9514 1404 393
Answer:
(x, y) = (2, 3)
Step-by-step explanation:
The first step is to find the least common multiple of the denominators of each of the equations. If the denominators have no common factors, a reasonable choice is their product. Here, it works to start with the fractions that must be added, then compare the LCM found to the denominator on the right to see if any further factors must be included.
First equation:
LCM = 3×4 = 12
12(2x/3 -y/4) = 12(7/12) . . . . . multiply the equation by 12
8x -3y = 7 . . . . . . . . . simplify
Second equation:
LCM = 4×5 =20
20(3x/4 -2y/5) = 20(3/10) . . . . multiply equation by 20
15x -8y = 6 . . . . . . simplify
Solve by elimination
We can eliminate the y-variable by subtracting 3 times the second equation from 8 times the first:
8(8x -3y) -3(15x -8y) = 8(7) -3(6)
19x = 38 . . . . . simplify
x = 2 . . . . . . . divide by 19
Substituting into the first equation gives ...
8(2) -3y = 7
3y = 9 . . . . . . add 3y-7
y = 3 . . . . . divide by 3
The solution is ...
(x, y) = (2, 3)
_____
There are many ways to solve such a system of equations. Using the LCM to eliminate fractions is one way to start. You can also do the arithmetic with the fractions intact, though most folks don't care to. In addition to the elimination method used here, you can use matrix or graphical methods, substitution, or any of the variations of Cramer's Rule.
What’s the slope and equation
Answer:
slope = -5 equation= y=-5x+100
Step-by-step explanation:
pick the x and y intercepts as your points to find the gradient that is
(20,0) and (0,100)
slope =∆y/∆x
=100/-20
= -5
take point(20,0) and (x,y) to find equation using the slope
equation becomes y= -5x+100
The terms central location or central tendency relate to the way quantitative data tend to cluster around some middle or central value.
a. True
b. False
Answer:
A: True
Step-by-step explanation:
It's true because central tendency is defined as a branch of descriptive statistics that shows the centre of the data distribution.
This central tendency could be mean, median or mode.
At the market, he spends $5.58 on red potatoes and $4.68 on yellow potatoes. If each type of potato costs $0.90 per pound, how many total pounds of potatoes does he buy?
Answer:
11.4pounds
Step-by-step explanation:
(5.58+4.68)÷0.90
=11.4(pounds)
Espanol
At the movie theatre, child admission is $5.70 and adult admission is $9.40. On Sunday, 135 tickets were sold for a total sales of S1080.30. How many adult
tickets were sold that day?
9514 1404 393
Answer:
84 adult tickets
Step-by-step explanation:
Let 'a' represent the number of adult tickets sold. Then (135-a) is the number of child tickets sold, and total revenue is ...
5.70(135 -a) +9.40(a) = 1080.30
3.70a = 310.80 . . . . . . . . subtract 769.50 and simplify
a = 310.80/3.70 = 84
84 adult tickets were sold on Sunday.
A recent study at Winthrop University was done to determine the ratio of democrats to republicans. Use the information in each problem to come up with an appropriate sample size to accurately estimate the mean. Let a republican represent a success r. If no preliminary sample is taken, how large should the sample be to be 90% sure that the estimate is within .03 of the population proportion?
Answer:
A sample of 752 should be taken.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
No preliminary sample is taken
This means that [tex]\pi = 0.5[/tex]
How large should the sample be to be 90% sure that the estimate is within .03 of the population proportion?
This is n for which M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645*0.5[/tex]
[tex]\sqrt{n} = \frac{1.645*0.5}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*0.5}{0.03})^2[/tex]
[tex]n = 751.7[/tex]
Rounding up:
A sample of 752 should be taken.
if loga (n) = 16, find loga (sqrtt n)
Answer:
8
Step-by-step explanation:
by definition:
[tex]log_an=16\\\\log_a\sqrt{n}=log_a n^{\frac{1}{2}}=\frac{1}{2}log_a n=\frac{1}{2}(16)=8[/tex]
List all the factors of 9. The factors of 9, from least to greatest, are and
Answer:
1 9 3
Step-by-step explanation:
i think only this much
Answer:
1,3 and 9
As Nine is divisible by 1,3 and 9
Pls help again thanks
Answer:
d.156.
x+24=180 ( being staright angle)
Jenny is taking a vacation from Florida. She travels 70 kilometers per hour for 2 hours, and 63 kilometers per hour for 5 hours. Over the 7 hours time period what was Jenny's average speed?
Answer: 65 kmh
Step-by-step explanation:
70 kmh for 2 hours = 140 km.
63 kmh for 5 hours = 315 km
140 + 315 = 455/7 total hours = 65 kmh
If four pounds of potatoes cost $6.00, how much would 10 pounds of potatoes cost
Answer:
I think is 15 dollars.
Step-by-step explanation:
each pound cost 1.5 multiply it by 10
Answer:
$15
Step-by-step explanation:
4 pounds are $6
10pounds are $?
1 pound would be $1.5, because 6/4 = 3/2= 1.5
If one pound is 1.5 dollars, 10 pounds would be 10*1.5=$15
as central angle is to 360 degrees.Arc length is to
A.circumference
B.area
C.sector
D. Diameter
If central angle is 360° then Arc length is circumference.
What is the central angle of a Circle?
An angle with the circle's center as its vertex is referred to as a central angle. The radius refers to each side of the angle that extends outward from the center to a particular point on the circle.
What is circumference?A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.
How to solve it?Since, when considering the circle's central angle we consider 360° which is the central angle of the whole circle.
So, when considering the arc length of a sector, we consider the arc length of the whole circle which is the circumference.
Learn more about circles here-
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Under an insurance policy, a maximum of five claims may be filed per year by a policyholder. Let Pn be the probability that a policyholder files n claims during a given year, where n 0,1,2,3,4,5. An actuary makes the following observations:
i) Pn≥ 2pn+1 for n= 0, 1,2, 3,4
ii) The difference between pn and pn+1 is the same for n 0,1,2, 3,4
iii) Exactly 40% of policyholders file fewer than two claims during a given year Calculate the probability that a random policyholder will file more than three claims during a given year.
A) 0.14
B) 0.16
c) 0.27
D) 0.29
E) 0.33
Help!!!
I will mark you
Answer:
832.6lbs
Step-by-step explanation:
10.6.23
Question Help
Becky would like to be a millionaire in 40 years. How much would she need to invest quarterly in a sinking
fund paying a 3% interest rate compounded quarterly to accumulate $1,000,000 in 40 years?
I = $ 1,200,000.00
Equation:
I = Prt
Calculation:
First, converting R percent to r a decimal
r = R/100 = 3%/100 = 0.03 per year,
then, solving our equation
I = 1000000 × 0.03 × 40 = 1200000
I = $ 1,200,000.00
The simple interest accumulated
on a principal of $ 1,000,000.00
at a rate of 3% per year
for 40 years is $ 1,200,000.00.
The perimeter of the triangle below is 80 units. Find the length of side PR
Answer:
32
Step-by-step explanation:
The perimeter is equal to sum of side lengths
4x + z + 3 + 5z - 3 = 80 add like terms
10z = 80 divide both sides by 10
z = 8 PR is 4z so 8*4 = 32
Here is the problem
Answer:
5 =x
Step-by-step explanation:
The top and the bottom are the same length
17 = 3x+2
Subtract 2 from each side
17-2 = 3x+2-2
15 =3x
Divide by 3
15/3 = 3x/3
5 =x
Answer:
x = 5
Step-by-step explanation:
3x + 2 = 17
3x + 2 - 2 = 17 - 2
3x = 15
3x ÷ 3 = 15 ÷ 3
x = 5
What is the surface area of the rectangular prism?
5 ft
5 ft
8 ft
Garcia bought 3 packs of red notebooks, 5 packs of yellow notebooks, and 8 packs of green notepads. There were 3 notepads in each package. How many notepads in all?
What is the expression?
The answer is 48 notepads.
simplify: x0 y-3 / x2 y-1
[tex] \frac{x {}^{0}y {}^{ - 3} }{x {}^{2}y {}^{ - 1} } \\ = \frac{1y {}^{ - 3} }{ {x}^{2}y {}^{ - 1} } \\ = \frac{1 \times 1}{ {x}^{2} y {}^{2} } \\ \\ = \frac{1}{ {x}^{2}y {}^{2} } [/tex]
Step by Step Explanation:
Evaluate the power: Any non-zero expression raised to the power of 0 equals 1Simplify: Simplify the expressionCalculate the product: Any expression multiplied by 1 remains the same. ☆彡Hanna#CarryOnLearning
PLEASE HELP!
WILL MARK BRAINLIEST!
Find the measure of the indicated angle to the nearest degree.
Please provide an explanation, I’m trying to learn.
Answer:
B =53.15010235
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan B = 20 /15
Take the inverse tan of each side
tan ^ -1 ( tan B) = tan ^-1( 20/15)
B =53.15010235
HELP TIMER Write the equation of a hyperbola centered at the origin with x-intercept +/- 4 and foci of +/-2(squareroot 5)
Answer:
[tex]\frac{x2}{a} - \frac{y2}{b2} = 1[/tex]
Step-by-step explanation:
A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.
The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:
[tex]\frac{X2}{16} - \frac{b}{4} = 1[/tex]
The coordinates of the foci is at (±c, 0), where c² = a² + b²
Given that a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:
I don't feel like explaining so...
a. = 4
The foci c is at +/-2√5, using c² = a² + b²:
B = 2
Substituting the value of a and b to get the equation of the hyperbola:
[tex]\frac{x2}{a2} - \frac{y2}{b2} = 1[/tex]
[tex]\frac{x2}{16} - \frac{b2}{4} = 1[/tex]
What is the value of h?
Answer:
35
All angles of a triangle = 180 degrees subtract 40 from 180 and you get 140
180-40=140 because the other angles are equal with the same equation to get them divide 140 by 2 140/2=70 then you have to get h alone so you divide by the other 2 in the equation 70/2=35 h=35
Answer:
55
Step-by-step explanation:
In triangle ABC (LET'S SAY TRIANGLE IS ABC)
Angle A=40
Angle B = Angle C = x (since 2h is beside B and C both)
40+x+x=180 (Angle sum property)
40+2x=180
2x=140
x=70
2h+70=180 (Angle in a straight line=180)
2h=110
h=55
A rectangular auditorium seats 1564 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row
Answer:
# of rows: 34
# of seats in each row: 46
Step-by-step explanation:
r - # of rows
s - # of seats in each row
r * s = 1564
s = r + 12
(34) * (46) = 1564
(46) = (34) + 12
Hope this helps!
Which one hurry
A.50
B.80
C.90
D.100
Answer:
I think its
im not sure
Step-by-step explanation:
What are 3 attributes of a Square based pyramid
Answer:
It has 5 Faces.
The 4 Side Faces are Triangles.
The Base is a Square.
It has 5 Vertices (corner points)
It has 8 Edges.
Step-by-step explanation:
btw you can choose 3
5.Square Given:a =12m,A=
Pa help po
If s=side, then each side is 12m.
It got cut off but
12mx12m=144m^2 because mxm=m^2.
heart if helpful
I need help finding the value of X.
Answer:
x=25
Step-by-step explanation:
43=2x-7 (since the midpoint separate a line into two equal halves)
43+7=2x
50/2=x
25=x
Answer:
x=25
Step-by-step explanation:
Since M is the midpoint, you can set your formula up as
43 = 2x-7
43+7=2x
50/2=x
25=x
What is the quotient?
x-3) 4x2+3x+2
+2
O 4X2 + 15 +
47
X-3
43
0 4x + 15 +
X-3
O 4x2 + 15 +
43
X-3
0 4x + 15 +
47
X-3
Answer:
13
Step-by-step explanation:
the answer is 13
the answer is 13
the answer is 13
the answer is 13
the answer is 13
The quotient obtained by dividing 4x²+3x+2 will be 4x + 15 hence option (A) will be correct.
What is the equation?An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
A formula known as an equation uses the same sign to denote the equality of two expressions.
In another word, the equation must be constrained with some constraint.
Given that
dividend = 4x²+3x+2
divider = x -3
⇒ (x - 3) / 4x²+3x+2
⇒ (x - 3) / 4x²+3x+2
→ First it will goes for 4x time so 4x × (x - 3) = 4x² - 12x
Quotient = 4x
so (4x²+3x+2) - ( 4x² - 12x ) = 15x + 2
(x - 3) / 4x²+3x+2
→ Second time it goes for 15 so 15 × (x - 3) = 15x -45
Quotient = 15
so (15x + 2 ) - ( 15x -45 ) = 47
Hence, 47 will be the remainder and the quotient will be (4x + 15).
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Can someone help me with 8,9 ??!!
Answer:
15 / 2437/52Step-by-step explanation:
8 .) Probability of students has no pets in senior = No. of outcomes favourable / Total no.of outcome
= 15 / 24
9.) Probability of students has pets in junior = No.of outcomes favourable / Total no. of outcomes
= 37/52
What is the factored form of y=-2x^2-8x+0
Answer:
(2x-4()(x-2)
Step-by-step explanation:
this is how it looks when factorised
Answer:
y=-2x^2-8x
you can use a factor form helper and from that it can show you examples on how to solve it