You buy 2 shirts and 3 pairs of pants for $50. Your friend buys 3 shirts and 1 pair of pants for $40. What is the cost of
each shirt? of each pair of pants?
Shirts = 10$ Pants = 10$
Step-by-step explanation:
50 / 5 = 10$
3/1 = 10$
In this system of simultaneous equations, the cost of each shirt (x) equals $5 and the cost of each pair of pants (y) is $25.
Explanation:This is a system of simultaneous equation problems in Mathematics. Let's denote the cost of one shirt as x and one pair of pants as y. Based on the problem information, you have these two equations:
1) 2x + 3y = 50
2) 3x + y = 40
To solve for x, you can multiply the second equation by three and subtract the first equation from it:
3*(3x + y) - (2x + 3y) = 50
After simplifying, you find that x (cost of each shirt) equals 5.
In order to find y (cost of each pair of pants), you can now substitute x = 5 into the second original equation: 3*5 + y = 40, which gives you y = $25, the cost of each pair of pants.
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In a right triangle, given legs of lengths 5 and 12, find the length of the hypotenuse.
The length of the hypotenuse is 13 units
How to find the length of the hypotenuse.From the question, we have the following parameters that can be used in our computation:
Legs = 5 and 12 units
The length of the hypotenuse of the right triangle can then be calculated using
Hypotenuse² = Leg 1² + Leg 2²
Substitute the known values in the above equation, so, we have the following representation
Hypotenuse² = 5² + 12²
So, we have
Hypotenuse² = 169
Take the square roots
Hypotenuse = 13
Hence, the hypotenuse is 13 units
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nominal exchange rate
(or simply called exchange rate)
If the nominal exchange rate between the U.S. dollar and the Japanese yen is: 90 YEN per $ dollar.
So, 1$ can buy 90 YEN in the foreign exchange market.
The price of foreign currency in relation to the local currency is referred to as the Nominal Exchange rate. It displays how many units of local money must be renounced in order to obtain one unit of foreign cash.
The amount of local currency required to buy foreign currency is known as the nominal exchange rate. The NEER is a measure of a nation's ability to compete internationally in the foreign exchange (forex) market.
Yes, you can exchange 1 USD for 90 YEN on the foreign exchange market, and vice versa. Nominal currency appreciation is the term used to describe a decline in this measure.
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What is the Nominal Exchange Rate?
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K
X
If the price of gasoline increased by 0.3% per month, which
equation models the future cost of gasoline?
X
Ay=1.19(z)1.03
Ix B
By=1.19(z) 1.003
C y = 1.19(1.03)"
D
y = 1.19(1.003)
The equation that models the future cost of gasoline, if the price increases by 0.3% per month, is option D: y = 1.19(1.003)
In this equation, y represents the cost of gasoline at a certain time (measured in months) in the future. The initial cost of gasoline is represented by 1.19 (since this is the base value we are starting with), and the increase in price over time is represented by (1.003)^z where z represents the number of months in the future.
The equation 1.19(1.003)^z to model the future cost of gasoline is correct, the base cost multiplied by a number representing an increase in the price each month (1.003) raised to the power of the number of month. Each time z increases by 1, the price increases by 0.3%
Therefore, increasing z by 1 increases the price of gasoline by 0.3%. If you want to calculate the price for a certain number of months in the future, you can plug in that number for z in the equation and calculate the result.
Answer:y=1.19(1.003)x
Step-by-step explanation:
4(6-b)=4
Use distributive property
Answer:
b is 5
I wish you luck in your assignments.
6x = 18 what does x =
Answer:
x= 3
Step-by-step explanation:
6x =18
divide 6 by both sides.
x=3
How much more does the cat eat than the parrot? The Parrot eats 3/8 pounds of food, and the cat eats 7/8 pounds of food. Write and solve an equation to represent the problem?
The equation and solution of the problem are 3/8-7/8 and 1/2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given;
The food parrot eats = 3/8pounds
The food cat eats = 7/8pounds
Now, food eaten more by cat =7/8-3/8
=(7-3)/8
=4/8
=1/2
Therefore, the answer to equation will be 1/2.
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There are 5 gallons of lemonade in the container. How much is remaining in the container after Coach Miller pours g gallons for the players?
The remaining lemonade in the container after Coach Miller pours g gallons for the players is, (5 - g) gallons.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
There are 5 gallons of lemonade in the container.
Now, Initially lemonade available in Container = 5 gallons
Here, Coach Miller pours g gallons for the players.
Hence, Lemonade remaining in Container = (5 - g) gallons
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help
What is the slope of the line that passes through the points (2, 8) and (-3, 14)?
Write your answer in simplest form.
The slope of the line that passes through the points (2, 8) and (-3, 14) is -6/5 in the simplest form.
Define Slope.A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).
What are coordinate pairs?An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
The slope of a line is given by the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Plugging in the given points, we get:
m = (14 - 8) / (-3 - 2)
m = 6 / -5
m = -6/5
so the slope of the line that passes through the points (2, 8) and (-3, 14) is -6/5 in the simplest form.
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simplify expression 8y^2+9y^2+6y
Answer
17y^2 + 6y
Step-by-step explanation:
I need the minimum interval on [-10,6]
The minimum of the function is at x = -10. The minimum on the interval [-10,6] is -2.67.
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
Given function is f(x) = ³√(x-9)
The graph of the given function increases with the increase of the value of x and decreases with the decrease of the value of x.
Thus the minimum value of f(x)on the interval [-10,6] is at x = -10
Putting x = -10 in the given function.
f(-10) = ³√(-10-9)
f(-10) = ³√(-19)
f(-10) = -2.668
f(-10) = -2.67 (rounded to 2 decimal places).
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Find the scale length of the following:
actual length is 36 ft
scale is 3 in. : 24 ft
The requried scaled length of the actual length is given as 4 inches.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
here,
In the question,
Scale 3 in = 24ft
Scale factor = modified length / original length
Scale factor = 3 / 24 = 1/8
Now,
For an actual length of 36 ft,
Scaled length is given as = 36 × 1/8 = 4 inches
Thus, the requried scaled length of the actual length is given as 4 inches.
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You roll a number cube and record an odd number 12 times in a row. As the number of times you roll an odd number increases, what happens to the theoretical probability that you roll an even number? (Please show step by step explanation)
When the number of times you roll an odd number increases, the theoretical probability that you roll an even number would decrease.
How is the probability of rolling an even number affected ?As the number of times you roll an odd number increases, the theoretical probability that you roll an even number decreases. This is because the probability of rolling an even number is inversely proportional to the number of times you roll an odd number.
If you are rolling a fair die, the probability of rolling an even number is 3/6 or 1/2, and the probability of rolling an odd number is also 3/6 or 1/2.
As the number of times you roll an odd number increases, the number of rolls that are left for an even number decreases, thus the probability of rolling an even number decreases as well.
For example, if you roll the die 10 times and 6 of them are odd numbers, the probability of rolling an even number in the remaining 4 rolls is 4/4 or 1 (100%) because you are guaranteed to roll an even number.
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Please help I’m struggling
Answer:
The answer to both parts is (C)
In the first 9/3.9 = 2.31 half lives elapsed
(1/2)^2.31 = .5^2.31 = .202 pressure at 9 mi above sea level
P = .202 * 31 = 6.26 mi
In the second:
19/5 = 3.8 half-lives
.5^3.8 = .072 left after 3.8 half lives
635.8 * .072 = 45.6
X^2+2xy-2y^2+x=2 find gradient at point (-4,1)
Therefore , the solution to the given problem of slope intercept comes out to be dy/dx = -1/2.
A slope-intercept form is precisely what?After you are certain if Y = mx + b, the gradient intercept approach can be employed. By using just one particular point on the line and its slope, the direction form is a way to represent an axiom for a line. The slope is defined as such rise across run and is represented first by point form (x,y), and may be calculated using the slope intercept method, y = mx + b. (0, b). By using just one specific statement on the vector and its slope, the direction form is a technique to write a linear model for a line.
Here,
Given : x² +2xy - 2y² +x =2
thus,
To find the gradient at point (-4,1) :
We have to find the dy/dx
so,
=> 2x + 2y + 2xdy/dx -2ydy/dx +1 =0
=> dy/dx (2x-2y) = -(2x+ 2y) -1
=>dy/dx = -(2x+2y) -1 / (2x-2y)
So , at the point (-4,1)
=> dy/dx = -(-8 + 2) -1 / (-8 -2)
=>dy/dx = 5/-10
=>dy/dx = -1/2
Therefore , the solution to the given problem of slope intercept comes out to be dy/dx = -1/2.
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18.
A button is circular, as shown. The
button has a diameter of 6.4
centimeters What is the area of the
button in square centimeters?
The area of the circle with diameter 6.4 is 32.15 square centimeters.
What is area of the circle?A circle closed plane geometric shape. In technical terms, a circle is a locus of a point moving around a fixed point at a fixed distance away from the point.
Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula:
[tex]A = \pi r^2[/tex]
Given that the diameter of the circle is 6.4 centimeters.
The radius of the circle is thus half of the diameter that is 3.2 centimeters.
The area of the circle is given by the formula:
[tex]A = \pi r^2[/tex]
Substitute the value of r = 3.2 in the formula:
[tex]A = (3.14) (3.2)^2\\\\A = 32.15[/tex]
The area of the circle is 32.15 square centimeters.
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A basketball player's chance of scoring a free throw is estimated to be 25. The player tries 20 shots and the number of baskets is recorded. This event is a binomial experiment because
A. there are only two outcomes; the number of trials is not fixed; the probability is the same for each trial; the trails are independent of each other.
B. there are only two outcomes; the number of trials are fixed; the probability is not the same for each trial; the trails are independent of each other.
C. there are only two outcomes; the number of trials are fixed; the probability is the same for each trial; the trails are independent of each other.
D. there is only one outcome; the number of trials are fixed; the probability is not the same for each trial; the trails are independent of each other.
This event is a binomial experiment because C. there are only two outcomes; the number of trials is fixed; the probability is the same for each trial; the trials are independent of each other.
What is a binomial experiment?A binomial experiment is a random experiment with a fixed number of repeated trials with independent outcomes, successes or failures, yes or no, and heads or tails.
In a binomial experiment, the probability of "success" p is the same for each outcome as the chance of "failure" q is the same for each outcome.
The number of free throw shots in this experiment is 20 and they are either missed or scored.
Thus, the fixed number of trials with only two outcomes satisfied as a binomial experiment.
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what do you mean by quadratic polynomials ?
Step-by-step explanation:
it us a polynomial with a second degree variable
Let the random variable X be a random number with the uniform density curve in the figure below. Find the following probabilities. O P(X 2 0.35) O P(X = 0.35) O P(0.35 < X < 1.25) O P(0.10 < X < 0.20 or 0.6 < X < 0.9) O X is not in the interval 0.5 to 0.6.
A continuous random variable is one that has a range of possible values. In other words, if a random variable adopts a value that fits within a specific range, it is said to be continuous.
Measurements like height, weight, and time are all represented by continuous random variables. A continuous random variable is represented as the area under a density curve. The concept of a continuous random variable, as well as its mean, variance, types, and related examples
P(X < 0.35) = 0.35
P(X = 0.35) = 0 since X is a continuous random variable and the probability of a specific value is 0.
P(0.35 < X < 1.25) = 1.25 - 0.35 = 0.9
P(0.10 < X < 0.20 or 0.6 < X < 0.9) = (0.20 - 0.10) + (0.9 - 0.6) = 0.3
P(X < 0.5 or X > 0.6) = (0.5 - 0) + (1 - 0.6) = 0.9
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Considering both dividends paid and capital gains, Dylan's pretax profit from his investment is $
Dylan's pretax return on investment (ROI) is
96.
Type the correct answer in each box. Use numerals instead of words.
Therefore ,the return on investment prior to deducting taxes is known as the net income rate of return.
What distinguishes taxable income from pretax income?The amount a company makes prior to taxes is known as pretax investment gains, on the other hand. Income that is subject to taxation is referred to as taxable income.
Here,
Investment income generally refers to, but is also limited to, earnings, profits, corporate taxes, rental and royalty revenues, non-qualified leases, income from businesses that trade investment products or commodities, and businesses which are passive for such taxpayer.
Pretax rates of return refers to an investment's profit or loss before taxes are taken into account.
The government imposes taxes on investment on any extra money made from buying or selling investments. Capital gains taxes must be paid on securities that are successfully sold.
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Answer: Considering both dividends paid and capital gains, Dylan’s pretax profit from his investment is $30. Dylan’s pretax return on investment (ROI) is 24%.
Step-by-step explanation: To determine Dylan’s profit from his investment, add his dividends of $5 and his capital gains of $25.total profit = $25 + $5= $30Before taxes are applied, Dylan can calculate his return on investment (ROI) by dividing his profit by the cost of his investment:30125 = 0.24, or 24%.
what is the direct answer to this equation?
13 + n-26 < 38
[tex]13 + n-26 < 38[/tex]
Simplify:
[tex]n-13 < 38[/tex]
Add 13 to both sides:
[tex]n-13+13 < 38+13[/tex]
[tex]\fbox{n} < \fbox{51}[/tex]
Answer:
n<51 but what I got was n+25
Let V be the vector space of symmetric 2 Times 2 matrices and W be the subspace W = span{ , }. Find a nonzero element X in W. X = Find an element Y in V that is not in W. Y =
The solutions are - X = [5 5; 5 -2] is a nonzero element in W and Y = [1 1; 1 1] is the element in V that is not in W.
A nonzero element X in W can be any linear combination of the given basis vectors:
X = a[5 5; 5 -2] + b[5 -4; -4 1]
Where a and b are nonzero scalars. For example, X = [5 5; 5 -2] is a nonzero element in W.
An element Y in V that is not in W can be any symmetric 2x2 matrix that cannot be written as a linear combination of the given basis vectors. For example, Y = [1 1; 1 1] is not in W as it cannot be written as a linear combination of [5 5; 5 -2] and [5 -4; -4 1].
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The complete question is -
Let V be the vector space of symmetric 2 Times 2 matrices and W be the subspace W = span{[5 5; 5 -2], [5 -4; -4 1]}. Find a nonzero element X in W. Find an element Y in V that is not in W.
Percy has 50 flowers. He will put 8 flowers in
each centerpiece. How many centerpieces can
Percy make? How many flowers will be left over?
Answer:
6 and 2
Step-by-step explanation:
50 divided by 8 is 6.25 and since you can't make .25 of a centerpiece he can only make 6 centerpieces
there will be 2 flowers left over because .25 of 8 is 2 (.25 times 8)
20 pairs of atletics shoes and 10 pair of casual shoes are 750. how much is each shoe
Each pair of athletic shoe cost $20 and each pair of athletic shoe cost $35, in the given arithmetic problem.
What is arithmetic?By doing addition, subtraction, multiplication, and division on numbers, arithmetic is defined as the study of numbers.
Let 20x be the cost of manufacturing 20 athletic shoes and 10y be the cost of manufacturing 10 casual shoes, then
20x + 10y = 750
10y = 750 - 20x
y = 75 -2x
Let 25x be the cost of manufacturing 25 athletic shoes and 20y be the cost of manufacturing 20 casual shoes, then
25x + 20y = 1200
20y = 1200 - 25x
y = 60 - 25x/20
y = 60 - 1.25x
Equalise the y terms
75 -2x = 60 - 1.25x
75 - 60 = -1.25x + 2x
15 = 0.75x
x = 15/ 0.75
x = 20
Substitute the value of x in y = 75 -2x
y = 75 -2(20)
y = 75 - 40
y = 35
Thus, each pair of athletic shoe cost $20 and each pair of athletic shoe cost $35.
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Full question:-
Ranger Shoe Company manufactures two types of shoes, athletic shoes and casual shoes. The cost of manufacturing 20 pairs of athletic shoes and 10 pairs of casual shoes is $750. If 25 pairs of athletic shoes and 20 pairs of casual shoes were manufactured, the cost would be $1200. How much does it cost to manufacture each type of shoe?
How to solve and the equation
Answer:19
Step-by-step explanation:
I think this is right
Can you please solve this problem.
Answer: 10y
Step-by-step explanation:
4(y-2)+6y+8
4(y-2)=4y-8
4y-8+6y-8
*8's cancel out*
6y+4y=10y
Thomas swam 5 laps in two and one-half minutes. At this rate, how many laps would he swim in 8 minutes?
5 laps
8 laps
14 laps
16 laps
At this rate, how will swim 16 laps in 8 minutes.
What is rate?A rate is a ratio in which the two terms being compared have different units.
Instead of using the "to" form for ratios (for example, 3 red ball to 2 blue balls), rates often use the word per. Rate is a ratio that compares two different quantities which have different units.
When two quantities of different units are compared and expressed as a ratio, we refer to it as 'Rate'.
5:2 1/2
x:8
x = (5 x 8) /5/2
x = (40) / 5/2
x = 16laps
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Jim is recording the number of points he misses on each math quiz. Here are his results for the last nine quizzes. 8, 3, 8, 6, 3, 3, 3, 6, 7 Find the range and the mode for the data.
Answer:
See below!
Step-by-step explanation:
Data:8, 3, 8, 6, 3, 3, 3, 6, 7
Range:The difference between highest value and lowest value in a data is called range.Here, Range is:
= Highest value - Lowest value
= 8 - 3
= 5
Mode:The most frequently occurring value in a data is called mode.Here, the mode is:
= 3 (occurring 4 times)
[tex]\rule[225]{225}{2}[/tex]
The physician orders Mylanta 0.5 oz how many milliliters would you give
Answer: 14.7868
Step-by-step explanation: There are 29.5734 milliliters in a US fluid ounce. Since we need .5 oz, we multiply this number by .5.
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X and y are both 20 degrees because all triangles = 180 degrees and 140 + 20+20= 180
Answer:
Step-by-step explanation:
if you may, try finding 180 degrees, which y is 40 and x is 0