Answer:
(a) 1024 ways
(b) 243 ways
Step-by-step explanation:
When answers are independent, the total number of ways all questions can be answered is the product of the number of ways each question can be answered.
__
(a)The first question can have one answer 4 ways. The second question can be answered 4 ways for each of the ways the first question was answered. That is, the two questions can be answered 4×4 = 16 ways. Similarly, each additional question multiplies the number of ways the questions can be answered by 4.
The 5 questions can be answered 4×4×4×4×4 = 4^5 = 1024 ways.
__
(b)There are 3 ways to answer the first question incorrectly. Each additional question can be answered incorrectly 3 ways for each of the ways previous questions were answered. The total number of ways all questions can be answered incorrectly is ...
3^5 = 243
A student can answer all questions wrong in 243 different ways.
jackie decided to open a restaurant. she borrowed 25000 for 5 years. after 5 years, she had paid back 35000. what was her simple i terest rate
The simple interest rate is 8% if the Jackie decided to open a restaurant. She borrowed 25000 for 5 years. After 5 years, she had paid back 35000.
What is simple interest?It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.
We have:
Jackie decided to open a restaurant. She borrowed 25000 for 5 years. After 5 years, she had paid back 35000.
We know the formula for simple interest is:
A = p(1 + rt)
We have A(final amount) = 35000
P(initial amount0 = 25000
t(time) = 5 years
35000 = 25000(1 + 5r)
1.4 = 1 + 5r
0.4 = 5r
r = 0.08 or
r = 8%
Thus, the simple interest rate is 8% if the Jackie decided to open a restaurant. She borrowed 25000 for 5 years. After 5 years, she had paid back 35000.
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how do you Simplify this question (5q4)(9q6) =
Answer:
45q^10
Step-by-step explanation:
First, we can separate the equation to make it simpler to understand.
5*q^4*9*q^6
Then we group terms that we can multiply:
(5*9)*(q^4*q^6)
Then we simplify
45*q^10
45q^10
Calculate the discriminant to determine the number of real roots of the equation.
y = x2 + 3x + 9
one real root
no real roots
three real roots
two real roots
find D which is the discriminant and with D < 0.
therefore the equation has an imaginary root and not a real root.
Answer this for me please?
The volume of the rectangular prism is exactly (3/8) of a cubic inch.
How to get the volume of the rectangular prism?
Remember that for a rectangular prism of height H, length L, and width W, the volume is:
V = H*L*W
In this case, we have:
H = 1 inL = (3/4) inW = (1/2) in.Then the volume of the rectangular prism is given by:
[tex]V = (1 in)*(\frac{3}{4} in)*(\frac{1}{2} in)= \frac{3}{4*2} in^3 = \frac{3}{8} in^3[/tex]
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Use prime factorizations to find the GCF of 18 and 33.
Prime factorization of 18: 2 × 3 × 3
Prime factorization of 33: 3 x 11
The GCF of 18 and 33 is
Answer:
Use prime factorizations to find the GCF of 18 and 33.
Prime factorization of 18: 2 × 3 × 3
Prime factorization of 33: 3 x 11
The GCF of 18 and 33 is
Step-by-step explanation:
Use prime factorizations to find the GCF of 18 and 33.
Prime factorization of 18: 2 × 3 × 3
Prime factorization of 33: 3 x 11
The GCF of 18 and 33 is
Answer:
3 XD
Step-by-step explanation:
What is 60/50 as a percentage?
Answer: Heyaa! :))
60/50 as a percentage is.. 120%
Step-by-step explanation:
Solution and how to convert 60 / 50 into a percentage 1.2 times 100 = 120.Hopefully this helps you! ~
Can someone please help me with these questions!
The line that contains an example of assonance is C. He fell asleep under the oak tree, feeling fine.
What is Assonance?This refers to the similarity of sounds that can be found in nearby words in a sentence, between their vowels and/or consonants.
Furthermore, alliteration means the occurrence of similar words or sounds in a sentence at the beginning of closely connected words.
With this in mind:
The line that contains an example of alliteration is A. Tom tried learning a new tune.The line that contains an example of consonance is D. Phillipe hoped for a copper cup.Read more about alliteration here:
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Which of the following is an example of a quadratic equation?
OA. x²-64-0
OB. y - 4x+6
O C. y6
OD. x+10=33
ASAP PLS
Answer:
A
Step-by-step explanation:
hope this help
40 POINTS!!
Which statement matches the vector operation shown on the coordinate grid?
The statement that matches the vector operation shown on the coordinate grid is v + w = u.
How to add two vectors graphically?In order to add two vectors a and b graphically by using the tail and tip method, we must draw the tail of b at the tip of vector a.
Then we must draw a line that goes from the tail of vector a to the tip of vector b.
This line represents the sum of a + b.
In the given problem, we notice that the tail of the vector w is on the tip of the vector v.
The line that joins the tail of vector v with the tip of vector w is vector u.
Therefore we can say that v + w = u
The statement that matches the vector operation shown on the coordinate grid is v + w = u.
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Question 4 of 10
Which of the following is most likely the next step in the series?
A.
B.
C.
D.
QUICKKK
If $-3\le x+5 \le 8$ and $x$ is an integer, what is the sum of all the possible solutions?
Add -5 to each side of the inequality:
-3 ≤ x + 5 ≤ 8
-3 - 5 ≤ x + 5 - 5 ≤ 8 - 5
-8 ≤ x ≤ 3
Since x is an integer, there are 12 possible solutions belonging to {-8, -7, ..., 1, 2, 3}. In the sum of these solutions, the integers -3 to 3 cancel out, and the rest give
-8 - 7 - 6 - 5 - 4 = -30
Solve for x to the nearest tenth.
[tex]3^2+y^2=8^2\\9+y^2=64\\y^2=55\\\\x^2+3^2=y^2\\x^2+9=55\\x^2=46\\x=\sqrt{46}=2\sqrt5\approx6,8[/tex]
In isosceles triangle ABC, AC=BC=20, the measure of angle A=68, and CD is the altitude to side AB. What is CD to the nearest 10th
Answer:
Step-by-step explanation:
Comment
The way the diagram looks when it is drawn is that you are going to need the sine function to solve for the side opposite which is CD.
Formula
Sin(A) = Sin(68 = opposite / hypotenuse Substitute values.
Solution
sin(68) = altitude (side opposite) / 20 multiply both sides by 20
20*sin(68) = 20* altitude / 20 substitute for sin(68)
20* 0.9272 = altitude
altitude = 18.5
Answer: 18.5 to the nearest tenth
100 POINTS
Do the points (0,0) (a,0) (a,a) and (0,a) represents a special quadrilateral? If so, which one?
If not, explain why not and what should be changed? Be sure to sketch the quadrilateral.
If it does represent a special quadrilateral, use the formulas from this module to prove one
of the properties from section 6.01a. Show and explain your work including a sketch.
Answer:
see the attachment photo!
Answer:
b
Step-by-step explanation:
Can someone at lest help me with the 2nd question a) b) and c) PLEASE AND THANKYOU
What are the ages of Lilian and May?
Let May's age be represented with m
Lilian's age 2/3m
Ratio of May's age to Lilian's age = m : 2/3m
Multiply both sides by 3 : 3 : 2
Ratio of Lilian's age their total age: 2 : 5
Lilian's age = 2/5 x 25 = 10 years
May's age = 3/5 x 25 = 15 years
What is the total mass of both ingredients?Let the mass of carrots be represented with c
The mass potatoes would be represented with 5/2c
Ratio of carrots to potatoes : 2 : 5
Ratio of the mass of potatoes to the total mass : 5 : 7 = 5/7
Mass of carrots = 5/2c - c = 9
3/2c = 9
3c = 18
c = 6
Mass of potatoes = 5/2 x 6 = 15
Total mass = 15 + 6 = 21 kilograms
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Given Segment AC with point B contained on the segment, as shown below.
Write a complete two-column proof for following information:
Given: Segment AB = x + 16, Segment BC = 4x + 11
Segment AC = 77
Prove: AB = 26
It is true that the line segment AB equals 26
How to prove that line segment AB = 26?The given parameters are:
AB = x +16
BC = 4x + 11
AC = 77
The two-column proof is as follows:
AC = AB + BC Line segment formula
77 = x + 16 + 4x + 11 Substitution property of equation
77 = 5x + 27 Addition property of equation
5x = 50 Subtraction property of equation
x = 10 Division property of equation
AB = 10 +16 Substitution property of equation
AB = 26
Hence, the line segment AB has been proved to equal 26
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Which rational number represents the number of months that Callie has to pay off the bill? what does the sign on the number mean?
Callie will have $104.12 less than what she earned each month.
What are Rational Numbers ?A number which can be represented in the form p/q where q ≠ 0 are called Rational Numbers.
The complete question is
Callie was billed $416.48 for car repairs. She will pay the service center in 4 equal monthly installments from her bank account.
What is the net change in her bank account balance after each monthly payment? The net change to Callie’s bank account is -$416.48.
The negative sign indicates money leaving Callie’s account. Which rational number represents the number of months that Callie has to pay off the bill? What does the sign on the number mean?
Write an expression to represent the net change to Callie’s account balance each month.
The number of months Callie has to pay the bill is for 4 months, as there are 4 equal installments
The net change in account in Callie's Account balance each month is
-$416.48 / 4 = -$104.12.
The (-) sign indicate the reduction of the net balance from her account.
Callie will have $104.12 less than what she earned each month.
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Please help me, will give 20 points
Answer: 64
Step-by-step explanation:
[tex]10x+8+5x-4=12x+16\\15x+4=12x+16\\3x+4=16\\3x=12\\x=4\\\\LN=12(4)+16=\boxed{64}[/tex]
he graph of the function f(x) = –(x + 6)(x + 2) is shown below.
The domain of the function is all real numbers, the range of a function is y ≤ 4
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = –(x + 6)(x + 2)
If we plot this function on the coordinate plane, we will see it is a graph of a quadratic function.
Here the no other details are given.
But we can say:
The domain of the function is all real numbers.The range of a function is y ≤ 4The x-axis intercept will be at (-6, 0) and (-2, 0).Thus, the domain of the function is all real numbers, the range of a function is y ≤ 4
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what is the mean of 12342634
Answer:
Mean = 3.125 ≈ 3.13
Step-by-step explanation:
Mean = Sum of numbers = 1 + 2 + 3 + 4 + 2 + 6 + 3 + 4 = 25 = 3.125≈3.13
Amount of number 8 8
A shipment of 50,000 transistors arrives at a manufacturing plant. The quality control engineer at the plant obtains a random sample of 500 resistors and will reject the entire shipment if 10 or more of the resistors are defective. Suppose that 4% of the resistors in the whole shipment are defective. What is the probability the engineer accepts the shipment? Do you believe the acceptance policy of the engineer is sound?
Step-by-step explanation:
remember, the number of possible combinations to pick m out of n elements is C(n, m) = n!/(m! × (n-m)!)
50,000 transistors.
4% are defective, that means 4/100 = 1/25 of the whole.
so, the probability for one picked transistor to be defective is 1/25.
and the probability for it to work properly is then 1-1/25 = 24/25.
now, 500 picks are done.
to accept the shipment, 9 or less of these 500 picks must be defective.
the probability is then the sum of the probabilities to get
0 defective = (24/25)⁵⁰⁰
1 defective = (24/25)⁴⁹⁹×1/25 × C(500, 1)
= 24⁴⁹⁹/25⁵⁰⁰ × 500
2 defective = (24/25)⁴⁹⁸×1/25² × C(500, 2)
= 24⁴⁹⁸/25⁵⁰⁰ × 250×499
3 defective = 24⁴⁹⁷/25⁵⁰⁰ × C(500, 3) =
= 24⁴⁹⁷/25⁵⁰⁰ × 250×499×166
...
9 defective = 24⁴⁹¹/25⁵⁰⁰ × C(500, 9) =
= 24⁴⁹¹/25⁵⁰⁰ × 500×499×498×497×496×495×494×493×492×491 /
9×8×7×6×5×4×3×2 =
= 24⁴⁹¹/25⁵⁰⁰ × 50×499×166×71×31×55×494×493×41×491
best to use Excel or another form of spreadsheet to calculate all this and add it all up :
the probability that the engineer will accept the shipment is
0.004376634...
which makes sense, when you think about it, because 10 defect units in the 500 is only 2%. and since the whole shipment contains 4% defect units, it is highly unlikely that the random sample of 500 will pick so overwhelmingly the good pieces.
is the acceptance policy good ?
that completely depends on the circumstances.
what was the requirement about max. faulty rate in the first place ? if it was 2%, then the engineer's approach is basically sound.
it then further depends what are the costs resulting from a faulty unit ? that depends again on when the defect is usually found (still in manufacturing, or already out there at the customer site, or somewhere in between) and how critical the product containing such transistors is. e.g. recalls for products are extremely costly, while simply sorting the bad transistors out during the manufacturing process can be rather cheap. if there is a reliable and quick process to do so.
so, depending on repair, outage and even penalty costs it might be even advisable to have a harder limit during the sample test.
in other words - it depends on experience and the found distribution/probability curve, standard deviation, costs involved and other factors to define the best criteria for the sample test.
Index Number:
b) A trader bought ar bags of rice at a cost, c= 24x+103 and sold them at a price.
x = 33x-x^2/20
(1)
Find the expression for the profit.
(i) If 20 bags of rice were sold, calculate the percentage profit.
The expression for the profit is -x^2/30 + 9x - 103 and the percentage profit on 20 bags of rice is 11.1%
How to determine the profit expression?The cost and the selling price are given as:
C(x) = 24x + 103
S(x) = 33x - x^2/30
The profit is calculated using:
P(x) = S(x) - C(x)
This gives
P(x) = 33x - x^2/30 - 24x - 103
Evaluate the like terms
P(x) = -x^2/30 + 9x - 103
Hence, the expression for the profit is -x^2/30 + 9x - 103
The percentage profitWhen x = 20, we have:
Cost: C(20) = 24 * 20 + 103 = 583
Profit: P(20) = -(20)^2/30 + 9(20) - 103 = 64.67
The percentage profit is then calculated as:
Percentage = P(x)/C(x) * 100%
This gives
Percentage = 64.67/583 * 100%
Evaluate
Percentage = 11.1%
Hence, the percentage profit on 20 bags of rice is 11.1%
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Help please and thanks! I'll award brainliest if you show your work as well :)
Answer:
6 inches
Step-by-step explanation:
Formula for surface area of a cylinder:
[tex]SA=2\pi r^{2} +2\pi rh[/tex]
Plug in values and solve for the radius:
[tex]180\pi =2\pi r^{2} +2\pi r(9)\\[/tex]
Divide both sides by [tex]2\pi[/tex]
[tex]90=r^{2} +r(9)[/tex]
Subtract 90 from both sides
[tex]0=r^{2} +9r-90[/tex]
Use the quadratic equation to find the roots
[tex]x=(-b[/tex]±[tex]\sqrt{b^2-4ac})*\frac{1}{2a}[/tex] (sorry for formatting, Brainly doesn't
allow equations with ± in them)
[tex]x=\frac{-9+\sqrt{9^2-4*1*90} }{2(1)}[/tex] and [tex]x=\frac{-9-\sqrt{9^2-4*1*90} }{2(1)}[/tex]
[tex]x=\frac{(-9+\sqrt{81+360})}{2}[/tex] and [tex]x=\frac{(-9-\sqrt{81+360})}{2}[/tex]
[tex]x=\frac{(-9+\sqrt{441})}{2}[/tex] and [tex]x=\frac{(-9-\sqrt{441})}{2}[/tex]
[tex]x=\frac{(-9+21)}{2}[/tex] and [tex]x=\frac{(-9-21)}{2}[/tex]
[tex]x=\frac{12}{2}[/tex] and [tex]x=\frac{-30}{2}[/tex]
[tex]x=6[/tex] and [tex]x=-15[/tex]
We can't have a negative radius, so that leaves us with r=6 in.
Consider two spinners I have the colors gray orange blue and yellow to make an area model what letter combination will go in the box highlighted in yellow below GB BB BG OY
Answer:
BB
Hope that helps!
find the probability of selecting a Jack on the 1st draw and a queen on the second draw after replacing the first card.
The probability of selecting a jack and a queen is 1/169.
What is the probability?Probability calculates the odds that an event would happen. The odds that the event would happen lies between 0 and 1.
The probability of selecting a jack and a queen = (number of jacks / number of cards in a deck) x (number of queens / number of cards in a deck)
4/52 x 4/52 = 1/169
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D. -1 7. A weaver bought a bundle of grass for $50.00 from which he made 8 mats. If each mat was sold for $ 15.00, find the percentage profit. 10 %
Profit percentage for weaver after selling mat is equals to 140%.
What is percentage ?" Percentage is defined as the hundredth part of the whole given quantity. It is represented by symbol %."
Formula used
Profit% = [tex](\frac{Profit }{cost price} )[/tex]× 100
According to the question,
Given,
Cost price of bundle of grass = $50.00
Number of mats made = 8
Selling price of each mat = $15.00
Therefore,
Selling price of 8 mats = 15 × 8
= $120
Selling price > Cost price
Therefore,
Profit = Selling price - Cost price
= 120 - 50
= $70
Substitute the value in the formula to get profit percentage we get,
Profit% = [tex]\frac{70}{50}[/tex] ×100
= 140%
Hence, profit percentage for weaver after selling mat is equals to 140%.
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Solve √x-1= x-3. Check for extraneous solutions.
A.No solution
B.x=2,5
C.x=5
D.x=2
Answer is C x=5
Step-by-step explanation:
so, "- 1" is also part of the square root ?
sqrt(x - 1) = x - 3
it is clear that for any value x < 1 we have no solution in R (as this makes the argument of the square root negative, and there is so real number solution for the square root of negative numbers).
now square the whole equation.
x - 1 = (x - 3)² = x² - 6x + 9
x² - 7x + 10 = 0
the general solution for quadratic equations is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -7
c = 10
x = (7 ± sqrt(49 - 4×1×10))/(2×1) =
= (7 ± sqrt(49 - 40))/2 = (7 ± sqrt(9))/2
x1 = (7 + 3)/2 = 10/2 = 5
x2 = (7 - 3)/2 = 4/2 = 2
x2 is probably (given the answer options) not a valid solution for the original problem, as it represents the negative solution of sqrt(x - 1).
sqrt(2 - 1) = 2 - 3
± 1 = -1
remember, every square root has always 2 solutions : a positive and a negative one.
your teacher clearly only wanted the positive solution, which is x1 = 5.
so, yes,
C. x = 5
is the correct answer.
but please send your teacher my regards and comments. he/she has to state that only the positive solution to the square root is required/allowed.
because, formally, also x = 2 is a valid solution.
and therefore, C. AND D. are correct answers !!!!
Find the APR, rounded to the nearest tenth of a percent (one decimal place) for the loan. Purchase a living room set for $4,900 at 8% add-on interest for 4 years. Enter only the number without % sign.
The annual percent rate(APR) to purchase a living room set for $4,900 at 8% add-on interest for 4 years is 8. 6
How to calculate the annual interest rate
Using the formula
APR = ((Interest + Fees / Loan amount) / Number of days in loan term)) x 365 x 100
Note that Interest expense = Original amount / interest rate
Interest amount = $4, 900
Rate = 8% = 0. 08
Interest expense = $4, 900× 0. 08 = $392
Loan amount is also the principal amount , P = I / (RT)
where I is Interest Amount, R is Rate of Interest and T is Time Period.
Principal amount = $4, 900 ÷ 0. 08 × 4 = $4, 900 ÷ 0.32 = $ 15,313. 5
Substitute the values into the formula for APR
APR = [tex]\frac{392+ 4900}{15312.5} / 1460 * 365* 100[/tex]
APR = [tex]0.345 / 1460 *365*100[/tex]
APR = [tex]2. 36* 10^-4 *365* 100[/tex]
APR = [tex]8. 625[/tex]
To the nearest tenth is, 8. 6
Therefore, the annual percent rate(APR) is 8. 6
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f(x) = -3x+1
g(x) = 3x² + 4x - 15
Find: f(g(x))
if you wanted to make the graph of y=6x+7 less steeps which equation could you use
Answer:
[tex]y = mx + b[/tex]
≡ For instance, I have the equation, y = 9x + 5, and I must find the slope. The slope is 9, because 9 is in the m area of the equation, making these equations easier to determine and have less steps than before.