Erica earned a total of 67,150 last year from her two jobs. The amount she earned from her job at the store was 1,550 more than three times the amount she earned from her job at the college. How much did she earn (in dollars) from her job at the college
The amount Erica earned (in dollars) from her job at the college is 16400.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The amount she earned from her college job is, 'x'.
Therefore, The numerical form of the statement can be formed as,
(3x + 1550) + x = 67150.
4x = 65600.
x = 65600/4.
x = 16400.
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A rectangular box, half filled, holds 200 cubic feet of grain. If the box is 8 feet wide and 5 feet long, how deep is it?
The rectangular bin has a depth of 20 feet.
A cuboid is a three-dimensional shape with rectangles on all sides. A cuboid has six faces, eight vertices, and twelve edges. All of the angles formed at a cuboid's vertices are right angles. The opposing edges are perpendicular to each other.
For the given situation,
A rectangular bin is in the shape of a cuboid.
Volume of the rectangular bin, V = 1200 cubic feet
Length of the rectangular bin ,l = 10 feet
Width of the rectangular bin,w = 6 feet
Let the height of the rectangular bin be h.
The formula of volume of cuboid is
[tex]v=lwh[/tex]
Now substitute the above values,
⇒ 1200= (10)(6)h
⇒ [tex]h=\frac{1200}{60}[/tex]
⇒ h= 20
Hence we can conclude that the rectangular bin is 20 feet deep.
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The depth of the box is found through the volume formula for a rectangular prism, which involves multiplying the length, width and depth. Knowing the volume when half-filled, and the length and width, we can calculate the box is 10 feet deep.
Explanation:This problem deals with the concept of volume in mathematics. First, the formula for the volume of a rectangular prism (or a box) is length multiplied by width multiplied by height. In this case, we know that the box is half filled with grain and that the total volume of that grain is 200 cubic feet. So, if the box was filled completely, it would have a volume of twice that, or 400 cubic feet.
Now we know that the box's volume is 400 cubic feet and its length is 8 feet and width is 5 feet. So to find the height (which is what we're calling 'depth' in this case), we can use our volume formula. We divide the total volume by the product of the length and width (400/40) to find the height or depth, resulting in a depth of 10 feet.
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Find a counterexample to show that the statement is false. (Select all that apply.)
x³ 2x
x = 1
-1
none of these
1 < x
x < -1
0
X
A counterexample to show that the statement is false is -1<x<0 or >1
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
EXPLANATION;
Rearrange unknown terms to the left side of the equation: x^3-x>0
Factor the expression:x(x+1)(x-1)>0
Convert inequality to equation:x(x+1)(x-1)=0
Apply Zero Product Property: x=0 or x+1=0 or x-1=0
Rearrange unknown terms to the left side of the equation:x=-1
Rearrange unknown terms to the left side of the equation:x=1
Combine the results: :x=0 or :x=1 or- :x=1
Order x-intercepts from smallest to greatest: x1=-1or x2=0 or x3=1
EXPLANATION;
Rearrange unknown terms to the left side of the equation:
Factor the expression:
Convert inequality to equation:
Apply Zero Product Property: or or
Rearrange unknown terms to the left side of the equation:
Rearrange unknown terms to the left side of the equation:
Combine the results: or or
Order x-intercepts from smallest to greatest: or or
Plot: As shown in figure
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What is 1% of 800?
Hint: We can think of 1% as a common fraction.
Reason:
1% converts to the decimal form 0.01
0.01*800 = 8
Basically we move the decimal point two spots to the left
So the 800.0 becomes 8.000 or simply 8
Answer:
8
Step-by-step explanation:
Anything in percentage format can be expressed as a fraction by dividing by 100
Thus
[tex]\textrm{1\% }= \dfrac{1}{100}[/tex]
1% of 800 is found by multiplying 800 by the above fraction
[tex]\textrm{1\% of 800 } = 800\cdot \dfrac{1}{100} = 8[/tex]
Suppose a parabola has an axis of symmetry at x = 8, a maximum height of 1 and also passes through the point (9, –1). Write the equation of the parabola in vertex form.
Answer:
Below
Step-by-step explanation:
Vertex at 8,1 and includes point 9,-1 <=====given
Vertex form :
y = a (x-8)^2 + 1
Plug in the point (9,-1) to find 'a'
-1 = a ( 9-8) + 1
a = -2
Parabola equation is then y = -2(x-8)^2 + 1
Two families visit a museum. A family of two adults and four children pay £43.50. for entry. Another family of five adults and three children pay £65. for entry. Find, in pounds, the price of one adult ticket and one child ticket.
Answer:
22.75
Step-by-step explanation:
2a + 4c = 43.5
5a + 3c = 65
10a + 20c = 217.5
subtract
10a +6c = 130
= 14c = 87.5
c = 6.25
2a + 25 = 43.5
2a = 18.5
a = 16.5
16.5 + 6.25 = 22.75
Answer:
One adult ticket costs £9.25, and one child ticket costs £6.25.
Step-by-step explanation:
Let a = price of 1 adult ticket.
Let c = price of 1 child ticket.
"A family of two adults and four children pay £43.50. for entry."
2a + 4c = 43.5
"Another family of five adults and three children pay £65."
5a + 3c = 65
We have a system of simultaneous equation in two unknowns.
2a + 4c = 43.5
5a + 3c = 65
Let's solve the system by the method of elimination. We need to add multiples of the two equations in a way that one variable will be eliminated (add to zero).
Let's eliminate the variable a. Multiply both sides of the first equation by -5 Multiply both sides of the second equation by 2. Then add them.
-10a - 20c = -217.5
+ 10a + 6c = 130
----------------------------------
-14c = -87.5
c = 6.25
Now substitute 6.25 for c in the first original equation and solve for a.
2a + 4c = 43.5
2a + 4(6.25) = 43.5
2a + 25 = 43.5
2a = 18.5
a = 9.25
Answer: One adult ticket costs £9.25, and one child ticket costs £6.25.
Standard form of a circle
Answer:
(x−h)2+(y−k)2=r2
Step-by-step explanation:
Standard form for the equation of a circle is (x−h)2+(y−k)2=r2. The center is (h,k) and the radius measures r units. To graph a circle mark points r units up, down, left, and right from the center.
How many tons is 245 pounds
Answer:
IT is 245 pounds
Step-by-step explanation:
The solution is: 0.1225 tons is 245 pounds.
Here, we have,
given that,
245 pounds
we need to find the value in ton
we know that,
1 pound = 1/2000 ton
= 0.0005 ton
let, 245 pounds = x ton
so, we get,
1 pound = 0.0005 ton
245 pounds = 0.0005 * 245 tons
= 0.1225 tons
so, x = 0.1225 tons
Hence, The solution is: 0.1225 tons is 245 pounds.
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This table represents a function.
Plot points to represent the function as a graph.
x y
-4 9
-1 3
0 1
2 -3
The graph solution of the function is attached below;
What is a solution to a system of equations? (SOLUTION GRAPHICALLY)For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)
Given in the question;
points to be plotted;
(-4,9) , (-1,3) , (0,1) , (2,-3)
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HELP PLSSS URGENT
IMMAGE ATTACED
The correct statement regarding the addition of the fractions is given as follows:
A. (3x² + 14x + 196)/[(x + 14)(x - 14)], x ≠ -14, x ≠ 14.
How to add the fractions?The addition of fractions for this problem is given as follows:
[tex]\frac{2x}{x + 14} + \frac{x + 14}{x - 14}[/tex]
They have different denominators, hence the least common factor of the denominator is used.
The terms at the denominator have no common factor, hence the least common factor is the multiplication of them.
Dividing the least common factor by the denominator and multiplying at the numerator, the addition of the fractions is given as follows:
[2x(x - 14) + (x + 14)(x + 14)]/[(x + 14)(x - 14)]
Expanding the numerator, we have that:
2x² - 14x + x² + 28x + 196.
Combining the like terms, the added fraction is given as follows:
(3x² + 14x + 196)/[(x + 14)(x - 14)]
The denominator cannot be zero, hence the restrictions are given as follows:
x ≠ -14, x ≠ 14.
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4cos(x)+ 3 = 6 with - π< x < π
Answer:
x = arccos(3/4) + 2πn where n = 0,1,2,3,4, ....
Step-by-step explanation:
We can solve the equation 4cos(x) + 3 = 6 by isolating the cos(x) term on one side of the equation.
4cos(x) + 3 - 3 = 6 - 3
4cos(x) = 3
cos(x) = 3/4
Now we can find the solutions of the equation by finding the values of x that make cos(x) equal to 3/4. Since -π < x < π, we can find the solutions in the range of -π < x < π.
x = cos^-1(3/4) + 2πn, where n is an integer
x = cos^-1(3/4) + 2πn, where n = 0, 1, 2, ...
The solutions are x= cos^-1(3/4) and x = cos^-1(3/4) + 2π, x = cos^-1(3/4) + 4π
Keep in mind that cos^-1(3/4) is the inverse cosine function or arccos(3/4) so the final solution is x = arccos(3/4) + 2πn where n = 0,1,2,3,4, ....
the NC lottery has a game called picked three numbers in exact order. It cost a dollar to play and if you win you get 500 dollars. respond to the two queations.
what is the expected value playing in the long run?
is it wise investment to play the NC pick 3 in the long run?
The expected value of playing a single game is given as follows:
-$0.499.
As the expected value is negative, it is not a wise investment to play the NC pick 3 in the long run.
How to obtain the expected value of a discrete distribution?The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.
You have to pick three digits in correct order. Considering that for each digit there are 10 possible outcomes, the probability of winning is given as follows:
1/10 x (1/10) x (1/10) = 1/1000 = 0.001.
The probability of losing is given as follows:
1 - 1/1000 = 1000/1000 - 1/1000 = 999/1000 = 0.999.
Considering that you get $500 winning, while you lose $1 losing, the distribution is given as follows:
P(X = 500) = 0.001.P(X = -1) = 0.999.Hence the expected value of the distribution is given as follows:
E(X) = 500 x 0.001 - 1 x 0.999
E(X) = -$0.499.
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Accounting department of “NERDS” company has 120,000 hours of work to complete for the next year.80,000 hours can be completed in the first 8 months, then the remaining 40,000 hours must be completed in the last 4 months. Company plans to add freelancers to handle the additional work in the last 4 months. A Freelancer works 200 hours per month. Approximately how many freelancers will company need to hire?
*
5 points
Answer:
Step-by-step explanation:
The company will need to hire approximately 200 freelancers in order to complete the remaining 40,000 hours of work. This is because each freelancer works 200 hours per month, so in order to complete the 40,000 hours of work in the last 4 months, the company will need to hire 200 freelancers.
what is the fraction of 0.3
Answer:
3/10
This is to reach the character limit
Answer:
3/10
Step-by-step explanation:
0.3 =
3/10 ==> since there is a non-zero number before the decimal, the
number is being divided by 10. If there was an extra 0, add a 0 to 10 and divide the number by 100. (0.3 = 3/10. 0.03 = 3/100)
Add another 0 to make 0.003, which is 3/1000 (add an extra 0 to 100 to make 1000, 10->100->1000).
What are the minimum and maximum values, over the interval x ≥ 3, for the function f(x) = -|x - 1| + 1 graphed below?
The minimum and maximum values, over the interval x ≥ 3, for the function f(x) = -|x - 1| + 1 graphed are -36 and 64 respectively.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Here Relative minimum are the minimum values in the interval
Looking at the graph, we find the lowest point in the interval
Relative minimum : (-3, -36) and (3,-36)
y value -36
Looking at the graph, we can find the highest point in the interval
Relative maximum : (0,64)
y value 64
The minimum and maximum values, over the interval x ≥ 3, are -36 and 64 respectively.
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I need help with these questions
In mathematics, the value for x is 9.38 in Example 1 and 11.40 in Example 2.
What are the value signifies?
The value in mathematics refers to the numerical representation of a quantity or concept. It represents the numerical magnitude of a mathematical expression, equation, or quantity.
For example, in the expression 2 + 3 = 5, the value of 2, 3, and 5 all represent specific numerical magnitudes. The value of a variable, such as x or y, can change depending on the context or equation it is used in, but it still represents a specific numerical value.
Values can be represented in different forms, such as integers, fractions, decimals, or real numbers, and they are used to perform mathematical operations and solve mathematical problems.
a) Example 1
AB is a diameter
PQ is a chord
AO = 13
AO is perpendicular to PQ (2AP=AQ)
In Δ APO
[tex](AO)^2 =(AP)^2+ (PO)^2[/tex]
[tex](13)^2 = (9)^2 + X^2[/tex]
[tex]169 = 81 +X^2[/tex]
X^2 = 169-81
X^2 = 88
X = √88
X = 9.38
As a consequence, 9.38 is equal to x.
b) Example 2
LM = 18
KN = 7
LK = ?
LN = 9
In Δ LKN:
[tex]X^2 = (KN)^2 + (LN)^2[/tex]
[tex]X^2 = (7)^2 + (9)^2[/tex]
X^2 = 49 + 81
X^2 = 130
X =√ 130
X = 11.40
As a consequence, 11.40 is equal to x.
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After 1 year in busines, NetPix has 250 subscribers. They now expect to triple their number of subscribers each year. At that rate, how many subscribers would they have after 10 years in business?
Using the rate of the exponential growth to calculate the exponential function, the number of subscribers after 10 years is 3446
What is an Exponential FunctionAn exponential function is a function in which the variable appears in an exponent. It is of the form f(x) = aˣ, where a is a constant and x is the independent variable. The graph of an exponential function is a curve that increases or decreases at an increasing rate.
To solve this problem, we have to find the rate and then calculate the number subscribers after 10 years.
In a given exponential function;
A = P(1 + x)ⁿ
Since this is an exponential growth, we can calculate the rate as;
1 year = 250 subscriber
2 years = 3 * 250
rate = (250 / 750) * 100
rate = 30%
We can substitute the values into the formula and solve
A = 250(1 + 0.3)¹⁰
A = 3446.46
They are expected to have 3446 subscribers after 10 years
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A line intersects the points (4, -2) and (3, 3). What is the slope of the line in simplest form? m = [?] Enter
Answer: -5
Step-by-step explanation:
y2 - y1/x2 - x1
3 + 2/3 - 4
5/-1
-5
Draw a pair of parallel lines intersected by a transversal so at least one angle is a 45° angle.
Label all of the angle measures in your drawing.
The pair of parallel lines intersected by a transversal so at least one angle is 45 degrees has an angle B'EB as 45 degrees.
What are parallel lines?In terms of geometry, parallel lines are two separate lines that never cross each other and are located in the same plane. They may be vertical or horizontal.
What are intersecting lines?They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.
The pair of parallel lines intersected by transversal is as shown:
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Suppose that 12 inches of wire costs 72 cents. At the same rate, how many inches of wire can be bought for 54 cents?
Answer: 9 inches of wire may be botten.
Step-by-step explanation: First I divided 72 by 12 to find the rate of cents for every inch of wire. I found the rate was 6 cents per inch so I did 6x9= 54.
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Solve for y. -10 - 8y = 2y - 5
Answer:
y = -1/2
Step-by-step explanation:
Pre-SolvingWe are given the equation -10 - 8y = 2y - 5.
We want to solve this equation for y.
To do that, we need to isolate y on one side of the equation.
SolvingTo start, add 10 to both sides.
-10 - 8y = 2y - 5
+10 +10
________________
-8y = 2y + 5
Subtract 2y from both sides.
-10y = 5
Divide both sides by -10.
y = -5/10
-5/10 can be simplified to -1/2.
Hence, y = -1/2.
Which algebraic rule describes the reflection of FG?
The algebraic rule for the reflection of FG is solved to be
D. (x, y) → (x, -y)What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Reflection is one of the movements in transformation that involve creation of mirror image
Transformation rule for reflection over x-axis at origin (0, 0)) is
(x, y) → (x, -y)
Transformation rule for reflection over line y-axis at origin (0, 0)) is
(x, y) → (-x, y)
The reflection of line FG is done across the x axis hence the transformation rule to be used is (x, y) → (x, -y)
This is equal to the last option
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Which description best matches the image?
A.Most of the time, you should drive in this lane position.
B.The operating space of the blue car is closed because the driver's line of sight is restricted.
C.This is the best lane position when approaching a hill or a curve.
D.This depicts the size of the driver's central or straight-ahead vision.
Answer:
B.The operating space of the blue car is closed because the driver's line of sight is restricted.
Step-by-step explanation:
it is not the best lane because lanes depend on which direction you are going so neither a nor c were correct and the driver's straight-ahead vision is not at this angle for there is a car roof and the driver can't see it like this as if you were above the cars this perspective is from above and also not a central vision
I need help understanding how to solve questions 5-8
Answer:2√5
Step-by-step explanation:
5. If OR is perpendicular to PQ and O its the center of the cincunference it means that RP has the same size of QR, then all you have to do its a Pythagorean theorem
H^2=C^2+C^2
OP^2=(2√3)^2+(2√2)^2
(=)OP^2= 12+8
(=)OP^2=20
(=)OP=±√20 ∧ OP>0
(=)OP=2√5
I'm Sorry for the bad english
A book sold 34,500 copies in its first month of release. Suppose this represents 9.8% of the number of copies sold to date. How many copies have been sold to
date?
Round your answer to the nearest whole number.
Answer: If 34,500 copies sold in the first month of release represent 9.8% of the number of copies sold to date, we can use this information to find the total number of copies sold to date. We can set up the equation as:
(34,500 copies) / (9.8%) = (Total number of copies sold to date)
To solve for the total number of copies sold to date, we can cross-multiply and divide by 0.098:
(34,500 copies) * (100%) / (9.8%) = (Total number of copies sold to date)
(34,500 copies) * (100/9.8) = (Total number of copies sold to date)
This simplifies to:
(34,500 copies) * 10.20408163 = (Total number of copies sold to date)
Total number of copies sold to date = 353878.163.
Rounding the answer to the nearest whole number we get:
Total number of copies sold to date = 353878.
So the book has sold 353878 copies to date.
Step-by-step explanation:
352,041
Take 34,500 and divide it be 9.8.
Next, multiply it by 100.
not sure if this is the answer
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
230p – 1010 = 650p – 400 – p and 2.3p – 10.1 = 6.49p – 4 are the equations after rewriting their properties have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p.
What is equations?As with other words like "equal," "equality," and "equate," the word "equa" at the start of the equation will sound familiar to you. Making things balance out is the theme of all these words. A statement of two quantities' equality is expressed by an equation.
You might still attempt to make the two sides equal even if the equation is not mathematical but rather, say, interpersonal. It might be simpler for two people to decide to remain together for a while if marriage is removed from the picture, for instance.
Given the equation 2.3p – 10.1 = 6.5p – 4 – 0.01p
When multiplied by 100, it becomes
230p – 1010 = 650p – 400 – p
And 6.5p - 0.01p = 6.49p
So, 2.3p – 10.1 = 6.49p – 4
Thus, 230p – 1010 = 650p – 400 – p and 2.3p – 10.1 = 6.49p – 4 are the equations after rewriting their properties have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p.
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Write 40 cm as a fraction of 2.4 m. Give your answer in its simplest form.
40cm as a fraction of 2.4m is 1/6
What are fractions?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. In a proper fraction, the numerator is less than the denominator. e.g . 2/7, 4/5, 3/10 e.t.c
An improper fraction had it's numerator higher than it's denominator .Example is 5/2 , 7/3 e.tc.
By expressing 40 cm as a fraction of 2.4m. The first thing we have to do is making both of thesame unit. therefore ;
2.4m = 2.4×100 = 240cm
40 as a fraction of 240 = 40/240
divide through by 40
= 1/6
therefore the fraction of 40 in 240 is 1/6 i.e 240×1/6 = 40
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I'll Give brainliest to whoever answers is correct
Answer:
52
Step-by-step explanation:
RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.
Answer:
52 degrees
Step-by-step explanation:
right angle = 90
90-38=52
So RTQ = 52 degrees
If you dissolved 50 g of sugar in 30 g of water what would the sugar concentration be
Answer:
62.5%
Step-by-step explanation:
(mass of solute/mass of solution) x 100 = 62.5%
what is the value of JK?
Answer:
x = √52
Step-by-step explanation:
Triangle PLM and JLK are connected together at L, which means that they share the same vertex L and therefore, the angle at L is the same for both triangles.
Since PLM and JLK are both triangles, we know that the sum of the angles in each triangle is always 180 degrees.
Let's call the angle at L as a. So we have:
a + (180-a) = 180
We know that PL = 6 and PM = 12, so we can use the Law of Cosines to find the value of the angle a:
c^2 = a^2 + b^2 - 2ab*cos(C)
where c is the hypotenuse, a and b are the other two sides and C is the angle opposite to c.
c = PL = 6
a = PM = 12
b = JL = 4
c^2 = 12^2 + 4^2 - 2124cos(a)
36 = 144 - 48cos(a)
cos(a) = (144 - 36)/48 = (108/48) = 9/4
a = arccos(9/4)
Now we know the measure of angle a and we can use it in the equation of the sum of angles in a triangle.
a + (180-a) = 180
We also know that JL = 4 and JK = x and we can use the Law of Cosines again to find the value of x.
x^2 = 4^2 + 6^2 - 246cos(a)
x^2 = 16 + 36 - 24(9/4)
x^2 = 52
x = √52
