Answer:
Solution Given:
let pitcher which is small be S medium be M and large be L and barrel be B.
By question
6S+3M+1L= 1B...... eq. 1
2S+1M+3L=1B.......eq. 2
The difference in 2L from the first to the second is 4S and 2M
Therefore, each L=2S+M
In equation 2
2S+1M+3L=1B
replacing 2S +1M by L,we get
L+3L=1B
4L=1B
Therefore, 4 large pitcher is required
Answer:
4 large pitchers
Step-by-step explanation:
Define the variables:
Let x = volume of a small pitcherLet y = volume of a medium pitcherLet z = volume of a large pitcherLet b = volume of a barrelCreate two equations with the given information and the defined variables.
Equation 1
If the barrel can be filled with 6 small pitchers, 3 medium pitchers and 1 large pitchers:
⇒ 6x + 3y + z = b
Equation 2
If the barrel can be filled with 2 small pitchers, 1 medium pitcher and 3 large pitchers:
⇒ 2x + y + 3z = b
Substitute Equation 2 into Equation 1
⇒ 6x + 3y + z = 2x + y + 3z
Subtract 6x from both sides:
⇒ 3y + z = -4x + y + 3z
Subtract y from both sides:
⇒ 2y + z = -4x + 3z
Subtract z from both sides:
⇒ 2y = -4x + 2z
Divide both sides by 2:
⇒ y = -2x + z
Substitute the found expression for y into Equation 1:
⇒ 6x + 3(-2x + z) + z = b
⇒ 6x - 6x + 3z + z = b
⇒ 4z = b
Therefore, 4 large pitchers are needed to fill the barrel.
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- 5x - 5 = 3x + 19 what would X be?
-5x - 5 = 3x + 19
---Move the x's to one side
-5x - 3x - 5 = 3x - 3x + 19
-8x - 5 = 19
---Isolate the -8x by removing the -5 from the left side
-8x - 5 + 5 = 19 + 5
-8x = 24
---Divide both sides by -8 to get x by itself
x = -3
Hope this helps!
-5x-5= 3x+19
= > -5x-3x= 19+5
= > -8x= 24
= >-x=24/8
= >x= -3
Which expression is equivalent to the given expression?
Assume the denominator does not equal zero.
a^3b^5 / a^4b
A. b^4 / a
B. a / b^4
C. 1 / ab^4
D. ab^4
The expression which is equivalent to the given expression by means of evaluation using the laws of indices is; Choice A; b⁴/a.
Which of the answer choice represents an expression which is equivalent to the given expression?The given expression according to the task content is; a³b⁵/a⁴b.
It therefore follows from the laws of indices that each variable can be evaluated by means of their exponents as follows;
a^(3-4)b^(5-1)
Consequently we have;
b⁴/a.
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Mary's tube of red paint is five sevenths full and her blue paint is four sevenths full. How much red and blue paint does Mary have in total? Use the benchmark fraction one half, 1, and 0 to help you estimate each answer before you solve.
one seventh tube
seven ninths tube
one and two sevenths tubes
one and one seventh tubes PLEASE HELP! (Ill give brainnliest!!)
By adding fractions, we conclude that the correct option is the third one:
"one and two sevenths tubes"
How much red and blue paint does Mary have in total?We know that:
She has 5/7 of the red paint tube.She has 4/7 of the blue paint tube.The total amount of paint will be given by the direct addition of these two fractions, notice that the denominator is the same in both cases, so we can just add the numerators.
5/7 + 4/7 = (5 + 4)/7 = 9/7
We can rewrite this as:
9/7 = 7/7 + 2/7 = 1 + 2/7
Thus, the correct option is the third one
"one and two sevenths tubes"
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18 times the quantity g plus 5
Answer:
Step-by-step explanation:
Comment
The first thing you should notice once you have read it, is there is a plus sign required. That means you are likely to get a binomial (two different things that won't reduce or combined).
So what you get is
18*g + 5
Notice where the place sign is. It is between 18g and 5. The result cannot be simplified any further.
Answer
18g + 5
Worth 15 points!!!!!!!!!!!!!!
Trigonometry Question
A boat sails on a bearing of 63 for 124 miles and then turns and sails 201 miles on a bearing of 192. Find the distance of the boat from its starting point.
The distance of the boat from its starting point is 156.226 .
According to the question
A boat sails on a bearing of 63 degree for 124 miles
i.e
By making 63 degree covers 124 miles
therefore ,
In figure below
AC = 124 miles
Then turns and sails 201 miles on a bearing of 192 degree
therefore ,
In figure below
CD = 201 miles
Now,
According to the sum of triangle
∠ACB + ∠ABC + ∠BAC = 180°
∠ACB + 90° + 63° = 180°
∠ACB = 27°
CE = 180° (Straight line )
therefore,
∠DCE = 192° - 180°
= 12°
As ∠C = 90°
therefore
∠ACD = ∠C - ∠DCE - ∠ACB
= 90° - 12°- 27 °
= 51°
Now,
The distance of the boat from its starting point = AD
By using Law of Cosines
As
The Law of Cosines can be used to find the unknown parts of an oblique triangle(non-right triangle), such that either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are given.
The Law of Cosines (also called the Cosine Rule) says:
c² = a² + b² − 2ab cos(C)
As we have 2 sides and one angle available we can use Law of Cosines
Therefore,
by substituting the value
(AD)² = (AC)² + (CD)² − 2(AC)(CD) cos(∠ACD)
(AD)² = (124)² + (201)² − 2*124*201 cos(51)
AD = 156.226
Hence, the distance of the boat from its starting point is 156.226 .
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Consider the interval [2, 3) = {x € r : 2 <= x < 3}. Find the complement of this interval where the universal set is taken to be r, the set of real numbers.
The complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
According to the given question.
We have an interval [2, 3).
Let A = [2, 3)
Which is defined as
[2, 3) = {x ∈ r : 2 ≤ x < 3}
This means that the interval [2, 3) contains all the real numbers which are greater and equal to 2 and less than 3.
And, here it is also given that the universal set is r ( set of real numbers).
As we know that " the complement of an interval is a set A of real numbers that conatins all the elements of universal set U except the number that lying between the given two numbers in the inerval" i.e.
[tex]A^{c} = U - A[/tex]
Where,
[tex]A^{c}[/tex] is the complement of interval A
Thereofre, the complement of the given interval [2, 3) will be all the elements of universal set i.e real numbers except 2 and the real numbers which lies in between 2 and 3.
So, we can say that
[tex]A^{c} = (-\infty, 2) \cup(3, \infty)[/tex]
Where, [tex]A^{c}[/tex] is the complement of the interval A.
Hence, the complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
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can someone help with this algebra problem?
Answer:
g(1) = 1
Step-by-step explanation:
Since 1 ≠ -2 and 1 ≠ -1
Then we must use the expression:
g(x) = x³ - x² + 1 ,to calculate g(1).
Therefore
g(1) = (1)³ - (1)² + 1
= 1 - 1 + 1
= 0 + 1
= 1
What is the sign of s^67/t^9 when s < 0 and t > 0?
possible answers:
. positive
. negative
. zero
Answer:
negative
Step-by-step explanation:
[tex]s^{67}<0 \\ \\ t^9>0 \\ \\ \implies \frac{s^{67}}{t^9}<0
[/tex]
Answer:
negativeStep-by-step explanation:
The sign of a product or quotient cannot be determined by the positive number (t), so we can ignore it. The sign of the expression will be negative if and only if there are an odd number of negative factors.
Here, there are 67 (an odd number) negative factors, so the expression will be negative.
What is the approximate radian measure
of an angle with a degree measure of
59.6°?
Answer:
The approximate radian measure of the angle. So we have 15 nine 0.6 degrees convert degrees to radiance. You have to multiply by pi over 1 80. So if we did that, that'd be 59.6 pi over 1 80. So if we want to know the approximate value, we're going to use the pi button on our calculator to figure out what 59.6 times pi is. That's approximately 187.2389, Divided by 1 80. So now I would divide that number by 180 and that gives me 1.04 radiance, 1.04 radiance is the answer.
If these two shapes are similar, what is the measure of the missing length w 20 in 15 in 12 in
Answer:
Step-by-step explanation:
What is the probability that a class of 50 has an average midterm mark that is less than 75?
The probability that a class of 50 has an average midterm mark that is less than 75 is value=0
Average is the mathematics mean, and is calculated by means of adding a group of numbers and then dividing with the aid of the count of these numbers. for instance, the average of 2, three, three, five, 7, and 10 is 30 divided with the aid of 6, that is five.
The common is described as the implied value that is identical to the ratio of the sum of the number of a given set of values to the whole wide variety of values gift within the set.
There are three primary sorts of common: imply, median, and mode. each of those techniques works slightly differently and frequency effects in barely specific regular values. The suggestion is the maximum normally used average. To get the suggested fee, you add up all of the values and divide this total by using the number of values.
The probability that a class of 50 has an average midterm mark that is less than 75
n = 50
P(<75)=P(Z<75)
P(Z<75−786√50)
P(Z<−3.5355)
We will look for the value in the StandardNormal able. We will get the value=0
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Simplify (64/125)-2/3 + (256/625)-1/4 + (7/3)
Step-by-step explanation:
part 1: 64/125 - 2/3
make the denominator ( bottom number) the same
x/125 and x/3
125×3 and 3×125
x/375 and x/375
whatever we do to the denominator we have to do to the numerator ( top number)
64/125
125 × 3
so
64 ×3
=64×3/125×3
=192/375
2/3
3 × 125
so
2 × 125
=2×125/3×125
=250/375
put together:
192/375 - 250/375
denominator is the same so we can simply take 192 from 250
192 - 250 = -58
= -58/375
part 2: + (256/625)-1/4
-58/375 + (256/625)-1/4
do the same for (256/625)-1/4 as in part 1
then add it to -58/375 by making the denominator the same
part 3: + (7/3)
make the denominator the same and add
part 4: simplify
divide a number from both the top and bottom till there is nothing you can divide from both
Evaluate the expressions. 32) 12+ 32÷3-6
Answer:
16.66666667
Step-by-step explanation:
=12+10.66666667-6
=22.66666667-6
=16.66666667
(ASAP PLEASE) Peter had some triangular tiles with sides 3 cm long. He placed them side by side to make a trapezium. If the perimeter of the trapezium was 27 cm, how many tiles did Peter use?
Answer:
She used 9 tiles which are 3 cm long
Step-by-step explanation:
cuz 3x9=27 and yea
On a map, point C is 4.3km due east of point B , and point B is 2.7km on a bearing of 143° from point A . Give your answer to 2 decimal places for the following. a Find how far east point B is from A. b Find how far east point C is from A. c Find how far south point C is from A
Based on the bearings of the direction and the distances given, the distance of point B from A is 1.62 km. Point C's distance from A is 5.92 km east and 2.16 km south.
How far are points B and C from A?To find the distance from point B to point A, the Cos function should be used.
Point A's distance from B can be found as:
= Cos (143 - 90) x distance from point A
= Cos (53°) x 2.7
= 1.62 km
The distance of C from A eastward is:
= 1.62 + 4.3
= 5.92 km
As C is southward from point A, the function to be used is the Sin function.
The distance southward of c from A is:
= Sin(53°) x 2.7
= 2.16 km
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20 POINTS & BRAINLIEST TO WHO EVER SOLVE
Answer:
PQ = 20 cm
QR = 15 cm
Step-by-step explanation:
A and b are monomials where a = 125 and b = 27p12. what is the factored form of a – b?
The factored form of a - b is [tex]\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)[/tex].
What is monomial factorization ?A monomial is an expression that is the product of constant and non-negative integer powers of x, like [tex]3x^{2}[/tex]..
A monomial is expressed as a product of two or more other monomials when it is factored.
Here,
a = 125
[tex]$b=27 p^{12}$[/tex]
To find: a - b
a - b = 125 - [tex]27 p^{12}$[/tex]
a - b = [tex]5^{3}-\left(3 p^{4}\right)^{3}$[/tex]
We know that,
[tex]$x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$[/tex]
Finding the factored form of a - b using this method:
[tex]$a - b=\left(5-3 p^{4}\right)\left(5^{2}+5\left(3 p^{4}\right)+\left(3 p^{4}\right)^{2}\right)$[/tex]
[tex]$a-b=\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex]
So, factored form of a - b is [tex]$\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex].
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A coin is tossed 10 times. given that the first 9 tosses were heads, find the percent chance of getting 10 heads in a row?
Answer:
1/2
Step-by-step explanation:
Assume the coin is a fair coin.
Since we already know that the first 9 tosses were heads, the probability of 9 straight heads in the first 9 tosses is 1.
It all depends on the last toss. There is an equal probability of heads and tails in a single toss of a fair coin.
p(heads) = 1/2
p(10 heads) = 1/2
Ok so the answer is 1/2
The volume of a pyramid that fits exactly inside a cube is 18 cubic feet. what is the volume of the cube? 6 cubic feet 18 cubic feet 54 cubic feet 72 cubic feet
The volume of the cube that perfectly fits an 18 ft³ pyramid is calculated as (C) 54 ft³.
What is a cube?A cube is a three-dimensional solid object with six square faces, facets, or sides, three of which meet at each vertex. The cube is one of the five Platonic solids and the only regular hexahedron. It has six faces, twelve edges, and eight vertices.To find the volume of the cube that perfectly fits an 18 ft³ pyramid:
We have been provided that:
18 cubic feet is the volume of the pyramid.Now, in order for this pyramid to fit exactly into a cube, the base of the pyramid must be square, and the height of the pyramid must be equal to the height of the cube.We can conclude from this that the volume of a cube equals three times the volume of a pyramid.So, the volume of the cube = 3 × 18The volume of Cube = 54 ft³Therefore, the volume of the cube that perfectly fits an 18 ft³ pyramid is calculated as (C) 54 ft³.
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The correct question is given below:
The volume of a pyramid that fits exactly inside a cube is 18 cubic feet. what is the volume of the cube?
(A) 6 cubic feet
(B) 18 cubic feet
(C) 54 cubic feet
(D) 72 cubic feet
Please helpp with my math hw I’ll give brainlest
Answer:
20 percent
40 percent
20 percent
20(.008) percent
Step-by-step explanation:
6) 54 - 45 = 9
45 / 9 = 5
100 / 5 = 20
20 percent
7) 60 - 36 = 24
60 / 24 = 2.5
100 / 2.5 = 40
40 percent
8) 30 - 24 = 6
30 / 6 = 5
100 / 5 = 20
20 percent
9) 24.99 - 19.99 = 5
24.99 / 5 = 4.998
100 / 4.998 approx. = 20.008
20.008 percent (or rounded 20 percent)
the x and y intercept
Answer:
Step-by-step explanation:
X-INTERCEPT
Plug y=0 into the equation and solve the resulting equation −6x=−7 for x.
The x-intercept:
[tex]\left(\frac{7}{6},0\right)\approx \left(1.16666666666667,0\right)[/tex]
Y-INTERCEPT
Plug x=0 into the equation and solve the resulting equation 3y=−7 for y.
The y-intercept:
[tex]\left(0, - \frac{7}{3}\right)\approx \left(0,-2.33333333333333\right)[/tex]
Answer:
[tex]x[/tex]-intercept = ([tex]-\frac{7}{6}[/tex] , 0)
[tex]y[/tex]-intercept = (0 , [tex]-\frac{7}{3}[/tex])
Step-by-step explanation:
[tex]6x + 3y = -7[/tex]
• The x-intercept is the point at which the line crosses the x-axis, that is, where y = 0.
∴ [tex]6x + 3(0) = -7[/tex]
⇒ [tex]6x = -7[/tex]
⇒ [tex]x = \bf -\frac{7}{6}[/tex]
∴ The x-intercept is at the point ([tex]-\frac{7}{6}[/tex] , 0).
• Similarly, the y-intercept is the point at which the line crosses the y-axis, that is, where x = 0.
∴ [tex]6(0) + 3y = -7[/tex]
⇒ [tex]3y = -7[/tex]
⇒ [tex]y = \bf - \frac{7}{3}[/tex]
∴ The y-intercept is at the point (0 , [tex]-\frac{7}{3}[/tex]).
WILL MARK U BRAINLIEST
Answer:
90
Step-by-step explanation:
First, we should find the area of the trapezoid, and then subtract the area of the removed triangle in order to find the shaded area.
Area of the trapezoid
1) Area of the rectangle in the middle.
Base Length: 10
Height Length: 10
Area: 10 x 10 = 100
2. Area of the triangles on the side
Base Length: (14 - 10)/2 = 2
Height Length: 10
Area: 2 x 10 x 1/2 = 10
There are two triangles: 10 x 2 = 20
Area of the trapazoid: 100 + 20 = 120
Area of the triangle that's been removed
Base Length: 10
Height Length: 10 - 4 = 6
Area: 10 x 6 x 1/2 = 30
Shaded area
Area of the trapezoid - Area of the triangle
120 - 30 = 90
Area of the shaded region is 90.
The booster club sold 36,276 tickets on Friday, 34,012 tickets on Saturday, and 29,879 tickets on Sunday. If you were going to find out how many fewer tickets were sold on Sunday than Saturday, which operation would you perform?
Answer:subtraction
Step-by-step explanation: to find out how many fewer tickets were sold on Sunday you would need to subtract 34012 by 29879. The solution would be how many fewer tickets were sold on Sunday compared to Saturday.
Briefly describe each of the eight guidelines for evaluating statistical studies.
8 Guidelines for Critically Evaluating a Statistical Study
1. Identify the Goal, Population, and Type of Study
2. Consider the Source
3. Examine the Sampling Method
4. Look for Problems in Defining or Measuring the Variables of
Interest
5. Watch Out for Confounding Variables
6. Consider the Setting and Wording of Any Survey
7. Check That Results Are Fairly Represented in Graphics or
Concluding Statements
8. Stand Back and Consider the Conclusions
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Beth is going to enclose a rectangular area in back of her house. the house wall will form one of the four sides of the fenced in area, so beth will only need to construct three sides of fencing. beth has 48 feet of fencing. she wants to enclose the maximum possible area. what amount of fence should beth use for the side labeled x?
The maximum possible area would have a length of 24 feet and width of 12 feet.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let x represent the length and y represent the width, hence:
Since beth has 48 ft fencing and cover 3 sides, hence:
x + 2y = 48
x = 48 - 2y (1)
Also:
Area (A) = xy
A = (48 - 2y)y
A = 48y - 2y²
The maximum area is at A' = 0, hence:
A' = 48 - 4y
48 - 4y = 0
y = 12 feet
x = 48 - 2(12) = 24
The maximum possible area would have a length of 24 feet and width of 12 feet.
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Write the following in interval notation
x < 8
Answer:
Yup Yup
Step-by-step explanation:
yessah
Inequalities help us to compare two unequal expressions. The given inequality x<8 can be written in the interval notation as x=(-∞,8).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways. They do not, however, intend to indicate any particular location. Instead, they serve as a concise approach to expressing an inequality or a set of inequalities.
The given inequality x<8 can be written in the interval notation as,
x = (-∞,8)
Hence, The given inequality x<8 can be written in the interval notation as x=(-∞,8).
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What are the solutions of the system of equations y = –(x 2)2 1 and y = 4x 9? (–2, 1) and (6, –15) (–2, 1) and (–6, –15) (2, 1) and (6, –15) (2, 1) and (–6, –15)
The equations exist [tex]$y =-(x+2)^2+1[/tex] and [tex]y =4x+9[/tex] then the value of
x = -6, x = -2 and y = -15, y = 1.
How to solve the system of equations [tex]$y =-(x+2)^2+1[/tex] and
[tex]y =4x+9[/tex] ?
The given equations are [tex]$y =-(x+2)^2+1[/tex] and [tex]y =4x+9[/tex]
[tex]$-\left(x\:+\:2\right)^2\:+\:1\:=\:4x\:+\:9[/tex]
[tex]$-x^{2}-4 x-3=4 x+9[/tex]
Subtract 9 from both sides, we get
[tex]$-x^{2}-4 x-3-9=4 x+9-9[/tex]
Simplifying the equation, we get
[tex]$-x^{2}-4 x-12=4 x[/tex]
Subtract 4x from both sides
[tex]$-x^{2}-4 x-12-4 x=4 x-4 x[/tex]
[tex]$-x^{2}-8 x-12=0[/tex]
Solve with the quadratic formula
[tex]$x_{1,2}=\frac{-(-8) \pm \sqrt{(-8)^{2}-4(-1)(-12)}}{2(-1)}[/tex]
[tex]$\sqrt{(-8)^{2}-4(-1)(-12)}=4[/tex]
[tex]$x_{1,2}=\frac{-(-8) \pm 4}{2(-1)}[/tex]
Separate the solutions
[tex]$x_{1}=\frac{-(-8)+4}{2(-1)}, x_{2}=\frac{-(-8)-4}{2(-1)}[/tex]
[tex]$x=\frac{-(-8)+4}{2(-1)}=-6[/tex]
[tex]$x=\frac{-(-8)-4}{2(-1)}= \quad-2[/tex]
The solutions to the quadratic equation are x = -6, x = -2
From the above equation [tex]y =4x+9[/tex],
substitute the value of x, then we get
Put, x = -6 then y = 4(-6) + 9 = -15
Put, x = -2 then y = 4(-2) + 9 = 1
The system of equations exists (–2, 1) and (–6, –15).
Therefore, the correct answer is (–2, 1) and (–6, –15).
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Answer:
(–2, 1) and (–6, –15)
Step-by-step explanation:
flvs testing (i am not completely sure btw)
just substitute that into a last equations (seperatly if you understand=== -2 and 1 as x and y; -6 and -15 as x and y)
please help if u can! greatly appreciated
don't answer if u dont know PLEASE
a. log₈8 = 1
b. log₇6/5
c. log₉3¹
The solution to the problem are1. log₈ 2 * 4 would produce an integer
= log₈8 = 1
The output is an integer
2. log₇6/5 would give us an irrational number
= log₇1.2
This would give us an irrational number
3. log₉3¹ would give us a rational number
= log₉9^[tex]^\frac{1}{2}[/tex] = 1/2 log⁹9
= 1/2
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