By solving a quadratic equation we will see that the number can be:
8 or -5.
How to find the number?The product of a number N, and 3 less than the number, is equal to 40.
This is written as:
[tex]N*(N - 3) = 40[/tex]
Now we need to solve this for N.
[tex]N^2 - 3N = 40[/tex]
[tex]N^2 - 3N - 40 = 0[/tex]
Then we need to solve this quadratic equation:
[tex]N = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*1*(-40)} }{2} \\\\N = \frac{3 \pm 13 }{2}[/tex]
Then we have two solutions:
N = (3 - 13)/2 = -5N = (3 + 13)/2 = 8These are the two possible solutions.
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What are the quartiles of the data
The quartiles of the data are: 60.5,64,66
Option(b) is correct.
The quartile divides the distribution into four groups and calculates the range of values above and below the mean.
A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.
Similar to how the median divides the data in half, with 50% of the measurements falling below it and 50% falling above it, the quartile divides the data into fourths, with 25% of the measurements falling below the lower quartile, 50% falling below the median, and 75% falling below the upper quartile.
The interquartile range, a measurement of variation around the median, is calculated using quartiles.
For the given data set: 58,60,60,61,62,64,64,64,66,70,72
Median = 64
Lower quartile = Median of the lower half = 60.5
Upper quartile = Median of the upper half = 66
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An online store sells two types of speaker docks for smartphones. The higher-priced speaker dock sells for $170 and the lower-priced speaker dock sells for $80. Last week the store sold four times as many lower-priced speaker docks as higher-priced speaker docks. Combined sales totaled $4,410. How many lower-priced speaker docks did it sell?
The lower-priced speaker docks and higher-priced speaker docks is 9 and 36 respectively.
AlgebraCost of higher-priced speaker = $170Cost of lower-priced speaker = $80Number of lower-priced speaker = 4xNumber of higher-priced speaker = xHigher-priced speaker = 170 × x
= 170x
Lower-priced speaker = 80 × 4x
= 320x
Total sales = $4,410
170x + 320x = 4,410
490x = 4,410
divide both sides by 490
x = 4,410 / 490
x = 9
So,
Number of lower-priced speaker = 4x
= 4 × 9
= 36
Number of higher-priced speaker = x
= 9
Therefore, the lower-priced speaker docks and higher-priced speaker docks is 9 and 36 respectively.
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4. Find the number of paths between c and d in the graph of length
The number paths between c and d of length 2.
What are the number paths?A counting model is a number path. Rectangles symbolize numbers, and it is possible to count each rectangle. Like a ruler, a number line is a model of length. The length starting at zero is used to represent each integer.A number path offers a more reassuring representation of numbers, which is crucial since we want representations that constantly assist pupils in gaining confidence and correctly resolving issues.Start adding the first number in the number sentence and work your way to the right after that. Starting with the largest number in the number sentence, go to the left on the number line to subtract. Skip counting by the number you are multiplying by when you multiply.Find the number of paths between c and d in the graph of length:
The number of paths between c and d is 0.
There is the number of paths between c and d of length 2.
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SUPER URGENT PLEASE ANSWER ASAP
Answer:
shown below
Step-by-step explanation:
Look at the white squares, count them. 1, 2, 3. the next will be 4 and 5. draw 4 white squares, then house it in black squares like the others. to know if u did it right, count the black squares, there should be 8, then 9.
Karin has 13 coins (2 quarters, 6 dimes, 4 nickels, and 1 penny) in a piggy bank. She turns the bank
upside down and shakes the bank until a coin falls out, puts it aside, and the shakes until another coin
falls out.
What is the probability that the first coin is a nickel and the second coin is a quarter?
Select one:
a. 2/30
b. 6/13
c. 2/13
d. 1/8
Using it's concept, the probability that the first coin is a nickel and the second coin is a quarter is:
2/39.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
For the first coin, 4 out of 13 will be nickels.For the second coin, considering a nickel was taken with the first coin, 2 out of 12 will be quarters.Hence the probability will be given as follows:
p = 4/13 x 2/12 = 4/13 x 1/6 = 2/13 x 1/3 = 2/39.
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A particle is moving with the given data. Find the position of the particle. a(t) = t2 − 7t + 6, s(0) = 0, s(1) = 20
The function position of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.
What are the parametric equations for the motion of a particle?
By mechanical physics we know that the function velocity is the integral of function acceleration and the function position is the integral of function velocity. Hence, we need to integrate twice to obtain the function position of the particle:
Velocity
v(t) = ∫ t² dt - 7 ∫ t dt + 6 ∫ dt
v(t) = (1 / 3) · t³ - (7 / 2) · t² + 6 · t + C₁
Position
s(t) = (1 / 3) ∫ t³ dt - (7 / 2) ∫ t² dt + 6 ∫ t dt + C₁ ∫ dt
s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + C₁ · t + C₂
Now we find the values of the integration constants by solving the following system of linear equations:
0 = C₂
63 / 4 = C₁ + C₂
The solution of the system is C₁ = 63 / 4 and C₂ = 0. The function position of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.
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I am confused. Can somebody explain this to me?
Maryann can paint a wall in 45 minutes. It takes her brother Junior 1 hour and 45 minutes to paint the same wall. How many minutes would it take Maryann and Junior to paint the wall, if they work together? Answer as a decimal to the nearest tenth.
Answer: If they worked together, it would take 31.5 minutes
Step-by-step explanation:
There's a certain formula for equations like this:
[tex]\frac{1}{t1} +\frac{1}{t2}=\frac{1}{tb}[/tex]
t1= the time it took for the first person to complete the task.
t2= the time it took for the second person to complete the task.
tb= the time it took for both of them to complete the task.
We have the values for both t1 and t2, but not for tb.
t1= 45
t2= 105
tb= x
[tex]\frac{1}{45} +\frac{1}{105} = \frac{1}{x}[/tex]
Now it's simple algebra, and all we need to do is solve for x
The LCM for both fractions is 315, so now we multiply BOTH sides of the equation by 315.
[tex]\frac{315}{45} + \frac{315}{105} = \frac{315}{x}[/tex]
This will simplify nicely, so now we just need to get x on the other side.[tex]7 + 3 = \frac{315}{x} \\\\\ 10*x = \frac{315}{x} * x[/tex]
[tex]10x = 315 \\\\x = 31.5[/tex]
need heeeelp please
Answer: [tex]\Large\boxed{x=-\frac{4}{5} }[/tex]
Step-by-step explanation:
Given equation
[tex]-9+log_{4}(-5x)=-8[/tex]
Add 9 on both sides
[tex]-9+log_{4}(-5x)+9=-8+9[/tex]
[tex]log_{4}(-5x)=1[/tex]
Simplify the logarithm
[tex]-5x=4^1[/tex]
[tex]-5x=4[/tex]
Divide -5 on both sides
[tex]-5x\div-5=4\div-5[/tex]
[tex]\Large\boxed{x=-\frac{4}{5} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Consider a triangle ABC
like the one below. Suppose that a=75, b=63, and c=69.
The figure is not drawn to scale.) Solve the triangle.
round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
The given triangle has three angles with measurements: ∠A = 69°, ∠B = 52°, and ∠C = 59° respectively. Using the law of cosines, these angles are calculated from the given lengths of the triangle.
What is the law of cosines?The law of cosines gives the relationship between the lengths of sides and the angles of the triangle ABC.
According to the law of cosines:
Cos A = (b² + c² - a²)/2bc
Cos B = (a² + c² - b²)/2ac
Cos C = (a² + b² - c²)/2ab
Calculation:For the given triangle ABC,
a = 75, b = 63, and c = 69
So, using the law of cosines,
Cos A = (b² + c² - a²)/2bc
⇒ Cos A = (63² + 69² - 75²)/2×63×69
⇒ Cos A = 5/14
⇒ A = Cos⁻¹(5/14) = 69.07
∴ ∠A = 69°
Similarly,
Cos B = (a² + c² - b²)/2ac
⇒ Cos B = (75² + 69² - 63²)/2×75×69
⇒ Cos B = 31/50
⇒ B = Cos⁻¹(31/50) = 51.6 ≅ 52
∴ ∠B = 52°
Cos C = (a² + b² - c²)/2ab
⇒ Cos C = (75² + 63² - 69²)/2×75×63
⇒ Cos C = 179/350
⇒ C = Cos⁻¹(179/350) = 59.2
∴ C = 59°
Thus, the angles of the triangle ABC are 69°, 52°, and 59° respectively.
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2w+w^3-1/2w^2 for w=2
The required value is 8
How can we find value?
We will find the value by putting the value of w in the given function to get the required value.
We can find the value of given function foe w=2 as shown below:
Given, function is 2w+w^3-1/2w^2
Let A=2w+w^3-1/2w^2
for w=2
A=2(2)+(2)^3-1/2(2)^2
= 2+8-1/2(4)
=2+8-2
=8
Hence, the required value is 8.
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A sundae requires 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries. Ramses wants to make sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries. Let S denote the number of sundaes he makes and M the number of milkshakes he makes. Write an inequality that represents the condition based on the number of ice-cream scoops. Write an inequality that represents the condition based on the number of strawberries.
The system of inequalities be
3x+2y ≤ 25, 4x+6y ≤ 37
1) Maximum number of sundaes possible exists 9.
2) Maximum number of milkshakes possible exists 6.
3) Combination that uses the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.
What is system of inequalities?A system of inequalities exists the system where the set of more than one inequalities in more than or equivalent to one variable.
Given: A sundae needs 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries.
Ramses have to create sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries.
Let x represent the number of sundaes he creates and y the number of milkshakes he creates.
We represent in tabular form,
Sundae(x) Milkshake(y) Total
Ice-cream 3 2 3x+2y
Strawberries 4 6 4x+6y
System of inequalities:
Sundaes and milkshakes with at most 25 ice-cream scoops exist
33x+2y ≤ 25.
Sundaes and milkshakes with at most 37 strawberries exist 4x+6y ≤ 37.
1) Maximum number of sundaes possible:
Maximum number of sundaes possible when y = 0
From the graph y = 0 at x = 9.25
Therefore, the maximum number of sundaes possible exists at 9.
2) Maximum number of milkshakes possible:
Maximum number of milkshakes possible when x = 0
From the graph x = 0 at y = 6.167
Therefore, the maximum number of milkshakes possible exists at 6.
3) Combination that utilizes the most of both Ice-cream and Strawberries:
A combination of both is possible there exists an intersection of both the equation.
From the graph, the intersection point exists x = 7.6 and y = 1.1.
Therefore, the Combination that utilizes the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.
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3. In AABC, a = 35, c = 25, and m can be drawn given these measurements?
Only one triangle possible with angle 38.2° at C.
According to the given statement
we have to seek out that the measurement of m with the help of the a and c.
Then for this purpose, we all know that the
The ambiguous case occurs when one uses the law of sines to see missing measures of a triangle when given two sides and an angle opposite one in every of those angles (SSA).
According to the this law
The equation become
35/sin(60) = 25/sinC
sinC = 0.6185895741
C = 38.2, 141.8
Since 141.8+60 = 201.8 > 180
It will not form a triangle.
So, only 1 triangle possible with angle 38.2° at C
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Law of Sines and the Ambiguous Case.
In ∆ ABC, a =35, c = 25, and m < A = 60*
How many distinct triangles can be drawn given these measurements?
SOMEONE PLEASE HELLPPPP
Answer:
93.39
Step-by-step explanation:
So the sum of exterior angles of the convex octagon is: 360 degrees
This means if we add all the equations that represent each angle, we can set it equal to 360 and solve for x
[tex](x+14) + (2x-3) + (3x+8) + (3x+16) + (2x-17) + (3x-4) + (3x-12) + (6x)[/tex]
Group like terms
[tex](x+2x+3x+3x+2x+3x+3x+6x) + (14-3+8+16-17-4-12)[/tex]
Add like terms
[tex]23x+2[/tex]
Now let's set the sum of exterior angles to 360
[tex]23x+2 = 360[/tex]
Subtract 2 from both sides
[tex]23x=358[/tex]
Divide both sides by 23
[tex]x\approx 15.565[/tex]
So by looking at all these, it appears that 6x is the highest value, given that x is positive. The way I estimated, is approximately 15.5, whenever I saw an equation like x+14, I estimated it's about 2x, since 14 is not exactly, but close to 15.5. I did this with each polynomial given. You could also manually check each one
Original equation
6x
Subsitute
6(15.565)
Simplify
[tex]93.39[/tex]
-20, 10, -5,
I need the next sequence
Answer:
The next term in the sequence is 5/2 or 2.5.
========================
Given series:
-20, 10, - 5, ...We notice that this is a geometric progression.
The common ratio is:
r = -5/10 = 10/ -20 r = - 1/2To find the next term multiply the last term by the common ratio:
[tex]t_n=rt_{n-1}[/tex]The 4th term is:
[tex]t_4=(-1/2)*(-5)=5/2=2.5[/tex]BECKY KUBIAK WISHES TO PURCHASE NEW APPLICANCES FOR HER HOME. THE
TOTAL COST FOR THE APPLICANCES IS $2900. TO FINANCE THE PURCHASE, BECKY
MUST PAY 20% DOWN, WITH THE BALANCE BEING FINANCED WITH A 24-MONTH
INSTALLMENT LOAN WITH AN APR OF 8.5%. DETERMINE BECKY’S TOTAL FINANCE
CHARGE AND HER MONTHLY PAYMENT.?
Using the monthly payment formula, it is found that:
Her monthly payments are of $105.46.The total finance charge is of $3,111.04.What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.Considering that she must pay 20% down, the parameters are given by:
P = 0.8 x 2900 = 2320, r/12 = 0.085/12 = 0.007083, n = 24.
Hence the monthly payments are found as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 2320\frac{0.007083(1.007083)^{24}}{(1.007083)^{24} - 1}[/tex]
A = $105.46.
The total finance charge is composed by the down payment plus the 24 monthly payments, hence:
F = 0.2 x 2900 + 24 x 105.46 = $3,111.04.
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Paolo helped in the community garden for 2 3/4 hours this week. This was 1 5/6 equal length shift, because Paolo stopped early one day when it started to rain. How long is a single shift?
If 2+3/4 hours is equal to 1+5/5 equal length shift then the single shift is 1.5 hours long.
Given that Paolo helped in the community garden for 2 +3/4 hours this week which is 1+5/6 times length shift.
We are required to find the length of a single shift.
First we have to find the proper fraction of the given mixed fractions.
Fraction is combination of numerator and denominator.The number that is present above the division sign is known as numerator and the number that is present below the division sign is known as denominator.
2+3/4=(8+3)/4=11/4
1+5/6=(6+5)/6=11/6
let the length of a shift is x hours.So,
11/4=11*x/6
11/4=11/6 x
66/44=x
x=3/2
x=1.5 hours.
Hence if 2+3/4 hours is equal to 1+5/5 equal length shift then the single shift is 1.5 hours long.
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Find center,foci and vertices of ellipse for 4x2+y2+2x-10y=6
Answer:
center:
(-0.25, 5)
foci :
(-0.25, 0.158771) | (-0.25, 9.84123)
vertices :
(-0.25, -0.59017) | (-0.25, 10.5902)
wolframramalpha
Determine the inverse of the function: h(x)= 2x-3/1-x
Find the midpoint of the segment with the following endpoints.
(10, 3) and (2, 9)
a tree 20 feet tall with a circumference of 3 ft has a vine wound around 7 times. How long is the vine?
The length of the vine is 21 ft
what is the circumference of a circle?
the circumference is the perimeter of a circle
the perimeter of the circle = 2πr = 3 ft
the vine is 7 times the perimeter
length of vine = 7×3= 21 ft
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If the tree is 20 feet tall with circumference 3 feet then the length of vince is around 21 feet.
Given the height of tree is 20 feet and the circumference of tree is 3 feet.
We have to find the length of vine.
Circumference is the perimeter of a circular object. Because the trunk of a tree is in shape of circle so the perimeter of the trunk is 2πr.
We have been given the circumference of tree be 3 feet.
Circumference=2πr
Because vine is 7 times the circumference so the length of vine being:
Length of vine=7*3
=21 feet.
Hence if the tree is 20 feet tall with circumference 3 feet then the vince is around 21 feet long.
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Geometry: Explaining Volume Formulas
Step-by-step explanation:
volume = area of circle × hight of cylinder ....
V = πr² × h
so V = πr²h
Answer:
10831 mm³
Step-by-step explanation:
The volume of any solid figure with a uniform cross section parallel to the base can be found using the volume formula ...
V = Bh
where B is the area of the base, and h is the height perpendicular to the base.
Base areaThe base of this cylindrical stack of pennies is a circle of diameter 19.05 mm. The area formula for a circle in terms of diameter is ...
A = (π/4)d²
The stack of pennies has a base area of ...
A = (π/4)(19.05 mm)² ≈ 285.023 mm²
VolumeThe volume formula tells us the stack of pennies has a volume of ...
V = Bh
V = (285.023 mm²)(38 mm) ≈ 10830.9 mm³
The volume of the stack of pennies is approximately 10831 mm³.
Which expression can be used to find the sum of the polynomials?
(9 - 3x2) + (-8x2 + 4x + 5)
The expression which can be used to determine the algebraic sum of the given polynomials as in the task content is; -11x² +4x +14.
Which expression can be used to find the sum of the given polynomials?It follows from the task content that the polynomials whose sum are to be determined are; (9 - 3x2) + (-8x2 + 4x + 5).
Hence, the sum can be evaluated as follows;
= 9 - 3x² + -8x² + 4x + 5
= -11x² +4x +14.
Consequently, the required expression is; -11x² +4x +14.
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Answer:
Step-by-step explanation:
is 100 for the points
Which expression is equivalent to sec²x - 1?
O A. cot²x
OB. tan²x
OC. CsC²x
OD. cos²x
[tex]l = sec {}^{2} x - 1 \\ l = \frac{1}{cos {}^{2} x} - \frac{cos {}^{2} x}{cos {}^{2} x} \\ l = \frac{1 - cos {}^{2} x}{cos {}^{2}x } \\ l = \frac{sin {}^{2} x}{cos {}^{2} x} = ( \frac{sinx}{cosx} ) {}^{2} = tan {}^{2} x[/tex]
BWhat are two ordered pairs that the midpoint is (4, -10)? Please show that your points work.
The two ordered pairs that the mid point is (4,-10) are (4,-20),(4,0) & (4,0),(4,-20).
Given the coordinates of mid point be (4,-10).
We are required to find the ordered pairs that the mid point is (4,-20).
Coordinates show positions of points or something else on a surface.
There are various combinations whose mid point is (4,-10).
First are (4,-20),(4,0).
Mid point =[(4+4)/2,(-20+0)/2]
=(4,-10)
Second are (4,0) , (4,-20)
Mid point=[(4+4)/2,(0-20)/2]
=(4,-10)
Third are (8,-20),(0,0)
Mid point=[(8+0)/2,(-20+0)/2]
=(4,-10)
Fourth are (0,-20),(8,0)
Mid point =[(0+8)/2,(-10+0)/2]
=(4,-10)
Hence the ordered pairs that the mid point is (4,-10) are (4,-20),(4,0) & (4,0),(4,-20)& (8,-20),(0,0)&(0,-20),(8,0)&(0,0),(8,-20).etc.
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Once a delay or disability is diagnosed, the best thing to do is to continue to be a family’s knowledgeable and reliable partner in child care.Once a delay or disability is diagnosed, the best thing to do is to continue to be a family’s knowledgeable and reliable partner in child care.
Once you detect that there is a delay or disability, then you should continue to be the reliable partner in child care to the family so this is True.
What should be done when a delay in child development is seen?The observation and screening process can lead to a child care partner discovering a delay or disability.
When this happens, you should report to your supervisor to check if the child is eligible for federal and state programs related to their condition. Whatever the case, you should remain accessible to the family as their partner in child care.
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Pls help answer this before 8pm
Answer:
Step-by-step explanation:
16 + 12 + 5 + 3 = 36
16 prefer email, 36 total students surveyed
16:36 / 4 = 4:9
4 out of 9 students prefer email
4:9 x 680 = 302.222
302 students can be expected to prefer email.
About 5% of the population has a particular genetic mutation. 300 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 300. Round your answer to two decimal places.
The standard deviation for the number of people with the genetic mutation is 3.77
How to determine the standard deviation?The given parameters are:
Sample size, n = 300
Proportion that has the particular genetic mutation, p = 5%
The standard deviation for the number of people with the genetic mutation is calculated as:
Standard deviation = √np(1 - p)
Substitute the known values in the above equation
Standard deviation = √300 * 5% * (1 - 5%)
Evaluate the product
Standard deviation = √14.25
Evaluate the exponent
Standard deviation = 3.77
Hence, the standard deviation for the number of people with the genetic mutation is 3.77
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A rectangle is 6x-4 feet long and 2x + 3 feet wide. What is the perimeter of the rectangle?
Answer:
Perimeter o the rectangle = 16x - 2
Step-by-step explanation:
Perimeter of a rectangle = 2(long+ wide)
Then:
Perimeter = 2((6x-4)+(2x+3))
Perimeter = 2(6x+ 2x + 3 - 4)
Perimeter = 2(8x - 1)
Perimeter = 2*8x + 2*-1
Perimeter = 16x - 2
Show all work to write the expression in simplified rational exponent form:
[tex](\sqrt[4]{x^{2}+4 } )^{3}[/tex]
(Fourth root of x squared plus four, cubed)
Answer:
[tex]x^{\frac{1}{2} } + 48[/tex]
Step-by-step explanation:
This is hard to explain, but basically you use exponent rules to switch it to an exponent
[tex](\sqrt[4]{x^{2} +4} )^{3}[/tex]
It's easiest if you calculate [tex]4^{3}[/tex] first
4³ = 4 x 4 x 4 = 48
Then convert the root to a fraction exponent
[tex]\sqrt[4]{x^{2}} = x^{\frac{2}{4}} = x^{\frac{1}{2} }[/tex]
Combine them using addition, since addition was in the problem
[tex]x^{\frac{1}{2} } + 48[/tex]
I hope this helps!
In a secondary school class, 23 students study Economics, 6 students study both government and economics. 48 students study either government or Economics or both. what is the total number of students who study government? How many study only economics? How many study only government?
If there are 23 students study Economics,6 students study both government and economics and 48 students study either government or economics or both then there are 31 students study government, 17 students study economics only and 25 students are there who study government only.
Given that in a secondary school class, 23 students study Economics, 6 students study both government and economics. 48 students study either government or Economics or both.
We are required to find :
what is the total number of students who study government? How many study only economics? How many study only government?Suppose E represents economics students and G students government students. In this way:
E=23
G∩E=6 (And represents intersection between sets)
G∪E=48 (Or represents union of sets)
G∪E=G+E-G∩E
48=G+23-6
G=48-17
G=31
Economics only=E-G∩E
=23-6
=17
Governments only=G-G∩E
=31-6
=25
Hence if there are 23 students study Economics,6 students study both government and economics and 48 students study either government or economics or both then there are 31 students study government, 17 students study economics only and 25 students are there who study government only.
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