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Related Questions
HELP I HAVE 25 POINTS AND I WILL MARK U AS BRAINLIST A granola recipe calls for 3 cups of oats, 1 cup of almends. 1 cup of pecans, and 1 cup of dried fruit. What is the ratio of fruit to eats? Yolanda says that for every 2 cups of nuts, there are 2 cups of fruit. Explain why her answer is incorrect and give the correct ratio of nuts to fruit. Explain your answer.
Answers
Answer:
Yolanda's answer is incorrect because the recipe calls for 1 cup of almonds, 1 cup of pecans, and 1 cup of dried fruit, which totals 3 cups of nuts. The correct ratio of nuts to fruit in this recipe is 3:1. This means that for every 3 cups of nuts, there is 1 cup of fruit.
Which equation can be used to determine the line that passes through the points (-1, -2) and (3, 10)?Justify your reasoning using new and prior concepts. Use math vocabulary to explain your thinking.
Answers
The equation the line is, y-3x=1
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have to points (-1,-2) and, (3,10)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>(y+2)/(x+1)=(10+2)/(3+1)
=>y+2=3x+3
=>y-3x=1
Hence, the required equation is, y-3x=1
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A large cuboid-shape box has dimensions of 70cm by 40cm by 40cm. Work out the maximum number of smaller cube-shaped boxes with sides of length 10cm that will fit in the large box
Answers
Given ,
A large cuboid-shape box has dimensions of 70cm by 40cm by 40cmLength of the cube shaped boxes are 10cmTo Find : Maximum number of small cube shaped boxes that can fit in the cuboid
Volume of the Cuboid = [tex]2(lb+bh+lh)[/tex]
Volume of the cuboid = [tex]2(70X40+40X40+70X40)[/tex]
= [tex]14400cm^{3}[/tex]
Now to find the volume of a cube,
[tex]V = a^{3}[/tex]
[tex]V = 10X10X10[/tex]
[tex]V = 1000cm^{3}[/tex]
Number of boxes that can fit in a cuboid = [tex]\frac{14400}{1000}[/tex]
= [tex]14boxes[/tex]
Hence , the number of cube shaped boxes that can fit in a cuboid are 14
Manuel says 25 5/8 ft of fencing is enough for a rectangular flower bed that measures 9 7/8 ft by 15 3/4 feet is this correct explain
Answers
Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Given that, Manuel says [tex]25\frac{5}{8}[/tex] feet of fencing is enough for a rectangular flower bed that measures [tex]9\frac{7}{8}[/tex] feet by [tex]15\frac{3}{4}[/tex] feet
Here, perimeter =2([tex]9\frac{7}{8}[/tex] + [tex]15\frac{3}{4}[/tex]) feet
= 2(79/8 + 63/4)
= 2(79/8 + 126/8)
= 2(205/8)
= 410/8
= [tex]51\frac{1}{4}[/tex] feet
Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.
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In AJLP. m/JMP = (3x −6)°, JK = 3y-2, and LK = 5y-8. Find LK if PK is a median.
LK=
Answers
On solving the provided question, we can say that - the value ox in the following angle = 3x = 84 => x = 28
what are angles?In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.
here
angle JMP = 3x-6 - 90
3x = 84
x = 28
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Help asappppp please
Answers
Answer:
the answer is a
and the correct answer is letter C
Step-by-step explanation:
I don't know that is the answer
What is the answers for 9 and 11?
Answers
The total amount in the bank after the specific number of years is;
9. $476. 1
11. $7, 128. 8
How to determine the amountThe formula for calculating simple interest is expressed as;
I = PRT/100
Where;
I is the simple interestP is the principal amountR is the interest rateT is the time takenFrom the information given, we have that;
9.Principal amount = $450
Interest rate = 1.45
Time = 5
Substitute the values into the formula
SImple interest = $450 ×1. 45× 5/100
Multiply the values, we get;
Simple interest, I = 2610/100
Divide through
Simple interest = $26. 1
Total amount = $450 + $26.1 = $476. 1
11. Principal amount = $5600
Interest rate = 3.9
Time = 7 years
Substitute the values
Simple interest = $5600× 3. 9 × 7/100
Multiply the values
Simple interest = 152,880/100
Simple interest = $1528. 8
Total amount = $7, 128. 8
Hence, the values are $476. 1 and $7, 128. 8
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Olivia is making greeting cards, which she will sell by the box at an arts fair. She paid $24 for a booth at the fair, and the materials for each box of cards cost $2. She will sell the cards for $6 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How much will the sales and expenditures be? How many cards will that take?
Answers
Answer:
$8
Step-by-step explanation:
A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number less than 2.
35 over 60
25 over 60
13 over 60
12 over 60
Answers
Experimental probablity will be - 12 over 30
Answer: D: 12/60 (12 over 60)
Step-by-step explanation:
6. Find the quotients.
a. 0.024 ÷ 0.015
b. 0.24 0.015
c. 0.024 ÷ 0.15
d. 24 ÷ 15
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Answer:
a. 1.6
b. 16
c. 0.16
d. 1.6
A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red. The deck is randomly arranged. What is the probability that the top card is a $\heartsuit$
Answers
The probability that the top card is a suit of heart as calculated from the data given is found to be 4 / 663.
We are given that ,
The number of cards in the deck = 52
Number of 3's in the deck = 4
Number of 8's in the deck = 4
As because all the card deck's have 4 cards of same number in different suits.
Probability is calculated as ,
P = required outcome / Total possible outcomes
Therefore, when we can choosing cards without replacing them we get,
P(top card is a 3) = 4 / 52
P(second being 8) = 4 / 51
P(top card is a 3 and second 8)
=4/52 x 4/51
= 16 / 2652
= 4 / 663.
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Find the mean, variance and standard deviation for the probability distribution given below:
X -1 3 9 12
P(X) 0.587 0.115 0.21 0.088
A. Mean = B. Variance = C. Standard Deviation =
Answers
The mean, variance, and standard deviation for the probability distribution given are A. Mean = 5.5; B. Variance = 13.875; C. Standard Deviation = 3.722.
The mean, variance and standard deviation of the probability distribution can be calculated using the formula. The mean is calculated by summing up the product of all the values and their respective probabilities and then dividing it by the total probability. In this case, the mean is calculated as:
(1*0.587 + 3*0.115 + 9*0.21 + 12*0.088)/(0.587 + 0.115 + 0.21 + 0.088) = 5.5.
The variance is calculated by summing up the product of the squares of the values and their respective probabilities and then dividing it by the total probability. In this case, the variance is calculated as:
(1^2*0.587 + 3^2*0.115 + 9^2*0.21 + 12^2*0.088)/(0.587 + 0.115 + 0.21 + 0.088) = 13.875.
The standard deviation is the square root of the variance and it is calculated as √13.875 = 3.722.
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You lose 0.3 point for stepping out of bounds during a gymnastics floor routine. Your final score is 9.124. Write and solve an equation to find your score x without the penalty.
Answers
The equation is x + 0.3 = 9.124 and the value of x is 8.824.
The following is a linear equation in one variable. It can be expressed in the form of ax+b=0. Here a and b are integers and x is a variable that has only one solution. In these type of equations only one variable is present.
We can write an equation to find the score without the penalty by using the information provided. Let x be the score without the penalty. We know that the final score (with the penalty) is 9.124 and that the penalty is 0.3 points. Therefore, we can set up the equation:
x + 0.3 = 9.124
To find the score without the penalty, we need to subtract 0.3 from both sides of the equation:
x = 9.124 - 0.3
x = 8.824
So, the score without the penalty is 8.824
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Aiden ha a gro income of 63,000 and take the tandard deduction. Their total taxe due are 6,628
A) what i their taxable income
B) what i their marginal rate
C) what i their effective rate? Round to the nearet hundredth of a percent
Answers
If their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.
What is your taxable income?The term taxable income refers to any gross income earned that is used to calculate the amount of tax you owe. Put simply, it is your adjusted gross income less any deductions. This includes any wages, tips, salaries, and bonuses from employers.
What is minimum taxable income?The minimum income amount depends on your filing status and age. In 2022, for example, the minimum for single filing status if under age 65 is $12,950. If your income is below that threshold, you generally do not need to file a federal tax return. Review the full list below for other filing statuses and ages.
Taxable income
a. Taxable income:
Taxable income=Gross income - Total taxes due
Taxable income=$63,000-$6,847.50
Taxable income=$56,152.5
b. The marginal tax rate for taxable income under the income bracket of of $40,526 to $86,375 is 22%.
c. Effective tax rate:
Effective tax rate = Total taxes due/ Taxable income×100
Effective tax rate =$6,847.50/$56,152.5×100
Effective tax rate =10.869%
Effective tax rate =10.87% (Approximately)
Inconclusion if their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.
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In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels. This point is circled on the graph.
What effect will the circled point have on the y-intercept?
The y-intercept will not change with the addition of this point.
The y-intercept will decrease because the point pulls the least-squares regression line toward it.
The y-intercept will increase because the point pulls the least-squares regression line toward it.
The y-intercept will increase because this point represents an extremely high number of pretzels grabbed with the dominant hand.
answer is B
Answers
We can see here that the effect that the circled point will have on the y-intercept is: B. The y-intercept will decrease because the point pulls the least-squares regression line toward it.
What is an intercept?In statistics, an intercept is the value of the dependent variable when the independent variable(s) is equal to zero. It is often represented by the symbol "b" in a linear equation.
For example, a simple linear equation has the form y = mx + b, where "y" is the dependent variable, "x" is the independent variable, "m" is the slope of the line, and "b" is the y-intercept. The y-intercept is the point where the line crosses the y-axis.
We see here that the answer above is the correct answer.
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Rover it’ 3/4 of a can of cat food each day Bobo it’ 1/2 of a can of cat food each day cat food cot five dollar for three can it i only aw three can’t fox how much doe it cot for Karen for a 60 day upply of cat food for her to count cat
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this question is related to numbers and the solution is as follows,
Rover eats 3/4 can of cat food in a day.
given
in 60 days it will consume 60 x 3/4 cans = 45 cans of cat food
3 cans cost = $5 and a pack contains 3 cans
45 cans is equivalent to= 45/3
= 15 packs
15 packs cost = 15 x $5 = $75
So it will cost $ 75 to feed Rover for 60 days
Bobo eats 1/2 of a can of cat food per day
in 60 days it will consume 60 x 1/2 cans = 30 cans of cat food
3 cans cost $5 and a pack contains 3 cans
30 cans are equivalent to 30/3 = 10 packs
10 packs will cost = 10 x $5 = $50
So it will cost $50 to feed Bobo for 60 days
In total, in 60 days it will cost $75 +$ 50 = $125 to feed both cats in 60 days.
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As calculated from the data we get the result as that $ 125 is required for the cat food of both the cats in a month.
We are given that in 60 days he will consume ,
60 x 3/4 cans
= 45 cans of cat food
The cost of 3 cans cost = $5
and one pack has 3 cans in it.
Therefore, 45 cans is equivalent to
= 45/3
= 15 packs
So , the cost of 15 cans will be ,
15 packs cost = 15 x $5 = $75
Therefore ,$75 is used for 60 days of cat food for Rover.
Now , we know that Bobo eats 1/2 of a can food in a day.
Therefore, in 60 days he will eat,
60 x 1/2 cans
= 30 cans of food
As we know, 3 cans cost $5 and a pack contains 3 cans
Therefore, 30 cans = 30/3 = 10 packs
10 packs will cost = 10 x $5 = $50
So , $50 is spend to feed Bobo , in a month.
Therefore , if will combine their cost we will get that ,
$75 +$ 50 = $125 is required to feed both the cats in one month.
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for large parties a restaurant adds a 15 service charge. how much would be added to a bill of $638.40
Answers
Answer: $95.76
Step-by-step explanation:
If the 15 is referencing 15%.
15% of 638.40 can be found by making 15% a decimal by moving the decimal to the left twice.
.15 X 638.40= 95.76
can someone answer this question really quick
Simplify the expression by combining like terms.
43a−12b+13a+52b
Enter your answer as an expression, like this: 42x+53
Answers
Answer:
56a+40b
Step-by-step explanation:
43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b
Given two points, (3, 2) and (7, 18), determine both the linear and quadratic equations crossing both points. Let f(x) and f(k) be the linear and quadratic equation respectively. Write both in standard form
Answers
The linear equation f(x) is 4x - 10 and the quadratic equation f(k) is -5/2k^2 + 4k - 1 for the two given points.
The linear equation can be found using the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept. To find the slope (m) we can use the two points given:
m = (y2 - y1) / (x2 - x1) = (18 - 2) / (7 - 3) = 16/4 = 4
The y-intercept (b) can be found using one of the points and the slope:
b = y - mx = 2 - 4(3) = -10
So the linear equation in standard form is:
f(x) = 4x - 10
For the quadratic equation, we know that it's in the form of y = ax^2 + bx + c. We have 2 points, so we have 2 equations with 2 unknowns. We can use this information to solve for a, b and c.
Let's (3,2) point 1 and (7,18) point 2.
f(k) = ak^2 + bk + c....(1)
point 1: f(3) = 2 = 9a + 3b + c...(2)
point 2: f(7) = 18 = 49a + 7b + c...(3)
Now we have 2 equations and 3 unknowns.
using theirs first equation and substitute it in the second and third equation
18 = 49a + 7b + c
2 = 9a + 3b + c
c = 2 - 9a - 3b
18 = 49a + 7b + (2 - 9a - 3b)
18 = 49a + 7b + 2 - 9a - 3b
18 = 40a + 4b + 2
16 = 40a + 4b
now this equation is used to solve for a and b
b = (16 - 40a) / 4
so a,b and c are
a = -5/2
b = 4
c = -1
so the quadratic equation in standard form is:
f(k) = -5/2k^2 + 4k - 1
4x - 10 is the linear equation f(x) and -5/2k^2 + 4k - 1 is the quadratic equation f(k) for the two given points.
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What is the mirror image of 2 5 in y-axis?
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The mirror image of (2,5) in y-axis is (-2,5)
The term mirror image of the point is a reflected duplication that appears identical but in reverse.
Here we have given point is (2, 5).
And we have to find the mirror image of this point with respect to the y-axis that is the mirror image is a point whose distance is same from the origin O (0, 0) and same from both axes as of the point (2, 5) is.
As we all know that (2, 5) lies on the first quadrant, then the mirror image with respect to the y-axis must lie on the second quadrant.
And we all also know that In second quadrant, here the x-coordinate of any point (x, y) is negative.
Therefore, while we looking into the given graph we have identified that the mirror image is (- 2, 5).
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Solve for 2 |v+2|-41=-9
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution"
Answers
Answer:
[tex]v=-18,14[/tex]
Step-by-step explanation:
[tex]2|v+2|-41=-9\\2|v+2|=32\\|v+2|=16\\\\v+2=16\\v=14\\\\v+2=-16\\v=-18[/tex]
HURRY!!
The height of a cylinder is 5 centimeters. The circumference of the base of the cylinder is 167 centimeters.
Which measurement is closest to the volume of the cylinder in cubic centimeters?
A. 251. 3
B. 4,021. 2
C. 1,005. 3
D. 628. 3
Answers
Since the circumference of the base is given, the radius can be calculated as r = (circumference / 2π) and the volume as V = πr2h. The volume of the cylinder is therefore approximately 628.3 cubic centimeters.
1. Calculate the radius of the base of the cylinder. The circumference of the base is 167 centimeters. Rearranging this gives
r = C / 2π. Therefore,
r = (167 / 2π)
= 26.6 cm.
2. Calculate the volume of the cylinder. The formula for volume is V = πr2h. Therefore,
V = π(26.6)2 * 5
= 628.3 cubic centimeters.
or
r = (167 / 2π) = 26.6 cm
V = π(26.6)2 * 5 = 628.3 cubic centimeters
To calculate the volume of the cylinder, the radius of the base must first be calculated. This can be found by using the formula C = 2πr, where C is the circumference and r is the radius The circumference of the base of the cylinder is 167 centimeters, so the radius can be calculated as r = (167 / 2π) = 26.6 cm. The volume of the cylinder can then be calculated using the formula V = πr2h, where h is the height of the cylinder. In this case, the height is 5 centimeters, so the volume is V = π(26.6)2 * 5 = 628.3 cubic centimeters. This is the closest measurement to the volume of the cylinder.
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?
Kadeesha left her house at time zero and drove for 3 minutes to the store, at a speed
of 1 blocks per minute. Then she stopped and went into the store for 3 minutes. From
there, she drove in the same direction at a speed of 2 blocks per minute until she got
to the bank, which is 6 blocks away from the store. She stopped at the bank for 5
minutes. Then she drove home at a speed of 3 blocks every minute. Make a graph of
showing the number of blocks away from home that Kadeesha is a minutes after she
leaves her house, until she gets back home.
Graph Stories (Level 1)
Jan 08, 3:36:47 PM
Watch help video
Click twice to plot a segment.
Click a segment to delete it.
Answers
Therefore ,As a result, the answer to the above equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).
Equation : what is it?An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.
Here,
Given :
At time zero, Kadeesha stepped outside and drove 3 minutes at a speed of 1 block per minute to the store.
after traveling six blocks at her normal speed of three blocks per minute
She spent 5 minutes stopping at the bank as a result. She then sped home at a rate of three blocks per minute.
She therefore begins at (19,8), travels 8 blocks back in 2 minutes, and ends at (21,0).
Therefore ,As a result, the answer to the above equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).
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Simplify: [tex]\frac{10m}{5m}[/tex]
Answers
Answer:
2
When you cancel out the m (cause its the common factor) the only thing left is to simplify 10/5 which is 2.
1. To find members for her skate team, Heather prints flyers to display around town. She posts 6 flyers
at her school and f flyers at each of the 3 nearest skate parks. Write two different expressions that
represent the total number of flyers posted.
Find the total number of flyers posted if f= 5.
Answers
Recently, the Town of Aberdeen announced they were going to acquire a large parcel of land for a new park initiative.
What is piecewise function?To fully understand what piecewise functions are and how we can construct our own piecewise-defined functions, let’s first dive into a deeper understanding of how it works.A piecewise function is a function that is defined by different formulas or functions for each given interval. It’s also in the name: piece. The function is defined by pieces of functions for each part of the domain.In mathematics, a piecewise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself.To learn more about piecewise function refer to:
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Denise dusted a square tabletop with an area of 36x^16y^4 units write an expression to represent one side length of the table top
Answers
The length of the side of the table top as calculated from the given data will be 6x⁴y².
To calculate the area of the table top we will have to square of the sides given .
area =(36x.16y^4 )²
side =√(36x.16y^4 )²
= 6x⁴y².
In mathematics the product of a number multiplied by itself is considered to be its square. Eg.) 6 multiplied by 6 gives 36 which is known as its square.
The given table is square in shape and hence its area will be given my multiplying its side with itself.
Area of a square = side x side.
To find its length we can simply find the square root of the number.
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An aircraft hangar is semi-cylindrical with
diameter 40 m and length 50 m. A helicopter
places a cable across the top of the hangar, and
one end is pinned to the corner at A. The cable
is then pulled tight and pinned at the opposite
corner B. Determine the length of the cable.
Answers
On solving the provided question, we can say that - the volume of the cylinder will be V = 3.14 * 20*20*50 = 62800
what is radius?The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle. Diameter
volume of the cylinder -
V = [tex]\pi r^2h[/tex]
r = 40/2 = 20
h = 50
V = 3.14 * 20*20*50 = 62800
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Write a rule to describe each transformation.
S(1,-4), R(2,0), 2(3,0), P(3,-2)
to
S'(-5,-2), R'(-4, 2), Q'(-3, 2), P(-3,0)
Answers
The transformation of S(1,-4), R(2,0), 2(3,0), and P(3,-2) is S(-6, -2), R(-6, 2), as well as the category is rotation transformation.
what is transformation ?Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image, which refers to the object's initial shape, and the Image, which refers to the object's ultimate shape and location after transformation, are both terms. Transformations can be divided into three categories: translations, reflections, and dilations. There are two types of transformations that can be done to a function: vertical (which affects the y-values) and horizontal (affects the x-values). The four transformation variables are included in the equation of a function that is shown below (a, b, h, and k). changing the log. Take the log of every observation as an example. Transposition by the square root. The square root of each observation is what is need for this.
given
Translation or shift vector refers to the pair (tx, ty). Column vectors are another way to visualize the aforementioned equations.
S(1,-4), R(2,0), 2(3,0), P(3,-2) to S'(-5,-2), R'(-4, 2), Q'(-3, 2), P(-3,0)
is S (-6, -2) , R( -6 , 2)
The transformation of S(1,-4), R(2,0), 2(3,0), and P(3,-2) is S(-6, -2), R(-6, 2), as well as the category is rotation transformation.
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Drag each tile to the correct box. Arrange the steps in the correct order to solve this trigonometric equation3 sin 2 ( x )
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For a trigonometric equation. Cos^2x=3sin^2x, the solution is mathematically given as x = π/6 + 2nπ.
What is trigonometry?Trigonometry is the study of angles and the angular connections of planar and three-dimensional shapes. Trigonometry is made up of trigonometric functions (also known as circle functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.
What is the solution of the trigonometric equation?Generally, the equation for the trigonometric equation is mathematically given as:
Cos^2x=3sin^2x
Therefore
1 - sin^2(x) = 3 sin^2(x)
1/4 = sin^2(x)
Hence introducing \pi
x = arcsin(1/2) + 2nπ
x = π/6 + 2nπ
In conclusion,
x = π/6 + 2nπ
For a trigonometric equation. Cos^2x=3sin^2x, the solution is mathematically given as x = π/6 + 2nπ.
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Suppose $PABCD$ is a right square pyramid with apex $P$ and base $ABCD$. If $PBD$ is an equilateral triangle with side length 6, then what is the volume of $PABCD$
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The volume of a right square pyramid PABCD is 50.91 cubic units
Let l be the side length of right squared pyramid and h be the height.
We know that the formula for the volume of the right squared pyramid.
V = a²h / 3
And the formula for the height of right squared pyramid.
h = (1/√2)a
Here, the side length (a) = 6 units
So, using above formula of height,
h = (1/√2) × 6
h = 6/√2
h = 3√2 units
Now using the formula for the volume of the right squared pyramid, the volume of pyramid PABCD would be,
V = (6² × 3√2) / 3
V = 6² × √2
V = 36√2
V = 50.91 cubic units
Therefore, the volume of PABCD is 50.91 cubic units
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