From the trigonometric identity of the sum of angles
[tex]\sin (\alpha-\beta)=\sin \alpha\cos \beta-\cos \alpha\sin \beta[/tex]we ca note that
[tex]\begin{gathered} \alpha=\frac{11\pi}{36} \\ \beta=\frac{\pi}{18} \end{gathered}[/tex]Then, by substituting these values into the formula, we have
[tex]\sin (\frac{11\pi}{36}-\frac{\pi}{18})=\sin \frac{11\pi}{36}\cos \frac{\pi}{18}-\cos \frac{11\pi}{36}\sin \frac{\pi}{18}[/tex]which is the same given expression. Then, we have that
[tex]\sin (\frac{11\pi}{36}\frac{\pi}{18})=\sin (\frac{11\pi}{36}-\frac{2\pi}{36})=\sin (\frac{11\pi}{36}-\frac{2\pi}{36})=\sin \frac{9\pi}{36}=\sin \frac{\pi}{4}[/tex]Then, the answer is:
[tex]\sin \frac{\pi}{4}=\frac{\sqrt[]{2}}{2}[/tex]
Which is less (_25)+12 or 40 +(_63)
The answer is 40 + (- 63). Addition is a method of combining items and counting them as a single large group. In mathematics, addition is the process of combining two or more numbers.
What is meant by equation?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Therefore,
First calculate (- 25) + 12(- 25) + 12 = - 13
Calculate 40 + (-63)40 + (- 63) = - 23
we get - 13 and -23 ,
-23 is lesser than -13
-23 < -13.
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Solve the inequality for u.u +8 > 24Simplify your answer as much as possible.DDDD
Answer:
[tex]u\text{ }>\text{ 16}[/tex]Explanation:
Here, we want to solve the given inequality for u
What we have to do is to bring like terms together
We bring 8 to the right which causes a sign change
Mathematically, we have that as:
[tex]\begin{gathered} u\text{ }>\text{ 24-8} \\ u\text{ }>\text{ 16} \end{gathered}[/tex]which function is used to find y, the remaining balance after x number of payments have been made?
Given data:
The first point on the graph is (0,20,000).
The second point on the graph is (40,0).
The equattion of the line is,
(y-20,000)/(x-0)=(0-20,000)/(40-0)
(y-20,000)/(x)=-500
y-20,000=-500x
y=-500x+20,000
Thus, the equation of the line is y=-500x+20,000
help me please
thank you
Answer:
Domain: [tex](-\infty, \infty)[/tex]
Range: [tex][0, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Which set represents a Pythagorean triple? 27,38,42. 33,44,55. 35,38,42. 68,72,81
The sets that represents a Pythagorean triple is 33,44,55.
How to represent Pythagorean triple?Pythagorean triple is used to find the side of a right angle triangle.
The Pythagoras theorem is represented as follows;
c² = a² + b²
where
c is the hypotenuse sidea and b are the other legs of the right triangle.Therefore, the Pythagorean triple must follow the principle : c² = a² + b²
Hence,
33² + 44² = 55²
1089 + 1936 = 3025
Therefore, the Pythagorean triple is 33,44,55.
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Find the domaine and range of each relation. Determine if the relation is a function .
D: {-5, -2, 1, 2}
R: {-4, 0, 3}
The relation is a function
Explanation:Given:
5) Ordered pairs on a coordinate plane
To find:
the domain, range, and the type of relation
[tex]\begin{gathered} The\text{ domain is the input of a funcion \lparen x values\rparen} \\ The\text{ range is the output of the function \lparen y values\rparen} \end{gathered}[/tex]To determine the domain and range, we will list the ordered pairs:
(-5, 3), (-2, -4), (1, 0), (2, 3)
The first number in each pair represents the x values (domain), while the 2nd number in each pair represents the y values (range)
The domain: {-5, -2, 1, 2}
The range: {3, -4, 0, 3}
Rearranging and picking one of the repetitions:
The range: {-4, 0, 3}
For a relation to be a function, each input will have only one output.
None of the inputs appears more than once. Hence, each input has only one output. It is a function
1. Liezl bought 2 1/4 kilograms of pork, 5 1/2 kilograms of chicken and 1 1/3 kilograms of beef. How many kilograms of meat did she buy in all?
2. Roel travelled 1 1/2 km while Arnel 1 1/2 km more than the distance covered by Roel. How many kilometers did the two travel together?
3. Kenneth and Ian have 20 kilograms of fruits. Kenneth has 9 5/8 kilograms of fruits. How many kilograms of fruits does Ian have?
4. Father has a 17 3/7 m of nylon string. He gave 10 m of it for his brother’s fishing net. How long is the nylon string that is left?
5. Althea is working in a bakeshop. She put two cheesecakes on display. The first cheesecake was cut into 8 slices and there are 5 slices left. The other was cut into 12 slices and there are 4 slices left. How much cheesecake is left.
1. Liezl bought the total amount of meat = 118 / 12 kilograms.
2. Roel travel 3 kilometer.
3. Lan have 83/8 kilograms fruits.
4. Her father left 52 / 7 nylon.
5. The left cheesecake is 9 slices.
What is Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Now,
1. For first condition;
Amount of pork = 2 1/4 kilograms
Amount of chicken = 5 1/2 kilograms
Amount of beef = 1 1/3 kilograms
So, Total meat = 2 1/4 + 5 1/2 + 1 1/3
= 9/4 + 11/2 + 4/3
= 36/12 + 66/12 + 16/12
= 118 / 12
Thus, The total amount of meat = 118 / 12 kilograms.
2. Total distance cover by Roel = 1 1/2 + 1 1/2
= 3/2 + 3/2
= 6/2
= 3 kilometer.
So, Roel travel 3 kilometer.
3. Kenneth and Lan have fruits = 20 kilograms.
Kenneth have fruits = 9 5/8 kilograms.
So, Amount of fruits does Lan have = 20 - 9 5/8
= 20 - 77/8
= (160 - 77) / 8
= 83 / 8 kilograms.
Thus, Lan have 83/8 kilograms fruits.
4. Father have nylon string = 17 3/7 m
And, He gave 10 m of it for his brother’s fishing net.
So, Left amount of the nylon string = 17 3/7 - 10
= 122/7 - 10
= 122 - 70 / 7
= 52 / 7
Thus, He left 52 / 7 nylon.
5. Since, Althea have left in first cheesecakes = 5 slices
And, In second cheesecakes = 4 slices.
So, Total left cheesecake = 5 + 4
= 9 slices.
Thus, The cheesecake is 9 slices.
Therefore,
1. Liezl bought the total amount of meat = 118 / 12 kilograms.
2. Roel travel 3 kilometer.
3. Lan have 83/8 kilograms fruits.
4. Her father left 52 / 7 nylon.
5. The left cheesecake is 9 slices.
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help meeeeeeee pleaseee
thank you
Part a: The equation is y=-500x+3000
Part b: The prediction of sales is 2750 at a price of $6.5
The equation of a line is given by:
y=mx+b
In which
m is the slope, representing the rate of change.
b is the y-intercept, which is the value of y when x = 0.
Part a:
In this problem:
There are two points (6, 3000) and (8, 2000).
The slope is given by: Change in y/Change in x
m = 2000-3000/8-6
m = -500
Thus
y = -500x+b
Point (6,3000) means that when x=6, y=3000, which we use to find b.
3000 = -500(6)+b
3000=-3000+b
b = 6000
So, y = -500x+6000
Part b:
The sales are y when x = 6.5, thus:
y = -500(6.5)+6000
= -3250+6000
The prediction is 2750 sales with a price of $6.50.
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How do yu solve -8w times -w
The result of the expression -8w times -w is [tex]8w^{2}[/tex]
The expression is -8w times -w
Expressions is the mathematical statements that have a minimum of two terms containing numbers or variables, connected by an operator in between. The operator maybe addition, subtraction, division or multiplication.
Here the expression is -8w times -w
Here -8w times -w means, we have to multiply the -8w by -w
Therefore the expression is
-8w × -w
We know when we multiply the a negative number by negative number the result will be positive number
-8w × -w = [tex]8w^{2}[/tex]
Hence, the result of the expression -8w times -w is [tex]8w^{2}[/tex]
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200 lottery tickets are sold for $6 each. The person with the single winning ticket will get $90. What is the expected value for a ticket in this lottery?
The probability of winning is 1/200.
The probability of losing is 199/200.
The gain of winning is
($90 - $6) that is $90 of the winning ticket minus the $6 ticket cost.
The loss of lossing is -$6 that is a player loses $6 for the ticket.
The expected value therefore is calculated as
[tex]\begin{gathered} E(X)=(90-6)(\frac{1}{200})+(-6)(\frac{199}{200}) \\ E(X)=(84)(\frac{1}{200})+(-6)(\frac{199}{200}) \\ E(X)=0.42-5.97 \\ E(X)=-5.55 \end{gathered}[/tex]Therefore, the expected value for a ticket in this lotter is -$5.55 or an average loss of $5.55.
Table 1 shows two variables m and n that are related by an equation n ab^m where a and b are constantBelow shows table 1:m : 1 2 3 4 5n : 24 48 96 192 384a) plot the graph of log10 n against m by using a scale of 2 cm to 1 unit on the x-axis and 2cm to 1.2 unit on the y-axisb) hence, find the value of a and b
Answer
a) The plotted graph is shown in the Explanation below.
b) a = 12, b = 2
Explanation
n = a(b^m)
Taking the logarithm of both sides
log n = log [a(b^m)]
log n = log a + log (b^m)
log n = log a + m log b
So, to first plot the graph, we know we need to rewrite this equation to match the equation of a straight line. Equation of a straight line is
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
log n = (log b) m + log a
y = mx + b
y-axis = log n
slope = log b
x-axis = m
intercept = log a
So, we need to plot log n (on the y-axis) against m (on the x-axis)
m | n | log n
1 | 24 | 1.38
2 | 48 | 1.68
3 | 96 | 1.98
4 | 192 | 2.28
5 | 384 | 2.58
The values for log n are then plotted against the corresponding value of m
The image is presented below.
From the graph, we can easily see that
Intercept = 1
To obtain the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
Using the two farthest points,
(x₁, y₁) and (x₂, y₂) = (1, 1.38) and (5, 2.58)
[tex]\begin{gathered} Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope = }\frac{2.58-1.38}{5-1}=\frac{1.2}{4}=0.3 \end{gathered}[/tex]b) Intercept = log a = 1.08
a = log⁻¹ (1.08) = 12
Slope = log b = 0.3
b = log⁻¹ (0.3) = 1.995 = 2
n = 12 (2^m)
We can test this by putting values of m in the expression looking to get n
when m = 1,
n = 12 (2^1)
n = 12 (2) = 24
when m = 5
n = 12 (2^5)
n = 12 (32) = 384
So, our model works!!!
Hope this Helps!!!
A radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t)=100(1.3)^-tWhat is the Half-Life of this substance?
Explanation:
The dunction is given below as
[tex]A(t)=100(1.3)^{-t}[/tex]To figure out the half life,
The new mass of the decayed substance will be half that of the initial substance
[tex]\begin{gathered} A(t)=100\left(1.3\right)^{-t} \\ A(t)=\frac{100}{2}=50 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A(t)=100(1.3)^{-t} \\ 50=100(1.3)^{-t} \\ \frac{50}{100}=1.3^{-t} \\ \frac{1}{2}=1.3^{-t} \end{gathered}[/tex]Apply exponent rules
[tex]\begin{gathered} \frac{1}{2}=1.3^{-t} \\ ln(\frac{1}{2})=-tln(1.3) \\ t=\frac{ln(2)}{ln(1.3)} \\ t=2.64years \end{gathered}[/tex]Hence,
The final answer is
[tex]2.64years[/tex]T
A metal worker traced a triangular piece of sheet metal on a coordinate plane, as shown. The un
represent inches. What is the length of the longest side of the metal triangle? Approximate the length
of the longest side to the nearest tenth of an inch using a calculator
The length of the longest side of the metal triangle is 7.8 inches
What is a triangle called ?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. Triangles can be divided into three groups based on the lengths of their sides, and these groups are as follows: Scalene. Isosceles. Equilateral. Interior angles in triangles all add up to 180°, 180°, 180°, etc. A triangle's angles are equal to the sum of the angles at each of its three vertices. Three diagonals must meet at three different locations to form a triangle. There are five possible arrangements of three diagonals.
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are z^3 and 3z eqivalent expressions? explain
Given the expressions:
[tex]\begin{gathered} z^3 \\ 3z \end{gathered}[/tex]these two expressions are not equivalent, since one is thrice a number and the other is a cubic number. We can see this if we write completely each expression:
[tex]\begin{gathered} z^3=z\cdot z\cdot z \\ 3z=z+z+z \end{gathered}[/tex]thus, the expressions are not equivalent
Is 5 a solution to 3x-8=0?
The equation is 3x - 8 = 0.
So, 5 is a solution if we replace x by 5 and we get 0 on the left side of the equation.
Then, replacing x by 5, we get:
3x - 8 = 0
3*5 - 8 = 0
15 - 8 = 0
7 = 0
Since 7 is different from 0, 5 is not a solution.
Answer: 5 is not a solution
155 divided by 12 step-by-step explanation
Answer:
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 12 on the left side and the dividend 155 on the right side like this:
1 2 ⟌ 1 5 5
Step 2:
The divisor (12) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:
0
1 2 ⟌ 1 5 5
Step 3:
Multiply the divisor by the result in the previous step (12 x 0 = 0) and write that answer below the dividend.
0
1 2 ⟌ 1 5 5
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.
0
1 2 ⟌ 1 5 5
- 0
1
Step 5:
Move down the 2nd digit of the dividend (5) like this:
0
1 2 ⟌ 1 5 5
- 0
1 5
Step 6:
The divisor (12) goes into the bottom number (15), 1 time(s). Therefore, put 1 on top:
0 1
1 2 ⟌ 1 5 5
- 0
1 5
Step 7:
Multiply the divisor by the result in the previous step (12 x 1 = 12) and write that answer at the bottom:
0 1
1 2 ⟌ 1 5 5
- 0
1 5
1 2
Step 8:
Subtract the result in the previous step from the number written above it. (15 - 12 = 3) and write the answer at the bottom.
0 1
1 2 ⟌ 1 5 5
- 0
1 5
- 1 2
3
Step 9:
Move down the last digit of the dividend (5) like this:
0 1
1 2 ⟌ 1 5 5
- 0
1 5
- 1 2
3 5
Step 10:
The divisor (12) goes into the bottom number (35), 2 time(s). Therefore put 2 on top:
0 1 2
1 2 ⟌ 1 5 5
- 0
1 5
- 1 2
3 5
Step 11:
Multiply the divisor by the result in the previous step (12 x 2 = 24) and write the answer at the bottom:
0 1 2
1 2 ⟌ 1 5 5
- 0
1 5
- 1 2
3 5
2 4
Step 12:
Subtract the result in the previous step from the number written above it. (35 - 24 = 11) and write the answer at the bottom.
0 1 2
1 2 ⟌ 1 5 5
- 0
1 5
- 1 2
3 5
- 2 4
1 1
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 155 divided by 12 calculated using Long Division is:12
11 Remainder
which expression can be used to find the surface area of the following rectangular prism A 15+10+6B 15+15+15+6 C 6+6+10+10+15+15D 6+10
Answer:
C. 6 + 6 + 10 + 10 + 15 + 15
Explanation:
The surface area of a rectangular prism can be calculated as:
Surface Area = lw + lw + wh + wh + lh +lh
Where l is the length, w is the width, and h is the height.
So, replacing l by 3, w by 2, and h by 5, we get:
Surface Area = 3(2) + 3(2) + 2(5) + 2(5) + 3(5) + 3(5)
Surface Area = 6 + 6 + 10 + 10 + 15 + 15
Therefore, the expression that can be used to find the surface area is:
Surface Area = 6 + 6 + 10 + 10 + 15 + 15
help me please
thank you
Answer:
Domain: [tex)(-\infty, \infty)[/tex]
Range: [tex][0, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Let A = {a,b,c), B = {4,5,6), and/= {(a ,6), (b,4), (c,6)). Is f a function from A to B? Explain.
The condition for a group of paired values to be a function is that for each value of the independent variable exists one and only one value of the dependant variable.
In this case, A is the group of points that represent the independent variable, and B, the dependent variable.
As each value of A has one and only one value of B, f is a function from A to B.
The inverse is not true, as 6 would have 2 values (a and c) in the image (A).
A is the domain of the independent variable.
f is the function that transform the values present in the group A in some of the elements of the image, that is group B.
The conditions for that relation to be a function is that each of the values in the domain has one and only one value in the image.
Bob's new machine for work cost him £6700. It will depreciate at 28% each year. After how many years will it be worth less than £1000?
It will be valued less than £1000 after x = -0.8260748 years.
Based on the given conditions, formulate:
6700 × (1 - 28%) = 1000
Calculate the sum or difference:
6700 ×0.72ˣ = 1000
Reduce the greatest common factor on both sides of the equation:
67 × 0.72ˣ = 10
Divide both sides of the equation by the coefficient of variable:
67 × 0.72ˣ / 67 = 10 / 67
Rewrite as fraction:
0.72ˣ = 10 / 67
Convert exponential to logarithm form:
x = log°.₇₂ 10 / 67
Convert decimal to fraction:
x = log°₍₇₂/₁₀₀₎ 10 / 67
After simplifying -
get the result:
x = -0.8260748
Hence , After x = -0.8260748 years will it be worth less than £1000.
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A population of values has a normal distribution with μ=62.9 and σ=25.8. You intend to draw a random sample of size n=22.
In a population of values having a normal distribution with (μ = 62.9) and (σ = 25.8), and we intend to draw a random sample of size (n = 22),
(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3) is 0.2476
(ii) The probability that a sample of size (n = 22) is randomly selected with a mean less than 45.3 [P(M < 45.3)] is (0.0007)
As per the question statement, a population of values has a normal distribution with (μ = 62.9) and (σ = 25.8) and we intend to draw a random sample of size (n = 22).
We are required to calculate:
(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3)
(ii) The probability that a sample of size (n = 242) is randomly selected less than 45.3 [P(M < 45.3)].
Let us assume that, a random variable "X" follows normal distribution with mean (μ = 62.9), standard deviation (σ = 25.8) and a sample size of (n = 22).
(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3) is,
P (X < 45.3) = P[{(X - μ)/σ} < {(45.3 - 62.9)/25.8}]
= [P{Z < (-0.6822)}]
=0.247556247343...[Using Excel Function "NORMSDIST (-0.6822)]
≈ 0.2476
(ii) The probability that a sample of size (n = 22) is randomly selected with a mean less than 45.3 [P(M < 45.3)] is,
P(M < 45.3) = P[{(M - μ)/(σ/√n)} < {(45.3 - 62.9)/25.8/√22)}]
= P[{(M - μ)/(σ/√n)} < {(45.3 - 62.9)/5.5006}]
=P[Z < (-3.19965)]
= (0.000687972836)...[Using Excel Function "NORMSDIST (-1.49)]
≈ 0.0007
Probability: Probability is the branch of mathematics concerning numerical descriptions about the extent to which an event is likely to occur, or how likely it is that, a proposition is true, and is measured by the ratio of the favorable cases to the whole number of cases possible.Sample: In statistics, quality assurance, and survey methodology, sampling is a logical selection of a subset (a statistical sample) of individuals from within a larger statistical population to estimate characteristics of the whole population.To learn more about Samples and Probability, click on the link below.
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can you explain to me how to solve this please
To solve the exercise you can use the following properties of exponents and radicals
[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex][tex]a^ma^n=a^{m+n}[/tex][tex]\frac{a^m}{a^n}=a^{m-n}[/tex]So, you have
[tex]\begin{gathered} \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=\frac{7^{\frac{1}{3}}\cdot7^{\frac{1}{2}}}{\sqrt[6]{7^5}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=\frac{7^{\frac{1}{3}+\frac{1}{2}}}{7^{\frac{5}{6}}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=\frac{7^{\frac{5}{6}}}{7^{\frac{5}{6}}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=7^{\frac{5}{6}-\frac{5}{6}} \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=7^0 \end{gathered}[/tex]By definition
[tex]\begin{gathered} a^0=1 \\ \text{Where a }\ne0 \end{gathered}[/tex]So
[tex]\begin{gathered} \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=7^0 \\ \frac{\sqrt[3]{7}\sqrt[]{7}}{\sqrt[6]{7^5}}=1 \end{gathered}[/tex]Therefore, the correct answer is b. 1.
3. Jill made 20 muffins. She put them into 3 boxes and has two muffins left. How many are in
each box if they all contain the same amount of muffins?
Answer: 6
Step-by-step explanation:
20 (amount of muffins) - 2 (muffins left) = 18 (total in boxes)
18 ÷ 3 = 6
Three glasses of milk and 4 snack bars have a total of 80 carbohydrates (carbs), and 4 glasses of milk and 3 snack bars have a total of 81 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
Let m be a glass of milk and s be a snack bar.
3 glasses of milk and 4 snack bars have a total of 80 carbohydrates. So, the expression is,
[tex]3m+4s=80\ldots..(1)[/tex]4 glasses of milk and 3 snack bars have a total of 81 carbs.
[tex]4m+3s=81\ldots\ldots.(2)[/tex]The above equation can be rewritten as,
[tex]\begin{gathered} 4m=81-3s \\ m=\frac{81-3s}{4}\ldots..(3) \end{gathered}[/tex]Put equ (3) in (1) to find s.
[tex]\begin{gathered} 3\times(\frac{81-3s}{4})+4s=80 \\ \frac{243-9s}{4}+4s=80 \\ \frac{243-9s+16s}{4}=80 \\ 243-9s+16s=320 \\ 7s=77 \\ s=11 \end{gathered}[/tex]Now, put 11 for s in equ (1) to find m.
[tex]\begin{gathered} 3m+4\times11=80 \\ 3m+44=80 \\ 3m=36 \\ m=12 \end{gathered}[/tex]So, there are
Neveah orders a square pizza. 2/3 of the pizza has pepperoni. 2/3 of the pepperoni also has
green peppers. How much of the whole pizza has both pepperoni and green peppers?
The fraction of whole pizza has both pepperoni and green peppers exists 1/2.
What is meant by a fraction?A number is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction exists less than the denominator.
Given that:
3/4 of the pizza contains pepperoni
2/3 of the pizza with pepperoni contains green pepper ;
The fraction of the whole pizza that contains both pepperoni and green pepper;
The fraction with pepperoni = 3/4
Fraction of whole with green pepper and pepperoni: 2/3 of 3/4
simplifying the above equation, we get
= 2/3 × 3/4
= (2 × 3) / (3 × 4)
= 6/12 = 1/2
Therefore, the fraction of whole pizza has both pepperoni and green peppers exists 1/2.
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Which is a polar form of the following parametric equations?x=5cos² thetay = 5 cos theta sin theta
ANSWER
[tex]r(\theta)=5cos\theta[/tex]EXPLANATION
Given;
[tex]\begin{gathered} x=5cos^2\theta \\ y=5cos\theta\:sin\theta \end{gathered}[/tex]Convert from polar form to parametric form.
[tex]\begin{gathered} x(\theta)=r(\theta)cos\theta \\ y(\theta)=r(\theta)sin\theta \end{gathered}[/tex]Here;
[tex]\begin{gathered} x(\theta)=5(cos\theta)^2=5cos\theta\times cos\theta \\ y(\theta)=5cos\theta s\imaginaryI n\theta=5cos\theta sin\theta \\ \Rightarrow r(\theta)=5cos\theta \end{gathered}[/tex]Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
what is the total number of digits required in numbering the pages of a book, if the books has 1150 pages?
Base= 5.4 cm, Height= 2 cm. Find the area of the triangle. A.21.6 cm2 B. 10.8 cm2 C. 7.4 cm2 D. 5.4 cm2
Step 1
Given;
[tex]\begin{gathered} width=5.4cm \\ length=2cm \end{gathered}[/tex]Required; To find the area of the triangle
Step 2
State the area of a triangle
[tex]\begin{gathered} A=\frac{1}{2}\text{ base x height} \\ A=\frac{1}{2}\times5.4\times2 \\ A=5.4cm^2 \end{gathered}[/tex]Answer;
[tex]Area=5.4cm^2[/tex]just need help solving this ( not graded just a review)
Given
jenny mixed 4kg of mixed nuts containing 16% of peanuts with 12kg of mixed nuts containing 40% of peanuts .
Find
Percent in the new mixture of peanuts
Explanation
we are given 4kg of mixed nuts containing 16% of peanuts
Amount of quantity =
[tex]\frac{percentage}{100}\times totalamount[/tex]so,
[tex]\frac{16}{100}\times4=0.64kg[/tex]and also 12kg of mixed nuts containing 40% of peanuts .
so,
[tex]\frac{40}{100}\times12=4.8kg[/tex]so,total weight
[tex]0.64+4.80=5.44kg[/tex]let total mass pf mixture containing x % peanuts.
so,
[tex]\begin{gathered} \frac{5.44}{16}=\frac{x}{100} \\ 34=x \end{gathered}[/tex]Final Answer
Percent in the new mixture of peanuts = 34%
