If an artist uses gold leaf foil in his work and he wants to cover a piece of canvas that is 22.5 by 34 inches with this foil and the foil costs $4.15 per square inch, then the money the artist spent on gold leaf foil for this project is equal to $3174.75
The money spent on gold leaf foil for the project can be calculated by the multiplication of the area or square inch of the foil needed to cover the piece of canvas with the price per square inch.
The area or square inches can be calculated by multiplying the length in inches by the width in inches.
Area = 22.5 × 34
Area = 765 square inches
Now, money spent on gold leaf foil can be calculated by multiplication of the area of the need with the price per square inch.
Area × price per square inch
765 × 4.15 = $3174.75
Hence the money the artist spent on gold leaf foil is calculated to be $3174.75
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What is f(-3) for the function f(x)=-3 x+6 ?
The value of f(-3) is 15.
The given function is f(x) = -3x+6. Now, f(-3) = x = -3
Substituting and Evaluating the value of x in the equation f(x) = -3x+6, we get
f(-3) = -3(-3)+6f(−3)=−3(−3)+6
f(-3) = 9+6f(−3)=9+6
f(-3) = 15f(−3)=15
∴ The value of f(-3) for the function f(x) = -3x+6 is equal to 15.
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i need help please
Y=CD-8 for C
Answer:
c = (y+8)/d
Step-by-step explanation:
Hence, or otherwise, express 0.372 as a fraction.
Answer:
93/250
3/8
0,375 has three numbers after a decimal so we will multiply and divide 0,375 by 1000
Find the value of x.
Answer:
43
Step-by-step explanation:
the plane is 180 degrees
subtract 2x4
172
divide by 4
43
BOOM
(-8) x (-2/3) =
1/3a = -5
URGENTTT
Answer: -8
Step-by-step explanation:
= 12 * (-2/3)
= -24/3
= -8
(−8) ⋅ (−2/3) = 1/3a = −5
The formula weights=mass of 1 mole of (−8) ⋅ (−2/3) = 1/3a = −5 = 0g
Please help with this answer! Thank you so much guys really thanks
What is the equation of the line that passes through the point (-2,-1)(−2,−1) and has a slope of 5/2
The equation of line having slope of 5/2 is given as 2y -5x = 8.
What is termed as the equation of line in point-slope form?A line's equation written in point slope form is (y - y₁) = m(x – x₁).When the line passing through the origin the equation of a line with slope m is: y - 0 = m(x = 0), i.e. y = mx.where m is the slope and (x₁, y₁) are the coordinates passing point on the line .As, per the given question;
The slope of the line is given as; m = 5/2
The coordinates of the passing points (-2, -1).
Thus, (x₁, y₂) = (-2, -1).
The equation of the becomes.
(y - y₁) = m (x – x₁)
Put the values;
y - (-1) = (5/2)(x - (-2))
Simplifying
y + 1 = (5/2)(x + 2)
2y + 2 = 5x + 10
2y -5x = 8
The equation of line is calculated as 2y - 5x = 8.
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If the measure of angle 1 = (7x-19), and the measure of angle 2 = (x+5) find the measure of angle 2
We can say that if the measure of angle 1 = (7x-19), and the measure of angle 2 = (x+5), then the measure of angle 2 is 18°.
Define supplementary angle.
Supplementary angles are those two angles whose sum is always equal to 180 degrees.
Mathematically, a supplementary angle is calculated as follows:
Q + R = 180
Since the angles on this line segment are supplementary angles, we have:
Angle (1) + Angle (2) = 180° - Angle 3
Substituting the given values into the formula, we get;
7x - 19 + x + 5 = 180 - 90
8x - 14 = 90
8x = 90 + 14
8x = 104
x = 104/8
x = 13
Now, we can calculate the length of angle 2 by putting the 'x' value:
Angle 2 = x + 5
Angle 2 = 13 + 5
Angle 2 = 18°
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5. A city has a population of 350,000.
The
population has decreased by 30% in the past
ten years. What was the population of the city
ten years ago?
The population of city 10 years ago before 30% decrease in population was 500,000
In the given statement is :
A city has a population of 350,000.The population has decreased by 30% in the past ten years.
The formula for calculating the percent change between two values over the time is given by:
[tex]p=\frac{A-B}{B}[/tex]×[tex]100[/tex]
where,
'p' represents the percent change
'A' represents the New value
'B' represents the Old value
Since, p is the percent (decreased) = -30
Substitute the given values and solve for B;
then;
[tex]-30=\frac{350,000-B}{B}[/tex] × 100
Divide both sides by 100 we get;
[tex]-0.3=[/tex] [tex]\frac{350,000-B}{B}[/tex]
By cross multiply we get;
-0.3B = 350,000 - B
Add both sides B, we get
-0.3B + B = 350,000
0.7B = 350,000
Divide both sides by 0.7 we get;
B = 500,000
Therefore, The population of city 10 years ago before 30% decrease in population was 500,000
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Given two functions
F(x) = 2x+1 and G(X) = x^2-40
Find f(-4) + g(-7)
Answer:
f(-4) = -7
g(-7) = 9
Step-by-step explanation:
f(x) = 2x + 1
f(-4) = 2(-4) + 1 = -8 + 1 = -7
g(x) = x^2 - 40
g(-7) = (-7)^2 - 40 = 49 - 40 = 9
Which is the first step in simplifying the expression 2(x 3) 5? 2x 2(3) 5 2x 3 5 2 x 3 5 2(5) x 3
The first step in simplifying the expression 2(x+3)+5 = 2x+2(3)+5.
Given expression in 'x' is 2(x+3)+5.
In order to simplify this expression, we need to expand it by opening the parenthesis. That is, we need to distribute 2 over (x+3) first. For this we multiply 2 into (x+3) and then only we can add 5 to it.
So, 2(x+3) +5 = 2x + 2(3) +5
= 2x +6 +5
= 2x+11
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Please help (show steps too)
Answer:
5
Step-by-step explanation:
[tex]d=\frac{|-3(5)-4(5)+10|}{\sqrt{(-3)^2+(-4)^2}}=5[/tex]
Lee is laying out a design for the tiles of a section of his bathroom floor. he will use 1 white tile for every 6 black tiles to have a total of 28 tiles in the design. how many of each type of tile will lee use?
If Lee is laying out a design for the tiles of a section of his bathroom floor and he will use 1 white tile for every 6 black tiles to have a total of 28 tiles in the design then the number of white and black tiles Lee will use is equal to 4 and 24 respectively.
The number of white and black tiles Lee will use can be determined by using an algebraic expression.
As 1 white tile is used for every 6 black tiles, an algebraic expression can be represented as,
x + 6x = 28
By solving the value of x, the number of each type of tile that Lee will use can be calculated,
x + 6x = 28
7x = 28
x = 28 ÷ 7
x = 4
As there is one white tile for every six black tiles,
White tiles = 1(x) = 1(4) = 4
Black tiles = 6(x) = 6(4) = 24
Hence the number of white tiles Lee will use is equal to 4 and the number of black tiles Lee will use is equal to 24.
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Peter bought three items at a store. Here are their prices (in dollars):
18.23, 6.39, and 15
What is the total amount Peter paid at the store? Do not round your answer.
$____
Type your numerical answer below.
-
Answer: $39.62
Step-by-step explanation: To get the answer to the cost of Peter's three items, I took the prices of the three and added them together. This amount would be the amount he paid WITHOUT TAX.
Piecewise defined functions
Part a
[tex]\frac{\pi}{3} > \frac{\pi}{4} \implies f(\pi/3)=\sin(\pi/3)=\boxed{\frac{\sqrt{3}}{2}}[/tex]
Part b
[tex]\frac{\pi}{6} \leq \frac{\pi}{4} \implies f(\pi/6)=2+\cos(\pi/6)=\boxed{2+\frac{\sqrt{3}}{2}}[/tex]
Part c
[tex]\frac{\pi}{4} \leq \frac{\pi}{4} \implies f(\pi/4)=2+\cos(\pi/4)=\boxed{2+\frac{1}{\sqrt{2}}}[/tex]
(PLEASE HELP!!)
Solve the following system of equations using either Gaussian elimination or a matrix. Write your answer as a point and explain how you would check your work:
2xy + 4z = 33
x + 2y - 3z = -26
-5x - 3y + 5z = 23
Using Gaussian elimination, the solution to the given system of equations is given as follows:
x = 5, y = -11, z = 3.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the equations are given as follows:
2x - y + 4z = 33.x + 2y - 3z = -26.-5x - 3y + 5z = 23.(I suppose there was a typing mistake on the first equation, as Gaussian elimination can only be applied to solve linear systems).
For Gaussian elimination, the first step is building the matrix of the system, in which:
The first three columns contain the coefficients of x, y and z, respectively.The last column contains the results of the operations.Hence, the matrix of the system is given as follows:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]
Then, we need to make the coefficient of x zero in the second and third rows, hence:
R2 -> 2R2 - R1.R3 -> 5R1 + 2R3.Then the matrix will be given by:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]
Now we need to make the coefficient of y on the third row zero, hence:
R3 -> 11R2 + 5R3.
Then:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]
From the third row, we have that:
40z = 120
z = 120/40
z = 3.
From the second row, we have that:
5y - 10z = -85
5y - 30 = -85
5y = -55
y = -11.
From the first row, we have that:
2x - y + 4z = 33
2x + 11 + 12 = 33
2x = 10
x = 5.
Hence the solution of the system is given by:
x = 5, y = -11, z = 3.
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Use the formula for the probability of two dependent events P(A and B) to derive the conditional probability formula for P(B | A) .
The conditional probability formula for P(B | A) has been derived from two dependent events P(A and B).
What is said to be dependent events?When the outcome from one event influences the outcome of the other, two events are referred to as dependent.
Dependent events in probability are generally real-life events that depend on another event to occur. Sam, for example, did well on his math test because he prepared; the gym class used to have a football session even though Adam brought a football from home. When you look at these examples, you will realize that one occurrence is dependent on the other.Derivation of conditional probability from two dependent events P(A and B) is-
The probability multiplication rule is used to derive the conditional probability formula, P(A and B) = P(A)×P(B|A).
This rule is also known as P(AB). The Union symbol (∪) represents "and," as in event A occurring and event B occurring.
Step 1: Write the multiplication rule down:
P(A and B) = P(A)*P(B|A)
Step 2: P(A) divides both sides of the equation:
P(A and B) / P(A) = P(A)*P(B|A) / / P(A)
Step 3: On the right side of the equation, cancel P(A):
P(A and B) / P(A) = P(B|A)
Step 4: Rewrite the equation as follows:
P(B|A) = P(A and B) / P(A)
Therefore, P(B | A) conditional probability formula is compiled from two dependent events P (A and B).
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Find 1, 305 x 81. Then estimate to check your answer.
A. 1, 305 x 81 = 85, 705 Check: 1,000 × 8 = 80,000
B. 1, 305 x 81 = 105, 705. Check: 1,400 x 90 = 12, 600 :
C. 1,305 x 81 = 105, 705 Check: 1, 200 × 80 = 96,000
D. 1, 305 x 81 105, 705 Check: 1,300 x 80 = 104, 000
the estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104,000 and Actual 1,305 × 81 = 105,706
The correct option is D.
In the given statement is:
Find 1, 305 x 81. Then estimate to check your answer.
The estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104000 and Actual 1,305 × 81 = 105706
How to estimate and then compute the product check that your answer is reasonable?
The product expression is given as
1,305 × 81
As an estimate, we have
1305 = 1300
81 = 80
So, we have:
1,305 × 81 ≈ 1300 * 80
Evaluate the product
1,305 × 81 ≈ 104000
For the actual product, we have
The estimate and the actual product both approximate to 100000
Hence, the estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104,000 and Actual 1,305 × 81 = 105,706
The correct option is D.
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PLs solveg g g g g g g g g g g g
Answer:
4°=1
g g g g g g g g g g
Step-by-step explanation:
Three divers kept track of the number of crabs they've seen this year.
Diver Crabs observed Dives
Scuba Sam 33 11
Wet Suit Willy 81 18
Deep Diving Dan 104 26
Which diver saw the most crabs per dive?
Choose 1 answer:
The diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.
What is an average?An average is a mean or the central value obtained by dividing the sum of all data values by the number of data values.
Data and Calculations:Diver Crabs observed Dives Average Crab per dive
Scuba Sam 33 11 3
Wet Suit Willy 81 18 4.5
Deep Diving Dan 104 26 4
Thus, the diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.
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find the value of x
2x+5=6x-3
Answer:
Step-by-step explanation:
2x+5=6x-3
subtract 6x
2x-6x+5=6x-6x-3
-4x+5=-3
subrtract-5
-4x+5-5= -3-5
-4x=-8
divide-4
-4x÷-4=-8÷-4
x=2
For any correlation, people often assume that change in one quantity causes change in the second quantity. This is not always true. For each situation, do you think that change in the first quantity causes change in the second quantity? What else may have affected the change in the second quantity?
a person's age and the number of cassette tapes he or she owns
For the given situation, we can clearly say that the change in one quantity will cause a change in the second quantity as well.
Correlation is a relationship between the values of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.
Causality means that one event causes another. Causality can only be determined by well-designed experiments. In such experiments, similar groups receive different treatments, and the results of each group are examined.
From the above information, we concluded that a person's age and the number of cassette tapes he/she owns are correlated more he lives the more he buys the cassette tapes. So we can make relation from this,
Person's Age ∝ Number of Cassette
This clearly states that by increasing/changing one quantity we will increase/change the other quantity as well.
Similarly, now that they have a direct relation if we decrease the Age of the person, the number of Cassette's will also decrease. A positive correlation we can call it.
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Find the sum of each finite series. Σ¹° n = 5 (20-n)
The sum of the given finite series is 75
The given series is:
[tex]\sum\limits^{10}_{n=5} {(20-n)}}[/tex]
To find the sum of this series,
Expand the summation notation by using the properties of sum operator:
Σ(a+b) = Σa + Σb
Hence,
[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]
If a is a constant, then Σa = k. a, where k is the number of terms = upper limit - lower limit + 1
Using this property:
[tex]\sum\limits^{10}_{n=5} {20} = (10 - 5+1)\times20=6\times20=120[/tex]
Expand
[tex]\sum\limits^{10}_{n=5} {n}=5+6+7+8+9+10=45[/tex]
Hence,
[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]
= 120 - 45 = 75
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Apparently a math question.
Answer:
Since Ian has $75 dollars, it would be enough to buy at least one DVD box set. However, there's not that much information in the statement.
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A small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters. A larger and similar can of tuna has a radius of 5.2 centimeters.
a. What is the scale factor of the cylinders?
The scale factor of the two similar cylindrical cans of tuna is 13/10.
Solids of the same type that have proportional corresponding linear measures are similar solids. In the case of similar cylinder:
height of A / height of B = radius of A / radius of B
Scale factor refers to the ratio of the corresponding dimensions of similar solids.
If the smaller cylindrical can of tuna has a radius of 4 centimeters and the larger and similar can of tuna has a radius of 5.2 centimeters, then the scale factor is:
scale factor = radius of larger can/ radius of smaller can
scale factor = 5.2 cm / 4 cm
scale factor = 13/10
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Identify the property illustrated by the equation.
5+(-5)=0
Identify the property illustrated by the equation.5+(-5)=0 Additive Inverse
What is an additive Inverse ?
The number that produces zero when added by -a is known as the additive inverse of a number, or a, in mathematics. The opposite, a shift in the sign, and negation are other names for this number.The definition of the additive inverse, which permits a wide application to mathematical objects other than numbers, is its inverse element under the binary operation of addition.Double additive inverse has no net effect, as with any inverse operation: −(−x) = x.To learn more about additive inverse, refer:
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Find the coordinates of the midpoint of the segment with the endpoints (5, 24) and
(-1, 10).
The radius, diameter, or circumference of a circle is given. Find the missing measure to the nearest hundredth.
r = x/8,d= ___, C=?
A circle is a curve sketched out by a point moving in a plane. The diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that radius of the circle is x/8 units. Therefore, the diameter and the circumference of the circle can be written as,
Diameter of circle = 2 × (Radius of the circle)
= 2 × (x/8) units
= x/4 units
Circumference of circle = 2 × π × (Radius of the circle)
= 2 × π × (x/8) units
= (x/4)π units
Hence, the diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.
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Question 7 of 10
Given NELR, solve for x.
R
(7x+33)
N
OA. 8
B. 7
O C. 6
O D. 5
(11x+21)
E
For the parallelogram NELR, we get the value of x as 7°.
We are given a parallelogram NELR.
We know that , the adjacent angles of a parallelogram are supplementary.
So, we get that:
∠ N + ∠ E = 180°
Substituting the values, we get that:
7 x + 33 + 11 x + 21 = 180
18 x + 54 = 180
18 x = 180 - 54
18 x = 126
x = 126 / 18
x = 7°
Therefore, for the parallelogram NELR, we get the value of x as 7°.
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Eileen is 3y years old now. Her mother is 4 times as old as her. Find their total age in 7 years' time. Give your answer in terms of y.
Answer:
15y+14
Step-by-step explanation
Answer: 14 + 15y
Step-by-step explanation:
E = Eileen’s age = 3y
M = Mum’s age
Total Age = 14 + 3y + 4(3y)
= 14 + 15y
Total age in 7 years time is their current ages plus 7 years for each (14 years)
Eileen is 3y, and her mum is 4 times that, which is 12y, meaning that their total ages are 3y + 12y, or, 15y.
Total age is then 15y + 14. Since we don’t know what y equals, we cannot add these two terms, and we can just leave them like that!
So, the answer is 14 + 15y.
