Step 1:
Equivalent fractions are fraction that are equal in ratio.
1/3 is equivalent to 4/12
4/12 can be simplify to 1/3 because 4 is a highest common factor of 4 and 12
When you divide by numerator ( 4) and denominator (12) by 4, the fraction result to 1/3.
Hence, 1/3 is equivalent to 4/12.
Final answer
[tex]\frac{1}{3}\text{ = }\frac{4}{12}[/tex]
work out sues total pay
Sue's total pay for the year given the salary, bonus and share of profit is £38,110.
What is the total pay?Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.
Salary for the year = monthly salary x number of months in a year
£1410 x 12 = £16,920
The next step is to determine the profit last year
Profit = total revenue - total cost
£549,000 - £473,500 = £75,500
Now determine the share of profit that Sue would earn.
Share of profit = 26% x £75,500
0.26 x £75,500 = £19,630
Now determine the total bonus she would earn : 4 x £390 = £1560
Total salary = £1560 + £19,630 + £16,920 = £38,110
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How do you solve #16?
∠A + ∠B + ∠C = 180°
reason : Sum of all angle of triangle is 180°
72° + 86° + ∠C = 180°
158° + ∠C = 180°
∠C = 180° - 158°
∠C = 22°
hence the value of ∠3 is 22°
Now ,
∠3 =∠4
reason : Being vertically opposite angle
4 = 22°
hence the value of ∠4 is 22°
Again ,
∠C + ∠D + ∠E = 180°
reason : Sum of all angle of triangle is 180°
22° + ∠D + 70° = 180°
92° + ∠D = 180°
∠D = 180° - 92°
∠D = 88°
hence the value of ∠5 is 88°..
[tex]...[/tex]
hope it helps ....☘✨
Mrs. Maria's Market buys 75% of eggs from farm A and the rest from farm B. Of the eggs from A,8% are green, and of those from B, 3% are green. If an egg is chosen at random and found to begreen, what is the probability that the egg is from farm B? Enter your answer as a decimal numberrounded to TWO digits after the decimal point.
0.12
Explanations:What is probability?Probability is the likelihood or chance that an event will occur. It ca be expressed as:
[tex]Probability=\frac{n(E)}{n(S)}[/tex]where:
n(E) is the expected event
n(S) is the total sample space
If Mrs. Maria's Market buys 75% of eggs from farm A and the rest from farm B, the percentage amount of egg bought from B will be 25% (100-75)
n(S) = 25%
If 3% of the eggs from B are green, hence n(E) = 3%
Determine the required probability
Pr(egg is from farm B) = n(E)/n(S)
Pr(egg is from farm B) = 3/25 = 0.12
Hence the probability that the egg is from farm B is 0.12
Send me Answers for Questions A, B, and C
Answer: A) 4 B) 30 C) 6
Step-by-step explanation:
For question A, you subtract the highest number and the lowest number (10-6)
For question B, you add all the frequency numbers together
For question C, you use your answer on B and divide it by 5
The fraction models below represent two fractions of the same whole: How much of the8음을16
So 4/5 times 5/8 is 1/2.
We have seen the isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use information to the right to help the measure of angles 1, 2, 3, 4, and 5.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
triangle diagram
Step 02:
angles:
we must analyze the diagram to find the solution
angle 1:
angle 1 = 180° - 155° = 25°
angle 2:
angle 2 = angle 1 = 25°
angle 3:
angle 3 = 180° - 25° - 25° = 130°
angle 4:
angle 4 = 155°
angle 5:
angle 5 = 180° - 25° = 155°
That is the full solution.
8y = 0.2(3x - 5) answer in slope intercept and y-intercept
The slope of the given equation is 0.075 and y-intercept is 0.125
What is slope of line ?
Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.
The point with coordinate having same slope as with given coordinates can be plotted on the same line.
First writing the given equation in standard slope intercept form :
y = mx + c.........(1)
In which:
• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
• c is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function
8y = 0.2(3x - 5)
8y = 0.6x - 1
y = 0.6/8x - 1/8
y = 0.075x - 0.125
Now, comparing it with equation (1) we get :
m = 0.075 and c = - 0.125
hence the slope of the given equation is 0.075 and y-intercept is 0.125
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SOMEONE PLEASE HELP ME QUICKLY WITH THIS,ITS AN EMERGENCY!!!!! pls explain how you get the solution as well, sorry!
Thank you <3
The statement that reflects the running rates is Pepe ran 9/8 mile in 1/2 hour and Paul ran 19/24 mile in 1/3 of an hour.
What is the speed?Speed is the total distance run per time. It can be determined by dividing the total distance travelled by the total time.
Speed = distance / time
Speed if Paul ran 1/5 mile in 4/15 hour
Speed = 1/5 ÷ 4/15
1/5 x 15/4 = 3/4 miles per hour
Speed if Pepe ran 8/10 mile in 1/4 of an hour
Speed = 8/10 ÷ 1/4
8/10 x 4 = 16/5 = 3 1/5 mile per hour
Difference in speeds =
[tex]3\frac{1}{5}[/tex] - [tex]\frac{3}{4}[/tex]
[tex]3\frac{4 - 15}{20}[/tex] = [tex]2\frac{9}{20}[/tex]
Speed if Paul ran 4/15 mile in 1/5 hour
Speed = 4/15 ÷ 1/5
4/15 x 5 = 4/3 = 1 1/3 miles per hour
Speed if Pepe ran 1/4 mile in of 8/10 an hour
Speed = 1/4 ÷ 8/10
1/4 x 10/8 = 5 / 16
Difference in speeds = [tex]1\frac{1}{3} - \frac{5}{16}[/tex] = [tex]1\frac{1}{48}[/tex]
Speed if Paul ran 1/3 mile in 19/24 hour
Speed = 1/3 ÷ 19 / 24
1/3 x 24/19 = 8/19 miles per hour
Speed if Pepe ran 1/2 mile in of 9/8 an hour
Speed = 1/2 ÷ 9/8
1/2 x 8/9 = 4/9 mile per hour
Difference = 4/9 - 8/19 = 4/171
Speed if Pepe ran 9/8 mile in 1/2 hour
Speed = 9/8 ÷ 1/2
9/8 x 2 = 2 1/4 miles per hour
Speed if Paul ran 19 / 24 mile in of 1/3 an hour
Speed = 19 / 24 ÷ 1/3
19 / 24 x 3 = 2 3/8 miles per hour
Difference =
[tex]2\frac{3}{8} - 2\frac{1}{4}[/tex]
[tex]\frac{3 - 2}{8}[/tex] = [tex]\frac{1}{8}[/tex] miles per hour
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Four points are labeled on the number line. M K L zo 0.5 1 Which point best represents 3? F. Point K G. H. Point 2 Point M Point N J.
The point that best represents 1/3 is point M .
The number line ranges from 0 to 0.5 with 10 divi
Hello! I need a little bit of help with this question please. (This information is not from an open test, it is a book as I'm studying for the ASVAB I am going to take later on.)
Given:
[tex]\sqrt{100}-\sqrt{64}[/tex]To find:
We need to solve this sum and find the final answer
Step-by-step solution:
To solve this problem, we need to know the square root of 100 and 64.
√100 = 10
√64 = 8
[tex]\begin{gathered} =\sqrt{100}-\sqrt{64} \\ \\ =10\text{ - 8} \\ \\ =2 \end{gathered}[/tex]Final answer:
Thus 2 (Option A) is the correct answer.
An envelope is 15 centimeters wide, and it measures 17 centimeters along the diagonal. The envelope is __ centimeters tall.
An envelope is rectangular in shape.
Given the width = 15cm, and diagonal = 17cm
Let h represent the tall length of the envelope
Applying Pythagoras theorem, we have
[tex]\begin{gathered} 17^2=15^2+h^2 \\ 289=225+h^2 \\ h^2=289-225 \\ h^2=64 \\ h=\sqrt[]{64} \\ h=8\operatorname{cm} \end{gathered}[/tex]The envelope is 8cm tall
Hello, I really need help on this assignment I don't understand what to do.
Answer:
-2 and -10
Explanation:
There are two numbers at a distance of 4 units from -6, the number that is 4 units to the right and the number that is 4 units to the left.
So, the number that is 4 units to the right is equal to
-6 + 4 = -2
And the number that is 4 units to the left is equal to
-6 - 4 = -10
Therefore, the numbers are -2 and -10 and they are represented as
what is the y intercept of y = 250 + 15x
The y-intercept of y = 250 + 15x is (0,250)
What is y-intercept?A line's y-intercept is the distance in y coordinates from the line's intersection with the y-axis at its origin. A location on the graph where x is 0 is known as the y-intercept. The y-intercept of a line that is perpendicular to the x-axis is undefined.
This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).
Here to determine the y-intercept put x=0,
Given, y = 250 + 15x
Replacing x by 0 in the above equation we get,
y = 250 + 15×0
y=250 +0
y=250
Therefore, the y-intercept of y = 250 + 15x is (0,250)
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help meeeeeeeeee pleaseee !!!!!
The value of the composite function is determined as: (g o f)(5) = 6.
How to Determine the Value of a Composite Function?To determine the value of a composite function, first evaluate the inner function by plugging in the value of x given, then use the output of the inner function as an input to evaluate the outer function.
Given the following:
f(x) = x² - 6x + 2
g(x) = -2x
Therefore:
(g o f)(5) = g(f(5))
Find f(5):
f(5) = (5)² - 6(5) + 2
f(5) = 25 - 30 + 2
f(5) = -3
Find g(f(5)) by substituting x = -3 into g(x) = -2x:
g(f(5)) = -2(-3)
g(f(5)) = 6
Therefore, (g o f)(5) = 6.
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Please help! I have 3 questions that I'm not sure what to do about :( if you could answer them that would be great
The resultant matrix for the given expressions are as follows -
[A] → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]
[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]
[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]
What is a Matrix?Matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. A matrix has [n] rows and [m] columns. The order of a matrix is given by - [m] x [n].
Given are the three different matrices as -
A = [tex]\left[\begin{array}{ccc}9&-6\\7&5\\\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}4&3\\-7&-6\\\end{array}\right][/tex]
C = [tex]\left[\begin{array}{ccc}0.5&3.6\\2.4&-3.2\\\end{array}\right][/tex]
We can solve the given expressions as follows.
[A] → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]
[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]
[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]
Therefore, the resultant matrix for the given expressions are as follows -
[A] → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]
[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]
[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]
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what property is used to solve this?
4x-3
x=2
4(2)-3
I need help with this question... it's about special triangles and I need to find y and z.. it should also not be a decimal.
To find z, consider the right-angled triangle at the botton in the diagram showm
[tex]\begin{gathered} \sin 45\text{ = }\frac{z}{20} \\ z\text{ = 20 }\sin 45 \\ z\text{ = }20\text{ }\times\frac{1}{\sqrt[]{2}} \\ z\text{ = }\frac{20}{\sqrt[]{2}} \\ z\text{ = }\frac{20}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ z\text{ = }\frac{20\sqrt[]{2}}{2} \\ z\text{ = 10}\sqrt[]{2} \end{gathered}[/tex]Let the common base of both triangles be m
[tex]\begin{gathered} \cos 45\text{ = }\frac{m}{20} \\ m\text{ = 20 }\cos 45 \\ m\text{ = }\frac{20}{\sqrt[]{2}} \\ m\text{ = }\frac{20}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ m\text{ = 10}\sqrt[]{2} \end{gathered}[/tex]To find y:
[tex]\begin{gathered} \tan 30\text{ = }\frac{y}{m} \\ \tan 30\text{ = }\frac{y}{10\sqrt[]{2}} \\ \frac{1}{\sqrt[]{3}}=\text{ }\frac{y}{10\sqrt[]{2}} \\ y\text{ = }\frac{10\sqrt[]{2}}{\sqrt[]{3}} \\ y\text{ = }\frac{10\sqrt[]{6}}{3} \end{gathered}[/tex]To find x:
[tex]\begin{gathered} \sin 30=\frac{y}{x} \\ \frac{1}{2}=\frac{10\sqrt[]{6}}{3}\div x \\ \frac{1}{2}=\frac{10\sqrt[]{6}}{3}\times\frac{1}{x} \\ x\text{ = }\frac{20\sqrt[]{6}}{3} \end{gathered}[/tex]In an arithmetic sequence with a1=-5 and d=-3, which term is -24?The term -24 is the ___th term of the sequence
Given:
[tex]\begin{gathered} a_1=-15 \\ d=-3 \\ a_n=-24 \end{gathered}[/tex]To find:
The value of n.
Explanation:
The nth term formula for the arithmetic sequence is,
[tex]a_n=a_1+(n-1)d[/tex]Substituting the given values we get,
[tex]\begin{gathered} -24=-15+(n-1)(-3) \\ -24=-15-3n+3 \\ -24=-3n-12 \\ -3n=-24+12 \\ -3n=-12 \\ n=4 \end{gathered}[/tex]Thus, -24 is the 4th term of the sequence.
Final answer:
The term -24 is the 4th term of the sequence.
(a) Teresa owns 9 shares of a certain stock. Yesterday the total value of her shares went down by90 dollars. What was the change in value for each share?dollarsHelp ASAP PLEASE
we have that
Divide $90 by the number of shares
so
90/9=$10
the answer is $10
I am struggling with this question. could you help me please??
Problem
Solution
Let x = age, W= weight the two variables of interest
We have the following probabilities given:
P(x<37) =0.142
P(W< 2500) = 0.051
P(x <37 AND W<2500)= 0.031
And we want the following probability and we can use the total probability rule:
P(x < 37 OR W< 2500) = P(x<37) +P(W< 2500) -P(x<37 AND W<2500)
If we replace we got:
P(x < 37 OR W< 2500)= 0.142+ 0.051- 0.031= 0.162
compare and contrast the graphs y=2x+1 with the domain {1,2,3,4} and y=2x+1 with the domain of all real numbers
Comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :
Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.
Contrast is range is different:
Range = { 3, 5, 7, 9} for domain {1,2,3,4}
Range = set of all real numbers for domain all real numbers.
As given in the question,
Given function for the graphs are:
y =2x+1
Different domains
Domain ={1,2,3,4}
Domain =All real numbers
Compare with y=mx +c
Slope m =2
For y-intercept put x=0
y=2(0) +1
=1
For x-intercept put y=0
0 =2x+1
⇒x=-1/2
Contrast:
For domain ={1,2,3,4}
Range is :
y = 2(1)+1
=3
y=2(2)+1
=5
y=2(3) +1
=7
y=2(4)+1
=9
Range ={ 3, 5, 7,9}
For domain= all real numbers
Range = set of all real numbers
Therefore, comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :
Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.
Contrast is range is different:
Range = { 3, 5, 7, 9} for domain {1,2,3,4}
Range = set of all real numbers for domain all real numbers.
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A toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 32 feet
per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function
h(t)=1612 +32t+5. How long will it take the rocket to reach its maximum height? What is the maximum height?
22The value of the hypotenuse in the right triangle shown isinches.14 in48 inFigure not drawn to scale
SOL
Step 1 :
In this question, we are meant to find the value of
the hypotenuse in the right angle below:
Before, we proceed, we still need to remind ourselves of Pythagoras' theorem,
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Step 2 :
From the above theorem, we can see that that the two adjacent sides are :
14 inches and 48 inches.
From the principle of Pythagoras' Theorem,
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{where a = 14 inches} \\ b\text{ = 48 inches} \\ c^2=14^2+48^2 \\ c^2\text{ = ( 14 x 14 ) + ( 48 x 48 )} \\ c^2\text{ = 196 + 2304} \\ c^2\text{ = 2500} \\ \text{square root both sides, we have that :} \\ c\text{ = 50 inches} \end{gathered}[/tex]
CONCLUSION :
The value of the hypotenuse in the Right angle, c = 50 inches.
8. Anna withdrew $50 from her checking account. She spent $28 on a pair of shoes. What fraction of her money does Anna have left?
Explanation:
If she spent $28 of the $50 she withdrew, she now has:
[tex]50-28=22[/tex]$22
The fraction is:
[tex]\frac{22}{50}=\frac{11}{25}[/tex]Answer:
Anna has 11/25 of her money left.
Fill in the missing statements and reasons in each proof shown below. You must mark the diagram forcredit.15.Given: g | h and 21 22Prove: p | r3рStatementReason2.ghgh21 2 2321 2222 223pllr
To prove that p || r, we will complete the data in the given table
[tex]\begin{gathered} \text{Statement: g}\mleft\Vert h\mright? \\ R\text{eason : Given} \end{gathered}[/tex][tex]\begin{gathered} \text{Statement: <1}\cong<3 \\ \operatorname{Re}\text{ason: Corresponding angles} \end{gathered}[/tex][tex]\begin{gathered} \text{Statement: <1}\cong<2 \\ \operatorname{Re}\text{ason:Given} \end{gathered}[/tex][tex]\begin{gathered} Statement\colon\text{ <2}\cong<3 \\ Re\text{ason: Alternate exterior angle} \end{gathered}[/tex][tex]\begin{gathered} \text{Statement: P}\mleft\Vert r\mright? \\ \operatorname{Re}\text{ason:<2}\cong<3 \end{gathered}[/tex]what would be an equation for a decrease of 75% using the y=kx format?
Input data
75% = 0.75
format
y = kx
Procedure
The k factor would be equal to 0.25
The answer would be
[tex]y=0.25x[/tex]Given ΔABC with m∠B = 62°, a = 14, and c = 16, what is the measure of A?
1) Let's sketch this out to better grasp it
2) We can see that there are two legs and two angles (one of them is missing) so let's solve it using the Law of Sines:
[tex]undefined[/tex]A red maple sapling was 3 feet tall when planted in 2010. Six years later, the tree was 24 feet tall. The growth rate of the tree is constant over time. Find a linear model for the height H (in ft) of the red maple t years after 2010. Let t = 0 represent 2010.H = __________What is the expected height (in ft) of the red maple in 2020?________ ft
Since the growth rate is linear and constant over time, it means that the sequence formed is an arithmetic sequence. The formula for finding the nth term of an arithmetic sequence is expressed as
an = a1 + d(n - 1)
where
a1 is the first term of the sequence
n = number of terms
d = common difference
In this case, n would be t(number of years
From the information given,
a1 = 3
Since the first term is at t = 0 and it represents 2010, six years letter would be represented by t = 7. Thus, we would took for d given that a7 = 24
We have
24 = 3 + d(7 - 1)
24 = 3 + 6d
6d = 24 - 3 = 21
d = 21/6 = 3.5
The linear model would be
an = 3 + 3.5(t - 1)
Substituting H for an, the linear model is
H = 3 + 3.5(t - 1)
At 2020, t = 11
H = 3 + 3.5(11 - 1) = 3 + 35
H = 38
Use the following data set to answer the question below.8 12 15 9 101212 18 14 1510 11 12 9 17What is the range for the data set?
Given the following set of data:
8 12 15 9 10 12 12 18 14 15 10 11 12 9 17
We will find the range of the data.
We need to find the maximum and the minimum
The maximum = 18
The minimum = 8
So, the range = maximum - minimum = 18 - 8 = 10
So, the answer will be The range = 10
I will show you a pic
GIven the table above :
We have that
x y
2 8
4 4
6 0
8 4
The table represents a Non - Linear Function
Reason: It is because there is no constant ratio or proportion between x and y.