3*2)x^(3*3)y^(5*3) * 4^5x^5
= x^(93)y^(93) * 32^31x^(403)y^(558) / 2^6x^6y^6 * 2^6x^6y^6 * 2^2x^2 * 2^6x^9y^15 * 4^5x^5y^25 * 2^6x^9y^15 * 4^5x^5
= x^(93+403)y^(93+558) * 32^31 / 2^6 * 2^6 * 2^2 * 2^6 * 4^5 * 2^6 * 4^5 * x^(6+6+2+9+5+9+5) * y^(6+6+15+25+15)
= x^(496)y^(651) * 32^31 / 2^(6+6+2+6+6) * 4^(5+5) * x^42 * y^67
= x^(496-42)y^(651-67) * 32^31 / 2^26 * 4^10
= x^(454)y^(584) * 32^31 / 2^26 * 4^10
= x^(454)y^(584) * 2^(5*31) / 2^26 * 2^(2*10)
= x^(454)y^(584) * 2^(155) / 2^(26+20)
= x^(454)y^(584) * 2^(155-46)
= x^(454)y^(584) * 2^(109)
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List the members of the following sets: (2 marks)
y|y=(x/x+1), x ϵ Z+, x<12) (Hint: 0 is considered a positive integer)
{x | x is the square of a whole number and x < 100} (Hint: Whole numbers include all positive integers along with zero)
The members of the second set are 0, 1, 4, 9, 16, 25, 36, 49, 64, and 81.
The members of the first set, y|y=(x/x+1), x ϵ Z+, x<12, are the values of y that satisfy the given equation and conditions. The members of the second set, {x | x is the square of a whole number and x < 100}, are the values of x that satisfy the given conditions.
For the first set, we need to find the values of y that satisfy the equation y=(x/x+1) for positive integers x less than 12. The values of x that satisfy this condition are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. We can plug these values into the equation to find the corresponding values of y:
y = (1/1+1) = 0.5
y = (2/2+1) = 0.6667
y = (3/3+1) = 0.75
y = (4/4+1) = 0.8
y = (5/5+1) = 0.8333
y = (6/6+1) = 0.8571
y = (7/7+1) = 0.875
y = (8/8+1) = 0.8889
y = (9/9+1) = 0.9
y = (10/10+1) = 0.9091
y = (11/11+1) = 0.9167
Therefore, the members of the first set are 0.5, 0.6667, 0.75, 0.8, 0.8333, 0.8571, 0.875, 0.8889, 0.9, 0.9091, and 0.9167.
For the second set, we need to find the values of x that are the square of a whole number and less than 100. The whole numbers that satisfy this condition are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We can square these values to find the corresponding values of x:
x = 0^2 = 0
x = 1^2 = 1
x = 2^2 = 4
x = 3^2 = 9
x = 4^2 = 16
x = 5^2 = 25
x = 6^2 = 36
x = 7^2 = 49
x = 8^2 = 64
x = 9^2 = 81
Therefore, the members of the second set are 0, 1, 4, 9, 16, 25, 36, 49, 64, and 81.
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Use the image to determine the line of reflection. Graph of polygon ABCDE with point E at negative 6 comma 3. A second polygon A prime B prime C prime D prime E prime with E prime at negative 6 comma negative 1. Reflection across x = −6 Reflection across y = 1 Reflection across the x-axis Reflection across the y-axis
The point E' will have a y-value of -1 instead of 3 and x-value of 6 instead of -6.
What is a polygon?A polygon is a two-dimensional shape composed of straight line segments that close in a loop to form a single shape. Generally, polygons have three or more sides and angles. Depending on the number of sides, polygons can be classified as triangles, quadrilaterals, pentagons, hexagons, and so on.
A reflection across the x-axis of the graph of polygon ABCDE with point E at (-6,3) would result in the creation of a second polygon A'B'C'D'E' with E' at (-6,-1). This is because the reflection flips the points across the x-axis, meaning all of the y-values of the points will be converted to the opposite sign. Therefore, in the new polygon, point E' will have a y-value of -1 instead of 3. This is because the reflection across the x-axis will cause the y-values of each point to flip signs, with the y-value of E increasing from -3 to -1.
Similarly, a reflection across the y-axis of polygon ABCDE with point E at (-6,3) would result in the creation of polygon A'B'C'D'E' with E' at (6,1). This is because the reflection flips the points across the y-axis, meaning all of the x-values of the points will be converted to the opposite sign. Therefore, in the new polygon, point E' will have an x-value of 6 instead of -6. This is because the reflection across the y-axis will cause the x-values of each point to flip signs, with the x-value of E increasing from -6 to 6.
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Answer:
Reflection across y = 1
Step-by-step explanation:
i got this right on the flvs test!
5. CREATE A GRAPH AND WRITE AN
EQUATION to represent the list of
ordered pairs listed below. y = mx
+ b
(2, -3) (1, -1) (-1, 3) (3, -5)
To create a graph and write an equation to represent the list of ordered pairs given, we need to plot each point on a coordinate system.
x | y
--|--
2 |-3
1 |-1
-1| 3
3 |-5
Plotting these points on a coordinate plane, we get:
![Graph of ordered pairs]
To write an equation to represent these ordered pairs in the form y = mx + b, we need to find the slope of the line and the y-intercept.
To find the slope:
m = (y2 - y1) / (x2 - x1)
Let's use the points (1, -1) and (3, -5) to find the slope:
m = (-5 - (-1)) / (3 - 1)
m = -4 / 2
m = -2
Now that we know the slope, we can use any point and the slope to find the y-intercept (b).
Using the point (1, -1):
y = mx + b
-1 = (-2)(1) + b
b = 1
So the equation that represents these ordered pairs in the form y = mx + b is:
y = -2x + 1
And the graph of this equation looks like:
![Graph of equation y = -2x + 1]
You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.49. Thus you are performing a two-tailed test. Your sample data produce the test statistic z=2.517z=2.517. Find the p-value accurate to 4 decimal places.
p-value =
The p-value for our test is 0.0120, accurate to 4 decimal places.
We are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.49. We are performing a two-tailed test and our sample data produce the test statistic z=2.517.
To find the p-value, we need to use a standard normal distribution table or calculator. We will use the table for this answer.
The first step is to find the area to the left of the test statistic z=2.517 in the standard normal distribution table. This gives us the probability of obtaining a z-score less than or equal to 2.517. The closest value in the table is 2.51, which gives us an area of 0.9940.
Since we are conducting a two-tailed test, we need to find the area in both tails of the distribution. To do this, we subtract the area to the left of the test statistic from 1: 1-0.9940 = 0.0060. This gives us the area in the right tail of the distribution.
Finally, we multiply this value by 2 to get the p-value for our two-tailed test: 0.0060 * 2 = 0.0120.
Therefore, the p-value for our test is 0.0120, accurate to 4 decimal places.
p-value = 0.0120
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Michael, a farmer, wants to buy a new tractor using the US$ he received from his daughter in America for his birthday. The price of the tractor is R160 000, VAT excluded. b) If the exchange rate is US$1 = R17.96, calculate how much USS Michel must change for him to pay cash for the tractor. Round off your answer to the nearest USS.
For Michael to pay cash for the tractor priced at R160,000 with the exchange rate as US$1 = R17.96, the amount he must change is US$8,908. 69.
What is an exchange rate?An exchange rate is the unit rate at which one country's currency is exchanged for another.
Exchange rates are based on a country's economic performance or indices in comparison to other countries.
The price of the tractor = R160,000
Exchange Rate: US$ = R17.96
R160,000 = US$8,908. 69 (R160,000/R17.96)
Thus, Michael needs to exchange US$8,908. 69 to purchase the tractor costing R160,000.
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5. Write an expression for the area of a rectangle with length & and width w.
6. Imagine dilating the rectangle with length & and width w by a factor of k.
7. Write an expression for the area of the dilated rectangle.
8. Use your work to draw a conclusion about what happens to the area of a rectangle when it's dilated by a scale factor of k.
5. The expression fοr the area of a rectangle with length l and width w is l × w.
What is a rectangle?
In Euclidean plane geοmetry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all οf its angles are equal.
5. The area of a rectangle is given by the prοduct of its length and width. Therefore, the expressiοn for the area of a rectangle with length l and width w is:
Area = l x w
6. Imagine dilating the rectangle with length & and width w by a factοr of k.
⇒ (l × k) × (w × k)
7. An expression fοr the area of the dilated rectangle.
⇒ l × w × k²
⇒ k²lw
8. Vοlume = l × w
Volume' = k²lw
Then we have
Volume/Volume' = (l × w)/k²lw
Vk²lw = V'lw
Divide bοth sides by lw
Vk² = V'
Thus, The area ο a rectangle when it's dilated by a scale factor of k will be dilated k² times
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The average rate of change of f(x) = x² = x + 4 from x= 2 to x = 4 is
A)2
B)10
C)5
D)3
Answer: 7
Step-by-step explanation: The average rate of change of a function f(x) over an interval [a,b] is defined as the ratio of “change in the function values” to the "change in the endpoints of the interval"1. In other words, it is the slope of the line that passes through two points on the graph of f(x)2.
To find the average rate of change of f(x) = x² + x + 4 from x = 2 to x = 4, we can use this formula:
Average rate of change = [f(4) - f(2)] / (4 - 2)
First, we need to plug in x = 4 and x = 2 into f(x) and simplify:
f(4) = (4)² + (4) + 4 f(4) = 16 + 8 f(4) = 24
f(2) = (2)² + (2) + 4 f(2) = 4 + 6 f(2) = 10
Next, we need to subtract f(2) from f(4), and divide by (4 - 2):
Average rate of change = [24 - 10] / (4 - 2) Average rate of change = 14 / 2 Average rate of change = 7
Joseph places $5,500 in a savings account for 30 months. He earns $893.75 in interest. What is the annual interest rate?
The annual interest rate is 6.5%
How to calculate the annual interest rate?The first step is to write out the parameters given in the question
Joseph places $5500 in a savings account for 30 months
He rans $893.75 in interest
The annual interest rate can be calculated by multiplying the amount in the savings by the number of months which is 30
= 5500 × 30y
= 165,000y
= 165,000y/12
= 13,750y
Equate 13,750y with the amount of interest
13,750y= 898.75
y= 898.75/ 13,750
y= 0.065 × 100
= 6.5%
Hence the annual interest rate is 6.5%
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a 20
b 15
c 5
d 10
i need sum help on this real quick
Answer:
C
Step-by-step explanation:
6x° and 60° form a right angle and sum to 90° , that is
6x + 60 = 90 ( subtract 60 from both sides )
6x = 30 ( divide both sides by 6 )
x = 5
The rate of change of f(x) = 2(2) is __ the rate of change of the function in the graph:
A. equal to
B. less than
C. greater than
The rate of change of f(x) = 2(2) is equal to the rate of change of the function in the graph.
What is a function?A function is a relation between two sets of values in mathematics. It is a mathematical process that takes an input and produces an output. It is represented as an equation which describes the relationship between the input and the output. A function can also be used to represent a mathematical rule or procedure that takes a set of inputs and produces a set of outputs.
The rate of change, or slope, is the measure of how quickly one variable changes when the other changes. In the graph, the rate of change is a constant, meaning that for every one unit the x-value increases the y-value increases by two. This is the same as the rate of change of f(x) = 2(2), as for every two units the x-value increases the y-value increases by four. Both the graph and the equation of the function have a constant rate of change which is equal to two, so the rate of change of f(x) = 2(2) is equal to the rate of change of the function in the graph.
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A coin with P[H]=0. 3 is flipped 3 times. Define N to be the total number of heads. Find the CDF FN(n), the cumulative distribution function for N. (please provide an explanation for the answer)
The cumulative distribution function for N when a coin is flipped 3 times with P[H]=0. 3 is given by ,
F(N≤ 0) = 0.343 , F(N≤1) = 0.784 , F(N≤2) = 0.973 , F(N≤3) = 1.000.
Cumulative distribution function (CDF) of N,
Probability of getting n or fewer heads in three coin flips,
(All values of n from 0 to 3)
Probability of getting exactly n heads in three flips.
Apply binomial distribution,
P(N = n) = ³Cₙ ×(0.3)ⁿ × (0.7)³⁻ⁿ
For cumulative distribution function, add up the probabilities of getting 0, 1, 2, or 3 heads in three flips,
F(N≤ 0)
=P(N=0)
=³C₀ × (0.3)⁰ × (0.7)³
= 1 × 1 × 0.343
= 0.343
For F(N≤1) is equal to,
⇒F(N≤1)
= P(N=0) + P(N=1)
= ³C₀ × (0.3)⁰ × (0.7)³ + ³C₁ × (0.3)¹ × (0.7)²
= 0.343 + 0.441
= 0.784
F(N ≤ 2)
= P(N=0) + P(N=1) + P(N=2)
= ³C₀ × (0.3)⁰ × (0.7)³
+ ³C₁ × (0.3)¹ × (0.7)²
+³C₂ × (0.3)² × (0.7)¹
= 0.343 + 0.441 + 0.189
= 0.973
This implies CDF for N is equal to,
F(N ≤n) = [tex]\sum_{0}^{x}[/tex]³Cₓ × (0.3)ˣ × (0.7)³⁻ˣ
And F(N≤3) is equal to,
⇒F(N≤3)
= P(N=0) + P(N=1) + P(N=2) + P(N=3)
= ³C₀ × (0.3)⁰ × (0.7)³
+ ³C₁ × (0.3)¹ × (0.7)²
+ ³C₂ × (0.3)² × (0.7)¹
+ ³C₃× (0.3)³ × (0.7)⁰
= 0.343 + 0.441 + 0.189 + 0.027
= 1.000
Therefore, the cumulative distribution function for N is equal to,
F(N≤ 0) = 0.343
F(N≤1) = 0.784
F(N≤2) = 0.973
F(N≤3) = 1.000
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Point X is located at (3, 2). Point Y is located at (3, -8). What is the distance form point X to point Y.
In response to the aforementioned query, we may say that D is equal to equation sqrt((3 - 3)2 + (-8 - 2)2 = sqrt(0 + (-10)2) = sqrt(100) = 10. As a result, it takes 10 units to get from position X to point Y.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The distance formula may be used to determine the separation between two points:
Sqrt((x2 - x1) + (y2 - y1)) = sqrt(d)
where d is the distance between the two locations, and (x1, y1) and (x2, y2) are the coordinates of the two points.
We may get the separation between points X at (3, 2) and Y at (3, -8), using the following formula:
D is equal to sqrt((3 - 3)2 + (-8 - 2)2 = sqrt(0 + (-10)2) = sqrt(100) = 10.
As a result, it takes 10 units to get from position X to point Y.
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Plssss solve them all
The table can be filled up accordingly:
1. 5 years compounded semi-annually:
b = (1 + 0.06/2)
y= 1800 (1 + 0.03)^10
x = 2
2. For the 5 years compounded quarterly:
b = (1 + 0.06/4)
y = 1800 (1 + 0.015)^20
x =4
3. For the 5 years compounded monthly:
b = (1 + 0.06/12)
y = 1800 (1.005)^60
x = 12
4. For 10 years compounded annually:
b = (1 + 0.06/1)
x = 1800 (1.06)^10
y = 1
5. For 10 years compounded quarterly:
b = (1 + 0.06/4)
y =1800 (1 + 0.005)^60
x = 4
6. For 10 years compounded monthly:
b = (1 + 0.06/12)
y = 1800 (1 + 0.005)^120
x = 12
How to solve the interestTo solve the compound interest we use the formula:
P(1+r/n)^(n*t).
For the 5 years compounded semi-annually:
A = 1800 (1 + 0.06/2)^2*5
A = 1800 (1 + 0.03)^10
A = 1800 (1.03)^10
A = 1800 (1.344)
A = 2419
For the 5 years compounded quarterly:
A = 1800 (1 + 0.06/4)^4*5
A = 1800 (1 + 0.015)^20
A = 1800 (1.015)^20
A= 1800 (1.3468)
A= 2424.24
For the 5 years compounded monthly:
A = 1800 (1 + 0.06/12)^12*5
A = 1800 (1 + 0.005)^60
A = 1800 (1.005)^60
A = 1800 (1.34885)
A = 2427.93
For 10 years compounded annually:
A= 1800 (1 + 0.06/1)^10
A = 1800 (1.06)^10
A = 1800 (1.7908)
A = 3223.53
For 10 years compounded semi-annually:
A = 1800 (1 + 0.06/2)^20
A = 1800 (1 + 0.03)^20
A = 1800 (1.03)^20
A =1800 (1.806)
A = 3251
For 10 years compounded quarterly:
A= 1800 (1 + 0.06/4)^4*10
A = 1800 (1 + 0.015)^40
A= 1800 (1.015)^40
A = 1800 (1.814)
A = 3265.23
For 10 years compounded monthly:
A= 1800 (1 + 0.06/12)^120
A = 1800 (1 + 0.005)^120
A = 1800 (1.005)^20
A= 1800 (1.8194)
A = 3274.9
The best pay period is that with the highest returns which is 10 years compounded monthly.
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State your yes/no research question. Do you play sports? No Make a frequency table with the headings: Frequency Percent Male Female Yes Yes No 16 9 7 14 Is it better to use frequencies or percentages to compare groups when you make your graph? Percentages are better to use when comparing the groups. Gramm: Please relo for Gramme Construct a side by side bar graph showing the men's and women's responses to your question. What do your graphs indicate about students? 5 points
Yes, it is better to use percentages to compare groups when making a graph. This is because percentages allow for a more accurate comparison of the data, as they take into account the relative size of each group. If we only use frequencies, we may get a skewed view of the data, as one group may be much larger than the other.
Here is the side by side bar graph showing the men's and women's responses to the question "Do you play sports?":
Gender Yes No
Male 9 7
Female 7 14
The graph indicates that a higher percentage of males play sports compared to females. However, it also shows that there are more females who do not play sports compared to males. This suggests that there may be a gender difference in the participation of sports among students.
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How do I do this I’ve tried so many times please help
Answer:
100°
Step-by-step explanation:
∠A and ∠B are supplementary angles, which means:
∠A° + ∠B° = 180°
[tex](2x) + (2x + 20) = 180[/tex]
Expand the parenthesis and solve for x:
[tex]2x + 2x + 20 = 180[/tex]
[tex]4x + 20 = 180[/tex]
[tex]4x = 180 - 20[/tex]
[tex]4x = 160[/tex]
[tex]x = \frac{160}{40}[/tex]
∴[tex]x = 40[/tex]
Substitute the value of x to determine the measurement of ∠B:
[tex]2(40) + 20[/tex]
[tex]80 + 20[/tex]
= 100°
A circle has a radius of \( 11 \mathrm{in} \). Find the length \( s \) of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians. Do not round any intermediate computations, and round y
The length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).
To find the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \), we can use the formula for arc length: \( s = r\theta \), where \( s \) is the arc length, \( r \) is the radius of the circle, and \( \theta \) is the central angle in radians.
Plugging in the given values, we get:
\( s = (11 \mathrm{in})(\frac{\pi}{2}) \)
Simplifying, we get:
\( s = \frac{11\pi}{2} \mathrm{in} \)
Therefore, the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).
Note: If the question asks for the answer to be rounded, you can use a calculator to find the approximate value of \( \frac{11\pi}{2} \) and round to the desired number of decimal places. For example, if the question asks for the answer to be rounded to the nearest tenth, the answer would be \( 17.3 \mathrm{in} \).
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Kendra’s water bottle contains 2 quarts of water.she wants to add drink mix to it, but he directions for the drink mix give the amount of water in fluid ounces.how many fluid ounces are in her bottle
By answering the above question, we may infer that So Kendra's water equation bottle holds 64 fluid ounces.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The volume of a quart is 32 fluid ounces. Kendra's water bottle, which holds 2 quarts of water, therefore has:
64 fluid ounces are equal to 2 quarts when each is 32 fluid ounces.
So Kendra's water bottle holds 64 fluid ounces.
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A contractor bids a job at $680 for materials plus $42 per hour
for labor. The total cost for the job can be modeled by: C = 42H +
680.
Find the number of hours that he has for the job if the owner wo
The contractor has 5.95 hours for the job if $930 is spent by him.
The total cost for the job can be modeled by C = 42H + 680, where C is the total cost of the job, H is the number of hours of labor, and 680 is the cost of materials.
If the owner wants to spend $930 for the job, then the number of hours that the contractor has for the job can be found by solving the equation C = 42H + 680 for H.
Thus, 42H + 680 = 930. Subtracting 680 from both sides gives 42H = 250. Dividing both sides by 42 gives H = 250/42 = 5.95 hours.
Therefore, the contractor has 5.95 hours for the job if the owner wants to spend $930.
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Evaluating Trigonometric Functions In Exercises 15-30, find the exact values of the sine, cosine, and tangent of the angle.
15. 105 deg = 60 deg + 45 deg
17. 195 deg = 225 deg - 30 deg
19. (11pi)/12 = (3pi)/4 + pi/6
12 21. - pi/12 = pi/6 - pi/4
23. 75°
25.-285°
27. (13pi)/12
222 29. - (7pi)/12
16. 165 deg = 135 deg + 30 deg
18. 255 deg = 300 deg - 45 deg
20. (17pi)/12 = (7pi)/6 + pi/4
22. - (19Y)/12 = (2pi)/3 - (9pi)/4
24. 15°
26.-165°
28. (5pi)/12
30. - (13pi)/12
For 15:
Sine: √2/2
Cosine: √2/2
Tangent: 1
For 17:
Sine: -1/2
Cosine: √3/2
Tangent: -1/√3
For 19:
Sine: (1+√3)/2
Cosine: (1-√3)/2
Tangent: √3
For 21:
Sine: -1/2
Cosine: -√3/2
Tangent: 1/√3
For 23:
Sine: √3/2
Cosine: 1/2
Tangent: √3
For 25:
Sine: -√2/2
Cosine: -√2/2
Tangent: -1
For 27:
Sine: (1-√3)/2
Cosine: (1+√3)/2
Tangent: -√3
For 29:
Sine: -(√3-1)/2
Cosine: (1+√3)/2
Tangent: -√3
For 16:
Sine: √3/2
Cosine: -1/2
Tangent: -√3
For 18:
Sine: -√2/2
Cosine: √2/2
Tangent: -1
For 20:
Sine: (√3-1)/2
Cosine: (1+√3)/2
Tangent: √3
For 22:
Sine: -(1+√3)/2
Cosine: (√3-1)/2
Tangent: -1/√3
For 24:
Sine: 1/2
Cosine: √3/2
Tangent: 1/√3
For 26:
Sine: √2/2
Cosine: -√2/2
Tangent: 1
For 28:
Sine: (√3+1)/2
Cosine: (1-√3)/2
Tangent: -1/√3
For 30:
Sine: -(1-√3)/2
Cosine: (√3+1)/2
Tangent: √3
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1/2 + 3y = y/5 what number is y in this equation
The solution to the equation 1/2 + 3y = y/5 is y = -3/14.
What is the linear equation in one variable?
A linear equation in one variable is an equation that can be written in the form:
ax + b = 0
where x is the variable, a and b are constants, and a is not equal to zero. The solution to the equation is the value of x that makes the equation true.
To solve for y in the equation 1/2 + 3y = y/5, we need to isolate y on one side of the equation.
First, we can simplify the left side of the equation by combining the like terms:
1/2 + 3y = (6/10) + (30y/10) = (6 + 30y)/10
Now we can rewrite the equation as:
(6 + 30y)/10 = y/5
To solve for y, we can start by multiplying both sides of the equation by 10, to eliminate the denominators:
6 + 30y = 2y
Next, we can simplify by subtracting 2y from both sides:
6 + 28y = 0
Finally, we can solve for y by subtracting 6 from both sides and then dividing by 28:
28y = -6
y = -6/28
Simplifying the fraction, we get:
y = -3/14
Therefore, the solution to the equation 1/2 + 3y = y/5 is y = -3/14.
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Find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets the plane 3x - 5y + 2z = 6. - . - -
The point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets the plane 3x - 5y + 2z = 6 is (4/3, -2/3, -2/3).
To find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets the plane 3x - 5y + 2z = 6, we can use the following steps:
Find the normal vector of the plane 2x - y - z = 4. This is given by the coefficients of the x, y, and z terms, which are 2, -1, and -1, respectively. So the normal vector is (2, -1, -1).
Since the line through the origin is perpendicular to the plane, it must be parallel to the normal vector of the plane. Therefore, the direction vector of the line is (2, -1, -1).
The equation of the line through the origin with direction vector (2, -1, -1) is given by x = 2t, y = -t, and z = -t, where t is a parameter.
Substitute the equations of the line into the equation of the plane 3x - 5y + 2z = 6 to find the value of t:
3(2t) - 5(-t) + 2(-t) = 6
6t + 5t - 2t = 6
9t = 6
t = 2/3
Substitute the value of t back into the equations of the line to find the point of intersection:
x = 2(2/3) = 4/3
y = -(2/3) = -2/3
z = -(2/3) = -2/3
Therefore, the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets the plane 3x - 5y + 2z = 6 is (4/3, -2/3, -2/3).
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Is the equation, y = 9x + 3 a proportional or non-proportional linear relationship?
A chemist has 42 grams of aluminum. There are 2.70 grams/milliliter for aluminum. How many milliliters of aluminum does the chemist have? Set this up either as a proportion or unit analysis.
a. the chemist has 133 milliliters
b. the chemist has 155 milliliters
c. the chemist has 58 milliliters
d. the chemist has 16 milliliters
The 42 grams of aluminum implies that the chemist has 0.06429ml of aluminum
What is density ?The density of material shows the denseness of that material in a specific given area. A material’s density is defined as its mass per unit volume. Density is essentially a measurement of how tightly matter is packed together. It is a unique physical property of a particular object. The principle of density was discovered by the Greek scientist Archimedes. It is easy to calculate density if you know the formula and understand the related units The symbol ρ represents density or it can also be represented by the letter D.
How to determine the amount of aluminum?
The mass is given as: Mass = 42 grams
The density of aluminum is: Density = 2.7 g/cm³
So, we have: Volume = Density/Mass
This gives, Volume = 2.7/42
Evaluate : Volume = 0.06429cm³
Convert to ml
Volume = 0.06429ml
Hence, the chemist has 0.06429ml of aluminum
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PLEASE EXPLAIN AND SHOW WORK
Correct statements are m∠C = m∠F, ΔABC ~ ΔDEF and 3/5 = y/z
What are similar triangles?Similar triangles are triangles that have the same shape but can be of different sizes. All equilateral triangles and squares of any length are examples of similar objects. That is, if two triangles are similar, their corresponding angles are congruent and their corresponding sides have the same proportions. Here, triangle similarity is indicated by the symbol '~'.
Given,
two triangles ABC and DEF
m∠A = m∠D = 40°
m∠B = m∠E = 60°
Sum of all interior angles of a triangle is equal to 180°
m∠A + m∠B + m∠C = m∠D + m∠E + m∠F = 180°
40 + 60 + m∠C = 40 + 60 + m∠F
m∠C = m∠F
All three angles are congruent
By A-A-A rule
ΔABC ~ ΔDEF
ratio of corresponding sides will be equal
6/10 = y/z
3/5 = y/z
Hence, m∠C = m∠F, ΔABC ~ ΔDEF and 3/5 = y/z are the correct statement.
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The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.
Is the relation a function? Explain.
A. No, because for each input there is not exactly one output
B. No, because for each output there is not exactly one input
C. Yes, because for each input there is exactly one output
D. Yes, because for each output there is exactly one input
No function exists in this relation. No, since there isn't always a single output for every input.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Here, we have
Given: The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.
We have to show the relation between a function.
The x-values are entered into the function machine. The function machine generates the y-values after its operations are complete. Any internal function is possible.
A mapping diagram with arrows pointing from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5, as well as two circles with the numbers 0, and labels for the x and y values, respectively
but according to the definition of y, it should give only one value
Hence, it is not a function.
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Image attached - thanks for helping!
Answer:
Ans = (1.50 x 29 movies) + 16
Step-by-step explanation:
y represents total costs
x represents how many movie he rents
$1.50 is the rent of each movie
$16 is the fixed fee
thus
y = 1.50 x + 16
Ans = (1.50 x 29 movies) + 16
Question 7
Find the center and radius of the circle with the equation x² + y² =4
Answer:A
Step-by-step explanation:
because
Suppose that f ( x ) = 7 x − 7 . Complete the following
statements.
As x → 7 − , f ( x ) →
As x → 7 + , f ( x ) →
Based on the calculation we know that
The value of x as 7− is 35.
The value of x as 7+ is 35.
Suppose that f( x ) = 7 x − 7. We can complete the following statements by plugging in the values of x and evaluating the function.
As x → 7 − , f ( x ) → 42 − 7 = 35
As x approaches 7 from the left, the function f(x) approaches 35.
As x → 7 + , f ( x ) → 42 − 7 = 35
As x approaches 7 from the right, the function f(x) also approaches 35.
Therefore, the function f(x) = 7x - 7 has a horizontal asymptote at y = 35 as x approaches 7 from both the left and the right.
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