The smallest integer is 10, the middle integer is 11, and the largest integer is 12.
What is the consecutive integers in algebra?
In algebra, consecutive integers are a sequence of numbers that follow each other in order, where each number is one more than the previous number.
Let's call the smallest integer "x". Then, the middle integer is "x + 1" and the largest integer is "x + 2".
Now, using the given information, we can set up an equation:
x + 2(x + 1) = 56 - 3(x + 2)
Expanding the equation and simplifying:
3x + 2 = 56 - 3x - 6
6x = 62
x = 10
So, the three consecutive integers are 10, 11, and 12.
Hence, The smallest integer is 10, the middle integer is 11, and the largest integer is 12.
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The table below shows the favorite soft drink of each student in a statistics class. Find the frequency of each drink
Drinks
Sprite Sprite Dr Pepper
Dr Pepper Coke Coke
Coke Pepsi Mtn Dew
Pepsi Sprite Pepsi
Sprite Sprite Sprite
Pepsi Coke Pepsi
Dr Pepper Coke Coke
Coke Coke Pepsi
Dr Pepper Coke Dr Pepper
Coke Coke Pepsi
The frequency of each drink in the statistics class can be found to be :
Sprite - 6 Dr Pepper - 5Coke - 11Mtn Dew - 1 Pepsi - 7 How to find the frequency ?The frequency of something refers to the number of times that thing happens. In this case, it therefore means the number of students who prefer a certain drink over the other ones.
From the table, the number of students who chose Sprite was 6 students. 5 students chose Dr Pepper and 11 students chose Coke. Then only a single student chose Mtn Dew while 7 students chose Pepsi.
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Please help will mark brainy
Area of a parallelogram when base is 25ft and height is 17.4 ft
Answer: 435
Step-by-step explanation:
Help me for this question. I just want to know if it’s right or not!
find the value of x in the solution to the system of equations shown
y = 12x + 7
y = -6 + 25
Answer:
Substitute y = 12x + 7
12x+7=-6+25
Simplify
12x+7=19
Solve
19-7=12
12x=12
x=1
From 15 men and 11 women, how many committees of 10 persons can be chosen if each committee is to have exactly 8 men?
Answer:
1
Step-by-step explanation:
There are 15 men in total;
If each committee is to have 8 men (and assuming one man cannot be in multiple committees), we can simply do the following:
15/8 = 1.875
This means only 1 committee can be made containing exactly 8 men.
You can also think of it like this:
If 8 men make up 1 committee, then this leaves 7 (15 - 8) men left;
Since you need 8 men, there is not enough for a second committee (once again, assuming that one man cannot be in more than one committee).
the following angles are given in degrees, arcminutes, and arcseconds. rewrite them in degrees and decimal fractions of degrees.
Angles given in degrees, arcminutes, and arcseconds converted to decimal fraction of degrees.
A. 2 degrees 18′ 36′′ can be rewritten in decimal fraction of degrees as :
2 + (18/60) + (36/3600) = 2.3111 degrees.
B. 36′ 18′′ can be rewritten in decimal fraction of degrees as :
(36/60) + (18/3600) = 0.6050 degrees.
C. 7 degrees 59′ 59′′ can be rewritten in decimal fraction of degrees as:
7 + (59/60) + (59/3600) = 7.9999 degrees.
D. 1′ can be rewritten in decimal fraction of degrees as:
(1/60) = 0.0167 degrees.
E. 1′′ can be rewritten in decimal fraction of degrees as:
(1/3600) = 0.0003 degrees.
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The complete question is :
The following angles are given in degrees, arcminutes, and arcseconds. Rewrite them in degrees and decimal fractions of degrees.
A. 2 degrees 18 ′ 36 ′′
B. 36 ′ 18 ′′
C. 7 degrees 59′ 59′′
D. 1′
E. 1′′
If m/n ,in lowest terms, be the probability that a randomly chose positive divisor of 10^99 is an integral multiple of 10^88 than find the value of (m+n).
m and n are the two numbers that form the fraction which is the probability of a randomly chosen positive divisor of [tex]10^99[/tex] being an integral multiple of [tex]10^88[/tex].
Let the probability of a randomly chosen positive divisor of [tex]10^99[/tex]being an integral multiple of 10^88 be represented as m/n.
Since [tex]10^99[/tex]is a multiple of [tex]10^88[/tex], its positive divisors will also be multiples of [tex]10^88[/tex].
Therefore, the probability that a randomly chosen divisor of [tex]10^99[/tex]is an integral multiple of [tex]10^88[/tex] will be 1, i.e., m/n = 1.
Therefore, m+n = 1+1 = 2
Hence, the value of (m+n) is 2.
m and n are two numbers that form a fraction in lowest terms, which is the probability that a randomly chosen positive divisor of [tex]10^99[/tex] is an integral multiple of [tex]10^88[/tex]. To find the value of (m+n), we need to first determine the value of m and n. To do this, we must first calculate the total number of positive divisors of [tex]10^99[/tex]that are integral multiples of [tex]10^88[/tex]. We can then divide this number by the total number of positive divisors of [tex]10^99[/tex] to get the fraction. The numerator of this fraction is m and the denominator is n. The sum of m and n is the answer to the question. This is because the fraction gives us the probability that a randomly chosen positive divisor of [tex]10^99[/tex] is an integral multiple of [tex]10^88[/tex], and the sum of m and n is the total number of positive divisors of[tex]10^99[/tex], which is the denominator of the fraction. Therefore, the value of (m+n) is the sum of the numerator and denominator of the fraction.
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Use the graph to determine
(a) open intervals on which the function is increasing, if any.
(b) open intervals on which the function is decreasing, if any.
(c) open intervals on which the function is constant, if any.
a) The function is increasing on the following interval: (3, ∞).
b) The function is not decreasing on any interval of it's domain.
c) The function is not constant on any interval of it's domain.
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.More can be learned about functions at brainly.com/question/24808124
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Geometry question, question in photo attachment
Answer:
323/7 or about 46.143
Step-by-step explanation:
We can infer that the measure of B + C is 90 degrees, so 6x + 1 + 8x - 11 must be equal to 90.
6x + 1 + 8x - 11 = 90
14x - 10 = 90
14x = 100
x = 100/14
x = 50/7
Solve for the measure of C by substituting x with 50/7.
50/7 * 8 = 400/7
400/7 - 11 = 323/7
the measure of C is 323/7
In each of the following problems, type the price per unit per oz in blanks a. and b, then pick the best buy. a. Bread, 1 lb. loaf for 80¢ would = b. Bread, 2 lb. loaf for $1.95 would = c. The best buy would be
Answer:
a) $0.05 per ounce
b) $0.06 per ounce
c)The best buy would be 1lb for .80
Step-by-step explanation:
.80/16 = .05 16 ounces in a pound
1.95/32 = .06 32 ounces in 2 pounds
(3x−1)(2x 3 +4x 2 −5) in standard form
The standard form is 6[tex]x^4[/tex] + 10x³ - 4x² - 15x + 5.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(3x−1) (2x³ +4x² −5)
Simplifying
3x (2x³ +4x² −5) - 1 (2x³ +4x² −5)
6[tex]x^4[/tex] + 12x³ - 15x - 2x³ - 4x² + 5
Adding the like terms.
6[tex]x^4[/tex] + 10x³ - 4x² - 15x + 5
Thus,
6[tex]x^4[/tex] + 10x³ - 4x² - 15x + 5
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Kunle and Peter shared 180 marbles in the ratio 5:7, how many will Peter receive
Answer: 108
Step-by-step explanation:
5+7 = 12
They split it into 12 parts.
Kunle gets 5/12, Peter gets 7/12
7/12 of 180
Divide by the bottom, multiply by the top
180/12 = 15
15x7 = 105
Therefore, Peter gets 108 marbles.
Please make me brainliest!
Answer:
k:p 5+7=7/12×180=15×7=105
How many starting points does a ray have?
0
1
2
infinite
The number of starting points a ray has is one.
Option B is the correct answer.
What is a ray?A ray is a line that has a starting point and no end.
We have,
A ray is a line that has one fixed point and the other point is endless.
So,
A ray has one starting point.
Thus,
A ray has one starting point.
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Help please!
Slope of one of the dotted lines:
Slope of the line reflection:
Answer:
see explanation
Step-by-step explanation:
calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
consider the slope of the middle dotted line
with (x₁, y₁ ) = (- 3, - 4) and (x₂, y₂ ) = (3, - 2) ← 2 points on the line
m = [tex]\frac{-2-(-4)}{3-(-3)}[/tex] = [tex]\frac{-2+4}{3+3}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
consider the slope of the line of reflection ( the solid line )
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (- 2, 3) ← 2 points on the line
m = [tex]\frac{3-0}{-2-(-1)}[/tex] = [tex]\frac{3}{-2+1}[/tex] = [tex]\frac{3}{-1}[/tex] = - 3
note the product of the slopes = [tex]\frac{1}{3}[/tex] × - 3 = - 1
indicating the lines are perpendicular to each other
Find the value of a.
Show your answers
4a - 8 + 4a - 8 + 4a - 8 = 180°
The sum of interior angle of triangle is 180°
12a - 24 = 180°
12a = 204
[tex]a = \frac{204}{12} \\ [/tex]
a = 17°
1. How does an annual percentage rate (APR) for mortgages differ from a
more traditional interest rate?
Annual percentage rate (APR) for mortgages differs from a
more traditional interest rate as APR includes other charges and fees while interest rates do not include it.
How is this determined?The annual cost of a loan to a borrower is referred to as interest rate, and it is indicated as a percentage.
APR represents the total yearly cost of a loan to the borrower, including all fees. The APR is stated as a percentage, just like an interest rate. It does, however, contain other costs or fees such mortgage insurance, the majority of closing costs, discount points, and loan origination fees, unlike an interest rate.
Hence, Annual percentage rate (APR) for mortgages differs from a
more traditional interest rate as APR includes other charges and fees while interest rates do not include it.
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100 POINTS PLEASE HELP WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
The entry "EQUIPMENT $12,000" is listed as a debit in the T-account, which means it is an increase in assets. Therefore, the correct answer is (b) increase in assets.
evaluate (8+2)^3-6 for IReady Math
100 POINTS PLEASE HELP A business buys equipment with $150 cash and puts $425 on credit. What is the value of this asset?
A. $275
C. $575
B. $150
D. $425
Answer:
The correct answer is C. $575. The business bought equipment with $150 cash and put $425 on credit, so the total value of the asset is $575 ($150 + $425).
Math work I hope you can see
What is the rationale for the above responses?
1) to obtain the value of x, we must equate AC and BD based on the diagonal properties of a rectangle. Note that a rectangle's diagonal divides it into two congruent right triangles.
A rectangle's diagonals are all the same length. A square is a quadrilateral whose diagonals bisect each other, intersect at right angles, and are congruent.
Thus,
Since BD = AC
2x + 19 = 5x - 2
To solve the equation 2x + 19 = 5x - 2, we need to isolate x on one side of the equation.
First, we can simplify both sides by combining like terms. Subtracting 2x from both sides gives:
19 = 3x - 2
Next, we can isolate x by adding 2 to both sides:
21 = 3x
Finally, we can solve for x by dividing both sides by 3:
x = 7
Therefore, the solution to the equation 2x + 19 = 5x - 2 is x = 7
b) The Properties of Parallel Lines Intersected by a Transverse Postulate states that when a transversal intersects two parallel lines, the corresponding angles are congruent, the alternate interior angles are congruent, and the same-side interior angles are supplementary. This means that
∠LMN + ∠MNK = 180°
Thus,
115 + ∠MNK = 180
∠MNK = 180 - 115
∠MNK = 65°
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A diff diver plunges from a height of 25 ft above the water surface. The distance the diver falls in t seconds is given by the function (t) - 16eft. Which equation can be solved fort to find the time (in seconds) when the diver hits the water?
Answer: The equation that can be solved for t to find the time (in seconds) when the diver hits the water is:
h(t) = 25 - 16e^(-ft) = 0
Where h(t) is the height of the diver in feet at time t, and f is a positive constant related to the speed of the fall.
To find the time when the diver hits the water, we set h(t) equal to zero and solve for t. This gives us the time when the height of the diver is equal to the water surface.
25 - 16e^(-ft) = 0
25 = 16e^(-ft)
e^(-ft) = 25/16
-ft = ln(25/16)
t = -ln(25/16)/f
Note that the negative sign in the equation for t indicates that the time is counted from the moment the diver starts falling. The constant f can be determined from the physical characteristics of the diver and the conditions of the fall, but it is not necessary to know the exact value of f to find the time when the diver hits the water.
Step-by-step explanation:
A maintenance worker needs to wax a restaurant floor shaped like the image shown.
A six-sided figure. There is a horizontal base of 28 feet then another horizontal base below it of 16 feet. The longest side is to the right and is 32 feet. The top is 24 feet. There is a perpendicular from the vertex of the top to the first base of 28 that is labeled 12 feet.
If the wax cost $2.25 a square foot, how much will the wax cost to cover the floor?
$3,096
$2,106
$1,638
$1,530
Answer: 1,638
Step-by-step explanation:
Answer:
1638
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At the ice cream shop, there are 14 shakes sold for every 6 malts. What is the ratio from malts to shakes and malts to total?
The ratio of malts to shakes is 3:7 if 14 shakes are sold for every 6 malts.
What is meant by ratios?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. A ratio is a tool for comparing like-kind quantities or illustrating relationships between them. To compare similar items, we employ ratios.
Let the number of shakes be S and the number of malts be M.
Given: Number of shakes sold = 14 shakes
Number of malts sold = 6 malts
To find the ratio of malts to shakes:
The ratio of malts to shakes exists given by the expression:
M/S = Number of malts sold/Number of shakes sold
Substituting the given parameters into the formula, we have;
M/S = 6/14
M/S = 3/7
Therefore, the ratio of malts to shakes is 3 : 7.
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HELP PLEASE I REALLY NEED THIS
Answer:
Step-by-step explanation:
Part A:
x = # of days
R: 1 hr + 3/4 hr/day(x)
J: 4 hr + 1/2 hr/day(x)
1 + 3/4x = 4 + 1/2x
3/4x - 2/4x = 3
1/4x = 3
x = 12 days
After 12 days of practicing (not including the first Saturday), they each will have practiced 10 hours
Part B:
Saturday plus 12 more days →
Saturday 1-Sun 2- Mon 3-Tues 4-Wed 5-Thurs 6-Fri 7-Sat 8-Sun 9-Mon 10-Tues 11-Wed 12-Thursday
They both will have practiced 10 hours on the second Thursday after they started on Saturday
anita can type 60 words to 75 words per minute it took her 43 minutes to type a 12 page report which could be the total number of words in the report
Anita can type between 60 and 75 words per minute and it took her 43 minutes to type a 12 page report.
The formula to calculate the total number of words in a report is: (words per minute * minutes) = total words. In this case, anita can type between 60 and 75 words per minute, so to solve for the total words in the 12 page report, we need to average her words per minute. This would be (60 + 75) / 2 = 67.5 words per minute. So, now the equation looks like this: (67.5 words per minute * 43 minutes) = 2,888.5 total words in the report.
To break the equation down further, we can say that for every minute Anita types, she is typing 67.5 words. This means that for every minute she types, she is typing 1.125 pages. In other words, for every 8 minutes she types, she is typing 9 pages. Therefore, to type 12 pages in 43 minutes, Anita is typing approximately 9.2 pages per 8 minutes.
To summarize, Anita can type between 60 and 75 words per minute and it took her 43 minutes to type a 12 page report. Using the formula (words per minute * minutes) = total words, we can calculate that the total number of words in the report is 2,888.
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Valentino is buying a movie at an online store. He can choose to use one of the three deals that are shown below or to just buy the movie without a deal. The online store charges a flat rate of $2.99 for shipping. Valentino is buying a movie for $12.99. He could buy the same movie with a digital download for $2.50 more.
The cheapest alternative that Valentino can select is to make the computation and discover which is less expensive when compared to others.
What is Algebra?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.
Given that the info is incomplete, Valentino needs to analyze the three options and make additions for extra charges or deductions for discount and make a purchase of the cheapest alternative.
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Daniel wants to predict how far he can hike based on the time he spends on the hike. He collected some data on the time (in hours) and distance (in kilometers) of some of his previous hikes. Which of linear equations best describes the given model?
When Daniel creates the linear equation, he will notice that the relationship between time spent and distance travelled is proportional.
What exactly is a linear equation?The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
When we create a linear equation for the distance of the hike, we will get a graph with a straight line.
A straight line's general equation is
y = mx + c
where m = is the slope of the line and
c = is the y-intercept
y = the distance covered
x = the time taken
Because distance is directly proportional to time,
more distance is covered in less time
Distance ∝ time
Hence,
Daniel will notice that the relationship between the time spent and distance covered are proportional.
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Microeconomics
The total cost function of a monopolist is (Q) = 3Q. The inverse demandfunction for
the monopolist’s products is P (Q) = 12 − Q.
A. find the profit-maximizing level of price and output
B. Find the maximum profit of the firm at an equilibrium price level
Step-by-step explanation:
A. To find the profit-maximizing level of price and output, we need to find the equilibrium point where the marginal revenue equals marginal cost.
The marginal cost of production is the derivative of the total cost function: MC = dC/dQ = 3.
The marginal revenue is the derivative of the inverse demand function: MR = dP/dQ = -1.
So at the profit-maximizing level of output, MC = MR.
3 = -1
Q = 6
Then we can substitute Q = 6 back into the inverse demand function to find the price:
P (Q) = 12 - Q
P (6) = 12 - 6
P = 6
So the profit-maximizing level of output is 6 units at a price of $6.
B. To find the maximum profit of the firm, we need to calculate the total revenue and the total cost at the profit-maximizing level of output.
The total revenue is the product of the price and the quantity:
TR = P * Q
TR = 6 * 6
TR = 36
The total cost is given by the total cost function:
TC = C (Q)
TC = 3 * Q
TC = 3 * 6
TC = 18
So the maximum profit is the difference between the total revenue and the total cost:
Profit = TR - TC
Profit = 36 - 18
Profit = 18
The maximum profit of the firm is $18 at an equilibrium price level of $6 and an output level of 6 units.
Imagine this:
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the
airplane and x represents the number of minutes the plane has been descending:
| = -5x + 150
Part C:
Which ordered pair (from the table in part A) represents the initial value? What does the initial value represent in this problem? (1-2 sentences)
Part D:
What is the rate of change in this equation? What does the rate of change represent in this problem? (1-2 sentences)
Part C: The ordered pair (0, 150) represents the initial value in the table. The initial value represents the altitude of the airplane when it started descending, i.e., the altitude of the airplane before it began its descent.
Part D: The rate of change in this equation is -5, which is the coefficient of x. The rate of change represents the decrease in altitude, in feet, per minute as the airplane descends for a landing. In other words, the altitude decreases by 5 feet for every minute that the airplane descends.