Step-by-step explanation:
-3x² - 6x + 24
this is an expression, not an equation.
for an equation this would have to look like e.g.
-3x² - 6x + 24 = 0
anyway, yes, we can factor this expression :
-3x² - 6x + 24 = -3(x² + 2x - 8) = -3(x + 4)(x - 2)
why ?
x² + 2x - 8 corresponds to
(x + a)(x + b) = x² + (a+b)x + ab
so which factors a and b multiply to ab = -8 and add to (a+b) = 2 ?
-8 has the factors
4, -2
-4, 2
8, -1
-8, 1
only (4, -2) covers the both criteria.
therefore, the correct factorization is
-3(x + 4)(x - 2)
Sam wanted to graph the equation
y = 2x -7. She plotted her y-intercept
point and started to count the slope.
Which of the following should she do?
A. count up 2, and left 1
B. count down 2, over 0
C. count down 2, and right 1
D. count up 2, and right 1
We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.
How can we find the intercepts and slope of the equations?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula. We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.
y=mx+b is the slope intercept formula
CalculationThe given equation is y=2x-7.
By comparing to slope intercept formula y=mx+b,
m=2 and b=-7.
So the slope of the given equation is 2 and y-intercept is (0,-7).
we know that,
m=rise/run
so rise=2 and run=1 that means Sam needs to count up 2 and right 1 to graph the equation using the given slope.
We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.
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At any given time there are N people on an elevator, N being a discrete random variable with mean E(N)=n. The weight of the i th person in the elevator Is a continuous random variable Y, with mean E(Yi)=w. The random variable N and the random variables Yi are independent. Let W be the total weight of all people in the elevator at a given time. Prove that E(w)=w. (Hint: This is very simple to prove if you use properties of conditional expectation).
At any given time there are N people on an elevator, N being a discrete random variable with mean E(N)=n, then E(Y1) = w
Let W be the total weight of all people in the elevator at a given time and N be the number of people in the elevator at a given time.
E(W) = E[E(W|N)]
Since N and Y are independent, we can also write with mean:
E(W|N) = E[E(W|N,Y)]
Since the weight of each person is independent of the others, we can write:
E(W|N,Y) = E[E(W|N,Y1)]
Since Y is a continuous random variable and the weights of each person are independent, we can further write:
E(W|N,Y1) = E(Y1) = w
Therefore, we can conclude that:
E(W) = E[E(W|N)] = E[E(W|N,Y)] = E[E(W|N,Y1)] = E(Y1) = w
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The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f(p).^1(a) What is the meaning of the derivative f^1(8)? What are its units?
The derivative f'(8) gives the rate of change of the quantity (in pounds) of coffee sold as we increase the price (in dollars).
The units of the derivative are always output units from original function input units from original function . For the original function, the output is pounds of coffee sold, and the input is the price in dollars per pound.
Thus the units for f′(8) are pounds dollars/pound.(b) Is f′(8) positive or negative? Explain. We interpret the rate given by the derivative as the input increases, so the price per pound is increasing. From the law of supply and demand, as the price increases, the quantity sold decreases. Thus we expect
f′(8) to be negative.
The answers to both subparts are shown:
(A) The derivative of f'(5) means the pace at which the price per pound changes in relation to the weight of coffee sold at $5 per pound.
(B) The unit of f'(5) is pounds/dollar.
What is derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument.
Calculus's core tool is the derivative.
We may find the slope of a function at any point by using its derivative. We can find numerous derivatives by adhering to certain rules.
For instance: A constant value, such as 3, always has a slope of 0.
(A) Meaning of derivative of: f'(5)
We have: Q = f(p) ...(1)
Differentiating Q in relation to p results in:
qQ/dp = f'(p) ...(2)
The rate of change of the price per pound in relation to the volume of coffee sold is implied by equation (2).
If p = 5, we get:
qQ/dp = f'(5) ...(3)
The rate at which the price per pound changes in relation to the amount of coffee sold at $5 per pound is implied by equation (3).
(B) Unit of f'(5):
Equation (3)'s result that qQ/dp = f'(5) suggests that f'(5) units are pounds/dollar.
Therefore, the answers to both subparts are shown:
(A) The derivative of f'(5) means the pace at which the price per pound changes in relation to the weight of coffee sold at $5 per pound.
(B) The unit of f'(5) is pounds/dollar.
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Correct question:
The quantity (in pounds) of gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f(p). (a) What is the meaning of the derivative f '(5)? The rate of change of the price per pound with respect to the quantity of coffee sold. The supply of coffee needed to be sold to charge $5 per pound. The rate of change of the quantity of coffee sold with respect to the price per pound when the price is $5 per pound. The rate of change of the price per pound with respect to the quantity of coffee sold when the price is $5 per pound. The price of the coffee as a function of the supply. What are the units of f '(5)? dollars dollars/pound pounds/(dollars/pound) pounds dollars/(pound/pound) pounds/dollar
the positive integers are arranged in the patterm illustrated below: if this pattern continues indifinetely, what is the number immediately above 39863
Answer:
Step-by-step explanation:
986
Ajay and deepak can do an allocated work in 15 days and 10days respectively. They stated the work together but Deepak left after sometimes and ajay finished the remaining work in 5 days. After how many days (from the start)did Deepak leave
Answer:
Deepak have taken 5 days leave from the start of the work.
Suppose that $800 was budgeted for the month. Determine the exact amount for each category
The exact amounts for each category are given as follows:
Landline: $120.Water: $104.Electric: $200.Gas: $136.Sanitation: $80.Cell phone: $160.How to obtain the exact amounts?The exact amounts for each category are obtained applying the proportion relative to the percentage of each category, that is, multiplying the decimal equivalent of the percentage by the total amount of $800.
Hence the amounts are given as follows:
Landline: 0.15 x 800 = $120.Water: 0.13 x 800 = $104.Electric: 0.25 x 800 = $200.Gas: 0.17 x 800 = $136.Sanitation: 0.1 x 800 = $80.Cell Phone: 0.2 x 800 = $160.Missing InformationThe pie chart with the categories and their percentages is given by the image shown at the end of the answer.
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The telephone company offers two billing plans for local calls. Plan 1 charges $25 per month for unlimited calls and Plan 2 charges $18 per month plus $0.05
per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part
a.
For the number of calls greater than 140, the plan [1] is more economical than plan [2].
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a telephone company offers two billing plans for local calls. Plan 1 charges $25 per month for unlimited calls and Plan 2 charges $18 per month plus $0.05 per call.
For the part [1] -
25 < 18 + 0.05x
25 < 18 + 0.05x
25 - 18 < 0.05x
7 < 0.05x
x > (7/0.05)
x > 140
For part [2] -
For the number of calls greater than 140, the plan [1] is more economical than plan [2].
Therefore, for the number of calls greater than 140, the plan [1] is more economical than plan [2].
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A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm) , and the foot length, in cm , for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown.
The figure presents a scatterplot in a coordinate plane. The horizontal axis is labeled Foot Length, in centimeters, and the numbers 18 through 34, in increments of 2, are indicated. The vertical axis is labeled Height, in centimeters, and the numbers 150 through 190, in increments of 10, are indicated. There are 65 data points in the scatterplot, and a trend line is given as follows. Note that all values are approximate. The data points begin in the lower left part of the plane at the point with coordinates 19 comma 160. The data points trend upward and to the right and end with the coordinates 33 comma 190. The least-squares regression line begins at the point 18 comma 153, and slants upward and to the right at a constant rate to end at the point 35 comma 197.
Term Coef (SE) Coef T -Value P -Value
Constant 105.08 6.00 17.51 0.000
Foot length 2.599 0.238 10.92 0.000
S=5.90181 R–sq=65.42%
(a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm .
(b) The standard deviation of the residuals is s=5.9 . Interpret the value in context.
Unit 2 Progress Check: FRQ
Aubree Flores
As per the least-squares regression,
a) The residual for the high school senior with a foot length of 20cm and a height of 160cm is 2.94
b) As per the given standard deviation, the value of the context 5.9
The term standard deviation in math is defined as a measure of how dispersed the data is in relation to the mean.
Here we have given that the random sample of 65 high school seniors was selected from all high school seniors at a certain high school.
And we need to find following.
While we looking into the given question, as per the least-squares regression line, here the estimated height for a high school senior with a foot length of 20 cm is calculated as,
=> y = 2.599x + 105.08
Now, we have to apply the value of x as 20, then we get,
=> y = 2.599(20) + 105.08
=> y = 157.06
Therefore, the residual is calculated as,
=> 160 − 157.06 = 2.94
b) As per the given standard deviation, here the differences between each data point and its corresponding estimate varies with a standard deviation of 5.9 cm.
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Help as soon as possible
The value of /BD/ in the quadrilateral is 16.9m
How to determine length in a triangle?A quadrilateral is polygon with four sides, four angles, four vertices, two diagonals whose sum of angles is 360 degrees
The diagonal of the quadrilateral forms a triangle.
From the triangle ΔABD, two sides are given with an included angle.
/AB/=16m
/AD/=19m
/BD/=?
To find the length /BD/
let it be a.
Using cosine rule, we have
a²=b²+d²-2bdcosA
a²=19²+16²-2*19*16*cos57⁰
Simplifying the formula
a²=361+256-608*0.5446
a²=617-311.1168
a²=285.8832
taking the square of both sides we have
a=√285.8832
a=16.9m
Therefore the length of the side /BD/ = 16.9m
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suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. the time t is measured in seconds and the units for r(t) are measured in tonnes (metric tons) per second. note that r(t) is increasing over the interval [0, 6]. t 0 1 2 3 4 5 6 r(t) 2 10 18 32 44 54 60 (a) give upper and lower estimates (in tons) for the total quantity q(6) of erupted materials after six seconds. (use six equal subintervals.)
The lower estimate and upper estimate of the erupted materials of total q(6) quantity after 6 seconds is equal to 160 metric tons and 218 metric tons respectively.
As given in the question,
Reading of the rate is represented by r(t) in metric tons
Time interval in seconds:
t : 0 1 2 3 4 5 6
r(t) : 2 10 18 32 44 54 60
Lower estimate for the q(6) quantity of the erupted material after 6 seconds.
= r(0)(1) + r(1)(1) + r(2)(1) + r(3)(1)+ r(4)(1) + r(5)(1)
= 2 + 10 + 18 + 32 + 44 + 54
= 160
Upper estimate for the q(6) quantity of the erupted material after 6 seconds.
= r(1)(1) + r(2)(1) + r(3)(1)+ r(4)(1) + r(5)(1) + r(6)(1)
= 10 + 18 + 32 + 44 + 54 + 60
= 218
Therefore, the lower estimate and upper estimate of the total q(6) quantity after 6 seconds is equal to 160 metric tons and 218 metric tons respectively.
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Help please fast!! What is the measure of angle C? I’m confused please help!
Answer:
[tex]61.8^{\circ}[/tex]
Step-by-step explanation:
Vertical angles are congruent
Answer:
61.8
Step-by-step explanation:
The measure of angle C is 61.8 degrees.
Vertical angles are a pair of nonadjacent angles formed by two intersecting lines. They are called "vertical" because they are opposite each other and share the same vertex (the point at which the two lines intersect). Because vertical angles share the same vertex, they are always congruent, which means that they have the same measure.
In this case, angles C and E are a pair of vertical angles, so they are congruent. Since the measure of angle E is 61.8 degrees, the measure of angle C must also be 61.8 degrees. Therefore, the answer is 61.8 degrees.
Graph line segment BC with endpoints B(8 and
C(-4,5) and label the points.
Steps for solving:
Draw and label an x and y axis (make sure you include arrows).
Plot the given points.
Label the given points.
The graph of the Line Segment BC with the endpoints B(8,9) and C(-4,5) is shown below.
In the question ,
it is given that ,
the end points of the line segment is B(8,9) and C(-4,5) .
we have to graph the line segment BC.
first we mark the point on the coordinate plane , with point B and point C .
after that we join the points .
and the equation of the line segment is
(y - 5) = (9-5/8+4)*(x + 4)
(y - 5) = (1/3)*(x + 4)
3y - 15 = x + 4
x - 3y + 19 = 0
Therefore, the graph of the line segment BC is shown below.
The given question is incomplete , the complete question is
Graph line segment BC with endpoints B(8,9) and C(-4,5) and label the points.
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Judy purchased a home in 1956. The
function represents y, the value of the home
x years since 1956.
f(x) = 11,500(1.09)^x
A. Judy purchased the home for
$109,000.
B. The value of the home increases by 9%
each year.
C. In 1986, Judy's home had a value over
$150,000.
After 26 years Judy purchased the home for $109,000.
What is function?
A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, and the set Y is known as the function's codomain.
A function is a relationship between a set of inputs and a set of potential outputs, where each input is related to exactly one output.
Given:
Judy purchased a home in 1956.
The function represents y, the value of the home x years since 1956.
f(x) = 11,500(1.09)^x
Let Judy purchased the home for $109,000.
We have to find the the number of years when Judy purchased the home for $109,000.
Plug f(x) = 109,000 in the above equation.
109,000 = 11,500(1.09)^x
218/23 = (1.09)^x
Taking log on both sides,
ln(218/23) = ln(1.09)^x
ln(218/23) = x ln(1.09)
x = ln(218/23)/ln(1.09)
x = 26.097
⇒ x ≈ 26
Hence, after 26 years Judy purchased the home for $109,000.
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(30 points) The fixed costs of manufacturing basketballs in a factory are $1,400.00 per day. The variable costs are $5.25 per basketball. Which of the following
expressions can be used to model the cost of manufacturing b-basketballs in 1 day?
O $1,405.25b
o $5.25b-$1,400.00
O $1,400.00b+$5.25
O $1,400.00-$5.25b
The correct expression to model the cost of manufacturing b basketballs in 1 day is:
O $5.25b-$1,400.00
The fixed costs of manufacturing the basketballs are $1,400.00 per day, and the variable costs are $5.25 per basketball. To find the total cost of manufacturing b basketballs in 1 day, you need to add the fixed costs and the variable costs for each basketball.
The variable costs for b basketballs would be $5.25 * b. To find the total cost, you need to subtract the fixed costs of $1,400.00 from this amount. This can be represented by the expression $5.25b - $1,400.00.
The other expressions do not correctly represent the cost of manufacturing b basketballs in 1 day because they do not correctly account for both the fixed costs and the variable costs.
Pentagons ABCDE and FGHIl are similar. The ratio of each side of pentagon ABCDE to its corresponding side of pentagon FGHIJ is 4:1. If AB and FG are corresponding sides, and the length of AB is 4x + 4, what is the length of FG?
Pentagons ABCDE and FGHIl are similar. The ratio of each side of pentagon ABCDE to its corresponding side of pentagon FGHIJ is 4:1. the length of FG is x + 1.
What is the length of FG?Generally, A distance may be measured in terms of its length. A quantity that has the dimension distance in the International System of Units is referred to as length. In the vast majority of measuring systems, a length base unit is selected, and it is from this unit that all other units are derived.
The meter serves as the fundamental measuring device for length in accordance with the International System of Units.
Since the ratio of the sides of the two pentagons is 4:1, the length of FG is 1/4 of the length of AB.
Therefore, the length of FG is
(1/4)(4x + 4) = x + 1.
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Complete Question not found
Image not found
Answer:
its 1/4
Step-by-step explanation:
Step 1: Calculate the ratio of the side lengths for the original image to the corresponding side lengths of the transformed image using side FG and its corresponding side in
in a recent poll of 1,000 homeowners in the united states, one in eight homeowners reports having a home equity loan that he or she is currently paying off. using a confidence coefficient of 0.99, construct the confidence interval for the proportion of all homeowners in the united states that hold a home equity loan.
Use Table 1. (Round intermediate calculations to 4 decimal places. Round "z-value" and final answers to 3 decimal places.)
Confidence interval to
For the proportion of all hometowners in the united states that hold a home equity loan, confidence interval is (0.0992, 0.1508).
We have given that in a recent poll of 1000 homeowners in the United states, one in eight homeowners reports havinf a home equity loan that he or she is curently paying off.
If one in eight reports having a home equity loan then for 1000 hometowners = 1000/8 = 125.
Sample proportion p = 125/1000 = 0.125
given that confidence coefficient = 0.99
α = 1 - confidence coefficient = 1 - 0.99
α = 0.01
z₀.₀₁ / 2 = 2.58
Therefore the interval estimate for the proportion of all homeowners in the United states that hold a home equity
= p ± z₀.₀₁/2 √p(1-p)/n
= 0.125 ± 2.58 √0.125(0.875)/1000
= 0.125 ± 2.58 √0.0001
= 0.125 ± 0.0258
= (0.125 - 0.0258,0.125 + 0.0258)
= (0.0992, 0.1508)
Hence (0.0992, 0.1508) is the confidence interval.
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is it possible to use the law of cosines to solve for one angle in a triangle?
Yes, it is possible to use the law of cosines to solve for one angle in a triangle.
The law of cosines states that in any triangle, the square of the length of any side (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) minus twice the product of those sides and the cosine of the angle between them (C):
c^2 = a^2 + b^2 - 2ab * cos(C)
If you know the lengths of all three sides of a triangle (a, b, and c), you can use the law of cosines to solve for the cosine of one of the angles (C). Once you have the cosine of the angle, you can use the inverse cosine function (also known as the arccosine) to find the measure of the angle in degrees.
For example, if you know the lengths of sides a and b and the measure of angle C in a triangle, you can use the law of cosines to find the length of side c:
c = sqrt(a^2 + b^2 - 2ab * cos(C))
Alternatively, if you know the lengths of sides a and c and the measure of angle B in a triangle, you can use the law of cosines to find the length of side b:
b = sqrt(c^2 - a^2 - 2ac * cos(B))
In both cases, once you have found the value of one of the sides, you can use the law of sines to find the measure of the remaining angle in the triangle.
find the value of x. (4x-101)° (2x+3)
The value of x in . (4x-101)° = (2x+3) is 52°.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
The value of x. (4x-101)° = (2x+3)
Collect the like terms
4x - 2x = 3 + 101
2x = 104
Divide
x = 104 / 2
x = 52°
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Complete question
Find the value of x. (4x-101)° = (2x+3)
3. Carissa is considering job offers from two companies. Company A offered her a starting salary of $45,000 with a $2100 raise at the end of each year. Company B offered her a starting salary of $45,000 with a 4.2% raise at the end of each year. Let f(t) represent Carissa's salary at Company At years after accepting a position at Company A, and let g(t) represent Carissa's salary at Company B t years after accepting a position at Company B. a. Find a function formula for f. b. Find a function formula for g. C. If Carissa was expecting to work for 5 years before going back to school, which company do you think she should work for? Use your functions to justify your answer. I d. If Carissa was expecting to work for 10 years before going back to school, which company do you think she should work for? Use your functions to justify your answer.
Let f(t) be 51000+ (2100)t which represent Chelsea's salary at Company A and g(t) be 45000(1.041)t which Chelsea salary at Company B.
Chelsea's offer from company A includes a raise of $2100 annually and a starting salary of $45,000.
Since the increase is constant, the salary of Chelsea from Company A is a linear function, as can be seen here.
f(t) is salary of chelsea from company A after t years.
f(t) = 45000+ (2100)t
The offer made to Chelsea by company B includes a starting salary of $45,000 and an annual raise of 4.1%.
we can see here that raise is exponential, so raise is:
(1+4.1/100) = (1+0.041) = (1.041) per year.
Consequently, the salary of Chelsea from Company B is a function that is exponential.
g(t) is salary of chelsea from company B after t years.
g(t) = 45000(1.041)t
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Select ALL solutions
Answer:
in the picture
Step-by-step explanation:
in the picture
96% of Americans report eating a diet that includes meat, 3.5% of Americans claim to be exclusively vegetarian, and 0.5% claim to be strictly vegan. Of a random sample of undergraduates in the University of Virginia dining hall (n = 175), 156 students report eating a diet that includes meat, 11 report being exclusively vegetarian, and 8 are strictly vegan.
5. State the test you would use to determine if the observed and expected frequencies of diets are consistent. List the conditions required for this test and verify that they are satisfied.
6. How many students would you expect to eat meat, be exclusively vegetarian, and be a strict vegan?
7. Calculate the chi-square statistic, the degrees of freedom associated with it, and the p-value.
8. Based on the p-value calculated in Question 7, what is the conclusion of the hypothesis test at α = 0.05? Interpret your conclusion in context of the question.
A study about the diet of undergraduate students,
5) Chi-square statistic test , would use to determine if the observed and expected frequencies of diets are consistent. With null hypothesis as the observed and expected frequencies of diets are consistent.
6) The excepted students to eat
meat = 165
exclusively vegetarian= 6
strict vegetarian= 1
7) Chi-square statistic value is 62.755 and degree of freedom are 2 . The critical value for Chi-square statistic is 0.00001
8) P-value< 0.05, so reject the null hypothesis.
Therefore there is no sufficient evidence to support that the observed and expected frequencies of diets are consistent.
A random sample of undergraduates in the University of Virginia dining hall.
Sample size , n = 175
Three categories are given as shown in above table with percentage of report eating a diet.
Report also consists observed values about the number of students diet including the three different categories
5) The Chi-square test would use to determine the required result. Consider Null and alternative hypothesis as :
H₀ : the observed and expected frequencies of diets are consistent
Hₐ : the observed and expected frequencies of diets are not consistent
χ² =∑(Oᵢ - Eᵢ)²/Eᵢ
where, χ² --> chi-square cofficient or value
Oᵢ --> observed values which are provided
Eᵢ --> excepted values
Excepted values , Eᵢ = n× p
here we assume that,
These categories are independentindividuals are selected randomly6) The number of students would you expect to eat meat = 168
The number of students would you expect to eat exclusively vegetarian
= 6.125 ~ 6
The number of students would you expect to eat strict vegetarian = 0.875 ~ 1
7) Degree of freedom,df = k - 1 = 2, where k denotes total number of categories here
Chi-square statistic, χ² = ∑(Oᵢ - Eᵢ)²/E
χ² = 62.755
Using chi-square table, the critical chi-square value for χ² = 62.755 and degree of freedom 2 is 0.00001 ..
8) Significance level, alpha = 0.05
As we see that p-value = 0.00001< alpha = 0.05
So, we reject the null hypothesis.
Thus, there is no sufficient evidence to support null hypothesis.
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for an closed cylinder with radius r cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 6 cm3
The dimensions giving the minimum surface area are r = 0.98 cm approx. and h = 1.998 cm .
What is surface area?
The surface area of a solid object could be a live of the full area that the surface of the article occupies.
Main body:
The surface area of the closed cylinder is given by,
S = 2πr²+2πrh
And volume is given by,
V = πr²h
Where, R is radius and h is height of cylinder.
Volume is given to be 6 cm³.
V = πr²h = 6
h = 6/πr²
Inserting this value of h in Surface area equation, we get,
S = 2πr²+ 2πr ( 6/πr²)
S = 2πr² + 12 /r
Now differentiating wrt x to find minimum, inserting ds/dr = 0 , we get,
4πr = 12/r²
r = (3/π)¹/³
r = 0.98 cm approx.
h = 6/π *(0.98)²
h = 6/3.017
h = 1.998 cm
Hence ,the dimensions giving the minimum surface area are r = 0.98 cm approx. and h = 1.998 cm .
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The measures of the acute angles in the isosceles trapezoid are one-half times the measures of the obtuse angles. Write and solve a system of equations to find the measures of all the angles.
Answer:
[tex]\textsf{System of equations: \quad }\begin{cases}x=\dfrac{1}{2}y\\\\2x+2y=360\end{cases}[/tex]
[tex]\begin{aligned} \textsf{Solutions}: \quad x &= 120^{\circ}\\y &= 60^{\circ}\end{aligned}[/tex]
Step-by-step explanation:
An obtuse angle is greater then 90° and less than 180°.
An acute angle is less than 90°.
Therefore, from inspection of the given diagram:
x = obtuse angley = acute angleIf the measures of the acute angles are one-half times the measures of the obtuse angles:
[tex]\implies x=\dfrac{1}{2}y[/tex]
Angles in a quadrilateral sum to 360°.
[tex]\implies 2x+2y=360[/tex]
Therefore, the system of equations is:
[tex]\begin{cases}x=\dfrac{1}{2}y\\\\2x+2y=360\end{cases}[/tex]
Substitute the first equation into the second equation and solve for y:
[tex]\implies 2\left(\dfrac{1}{2}y\right)+2y=360[/tex]
[tex]\implies y+2y=360[/tex]
[tex]\implies 3y=360[/tex]
[tex]\implies \dfrac{3y}{3}=\dfrac{360}{3}[/tex]
[tex]\implies y=120[/tex]
Substitute the found value of y into the first equation and solve for x:
[tex]\implies x=\dfrac{1}{2} \cdot 120[/tex]
[tex]\implies x=60[/tex]
a die is rolled until the first time t that a six turns up, what is the probability distribution for t
The probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.
What is a probability distribution?
A probability distribution is a function that describes the probabilities of different outcomes in a random event or experiment. It is used to represent the likelihood of different outcomes occurring in a given situation.
In the case of rolling a die until the first time that a six turns up, the probability distribution for t (the number of rolls it takes to get a six) would describe the probability of getting a six on each roll.
The probability of getting a six on the first roll is 1/6, since there is a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the second roll is 1/6, since there is still a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the third roll is also 1/6, and so on.
The probability distribution for t in this case can be represented by the following table:
t Probability
1 1/6
2 1/6
3 1/6
4 1/6
5 1/6
... ...
This probability distribution indicates that the probability of getting a six on the first roll is 1/6, the probability of getting a six on the second roll is 1/6, and so on.
Hence, the probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.
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which measures do not represent the length of 3 sides of a triangel
Answer: correct answer is A
Step-by-step explanation:The numbers of sets which cannot represent the lengths of the sides of a triangle are 8, 9, 11.We have to determineWhich set of numbers cannot represent the lengths of the sides of a triangle?According to the questionThe length of sides which can not form a triangle is determined in the following steps given below.
Answer:
The correct answer is A.
Step-by-step explanation:
You have to look at the triangle inequality theorem where a + b ≥ c. Any two sides of a triangle must be greater than or equal to the third, in this case, 1 ft + 3 ft only = 4. Therefore A does not represent the length of 3 sides of a triangle.
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Sharon wants to make keychains with different colored beads as shown below.
Each key-chain will look the same Sharon will use a total of 20 green beads to make all her keychains. What is the number of red Beads and the number of blue Beads she will need to make all of the keychains
The numbers of each beads that Sharon will need to make all of the key chains is given as follows:
Red beads: 15.Blue beads: 30.How to obtain the amounts needed of each bead?The amounts for each bead are obtained applying the proportions built from the image given at the end of the answer.
From the images, for a single key chain, the amounts needed are given as follows:
4 green beads.3 red beads. 6 blue beads.Hence, for each 4 green beads, 3 red beads are needed. For 20 green beads, the number of red beads needed is given as follows:
3/4 x 20 = 60/4 = 15 red beads.
For each 4 green beads, 6 blue bears are needed. For 20 green beads, the number of blue beads needed is given as follows:
6/4 x 20 = 120/4 = 30 blue beads.
Missing InformationThe image is given at the end of the answer.
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Is it true n ⊥ p? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.
No, the lines are not perpendicular because Line m has a slope of 2/3 and line n has a slope of 3/5.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
For two lines to be perpendicular if the slopes are reciprocal of each other.
line m: 2/3
line n: 3/5
Therefore,
n ⊥ p is False.
The slopes are not negative reciprocal of each other. so the lines are not perpendicular.
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Given the function:
f(x) = (3x+7)
What is the output of the function when the input is x = 9?
A 9
B 15
C 17
D 21
Answer isn't one of your options, it is 34.
Step-by-step explanation:1. Write the function.[tex]f(9) = (3(9)+7)[/tex]
3. Calculate.[tex]f(9) = (27+7)\\ \\f(9) = 34[/tex]
4. Conclude.[tex]f(9) = 34[/tex].
34. selecting from urns an urn contains four red marbles and three green marbles. one marble is removed, its color noted, and the marble is not replaced. a second marble is removed and its color noted.
The probability states that- (r+w+b+g)min =21,
What is probability ?Probability refers to possibility.
A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
According to our question-
r−3=4w,r−2=3b,r−1=2g
r=4w+3,r=3b+2,r=2g+1
rmin=11⇒w min=2⇒bmin=3⇒g min =5
Hence, (r+w+b+g)min =21,
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The integer 5 makes which of the following equation false
Answer:
(a) 3m +4 = 6m
Step-by-step explanation:
You want to know which of the equations is false when the value of the variable is 5.
3m +4 = 6m3(5) +4 = 19 ≠ 6(5) . . . . . the given equation is false for m=5
-5(t -7) = 10-5(5 -7) = -5(-2) = 10 . . . . true
17 = 4x -317 = 4(5) -3 = 20 -3 . . . . true
t +9 = 145 +9 = 14 . . . . true