Therefore;`a < b < c`The sides of the triangle are listed in order from shortest to longest as follows:
`Side a < Side b < Side c`
Let's apply the angle sum property to ∆ABC such that;
`[tex]\angle A + \angle B + \angle C = 180[/tex]`We can now substitute the angle measures provided by the problem statement to get an equation in terms of x such that;`(9x+29)+(93-5x)+(10x+2)=180`Simplify and solve for x:`9x+29+93-5x+10x+2=180`Simplify like terms to get;`14x+124=180`Subtract 124 from both sides of the equation to get;`14x=56`Divide both sides of the equation by 14 to get:`x=4`Now that we know x, we can use it to determine the measures of the angles.
Therefore;`m∠A = 9x + 29 = 9(4) + 29 = 65°``m∠B = 93 - 5x = 93 - 5(4) = 73°``m∠C = 10x + 2 = 10(4) + 2 = 42°`
We are now going to list the sides of the triangle in order from shortest to longest using the information provided in the problem statement. Here's how to do it:
From angle A, we know that the side opposite it, which is side a, is the shortest side of the triangle.
Therefore;`a < b < c
`From angle B, we know that the side opposite it, which is side b, is longer than side a. We can now rewrite our inequality to show the relationship between sides a, b, and c such that;`a < b < c`We can then use the information provided by angle C to figure out which side is the longest. Since angle C is the largest angle of the triangle, we can assume that side c is the longest side.
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Brenda found a store online where he can buy a package of 8-tshirts .these t-shirts sell at the time rate as the t-shirts jacob bought .how much does brendan pay for the package of 8t-shirts?
The amount that Brenda would pay for the 8 t- shirts at the same rate would be $ 37. 60.
How to find the amount paid ?To determine how much Brenda pays for the package of 8 T-shirts, we need to calculate the price per T-shirt based on Jacob's purchase and then multiply it by 8.
Jacob bought 7 T-shirts for $32.90, so the price per T-shirt can be calculated as:
Price per T-shirt = Total cost / Number of T-shirts
Price per T-shirt = $32.90 / 7
Price per T-shirt = $4.70
The cost of 8 shirts is therefore:
Total cost = Price per T-shirt * Number of T-shirts
Total cost = $4.70 x 8
Total cost = $37.60
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Missing detail is:
Jacob bought 7 T shirts for $32.90 Kyle bought 12 T shirts for $60.00
It costs the developer $300,000 to build each townhouse and $450,000 to build each single-family home. Write a function that can be used to determine the minimum cost.
The function for determining the minimum cost of townhouse and single-family home development is min_cost = (num_townhouses x 300000) + (num_homes x 450000).
A function is a self-contained block of code that performs a specific task. In the given problem, we need to determine the minimum cost of developing townhouses and single-family homes. Here, the cost of building a townhouse is $300,000 while the cost of building a single-family home is $450,000. We need to determine the minimum cost by multiplying the number of townhouses and single-family homes by their respective costs.
Therefore, the function for determining the minimum cost of townhouse and single-family home development is given by: min_cost = (num_townhouses x 300000) + (num_homes x 450000) where num_townhouses and num_homes are the number of townhouses and single-family homes, respectively. This function takes two arguments and returns the minimum cost for developing the given number of townhouses and single-family homes.
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Sam road his bike 2/5 of a mile and walked another 3/4 of a mile . How far did he travel ?
The distance Sam traveled is 1.15 miles.
Given: Sam road his bike 2/5 of a mile and walked another 3/4 of a mile.
To find the total distance Sam traveled,
we need to add the distance he traveled while riding his bike to the distance he traveled on foot.
To do that, we need to find a common denominator for 2/5 and 3/4.
The smallest common multiple of 5 and 4 is 20.
So, we'll rewrite 2/5 and 3/4 with a denominator of 20.2/5 = 8/20 (multiply the numerator and denominator by 4)
3/4 = 15/20 (multiply the numerator and denominator by 5).
Now, we can add these two fractions together: 8/20 + 15/20 = 23/20.
So, Sam traveled 23/20 of a mile, which is equivalent to 1 3/20 miles or 1.15 miles (rounded to the nearest hundredth).
Therefore, the distance Sam traveled is 1.15 miles.
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The scatter plot below shows data that were collected to compare the amount of television a student watched (hours per week ) and his or her GPA
A reasonable correlation coefficient for these data would be
The scatter plot shows a comparison between the amount of television watched by students (in hours per week) and their GPA. a reasonable correlation coefficient for these data would be close to 0, indicating a weak or negligible correlation.
Based on the scatter plot, we can observe the general trend of the data points. If the points on the plot are more closely clustered around a straight line, it indicates a stronger correlation between the two variables. Conversely, if the points are more spread out and do not follow a clear pattern, it suggests a weaker correlation. To determine the correlation coefficient, we need to assess the direction and strength of the relationship.
If the data points on the scatter plot exhibit a clear upward or downward trend, it indicates a positive or negative correlation, respectively. The correlation coefficient ranges between -1 and 1, with values closer to -1 or 1 indicating a stronger correlation. A correlation coefficient of 0 indicates no linear relationship. Given that the scatter plot does not show a clear pattern or trend, it suggests a weak or no correlation between the amount of television watched and GPA. Therefore, a reasonable correlation coefficient for these data would be close to 0, indicating a weak or negligible correlation.
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Three minus eleven times a number is more than twenty one minus five times the number (show work)
The solution to the equation is x is less than 1.
Let's assume the number as "x".
The given statement can be translated into an equation as follows:
3 - 11x > 21 - 5x
To solve this equation, we can start by simplifying both sides:
3 - 11x > 21 - 5x
Next, let's gather the terms with x on one side and the constant terms on the other side by adding 11x and subtracting 21 from both sides:
3 - 11x + 11x - 5x > 21 - 5x + 11x - 21
Simplifying further, we get:
-16x > -x
Now, we can divide both sides by -16, but since we are dividing by a negative number, we need to reverse the inequality sign:
-16x / -16 < -x / -16
x < 1
Therefore, the solution to the equation is x is less than 1.
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Milo wants to make a mixture that is 50% lemon juice and 50% lime juice. How much 100% lemon juice should he add to a juice mixture that is 20% lemon juice and 80% lime juice to make 4 gallons of the 50% lemon/50% lime juice mixture? 0. 5 gallon 1. 5 gallons 2 gallons 2. 5 gallons.
To solve this problem, we can set up an equation based on the volume of lemon juice in the mixture:
Let's assume Milo needs to add x gallons of 100% lemon juice.
The total volume of the final mixture is given as 4 gallons, and it should be a 50% lemon juice and 50% lime juice mixture.
The initial mixture contains 20% lemon juice, which means it contains 20% of 4 gallons = 0.2 * 4 = 0.8 gallons of lemon juice.
So, the equation becomes:
0.8 gallons (initial lemon juice) + x gallons (additional 100% lemon juice) = 0.5 * 4 gallons (final lemon juice)
Simplifying the equation:
0.8 + x = 2
Subtracting 0.8 from both sides:
x = 2 - 0.8
x = 1.2
Therefore, Milo needs to add 1.2 gallons of 100% lemon juice to make 4 gallons of the 50% lemon/50% lime juice mixture.
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What is the value of n when 3/5 of n is 27? Enter answer in the box
n = 45 satisfies the equation, and it is the value that makes 3/5 of n equal to 27. The value of n can be determined by setting up an equation based on the given information that 3/5 of n is equal to 27.
By solving the equation, we can find the value of n. Let's set up the equation based on the given information:
(3/5) * n = 27
To solve for n, we need to isolate n on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of 3/5, which is 5/3:
n = 27 * (5/3)
Simplifying the right side of the equation:
n = (27 * 5) / 3
n = 135 / 3
n = 45
Therefore, the value of n is 45. We can confirm this by substituting n = 45 back into the equation:
(3/5) * 45 = 27
(3/5) * 45 = 135/5 = 27
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A hockey goalie loses 235rating points each time his team loses. If his team loses 8 games in a row, what number represents the change in the goalie's rating points?Negative 20 and StartFraction 4 over 5 EndFractionNegative 4 and StartFraction 4 over 5 EndFraction16 and three-fifths20 and four-fifths
The change in the goalie's rating points after his team loses 8 games in a row is -20 and 4/5.
The goalie loses 235 rating points each time his team loses. If his team loses 8 games in a row, we need to calculate the total change in his rating points.
To find the total change, we multiply the loss per game (235) by the number of games lost (8).
235 * 8 = 1880
Therefore, the goalie's rating points decrease by 1880. However, the answer options provided are in mixed number format, so we need to convert 1880 to a mixed number.
To convert 1880 to a mixed number, we divide 1880 by the denominator (5) and express the remainder as the numerator:
1880 ÷ 5 = 376 with a remainder of 0
Hence, the mixed number representation of 1880 is 376 and 0/5, which simplifies to 376.
Therefore, the change in the goalie's rating points after losing 8 games in a row is -376, or in mixed number form, -376 and 0/5, which further simplifies to -376 and 4/5.
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Let b cannot equal 1 and consider the integral 1 to b (6x-9) dx a) what value of b will make this integral equal to 0? b) sketch a graph of y=6x-9 on the interval from x=1 to x=b to verify your answer in (a)
a) To find the value of b that makes the integral equal to 0, we need to solve the integral:
∫(1 to b) (6x - 9) dx = 0
Applying the fundamental theorem of calculus, we can find the antiderivative of the integrand and evaluate it at the limits of integration:
[3x² - 9x] (from 1 to b) = 0
Substituting the limits, we have:
(3b² - 9b) - (3(1)² - 9(1)) = 0
Simplifying further:
3b² - 9b - 6 = 0
Now we can solve this quadratic equation for b using the quadratic formula or factoring:
b² - 3b - 2 = 0
Factoring the quadratic equation, we get:
(b - 2)(b + 1) = 0
Setting each factor to zero, we find two possible values for b:
b = 2 or b = -1.
However, since b cannot equal 1 (as stated in the problem), the only valid solution is b = 2.
b) To verify our answer, we can sketch a graph of y = 6x - 9 on the interval from x = 1 to x = b = 2. The graph will be a straight line with a slope of 6 and y-intercept at -9.
On the interval [1, 2], the line starts at the point (1, -3) and ends at the point (2, 3). By calculating the area under this line, we find that the integral from 1 to 2 of (6x - 9) equals 0, confirming our previous result.
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On Monday, you bought 4 cheeseburgers and 6 fries for $62. Tuesday, you bought 7 cheeseburgers and 4 fries for $76. What is the cost of a (cheeseburger, fry)?
The cost of cheeseburgers = $4
And, The cost of fries = $5
We have,
On Monday, you bought 4 cheeseburgers and 6 fries for $62.
And, On Tuesday, you bought 7 cheeseburgers and 4 fries for $76.
Let us assume that,
The cost of cheeseburgers = x
And, The cost of fries = y
Hence, We get;
4x + 6y = 62 .. (i)
7x + 4y = 76 .. (ii)
From (i);
4x + 6y = 62
2x + 3y = 31 .. (iii)
Multiply by 2 in (ii) and multiply 7 in (iii), then subtract,
8y - 21y = 152 - 217
- 13y = - 65
y = 5
From (i);
4x + 3 (5) = 31
4x + 15 = 31
4x = 31 - 15
4x = 16
x = 4
Thus, The cost of cheeseburgers = $4
And, The cost of fries = $5
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A grocer mixes together some cashews costing $8 per kilogram with some Brazil nuts costing
$10 per kilogram. The grocer sold 12 kg if the mixture for $8.50 per kilogram. How many
kilograms of cashews were in the mixture the grocer sold?
I know the answer is 9 but how do i get that?
9 kilograms of cashews were in the mixture the grocer sold.
To solve the given problem, let x represent the number of kilograms of cashews.
Hence, the number of kilograms of Brazil nuts would be (12 - x) as the grocer sold 12 kg of the mixture.
Therefore, the cost of the cashews at $8 per kilogram is 8(x)
and the cost of the Brazil nuts at $10 per kilogram is 10(12 - x).
Hence, the cost of the mixture at $8.50 per kilogram is:
8.5*(12) = 8(x) + 10(12 - x)
We solve this equation for x:
102 = 8(x) + 120 - 10(x)
2(x)= 18
x = 9
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A Mad Professor has created a new kind of creature called a Blorg. For each Blorg, one hour after it is born, it gives birth to a new Blorg. Two hours after it is born, it gives birth to two more new Blorgs and then it immediately dies. If the Professor starts with one newborn Blorg at noon, how many live Blorgs does he have at 4:05 PM that afternoon after the new Blorgs have been born and the 2-hour-olds have died?
Blorgs have a lifespan of two hours, and after that, they die. The newborn Blorgs continue the reproductive cycle, but all Blorgs born before 3 PM would have reached their lifespan and died by 4:05 PM.
To determine the number of live Blorgs the Mad Professor has at 4:05 PM, we need to understand the pattern of Blorg reproduction and lifespan.
From the given information, we know that one hour after a Blorg is born, it gives birth to a new Blorg. Two hours after birth, it gives birth to two more new Blorgs and then immediately dies.
Let's break down the timeline:
At noon, the Professor has one newborn Blorg.
One hour later, at 1 PM, the initial Blorg gives birth to a new Blorg. So, there are two Blorgs now.
Two hours after birth, at 2 PM, the initial Blorg dies, but the newborn Blorg from 1 PM gives birth to two more Blorgs. So, there are four Blorgs now.
At 3 PM, the two newborn Blorgs from 1 PM give birth to two more Blorgs each, resulting in a total of eight Blorgs.
At 4 PM, the four Blorgs that were born at 2 PM die, while the four Blorgs born at 3 PM are still alive. The four living Blorgs are from the second generation.
Now, let's calculate the number of live Blorgs at 4:05 PM:
At 4 PM, there are four living Blorgs.
Since each Blorg lives for two hours, at 4:05 PM, it has been 5 minutes past their lifespan, and all the living Blorgs from the 3 PM generation would have died.
Therefore, at 4:05 PM, the Mad Professor would have zero live Blorgs.
It is important to note that Blorgs have a lifespan of two hours, and after that, they die. The newborn Blorgs continue the reproductive cycle, but all Blorgs born before 3 PM would have reached their lifespan and died by 4:05 PM.
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Write it as a fact family
12. 4-3. 2=9. 2
The fact family 12, 4, 3, 2, and 9 demonstrates the relationship between addition and subtraction. In this fact family, when we subtract 3 from 4, the result is 1. If we then add 2 to 1, we get 3. Furthermore, when we subtract 2 from 9, the result is 7. If we add 7 and 2 together, the sum is 9.
In the given fact family, the numbers 4 and 3 are related through subtraction. When we subtract 3 from 4, we get 1. This is represented by the equation 4 - 3 = 1.
On the other hand, the numbers 2 and 1 are related through addition. If we add 2 to 1, the sum is 3. This is represented by the equation 1 + 2 = 3.
Similarly, the numbers 9 and 2 are related through subtraction and addition. When we subtract 2 from 9, we get 7, represented by the equation 9 - 2 = 7. By adding 7 and 2 together, the sum is 9, represented by the equation 7 + 2 = 9.
Therefore, the fact family 12, 4, 3, 2, and 9 demonstrates the relationship between addition and subtraction within the given numbers.
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Molly has biweekly gross earnings of $839. 52. By claiming 1 more withholding allowance, Molly would have $16 more in her take home pay. How many withholding allowances does Molly currently claim? a. 1 b. 2 c. 3 d. 4 Please select the best answer from the choices provided A B C D.
Molly currently claims 2 withholding allowances which can be determined by using rules of allowance.
Given that,
Molly has biweekly gross earnings of $839. 52.
By claiming 1 more withholding allowance,
Molly would have $16 more in her take-home pay.
We have to determine,
How many withholding allowances does Molly currently claim?
According to the question,
Molly has biweekly gross earnings of $839. 52.
By claiming 1 more withholding allowance,
Molly would have $16 more in her take-home pay.
The withholding allowance is used by a person to pay less amount of tax on his or her income to the government.
Molly has biweekly gross earnings of $839. 52.
By claiming 1 more withholding allowance,
Molly would have $16 more in her take-home pay.
Therefore,
It is given that Molly has taken 1 more withholding allowance to pay tax less by the amount of $16.
So he must have possessed at least 1 allowance previously and added 1 more.
So, the minimum number of allowance possessed by Molly = 2
Hence, Molly currently claims 2 withholding allowances.
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Walter had new carpeting installed in his 13-foot by 18-foot family room. He paid $7 per square foot for the carpet and $2 per square foot for the pad under the carpet. What was the total cost for the carpet and pad
Walter had new carpeting installed in his 13-foot by 18-foot family room. He paid $7 per square foot for the carpet and $2 per square foot for the pad under the carpet.
The total area of the room will be A
= l × w= 13 × 18= 234 sq. feet The cost of carpet per square feet is $7. The cost of carpeting the family room is:Total cost of carpeting
= Cost of carpet per sq. ft. × Area of the room
= $7 × 234
= $1638The cost of the pad per square feet is $2.Therefore, the cost of padding the family room is: Total cost of padding
= Cost of pad per sq. ft. × Area of the room
= $2 × 234
= $468The total cost of the carpet and pad will be the sum of the cost of the carpeting and the cost of the padding. Total cost of carpet and pad
= Total cost of carpeting + Total cost of padding
= $1638 + $468
= $2106Hence, the total cost of the carpet and pad is $2106.
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Three vertices of parallelogram WXYZ are W(-5,2), X(2,4), and Z(-7, -3). Find the coordinates of vertex Y
The coordinates of Y are (-1,0). Answer: The coordinates of vertex Y are (-1,0).
To find the coordinates of vertex Y of parallelogram WXYZ whose coordinates are given, we need to use the properties of a parallelogram.
A parallelogram is a quadrilateral in which opposite sides are parallel and congruent.
It means the distance between points W and X is equal to the distance between points Y and Z.
W(-5,2), X(2,4), Y(a,b), and Z(-7,-3).
Therefore, the length of side WX is given as,
WX = √ [(2 - (-5))²+ (4 - 2)²]
= √(49 + 4) = √53. ..(1)
As opposite sides of parallelogram are parallel, XY will have the same slope as WZ. The slope of line WZ is given as
(2 - (-3))/(-5 - (-7)) = 5/2.
Therefore, the slope of XY is also 5/2.
(a, b) is on line XY. The equation of line XY can be written as
y - b = 5/2(x - a) ...(2)
It is given that the length of side WZ is equal to the length of side WX. Therefore,
WZ = WX = √53.
Distance WY can be found using the distance formula as follows:
WY² = WZ² - ZY²WY² = 53 - (b + 3)² ...(3)
Similarly, distance XY can be found as,
XY²= WX²- WY²XY²
= 53 - (a - 2)² - (b - 4)² ...(4)
By solving equations (2), (3), and (4) for a and b, we can get the coordinates of Y.a = -1, b = 0
Therefore, the coordinates of Y are (-1,0). Answer: The coordinates of vertex Y are (-1,0).
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The shape shown is made up of three similar right-angled triangles.
Click to insert IMC 2022 KF3a
The smallest triangle has two sides of side-length 2, as shown.
What is the area of the shape?
To calculate the area of the shape made up of three similar right-angled triangles, we need additional information about the scale factor or proportions of the triangles. Without that information, we cannot determine the exact area of the shape.
The given information states that the shape is composed of three similar right-angled triangles, and the smallest triangle has two sides of side-length 2. While we know the dimensions of the smallest triangle, we do not have any information about the scale factor or proportions of the other two triangles. Since the shape is formed by three similar triangles, the areas of the triangles would be proportional, but we cannot determine the exact proportions without additional information. Consequently, we cannot calculate the area of the shape accurately based solely on the given information.
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Which expressions are equivalent to 8. 9 x 6. 2 8. 7? Check all that apply. 9 x 6 9 8. 9 6. 2 8. 7 x 8. 9 x 8. 7 6. 2 8. 7 8. 9 x 6. 2 6. 2 8. 7 8. 9 6. 2 8. 7 8. 9 x 8. 9 6. 2 x 8. 7.
The following expressions are equivalent to 8.9 x 6.28.7: 9 x 6; 6.28.7; 8.9 x 6.2. The product of two numbers, in general, is the outcome when we multiply the numbers together.
It means, when we take two quantities and multiply them, we get the result as a product. Let us understand how the multiplication of numbers works with an example. When we multiply 3 and 4, we get:3 × 4 = 12Here, 3 and 4 are called factors, and the result, 12, is called the product. Equivalent expressions are the expressions that have the same value, but their structures may differ. The expressions can be equivalent if they have the same value, but their format is different .Let's list the expressions that are equivalent to 8.9 x 6.28.7:The product of 9 and 6 is equal to 54. The product of 8.9 and 6.2 is equal to 55.18.The expression 6.28.7 is the same as 55.18. The product of 8.9 and 6.2 is the same as 6.28.7.Therefore, the following expressions are equivalent to 8.9 x 6.28.7:9 x 66.28.78.9 x 6.2.
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If the frequency of a FM wave is 8. 85 × 107 hertz, what is the period of the FM wave? A. 2. 58 × 10–8 seconds B. 1. 13 × 10–8 seconds C. 1. 25 × 10–7 seconds D. 5. 82 × 10–7 seconds.
The period of the FM wave is 1.13 × 10–8 seconds.
The correct option is B. 1. 13 × 10–8 seconds.
How to find the period of an FM wave.
The period of a wave can be defined as the time required to complete one cycle.
The period is represented by the symbol T.
It is measured in seconds (s).
Frequency is the number of cycles per second. It is measured in Hertz (Hz).
It is represented by the symbol f.
The formula for finding the period of a wave is given by:
T = 1/f
Given that the frequency of a FM wave is 8.85 x 10⁷ Hertz.
We have to find the period of the FM wave.
The period of the FM wave can be found using the formula:
T = 1/f
Where frequency
= 8.85 × 107 Hz
T = 1/fT
= 1/8.85 x 10⁷T
= 1.13 × 10–8 seconds
Therefore, the period of the FM wave is 1.13 × 10–8 seconds.
Thus, option B is the correct answer.
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CERAMICS Josh has 8 days to make pots and plates to sell at a local fair. Each potweighs 2 pounds and each plate weighs 1 pound. Josh cannot carry more than 50 poundsto the fair. Each day, he can make at most 5 plates and at most 3 pots. He will make $12profit for every plate and $25 profit for every pot that he sells.a. Write linear inequalities to represent the number of pots p and plates a Josh maybring to the fair.b. List the coordinates of the vertices of the feasible region.c. How many pots and how many plates should Josh make to maximize his potentialprofit?
The given restrictions can be written as follows:Maximum weight carried by Josh: 2p + 1a ≤ 50Maximum number of plates per day: p ≤ 3his objective function would be:Profit = 12a + 25pWe need to find the values of a and p which can maximize his profit.
Thus, the linear inequalities to represent the number of pots p and plates a that Josh may bring to the fair is:2p + 1a ≤ 50, a ≤ 5 and p ≤ 3.b) The feasible region can be found by plotting the given constraints on the coordinate plane. Here is the graph for the same:From the graph, we can see that the vertices of the feasible region are (0,0), (3,5), (8,0), and (16,0).c) Josh wants to maximize his profit.
Therefore, To do so, we can substitute the vertices of the feasible region and calculate the profit to identify the combination of pots and plates that gives the maximum profit.
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What is the surface area of the prism in square inches?A rectangular prism has a height of 2 inches, width of 8 inches, and depth of 11 inches. 90 square inches126 square inches176 square inches252 square inches
The surface area of the prism is 252in²
Given,
Dimensions of rectangular prism:
Height = 2 in
width = 8 in
depth = 11 in
Now,
The surface area of a rectangular prism is given by:
A = 2 * (x * y) + 2 * (x * z) + 2 * (y * z)
where,
x, y, z: are the sides of the rectangular prism
Substituting values we have:
A = 2 * (2 * 8) + 2 * (2 * 11) + 2 * (8 * 11)
A = 252 in²
Hence the surface area of the prism in square inches will be 252 .
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Karen drew a plan for a rectangular piece of material that she will use for a blanket. Three of the vertices are (−1.3,−3.1), (−1.3,1.2), and (1.1,1.2). What are the coordinates of the fourth vertex?
The coordinates of the fourth vertex are (1.1, -3.1).
We know that a rectangular piece of material has two pairs of parallel sides and four right angles. Therefore, we can calculate the distance between two opposite sides by using the distance formula. The two sides that are parallel to the x-axis have the same y-coordinate, and the two sides parallel to the y-axis have the same x-coordinate.
Thus, the distance between opposite sides is given by the difference between the x-coordinates or the difference between the y-coordinates. The x-coordinates of the vertices are −1.3, −1.3, and 1.1. So the difference between them is 1.1 − (−1.3) = 2.4. The y-coordinates of the vertices are −3.1, 1.2, and 1.2. So the difference between them is 1.2 − (−3.1) = 4.3. The fourth vertex is located at the point with an x-coordinate of 1.1 and a y-coordinate of −3.1. Therefore, the coordinates of the fourth vertex are (1.1, -3.1).
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A shop sells two brands of eggs. Brand A and Brand B , Their prices are given in the ratio 4:7, if a baker buys 8 trays of brand A and 6 trays of Brand B at a total cost of R279,45
How much did the baker pay for the 8 trays of brand
The baker paid approximately R15.08 for each tray of Brand A.
Understanding Word ProblemLet:
x = price of each tray of Brand A
y = price of each tray of Brand B
Given that the prices are in the ratio 4:7, we can write the equation:
x/y = 4/7
To find the individual prices of Brand A and Brand B, we can introduce a constant k:
x = 4k
y = 7k
The total cost of 8 trays of Brand A (8x) and 6 trays of Brand B (6y) is R279.45:
8x + 6y = 279.45
Substituting the expressions for x and y:
8(4k) + 6(7k) = 279.45
32k + 42k = 279.45
74k = 279.45
Dividing both sides by 74:
k = 279.45 / 74
k ≈ 3.77
Now we can find the price of each tray of Brand A:
x = 4k ≈ 4 * 3.77 ≈ R15.08
Therefore, the baker paid approximately R15.08 for each tray of Brand A.
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Use the Pythagorean Theorem to determine the lengths of QT and RS Show your work
(HURRY I WILL GIVE BRAINLEST)
To determine the lengths of QT and RS using the Pythagorean Theorem, we need additional information such as the lengths of the other sides or the measurements of angles in the triangle. Without this information, we cannot accurately calculate the lengths of QT and RS.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. However, in the given question, we are not provided with any measurements or information about angles in the triangle or the lengths of the other sides.
Therefore, without additional information, we cannot determine the lengths of QT and RS using the Pythagorean Theorem.
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When performing a dilation or a composition of a dilation and rigid transformations on a triangle, what properties of the original triangle preserved?
When performing a dilation or a composition of a dilation and rigid transformations on a triangle, several properties of the original triangle are preserved. In both cases, the shape and orientation of the triangle remain the same while the size and location of the triangle change.
During a dilation, the original triangle is extended or shrunk in size uniformly. All sides of the triangle are extended or shrunk by the same factor, which is the scale factor of the dilation. The angle measures of the triangle remain unchanged during dilation, and the corresponding angles of the dilated triangle remain equal.In a composition of a dilation and rigid transformation, the original triangle is first dilated and then subjected to a rigid transformation like rotation, translation, or reflection.
The shape and orientation of the original triangle are preserved, and the size and location of the dilated triangle change. The angle measures of the triangle remain unchanged during dilation, and the corresponding angles of the dilated triangle remain equal. During the subsequent rigid transformation, the corresponding sides and angles of the dilated triangle are also preserved.
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Does the table represent a function? Why or why not?
xy
3 1
4 3
5 2
6 5
6 6
A. Yes, because every x-value corresponds to exactly one y-value.
B. No, because one x-value corresponds to two different y-values.
C. Yes, because there are different y-values.
D. No, because the y-values are positive.
Option A, "Yes, because every x-value corresponds to exactly one y-value," accurately describes the situation presented in the table. Option A is the proper response, so.
The table represents a function.
A mathematical relationship known as a function is one in which every input (x-value) has exactly one corresponding output (y-value). In the given table:
xy
3 1
4 3
5 2
6 5
6 6
Every x-value in the table corresponds to exactly one y-value. There are no repeated x-values, and for each x-value, there is only one corresponding y-value. The definition of a function is met by this.
The answer given in Option A, "Yes, because every x-value corresponds to exactly one y-value," appropriately sums up the situation shown in the table. Option A is the proper response, so.
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The music for Savannah’s dance routine lasts for exactly 4 minutes. When Savannah dances
her routine, she starts with her music and finishes 12 seconds before the music ends.
What percent of the time the music is playing is Savannah dancing?
The answer is that Savannah is dancing 95% of the time the music is playing. Duration of music = 4 minutes Duration of Savannah's dance routine = 4 - (12/60) = 3.8 minutes. Now, we need to find the percentage of time the music is playing is Savannah dancing.
To find the percentage of time, we need to divide the time for Savannah's dance routine by the duration of the music and then multiply the quotient by 100.Percentage of time Savannah is dancing = (time for Savannah's dance routine / duration of music) × 100= (3.8 / 4) × 100= 95%.
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If 15. 0 g of CaCl2 are present in 250 mL of aqueous solution, what is the concentration of CaCl2 in % (w/v)?
The concentration of CaCl2 in % (w/v) can be calculated by dividing the mass of CaCl2 by the volume of the solution and multiplying by 100. In this case, if 15.0 g of CaCl2 is present in 250 mL of solution, the concentration of CaCl2 can be determined.
The concentration of a solution is commonly expressed as a percentage by weight/volume (% w/v), which represents the mass of solute (in this case, CaCl2) in a given volume of solution. To calculate the concentration, divide the mass of CaCl2 (15.0 g) by the volume of the solution (250 mL) and multiply by 100.
Concentration of CaCl2 in % (w/v) = (Mass of CaCl2 / Volume of Solution) x 100
Substituting the given values:
Concentration of CaCl2 in % (w/v) = (15.0 g / 250 mL) x 100
Simplifying the expression:
Concentration of CaCl2 in % (w/v) = 6.0% (rounded to one decimal place)
Therefore, the concentration of CaCl2 in the given solution is 6.0% (w/v).
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Que es la circunferencia
Answer: you can also search what you said in eniglish aand it would give u a calculater _--_- (
Step-by-step explanation:The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its centre. A meridian is any great circle passing through a point designated a pole.
Which histogram depicts a higher standard deviation.
Histograms visualize the distribution and spread of data. A higher standard deviation implies greater variability in the data points. In a histogram, a wider shape indicates a larger spread of data and thus a higher standard deviation. Therefore, the histogram with a broader shape depicts a higher standard deviation.
To determine which histogram depicts a higher standard deviation, we need to look for the histogram with a greater spread or dispersion of data. In a histogram, a higher standard deviation indicates that the data points are more spread out or have a larger variability. This means that the values are more scattered from the mean. Therefore, the histogram with a wider and more spread-out shape would depict a higher standard deviation, as it indicates a greater variability in the data.
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