By solving a system of equations, we will see that you must use 6.67 pounds of chocolate-covered almonds.
How to solve the system of equations?
First, we need to define the two variables:
x = number of pounds of the $9.99 chocolate-covered almonds used.y = number of pounds of the $5.99 chocolate-covered raisins used.If we mix that, we will get:
x*$9.99 + y*$5.99 = (x + y)*C
That equation means that the cost of the individual elements of the mixture, must be equal to the total cost of the mixture. Where C is the cost of each pound of the mixture, and we know that:
C = $8.75
y = 3
Replacing that, we get:
x*$9.99 + 3*$5.99 = (x + 3)*$8.75
Now we can solve that for x:
x*$9.99 - x*$8.75 = 3*$8.75 - 3*$5.99
x*$1.24 = $8.28
x = $8.28/$1.24 = 6.67
Then you must use 6.67 pounds of the chocolate-covered almonds.
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What is the sum of 6dm, 40mm, 2m and 10cm in meters?
Answer:
2.74 mStep-by-step explanation:
convert to meters
6 dm = 0.6 m
40 mm = 0.04 m
2 m = 2 m
10 cm = 0.1 m
sum
0.6 + 0.04 + 2 + 0.1 =
2.74 m
Answer:
2.74m
Step-by-step explanation:
Convert all values to meters.
6dm = 0.6m
40mm = 0.04m
2m = 2m
10cm = 0.1m
sum = 0.6+0.04+2+0.1
= 2.74
Zoe is painting the outside surfaces of the cylinder for an art project. Find the surface area of the cylinder. Use the formula SA = 2B + Ph. Use 3.14 for π
, and round to the nearest tenth.
PLEASE ANWSER ABOUT TO FAIL
The surface area of the cylinder is 131.88 in².
A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm
We have,
The surface area of the cylinder = 2B + P h
Where B is the base area and P is the perimeter.
B = πr² and P = 2πr
Now,
We will assume that,
The radius of the cylinder = 3 in.
The height of the cylinder = 4 in.
So,
The surface area of the cylinder.
= 2B + P h
= 2πr² + 2πrh
= 2 x 3.14 x 3² + 2 x 3.14 x 3 x 4
= 56.52 + 75.36
= 131.88 in²
Thus,
131.88 in² is the surface area of the cylinder.
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tickets for a school play have one price for students, x, and a different price for non-students, y. The system of equations shown is based on two different ticket orders in which the prices x and y are in dollars. 2x + 3y = 49 and x + 2y = 30
A. What is the first step in solving the system by substitution?
B. Solve the system and explain what your solution represents.
A) x+2y=30
x=30-2y
B) x=8, y=11 and the solutions x and y represent the prices of tickets for students and non students.
What is meant by an equation?An equation in French is defined as having one or more variables, whereas an equation in English is any well-formed formula consisting of two expressions combined with an equals sign.
Solving a variable equation includes determining which variables' values result in equality. Unknowns are the variables for which the equation must be solved, while equation solutions are the unknown values that satisfy the equality. An equation is a mathematical phrase with two equal sides separated by an equal sign. An equation is 4 + 6 = 10. We can see 4 + 6 on the left side of the equal sign and 10 on the right.
Given equations are:
2x + 3y = 49
x + 2y = 30
A) From eq 2,
x+2y=30
x=30-2y
B) x and y represents the prices of tickets for students and non students.
2(30-y)+3y=49
60-4y+3y=49
y=60-49
y=11
x=30-2y
x=30-2(11)
x=30-22
x=8
The solutions x and y represent the prices of tickets for students and non students.
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Given a mean of 34 and a standard deviation of 5. Find the following z-scores.
The z-score for the raw score of 39 is 1.The z-score for the raw score of 30 is -0.8.Z-scores measure the number of standard deviations a raw score is from the mean. A positive z-score indicates a raw score above the mean, while a negative z-score indicates a raw score below the mean.
To find the z-scores, we need to use the formula:
z = (x - μ) / σ
where:
z is the z-score,x is the raw score,μ is the mean, andσ is the standard deviation.
Let's calculate the z-scores for the given mean of 34 and standard deviation of 5.For a raw score of 39:
z = (39 - 34) / 5
z = 5 / 5
z = 1
So, the z-score for the raw score of 39 is 1.For a raw score of 30:
z = (30 - 34) / 5
z = -4 / 5
z = -0.8
The z-score for the raw score of 30 is -0.8.
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Find an equation for the nth term of the arithmetic sequence.
-13, -8, -3, 2, ...
Answer:
An = 5n-18
Step-by-step explanation:
hello :
note : the n th term of an arithmetic sequence is :
An =A1+(n-1)d ....a common difference is : d and A1 the first term
in this exercice : d = 2-(-3)=-3-(-8) =5 A1 = -13
the n th term of an arithmetic sequence is :An =-13+(n-1)(5)
An = 5n -5 -13
An = 5n-18
Complete the equation involving x. Order terms like the physical situation, and don't simplify.
A 5 foot wide painting should be centered on a 15 foot wide wall. Type the left side of an equation that can be used to determine how many feet (x) should be on each side of the painting.
Therefore, the painting should be placed 5/4 feet on each side of the wall.
In the given problem, a 5-foot wide painting should be centered on a 15-foot wide wall. We can determine the length of each side of the painting by subtracting x from each side of the wall.
Therefore, the left side of the equation can be written as:
\(15 - x - 5 - x\)
The physical situation given is that the painting is to be centered on the wall. This means that each side of the wall will have the same amount of space as the painting.
Therefore, the length of each side of the painting can be determined by subtracting x from each side of the wall. The total width of the wall is 15 feet, and the painting is 5 feet wide.
Therefore, the total length of the space on each side of the painting is 5 + x.To find the value of x, we can equate the length of each side of the painting. Therefore, the equation can be written as:
\(15 -x - 5 - x = 5 + x + x\)
Simplifying the equation, we get:
\(10 - 2x = 2x + 5\)
Solving for x, we get:
\(4x = 5x = \frac{5}{4}\)
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Gameron wants to measure a poster frame, but he only has a sheet of
paper that is 8 1/2 by 11 inches
a.
He lays the long edge of the paper along the long edge of the frame several times
and finds the frame is 4 papers long. How long is this in inches?
In feet?
b.
He lays the short edge of the paper along the short edge of the frame several times
and finds the frame is 3 papers wide. How long is this in inches?
In feet?
plsss help!
The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: The measure of the frame is 8.5 inches and 11 inches
a) if the frame is 4 papers long then we have the length of the frame as
11×4=44 inches (since he lays the paper along the edge of frame)
We know 1 inch= 0.0833 foot
Thus 44 inches= 3.66667 foot
b) Again if he lays the paper along the short edge than the width of the frame is 3×8.5=25.5 inches
∴25.5 inches= 2.125 feet
Hence, The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.
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Mark and Heather Starr are celebrating their 25th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall charges a $50 cleanup fee plus $30 per person, find the greatest number of people that they may invite and still stay within their budget
Write the quadratic equation in standard form:
3x2 – 3x = 11
Answer:
\(3x^{2} -3x-11 = 0\)
Step-by-step explanation:
Solve the two simultaneous equations.
You must show all your working.
3t+2p=15.5
5t+4p=28.5
Answer:
Given equations are,
5x+2y=−2 (1)
3x−5y=17.4 (2)
Multiply equation (1) by 5 and equation (2) by 2, we get,
5(5x+2y)=5×−2
∴25x+10y=−10 (3)
2(3x−5y)=2×17.4
∴6x−10y=34.8 (4)
Adding equations (3) and (4), we get,
31x=24.8
∴x=
31
24.8
Put this value in equation (1), we get,
5(
31
24.8
)+2y=−2
∴
31
124
+2y=−2
∴2y=−2−
31
124
∴2y=
31
−186
∴y=
31
−93
Step-by-step explanation:
Determine if the ratios are equivalent. 8/6 and 20/15
Answer:
Yes
Step-by-step explanation:
8/6 simplified is 4/3
20/15 simplified is 4/3
Choose me as smartest
I really need help with this I would be really happy happy If you could help me
as the picture say, we need to do constant/variable
the input variable i
What is the value of x?
Enter your answer in the box.
Answer:
x = 25
Step-by-step explanation:
Use Pythagoras' Theorem \(a^s+b^2=c^2\)
where a and b are the legs and c is the hypotenuse of a right triangle
\(\implies 7^2+24^2=x^2\)
\(\implies 49+576=x^2\)
\(\implies 625=x^2\)
\(\implies x=\sqrt{625}\)
\(\implies x=\pm25\)
\(\implies x = 25\) only, as distance is positive
Use Pythagorean theorem
\(\\ \rm\longmapsto x^2=24^2+7^2\)
\(\\ \rm\longmapsto x^2=576+49\)
\(\\ \rm\longmapsto x^2=625\)
\(\\ \rm\longmapsto x=25\)
20 points!! what is m∠A?
The unknown angle of the triangle is 58 degrees.
How to find the angle of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
Therefore, the unknown angle can be found using the external angle theorem.
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle
Hence,
138 = x + 80
x = 138 - 80
x = 58 degrees
Therefore, the unknown angle is 58 degrees.
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Consider the chart of LCD Television sets and population below. Round your ratio as a decimal to 6 places. Round the Owners per 100 to one decimal.
City
Number of Owners
Total Population
Ratio as decimal
Owners per 100
Indianapolis
6,245
0.90 million
New York
911,216
18.6 million
Cairo
10,598
19.1 million
Beijing
959,611
21.2 million
Tokyo
1,700,510
26.5 million
To calculate the ratio as a decimal, we divide the number of owners by the total population for each city.
For Indianapolis: Ratio = 6,245 / 0.9 million = 0.006938
For New York: Ratio = 911,216 / 18.6 million = 0.049019
For Cairo: Ratio = 10,598 / 19.1 million = 0.000554
For Beijing: Ratio = 959,611 / 21.2 million = 0.045270
For Tokyo: Ratio = 1,700,510 / 26.5 million = 0.064234
To calculate the owners per 100, we multiply the ratio by 100.
For Indianapolis: Owners per 100 = 0.006938 * 100 = 0.7 (rounded to one decimal place)
For New York: Owners per 100 = 0.049019 * 100 = 4.9 (rounded to one decimal place)
For Cairo: Owners per 100 = 0.000554 * 100 = 0.1 (rounded to one decimal place)
For Beijing: Owners per 100 = 0.045270 * 100 = 4.5 (rounded to one decimal place)
For Tokyo: Owners per 100 = 0.064234 * 100 = 6.4 (rounded to one decimal place)
Therefore, the ratio as a decimal and the owners per 100 for each city are as follows:
Indianapolis: Ratio = 0.006938, Owners per 100 = 0.7
New York: Ratio = 0.049019, Owners per 100 = 4.9
Cairo: Ratio = 0.000554, Owners per 100 = 0.1
Beijing: Ratio = 0.045270, Owners per 100 = 4.5
Tokyo: Ratio = 0.064234, Owners per 100 = 6.4
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Write a quadratic function in vertex form whose graph has the vertex (1,2) and passes through the point (3,10)
Answer:
y= 2(x-1)^2 +2
Step-by-step explanation:
a= y-2/(x-1)^2
a=10-2/ (3-1)^2 = 8/4 =2
y= 2(x-1)^2 +2
Please show me how to work out these math problems. Only the ones with stairs next them please. Thank you. Don’t understand how to work it out.
The areas of the composite figures are 36 square units, 27 square units, 66 square units, 32+2π square units and 68 square units respectively.
What are composite figures?
A composite figure is a shape that is produced from two or more fundamental shapes. Composite figures are also referred to as compound and complex shapes frequently.
Figure 1
This figure can be broken into two rectangles.
First rectangle with length 5 and width 4.
Second rectangle with length 8 and width 2 (as 6-4 is 2).
Area of rectangle= length*width
So, area of first rectangle= 5*4= 20 square units
Area of second rectangle= 8*2= 16 square units
Thus,
Area of figure= 20+16= 36 square units
Figure 2
This figure can be broken into two rectangles.
First rectangle with length 7 and width 3(as 6-3 is 3).
Second rectangle with length 2 and width 3.
Area of rectangle= length*width
So, area of first rectangle= 7*3= 21 square units
Area of second rectangle= 2*3= 6 square units
Thus,
Area of figure= 21+6= 27 square units
Figure 3
This figure can be broken into two rectangles.
First rectangle with length 12 and width 5.
Second rectangle with length 3 and width 2(as 12-(6+4) is 2).
Area of rectangle= length*width
So, area of first rectangle= 12*5= 60 square units
Area of second rectangle= 3*2= 6 square units
Thus,
Area of figure= 60+6= 66 square units
Figure 4
This figure can be broken into a rectangle and a semicircle.
Rectangle with length 8 and width 4.
Semi-circle with radius 2 ( as diameter is 4).
Area of rectangle= length*width
So, area of rectangle= 8*4= 32 square units
Area of semi-circle= 1/2πr^2
So, area of semi-circle= 1/2π(2)^2= 2π square units
Thus,
Area of figure= 32+2π square units
Figure 5
This figure can be broken into a rectangle and two squares.
Rectangle with length 10 and width 6(as 8-2 is 6).
Both squares with side 2.
Area of rectangle= length*width
So, area of rectangle= 10*6= 60 square units
Area of square= side^2
So, area of first square= 2^2= 4 square units
area of second square= 2^2= 4 square units
Thus,
Area of figure= 60+4+4= 68 square units
Hence, the areas of the composite figures are 36 square units, 27 square units, 66 square units, 32+2π square units and 68 square units respectively.
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a fruit store purchases 10000 apples. it sells of the 1/2 remaining apples per day. calculate the number of apples left.
can someone help?
Answer:
Step-by-step explanation:
The fruit store sells 10,000 apples....
it sells 1/2 apples per day......
what is half of 10,000? It’s 5,000
so, I think it’s 5,000.... I don’t know bc it does not tell how many days........
Answer:
10000 divided by 2 equals
5000 divided by 2 equals
2500 divided by 2 equals
1250 divided by 2 equals
625 which divided equals half apples
Represent the following sentence as an algebraic expression,
Where “a number " is the letter x. You do not need to simplify,
3 plus four times a number.
Answer:
4x+3
Step-by-step explanation:
First, you need to take the 4 times a number part, which gives you 4x. Then you know you need to add 3 to that, so you end up with 4x+3
arjun has to stick by his budget. his salary is $112,000 after taxes. he divides his
salary in the following ratio, 3:4:5 for savings, bills and food respectively. calculate
his spending for the different items on his budget
A company is developing packaging for a new product as shown below.
Choose all of the expressions that can be used to find the volume of the packaging.
Packaging is made up of 2 cuboids. First cuboid has length as 2 m, height as 9 m and width as 4 m. Second cuboid has length as 2 m, height as 3 m and width as 4 m.
A. (2 × 3 × 4) + (2 × 9 × 2)
B. (2 × 4 × 3) + (2 × 9 × 4)
C. (2 × 4 × 3) + (4 × 9 × 4)
D. (3 × 4 × 4) + (2 × 9 × 2)
E. (3 × 4 × 4) + (6 × 4 × 2)
Step-by-step explanation:
B and E
B-2 × 4 × 3) + (2 × 9 × 4)=96
E-3 × 4 × 4) + (6 × 4 × 2)=96
answer correct B and E
Divide: 7 5/6 ÷ 2/3 need help
To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.
Step 1: Convert the mixed number to an improper fraction:
7 5/6 = (6 * 7 + 5) / 6 = 47/6
Step 2: Multiply the improper fraction by the reciprocal of the fraction:
47/6 ÷ 2/3 = 47/6 * 3/2
Step 3: Simplify the fraction if possible:
47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12
Step 4: Simplify the fraction further, if necessary:
141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4
Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.
If the sum of x and y is 90 and y is 6 more than four times x, which of the following systems of equations could be used to solve for x and y?
A.x+y=90
x−4y=6
B.x+y=90
4x−y=−6
C.x+y=90
6x−y=−4
D.x+y=90
4x−y=6
Answer:
B
Step-by-step explanation:
x + y =90
y= 4x +6
_______
x + y = 90
4x − y = -6
The equations are \(\rm x + y = 90\) and \(\rm 4x - y = -6\). Then the correct option is B.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
The sum of x and y is 90.
And y is 6 more than four times x.
Let x and y be the numbers.
Then according to the first condition, we have
\(\rm x + y = 90\)
Then according to the second condition, we have
\(\rm y = 4x + 6\)
It can be written as
\(\rm 4x - y = -6\)
Then the equations are \(\rm x + y = 90\) and \(\rm 4x - y = -6\).
Thus, the correct option is B.
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Who can solve this?
Answer:
$1000
Step-by-step explanation:
Check answers
1000x .03= 30
1000 - 30 = 970
Find the volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0). Slices perpendicular to the x-axis are semicircles. Enter answer using exact values.
The volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0) is 25π/12 cubic units.
What is a triangle?
A triangle is a closed geometric shape that is formed by connecting three line segments. These line segments are called sides, and the points where they meet are called vertices. A triangle has three sides, three angles, and three vertices.
To start, let's graph the triangle to get a better understanding of the problem:
(0,3) *
|\
| \
| \
| \
| \
(0,0) *-----*-----> x
(5,0)
The height of this slice is given by the line from the point (x,0) to the point (0,3), which has equation y = 3/5 * x + 0. The radius of the semicircle is half the height of the slice, which is given by the equation r = 3/10 * x.
The area of a semicircle is πr²/2, so the volume of this slice is:
V(x) = π * (3/10 * x)² / 2 * dx
To find the total volume of the solid, we need to integrate this expression over the range of x values that covers the entire base of the solid, which is from x=0 to x=5:
V = ∫₀₅ π * (3/10 * x)² / 2 dx
V = π/20 * ∫₀₅ x² dx
V = π/20 * [x³/3] from 0 to 5
V = π/20 * (5³/3)
V = π/4 * (25/3)
V = 25π/12
Therefore, the volume of the solid is 25π/12 cubic units.
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Identify all of the root(s) of g(x) = (x2 + 3x - 4)(x2 - 4x + 29).
-1
1
-4
4
2 + 5i
2 - 5i
-2 + 10i
-2 - 10i
Answer:
The answer is 1, -4, 2+5i, 2-5i
Step-by-step explanation:
Answer:
B,C,E,F
Step-by-step explanation:
Edge 2020
pls help me with this
Part 1.1.1. The mean of Angel's marks is 68.5%
Part 1.1.2 The median of Angel's marks is 68.5%
Part 1.1.3 The range of her marks is 23%
Part 1.1.4 Angel's mark on the third test are 81%
Part 1.1.1:
To find the mean of her marks, we use the following formula:
Mean = Sum of marks/ Total number of subjects
= 75+80+57+62/4 = 68.5%
So, the mean of her marks is 68.5%
Part 1.1.2:
To find the median of the data we first need to arrange the data in ascending order:
So, the ordered set will be 57%, 62%, 75% and 80%
Now, using the formula for finding the median of even data set:
Median = (n/2th observation + (n/2 + 1)th observation)/2
where n is the number of observations in the data set
Median = (4/2 + (4/2 + 1))/2
= (2th obs + 3th obs)/2
= (62 + 75)/2
= 68.5%
So, the Median is 68.5%
Part 1.1.3
To find the range we subtract the lowest from the highest value from the data set
Range = Highest - lowest
= 80 - 57
= 23%
Part 1.1.4
Given average = 74.5%
Average = Sum of observations/Total number of observations
74.5 = Sum of observations/4
298 = Sum of observations
Subtracting test 1, test 2 and test 4 values to get test 3 values:
298 - 75 - 80 - 62 = Sum of observations
81 = Sum of observations
Therefore, Angel's mark on the third test is 81%
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devide 255 in the ratio 3:7:7:10
Answer:5
Step-by-step explanation:
5098
wat factor of 26 is between 4 and 26
Answer:
13
Step-by-step explanation:
cos 13 x 2 = 26
13 is a factor that is more than 4 and less then 26
The factor of the number 26 that is between 4 and 26 is 13. Factors are the numbers that can divide into a number without leaving a remainder. In this case, the factors of 26 are 1, 2, 13, and 26.
Explanation:In mathematics, a factor of a number is a number that divides into another number without leaving a remainder. In the case of the number 26, its factors include 1, 2, 13, and 26. The factor of 26 that is between 4 and 26 is 13.
To find this, you can go through the factors of 26 one by one. The factors are found by dividing 26 by all the numbers up to 26, and the numbers that give a remainder of 0 are the factors. In this case, 1, 2, 13, and 26 divide evenly into 26, and so are the factors of 26. Of these, only 13 lies between 4 and 26.
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Help
look at the picture
\(x7 - 2 \: or \: x \leqslant - 3\)