Answer: A. U.S. Landmarks to European Landmarks
Maria has 25 U.S. landmark postcards and 20 European landmark postcards. The ratio of U.S. landmarks to European landmarks can be written as 25:20 or as 25/20.
Alternatively, we can express the ratio as a fraction. If we divide the number of U.S. landmark postcards by the total number of U.S. and European landmark postcards, we get 25/(25+20)=25/45
The last way we can express the ratio as a decimal. By dividing the number of U.S. landmark postcards by the total number of U.S. and European landmark postcards, we can find that the ratio of U.S. landmarks to European landmarks is 25/45 =0.555 or 55.5%
Step-by-step explanation:
Alana and Petra go to a used book sale , where every book is the same price. Alana buys 4 books and Petra buys 2 books. They run into their friend angus, who really loves to read, and discover that he has bought 16 books. Angus received a $15 discount, but he still spent $5 more than Alana and Petra combined. How much does one book cost?
Answer:
$2
Step-by-step explanation:
A line passes through the points (-2, 9) and (1, 3).
Click “show your work” and provide work for calculating the slope and y-intercept. Then, write the equation for the line in slope-intercept form. Please write your answers on the lines provided in the whiteboard.
The equation of the line passing through the points (-2,9) and (1,3) is
y = -2x + 11 where the slope is -2 and the y-intercept is +11
What is the Equation of a Line?The equation of a line can be formed with the help of the slope of the line and a point on the line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.
m = (y2 - y1) / (x2 - x1)
y1 = 9
y2 = 3
x1 = -2
x2 = 1
m = (3 - 9) / (1 - (-2))
m = - 6 / 3
m = - 2
The equation of the line;
m = (y - y1) / (x - x1)
-2 = y - 9 / x - 1
y - 9 = -2(x - 1)
y - 9 = -2x + 2
y = -2x + 11
Therefore the y-intercept is +11.
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Keshia goes to the post office to mail a package and a few letters. Stamps cost 49 cents each. It will cost $7.65 to mail the package. Keshila has 10.00. a. Write an inequality to represent this situation, where x is the number of stamps.
The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:
0.49x + 7.65 <= 10.00
Define Inequality.An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Define expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:
0.49x + 7.65 <= 10.00
This inequality can be read as "the cost of x number of stamps plus the cost of the package is less than or equal to Keshia's budget of $10.00."
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6+√-18 simplified for edmentum
Answer:
= 18√2
decimal =25.45584412
I need an answer fast
Alright I got it.
So first what I did was I made an equation that match did the word problem.
The equation was 15x=250+10x
When I solved it the answer was 50.
so they would need to sell 50 Tshirts (x=50)
Let L be the line through A = (1, 2,−1) and B = (5,−3, 4).
Answer the following questions below:
1. Find a direction vector of L
2. Find a parameterization of L.
3. Find the two points on L that are at distance 2 away from A.
4. Find a unit speed parameterization of L.
Answer:
(4, -5, 5)L = (1+4t, 2-5t, -1+5t)(1+4√66/33, 2-5√66/33, -1+5√66/33), (1-4√66/33, 2+5√66/33, -1-5√66/33)(1-2t√66/33, 2+5√66/66, -1-5√66/66)Step-by-step explanation:
Given L is the line through A(1, 2, -1) and B(5, -3, 4), you want its direction vector, a parameterization of L, 2 points on L that are 2 units from A, and a unit speed parametrization of L.
1. Direction vectorA direction vector for L will be the vector AB.
[tex]\overrightarrow{AB}=B-A=(5,-3,4)-(1,2,-1)\\\\\boxed{\overrightarrow{AB}=(4, -5,5)}[/tex]
2. Parameterized lineThe parameterized equation will be ...
[tex]L=A+t\cdot\overrightarrow{AB}\\\\\boxed{L=(1+4t,2-5t,-1+5t)}[/tex]
3. Distance 2The direction vector has length √66, so we can find two points on L that are 2 units from A by using t = ±2/√66 in the parameterized equation.
Here, they are:
P1 = L(2/√66) = (1 +8/√66, 2 -10/√66, -1 +10/√66)
P2 = L(-2/√66) = (1 -8/√66, 2 +10/√66, -1 -10/√66)
In the Answer section above, these are written with rationalized denominators.
4. Unit speedThe unit speed parametrization uses the unit direction vector instead of the unnormalized direction vector in the parameterized equation. Effectively, t is scaled by a factor of 1/√66.
L = (1 +4t/√66, 2 -5t/√66, -1 +5t/√66)
In the Answer section above, this is written with rationalized denominators.
You might notice here that it is easier to answer part 3 if you have this equation. You need only substitute t=±2 to get the points 2 units from A.
help me pls i need it fastest for my math project !!!!!! please help
Part A
g(x) = 9.25x
g(8) = 9.25*8
g(8) = 74
He would make $74 before taxes if he worked 8 hours.
------------------------------------------------------
Part B
g(x) = 9.25x
g(14) = 9.25*14
g(14) = 129.50
He would make $129.50 before taxes if he worked 14 hours.
------------------------------------------------------
Part C
g(x) = 9.25x
g(27.5) = 9.25*27.5
g(27.5) = 254.375
g(27.5) = 254.38
He would make $254.38 before taxes if he worked 27.5 hours.
Answer:
Solution below.
Step-by-step explanation:
SolutionThis question is basically asking you to substitute corresponding x values to find g(x).
Given the function from the question:
g(x) = 9.25x where x is the work hours and g(x) is the wages.
Given x = 8,
g(8) = 9.25 * 8 = $74.00
Given x = 14,
g(14) = 9.25 * 14 = $129.50
Given x = 27.5,
g(27.5) = 9.25 * 27.5 = $254.38 (rounded off to nearest cent)
Denise and Gabe met for dinner in downtown Belmont. Denise did flat-rate valet parking for $20. Gabe went to another valet and paid $4 up front and $4 for every hour, including the first hour. Ultimately, the friends ended up paying the same amount. How long did they stay? How much did each one pay?
What is the equation of the line that passes through the point (6,-5) and has a
slope of 1/3?
Answer:
y = 1/3x - 7
Step-by-step explanation:
start with the point-slope form:
(y-y1) = m(x-x1)
substitute the values of (x,y) into the formula:
(y-(-5)) = 1/3(x-6)
y+5 = 1/3x - 2
now write in slope-intercept form:
y = 1/3x - 2 - 5
y = 1/3x - 7
A train traveled 250 mi in 2 hours. If it traveled at the same rate of speed how long would it take the train to travel 600 mi
4.8
Divide 250 by 2 which is 125 then do 600 divided by 125. Then your answer should be 4.8.
(c) Ben changes £800 to Euros before he goes on holiday.
£1 = 1.25 Euro
He spends 895 Euros.
He changes the Euros that he has left to Pounds (£).
The exchange rate is now £1 = 1.40 Euro
How many Pounds does he get back?
Amount of pounds that Ben get back is £75.
What is Exchange Rate?Exchange rate is defined as the value of a currency with respect to another currency in order to convert the currency.
Ben changes £800 to Euros before he goes on holiday.
Before holiday, exchange rate is, £1 = 1.25 Euro
£800 = 800 × 1.25 Euros = 1000 Euros
He spends 895 Euros.
Euros left = 1000 - 895 = 105 Euros
Now, the exchange rate is £1 = 1.40 Euro.
or 1.40 Euro = £1
⇒ 1 Euro = £ 1/1.40
⇒ 105 Euros = £ (1/1.40) × 105 = £75
Hence Ben got £75 of pounds back.
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One pair of base angles of an isosceles trapezoid each have a measure of 2(x–10)°. The other pair of base angles of the trapezoid each have a measure of (4x+8)°. What is the value of x?
Answer:
x = 32
Step-by-step explanation:
• any lower base angle is supplementary to any upper base angle.
here base angle = 2(x - 10) and upper base angle = 4x + 8
supplementary angles sum to 180°
sum the base and upper base angles and equate to 180
2(x - 10) + 4x + 8 = 180
2x - 20 + 4x + 8 = 180
6x - 12 = 180 ( add 12 to both sides )
6x = 192 ( divide both sides by 6 )
x = 32
4) You are hired to work for a company at age 25 and the company has a retirement plan
where you can put up to 6% of your salary into the plan each month and they will match
that amount. Your starting monthly salary is $6,100, assume for simplicity sake you
never get a raise, and the retirement plan guarantees a 6.28% interest rate over the life of
the plan.
Scenario 1: You decide to start the retirement plan right away and you can afford
to put the full amount (6% of your salary) into the plan each month.
a) What is 6% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
Scenario 2: You decide to start the retirement plan right away, but you can only
afford to put 3% of your salary into the plan each month.
a) What is 3% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
What is the difference in the amount of money you will have at age 62 between scenarios
1 and 2? ________________
What is the difference in the amounts of money you put into retirement between
scenarios 1 and 2? _______________
How much more money did you get from your employer in scenario 1 than 2? ________
6% of the salary is $366
The total amount that would in the retirement account in the account each month is $732.
The amount that would be in the retirement account when you retire is $345,418.50.
The amount of money that you put in the account is $162,504.
The amount of money that the employer put in the account is $162,504.
The interest that was gained over the years is $20,410.50.
3% of the salary is $183.
The total amount that would in the retirement account in the account each month is $366.
The amount that would be in the retirement account when you retire is $172,709.25.
The amount of money that you put in the account is $81,252
The amount of money that the employer put in the account is $81,252
The interest that was gained over the years is $10,205.25.
How much would be in the retirement account?6% of the salary = salary x percentage
6% of the salary = 6% x $6,100
6% of the salary = 0.06 x $6,100 = $366
The amount in your account at the end of the month = amount the company puts + amount you deposit
= $366 + $366 = $732
Amount that would be in your retirement account = (1 + interest rate) x amount in the account
Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year
Amount in the account at retirement = $732 x 12 x (62 -25)
$732 x 12 x 37 = $325,008
Amount in the account at retirement = (1 + 0.0628) x $325,008 = $345,418.50
Amount the employer put in the account = $325,008 \ 2 = $162,504
Interest earned = $345,418.50 - $325,008 = $20,410.50
3% of the salary = salary x percentage
3% of the salary = 3% x $6,100
3% of the salary = 0.03 x $6,100 = $183
The amount in your account at the end of the month = amount the company puts + amount you deposit
= $183 + $183 = $366
Amount that would be in your retirement account = (1 + interest rate) x amount in the account
Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year
Amount in the account at retirement = $366 x 12 x (62 -25)
$366 x 12 x 37 = $162,504
Amount in the account at retirement = (1 + 0.0628) x $325,008 = $172,709.25
Amount the employer put in the account = $162,504 \ 2 = $81,252
Interest earned = $172,709.25 - $162,504 = $10,205.25
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if 6p = 120 what is p
Answer:
p = 20
Step-by-step explanation:
120 divided by 6 would = 20
Answer: p = 20
Step-by-step explanation:
120/6=20
6x20=120
leila says that 75% of a number will always be greater than 50% of any other number
support
75% of ____>50% of _____
refute
75%of ____ < 50% of_____
Answer:
it is not always true that 75% of a number will be greater than 50% of any other number
Step-by-step explanation:
Leila's statement is not true. It is possible for 50% of a number to be greater than 75% of another number.
For example, consider the numbers 10 and 100. 50% of 10 is 5, and 75% of 100 is 75. In this case, 50% of 10 (5) is greater than 75% of 100 (75).
Here's another example: 50% of 20 is 10, and 75% of 30 is 22.5. In this case, 50% of 20 (10) is again greater than 75% of 30 (22.5).
Therefore, it is not always true that 75% of a number will be greater than 50% of any other number.
Fill in the blanks to write the solutions to the quadratic equation.Fill in the blanks to write the solutions to the quadratic equation.Fill in the blanks to write the solutions to the quadratic equation.Fill in the blanks to write the solutions to the quadratic equation.x^2+2x+10 = 0
The solution to the given quadratic equation is x = -1 + 3i OR x = -1 - 3i
Solving Quadratic equationsFrom the question, we are to solve the given quadratic equation
From the given information,
The quadratic equation is
x² + 2x + 10 = 0
Using the Quadratic formula,
x = [-b ± √(b² - 4ac)] / 2a
From the equation,
a = 1, b = 2, and c = 10
Then,
x = [-b ± √(b² - 4ac)] / 2a
x = [-(2) ± √((2)² - 4(1)(10))] / 2(1)
x = [-2 ± √(4 - 40)] / 2
x = [-2 ± √(-36)] / 2
x = [-2 ± -6i] / 2
x = -1 ± 3i
x = -1 + 3i OR x = -1 - 3i
Hence, the solution is x = -1 + 3i OR x = -1 - 3i
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Prove that for any natural n: a the number 7^(n+4) −7^n is divisible by 30.
For, n = 0, 1 we proved that 7⁽ⁿ⁺⁴⁾ - 7ⁿ hence by induction it is divisible by 30 for all n ∈ N.
What is mathematical induction?An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.
Given, We have to prove 7⁽ⁿ⁺⁴⁾ - 7ⁿ is divisible by 30 for all n ∈ N.
Let, n = 0.
Therefore,
7⁴ - 7⁰.
= 2401 - 1.
= 2400.
= 30×80, Divisible by 30.
Similarly for n = 1 we have,
7⁵ - 7¹.
= 16807 - 7.
= 16800.
= 30×560.
Hence by induction, the cycle will continue.
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What is the equation of this graph in slope intercept form
The slope-intercept form of the equations presented on the graph are;
y = 4
y = 3
What is the slope-intercept form of the equation of a line?The slope-intercept form of the equation of a line is; y = m·x + c, where;
m = The slope of the graph
c = The y-intercept of the graph
The equation of the lines in the graphs (blue line, and red line) are found as follows;
The slope of the blue line is found using the points on the graph as follows;
The coordinates of points on the blue line graph are; (0, 4), (2, 4), (4, 4)
The slope is therefore; m = (4 - 4)/(4 - 2) = 0
The y-intercept, obtained from the graph is; c = 4
The value of the slope, m = 0, indicates that the graph is an horizontal line with an equation y = c
c = 4
The equation of the blue line graph in slope-intercept form is therefore;
y = 4
The coordinates of points on the red line graph are; (0, 3), (2, 3), (4, 3)
The slope of the red line graph is therefore;
m = (3 - 3)/(4 - 2) = 0
The y-intercept of the red line graph is; c = 3
The value of the slope, m = 0, and the y-intercept, c = 3, indicates that the equation of the red line graph is therefore;
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Write an equation of a line that is perpendicular to 6x - 3y = -6 and passes
through the point (-12, 14).
I'm sorry but I didn't get that
HELP ASAP PLS
Question 2 of 5
Select all the correct answers.
Which expressions are prime polynomials?
Answer: There is no picture
Step-by-step explanation:
how long would it tak to go 75 miles if you can go 45 mph
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a jack or a ten
If you are dealt one card from a 52-card deck. The probability that you are not dealt a jack or a ten is 12/13.
How to find the probability?Since there are 4 aces in a deck of card 52 first step is to find the number of cards not aces in a deck of 52
Number of cards not aces in a deck = 52 -4
Number of cards not aces in a deck = 48
Now let find the probability that you won't draw an ace.
Probability = 48/52
Probability = 24/26
Probability = 12/13
Therefore we can conclude that the probability is 12/13.
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A local store is selling a tool for 35% off its normal price. If the tool costs $45, how much would you save by buying it on sale? A. $15.75, B. 18.25, C. 12.75, D. 16.50
an altitude is drawn from the vertex of an isosceles triangle forming a right angle and two congruent triangles. as a result, the altitude cuts the base into two equal segments. the length of the altitude is 30 inches, and the length of the base is 10 inches. find the triangles perimeter. round to the nearest tenth of an inch.
The perimeter of the isosceles triangle with altitude 30 inches and base 10 inches is calculated to be 70.82 inches
How to find the perimeter of the isosceles trianglePerimeter of a triangle refers to the surface dimensions, this is calculated by the formula
Perimeter, P = a + b + c
where
a, b, c are sides of the triangle
The third side of the triangle will be calculated using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
The right triangle consist 1/2 the isosceles triangle base = 5 inches and the altitude = 30 inches
plugging the values as in the problem
let x be the required distance
x² = 30² + 5²
x² = 900 + 25
x² = 925
x = √925
x = 30.41 inches
Perimeter of the isosceles triangle
= 30.41 + 30.41 + 10
= 70.82 inches
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What is the value of y in the equation y = 1/4 x divided by 2 when x =32
The value of y is 16 when x = 32 for equation y = (1/4)x divided by 2.
What is an equation?Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It displays how the expressions on the left and right sides are equally related. We have LHS = RHS in any mathematical equation. Equations can be solved to get the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol, a statement is not an equation.
The given equation is
y = 1/4 x divided by 2
So,
y = ((1/4)x)/ 2
y = (2/4) × x
Put x = 32
y = 2/4 ×32
y = 2 × 8
y = 16
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i am number between 47 and 53 no two of my factors are the same number what number am i
A number between 47 and 53 such that the prime factors are not repeated is:
3*17 = 51
How to find the number?Remember that any number can be written as a product of prime factors.
If we want to find a number between 47 and 53, such that there are no repeated factors, we just need to take different primes and multiply them.
For example:
2*3*5*7 = 210
There are no repeated factors, but the number is not in the desired range.
2*5*7 = 70
Still not in the range.
You can try some times until you get for example:
3*17 = 51
This a number in the desired range, such that their prime factors are not repeated.
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A machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long. What is the total length needed in inches?
The total length needed in inches will be 490.5 inches.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long The total length needed in inches will be:
= (3 ft 4 7/8 inch × 12)
Note that 1 feet = 12 inches
= (12 × 3) + (4 7/8) × 12
= (36 + 4.875) × 12
= 490.5 inches
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Fill in the sentence below with the description that most specifically applies to the quadrilateral below.
The figure with equal opposite sides and all the interior angles being right angles is a rectangle.
What is a quadrilateral?A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.
A rectangle is a special type of quadrilateral in which opposite sides are of equal length(not all sides are the same) and all the interior angles are right angles.
From the given diagram the opposite sides are equal and all the interior angles are right angles hence the figure is a rectangle.
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1 18. You have a --cup 4 1 measuring cup and a --cup measuring 2 cup. What are two ways you can 3 measure 2 cups of water? - 4
You buy 8.25 ounces of almonds and 7.5 ounces of cashews. You combine the nuts and divide them equally into 9 bags. How many ounces are in
Options are below
⬇️
1.75 ounces
9.5 ounces
15.5 ounces
17.5 ounces
PLS FOR 18 POINTS