The value of k is 4.
What is Proportion ?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Volume= 16
Width = 4
So, we can write the relation as
Volume= k (width)
k = Volume/ width
k= 16/4
k = 4
Hence, the value of k is 4.
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The ratio of the number of beads collected by Jane to the number of beads collected by Jill is 7: 3. Jane gave some beads to Jill. Is it possible for both Jane and Jill to have the same number of beads after Jane gave some beads to Jill? Explain why you think so
yes , it is possible for both Jane and Jill to have the same number of beads after Jane gave some beads to Jill and The number of beads Jane has is 7t/4 and Jill has 3t/4 bead's
The ratio of Jane's beads to Jill's beads is 7: 3
Let x be the number of beads Jane has
y be the number of beads Jill has
x/y = 7/3
When Jane's gives t of her beads away both will have the same number of beads so
x - t = y
substituting in the first equation
x/ ( x- t) =7/3
3x= 7x-7t
4x= 7t
x= 7t/4
y= 7t/4 -t
= 3t/4
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Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.
Based on the given ratio of modern and classical songs learned, the number of modern songs learned if 9 classicals have been learned is 15
What is the number of modern songs learned?Number of modern songs they learn = 5Number of classical songs = 3If the choir has learned 9 classical songs;
Number of modern songs learnt = xEquate the ratio of the number of modern songs to the number of classical songs
5 : 3 = x : 9
5/3 = x/9
cross product5 × 9 = 3 × x
45 = 3x
divide both sides by 3
x = 45/3
x = 15
In conclusion, the number of modern songs they have learned if they learn 9 classical songs is 15
Complete question:
Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.
If the choir has learned 9 classical songs, how many modern songs have they learned?
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i need to find the diameter and the area of this equation[tex]A=\pi \frac{d}{2} x^{2}[/tex]
Answer:
Step-by-step explanation:
Express 60 as the product of its prime factors.
60 = (Answer here)
Answer:
2x2x3x5= 60
I hope you like it
Answer:
2 X 2 X 3 X 5
Step-by-step explanation:
We divide 60 by 2 as many times as possible to get 60 = 15 x 2 x 2. 2 is a prime number so we don't need to break the 2's down any more. Instead we break 15 down. 15 doesn't divide by 2 so we try the next prime number: 3 Divide 15 by 3 to get 15 = 5 x 3, and so 60 = 5 x 3 x 2 x 2. Now we collect the factors, so our final answer is 60 = 5 x 3 x 22.
Tammy installs bathroom tiles. Her current job requires tiles that are equilateral triangles and all the tiles have to be congruent to each other. She has a big sack of tiles all in the shape of equilateral triangles. Although she knows that all the tiles are equilateral, she is not sure they are all the same size. What must she measure on each tile to be sure they are congruent? Explain.
Step-by-step explanation:
one side.
as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.
the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.
so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.
a box contains tiles. each tile has certain properties: each tile is made of wood or plastic. each tile is red, yellow, or blue. each tile is a triangle, square, pentagon, or circle. there is exactly one tile for each combination of properties. for example, there is one red circle that is made of wood. steve chooses one tile, and ellen chooses a different tile. what is the probability that the two chosen tiles differ with respect to all three properties?
1/24 is the probability that the two chosen tiles differ with respect to all three properties
1/2 chance that the tiles materials will be different (wood or plastic). 1/3 chance exists that the tiles will have different colors (r, y or b) 1/4 chance where the tile shapes will change (t, s, p or c)the probability that all three attributes of the two tiles will be different.1/2 * 1/3 * 1/4 = 1/24 The probability of an event occurring is a measure of its likelihood. It assesses the likelihood of an event. P(E) = Number of Favourable Outcomes/Total Outcomes is the probability formula.
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rationalise the denominator of \frac{26}{4+\sqrt{3}}
The rationalization of the denominator of the given fraction gives 8 -2√3
Rationalizing the denominatorFrom the question, we are to rationalize the denominator of the given fraction
The given fraction is
26 / (4+√3)
To rationalize the given expression, we will multiply both the numerator and the denominator of the fraction by the conjugate of the denominator.
The denominator is 4+√3
Thus,
The conjugate of the denominator is 4-√3
Now, multiply the numerator and the denominator by the conjugate.
That is,
(26 × (4-√3)) / ((4+√3) × (4-√3))
(104 - 26√3) / (16 - 3)
(104 - 26√3) / 13
= 104/13 - (26√3)/13
= 8 - 2√3
Hence,
The result of rationalizing is 8 -2√3
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Choose the linear equation that is parallel to the following line y =−1/4 x − 1
Answer:
Any equation that has the same slope as this line will be parallel to it. The slope is -1/4, so whichever equation has -1/4 x in it will be parallel to the line.
7(x+4)-2[x-3(5+x)]=2/3(x-6)
With detailed workings
. suppose the sides of a rectangle are changing with respect to time. the first side is changing at a rate of 2 in./sec whereas the second side is changing at the rate of 4 in/sec. how fast is the diagonal of the rectangle changing when the first side measures 16 in. and the second side measures 20 in.? (round answer to three decimal places.)
Diagonal of rectangle is changing by the rate of 4.373 in. /sec.
What is rate of change ?Rate of change (ROC) is the rate at which a variable changes over a particular period of time
To find the average rate of change, divide the change in the y-values by the change in the x-values . Finding the average rate of change is especially useful for identifying changes in measurable values such as average speed or average velocity.
A ratio is a special ratio in which the two terms have different units.
Calculationthe calculation part is shown in the below picture attached .
so after seeing the solution we come to an answer of = 4.373 in./sec
therefore diagonal of rectangle is changing by the rate of 4.373 in. /sec
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The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle.
Solve the equation for the variable w
When you have done that
state the value of 'w' if the perimeter of the rectangle is equal to 37 feet and the length is equal to 4 feet.
hurrryyyy pls
Answer:
14.5 feet
Step-by-step explanation:
To make subject as 'w' and solving:To make the subject as 'w', isolate w.
To isolate 'w', subtract 2L from both sides .2L + 2W =P
2W = P - 2L
Now, divide both sides by 2.[tex]\sf W = \dfrac{P-2L}{2}\\\\W =\dfrac{P}{2}-\dfrac{2L}{2}\\\\ \boxed{W = \dfrac{P}{2}-L}[/tex]
P = 37 feet
L = 4 feet
[tex]\sf W =\dfrac{37}{2}-4\\\\[/tex]
= 18.5 - 4
W = 14.5 feet
help for the rest pls
Answer :
9 girls and 18 boys don't have a voucher
Step-by-step explanation :
There are 38 boys and 22 girls. The total number of children is 60. We know that 33 children have a voucher. 27 children don't have a voucher. ( 60 - 33 = 27 ) .
"Twice as many boys as girls do not have a voucher."
We can now make an equation.
The girls who do not have a voucher will be x, boys who don't have a voucher will be 2x, since it says twice as many boys.
We can now make our equation.
x + 2x = 27
Add x and 2x
3x = 27
Divide both sides by 3
x = 9
We know now that girls who don't have a voucher is 9.
The boys who don't have a voucher is 2x, so we plug 9 instead of x.
2(9) = 18.
18 boys do not have a voucher.
If you would like the rest for the frequency tree...
Total students : 60
Boys : 38
Boys who don't have a voucher : 18
Boys who have a voucher : 20
Girls : 22
Girls who don't have a voucher : 9
Girls who have a voucher : 13
Hope this helped.
asking help for a friend again
To find the parallel line of y =3z+6 passing through the slope intercept points (-2,5).
For a line to be parallel to another line, by definition it must have the same slope.
Because the equation is in the slope-intercept form we can use the slope of the line.
The slope- intercept form of a linear equation is :
y=mx+b
Where m is the slope and b is the y− intercept value.
Therefore, for the given equation, the slope is 3.
Now we can use the point slope formula to determine the equation for the parallel line.
The point - slope formula states: (y−y1)=m(x−x1)
Where m is the slope and (x1,y1) is a point the line passes through.
Substituting the slope from the given line and the given point gives:
y−5=3(x+2)
Transforming this to the slope-intercept form by solving for y gives:
y−5=3x+6
y−5+5=3x+6+5
y=3x+11
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WILL GIVE BRAINLIST TO BEST ANSWER! EASY POINTS
write the point slope form of the equation of the line through the given points.
through (-1, -5) and (-5, 3)
LOTS OF POINTS coordinate proof explaining how the midsegment of a triangle forms a triangle with 1/4 of area
The coordinate geometry, the midsegment theorem shows that the midsegment of a triangle is 1/4 area of the triangle.
How to show that the midsegment of a triangle is 1/4 area?
The midsegment if a triangle is defined as a line that joins two midpoints of two opposite sides of a triangle.
The midsegment theory of a triangle states that in a triangle, the midsegments of 2 sides is parallel to, and half the length of the 3rd side.
The 3 midsegments of a triangle forms a small triangle within the larger triangle.
This therefore, forms 4 triangles.
Area of a triangle =base x height
Hence 4 triangles are formed,
The area of the larger triangle is [tex]\frac{bh}{4}[/tex] =1/4(bh)
Therefore; Area =1/4 of area.
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Given the speeds of each runner below, determine who runs the fastest.
i cant figure this out and its due soon pls help me
The person who runs fastest is Zach.
How to find the speed?Ron runs 9 feet per second: 9 ft/s
Zach runs 410 feet in 49 seconds:
410/49 ft/s
=8.36 ft/s
= 8.4 ft/s (Approximately)
Katie runs 1 mile in 412 seconds:
1 mile = 5280 ft
5280/412 ft/s
=12.8 ft/s
Noah runs 870 feet in 1 minute:
= 870/60 ft/s
= 14.5 ft/s
Hence,
Ron 9 feet per seconds
Zach 8.4 feet per seconds
Katie 12.8 feet per seconds
Noah 14.5 feet per seconds
So, Zach is the fastest.
Therefore the fastest is Zach.
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Can someone please help me
Tanks are used to deliver liquid fuel to a factory. each tank holds 22.5 cubic yards of fuel. the weight of 1 cubic yard of fuel is 0.74 tons. the fuel will be stored in containers that each holds 7.4 tons of fuel. how many containers of this size are needed to hold all the fuel from 12 tanks?
27 containers are needed to hold all the fuel from 12 tanks.
How do you prove that?We are given that each tank holds 22.5 cubic yard of fuel, the weight of 1 yd³ (cubic yard) of fuel is equal to .74 tons, and each container holds 7.4 tons of fuel. Solving this problem would involve converting units.
In order to find out how many containers of the size are needed to hold all the fuel from 12 tanks, first we need to find how much fuel is delivered by 12 tanks. Since 12 x 22.5 = 270, 12 tanks are used to deliver 270 yd³ of fuel.
Next we convert it to tons. Recall that 1 yd³ of fuel is equal to .74 tons. Therefore, 270 yd³ = 270 x .74 = 199.8 tons.
A container holds 7.4 tons of fuel. 199.8 ÷ 7.4 = 27, hence 27 containers are needed to hold all the fuel.
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if f(x) = 2x - 4 find f(3x)
Answer: the answer would be 2
Step-by-step explanation: f(x) means that for every x you are going to multiply it by the value it gives you in this case it is 3.
2x3=6-4=2
The identification of a relationship using
multiplication and the prediction of the value of one
quantity based on the value of another.
Utilizing multiplication to find relationships and predicting that value of one "Linear regression" is a quantity derived from the value of another.
Define the term Linear regression?The relationship in between magnitude of one parameter and that of a second is modeled by simple linear regression.
For instance, as X rises, Y also increases. or Y declines as X rises. 1 Regression defines the nature of the link, whereas correlation evaluates the strength of such a linking between two variables.Simple linear regression calculates the precise amount by which Y will alter when X alters by a specific amount. The variables X and Y remain interchangeable with the correlation coefficient. Regression uses a linear relationship, or a line, to try and predict any Y variable from the X variable:Y = b 0 + b 1 X.Thus, finding correlations via multiplication and assuming that the value of one "Linear regression" is a number obtained as from value of another
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To compleate a task in 16 days a company needs 5 workers each working 6 hours per day
The company decides to have 8 people each working 4 hours per day
Assuming that each person works at the same rate
How many days will the task take to complete?
Answer:
10 days
Step-by-step explanation:
This is a type of proportion either direct or indirect .16 days for 5 workers.so for 8 workers the days will reduce .Now for 8 workers it will be 10daysA sample survey of 54 discount brokers showed that the mean price charged for a trade of 100shares at 50 per share was $33. 77 (AAII Journal, February 2006). The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.
a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share
a) The margin of error associated with a 95% confidence interval is 4.
b) The 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
a) We are given with the information that the mean for 54 discount brokers is $50 for 100 shares is $33.77 Also the population standard deviation is $15.
The formula for margin of error is Z = zα/2 σ √ n
Now we know from our z-table that value of zα/2 for 95% confidence interval is 1.96
So, the value of error margin is zα/2 σ √ n =1.96 (15/√54) = 1.96 x 2.04
= 4
b) We know from part a that margin of error is 4.
Also, the mean price charged for a trade of 100shares at 50 per share was $33. 77
The value of confidence interval for population mean is,
x ± zα/2 σ √ n = 33.77 ± 4 = (29.77,37.77)
Thus, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
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The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (Choose from: shift up, shift down, shift right, shift left). Part B: Solve for k in each type of transformation. (This means tell me how many units you are shifting for each transformation you picked in part A). Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (This would be f(x) + k, f(x) - k, f(x -k), or f(x+k) but replace k with the values from part B).
A. The translations used in the transformation of f(x) to g(x) can be given as follows:
Left 6 units.Up 18 units.B. The solutions for k are given as follows:
Left 6 units: k = 6.Up 18 units: k = 18.C. The rules are given as follows:
Left 6 units: g(x) = f(x + 6).Up 18 units: g(x) = f(x) + 18.What are the translations to an image?There are four cases for the translation of an image, and they can be represented as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.From the graph of the linear functions shown at the end of the answer, two translations are possible, listed as follows:
Left 6 units: As the x-intercept of g(x) is of -6 and the x-intercept of f(x) is of x = 0.Up 18 units, as the y-intercept of g(x) is of 17 and of f(x) is of -1, 17 - (-1) = 18.The values of k are equivalent to the values of a in the bullet points listing the translations above, and the equations were also built from those bullet points.
Missing InformationThe lines are shown by the image at the end of the answer.
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. Which is the better investment?
a. $1,200 at 9% simple interest for 2 years
b. $1,200 at 8% compound interest for 2 years
Answer:
200 at 9% simple interest for 2 years
Answer:
a
Step-by-step explanation:
Hope it helps and have a nice day!!!! :)
Find the missing side lengths. Leave your answers as radicals in simplest form
Answer:
Step-by-step explanation:
Hi Mia, are you aware that the last name Hamilton is a famous math person? :) anyway,
The triangle in the picture is an isosceles triangle, we know that b/c the angle of the one is 45° meaning the other side must also be a 45° angle. So we know the two sides are the same length.
side n = 7 [tex]\sqrt{2}[/tex] / 2
then use Pythagoras to find m
[tex]c^{2}[/tex] = ( 7 [tex]\sqrt{2}[/tex] / 2)^2 + ( 7 [tex]\sqrt{2}[/tex] / 2)^2
[tex]c^{2}[/tex] = 49*2/4 + 49*2/4
[tex]c^{2}[/tex] = 49/2 + 49/2
[tex]c^{2}[/tex] = 98/2
[tex]c^{2}[/tex] = 49
c = 7
side m = 7 :) nice, huh ?
a) Sin X = O/H
Sin 45 = [tex]7\sqrt{2}[/tex]/2/H
H= [tex]7\sqrt{2}[/tex]/2/ Sin 45
m= 7
b) cos X = A/H
cos 45= A/7
A= cos45*7
n= 4.95
If the area of the rectangle is 42 square units, what is the area of the shaded part?
Answer: 16
Step-by-step explanation:
The first triangle has an area of [tex]\frac{1}{2}(7)(2)=7[/tex].
The second triangle has an area of [tex]\frac{1}{2}(6)(3)=9[/tex].
Adding these areas together yields an area of 16.
Arrange the pairs of points in increasing order of the slopes of the lines joining them.
(15, 30) and (20, 40)
(12, 32) and (18, 48)
(27, 12) and (72, 32)
(45, 15) and (60, 20)
(27, 2) and (243, 18)
(18, 63) and (24, 84)
(63, 9) and (84, 12)
↓
↓
↓
↓
↓
↓
The arrangement of the points in increasing order of the slopes are (27, 2) and (243, 18), (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40), (12, 32) and (18, 48), (18, 63) and (24, 84)
How to Arrange the points in increasing order of the slopes of the lines joining them?
Slope is defined as the change in y divided by the change in x. Mathematically:
Slope = (y2 - y1) / (x2 -x1)
To arrange the pair of points. You need to find the slope:
For (15, 30) and (20, 40):
x1 = 15, y1 =30 and x2 =20, y2=40
slope = (40-30)/(20-15) = 10/5 =2
For (12, 32) and (18, 48):
slope = (48-32)/(18-12) = 16/6 = 2.67
For (27, 12) and (72, 32):
slope = (32-12)/(72-27) = 20/45 = 0.44
For (45, 15) and (60, 20):
slope = (20-15)/(60-45) = 5/15 = 1/3 = 0.33
For (27, 2) and (243, 18):
slope = (18-2)/(243-27) = 16/216 = 0.07
For (18, 63) and (24, 84):
slope = (84-63)/(24-18) = 21/6 = 7/2 = 3.5
For (63, 9) and (84, 12):
slope = (12-9)/(84-63) = 3/21 = 1/7 = 0.14
Therefore, the pairs of points in increasing order of the slopes are (27, 2) and (243, 18), (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40), (12, 32) and (18, 48), (18, 63) and (24, 84)
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If the line of best fit is y = 1.416x − 0.76, what is the residual value for the coordinate (10, 14)? −0.16 0.16 0.6 −0.6
The residual value is 0.6.
What is Residual?The estimated value of a fixed asset at the conclusion of its useful life or lease term is known as the residual value, also known as salvage value. In lease agreements, one of the lessor's main methods for figuring out how much the lessee must pay in periodic lease payments is the residual value.
Given:
y = 1.416x − 0.76
For (7, 8):
As, residual value = Measured value - Predicted value
or, residual value = (actual y-coordinate of the point) - (value of y from the
equation)
When x = 10:
So, the value of y from the equation,
[tex]y_1[/tex] = 1.416 x 10 - 0.76
[tex]y_1[/tex]= 14.16 - 0.76
[tex]y_1[/tex]= 13.4
and, actual y-coordinate of the point, [tex]y_2[/tex]= 14
Residual value = 14 - 13.4
Residual value = 14 - 13.4
Residual value = 0.6
Hence, the residual value is 0.6
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Answer:
0.6
Step-by-step explanation:
im taking the test rn
the profit y (in dollars) for a business from selling x games is represented by y=33x graph the equation
THIS IS URGENT!!! SOMEONE PLEASE RESPOND!!!!
ty!
Answer: check the image attached
Step-by-step explanation:
Hope this helps
Answer:
Just point the graph on Y=33x+0
Step-by-step explanation:
There's no B or starting point, so you would just plant the point on 0,33
Determine the smallest integer value of x in the solution of the following inequality.
-4x - 1 ≤ 13
Answer:
-3.5
Step-by-step explanation:
-4x-1+1≤ 13+1
-4x/-4 ≤ 14/-4
x≤ -3.5
