The first of the three consecutive integers is 52. The next two are 53 and 54. These are three consecutive integers such that the sum of the first two is 51 more than the third integer.
Let's call the first of the three consecutive integers "x". The next two would then be "x + 1" and "x + 2".
According to the problem, the sum of the first two integers (x + (x + 1)) is 51 more than the third integer (x + 2), so we can write an equation:
x + (x + 1) = (x + 2) + 51
Expanding the left side and solving for x:
2x + 1 = x + 53
x = 52
So, the first of the three consecutive integers is 52. The next two are 53 and 54. These are three consecutive integers such that the sum of the first two is 51 more than the third integer.
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Which domain would be appropriate for the number of guests at an outside concert?
(1) integers
(2) whole numbers
(3) all real numbers
(4) positive real numbers
Answer:
(2) whole numbers
Step-by-step explanation:
Whole numbers include all natural numbers and 0. They are real numbers that do not include fractions, decimals, and negative integers.
how mant ways can a 7 members team be selected out of 9 girls and 5 boys if the members of the team only have only 3 boys
To select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys , there are 1260 ways.
To find the number of ways to select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys, you can use the formula for combinations:
C(n, k) = n! / (k! * (n - k)!)
where n is the total number of items (9 girls and 5 boys), k is the number of items to be selected (3 boys and 4 girls), and ! represents the factorial function.
So, the number of ways to select 3 boys out of 5 boys is:
C(5, 3) = 5! / (3! * (5 - 3)!) = 5! / (3! * 2!) = 10
And the number of ways to select 4 girls out of 9 girls is:
C(9, 4) = 9! / (4! * (9 - 4)!) = 9! / (4! * 5!) = 126
Finally, the number of ways to select a team of 7 members consisting of 3 boys and 4 girls is:
C(14, 7) = 10 * 126 = 1260
So, there are 1260 ways to select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys.
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Match the exponent expression with it's correct solution.
The correct order for the exponent expression is,
A-3, B-1, C-4, and D-2.
What is Exponential Function?The formula for an exponential function is f (x) = aˣ, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
Given functions to match,
for the functions using property,
aⁿ.aᵇ = aⁿ⁺ᵇ
A; x¹⁸.x¹⁴
x¹⁸.x¹⁴ = x¹⁸⁺¹⁴ = x³²
B: x⁸.x⁵ = x⁸⁺⁵
x⁸.x⁵ = x¹³
C: x³⁵.x⁴⁰ = x³⁵⁺⁴⁰
x³⁵.x⁴⁰ = x⁷⁵
D: x⁴⁵.x² = x⁴⁵⁺²
x⁴⁵.x² = x⁴⁷
Hence correct order is, A-3, B-1, C-4, and D-2.
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tyler can type twice as many words wpm as kyla
define variable=
Expression to represent problem=
if kyla can type 3 wpm how many wpm can Tyler type
Answer:
Your answer is: 6 wpm
Step-by-step explanation:
If Tyler types twice as fast as Kyla, you multiply the amount of wpm Kyla writes by 2. 3 multiplied by 2 equals 6. Therefore, Tyler writes 6 wpm.
You tried 8 of the frozen yogurt flavors shown. In which two ways can you write the fraction of flavors that you tried?
The solution is, 128 combinations.
What is combination?In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
here, we have,
We are told in the question that a frozen yogurt shop has:
8 flavors of frozen yogurt
2 kinds of syrup
8 toppings.
The combinations that can be made with one flavor of frozen yogurt, one syrup, and one topping is calculated as:
8 × 2 × 8
= 128 combinations
Therefore, the combinations that can be made with one flavor of frozen yogurt, one syrup, and one topping is 128 combinations.
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A store employee creates a display of gymnastics mats priced at $73 apiece. The store paid $50 for each gymnastics mat. What percentage is the mark-up?
How do you multiply fractions with a common denominator?
When multiplying fractions, multiply the numerator (top number), then the denominator (bottom number), and finally reduce to the lowest term if necessary.
Fractions are subsets of wholes. They are made up of a numerator (the number on top) and a denominator (the number on the bottom). The numerator represents the number of parts, while the denominator represents the total number of available parts.
To multiply two fractions, follow these three simple steps:
Step 1: Multiply the numerators of each fraction by themselves (the numbers on top). The answer's numerator is the result.
Step 2: Add the denominators of each fraction together (the numbers on the bottom). The answer's denominator is the result.
Step 3: Simplify or reduce your response.
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Nico wants to use a horizontal number line to compare 13 4 and 1. 5. He is unsure how to do it and asks you for help. How would you explain the process?
The order from smallest to largest is 1.5, 4, 13.
To compare numbers using a horizontal number line, simply need to place each number on the line and see which one is farther to the right (greater) or to the left (less).
Here's how to compare 13, 4 and 1.5 on a number line:
Draw a horizontal number line and label it with numbers, making sure to include the numbers you want to compare.Place each number on the line, with the smaller numbers to the left and the larger numbers to the right.Look at the position of each number relative to each other. The numbers farther to the right are greater, while the numbers farther to the left are less.So, in this case, 1.5 is to the left of 4, which is to the left of 13. Therefore, the order from smallest to largest is 1.5, 4, 13.
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for the figures below assume they are made of semicircle quarter circles and squares for each shape find the area and the perimeter. Give your answers as a completely simplified exact value in terms of pie (no approximations)
Thank you
The area of the combined figure is 98.64 sq cm and the perimeter of the combined figure is 91.88 cm.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
What are the area and perimeter of a rectangle?
We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know, The area of a triangle is (1/2)×base ×height and the area of the semicircle is (1/2)πr².
Also, the perimeter of a triangle is the sum of the lengths of all the sides and the perimeter of a semicircle is πr.
From the given figure The right angle triangle is an isosceles therefore, The length of the side BC is also 12 units.
Hence the area is = (1/2)×12×12 = 72 sq cm.
And The area of the semicircle is,
(1/2)×π×(√12² + 12²) sq cm.
= (1/2)×3.14×√(288) sq cm.
= 26.64 sq cm.
Therefore, The total area is (72 + 26.64) sq cm.
= 98.64 sq cm.
And the perimeter is,
= (12 + 12 + 16.97) + (3.14×16.97) cm.
= 91.88 cm.
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Off track biking charges an hourly rate for mountain bike lessons and adds a charge of $100 for insurance. The overvalued cost (C) is represented by the formula, C=40h + 100 where h is the number of hours of lessons. Ben has 7 hours of lessons with off track biking.
How much does he pay?
Answer:
Step-by-step explanation:
If Ben has 7 hours of lessons with Off Track Biking, we can find the total cost (C) using the formula:
C = 40h + 100
where h is the number of hours of lessons. Substituting h = 7, we get:
C = 40(7) + 100
C = 280 + 100
C = 380
Therefore, Ben pays $380 in total for his 7 hours of lessons with Off Track Biking.
Somebody knows how to do this exterior angle property question?
Answer:
see below
Step-by-step explanation:
the figure shows that GF = FH
so 5x+26 = ∠H
because sum of all angles in a triangle =180 (memorize this)
so then you have 2*(5x+26) + 3x+37 =180
solve for x
10x + 52 +3x +37 =180
13x = 91
x=7
so 5x+26 = 35+26 = 61
3x+37 =21+37 =58
suppose a researcher describes the age, race, and gender distributions for people who are charged with shoplifting. the unit of analysis is
The unit of analysis that supposed to use when researcher describes the age, race, and gender distributions for people who are charged with shoplifting is called individuals.
The entity that frames what is being investigated in a study, or the entity being studied as a whole is known as the unit of analysis. At the macro level of social science study, the state is the most frequently used analytical unit that is regarded as a society. Groups, organizations, and institutions are frequent observational units at the meso level, while individuals are the unit of observation at the micro level.
The individual unit of analysis could be either a human or an animal. A group might be made up of a single person or a number of people who communicate with one another. For instance, if we are interested in examining people's shopping behaviors, their learning outcomes, or their views about new technology, then the individual is the unit of analysis that we should use.
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I'm looking at data that show the number of new college programs in green studies, and a linear function appears to be a better choice than an exponential function for modeling the number of new college programs from 2005 through 2009.
The table represents the exponential function as f(x) = a(b)^3
What are exponential functions?When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.
Here we have the table:
Year number of new college programs
2005 3
2006 22
2007 27
2008 66
2009 100
Few things that are useful to identify this as an exponential equation are:
f(x) = a(b)^3
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What is the equation of the line that passes through thé point (-1, 3) and has a
slope of -3?
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of the line that passes through the point (-1, 3) and has a slope of -3, we can use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
Substituting the given values, we get: y - 3 = -3(x - (-1))
Expanding the right side, we get: y - 3 = -3x + 3
Adding 3 to both sides, we get: y = -3x + 6
So the equation of the line that passes through the point (-1, 3) and has a slope of -3 is y = -3x + 6.
Hope this helps,
- Jeron :- )
Answer: y=-3x+6
Step-by-step explanation:
The equation for slope intercept form is y=mx+b, and since you are given your y and x values from the point (-1, 3), you can plug those values into it. You are also given your slope of -3, and since m is your slope value, you would plug the -3 in as your m.
After you plug in your given values from the problem, you should should get 3 = -1 (3) + b.
Then, you isolate the b. Multiply the -1 and 3 to get -3.
3 = -1 (3) + b
3 = -3 + b
Next, add the 3 to both sides of the equation, and you should be left with b=6.
3 = -3 + b
+3 +3
--------------
6 = 0 + b
6 = b
Finally, you re-write the slope intercept equation with the y-intercept (b value) you just found along with the slope of -3 given by the problem to get y=-3+6.
Last week, Bill bought 12 pizzas and 6 cakes for a total of $186.
Today, Bill bought 29 pizzas and 24 cakes for a total of $554.
Assuming neither item has changed in price, what is the cost of a pizza in dollars?
Using a system of equations and assuming neither pizza nor cake has changed in price, the cost of a pizza in dollars is $10.56.
What is a system of equations?A system of equations is two or more equations solved at the same time or concurrently.
A system of equations is also called simultaneous equations.
Pizzas Cakes Total Cost
Last week 12 6 $186
Today 29 24 $554
Let the cost per pizza = x
Let the cost per cake = y
Equations:12x + 6y = 186 ... Equation 1
29x + 24y = 554 ... Equation 2
Multiply Equation 1 by 4:
48x + 24y = 744 ... Equation 3:
Subtract Equation 2 from Equation 3:
48x + 24y = 744
-
29x + 24y = 554
18x = 190
x = 10.56
= $10.56
Substitute x = $10.56 in Equation 1:
12x + 6y = 186
12(10.56) + 6y = 186
126.72 + 6y = 186
6y = 59.28
y = 9.88
= $9.88
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3. Zachary earned $4, 236 in August as a salesman at the racetrack. His earnings include his monthly salary of $700 and commission. If Zachary's sales totaled $10, 654, what is his rate of commission?
-approximately 30.6%
-approximately 28.4%
-approximately 29.8%
-approximately 33.2%
Answer:
approximately 33.2%
Step-by-step explanation:
Find Zachary's commission by subtracting his basic salary from total monthly earnings.
Commission = 4236 - 700
= $ 3536
[tex]\sf rate \ of \ commission = \dfrac{commission}{total \ sales}*100[/tex]
[tex]\sf = \dfrac{3536}{10654}*100\\\\ = 33.19 \%\\ = 33.2 \%[/tex]
A boat traveled 140 miles downstream and back. The trip downstream took 7 hours. The trip
back took 70 hours. Find the speed of the boat in still water and the speed of the current.
On solving the provided question, we can say that the speed of the boat in still water is 11 miles per hour, and equation the speed of the current is 9 miles per hour.
What is equation?A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the calculation 3x + 5 = 14, the equal sign places a space between the values 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The logo and the specifically software are frequently the same. as in, 2x - 4 Equals 2, for instance.
distance = rate × time
to set up two equations using the given information:
Equation 1: 140 = (b + c) × 7 (downstream trip)
Equation 2: 140 = (b - c) × 70 (upstream trip)
b + c = 20 (dividing both sides by 7)
b - c = 2 (dividing both sides by 70)
Now we have two equations with two variables. We can solve for "b" and "c" by adding the two equations together:
[tex](b + c) + (b - c) = 20 + 2\\2b = 22\\b = 11\\[/tex]
So the speed of the boat in still water is 11 miles per hour.
We can then use either Equation 1 or Equation 2 to solve for the speed of the current. Let's use Equation 1:
[tex]140 = (11 + c) × 7\\20 = 11 + c\\c = 9[/tex]
So the speed of the current is 9 miles per hour.
Therefore, the speed of the boat in still water is 11 miles per hour, and the speed of the current is 9 miles per hour.
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Taco Johns is soon opening in Caledonia. It's massive news. Right now Caledonia has 13 fast food
restaurants. It's expected over the next 4 years the number of fast food restaurants in Caledonia will increase
to 21 restaurants. Write an equation to relate the number of fast food restaurants in Caledonia as a function of
time.
Step-by-step explanation:
let's say x stands for years.
FFR(x) is a function that calculates the number of fast food restaurant after x years.
FFR(x) = 2x + 13
they have 13 fast food restaurants right now (x = 0).
in 4 years (x = 4) they think they will have 21. that is 8 more than now. that means 2 more per year (2×4 = 8). therefore the factor 2 for every year (x).
FFR(4) = 2×4 + 13 = 8 + 13 = 21
In the figure below,m<1=29 and m<2=33. Find
Answer:
62 degrees
Step-by-step explanation:
To find the answer simply add both measures of angles 1 and 2 (29 + 33) to get 62 degrees.
Iready comprehension check lesson 19
Based on the information, it can be inferred that the correct fraction is 8/8 - 3/8 (option B).
How to select the correct fraction?To select the correct fraction we must perform the following procedure:
Analyze the fraction that we have as reference. Once we know its elements (numerator and denominator) we can identify any fracture that is related to it.
We analyze the options and identify the one that is related to the reference fraction. In this case the correct fraction would be 8/8 - 3/8 because we leave the same denominator and do the subtraction with the numerators.
So it would be 8 - 3 = 5. So the correct fraction is option B.
Note: This question is incomplete. Here is the complete information:
Question: Which expression has a value of 8/8 - 3/8?
Options:
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Jack want to buy a coat that 74.95. the sales tax rate in the city is 6 1/2% what is the total cost
Answer:
$79.82 (to 2 d.p.)
Step-by-step explanation:
100%=$74.95
1%=$74.95÷100
=$0.7495
100%+6.5%=106.5%
106.5%=$0.7495×106.5
=$79.82 (to 2 d.p.)
from a group of 8 men and 7 women, 5 persons are to be selected to form a committee so that at least 3 men are there on the committee. in how many ways can it be done?
5 persons are to be selected to form a committee so that at least 3 men are there on the committee, in 3192 ways the committee can be formed.
Combinations are decisions that are made by choosing some or all of a group of objects, regardless of how they are arranged. the variety of n distinct combinations, each taken r at a time,
We may have four males and one lady or three men and two women (5 men only).
∴ Required number of ways = (⁸C₃ x ⁷C₂) + (⁸C₄ x ⁷C₁) + ⁸C₅
= [tex]\frac{8*7*6}{3*2*1} *\frac{7*6}{2*1} + \frac{8*7*6*5*4}{4*3*2} *\frac{7}{1} + \frac{8*7*6}{3*2}[/tex]
= 1176 + 1960 + 56
= 3192
Therefore, at least 3 men are there on the committee can be formed 3192 times.
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Your family purchases a new car for $20,000. Its value decreases by 15% each year. During what interval does the car's value exceed $10,000? Round your answer to the nearest hundredth.
From the time it was purchased until about years later.
The car's value will exceed $10,000 during the interval of 6.97 years to 12.97 years.
To find the interval during which the car's value exceeds $10,000, we can use the following formula to calculate the value of the car after n years:
Value = $20,000 × [tex](1 - 0.15)^n[/tex]
We want to find the number of years, n, such that Value > $10,000. Rearranging the equation, we get:
n = (log(Value / $20,000)) / (log(1 - 0.15))
Substituting Value = $10,000, we find that n = approximately 6.97 years.
So, the car's value will exceed $10,000 from approximately 6.97 years after it was purchased until about 12.97 years after it was purchased.
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Given the equation 3x + y = 6, write a second equation that, together with the first,
will create a system of equations that
(a) has one solution;
(b) has an infinite number of solutions;
(c) has no solution;
(d) has the ordered pair (4, -6) as its only solution.
This system of equations has the ordered pair (4, -6) as its only solution, as the two lines intersect only at that point.
What is the system of equations?
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
To create a system of equations that has one solution, we can write a second equation that intersects with the first equation in exactly one point.
One way to do this is to solve the first equation for y, then substitute the expression for y into a second equation. For example:
3x + y = 6
y = -3x + 6
This system of equations has one solution, as the two lines intersect at exactly one point.
To create a system of equations that has an infinite number of solutions, we can write a second equation that is identical to the first equation:=
3x + y = 6
3x + y = 6
This system of equations has an infinite number of solutions, as the two lines are coincident and overlap exactly.
To create a system of equations that has no solution, we can write a second equation that is parallel to the first equation:
3x + y = 6
3x + y = 8
This system of equations has no solution, as the two lines are parallel and do not intersect.
To create a system of equations that has (4, -6) as its only solution, we can write a second equation that passes through the point (4, -6):
3x + y = 6
y = -3x - 6 + 12
y = -3x + 6
Hence, This system of equations has the ordered pair (4, -6) as its only solution, as the two lines intersect only at that point.
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what is the value of x if 10 % of x is equal to x-405
Answer:
-4050
Step-by-step explanation:
you have to do inverse operation
so divide by 10 and times by 100
you can test it out by taking 10 percent of -4050
by dividing it by 100 and times by 10.
the answer comes out as -405
Two part question.
Use the real-world situation below to answer both parts of the question.
Randy needs to buy school supplies. He needs a headset that costs $30.00. He also needs notebooks that cost $3.00 each.
Part 1
Complete the table to determine his total cost for a given number of notebooks.
Format your response using 2 decimal places and NO symbols. Example: 25.00
Part 2
Graph the linear relationship
Part 1 is given in the attached image.
Part 2:
The linear equation is y = 3x
The graph of the equation is given in the attached image.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
Randy needs to buy school supplies.
He needs a headset that costs $30.00.
He also needs notebooks that cost $3.00 each.
Part 1 is given in the attached image.
Part 2:
The linear equation is y = 3x
The graph of the equation is given in the attached image.
Hence, all the solution of part 1 and 2 is given above.
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HELPPPPPPPPPPPPPPPPPPPP
Answer:
i wish i knew but try just posting the pictures on the math page and boom
Answer: it should just be (x, -y)
Step-by-step explanation:
Greenlings are a group of fish that share common features.
The function
G(×) = -10×€2 +100× +44
What does the variable x represent? Include the units.
The variable x shows fish with common features.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.
Given:
G(x) = -10x² + 100x +44
Now solving the Quadratic Equation we have
D = √(100)² - 4(-10)(44)
D = √10000 + 1760
D = √11760
D= 108.44
Now, x= -b ± D/2a
x= -100 ± 108.44 /2(-10)
x= -100 ± 108.44 / (-20)
x = -100 + 108.44 / (-20) or x= -100- 108.44 / (-20)
x= -0.422 or x= 10.422
Here x represents the fish with common features.
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I need help with this problem p
The initial value is 20000 and it is a growth function
The rate is 14%
How to determine the initial valueFrom the question, we have the following parameters that can be used in our computation:
v(t) = 20000(1.14)^t
A function represented as
v(t) =ab^t has teh following features
Initial value = a
Growth/Decay factor = b
This means that
Initial value = 20000
Also, we have
Growth factor = 1.14
This means that
Percentage rate = 1.14 - 1
Percentage rate = .14
So, we have
Percentage rate = 14%
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Here is a point on a circle centered (0,0) at .
Which equation defines the circle?
The equation of circle is,
⇒ x² + y² = 100
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
Here is a point (6, 8) on a circle centered (0,0) at.
Now, Distance between the point (6, 8) and (0, 0) is,
⇒ D = √(6 - 0)² + (8 - 0)²
⇒ D = √36 + 64
⇒ D = √100
⇒ D = 10
We know that;
Distance between the point (6, 8) and (0, 0) is the radius of circle.
And, The equation of circle is,
⇒ (x - a)² + (y - b)² = r²
Where, (a, b) is center of circle and r is radius of circle.
Here, Center of circle = (0, 0)
And, Radius of circle = 10
So, We get;
The equation of circle is,
⇒ (x - a)² + (y - b)² = r²
⇒ (x - 0)² + (y - 0)² = 10²
⇒ x² + y² = 100
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