Answer:
A. 1 + 3x = -89
B. x = -30
Step-by-step explanation:
Let the unknown variable be x.
A. Translating the word problem into an algebraic expression, we have;
1 + 3x = -89
B. To solve for the unknown variable;
1 + 3x = -89
3x = -89 -1
3x = -90
x = -90/3
x = -30
Check:
1 + 3x = -89
Substituting the value of x;
1 + 3(-30) = -89
1 + (-90) = -89
1 - 90 = -89
-89 = -89
The average cost when producing x items is found by dividing the cost function, C(x), by the number of items,x. When is the average cost less than 100, given the cost function is C(x)= 20x+160?
A) ( 2, infinit)
B) (0,2)
C) (-infinit,0) U (2,infinit)
D) (- infinit,0] U [2,infinit)
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Answer:
A) (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it
Step-by-step explanation:
We want ...
C(x)/x < 100
(20x +160)/x < 100
20 +160/x < 100 . . . . . separate the terms on the left
160/x < 80 . . . . . . . subtract 20
160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0
x > 2 . . . . . . simplify
In interval notation this is (2, ∞). matches choice A
__
Technically (mathematically), we also have ...
160/80 > x . . . . and x < 0
which simplifies to x < 0, or the interval (-∞, 0).
If we include this solution, then choice C is the correct one.
_____
Comment on the solution
Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.
*REVERSE PROPORTION*
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Answer:
33.3%
Step-by-step explanation:
The selling price of £42 is (1 +40%) times the total purchase price.
1.40 × purchase price = £42
purchase price = £42/1.40 = £30
The total profit is 40% of this, so is ...
£30 × 40% = £12
The purchase price of the skirt is ...
total cost - glove cost = skirt cost = £30 -3 = £27
The profit on the skirt is ...
total profit - glove profit = skirt profit = £12 -100% × £3 = £9
Then the percentage profit on the skirt is ...
skirt profit % = skirt profit / skirt cost × 100% = £9/£27 × 100% = 33.3%
The percentage profit on the cost of the skirt was 33.3%.
At the gas station, each liter of gas costs $3 but there's a promotion that for every beverage you purchase you save $0.20 on gas.
The side lengths of a triangle are 5,10, and 13. Is this a right Triangle?
No because 5^2 +10^2 is not equavalent to 13^2
by using the pythagoras' theorem
What is the product? (–3s + 2t)(4s – t)
Answer:
[tex] - 12 {s}^{2} + 11st - 2 {t}^{2}[/tex]Step-by-step explanation:
(–3s + 2t)(4s – t)
= -3s (4s - t) + 2t(4s - t)
[tex] = - 12 {s}^{2} + 3st + 8st - 2 {t}^{2} [/tex]
[tex] = - 12 {s}^{2} + 11st - 2 {t}^{2} (ans)[/tex]
Answer: -12s^2 + 11st -2t^2
Step-by-step explanation:
= (-3s + 2t)(4s - t)
= -12s^2 + 3st + 8st -2t^2
= -12s^2 + 11st -2t^2
Answer Provided by GauthMath please heart and comment thanks if you like.
What is the derivative of x^2?
Answer:
[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x^2[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = 2x^{2 - 1}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
please show steps in solving: B/3 + B/4 + B/6 =
Answer:
= 3b/4
Step-by-step explanation:
= b . 4/12 + b . 3/12 + b . 2/12
Apply the fraction rule: a/c + b/c = a + b/c
= b . 4 + b . 3 + b . 2/12
= 4b + 3b + 2b/12
Add similar elements: 4b + 3b + 2b = 9b
= 9b/12
Cancel 9b/12: 3b/4
= 3b/4
find the missing side lengths
Answer:
x = 11 * sqrt(3)
y = 11
Step-by-step explanation:
Use the ratio of the lengths of the sides of a 30-60-90 triangle.
y = 22/2 = 11
x = 11 * sqrt(3)
Answer: x = 11√3
y = 11
Step-by-step explanation:
Let the reference angle be 60
b = y
h = 22
p = x
so
sin60 = p/h
[tex]\sqrt{3} /2[/tex] = x/22
so x =( 22[tex]\sqrt{3}[/tex] )/ 2
so x = 11√3
so
[tex]h^2 = p^2 + b^2\\22^2 = (11\sqrt{3)}^2 + b^2\\or, 484 = 363 + b^2\\or, 484-363 = b^2\\or, 121 = b^2\\or, \sqrt{121} = b\\so b = 11[/tex]
write two properties of 1
The identity property of 1 says that any number multiplied by 1 keeps its identity. In other words, any number multiplied by 1 stays the same. The reason the number stays the same is because multiplying by 1 means we have 1 copy of the number. For example, 32x1=32.
in a group of boys the number of arrangments of boys 4 boys is 12 times the number of arrangment of 2 boys the number of boys in the group is
Answer:
4*12*2
Step-by-step explanation:
it will be the right answer
Answer:
There are 6 boys in group.
Step-by-step explanation:
Since we have given that
Number of arrangement of 4 boys = 12 times the number of arrangement of 2 boys.
So, Let the number of boys in the group be 'x'.
So, Number of boys in the group will be
\begin{gathered}x=\frac{12\times 2}{4}\\\\x=\frac{24}{4}\\\\x=6\end{gathered}
x=
4
12×2
x=
4
24
x=6
Hence, there are 6 boys in the group.
hope it helps you a follow would be appreciated
A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 16.3 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23.
Answer:
Hence, we reject H_0 as There is sufficient evidence to show that population variance is not 23
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=30[/tex]
Variance [tex]\sigma= 16.8[/tex]
Significance Level [tex]\alpha=0.05[/tex]
[tex]\sigma = 23[/tex]
Genet=rally the Hypothesis are as follows
Null [tex]H_0=\sigma^2=23[/tex]
Alternative [tex]H_a=\sigma^2 \neq 23[/tex]
Generally the equation for Chi distribution t is mathematically given by
t test statistics
[tex]X^2=\frac{(n-1)\sigma}{\sigma^2}[/tex]
[tex]X^2=\frac{(30-1)16.8^2}{23}[/tex]
[tex]X^2=355.86[/tex]
Therefore
Critical Value
[tex]P_{\alpha,df}[/tex]
Where
[tex]df=29[/tex]
[tex]P_{\alpha,df}=16.0471 and 45.7223[/tex]
[tex]X^2=45.7223[/tex]
Hence, we reject H_0 as There is sufficient evidence to show that population variance is not 23
In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is with a standard deviation of days. Assume the data to be approximately bell-shaped.
Required:
a. Between what two values will approximately 68% of the numbers of days be?
b. Estimate the percentage of customer accounts for which the number of days is between 18 and 46.
c. Estimate the percentage of customer accounts for which the number of days is between 11 and 53.
A finance journal, which publishes research on current financial topics, states that the maturity term for a certificate of deposit is, on average, 10 years. A banker believes the average maturity term at their bank is different than the amount quoted in the finance journal. After completing a study, the banker found that the average maturity term for a certificate of deposit is 8 years, on average.
Required:
As the banker sets up a hypothesis test to determine if their belief is correct, what is the banker's claim?
Answer:
Following are the solution to the given question:
Step-by-step explanation:
In this the hypothesis is:
[tex]H_{0}:\mu=10\\\\H_{1}:\mu\neq10[/tex]
The bankers assert that their bank's average maturity was distinct from that of ten years, that's why the hypothesis of the alternative.
PLEASE CORRECT BEFORE ANSWERING I AM HAVING TROUBLE GETTING THINNGS RIGHT SO PLEASE HELP
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Answer:
3
Step-by-step explanation:
AB is 1 unit long.
A'B' is 3 units long.
The scale factor is the ratio of these lengths:
scale factor = A'B'/AB = 3/1 = 3
ABC is dilated by a factor of 3 to get A'B'C'.
Which of the following functions is graphed below?
20
15
10
-8-84
-2
42
-5
-10
-15
-20
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Answer:
D.
Step-by-step explanation:
The linear portion of the curve is in the region x ≥ 2. The only function defined that way is the one in choice D.
Consider the lists of length six made with the symbols P, R, O, F, S, where repetition is allowed. (For example, the following is such a list: (P,R,O,O,F,S).) How many such lists can be made if the list must end in an S and the symbol O is used more than once?
Answer:
96
Step-by-step explanation:
COMBINATIONS & PERMUTATIONS can be confusing but they always have a solution.
Key 1: Understand and/or rewrite the question
Consider the lists of 6 items (out of the 5 letters P,R,O,F, and S; where O is used twice).
NOTE: When they say O is used more than once, don't forget that each list must not exceed 6 items in total. So, O is used twice. Simple!
How many such lists can be made if each list must end in an S?
NOTE: This instruction requires that S doesn't move. It won't change position, and it won't be involved in the rearrangement!
Key 2: Solve the mysteries
Now, S won't move and O is doubled. These rules put a form of restriction on the "n" which is the total number of items involved in the operation. We are supposed to create lists of 6 items but the reality is - only 5 are moving. Recall also that the original number of items involved in the operation is 5.
In this case, n = 5
Then we have 4 items rotating - P, R, O and F - with 1 repeated.
What this means is that for every list starting with the first O, the different arrangements apply to the second O as well.
There is no distinction such as O₁ and O₂. O is O!
Let k = the extra O
(n - k) = 5 - 1 = 4
So each of these 4 letters has 4! (4 factorial) arrangements, that is (4 x 3 x 2 x 1) = 24 arrangements
Multiply 24 by 4 to get 96
Complete this
sentence: The shortest side
of a triangle is always opposite the
A. longest side
B. angle with the smallest measure
• C. second-longest side
•
D. angle with the greatest measure
Answer:
B
Step-by-step explanation:
The shortest side of a triangle is opposite the smallest angle
The longest side of a triangle is opposite the largest angle
please help
abd=58 and bdc=32 what is the measure of adb
Answer:
<ADB = 61degrees
Step-by-step explanation:
From the diagram shown, triangle ADB is isosceles since they projected out from the chord AD. Hence;
<ABD + <ADB + <BAD = 180
Since <ADB = <BAD, then;
<ABD + <ADB + <ADB = 180
Given that:
<ABD = 58degrees
58 + 2<ADB = 180
2<ADB = 180 - 58
2<ADB = 122
<ADB = 122/2
<ADB = 61degrees
Answer90 degrees
Step-by-step explanation:
x -3,4,11,18 y -3,1,5,9
Is the relationship linear, exponential, or neither?
Choose 1 answer:
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Answer:
linear
Step-by-step explanation:
The points all lie on a straight line. The relationship is linear.
Tim took a random survey of 20 sixth graders and 20 eighth graders. He asked how many hours a week each played sports. His data is shown in the two dot plots below.
What is the difference between the median number of hours that 6 graders play sports and the median number of hours that 8 graders play sports?
Answer: 4 hours
Step-by-step explanation:
The median number is always in the middle the other numbers have to be equal on both sides 5 is the middle number on the plot 6th graders have 4 dots and 8th graders have 0 dots which means the hourly difference is 4
There are 84 students in a speech contest. Yesterday, 1/4 of them gave their speeches. Today, 3/7 of the remaining students gave their speeches. How many students still haven't given their speeches?
Answer:
36
Step-by-step explanation:
Total students un the contest = 84
Number of students who gave their speech yesterday:-
[tex] \frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21[/tex]
so 21 students gave their speech yesterday
remaining students = 84 - 21= 63
Number of students who gave their speech today:-
[tex] \frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27[/tex]
Number of students who have given their speech:-
= 21 + 27
= 48
Number of students who still haven't given their speech :-
= total - 48
= 84 - 48
= 36
find the area of the figure sides meet at right angles 8 cm, 3cm, 4cm, 5cm, 9cm
Answer:
umm is it a quadrilateral
Step-by-step explanation:
Answer:
if it's 8cm, 3m, 4cm, 5cm, and 9cm it's probably a quadrilateral
(2/3)x-1=27/8,find x
Answer:
x = 105/16
Step-by-step explanation:
2/3x - 1 = 27/8
Add 1 to each side
2/3x - 1+1 = 27/8+1
2/3x = 27/8 + 8/8
2/3x = 35/8
Multiply each side by 3/2
3/2 * 2/3x = 35/8 *3/2
x = 105/16
In the context of the Pearson r correlation coefficient, the absolute size of r is the:_____.
a. coefficient that indicates the measurement scale that applies to two variables.
b. direction of the relationship between two variables.
c. strength of the relationship between two variables.
d. curvilinear relationship between two variables.
Answer:
strength of the relationship between two variables.
Step-by-step explanation:
The Pearson r correlation Coefficient used to measure the relationship or association between two variables. The correlation Coefficient, R ranges between - 1 and 1. As it provides information on both the strength and type of the relationship. The type of relationship could be positive or negative.
The absolute size of r measures Tha strength of the relationship as it ignores the sign. As the Pearson r value moves closer to 1, the higher the strength of the relationship.
Find the length of XW.
Answer:
XW = 78
Step-by-step explanation:
Both triangles are similar, therefore based on triangle similarity theorem we have the following:
XW/XZ = VW/YZ
Substitute
XW/6 = 104/8
XW/6 = 13
Cross multiply
XW = 13*6
XW = 78
how all work.
A) What is the average rate of change of the function g(x) = 14x + 6 over the interval [0, 5]?
B) What is the average rate of change of the function g(x) = 3(2x) - 6 over the interval [0,5]?
C) How does this compare to your Answers for Problem 4?
Answer:
Here we can only answer A and B.
For a given function f(x), the average rate of change in a given interval [a, b] is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
A) we have g(x) = 14*x + 6, and the interval [0, 5], the average rate of change is:
[tex]r = \frac{g(5) - g(0)}{5 - 0} = \frac{(14*5 + 6) - (14*0 + 6)}{5} = \frac{14*5}{5} = 14[/tex]
The average rate of change is 14.
B) We have g(x) = 3*(2x) - 6
we can rewrite this as:
g(x) = 3*2*x - 6 = 6x - 6
And we want to find the rate of change in the interval [0, 5]
is:
[tex]r = \frac{g(5) - g(0)}{5 - 0} = \frac{(6*5 - 6) - (6*0 - 6)}{5} = 6[/tex]
simplify. can someone help i am lost
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Answer:
[tex](S)\cdot(H)\cdot(E)\cdot(e)\cdot(\theta)\cdot(\epsilon+1+1)\cdot(\xi)\cdot(s)\cdot(h)[/tex]
Step-by-step explanation:
The inverse function of fun(x) is indicated using a -1 exponent. That is ...
[tex]\text{fun}(\text{fun}^{-1}(x)) = x\\\text{fun}^{-1}(\text{fun}(x)) = x[/tex]
The usual trig identities apply:
sin²(x) +cos²(x) = 1
sec²(x) -tan²(x) = 1
sin(x) = 1/csc(x)
__
So, the expression simplifies to ...
[tex](S)\cdot(H)\cdot(E)\cdot(e)\cdot(\theta)\cdot(\epsilon+1+1)\cdot(\xi)\cdot(s)\cdot(h)[/tex]
find the result when six times the difference of 5 and 3 is added to the quotient of 12 by 3.with process
6. A boy pushes his little brother in a box with a force of 500 N for 324 m How much work is this if the force of
friction acting on the sliding box is (a) 100 N (6) 250. N?
Answer:
(a) 129600 J
(b) 81000 J
Step-by-step explanation:
The work done is given by the product of force and the displacement in the direction of force.
Force, F = 500 N
distance, d = 324 m
(a) friction force, f = 100 N
The work done is
W = (F - f) x d
W = (500 - 100) x 324
W = 129600 J
(b) Friction, f = 250 N
The work done is
W = (F - f) d
W = (500 - 250) x 324
W = 81000 J
If land the domain of the following peicewise function f(x)={x^2 +2 if -6
Answer:
? what is this question asking
Step-by-step explanation:
