Answer:
ab - a - b + 1 = (a - 1)(b - 1)
Step-by-step explanation:
Let us explain factorization by grouping
In the expression of 4 terms ax + by + bx + ay
Take every two terms have a common factor in a bracket
(ax + ay) + (bx + by)Take the common factor out of the brackets
a(x + y) + b(x + y)Take the bracket as a common factor
(x + y)(a + b)Let us do these steps with our question
∵ ab - a - b + 1 is an expression of 4 terms
→ Take ab and a in a bracket, -b and 1 in another bracket
∴ ab - a - b + 1 = (ab - a) + (-b + 1)
→ Take a as a common factor from the 1st bracket and -1 from
the 2nd bracket
∴ (ab - a) + (-b + 1) = a(b -1) + -1(b - 1)
→ Take the bracket (b - 1) as a common factor
∴ a(b -1) + -1(b - 1) = (b - 1)(a + -1)
∵ (+)(-) = (-)
∴ (b - 1)(a + -1) = (b - 1)(a -1)
→ Change the order of the bracket
∴ (b - 1)(a -1) = (a - 1)(b - 1)
∴ ab - a - b + 1 = (a - 1)(b - 1)
4 people equally share 2/3 of a pizza. How much of the pizza does each person eat?
Answer:
3/16
Step-by-step explanation:
Savannah sells character images online. Small images take one hour to make and she sells them for $15. Large images sell for $25 and take two hours to make. Each week, Savannah can work up to 20 hours making images, and she wants to earn at least $400.
Let x represent the number of small images Savannah makes in a week, and let y represent the number of large images. Which of the following systems of inequalities models the constraints of this situation?
Answer:
15x + 25y ≥ 400
x + 2y ≤ 20
x ≥ 0, y ≥ 0
Step-by-step explanation:
Here, we are modelling the total number of hours she can use in making images in a week and the total amount that can be earned in a week, considering the given constraints.
Number of small images in a week = x
Number of hrs in making images if it takes 1 hr to make 1 = 1*x = x
Number of large images in a week = y
Number of hrs in making large images if it takes 2 hrs to make 1 = 2*y = 2y
Given that she has up to 20 hrs to make the images, therefore, the inequality that models this situation would be:
x + 2y ≤ 20
This implies that, the hours spent altogether can be less than or equal to 20hrs
Amount for small images = $15
Amount in total for all images made in a week = $15*x = 15x
Amount for large images = $25
Amount in total for all images made in a week = $25*y = 25y
Given that she can earn AT LEAST $400 in a week, therefore, the inequality that models this situation would be:
15x + 25y ≥ 400
This implies that, the amount she wants to make in a week would be $400 or more.
The system of inequalities would be:
x + 2y ≤ 20
15x + 25y ≥ 400
x ≥ 0, y ≥ 0
A 2 3/4 inch candle burns down in 11 hours. At what rate does the candle burn, in inches per hour?
Answer:
1/4 or or 0.25
1Step-by-step explanation:
just do 2.75 divided by 11 and you get your answer
At rate 0.25 inch per hour the candle burn.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
A 2 3/4 inch candle burns down in 11 hours.
Now,
Since, A 2 3/4 inch candle burns down in 11 hours.
Hence, The rate in which the candle burn, in inches per hour is;
= [tex]2 \frac{3}{4}[/tex] ÷ [tex]11[/tex]
= 11/4 ÷ 11
= 11/4 x 1/11
= 1/4 inches per hour.
Thus, At rate 0.25 inch per hour the candle burn.
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Cash versus accrual accounting
Newman Consulting Company maintains its records on a cash basis. During 2011 the following cash flows were recorded: cash received from customers, $420,000; and cash paid for salaries, utilities, and advertising, $240,000, $35,000, and $12,000, respectively. You also determine that customers owed the company $52,000 and $60,000 at the beginning and end of the year, respectively, and that the company owed the utility company $6,000 and $4,000 at the beginning and end of the year, respectively. Determine accrual net income for the year.
Answer:
$143,000
Step-by-step explanation:
Newman consulting company maintains its record on its cash basis
The first step is to calculate the revenue
$420,000+($60,000-$52,000)
= $420,000+$8,000
= $428,000
The expenses can be can be calculated as follows
Utilities expenses = $35,000-($6,000-$4,000)
= $35,000-$2,000
= $33,000
Advertising expenses= $12,000
Salaries expenses= $240,000
Total expenses= $240,000+$12,000+$33,000
= $285,000
Therefore the accural net income for the year can be calculated as follows
= revenue - expenses
= $428,000-$285,000
= $143,000
Hence the accrual net income for the year is $143,000
Write the b expanded form of 0.031 with fractions
Answer:
31/1000
Step-by-step explanation:
Equivalent fraction would be 31/1000
Approximate value would be 4/129 or 3/97
2. Which statement is represented by the equation 4 * 9 - 36?
a 36 is 4 more than 9.
b. 36 is 9 times as many as 4.
o. 9 is 4 less than 36.
d. 9 is 36 less than 4.
7 Thousands= _ Hundreds
7
70
.07
700
What is the answer
7 thousands = 7,000
70 hundreds = 7,000
These two numbers are both equivalent.
They both give a total of 7,000.
Hope this helps!
can somebody find this out
Answer:
???
Step-by-step explanation:
?????what's the question
What is the x and y-intercept 15x + 8y = 120x
Answer:
x=(0,8)
y=(15,0)
Step-by-step explanation:
Brice has $30 to take his brother and his friends to the movies. If each ticket costs $4.00, and he must buy tickets for himself and his brother, what is the
greatest number of friends he can invite?
Answer:
5 friends
Step-by-step explanation:
beacuse it costs $8.00 for himself and his brother, and he can only invite 5 friends because $30 - $8 is $22
so $22 divided by 4 is 5
Answer:
5
Step-by-step explanation:
You start with $30, and each ticket cost $4.
You have to buy AT LEAST 2 tickets for Brice (yourself in the story) and Brice's brother. That 30-8=22.
22/4=5 (without going over 22)
what is 56897712937e+ - (-73618260) ??
Your answer is 1.54737637e11
Answer:
154737637418
Step-by-step explanation:
Find the value of 5x-2 given that --3x+6=3.
Simplify your answer as much as possible.
Answer:
-37
Step-by-step explanation:
-3x/-3=x
3/-3=-1
-1-6=-7
x=-7
5(-7)=-35
-35-2=-37
Sally just purchased a beautiful home on a riverbank for what she thought was a very good deal. She later learned that her house was very susceptible to flood damage during the rainy season. Which of the following statements best describes the effect the location of Sally’s new home will have on her homeowners insurance premium?
a.
Financial loss due to flood damage is likely. Her insurance premiums will be higher than homes not on the waterfront.
b.
Since floods are likely, the value of the home decreases significantly, lowering the insurance premium at the same time.
c.
Since floods happen so infrequently, they are not considered a real threat to the value of the home. Sally’s insurance premium will not be affected.
d.
While extremely annoying, flood damage is usually inexpensive and will not affect the value of the home. Sally’s insurance premium should not be affected.
Answer:
A .Financial loss due to flood damage is likely. Her insurance premiums will be higher than homes not on the waterfront.
Step-by-step explanation:
Got it right on the quiz hope this helps. :)
Statements which best describes, effect the location of Sally’s new home is, (A) Financial loss due to flood damage is likely. Her insurance premiums will be higher than homes not on the waterfront.
What is natural disaster insurance?The natural disaster insurance is the type of insurance in which the insurance company pay the total amount of loan to the beneficiary in case of loss of his property or life in a natural disaster such as earth quack, flood etc.
The face value of natural disaster insurance is depends on following factor:
The face value of natural disaster insurance depends on the location of the house or property.If it is based on the place where the risk of loss due to natural disaster is low, then face value is high and vice versa.Insurance premiums of such places is low, than the place which are at high risk of natural disaster.Sally just purchased a beautiful home on a riverbank for what she thought was a very good deal.
She later learned that her house was very susceptible to flood damage during the rainy season.
In this case, the face value or insurance premiums is high as her house was very susceptible to flood damage during the rainy season.
Thus, the statements which best describes the effect the location of Sally’s new home will have on her homeowners' insurance premium is, (A) Financial loss due to flood damage is likely.
Her insurance premiums will be higher than homes not on the waterfront.
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A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 50, p = 0.97, x= 48
P(48) =
I can't find the right answer I keep getting it wrong
Answer:
not sure ia may give wrong answer
Cherry cuts 6 pieces of tape, each 4/5 m long ,from a roll of tape 5m long . How many meters of tape are left in the roll?
The meters of tape left in the roll will be equal to 1/5 meters.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the information given in the question,
The total length of Tape = 5 m
Total number of pieces = 6
Length of each piece = 4/5 m
Then, the total length of the pieces will be,
6 × 4/5
= 24/5
Then, the amount of tape left in the roll will be,
= 5 - 24/5
= (25 - 24)/5
= 1/5
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Can someone help me answer this
Add up the times spent
Data on pull-off force (pounds) for connectors used in an automobile engine application are as follows: 79.3, 75.1, 78.2, 74.1, 73.9, 75.0, 77.6, 77.3, 73.8, 74.6, 75.5, 74.0, 74.7, 75.9, 72.9, 73.8, 74.2, 78.1, 75.4, 76.3, 75.3, 76.2, 74.9, 78.0, 75.1, 76.8. (a) Calculate a point estimate of the mean pull-off force of all connectors in the population. State which estimator you used and why. (b) Calculate a point estimate of the pull-off force value that separates the weakest 50% of the connectors in the population from the strongest 50%. (c) Calculate point estimates of the population variance and the population standard deviation. (d) Calculate the standard error of the point estimate found in part (a). Interpret the standard error. (e) Calculate a point estimate of the proportion of all connectors in the population whose pull-off force is less than 73 pounds
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
79.3, 75.1, 78.2, 74.1, 73.9, 75.0, 77.6, 77.3, 73.8, 74.6, 75.5, 74.0, 74.7, 75.9, 72.9, 73.8, 74.2, 78.1, 75.4, 76.3, 75.3, 76.2, 74.9, 78.0, 75.1, 76.8
a) Calculate a point estimate of the mean pull-off force of all connectors in the population. State which estimator you used and why.
The mean can be used as a point estimate for the pull of force.
Using a calculator :
The mean(m) :
Σx /n = 1966/26
= 75.62 pounds
(b) Calculate a point estimate of the pull-off force value that separates the weakest 50% of the connectors in the population from the strongest 50%.
To obtain this, we calculate the median:
Median = 0.5(n + 1)th term
Median = 0.5(27)th term = 13.5
Take the 13th and 14th term:
(75.1 + 75.3) / 2 = 75.2 pounds
(c) Calculate point estimates of the population variance and the population standard deviation.
Using calculator ; the variance (s²) = 2.73815
The standard deviation (s) = √variance
s = √2.73815 = 1.655
(d) Calculate the standard error of the point estimate found in part (a). Interpret the standard error.
Standard Error = standard deviation / √n
Standard Error = 1.655 / √26
= 0.3245
(e) Calculate a point estimate of the proportion of all connectors in the population whose pull-off force is less than 73 pounds
Number of Proportions less than 73 pounds / number of samples
= 1 / 26
= 0.0385
19c + 31 = 26c - 74
solve for c
Answer:c
c = - 15
Step-by-step explanation:
Simplifying
19c + 31 = 26c + -74
Reorder the terms:
31 + 19c = 26c + -74
Reorder the terms:
31 + 19c = -74 + 26c
Solving
31 + 19c = -74 + 26c
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '-26c' to each side of the equation.
31 + 19c + -26c = -74 + 26c + -26c
Combine like terms: 19c + -26c = -7c
31 + -7c = -74 + 26c + -26c
Combine like terms: 26c + -26c = 0
31 + -7c = -74 + 0
31 + -7c = -74
Add '-31' to each side of the equation.
31 + -31 + -7c = -74 + -31
Combine like terms: 31 + -31 = 0
0 + -7c = -74 + -31
-7c = -74 + -31
Combine like terms: -74 + -31 = -105
-7c = -105
Divide each side by '-7'.
c = 15
Simplifying
c = - 15
in this image, what is Janelle's position relative to sea level while hiking? what should the altimeter read a this position?
Answer:
janelle is 2,015.75 ft above sea level the altimeter should read plus 2,015.75
2,015.75 ft is the Janelle's position relative to sea level while hiking and the altimeterread this position as 2,015.75.
hope this hep you
SKILL
Given that one side of an equilateral triangle is 16, what is the area of the triangle?
Answer:
approximately 55.43 or [tex]4\sqrt{192}[/tex]
Step-by-step explanation:
1) draw line down middle of said triangle and split it in half
2) since the area of the triangle is 1/2 b * h we can solve
3) we know that the base is 8 (16 split in 1/2)
4) use the Pythagorean theorem (a^2 +b^2 = c^2) to solve for the height
5) a= 8 b= ? c= 16
6) 16^2=256 8^2= 64 256-64=b^2
7) b=[tex]\sqrt{192}[/tex]
8) [tex]\frac{1}{2} *\sqrt{192} *8= 4\sqrt{192}[/tex] or approximately 55.43
You can check by substituting the numbers back into the Pythagorean theorem and see if they match up
what is the missing number in the
sequence -10,-6, -2,_ 6, 10?
Answer:
It would be a positive 2.
Step-by-step explanation:
This is because if you start with -10 and add 4, the number 2 would go in the blank. Also if you start at positive 10 you just subtract 4 and the number 2 would still go in the blank.
Hope this helps!
Given the functions:
f(x) = x2 - 9, and g(x) = x3 + 4x² + 8x – 7, find h(x) = f(x) + g(x).
h(x) = - x3 +5x2 + 8x - 16
h(x) = x3 + 3x² + 8x + 2
h(x) = x3 + 5x² + 8x – 16
h(x) = -x3 - 3x2 – 8x - 2
h(x) = -x3 + 3x2+8x+2
Answer: h(x)=x³+5x²+8x-16
Step-by-step explanation:
In this problem, we are given f(x) and g(x). The problem asks to find h(x)=f(x)+g(x). Since we are given f(x) and g(x), we can directly add them together.
h(x)=x²-9+x³+4x²+8x-7 [combine like terms]
h(x)=x³+5x²+8x-16
Now, we know that h(x)=x³+5x²+8x-16 after we have combined like terms.
a car can travel 476 miles on 14 gallons of gas. write an equation relating the distance to the number of gallons. how many gallons of gas does this car need to travel 578 miles .
6A. what is the equation?
6B. how many gallons of gas does this car need to travel 578 miles?
2
¿Cuál de los siguientes causa que un sólido cambie a liquido
Answer:heat
Step-by-step explanation:heat turns solid into liquid
How to add/Subtract fractions With an Example and explain good
Answer:
The first example is adding fractions. The last is Subtraction.
Step-by-step explanation:
The first step is finding the LCD or Least Common Denominator. In this case, we multiply both denominators by each other 2 x 3 = 6 before we proceed.
Secondly, we multiply the bottom denominator on the right (which is three) and multiply it by numerator and denominator on the left.
[tex]\frac{1}{2}[/tex] x 3= Multiply the numerator and denominator and you should get this
[tex]\frac{3}{6}[/tex]
Next multiply [tex]\frac{1}{3}[/tex] by 2. You should get [tex]\frac{2}{6}[/tex]
The final step is just to add the numbers on the very top. You should get [tex]\frac{5}{6}[/tex]
*Also note, pay attention to your question. Some may require decimal form or simplification.
1. [tex]\frac{1}{2} + \frac{1}{3} = \frac{5}{6}[/tex]
2. [tex]\frac{3}{6}[/tex] +[tex]\frac{2}{6}[/tex] = [tex]\frac{5}{6}[/tex]
3. The answer is [tex]\frac{5}{6}[/tex]
_________________________________________
The next example is subtraction.
Find the LCD.
Next, start by multiplying [tex]\frac{3}{5}[/tex] by 3. Penultimately, multiply [tex]\frac{1}{3}[/tex] by 5. Finally, subtract 9-5 to get 4. The answer should be [tex]\frac{4}{15}[/tex]
1. [tex]\frac{3}{5} - \frac{1}{3}[/tex]
2. [tex]\frac{9}{15}[/tex] - [tex]\frac{5}{15}[/tex] = [tex]\frac{4}{15}[/tex]
A certain car has a fuel efficiency of 55 miles per gallon when travelling at 70 miles per hour. How many miles will the car travel using 3 gallons?
9514 1404 393
Answer:
165 miles
Step-by-step explanation:
miles = miles/gallon × gallons
(55 mi/gal) × (3 gal) = 165 mil
The car will travel 165 miles on 3 gallons.
Helpp? Please! What’s the area of this triangle?
ES LA B
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Games Played
So far this season, a team has won 51 out of 68 games.
Identify the values of a, b, c, and d that complete the bar
diagram for this situation.
a =
b =
a%
a%
a%
a%
b%
C-
d=
e
с
с
с
d.
Answer:
a=25 b=100 c=17 d=68
Step-by-step explanation:
the test said so
I need help with thisssssssssssssssss
9514 1404 393
Answer:
(a) 90°, 90°
(b) 5, 1
(c) 10°, 20°
(d) 10°, 20°, 150°
Step-by-step explanation:
You need to consider ways in which each statement might not apply.
(a) An obtuse angle is greater than 90°. If both angles are 90°, then neither is obtuse.
counterexample: m∠1 = 90°, m∠2 = 90°
__
(b) If the perimeter is 12, the sum of the side lengths must be 6. There are many ways to get two numbers that have a sum of 6. Here's one:
counterexample: length = 5, width = 1
__
(c) All that is required is that the sum of angles be 30°. They don't have to be equal.
counterexample: m∠ABC = 10°, m∠CBD = 20°
__
(d) We know the three angles of a triangle have a sum of 180°, but that does not require it to be an acute triangle. A triangle can also be right or obtuse.
counterexample: m∠P = 10°, m∠Q = 20°, m∠R = 150°
