Answer:
x = −2.4
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Exact Form: x = −12/5
Decimal Form: x = −2.4
The difference of the product of 10 and x and the product of 6 and y is -8. The sum of the product of -5 and x and the product of 3 and y is -1. What are the values of x and y
The system of equations is inconsistent, meaning there is no solution for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfies both equations simultaneously.
The given information can be translated into equations:
1. "The difference of the product of 10 and (x) and the product of 6 and y is -8":
[tex]\[10x - 6y = -8\][/tex]
2. "The sum of the product of -5 and x and the product of 3 and y is -1":
[tex]\[-5x + 3y = -1\][/tex]
Now, we have a system of two equations with two variables:
[tex]\[ \begin{cases} 10x - 6y = -8 \\ -5x + 3y = -1 \end{cases} \][/tex]
Let's solve this system step by step:
Step 1: Eliminate one variable from one of the equations.
Multiply the second equation by 2 to make the coefficients of [tex]\(y\)[/tex] in both equations opposites:
[tex]\[ \begin{cases} 10x - 6y = -8 \\ -10x + 6y = -2 \end{cases} \][/tex]
Now, add the two equations to eliminate [tex]\(y\)[/tex]:
[tex]\[ 0 = -10 \][/tex]
The result is a contradiction, indicating that the system is inconsistent. This means there is no solution that satisfies both equations simultaneously.
Conclusion:
The system of equations is inconsistent, meaning there is no solution for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfies both equations simultaneously. The given information might contain an error or contradiction. Please double-check the equations and conditions provided.
A home security system is designed to have a 99% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. Find the probability that eight or fewer alarms are triggered.
Answer:
0.0865
Step-by-step explanation:
Binomial Problem with n = 9 and p(triggered) = 0.99
And the photo below is the full answer,
I could not insert the fomula and hope it will find you well.
Which of the following equations represents the line with a slope of 5/2 and a y-intercept of 1?
y = 5/2x + 1
y = 2/5x - 1
y = 2/5x + 1
y = 5/2x - 1
Answer:
[tex]y = \frac{5}{2} x + 1[/tex]HOPE U UNDERSTOOD
MARK AS BRAINLIEST ONE
Any doubts? please COMMENT
Jane invested $2500 into an RRSP that earned interest at 6% compounded semi annually for ten years a) find the balance of account at end of peroid b)how much interest is earned c) what is effective rate of interest
Answer:
Step-by-step explanation:
PV = $2500
r = 6%
Compounded semi annually for ten years => number of periods: 10*2 = 20
a. the balance of account at end of peroid (FV)
FV = PV [tex](1+r)^{n}[/tex] = 2500[tex](1+0.06)^{20}[/tex] = 8017.8386
b. How much interest is earned; FV - PV = 8017.8386 - 2500 = 5517.8686
c. what is effective rate of interest :
Answer:
The answers to the question are
a) The balance of account at end of period $4515.278
b) The interest earned $2515.278
c) The effective rate of interest is 0.0609 or 6.09 %
Step-by-step explanation:
To solve the question
a) Here we have the compound interest formula given by
[tex]A = P(1+\frac{r}{n})^{nt}[/tex] Where,
P = Initial investment = $2500
r = Annual interest rate = 6% =0.06
n = Number of compounding periods per year = 2
t = Number of years 10
From which we have
[tex]A = 2500*(1+\frac{0.06}{2})^{2*10}= 2500(1.03)^{20}[/tex] = $4515.278
The balance of account at end of period $4515.278
b) Interest earned = Balance - initial investment = $4515.278 - $2500 = $2515.278
c)
The effective interest rate is the interest rate that accrues to an investment or loan as a result of the compounding the interest for a given time period of time. It is also known as the effective annual interest rate
The effective rate of interest is given by
Effective rate = [tex](1+\frac{r}{n} )^n -1[/tex]Where
r = Annual interest rate
n = Number of annual compounding periods
this gives [tex](1+\frac{0.06}{2} )^{2} -1[/tex] = 0.0609 = 6.09 %
HELP PLEASE!
Solve the system of equations
[tex]\left \{ {x+4y=-2} \atop {-5x+5y=10}} \right.[/tex]
Answer: x = - 2
y = 0
Step-by-step explanation:
The given system of linear equations is expressed as
x + 4y = - 2 - - - - - - - - - - - - - 1
- 5x + 5y = 10- - - - - - - - - - - - - 2
We would eliminate x by multiplying equation 1 by 5 and equation 2 by 1. It becomes
5x + 20y = - 10
- 5x + 5y = 10
Adding both equations, it becomes
25y = 0
Dividing both sides by 25, it becomes
y = 0/25 = 0
Substituting y = 0 into equation 1, it becomes
x + 4 × 0 = - 2
x = - 2
The system of equations have only one solution.
Kristen bought a Home Theater for $750 and rented movies every month. The cost of each rental is $4.49 and the membership charges are $12/month. Which equation gives the total amount, A, she spent during the first six months on the number of rented movies, r, including the cost of the Home Theater?
Answer:
A = $822 + $4.49r
Step-by-step explanation:
The question asks to know the equation that describes how much spent in the first six months and also the cost of the home theater.
Firstly, the equation asks to represent the total amount spent by A. She spent $4.49 per rental and made a total of r rentals in the first six months, thus, the total amount of money she spent on rentals is thus 4.49 * r = $4.49r. Now, she also spends $12/month as membership charges. The total membership charges in the first 6 months is thus 6 * 12 = $72
Lastly, she bought the home theater itself $750. Thus, the total amount of money spent A is $750 + $72 + $4.49r
This translates to $822 + $4.49r
In equation form, A = $822 + $4.49r
At a banquet, the ratio of the number of boys to the number of girls is 5 : 3. 20 boys leave and the ratio becomes 5 : 4. How many girls are at the banquet?
Answer:
There are 48 girls at the banquet
Step-by-step explanation:
Let the number of boys =x
Let the number of girls=y
Ratio Of boys to girls=5:3
Therefore, x:y=5:3......(1)
If 20 boys leave, the ratio becomes 5:4
Sine number of boys=x
If 20 boys leave, new number = x-20
Therefore, x-20:y=5:4......(2)
From (1),
3x=5y
From Equation (2),
4(x-20)=5y
Therefore: 3x=4x-80
x=80
From (1),
3x=5y
5y=3X80
y=240/5=48
Therefore, there are 48 girls at the banquet
Kate Alexander worked 40 hours last week. Her pay rate is $8.50 per hour. Assuming 7.65% social security withholding, how much should her employer withhold from her check for social security? a) 0.65 b) 6.50 c) 2.60 d) 26.01
Answer:
Her employer should withhold from her check for social security is d) 26.01
Step-by-step explanation:
Given:
Kate Alexander worked 40 hours last week. Her pay rate is $8.50 per hour. Assuming 7.65% social security withholding.
Now, to find the amount her employer should withhold from her check for social security.
Total number of hours = 40.
Pay rate per hour = $8.50.
Now, the total amount of total number of hours she worked in accordance of her pay rate:
[tex]40\times 8.50\\\\=\$340.[/tex]
Social security withholding = 7.65%.
So, to get the amount of social security withholding:
[tex]7.65\%\ of\ \$340[/tex]
[tex]=\frac{7.65}{100} \times 340[/tex]
[tex]=\frac{2601}{100}[/tex]
[tex]=\$26.01.[/tex]
The amount of social security withholding is $26.01.
Therefore, her employer should withhold from her check for social security is d) 26.01
Graph the function g(x)= -3/(x^2-4) . What is the domain of g(x)? Explain your reasoning. Do not completely trust calculator or computer graphs of this function.
can anyone help
Answer:
Find where the expression [tex]\frac{3}{(x+2)(x-2)}[/tex]
is undefined.
List all of the vertical asymptotes:
[tex]x=2, -2[/tex]
This is what your graph would look like:
PLEASE HELP ME, IF CORRECTLY ANSWERED I’LL GIVE BRAINLIEST
Answer:
c=f(x)−ax^2−bx
Step-by-step explanation:
Answer:
C=1
Step-by-step explanation:
Put the first point in the equation y=ax^2+bx+c where x=0 and y=1 you get
1=a*0+b*0+c
1=c
Most evenings after dinner Duarte spends 30 3030 minutes playing chess with his dad. Write an equation for the number of minutes, m mm, that Duarte spent playing chess with his dad if they played chess together e ee evenings
Answer:
im sorry but that question makes o sense
Step-by-step explanation:
A pair of children shoes comes in a box that measures 10.2 cm x 15 cm x 8 cm what is the volume of a shoebox A pair of children shoes comes in a box that measures 10.2 cm x 15 cm x 8 cm what is the volume of a shoebox
Answer:
1224 cm^3
Step-by-step explanation:
The shape of the box is a rectangular prism.
The volume of a rectangular prism is given by the formula below.
volume = length * width * height
volume = 10.2 cm * 15 cm * 8 cm
volume = 1224 cm^3
Final answer:
The volume of a shoebox with dimensions 10.2 cm x 15 cm x 8 cm is calculated by multiplying these three dimensions together, resulting in a volume of 1224 cm³.
Explanation:
To calculate the volume of a shoebox, you multiply its length by its width by its height. For a shoebox with dimensions of 10.2 cm, 15 cm, and 8 cm, the calculation would look like this:
Volume = Length × Width × Height
Volume = 10.2 cm × 15 cm × 8 cm
Volume = 1224 cm³
Therefore, the volume of the shoebox is 1224 cubic centimeters.
Faith and Shawna are shopping for shirts. The available styles are short sleeve (s), tank top (t), and long sleeve (L). they make a list to show all possible outcomes if each girl buys a new shirt. is the list complete? Explain. (s,t), (s,s), (s,L), (T,T), (T,S), (T,L), (L,L), (L,T), (L,S)
Answer:
The number of ways of selection of 3 items taking 2 at a time in addition to the possible ways in which each girl selects the same style is 9 different ways. Since the list contains 9 different ways in which each of them can select a style, the list is complete.
Step-by-step explanation:
Here we have the number of ways the available styles can be arranged between each girl is given by the number of permutation of 3 items, taking two at a time plus the number of possible selections where both of them select the same style as follows
We note that the formula for permutation is
[tex]_n[/tex]P[tex]_r[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]
Therefore ₃P₂ = [tex]\frac{3!}{(3-2)!}[/tex] = 6 different ways
The number of possible selections where both of them select the same style is given by
(T, T), (s, s), (L, L) = 3 different ways
Total number of ways = 6 + 3 = 9 ways
Number of different ways available in the list = 9 ways
Therefore the list is complete
According to the journal of irreproducible results, any obtuse angle is a right angle! c d b p here is their argument. given the obtuse angle x, we make a quadrilateral abcd with \dab = x, and \abc = 90 , and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = p
d. so the triangles p ad and p bc have equal sides and are congruent. thus \pad = \pbc. but pab is isosceles, hence \pab = \pba. subtracting, gives x = \pad \pab = \pbc \pba = 90 . this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?
Answer:
The mistake stems from the assumption that angle dab and abc are both 90 and ad = bc and that the perpendicular bisector of dc is different from the perpendicular bisector to ab because they are the same and abcd is a rectangle.
Step-by-step explanation:
If ∡dab = ∡abc and side ab is equal to side bc which are opposite sides, ten then ab is parallel to bc which means the quadrilateral is parallelogram. Also since two angles of the four angles of the parallelogram are 90 degrees then the parallelogram is a rectangle.
The bisector of one side of a rectangle will also bisect the opposite side of the rectangle. Therefore the bisector of dc is the same as the bisector of ab and it meets ab at the midpoint of ab. Therefore p is now at the midpoint of ab and there are no triangles pad and pbc.
Death Valley CA is 282 feet below sea level. Black Mountain, KY is 750 feet above sea level . How many more feet above sea level is Black Mountain than Death Valley?
From the Death Valley to Black Mountain, it rises 1032 feet because Death Valley is 1032 ft lower than Black Mountain in elevation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
Death Valley CA is 282 feet below sea level.
Black Mountain, KY is 750 feet above sea level.
Death Valley (282ft) + 282ft = sea level (0).
0 + 750ft = Black Mountain (750ft).
282ft + 750ft = 1032ft.
From Death Valley to Black Mountain, it rises 1032 feet. Death Valley is 1032 ft lower than Black Mountain in elevation.
Thus, from the Death Valley to Black Mountain, it rises 1032 feet because Death Valley is 1032 ft lower than Black Mountain in elevation.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
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one pipe fills a store pool in 12 hours. A second pipe fills the same pool in 6 hours. When a third pipe is added and all three are uset otill the pool, it only takes 3 hours. Find how long it takes the third pipe to do the job
Answer:
x = 12 hours
Step-by-step explanation:
If one pipe fills store pool in 12 hours in 1 hour will fill 1/12 of the pool
If one pipe fills a store pool in 6 hours in 1 hour will fill 1/6 of the pool
Let call " x " number of hours needed by the third pipe to fills the pool
then in 1 hour will fill 1/x
The three pipes working together in 1 hour will fill
1/12 + 1/6 + 1/x
Now we know that the three pipes take 3 hours to fill the pool then in 1 hour three pipes will fill 1/3 of the pool, therefore
1/12 + 1/6 + 1/x = 1/3
( x + 2*x + 12) /12*x = 1/3 ⇒ ( 3*x +12 )/ 12*x = 1/3
9*x + 36 = 12*x
- 3*x = - 36
x = 36/3
x = 12 hours
Final answer:
The third pipe, when operating alone, takes 12 hours to fill the pool. This is found by calculating the combined rate of the first two pipes, then the rate of all three, and deducting to find the third pipe's alone rate.
Explanation:
The question asks how long it takes for a third pipe to fill a pool when utilized alongside two other pipes, where one fills the pool in 12 hours, another in 6 hours, and all three together in 3 hours. This is a rate of work problem, commonly encountered in algebra and practical mathematics. To solve, we first find the rates at which each individual pipe fills the pool and then calculate the third pipe's rate.
Determine the rate at which each pipe fills the pool. The first pipe fills the pool at a rate of 1/12 of the pool per hour, and the second at 1/6 of the pool per hour.
Add these rates to determine the combined rate when the two pipes are working together: (1/12) + (1/6) = 1/12 + 2/12 = 3/12 = 1/4. So, the two pipes fill the pool at a rate of 1/4 of the pool per hour together.
When the third pipe is added, all three fill the pool in 3 hours, which means their combined rate is 1/3 of the pool per hour. The rate of the third pipe alone can be found by subtracting the rate of the first two pipes from this combined rate: (1/3) - (1/4) = 4/12 - 3/12 = 1/12.
Therefore, the third pipe fills the pool at a rate of 1/12 of the pool per hour on its own. To find the time it takes for the third pipe to fill the pool by itself, we take the reciprocal of its rate, resulting in 12 hours.
4 game dice have been rolled out. Find the probability that all of the same points will drop.
please
Answer:
1/216
Step-by-step explanation:
n{1111,2222,3333,4444,5555,6666}=6
number of every cases =6×6×6×6
6/6^4=1/6^3=1/216
Answer:
1/216.
Step-by-step explanation:
The probability that all the 4 dice will show a 1 = (1/6)^4.
There are also 5 other possible outcomes: 4 2's , 4 3's etc.
So the required probability = 6 * (1/6)^4
= 6 * 1/1296
= 1/216.
A parabola can be drawn given a focus of ( 6 , − 5 ) (6,−5) and a directrix of y = 1 y=1. Write the equation of the parabola in any form. -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12
Answer:
y = -(1/12)(x -6)² -2
Step-by-step explanation:
The vertex of the parabola is halfway between the focus and the directrix, so has y-coordinate (-5+1)/2 = -2. The difference in the y-coordinates between the focus and the vertex is ...
p = -5 -(-2) = -3
An equation of the parabola with vertex (h, k) and focus-vertex distance p can be written:
y = 1/(4p)(x -h)² +k
For (h, k) = (6, -2) and p = -3, the equation is ...
y = (-1/12)(x -6)² -2
g A group of people were asked if some psychics can help solve murder cases. 175 responded "Yes", and 474 responded "To". Find the probability that if a person is chosen at random, the person believes some psychics can help solve murder cases.
Answer:
0.2696
Step-by-step explanation:
Number of People who responded Yes=175
Number of People who responded No=474
Total Number of Respondents=175+474=649
We want to determine the Probability that a person chosen at random believes that psychic can help solve murder cases.
Now,
[TeX]Probability=\frac{Number of Possible Outcome}{Total Number of Outcomes}[/TeX]
Number who believe psychic can help solve murder cases=175
Total Number=649
Therefore:
P(a person chosen at random person believes some psychics can help solve murder cases) = [TeX]\frac{175}{649}=0.2696[/TeX]
Final answer:
The probability that a randomly chosen person believes some psychics can help solve murder cases is 175 divided by the total number of respondents (649), resulting in approximately 26.96%.
Explanation:
The question asks for the probability that a chosen person believes some psychics can help solve murder cases, given that out of a group, 175 said 'Yes' and 474 said 'No'. To find this probability, divide the number of people who believe psychics can help (175) by the total number of people asked (175 + 474).
Steps to Calculate the Probability:
Calculate the total number of responses: 175 (Yes) + 474 (No) = 649.
Calculate the number of positive responses (people who believe psychics can help): 175.
Divide the number of positive responses by the total number of responses: Probability = 175 / 649.
Perform the division to get the probability.
Therefore, the probability that a person chosen at random believes some psychics can help solve murder cases is 175/649 or approximately 0.2696, which can be expressed as 26.96%.
Multiply.
−3y(5y3+11y2−y+8)
Express the answer in standard form.
Final answer:
The result of multiplying −3y by the polynomial (5y³+11y²−y+8) is −15y⁴ − 33y³ + 3y² − 24y when expressed in standard form.
Explanation:
To multiply the expression −3y(5y³+11y²−y+8), we will distribute the −3y across each term inside the parentheses. The process involves the use of the distributive property, often also known as the multiplication of polynomials. Here are the steps:
Multiply −3y by 5y³ to get −15y⁴.
Multiply −3y by 11y² to get −33y³.
Multiply −3y by −y to get 3y².
Multiply −3y by 8 to get −24y.
Combining all these products gives us the expression in standard form:
−15y⁴ − 33y³ + 3y² − 24y
Local phone numbers consist of seven numerals, the first three of which are common to many users. A small town's phone numbers all start with 313, 359, or 387. How many phone numbers are available?
Answer:
30,000 phone numbers.
Step-by-step explanation:
If the first three numbers are already defined then it means that only the other 4 digits remain to be defined.
The solution would be the number of numbers between 0000 and 9999, because the order here matters, since each number is different.
Therefore between these two numbers there are a total of 10,000 numbers, that is to say that for each of the three initial numbers there are 10,000 numbers, therefore in the town there are a total of 30,000 numbers.
Final answer:
The small town has 30,000 available telephone numbers.
Explanation:
To calculate the number of available telephone numbers in the small town, we need to consider that local phone numbers have seven digits, with the first three being the telephone exchange numbers. The town uses three different telephone exchanges: 313, 359, and 387. Since the last four digits of a phone number can range from 0000 to 9999, that means there are 10,000 possible combinations for the last four digits.
Since there are three possible telephone exchanges, each with 10,000 combinations for the remaining four digits, we calculate the total number of available phone numbers by multiplying the number of exchanges by the number of combinations per exchange:
Number of exchanges x 10,000 (combinations per exchange) = Total number of phone numbers
3 x 10,000 = 30,000
Therefore, the small town has 30,000 available telephone numbers.
Diedre drew a quadrilateral with 4 right Angles and opposite sides of the same length. Name all the kinds of polygons that could be Diedre's quadrilateral.
Answer:
The answer to the question is
The kinds of polygons that could be Diedre's quadrilateral are rectangle and square
Step-by-step explanation:
We note the conditions of the polygon as thus
Number of sides = 4, Which include trapezoid, square, rectangle
Size of angles = 90 ° which eliminates trapezoid
Sizes of opposite sides = Equal opposite sides, includes square and rectangle
With the above we conclude that the possible polygons in Diedre's quadrilateral are rectangle and square
The vector r = xˆi + y ˆj + zkˆ, called the position vector points from the origin (0, 0, 0) to an arbitrary point in space with coordinates (x, y, z). Use what you know about vectors to prove the following: All points (x, y, z) that satisfy the equation Ax + By + Cz = 0, where A, B, and C are constants, lie in a plane that passes through the origin and that is perpendicular to the vector Aˆi + Bˆj + Ckˆ. Sketch this vector and the plane.
Answer:
The vectors r and p = Aˆi + Bˆj + Ckˆ are perpendicular between them. Thus, the plane equation come from the fact that the dot product is equal to zero.
Step-by-step explanation:
The dot product of r and p
r*p = (xˆi + y ˆj + zk)*(Aˆi + Bˆj + Ckˆ) = Ax + By + Cz = 0
For married couples living in a certain suburb, the probability that the husband willvote on a bond referendum is 0.21, the probability that his wife will vote in thereferendum is 0.28, and the probability that both the husband and wife will vote is0.15. What is the probability that:
Answer:
niglgapopfart
Step-by-step explanation:
12(5)6$78$???98
Of the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the bread-slicing machine, and 15 can use both machines. If one member of the crew is to be chosen at random, what is the probability that the member chosen will be someone who cannot use either machine?
Step-by-step explanation:
The total number of members in the crew = 20
The number of people able to use meat machine = 17 ⇒n (M) = 17
The number of people able to use bread machine = 18 ⇒n (B) = 18
The number of people able to use both machine = 15 ⇒n (M∩B) = 15
Now, a person is chosen at random:
Let us assume the number of people who cannot use either machine = K
Now,as we know:
[tex]n(A\cup B) = n(A) + n(B) - n(A\cap B)[/tex]
So, the number of people who can use either of the machines
=n (M) + n(B) - n(M∩B) = 17 + 18 - 15 = 20
So, there are 20 people who can use either of the two machines.
Also, as given the total number of people in the crew = 20.
Hence, from the above statement it is clear that there exists no person who can not use either of the machines.
So, such probability = 0
Nick likes to use 12 of a chocolate bar to make a s'more Tasha will only eat a s'more that is made with exactly 25 of a chocolate bar what fraction of a chocolate bar will nick and Tasha use in total if they each eat one s'more
Question:
Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mores, their favorite campfire dessert. Each of them has a different recipe for their perfect s’more. Nick likes to use 1/2 of a chocolate bar to make a s’more. Tasha will only eat a s’more that is made with exactly 2/5 of a chocolate bar.
Answer:
The fraction of a chocolate bar will Nick and Tasha will use in total if they each eat one s'more is [tex]\frac{9}{10}[/tex] bar.
Step-by-step explanation:
Here, we are meant to learn how to add fractions and to know about the essence of a common denominator
The portion of the chocolate that Nick makes an s'more with is 1/2
The portion of the chocolate that Tasha makes an s'more with is 2/5
Therefore the fraction of the chocolate bar Nick and Tasha use in total if they each eat one s'more is 1/2 + 2/5
Where [tex]\frac{1}{2}[/tex] + [tex]\frac{2}{5}[/tex] multiplying the fraction [tex]\frac{1}{2}[/tex] by [tex]\frac{5}{5}[/tex] and [tex]\frac{2}{5}[/tex] by [tex]\frac{2}{2}[/tex] wee have
[tex]\frac{5}{5}[/tex]× [tex]\frac{1}{2}[/tex] + [tex]\frac{2}{2}[/tex]× [tex]\frac{2}{5}[/tex] = [tex]\frac{5}{10}[/tex] + [tex]\frac{4}{10}[/tex] = [tex]\frac{9}{10}[/tex] bar
Therefore the fraction of the chocolate bar that would be left is
1 bar - [tex]\frac{9}{10}[/tex] bar = [tex]\frac{1}{10}[/tex] bar.
Here is the complete question
Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mores, their favorite campfire dessert. Each of them has a different recipe for their perfect s’more. Nick likes to use 1/2 of a chocolate bar to make a s’more. Tasha will only eat a s’more that is made with exactly 2/5 of a chocolate bar.
Answer:
Both Nick and Tacha will use 9/10 of the chocolate bar
Step-by-step explanation:
Nicks share of the chocolate bar is 1/2(fraction of the chocolate bar need to make the s'more
And Tasha requires 2/5 to make her own s'more.
Then if both of them share a single chocolate bar,then it will be:
2/5(Tasha's share) + 1/2(Nick's share)
= 9/10 of a single chocolate bar will be used.
In case they were interested to know the amount remaining, it will be:
1 - 9/10 = 1 1/10
A family has a rectangular back yard that measures 5x+4 by 3x-2 they are building a square patio with side lengths that measure x+3. write an expression for the area of grass that will be left in the back yard after the patio is built. show your work.
Answer: 14x² - 4x - 17
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
The rectangular back yard measures 5x + 4 by 3x - 2. This means that the area of the rectangular back yard would be
Area = (5x + 4)(3x - 2)
Area = 15x² - 10x + 12x - 8
= 15x² + 2x - 8
The formula for determining the area of a square is expressed as
Area = length²
Length of square patio = x + 3
Area of square patio = (x + 3)(x + 3)
= x² + 3x + 3x + 9
= x² + 6x + 9
The expression for the area of grass that will be left in the back yard after the patio is built is
15x² + 2x - 8 - (x² + 6x + 9)
= 15x² + 2x - 8 - x² - 6x - 9
= 15x² - x² + 2x - 6x - 8 - 9
= 14x² - 4x - 17
Which statement is true? Use the diagram to answer.
Select one:
a. are alternate interior angles.
b. are same-side interior angles.
c. are alternate interior angles.
d. are same-side interior angles.
The statement that is: a. ∠1 and ∠5 are alternate interior angles.
What is the alternate interior angles ?
A pair of angles that are inside the two parallel lines and on opposing sides of the transversal line are known as alternate internal angles. 1 and 5 are situated on opposite sides of the transversal line and inside the parallel lines in the diagram. They are thus different internal angles.
The fact that alternate inner angles have the same measure and are congruent is significant.
Therefore the correct option is A.
A company has 8 cars and 11 trucks.The state inspector will select 3 cars and 4 trucks to be tested for safety inspections in how many ways can this be done
Answer:
Number of ways to select 3 cars and 4 trucks = 18,480
Step-by-step explanation:
Let x be the number of ways to select 3 cars and 4 truck.
Given:
Total number of cars = 8
Total number of Trucks = 11
We need to find out how many ways can the inspector select 3 cars and 4 truck.
Solution:
Using combination formula.
[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
Where, n = Total number of object.
m = Number of selected object.
We need to find out how many ways can the inspector select 3 cars and 4 truck from 8 cars and 11 trucks.
So, we write the the combination as given below.
[tex]8C_{3}\times 11C_{4} = Number\ of\ ways\ to\ selection[/tex]
[tex]\frac{8!}{3!(8-3)!} \times \frac{11!}{4!(11-4)!}= x[/tex]
[tex]x = \frac{8\times 7\times 6\times 5!}{3!\times 5!} \times \frac{11\times 10\times 9\times 8\times 7!}{4!\times 7!}[/tex]
Factorial 5 and 7 is cancelled.
[tex]x = \frac{8\times 7\times 6}{6} \times \frac{11\times 10\times 9\times 8}{24}[/tex] ([tex]3! = 6\ and\ 4! = 24[/tex])
[tex]x = (8\times 7) \times (11\times 10\times 3)[/tex] ([tex]\frac{9\times 8}{24}=\frac{72}{24}=3[/tex])
[tex]x=56\times 330[/tex]
x = 18480
Therefore, the Inspector can select 3 cars and 4 trucks in 18,480 ways,
To determine how many ways the state inspector can select 3 cars from 8 and 4 trucks from 11, we need to calculate the combinations separately for each type of vehicle and then multiply them together to find the total number of ways to make both selections simultaneously.
### Selection of Cars:
The number of ways to choose 3 cars from 8 is a combination problem, because the order in which we select the cars does not matter. The formula for combinations, denoted as C(n, k), where n is the total number of items to choose from, and k is the number of items to be chosen, is given by:
C(n, k) = n! / (k! * (n - k)!)
Let's apply this formula to select 3 cars from 8:
C(8, 3) = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!) = (8 × 7 × 6) / (3 × 2 × 1)
Simplify the factorials by canceling out common terms:
C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = (8/2) × (7/1) × (6/3) = 4 × 7 × 2 = 56
So, there are 56 ways to choose 3 cars out of 8.
### Selection of Trucks:
Similarly, to choose 4 trucks out of 11 we use the combination formula again:
C(11, 4) = 11! / (4! * (11 - 4)!) = 11! / (4! * 7!) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1)
Simplify the factorials:
C(11, 4) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1) = (11/1) × (10/2) × (9/3) × (8/4) = 11 × 5 × 3 × 2 = 330
So, there are 330 ways to choose 4 trucks out of 11.
### Total Ways:
To find the total number of ways to select both the cars and trucks for inspection, we multiply the number of ways to choose the cars by the number of ways to choose the trucks:
Total number of ways = number of ways to choose cars × number of ways to choose trucks
Total number of ways = 56 (from choosing cars) × 330 (from choosing trucks)
Total number of ways = 56 × 330 = 18480
Therefore, the state inspector can select 3 cars out of 8 and 4 trucks out of 11 in 18,480 different ways.
Am I correct for the following questions? because I'm not sure if I am.
If not what are the correct choices?
Which of the lines are parallel?
(1) a and b
(2) a and c
(3) a and D
(4) b and c
(5) b and D
(6) c and D
Which of the lines are perpendicular?
(1) a and b
(2) a and c
(3) a and D
(4) b and c
(5) b and D
(6) c and D
Please show all the work on how you got your answers
Answer:
The answer to your question is C and D are parallel
B and C and B and D are perpendiculars.
Step-by-step explanation:
Data
Line A (-2, 3) (2, 2)
Line B (-3, 0) (3, -2)
Line C (2, 4) (0, -2)
Line D (0, 6) (-2, 0)
Process
1.- Calculate the slope of each line
m = (y2 - y1)/(x2 - x1)
Line A m = (2 - 3) / (2 + 2)
m = -1/4
Line B = (-2 - 0) / (3 + 3)
= -2/6
= -1/3
Line C = (-2 -4)/(0 - 2)
= -6/-2
= 3
Line D = (0 - 6) / (-2 - 0)
= -6/-2
= 3
2.- Conclusion
If the slopes are the same, the lines are parallel if are reciprocal, the lines are perpendicular
Line C ║ Line D
Line B ⊥ Line C and Line B ⊥ Line D