If a null hypothesis is not rejected at a significance level of 0.05, it will at a significance level of 0.01. a. Never b. Sometimes c. Always be rejected
he population standard deviation is unknown, and the population is assumed to be a normal distribution, the correct test statistic to use is a. z b. t c. r d. p-value
Answers
If a null hypothesis is not rejected at a significance level of 0.05 it will sometimes at a significance level of 0.01.
The population standard deviation is unknown, and the population is assumed to be a normal distribution, the correct test statistic to use is p value.
If a null hypothesis is not rejected at a significance level of 0.05, it may or may not be rejected at a significance level of 0.01.
The decision depends on the specific results of the hypothesis test and the level of evidence available.
When the population standard deviation is unknown and the population is assumed to be normally distributed, the correct test statistic to use is the t-test.
The t-test is appropriate for small samples or when the population standard deviation is unknown.
The z-test is used when the population standard deviation is known and the sample size is large.
The r-test is not a standard test statistic, and the p-value is a statistical concept used to measure the strength of evidence against the null hypothesis, not a specific test statistic.
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Related Questions
Solve the system of equations.
– 3y + 5x = 26
- 2 - 5x = -16
Answers
Answer:
\(y=-4,\:x=\frac{14}{5}\)
Step-by-step explanation:
\(\begin{bmatrix}-3y+5x=26\\ -2-5x=-16\end{bmatrix}\)
Isolate x for -2-5x=-16:
\(x=\frac{14}{5}\)
\(\mathrm{Substitute\:}x=\frac{14}{5}\)
\(\begin{bmatrix}-3y+5\cdot \frac{14}{5}=26\end{bmatrix}\)
\(Simplify\)
\(\begin{bmatrix}-3y+14=26\end{bmatrix}\)
Isolate y for -3y+14=26:
\(y=-4\)
\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)
\(y=-4,\:x=\frac{14}{5}\)
PLEASE HELP ME............THANKS
Answers
Answer:
i think it's c, I could be wrong djxndnxmmx
Answer:
{2,4,9,16}
Step-by-step explanation:
Range are the y values, which are on the right.
what is the area of this triangle? i’m mostly confused on how to find the height.
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Answer:
it 4968
Step-by-step explanation:
because you have to multiply 92 by 54 hopes this helped
factor completely
8y²+6y+1
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(4y + 1)(2y +1) this should be the answer: How to solve your problem
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Grouping
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Common factor from the two pairs
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Solution
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DETAILS PREVIOUS ANSWERS LARCALCET7 9.5.034. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Approximate the sum of the series by using the first six terms. (See Example 4. Round your answer to four decimal places.) (-1)^²+¹ 4" n=1 56 X SSS 0.1597 X Need Help? Read It
Answers
The sum of the series, using the first six terms, is approximately -0.0797.
The sum of a series refers to the result obtained by adding up all the terms of the series. A series is a sequence of numbers or terms written in a specific order. The sum of the series is the total value obtained when all the terms are combined.
The sum of a series can be finite or infinite. In a finite series, there is a specific number of terms, and the sum can be calculated by adding up each term. For
The given series is
\((-1)^(n²+1) * 4 / (n+56)\)
where n starts from 1 and goes up to 6. To approximate the sum of the series, we substitute the values of n from 1 to 6 into the series expression and sum up the terms.
Calculating each term of the series:
Term 1:
\((-1)^(1²+1) * 4 / (1+56) = -4/57\)
Term 2:
\( (-1)^(2²+1) * 4 / (2+56) = 4/58\)
Term 3:
\( (-1)^(3²+1) * 4 / (3+56) = -4/59\)
Term 4:
\(-1^(4²+1) * 4 / (4+56) = 4/60\)
Term 5:
\( (-1)^(5²+1) * 4 / (5+56) = -4/61\)
Term 6:
\((-1)^(6²+1) * 4 / (6+56) = 4/62\)
Adding up these terms:
-4/57 + 4/58 - 4/59 + 4/60 - 4/61 + 4/62 ≈ -0.0797
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Anyone know the answer ?x
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The probability of students chosen at random does not study chemistry is \(\frac{20}{41}\).
What is probability?
The likelihood of an event happening is gauged by probability. Many things are impossible to completely predict in advance. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
Total number of student = 6+7+2+5+4+8+6+3 = 41
Now number of chemistry students = 8+3+4+6 = 21
Then Non chemistry students = 41-21 = 20
So required probability = Non chemistry student/ Total number of students
=> probability = \(\frac{20}{41}\)
Hence the probability of students chosen at random does not study chemistry is \(\frac{20}{41}\).
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Can someone please help me i dont understand it.
Answers
Answer:
1. True
2. False
3. True
4. True
Step-by-step explanation:
match the terms to their definition. 1. kilometer one thousandth of a meter 2. centimeter one hundredth of a meter 3. millimeter one thousand meters
Answers
A kilometer is a unit of length in the metric system equal to one thousand meters
What is distance in math?
As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.
Kilometer: A kilometer is a unit of length in the metric system equal to one thousand meters. It is commonly used to measure long distances, such as the distance between two cities or countries.
Centimeter: A centimeter is a unit of length in the metric system equal to one hundredth of a meter. It is commonly used to measure small distances, such as the length of an object or the distance between two points.
Millimeter: A millimeter is a unit of length in the metric system equal to one thousandth of a meter. It is an even smaller unit of measurement than a centimeter and is commonly used to measure very small distances, such as the thickness of a sheet of paper or the diameter of a small object.
In the metric system, each unit of length is based on powers of 10. This means that each unit is ten times larger or smaller than the one next to it. Hence, This system of measurement makes it easy to convert between units and to measure distances of all sizes.
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A restaurant manager is listing 10 items on a menu. Of these menu items, 8 are appetizers and 2 are main courses. All of the appetizers will be listed before both of the main courses. In how many ways can the restaurant manager list the items
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The number of ways is an illustration of selections and arrangements.There are 16 ways to order a two-course meal.
What is arrangement?An arrangement is defined as a combination of things that make up a design or that are laid out in a certain way
The given parameters are
Appetizer=8
Main=6
A person can choose 1 a-piece from each menu.
This means that:
There are 8 ways of selecting appetizers, and 2 ways of selecting the main courses.
So, the number of ways (n) is:
\(\rm n=Appetizer\times Main\)
\(n=8\times 2\)
\(n=16\)
Hence, there are 16 ways to order a two-course meal
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How do I solve this?
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Answer:
About 10.54, sorry if im wrong
Step-by-step explanation:
c= the square root of a^2+b^2
1 Find m2R
2x + 106
16
Answers
Answer:
2(x+5308)
Step-by-step explanation:
Factor 2x+10616
2x+10616
=2(x+5308)
if f(x)=4(3x-5), find f^-1(x)
Answers
Answer:
f^-1(x) = (x+20) / 12
Step-by-step explanation:
f(x) = 4(3x-5)
Let y be the image of f.
y = 4(3x-5)
y = 12x-20
y+20 = 12x
x = (y+20) / 12
f^-1(y) = (y+20) / 12, so
f^-1(x) = (x+20) / 12
Which of the following must always be true about vertical angles
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Answer:
It is always a strait line going up.
Step-by-step explanation:
Answer:
vertical angels
angles opposite each other where two lines cross.
plz mark brainliest
Step-by-step explanation:
Find the dot product of ⟨4,1,
4
1
⟩ and 9. Given two displacement vectors ⟨6,−3,−8⟩ 8. For vectors
b
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and
a
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i
^
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a
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i
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j
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k
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+
b
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a
−
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i
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j
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−7.00
k
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d
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The dot product of ⟨4, 1, 4⟩ and 9 is 81. Displacement vectors a and b result in vectors of -4i^ + 2j^ and -2i^ + 2j^ respectively. Magnitudes and directions of vectors b, c = a + b, and d = 2a - b are approximately 7.87 with direction ⟨0.25, 0.38, -0.89⟩, 8.83 with direction ⟨-0.23, 0.57, -0.79⟩, and 12.73 with direction ⟨-0.63, -0.55, 0.55⟩ respectively.
To find the dot product of the vector ⟨4, 1, 4⟩ and 9, you multiply each component of the vector by 9 and sum them up. The dot product is given by:
⟨4, 1, 4⟩ ⋅ 9 = (4 * 9) + (1 * 9) + (4 * 9) = 36 + 9 + 36 = 81.
So, the dot product of ⟨4, 1, 4⟩ and 9 is 81.
Given the displacement vectors ⟨6, -3, -8⟩ and ⟨8⟩. If the second vector is ⟨8⟩, then it's a scalar and not a vector, so we can't perform vector operations on it.
For the vectors b = -i^ - 4j^ and a = -3i^ - 2j^, we can calculate the following:
(a) a + b:
-3i^ - 2j^ + (-i^ - 4j^) = -3i^ - 2j^ - i^ + 4j^ = (-3 - 1)i^ + (-2 + 4)j^ = -4i^ + 2j^
(b) a - b:
-3i^ - 2j^ - (-i^ - 4j^) = -3i^ - 2j^ + i^ + 4j^ = (-3 + 1)i^ + (-2 + 4)j^ = -2i^ + 2j^
For the vector b = ⟨2.00, 3.00, -7.00⟩, we can calculate the magnitude and direction:
Magnitude of b = √(2.00^2 + 3.00^2 + (-7.00)^2) = √(4 + 9 + 49) = √62 ≈ 7.87
Direction of b can be represented by the unit vector in the same direction:
b_hat = ⟨2.00/7.87, 3.00/7.87, -7.00/7.87⟩ ≈ ⟨0.25, 0.38, -0.89⟩
For the vector c = a + b, we can calculate the magnitude and direction:
c = -4i^ + 2j^ + 2.00i^ + 3.00j^ - 7.00k^ = (-4 + 2)i^ + (2 + 3)j^ - 7.00k^ = -2i^ + 5j^ - 7.00k^
Magnitude of c = √((-2)^2 + 5^2 + (-7.00)^2) = √(4 + 25 + 49) = √78 ≈ 8.83
Direction of c can be represented by the unit vector in the same direction:
c_hat = ⟨-2/8.83, 5/8.83, -7.00/8.83⟩ ≈ ⟨-0.23, 0.57, -0.79⟩
For the vector d = 2a - b, we can calculate the magnitude and direction:
d = 2(-3i^ - 2j^) - (2.00i^ + 3.00j^ - 7.00k^) = (-6i^ - 4j^) - (2.00i^ + 3.00j^ - 7.00k^) = (-6 - 2)i^ + (-4 - 3)j^ + 7.00k^ = -8i^ - 7j^ + 7.00k^
Magnitude of d = √((-8)^2 + (-7)^2 + 7.00^2) = √(64 + 49 + 49) = √162 ≈ 12.73
Direction of d can be represented by the unit vector in the same direction:
d_hat = ⟨-8/12.73, -7/12.73, 7.00/12.73⟩ ≈ ⟨-0.63, -0.55, 0.55⟩
So, the magnitudes and directions are as follows:
(a) a + b: Magnitude ≈ √((-4)^2 + 2^2) ≈ √20 ≈ 4.47
Direction ≈ ⟨-4/4.47, 2/4.47⟩ ≈ ⟨-0.89, 0.45⟩
(b) a - b: Magnitude ≈ √((-2)^2 + 2^2) ≈ √8 ≈ 2.83
Direction ≈ ⟨-2/2.83, 2/2.83⟩ ≈ ⟨-0.71, 0.71⟩
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PLEASE HELP I NEED THIS RIGHT NOW!!
Two pools are being filled with water. To start, the first pool had 972 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 17 liters per minute. Water is being added to the second pool at a rate of 44 liters per minute.
Let x be the number of minutes water has been added.
Answers
Answer: To find the number of liters of water in the first pool after x minutes have passed, we can use the formula:
972 + 17x
To find the number of liters of water in the second pool after x minutes have passed, we can use the formula:
44x
Note that both of these formulas assume that the pools are being filled continuously, without any interruptions. If the flow of water into either pool is interrupted at any point, the actual amount of water in the pools may be different from what these formulas predict.
Answer:
a)
17x + 972
44x
b)
972 + 17x = 44x
Step-by-step explanation:
there are 39 chocolates in a box, all identically shaped. there 16 are filled with nuts, 10 with caramel, and 13 are solid chocolate. you randomly select one piece, eat it, and then select a second piece. find the probability of selecting a solid chocolate candy followed by a nut candy.
Answers
The probability of selecting a solid chocolate candy followed by a nut candy is 0.126315789.
The probability of selecting a solid chocolate candy followed by a nut candy can be calculated using the formula for joint probability.
Joint Probability = P(Solid Chocolate) x P(Nut Candy given that the first candy was Solid Chocolate)
P(Solid Chocolate) = 13/39
P(Nut Candy given that the first candy was Solid Chocolate) = 16/38
Joint Probability = (13/39) x (16/38)
Joint Probability = 0.126315789
Therefore, the probability of selecting a solid chocolate candy followed by a nut candy is 0.126315789.
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NEED HELP QICK PLS
Answers
Answer:
uhm with what? there isn't anything here?
Step-by-step explanation:
F (x) = (2x + 3)^4
Expand the function
Answers
Answer:
\(f(x)=16x^4+96x^{3}+216x^{2}+216x+81\)
Step-by-step explanation:
The function f(x) = (2x + 3)⁴ is a fourth-degree polynomial function.
It can be expanded using the binomial theorem.
\(\boxed{\begin{minipage}{5cm} \underline{Binomial Theorem}\\\\$\displaystyle (a+b)^n=\sum^{n}_{k=0}\binom{n}{k} a^{n-k}b^{k}$\\\\\\where \displaystyle \binom{n}{k} = \frac{n!}{k!(n-k)!}\\\end{minipage}}\)
Comparing the given function with (a + b)ⁿ:
a = 2xb = 3n = 4Substitute these values into the binomial theorem formula:
\(\displaystyle (2x+3)^4=\binom{4}{0}(2x)^{4-0}3^{0}+\binom{4}{1}(2x)^{4-1}3^{1}+\binom{4}{2}(2x)^{4-2}3^{2}+\binom{4}{3}(2x)^{4-3}3^{3}+\\\\\\\phantom{wwww}\binom{4}{4}(2x)^{4-4}3^{4}\)
Solve:
\(\begin{aligned}\displaystyle (2x+3)^4&=\binom{4}{0}(2x)^4\cdot3^0+\binom{4}{1}(2x)^{3}\cdot3^1+\binom{4}{2}(2x)^2\cdot3^2+\binom{4}{3}(2x)^{1}\cdot3^3+\binom{4}{4}(2x)^0\cdot3^4\\\\&=\binom{4}{0}16x^4\cdot1+\binom{4}{1}8x^3\cdot3+\binom{4}{2}4x^2\cdot9+\binom{4}{3}2x\cdot27+\binom{4}{4}\cdot81\\\\&=\binom{4}{0}16x^4+\binom{4}{1}24x^3+\binom{4}{2}36x^2+\binom{4}{3}54x+\binom{4}{4}81\\\\&=1\cdot16x^4+4\cdot24x^3+6\cdot36x^2+4\cdot54x+1\cdot81\\\\&=16x^4+96x^3+216x^2+216x+81\end{aligned}\)
Therefore, the expanded function is:
\(f(x)=16x^4+96x^{3}+216x^{2}+216x+81\)
\( \Large{\boxed{\sf F(x) = (2x + 3)^4 = 16x^4 + 96x^3 + 216x^2 + 216x + 81 }} \)
\( \\ \)
Explanation:To expand the given function, we will apply the binomial theorem, which is the following:
\(\sf(a+b)^n =\sf\sum\limits_{k=0}^{n} \binom{n}{k}a^{n-k}b^{k} \\ \\ \sf \:Where\text{:} \\ \star \: \sf n \: is \: a \: positive \: integer. \: ( n \in \mathbb{N}) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \star \: k \: is \: a \: positive \: integer \: less \: than \: or \: equal \: to \: n. \: (k \leqslant n, \: k \: \in \: \mathbb{ N}) \\ \\ \\ \sf \star \: \displaystyle\binom{ \sf \: n}{ \sf \: k} \: \sf is \: a \: \underline{binomial \: coefficient} \: and \: is \: calculated \: as \: follows\text{:} \\ \\ \\ \sf \displaystyle\binom{ \sf \: n}{ \sf \: k} = \sf \dfrac{n! }{(n - k)! k ! }\)\( \\ \\\)
\( \\ \)
Let's identify our values\( \\ \)
\( \sf F(x) = (\underbrace{\sf 2x}_{\sf a} + \underbrace{3}_{\sf b})^{\overbrace{\sf 4}^{n}} \\ \\ \implies \sf a = 2x \: \: ,b = 3 \: \: ,n = 4 \)
\( \\ \)
Substitute these values into our formula:\( \\ \)
\( \sf (2x + 3)^4 = \displaystyle\sum\limits_{ \sf k=0}^{ \sf 4} \binom{ \sf 4}{ \sf k}( \sf 2x)^{4-k}(3)^{k} \\ \\ \\ \sf = \binom{ \sf 4}{ \sf 0}( \sf 2x)^{4-0}(3)^{0} + \binom{ \sf 4}{ \sf 1}( \sf 2x)^{4-1}(3)^{1} + \binom{ \sf 4}{ \sf 2}( \sf 2x)^{4-2}(3)^{2} + \binom{ \sf 4}{ \sf 3}( \sf 2x)^{4-3}(3)^{3} + \binom{ \sf 4}{ \sf 4}( \sf 2x)^{4-4}(3)^{4} \\ \\ \\ \sf = \binom{ \sf 4}{ \sf 0}( \sf 2x)^{4}(3)^{0} + \binom{ \sf 4}{ \sf 1}( \sf 2x)^{3}(3)^{1} + \binom{ \sf 4}{ \sf 2}( \sf 2x)^{2}(3)^{2} + \binom{ \sf 4}{ \sf 3}( \sf 2x)^{1}(3)^{3} + \binom{ \sf 4}{ \sf 4}( \sf 2x)^{0}(3)^{4} \\ \\ \\ \sf = \binom{ \sf 4}{ \sf 0}( \sf 16 {x}^{4} ) + \binom{ \sf 4}{ \sf 1}( \sf 24 {x}^{3}) + \binom{ \sf 4}{ \sf 2}( \sf 36x^{2}) + \binom{ \sf 4}{ \sf 3}( \sf 54x) + \binom{ \sf 4}{ \sf 4}(81) \)
\( \\ \)
Determine the value of each binomial coefficient\( \\ \)
\( \\ \star \: \displaystyle\binom{ \sf 4}{\sf \: 0} = \sf \dfrac{4! }{(4-0)!0 ! } = \dfrac{4!}{4!0!} = \dfrac{4!}{4!} = \boxed{\sf 1} \\ \\ \star\:\displaystyle\binom{ \sf 4 }{ \sf \: 1} =\sf \dfrac{4! }{(4 - 1)!1 ! } = \dfrac{4!}{3!1!}= \dfrac{2\times 3 \times 4}{2 \times 3} = \boxed{\sf 4} \\ \\ \star \: \displaystyle\binom{ \sf 4 }{ \sf \: 2} =\sf \dfrac{4! }{(4-2)!2!} = \dfrac{4!}{2!2!}=\dfrac{2 \times 3 \times 4}{2 \times 2} = \boxed{\sf 6} \\ \\ \star \:\displaystyle\binom{ \sf 4 }{ \sf \: 3}= \sf \dfrac{4! }{(4 - 3)!3!} =\dfrac{4!}{1!3!} = \dfrac{2 \times 3 \times 4}{2 \times 3 } = \boxed{\sf 4}\\ \\ \star \:\displaystyle\binom{ \sf 4 }{ \sf \: 4}= \sf \dfrac{4! }{(4 - 4)!4 !} =\dfrac{4!}{0!4!} = \dfrac{2 \times 3 \times 4}{2 \times 3 \times 4 } = \boxed{\sf 1} \)
\( \\ \)
Replace the binomial coefficients with their value\( \\ \)
\( \sf (2x + 3)^4 = \binom{ \sf 4}{ \sf 0}( \sf 16 {x}^{4} ) + \binom{ \sf 4}{ \sf 1}( \sf 24 {x}^{3}) + \binom{ \sf 4}{ \sf 2}( \sf 36x^{2}) + \binom{ \sf 4}{ \sf 3}( \sf 54x) + \binom{ \sf 4}{ \sf 4}(81) \\ \\ \\ \sf = (1)(16x^4) + (4)(24x^3) + (6)(36x^2) + (4)(54x) + (1)(81) \\ \\ \\ \boxed{\boxed{\sf = 16x^4 + 96x^3 + 216x^2 + 216x + 81}} \)
\( \\ \\ \\ \)
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Describe geometrically the sets of points zin the complex plane defined by thefollowing relations:(1) |z−z1|=|z−z2|where z1, z2∈C.(2) 1/z =z.(3) Re(z) = 3.(4) Re(z)> c, (resp., ≥c) where c∈R.(5) Re(az +b)>0 where a, b ∈C.(6) |z|= Re(z) + 1.(7) Im(z) = cwith c∈R.
Answers
The complex plane, also known as the Argand plane, is a graphical representation of complex numbers in mathematics. It is a two-dimensional plane with the real axis representing the real part of a complex number and the imaginary axis representing its imaginary part.
1. The set of points in the complex plane that satisfy the relation |z-z1| = |z-z2| forms a circle with its center at the midpoint of z1 and z2, and with a radius equal to half the distance between z1 and z2.
2. The set of points in the complex plane that satisfies the relation 1/z = z forms a pair of lines that intersect at the origin, with slopes equal to 1 and -1. These lines divide the complex plane into four quadrants, and the set of points consists of the complex numbers that lie on the unit circle.
3. The set of points in the complex plane that satisfies the relation Re(z) = 3 forms a vertical line at x=3. All points on this line have the same real part, equal to 3.
4. The set of points in the complex plane that satisfies the relation Re(z) > c (respectively, >=c) forms a half-plane to the right (respectively, including) of the vertical line x=c. All points in this region have real parts greater than (respectively, greater than or equal to) c.
5. The set of points in the complex plane that satisfies the relation Re(az + b) > 0 forms a line that is the image of the real axis under the transformation az + b. The set of points consists of those complex numbers that lie to one side of this line.
6. The set of points in the complex plane that satisfy the relation |z| = Re(z) + 1 forms a hyperbola. The foci of the hyperbola are on the real axis, at x = -1 and x = 1.
7. The set of points in the complex plane that satisfies the relation Im(z) = c forms a horizontal line at y=c. All points on this line have the same imaginary part, equal to c.
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HELP NO LINKS OR FILES DUE TODAY
Answers
Answer:
for every 13 dogs, there are 25 cats.
Step-by-step explanation:
It's simple you put dog on top since it came first and then cats on bottom. I hope this help :)
A jewelry box is shaped like a cube. One side of the box is 6.5 inches long. What is the volume of the jewelry box?
Answer options:
-274 in3
-274.5 in3
-274.375 in3
-274.625 in3
Answers
Answer:
274.625 in^3
Step-by-step explanation:
equation for volume LxWxH
6.5x 6.5x 6.5= 274.625
The equation c = 6m represents how many ice cream cones (c) are sold within a certain number of minutes (m) at a certain ice cream shop. determine the constant of proportionality. one-sixth 1 6 12
Answers
The constant of proportionality will be 6.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have a equation c = 6m represents how many ice cream cones (c) are sold within a certain number of minutes (m) at a certain ice cream shop
We can use the equation of a straight line to represent direct proportionality as -
y = mx + c
for -
c = 0
y = mx
m = y/x
Where [m] as constant of proportionality.
For -
c = 6m
constant of proportionality will be 6.
Therefore, the constant of proportionality will be 6.
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Answer:
YEs tis i, the simplifier
Step-by-step explanation:
its 6
Solving Systems
If (1,3), and (-8,6) are two solutions of f(x) = mx + b, find m and b.
Answers
To find the values of m and b in the equation f(x) = mx + b using the given solutions (1,3) and (-8,6), we can set up a system of equations and solve it. Substituting the coordinates into the equation, we can find that the values of m = -1/3 and b = 10/3 that satisfy both equations.
Let's substitute the coordinates of the first solution (1,3) into the equation:
3 = m(1) + b
And now let's substitute the coordinates of the second solution (-8,6) into the equation:
6 = m(-8) + b
We now have a system of two equations with two variables (m and b). We can solve this system of equations to find the values of m and b.
From the first equation, we can rewrite it as:
m + b = 3 (Equation 1)
From the second equation, we can rewrite it as:
-8m + b = 6 (Equation 2)
To solve this system, we can use various methods such as substitution or elimination. Let's use the elimination method to solve the system.
Multiplying Equation 1 by -1, we get:
-m - b = -3 (Equation 3)
Now we can add Equation 2 and Equation 3:
(-8m + b) + (-m - b) = 6 + (-3)
-9m = 3
m = -3/9
m = -1/3
Substituting the value of m into Equation 1:
(-1/3) + b = 3
b = 3 + 1/3
b = 10/3
Therefore, the values of m and b are:
m = -1/3
b = 10/3
So the equation f(x) = mx + b is f(x) = (-1/3)x + 10/3.
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A newspaper charges a flat
fee plus a charge per day to
place a classified ad.
Number
of Days
2
4
6
Total
Charges
($)
8
13
18
Answers
Answer: This problem can be represented by the equation y = mx + b, where y is the total charges, x is the number of days, m is the charge per day, and b is the flat fee.
To find the values of m and b, we can use the given data points to solve for the equation.
For x = 2, y = 8, so 8 = m * 2 + b
For x = 4, y = 13, so 13 = m * 4 + b
For x = 6, y = 18, so 18 = m * 6 + b
We can then use a system of equations to solve for m and b:
m * 2 + b = 8
m * 4 + b = 13
m * 6 + b = 18
Using substitution or elimination methods:
m = 2
b = 2
Therefore, the equation is: y = 2x + 2
This means that the flat fee is $2 and the charge per day is $2.
Step-by-step explanation:
tickets for a raffle cost $ 5. there were 832 tickets sold. one ticket will be randomly selected as the winner, and that person wins $ 1600 and also the person is given back the cost of the ticket. for someone who buys a ticket, what is the expected value (the mean of the distribution)?
Answers
The most appropriate choice for expectation will be given by-
Expected value for someone who buys the ticket = $\((-1591.2)\)
What is expectation?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Suppose x is a random variable with the probability function f(x). suppose
\(x_1. x_2,........,x_n\) are the values corrosponding to the actual occurance of the event and \(p_1, p_2.,,,, p_n\) be the corrosponding probabilities.
Expectation is given by the formula \(p_1x_1+p_2x_2+...+p_nx_n\)
Here,
Total number of tickets = 832
Number of prized tickets = 1
Probability of winning a ticket = \(\frac{1}{832}\)
Probability of losing a ticket = \(\frac{831}{832}\)
Gain of winning = $(1600 - 5) = $1595
Loss of losing = $(5 - 1600) = -$1595
Expected value for someone who buys the ticket
\(1595 \times \frac{1}{832} + (-1595)\times \frac{831}{832}\)
\(1595\times(\frac{1-831}{832})\\-1595\times \frac{830}{832}\\\)
$\((-1591.2)\)
Expected value for someone who buys the ticket = $\((-1591.2)\)
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Help with this question
Its about shapes
Answers
Answer:
a
Step-by-step explanation:
triangles are pyramids and it has 6 sides
Answer:
Hexagonal prism
Step-by-step explanation:
We can rule out B and D because if it was a pyramid, there would be a triangle in the net (The net of a 3D shape is what it looks like if it is opened out flat). We can also rule on C because it it was a cylinder, there would be a circle in the net. Therefore, our remaining answer is A.
the probability of at least one head in two flips of a coin is
Answers
The probability of getting at least one head in two flips of a coin is 3/4 or 0.75, which means that there is a 75% chance of getting at least one head in two flips of a coin.
To find the probability of at least one head in two flips of a coin, we can use the complement rule. The complement of the event "at least one head" is "no heads."
The probability of getting no heads in two flips of a coin is (1/2) x (1/2) = 1/4.
Therefore, the probability of getting at least one head in two flips of a coin is:
1 - (probability of no heads) = 1 - 1/4 = 3/4
The probability of getting at least one head in two flips of a coin is 3/4 or 0.75, which means that there is a 75% chance of getting at least one head in two flips of a coin.
In other words, if you flip a coin twice, the probability of getting at least one head is relatively high, and you are more likely to get at least one head than to get no heads at all.
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Lee made a scale drawing of a city. The scale of the drawing was 1 inch : 8 yards. The actual length of a neighborhood park is 96 yards. How long is the park in the drawing?
Answers
Answer:
12 inches
Step-by-step explanation:
Use a proportion.
1 inch is to 8 yards as x inches is to 96 yards
1/8 = x/96
Cross multiply.
8x = 96
x = 12
Answer: 12 inches
Which expression is equivalent to 10s+s-3s10s+s−3s?
Answers
Answer:
9s-3s10s or 3-10s
Step-by-step explanation:
10s+s-3s10s+s-3s
first of all, we collect like terms
10s+s+s-3s-3s10s
=9s-3s10s
it could also be equal to
9s/3s-(3s10s/3s)
3-10s
when we divide through by 3s
Please help giving up 20 points for answers
Answers
Answer:
Question 2: 6x-21
Question 1: -9x+3
Step-by-step explanation: