Answer:
108
Step-by-step explanation:
Since 3n is a perfect square, that means that n has to be a multiple of 3. Since 2n is a perfect cube, then n has to be divisible by 2^2=4. Since n is a multiple of 3, then n also has to be divisible by 3^3=27. Therefore, the smallest value for n is 4*27=108.
A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet.
A) The outcome for Event X or Y is expressed as; X ∪ Y = {D, A, B, E}
B) The outcome of Event X and Y is; X ∩ Y = {A, B, E}
How to use the sets notation?We are given the events;
Event X; The letter selected is found in the word "BEAD"
Event Y; The letter selected comes after D
Thus;
A) The outcome for Event X or Y is expressed as;
X ∪ Y = {D, A, B, E}
B) The outcome of Event X and Y is;
X ∩ Y = {A, B, E}
C) Complement of Event Y is;
Y^(c) = {D}
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Find the distance between the points (-9,0) and (2,5)
A. 12.08
B. 14.6
C. 8.6
D. 74
A. 12.08
9 + 2 = 11
(So, 11 across on our x - axis from - 9 to 2)
Then, up 5 from 2 on our x-axis
Join the 2 dots of coordinates, & creating a triangle. Base 11, height 5
Use Pythagoras Theorem, to find that distance between the coordinates (the hypotenuse)
Root 11^2 + 5^2 = 12.083056...
(root means square root)
Hope this helps!
Answer:
Hello! The answer to this question is A. 12.08.
Step-by-step explanation:
The distance formula is:
[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2 }[/tex]
With the distance formula, we can now substitute the values from the points provided:
[tex]\sqrt{(2 - (-9))^2 + (5 - 0)^2} \\= \sqrt{11^2 + 5^2\\\\\\\\= \sqrt{121 + 25} \\=\sqrt{146} \\= 12.08[/tex]
The distance between the points is 12.08.
What's the range of the graph? I have a menu that I could choose from and this is the option that I have.
Answer:
-∞ < x < 4
Step-by-step explanation:
→ The graph touches the y axis at 4, therefore 4 part of the range. As h ( x ) has a vertical asymptote it will never touch the line x = 1, therefore -∞.
From the triangle below, if AD = 5 and CD = 20, find the length of side BD.
Select one:
a.
10
b.
28
c.
7
d.
25
Answer: 10
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{BD}{5}=\frac{20}{BD}\\\\(BD)^2 = 100\\\\BD=10[/tex]
The length of side BD, given that AD = 5 and CD = 20 is 10 (Option A)
Data obtained from the questionLength of side AD = 5 Length of side CD = 20Length of side BD =?How to determine the length of side BDSince the triangles are similar, we can obtain the length of side BD as illustrated below:
CD / BD = BD / AD
20 / BD = BD / 5
Cross multiply
BD × BD = 20 × 5
BD² = 100
Take the square root of both sides
BD = √100
BD = 10
Thus, the length of side BD is 10
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New flowers are being planted
in the school garden. There
are 45 dandelions for each row
in the 15 row garden. How
many dandelions are being
planted?
Answer:
45 dandelion × 15 rows= 675
The expressionx^2-9/x2+6x+8 is equal to zero when x = .
Hello !
Answer:
When x = -3 or x = 3
Step-by-step explanation:
[tex] \frac{ {x}^{2} - 9}{ {x}^{2} + 6x + 8} = 0[/tex]
[tex]\Leftrightarrow \frac{ {x}^{2} - 9 }{ {x}^{2} + 6x + 8} \times ( {x}^{2} + 6x + 8) = 0 \times ( {x}^{2} + 6x + 8)[/tex]
[tex]\Leftrightarrow {x}^{2} - 9 = 0[/tex]
[tex]\Leftrightarrow(x - 3)(x + 3) = 0[/tex]
[tex]\Leftrightarrow \: x - 3= 0 \: or \: x + 3 = 0[/tex]
[tex]\Leftrightarrow \: x = 3 \: or \: x = - 3[/tex]
[tex]\boxed{S = {-3 \: \: or \: \: 3}}[/tex]
what is the volume of the regular pyramid below?
The volume of the regular pyramid is 128 unit³.
Option D) 128 unit³ is the correct answer.
This question is incomplete, the missing image is uploaded along this answer below.
What is the volume of the regular pyramid?The volume of pyramid is expressed as;
V = ( 1/3 ) × l × w × h
Given that;
Length l = 8Width W = 8Height h = 6We substitute our given values into the equation above.
V = ( 1/3 ) × 8 × 8 × 6
V = 128 unit³
The volume of the regular pyramid is 128 unit³.
Option D) 128 unit³ is the correct answer.
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Writing Exercises
352. How do you decide which pattern to use?
Answer:
Hence if the square of binomials needs to be find then we use square of binomial pattern and if the product of conjugate pair needs to determine then we use product of conjugate pattern.
Step-by-step explanation:
Explanation
We have to explain how we decide which pattern to use.If we need to determine the squares of binomials then we use the binomial square pattern for example [tex]$(x-y)^{2}$[/tex] or [tex]$(x+y)^{2}$[/tex] wherease when we need to find the product of the pair of the binomials each have the same first term and the same last term, but one binomial is the sum and the other is a diference then we the the product of conjugate pattern for example [tex]$(x+y)(x-y)$.[/tex]Brandon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Brandon scored a total of 16 points and made twice as many three point shots as two point shots. Write a system of equations that could be used to determine the number of two point shots Brandon made and the number of three point shots he made. Define the variables that you use to write the system
The system of equations are x+ y =16 and 2y=x.
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions
let the two points shots be x
let the three points shots be y.
According to question,
x+ y =16
and,
2y=x
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What is the equation, in point-slope form, of the line
that is parallel to the given line and passes through the
point (-3, 1)?
Oy-1= -(x+3)
Oy-1= -(x+3)
Oy-1= (x+3)
Oy - 1 = (x+3)
Answer:
The answer is B.
Step-by-step explanation:
I learned this last year.
The graph of f(x) = x² is shown.
Compare the graph of f(x) with the graph of d(x) = x² - 27.
Answer:
The graph of [tex]d(x)[/tex] is [tex]f(x)[/tex] shifted right by [tex]27[/tex] units.
The letters $A, B$ and $C$ are used to form every possible three letter ``word.'' When these ``words'' are arranged in alphabetical order and numbered so that $AAA$ is Word $1$ and $CCC$ is Word $27$, what number will correspond to the position of word $BAB$ on the list?
The number which would correspond to the position of the word; $BAB$ is; $2×1×2$ = 4.
What number will correspond to the position of word $BAB$ on the list?As evident in the task content, by observation, if follows that since; $AAA$ is Word $1 and $CCC$ is Word $27$.
Then, it can be inferred that A = 1 , B = 2 and C = 3.
On this note, the number which would correspond to the position of the word; $BAB$ is; $2×1×2$ = 4.
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68. REAL-WORLD APPLICATIONS
At noon, a barista notices that she has $20 in her tip jar. If she makes an average of $0.50 from each customer, how much will she have in her tip jar if she serves n more customers during her shift?
Answer:
The linear equation for tip barista gets in a day is f(n)=0.5n+20.
Step-by-step explanation:
It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,
It is required to find how much will she have in her tip jar if she serves n more customers during her shift. m=0.5. Bases on this write the equation for n more customers.
Step 1 of 1
It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,
To solve this let f(n) is the total tip barista has in her tip jar after a day.
When n is equal to 0 , that barista has $20,
Then if barista make 0.5 from each customer, then for the linear function m=0.5,
Bases on this write the equation for n more customers,
[tex]$$f(n)=0.5 n+20 .$$[/tex]
Use the given information to prove that
A line segment can be made up of the addition of different fractions of the line on a straight path i.e a given line segment can be broken into smaller parts.
Therefore, the required proof that EG = HK is shown below:
Given that: EF = JK
FG = HJ
But,
EG = EF + FG .............. 1
and
HK = HJ + JK ............. 2
From equation 1, we have:
EG = EF + FG
= JK + HJ (since EF = JK, and FG = HJ)
So that,
EG = JK + HJ ........... 3
Also from equation 2, we have:
HK = HJ + JK
= FG + EF (since EF = JK, and FG = HJ)
So that,
HK = FG + JK ........... 4
Therefore, comparing equations 1, 2, 3, and 4, it can be concluded that;
EG = HK
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Find the image of (-1, 2) reflected across the y-axis.
Answer: (1,2)
Step-by-step explanation:
Reflecting across the y-axis means [tex](x,y) \longrightarrow (-x,y)[/tex]
So, [tex](-1,2) \longrightarrow \boxed{(1,2)}[/tex]
Expand (x – 2)5 using the Binomial Theorem and Pascal’s triangle. Show all necessary steps.
Answer:
[tex](x-2)^5 = x^5 - 10x^4 + 40x^3 - 80x^2 + 80x - 32[/tex]
Step-by-step explanation:
Binomial Theorem
[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]
Given expression:
[tex](x-2)^5[/tex]
Compare with the Binomial Theorem:
[tex]a=x, \quad b=-2, \quad n=5[/tex]
Substitute the values into the formula:
[tex]\begin{aligned}(x-2)^5 & = x^5+\dfrac{5!}{1!4!}x^{4}(-2)+\dfrac{5!}{2!3!}x^{3}(-2)^2+\dfrac{5!}{3!2!}x^{2}(-2)^3+\dfrac{5!}{4!1!}x^{1}(-2)^4+(-2)^5\\\\& =x^5+\dfrac{120}{24}x^{4}(-2)+\dfrac{120}{12}x^{3}(4)+\dfrac{120}{12}x^{2}(-8)+\dfrac{120}{24}x(16)-32\\\\& =x^5-\dfrac{240}{24}x^{4}+\dfrac{480}{12}x^{3}-\dfrac{960}{12}x^{2}+\dfrac{1920}{24}x-32\\\\& =x^5-10x^{4}+40x^{3}-80x^{2}+80x-32\end{aligned}[/tex]
Pascal's Triangle
Pascal's triangle is an arrangement of binomial coefficients in triangular form. Each row has 1 at both ends, and each remaining number in the row is found by adding together the two numbers directly above it.
[tex]\phantom{-b)))))))}1\\\phantom{-b)))))}1 \:\quad 1\\\phantom{-b)))}1 \:\quad 2\: \quad 1\\\phantom{-b)}1 \:\quad 3\: \quad 3\: \quad 1\\\phantom{))}1 \quad 4 \:\: \quad 6 \quad \;4 \: \quad 1\\1 \quad 5 \quad 10 \quad 10 \quad 5 \quad 1[/tex]
(Note: The initial row with the single number 1 is row zero)
Each term in the binomial expansion using Pascal's triangle is the product of a coefficient, a with an exponent, and b with an exponent.
As we move through each term from left to right, the exponent of a decreases from the exponent of the expression down to zero, and the exponent of b increases from zero up to the exponent of the expression.
The coefficients of each term are the numbers which appear in the number of the row that corresponds with the exponent of the expression.
From the given expression, the power that we are expanding the bracket to is 5, so we need to look at line 5 of Pascal's triangle, which is:
1 5 10 10 5 1
Therefore, the expansion using Pascal's triangle to the power 5 of is:
[tex](a+b)^5=1a^5b^0+5a^4b^1+10a^3b^2+10a^2b^3+5a^1b^4+1a^0b^5[/tex]
Substituting the values of a and b:
[tex]\begin{aligned}(x-2)^5 & = 1x^5(-2)^0 + 5x^4(-2)^1 + 10x^3(-2)^2 + 10x^2(-2)^3 + 5x^1(-2)^4 + 1x^0(-2)^5\\\\ & = x^5 - 10x^4 + 40x^3 - 80x^2 + 80x - 32\end{aligned}[/tex]
Intervals of increasing and decreasing are written in terms of the_____value, and you will use the symbol for_______with the____–coordinate from the vertex.
The Intervals of increasing and decreasing are written in terms of the 'x' value, and you will use the symbol for 'x' with the 'y' coordinate from the vertex.
How to denote the termsThe increasing and decreasing intervals are written in the terms of the 'x' value of the function
They are represented thus;
Increasing interval = f (x) ≤ f (y)
Decreasing interval = f (x) ≥ f (y)
Thus, the Intervals of increasing and decreasing are written in terms of the 'x' value, and you will use the symbol for 'x' with the 'y' coordinate from the vertex.
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is 2(x+4)=4x+3-2x+5 no solution or infinite solutions?
Answer:
This is always true so there are infinite solutions
Step-by-step explanation:
2(x+4)=4x+3-2x+5
To find the solution, the first step is to distribute
2x+8 =4x+3-2x+5
Combine like terms
2x+8= 2x+8
Subtract 2x from each side
2x+8 -2x = 2x+8-2x
8 = 8
This is always true so there are infinite solutions
help asap!!!!!
Select the correct answer from each drop-down menu.
Consider polygon JKLMNO on the coordinate grid.
first: 12.5, 25, 17,07
second: 20, 30, 50
third: 47, 37, 61, 68.5
Answer:
12.5
30
68.5
Step-by-step explanation:
Let u = <-4, 3>. Find the unit vector in the direction of u, and write your answer in component form. (2 points)
Answer: < -4/5, 3/5>
This is equivalent to writing < -0.8, 0.6 >
======================================================
Explanation:
Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.
We have a right triangle with legs of 4 and 3. The hypotenuse is [tex]\sqrt{4^2+3^2} = \sqrt{16+9} = \sqrt{25} = 5[/tex] through use of the pythagorean theorem.
We have a 3-4-5 right triangle.
Therefore, the vector is 5 units long. This is the magnitude of the vector.
Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.
Therefore, we go from < -4, 3 > to < -4/5, 3/5 >
This is equivalent to < -0.8, 0.6 > since -4/5 = -0.8 and 3/5 = 0.6
Side note: Unit vectors are useful in computer graphics.
also need help with this question
Answer:
C
Step-by-step explanation:
In option c, the first block is divided into 3 pieces where 2 parts are shaded whereas the second block is divided into 6 pieces where 3 parts are shaded
For both to be equivalent, both of them should be the same
2/3 = x/6
x = 4
4 pieces should be shaded in in the second block to be equal to the first one, in the diagram only 3 parts are shaded thus the answer is c
help me solve this pls ?
Answer:
x = 2
Step-by-step explanation:
divide both sides by 2
then simplify
Apply exponent rule and vowla theirs your final answer of x = 2
Help me please I need a hand
The statements that are true are
The sum of A and C is negativeA + D = BThe quotient of D and B is -10/3 The product of A and B > the product of A and CNumber lineFrom the question, we are to determine the statements that are true
In the given number line,
A = -2 1/6
B = - 1/2
C = 1/3
D = 1 2/3
B - C = 1/6B - C = -1/2 - 1/3
B - C = -5/6
∴ B - C ≠ 1/6
The sum of A and C is negativeA + C = -2 1/6 + 1/3
A + C = -1 5/6
∴ The sum of A and C is negative
A + D = BA + D = -2 1/6 + 1 2/3
A + D = -1/2
B = -1/2
∴ A + D = B
Quotient of D and B1 2/3 ÷ - 1/2 = -10/3
∴ The quotient of D and B is -10/3
Product of A and B
A×B = -2 1/6 × -1/2
A×B = 13/12
Product of A and C
A×C = -2 1/6 × 1/3
A×C = -13/18
∴ The product of A and B > the product of A and C
|B| < |C||B| = 1/2
|C| = 1/3
|B| > |C|
|B| is NOT less than |C|
Hence, the statements that are true are
The sum of A and C is negativeA + D = BThe quotient of D and B is -10/3 The product of A and B > the product of A and CLearn more on Number line here: https://brainly.com/question/1545224
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hey guys please help me I'm lowkey confused on how to do this :)
Answer:
x = [tex]\frac{2}{7}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2}[/tex](7x+2) = 2
7x+2 = 2÷[tex]\frac{1}{2}[/tex]
= 2×2
= 4
7x = 4-2
= 2
∴x = 2÷7
= [tex]\frac{2}{7}[/tex]
Answer:
[tex]\displaystyle \frac{2}{7} = x[/tex]
Step-by-step explanation:
[tex]\displaystyle 2 = \frac{1}{2}(7x + 2) \Rightarrow 2 = 3\frac{1}{2}x + 1 \hookrightarrow \frac{1}{3\frac{1}{2}} = \frac{3\frac{1}{2}x}{3\frac{1}{2}} \\ \\ \boxed{\frac{2}{7} = x}[/tex]
I am joyous to assist you at any time.
(10 - d)^0
for d = 11
Answer:
1
Step-by-step explanation:
any number (except zero) raised to the 0th power is equal to 1.
Answer:
1
Step-by-step explanation:
(10 - 11)⁰ = ( -1)⁰ = 1
We have a⁰ = 1
Efraín es un vendedor de celulares, cada equipo cuesta 7500 pesos, el cuenta con su propia línea telefonica y tiene dos métodos de pago, una que es de contado y otra que es a creditó.
Si un cliente compra un celular a crédito aumenta un 20% a su costó inicial.
Samara quiere comprar un celular a crédito y otro de contado dando un total de 11 veces el 20%
¿Cuánto costará cada celular?
¿Cuanto es el valor de el 20%?
El celular de contado costará 7500 pesos, mientras que el celular a crédito tendrá un costo de 9000 pesos.
¿Cuál es el 20% de 7500?7500 / 100 = 75 (valor del 1%)
75 x 20 = 1500 pesos
¿Cuánto cuesta cada celular?Celular a contado: El precio no aumenta por lo que el valor sería de 7500 pesos.
Celular a crédito: 7500 + 1500 = 9000 pesos
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A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 4.20. A sample of 37 honors students is taken and is found to have a mean GPA equal to 4.30. The population standard deviation is assumed to equal 0.40. The parameter to be tested is __________.
The parameter to be tested is z.
We would set up the hypothesis test.
For the null hypothesis,
µ ≥ 4.2
For the alternative hypothesis,
µ < 4.2
It is a left tailed test.
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 4.2
x = 4.3
σ = 0.4
n = 37
z = (4.3 - 4.2)/(0.4/√37) = 1.53
Looking at the normal distribution table, the probability corresponding to the z score is 0.933
The p value gotten is to the right of the normal curve. Since it is a left tailed test, we need the p value to the left of the curve. Therefore,
p = 1 - 0.933 = 0.067
Since alpha, 0.05 < than the p value, 0.067, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, there is no significant evidence that mean GPA of these graduates does not exceed 4.30
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Which function has the given properties below?
The domain is the set of all real numbers.
One x-intercept is (2 pi, 0).
The amplitude is 4.
The point (StartFraction pi over 2 EndFraction, negative 4 EndFraction) is on the graph.
The y-intercept is (0, 0).
The function that has the given properties below is y = -4sin(x).
How to illustrate the function?It should be noted that a function can be used to illustrate the relationship between variables.
In this case, the domain is the set of all real numbers, the amplitude is 4, and one x-intercept is (2 pi, 0).
The appropriate function is y = -4sin(x).
The graph is attached.
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F(x) = x^2 + 4x. G(x) = 1 + e^2x. As a single logarithm find fg(x) = 21
Answer:
1/2 log2
Step-by-step explanation:
I hope you understand
Answer:
[tex]x & = \dfrac{1}{2} \ln 2[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=x^2+4x\\g(x)=1+e^{2x}\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
Therefore, the given composite function fg(x) means to substitute the function g(x) in place of the x in function f(x):
[tex]\begin{aligned}f[g(x)] & = [g(x)]^2 + 4[g(x)]\\& = \left(1+e^{2x}\right)^2+4\left(1+e^{2x}\right)\\& = 1+2e^{2x}+(e^{2x})^2+4+4e^{2x}\\& = e^{4x}+6e^{2x}+5\end{aligned}[/tex]
[tex]\textsf{Let }u=e^{2x}[/tex]
[tex]\implies e^{4x}+6x^{2x}+5=u^2+6u+5[/tex]
Set the composite function to 21 and factor:
[tex]\begin{aligned}f[g(x)] & = 21\\\implies u^2+6u+5 & = 21\\u^2+6u-16 & = 0\\u^2+8u-2u-16 & = 0\\u(u+8)-2(u+8) & = 0\\(u-2)(u+8) & = 0\\\end{aligned}[/tex]
Apply the zero-product property:
[tex]\implies (u-2)=0 \implies u=2[/tex]
[tex]\implies (u+8)=0 \implies u=-8[/tex]
[tex]\textsf{Substitute back in }u=e^{2x}:[/tex]
[tex]\implies e^{2x}=2[/tex]
[tex]\implies e^{2x}=-8[/tex]
As we cannot take logs of negative numbers, the only solution is:
[tex]\begin{aligned}e^{2x} & = 2\\\ln e^{2x} & = \ln 2\\2x \ln e & = \ln 2\\2x(1) & = \ln 2\\2x & = \ln 2\\\implies x & = \dfrac{1}{2} \ln 2\end{aligned}[/tex]
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Ted borrowed $5,600 from his bank for 4 months with interest at 9%. ted paid the note in full on its due date. how much was the check he gave to the bank for payment?
Ten gave the check of $5768 to the bank for payment.
What is simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a borrower will never have to pay interest on the interest already accumulated because a creditor will only pay interest on the principal amount.
Formula for simple interest is;-
Simple interest = (principal amount×rate of interest×time duration in years)/100
S.I = (P×R×T)/100
Calculation of the total amount paid by Ted to the bank-
The principal amount is $5,600.
The rate of interest is 9%.
Time duration is 4 months equals 4/12 = 1/3 years.
S.I = (5,600×9×1)/(3×100)
S.I = 168
The simple interest on amount is $168.
Thus, the total amount is S.I + principal amount
Total amount = 168 + 5600
= 5768
Therefore, the total amount paid by the Ted to the bank is $5768.
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