Answer: The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.
Step-by-step explanation:
Given, Farmer has 240 apples and 150 pears.
The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out = GCF(240,150)
Prime factorization of 240 and 150 :
[tex]240=2\times2\times2\times2\times3\times5\\150=2\times3\times5\times5[/tex]
Greatest common factor of 240 and 150 = [tex]2\times3\times5=30[/tex]
Hence, the largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.
YOU WILL GET 30 POINTS AND BRAINLIEST IF YOU GET THIS CORRECT AND ANSWER THIS IN 5 MIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 3 of the recall, the manufacturer fixed 391 cars. In week 13, the manufacturer fixed 361 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week by the mechanic. f(x) = 3x + 400 f(x) = 3x + 391 f(x) = −3x + 391 f(x) = −3x + 400
Answer:
f(x)= -3x + 400
Step-by-step explanation:
[tex]\frac{x-x_{1} }{x_{2}-x_{1} } = \frac{y-y_{1} }{y_{2}-y_{1} }[/tex]
[tex]\frac{x-3}{13-3} =\frac{y-391}{361-391}[/tex]
-3 ( x-3 ) = (y - 391 )
-3x + 400
Answer:
he is correct
Step-by-step explanation:
Write the first 4 terms of the sequence defined by the given rule f(n)=n2 -1
Answer:
0, 3, 8, 15Step-by-step explanation:
Substitute n = 1, n = 2, n = 3 and n = 4 to the equation f(n) = n² - 1:
f(1) = 1² - 1 = 1 - 1 = 0
f(2) = 2² - 1 = 4 - 1 = 3
f(3) = 3² - 1 = 9 - 1 = 8
f(4) = 4² - 1 = 16 - 1 = 15
Find the x-coordinates of the two points on the curve
y=x-1/x at which the tangent is parallel to the straight line 4y= x + 8. (4 marks)
Answer: x = {-2, 2}
Step-by-step explanation:
Tangent means it is touching. Find the intersection of the two equations.
Solve the linear equation for y, then set the two equations equal to each other.
[tex]4y=x+8\qquad \rightarrow \qquad y=\dfrac{x+8}{4}[/tex]
[tex]\dfrac{x-1}{x}=\dfrac{x+8}{4}\\\\\\\text{Cross multiply and solve for x:}\\4(x-1)=x(x+8)\\4x-4=x^2+8x\\.\qquad 0=x^2+4x+4\\.\qquad 0=(x+2)^2\\.\qquad 0=x+2\\.\qquad x=-2[/tex]
To find the next point that is parallel to the linear equation and tangent to the curve, we need to use the linear equation with slope (m) = [tex]\dfrac{1}{4}[/tex] and unknown b.
Let's try b = 0, then the equation of the linear equation is: [tex]y=\dfrac{1}{4}x[/tex]
Set the equations equal to each other and solve for x:
[tex]\dfrac{x-1}{x}=\dfrac{x}{4}\\\\\\4(x-1)=x^2\\4x-4=x^2\\.\qquad 0=x^2-4x+4\\.\qquad 0=(x-2)^2\\.\qquad 0=x-2\\.\qquad x=2[/tex]
This works!!! If it didn't work, we would have tried other values for b until we arrived at a solution.
Below are some of the scores on a math quiz given last week,
{82, 73, 74, 78, 46, 73}
What will happen to the mean of the quiz scores if the outlier is removed?
A
The mean will decrease.
OB
The mean will increase
C
There is not enough information given.
OD
The mean will not change.
Answer:
B: The mean will increase
Step-by-step explanation: The outlier is 46, which is way below all the other numbers, which is the definition of an outlier. If we remove a really low number from the set, then the mean(average) will increase.
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = x2 − 7x + 5
Answer:
F(x) = [tex]\frac{x^3}{3} - \frac{7x^2}{2} + 5x + c[/tex]
Step-by-step explanation:
The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;
F(x) = [tex]\int\limits{f(x)} \, dx[/tex]
From the question, f(x) = x² - 7x + 5
Therefore,
F(x) = [tex]\int\limits {(x^2 - 7x + 5)} \, dx[/tex]
F(x) = [tex]\frac{x^3}{3} - \frac{7x^2}{2} + 5x + c[/tex]
Where c is the constant of the integration (antiderivative).
PS: The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.
Solve the system by substitution. x−5y=13 4x−3y=1 Enter your answer as an ordered pair (x,y).
Answer:
(-2,-3)
Step-by-step explanation:
Well in the system,
x−5y=13
4x−3y=1
We need to find x or y in either equation.
Let's do x - 5y = 13 for x.
+5y to both sides
x = 5y + 13
Now we substitute 5y + 13 for y in 4x - 3y = 1.
4(5y + 13) - 3y = 1
20y + 52 - 3y = 1
17y + 52 = 1
-52 to both sides
17y = -51
Divide all by 17
y = -3
Now we can substitute -3 for y in 4x - 3y = 1.
4x - 3(-3) = 1
4x + 9 = 1
-9 to both sides
4x = -8
Divide 4 to both sides
x = -2
Thus,
the solution is (-2,-3).
Hope this helps :)
Answer:
( - 2 , - 3 )Step-by-step explanation:
x - 5y = 13
4x - 3y = 1
Solve the equation for x
[tex]x - 5y = 13[/tex]
Move '5y' to R.H.S and change it's sign
[tex]x = 13 + 5y[/tex]
Substitute the given value of X into the equation
4x - 3y = 1
[tex]4(13 + 5y) - 3y = 1[/tex]
Solve the equation for y
distribute 4 through the parentheses
[tex]52 + 20y - 3y = 1[/tex]
Collect like terms
[tex]52 + 17y = 1[/tex]
Move constant to R.H.S and change it's sign
[tex]17y = 1 - 52[/tex]
Calculate
[tex]17y = - 51[/tex]
Divide both sides of the equation by 17
[tex] \frac{17y}{17} = \frac{ - 51}{17} [/tex]
Calculate
[tex]y = - 3[/tex]
Now, substitute the given value of y into the equation
x = 13 + 5y
[tex]x = 13 + 5 \times ( - 3)[/tex]
Solve the equation for x
Multiply the numbers
[tex] = 13 - 15[/tex]
Calculate the difference
[tex] = - 2[/tex]
The possible solution of the system is the ordered pair
( x , y )
( x , y ) = ( - 2 , - 3 )
-----------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
[tex] - 2 - 5 \times ( - 3) = 15[/tex]
[tex]4 \times ( - 2) - 3 \times ( - 3) = 1[/tex]
Simplify the equalities
[tex]13 = 13[/tex]
[tex]1 = 1[/tex]
Since all of the equalities are true, the ordered pair is the solution of the system
( x , y ) = ( - 2 , - 3 )Hope this helps..
Best regards!!
What is the y-intercept of the line described by the equation below? Y=3x - 6
We are given the equation y = 3x - 6
The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.
The b value in this equation is -6, thus the y-intercept is -6.
Let me know if you need any clarifications, thanks!
-2x(x+3)-(x+1)(x-2)=
Answer:
-3x^2 -5x +2
Step-by-step explanation:
-2x(x+3)-(x+1)(x-2)=
Distribute
-2x^2 -6x -(x+1)(x-2)
Foil
-2x^2 -6x -(x^2 -2x +x -2)
Combine like terms
-2x^2 -6x -(x^2 -x -2)
Distribute the minus sign
-2x^2 -6x -x^2 +x +2
Combine like terms
-2x^2 -x^2 -6x +x +2
-3x^2 -5x +2
Answer:
[tex]\huge\boxed{-2x(x+3)-(x+1)(x-2)=-3x^2-5x+2}[/tex]
Step-by-step explanation:
[tex]-2x(x+3)-(x+1)(x-2)[/tex]
Use the distributive property: a(b + c) = ab + ac
and FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex]=(-2x)(x)+(-2x)(3)-\bigg[(x)(x)+(x)(-2)+(1)(x)+(1)(-2)\bigg]\\\\=-2x^2-6x-\bigg(x^2-2x+x-2\bigg)=-2x^2-6x-x^2-(-2x)-x-(-2)\\\\=-2x^2-6x-x^2+2x-x+2[/tex]
Combine like terms:
[tex]=(-2x^2-x^2)+(-6x+2x-x)+2=-3x^2+(-5x)+2\\\\=-3x^2-5x+2[/tex]
PLZ HELP ITS 20 POINTS Using the linear combination method, what is the solution to the system of linear equations 5 x + 3 y = negative 10 and Negative 20 x minus 7 y = 15? (–5, 1) (–1, 5) (1, –5) (5, –1)
Answer:
The answer is (1,-5). (i.e x=1 and y=-5).
Hope it helps..
Answer:
(1,-5)
Step-by-step explanation:
Question 5 of 13, Step 1 of 1
3/15
Correct
2
The Chandlers are moving across the country. Mr. Chandler leaves 2.5 hours before Mrs. Chandler. If he averages 75 mph and she averages 85 mph, how many hours
will it take Mrs. Chandler to catch up to Mr. Chandler?
Answer:
It will take Mrs Chandler 18 hours 45 minutes or 18.75 hours to catch up Mr Chandler
Step-by-step explanation:
What we want to know here is that at how many hours will they have traveled same distance.
Let the total time taken by Mrs Chandler to catch up be x hours
Since Mr Chandler left 2.5 hours earlier , then the total time taken by him would be x + 2.5 hours
Now, we know that distance = speed * time
Since it’s same distance covered;
For Mr Chandler, his distance is calculated as 75(x + 2.5)
For Mrs Chandler, her distance is calculated as 85x
We equate both since they are equal;
75(x + 2.5) = 85x
75x + 187.5 = 85x
85x -75x = 187.5
10x = 187.5
x = 18.75 hours or 18 hours 45 minutes
WILL GIVE BRAINLIEST IF CORRECT
A 10 ft ladder is propped up against a building at an angle of 39°. How far up the wall does the ladder go?
Answer:
6.3 ft
Step-by-step explanation:
The ladder lying on the wall with an elevation of 39° forms a right angled triangle.
Hypotenuse = length of ladder = 10 ft
Opposite = x = ?
θ = 39°
Use trigonometric ratio formula to find, x, which is how far the ladder goes up the wall.
The trigonometric ratio formula to use is:
sin(θ) = opposite/hypotenuse
Sin(39) = x/10
Multiply both sides by 10
10*sin(39) = x
x = 10*sin(39)
x = 6.29 ≈ 6.3 ft (to nearest tenth)
Answer:
6.3 ft
Step-by-step explanation:
did the quiz got it right
81^x^2=27^x solve for x
Step-by-step explanation:
81^x² = 27^x
(3^4)^x² = (3^3)^x
3^(4x²) = 3^(3x)
4x² = 3x
4x² − 3x = 0
x (4x − 3) = 0
x = 0 or ¾
The graphed line shown below is y = negative 4 x minus 12. On a coordinate plane, a line goes through (negative 3, 0) and (negative 2, negative 4). Which equation, when graphed with the given equation, will form a system that has no solution? y = 4 x + 12 y = negative 4 x y = negative 12 y = negative 4 (x + 3)
Answer:
y = -4x or the second option on edge.
This is because after you form it into the given equation, it equals y = -4x.
In order to clarify, edge also states that's the answer.
Answer:
2nd option
Step-by-step explanation:
A recipe for 1 batch of muffins used 2/3 of blueberries. Amir made 2 1/2 batches of muffins. How many cups of blueberries did he use? A. 1 4/6 B. 1 5/6 C. 2 2/6 D. 3 1/6. Please show your work.
Answer:
A. 1 4/6 cups of blueberries
Step-by-step explanation:
1 -- 2/3
Proportion, Batches to Blueberries
1*(2 1/2) -- (2/3)( 2 1/2)
Because we are now multiplying the 1 batch to 2 1/2 batches. So to keep the proportion balanced/equal we are using the same operation on the right side of the proportion
2 1/2 -- (2/3)( 5/2 )
2 1/2 -- 5/3
2 1/2 -- 1 2/3
Simplify
On the right side shows the blueberries for 2 1/2 batches. 1 2/3 = 1 4/6
Hope that helps! Tell me if you need more info
The floor of a shed given on the right has an area of 44 square feet . The floor is in the shape of a rectangle whose length is 3 less than twice the width. Find the length and width of the floor of the shed.
Answer:
The length and width of the floor of the shed are 8 feet and 5.5 feet, respectively.
Step-by-step explanation:
Given that the shape of the shed is a rectangle, the expression for the area is:
[tex]A = w \cdot l[/tex]
Where [tex]w[/tex] and [tex]l[/tex] are the width and length of the shed, measured in feet. In addition, the statement shows that [tex]l = 2\cdot w - 3\,ft[/tex]. Then, the equation of area is expanded by replacing length:
[tex]A = w\cdot (2\cdot w - 3)[/tex]
[tex]A = 2\cdot w^{2} - 3\cdot w[/tex]
If [tex]A = 44\,ft^{2}[/tex], then, a second-order polynomial is formed:
[tex]2\cdot w^{2}-3\cdot w - 44 = 0[/tex]
The roots of this equation are found via General Equation for Second-Order Polynomials:
[tex]w_{1} = \frac{11}{2}\,ft[/tex] and [tex]w_{2} = -4\,ft[/tex]
Only the first roots is a physically reasonable solution. Then, the length of the shed is:
[tex]l = 2\cdot \left(\frac{11}{2}\,ft \right)-3\,ft[/tex]
[tex]l = 8\,ft[/tex]
The length and width of the floor of the shed are 8 feet and 5.5 feet, respectively.
The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes. Calculate the rate that the water is draining out of the pool. (Hint: remember this line is sloping down to the right) (3 marks) Rate=0-45000/70-20 Rate = (0 - 45000) / 70-20 Rate = -45000 / 50 Rate=-900/minute b) Calculate how much water was in the pool initially (at time 0). (2 marks)
Answer:
there were 63,000L of water initially in the pool
Step-by-step explanation:
do 900L times the first 20 minutes to find out how much water was drained during the first 20 minutes and you get 18,000L drained
then, add 18,000L plus the rest of the 45,000L of water drained from the pool to get 63,000L of water intially in the pool
1000 randomly selected Americans were asked if they believed the minimum wage should be raised. 600 said yes. Construct a 95% confidence interval for the proportion of Americans who believe that the minimum wage should be raised.
a. Write down the formula you intend to use with variable notation).
b. Write down the above formula with numeric values replacing the symbols.
c. Write down the confidence interval in interval notation.
Answer:
a. p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]
b.0.6 ± 1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]
c. { -1.96 ≤ p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ≥ 1.96} = 0.95
Step-by-step explanation:
Here the total number of trials is n= 1000
The number of successes is p` = 600/1000 = 0.6. The q` is 1 - p`= 1- 0.6 = 0.4
The degree of confidence is 95 % therefore z₀.₀₂₅ = 1.96 ( α/2 = 0.025)
a. The formula used will be
p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ( z with the base alpha by 2 (α/2 = 0.025))
b. Putting the values
0.6 ± 1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]
c. Confidence Interval in Interval Notation.
{ -1.96 ≤ p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ≥ 1.96} = 0.95
{ -z( base alpha by 2) ≤ p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ≥ z( base alpha by 2) } = 1- α
13. If 6 times the 6th term of an A.P. is equal to
13 times the 13th term, prove that 19th term
of this A.P. is zero.
please give the answer as fast as you can
please
Answer:
see explanation
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given
6(a₁ + 5d) = 13(a₁ + 12d) ← distribute parenthesis on both sides
6a₁ + 30d = 13a₁ + 156d ( subtract 13a₁ from both sides )
- 7a₁ + 30d = 156d ( subtract 30d from both sides )
- 7a₁ = 126d ( divide both sides by - 7 )
a₁ = - 18d
Now
a₁₉ = a₁ + 18d = - 18d + 18d = 0 ← as required
6th grade math, help me please.
Answer:
a) [tex]\frac{2}{3} \,\frac{lb}{bread}[/tex]
b) [tex]1\frac{1}{4} \,\frac{in}{domino}[/tex]
Step-by-step explanation:
Part a:
every 4 lbs of flour, she makes 6 loaves of bread. this as a rate in simplest fraction form is:
[tex]\frac{4}{6} \,\frac{lb}{bread} = \frac{2}{3} \,\frac{lb}{bread}[/tex]
Part b:
every 10 inches , 8 dominoes can be placed. then the rate can be written as:
[tex]\frac{10}{8} \,\frac{in}{domino} = \frac{5}{4} \,\frac{in}{domino} =1\frac{1}{4} \,\frac{in}{domino}[/tex]
This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If = 4 cm, what is the smallest diameter of wrapper that will fit the candy bar?
Answer:
Step-by-step explanation:
No figure supplied, so lots of assumptions needed.
Assume side length of triangle is 4 cm.
( If = 4 cm means ??)
Assume ABC is equiangular, all three angles are 60 degrees.
(This is a cross-sectional view, but don't see any)
Side length = 4
altitude of triangle = 4 sin(60) = 2sqrt(3)
radius of circumscribed circle of equilateral triangle
R = (2/3) altitude
= (2/3)*2sqrt(3)
= (4/3)sqrt(3)
Diameter
D = 2R
= (8/3) sqrt(3)
Answer: 8 cm
Step-by-step explanation:
The figure in the image attached below shows that there are two specific angles that are congruent to each other, angles AD and CD.
We are given the length of one of these angles:
AD= 4 cm so we must multiply 4 by 2, since there are TWO angles measuring 4 cm.
4 cm x 2 angles (AD and CD) =8 cm.
Proof of answer is shown below!
If a transversal is perpendicular to one of two parallel lines, then it's ________ to the other line. Question 16 options: A) perpendicular B) congruent C) parallel D) supplementary
Answer: Perpendicular.
Step-by-step explanation:
Suppose that you have two perpendicular lines:
Remember that a line is something like:
y = a*x +b
and two lines are parallel if they have the same slope (a) but a different y-intercept(b)
Then our lines can be:
y1 = a*x + b1
y2 = a*x + b2.
Now, if we have a line:
y = a*x + b
Then a perpendicular line will have a slope equal to -(1/a):
yp = (-1/a)*x + c
So this only depends on the slope, and we know that our two parallel lines have the same slope. So if we construct a transversal line that is perpendicular to one of our lines, it also must be perpendicular to the other line.
Answer:
A
Step-by-step explanation:
A student is using the elimination method to solve the system of equations below. What is the best first
step?
4x - 5y = 2
2x + y = -3
Answer:
The best first step would be to multiply the second equation by -2
Step-by-step explanation:
The best first step would be to multiply the second equation by -2
then you would have the following
[tex]\ \ \ \ \ \ 4x - 5y = 2 \\-2*(2x)+ (-2)*y = (-2)*3[/tex]
and when you multiply it is easy to eliminate because you will get
[tex]4x - 5y = 2 \\-4x -2y = 6[/tex]
and if you sum the equations you get
-7y = 8
so that is a single variable equation which is easier to solve.
Create a circle such that its center is point a and b is a point on the circle
Step-by-step explanation:
The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.
Answer:
i think that this question is wrong
Step-by-step explanation:
The value of y varies inversely as the square of x, and y = 16, when I = 3.
Find the value of x when y = 1.
Answer:
x = 12Step-by-step explanation:
The statement
The value of y varies inversely as the square of x is written as
[tex]y = \frac{k}{ {x}^{2} } [/tex]
where k is the constant of proportionality
To find the value of x when y = 1 first find the formula for the variation
y = 16 x = 3
k = yx²
k = 16(3)²
k = 16 × 9
k = 144
The formula for the variation is
[tex]y = \frac{144}{ {x}^{2} } [/tex]
when y = 1
We have
[tex]1 = \frac{144}{ {x}^{2} } [/tex]
Cross multiply
x² = 144
Find the square root of both sides
We have the final answer as
x = 12Hope this helps you
174 people ate lunch at Alice’s restaurant yesterday, and 1/3 of them had dessert. How many people had dessert after lunch?Explain how you got your answer. (90 points!!!)
Answer:
58 people
Step-by-step explanation:
174 people ate lunch.
1/3 of the 74 people had dessert after lunch.
Multiplying 1/3 and 174.
1/3 × 74
= 58
58 people had desert after lunch.
Answer:
[tex]\boxed{ 58\ people}[/tex]
Step-by-step explanation:
People who ate lunch = 174 people
People among among them who had desserts = 1/3 of the total
(Remember "of" means to "multiply")
=> 1/3 * 174
=> 1 * 58
=> 58 people
A congressman wants to measure the level of support in his district for campaign finance reform and determine if there is a gender gap among voters with respect to this issue. One aid suggests that they find separate confidence intervals for the percent of men and the percent of women who favor reform and then see if the intervals overlap. Another aid suggests that they find a confidence interval for the difference in the proportions of men and women who favor reform. The question is: Is there a gender gap
Answer:
Campaign Finance Reform
Gender Gap among Voters in the District
There is a gender gap among women and men who favor campaign finance reform.
Step-by-step explanation:
In issues such as the above, a gender gap always exist between women and men who think that there is the need to reform the campaign finance. Women ordinarily favor a reduction in the campaign finance. On the other hand, men do not mind so much about the candidate expenditure in campaigns. Reducing the huge campaign finance will ensure that political campaigns and aspiration to political offices are not left to money bags. Many women would like to get involved, but they are limited by funding. So, anytime the issue of reforming the whole electoral system, especially with respect to campaigns, women favor the reforms more than men. The gap is always there. The main issue is how would this gap be measured?
Example 2: The GPAs of 20 students are listed.
Make a stem-and-leaf plot for this data.
1.8 2.9 0.9 4.0 3.3
2.4 2.3 1.6 1.6 4.0
1.7 0.5 3.6 3.4 1.9
4.0 2.1 1.9 1.1 0.5
How do I make a stem and leaf plot for these numbers?
Answer/Step-by-step Explanation:
To create a stem-and-leaf plot for the GPAs of the 20 students that were listed in the above question, take the following steps:
Step 1: for easy plotting, write down the GPAs in an ordered manner, that is, from the smallest value to the largest.
0.5, 0.5, 0.9, 1.1, 1.6, 1.6, 1.7, 1.8, 1.9, 1.9, 2.1, 2.3, 2.4, 2.9, 3.3, 3.4, 3.6, 4.0, 4.0, 4.0
Step 2: divide each set of data into a stem and a leaf. For example, for a GPA, 0.5, 0 would be the stem, while 5 would be the leaf.
For a GPA listed, 2.9, 2 is the stem, 9 is the leaf. Same applies to all the other GPAs.
Step 3: All stems should be written in ascending order, vertically, from the smallest to the largest. From the listed GPAs, you would observe that the highest stem value would be 4, while the lowest would be 0.
Therefore, write down your stems vertically, in ascending order as shown below:
0 |
1 |
2 |
3 |
4 |
Step 4: All leaves should be written also in ascending order to their corresponding stem, from the smallest to the largest, as shown below:
Stem | Leaf
0 | 5 5 9
1 | 1 6 6 7 8 9 9
2 | 1 3 4 9
3 | 3 4 6
4 | 0 0 0
Thus,
0 | 5 5 9 represents => 0.5, 0.5, 0.9
*See attachment below for the stem-and-leaf plot.
The ratio of oranges in a fruit salad to people it will serve is 9/40, or 9:40. If Lisa wants to serve 800 people, how many oranges will Lisa use?
The correct answer is 180 oranges
Explanation:
In mathematics, a ratio expresses two or more numbers that are related. In the case fo the ration 9: 40 this expresses 9 oranges are used to serve fruit salad for 40 people. Now, if you need to determine what is the number of oranges not for 40 people but for 800 people you can use cross multiplication. This process is explained below:
[tex]\frac{9}{40} = \frac{x}{800}[/tex] - 1. Multiply 9 x 800 and 40 x x (cross multiplication)
[tex]7200 = 40x[/tex] - 2. Solve the equation by diving 7200 into 40
[tex]\frac{7200}{40} = x[/tex]
[tex]x = 180[/tex] - 3. 180 represents the number of oranges to serve 800 people, which can be expressed as 180: 800
|x–5|=|x+5| If you answer this question before 2:35 pm on July 28, 2020, I will give 10 points!!
Answer:
[tex]\boxed{x=0}[/tex]
Step-by-step explanation:
[tex]|x-5|=|x+5|[/tex]
Solve absolute value.
There are two possibilities.
First possibility:
[tex]x-5=x+5\\0=10[/tex]
No solution.
Second possibility:
[tex]x-5=-(x + 5)\\x-5=-x-5\\2x=0\\x=0[/tex]
What is the following simplified product? Assume x>0
2 square root 8x^3(3 square root 10x^4-x square root 5x^2
Answer:
[tex] 24x^3\sqrt{5x} - 4x^3\sqrt{10x} [/tex]
Step-by-step explanation:
The product [tex]2\sqrt{8x^3} (3\sqrt{10x^4} - x\sqrt{5x^2})[/tex] can be simplified as follows:
Step 1: Use the distributive property of multiplication
[tex]2\sqrt{8x^3}(3\sqrt{10x^4)} - 2\sqrt{8x^3}(x\sqrt{5x^2})[/tex]
[tex] 2*3\sqrt{8x^3*10x^4} - 2*x\sqrt{8x^3*5x^2} [/tex]
[tex] 6\sqrt{80x^7} - 2x\sqrt{40x^5} [/tex]
Step 2: simplify further
[tex] 6\sqrt{16*5*x^3*x^3*x} - 2x\sqrt{4*10*x^4*x} [/tex]
[tex] 6*4*x^3\sqrt{5*x} - 2x*2*x^2\sqrt{10*x} [/tex]
[tex] 24x^3\sqrt{5x} - 4x^3\sqrt{10x} [/tex]