The volume of the solid right pyramid is, x²y cm³.
What is a pyramid?A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces.
The number of sides on its base is equal to the number of lateral faces.
The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.
We know, Area of a square is a product of it's any two sides.
Now, If we want to determine the volume we have to multiply the height also(another dimension).
Therefore, From the given information and options, A pyramid with square bases(x) and a height of 'y' will have a volume,
= x×x×y cm³.
= x²y cm³.
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A data set includes 103 body temperatures of healthy adult humans having a mean of 98.1°F and a standard deviation of 0.56°F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6°F as the mean body temperature?
The sample suggests that the true mean is likely to be between 98.0°F and 98.2°F, which is lower than 98.6°F. 98.6°F overestimates the mean body temperature of all healthy humans.
What is standard deviation?Standard deviation is defined as the measure of how spread out numbers are. It measures the average distance between each number in a set of data and the mean. It is used to measure the variation and dispersion of a set of data from its mean.
A 99% confidence interval estimate of the mean body temperature for all healthy humans can be calculated using the following formula: mean ± 2*standard deviation/square root of the sample size. In this case, the confidence interval is 98.1°F ± 0.12°F. This means that the mean body temperature of all healthy humans is likely to be between 98.0°F and 98.2°F.
This sample suggests that 98.6°F is not an accurate representation of the mean body temperature of all healthy humans.
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Drag the descriptions of each investment in order from which will earn the least simple interest to which will earn the most simple interest of 2000
1) investment of 2000 at 10% simple interest for 9 years
2) investment of 2000 at 3% simple interest for 20 years
3) investment of 2000 at 10% simple interest for 3 years
The response to the given question would be that Because it has a interest higher interest rate and a longer term than option 3, option 1 would generate the greatest interest.
what is interest ?By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The interest rate of the loan is defined as this ratio.
The following would be the order of 2000 simple interest generated on an investment, from least to most:
2000 invested for 20 years at 3% simple interest
2000 invested for three years at 10% simple interest
2000 invested at 10% simple interest for nine years
Because of its longer length and lower interest rate than the other two alternatives, Option 2 would yield the least amount of interest.
Due to its higher interest rate and longer period, option 3 would generate more interest than option 2.
Because it has a higher interest rate and a longer term than option 3, option 1 would generate the greatest interest.
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12a^4+ (-29a^4) simplify
Answer: -17a^4
Step-by-step explanation:
Combine like terms
12a^4 +(-29a^4)
(12a^4-12a^4) - (29a^4-12a^4) =
-17a^4
Hope this helps
round 53.121 nearest half
Therefore , the solution of the given problem of rational comes out to be 53.00 for the given rational number after rounding off.
What precisely are rational numbers?The percentage (not the percentage) of two integers can be used to represent rational numbers. A reasonable fraction is one with a non-zero denominator. Rational values are including 1/2, 1/5, but they also include 3/4. Additionally, "0" could be expression as a real purpose in a variety of forms, including 0/1, 0/2, and 0/3. However, 1/0, 2/0, 3/0, along with others. Seven is a reasonable amount. A rational number can be obtained by dividing two factors.
Here,
Given :
rational number or integer is 53.121
To round it to the nearest half so ,
According to rounding off the integer , we can round off to 54 when it is 53.5 or above .
But since it is below than that
We get answer as 53.00 for the given rational number after rounding off.
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find the slope of a line perpendicular to each given line.
y= -2x -2
Answer:
Using the slope-intercept form, the slope is −2 .
Step-by-step explanation:
Step-by-step explanation:
solution
Equation of line,
y=-2x-2
2x+y=2 - - - - - - -1
Now,
slope of line,
m= -x coefficient/ y coefficient
= -2/1
= -2
Slope of required line which is perpendicular to the line
m.m = -1
-2.m = -1
m = -1/-2
m =1/2
16. evaluate this equation
We simplify the summation to get:
S₄ = 8*(3ⁿ⁻¹)
How to evaluate the summation?Remember that the large sigma means that we need to add from the lower number to the larger number.
The particular problem here is that "n" is not the index in the summation, so we can't evaluate that variable, we will just have 4 terms (for k = 1 to k = 4) but the variable k does not appear, so we will have 4 times the same term:
S₄ = 2*(3ⁿ⁻¹) + 2*(3ⁿ⁻¹) + 2*(3ⁿ⁻¹) + 2*(3ⁿ⁻¹)
S₄ = 4*2*(3ⁿ⁻¹)
S₄ = 8*(3ⁿ⁻¹)
That is the simplification we can do.
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The quotient of ten and a number
Answer: 10 / 5 = 2
Step-by-step explanation:
The hypotenuse of a right triangle is 54 inches long. Find possible measures for the legs of the triangle.Round to the nearest tenth. Write an argument that can be used to defend your solution.
Using the Pythagorean theorem we know that the rest 2 sides of the given right triangle are 27 inches long.
The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry.
The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side.
So, we know the Pythagorean theorem which is:
H² = a² + b²
We know that:
H² = a² + b²
54² = a² + b²
Suppose that the given right triangle is also an isosceles triangle with the rest of the sides being of the same length. Then,
54/2 = 27
Similarly,
54² = a² + b²
54² = 27² + 27²
Therefore, using the Pythagorean theorem we know that the rest 2 sides of the given right triangle are 27 inches long.
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Can someone help me please? Thank you
Answer:
1. 6/18 = 1/3
9/21 = 3/7
2. 4/6 = 2/3
2/4 = 1/2
3. 6/12 = 1/2
8/12 = 2/3
4. 2/8 = 1/4
3/6 = 1/2
5. 7/21 = 1/3
8/10 = 4/5
6. 9/12 = 3/4
12/20 = 3/5
7. 8/16 = 1/2
10/25 = 2/5
A baker weighs some pieces of chocolate before he begins making a recipe. He writes the following weights measured in ounces: 2.6, 2.796, 2.94, 2.29, 2.064. How many ounces did the heaviest piece of chocolate weigh?
Answer:
The heaviest piece of chocolate weighed 2.94 ounces.
Step-by-step explanation:
Consider the parabola represented by this equation.
4x2 + 4x + 2y + 1 = 0
Which features are features of the parabola?
0
opens down
opens to the left
directrix at y = ㅎ
vertex at (-1,0)
directrix at x =
02/00
HELPPPP MEEEW
The key features of the parabola include the following:
A) opens down
C) directrix at y = 1/8
D) vertex at (-1/2, 0).
How to determine the equation of a parabola?Mathematically, the standard equation of the directrix lines for any parabola is given by this mathematical expression:
y = a(x - h)² + k.
Where:
h and k are the vertex.a represents the leading coefficient.Based on the information provided about the parabola, we have:
4x^2 + 4x + 2y + 1 = 0
2(y + 1/2) = -4(x + 1/2)^2 + 1
(y + 1/2) = -2(x + 1/2)^2 + 1/2
By comparing to the standard form, we have:
Vertex, (h, k) = (-1/2, 0).
Additionally, the distance between the vertex and the directrix is given by:
y = |1/(4a)|
y = |1/(4 × -2)|
y = |-1/8|
y = 1/8.
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Given ΔABC≈ΔPQR and your scale factor:
Complete the Hotspots
If youd like to show your work please do itll help me better understand.
∠1 = 68°
∠2 = 22°
side 3 = 5 cm
side 4 = 19.5 cm
5: perimeter of ΔABC = 45 cm
6: perimeter of ΔPQR = 30 cm
7: Area of ΔPQR = 30 cm²
How to complete the hotspots for the similar triangles?Similar triangles are triangles that have the same shape but may have different sizes. This means that corresponding angles of similar triangles are equal, and corresponding sides are in proportion.
The hotspots can be completed as follow:
∠1 = 180° - 22° - 90° = 68° (angle sum in a triangle)
∠2 = 22° (similar triangle)
side 3 = √(13²-12²) = 5 cm (Pythagoras)
side 4 = √(18²+7.5²) = 19.5 cm (Pythagoras)
5: perimeter of ΔABC = AB + BC + AC = 7.5 + 19.5 + 18 = 45 cm
6: perimeter of ΔPQR = PQ + QR + PR = 5 + 13 + 12 = 30 cm
7: Area of ΔPQR = 1/2 * base * height = 1/2 * 12 * 5 = 30 cm²
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Which retirement plan(s) is not managed by the U.S. government?
1. Fixed Annuity
II. Traditional IRA
III. Roth IRA
IV. Social Security
A. I, IV
B. II, III
C. I, III, IV
D. I, II, III
Answer:
I’m pretty sure 3
Step-by-step explanation:
Answer:
D. I, II, III
Step-by-step explanation:
Social security is the only plan managed by the government
what is the variability of the mean is 14 and the MAD is 3.2?
The variability of the mean is 0.154
What is mean?The total of all values divided by all of the values constitutes the result of a set, also called as the arithmetic mean. It is considered to be the most popular central trend indicator, and the word "mean" is commonly used to describe it. The average of a figure is known to as the average.
We are Given a normal distribution, the MAD and standard deviation (SD) are roughly inversely proportional to one another as follows:
=> MAD = 1.4826 × SD
Here we can calculate the standard deviation as follows:
=> SD = MAD / 1.4826
Since the MAD in this instance is provided as 3.2,
=> SD ≈ 3.2 / 1.4826 ≈ 2.16
The standard error of the mean (SEM), can be determined as follows, then gives the variability of the mean.
=> SEM ≈ SD / sqrt(n)
=> CV Equals SD/mean
2.16 / 14 ≈ 0.154
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A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 25 miles per gallon of gas. During one particular week, the two cars went a combined total of 1375 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of
the two cars that week?
Answer:
Step-by-step explanation:
Let's call the number of gallons of gas consumed by the first car "x" and the number of gallons of gas consumed by the second car "y". We can set up a system of two equations to represent the information given in the problem:
x + y = 45 (equation 1: total gas consumption is 45 gallons)
35x + 25y = 1375 (equation 2: total distance traveled is 1375 miles)
To solve for x and y, we can use the first equation to solve for one variable in terms of the other. For example, we can solve for y as:
y = 45 - x
We can then substitute this expression for y into the second equation, and simplify:
35x + 25(45 - x) = 1375
35x + 1125 - 25x = 1375
10x = 250
x = 25
So the first car consumed 25 gallons of gas that week. We can substitute this value into equation 1 to find the number of gallons consumed by the second car:
25 + y = 45
y = 20
Therefore, the second car consumed 20 gallons of gas that week.
Elena is selling tickets to a school play.she sells the tickets for $50 each.her goal is to raise more than $180 selling the tickets.she wants to know how many tickets she can sell to meet her goal
Answer:
15 + t = greather than 180
Step-by-step explanation:
line n passes through the points (-3, -7.5) and (2, -5). tahlia determined that the equation of line n is y = 0.5x. explain the error tahlia made while determining her equation. be sure to include the correct equation in your explanation
Answer:
Tahlia was correct in remembering that you can find the slope of a line using the slope formula.
She was also correct that the slope is 0.5.
However, if you use the slope-intercept formula y = mx + b, you still have to find b (the y-intercept) by plugging in one of the two points and the slope.
So, if we plug in the first point and the slope into the line, we can find b and thus the full equation of the line:
[tex]-7.5=0.5(-3)+b\\-7.5=-1.5+b\\b=-6\\\\y=0.5x-6[/tex]
Find z_{0} such that P(z_{0} < z < 2.2) = 0.7258 Use a TI T - 83Plus / T * 1 - 84 Plus calculator and round the answer to at least four decimal places z_{0} =
Using a standard normal distribution table, the value of z₀ is -0.64
What is the value of Z₀To find z₀, we need to use the standard normal distribution table or calculator. We know that the area under the standard normal curve between z₀ and 2.2 is 0.7258.
Using a standard normal distribution table or calculator, we can find the z-score corresponding to 0.7258.
From the table, we can find that the closest value to 0.7258 is 0.7257, and the corresponding z-score is approximately 0.61.
Therefore, we have:
P(z₀ < z < 2.2) = 0.7258
P(z < 2.2) - P(z < z₀) = 0.7258
Using the z-score table again, we can find that P(z < 2.2) is approximately 0.9861.
So we have:
0.9861 - P(z < z₀) = 0.7258
P(z < z₀) = 0.2603
Using the z-score table again, we can find that the z-score corresponding to 0.2603 is approximately -0.64.
Therefore, we have:
z₀ = -0.64
Rounding to at least four decimal places, we get:
z₀ = -0.6400
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I need help with number 1
Answer:
3,418.32yd³
Step-by-step explanation:
For volume you do the area (8)² multiplied by the height (17). 8 x 8 = 64. 64 x 17 = 1,088. you then multiply 1,088 by 3.14, the π, which is 3,416.32. We are using yards so the end result is 3,418.32yd³.
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Meena had a piece of fabric. She cut 2/9 of her fabric and used 8/9 of that piece for an art project. What fraction of her fabric did she use for her art project? 15 POINTS IF CORRECT!!!!
Answer:
Below
Step-by-step explanation:
x = original amount of fabric
2/9 * x = amount of cut fabric
8/9 * ( 2/9 * x) = amount of fabric used
8/9 * 2/9 * x = ( 8 *2) / ( 9 * 9) * x = 16 / 81 x
she used 16/81 of her fabric
Last year Amber went to gymnastics classes 21 days every month. This year she only went 19 days a month. How many more days did she go to gymnastics class last year than this year?
Answer:
Step-by-step explanation:
If you know how to subtract which you should the answer is 2.
How many more means subtraction.
Hope that is helpful!
5 students want pancakes and 13 students want waffles. What is the ratio of the number of students who want pancakes to the total number of students?
Answer: 5/18. or 5 over 18
Step-by-step explanation:
5 is the number of kids that want pancakes
13 is the number of kids that want waffles
18 is the total number of students
The question is asking what is the ratio of the number of students who want pancakes to the total number of students?
So you just do
5 kids that want pancakes over 18 kids total or 5/18
Find volume of triangular prism
I don’t know how to solve I know u use a b c base side and height but I don’t know which is each?
Explanation:
The front and back faces are triangles. They have a base of 10 ft and height of 4 ft.
area of triangular face = 0.5*base*height area = 0.5*10*4area = 20The front face has area 20 sq ft. The same applies for the back face as well.
Now imagine rotating the prism so that the front face is now laying on the floor. The floor and ceiling are triangles. Each wall is a rectangle.
volume of prism = (floor area)*(height)volume = (20 sq ft)*(5.5 ft)volume = 110 cubic feetAnswer: 110 ft^3
Step-by-step explanation:
Base is 10ft
Height is 4ft (distance from base to uppermost point)
0.5*10*4=20
20*5.5 (length)=110
A college professor randomly selects 10 of the 28 students in his statistics class and finds that
8 of them have part-time jobs in addition to being a full-time student.
He would like to construct a 90% confidence interval for the true proportion of students in his class who have part-time jobs in addition to being a full-time student.
Random condition:
✔ met
10% condition:
✔ not met
Large counts condition:
✔ not met
Are the conditions for inference met?
✔ no
(No one asked the question nor provided an answer, so here yous go FOR !!!!!EDGE2023!!!!!!!)
Answer:im confused
Step-by-step explanation:
Random condition:
✔ met
10% condition:
✔ not met
Large counts condition:
✔ not met
Are the conditions for inference met?
✔ no
If you invest $5,000 and after some time you receive $5,600, how much is the interest earned?
Answer:
The interest earned would be $600.
To calculate this, you would subtract the initial investment from the final amount:
$5,600 - $5,000 = $600.
Therefore, the interest earned is $600.
does inequality
2d+20<=120 explain?
The inequality 2d+20<=120 is a valid inequality. It means that some value of d can be substituted into the inequality to make it a true statement.
What is inequality?In mathematics, an inequality is a statement that compares two values and indicates how they are related in terms of magnitude or size. Inequalities use symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to show the relationship between the two values.
What is the types of inequality?Linear inequalities: These are inequalities in which the variables have a degree of one. For example, 2x + 3 < 7.Quadratic inequalities: These are inequalities in which the variables have a degree of two. For example, x^2 - 3x + 2 > 0.Rational inequalities: These are inequalities in which the variables appear in the denominator of a rational function. For example, (x + 3)/(x - 2) < 0.Absolute value inequalities: These are inequalities that contain absolute values. For example, |x + 2| < 5.In the given question,
Yes, the inequality 2d+20<=120 is a valid inequality. It means that some value of d can be substituted into the inequality to make it a true statement.
In this case, the inequality is saying that 2 times the value of d plus 20 is less than or equal to 120. To solve for d, we can subtract 20 from both sides to get:
2d <= 100
Then, we can divide both sides by 2 to isolate d:
d <= 50
So the solution to the inequality is that d must be less than or equal to 50 for the inequality to be true.
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Given that cos Ø= 2/5 determine the exact value of csc Ø
Answer:
below
Step-by-step explanation:
Given cos, you will have to use this to calculate sin because csc is 1/ sin
Remember cos^2 + sin^2 = 1
(2/5)^2 + sin^2 = 1
sin^2 = 21/25
sin = sqrt (21) / 5 (ignoring negative root)
csc = 1/sin = 5 / sqrt(21)
Please help me PLEASE HELPOP
Given - The expression as
[tex]\frac{3.07+2^4}{5.03-1.79}[/tex]
To find - the solution of the expression
Explanation To simplify the expression, we will simply the terms in the expression
[tex]\frac{3.07+2^4}{5.03-1.79} =\frac{3.07+16}{3.24} =5.885[/tex]
Hence the value of the expression is 5.885
Final answer- The value is 5.885
Two customers spent the same total amount of money at a restaurant.
- The first customer bought 8 hot wings and left a $4 tip.
- The second customer bought 10 hot wings and left a $2.80 tip.
- Both customers paid the same amount per hot wing.
How much does one hot wing cost at this restaurant in dollars and cents?
One hot wing costs 60 cents at this restaurant.
What are unknown variables?A variable in an equation that has to be solved for is known as an unknown.
A polynomial or formal power series may contain an indeterminate symbol, often known as a variable. In the polynomial ring or the ring of formal power series, an indeterminate is a constant rather than a variable. Nonetheless, many writers view indeterminates as a distinct class of variables because of the close connection between polynomials or power series and the functions that they describe.
Let's us assume that the cost of one hot wing is x dollars.
Then,
Total amount spent by each customer:
8x + 4 = 10x + 2.8
8x - 10x = 2.8 - 4
-2x = -1.2
x = 0.6
Therefore, one hot wing costs 60 cents at this restaurant.
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A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $21. The total cost to rent 8 chairs and 4 tables is $45. What is the cost to rent each chair and each table?
Let's say the cost to rent each chair is "x" and the cost to rent each table is "y". Then we can set up two equations based on the given information:
3x + 2y = 21 (for the first rental)
8x + 4y = 45 (for the second rental)
We can simplify the second equation by dividing both sides by 4:
2x + y = 11.25
Now we have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution:
3x + 2y = 21
2x + y = 11.25
From the second equation, we can solve for y in terms of x:
y = 11.25 - 2x
Then we can substitute this expression for y in the first equation:
3x + 2(11.25 - 2x) = 21
Simplifying and solving for x, we get:
3x + 22.5 - 4x = 21
-x + 22.5 = 21
-x = -1.5
x = 1.5
So the cost to rent each chair is $1.50. We can substitute this value back into either of the original equations to solve for y:
3(1.5) + 2y = 21
4.5 + 2y = 21
2y = 16.5
y = 8.25
So the cost to rent each table is $8.25. Therefore, the answer is $1.50 for each chair and $8.25 for each table.