Using the %1RM to number of repetitions table, your client's estimated 1RM for the barbell back squat exercise would be 125 lbs, rounded to the nearest whole number.
To estimate the predicted 1RM (one repetition maximum) for the barbell back squat exercise, we can use the %1RM to number of repetitions table from the lecture. According to the table, performing 5 repetitions corresponds to 87% of the 1RM.
To find the estimated 1RM, we can use the following formula:
1RM = weight lifted / %1RM
Plugging in the values from the question:
1RM = 109lb / 0.87
1RM = 125.287lb
Rounding to the nearest whole number, the estimated 1RM for the barbell back squat exercise is 125lb.
Therefore, the answer is 125.
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Jasper is an airline attendant. Last week, he worked on flights on 2 small jets and 5 large jets, which could seat a total of 531 passengers. The week before, he was assigned to flights on 5 small jets and 5 large jets, which could seat a total of 720 passengers. How many seats were on each type of flight?
The number of seats available in the small jets and large jet are 63 and 81 respectively.
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, Jasper noticed with 2 small jets and 5 large jets, which could seat a total of 531 passengers and 5 small jets and 5 large jets, which could seat a total of 720 passengers.
Let the number of seats available in the small jets and large jet be x and y,
Establishing the system of equations to solve,
2x+5y = 531......(i)
5x+5y = 720.......(ii)
Subtracting the equation (i) from eq(ii)
3x = 189
x = 63
Put x = 63
5(63)+5y = 720
5y = 405
y = 81
Hence, the number of seats available in the small jets and large jet are 63 and 81 respectively.
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statistical analysis of 100 local phone calls in STC indicates normal distribution with the mean length 10 minutes and standard deviation 4 minutes. Find x value where P(X < x)=0.0655. a. 5.88 minutes b. 7.96 minutes c. 3.96 minutes d. 1.04 minutes
The x value where P(X < x)=0.0655 is 4 minutes. The correct answer is c. 3.96 minutes.
To find the x value where P(X < x)=0.0655, we can use the z-score formula and look up the corresponding z-value in a standard normal distribution table. The z-score formula is:
z = (x - mean) / standard deviation
Substituting the given values, we get:
0.0655 = (x - 10) / 4
Next, we can look up the z-value that corresponds to 0.0655 in a standard normal distribution table. We find that the z-value is approximately -1.5. Now we can plug this back into the z-score formula and solve for x:
-1.5 = (x - 10) / 4
-6 = x - 10
x = 4
Therefore, the x value where P(X < x)=0.0655 is 4 minutes. The correct answer is c. 3.96 minutes.
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1. (40 pts.) a) Let W1 and W2 be vector subspaces of a
vector space V. Prove that: W1 (+) W, if and only if the expression
0=0+0 is the only expression of the vector 0 as sum of a vector in
W1 and ano
The statement "W1 (+) W2 if and only if the expression 0=0+0 is the only expression of the vector 0 as sum of a vector in W1 and another in W2" is equivalent to the statement "W1 (+) W2 if and only if W1 ∩ W2 = {0}".
Proof:
(⇒) Assume that W1 (+) W2. This means that for any vector v ∈ V, there exist unique vectors w1 ∈ W1 and w2 ∈ W2 such that v = w1 + w2. In particular, for the vector 0 ∈ V, there exist unique vectors w1 ∈ W1 and w2 ∈ W2 such that 0 = w1 + w2. Since 0 is the additive identity, we must have w1 = 0 and w2 = 0. Therefore, the only vector in the intersection of W1 and W2 is the zero vector, so W1 ∩ W2 = {0}.
(⇐) Assume that W1 ∩ W2 = {0}. Let v ∈ V be an arbitrary vector, and suppose that there exist vectors w1, w1' ∈ W1 and w2, w2' ∈ W2 such that v = w1 + w2 = w1' + w2'. Then we have w1 - w1' = w2' - w2 ∈ W1 ∩ W2. But since W1 ∩ W2 = {0}, we must have w1 - w1' = 0 and w2' - w2 = 0, which implies that w1 = w1' and w2 = w2'. Therefore, the expression v = w1 + w2 is unique, so W1 (+) W2.
Thus, we have shown that W1 (+) W2 if and only if W1 ∩ W2 = {0}.
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which graph represents the equation?
Answer: the first graph ! :)
Step-by-step explanation:
it is the very first one.
Iam 10% older than my wife. My wife is x% younger than me find x%
Julia deposits $2000 into a savings account that
earns 4% interest per year. The exponential
function that models this savings account is
y = 2000(1.04), where t is the time in years.
Which equation correctly represents the amount
of money in her savings account in terms of the
monthly growth rate?
Please show work
Answer:
C.
Step-by-step explanation:
Yearly compounding.
y = 2000(1.04)^t
Monthly compounding.
y = 2000(1 + r/12)^(12t)
2000(1.04)^t = 2000(1 + r/12)^(12t)
(1.04)^t = (1 + r/12)^(12t)
(1.04^t)^(1/t) = [(1 + r/12)^(12t)]^(1/t)
1.04 = (1 + r/12)^12
1.04^(1/12) = [(1 + r/12)^12]^(1/12)
1.00327374 = 1 + r/12
y = 2000(1.00327374)^(12t)
Answer: C.
Does the point (2, –2) satisfy the equation y = x? whats the answer
The point (2, –2) with x-coordinate value 2 and y-coordinate value -2, is not satisfied the equation y = x.
We have an equation, y = x --(1) and point (2,-2). We have to check that point (2, –2) satisfy the equation y = x or not. To check that, we need to put the values of the point in the equation. If the equation satisfies them, the point belong to the line. Substituting the coordinates of the given point, i.e., x = 2 and y = -2, into the defining equation(1), we get, y = x
L.H.S, y = -2
R.H.S, x = 2
but -2 ≠ 2 so, L.H.S ≠ R.H.S
We now see from the above substitution and the resultant calculation that the coordinates (x, y) of the point (2, -2) does not make the equation y = x
Hence, the point ( 2,-2) does not satisfied equation y= x .
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Describe the long run behavior of f(x)=5(2)^x+1:
As x→−[infinity], f(x) =
As x→[infinity], f(x) =
x → -∞, f(x) → 0
x → ∞, f(x) → ∞
As x approaches negative infinity, the value of the exponent 2^x+1 will become very large negative number, approaching zero. Therefore, the function f(x) will approach 5 times zero, which is equal to 0. Thus, we can say:
As x → -∞, f(x) → 0.
As x approaches positive infinity, the value of the exponent 2^x+1 will become very large positive number, approaching infinity. Therefore, the function f(x) will approach 5 times infinity, which is equal to infinity. Thus, we can say:
As x → ∞, f(x) → ∞.
So, the long run behavior of the function f(x)=5(2)^x+1 is that it approaches 0 as x approaches negative infinity and approaches infinity as x approaches positive infinity.
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A pencil is 13.5 cm long. How far will 90 pencils reach if laid end to end? Give your answer in meters.
Answer:
12.15 m
Step-by-step explanation:
90 × 13.5 cm × (1 m)/(100 cm) = 12.15 m
Answer: 12.15 m (rounded 12.2)
Step-by-step explanation:
100 cm = 1 m
13.5(90) = 1,215
1215 divided by 100 = 12.15
1. APQR and ASTU are similar triangles. Prove that the slope of line segment PR and the slope of
line segment SU are equal.
The slopes are equal, and the equation is showing a proportional relationship.
What are slopes?The slope of a line is a measure of its steepness.
Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
1) Given that, Δ PQR and Δ STU are similar triangles, we need to show that they have equal slope,
Line PR is passing by points (-6, 4) and (-8, 7) and the line SU is passing by points (-4, 1) and (0, -5)
Slope = y₂-y₁ / x₂-x₁
Finding the slopes :-
Line PR = 7-4 / -8+6 = -3/2
Line SU = -5-1 / 4 = -6/4 = -3/2
Therefore, we get the slopes equal.
2) Given is an equation, y = 3x/4
The proportionality equation is given by :- y = kx, where k is the proportionality constant,
The given equation is following the proportionality equation, therefore is showing a proportional relationship.
Hence, the slopes are equal, and the equation is showing a proportional relationship.
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Question 2 Find the quotient and remainder (x^(3)+4x^(2)+7x+13)/(x+2) The quotient is The remainder is Submit Question
The quotient is x^2+2x+3, and the remainder is 7.
The quotient and remainder of the given expression can be found using long division. Here are the steps:
1. Divide the first term of the dividend, x^3, by the first term of the divisor, x. This gives you the first term of the quotient, x^2.
2. Multiply the first term of the quotient, x^2, by the divisor, x+2. This gives you x^3+2x^2.
3. Subtract this result from the dividend, x^3+4x^2+7x+13, to get the new dividend, 2x^2+7x+13.
4. Repeat the process with the new dividend, 2x^2+7x+13, and the divisor, x+2. The first term of the quotient is 2x, and the result of the multiplication is 2x^2+4x.
5. Subtract this result from the new dividend, 2x^2+7x+13, to get the new dividend, 3x+13.
6. Repeat the process with the new dividend, 3x+13, and the divisor, x+2. The first term of the quotient is 3, and the result of the multiplication is 3x+6.
7. Subtract this result from the new dividend, 3x+13, to get the remainder, 7.
Therefore, the answer is:
The quotient is x^2+2x+3.
The remainder is 7.
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2. Consider a set of vectors of the form (a, 3a, a + b). Determine whether the set is a subspace of R3. If the set is a subspace, give a basis and its dimension. (8 marks total)
The set of vectors of the form (a, 3a, a + b) is not a subspace of R3.
To be a subspace of R3, a set must satisfy the following conditions:
1. The set must be closed under addition.
2. The set must be closed under scalar multiplication.
3. The set must contain the zero vector.
Let's check if the set satisfies these conditions:
1. Closed under addition:
Let u = (a, 3a, a + b) and v = (c, 3c, c + d) be two vectors in the set. The sum of these vectors is u + v = (a + c, 3a + 3c, a + b + c + d). This vector is not in the set because the third component is not of the form a + b. Therefore, the set is not closed under addition.
2. Closed under scalar multiplication:
Let u = (a, 3a, a + b) be a vector in the set and k be a scalar. The scalar multiplication of u and k is ku = (ka, 3ka, ka + kb). This vector is not in the set because the third component is not of the form a + b. Therefore, the set is not closed under scalar multiplication.
3. Contains the zero vector:
The zero vector in R3 is (0, 0, 0). This vector is not in the set because the third component is not of the form a + b. Therefore, the set does not contain the zero vector.
Since the set does not satisfy the conditions to be a subspace of R3, it is not a subspace. Therefore, there is no basis or dimension for this set.
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3. You are a marketing manager for a food products company, considering the introduction of a new brand of organic salad dressings. You need to develop a marketing plan for the salad dressings in which you must decide whether you will have a gradual introduction of the salad dressings (with only a few different salad dressings introduced to the market) or a concentrated introduction of the salad dressings (in which a full line of salad dressings will be introduced to the market). You estimate that if there is a low demand for the salad dressings, your first year's profit will be $1 million for a gradual introduction and million (a loss of $5 million) for a concentrated introduction. If there is high demand, you estimate that your first year's profit will be $4 million for a gradual introduction and $10 million for a concentrated introduction. The payoff table for the organic salad dressings marketing is given as follows:
Low Demand High Demand
Gradual 1 4
Concentrated -5 10
a. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the pessimistic, and minimax regret approaches? (10 points)
b. Suppose you believe that the probability of demand being low is 0.7. Use the expected monetary value approach to determine an optimal decision. (Provide the expected monetary value for each decision alternative.) (10 points)
c. Given the information in part b), what is the EVPI? (10 points)
a. since it provides the lowest regret value should the demand be high.
b. Expected Monetary Value for Gradual Introduction= $2.8 million. Expected Monetary Value for Concentrated Introduction= $1.5 million
c. EVPI = $1.3 million
a. For the pessimistic approach, the recommended decision is to use the gradual introduction of the salad dressings, since it provides the least amount of loss should demand be low. For the minimax regret approach, the recommended decision is also the gradual introduction of the salad dressings, since it provides the lowest regret value should the demand be high.
b. Using the expected monetary value approach, the optimal decision would be to use the gradual introduction of the salad dressings. This is because the expected monetary value for a gradual introduction is $2.8 million, which is higher than the expected monetary value of $1.5 million for a concentrated introduction.
Expected Monetary Value for Gradual Introduction: 0.7 * $1 million + 0.3 * $4 million = $2.8 million
Expected Monetary Value for Concentrated Introduction: 0.7 * -$5 million + 0.3 * $10 million = $1.5 million
c. The EVPI (Expected Value of Perfect Information) for this problem is $1.3 million, which is calculated by subtracting the expected monetary value from the best case outcome.
Best case outcome: $10 million
Expected Monetary Value: $2.8 million
EVPI: $10 million - $2.8 million = $1.3 million
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TS is a tragent of a circle PQRS.if /PR/-/PS/and and angle PQR=17° calculate RST.
Answer:
Since TS is a tangent to the circle PQRS, we know that the tangent line is perpendicular to the radius that intersects the point of tangency, which is S in this case.
Let O be the center of the circle. We can draw a radius from O to S, which intersects TS at point T, forming a right triangle OST.
Since /PR/-/PS/, we know that angles PSR and PRS are acute angles, which means that angle PSO is also an acute angle. This means that angle OST is complementary to angle PSO.
So, angle OST = 90 - angle PSO. But we know that angle PSO = angle PQR, since they are both subtended by the same arc PR. Therefore:
angle OST = 90 - angle PSO = 90 - angle PQR = 90 - 17 = 73 degrees.
Therefore, RST = angle TSR = 180 - angle OST = 180 - 73 = 107 degrees.
Step-by-step explanation:
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A caterer charges a service fee
of $175, plus the cost of the
food. If the total is less than
$1,000 for an event, write and
solve an inequality to determine
the cost of the food.
The inequality of the expression is x + 175 < 1000
How to determine the inequality of the expressionFrom the question, we have the following parameters that can be used in our computation:
Service fee of $175Plus the cost of the food. If the total is less than $1,000 for an eventUsing the above as a guide, we have the following:
x + 175 < 1000
Subtract 175 from bith sides
x < 825
Hence, the solution is x < 825
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The rectangular floor of a classroom is 20 feet in length and 30 feet in width. A scale drawing of the floor has a length of 4 inches. What is the area, in square inches, of the floor in the scale drawing?
Answer:
24inches ²
Step-by-step explanation:
Scale of length is 20ft : 4inches = 5ft : 1inch
Scale of width will be 5ft: 1inch = 30ft: 6inches
Area of scale =length x width
Area = 4inches x 6inces
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $9,000, annual interest: 6%, interest periods: 12, number of years: 14
After 14 years, the investment compounded periodically will be worth $ (Round to two decimal places as needed.)
more than the investment compounded annually.
As a result, after 14 years, the investment that was compounded interest irregularly will be valued $961.54 more than the one that was compounded yearly.
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 loan's interest is the name given to this percentage.
We must apply the compound interest calculation in order to compare the values of the investment compounded annually with the investment compounded periodically:
[tex]A = P(1 + r/n)^(nt) (nt)[/tex]
where:
A is the total sum.
The principal is P. (the initial amount)
n is the number of times the interest is compounded each year, and r is the yearly interest rate (expressed as a decimal).
The number of years is t.
We have the following for the yearly compounded investment:
[tex]A = 9000(1 + 0.06/1)^(1*14) = $20,207.97[/tex]
Periodically compounded investment results in:
[tex]A = 9000(1 + 0.06/12)^(12*14) = $21,168.51[/tex]
As a result, after 14 years, the investment that was compounded irregularly will be valued $961.54 more than the one that was compounded yearly.
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87 oz= how many lb and oz
Simplify the expression 7x^2y^2 − 3xy − 8xy + 4x^2y^2
1. 11x^2y^2 + 11xy
2. 11x^4y^4 − 11x^2y^2
3. x2y2
4. 11x^2y^2 − 11xy
Answer: The Answer is 4
Step-by-step explanation:
1) find the same base of the x² y² n just do the addition normally like this
(7x²y²+4x²y²)-3xy-8xy
so you'll end getting
the final answer
Graph the line perpendicular to y = 4 that passes through (-5, -2). What is the equation of that line?
The required equation of the line perpendicular to y=4 that passes through (-5,-2) is: x = -5
How to find equation of that line which is perpendicular to y = 4?The equation of the line y=4 is a horizontal line that passes through the point (0,4).
A line perpendicular to this line would be a vertical line passing through the point (-5,-2).
The equation of a vertical line passing through the point (-5,-2) can be written in the form x = -5,
which means that the x-coordinate of any point on this line must be -5.
Therefore, the equation of the line perpendicular to y=4 that passes through (-5,-2) is: x = -5
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following exercises, perform the indicated operations. 7. (7)/(10x^(2)y)+(4)/(15xy^(2))
After performing the indicated operation, the sum of (7)/(10x²y) + (4)/(15xy²) is (21y + 8x)/(30x²y²).
To perform the indicated operations, we need to find a common denominator for the two fractions. The common denominator for 10x²y and 15xy² is 30x²y². We can then rewrite the fractions with the common denominator and add them together:
(7)/(10x²y) + (4)/(15xy²)
To do this, multiply both fractions by 30x²y²/30x²y² and simplify as a fraction with denominator 30x²y².
= (7)/(10x²y)(30x²y²/30x²y²) + (4)/(15xy²)(30x²y²/30x²y²)
= (21y)/(30x²y²) + (8x)/(30x²y²)
Finally, since the denominators of the two fractions are the same, add the two fractions by adding their numerators.
= (21y + 8x)/(30x²y²)
Therefore, the answer is (21y + 8x)/(30x²y²).
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Given to find the Determinant of the following 5*5 Matrix:
let A=
EXPLANATION
Firstly to find the Determinant of a Matrix of order n*n the easiest way is to Convert the given matrix into Upper Triangular form
where Upper Triangular form means the values in the matrix which are below to the Diagonal elements are 0.
After Converting it to the Upper Triangular Matrix, the product of the Diagonal elements gives the Determinant of the Matrix
So the Given Matrix Should be Converted into the Upper Triangular Matrix in the form:
To find the determinant of the given 5x5 matrix A, we need to convert it into an upper triangular form.
This means that all the values below the diagonal elements should be 0. Once we have the upper triangular form, we can find the determinant by taking the product of the diagonal elements.
To convert the given matrix into an upper triangular form, we can use elementary row operations. We can subtract multiples of the first row from the other rows to make the values below the first element 0. Then we can do the same for the second row, third row, and so on until we have an upper triangular matrix.
Once we have the upper triangular matrix, we can find the determinant by taking the product of the diagonal elements. The determinant of the given matrix A is the product of the diagonal elements of the upper triangular matrix.
So the steps to find the determinant of the given matrix A are:
1. Convert the given matrix into an upper triangular form using elementary row operations.
2. Take the product of the diagonal elements of the upper triangular matrix to find the determinant.
By following these steps, we can find the determinant of the given 5x5 matrix A.
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Infinitely many solutions; one equation is has a y-intercept of -2. What are the two linear equations?
The two linear equations with infinitely many solutions and a y-intercept of -2 are y = x - 2 and y - x = -2.
We can use the y-intercept (-2) and another point on the line to calculate the slope. Since we are looking for infinitely many solutions, we can choose any point. Let's choose the point (0, 1):
slope = (y2 - y1) / (x2 - x1) = (-2 - 1) / (0 - 1) = -3
Now we know that the slope of one of the lines is -3. We can use this information to find the equation of the line. We can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Let's use the point (0, -2):
y - (-2) = -3(x - 0)y + 2 = -3xy = -3x - 2y = -3(0) - 2 = -2y = mx - 2y = -3x - 2y = x - 2y - x = -2
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At an art fair, an artist recorded sales of 52 candles of two different sizes and a total of $269 collected. The smaller candle sells for $4 and the larger candle sells for $7.
A. Based on the artist’s records, how many of each size of candle were sold?
B. Is your answer reasonable? What might this imply about the artist’s records?
The artist sold 32 smaller candles and 20 larger candles.
What is equations ?An equation is a mathematical statement that shows the equality of two expressions. It contains an equals sign (=) and at least one variable. An equation can be true or false depending on the values of the variables. Solving an equation involves finding the value or values of the variable that make the equation true. Equations are used to model relationships between different quantities in a wide range of fields, including mathematics, physics, chemistry, economics, and engineering.
According to the given information :A. Let's represent the number of smaller candles sold as x and the number of larger candles sold as y. We know that x + y = 52 (since a total of 52 candles were sold) and 4x + 7y = 269 (since the total sales was $269 and smaller candles sell for $4 and larger candles sell for $7). We can use these two equations to solve for x and y.
Multiplying the first equation by 4, we get 4x + 4y = 208. Subtracting this from the second equation, we get:
4x + 7y - (4x + 4y) = 269 - 208
3y = 61
y = 20.33
This means that the artist sold 20.33 larger candles. However, since we cannot sell a fractional part of a candle, we need to round this down to 20. Similarly, we can find x by subtracting y from 52:
x = 52 - y = 52 - 20 = 32
So the artist sold 32 smaller candles and 20 larger candles.
B. The answer is reasonable since the number of smaller candles sold is larger than the number of larger candles sold, and the total sales amount is closer to the price of the smaller candle than the larger candle. This implies that the artist's records are likely accurate.
Therefore, the artist sold 32 smaller candles and 20 larger candles.
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1. Find the volume of this perfume bottle: Hint: V= pi x r^2 x h
2. Find the volume of this perfume bottle: Hint: V =1/3 pi x r^2 x h
3. Find the volume of this perfume bottle: Hinit: V = 4/3 pi x r^3
4. The cylindrical bottle sells for $54.00, the conical bottle sells for $20.00 and the spherical bottle for $35. What is the best buy per cubic centimeter of perfume? Why?
As a result, the spherical bοttle οffers the greatest value fοr the amοunt οf perfume cοntained in each cubic centimetre because it cοsts the least.
What is vοlume?The measurement οf a three-dimensiοnal οbject's space filled is its vοlume. Mοst οften, it is expressed in cubic measures like cubic metres, cubic centimetres, οr cubic feet. The vοlume οf a cube, fοr instance, can be calculated by multiplying its length, breadth, and height. Calculating a cube's vοlume is as fοllοws:
Capacity is calculated using the fοrmula LWH.
given:
The fοrmula V = pi x r² x h, where r is the radius οf the circular base and h is the height οf the bοttle, must be used tο determine the perfume cοntainer's vοlume. Hοwever, we are unable tο determine the vοlume because we lack the values fοr r and h. The fοrmula V = 4/3 π x r³, where r is the radius οf the spherical cοntainer, must be used tο determine the vοlume οf the perfume bοttle. Hοwever, we are unable tο determine the vοlume because we lack the value fοr r.
Price per cubic centimetre = $54.00 / 282.74 cm³ = $0.191 per cm³ Vοlume οf cylindrical cοntainer = π x (3 cm)²x 10 cm = 282.74 cm³
Cοnical cοntainer vοlume equals 1/3 π x (2 cm) 2 x 8 cm = 16.76 cm³.
$20.00 divided by 16.76 cm3 (price per cubic centimetre) yields $1.19 per cm3.
The vοlume οf a sphere is equal tο 4/3 π x (4 cm)³ = 268.08 cm³.
$35.00 divided by 268.08 centimetres squared equals $0.13 per centimetre.
As a result, the spherical bοttle οffers the greatest value fοr the amοunt οf perfume cοntained in each cubic centimetre because it cοsts the least.
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#5
The frequency table shows the results of a survey that asked 175 high schoolers how they learn about news stories.
The relative frequency of a student being a tenth grader that gets their news from the internet is 0.79.
What is frequency ?
Frequency refers to the number of times that an event or value occurs within a specific period or dataset. It is a measure of how often a particular value or category appears in a set of data. The frequency can be expressed as an absolute count or as a proportion or percentage relative to the total number of observations in the dataset. Frequency is often used in statistical analysis to describe the distribution of data and to calculate various measures of central tendency and variability.
The relative frequency of a student being a tenth grader that gets their news from the internet is given by:
(number of tenth graders who get their news from the internet) / (total number of students)
So, the relative frequency for tenth graders is
34/175 = 0.194
Rounding to the nearest hundredth gives 0.19.
Therefore, the relative frequency of a student being a tenth grader that gets their news from the internet is 0.79.
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Which of the following is the correct way to name the figure shown?
PQ
A. PQ
B. PQ
C. QP
The correct way to name the figure shown is PQ. This figure consists of two perpendicular lines, P and Q, which intersect at a point. The lines are labeled P and Q, so the correct name for the figure is PQ.
What are perpendicular lines?Perpendicular lines are those two lines that intersect each other at a 90 degree angle. These lines are also known as orthogonal lines. When two lines intersect at a 90 degree angle, they are said to be perpendicular.
The figure is a basic geometric shape and is used to illustrate the concept of perpendicular lines. In the figure shown, the angle formed by the intersection of the two lines is a right angle, so the lines are perpendicular.
The figure can also be used to illustrate the concept of a transversal. A transversal is a line that intersects two other lines at different points. In the figure, the line PQ is a transversal intersecting the two lines P and Q.
In conclusion, the correct way to name the figure shown is PQ. This figure is used to illustrate the concepts of perpendicular lines, line segments, and transversals.
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find the measure of pbd? what is the value of k?
Answer:
Your answer is <PBD = 56
Step-by-step explanation:
That red square indicate that its a right triangle meaning that <PBH is 90°
Those two angle <PBD and <DBH are complementary angle meaning that those two angle add up to 90°
So,
<PBD + <DBH = 90°
(3k + 65°) + 34 = 90
3k + 65 + 34 = 90
3k = -9
k = -3
Plug in k = -3 in <PBD to solve for the measure angle.
<PBD = (3k + 65°) ; k = -3
<PBD = 3(-3) + 65
<PBD = -9 + 65
<PBD = 56
if both pipes are turned on by mistake, how long will it take to fill an empty pool?
It will take 1/4 of an hour, or 15 minutes, to fill an empty pool when both pipes are turned on by mistake.
What is the rate of change?The speed at which a variable changes over a specific amount of time is referred to as the rate of change. It is frequently represented in mathematics as a function's derivative, which gauges how quickly the function's output alters in relation to its input.
We must first ascertain the rates of each pipe in order to solve this issue using the rate of work formula. Let r in and r out represent the corresponding flow rates of the inlet and output pipes.
The rate of the inflow pipe is 1/3 of the pool per hour because it may fill the pool in three hours. The outlet pipe's rate is 1/12 of the pool each hour since it can drain the entire pool in 12 hours.
The net rate is the difference between the inlet and output rates because when both pipelines are operating, they compete with one another:
r_net = r_in - r_out = 1/3 - 1/12 = 1/4 of the pool per hour
This means that the pool will be filled with a net rate of 1/4 of the pool per hour. Using the rate of work formula, we can now solve for the amount of time it takes to fill the pool:
A = r / t
t = r / A
Substituting r_net = 1/4 and A = 1 (since we want to fill one pool), we get:
t = (1/4) / 1 = 1/4 hours
Hence, it will take 1/4 of an hour, or 15 minutes, to fill an empty pool when both pipes are turned on by mistake.
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Suppose 2022 balls are randomly distributed into 100 boxes. Let
X be the total number of balls in the first 20 boxes.
a) Find P(X = 90)
b) Find V arX.
Suppose 2022 balls are randomly distributed into 100 boxes. Let X be the total number of balls in the first 20 boxes. P(X = 90) ≈ 0. VarX = 323.52.
a) To find P(X = 90), we can use the binomial probability formula:
P(X = k) = C(n,k) * p^k * (1-p)^(n-k)
where C(n,k) = n! / (k! * (n-k)!)
In this case, n = 2022, k = 90, p = 20/100 = 0.2
P(X = 90) = C(2022,90) * 0.2^90 * 0.8^(2022-90)
P(X = 90) = 1.19 * 10^(-37)
Therefore, P(X = 90) ≈ 0.
b) To find VarX, we can use the formula for the variance of a binomial distribution:
VarX = n * p * (1-p)
In this case, n = 2022, p = 0.2
VarX = 2022 * 0.2 * 0.8
VarX = 323.52
Therefore, VarX = 323.52.
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