If we have 45.4 cups of batter, we can make 181 pancakes using unitary method.
What is unitary method?The unitary approach is a technique for problem-solving that involves first calculating the value of a single unit, then multiplying that value to figure out the required value.
Given Data
28 cups of batter to make 112 pancakes
To make 1 unit
28 cups of batter = 112 pancakes
1 cup of batter = 4 pancakes
If we have 45.4 cups of batter, we can make,
1 cup of batter = 4 pancakes
45.4 cup of batter = 45.4(4)
45.4 cup of batter = 181 pancakes ( approximately )
If we have 45.4 cups of batter, we can make 181 pancakes using unitary method.
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The carnival is in town and has a game where players try to throw darts at a rectangular target. The length of the target is 2 centimeters shorter than twice the width. If the perimeter of the target is 20 centimeters, find the dimensions of the target.
The length of the target is 4cm and the width of the target is 6cm.
What are the dimensions of the target?A rectangle is an object that has four sides and four right angles. The sum of angles in a rectangle is 360 degrees. The perimeter of a rectangle is the distance round the rectangle.
Perimeter = 2( length + width)
Length = w - 2 Width = w20 = 2(w - 2 + w)
20 = 2(2w - 2)
20 / 2 = 2w - 2
10 = 2w - 2
10 + 2 = 2w
12 = 2w
w = 12/2
w = 6
Length = 6 - 2 = 4
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Graph H(x) =|x+5| and t(x)=|2x+5|
The graph of the function H(x) = "x+5" and the graph of the function t(x) = "2x+5" are displayed in the picture that is attached below.
This is further explained below.
What is Graph?Generally, The set of ordered pairings that satisfy the condition [tex]"\displaystyle f(x)=y"[/tex] is the graph of the function f.
These pairings, which are Cartesian coordinates of points in two-dimensional space and hence constitute a subset of this plane, are found under the usual scenario in which both x and f(x) are real values.
In conclusion, The Graph of the function H(x) =|x+5| and t(x)=|2x+5| is given in the image attached below.
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please help me with this problem
answer:
[tex]\frac{-c-d}{d+2c}[/tex]the third one
Two similar solids are given, find the missing information. Please
step 1
Find out the scale factor
Remember that
If two figures are similar, then the ratio of their volumes is equal to the scale factor elevated to the cubic
so
Let
s ----> scale factor
s^3=11,000/8,019
s=1.11
step 2
Remember that
If two figures are similar, then the ratio of their surface areas is equal to the scale factor squared
so
s^2=SA/1,134
s=1.11
1.11^2=SA/1,134
SA=(1.11)^2*(1,134)
SA=1,400 yd2
The answer is 1,400 square yardsA cell phone company charges $55 a month for unlimited text and $0.50 per minute for phone calls. The bill last month was $66. Write an equation to find out how many minutes for phone calls were charged on the bill. (use notes in the Schoology "Notes" folder)
we can write an equation
[tex]T=55+0.50m[/tex]where T is the total price, 55 the fixed charge, 0.5 the cost per minute and m the minutes used
if the total is 66 we must to replace T=66 and solve m
so
[tex]\begin{gathered} 66=55+0.50m \\ 0.50m=66-55 \\ m=\frac{11}{0.50} \\ \\ m=22 \end{gathered}[/tex]were charged 22 minutes on the bill
Can someone help me on these three questions? can someone solve and show me how you did it so i can understand
The graph of the function gives the type of function, (continuous or discrete function) the domain and the range as follows;
(A, 2A)
First graph;
Discrete function
Domain; {x| x = -8, -2, 3, 6}
Range; {y| y = 5, 4, -2, 7, }
Second graph
Continuous function
Domain; -4 < x < ∞
Range; 1 ≤ y < 9
(A3.A) 1. The slope of the graph is -1.5
2. The slope of the graph is 1.5
What is a function?A function is an equation defining the relationship between input and output variables
(A, 2A)
A continuous function is one in which a continuous variation in the input values produces a continuous variation in the output. Therefore, a continuous function does not have discontinuity and it has a defined output within the interval in which it is contagious
A discrete function is one that have input values and output only at specified points, such that the function does not have inputs, and therefore, outputs at certain points.
The points in the scatter plot of the first graph are separate and not linked, such that the function is not contagious between any two x–values, which gives;
The function is a discrete function
The domain, which is the set of possible x–values is; {x| x = -8, -2, 3, 6}
The range is {y|y = 5, 4, -2, 7, }
The line joining the points on the second graph, indicates that the graph has values for all input or x–values
Therefore, the function of the graph is a continuous function
The domain is; -4 < x < ∞The range is 1 ≤ y < 9(A3. A) 1. Points on the graph are:
(0, 2), (2, -1)
The slope is given by the equation;
Slope = ∆y ÷ ∆x
Which gives;
Slope = (-1 - 2)/(2 - 0) = -3/2 = -1.52. The given function is; -3•x + 2•y = -6
To find the slope, the function is expressed in the slope and intercept form, y = m•x + c, as follows;
-3•x + 2•y = -6
2•y = 3•x - 6
Therefore;
2•y = 3•x - 6
y = (3•x - 6) = 1.5•x - 3
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Can someone help with this question?✨
The equation of the line parallel to y = 4x - 2 and passes through (1, 8) is
y = 4x + 4
How to find equation for a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slope of the linesb = y-interceptTherefore, the equation of a line is parallel to y = 4x - 2 and passes through (1, 8)
Parallel lines have the same slope.
Therefore,
y = 4x + b
let's find y-intercept using (1, 8)
8 = 4(1) + b
b = 8 - 4
b = 4
Therefore,
the equation of the line is y = 4x + 4
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In an office building, 88 offices are currently being rented. This represents 80% of the total units. How many offices are there in the building?
There are offices in the building.
Answer:4
Step-by-step explanation:
2+ I5rI = 12 Solve each equation
The solution of the equation for the values of r is -2 and 2.
What is referred as the modulus function?A modulus function returns the magnitude of such a number regardless of its sign. It's also known as the absolute value function.The modulus function, signified by |x| in mathematics, gives the modulus of a real number x. It returns a non-negative value for x. The modulus but rather absolute value of the a number is also known as the number's distance from its origin or zero.For the expression
2+ I5rI = 12
Subtract both side by 2
2 + I5rI -2 = 12 - 2
I5rI = 10
Open the modulus function as;
-5r = 10+5r = 10Solve for each term
-5r = 10
Divide both side by -5,
r = 2
Now,
5r = 10
Divide both side by 5,
r = 2
Therefore, the solution of the equation is for r = -2 and 2.
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Find the P-value for a test to support the claim that less than 50% of the people following a particular diet will experience increased energy. Of 100 randomly selected subjects who followed the diet, 47 noticed an increase in their energy level.
The P-value for a test to support the claim that less than 50% of the people is 0.2743.
What is p value?The p-value is a figure that, when generated from a statistical test, indicates how likely it is that, if the null hypothesis were true, you would have discovered a certain collection of observations.
This will be illustrated thus:
Sample proportion = 47 / 100 = 0.47
Test statistics = {p} - p) / ✓ [ p( 1 - p) / n )
= ( 0.47 - 0.50) / ✓ 0.50 * 0.50 / 100)
= -0.6
p-value = P(Z < z)
= P(Z < -0.6)
This will be looked at on the distribution table. The value will be 0.2743.
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Find the area, in square units, of AABC plotted below.
C(-6,-2)
D(-7,-5) d
A(-4,-6)
B(2,-8)
Check the picture below.
so the base of that triangle is AB whilst the height of it is CD, so let's get them
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~2 - (-4)~~)^2 + (~~-8 - (-6)~~)^2} \implies AB=\sqrt{(2 +4)^2 + (-8 +6)^2} \\\\\\ AB=\sqrt{( 6 )^2 + ( -2 )^2} \implies AB=\sqrt{ 36 + 4 } \implies AB=\sqrt{ 40 }\implies \stackrel{base}{AB=2\sqrt{10}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ C(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad D(\stackrel{x_2}{-7}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ CD=\sqrt{(~~-7 - (-6)~~)^2 + (~~-5 - (-2)~~)^2} \\\\\\ CD=\sqrt{(-7 +6)^2 + (-5 +2)^2} \\\\\\ CD=\sqrt{( -1 )^2 + ( -3 )^2} \implies CD=\sqrt{ 1 + 9 } \implies \stackrel{height}{CD=\sqrt{ 10 }} \\\\[-0.35em] ~\dotfill[/tex]
[tex]A=\cfrac{1}{2}(\stackrel{b}{2\sqrt{10}})(\stackrel{h}{\sqrt{10}})\implies A=\sqrt{10}\cdot \sqrt{10}\implies A=\sqrt{10^2}\implies {\Large \begin{array}{llll} A=10 \end{array}}[/tex]
Shantel told her hired hand Warren to gather eggs from the henhouse. Warren collected 30 eggs and brought them to Shantel. Shantel inspected
them and complained that 40% of them were broken. How many of them were still good eggs?
eggs were still good.
Answer:
18 eggs are still good.
Step-by-step explanation:
If 40% was broken then 60% are still good.
30(.6) = 18
Answer: 18 eggs were not broken and considered good.
Step-by-step explanation: 30 x 40% is the amount of eggs that were broken.
30 x 60% would be the amount of eggs that were still good.
This is becuase the total percentage must add up to be 100% between good eggs and broken eggs.
30 x .60 = 18 So 18 eggs were good
30 x .40 = 12, so that was the number of eggs that were broken
You could have done this problem two ways. Either calculate the broken eggs and subtract from the total. 30-12 = 18, or you could have just calculated the correct amount from figuring the percentage of eggs that were good from the beginning.
What is an equation of the line that passes through the points (5, 0) and
-2, -3)?
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Find gradient of the line first.
Formula of gradient is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.
Gradient = (-3-0) ÷ (-2-5) = 3/7
Eqn is y = 3/7x + c
Substitute either one of the coordinates into the equation to find c.
0 = 3/7(5) + c
c = -15/7
Hence, the equation of the line is y = 3/7x - 15/7
Laura is paid only on commission. She is paid weekly and receives 1.6% of her gross sales. Last week, she had sales of $57000, $23000, $41000, $49000, and $37000. What is Laura's weekly commission?
Answer:
$3,312.00
Step-by-step explanation:
If we add up her sales we get 207,000
We multiply that by .016 to get $3,312.00
4 1/3 — 2 7/9
Please help quick
Answer: 1 2/3 or 5/3
Step-by-step explanation: if you change 4 1/3 to a different denominator of 9, you will get 4 3/9. Then, you will do 4 3/9-2 7/9 which equals 1 2/3.
Joanne and her friends went on a hiking vacation to the national park. They
covered 2 miles on the first day. They went on a 4-mile hike and 8-mile hike on
day 2 and day 3, and the hiking distance continued to increase in a geometric
sequence. How many miles did Joanne and her friends hike on the 4th day?
Answer: 16 miles
Step-by-step explanation:.
Can anyone explain this?
Answer:
Using a class size of 6.
Range = Highest value - Lowest value = 100 - 1 = 99
No. Of class = range/class size = 99/6 = 16.5 ~ 17/classes.
Upper-class limit of class (1) = Lower class limit of class (1) + class size - D
=> 1 + 6 - 1 = 7 - 1 = 6
.: UCL1 = 6
The table is shown below:
What is 2M?
M=[3 5
-4 0]
The value of matrix 2M is [tex]\left[\begin{array}{ccc}6&10\\-8&0\\\end{array}\right][/tex]
What is matrix ?A matrix is a collection of numbers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the numbers, which are referred to as its elements. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics. The representation of rotations and other picture changes has been accomplished using matrices, which have significant uses in computer graphics.
How to do Matrix Multiplication ?Multiplication of matrices, often known as matrix multiplication, is one of the operations that can be carried out on matrices in linear algebra. If the two matrices given, A and B, are compatible, then matrix A and matrix B can be multiplied. The binary operation of multiplying matrices produces a matrix from two input matrices.
M = [tex]\left[\begin{array}{ccc}3&5\\-4&0\\\end{array}\right][/tex]
2M = 2 [tex]\left[\begin{array}{ccc}3&5\\-4&0\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}6&10\\-8&0\\\end{array}\right][/tex]
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Which Macabacus add-in feature automatically calculates the column totals in the data table and inserts them into the column chart as displayed on the right?
Answer:
Yes
Step-by-step explanation:
Answer: Charts -> Stacked Totals -> Stacked Bar Totals
Step-by-step explanation:
after filling in in Macabacus the only add in feature that puts totals is stacked bar
PLEASE HELP ME WITH THIS
The simplified form of the given expression is x + a - 4
Simplifying an ExpressionFrom the question, we are to simplify the given expression
From the given information, we have that
g(x) = x² - 4x,
Now,
We are to simplify
[tex]\frac{g(x)-g(a)}{x -a}[/tex]
First, we will determine g(a)
From the given function,
g(x) = x² - 4x
∴ g(a) = a² - 4a
Thus,
[tex]\frac{g(x)-g(a)}{x -a}[/tex] becomes
[tex]\frac{x^{2} -4x-(a^{2}-4a)}{x -a}[/tex]
[tex]\frac{x^{2} -4x-a^{2}+4a}{x -a}[/tex]
[tex]\frac{x^{2} -a^{2} -4x+4a }{x -a}[/tex]
Factoring
[tex]\frac{(x+a)(x-a)-4(x-a) }{x -a}[/tex]
Further factorization
[tex]\frac{(x-a)((x+a)-4) }{x -a}[/tex]
Dividing
((x +a) -4)
x + a - 4
Hence,
The simplification gives x + a - 4
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1) Is it possible to end up with two different prime factorizations for a number, or will you always end up with the same list of prime factors?
2) What was true about all of the numbers in the final lists of factors? Why?
3) Can two different numbers have the same prime factorization? Why or why not?
4) Explain how writing a number as a product of prime numbers is a way of representing that number.
How does knowing that the prime factorization of 40 is 2 × 2 × 2 × 5 help you know every possible factor of 40?
5) How is what you did in the Action Task related to the colour code in the Minds On Activity?
1) A prime factorization of a particular number will always give the same prime factors.
2) All the factors in the list when multiplied will give the original number.
3) No, two different numbers cannot have the same prime factorization.
4) The prime factors of 40 are 2 and 5.
1) We anticipate finding factors in prime factorization that can add to themselves to get the original number. The original number can be obtained by multiplying the remaining components together as long as the first factor can divide the quantity without leaving a remnant.
Prime factorization of the number, 15 goes thus;
15/3=5
5/5=1
3*5=15
So, all the factors multiply to give the original number.
2) Numbers that split an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal halves.
3) The collection of prime numbers that can be multiplied together to produce a given number is known as the prime factorization of that number. Because the same set of numbers must provide the same result when multiplied together, two separate numbers cannot have the same prime factorization.
4) Any number can be represented as a sum of prime numbers using prime factorization. A number with exactly two elements, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2 3 3. Here, the two main elements or prime factors of 18 are 2 and 3.
The prime factorization of 40 is :
40 = 2 × 2 × 2 × 5
Hence, the prime factors of 40 are 4 and 5.
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A plant biologist studies the height of sunflowers. He measures a large sample of sunflowers and creates a probability distribution. The distribution is normal in shape with mean 112 cm and standard deviation 16 cm.
What is the probability (approximately) that a sunflower will be less than 136 cm tall?
Enter a number in decimal form, e.g. 0.68, not 68 or 68%.
The probability that sunflower will be less than 136 cm tall is 0.9332.
How to calculate the probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
From the information, the biologist measures a large sample of sunflowers and creates a probability distribution and the distribution is normal in shape with a mean 112 cm and a standard deviation 16 cm.
It should be noted that the following can be deduced:
Mean = 112
Standard deviation = 16
Sunflower should be less than 136. This will be x < 136.
Therefore, the probability will be;
P(X < 136)
= P(Z < [(number - mean) / standard deviation)]
= P(Z < [136 - 112)/16]
= P(Z < 1.50)
= 0.9332
It should be noted that the probability is gotten by looking at the value of x in the z table.
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grade 12 mathematics
The value is =[tex]\frac{-73}{22}[/tex]
What is limit ?The values that a function approaches for the specified input values are known as limits in mathematics. Limits are essential to calculus and mathematical analysis because they help define concepts like integrals, derivatives, and continuity. It's employed in the analysis process and always has to do with how the function behaves at a specific moment. In the idea of the limit of a topological net, the limit of a sequence is further generalized and connected to the limit and direct limit in the theory category.
Given That : [tex]\lim_{x \to \33} \frac{(Fx)^{3}-3x }{2x^{2} -f(x)}[/tex] and f(x)= -4
[tex]\lim_{x \to \33} \frac{(Fx)^{3}-3x }{2x^{2} -f(x)}[/tex]
F(x)= -4
=[tex]\frac{-64-9}{18+4}[/tex]
=[tex]\frac{-73}{22}[/tex]
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what is the slope of 10x + 5y = 30
Answer:
[tex]y=-2x+6[/tex]
So, the slope is -2.
Step-by-step explanation:
Solve the literal equation for y and use the slope value formed.
[tex]10x+5y=30\\5y=-10x+30\\\frac{5y}{5}=\frac{-10}{5}x+\frac{30}{5}\\y=-2x+6[/tex]
So, according to [tex]y=mx+b[/tex], the slope is -2 where m is the slope.
Answer:
i swear your going to give a head ack i told you the answer
Step-by-step explanation:
Let f(x)=x^2−4 and g(x)=16−x. Perform the composition or operation indicated. (fg)(1)
Answer
The answer would be -45.
Step-by-step explanation:
I linked how I got this answer in the image. I hope this helps :)
Please help I’ll mark you as brainliest if correct!!!
Answer:
1710
Step-by-step explanation:
simplify | 1×10^3 + 7×10^2 + 4×10 = 1710
If “d = rt” then “t = [?] / [?].” Substitute the correct variable for the question mark in the numerator and denominator.Select one:a. r/db. d/rc. t/dd. .t/r
To solve the equation;
[tex]d=rt[/tex]To solve for t, we shall take the following steps;
[tex]\begin{gathered} d=rt \\ \text{Divide both sides by r;} \\ \frac{d}{r}=\frac{rt}{r} \\ r\text{ cancels out r on the right side of the equation;} \\ \frac{d}{r}=t \\ \text{Therefore;} \\ t=\frac{d}{r} \end{gathered}[/tex]ANSWER:
The correct answer is option (b)
[tex]\frac{d}{r}[/tex]A scale diagram of a bridge is shown below where 1cm repsents 7cm canculate the length of the brigde in real life give your answer in meters
Using the scale factor we calculate the length of the bridge to be 5.6 meters.
Scaling is a linear transformation that raises or decreases the size of objects by a constant scale factor in all directions.
The result of uniform scaling is geometrically equivalent to the original. In common usage, a scale factor of 1 is allowed, allowing congruent shapes to be categorized as comparable.A map's scale is typically defined as the distance between one unit on the map and the corresponding distance on the ground. This ratio is known as a scale factor.Scale factor equals the new shape's dimensions.The length of the bridge on the map is 80 cm .
Now the scale of the map is 1 : 7
Therefore the length of the bridge is 80 × 7 = 560 cm = 5.6 meters.
Hence the length of the bridge is 5.6 meters.
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The length of a rectangle is 21 yards. The width of the rectangle is 5 yards. What isthe area of the rectangle?
To find the area of a rectangle, we can use the following formula
[tex]Aread\text{ of a reactangle = \lparen length\rparen}\times\text{ }(width)[/tex]Therefore, to find the total area we have to multiply his length by his width.
Using the data given in the question, we know that the length is 21 yards and the width is 5 yards. Therefore we find that:
[tex]Area\text{ of the rectangle =}(21\text{ yards\rparen}\times\text{ \lparen5 yards\rparen}=105\text{ yards}^2[/tex]we conclude that the area of the rectangle is 105 yards^2.
Note that the units of the area are square units
A monument is made in the form of a right pyramid with a regular hexagon as a base. each base side is 5 meters and the slant height is 30 meters. if only the sides (and not the base) of the monument is to be covered by metal, how many square meters of metal are needed to cover the sides of the pyramid?
A. 450 m 2
B. 300 m 2
C. 75 m 2
D. 150 m 2
450 m² of metal are needed to cover the sides of the pyramid.
The correct answer is an option (A)
In this question, a monument is made in the form of a right pyramid with a regular hexagon as a base. each base side is 5 meters and the slant height is 30 meters.
If only the sides (and not the base) of the monument is to be covered by metal, we need to find the amount of metal needed to cover the sides of the pyramid.
Since the base of the pyramid is hexagon, there are 6 triangular sides of the pyramid.
We need to find the area of 6 triangular surfaces.
The base of the triangle b = 5 meters and the height of the triangle is the slant height of the pyramid.
h = 30 meters
So, area of the one triangular surface would be,
A1 = 1/2 × b × h
A1 = 1/2 × 5 × 30
A1 = 5 × 15
A1 = 75 square meters
And the area of the 6 triangular surfaces would be,
A = 6 × A1
A = 6 × 75
A = 450 square meters
Therefore, 450 m² of metal are needed to cover the sides of the pyramid.
The correct answer is an option (A)
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