Because domain restrictions apply to this rational expression, x cannot be equal to {-2, 2}.
What is domain?Domain restrictions are any points in the domain where the function will not have a value. This basically means that there is a point in the function where x will not work.
For the numerator, any value of x will suffice. We can have a value of 0 in the numerator, or a positive, negative, or decimal number.
However, the denominator cannot be equal to zero. This is due to the fact that a fraction bar represents division, and we cannot divide by zero.
Here,
x²-4=0
Add 4 to both sides:
x²-4+4 = 0+4
x² = 4
Take the square root of both sides:
√x² = √4
x = 2 or x = -2
The x cannot be equal to {-2, 2} as domain restrictions apply to this rational expression.
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Wendy spent 1/4of her paycheck on Monday and
3/7of it on Tuesday. She spent the rest of her
paycheck over the next 3 days. If Wendy spent $18 on each of the 3 days, what was the amount of
her paycheck
Answer:
$56.00
Step-by-step explanation:
Check:
1/4(56) + 3/7(56) + 18 =
14 + 24 + 18 = 56
See the picture below. I wanted to figure out what fraction of the paycheck was the 18.
I took 1 which is the whole pay check and subtracted out the fractions that I knew were spent 1/4 and 3/7. That left me with 9/28. So I knew 9/28 of the paycheck was 18 dollars. I drew out 28 squares. 9 of those squares was worth $18. That meant that each square was worth $2. 2 x 28 = 56
Justin, age 52, wants to pay no more than S800 a year in lite insurance. If the annual life insurance premium rate (per $1000 of face value) is $5.38, what is the largest 15-year term policy he ca
buy without spending more than S800 annually?
If Justin, age 52, wants to pay no more than S800 a year in lite insurance. The largest 15-year term policy he ca buy without spending more than S800 annually is:$148,700
What is insurance?Insurance can be defined as the coverage that help to cover the cost or expense of those that enroll under the insurance plan.
Now let find the largest 15-year term policy he can buy using this formula
Largest 15-year term policy = Lite insurance amount / Annual life insurance premium × Face value
Let plug in the formula
Largest 15-year term policy = $800 / $5.38 × $1,000
Largest 15-year term policy = $148,698.9
Largest 15-year term policy = $148,700 (Approximately)
Therefore the Largest 15-year term policy is $148,700.
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Three students are participating in a walkathon. The data for each student is shown.
Student A: The equation y = 13x represents the amount of money raised (y) for walking (x) miles.
Student B: $36 is raised after walking 3 miles.
Student C:
Miles Walked 4 5
Money Raised $52 $65
Determine which student raised the least amount of money after walking 7 miles.
Student A
Student B
Student C
All three students raised the same amount of money after walking 7 miles.
The student C raised the least amount of money after walking 7 miles .
What is meant by mathematical equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
A mathematical sentence with an equals sign is referred to as an equation. It informs us that two expressions that represent the same number or have the same meaning are equivalent. Constants and variables can both be found in an equation. Equations allow us to quickly solve problems and express math facts in condensed, easy-to-remember forms.
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Find the value of x. Show all work.
Area of the rectangle is 30 sq. Ft
Answer:
The answer is 3 ft
Step-by-step explanation:
Given;Area of rectangle (A) = 30 sq ft.Length (l) = xWidth (w) = 3x + 1To Find;Value of xNow, we know that
A = l × w
30 = (x) × (3x + 1)
30 = 3x² + x
3x² + x = 30
3x² + x - 30 = 0
3x² - 9x + 10x - 30 = 0
3x(x - 3) + 10(x - 3) = 0
(x - 3) (3x + 10) = 0
x = 3 ft
Thus, The value of x is 3
For Verification Only ;
30 = (x) × (3x + 1)
30 = (3) × (3*3 + 1)
30 = 3 × 10
30 = 30
Hence, L.H.S = R.H.S
a standard deck of cards contains 52 cards with a total of 12 face cards, 3 from each suit. three cards are dealt from a well-shuffled deck with replacement. find the probability that the cards are not all face cards. choose the closest answer. group of answer choices
The probability that out of 52 card the selected 3 cards are not a face card is 0.183.
There are 12 face cards in a deck of 52 cards.
The probability of selecting 3 cards which should not be a face card is ,
=30c3 / 52c3
= 4060 / 22,100
= 0.183
Combination is a means to choose items from a collection without worrying about their order. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.
It is easy to count the number of combinations in smaller cases, but the likelihood of a set of combinations is also higher in cases with many groups of components or sets. As a result, a formula has been developed to determine the number of items that could be chosen, i.e., nCr .
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Compute 5/6(43)+1/2(43)+2/4(43)
The value of the equation A = 5/6(43) + 1/2(43) + 2/4(43) is A = 78.83 and the improper fraction of the number A = 473/6
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the value of the equation be A
Now , the equation A is given as
A = 5/6(43) + 1/2(43) + 2/4(43)
So , on simplifying the equation , we get
Taking 43 as the common term of the expression , we get
The value of A = 43 [ 5/6 + 1/2 + 2/4 ]
The value of A = 43 [ 5/6 + 1/2 + 1/2 ]
The value of A = 43 [ 5/6 + 1 ]
So , on further simplification , we get
The value of A = 43 [ 11/6 ]
So , the value of A is A = ( 43 x 11 ) / 6
The value of A = 473/6
The value of A in decimal form is A = 78.83
Therefore , the value of A is 78.83
Hence ,
The value of the equation A = 5/6(43) + 1/2(43) + 2/4(43) is A = 78.83
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Answer:70.83 I think..
Step-by-step explanation:
suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. what is the probability that the penny and nickel both come up heads?
The probability of the coins penny and nickel both should show heads when four coins flip simultaneously is equal to 1/4.
As given in the question,
Number of coins flip simultaneously = 4
Possible outcomes on flipping a outcome = { head , tail}
Total outcomes = 2
Probability of getting a head for each coin = 1 /2
Probability of getting heads on both the coins penny and nickel
= ( 1 / 2 ) × ( 1 / 2 )
= ( 1 / 4 )
Therefore, the probability of getting heads on both the coins penny and nickel is equal to 1 / 4.
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Janet is shopping for silver as an investment. At her local silver shop she is presented with two options: round coins and rectangular bars. She looks at the
prices for each.
●
The silver shop will sell her round silver coins according to the equation p=
27s which shows the relationship between s, the number of ounces of silver
she buys, and p. what she will pay for the round coins.
The silver shop will sell her rectangular silver bars but they are more popular
so she has to pay a premium to acquire the rectangular bars. The equation p
= 27.5s +50 shows the relationship between s, the number of ounces of
silver she buys, and p, what she will pay for the rectangular bars.
Janet intends to buy 40 ounces of silver at the silver shop. How much money will
she save by purchasing only round coins instead of rectangular bars?
Answer:
To determine how much money Janet will save by purchasing round coins instead of rectangular bars, we need to find the difference in cost between the two options.
First, we can find the cost of the round coins by plugging 40 ounces into the equation p=27s:
p = 27 * 40 = 1080
Next, we can find the cost of the rectangular bars by plugging 40 ounces into the equation p = 27.5s + 50:
p = 27.5 * 40 + 50 = 1100
The difference in cost between the two options is 1100 - 1080 = $<<1100-1080=20>>20. Therefore, Janet will save $20 by purchasing round coins instead of rectangular bars.
Step-by-step explanation:
SELF EXPLANATORY
a) 3-8=
b) -6-4=
c) -2 + 6 =
Answer:
A= -5
B= -10
c= 4
Step-by-step explanation:
hope this helps
Answer:
a) -5
b)-10
c) 4
Hope this helps!
a car is sold for $18,000. after one year, the value of the car is $11,700. write an exponential function y to determine the value of the car after x years if the rate of decrease is the same each year.
The exponential function that determines the value of the car after x years is y = 18000(0.65)ˣ. Here the rate of decrease is the same each year.
What is the exponential function?The exponential function is the function that gives the relationship between the input and the output with a rate of increase or decreases exponentially. It is given by the formula,
y = abˣ
Where 'a' is the initial value, 't' is the time, and 'b' is the rate. If b > 1, then the function is said to be the exponential growth function, and if b < 1, the function is said to be the exponential decay function.
Calculation:Given that, a car is sold for $18,000.
So, the initial value a = 18000.
After one year (x = 1), the value of the car is $11,700 i.e., y = 11700. So we can write the exponential function as
11700 = 18000(b)¹
⇒ b = 11700/18000 = 0.65
Since b < 1, the function is exponentially decaying.
Then, the value of the car after 'x' years is given by the exponential decay function as
y = 18000(0.65)ˣ
(It is given that, the rate of decrease is the same each year).
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How many solutions are there to the inequality x₁ + x₂ + x₃ ≤ 11, where x₁, x₂, and x₃ are nonnegative integers?
There are 66 solutions to the inequality x₁ + x₂ + x₃ ≤ 11, where x₁, x₂, and x₃ are nonnegative integers.
To solve this inequality, we must find all the possible combinations of nonnegative integers x₁, x₂, and x₃ that add up to 11 or less. This can be done by breaking down the problem into a series of nested loops. The outermost loop will iterate through all possible values of x₁, while the two inner loops will iterate through all possible values of x₂ and x₃ that add up to the remaining value of 11 minus x₁. We know that the maximum value of x₁ is 11, so the outermost loop will run from 0 to 11. For each value of x₁, the inner loops will run from 0 to (11 - x₁), incrementing by 1 each time. This will ensure that all possible combinations of x₂ and x₃ that add up to 11 minus x₁ are tested. Once we have all the combinations, we can count them to get the total number of solutions. In this case, there are 66 solutions to the inequality.
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-4(n-6)= 12
What is the value of n?
Step-by-step explanation:
-4(n-6)=12
-4n+24=12
-4n=-36
4n=36
n=36/4
Kurt was trying to factor a polynomial and was having trouble. He wondered if the polynomial could even be factored. He got frustrated and tore his paper up, throwing the pieces away, but one piece fell to the floor. On it, you were able to see that the polynomial ended with “ + 12” Using this, you decide to create a polynomial that cannot be factored.
Your polynomial must have three terms:
something with x2, something with x, and ending with + 12.
What is your polynomial?
How do you know that it cannot be factored?
The polynomial with constant term of 12 that cannot be factored is given as follows:
y = x² - 3x + 12.
It cannot be factored because it has a negative discriminant.
How to factor a quadratic equation?The standard definition of a quadratic equation is given as follows:
y = ax² + bx + c.
The discriminant determines if the function can be factored, and is given as follows:
D = b² - 4ac.
If the discriminant is negative, the function cannot be factored.
In this problem, the function is defined as follows:
y = ax² + bx + 12.
Attributing a = 1, the function is:
y = x² + bx + 12.
Then the coefficients are:
a = 1, c = 12.
It cannot be factored when:
D < 0
Hence:
b² - 4ac < 0.
b² < 48
|b| < 7.
Hence one possible case is when b = -3, giving the equation shown at the answer.
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Which of the following pair of linear equations are consistent or inconsistent x - y = 8, 3x - 3y = 16?
Answer:
the equations listed are inconsistent because the do not intersect or overlap.
Step-by-step explanation:
use the desmos graphing calculator website to graph the two equations. if they are parallel then they are inconsistent. if the cross or overlap then they are consistent
The figure shows two lines cut by a transversal. What value of x shows that the lines parallel? Show your work.
Value of x shows that the lines parallel is x=60°
What is transversal and parallel line?
In geometry, a transversal line intersects two lines in the same plane at two different locations. In the Euclidean plane, transversals help establish the parallelism of two or more other straight lines. It crosses two lines at separate locations. Transversal intersection results in numerous angles. These include co-interior angles, matching angles, alternate interior angles, and alternate exterior angles.If you stretch a set of lines indefinitely, they will remain parallel and never cross one other even though they are on the same plane. The symbol || represents the collection of parallel lines. All parallel lines are always equally spaced apart. Investigate the characteristics of parallel lines.When two lines in a plane are stretched endlessly in both directions and do not cross, they are said to be parallel. If two straight lines have separate y-intercepts and equal slopes, they are said to be parallel. A few significant parallel line attributes that accurately describe their features are shown below.From the figure attached we can se that ∠A+ 2x+10= 180°
and ∠B+x-10 =180°
and we know that the is transversal line so ∠A=x-10 & ∠B=2x+10
There fore x-10 +2x+10 =180 °
3x=180°
x=60°
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The diameter of a hat is 6.8 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
Answer:
21.35 inches
Step-by-step explanation:
You want to know the circumference of a hat that has a diameter of 6.8 inches.
CircumferenceThe circumference is given by ...
C = πd
C = 3.14 × 6.8 in = 21.352 in
C ≈ 21.35 in
The distance around the hat is about 21.35 inches.
<95141404393>
Carolina is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus $6 for each hour of work. Her total fee for a 4-hour job, for instance, is $32 Let y represent Carolina's fee (in dollars) for a single job that took x hours for her to complete.
Complete the equation for the relationship between the fee and number of hours.
The linear equation that models how much Carolina earns depending on the number of hours that she works is:
y = 6*x + 8
How to find the equation between the fee and the number of hours?
Here we know that for every mowing job, Carolina charges $6, plus an initial fee. So if that initial fee is b, we can write the equation as:
y = 6*x + b
We also know that for a 4 hours job she charges $32, then we can replace x by 4 and y by 32 in the equation above.
32 = 6*4 + b
32 = 24 + b
32 - 24 = b
8 = b
Then the linear equation we wanted to find is:
y = 6*x + 8
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Please answer this question ty
Answer:
m<1 = 45 M<2 = 135 M<3 = 45
Step-by-step explanation:
Answer: M<1 = 45, M<2 = 135, m<4 = 45
Step-by-step explanation:
Angles such as 1 to 4 and 2 to 3 have the same angle, so you take the total of 3 and 2 (270) and subtract it from 360 to to get the values of angles 1 and 4 combined. divide this in half to separate the two angles to get 45 degrees.
135+135=270
360-270=90
90/2=45
24+6k<-6(-4-k) please help me :(
inequality will not be use in the given expression.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
The given information,
24+6k<-6(-4-k)
24+6k < 24+6k
It's can be seen that both expressions are equal, but in the question, it is given that the inequality which is not valid.
Hence, inequality will not be use in the given expression.
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Create a binomial probability experiment with the data from the public opinion poll experiment. Use the probability of success and failure from the experiment. Calculate the probability of the number of successes in 100 random tests. For example, if the probability of success is 0.20 and the number of trials is 100, then the number of successes is 20.
Please give and answer my grade has never depended on something more. thank you.
Binomial probability distribution for the given set of data is
[tex]100C_x (0.20)^x (0.80)^{100-x}[/tex]
What is binomial probability distribution?
"Binomial probability distribution is the representation of a probability with only two outcomes success and failure under given number of trials."
Binomial probability distribution is given by
[tex]nC_x p^x q^{n-x}[/tex]
n= number of experiments
x = 0, 1, 2, 3,.......
p = probability of success
q = probability of failure
According to the given question
Number of trials 'n' = 100
Probability of success 'p' = (20 / 100)
= 0.20
Probability of failure 'q' = 1 - p
= 1 - (20/100)
= (80 / 100)
Substitute the value in the formula we get
Required probability = [tex]100C_x (0.20)^x (0.80)^{100-x}[/tex]
Example:
Tossing a coin 6 times getting exactly two heads.
Number of trials 'n' = 6
Number of heads 'x' =2
Only two possible outcomes head or tail
Probability of getting head 'p' = 1 / 2
Probability of not getting head 'q' = 1 /2
Required probability = [tex]6C_2[/tex] (1/2)²(1/2) ⁶⁻²
= [tex]6C_2\\[/tex] (1/2)⁶
Hence, binomial probability distribution for the given set of data is
[tex]100C_x (0.20)^x (0.80)^{100-x}[/tex]
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how do i solve 4( К-8 ) = -3+4к
Answer:
No solutions, there is nothing that will make the equation true
Step-by-step explanation:
You need to isolate the variable
4(K-8) = -3+4K
First get ride of the parenthesis by distributing
(4 x k) - (4 x 8) =-3+4k
4k-32 = -3+4k
next rearrange the equation to have the variable on only one side
4k-32 = -3+4k (subtract 4k from one side)
-32 = -3
The variables canceled out, leaving an equation. If the equation is true there are infinite equations while if the equation is false there are no solutions
-32 is NOT equal to -3, meaning there are no solutions
9. The population of a city increases by 25% each year, and that city's initial population is 1250. Which function provides a model for P(t), this city's population after t years? A. P(t) = 1250(25)* B. P(t) = 1250(0.25)* C. P(t) = 1250+ (25)* D. P(t) = 1250(1.25)* 1
The function that provides a model for the function p(t) for the population of a city is
D. P(t) = 1250(1.25)*tHow to write an exponential function to model the dataThe given problem is solved using, f(x) = a (b)^x
the starting = a
the base = b
the exponents = x
considering the given problem
p(t) = a (b)^t
a = 1250
rate, r = 25%
r = 25 / 100
r = 0.25
for increasing rate, b = 1 + r = 1 + 0.25 = 1.25
substituting known variables
p(t) = 1250 (1.25)^t
the equation that models the population of a city is p(t) = 1250 (1.25)^t
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What is the volume of the figure below if a = 9 units and b = 7 units?
A.
760.5 cubic units
B.
1,296 cubic units
C.
1,012.5 cubic units
D.
364.5 cubic units
Base (cube): [tex]V=s^3[/tex]
[tex]V=9\cdot9\cdot9=729[/tex]
Top (triangular prism): [tex]V=\frac{1}{2}bhl[/tex]
[tex]V = \frac{1}{2}(9\cdot7)\cdot9=283.5[/tex]
Together:
[tex]V = 729+283.5 =1012.5[/tex]
C.
1012.5 cubic units.
determine if a-1 c = c a–1 given
CA ⁻¹ is undefined because there are more columns in A ⁻¹ than there are rows in C.
What is matrix?A matrix is a numerical arrangement that is divided into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements. A matrix is a rectangular array of integers divided into rows and columns. Matrix A, for example, contains two rows and three columns. A matrix is a rectangular organization of a collection of integers into a defined number of rows and columns. When the elements are arranged in a matrix horizontally, it forms the rows of a matrix. When the elements are arranged in a matrix vertically, it forms the columns of a matrix.
CA⁻¹ is undefined because A⁻¹ contains more columns than rows in C.
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Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop. How much she make in a workweek if she sold $4,800 worth of merchandise?
The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.
How to calculate the value?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.
The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:
= $365 + (5% × $4800)
= $605
The amount is $605.
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an engineering research center claims that through the use of a new computer control system, automo- biles should achieve, on average, an additional 3 miles per gallon of gas. a random sample of 100 automo- biles was used to evaluate this product. the sample mean increase in miles per gallon achieved was 2.4, and the sample standard deviation was 1.8 miles per gallon. test the hypothesis that the population mean is at least 3 miles per gallon. find the p-value of this test, and interpret your findings.
The test is proved that hypothesis that the population mean is atleast 3-miles per gallon.
What is hypothesis?A hypothesis is the proposed explanation for any kind of phenomenon.
So here are the values of X BAR i=2.4. S is 1.8.
Our sample n =100.
The null hypothesis here is that mu is greater than or equal to 3.
Against the alternative hypothesis that is less than three. Now the calculated value for the test statistic is going to be the equal to X bar is in (-) knots. That's 2.4 -3. divided by S over 2^2 of end. So 1.8 divided by the square root of the 100 gives us negative 3.33. So we can refer to that box of the T distribution and we are get the value. The p value for the test is going to be less than 0.5. Therefore we have the strong evidence that the not hypothesis is going to be the read checked it. So therefore we can reject to the null hypothesis and then it can accept the alternative by the hypothesis that is less than three. Where it is here is the mean of the population, the noting the average increase per gallon.
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What is the value(s) of x in the equation below? Simplify if necessary.
x² +5=30
Answer: x=25
Step-by-step explanation:
x²+5=30
30-5=25
x²=25
[tex]\sqrt{x^2}=\sqrt{25}[/tex]
x=25
Answer:
x = -5 or 5
Step-by-step explanation:
1. subtract 5 from both sides
x^2 = 25
2. take the square root of both sides and remember to use positive and negative roots
x = ± 5
3. separate both solutions
x = -5 or x = 5
The purchase price of a large 4K LED TV, including finance charges, was $1230. A down payment of $300 was made, and the remainder was paid in 12 equal monthly installments. Find the monthly payment.
The monthly installment is $ 77.5. We have to divide the annual rate by 12 to find monthly installments.The number of equated monthly installment is equal to the number of month in the repayment tenure.
What is finance purchase charges?
A purchase finance charge is a fee applied to purchase a credit account like a credit card .This typically takes the form of an interest charge, although some accounts have may other terms.
How do we made monthly installment?The installment is generally in equal month payments that include interest and portion of the principle.We schedule to be created by the lender detailing payment throughout the loan duration.
By solving :
1230=300+12 x
1230-300=12 x
x= $ 77.5 monthly payment
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Write the equation of the circle with a radius of 10 and a center at (3,-1)
Answer:
[tex]\textsf{b)} \quad (x-3)^2+(y+1)^2=100[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Given:
center = (3, -1)radius = 10Substitute the given center and radius into the formula to create the equation of a circle with the given parameters:
[tex]\implies (x-3)^2+(y-(-1))^2=10^2[/tex]
[tex]\implies (x-3)^2+(y+1)^2=100[/tex]
there are 8 people participating in a focus group for a new software product related to the health system, 3 of them are software engineers, 2 of them are nurses, 1 of them is a doctor, and the remaining 2 people are technicians. in how many ways they can be seated in a row so that no two software engineers are together?
Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.
What is combination?An alternative name for a combo is a choice. A combination is a choice made from a predetermined group of options. I won't organize anything here. They will be my choice. The number of distinct r selections or combinations from a set of n objects is indicated by the symbol [tex]^nC_{r}[/tex].
There are eight participants in the focus group, including three software engineers, two nurses, one doctor, and two technicians.
So the 3 software engineers =3! ways, 2 nurses =2! ways,
doctor =1! way , 2 technicians =2! ways.
We must determine how many different configurations are possible so that no two pieces of software may coexist.
In order to prevent two software engineers from being seated next to each other, we first arrange five persons in a row with a space between them.
[tex]We get that in 6 places they can sit in ^6C_{3} ways\\ xi.e ^6C_3 = 20 (by formula of combination)\\ Therefore total ways are,6 X 2 X 1 X2 X 20 = 480.[/tex]
Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.
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