a) The ratio system that models this situation which has an equation.
0.20 m + 1 (5 m) = 0.60 x (5)
0.80 m + 0 (5 m) = 0.40 x (5)
b) The system solution is:
m = 2.5 lb
p = 5-m = 2.5 lb
This is a mixing issue.
Mixture A of 20% peanuts + 80% almonds
Let's call the 100% peanut mixture B and the mixture C of 60% peanuts + 40% almonds
Adding mixture A and mixture B together gives mixture C, so we know that the pounds of mixture A and mixture B is 5 lb.
Let m be the amount in pounds of the 20% peanut and 80% almond mixture or mixture A
When 5-m = p is the amount of mixture B in pounds.
The system of equations that models this situation is, therefore:
0.20 m + 1 (5 m) = 0.60 x (5) ...... (1)
0.80 m + 0 (5 m) = 0.40 x (5) ...... (2)
Solving any of the above equations we find the value of m = 2.5 lb
Amount of mixture A in pounds = 2.5 lb
Amount of mixture B in pounds = 5-2.5 = 2.5 lb
The system solution is:
m = 2.5
p = 2.5
So, we can make 5 lbs of mixture C (60% peanuts + 40% almonds) from 2.5 lbs of mixture A (20% peanuts + 80% almonds) and 2.5 lbs of mixture B (100% peanuts).
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Solve #19 and show explanation
The next equation will be 6²-4²=2×10.
Here, we have given three equations and we have to find out the next equation.
The first three equations are like this
1. 3²-1²=2×4
2. 4²-2²=2×6
3. 5²-3²=2×8
Now,
As from the equation
On the L.H.S. we can see that every time it is creating a sequence
Like, every time it is subtracting square value of the one’s from the another number’s square
Which is the value we got from adding 2 in first value.
And on the R.H.S.
We can say that every time 2 multiplies with the next even number than the previous one
So,
The last equation was 5²-3²=2×8
Therefore,
The next equation will be
6²-4²=2×10
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Match the reasons to the statement ( will mark brainiest if optional)
Match the reasons to the statements.
a) Reflexive Property
b) Angle Congruence Postulate
c) Definition of Supplementary
d) Segment Addition Postulate
e) Definition of Right Angle
f) Symmetric Property
g) Substitution Property of Equality
h) Definition of Complementary
i) Segment Congruence Postulate
j) Angle Addition Postulate
k) Linear Pair Postulate
The reasons for the possible congruency statements obtained from a similar question on the website are as follows;
Statement [tex]{}[/tex] Reason
7. ∠BAD ≅ ∠CAD
[tex]\overline{AD}[/tex] ≅ [tex]\overline{AD}[/tex] ⇒[tex]{}[/tex] Reflexive property
8. ∠2 ≅∠3
m∠2 = m∠3 ⇒ [tex]{}[/tex] Angle congruency postulate
9. [tex]\overline{BE}[/tex] ≅ [tex]\overline{CE}[/tex]
[tex]\overline{DE}[/tex] ≅ [tex]\overline{AE}[/tex]
[tex]\overline{BE}[/tex] = [tex]\overline{CE}[/tex] [tex]{}[/tex] ⇒ Segment Congruence Postulate
[tex]\overline{DE}[/tex] = [tex]\overline{AE}[/tex] [tex]{}[/tex] ⇒ Segment Congruence Postulate
10. AE + BE = AB [tex]{}[/tex] ⇒ Segment Addition Postulate
11. [tex]\overline{AB}[/tex] ≅ [tex]\overline{DE}[/tex]
[tex]\overline{DE}[/tex] ≅ [tex]\overline{AB}[/tex] [tex]{}[/tex] ⇒ Symmetric property
What are congruent geometric figures?Geometric figures are congruent if their shape and or size are the same.
Reflexive property of congruency
The reflexive property of congruency states that a shape is congruent to itself.
Angle congruency postulate
The angle congruency postulate states that if the measure of two angles are the same, then they are congruent
Segment congruency postulate
The segment congruency postulate states that if the length of two segments are the same, then the segments are congruent
Segment Addition Postulate
The segment addition postulate states a point B is located on a segment AC if and only if AB + BC = AC
Symmetric property of congruency
The symmetric property congruency states that if a geometric figure, A, is congruent to another geometric figure, B, then B is congruent to A
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Lannie has 5 1/2 cups of chocolate chips. She needs 1 3/4 cups to make one batch of chocolate
chip cookies. How many batches of chocolate chip cookies can she make?
Has 5 1/2 cups or 11/2
Needs 1 3/4 or 7/4
Divide how much she has by how much she needs
(11/2) / (7/4)
Is also the same as
(11/2) * (4/7)
Which equals
= 44/14
= 22/7
or 3 1/7
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
A line that represent the "rise" and the "run" of the line is shown in the image attached below. Also, a slope of this line in simplest form is equal to 0.25.
How to determine the slope of a line?Mathematically, the slope of a line is also referred to as pitch or gradient and can be calculated by using this formula:
Slope, m = V/H
Where:
V represents the rising vertical distance (rise) of an object.H represents the horizontal distance (run) an object runs through.From the graph of this line, we would choose the following data points to represent both the rise and run:
Rise (x, y) = (-5, 0)
Run (x, y) = (7, 3)
Substituting the selected data points into the slope formula, we have;
Slope (pitch), m = (3 - 0)/(7 - (-5))
Slope (pitch), m = (3 - 0)/(7 + 5)
Slope (pitch), m = 3/12
Slope (pitch), m = 0.25
At point (-5, 0), the equation of this line would be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the data points.Substituting the parameters into the formula, we have;
y - 0 = 0.25(x - (-5))
y - 0 = 0.25(x + 5)
y = 0.25x + 1.25
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How do you find the margin of error for two samples?
Answer:
Step-by-step explanation:
The margin of error is obtained by multiplying the standard error by t*.
The margin of error can be calculated in two ways, depending on whether you have population parameters or sample statistics:
Margin of error (parameter) = critical value x population standard deviation Margin of error (statistic) = Critical value x Sample standard error
What is a margin of error?A margin of error is a statistical metric that accounts for the difference between actual and projected survey results in a random sample.
In layman's terms, the margin of error measures the degree of unpredictability in data and research results. The margin of error formula is calculated by multiplying a critical factor. The result is then divided by the square root of the sample's number of observations.
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The Book Club purchased a bundle of 12 books for $95.40. Calculate the unit rate per book.
Answer: $7.95
Step-by-step explanation:
95.40/12
= $7.95
Answer:
unit rate per book
= $95.40 ÷ 12 books
= $7.95 per book
How do I work out this question. Complete 24 : 8 = 3 : ?
The complete ratio is24:8=3:1.
What is ratio?
By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part to part ratio, whereas the second is a part to whole ratio. The relationship between two separate entities or organisations is shown by the part-to-part ratio. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio describes how one group compares to another. For instance, five people enjoy reading books out of every ten persons. Since the ratio of the component to the total is 5:10, 5 out of every 10 persons enjoy reading.
Here the given ratio 24:8=3:?
Let us take missing part as x then,
=> 24:8=3:x
=>24/8=3/x
=>x = 3*8/24
=> x=1
Hence the complete ratio is 24:8=3:1
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Rachel has 79 books in her collection. The average size
of each book is shown below. She wants to buy shelves
for her book collection. Each shelf is 34.5 inches wide
and costs $12.95. How much will it cost Rachel to shelve
her book collection? Explain how you found your
answer.
1.5 in.
9.2 in.
6 in.
The amount it would cost Rachel to shelve her book collection is $51.80.
What is the cost ?The first step is to determine the total width of the 79 books in the collection.
Total width = width of one book x total number of books
Total width = 1.5 x 79
Total width = 118.50 inches
The second step is to calculate the number of shelves that would be needed for the book collection.
Number of shelves that would be needed = total width of the collection / width of one shelf
Number of shelves that would be needed = 118.50 / 34.50
Number of shelves that would be needed = 3.4 ≈ 4
Total cost to shelve the book collection = cost of one shelf x total number of shelves needed
Total cost to shelve the book collection = 4 x $12.95 = $51.80
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This square root equation has 2 solutions. What is the extraneous solution?
2x+29−−−−−−√−7=x
Enter your answer in the box.
x =
Answer:
See below
Step-by-step explanation:
Sqrt(2x + 29) - 7 = x <===answering this version
add 7 to both sides to get
sqrt(2x+29) = x+7 square both sides
2x+29 = x^2 + 14x + 49 simplify
x^2 +12x + 20 = 0 factor
(x+10)(x+2) = 0 shows x can be -10 or -2
sub in these values in the original equation to find only the answer
x = -2 works then the answer x = -10 is extraneous answer
Q10
What is the value of angle a?
a
25°
105°
Answer:
Assuming this is a triangle, angles would equal up to 180 degrees
Step-by-step explanation:
105 + 25 = 135
180 - 135 = a, a = 45 degrees
Kayla is a basketball player who makes 50 of her 2 point shots and 20 of her 3 point shots find Kayla expected value for a 2 point shot
Kayla's expected value for a 2- point shot is 1 point.
What is expected value?
The expected value, also known as expectation, expectancy, arithmetical expectation, mean, average, first or moment, is a generalization of the weighted average in the field of probability theory. Informally, the estimation is the arithmetic mean of a significant number of values of a random variable that were independently chosen. A weighted average of all potential outcomes constitutes the expected value of the a random variable with such a finite number of outcomes. When there is a continuum of potential outcomes, integration defines the expectation. The expectation is provided by Lebesgue integration in the measure theory-based axiomatic foundation for probability.
Sol- The expected value is calcuated using the formula:
EV= x.P(x)
where x is the weight/value of the event, and P(x) is the probability of the event occurring.
For a 2-point shot, we have:
X=2
P(x) = 50/100 = 0.5
There for the expected value will be -
EV = 2×0.5 = 1
Thus,
The expected value will be 1 point.
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Question 10
Three students in the Math Club are analyzing the expressions (10x+8) and (x+13) + 3(x+5) for all values of x. Each student
claims the expressions are related according to the results in the table. Which student is correct?
Student 1 (10x+8)
Student 2(10x +¹8) >
Student 3 (10x+8)
=
<
Student Select Choice is correct.
-(x+13) + 3(x+5)
-(x+13) + 3(x+5)
-(x+13) + 3(x+5)
1/4(10x+8)= -(1/2x+13) + 3(x+5) being examined by three Math Club members for all possible values of x.
Given that,
The formulas 1/4(10x+8) and -(1/2x+13) + 3(x+5) are being examined by three Math Club members for all possible values of x. According to the findings in the table, each student asserts that the expressions are connected.
We have to find which student is right.
Take the
1/4(10x+8) = 10/4x+8/4 = 5/2x+2
-(1/2x+13) + 3(x+5) = -1/2x-13+3x+15 = 5/2x+2
So, 1/4(10x+8)= -(1/2x+13) + 3(x+5)
Therefore, 1/4(10x+8)= -(1/2x+13) + 3(x+5) being examined by three Math Club members for all possible values of x.
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Solve x² - 4x+1=0.
O x=2±2√5
O x=4± √√3
O x=2± √√3
Ox
x=-2± √3
Answer: x=2±√3
Step-by-step explanation:
[tex]\displaystyle\\x^2-4x+1=0\\\\ax^2+bx+c=0\\\\a=1\ \ \ \ \ b=-4\ \ \ \ \ c=1\\\\D=b^2-4ac\\\\D=(-4)^2-4(1)(1)\\\\D=16-4\\\\D=12\\\\\sqrt{D} =\sqrt{12}\\\\\sqrt{D}=\sqrt{3(4)} \\\\\sqrt{D}=2\sqrt{3}\\\\ Hence,\\\\x=\frac{-bб\sqrt{D} }{2c} \\\\x=\frac{-(-4)б2\sqrt{3} }{2(1)} \\\\x=\frac{4б2\sqrt{3} }{2} \\\\x=\frac{2(2б\sqrt{3}) }{2} \\\\x=2б\sqrt{3}[/tex]
The value of solution of equation is,
⇒ x = (2 ± √3)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
Quadratic equation is,
⇒ x² - 4x + 1 = 0
Now, We can simplify as;
⇒ x² - 4x + 1 = 0
⇒ x = - (-4) ± √(-4)² - 4×1×1 / 2
⇒ x = (4 ± √16 - 4) / 2
⇒ x = (4 ± √12) / 2
⇒ x = (4 ± 2√3) / 2
⇒ x = (2 ± √3)
Thus, The value of solution of equation is,
⇒ x = (2 ± √3)
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3 4 5
Hannah travels 5 times as many minutes to work as Raoul does. Together, they travel for 48
minutes. How many minutes does Hannah travel? Select the model that represents the
problem and complete the equation to solve.
A
B
12
Hannah m
Raoul m
Hannah
Raoul
xm = 48
Hannah travels
E
m
m
E
E
E
minutes to work.
m
m
Hannah travel for 40 minutes when Hannah travels 5 times as many minutes to work as Raoul does. Together, they travel for 48 minutes.
Define equation.In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.
Given,
Let Raoul travel in minutes be x
So, Hannah travel in minutes will be 5x
Together, they travel for 48 minutes.
Equation:
x + 5x = 48
6x = 48
x = 8
Hannah travel in minutes will be 5x.
Total travel by Hannah:
5(8)
40
Hannah travel for 40 minutes when Hannah travels 5 times as many minutes to work as Raoul does. Together, they travel for 48 minutes.
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√ 4(x+5)² - 130 = 0 , please solve
Answer:
x = 60, -70
Step-by-step explanation:
Let's move the constant (-130) to the right by adding it to both sides.
[tex]\sqrt{x} 4(x+5)^{2} =130[/tex]
Now, we can rewrite the equation as (since the square root and square cancel):
2 × | x + 5 | = 130
To get rid of the 2 multiplication, we can divide both sides by 2:
| x + 5 | = 65
This leaves us with 2 equations:
x + 5 = 65
x + 5 = -65
Simplify.
x1 = 60
x2 = -65
I need to know the z-score to percentile of 1
The z-score to percentile of 1 = -2.326
In this question, we need to find the z-score to percentile of 1
We know that a Z-scores is a normalized score that used to compare values relative to their population. z-score represents a specific location in the normal distribution, so that there is a certain area that is to the left of that z-score. The percentile associated to a z-score is nothing but the area to the left of that z-score.
the z-score to percentile of 1 = -2.326
Therefore, the z-score to percentile of 1 = -2.326
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2x + y = 4
x - y = 2
Value of x is 2 and y is 0 of the equations 2x + y = 4 and x - y = 2.
Define equation.A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
Given,
Equation:
2x + y = 4
x - y = 2
From equation 2,
x = 2 + y
Equating in equation 1,
Using substitution method,
2(2+ y) + y = 4
4 + 2y + y = 4
3y = 0
y = 0
x = 2 + y
x = 2+ 0
x = 2
Value of x is 2 and y is 0 of the equations 2x + y = 4 and x - y = 2.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer: 1: Congruent angles
2: Corresponding Angles
3: 7
Step-by-step explanation:
I'm not entirely sure if I got all of these correct due to the fact I'm not the best when it comes to math, but when I searched the word bank options and looked at the images, I made sure they looks the most similar.
The length of a rectangle is three times it’s width. The area of the rectangle is 108cm power of 2 what is its perimeter
The perimeter of the rectangle with area of 108 cm is 48 cm.
How to find the perimeter of a rectangle?The perimeter of a rectangle is the sum of the whole sides of the rectangle. A rectangle is a quadrilateral with opposite side equal to each other.
Therefore,
area of a rectangle = lw
where
l = side lengthw = widthTherefore,
l = 3w
108 = 3w(w)
108 = 3w²
w² = 108 / 3
w = √36
w = 6
Hence,
length = 3(6) = 18
Therefore,
perimeter of the rectangle = 2(l + w)
perimeter of the rectangle = 2(18 + 6)
perimeter of the rectangle = 2(24)
perimeter of the rectangle = 48 cm
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pie charts help is greatly apprieciated
Answer:
Brown 180°
Ginger 84°
Blonde 96°
Step-by-step explanation:
Brown 360 x 15/30 = 180
Ginger 360 x [tex]\frac{7}{30}[/tex] = 84
Blonde 360 x [tex]\frac{8}{30}[/tex] = 96
Morris’s family is selling their house. They want to have
$150,000 after paying 6% commission to the realtor. What
should be the sale price of the house?
Sale price of the house should be $141509
Amount = $150000
Commission% = 6 %
By formula
Selling price x commission rate = commission paid
SP × 6% = commission paid
(6·SP)/100 = commission paid …. (1)
Again by formula
Selling price – commission paid = net amount to seller
SP - (6·SP)/100 = 150000 (from equation 1)
SP ( 1 - 0.06) = 150000
SP = 141509.43 ≈ 141509
$141509 should be the sale price of the house.
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What is an equation of the line that passes through the point (-6,-7)(−6,−7) and is perpendicular to the line 6x+5y=306x+5y=30? math
The equation of the line that passes though the point (-6,-7) and is perpendicular to the line 6x + 5y = 30 is y = (5/6)x -2 .
In the question ,
it is given that
the required line is perpendicular to the line 6x + 5y = 30 ,
rewriting the line we get
5y = -6x + 30
y = (-6/5)x + 6
the slope of perpendicular is -6/5 ,
the slope of the required line will be 5/6 .
The equation of the line passing through (-6,-7) with slope 5/6 is written as
(y - (-7)) = (5/6)(x - (-6))
y + 7 = (5/6)(x + 6)
y + 7 = (5/6)x + 5
y = (5/6)x + 5 -7
y = (5/6)x -2
Therefore , the equation of the line is y = (5/6)x -2 .
The given question is incomplete , the complete question is
What is an equation of the line that passes through the point (−6,−7) and is perpendicular to the line 6x+5y=30 ?
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Do adjacency matrices have to be symmetric?
Adjacency matrices have to be symmetric. This is true.
What is an adjacency matrix?An adjacency matrix is a square matrix used to represent a finite graph in graph theory and computer science. The matrix's elements indicate whether or not two vertices in the graph are adjacent. The adjacency matrix of a finite simple graph is an a-matrix with zeros on its diagonal.
An adjacency matrix is a method of representing a graph as a boolean (0 or 1) matrix. Any graph's adjacency matrix is symmetric, for the obvious reason that there is an edge between Pi and Pj if and only if Pj and Pi have an edge (the same one).
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2. In an exponential function, f(x)= a(b)^x, it is known that f (5) = 20 and f (9) = 211. Which of the following
is closest to the value of b?
By solving a system of equations, we can see tha the value of b is 3.81
How to get the value of b?We know that we have a exponential function of the form:
f(x)= a*(b)^x
And we know that:
f(5) = 20 and f(9) = 211
Then we can write a system of equations:
20 = a*(b)^5
211 = a*(b)^9
If we take the quotient between the second equation and the first one, we get:
211/20 = (a*(b)^9)/(a*(b)^5)
211/20 = b^(9 - 5)
211 = b^4
(211)^(1/4) = b
3,81 = b
The value of b is 3.81
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How can i graph y=x+3
Answer:
The x-intercept is -3
Step-by-step explanation:
Answer:
x = -3, y = 3 ----> (-3,0) and (0, 3)
Step-by-step explanation:
Required: Find the X-intercept.
1) Let y = 0 to find the x-intercept (s):
0 = x + 3
2) Subtract 3 from both sides.
-3 = x
3) Switch sides.
x = -3
Just to find the y-intercept.
1) Let x = 0 to find the y-intercept (s):
y = 0 + 3
2) Simplify:
y = 3
Adjusted exponential smoothing forecasting includes an adjustment factor (T) which adjusts the exponential smoothing forecast for a:
Group of answer choices
a. Trend
b. Cycle
c. Seasonal Pattern
d. Random Variation
The adjustment factor (T) which adjusts the exponential smoothing forecast , does this adjustment for a. Trend.
What is the adjustment factor?A big part of the Adjusted exponential smoothing forecasting method is the use of an adjustment factor which has the purpose of adjusting the smoothing forecast for a trend.
If this trend is found, then there is a need to smoothen it out of the data so that the model is more trustworthy. It is important that this trend is removed to ensure that the forecast does not have a time bias.
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Antonia is making a cake.
She uses currants, raisins and sultanas in the ratio
currants: raisins: sultanas = 4:3:5.
The total mass of the three ingredients is 3.6 kilograms.
Calculate the mass of sultanas.
The mass of sultanas is 1.5 kilograms which were found using the given data and ratio.
What is the definition of ratio?Simply said, a ratio is a number that may be used to indicate one quantity as a fraction of another. A ratio's two numbers can only be compared if they share the same unit. To compare two objects, we utilize ratios.What are some examples of ratios?A ratio in mathematics displays the multiplicative relationship between two numbers. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio of 4:3).Given:
Ratio of currants: raisins: sultanas = 4:3:5.
The total mass of the three ingredients is 3.6 kilograms.
Let,
number of currants = 4x
number of raisins = 3x
number of sultanas = 5x
We know that,
4x + 3x + 5x = 3.6
12x = 3.6
x = 0.3
So, the mass of sultanas = 5x = 5(0.3) = 1.5
Therefore, the mass of sultanas is 1.5 kilograms which were found using the given data.
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How far is the distance from sprinkler head to ?
The distance from sprinkler head B to C is?
.B (-14,-5)
C(-14, 7)
The distance between the points B and C is 12m
What is the distance between two points?Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
for the coordinates B (-14,-5) and C(-14, 7), then x1 = -14 ,x-2= -14 , y1= -5 and y2= 7
therefore d =√((x2 – x1)² + (y2 – y1)²) = √((-14– -14)² + (-5 – 7)²)
d=√((0)² + 12²)
d=√144
d= 12m
therefore the distance between the points B and C is 12m.
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Graphing and Solving Inequalities
m-1<-3
————————➡️
-4y <-20
————————➡️
5+b>1
————————➡️
-18
————————/➡️
There are two arrows on each side. And little marks on the body of the graph. Could not paste graph. Thank you.
The Solutions for given inequalities are -2, 5, and -4
Inequalities:Inequalities are algebraic expressions in which both sides are not equal to each other. In inequality, we compare two values with signs like less than (<) (or less than or equal to), greater than (>) (or greater than or equal to), or not equal to sign(≠), etc.
Here we have three inequalities
m -1 < -3, - 4y < - 20, and 5 + b > 1
We can solve each equation and can give a graph as given below
m -1 < -3
Add 1 on both sides
=> m - 1 + 1 < -3 + 1
=> m < -2
- 4y < - 20
Divide both sides with - 4 on both sides
=> - 4y/4 < - 20/4
=> -y < - 5
Multiply with -1 on both sides
=> -1(-y) < -5(-1)
=> y < 5
5 + b > 1
Subtract - 5 on both sides
=> 5 + b - 5 > 1 - 5
=> b > -4
Therefore,
The Solutions for given inequalities are -2, 5, and -4
Learn more about Inequalities at
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If you are buying some food for a party. My food costs $130 but there is a 12% discount. If there is a 13% tax. Find the sale price I will pay?
Answer:
$129.27 Sale price Including tax
Step-by-step explanation:
Original Price - Discount = Sale Price
130 - 130(0.12) = 114.40
114.40 + 114.40(0.13) = 129.27 Include sale tax
