The number of tickets that the band have to sell for each concert to meet the goal is 76 tickets
How many tickets does the band have to sell for each concert to meet the goal?Based on the information given, the production costs, P , for a band to have a concert can be modeled by the equation P=850 + 5x.
x = the number of concert tickets sold.
Since the band earns $50 for each ticket sold. The band’s goal is for the amount earned on ticket sales minus production costs to equal $5,000 per concert.
This will be illustrated thus:
Revenue - Cost = Profit
50x - 850 + 5x = 5000
Collect like terms
55x = 5000 - 850
55x = 4150
Divide
x = 4150 / 55
x = 76
The tickets will be 76.
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Complete the fraction to make a true inequality, and explain your reasoning
4 × < 4
3
I know this because the fraction I made
Which of the following represents a one to one function?A.Students to thier height B.Students to their weight C.Students to their LRN D.Students to their age
(Option C. Students to their LRN) In this case, each student has a unique LRN, meaning that it can be used in a one-to-one function where each student is mapped to their LRN.
Which of the following represents a one-to-one function?Option C. Students to their LRNA one-to-one function is a type of function where each element in the domain has one and only one image in the range. In this case, each student can be mapped to their LRN (Learning Reference Number) in a one-to-one function. This means that for every student, there is a unique LRN, and for every LRN, there is a unique student. This type of function is useful for keeping track of individual student information, as each student has a unique LRN associated with them.
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Nationwide, the mean value of farm land per acre is $2200, with a standard deviation of $400. The data has a bell-shaped distribution. Assume that a random sample of 80 farms is selected. Use the Empirical Rule to estimate the expected number of farms in the sample whose land value per acre is between $1800 and $2600. Round to the nearest whole number. Group of answer choices a.54 b.76 c.79 d.68
we get the expected number of farms in the sample whose land value per acre is between $1800 and $2600 is 59.
The Empirical Rule (or 3 sigma rule) states that for a normal distribution (bell shaped distribution) 68% of the data falls within one standard deviation (μ ± σ), 95% percent within two standard deviations (μ ± 2σ), and 99.7% within three standard deviations from the mean (μ ± 3σ).
Given that the mean (μ) = $2200, standard deviation (σ) = $400
a) The percentage of data within one standard deviation = μ ± σ = (2200 ± 400) = (1800, 2600)
Hence 68% of the land are between $1800 and $2600.
Number of farms = 68% × number of sample = 0.68 × 80 = 54.4 ≈ 54 farms
Hence we get the expected number of farms in the sample whose land value per acre is between $1800 and $2600 is 59.
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Find all the zeroes of the function
y=x^4-7x^2+12
show your work
x=-[tex]\sqrt{3}[/tex] ,[tex]\sqrt{3}[/tex],-2,2
What is a quadratic equation ?
Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:
ax² + bx + c = 0
Given:
y=[tex]x^{4} -7x^{2} +12[/tex]
Let [tex]x^{2}[/tex] = k
So , y = [tex]k^{2}[/tex] -7k+12
On simplifying/factorising the given equation ,we get
y = [tex]k^{2}[/tex] - 4k - 3k +12
On taking common ,we get
y = k(k-4) -3(k-4)
y =(k-3)(k-4)
Thus , on factorising and equating it to zero we get
(k-3)=0 or (k-4)=0
k=3 or k=4
Now , replacing k by [tex]x^{2}[/tex] ,we get
[tex]x^{2}[/tex] = 3 or [tex]x^{2}[/tex] = 4
Further on solving ,we get
( [tex]x^{2}[/tex]-3)=0 or ( [tex]x^{2}[/tex]-4)=0
(x-[tex]\sqrt{3}[/tex])(x+ [tex]\sqrt{3}[/tex]) =0 or (x+2)(x-2)=0
x=-[tex]\sqrt{3}[/tex] ,[tex]\sqrt{3}[/tex] or x= -2,2
Thus , x=-[tex]\sqrt{3}[/tex] ,[tex]\sqrt{3}[/tex],-2,2
Hence ,the obtained values of y are the zeros of x .
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What is volume of the rectangular prism?; What is the formula to rectangular prism?; How do you find the length of a rectangular prism?; What is the surface area of a box with a length of 6 ft a width of 3 ft and a height of 2ยฝ ft?
The formula of the volume of the rectangular prism is,
V = l * w * h
The formula of the surface area of the rectangular prism is,
A = 2(lw + wh + lh)
the surface area of a box is 72 sq.ft.
For a rectangular prism with length(l), width(w) and height(h),
The formula of the volume of the rectangular prism is,
V = l * w * h
The formula of the surface area of the rectangular prism is,
A = 2(lw + wh + lh)
For a rectangular box with a length of 6 ft a width of 3 ft and a height of 2 ft,
here, l = 6 ft, w = 3 ft and h = 2 ft
using the formula for the surface area of a rectangular prism, the surface area of box would be,
A = 2(lw + wh + lh)
A = 2(6 * 3 + 3 * 2 + 6 * 2)
A = 2(18 + 6 + 12)
A = 2(36)
A = 72 sq.ft.
Therefore, the surface area of a box is 72 sq.ft.
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Which statement correctly compares -9 and 2?
A. 92 because 9 is to the left of 2 on a number line.
B. 9 is to the left of 2 on a number line. -9> 2 because 92 because
C. 9 is to the right of 2 on a number line. D. 9 > 2 because 9 is to the right of 2 on a number line.
The statement that correctly compares -9 and 2 is A. -9 < 2 because 9 is to the left of 2 on a number line.
What is a number line?In arithmetic, a number line is a depiction of a graduated straight line which functions as a graphic representation of real numbers. It is presumed that every number line point and every real number correspond to one another.
Horizontal straight lines termed number lines have integers along them spaced equally apart. All of the numbers in a series can be shown on a number line. This line extends indefinitely at both ends.
In this case, -9 is on the left of a number line since it's negative. In conclusion, the correct option is A
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which of these is the quadratic parent function
The quadratic parent function is f(x) = x^2. (Option A)
In mathematics, family of functions refers to a group of functions that have the same degree or form. The examples of families of functions include linear functions, quadratic functions, square root functions, and absolute value functions. A parent function refers to the simplest function of a family of functions that preserves the definition of the entire family where the graph does not experience any transformations. The parent function of a quadratic equation is f(x) = x^2, whose graph has a vertex at the origin and experiences no vertical stretch or shrink. The other three options would be translated or transformed, hence are not the parent function of the quadratic equation.
Note: The question is incomplete. The complete question probably is: Which of these is the quadratic parent function? A. f(x) = x^2 B. f(x) = x^2 + 3 C. f(x) = x^2 – 5 D. f(x) = –4x^2
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Next (1 point) A quiz consists of 20 multiple-choice questions, each with 6 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %. P(pass)
The probability of passing if the minimum passing grade is 50 %. P(pass) is 0.000035 .
Given :
A quiz consists of 20 multiple - choice questions, each with 6 possible answers. For someone who makes random guesses for all of the answers .
Probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Binomial problem with n = 20 and p = 1/6 , q = 5/6
50 % of 20 = 10
P ( x = 10 ) = C ( 20 , 10 ) ( 1/6 )^10 ( 5/6 )^10
= 184756 * ( 1/6 )^10 ( 5/6 )^10
= 0.000035
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sume of angles of a triangel greater than 180 degrees when teh triange is so large that it extends to cosmological scales
In hyperbolic geometry, the angle sum of a triangle is always less than 180 degrees.
A lune is a wedge of a sphere with angle θ, represented by L(θ) in the proof.
α, β, and γ are the three angles of the triangle.
4πr²+4area[αβγ]=2L(α)+2L(β)+2L(γ)
2(2πr²+2area[αβγ])=2(L(α)+L(β)+L(γ))
2πr²+2area[αβγ]=L(α)+L(β)+L(γ)
At this point, we need to use a theorem that states that a lune whose corner angle is θ radians has an area of 2θr².
2πr²+2area[αβγ]=2αr²+2βr²+2γr²
2πr²+2area[αβγ]=2r²(α+β+γ)
π+area[αβγ]r²=α+β+γ
At this point, it is clear that the sum of the angles is equal to π plus the area[αβγ]r² (which cannot be zero).
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A parallelogram is a quadrilateral with two pairs of parallel sides.
A quadrilateral is a parallelogram _[blank]_.
Which answer correctly fills in the blank in the previous sentence?
if it has only two pairs of parallel sides
if and only if it has two pairs of parallel sides
because it has only four sides and two of them are parallel
if it has two pairs of parallel sides and is a polygon
The quadrilateral is a parallelogram if and only if it has two pairs of parallel sides
What is parallelogram?
In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
It is given that:
A parallelogram is a quadrilateral with two pairs of parallel sides.
As we know,
The quadrilateral can be defined as the four-sided polygon in geometry having four edges and four corners.
The quadrilateral, has:
Two pairs of congruent sides.
It has one pair of opposite congruent angles.
The diagonals of a kite are perpendicular.
One diagonal is bisected.
The top and bottom angles are bisected but does not have congruent diagonals.
A quadrilateral is a parallelogram if and only if it has two pairs of parallel sides.
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There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 red?
Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine. (cos^4 (x) sin^4 (x))
The Trigonometric Expression can be written as :
cos⁴ x = 18(3 + 4cos2x + cos4x)
Power:
In mathematics, a power defines a base number raised to an exponent. The base is the factor multiplied by itself, and the exponent is the number of times the same base is multiplied.
Reducing / Lowering Power:
Power identities are trigonometric identities, allowing us to rewrite trigonometric expressions raised to powers in terms of simpler trigonometric expressions.
According to the question:
cos2x = 2cos²x -1
⇒ cos²x = 1/2 (1 + cos2x)
⇒ cos²2x = 1/2 (1 + cos4x)
⇒ cos⁴ x = (cos²x)²
= 1/4(1 + 2cos2x+cos²2x)
⇒ cos⁴ x = 1/4( 1 + 2cos2x + 1/2(1+cos4x))
⇒ cos4x = 1/8(3 + 4cos2x+cos4x)
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at a certain university, students who live in the dormitories eat at a common dining hall. recently, some students have been complaining about the quality of the food served there. the dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think that the quality of the food should be improved. one evening, the manager asked the first 100 students entering the dining hall to answer the following question. Many students believe that the food served in the dining hall needs improvement Do you think that the quality of food served here needs improvement; even though that would increase the cost of the meal plan? Yes No No opinion a) What is the population of interest? What is the population parameter of interest (that is, what number are you trying to estimate)? b) What sampling plan did the manager use to collect his data? c) In this setting; explain how bias may have been introduced based on the way this sample was selected. That is, explain how those chosen for the sample may be different from those who were not chosen with respect to their answers to the question being asked in the survey: d) How might the sample be selected differently to avoid the bias discussed in part c)? Use one of the methods from the Random Rectangle Activity: In this setting, explain how bias may have been introduced based on the way the question was worded_ That is, explain how the wording of the question might lead toward a specific answer 0 Give an alternative wording to the research question that will avoid the bias discussed in part e)?
To avoid bias - increase the sample size and take reviews randomly
The dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think that the quality of the food should be improved. one evening, the manager asked the first 100 students entering the dining hall
There is a bias if taken data contain only the first 100 students, primary reasons students come in a friend circle to the dining hall, possibly that whole friend circle did/ didn't like food. Chances are the first hundred students like the food and the remaining students don't like, vice - versa.
To avoid bias - increase the sample size and take reviews randomly
Therefore, the manager should increase the sample size and take reviews randomly to avoid sampling bias.
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Simplify the expression.
fraction with negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 as the denominator
ten fourths
negative ten fourths
8
−8
The simplified form of the given expression as required in the task content is; 8.
What is the simplified form of the expression as described?It follows from the task content that the simplified form of the given expression; -4 ( 2 - (³√8 × 6) ) / 5 is to be determined.
Therefore, By solving the innermost parentheses; we have;
-4 ( 2 - (2 × 6) ) / 5
= -4 ( 2 - 12 ) / 5
= -4 ( -10 ) / 5
= 40 / 5
= 8.
Therefore, the simplified form of the expression is; 8.
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Your classmate is starting a new fitness program. He is planning to ride his bicycle for 45 minutes every day. He burns 6 calories per minute bicycling at 11 mph and 9.25 calories per minute bicycling at 15 mph. How long should he bicycle at each speed to burn 400 calories?
He will spend 5 minutes bicycling at 11mph and 40 minutes bicycling at 15mph.
How to calculate the time taken?From the information, the person is planning to ride his bicycle for 45 minutes every day. He burns 6 calories per minute bicycling at 11 mph and 9.25 calories per minute bicycling at 15 mph
This will be illustrated as:
x + y = 45 ..... i
6x + 9.25y = 400 ..... ii
From equation i, x = 45 - y ..... iii
x = number of minutes cycling at 11mph
y = number of minutes cycling at 15mph
Put equation iii into ii
6x + 9.25y = 400
6(45 - y) + 9.25y = 400
270 - 6y + 9.25y = 400
3.25y = 130
Divide
y = 40
Since x + y = 45.
x = 45 - 50
x = 5
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In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 43 ) and matching the number on the gold ball (1 through 33). If one ticket is purchased, what is the probability of winning the jackpot?
Answer:
44
Step-by-step explanation:
Benefits of Exercise According to a study in a medical journal, 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that men who were very active (burning about 3,500 calories daily) were a fourth as likely to develop diabetes compared with men who were sedentary. Assume that one-half of all middle-aged men are very active, and the rest are classified as sedentary. What is the probability that a middle-aged man with diabetes is very active? (Round your answer to four decimal places.)
The probability that a man who developed diabetes is very active is 0.0625.
What is probability?
Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.
Main body:
You want P(a/d) where a means active, d means diabetic. Then Bayer's rule gives
P(a/d)=P(d/a)p(a)/P(d)
We know P(d)=202/5990.
P(a)=1/4 and P(d/a) we need to figure out.
But
P(d)=1/4P(d/a)+3/4p(d/s)=1/4P(d/a)+3/4∗5P(d/a)
P(D&A)/P(A) = 1/5*P(D&A')/P(A')
I am given P(A) = 1/4, so this can be reduced to
P(D&A)/(1/4) = 1/5*P(D&A')/(3/4) 15*P(D&A) = P(D&A')
The probability I am interested in is P(A|D) = P(D&A)/P(D) = P(D&A)/(P(D&A) + P(D&A')) = P(D&A)/(P(D&A) + 15*P(D&A)) = 1/16
Hence ,The probability that a man who developed diabetes is very active is 0.0625.
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f(x) = 3x² + 4x - 6
g(x) = 6x³5x² - 2
Find (f - g)(x).
O A. (f-g)(x) = 6x³ - 2x² + 4x - 8
O B. (f-g)(x) = -6x³ - 2x² + 4x - 8
O c. (f - g)(x) = 6x³ - 8x² - 4x + 4
O D. (f - g)(x) = -6x³ + 8x² + 4x - 4
The difference of the functions, f(x) = 3x² + 4x - 6 and g(x) = 6x³ - 5x² - 2, is: D. (f - g)(x) = -6x³ + 8x² + 4x - 4.
How to Find the Difference of Two Functions?Finding the difference of two functions involves combining like terms together and then simplify.
Given the functions:
f(x) = 3x² + 4x - 6
g(x) = 6x³ - 5x² - 2
To find (f - g)(x), it implies that we find the difference between f(x) and g(x).
(f - g)(x) = f(x) - g(x)
Substitute
f(x) - g(x) = (3x² + 4x - 6) - (6x³ - 5x² - 2)
Open the parentheses:
f(x) - g(x) = 3x² + 4x - 6 - 6x³ + 5x² + 2
Combine like terms
f(x) - g(x) = - 6x³ + 8x² + 4x - 4
Therefore, the answer is: D. (f - g)(x) = -6x³ + 8x² + 4x - 4
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the insure website reports that the mean annual premium for automobile insurance in the united states was $1,503 in march 2014. being from pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. a sample of 25 automobile insurance policies from the state of pennsylvania showed a mean annual premium of $1,430 with a standard deviation of s s = $165.
(a)
Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.
H0: ???? > 1,503
Ha: ???? ≤ 1,503
H0: ???? < 1,503
Ha: ???? ≥ 1,503
H0: ???? ≤ 1,503
Ha: ???? > 1,503
H0: ???? = 1,503
Ha: ???? ≠ 1,503
H0: ???? ≥ 1,503
Ha: ???? < 1,503
(b)
What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.)
$
(c)
At
???? = 0.05,
test for a significant difference.
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Reject H0. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
Do not reject H0. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
Do not reject H0. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
Reject H0. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
The hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium is between -2.064 and 2.064.
Hypothesis testing
The standard formula to calculate the hypothesis testing is given by the z test is
Z = (X – U) / (SD / √n)
Where:
X – Sample Mean
U – Population Mean
SD – Standard Deviation
n – Sample size
Given,
Here we have the the insure website reports that the mean annual premium for automobile insurance in the united states was $1,503 in march 2014. being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. a sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1,430 with a standard deviation of is $165.
Here we need to develop the a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.
While we looking into the given question we have identified the values of
Sample mean = 1430
Sample size = 25
Population mean = 1503
Standard deviation = 164
Then the hypothesis testing is calculated as,
=> Z = (1430 – 1503) / (164 / √25)
Therefore, if we reject the null hypothesis and accept the alternative hypothesis. The z score of -2.23 is within the rejection area.
And the 2 critical values (cutoff points) are -2.064 and 2.064. Since the z score, -2.23, is outside this interval, we reject the null hypothesis. We accept the alternative hypothesis.
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what is 1 +1 x 30(200-125) + 999² ÷2000
what i got when i looked it up: 2750.0005
what i got when i did it 500.0005
What is the solution to the system of equations y 2 3x 3 x?
The system of equations y 2 3x 3 x= -2 has a solution.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
y = -2*2/3+3
y= -4/3+3
now simplifying,
5/3
Hence, The system of equations y 2 3x 3 x= -2 has a solution.
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Complete question-
What is the solution to the system of equations y 2 3x 3 x?
If AB = BC in traingle ABC, then which of the following must be true?1. m^A < m^C 2. m^A = m^C 3. m^A > m^C 4. m^A > m^B
The condition which is must be true for the given triangle ABC is m∠A = m∠C. Option 2 is correct. If AB = AC, then the triangle is said to be an isosceles triangle.
What is an isosceles triangle?A triangle is said to be an isosceles triangle if it has two equal sides and two equal angles in measurement.
The angles in an isosceles triangle are acute. That means they are less than 90° each. So, their sum results in a total of 180°.
Calculation:Given a triangle, ABC has AB = BC.
So, that means the given triangle is isosceles.
As we know, in an isosceles triangle, two angles are formed between one of the similar sides with the odd side being equal.
I.e., m∠A = m∠C
So, option 2 is correct.
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Solve 0=5y2-60 , round your answer to the nearest hundredth
Answer: y=-3.46,3.46
Step-by-step explanation:
isolate y
5y^2=60
y^2=12
y=-3.46,3.46
If x = 7 units and h = 6 units, then what is the area of the rhombus pictured above? A 8 square units b 7 square units c 42 square units d 28 square units
The area of the rhombus is 42 square units, and the correct answer is C.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
We have given that side of the rhombus is 7 units and height is 6 units.
To find the area of rhombus:
Remember that a rhombus is any quadrilateral that has four equal sides.
As a rhombus is also a parallelogram.
Formula to calculate area of rhombus using base and height;
Area of the rhombus = base x height
We have base = 7 units
And height = 6 units.
Substituting the values to the formula,
Area of the rhombus = 7 x 6
Area of the rhombus = 42 unit squared.
Therefore, the area is 42 square units.
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I have tried many times and I just can't get it
Answer:
1) 60
2) 15
3) 45
4) 105
5) 75
Step-by-step explanation:
7y + 5y = 180 A straight angle is 180 Combine like terms
12y = 180 Divide both sides by 12
y = 15
The sum of the interior angles is 180
y = 15
180 - (5y + 3y) = x
180 -(5(15) + 3(15)) = x
180 - (75 + 45) = x
180 - 120 = x
60 = x
Angle c
3y
3(15)
45
Angle DBC
7y
7(15)
105
Angle CBA
5y
5(15)
75
If a = -2 and b = 3, what is the value of -3a²b?
Answer:
-36
Step-by-step explanation:
-3[tex]a^{2}[/tex]b Substitute -2 for a and 3 for b
-3[tex](-2)^{2}[/tex](3)
-3(4)(3)
-36
Answer:
= -36
Step-by-step explanation:
-3a²b
if:
a = -2
b = 3
Then:
= -3*-2²*3
= -3(-2*-2) * 3
= -3*4*3
= -36
A= 25 ft
B = 45 ft
A new arboretum was designed to contain two circular gardens. Garden A has a diameter of 25
ft and Garden B has a diameter of 45 ft.
a.
If the gardener wants to outline the gardens in edging, how many feet will be needed to
outline the smaller garden? (Express as an exact answer in terms of .)
Formula:
The perimeter of smaller circle is 78.5 ft
What is area?
Area is that the amount that expresses the extent of a vicinity on the plane or on a semicircular surface. space|the world|the realm} of a plane region or plane area refers to the world of a form or planate plate, whereas area refers to the world of associate degree open surface or the boundary of a three-dimensional object.
Main Body:
A new arboretum was designed to contain two circular gardens. Garden A has a diameter of 25 ft and Garden B has a diameter of 45 ft.
outline the smaller garden means circumference of the circle.
Perimeter of circle is 2πr.
diameter = 25 ft
radius = 25/2 = 12.5 ft
Radius = 2π *12.5
= 25 π
= 25*3.14
= 78.5 ft
Hence the perimeter of circle is 78.5 ft
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Usain Bolt masses 94 kg and runs at 10 m/s. How much kinetic energy does he have?
Usain’s brother, Insane Bolt, runs twice as fast and has the same mass. How much kinetic energy does he have?
If you double the mass of an object, how does this affect its kinetic energy?
You serve a volleyball with a mass of 2.1 kg. The ball leaves your hand with a speed of 30 m/s.
A car is traveling with a velocity of 40 m/s and has a mass of 1120 kg.
Determine the kinetic energy of a 1000-kg roller coaster car that is moving with a speed of 20.0 m/s.
Kinetic energy of Usain is 4700kg-m²/s².
Kinetic energy of Usain's brother is 18800kg-m²/s².
If we double the mass kinetic energy get doubled.
What is kinetic energy ?
Kinetic energy of an object is the energy that it possess due to its motion.
It is calculated as [tex]\frac{1}{2}mv^{2}[/tex] where m is mass and v is velocity.
In Usain's case m = 94kg and v = 10m/s.
So, kinetic energy = 4700kg-m²/s².
In Usain's brother case mass is same but velocity is doubled.
So, kinetic energy = 18800kg-m²/s².
From the formula we can see ,
if mass is doubled then kinetic energy get doubled.
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what is the volume of the rectangular pyramid shown? a square pyramid. the square base has side lengths 15 yards and the height is 12 yards.
The volume of the rectangular pyramid is 900 cubic yards.
The standard formula of the volume of the rectangular pyramid is written as
V = 1/3s²h
where s refers the base edge and h refers the height.
Here we have given that the square base has side lengths 15 yards and the height is 12 yards.
Now, we have to find the volume of the rectangular pyramid
As we know the the value of base edge is 15 yard and the height is 12 yards.
Now, we have to apply the values on the formula then we get,
=> V = 1/3 x 15² x 12
It can be simplified as,
=> V = 4 x 225
When we do the appropriate arithmetic operation, then we get,
=> V = 900 cubic yard.
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Macy's aunt makes raspberry jam using 6 tablespoons of sugar and 8 tablespoons of raspberries. What is the ratio of tablespoons of raspberries to tablespoons of sugar?
8 to 14
8 to 6
6 to 14
6 to 8
The ratio of tablespoons of raspberries to tablespoons of sugar should be considered as the 8 to 6.
What is ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
Calculation of the ratio:
Since Macy's aunt makes raspberry jam using 6 tablespoons of sugar and 8 tablespoons of raspberries.
So here the ration be like
= 8 raspberries tablespoons to 6 tablespoons of sugar
= 8 to 6
hence, the second option is correct.
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