Complex fraction 4²/₃ + 1/3 – 4¹/₃ = 2/3
A fraction defined as the part of the whole thing. For example, a pizza is divided into four equal pieces, then each piece is represented by ¼. Fractions help to distribute and judge the numbers easily and make the calculation faster.
Some steps to solve a fraction -
Step 1: Write the factors of numerator and denominator.
Step 2: Determine the highest common factor of numerator and denominator.
Step 3: Divide the numerator and denominator by their highest common factor (HCF). The fraction so obtained is in the simplest form.
For example -
4²/₃ + 1/3 – 4¹/₃
= (4 × 3 + 2)/3 + 1/3 – (4× 3 + 1)/3
= 14/3 + 1/3 – 13/3
= (14 + 1 - 13)/3
= (15 - 13)/3
= 2/3
Hence , in the mathematics problem can be solved by using the fractions.
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the table shows the estimated sales for two different prices of bags of chips. Calculate the profit per bag for the bags sold at 3$ each
The profit per bag for the bags sold at 3$ each is $1.5 per bag.
How to calculate the profit?The total cost will be:
= $300000 + (1 × $600000)
= $900,000
The revenue will be:
= $3 × 600000
= $1,800,000
Therefore, the profit per bag will be:
= ($1800000 - $900000) / 600000
= $900000/600000
= $1.5
The profit is $1.5.
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Is it possible to calculate the square root of a negative number?
Answer: It is impossible to find the square root of negative one, or the square root of any negative number because no number times itself can equal a negative number.
Step-by-step explanation:
Answer:
It is impossible to find the square root of negative one, or the square root of any negative number, because no number times itself can equal a negative number.
Step-by-step explanation:
The square root of a negative number does not exist among the set of Real Numbers.
When problems with negatives under a square root first appeared, mathematicians thought that a solution did not exist. They saw equations such as x2 + 1 = 0, and wondered what the solution n3 really meant.
Round 3.691 to the nearest hundredth
Answer: 3.69
Step-by-step explanation:
Answer:
3.69
Step-by-step explanation:
If the last digit in the fractional part of 3.691 is less than 5, then simply remove the last the digit of the fractional part.
write 25x + 2 as a verbal expression
The required verbal form of the expression is two more than 25 times of a number.
Given that,
An expression is given we have to determine the verbal expression of the given algebraic expression.
The algebraic expression consists of constant and variable. eg x, y, z etc.
Here,m
Given expression = 25x + 2
Where x is any variable number 25 times and further added 2.
So.
The verbal expression can be given as
two more than 25 times of a number.
Thus, the required verbal form of the expression is two more than 25 times of a number.
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Select the correct answer.
Why is the responsibility for maintaining roads and streets given to municipal governments?
O A.
The federal government would not have time to get to all the roads.
O B.
The local government has better knowledge about the needs in its area.
O C. The state government does not want to pay maintenance crews.
O D.
The county government does not have the power to pave roads.
Hurryyyyyyyy pls
Answer:
OA
Step-by-step explanation:
the federal government only manages the things about the country , that's why there are different types of government becuz each one of them has responsibilities
Ten times the sum of a number and nine is 290. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
Step-by-step explanation:
10+290=x is the answer
x=290-10
x=280#
"divide 9 by p, then multiply 2 by the result" i need the expression for this, thank you
Answer: The expression would look like this p/9 (2)
Step-by-step explanation: You should make it a fraction by putting the p on top and 9 on bottom and in parentheses you put in the 2!
Hope this helped! :D
on average max makes 45 out of 60 shots with the basketball, write an equation to represent the average number of shots made out of x attempts
Answer:
See below
Step-by-step explanation:
Avg shots made = (45/60) x = (3/4 ) x = .75 x
You're to prepare 850 mL of D8W form D10W and sterile water for injection. How many milliliters of D10W will you need?
The volume of D10W solution required to be diluted to make 850 mL of D8W solution is 680 mL.
How can the dilution contents be calculated?The dilution formula can be presented as follows;
[tex]C_1 \cdot V_1 = C_2 \cdot V_2[/tex]
Where;
[tex]C_1 = Initial \: concentration = D10W [/tex]
[tex]V_1 = Initial \: volume [/tex]
[tex]C_2 = Final \: concentration = D8W[/tex]
[tex]V_2= Final \: volume = 850 \: mL [/tex]
Which gives;
[tex]V_1 = C_2 \cdot V_2/C_1[/tex]
V1 = 8×850/10 = 680
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Answer the question.
The distance from the Earth to the Sun is about 1.5 x 108 km, while the distance from the Earth to the
moon is about 3.8 x 105 km. If a scale model of the solar system is constructed so that the distance
from the Earth to the Sun is 100 meters, what will be the distance from the Earth to the moon?
Select one:
O a. 39, 474 m
O b.
39.5 m
O c. 6.36 m
O d. 0.25 m
The distance from the Earth to the moon, in the scale model, is d. 0.25 m
As per the known fact, ratio of measurement in real is equal to the ratio of measurement on scale. Further, ratio will be calculated in this case as -
Distance from Earth to Sun in real : Distance from Earth to Moon in real = Distance from Earth to Sun on scale : Distance from Earth to Moon on scale
Keep the values in mentioned relation to find the distance from Earth to Moon.
1.5×10⁸:3.8×10⁵ = 100:distance from Earth to Moon on scale
Distance from Earth to Moon on scale = 100×3.8×10⁵/1.5×10⁸
Distance from Earth to Moon on scale = 0.25 m
Therefore, the correct option for distance is d. 0.25 m.
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The line graph below shows the number of times Maria drove her car each day of the week.
How many times did Maria drive her car on day 4?
The number of times Maria drove the car on day 4 is 9 times.
How many times did Maria drive her car on day 4?A line graph is a graph that connects different data points on a graph using a straight line. A line graph is made up of a x-axis and a y-axis. In the line graph given, the number of days is on the x-axis and the number of times the car was driven is on the y-axis. A line graph is used to show quantitative data. Line graphs are used to visualise data.
In order to determine the number of times Maria drove the car on day 4, locate where day 4 is on the x-axis. Then trace 4 upward toward a data point. When the data point is located, trace it to the y-axis. When day 4 is traced to the y-axis, the value gotten is 9.
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Building A is 251 meters taller than building B. If the height of building A is subtracted from twice the height of building B, the result is 223 meters. How tall is each skyscraper?
Answer:
Step-by-step explanation:
A patient's order is 70 milligrams of a drug. Available in stock is 80 milligrams in 1 milliliter of liquid. How many milliliters should be administered?
The required milliliters should be administered is 0.875 milliliter .
What is Volume?Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units or by various imperial units. The definition of length is interrelated with volume.
Given:
A patient's order is 70 milligrams of a drug.
Available in stock is 80 milligrams in 1 milliliter of liquid.
According to given question we have
80 milligrams = 1 milliliter
70 milligrams =1*70/80 milliliter
70 milligrams = 0.875 milliliter
Therefore, the required milliliters should be administered is 0.875 milliliter .
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Find the slope of the regression line.
Shots on goal 22, 25, 28, 29, 33
Points scored 5, 7, 7, 9,8
A -0.561
B 0.283
C. 0.631
D. 0.794
Why is adding two fractions different from multiplying the two fractions?
Answer:
Step-by-step: The reason we cross multiply fractions is to compare them. Cross multiplying fractions tells us if two fractions are equal or which one is greater. This is especially useful when you are working with larger fractions that you aren't sure how to reduce.
Answer:
adding two fractions is different than multiplying two fractions bc after adding the fractions, you have to simplify them and it is not easy but with multiplying, you multiply from left to right.
Step-by-step explanation:
example: 1/2+3/4
4/8+6/8=10/8=1 1/4
another example: 6/10*4/6=24/60
Graph the image of the figure after a dilation with a scale factor of 3 centered at the origin.
Use the polygon tool to graph the dilated figure.
Answer: (3, 3), (3, 9), (-6, 9), (-6, 3)
Step-by-step explanation:
With a dilation of 3 centered about the origin-
the point (1, 1) would go to (3, 3)
the point (1, 3) would go to (3, 9)
the point (-2, 3) would go to (-6, 9)
the point (-2, 1) would go to (-6, 3)
simply multiply the original coordinates all by 3.
Subtract Integers
1. FOOTBALL A team gained 5 yards on
their first play of the game. Then they
lost 6 yards. Find the total change in
yardage.
total change is -1
The total change in yard is -1
By this question we can get
The football A team gained 5 yard on their first day of the game
Then they lost 6 yards
The total change in yard is
We all know
The formula of find change is
Total-loss
So,
5-6=-1
Gain 5 yards
Lost 6 yards
Total change 5-6=-1 (ans)
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Cameron said that the y-intercept of a quadratic function always tells the maximum value of that function.
Explain Cameron's error.
The y-intercept is where the graph crosses the y-axis and is not necessarily where the maximum is. For instance, consider the graph of [tex]y=x^2 +2x+4[/tex].
the cost of 1 dorzen of pencils is rs 80 find the cost of 18 pencil
Answer:
soln
given,
1dozen=rs 80
therefore,cost of 18 dozen pencils =80 × 18
=1440 Rs
Write a slope-intercept equation for a line passing through the point (4,7) that is parallel to y=x+1. Then write a
second equation for a line passing through the given point that is perpendicular to the given line.
Answer:
y = x + 3
y = -x + 11
Step-by-step explanation:
When the slopes are parallel they are the same. When slopes are negative, the slope is the negative reciprocal.
Parallel: The slope is 1. This is the coefficient of the x in the equation given. If you do not see a number before the x like in y = x + 1, then number is 1.
Use this form:
y =mx + b Us the slope of 1 to put in for m. Use 4 for x and 7 for y
7 =(1)4 + b Solve for b.
7 = 4 + b Subtract 4 from both sides.
3 = b
The equation for the parallel line is
y = x + 3.
Perpendicular:
y = mx + b This time the slope is -1 Still use 4 for x and 7 for y
7 = (-1)4 + b
7 =-4 + b add 4 to both sides
11 = b
The equation would be y = -x + 11
20 cm
13 cm
7 cm what is the area of the shape?
Answer:
270cm2
Step-by-step explanation:
you have to split the figure into 2.
the triangle above is = 1/2 x20cmx13cm=130cm2
the rectangle is = 20cmx7cm=140cm2
total area=140cm2+130cm2
=270cm2
Kim went to the store and bought three shirts.
She spent $26.30. One shirt cost $8.72, and
another cost $10.79. How much did the third shirt
cost?
Answer:
$6.79
Step-by-step explanation:
You add the cost of the first two then subtract that by the total she spent to get the answer
$10.79 + $8.72 = $19.51
$26.30 - $19.51 = $6.79
0.36 converted into a fraction
Answer:
9/25
Step-by-step explanation:
0.36 = 36/100
36 / 4 = 9
100 / 4 = 25
9/25
Explain how you would estimate the value of 57−−√ by determining the two consecutive whole numbers that it lies between. Write the two numbers and explain the process you used to select them.
The two consecutive whole numbers that it lies between are 28 and 29.
What are the consecutive numbers?The consecutive numbers are those number which follow each other continuously in the order from smallest to largest numbers.
Let the two consecutive numbers be x and x + 1
x + x + 1 = 57
Combine like terms;
2x + 1 = 57
Now Subtract 1 from both sides;
2x = 57- 1
2x = 56
Divide both sides by 2
x = 56/2
x = 28
Thus, x + 1 = 28 + 1 = 29
The two consecutive whole numbers that it lies between are 28 and 29.
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If the average of 292, 305, 415, and x is 343, what is the value of x?
Henry will paint 5 birdhouses with 1 quart of paint. How many quarts of paint will Henry use to paint 42 birdhouses?
Answer:
8
Step-by-step explanation:
because you can't count before 42 so eight
Solve first principle of y=X^3
Answer:
3x^2
Step-by-step explanation:
Explained in image.
Simplify the equation, [tex](x^{4})^{\frac{5}{6} }[/tex], to a simplified radical. Show work
The simplified radical form of the equation [tex](x^{4})^{\frac{5}{6} }[/tex] is [tex]x^{\frac{10}{3} }[/tex]
The exponentiation is written as [tex]a^{n}[/tex], where a is the base and n is the exponent or power. We say as "a by n". Exponent means the number of times the base is used as a factor.
The expression = [tex](x^{4})^{\frac{5}{6} }[/tex]
Here we have to apply the exponent rule
We know,
The power rules for the exponent [tex](a^{m})^{n}=a^{mn}[/tex]
Here multiply the exponent times the power.
Simplify it
[tex](x^{4})^{\frac{5}{6} }=(x)^{4(\frac{5}{6}) }[/tex]
=[tex]x^{\frac{20}{6} }[/tex]
Divide both 20 and 6 by 2 to make it to simplest form, then the result
=[tex]x^{\frac{10}{3} }[/tex]
Hence, the simplified radical form of the equation [tex](x^{4})^{\frac{5}{6} }[/tex] is [tex]x^{\frac{10}{3} }[/tex]
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If tan a = x + 1 and tan ß = x - 1, then verify that: 2cot(a - B) = x²
[tex]
\cot(a-b)=\frac{\frac{1}{(x+1)(x-1)}+1}{\frac{1}{x-1}+\frac{1}{x+1}} \\ \\ =\frac{1-1+x^2}{2} \\ \\ =\frac{x^2}{2} \\ \\ \therefore 2\cot(A-B)=x^2[/tex]
Answer:
See below for proof.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\cot \theta=\dfrac{1}{\tan \theta}$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\implies 2\cot (\alpha - \beta) & =\dfrac{2}{\tan (\alpha - \beta)}\\\\ & =\dfrac{2}{\dfrac{ \tan \alpha - \tan \beta}{1+\tan \alpha \tan \beta}}\\\\ & =\dfrac{2(1+\tan \alpha \tan \beta)}{ \tan \alpha - \tan \beta}\\\\ & =\dfrac{2(1+(x+1)(x-1))}{ (x+1) - (x-1)}\\\\& = \dfrac{2(1+(x^2-x+x-1))}{x+1-x+1}\\\\& = \dfrac{2(1+(x^2-1))}{2}\\\\& = \dfrac{2x^2}{2}\\\\& = x^2\end{aligned}[/tex]
Hence verifying that 2cot(α - β) = x².
if log4^u - log8^v =1 find u in terms of v
u in terms of v will be represented with the logarithm function as v = u log (- 4 ) - ( log 8) ⁻¹
We are given that:
log 4 ^ u - log 8 ^ v = 1
This can also be written in another way using the logarithm properties. We get that:
u log 4 - v log 8 = 1
Subtract v log 8 from both the sides:
u log 4 = 1 + v log 8
v log 8 = u log 4 - 1
v = ( u log 4 - 1 ) / log 8
v = u log (- 4 ) - ( log 8) ⁻¹
Therefore, we get that, u in terms of v will be represented with the logarithm function as v = u log (- 4 ) - ( log 8) ⁻¹
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