The volume of the cone is1527.1 cm³
And the correct answer is an option (c)
We know that he formula for the volume of the cone is:
V = 1/3(π × r² × h)
Here, the diameter of the base of the cone is 15 cm
so, the radius of the cone would be,
r = 15/2 cm
r = 7.5 cm
And the slant heihgt of the cone is l = 27 cm
Using Pythagoras theorem the height h of the cone would be,
h = √(l² - r²)
h = √(27² - 7.5²)
h = √(672.75)
h = 25.94 cm
Using above formula, the volume of the cone would be,
V = 1/3(π × r² × h)
V = 1/3(π × (7.5)² × 25.94)
V = 1527.99 cm³
V = 1527.1 cm³
Therefore, the correct answer is an option (c)
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Find the complete question below.
does anyone know the answer to this?
The probability of selecting a J or an A on the second draw, given that an E was selected on the first draw is 0.101.
How to find the probability ?The number of tiles which have an E on them are shown to be 12 which means that if an E was selected on the first draw, there are now 99 tiles left.
The probability that an A or J will be selected in this second draw would be :
= ( Number of A tiles and J tiles ) / 99
Number of A tiles = 9
Number of J tiles = 1
The probability is then :
= ( 9 + 1 ) / 99
= 10 / 99
= 10.1%
= 0.101
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Question 1: A gardener uses a total of 81.5 gallons of gasoline in one month. Of the total amount of
gasoline, 2/5 was used in his lawn mowers. How many gallons of gasoline did the gardener use in his
lawn mowers in the one month?
A. 12.3 gal
B. 203.75 gal
C. 0.326 gal
D. 32.6 gal
Answer: D
Step-by-step explanation:
The amount of gasoline used in the lawn mowers is 2/5 of the total amount of gasoline used. Therefore:
Gasoline used in lawn mowers = (2/5) x 81.5 gallons
Gasoline used in lawn mowers = 32.6 gallons
Therefore, the answer is D. 32.6 gal.
A wall 12 feet long makes a corner with a wal
that is 14 feet long. The other ends of the walls
are about 18.44 feet apart. Do the walls form a
right angle? Explain.
Yes, the walls form a right angle.
To determine if the walls form a right angle, we can use the Pythagorean theorem. The question states that a wall 12 feet long makes a corner with a wall that is 14 feet long, and the other ends of the walls are about 18.44 feet apart.
The Pythagorean theorem states that in a right-angled 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. In this case, let's consider the 12-foot and 14-foot walls as the two shorter sides, and the 18.44-foot distance as the potential hypotenuse.
Step 1: Calculate the square of the lengths of the 12-foot and 14-foot walls.
12² = 144
14² = 196
Step 2: Calculate the sum of the squares of these two sides.
144 + 196 = 340
Step 3: Calculate the square of the length of the 18.44-foot distance.
18.44² ≈ 339.95
Since 339.95 is very close to 340, we can conclude that the walls form a right angle.
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Rewrite 4.86 x 104 in decimal notation.
O48,600
O4, 860,000
O 0.000486
O 4.86
If we rewrite 4.86 x 104 in decimal notation, we will have 48,600. The Option A.
What is the decimal notation of 4.86 x 104?In decimal notation, 4.86 x 104 is equivalent to 48600. To convert scientific notation to decimal notation, you simply move the decimal point to the right by the number of places indicated by the exponent.
In this case, since the exponent is 4, you move the decimal point four places to the right of the digit 4, resulting in 48600. Therefore, 4.86 x 104 in decimal notation is 48600.
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Simplify the radical
-√81m^3
Answer:
9m^3
Step-by-step explanation:
since there is a square root remove it and find it square which is 9
Michael fills a plastic ball with air until it is a sphere with a radius of 6 cm. What is the volume of the ball?
The volume of the ball is 904.78 cubic cm
We know that the formula for the volume of sphere is:
V = (4/3) × π × r³
where r is the radius of the sphere
Here, Michael fills a plastic ball with air until it is a sphere with a radius of 6 cm.
So, the radius of spherical ball r = 6 cm
Using above formula of volume of sphere, the volume of the ball would be,
V = (4/3) × π × r³
V = (4/3) × π × (6)³
V = (4/3) × π × 216
V = 904.78 cubic cm
Therefore, the required volume = 904.78 cubic cm
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Question 3(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
The IQR of 13 is more appropriate to use than the range of 13, as it provides a more accurate representation of the variability in the data when the data is skewed. Thus, option B is correct.
What is the accurate and IQR?The range is the difference between the maximum and minimum values in a dataset, and it is affected by extreme values, which can result in a misleading representation of the variability in the data.
if the data is skewed or contains outliers, the range may not accurately represent the variability in the data.
However, it is not appropriate to use the range of 20 to show that they have plenty of money or the IQR of 20 to show.
Therefore, in this case, the IQR of 13 is more appropriate to use than the range of 13, as it provides a more accurate representation of the variability in the data when the data is skewed.
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Marina is drawing a plan for a new garden. The rectangle plotted in the coordinate plane represents the garden, measured in feet. To surround the garden with a stone path, how many feet of stone does she need? 4 feet 6 feet 10 feet 20 feet
If Mariana needs to surround the garden with a stone-path, then she would need 20 feet of stone, Option (d) is correct.
The "Perimeter" of a rectangle is defined as the "total-length" of the outer boundary.
The length of the rectangle can be calculated as the difference between the x-coordinates of the vertices on the same vertical side.
In this case, the "x-coordinates" of vertices on same vertical side are 4 and -2.
So, the length of the rectangle is = 4 -(-2) = 6 feet.
Similarly, the width of rectangle is calculated as difference between "y-coordinates" of vertices on same horizontal side.
In this case, the "y-coordinates" of vertices on same horizontal side are 1 and -3.
So, the width of the rectangle is = 1 -(-3) = 4 feet,
To surround rectangle with a stone path, Marina need to add length of stone needed for the perimeter of rectangle, which is sum of all four sides.
The perimeter (P) is ⇒ P = 2(length + width),
Substituting the values,
We get,
⇒ P = 2(6 + 4) = 2(10) = 20 feet
Therefore, the correct option is (d).
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The given question is incomplete, the complete question is
Marina is drawing a plan for a new garden. The rectangle with the vertex (4,1) , (4,-3) , (-2,-3) , (-2,1)in the coordinate plane represents the garden, measured in feet. To surround the garden with a stone path, how many feet of stone does she need?
(a) 4 feet
(b) 6 feet
(c) 10 feet
(d) 20 feet
Answer:
20 feet because ik from experience
In which quadrant of the coordinate plane will you find the point (-3, -2)?
Answer:
Quadrant III
Step-by-step explanation:
The point has a negative x AND y value, so it would be in Quadrant III
Taking a look at the quadrant graph will help you.
What is the equation of this circle in general form?
Responses
x2+y2−2x−6y−26=0
x squared plus y squared minus 2 x minus 6 y minus 26 equals 0
x2+y2+2x+6y−26=0
x squared plus y squared plus 2 x plus 6 y minus 26 equals 0
x² + y² + 2x + 6y + 4 = 0
x, ² +, y, ² + 2, x, + 6, y, + 4 = 0
x2+y2−2x−6y+4=0
x squared plus y squared minus 2 x minus 6 y plus 4 equals 0
The equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36
How to find the equation of the circle in general formTo find the equation of a circle in general form, we need to complete the square for both x and y terms.
x^2 + y^2 - 2x - 6y - 26 = 0
First, we will complete the square for x terms:
x^2 - 2x + y^2 - 6y - 26 = 0
(x - 1)^2 - 1 + y^2 - 6y - 26 = 0
(x - 1)^2 + y^2 = 27
Now, we will complete the square for y terms:
(x - 1)^2 + (y - 3)^2 = 36
Therefore, the equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36
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Answer:
x2+y2−2x−6y−26=0
Step-by-step explanation:
Just took the test.
LOT OF POINTS AND BRAINLIEST IF YOU'RE RIGHT:
Public opinion in the large city of Hillwood is that 62 percent of the residents are in favor of increasing taxes to fund afterschool programs and 38 percent are against the increase. What is the approximate probability that more than 180 of the residents surveyed will be against increasing taxes if a random sample of 450 residents are surveyed? (4 points)
Answer:
0.16%
Step-by-step explanation:
Imagine you are a politician who wants to increase taxes in your city. You decide to conduct a survey among 450 residents to see how many of them are against your proposal. You know that the probability of finding someone who is against increasing taxes is 0.38. You hope that the survey will show that most people support your idea, or at least that the opposition is not too strong. However, when you get the results, you are shocked to see that more than 180 people are against increasing taxes. How unlucky are you? Well, let's do some math. This is a binomial probability problem. The probability of success (being against increasing taxes) is p = 0.38 and the number of trials (residents surveyed) is n = 450. The question asks for the probability of more than 180 successes, which is equivalent to the probability of at least 181 successes. Using a binomial calculator, the answer is approximately 0.0016 or 0.16%. That means that there is only a 0.16% chance of getting at least 181 people against increasing taxes in a sample of 450 residents. That's very rare and unlucky indeed! You might want to reconsider your proposal or find a better way to convince people that paying more taxes is good for them.
a cube is made up of 27 equal sized cubes. if all faces of the large cube are painted, how many small cubes will not have any paint on any of their faces?
If a large cube is made up of 27 equal-sized smaller cubes, and all faces of the large cube are painted, then the cubes on the interior of the large cube will not have any paint on any of their faces.
The large cube consists of 27 smaller cubes arranged in a 3x3x3 pattern. The smaller cubes on the exterior faces of the large cube will have some of their faces painted, while the smaller cubes on the interior will not have any of their faces painted.
To calculate the number of smaller cubes that will not have any paint on any of their faces, we need to subtract the smaller cubes on the exterior faces from the total number of smaller cubes in the large cube.
The number of smaller cubes on the exterior faces of the large cube can be calculated as follows:
There are 9 smaller cubes on each of the six faces of the large cube (3x3=9), for a total of 54 smaller cubes on the exterior faces.
So, the total number of smaller cubes in the large cube is 27, and the number of smaller cubes on the exterior faces is 54. Therefore, the number of smaller cubes that will not have any paint on any of their faces is:
27 - 54 = -27
Since we cannot have a negative number of cubes, the correct answer is 0. There will be 0 smaller cubes that will not have any paint on any of their faces.
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i need help please help me
You can take a look at this, the image that I attached might help.
For example, the first one shifts left because the h value is positive 3. -(3) = -3.
Enter the surface area of the figure
The surface area of the figure, given the diameter of the base and the height, would be 353.43 square millimeters.
How to find the area ?We can use the formula for the surface area of a cone:
Surface Area = πr² + πr√(r² + h²)
where r is the radius of the base and h is the height of the cone.
Since the diameter of the base is 9mm, the radius is half of that, or 4.5mm. The height of the cone is 20mm. Plugging these values into the formula, we get:
Surface Area = π(4.5)² + π(4.5)√(4.5² + 20²)
Surface Area = π(20.25) + π(4.5)√(436.25)
Surface Area = 353.43 millimeters²
Therefore, the surface area of the cone is approximately 353.43 square millimeters.
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Use the normal approximation to the binomial for a binomial probability distribution with p =.20 and n = 60 to determine the probability of exactly 17 successes?
The probability of exactly 17 successes in a binomial distribution with p=0.20 and n=60, using normal approximation to the binomial, is approximately 0.0129.
To use the normal approximation to the binomial, we need to check if the conditions for the approximation are met
np = 60 x 0.20 = 12 ≥ 10
n(1-p) = 60 x 0.80 = 48 ≥ 10
Both conditions are met, so we can use the normal approximation to the binomial.
The mean of the binomial distribution is μ = np = 12, and the standard deviation is σ = √(np(1-p)) = √(60 x 0.20 x 0.80) ≈ 2.19.
To find the probability of exactly 17 successes, we can use the normal distribution with mean μ = 12 and standard deviation σ ≈ 2.19, and approximate the discrete binomial distribution with a continuous normal distribution
P(X = 17) ≈ P(16.5 < X < 17.5)
where X is a continuous random variable that follows a normal distribution with mean μ = 12 and standard deviation σ ≈ 2.19.
Using the standard normal distribution, we can calculate the z-scores for 16.5 and 17.5
z1 = (16.5 - 12) / 2.19 ≈ 1.83
z2 = (17.5 - 12) / 2.19 ≈ 2.28
Using a standard normal distribution table or a calculator, we can find the probabilities associated with these z-scores
P(1.83 < Z < 2.28) ≈ P(Z < 2.28) - P(Z < 1.83) ≈ 0.0129
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Populations that can be modeled by the modified logistic equation dt can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b 0.0015 and a 0.2, use phase portrait analysis to determine which of the two limiting behaviors will be exhibited by populations with the indicated initial sizes Initial population is 286 individuals Initial population is 16 individuals a. Doomsday scenario: Population will exhibit unbounded growth in finite time b. Population will trend towards extinction
We can conclude:
a) For an initial population size of 286, the population will trend towards extinction.
b) For an initial population size of 16, the population will exhibit unbounded growth in finite time.
What is differential equations?
Differential equations are mathematical equations that describe the relationship between an unknown function and its derivatives (or differentials).
The modified logistic equation is given by:
dP/dt = aP - bP²
where P is the population size, and a and b are positive constants.
To determine the limiting behavior of the population, we need to analyze the phase portrait of the differential equation. This can be done by finding the equilibria of the system, and then examining the direction of the vector field near each equilibrium.
The equilibria of the system occur when dP/dt = 0. This leads to two possible equilibria:
P = 0, and P = a/b
The direction of the vector field near each equilibrium can be determined by examining the sign of dP/dt for values of P slightly greater and less than the equilibrium value.
Near P = 0, dP/dt = aP > 0 for P > 0, indicating that the population will grow in this region.
Near P = a/b, dP/dt = -bP² < 0 for P slightly greater than a/b, indicating that the population will decrease in this region.
Based on this analysis, we can conclude:
a) For an initial population size of 286, the population will trend towards extinction. This is because 286 is larger than a/b, so the population starts in the region where the vector field is pointing towards extinction.
b) For an initial population size of 16, the population will exhibit unbounded growth in finite time.
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Suppose that we would like to determine the proportion of U.S. citizens who have brown hair. To estimate this, we randomly select 100 people and we find that 63 of them have brown hair. Construct a 95% confidence interval for the proportion of people with brown hair in the U.S.
we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.
To construct a 95% confidence interval for the proportion of people with brown hair in the U.S., we can use the following formula:
[tex]Confidence Interval = p± z \sqrt{\frac{p(1-p)}{n} }[/tex]
where p is the proportion of people with brown hair in our sample, z is the critical value for a 95% confidence level (which is 1.96), and n is the sample size.
In this case, our sample proportion is , and our sample size is 100. Plugging these values into the formula, we get:
[tex]Confidence Interval = 0.63 ± 1.96\sqrt{\frac{0.63(1-0.63)}{100} }[/tex]
Simplifying the expression inside the square root, we get:
[tex]Confidence Interval= 0.63 ± 0.098[/tex]
Therefore, the 95% confidence interval for the proportion of people with brown hair in the U.S. is:
[tex]\frac{63}{100} = 0.63[/tex](0.532, 0.728)
This means that we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.
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help me plsssssssss
Answer: 13. 30
Step-by-step explanation:
13. Area = 18x * 10y = 180xy
Length = 6th
With ?
180xy = 6xy x width
180 x/6xy
Width = 30
14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver
3^5
____ is the formula x=-b±b2-4ac2a, used to find the solutions to a quadratic equation of the form ax2+bx+c=0.
The quadratic formula x = (-b ± √ ( [tex]b^2[/tex] - 4ac) / (2a) is used to find the solutions (or roots) of a quadratic equation of the form [tex]ax^2[/tex] + bx + c = 0.
In this formula, "a", "b", and "c" are coefficients of the quadratic equation, and the ± symbol indicates that there are two possible solutions, one with a positive square root and one with a negative square root. By plugging in the values of "a", "b", and "c" from the given quadratic equation, one can use the quadratic formula to calculate the solutions for x that satisfy the equation.
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x = (-b ± √(b² - 4ac)) / (2a) is the formula x=-b±b2-4ac2a, used to find the solutions to a quadratic equation of the form ax2+bx+c=0.
The formula x = (-b ± √(b² - 4ac)) / (2a) is known as the Quadratic Formula, used to find the solutions to a quadratic equation of the form ax² + bx + c = 0.
The formula x=-b± b2 -4ac2a, is called the quadratic formula, which is used to find the solutions (or roots) to a quadratic equation of the form ax2+bx+c=0,
where a, b, and c are coefficients of the equation.
The term under the square root sign (b2-4ac) is called the discriminant and can tell you whether the quadratic equation has two real solutions (if the discriminant is positive), one real solution (if the discriminant is zero), or two complex conjugate solutions (if the discriminant is negative).
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An architect is designing a house. He wants the bedroom to have the dimensions of 9 ft by 5 ft by 7 ft. The architect doubles one dimension to create the den. Does that mean the den will have double the volume of the bedroom?
Answer:
Yes
Step-by-step explanation:
The definition of dimension is Length, Width, and Height so if he doubles the dimensions it will be double. The volume is 630.
how do I do 3 + 2n = 7
In the given equation which is 3 + 2n = 7, the value of n = 2.
For, further explanation to find the value of the variable in the given equation, we can solve the given equation by transferring the non-variable digits to one side either to L.H.S or R.H.S.
Given equation = 2n + 3 =7
In the above equation, the variable is 'n' and the non-variable digits are '3' and '7'. To find the value of 'n', we can transfer the non-variable digits to the R.H.S (Right Hand Side) as shown below:
2n + 3 = 7
2n = 7 - 3
2n = 4
n = [tex]\frac{4}{2}[/tex]
n = 2.
So, from the above solution the value of 'n' is 2.
Given question is incomplete/incorrect, I assume the given question was to "obtain the value of n from the linear equation 3 + 2n = 7"
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Rewrite the equation in slope-intercept form: 5x + 9y = 30
Answer:
y = (-5/9)x + 30/9
Step-by-step explanation:
To rewrite the equation 5x + 9y = 30 in slope-intercept form, we need to isolate y on one side of the equation.
5x + 9y = 30
Subtract 5x from both sides of the equation to isolate 9y:
5x - 5x + 9y = -5x + 30
9y = -5x + 30
Divide both sides of the equation by 9 to solve for y:
9y/9 = (-5x + 30)/9
y = (-5/9)x + 30/9
1 individuals in a tetrahybrid cross is AaB-bCcDd. Assuming independent assortment of these four genes, what are the probabilities that F2 offspring will have the following genotypes?
1. AABBCCDD: The probability of this happening is [tex]1/16[/tex], since each parent would need to contribute a dominant allele for each gene.
2. AABBCcDD: This genotype can be produced in two ways:
a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.
The probability of this happening is = 1/128.
b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.
3. The probability of this happening is 1/32.
AaBbCcDd : The probability of this happening is 1/256.
4. aaBBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is 1/128.
b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is 1/32.
To solve this problem, we need to use the principles of probability and Punnett squares.
For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.
Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:
A | A | a | a
---|-----|-----|----
B | B | b | b
---|-----|-----|----
C | C | c | c
---|-----|-----|----
D | D | d | d
Each box in the Punnett square represents a possible combination of alleles from the two parents.
For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.
We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.
AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.
The probability of this happening is [tex](1/2)^4 = 1/16[/tex] , since each parent would need to contribute a dominant allele for each gene.
AABBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.
The probability of this happening is[tex](1/2)^4 * 1/2 * (1/2)^3 = 1/128[/tex]
b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is[tex]2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32[/tex]
AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).
The probability of this happening is [tex](1/2)^8 = 1/256.[/tex]
aaBBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is[tex](1/2)^4 * 1/2 * (1/2)^3 = 1/128.[/tex]
b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is [tex]2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.[/tex]
Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.
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3. A composite figure is created using
rectangle and a semicircle. What is the area
of the figure?
12 in
18 in
A=r²
The area of the composite figure is 343.62 square inches.
What is a 3D composite shape's area?
Composite things that are three dimensional (3D) are created by joining two or more objects. Finding each object's outside surface area and adding the surface areas together will yield the surface area of a 3D composite object.
Area of rectangle = length x width = 12 x 18 = 216 sq in
As a result, the radius is equal to 9 inches, or half the diameter.
[tex]Area \ of\ semicircle = (1/2) * \pi * r^{2} \\\\Area \ of \ semicircle = (1/2) * 3.14 * 9^{2} \\\\Area \ of \ semicircle = 127.62\ sq\ in[/tex]
The combined area of the rectangle and the semicircle is therefore equal to the area of the composite figure as a whole:
Total area = 216 sq in + 127.62 sq in = 343.62 sq in
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select the correct answer from each drop-down menu. a candy company designs a package to hold chocolates. the height of the container is 13 inches and the diameter of its bottom is 9 inches. diagram shows a shape with circular base and curved surface meeting at a point. the diameter of the base is labeled 9 inches and the height of the shape is labeled 13 inches. which shape best models the package, and what is the approximate surface area of the package? the best model for the package is a . the approximate surface area is square inches.
The candy company's package can be modeled as a right circular cone with a height of 13 inches and a base diameter of 9 inches.
The circular base of the cone holds the chocolates, while the curved surface extends up to a point at the top. To calculate the surface area, we need to find the area of the circular base and the area of the curved surface. The formula for the area of a circle is pi times the radius squared, so the radius of the base is 4.5 inches.
The area of the base is pi times the radius squared, or approximately 63.62 square inches. The formula for the curved surface area of a cone is pi times the radius times the slant height, which is the square root of the height squared plus the base radius squared. Substituting the given values into the formula, the curved surface area is approximately 207.35 square inches. Thus, the approximate surface area of the package is the sum of the area of the base and the curved surface area, or approximately 271.97 square inches.
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Select the correct answer.
Kristen gathered data from her classmates about the age and contents of their backpacks. She displayed the data in two scatter plots.
Does either scatter plot indicate a positive correlation between the variables?
A. Only plot A
B. Only plot B
C. Both plot A and plot B
D. Neither plot A nor plot B
Plot B shows a negative correlation between the age and the number of items in the backpack, while plot A does not show any clear correlation. Therefore, the correct answer is B. Only plot B.
In plot A, the data points appear scattered and do not show a clear trend or pattern.
In plot B, the data points are mostly clustered around a diagonal line that slopes downward from left to right, indicating a negative correlation between the age and the number of items in the backpack. Since the question asks for a positive correlation, the correct option is B. Only plot B.
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--The given question is incomplete, the complete question is given
" Question
Select the correct answer.
Kristen gathered data from her classmates about the age and contents of their backpacks. She displayed the data in two scatter plots.
Does either scatter plot indicate a positive correlation between the variables?
A. Only plot A
B. Only plot B
C. Both plot A and plot B
D. Neither plot A nor plot B"--
Please help! The question is on the screenshot link.
The amount of interest that is earned on Sandra's card after 1 year if Sandra makes no payment is: $538.48.
How to obtain the interestWe can obtain the right answer by using using the formula for compound interest as follows: A = P(1 + r/n)^(nt)
where:
P = $2,500
r = 0.1999 (since the APR is 19.99%)
n = 4 (since the interest compounds quarterly)
t = 1 (since we're looking at the interest earned after 1 year)
Substituting these values into the formula, we get:
A = $2,500(1 + 0.1999/4)^(4*1)
A = $2,500(1.049975)^4
A = $2,500(1.207789)
A = $3,019.47
So after 1 year, Sandra will owe $3,019.47 on her credit card. The interest earned is the difference between this amount and the initial amount charged, which is:
Interest = $3,019.47 - $2,500
Interest = $519.47
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Lucy made tables of values to approximate the solution to a system of
equations. First she found that the x-value of the solution was between 1 and
2. And then she found that it was between 1. 5 and 2. Next, she made this
table,
1. 5
16
1. 7
18 T
1. 9
y=-3x + 6
1. 5
12
09
0.
6
03
y = 4% - 5
1
14
18
22
2. 6
If Lucy made "tables-of-values" to approximate the solution to "system-of-equations", then the "ordered-pair" which is the best approximation of exact solution is (b) (1.6 , 1.3).
An "Ordered-Pair" is defined as a pair of values which are arranged in a specific order, generally denoted as (x, y), where x represents the first value and y represents the second value.
We are finding an ordered pair that satisfies the following conditions:
(i) The x-value falls within the given range of x-values between 1 and 2.
(ii) The y-value for the equation y = -3x + 6 is closest to the given y-value for the equation y = 4x - 5.
In Option (a) : (1.7, 0.9);
The "x-value" of 1.7 falls within the given range of x-values between 1 and 2.
For the equation "y = -3x + 6", the corresponding "y-value" at x = 1.7 is 0.9, which is not as close to the given y-value for the equation y = 4x - 5, which is 1.4.
So, (1.7, 0.9) is not the best approximation.
In Option (b) : (1.6, 1.3);
The "x-value" of 1.6 falls within the given range of x-values between 1 and 2.
For the equation "y = -3x + 6", the corresponding y-value at "x = 1.6" is 1.2, which is closest to the given y-value for the equation y = 4x - 5, which is 1.4.
So, the ordered pair (1.6, 1.3) is best-approximation.
In Option(c) : (1.5, 1.8);
The "x-value" of 1.5 falls within the given range of x-values between 1 and 2.
For the equation "y = -3x + 6", the corresponding "y-value" at x = 1.5 is 1.5, which is away from the y-value for equation "y = 4x - 5", which is 1.4.
So, (1.5, 1.8) is not the best approximation.
In Option (d) : (1.9, 1.5);
The "x-value" of 1.9 falls within the given range of x-values between 1 and 2.
For the equation "y = -3x + 6", the corresponding y-value at x = 1.9 is "0.3", which is not as close to the given y-value for the equation "y = 4x - 5", which is 1.4.
So, (1.9, 1.5) is not the best approximation.
Therefore, the correct option is (b).
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The given question is incomplete, the complete question is
Lucy made tables of values to approximate the solution to a system of equations. First she found that the x-value of the solution was between 1 and 2. And then she found that it was between 1. 5 and 2. Next, she made this table,
x y = -3x + 6 y = 4x - 5
1.5 1.5 1
1.6 1.2 1.4
1.7 0.9 1.8
1.8 0.6 2.2
1.9 0.3 2.6
2.0 0 3
Which ordered pair is the best approximation of the exact solution?
(a) (1.7 , 0.9)
(b) (1.6 , 1.3)
(c) (1.5 , 1.8)
(d) (1.9 , 1.5)
helicopters The four blades of a helicopter meet at right angles and are
all the same length. The distance between the tips of two adjacent blades
is 36 ft. How long is each blade? Round your answer to the nearest tenth.
Britney had a math quiz yesterday. She got 7 questions correct for every 2 that she got incorrect.
If Britney got 10 more questions correct than she got incorrect, how many questions were on the quiz?
Answer:18
Step-by-step explanation: