Given:
The ratio of the amount of money Kate has to that of Nora is 3 : 5.
After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9.
To find:
The sum of money Kate had initially.
Solution:
Let the initial amount of money Kate and Nora have are 3x and 5x respectively.
After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9.
The amount of Kate = 3x+150
The amount of Nora = 5x-150
Now,
[tex]\dfrac{3x+150}{5x-150}=\dfrac{7}{9}[/tex]
[tex]9(3x+150)=7(5x-150)[/tex]
[tex]27x+1350=35x-1050[/tex]
[tex]1350+1050=35x-27x[/tex]
[tex]2400=8x[/tex]
Divide both sides by 8.
[tex]300=x[/tex]
Putting x=300 in 3x, to get the amount of money Kate has initially.
[tex]3(300)=900[/tex]
Therefore, the Kate initially had $900.
Eli wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. Eli only has $37 to spend.
Let n represent the number of notebooks that Eli buys.
Which inequality describes this scenario?
37<2n+24 , 37<2n+24
37≤2n+24 , 37 is less than or equal to 2 n plus 24
37>2n+24 37 is greater than 2 n plus 24
37≥2n+24
Answer: the second one
Step-by-step explanation:
The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:
37 ≥ 2n + 24
Option D is the correct answer.
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
We have,
Cost of the calculator = $24
Cost of a notebook = $2
Total amount to spend = $37
Number of notebooks = n
The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:
37 ≥ 24 + 2n
The number of possible notebooks to buy:
37 24 + 2n
37 - 24 ≥ 2n
13 ≥ 2n
13/2 ≥ n
6.5 ≥ n
The number of notebooks can be 6 or fewer.
Thus,
The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:
37 ≥ 2n + 24
Option D is the correct answer.
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Simplify (24)−1. one over two raised to the power of negative four one over two raised to the fourth power −24 23
The simplified form of the expression (2⁴)⁻¹ is 1/2⁴ (one over two raised to the power of four).
The integers exponents are the exponents that should be an integer. It can be either a positive integer or a negative integer. In this, the positive integer exponents describe how many times the base number should be multiplied by itself.
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
It is given that the expression is (2⁴)⁻¹
Now,
using the integer exponent properties,
=> (2⁴)⁻¹
=> (2)⁴* ⁻¹
=> (2)⁻⁴
=> 1/2⁴
Therefore, the answer is 1/2⁴ (one over two raised to the power of four) derived using the properties of integer exponents.
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suppose that you decided to go skiing this weekend. it costs $50 for transportation, $50 for lodging, $50 for ski lift tickets and you could have earned $100 as a waiter at a job you love so much you would do it as a volunteer if you had nothing better to do. what is the total cost of the ski weekend?
The total cost of the ski weekend comes out to be $250.
What is the total cost of expenses?Total expenses for just a given period are the sum of all gross cash expenditures and furthermore any pending subsidiary items like operating expenses, reward fees, interest, & taxes.
Some key features regarding the total cost are-
In economics, total cost is the sum of all costs a company incurs in generating a certain output level. It is generally expressed as the sum of all fixed costs (for example, the costs of a construction lease and heavy machinery) that do not vary with the amount of output produced and all variable costs (for example, the costs of labor and raw materials) that change with the of output. If fixed costs are not changed (for example, by acquiring a larger building or more industrial equipment), the rate at which of variable costs to increasing output will become progressively greater with in long run, due to decreasing returns on additional units of production.Now, according to the question;
The cost of all spending are-
$50 for transportation
$50 for lodging
$50 for ski lift tickets
$100 for waiter.
Total cost = transportation cost + lodging cost + ski lift tickets cost + waiter cost.
Total cost = $50 + $50 + $50 + $100
Total cost = $250.
Therefore, the total spending in the ski weekend are $250.
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what trigonometric expression can be used to find the value of x? replace a and b with the correct values.
The trigonometric function that can be used to find the value of x is 12 / tan ( 25 ) . The correct values of a and b will be 12 and 25 resp . .
Given :
A right angle triangle , one angle = 25 ° and side opposite given angle = 12 units .
Trigonometric Formula for Tan θ
tan θ = perpendicular / base , tan θ = ( sin θ / cos θ ) , tan θ = ( 1 / cot θ ) .
where θ = 25 , perpendicular = 12 , base = x .
Substituting values in above first formula ,
tan 25 = 12 / x
Therefore , x = 12 / tan ( 25 ) .
Hence , a = 12 and b = 25 .
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A company makes a profit of $55 per software program and $45 per video game. The company can produce at most 225 software programs and at most 275 video games per week. Total production cannot exceed 450 items per week. How many items of each kind should be produced per week in order to maximize the profit?
Use linear programming to solve. Show all your work.
Answer:
they should produce 225 software programs and 225 video games per week.
Step-by-step explanation:
limit 450
there are 2 factors the software and video games.
450•2= 225
identify the set of values for which will be a real number. the set of values for which will be a real number is
Except for x = 3, the set of x values for that y will become a real number as per Y=8/x-3 contains all real numbers.
What is real number?A real number is any number which can be found with in real world. Numbers can be found all around us.
Natural numbers are used to count objects, rational numbers for fraction representation, irrational numbers for determining the square root of the a number, integers for temperature measurement, and so on. These various types of numbers combine to form a gathering of real numbers.The union of a set of rational numbers (Q) or the set of irrational numbers yields the set of real numbers (R).Now according to the question;
In actuality, the expression Y=8/x-3 stops producing a real numerical value for y when the denominator has become zero.
When the denominator is zero, the y value is undefined and thus not a real number.
As a result, if we set;
x - 3 = 0
x = 3
Therefore, except for x = 3, the set of x values for which y is a real number per the Y=8/x-3 includes all real numbers.
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The complete question is-
Y=8/x-3
Identify the set of values x for which y will be a real number
Ari has a total of 22 coins consisting of pennies and nickels. The total value of the coins is $0.54.
Answer:
8 nickels and 14 pennies
Step-by-step explanation:
Let p = number of pennies
Let n = number of nickels
p + n = 22 .01p + .05n =.54
Take the second equation and multiple it through by 100 to clear the decimals.
100(.01p + .05n( = .54(100)
p + 5 n = 54 Multiply this through by -1 so that I can add it to the first equation.
-p -5n = -54
p + n = 22 Add these together
-4n = -32 Divide both sides by -4
n = 8 We have solved for n. We have 8 nickels.
Plug 8 in for n in the first equation and solve for p.
p + n = 22
p + 8 = 22 Subtract both sides by 8
p = 14 There are 14 pennies.
Check:
p + n = 22
14 + 8 = 22
22 = 22 Checks
.01p + .05n = .54
.01(14) + .05(8) = .54
.14 + .40 .54
.54 .54 check
The Evans family drives 21 miles in the first miles in the first 20 minutes of their trip. what is their speed in miles per hour during this time? create a representation to show your work.
The measure of the speed during the time is 63. 64 miles per hour
How to determine the speedThe formula for speed is expressed as;
Speed = distance/ time
Given that;
Distance traveled = 21 milesTime = 20 minutesLet's convert the time in minutes to hour
60 minutes = 1 hour
20 minutes = x hour
cross multiply
x = 20/ 60
x = 0. 33 hours
Substitute the values
Speed = 21/ 0. 33
Speed = 63. 64 miles per hour
Thus, the measure of the speed during the time is 63. 64 miles per hour
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which measurements best approximate the lengths of the legs, to the nearest tenth of a centimeter, of a right triangle if the hypotenuse is 70 cm and the shorter leg is one-third the length of the longer leg?
The length of the base will be equal to 65.99 centimeters.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The formula for the Pythagorean theorem is given below:-
H² = B² + P²
Given that in a right triangle if the hypotenuse is 70 cm and the shorter leg is one-third the length of the longer leg.
P = 70/ 3 cm
H = 70 cm
The value of the leg will be calculated as:-
H² = B² + P²
70² = B² + (70/3)²
B² = 70² - (70/3)²
B = √4355
B = 65.99 cm
Therefore, the length of the base will be equal to 65.99 centimeters.
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a bucket holds 10 liters.about how many gallons does the buket hold?round to the nearest tenth,if necessary
For the bucket to hold the 10 litres, then it s said to contains 2.64 gallons.
What is termed as units and unit conversion?A multi-step procedure encompassing multiplication as well as division by a mathematical factor is known as unit conversion. We can measure weight, length, and temperature in a variety of ways.
Before performing any arithmetic operations on 2 variables, we should always convert all of their values to a common unit.Unit conversion is the process of converting one unit of measurement to another measurement unit for the same amount by multiplying/dividing by conversion factors.Scientific notation is used to express the units, which are then converted into numerical based on the quantities.Now, per the given question;
The total amount a bucket contains is 10 litres.
Noe, the conversion of litres in gallons is given as;
1 litres = 0.26 gallons.
Thus, 10 litres = 10×0.264
= 2.64 gallons.
Therefore, the bucket will contain 2.64 gallons.
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In 1975, a person earning minimum wage made $80 for a 40-hour work week. what was the minimum wage per hour in 1975?
The minimum wage per hour = $2
Here we need to find the value of minimum wage per hour in 1975
As is given that the earning minimum wage is $80 for working 40 hours.
40-hour work gives = $80
1-hour work gives = $80/40
= $2
Therefore the minimum wage per hour in 1975 is $2
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Kaylee drove 160 miles in 5 hours. If she continued at the same rate, how far would
she travel in 17 hours
Answer:
544 miles
Step-by-step explanation:
160 miles= 5 hours in order to see how much she traveled in 1 hour you need to divide so do 160 divided by 5 = 32 then do 32x17 which would be 544.
I hope it helps you!
~XxBells is a cute girlxX~
Kaylee would travel 544 miles in 17 hours if she continued at the same rate.
What is the distance?A mathematical number is known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.
distance = rate × time
We know that Kaylee drove 160 miles in 5 hours, so her rate is:
rate = distance / time = 160 miles / 5 hours = 32 miles/hour
Now we can use this rate to find out how far she would travel in 17 hours:
distance = rate × time
distance = 32 miles/hour × 17 hours
distance = 544 miles
Therefore, Kaylee would travel 544 miles in 17 hours if she continued at the same rate.
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What is the slope of the line that passes through the points (5, -6) and (9, -6) Write your answer in simplest form.
Answer:
slope=y2-y1/x2-x1
=-6-(-6)/9-6
=0/3
any fraction in which numerator is 0 is 0.
90% of what number is 45?
Answer:
40.5
Step-by-step explanation:
The shaded diagram represents a block of land.
What is the area of the block?
By using Heron's formula and standard formula for the area of a triangle, the area of the composite figure is 921006.497 square meters.
What is the area of a composite figure?
In this problem we must determine the area of a composite figure, which consists in subtracting the area of an isosceles triangle from the area of the equilateral triangle:
Big triangle
The area of the big triangle is determined by Heron's formula:
s = [3 · (520 m)] / 2
s = 780 m
A = √[(780 m) · (1560 m - 520 m)³]
A ≈936693.077 m²
Small triangle
H = (520 m) · sin 60°
H ≈ 450.333 m
h = 450.333 m - 390 m
h = 60.333 m
A = 0.5 · (520 m) · (60.333 m)
A = 15686.580 m²
Then, the area of the composite figure is 921006.497 square meters.
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9. Mr. Crowley bought lunch for himself and eight of his employees.
Each had a sandwich platter that costs $5.85 and a drink that
costs $1.25. Five of the employees had dessert that costs $1.50.
Mr. Crowley gave the delivery person $80 and told her to keep
the change as a tip. How much was the delivery person's tip?
Answer:
$8.60
Step-by-step explanation:
Let x = the tip
80 - x = 9(5.85 + 1.25) + 5(1.50)
80 -x = 63.90 + 7.5
80 - x = 71.40 Subtract 80 from both sides
-x = -8.60 Divide both sides by -1
x = 8.60
Answer please, thanks.
Answer:2
Step-by-step explanation:
M, N and P are points on a circle, centre O.
MON is the diameter of the circle.
MP = 3.5 cm
PN = 9.7 cm
Angle = 90º
Work out the circumference of the circle.
Give your answer correctly to 3 significant figures.
Step-by-step explanation:
just draw what I have done
Please Help
Thanks In advance
Answer:
4
Step-by-step explanation:
you do cross multiplication
you do 3x12÷9
Can someone please help mee (20 points
brainliest!!!)
Answer:
60,000
Step-by-step explanation:
going straight across the line we can see that for $140 the demand in thousands 60
so
you can buy 60,000 units
Answer:
60 because oficial the line goes to 60
ngozi earns \$24{,}000$24,000dollar sign, 24, comma, 000 in salary in the first year she works as an interpreter. each year, she earns a 3.5\%3.5%3, point, 5, percent raise.
The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by [tex]S = 24000 * (1.035)^t[/tex].
What is a function?
A function in mathematics from a set X(ax) to a set Y allocates exactly one element of Y to each element of X(ax). A relation between a collection of inputs and labor is known as a function.You can use the fact that the raise is done on the previous year's salary.
Let the initial salary be P = $24000
After 1 year, her salary increased by R = 3.5% which, thus,
Total salary = P + increment
Similarly going on, we get
[tex]P_t = P(1+ \frac{R}{100})^t = S[/tex] (we can say)
Putting values of P(value of P) and R(value of R), we get
[tex]S = 24000(1 + 0.035)^t = 24000 *(1.035)^t[/tex]
Thus,
The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by
[tex]S = 24000 * (1.035)^t[/tex]
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What are the key features of the quadratic function f(x) = 2(x - 3)2 + 4
The vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.
The given quadratic function is f(x) = 2(x - 3)² + 4.
We need to find the key features of the given quadratic function.
What is the quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.
Now, the key features of the given quadratic function as follows:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (3, 4)
Focus: (3, 33/8)
Axis of Symmetry: x=3
Directrix: y=31/8
Plot these points (1, 12), (2, 6), (3, 4), (4, 6) and (5, 12) on the graph.
Therefore, the vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.
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will the sum of 5 + (-2) be positive or negative? what is the sum? show your work.
Answer:
positive the answer is 3
Step-by-step explanation:
Solve the equation
A =2πr*2 + 2πrh, for h
lindsay bedford works at the baseball cap shop she is paid $6.50 per hour plus $0.45 for each cap she embroiders how many caps must she embroider to earn at least $85
Lindsay Bedford should embroider 73 caps.
Let us assume the number of number of caps needed to be embroidered for desired earning be x. Now, forming the equation to solve for x, thus, finding the required number of caps.
Equation -
6.50*8 + 0.45*x = 85
Now solving this equation for the value of x.
Performing multiplication of numbers on Left Hand Side
52 + 0.45x = 85
Shifting the product from Left Hand Side to Right Hand Side
0.45x = 85 - 52
Performing subtraction on Right Hand Side to find the value of x
0.45x = 33
Shifting 0.45 to denominator on Right Hand Side
x = 33÷0.45
Performing division to find the value of x
x = 73.3
The number of caps can not be in fraction. So, we will round off the digit to find exact number of caps.
Number of caps = 73
Therefore, Lindsay Bedford needs to embroider 73 caps.
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The complete question is -
Lindsay Bedford works at a baseball cap shop. She is paid $6.50 per hour plus $0.45 for each cap she embroiders. How many caps must she embroider to earn at least $85 in an 8-hour day?
7+(2x3) 5-6(9 divided by 5)=
Answer:
26.2
Step-by-step explanation:
7 + (2x3) 5-6 (9/5)
7 + 6*5-6*1.8
7 + 30-10.8
37 - 10.8
26.2
Raven is deciding between two plumbing services. service provider a multiplies the average number
Based on the fact that Raven is trying to decide between two plumbing services, the costs of the service charge are:
Service provider A - $83.33Service provider B - $105What is the service cost?The Service cost for Service provider A is:
= 50 x 1.5 + (50 x ((1.75 / 1.5) - 1)
= $83.33
Service cost for Service provider B is:
= Number of hours x Cost per hour
= 60 x 1.75
= $105
The cheaper plumber is Service provider A.
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Which statement is true?
The Mississippi River in Iowa is at an elevation of 279 and Death Valley, in California is at an elevation of -282 feet. Which statement is true?
A |279| > |-282|
B |279| < |-282|
C 279 = 282
D 279 < -282
Answer:
Step-by-step explanation:
if we consider mod then the negative turns to positive and positive remains positive so it will be
279 < 282 which is l279l < l-282l
Quadrilateral ABCD is dilated at center (0, 0) with scale factor to form quadrilateral 1/2; A^ prime B^ prime C^ prime D^ prime . What is the length of overline A^ prime B^ prime ?
The length with scale factor to form quadrilateral 1/2, A'B' is √5 units when AB is √20.
What is distance formula?The formula to find the distance between the two points is usually given by
d=√((x2 – x1)² + (y2 – y1)²).
Given :
Quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2 to form quadrilateral A'B'C'D'.
Points - A(0,4), B(4,2), C(4,-4), and D(-2,-2).
So, the points of the quadrilateral ABCD becomes:
A' (0, 2)B' (2, 1)C'( 2, -2)D'(-1 , -1)So, length of A'B'
AB = √(4-0) ² +(2 -4)²
AB = √16 + 4
AB = √20
AB = 2√5
A'B' = 1/2 AB
A'B' = √5
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I need help asap (Fractions)
Answer:
Step-by-step explanation:
3 3/4 = 15/4
15/4 divided by 3/4 = 5