The value of expression -23 +-15+|-17| + -35 is -56
In this question, we have been given a numerical expression.
-23 +-15+|-17| + -35
We need to find the value of given numerical expression.
Consider given numerical expression,
-23 +-15+|-17| + -35
= -23 + (-15) + |-17| + (-35)
= -23 - 15 + |-17| - 35
We know that for any real number a, |±a| = a
So, |-17| = 17
= -38 + 17 - 35
= -56
Therefore, the value of expression -23 +-15+|-17| + -35 is -56
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a rectangular lot is to be bounded by a fence on three sides and by a wall on the fourth side. two kinds of fencing will be used with heavy duty fencing selling for $4 a foot on the side opposite the wall. the two remaining sides will use standard fencing selling for $3 a foot. what are the dimensions of the rectangular plot of greatest area that can be fenced in at a cost of $6600?
An area 825 by 550 ft gives max area for $6600.
What is the area of rectangle?Any shape's area can be calculated by counting how many unit squares will fit inside of it.A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area. Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangle floor's area.acc to our question-
he perimeterP = L + 2WThe cost4L + 3(2W) = $66004L + 6W = $66004L = (6600-6W)divide both sides by 4L = 1650 - 1.5WReplace L with (1650-1.5w)A = W(1650-1.5W)A quadratic equationA = -1.5w^2 + 1650wFind the axis of symmetry: x = -b/(2a); In this equation: a=-1.5; b=1650w = %28-1650%29%2F%282%2A-1.5%29w = +550 ft is the widthfind the lengthL = 1650 - 1.5(550)L = 825 ft is the lengthhence, 3300 + 3300 = $6600
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A primary school had 1200 students enrolled in 2013 and 1500 students in 2016.if the students population grows as a linear function of time t,where t is the number of years after 2013.how many will be enrolled in the school in 2020?and find the linear function that relates the students population to time t.
Answer:
y=100t+1200, where t is years since 2013 and
Step-by-step explanation:
We only have two points from which to form an equation. Since we are told that it is a linear equation, two points is all we need to find an equation in the form of y=mx+b, where m is the slope (the rate of change) and b is the y-intercept (the value of y when x=0). Let's make the x axis the year and y the student population.
Let's put the data into an x,y format, but before we do, lets be sure to adopt the problem's fervent wish that we treat the x variable, t, as the years since 2013. "t is the number of years after 2013." (0,1200) becomes is the data point for 2013. The school's population will be the y-axis.
(0,1200) [primary school had 1200 students enrolled in 2013], and
(3,1500) [1500 students in 2016]
---
First calculate m, the slope. Slope is the Rise/Run between the two points (the change in y over the change in x)
Going from (2013,1200) to (2016,1500) we find that:
Rise (in y) = (1500 - 1200) = 300 students
Run (on x) = (2016 - 2013) = 3 years
The Rise/Run, or slope, m, is 300/3 or 100: m = 100
Lets put that into our equation format:
y = 100x + b
X will be the time, in years. The problem asks that we define x in terms of years after 2013, and that this be assigned the variable, t:
y = 100t +b, where t is years after 2013.
(The 100 tells us that the student population increases by 100 per year)
We now need b, the y-intercept. One can either graph this and look for the value of y when x=0, of simply input either of the data points. This looks easy enough to input a point and solve for b:
Remember that t is the (year - 2013)
y = 100t +b Solve for (2013,1200)
t = 2013 - 2013 = 0
1200 = 100*(0) + b
b = 1200
Actually, b was easy enough to find without either calculating or graphing, since one of our two points tells us the y-intercept (0,1200).
The equation becomes y = 100t + 1200
See the attached graph.
2 1. The drama teacher is making bandanas for costumes. She is cutting yard of fabric into 6 bandanas of the same size. Write and solve an equation to find how much fabric there will be for each bandana. (Example 1)
The equation which can be used to find how much fabric is used in each bandana is [1/2 ÷ 6 = x].
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the equation to get fabric used in each bandana:
Fabric cutting out to make 6 bandanas is 1/2 yards.Then, the fabric in each bandana will be:
1/2 ÷ 6 = xSolve as follows:
1/2 ÷ 6 = x1/2 × 1/6 = x1/12 = xSo, 1/12 yards of fabric is used in each bandana.
Therefore, the equation which can be used to find how much fabric is used in each bandana is [1/2 ÷ 6 = x].
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Complete question:
The drama teacher is making bandanas for costumes. She is cutting 1/2 yard of fabric into 6 bandanas of the same size. Write and solve an equation to find how much fabric there will be for each bandana.
government employees: in 2013 about 66% of full-time law enforcement workers were sworn officers, and of those, 88.4% were male. females however make up 60.7% of civilian employees. choose one law enforcement worker at random and find the following. b. the probability that he is a male civilian employee
The probability that he is a male civilian employee is 0.13362.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given that 66% of full-time law enforcement employees are sworn officers, 34% of them are civilian employees (100 - 66).
Given that 60.7% of civilian employees are women. Therefore, the percentage of men is (100 - 60.7)% or 39.3%.
Therefore, the likelihood that he works as a male civilian is 39.3% of 34%, which equals 0.393 * 0.34, = 0.13362.
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What are the domain and range of the function f(x) = -
OD: {X E R | X + -2},R: {ye Rly +-8}
E
OD: (x = R X
4),R: {ye Rly -2}
OD: {x € R | x # 2},R: {y = R | y + 8)
x² - 4x-12?
X+2
OD:{X = R | x # -4},R: {y = R | y + 2}
The domain is { x ∈ R | x ≠ -2 }.
The range is { y ∈ R | x ≠ -8 }.
What are the domain and range of a function?
The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.
A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)
Find domain:
Set the denominator equal to zero and solve for x.
x+2=0
x=-2
This means, domain is set of all real numbers except x=2.
Set builder notation: { x ∈ R | x ≠ -2 }. R= real numbers
Find range:
Replace f(x) by y in the given equation and solve for x.
[tex]y=\frac{x^2-4x-12}{x+2}[/tex]
Write the factors of the numerator
[tex]y=\frac{(x+2)(x-6)}{x+2}[/tex]
common terms x+2 cancel out
y=x-6
x=y+6
substitute x=-2
-2=y+6
y= -8
This means range is the set of all real numbers except y= -8.
Set builder notation: { y ∈ R | y ≠ -8 }. R= real numbers
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Simplify the power.
(-3x²y)^4
Using exponents, the resultant expression after simplification is 81x⁸y⁴.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.For instance, the number 6 is multiplied by itself four times, yielding 6 × 6 × 6 × 6. You can write this as 6⁴. In this case, the exponent is 4 and the base is 6.So, the expression is:
(-3x²y)⁴Now, simplify the power as follows:
(-3x²y)⁴(-3x²y)⁴ = (3x²y)⁴ (Exponent rule)3⁴(x²)⁴y⁴ (Exponent rule)81((x²)⁴y⁴ (3⁴ = 81)81x⁸y⁴Therefore, using exponents, the resultant expression after simplification is 81x⁸y⁴.
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Please help!!
Solve this system of equations by graphing. First graph the equations, and then type the solution.
x+2y=2
y=–x+4
(you'll need to graph this).
By graphing, the solution of the system of equations is: (6, -2).
How to Solve a System of Equations by Graphing?To solve the system of equations by graphing, plot each of the line of the equations, then find the coordinates of the point where both lines intersect. Where they intersect is the solution to the systems of equations.
Given the following equations:
x + 2y = 2
y = -x + 4
x + 2y = 2 can be rewritten as y = -1/2x + 1. The graph for x + 2y = 2 will intercept the y-axis at 1 and also has a slope of -1/2. (It is the red line in the image below).
The graph of y = -x + 4 will also have a slope of -1 and intercept the y-axis at 4. (It is the blue line in the image below).
The graph of the equations are shown below, and they intersect at (6, -2), which is the solution to the system of equations.
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Is -1 8/9 a repeating decimal or Terminating
A rectangle with dimensions 60 units * 40 units is drawn on a grid paper that has a 1 unit * 1 unit grid. Each vertex of the rectangle is on a node, and each side of the rectangle is on a gridline. Then a diagonal of the rectangle is drawn. How many cells are cut into two(not necessarily equal) parts? PLEASE ANSWER ASAP!!!!!!!
The number of cells cut into two by the diagonal of the rectangle, found by using Pythagorean theorem, are approximately 51 cells
What is Pythagorean theorem?Pythagorean theorem can be expressed as the square of the hypotenuse side of a right triangle is equal to the sum of the square of the legs of the triangle.
The dimensions of the rectangle = 60 units by 40 units
The dimensions of each grid = 1 unit by 1 unit
The vertices of the rectangle are (0, 0), (60, 0), (60, 40), (0, 40)
The slope of the diagonal is therefore;
m = 40/(60) = 2/3
The equation of the line is; y - 0 = 2/3·(x - 0) = 2/3·x
y = 2/3·x
The number of cells in the diagonal is found using Pythagorean theorem as follows as follows;
Length the diagonal, l = √(60² + 40²) ≈ 72.1
Length of the diagonal of a unit = √(1 + 1) =√2
Number of units in the diagonal, n = 72.1/√(2) ≈ 51 units
The number of cells cut into two ≈ 51 cells
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9) For a job, Phillippa is paid three times as much as Peter. Pavin is paid £10 more than Phillippa, Write an algebraic expression for the total of everyone's wages
Answer:
Step-by-step explanation:
Peter=x
Phillippa= 3x then x
Palvin= 10 then Phillippa
Step 2: Answer: Phillipa 3x+x+10
7. Hannah invests £750 and after 4 years has £844.13. Find the compound interest rate.
If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Hannah contributes £750 and following 4 years has £844.13. Then the compound interest rate is given as,
844.13 = 750 (1 + r)⁴
(1 + r)⁴ = 1.1255
1 + r = 1.02999
r = 0.0299
r = 2.99%
r ≈ 3%
If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.
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Select the correct symbol to make 11⎯⎯⎯⎯√ , 1 of 1.
Select Choice
323 a true statement.
The correct inequality symbol that makes the statement true is:
1000 < (6²)³.
How to choose the inequality symbol?The inequality symbols, and their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.In the context of this problem, the numbers being compared are presented as follows:
1000 and (6²)³.
The power of power property of a number with multiple exponents means that the base is kept while the exponents are multiplied.
The number in which this property is applied in this problem is (6²)³, in which:
The base is of 6.The exponents are of 2 and 3.Hence the equivalent number is given as follows:
(6²)³ = 6^6 = 6 x 6 x 6 x 6 x 6 x 6 = 46,656
Which is a greater number than 1,000, meaning that 1,000 is less than the number, and the inequality is:
1000 < (6²)³.
Missing InformationThe problem is given by the image at the end of the answer.
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jacob has a jar of nickels and dimes. he has twice as many nickels as dimes. he has 310. how many of each type of coin does he have
No. of coins in jar of nickels is 207 and of dimes is 103.
Let the no. of coins of dimes = x
No. of coins of nickels = 2x
Total = 310
x + 2x = 310
3x = 310
x = 310/3
= 103.33
≈ 103
No. of coins of dimes = 103
No. of coins of nickels = 310 - 103
= 207
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a deli bar offers sandwiches with four types of bread, three types of cheese and four types of meat. how many different sandwich combinations are possible?
Exactly one type of meat required = 5 choices
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
Exactly one type of meat required = 5 choicesAny number (0–5) of types of meat allowed: 2^5 (ie. binary, eat type of meat is either ‘on’ or ‘off’At least on type of meat required 2^5 - 1 (remove the zero choice)Do similarly for bread and cheese and number of sandwiches combinations =bread combinations X cheese combinations X meat combinationslearn more about probability click here:
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Given the function below, find value (a) of x if f(x)=7
The function f(x) = 2x + 1 has its value of x to be 3 when f(x) = 7
How to determine the value of the function?From the possible question, the definition of the function is given as
f(x) = 2x + 1
Also, from the question, we have:
f(x) = 7
Substitute 7 for x in the equation f(x) = 2x + 1
So, we have the following representation
2x + 1 = 7
Subtract 1 from both sides of the equation
This gives
2x = 6
Divide both sides by 2
x = 3
So, we can conclude that the value of x is 3
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Possible question
Given the function below, find the value of x if f(x)=7
f(x) = 2x + 1
(y+6) (y+13) find the product
step by step explanation pls
Answer:
(y + 6)(y + 13) = y² + 19y + 78
Step-by-step explanation:
[tex] \rm \implies (y + 6)(y + 13) \\ \\ \rm \implies y(y + 13) + 6(y + 13) \\ \\ \rm \implies {y}^{2} + 13y + 6y + 78 \\ \\ \rm \implies {y}^{2} + 19y + 78[/tex]
What is the slope of the line that passes through the points (7,-5) and (16,7) in simplest form ?
Answer:
4/3
Step-by-step explanation:
look for gradientgradient=
[tex] \frac{change \: in \: y}{change \: in \: x?} [/tex]
change in y7--5=12
change in x16-7=9
gradient12÷9=4/3
the gradient is the same as slope
thus the answer is 4/3
Which equation represents a line which is perpendicular to the line y=2x-5y?
A.2x-y=-42x−y=−4
B.2y−x=4
C.x+2y=−6
D.2x+y=−2
Answer:
C) x + 2y = - 6Step-by-step explanation:
We know that perpendicular lines have opposite-reciprocal slopes.
Given line:
y = 2x - 5Its slope is 2 and the perpendicular line has a slope of - 1/2.
Let's find the line with the slope of - 1/2:
A) 2x - y = - 4y = 2x + 4, the slope is 2, the answer is NOB) 2y - x = 42y = x + 4y = 1/2 x + 2, the slope is 1/2, the answer is NOC) x + 2y = - 62y = - x - 6y = - 1/2 x - 6, the slope is - 1/2, the answer is YESD) 2x + y = - 2y = - 2x - 2, the slope is - 2, the answer is NOAnswer:
c
Step-by-step explanation:
im 68inches tall so how much is that into feet?
Answer:
5.68 ft
Step-by-step explanation:
12 inches = 1 feet
[tex]68 \: inches \: *\: \frac{1 feet}{12 \: inches} =\frac{68}{12} \: feet= 5.6777...\\\\68 \: inches \approx 5.68 \: feet[/tex]
true or false? a large number of mba applicants are given an aptitude test. scores are normally distributed with a mean of 460 and standard deviation of 80. the probability that an applicant scores below 552 is 0.8329.
It is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.
Given, a large number of MBA applicants are given an aptitude test. scores are normally distributed with a mean of 460 and standard deviation of 80.
We are asked the probability that an applicant scores below 552.
Now, using the formula of probability, we get
P(X < 552) = 0.8329
when the mean is given i.e. 460 and standard deviation is given i.e. 80.
Hence, it is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.
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The length of a rectangle is 5 more than twice the width . If the length is 60 inches ,what is the width?
Answer:27.5 inches
Step-by-step explanation:
Question 2 options:
Multiply the radicals.
What is the product in simplest form?
The product in simplest form is [tex]-250\sqrt[3]{50}[/tex] .
In the question,
It is given that,
[tex]5*\sqrt[3]{5} * (-10\sqrt[3]{50})[/tex]
By radical laws, [tex]\sqrt{a} * \sqrt{b} = \sqrt{ab}[/tex]
So,
The given question becomes:
[tex]-50*\sqrt[3]{50*5} = -50*\sqrt[3]{250} = -250\sqrt[3]{5} }[/tex]
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I need help on solving these equations linear. Please helpppp
The solution of the first set of equations is x = 15 and y = 5 and the second is x = 14.25 and y = 7.75.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation.
a)
As per the given first system of equation,
2x - 4y = 10
x + 5y = 40 → 2x + 10y = 80
Subtract both
10y + 4y = 80 - 10
14y = 70
y = 5
And, x = 40 - 5(5) = 15
b)
As per the given first system of equation,
3x - 5y = 4 and
-2x + 6y = 18 → -x + 3y = 9 → -3x + 9y = 27
Add both
-5y + 9y = 4 + 27
4y = 31
y = 7.75
x = (4 + 5(7.75))/3 = 14.25
Hence "The solution of the first set of equations is x = 15 and y = 5 and the second is x = 14.25 and y = 7.75".
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a survey of 500 high school students was taken to determine their favorite chocolate candy. of the 500 students surveyed, 118 like snickers, 185 like twix, 179 like reese's peanut butter cups, 60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups, and 17 like all three kinds of chocolate candy. how many students like snickers, but not twix or reese's peanut butter cups? a) 118 b) 101 c) 100 d) 18 e) 83 f) none of the above.
There are 18 students who like snickers but not twix or reese's peanut butter cups.
Given, that 500 high school students was taken to determine their favorite chocolate candy.
118 like snickers, 185 like twix, 179 like reese's peanut butter cups,
60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups,
and 17 like all three kinds of chocolate candy.
Let A = Set of students like snickers
B = Set of students like twix
C = Set of students like reese's peanut butter cups
Now, we have to find the number of students like snickers but not twix or reese's peanut butter cups i.e. A - A∩B - A∩C + A∩B∩C
A - A∩B - A∩C + A∩B∩C = 118 - 60 - 57 + 17
A - A∩B - A∩C + A∩B∩C = 135 - 117
A - A∩B - A∩C + A∩B∩C = 18
Hence, there are 18 students who like snickers but not twix or reese's peanut butter cups.
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How much would it cost for 3 slices of pizza and 4 orders of French fries?
Answer:
1 piece = 1 slice then the answer is 4/3 = $1.33 (still … 3 slices will be $3.99 rounded to 4). A pizza costs £5.50 and fries cost £1.00, John orders 3 pizzas and 5 fries but the …
A rectangular tank with a square base, an open top, and a volume of is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
The tank with the smallest surface area has dimensions of 6ft.
s = 12ft and h = 6ft.
A(s) = s² + 4 × (V ÷ s)
The rectangular tank has a capacity of 864 feet.
Let the square base's long sides be.
Let h represent the tank's height.
Let A represent the tank's whole area.
A = (Base Area) + (4 × Lateral Area)
Lateral Area = s × h
Lateral Area = s × (V ÷ s²)
Lateral Area = (V ÷ s)
Base Area = s²
Compared to the objective function,
A(s) = s² + 4 × (V ÷ s)
A(s) = s² + 4 × (864 ÷ s)
The area function's derivative,
A'(s) = 2s - (3456 ÷ s²)
The smallest surface area is now.
A'(s) = 0
2s - (3456 ÷ s²) = 0
2 × [tex]s^{3}[/tex] = 3456
[tex]s^{3}[/tex] = 3456
s = [tex]\sqrt[3]{3456}[/tex]
s = 12ft
The volume is,
V = s² × h
864 = 12² × h
h = 6ft
As a result, the tank's height is 6 feet, and the square base's long sides measure 12 feet.
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The question is -
A rectangular tank with a square base, an open top, and a volume of 864 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.
Which equation can equal 107 for some value of n or x? t(n)= 2n + 7 or f(x) = 2x + 7
Ot(n)
Of(x)
O neither
O both
For some n or x value, neither equation can equal 107. f(x) = 2x + 7 or
t(n) = 2n + 7.
What is Function Notation?Function notation is a method for writing functions that are simple to read and understand. When we use function notation, the independent variable is typically x, and the dependent variable is F. (x).Notation for Functions When expressing a function as an equation, it is often written as "f(x)." When creating a table of values for an equation, such as y = 5x - 1, we use the rule "multiply by five and subtract one" to transform an input x value into the single resulting y value.Function notation is a method for writing functions that are simple to read and understand. When we use function notation, the independent variable is typically x, and the dependent variable is F. (x)To learn more about Function Notation, refer to:
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Francisco just got his driver's license and wants to rent a car. The platinum car rental company charges $180 plus $92 per hour to rent a car. The plastic car rental company charges $250 plus $75 per hour. For what number of hours would the companies charge the same amount?
6900 hours, make a list of multiples until lcm is found
Catseby ran up 16 flights of stairs. Write an integer to represent this situation
Zero means ????
Answer: 16
Step-by-step explanation:
NEED HELP WRITING THE EQUATION!!!
The equation of line with undefined slope and passes through the point
(1/2, 5) will be;
⇒ x = 1/2
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point = (1/2 , 5)
And, The slope = undefined
Now,
Since, We know that;
The equation of line with undefined slope and passes through the point will be;
⇒ x = a
Where, 'a' is the x - intercept.
Here, The point = (1/2 , 5)
The slope = undefined
And, The x - intercept = 1/2
So, The equation of line with undefined slope and passes through the point (1/2, 5) will be;
⇒ x = 1/2
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