Solve the inequality: −2x > −6
Answer:
x < 3
Step-by-step explanation:
42. Let f be a function from the set A to the set B. Let S and T be subsets of A. Show that
a) f(S ∪ T)=f(S) ∪ f(T).
b) f(S ∩ T) ⊆ f(S) ∩ f(T).
Start with any random elements of sets and compute LHS and RHS individually.
a) The proof of f(S ∪ T) = f(S) ∪ f(T) is explained below.
b) The proof of f(S ∩ T) ⊆ f(S) ∩ f(T) is expliane dbelow.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Let, The set A = {1, 2, 3, 4, 5} and B = {2, 4, 5}.
Therefore, S = {1, 2, 3} and T = {1, 4, 5}.
Now, f(S ∪ T) = {1, 2, 3, 4, 5} and f(S) ∪ f(T) = {1, 2, 3} ∪ {1, 4, 5}.
Hence, f(S ∪ T)=f(S) ∪ f(T).
Now, f(S ∩ T) = {1} and f(S) ∩ f(T) = {1, 2, 3} ∩ {1, 4, 5} = {1}.
Therefore, f(S ∩ T) ⊆ f(S) ∩ f(T). (⊆ implies improper subset)
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A theater has 20 rows of seats. If there are 4 seats in the 1st row 12 in the 2nd row, 20 in the 3rd row . How many seats are there in total? Show and explain all work.
Answer:
164 seats
Step-by-step explanation:
you make the equation 4+ 8X to deteremine the seats and x equals the rows and you get your answer.
An arithmetic sequence is a sequence where each consecutive term has a common constant difference. The total number of seats that the theatre has is 156 seats.
What is the sum of terms of an arithmetic sequence?An arithmetic sequence is a sequence where each consecutive term has a common constant difference.
An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.
Let the starting term be 'a' and the common difference be 'd', then we get the arithmetic sequence as:
a, a+d, a+2d, .....
The sum of those 'n' terms is:
[tex]\rm a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n}{2}[2a + (n-1)d ][/tex]
The condition is a case of an arithmetic progression. Therefore, the common difference in the progression is of 8 and the first term of the sequence is 4. Therefore, the sum of the series for the first 20 terms will be,
aₙ = 4 + (20-1)8
= 4 + (19)8
= 4 + 152
= 156
Hence, the total number of seats that the theatre has is 156 seats.
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Chen tosses a number cube 19 fewer times than Jayden. Chen tosses a number cube 38 times. How many times does Jayden toss a number cube?
Use partial quotients to solve 5,140 ÷ 9 = ___.
The correct answer is 571 quotient and 1 is remainder.We can solve easily by partial quotients.
What are partial quotients division?Partial quotients division is a deviation from the standard method. The divisor is multiplied with a number and the multiple obtained is deducted from the dividend. This multiple of the divisor is as close as possible to the dividend, that is less than or equal to the dividend.
Why do we use partial quotient division?Partial quotient division provides natural differentiation because we can have students solve at a level they are comfortable with and then we can challenge them to find a more efficient way. And this means using fewer steps and solve easily.
Now we solve
first 9 multiply with 500 so we get 4500. 5140-4500=640
then 9 multiply with 70 so we get 630. 640-630=10
then 9 multiply with 1 so we get 9. 10-9=1
Hence 500+70+1=571
And our remainder is 1.
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Which is a rational function?
A. Y= 2/x
B. Y=x^2 - x + 4
C. Y= x-3^x/x^2
D. Y= x-5/2
A rational function is the algebraic expression y = 2 / x. (Correct choice: A)
What function is a rational function?
Rational functions are algebraic expressions, whose form is described below:
R(x) = P(x) / Q(x)
Where:
P(x) - Numerator polynomic function.Q(x) - Denominator polynomic function.Please notice that Q(x) must be a polynomial whose grade is greater than zero.
Polynomials are algebraic expressions of the form:
P(x) = ∑ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., n, ..., m}, where m is the grade of the polynomial.
Therefore, by direct inspection, we conclude that algebraic expression y = 2 / x is a rational expression.
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a family buys a new home for $212,500 and pays a 20% down payment ($42,500). if the mortgage is for 15 years at 5.75% interest which is their monthly house payment
Answer:
Their monthly house payment is of $2,184.65.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
A family buys a new home for $212,500 and pays a 20% down payment ($42,500).
This means that the loan is of 212,500 - 42,500 = $170,000, that is, [tex]P = 170,000[/tex]
Value of the loan in 15 years:
15 years means that [tex]t = 15[/tex]
5.75% interest means that [tex]r = 0.0575[/tex]
Compounded yearly, so [tex]n = 1[/tex]
Then
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(15) = 170000(1 + \frac{0.0575}{1})^{15}[/tex]
[tex]A(15) = 393237[/tex]
Monthly payment:
Total of $393,237 in 15*12 months. So
[tex]M = \frac{393237}{15*12} = 2184.65[/tex]
Their monthly house payment is of $2,184.65.
which of the following is the solution to the equation 3^X+9=81^X
a) x=-6
b)x=6
c)x=-3
d)x=3
9514 1404 393
Answer:
d) x = 3
Step-by-step explanation:
The given equation resolves to a quartic equation in (3^x). It has a solution near ...
x = 0.541770946714
__
Perhaps you want the solution to ...
3^(x+9) = 81^(x)
Rewriting in powers of 3, this is ...
3^(x+9) = (3^4)^x = 3^(4x)
Taking logarithms base 3 gives ...
x +9 = 4x
9 = 3x . . . . . . subtract x
3 = x . . . . . . . divide by 3 . . . . matches choice D
_____
Additional comment
The Order of Operations requires that exponential terms be evaluated before addition and subtraction. That means (3^x) must be evaluated before the sum (3^x) + 9. If you want the sum of x and 9 to be evaluated first, it must be in parentheses: 3^(x+9).
In typeset equations, the superscript font serves to group parts of the exponent. In plain text, a grouping symbol (parentheses) must be used.
A parallelogram has two
adjacent angles that are
supplementary. One
angle is 55° less than the
other. What is the
measure of the smaller
angle?
Answer:
x + (x + 55) = 180
2x =125
The angle is 62.5 degrees
Double-Check
62.5 + (62.5 + 55) = 180
125 + 55 = 180
62.5 is the smaller angle
Step-by-step explanation:
Answer:
62.5
Step-by-step explanation:
Plz help me plz help
Answer:
46
Step-by-step explanation:
26+20
The ladder is 26ft long, there is still 20ft to go, so 20+26
I need help with this, I need to simplify but I don't know how
Answer: solve the same variables
Step-by-step explanation:
1. 3y + 4.1
2. 4x +
3. 5x + 22½
4. 4y²
5. + 25
6. 0
(4 x 5) + ( 4 x 2) = 4 x (5 + n)
Answer:
Step-by-step explanation:
1. (4x5) is 20
2. (4x 2) is 8
3. 20 plus 8 is 28
4. 28= 4x (5+n)
5. isolate n by dividing 4 on both sides= 28/4= 4+n
6. subtract 4 on both sides to get 7-4=n
7. n=3
The next model of a sports car will cost 12.8% more than the current model. The current model costs $42,000. How much will the price increase
in dollars? What will be the price of the next model?
Answer:
$5,376
$47,376
Step-by-step explanation:
Given :
Price of current model = $42,000
Percentage increase in price = 12.8%
Price increase in dollars :
12.8% of $42000
0.128 * $42000
= $5,376
Price of the next model :
Price of current model + increase in price
$42000 + $5376
= $47,376
i’m need help !!!! thanksss
Answer:
x=77
Step-by-step explanation:A triangle is always 180 degreesin total so u would take 26 away from 180 witch is 154 then devide it as the angles that are left are corresponding angles. Then you dwvide 154 by 2 witch is 77. X=77
y=x-4 and y=4x+2 graph solution of the systems
Answer:
(-2,-6)
Step-by-step explanation:
we can solve this system of equations with the substitution method because y is already by itself.
since they are both equal to y, we can set both equations equal to each other.
4x+2=x-4
subtract 2 from both sides
4x=x-6
subtract x from both sides
3x=-6
divide both sides by 3
x = -2
now that we know x, we can plug this value into one of the original equations and solve for y.
y=-2-4
y=-6
so on a graph, these two equations will intersect at the point (-2,-6)
Please help me with this
9514 1404 393
Answer:
3025
Step-by-step explanation:
We observe that increasing x by 1 from 0.5 to 1.5 causes the function value to be multiplied by 55 (from 1 to 55).
So, increasing the x-value by 1 again, from 1.5 to 2.5, will again multiply the function value by 55.
f(2.5) = 55·f(1.5) = 55^2
f(2.5) = 3025
Based on past experience, the daily revenue, X, for a coffee shop in a city is a normally distributed random variable with a mean daily revenue of $900. The first co-owner of the shop feels that the shop is known throughout the city and as such they could reduce the amount of money spent on advertising without causing a decrease in the population mean daily revenue. The second co-owner is concerned that a reduction in advertising would in fact result in a decrease in the population mean daily revenue. To settle the issue, the first co-owner decides to decrease the advertising dollars for a period of time, during which she will select 64 days at random and compute the sample mean daily revenue. She will then perform a hypothesis test to determine if the sample mean daily revenue provides significant evidence to conclude that the population mean daily revenue is less than $900 when the advertising dollars are reduced. The first co-owner observes a sample mean daily revenue of $892.50 with a sample standard deviation of $24 when the advertising dollars have been reduced. What is the p-value for her test
Answer:
The p-value for her test is 0.0075.
Step-by-step explanation:
She will then perform a hypothesis test to determine if the sample mean daily revenue provides significant evidence to conclude that the population mean daily revenue is less than $900 when the advertising dollars are reduced.
At the null hypothesis, we test that the mean is less than 900, that is:
[tex]H_0: \mu = 900[/tex]
At the alternate hypothesis, we test that the mean is less than 900, that is:
[tex]H_a: \mu < 900[/tex]
The test statistic is:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
900 is tested at the null hypothesis:
This means that [tex]\mu = 900[/tex]
Sample of 64 days. The first co-owner observes a sample mean daily revenue of $892.50 with a sample standard deviation of $24 when the advertising dollars have been reduced.
This means that [tex]n = 64, X= 892.50, s = 24[/tex]
Value of the test:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{892.50 - 900}{\frac{24}{\sqrt{64}}}[/tex]
[tex]t = -2.5[/tex]
What is the p-value for her test?
The pvalue of the test is the probability of a sample mean below 892.5, which is a left-tailed test for t = -2.5 with 64 - 1 = 63 degrees of freedom.
Using a calculator, the p-value for her test is 0.0075.
Write 1 6/7 as an improper fraction.
Answer:
13/7
Step-by-step explanation:
multiply the 7 x 1 then add 6. 13 would be the numerator.
mark me brainliest please
Help pls pls help pls pls help
It's 8, it gave Y so pretty easy from there on
y = 4
y = 1/4 x + 2
______________
4 = 1/4 x + 2
4 - 2 = 1/4 x + 2 - 2
2 = 1/4 x
2 × 4 = 4 × ( 1/4 ) × x
x = 8
Thus the correctly answer is option D.
Q6.4☆ Points: 2 Suppose that Angela wants to use her sample to create a 68% confidence interval for the true population median of boba weight per drink and she knows that the population SD is 2 grams. What is the minimum sample size she needs to create a confidence interval that has a width of 0.4 grams?
Answer:
She needs a sample size of 25.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.68}{2} = 0.16[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.16 = 0.84[/tex], so Z = 0.995.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The population SD is 2 grams.
This means that [tex]\sigma = 2[/tex]
What is the minimum sample size she needs to create a confidence interval that has a width of 0.4 grams?
She needs a sample size of n.
n is found when M = 0.4. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.4 = 0.995\frac{2}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = \frac{0.995*2}{0.4}[/tex]
[tex](\sqrt{n})^2 = (\frac{0.995*2}{0.4})^2[/tex]
[tex]n = 24.8[/tex]
Rounding up:
She needs a sample size of 25.
Answer please for brainliest
Answer:
the answer is 0.7 by the way!
Step-by-step explanation:
This is talking about the distance from zero sooo...
6. Find the greatest odd integer value of x that satiste the inequality 3x < -105.
Answer:
x<-35
Step-by-step explanation:
Find perimeter
Simplify answer completely
Answer:
[tex]perimeter = 14 \frac{3}{4} + 4 \frac{1}{2} + 8 \frac{1}{2} + 10 \frac{2}{5} + 10 \frac{2}{5} + 12 \frac{4}{5} \\ = \frac{59}{4} + \frac{9}{2} + \frac{17}{2} + \frac{52}{5} + \frac{52}{5} + \frac{64}{5} \\ = 61 \frac{7}{20} \: units[/tex]
A phone company offers two monthly plans. Plan A costs $13 plus an additional $0.14 for each minute of calls. Plan B costs $24 plus an additional $0.10 for each minute of calls.
For what amount of calling do the two plans cost the same? Minutes
What is the cost when the two plans cost the same? $
Answer:
m = number of minutes calls
Plan A : 30 + 0.15 m
Plan B: 16 + 0.20 m
For what amount of calling do the two plans cost the same?
30 + 0.15m = 16 + 0.20m
0.05m = 14
m = 280
280 minutes of calling, the two plans cost the same
What is the cost when the two plans cost the same?
Plan A: 30 + 0.15 m = 30 + 0.15 (280) = 72
Plan B: 16 + 0.20 m = 16 + 0.20 (280) = 72
It's cost $72 when the two plans cost the same
The solid below is made of twelve identical rectangular prisms. The overall dimensions of the composite solid are 36 inches (in.) by 36 inches by 24 inches. What is the volume, in cubic inches, of a single prism?
Whoever answers correctly will get Brainliest.
Answer:
A
Step-by-step explanation:
Volume of the solid = base x width x height = 36 x 36 x 24 = 31 104 in^3
Volume of one prism = total volume / 12 = 31 104 / 12 = 2592 in^3
Get it right I need this bro
Write an equation and solve for b using the diagram
below. YOU MUST WRITE THE EQUATION IN
ORDER TO GET CREDIT.
(3b + 18)°
93°
Step-by-step explanation:
hope this is right hehe.....
evaluate - [tex]6^{2}- 2(5+1+3[/tex]
The expression 6² - 2(5 + 1 + 3) after evaluation gives 18.
What is BODMAS rule?BODMAS rule is rule for operation of numbers in a specific order when more than one type of operations is involved.
BODMAS is the abbreviated form for Brackets, Order including powers and exponents, Division, Multiplication, Addition and Subtraction.
Given expression is, 6² - 2(5 + 1 + 3).
First we should do the operation in brackets.
6² - 2(5 + 1 + 3) = 6² - 2 (9)
Now we should do the power operations.
6² - 2 (9) = 36 - 2 × 9
Now we do multiplication.
36 - 2 × 9 = 36 - 18
Now we do subtraction.
36 - 18 = 18
Hence the answer of the expression given is 18.
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Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?
Answer:
The slope of the line through these two points is 0.5, which means that for each hour moving a lawn, 0.5 more lands of area are mowed.
Step-by-step explanation:
Slope of a line:
Suppose we have two points in a line. The slope is the change in y divided by the change in x. It states how much y changes when x changes by 1.
In this question:
x: Time in hours to move a lawn.
y: Area of land.
Two of his points are (3, 1.5) and (5, 2.5).
Change in y: 2.5 - 1.5 = 1
Change in x: 5 - 3 = 2
Slope: 1/2 = 0.5
The slope of the line through these two points is 0.5, which means that for each hour moving a lawn, 0.5 more lands of area are mowed.
To determine the inverse of function f,
change f(x) to y, switch
and y,
and solve for
The resulting function can be written as
f(x) = (x - 3.
Answer:
To determine the inverse of function f, change f(x) to y, switch x and y, and solve for y.
[tex]\frac{1}{8} (x-4)^3[/tex]
Step-by-step explanation:
f(x) = [tex]\sqrt[3]{8x} +4[/tex]
Change f(x) to y: y = [tex]\sqrt[3]{8x} +4[/tex]
Switch x and y: x = [tex]\sqrt[3]{8y} +4[/tex]
Solving for y: x - 4 = [tex]\sqrt[3]{8y}[/tex]
(x-4)^3 = 8y
y = [tex]\frac{1}{8}[/tex][tex](x-4)^3[/tex]
Therefore: inverse of function f = [tex]\frac{1}{8} (x-4)^3[/tex]
The inverse function of f(x) will be f⁻¹(x) = 1/8(x - 4)³.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function f(x) is given below.
f(x) = ∛(8x) + 4
Then the inverse function of f(x) will be
Put x = f⁻¹(x) and f(x) = x. Then we have
x = ∛{8f⁻¹(x)} + 4
∛{8f⁻¹(x)} = x - 4
Cube on both sides, then we have
8f⁻¹(x) = (x - 4)³
f⁻¹(x) = 1/8(x - 4)³
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