what do parallel and perpendicular cross sections of a sphere look like?
Parallel cross sections of a sphere look like circles with the same radius as the sphere, while perpendicular cross sections look like points. Cross sections taken at other angles will be ellipses.
What you understand by sphere?A sphere is a three-dimensional geometric shape that is perfectly round in shape, like a ball. It is defined as the set of all points in three-dimensional space that are at a constant distance (the radius) from a given point called the center.
If we take a cross section of a sphere, the resulting shape will depend on the angle at which the section is taken relative to the center of the sphere.
If we take a plane that is parallel to the base of the sphere, the cross section will be a circle with the same radius as the sphere. This is because the intersection of the plane with the sphere will be a circle, and since the plane is parallel to the base of the sphere, the circle will have the same radius as the sphere.
On the other hand, if we take a plane that is perpendicular to the base of the sphere, the cross section will be a point. This is because the plane will intersect the sphere at only one point, which is the point at which the plane is perpendicular to the sphere.
If we take a plane that is neither parallel nor perpendicular to the base of the sphere, the resulting cross section will be an ellipse. The size and shape of the ellipse will depend on the angle at which the plane intersects the sphere.
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Area use a 7. 2 pans of blue pink and white paint to paint her bedroom walls 1/4 of this month is blue pants and the rest is wipe it how many pensive white paint did you use to paint her bedroom walls
If 1/4 of this amount is blue paint, and the rest is white paint, Area used 5.4 pints of white paint to paint her bedroom walls.
Given that Area used a total of 7.2 pints of blue and white paint to paint her bedroom walls. And 1/4 of the amount is blue paint, then the remaining 3/4 of the amount must be white paint.
To find the amount of white paint used, we can use the following formula:
Amount of white paint = Total amount of paint - Amount of blue paint
Since we know that the total amount of paint used is 7.2 pints and 1/4 of that amount is blue paint, we can calculate the amount of blue paint as:
Amount of blue paint = (1/4) x 7.2 = 1.8 pints
Now we can substitute these values in the formula to find the amount of white paint used:
Amount of white paint = 7.2 - 1.8 = 5.4 pints
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The answer is "The IQR is the best measure of variability, and it equals 7. because the best measure of variability for the data is the IQR, and its value is 7
What is the linear function?A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
According to the given information:The given plot displays the distribution of the number of roses purchased per day at a grocery store. The best measure of variability for this data would be the interquartile range (IQR) since it is robust to outliers and provides a measure of the spread of the middle 50% of the data.
To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.
From the plot, we can see that there are a total of 11 data points: one at 1, two at 2, three at 6, three at 7, two at 8, and three at 9. The median (Q2) is 7 since it is the middle value when the data are arranged in order.
To find Q1, we need to find the median of the lower half of the data. Since there is one data point below 6 and three data points at 6, the lower half of the data consists of four points: 1, 2, 6, and 6. The median of this set is (1+2)/2 = 1.5.
To find Q3, we need to find the median of the upper half of the data. Since there are two data points at 8 and three data points at 9, the upper half of the data consists of five points: 8, 8, 9, 9, and 9. The median of this set is (8+9)/2 = 8.5.
Therefore, the IQR is Q3-Q1 = 8.5-1.5 = 7.
Therefore, the answer is "The IQR is the best measure of variability, and it equals 7. because the best measure of variability for the data is the IQR, and its value is 7
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48 students took an arithmetic test. If 36 students passed the test, what percent of students have passed? Show your work using the
scratchpad.
The percentage of the students who passed the test is
5. A cylinder has radius 3 inches and height 5 inches. A cone has the same radius and height. (Lesson 5-13)
b. Find the volume of the cone.
c. What fraction of the cylinder's volume is the cone's volume?
Joe’s broker’s fee schedule is given in the table. Joes current portfolio is worth $50,000. He wants to purchase 50 shares of a company’s stock fir a purchase price of $15 per share.
Joe will need to pay a commission of _____.
The total amount charged by the broker will be ______.
Space 1: $7. 50, $5. 00, $1. 50
Space 2: $17. 50, $15. 50, $15. 0
Jow will need to pay a commision of $7.50. The total amount charged by the broker will be $17.50
Joes current portfolio is worth $50,000
A purchase price one share = $15
He wants to purchase 50 shares of a company's stock
Using unitary method the cost of 50 shares would be,
C = 50 × 15
C = $750
Since his portfolio is less than $100000 the amount chanrged by the broker would be equal to the 1% commision plus fees per trade.
First we find the commision.
1 percent of $750
= 1/100 × 750
= $7.5
And the fees per trade = $10
So, the total amount charged by the broker = $10 + $7.5
= $17.5
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Find the complete question below.
What are the coordinates of F' and G' for D(6.(2,5)) [F (3,11), G (2,8)]?
Answer: To find the coordinates of F' and G', we need to reflect points F and G across the line y = 5, since point D is located on this line.
For point F, the y-coordinate changes from 11 to -1, since the distance between the line y = 5 and point F is 6 units (2 times the distance between D and the line). Therefore, the coordinates of F' are (3,-1).
For point G, the y-coordinate changes from 8 to 2, since the distance between the line y = 5 and point G is 3 units (1.5 times the distance between D and the line). Therefore, the coordinates of G' are (2,2).
Thus, the coordinates of F' are (3,-1) and the coordinates of G' are (2,2).
13 Which polynomial is twice the sum of 4x^2-x + 1 and -6x^2 + x - 4?
(3)-4x²-6
(4)-2x²+x-5
(1)-2r²-3
(2)-41²-3
Answer: is option (3) -4x²-6.
Step-by-step explanation: First, we need to add the two given polynomials:
4x^2 - x + 1 + (-6x^2 + x - 4) = -2x^2 - 3
Now, we need to multiply this sum by 2:
2(-2x^2 - 3) = -4x^2 - 6
Therefore, the polynomial that is twice the sum of 4x^2-x+1 and -6x^2+x-4
You want to estimate the proportion of individuals in your area who think the public school system needs major overhauling. If you believe the proportion will be about 35%, how many individuals will you need to sample if you want a 95% margin of error to be no more than 3%? at least 30 at least 1068 at least 972
We cannot have a fraction of a person in the sample, we need to round up to the next whole number, which is 1022.
So, you will need to sample at least 1022 individuals to achieve a 95% confidence level with a margin of error no more than 3%.
This means that the correct answer among the given options is "at least 1068".
To estimate the sample size needed for survey, you can use the formula for sample size calculation in a proportion estimation problem.
The formula is:
[tex]n = (Z^2 * p * (1-p)) / E^2[/tex]
where:
n = required sample size
Z = Z-score, which corresponds to the desired confidence level (1.96 for a 95% confidence level)
p = estimated proportion (0.35 in this case)
E = desired margin of error (0.03 in this case)
Now, let's plug the values into the formula:
[tex]n = (1.96^2 * 0.35 * (1-0.35)) / 0.03^2[/tex]
n = (3.8416 * 0.35 * 0.65) / 0.0009
n = 0.919326 / 0.0009
n ≈ 1021.473.
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What is the volume and total surface area of each shape combined?
The volume and total surface area of each shape combined is calculated below.
How to find the volume and total surface area of each shape combined?For cone-hemisphere shape
Volume = volume of cone + volume of hemisphere
Volume = 1/3πr²h + 2/3πr³
where r = 9/2 = 4.5 m
h = √(13² - 4.5²) (Pythagoras)
h = 12.20 m
Volume = 1/3πr²h + 2/3πr³
Volume = (1/3 * 3.14 * 4.5² * 12.2) + (2/3 * 3.14 * 4.5³)
Volume = 449.33 m³
Surface area = curved surface area of cone + curved surface area of hemisphere
Surface area = πrl + 2πr², where l = 13 m
Surface area = (3.14 * 4.5 * 13) + (2 * 3.14 * 4.5²)
Surface area = 310.86 cm²
For hemisphere-cylinder shape
Volume = volume of hemisphere + volume of cylinder
Volume = 2/3πr³ + πr²h
where r = 22/2 = 11 ft
height of cylinder (h) = 45 - 11 = 34 ft
Volume = (2/3 * 3.14 * 11³) + (3.14 * 11² * 34)
Volume = 15704.19 ft³
Surface area = curved surface area of hemisphere + curved surface area of cylinder + curved surface area circular base of cylinder
Surface area = 2πr² + πr² + 2πrh
Surface area = 3πr² + 2πrh
Surface area = (3 * 3.14 * 11²) + (2 * 3.14 * 11 * 34)
Surface area = 3488.54 ft²
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Find the quotient. Assume that no denominator has a value of 0.
5x^2/7÷10x^3/21
The quotient of the expression 5x^2/7÷10x^3/21 is 3/(2x)
Finding the quotient of the expressionFrom the question, we have the following parameters that can be used in our computation:
5x^2/7÷10x^3/21
Assume that no denominator has a value of 0, we have
5x^2/7÷10x^3/21 = 5x^2/7 ÷ 10x^3/(7 * 3)
Express as products
So, we have the following representation
5x^2/7÷10x^3/21 = 5x^2/7 * (7 * 3)/10x^3
When the factors are evaluated, we have
5x^2/7÷10x^3/21 = 5 * 3/10x
So, we have
5x^2/7÷10x^3/21 = 15/10x
This gives
5x^2/7÷10x^3/21 = 3/(2x)
Hence, the solution is 3/(2x)
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Jazmin and Justine went shopping for back to chool clothes. Jazmin purchasrd three shirts and one pair of shorts ans spent $38. 0. Justine bought four shirts and three pairs of shorts and spent $71. 50.
Part A: Assumibg all the shirts cost the same amount and all the shorts cost the same amount, write a system os equations to represent each girl's shoppins spree
Part B: Use the elimination method to solve for the price of one pair of shorts
The equations to represent each girl's shoppins spree is 3x + y = 38.0 and 4x + 3y = 71.50. Price of one shirt costs $8.50 and price of one pair of shorts costs $12.50.
Let x be the price of one shirt, and y be the price of one pair of shorts. Then, we can write the following system of equations
For Jazmin
3x + y = 38.0
For Justine
4x + 3y = 71.50
To solve for the price of one pair of shorts using elimination method, we need to eliminate one of the variables. We can do this by multiplying the first equation by 3 and the second equation by -1, and then adding them together
9x + 3y = 114.0
-4x - 3y = -71.50
5x = 42.50
x = 8.50
So, one shirt costs $8.50.
To find the price of one pair of shorts, we can substitute the value of x into either of the original equations and solve for y. Using the first equation
3(8.50) + y = 38.0
25.50 + y = 38.0
y = 12.50
Therefore, one pair of shorts costs $12.50.
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1.6 Give a reason why the bank is legible to charge service fees?
Answer:
Banks are eligible to charge service fees to cover the costs of providing and maintaining various banking services such as account maintenance, ATM access, online banking, and customer support. These fees help banks to generate revenue and continue to offer their services to customers. The specific fees and their amounts can vary depending on the bank and the type of account or service being used.
Write a short paragraph about correlation coefficient. Describe what it is, how to find it, what it looks like, and how it is used.
The correlation coefficient is a statistical measure that indicates the strength and direction of the relationship between two variables.
Correlation coefficient is denoted by the symbol "r" and ranges from -1 to 1.
A correlation coefficient of 1 indicates a perfect positive correlation, where as one variable increases, the other variable also increases at the same rate.
A correlation coefficient of -1 indicates a perfect negative correlation, where as one variable increases, the other variable decreases at the same rate.
A correlation coefficient of 0 indicates no correlation between the two variables.
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twice a certain number is added to 10.if the result is minus 14, find the number
The value of the unknown number -12.
What is the value of the unknown number?Given that: twice a certain number is added to 10 and the result is minus 14.
Let's assume that the number we are trying to find is "x".
We can represent the statement twice this number (2x) is added to 10, and the result is -14 in an algebraic equation.
2x + 10 = -14
We can solve for x by isolating it on one side of the equation. We can start by subtracting 10 from both sides of the equation:
2x + 10 - 10 = -14 - 10
2x = -14 - 10
Simplifying the right side of the equation, we get:
2x = -24
Finally, we can solve for x by dividing both sides of the equation by 2:
2x/2 = -24/2
x = -12
Therefore, the number we are looking for is -12.
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The question is: Emily sold 56 of the 145 bracelets. What percent of the bracelets did she sell? Show your strategy.
Answer:
[tex]percentage = \frac{56}{145} \times 100[/tex]
56/145×100
0.386...×100
38.6%
Starting at the same point Tom and Juanita goes biking in opposite directions if Tom rides at the speed of 30mph and Tom rides at the speed 30mph how far apart will they be in 3 hours
Starting from the same point when bike riding, two individuals are riding. Tom and Juanita goes on biking in opposite directions to each other. Tom rides at speed of 30 mph and Juanita rides at speed of 30 mph in one hour. This will both be added together. And later will be add both speed in third hour that gives us the final value. The answer of this will be seventy two miles.
[tex]30+30[/tex] in one hour
[tex]30+30[/tex] in second hour
[tex]30+30[/tex] in the third hour
[tex]\boxed{\bold{= 270 \ miles}}[/tex]
Solve the inequality for the variable: 2(3c + 15) + 4c > 100
Answer:
c > 7
Step-by-step explanation:
Now we have to,
→ Find the required value of c.
The equation is,
→ 2(3c + 15) + 4c > 100
Then the value of c will be,
→ 2(3c + 15) + 4c > 100
Applying Distributive property:
→ 2(3c) + 2(15) + 4c > 100
→ 6c + 30 + 4c > 100
Combining the like terms:
→ 10c + 30 > 100
→ 10c > 100 - 30
→ 10c > 70
Dividing the value 70 with 10:
→ c > 70 ÷ 10
→ [ c > 7 ]
Hence, the answer is c > 7.
Hello !
Answer:
[tex]\boxed{\sf c > 7 \ \ \ ||\ \ \ \sf (7,+\infty)}[/tex]
Step-by-step explanation:
We are looking for the values of c that satisfy the following inequality :
[tex]\sf 2(3c + 15) + 4c > 100[/tex]
Let's expand the left side of the inequality.
[tex]\sf 2\times 3c +2\times 15+4c > 100\\6c+30+4c > 100[/tex]
Now we will combine like terms :
[tex]\sf 10c+30 > 100[/tex]
Let's substract 30 from both sides of the inequality.
[tex]\sf 10c+30-30 > 100-30\\10c > 70[/tex]
Finally, let's divide both sides by 10.
10>0 so the inequality remains the same.
[tex]\sf\frac{10c}{10} > \frac{70}{10} \\\boxed{\sf c > 7}[/tex]
Have a nice day ;)
What is 10/9 minus negative 1 1/3 equal?
hi
10/9 - 11/3 = 10/9 - 33/9 = -23/9
Answer:
-23/9
Step-by-step explanation:
You would need to find a common denominator which would be 9.
The next step would be to combine the top 10-11 (times)3 over 9
Then you multiply -11 by 3 tp get 10 -33 /9
The last and final step would be tp subract 33 from 10 to get 33 -10
Which will led you to your final awnser which is -23/9
see the scatter plot of Wins compared to Free Throw Attempts per Game.
Then use the scatterplot to write your line of best fit and determine the correlation.
I'm confused what's being asked here...but if you're looking for someone to check it then:
The line of best fit is drawn correctly; there are about the same amount of dots on the top and bottom of the line.
And the correlation is positive
Part A: Complete the square to rewrite the following equation in standard form. Show all
necessary work. (6 points)
x² - 4x + y² + 8y = -4
Part B: What are the center and radius of the circle? (4 points)
Answer:
A) (x - 2)² + (y + 4)² = 4²B) The center is (2, - 4), radius is r = 4 units-----------------------------
Standard form for the equation of a circle is:
(x − h)² + (y − k)² = r²,where the center is (h, k) and the radius is r units.
Part AComplete the square by adding missing parts of the identity:
(a ± b)² = a² ± 2ab + b²Apply this to the given equation:
x² - 4x + y² + 8x = - 4x² + 2(-2)(x) + (-2)² + y² + 2(4)(y) + 4² = - 4 + (-2)² + 4²(x - 2)² + (y + 4)² = - 4 + 4 + 4²(x - 2)² + (y + 4)² = 4²Part BAs per the standard form, the center is (h, k) = (2, - 4) and radius is r = 4 units.
What is the area of each shape?
Answer:
19.25
Step-by-step explanation:
You add up all three sides which would be 10+3.25+6 to get the awnser 19.25
If I was asked to think of a number and multiply it by 2, I could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, add 3 to it and multiply the result by 7."
Find the surface area of this triangular prism! Hurry!
Answer:
240m
Step-by-step explanation:
You need to find the area of each surface.
FORMULAS
A= L × W
A= 1/2(L × W)
SIDES
Base = 12×6 = 72
Top of triangle = 6×13 = 78
Side of triangle = 5×6 = 30
Triangular side 1 = 1/2(5×12) = 30
Triangular side 2 = 1/2(5×12) 30
Now you need to add all of the surface areas together.
72+78+30+30+30 = 240
Therefore, the surface area of the triangular prism is 240m.
IM SO SORRY IF THIS DOESN'T MAKE ANY SENSE!
Ana dives into a pool off of a springboard high dive.
Her height (in meters above the water), seconds after diving, is modeled by
h(x)=−5(x+1)(x−3)h, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 3, right parenthesis
How many seconds after diving will Ana hit the water?
Ana will hit the water 3 seconds after diving.
To find when Ana will hit the waterWe need to solve for when her height is 0. We can set h(x) = 0 and solve for x:
-5(x+1)(x-3) = 0
This expression equals zero when either (x+1) = 0 or (x-3) = 0. Solving for these values gives:
x+1 = 0 or x-3 = 0
x = -1 or x = 3
The negative value for x doesn't make sense in this context since it represents a time before Ana even jumped off the board, so we can ignore it.
Therefore, Ana will hit the water 3 seconds after diving.
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USE A MODEL In a mathematics exam with a maximum score of 100, Machelle loses less than 27 points. The table shows the grade that matches the exam score. Compare points to grades and identify which grade Machelle can get.
Machelle can get a grade of D or higher on her exam.
Describe Inequality?In mathematics, an inequality is a mathematical statement that describes a relationship between two quantities that are not necessarily equal. An inequality can express that one quantity is less than, less than or equal to, greater than, greater than or equal to, or not equal to another quantity.
Inequalities can be represented using various symbols. For example, the symbol < represents "less than," the symbol > represents "greater than," the symbol ≤ represents "less than or equal to," and the symbol ≥ represents "greater than or equal to." The symbol ≠ represents "not equal to."
Inequalities are also used in algebra to solve equations and to represent the solution set of an equation. In this context, an inequality can represent all the possible values of a variable that satisfy the equation. For example, the inequality x > 5 represents all the values of x that make the expression x - 5 positive.
We can write an inequality to represent the number of points, m, obtained by Machelle on her exam:
m > 100 - 27
Simplifying this expression, we get:
m > 73
This means that Machelle must have scored more than 73 points on her exam. Based on the table, we can see that a score of more than 73 points corresponds to a grade of at least a D. Therefore, Machelle can get a grade of D or higher on her exam.
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The complete question is:
The diameter of a circle is 18 inches. What is the area of a sector bounded by a 30° arc?
Answer: [tex]6.75\pi[/tex] inches^2
Step-by-step explanation:
If the diameter is 18 inches, the radius must be 18/2 = 9 inches.
Thus, we can calculate the area using the area of a circle = [tex]\pi r^{2}[/tex].
Plugging in the values, we get the area = [tex]81\pi[/tex] inches^2.
Since 30 degrees is 1/12 of 360 degrees, a 30-degree sector would be equal to 1/12 the area of the circle.
Therefore, we divide [tex]81\pi[/tex]/12 to get the area of the sector = [tex]6.75\pi[/tex] inches^2.
please give a step by step ASAP
The correct option is the fourth one, the slope and y-intercept are different.
Which statement is correct?Here we have the linear equation:
3x - 5y = 4
We know that it is dilated by a scale factor of 5/3, so let's find the dilation.
We can rewrite the linear equation as:
-5y = 4 - 3x
y = (3/5)x - 4/5
Now let's apply the dilation:
y = (5/3)*[ (3/5)x - 4/5]
y = x - 4/3
Then we can see that the slope and the y-intercept are different, the correct option is 4.
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what value of c is such that 99% of all parcels are at least 1 lb under the surcharge weight? (round your answer to four decimal places.)
the value of c is 11.165 lbs. This was calculated using the z-score formula, assuming a normal distribution with a mean weight of 10 lbs and a standard deviation of 0.5 lbs. This ensures that 99% of all parcels are at least 1 lb under the surcharge weight.
To find the value of c, we need to use the standard normal distribution and the z-score formula. Since we know that 99% of all parcels are at least 1 lb under the surcharge weight, we can use the z-score associated with the 99th percentile, which is 2.33 (from a z-score table).
The formula for the z-score is:
z = (x - μ) / σ
where x is the weight of the parcel, μ is the mean weight, and σ is the standard deviation.
In this case, we want to find the weight of the parcel that is at the 99th percentile, which is 1 lb under the surcharge weight. Let's call this weight x. We know that the surcharge weight is c, so the weight of the parcel that is 1 lb under the surcharge weight is (c - 1).
Using the z-score formula and substituting the values we know, we get:
2.33 = ((c - 1) - μ) / σ
We want to solve for c, so we need to rearrange the equation:
c - 1 = 2.33σ + μ
c = 2.33σ + μ + 1
We don't know the values of μ and σ, but we can use the fact that the distribution is normal to estimate them. We can assume that the distribution is centered at the mean weight of all parcels, and that the standard deviation is equal to the average difference between the weight of each parcel and the mean weight.
Let's say that the mean weight is 10 lbs, and the standard deviation is 0.5 lbs. Then, we can plug these values into the equation for c:
c = 2.33(0.5) + 10 + 1
c = 11.165
So, the value of c that ensures that 99% of all parcels are at least 1 lb under the surcharge weight is approximately 11.165 lbs.
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Consider the triangle with vertices (-7, -2), (-2, -5) , and (2, 3). What is the approximate perimeter of the triangle?
The perimeter of the triangle is 23.623 units.
What is perimeter of triangle?
Finding the distance around a triangle entails determining its perimeter. The distance formula can be used to calculate the side lengths if you don't already know all of them. The simplest way to find a triangle's perimeter is to add up all of its sides' lengths.
The distance between two points (x1,y1) and (x2,y2) can be determined using the following formula: √(x₂-x₁)² + (y₂ - y₁)²
Let the given vertices are (-7, -2), (-2, -5) , and (2, 3).
Distance formula for two points is = √(x₂-x₁)² + (y₂ - y₁)²
Using the formula,
AB = √((-2)-(-7))² +((-5)-(-2))²
= √(-2+7)² + (-5+2)²
= √5² + (-3)²
= √25 + 9
= √31
Similarly, BC = √(2 - (-2))² + (3-(-5))²
= √(2+2)² + (3+5)²
= √4² + 8²
= √16+64
= √80
CA = √((-7)-2)² + (-2 + 3)²
= √(-9²) + 1
= √81+1
=√82
Perimeter of triangle = AB + BC + CA
= √31 +√81 +√82
= 5.5677 + 9 + 9.0553
= 23.623
Therefore, the perimeter of the triangle is 23.623 units.
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