If product of two numbers is 19,200 and HCF is 40, then the LCM is 480
Given that the product of two numbers is 19,200 and the highest common factor (HCF) is 40.
Let us assume the two numbers to be x and y.
Therefore, x × y = 19,200
Also, HCF of x and y is 40.
We can write x = 40a and y = 40b, where a and b are co-prime.
Then, x × y = 40a × 40b = 1600ab = 19,200
Therefore, ab = 12
Now, we need to find the LCM of x and y.
LCM(x, y) = (x × y)/HCF(x, y) --- (1)
Substituting the values of x, y and HCF in the above equation, we get,
LCM(x, y) = (40a × 40b)/40 = 40ab
= 40 × 12 (as ab = 12)
= 480
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Calculate the volume of iron needed to create a rectangular prism with a base area of
2250 square cm. The prism has a cylinder missing through the center of the prism. The
radius of the cylinder is 25 cm and the height of the cylinder and the prism are both
100cm. Find the volume to the nearest tenth of a cubic cm.
The volume of iron needed to create the rectangular prism is approximately 28650.5 cubic cm.
what is volume?
Volume is the amount of space occupied by a three-dimensional object. It is a measure of how much an object can hold or how much space it takes up. The volume of a solid object is typically measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).
The volume of the rectangular prism without the cylinder can be calculated as:
[tex]$$V_1 = A \times h$$[/tex]
where A is the base area and h is the height
[tex]$$V_1 = 2250 \times 100$$[/tex]
[tex]$$V_1 = 225000 \ \text{cubic cm}$$[/tex]
The volume of the cylinder can be calculated as:
[tex]$$V_2 = \pi r^2 h$$[/tex]
where r is the radius and h is the height
[tex]$$V_2 = \pi \times 25^2 \times 100$$[/tex]
[tex]$$V_2 = 196349.54 \ \text{cubic cm}$$[/tex]
The volume of the rectangular prism with the cylinder missing can be calculated as:
[tex]$$V = V_1 - V_2$$[/tex]
[tex]$$V = 225000 - 196349.54$$[/tex]
[tex]$$V = 28650.46 \ \text{cubic cm}$$[/tex]
Therefore, the volume of iron needed to create the rectangular prism with a base area of 2250 square cm, a cylinder missing through the center of the prism with a radius of 25 cm, and the height of the cylinder and the prism being 100 cm, is approximately 28650.5 cubic cm (rounded to the nearest tenth of a cubic cm).
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For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1. (b) A study was performed to examine the personal goals of children in elementary school. A random sample of students was selected and the sample was given a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Each student's sex (boy or girl) was also recorded. If a contingency table for the data is evaluated with a chi-squared test, what are the hypotheses being tested? A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades. OB. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. C. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship. OD. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis is that the means differ. O E. None of the above. (C) The variables considered in a chi-squared test used to evaluate a contingency table A. are normally distributed. B. are categorical. C. can be averaged. OD. have small standard deviations. E. have rounding errors.
a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.
b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.
c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.
(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.
(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.
(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.
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10 is 30% of what number?
Solution:
Part:
whole
percent:
The number 10 is 30% of the following number: 33.33.
What is a percentage?In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
How to calculate the percentage of a number?In order to determine the whole number which 10 is 30%, we would apply the following mathematical expression (formula);
Quantity = percent × number
Substituting the given parameters into the percentage and quantity formula, we have the following;
10 = 30/100 × number
10 = 0.3 × number
Number = 10/0.3
Number = 33.33.
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As just a motion in the x-direction is needed for this transition, the motion is stiff: d.(x, y) → (x - 2, y) (x - 2, y).
What is motion referred to as?A body's ability to change its location with respect to time is known as motion. The various motions include: 2.1 Straight line motion Particles in linear motion are those that move through one point to the other along a straight or curved path.
a.(x, y) → (2x, y + 2)
As this transformation only comprises a y-direction translation and an x-direction scaling, it is a stiff motion.
b.(x, y) → (2x, 2y)
Since this transformation involves scaling both the x and y axes without any translation, it is a dilation.
c.(x, y) →(x + 2, y + 2)
As this transformation only requires a translation in the x and y dimensions, it is a stiff motion.
d.(x, y) → (x - 2, y)
As this transformation solely requires a movement in the x-direction, it is a stiff motion.
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the area of rectange is 297 sq cm if its length is increased by 3 cm and width decreases by 1 cm its area increased by 3 cm. sq. find the length and width of rectangle
The length and width of the rectangle is about 33cms and 9cms. This can be calculated with the help of the given area of the rectangle.
What is the width and length of rectangle?Let the original length and width of the rectangle be L and W respectively.
The given area of the rectangle is 297 square cm.
Area = L × B
297 = L × B
As per the question, the length is increased by 3 cm and the width is decreased by 1 cm.
Therefore, the new length and width are L + 3 and W - 1 respectively.
The new area is 3 square cm more than the original area.
So, (L + 3) × (W - 1) = 297 + 3
L×W -L +3W - 303 = 0
297 - L +3W - 303 = 0
-L + 3W - 6 = 0
-297/W + 3W = 6
-297 + 3W² = 6W
W² - 2W - 99 = 0
Using the quadratic formula, we get,
W = -2±[tex]\sqrt{ 2^2 - 4X1 X ( -99 ) ] ) / 2 X1 }[/tex]
[tex]W =\frac{-2±\sqrt{ (4+396)}}{2}[/tex]
[tex]W =\frac{-2±20}{2}[/tex]
Width can't be negative so, W = 9 cm
So, L 297/W
L = 297/9
L = 33cm
Therefore, the length and width of the rectangle are 33 cm and 9 cm respectively.
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Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
The statement that is true is: Player 2 has the highest likelihood of getting a hit in their at-bats.
How to determine the true statement from the optionsBy comparing the probabilities, we can interpret the likelihood of each player getting a hit in their at-bats. The highest probability indicates the highest likelihood of getting a hit.
Comparing the probabilities of the three players, we can see that:
Player 2 has the highest probability (5/8), which means they are the most likely to get a hit in their at-bats.
Player 1 has a lower probability (4/7) than Player 2, but a higher probability than Player 3. This means they are less likely to get a hit than Player 2, but more likely to get a hit than Player 3.
Player 3 has the lowest probability (3/6 = 1/2) of getting a hit, which means they are the least likely to get a hit in their at-bats.
Therefore, the statement that is true is: Player 2 has the of getting a hit in their at-bats.
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15 workmen can complete a piece of work in 12 days working 10 hours a day. How many workmen should be added to complete the same work in 6 days working 12 hours a day?
Answer:
25 workmen
Step-by-step explanation:
C = work completion
Half the number of days
6/5 (= 12/10) the hrs/day
½ × 6/5 × C = ⅗C
C/(⅗C) = 5/3
5/3 × 15 = 25
Nine hundred-thinty-nine divided by forty-two?
999 divided by 42 is equal to 23 with a remainder of 33.
What is division?
Division is a basic arithmetic operation that involves splitting a number into equal parts or groups. It is the inverse operation of multiplication, and is used to find out how many times one number (the divisor) can be divided into another number (the dividend) without leaving a remainder. The result of division is called the quotient.
To simplify the division of 999 by 42, we can use the fact that 42 is a divisor of 84, which is a multiple of 42. We can write:
999 ÷ 42 = (42 × 23) + 33
= 966 + 33
= 999
Therefore, 999 divided by 42 is equal to 23 with a remainder of 33, or in other words, 999 ÷ 42 = 23 33/42.
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The volume of the solid is 2160ft^3
Define the volume of cuboid?Volume of Cuboid is the multiplication of length breath and height.
We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=1800ft^3
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=360ft^3
Total volume= 1800 + 360
= 2160ft^3
Therefore, the volume of the solid is 2160ft^3
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Cuboid: According to the question the volume of the solid is [tex]2160ft^3[/tex].
What is cuboid?A cuboid is a three-dimensional geometric shape which is composed of six rectangular faces. It has 12 edges and 8 vertices. It is also referred to as a rectangular prism. The three dimensions of a cuboid are its length, width, and height. The cuboid is a versatile shape that can be used in many different ways and can be seen in everyday objects such as boxes, desks, and bookshelves. It is also a common shape for mathematically-based problems such as calculating the volume of a cuboid.
We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=[tex]1800ft^3[/tex]
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=[tex]360ft^3[/tex]
Total volume= 1800 + 360
= [tex]2160ft^3[/tex]
Therefore, the volume of the solid is [tex]2160ft^3[/tex]
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Here is a solid.
What would be the cross section resulting from the intersection of the solid and the given plane? Be specific about the resulting shape.
Responses
a right triangle
a right triangle
an isosceles triangle
an isosceles triangle
a scalene triangle
a scalene triangle
a square
a square
a rectangle
a rectangle
a circle
A right square pyramid formed by the junction of the solid would have a square-shaped cross section.
Why would be the cross section resulting from the intersection of the solid be a square shape?This is thus because a square pyramid has four triangular sides that meet at a shared vertex on its square base. The cross section of a pyramid formed when a plane meets it parallel to the base and perpendicular to one of the triangular sides is a square. Because the pyramid's base is square, the intersecting plane will cut all four of the triangle faces at the same distance from the peak, giving the pyramid a square shape.
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write down the name of shape W
A hexagon with two lines
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Laura has done a two-factor factorial completely randomized design. From her experiment, Laura has constructed the following incomplete ANOVA display: Source SS DF MS F A 350.00 2 B 300.00 150 AB 200.00 50 Error 150.00 Total 1000.00 18 a. How many levels of factor B did she use in the experiment? b. How many degrees of freedom are associated with interaction? c. The error mean square is d. The mean square for factor A is e. How many replicates of the experiment were conducted? f. What are your conclusions about interaction and the two main effects? g. An estimate of the standard deviation of the response variable is h. If this experiment had been run in blocks (CRBD) there would have been degrees of freedom for blocks.
a. Two levels of factor B were used in the experiment.
b. The degrees of freedom associated with interaction are 50.
c. The error mean square is 6.00. d. The mean square for factor A is 175.00.e. The experiment was conducted with three replicates.f. The interaction is significant. Factor A is significant. Factor B is not significant.g. An estimate of the standard deviation of the response variable is 2.449. h. If the experiment had been run in blocks (CRBD) there would have been 12 degrees of freedom for blocks.Solution:Factorial design: A factorial design is an experimental design that consists of two or more factors, each with two or more levels, and each subject is assigned to one and only one level of each factor. The objective of a factorial experiment is to analyze the effect of each factor on the response variable and to examine if there is any interaction between factors.a. Two levels of factor B were used in the experiment.b. Interaction degrees of freedom = AB = 50.c.
Mean square for error: MSE = 150/10 = 15.d. Mean square for factor A: MS(A) =[tex]SSA/dfA = 350/2 = 175.e.\\[/tex] Three replicates were conducted (from the error df = 10).f. Interaction is significant. Factor A is significant. Factor B is not significant.g. Estimate of the standard deviation of the response variable: sqrt(15/2) = 2.449.h. If the experiment had been conducted in a CRBD, there would have been 12 degrees of freedom for the block.
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Which of the following is the most appropriate inference procedure for the researchers to use to analyze the results? A. A one-sample zz-interval for a population proportionB. A one-sample tt-interval for a sample mean differenceC. A matched-pairs tt-interval for a population mean differenceD. A matched-pairs tt-interval for a sample mean differenceE. A two-sample tt-interval for a difference between means
The appropriate inference procedure for the researchers to analyze the results depends on the specific research question and the nature of the data.
A one-sample zz-interval for a population proportion is appropriate when the research question involves estimating the proportion of a population that has a particular characteristic or attribute.
A one-sample tt-interval for a sample mean difference is appropriate when the research question involves estimating the difference between a sample mean and a known population mean.
A matched-pairs tt-interval for a population mean difference is appropriate when the research question involves estimating the difference between two related population means.
A matched-pairs tt-interval for a sample mean difference is appropriate when the research question involves estimating the difference between two related sample means.
A two-sample tt-interval for a difference between means is appropriate when the research question involves estimating the difference between two independent sample means.
Therefore, without knowing the specifics of the research question and the data, it is impossible to determine the most appropriate inference procedure.
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an ore sample weighs 18.5 n n in air. when the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.8 n n .find the total volume and density of the sample
The total volume of the sample is 0.0067 m³ and the density of the sample is 2753.73 kg/m³.
An ore sample weighs 18.5 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.8 N. When the ore sample is immersed in water, the tension in the cord is given as 11.8 N.
Thus, the buoyancy force experienced by the ore sample is given by the difference between the weight of the sample in the air and the tension in the cord.
Buoyancy force experienced by the ore sample = Weight of the sample in the air - Tension in the cord
Buoyancy force experienced by the ore sample = (18.5 N) - (11.8 N)
Buoyancy force experienced by the ore sample = 6.7 N
Also, we know that the weight of the ore sample in air is equal to the weight of the ore sample when immersed in water.
Weight of the ore sample = Weight of the displaced water
Weight of the ore sample = Buoyancy force experienced by the ore sample
Weight of the ore sample = 6.7 N
The density of the ore sample
Density is given by the formula Density = Mass/Volume
Where Density is measured in kg/m³
Mass is measured in kg
Volume is measured in m³
Also, the density of water is given as 1000 kg/m³.
The density of the ore sample = Mass/Volume
Mass = Density x Volume
Volume of the ore sample can be obtained from volume of the displaced water.
Volume of the displaced water = Weight of the ore sample/Density of water
Volume of the displaced water = (6.7 N)/(1000 kg/m³)
Volume of the displaced water = 0.0067 m³
Density of the ore sample = (18.5 N)/(0.0067 m³)
Density of the ore sample = 2753.73 kg/m³
Therefore, 0.0067 m³ is the sample's total volume and 2753.73 kg/m³ is the density of the sample.
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Multiply the polynomials.
(2x² + 6x+6)(3x - 2)
_____________
A. 6x³14x²2 + 6x + 12
B. 6x³ + 14x² + 6x + 12
Wan
C. 6x³22x² - 30x - 12
D. 6x³ + 14x² + 6x - 12
exponential law of heating and cooling
Answer:
A) k = 0.037
B) 186°F
Step-by-step explanation:
List initial (T₀) and air (Tₐ) temperature
[tex]T_0=280^\circ\\T_a=67^\circ\\[/tex]
Part A
[tex]T=T_a+(T_0-T_a)e^{-kt}\\193^\circ=67^\circ+(208^\circ-67^\circ)e^{-k(3)}\\193=67+141e^{-3k}\\126=141e^{-3k}\\\frac{126}{141}=e^{-3k}\\\ln(\frac{126}{141})=-3k\\-\frac{1}{3}\ln(\frac{126}{141})=k\\k\approx0.037[/tex]
Part B
[tex]T=T_a+(T_0-T_a)e^{-kt}\\T=67+(208-67)e^{-0.037(4.5)}\\T\approx186^\circ\text{F}[/tex]
I need help please I need to show my work
Answer:
18
Step-by-step explanation:
We can safely assume EGF and EGD are congruent by SAS (EG = EG reflexive property, and the angle and side given)
that must mean FG AND GD are congruent (CPCTC)
3a = a+6
2a = 6
a = 3
plug this into 3a+a+6 (DF is the sum of the two segments)
4a+6
4(3)+6
18
The ratio of shells to driftwood Gus found is shown on the ratio table. Complete the ratio table to make an equivalent ratio.
Shells 9 36
Driftwood 3 (blank)
Answer:
12
Step-by-step explanation:
Given the ratio [tex]9:36[/tex], we can say that the ratio of driftwood is divided by 3 for the number of shells.
[tex]\frac{9}{3} =3\\\frac{36}{3}=12[/tex]
So, to fill the blank and create an equivalent ratio, you need to input 12.
Which graph matches the equation y+6 = 3/4 (x + 4)
A graph that matches the equation include the following: A. graph A.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be determined by using this mathematical equation:
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.Based on the information provided about the equation of this line, we can logically deduce the following parameters;
y + 6 = 3/4(x + 4)
y = 3x/4 + 3 - 6
y = 3x/4 - 3
Therefore, the slope, m is equal to 3/4 while the y-intercept is at point (0, 3).
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Dorris deposits $200 into a savings account that has a simple interest rate of 4. 1% Max deposits 300 dollars into a savings account that has a simple interest rate of 1. 9%, who earn more interest in 15 months round to the nearest cent if necessary
Dorris earns $12.25 in interest over 15 months, while Max earns $2.84 in interest over the same period. So, Dorris earns more interest than Max.
To find out who earns more interest in 15 months, we can calculate the interest earned by each person using the formula:
Interest = Principal x Rate x Time
For Dorris, we have:
Interest = $200 x 0.041 x (15/12)
Interest = $12.25
For Max, we have:
Interest = $300 x 0.019 x (15/12)
Interest = $2.84
Interest refers to the cost of borrowing money, usually expressed as a percentage of the amount borrowed over a specific period of time. When someone borrows money, they are required to pay back not only the amount borrowed but also an additional amount, which is the interest. Interest is how lenders make money and is an important component of the financial system.
There are different types of interest rates, including fixed and variable rates. A fixed interest rate remains the same throughout the loan term, while a variable interest rate may change based on market conditions. Interest rates can also be compounded, which means that interest is added to the principal amount, and future interest payments are calculated based on the new higher amount.
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factoring integers with sublinear resources on a superconducting quantum processor
Factoring integers with sublinear resources on a superconducting quantum processor can be achieved using quantum approximate optimization algorithm" (QAOA) or quantum phase estimation algorithm (QPE) approach.
Factoring integers with sublinear resources on a superconducting quantum processorFactoring large integers is a problem of significant importance in the field of cryptography.
Classical computers have limited efficiency in solving this problem, and their performance is expected to decline further as the size of the integers to be factored increases.
In contrast, quantum computers are expected to have exponential speedup in factoring large integers, thanks to Shor's algorithm.
Recently, researchers have been exploring the possibility of using superconducting quantum processors to factor integers with sublinear resources.
One approach is to use a so-called "quantum approximate optimization algorithm" (QAOA), which maps the problem of factoring integers to a problem of finding the ground state of a certain Hamiltonian.
The QAOA can be implemented using a superconducting quantum processor, with the problem Hamiltonian implemented by a set of two-qubit gates.
Another approach is to use the quantum phase estimation algorithm (QPE) to estimate the eigenvalues of the problem Hamiltonian.
This can be used to factor integers by finding the period of a certain function using the quantum Fourier transform, as in Shor's algorithm. QPE can be implemented on a superconducting quantum processor using phase estimation circuits, which require only polynomial resources.
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Arrange the steps in the correct order to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm. a = 55, m= 89 Rank the options below. The steps to find gcd(55, 89) using the Euclidean algorithm are listed below. 89 = 1.55 +34 55 = 1.34 +21 34 = 1.21 + 13 21 1 . 13 + 8 13 = 1.8+5 8 = 1.5+ 3 5 = 1.3+2 3 = 1.2+1 2 = 1.2 The Bézout coefficient of 55 is 34, and it is an inverse of 55 modulo 89. The Bézout coefficients of 55 and 89 are 34 and -21, respectively. -21, respectively. The ged in terms of 55 and 89 is written as 1 = 3-1.2 = 3-1. (5-1.3) = 2.3-1.5 = 2. (8-1.5) - 1.5 = 2.8-3.5 = 2.8-3. (13-1-8)= 5.8-3.13 = 5. (21-1.13) - 3.13 = 5.21-8. 13 = 5.21-8. (34-1.21) = 13.21-8.34 = 13. (55 - 1. 34)- 8. 34 = 13.55 - 21 34 = 13.55 - 21 - (89-1. 55) = 34.55 -21.89
The correct order of steps is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
To find the inverse of 55 modulo 89 using the Euclidean algorithm, the steps are:
1. 89 = 1.55 +34
2. 55 = 1.34 +21
3. 34 = 1.21 + 13
4. 21 = 1.13 + 8
5. 13 = 1.8 +5
6. 8 = 1.5 +3
7. 5 = 1.3 +2
8. 3 = 1.2 +1
9. 2 = 1.2
10. The Bézout coefficient of 55 is 34, and it is an inverse of 55 modulo 89.
11. The Bézout coefficients of 55 and 89 are 34 and -21, respectively.
12. The gcd in terms of 55 and 89 is written as 1 = 34-21.89 = 34-21. (55-1.34) = 13.34-21.55 = 13. (21-1.13) - 3.13 = 5.21-8. 13 = 5. (8-1.5) - 1.5 = 2.8-3.5 = 2. (3-1.2) = 2.3-1.5 = 2. (2-1) = 3-1.2 = 3-1. (1-0) = 34-21.89
The correct order of steps is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
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Ray has 9 identical shoe boxes like the one shown. What is the total volume of all the shoe boxes?
Answer:
Step-by-step explanation:
You need to find the volume if one shoe box by doing:
Length x Width x Height
Of the shoe box
Then multiply by 30 to get the volume for all the shoe boxes
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a single letter from the word aardvark is chosen. what is the probability of choosing an r or an a? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability of choosing an r or an a is 0.7143. A single letter from the word aardvark is chosen.
What is the probability of choosing an r or an a?The probability of choosing an r or an a from the word aardvark can be calculated as follows:
First, calculate the total number of letters in the word aardvark.
Aardvark is a seven-letter word. As a result, there are seven letters available.
Next, calculate the number of r's and a's in the word aardvark.
There are five letters that are either an r or an a in aardvark.
As a result, there are two r's or three a's in aardvark.
So, the probability of choosing an r or an a is:
[tex]P("r" or "a") = \frac{number of r's or a's in aardvark}{total number of letters in aardvark} \\ = 5/7\\=0.7143[/tex]
The probability of choosing an r or an a is 0.7143.
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[LAST QUESTION, OFFERING BRAINLIEST]
??? PTS
Answer:
Step-by-step explanation:
Let h be the height of the trapezoid.
The area of a trapezoid is given by the formula:
Area = (1/2) × (sum of parallel sides) × (height)
In this case, we know that the area is 21 cm², one base length is 5 cm, and the other base length is 9 cm. So we can write:
21 = (1/2) × (5 + 9) × h
Simplifying this equation, we get:
21 = 7h
Dividing both sides by 7, we get:
h = 3
Therefore, the height of the trapezoid is 3 cm.
Answer:
Height of Trapezium is 3 cm.Step-by-step explanation:
Area of Trapezium is 21 cm². Parallel sides are 5 cm and 9 cm .
Shorter parallel side is 5 cm and the Longer Side is 9 cm.
As we know that formula of area of Trapezium is,
Area of Trapezium = ½ (a + b) hWhere,
a and b are Parallel sides and h is the height.On substituting the values of area and the two parallel sides in the above formula we will get the required Height.
Substituting the values,
21 = ½ (5 + 9)h
21 = ½ × 14 × h
21 = 7 × h
h = 21/7
h = 3 cm
Therefore, Height of the Trapezium will be 3 cm respectively.
when an automatic press is a manufacturing process is operaing properly, the lengths of the component it produces are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches. what is the probability thata randomly selected component is shorter than 7 inches long? (report your answer to 4 decimal places.)
The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.
What is the probability of randomly selected component?We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.
We need to find the probability that a randomly selected component is shorter than 7 inches long.
We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:
z = (7 - 8) / 1.5 = -0.67
Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:
P(z < -0.67) = 0.2514
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Find the mean, median, mode, and range for the data set given.
112, 122, 132, 142, 152
Find a particular solution to the differential equation day dy 8 dt + 20y = 68 – 20t dt2 You do not need to find the general solution. y(t) = symbolic expression
The particular solution to the differential equation is given by: y(t) = y_ h(t) + y_ p(t) = c exp (-5/2 t) + t + 3Here, y_ h(t) is the homogeneous solution, which we don't need to find for this problem.
To solve the given differential equation, we'll need to use the method of undetermined coefficients. In this method, we assume that the particular solution to the differential equation has the same form as the forcing term. Here's how we can solve the given differential equation: Identify the forcing term and its derivatives. The forcing term is given by: f(t) = 68 - 20tWe can find its first derivative as follows: f'(t) = -20We can find its second derivative as follows: f''(t) = Guess the form of the particular solution We assume that the particular solution has the same form as the forcing term.
Since the forcing term is a first-degree polynomial, we assume that the particular solution also has the form of a first-degree polynomial: y_ p(t) = At + B Here, A and B are constants that we need to determine. Find the derivatives of the assumed form of the particular solution. Here are the first and second derivatives of the assumed form of the particular solution: y_ p(t) = At + B ==> y_ p'(t) = A ==> y_ p''(t) = 0. Substitute the assumed form of the particular solution and its derivatives into the differential equation Substituting y_ p(t), y_ p'(t), and y_ p''(t) into the differential equation, we get:8A + 20(At + B) = 68 - 20t Simplifying the above equation, we get: (8A + 20B) + (20A - 20)t = 68Comparing the coefficients of t and the constant terms on both sides,
we get two equations:8A + 20B = 68 (1)20A - 20 = 0 (2)Solving equation (2) for A, we get: A = 1 Substituting A = 1 into equation (1), we get:8 + 20B = 68Solving for B, we get: B = 3. Write the particular solution to the differential equation Substituting A = 1 and B = 3 into the assumed form of the particular solution, we get :y_ p(t) = t + 3Therefore, the particular solution to the differential equation is given by: y(t) = y_ h(t) + y_ p(t) = c exp (-5/2 t) + t + 3Here, y_ h(t) is the homogeneous solution, which we don't need to find for this problem.
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Cheryl builds cylindrical pools according to measurements given by her customers. Cheryl uses the volume formula for a cylinder, V = pi R squared^2H to determine how big to build the pool If Cheryl is given the volume and height requirements, how would she rewrite the formula to determine the radius of the pool?
The radius of a cylindrical pool when given the volume and height is √{(V / (πh))}.
Cheryl can rewrite the volume formula for a cylinder in terms of the radius.
The volume formula for a cylinder is: V = πr²h
Where V is the volume of the cylinder,
r is the radius of the cylinder,
h is the height of the cylinder.
To determine the radius of the cylindrical pool, we can rearrange the formula for the volume of a cylinder,
V = πr²h, to solve for r.
Starting with the formula for the volume of a cylinder:
V = πr²h
Divide both sides by πh:
V / (πh) = r²
Take the square root of both sides:
√{(V / (πh))} = r
Therefore, the formula to determine the radius of the pool given the volume V and height h is:
r = √{(V / (πh))}
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Why is pi important in math?