The points are known to intersect the curve at
(smaller t-value) (x, y, z) = 0, 0, 0(larger t-value) (x, y, z) = 2, 0, 4How to find the pointsWe have our equation as: r(t)=ti+(4t-t2)k (4t - t2)k
From r(t)
We have x to be t, y to be 0 and z=4t-t2
The given paraboloid can be defined to be
z=x^2+y^2
We are to put the values in the equation
4t-t²=t²+0
2t²=4t
Then t wuld be 2 or 0
Hence we have to conclude that ours points of intersection are at (0,0,0) and (2,0,4).
The 0,0,0) and (2,0,4) points is where the intersection of the paraboloid take place.
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If the solutions of f(x)=0 are -1 and 2
then find the solutions of f(x/2)=0
Answer: -2 and 4
Step-by-step explanation:
Let [tex]t=x/2[/tex].
[tex]f(t)=0 \longrightarrow t=-1, 2\\\\\therefore x=-2, 4[/tex]
the domain of f(x)= logb x is the set of all real numbers true or false pls need now
Answer: False
Step-by-step explanation:
The only number that makes this impossible to solve is x = 0
A random sample of n D 225 and xN D 21 was drawn from a normal population with a known
standard deviation of 26:8: Calculate the 95% confidence interval of the population mean.
Using the z-distribution, the 95% confidence interval of the population mean is: (17.5, 24.5).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For this problem, the other parameters are:
[tex]\overline{x} = 21, \sigma = 26.8, n = 225[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 21 - 1.96\frac{26.8}{\sqrt{225}} = 17.5[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 21 + 1.96\frac{26.8}{\sqrt{225}} = 24.5[/tex]
The interval is: (17.5, 24.5).
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Fill in the blank
Timothy runs a public transportation service in his town. He has learned from his accountant that his organization is a liable to a special kind of tax. Which tax would Timothy have to pay from his organization?
Timothy would have to pay the _______ tax for his transportation service.
Answer:
road
Step-by-step explanation:
A bank gives an interest of 12% per annum.How long will it take to double one's interest?
Mike, Luke, and Alex each own a white hat marked with the first letter of their name. Winter owns a plain red hat, which is not marked with any letter.
How many ways can the four people wear these four hats so each person is wearing a different hat, and no one is wearing a hat marked with the first letter of their name?
Answer:switch mikes Luke’s and Alex in between each other and let winter keep her own
Step-by-step explanation:
Determine whether the relationship is linear, quadratic, or neither by completing each table. Be sure to give
a reason for your choice.
The 1st table represents a linear as well as the quadratic relationship, the 2nd table represents neither and the 3rd table also represents neither relationship.
Why do the given tables have the above relationship?The first table is having linear as well as quadratic because the 1st table has its first difference equal as well as the second difference is also equal i.e., why it is linear and quadratic respectively.The second table is having neither because 1st difference is not equal to each other as well as 2nd the difference is also not equal.The third table is having neither because 1st difference is not equal to each other as well as 2nd the difference is also not equal to each other. Therefore, the 3rd table is neither.Hence, the 1st table represents a linear as well as a quadratic relationship, the 2nd table represents neither and the 3rd table also represents neither relationship.
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Suppose Mai places $3500 in an account that pays 19% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
S
(b) Find the amount in the account at the end of 2 years.
Answer:
a.$4165
b.$4956.35
Step-by-step explanation:
a)19% × 3500 = 665.
3500+665 =4165
b)19% × 4165 = 791.35
4165+791.35= 4956.35
The sum of three consecutive integers is -15.
If 1 is added to each integer, what is the product.
of the three resulting integers?
60 POINTS IF CORRECT AND BRAINLIEST ANSWER FOR COMPLETE ANSWER
1. The solution to the first percent puzzle is as follows:
75% 66²/₃ 11¹/₉
33¹/₃% 25% 22¹/₅% 3⁷/₁₀%
50% 37¹/₂% 33¹/₃% 5¹/₂%
50% 37¹/₂% 33¹/₃% 5¹/₂%
2. The solution to the second percent puzzle is as follows:
10% 90%
50% 5% 45%
50% 5% 45%
What is a percent puzzle?A percent puzzle is a puzzle that engages students to practice working with percentages.
The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.
The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.
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What is the volume of this prism if a scale factor of 1.25 is applied to its dimensions?
A. 17.00 cubic units
B. 33.20 cubic units
C. 21.25 cubic units
D. 13.60 cubic units
Answer: B
Step-by-step explanation:
1: 5 × 1.25 = 6.25
2 × 1.25 = 2.5
1.7 × 1.25 = 2.125
2: L × W × H = 6.25 × 2.5 × 2.125 = 33.20 cubic
Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part.
The function is illustrated below based on the information.
How to describe the function?When x <= 8000
The cost remains constant at 0.35 when x increases from 0 to 8000. The slope of the cost function over this part is 0
When 8000 < x <= 20000
The cost remains constant at 0.75 when x increases from 8000 to 20000 and the slope of the cost function over this part is 0.
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root of polynomial function f(x)=(x-3)^4(x+6)^2
log a^x² - 9log a³√x simplify
Answer:
log(a^x^2-27(radicalx))
Step-by-step explanation:
Assuming you have written your question correctly, this is it.
Consider the probability that exactly 90 out of 147 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 56%.
Approximate the probability using the normal distribution. Round your answer to four decimal places.
Answer:
Step-by-step explanation:
i didnt do anything bro why u delete my answer
Determine the domain and range of the following and show/explain your work.
5 y = - x^4 + 4 Provide a graph to verify your answer.
6 y = 2x^3 - 1 Provide a graph to verify your answer.
7 y = 3√(2x+8) Provide a graph to verify your answer.
See below for how the domain and the range are calculated
How to determine the domain and the range?Function, y = -x^4 + 4
The function is given as:
y = -x^4 + 4
See attachment for the graph
From the attached graph, we have:
Domain = Set of all real numbersRange = Set of real numbers less than or equal to 4Function, y = 2x^3 - 1
The function is given as:
y = 2x^3 - 1
See attachment for the graph
From the attached graph, we have:
Domain = Set of all real numbersRange = Set of all real numbersFunction, y = ∛(2x + 8)
The function is given as:
y = ∛(2x + 8)
See attachment for the graph
From the attached graph, we have:
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I need to see the steps to the problem for me to fully get it
The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)
How to find the result of a multiplication of two matrices
In this question we must apply the operation of multiplication of two matrices, whose definition is shown below:
[tex]\vec B\, \cdot \, \vec A[/tex], where [tex]\vec B \in \mathbb {R}_{n \times p}[/tex] and [tex]\vec A \in \mathbb{R}_{p \times n}[/tex] (1)
Where each element of the resulting matrix is equal to the following expression:
[tex]c_{(i, j)} = b_{(i, p)} \,\bullet\, a_{(p, j)}[/tex] (2)
Where the operator "[tex]\bullet[/tex]" represents a dot product.
Now we proceed to calculate each element of the matrix:
[tex]c_{(1, 1)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
5 · 1 + 7 · 5 + 3 · (- 1)
37
[tex]c_{(1, 2)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
5 · 7 + 7 · 2 + 3 · 2
55
[tex]c_{(1, 3)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
5 · (- 3) + 7 · 1 + 3 · (- 4)
- 20
[tex]c_{(2, 1)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
(- 3) · 1 + 7 · 5 + 9 · (- 1)
23
[tex]c_{(2, 2)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
(- 3) · 7 + 7 · 2 + 9 · 2
11
[tex]c_{(2, 3)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
(- 3) · (- 3) + 7 · 1 + 9 · (- 4)
- 20
[tex]c_{(3, 1)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
2 · 1 + 5 · 5 + 2 · (- 1)
25
[tex]c_{(3, 2)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
2 · 7 + 5 · 2 + 2 · 2
28
[tex]c_{(3, 3)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
2 · (- 3) + 5 · 1 + 2 · (- 4)
- 9
The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)
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question in the picture below
The doubling time after 4 and 7 years is 400 months and 700 months respectively
How to determine the doubling timeThe formula for finding doubling time is given as;
Doubling time = [tex]t \frac{In 2}{In 1 + \frac{r}{100} }[/tex]
Where t = time = 4 and 7 years
r = rate
For 4 years, we have
Doubling time = [tex]4 * \frac{In 2}{In ( 1 + \frac{0.7}{100}) }[/tex]
⇒ [tex]4 * \frac{In 2}{In 1. 0074}[/tex]
⇒ [tex]4 * \frac{0. 6931}{0. 0074}[/tex]
⇒ [tex]4[/tex] × [tex]93. 66[/tex]
⇒ 374. 65
⇒ 400 months in the nearest hundredth
For 7 years
⇒ [tex]7[/tex] × [tex]93. 66[/tex]
⇒ [tex]655. 62[/tex]
⇒ 700 months in the nearest hundredth
Thus, the doubling time after 4 and 7 years is 400 months and 700 months respectively
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How many more people attended from the 40-60 class than the 60-80
Answer:7 people
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
PLEASE help me with this question, and preferably leave your handwritten answer
(Easier for me to understand) but typed is also ok :)
Help is greatly appreciated!!
Using a system of equations, it is found that there were 100 students at the bus stop.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of boys in the bus stop.Variable y: Number of girls in the bus stop.Considering the first paragraph, the equation is:
[tex]\frac{x}{y - 25} = \frac{3}{2}[/tex]
Considering the second paragraph, the equation is:
y - 25 = x - 15.
Hence:
y = x + 10.
Replacing on the first equation:
[tex]\frac{x}{x - 15} = \frac{3}{2}[/tex]
3x - 45 = 2x
x = 45.
y = x + 10 = 55.
The total number was:
45 + 55 = 100.
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Graph the function f(x) = x3 – 3x – 2. Based on the graph, which value for x is a double root of this function?
–2
–1
1
2
The value for x that is a double root of this function is x = -1
How to determine the double root?The function is given as:
f(x) = x^3 - 3x - 2
From the graph of the above function (see attachment), we have the following highlights:
The curve crosses the x-axis at x = 2The curve touches the x-axis at x = -1The point that it touches the x-axis is the double root point
Hence, the value for x that is a double root of this function is x = -1
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There are 20 students in Mrs. Tanya's class and 24 kids in Mrs. Olga's class. The students need to be placed on teams of equal size with students from only their own class. What's the largest size of a team?
The largest size of a team according to the task content is; 20 kids.
What is the largest size of a team?It follows from the task content that the population is; 20 students in Mrs. Tanya's class and 24 kids in Mrs. Olga's class.
However, since, the team forming condition states that students be placed on teams of equal size with students from only their own class.
It therefore follows that the largest size of a team is 20 as only 20 students are in Mrs. Tanya's class hence leaving 4 kids in Mrs. Olga's class without a team.
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The games have been sorted into video games and board games. The number of video games is 28 less than 6 times the number of board games. The games are 80% video games. How many board games are there?
8
10
13
14
The number of board game sorted is 14
How to find the number of games?The games have been sorted into video games and board games.
The number of video games is 28 less than 6 times the number of board games.
Therefore,
the number of board games = x
number of video game = 6x - 28
The games are 80% video games. Hence,
80 / 100 × x + 6x - 28 = 6x - 28
4 / 5 × 7x - 28 = 6x - 28
4 / 5 (7x - 28) = 6x -28
28 / 5 x - 112 / 5 = 6x - 28
28 / 5 x - 6x = -28 + 112 / 5
28x - 30x / 5 = - 28 + 112 / 5
-2x / 5 = -28 / 5
-10x = -140
x = 14
Therefore, the number of board game sorted is 14.
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Answer:
14
Step-by-step explanation:
80 / 100 × x + 6x - 28 = 6x - 28
4 / 5 × 7x - 28 = 6x - 28
4 / 5 (7x - 28) = 6x -28
28 / 5 x - 112 / 5 = 6x - 28
28 / 5 x - 6x = -28 + 112 / 5
28x - 30x / 5 = - 28 + 112 / 5
-2x / 5 = -28 / 5
-10x = -140
x = 14
necesito ayuda con estas operaciones
3x=12
3x= -5=0
x+4=17
9y+3=21
5(x-2)=20
x÷2=4
2x÷=4
5÷x=2
4x+5=3x-6
3(x-2) =0
x÷3-4=0
5(7-x) =31-x
3(2x-2) =2(3x+9)
The expressions are illustrated below.
How to compute the expression?3x = 12
x = 12/3
x = 4
x + 4 = 17
x = 17 - 4
x = 13
9y + 3 = 21
9y = 21 - 3
9y = 18
y = 18/9
y = 2
x ÷ 2 = 4
x = 4 × 2
x = 8
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The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 31 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:
The equation that can be used to find the height of the tree is as follows:
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
The height of the tree is 35.6 m
How to use sine rule to find height of the tree?Th equation that can be used to find the height of the tree uses the principle of sine rule.
Therefore,
[tex]\frac{h}{sin 29} =\frac{40}{sin(180-4-29)}[/tex]
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
Therefore,
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
cross multiply
h sin 147 = 40 sin 29°
h = 40 sin 29° / sin 147
h = 19.3923848099 / 0.54463903501
h = 35.6015636045
h = 35.6 m
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Membership selection. A town council has members, Democrats and Republicans.
(A)
If the president and vice-president are selected at random, what is the probability that they are both Democrats?
(B)
If a 3-person committee is selected at random, what is the probability that Republicans make up the majority?
The probability that they are both Democrats is approximately
enter your response here.
(Type a decimal. Round to three decimal places.)
Using the hypergeometric distribution, the probabilities are given as follows:
a) 0.2 = 20%.
b) 0.5539 = 55.39%.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.Researching this problem on the internet, it is found that the council has 15 members, of which 7 are Democrats and 8 are Republicans.
Item a:
The parameters are:
N = 15, n = 2, k = 7.
The probability is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]
Item b:
At most one Democrat, with n = 3, hence:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which:
[tex]P(X = 0) = h(0,15,3,7) = \frac{C_{3,0}C_{8,3}}{C_{15,3}} = 0.1231[/tex]
[tex]P(X = 1) = h(1,15,3,7) = \frac{C_{3,1}C_{8,2}}{C_{15,3}} = 0.4308[/tex]
Then:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1231 + 0.4308 = 0.5539[/tex]
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Evaluate bh for b = 12 and h = 2. Type a numerical answer in the space provided.
The value of bh for b =12 and h = 2 is 24
How to evaluate the expression?The expression is given as:
bh
Where
b = 12 and h = 2
So, we have:
bh = 12 * 2
Evaluate
bh = 24
Hence, the value of bh for b =12 and h = 2 is 24
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Tyler wants to have $250,000 in his retirement account by the time he retires in 30 years. The interest rate is 5%. Use the annuity formula to calculate the amount Tyler needs to deposit on a monthly basis in order to reach his goal. When solving, round numbers to the nearest hundred-thousandth. Round your final answer to the nearest cent.
Using the monthly payment formula, he needs to deposit A = $1,342.12 a month to reach his goal.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are:
P = 250000, r = 0.05, n = 12 x 30 = 360.
Then:
r/12 = 0.05/12 = 0.004167.
Then:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 250000\frac{0.004167(1+0.004167)^{360}}{(1+0.004167)^{360} - 1}[/tex]
A = $1,342.12
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solve the system of equations. y=3x+2 y=x^2-4+2
The solutions to the system of equations are (4, 15) and (-1,-1)
How to solve the system of equations?The system of equations is given as:
y=3x+2
y=x^2-4+2
Substitute y=3x+2 in y=x^2-4+2
3x + 2=x^2-4+2
Simplify
x^2 - 3x - 4 = 0
Expand
x^2 + x - 4x - 4x = 0
Factorize
x(x + 1) - 4(x + 1) = 0
This gives
(x - 4)(x + 1) = 0
Solve for x
x = 4 and x = -1
Substitute these values in y=3x+2
y = 3(4)+2 = 15
y = 3(-1)+2 = -1
Hence, the solutions to the system of equations are (4, 15) and (-1,-1)
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Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level 95%, sample size 10.
Using the t-distribution, the critical value needed is: t = 2.2622.
How to find the critical value for the t-distribution?The critical value is found using a calculator, with two parameters:
The confidence level.The number of degrees of freedom, which is one less than the sample size.For this problem, we have a confidence level of 95% and 10 - 1 = 9 df, hence the critical value is t = 2.2622.
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