The response will be P(neither blue nor white) = 0, in accordance with the information provided.
In math, what is a fraction?A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, in which the both the numerator and the denominator are divided. In a simple fraction, both are integers. The numerator or decrease of a complicated fraction contains a fraction. The numerator of an appropriate fraction is less than the denominator.
The total probability of all potential outcomes must equal 1. As P(blue) and P(white) are both 1, there cannot be any other card colors. P(neither blue nor white) is therefore equal to zero.
If there are additional cards of different colors and the information provided is insufficient or inaccurate, we can also apply the following formula:
P(neither blue nor white) = 1 - P(blue) - P(white)
Assuming that there are just three possible card colors (blue, white, and another color), the following equation can be constructed using the provided data:
P(blue) + P(white) + P(another color) = 1
P(white) and P(blue) are both 1, so we have:
1 + 1 + P(another color) = 1
When we simplify this equation, we obtain:
P(another color) = -1
The presented information does not support the notion that there are merely three possible card colors, hence this is not a legitimate probability. Hence, the only viable response is.
P(neither blue nor white) = 0
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The answer is 0/1, which can be simplified to 0.
what is probability?
Probability is a measure of the likelihood or chance of an event occurring.
If P(blue) and P(white) are both 1, it means that all the cards are either blue or white.
Let's assume there are a total of n cards. Then,
P(blue) + P(white) = 1
=> Number of blue cards + Number of white cards = n
Given that P(blue) = P(white) = 1, we can conclude that there are n/2 blue cards and n/2 white cards.
Therefore, the probability of choosing a card that is neither blue nor white is the probability of choosing a card of a different color. There are no other colors given, so we can assume that there are no cards of any other color.
Hence, the probability of choosing a card that is neither blue nor white is 0.
So, P(neither blue nor white) = 0.
Therefore, the answer is 0/1, which can be simplified to 0.
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What is the value of x?
The value of x in the triangle is 2√3
What are right trianglesRight triangles are triangles with one angle measuring 90 degrees.
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
The triangle
From the triangle, we have the following equation
x/2 = 6/x
Cross multiiply the equation
So, we have the following representation
x^2 = 12
Take the square roots of both sides
So, the equation becomes
x = 2√3
Hence, the value of x is 2√3
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please help me i don't understand my homework
Answer:
The final answer is 18-2 = which is 16
Step-by-step explanation:
x =3
y =2
6(3) -2
Then do 18-2
You have to multiply 6 and 3, after that, subtract by 2
Just substitute your value in!
Answer:
16
Step-by-step explanation:
replace x with 3 and y with 2
6x - y =
6 * 3 - 2 =
18 - 2 =
16
Gauss Jordan elimination method step by step 0. 99x-0. 04y-0. 2z=4
-0. 1x+0. 97y=6
-0. 2x-0. 01y+0. 96z=3
[ 1 -0.0004 -0.00202 | 0.0404 ] [ 0 1 -0.00020828 | 6] this is the Gauss Jordan elimination method step by step of the given linear equation.
The Gauss Jordan elimination method is a systematic way of solving a system of linear equations by performing elementary row operations on an augmented matrix. The augmented matrix is formed by combining the coefficients and constants of the linear equations.
The given system of linear equations can be written in matrix form as:
[ 99 -0.04 -0.2 | 4 ]
[ -0.1 0.97 0 | 6 ]
[ -0.2 -0.01 0.96 | 3 ]
The goal of the Gauss Jordan elimination method is to transform the augmented matrix into reduced row echelon form, which is a unique form that represents the solution of the system of linear equations.
The following steps outline the Gauss Jordan elimination method to solve the given system of linear equations:
Step 1: Begin with the first column and eliminate the coefficients below the first row by using row operations.
Divide the first row by 99 to make the leading coefficient equal to 1:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ -0.1 0.97 0 | 6 ]
[ -0.2 -0.01 0.96 | 3 ]
Add 0.1 times the first row to the second row:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 0.9704 -0.000202 | 6.00404]
[ -0.2 -0.01 0.96 | 3 ]
Add 0.2 times the first row to the third row:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 0.9704 -0.000202 | 6.00404]
[ 0 -0.00018 0.960396 | 3.00808]
Step 2: Continue with the second column and eliminate the coefficients below the second row by using row operations.
Divide the second row by 0.9704 to make the leading coefficient equal to 1:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 1 -0.00020828 | 6.18377]
[ 0 -0.00018 0.960396 | 3.00808]
Add 0.00018 times the second row to the third row:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 1 -0.00020828 | 6.18377]
[ 0 0.0000324 0.96052174| 3.01998]
Step 3: Continue with the third column and eliminate the coefficients above the third row by using row operations.
Divide the third row by 0.96052174 to make the leading coefficient equal to 1:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 1 -0.00020828 | 6]
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Are all of the diagonals of a regular polygon congruent?
Yes, a regular polygon's diagonals are all congruent.
In geometry, a shape's diagonals are its building blocks. In mathematics, a diagonal is a line that connects two solids or polygons whose vertices are not next to one another's edges. In general, a diagonal connects the vertices of a form via sloping or slanting lines. Shapes with lateral sides, edges, and corners are referred to as "diagonals" in this context. Diagonals can be found in curved objects like circles, spheres, cones, and so on.
The diagonals of a square are the segments of lines joining its opposite vertices. A square is made up of two diagonals. The two diagonals of the square are parallel to one another. The diagonals of a square divide one another in half. Each diagonal divides the square into two identical, isosceles right triangles.
Yes all of the diagonal of a regular polygon is congruent , because all sides of regular shape are congurent.
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A box is subject to the forces shown in the diagram below.
5N Up
7.5N Left
7.5N Right
10N Down
Calculate the size and direction of the resultant force on the box.
Show your working.
Resultant force =?
The resultant force on the box, along with it's direction, is given as follows:
5N Down.
How to obtain the resultant force on the box?The resultant force on the box is obtained as the vector sum of all the forces in the box.
The forces are given as follows:
5N Up7.5N Left7.5N Right10N DownThe horizontal forces are the same force in opposite directions, hence the horizontal forces are of zero.
The sum of the vertical forces is given as follows:
5 - 10 = -5N.
As the sum is negative, the direction is in the down direction, hence the resultant force is of -5N down.
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Martin is x years old. Jennifer is 3 years younger than Martin. Connor is twice as old as Martin. Write an expression for Jennifer’s age.
Answer: x-3
Step-by-step explanation: if Martin's age is unknown and we have to use x for it, you could only plug in x-3 to figure out Jennifer's age. And if we have to write an expression for Connor's age it would be x*2
martin = x years
jennifer = x - 3
The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute.
Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30
Answer:
Step-by-step explanation:
The sine model is y=10 sin(1/30 t) + 30. The 30 represents default distance from the ground, and the ten is required to represent the length of the blades. Every 30 seconds, one rotation completes, so t must be multiplied by 1/30.
By first making the powers of 10 the same,
work out (3 x 10 6) + (5 × 10 7)
Give your answer in standard index form.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(3\times10^6) + (5\times10^7)}\\\mathsf{= (3\times10\times10\times10\times 10\times10\times10) + (5\times 10\times10\times10 \times 10\times10\times10 \times 10)}\\\mathsf{= (3\times 100\times100\times100) + (5\times100\times100\times100\times10)}\\\mathsf{= (3\times10,000\times100) + (5\times10,000\times1,000)}\\\mathsf{= (3\times1,000,000) + (5\times10,000,000)}\\\mathsf{= (3,000,00) + (50,000,000)}\\\mathsf{= 3,000,000 + 50,000,000}\\\mathsf{= 53,000,000}\\\mathsf{= 5.3\times10^7}[/tex]
[tex]\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{5.3\times10^7}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A coin bank in the shape of a triangular pyramid has a volume of 65 cubic inches. The bank has a height of 9.75 inches. What is the area of the base?
In response to the query, we can state that Therefore, the area of the base of the triangular pyramid is 21 square inches.
what is pyramid?A pyramid is a polygon in mathematics, formed by connecting points referred to as bases and polygonal vertices. For each hace and vertex, a triangle called a face is formed. a cone with a polygonal form. A pyramid with a floor and n pyramids has 2n edges, n+1 vertices, and n+1 vertices. Each pyramid is dual in itself. Pyramids can be seen in three dimensions. The vertex, the intersection of a pyramid's flat tri face and polygonal base, is where they come together. The base and apex are connected to form a pyramid. Triangle faces that connect to the top are formed by the edges of the base.
volume of a triangular pyramid
V = (1/3) * Base Area * Height
65 = (1/3) * Base Area * 9.75
Area = 65 / (1/3) / 9.75
Area = 21
Therefore, the area of the base of the triangular pyramid is 21 square inches.
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A brick of mass 6 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 5 cm. The spring is then stretched an additional 3 cm and released. Assume there is no air resistance. Note that the acceleration due to gravity, g, is g = 980 cm/s^2.
Set up a differential equation with initial conditions describing the motion and solve it for the displacement s(t) of the mass from its equilibrium position (with the spring stretched 5 cm).
The differential equation with initial conditions describing the motion is F = -k * (s(t) + 5) - 6g and the displacement of the mass from its equilibrium position as a function of time s(t) = (3 * r2 * e^(r1*t)) / (r2 - r1) + (3 * r1 * e^(r2*t)) / (r1 - r2)
The differential equation for the motion of the mass is given by Newton's Second Law, F = ma:
F = -k * (s(t) + 5) - 6g
where k is the spring constant, s(t) is the displacement from the equilibrium position, and g is the acceleration due to gravity. The initial conditions are s(0) = 3 and s'(0) = 0, since the spring is initially stretched an additional 3 cm and released from rest.
We can rearrange the equation to get:
s''(t) + (k/6) * s(t) = -5k/6 - g
This is a second-order linear homogeneous differential equation with constant coefficients. The general solution is:
s(t) = C1 * e^(r1*t) + C2 * e^(r2*t)
where r1 and r2 are the roots of the characteristic equation:
r^2 + (k/6) * r = -5k/6 - g
Using the quadratic formula, we get:
r1,2 = -(k/12) ± √((k/12)^2 + 5k/6 + g)
We can find the values of C1 and C2 by applying the initial conditions:
s(0) = C1 + C2 = 3
s'(0) = C1 * r1 + C2 * r2 = 0
Solving for C1 and C2, we get:
C1 = (3 * r2) / (r2 - r1)
C2 = (3 * r1) / (r1 - r2)
Substituting back into the general solution, we get:
s(t) = (3 * r2 * e^(r1*t)) / (r2 - r1) + (3 * r1 * e^(r2*t)) / (r1 - r2)
This is the displacement of the mass from its equilibrium position as a function of time.
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2. Which expression below can be simplified to 2x + 11?
A. x + x + 11
B. x + 2 + 11
C. x + 7 + 4
A. x+x+11 is the expression can be best simplified for equation 2x+11
Explain equationA statement that establishes the equivalence of two expressions is known as an equation in mathematics. It has two sides containing expressions on each, each separated by the equals symbol (=).
For example, the equation x + 2 = 5 asserts that the expression on the left side, x + 2, is equal to the expression on the right side, 5. This equation can be solved for the variable x, by subtracting 2 from both sides, to obtain x = 3, which is the value that satisfies the equation.
Given equation 2x+11
2x can be written as x+ x
So, expression can be written as
x+x+11
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Elizabeth is mountain climbing with Frank and has just climbed a 16-meter vertical rock face. Frank is standing 30 meters away from the bottom of the cliff, looking up at Elizabeth. How far away are Elizabeth and Frank?
The Pythagorean theorem
‘I’m just not sure which equation to use.”
Answer: 34
Step-by-step explanation:
based on the given conditions , formulate
[tex]\sqrt{16^2+30^2}[/tex]
x= [tex]\sqrt{(16)^2f(30)^2}[/tex]
x= [tex]\sqrt{256+900}[/tex]
x= [tex]\sqrt{11 56}[/tex]
x= 34
The attorney does not accept legal cases involving litigation that would result in less than a $45,000 fee. The attorney has the opportunity to represent a client who will pay him $175 per hour plus 25% of the settlement. What is the minimum acceptable settlement on a case on which the attorney spent 110 hours?
In linear equation, 103000 is the minimum acceptable settlement on a case on which the attorney spent 110 hours.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Let x be the amount settlement.
amount he earn from client = 175 * 110
= 19250
amount he earn from settlement = x * 25/100 = x/4
according to given condition
19250 + x/4 ≥ 45000
x/4 ≥ 45000 - 19250
x/4 ≥ 25750
x ≥ 25750 * 4
x ≥ 103000
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This is for highschool geometry
Answer:
i dont
Step-by-step explanation:
never mind sorry for bothering you! :(
Jacob is putting carpet in his house. He wants to carpet the living room, which measures 15 ft x 12 1/3 ft. He also wants to carpet the dining room, which is 10 1/4 ft x 10 1/3 ft
Jacob needs 290.92 ft² of carpet in total to cover both the living room and the dining room.
To find out how much carpet Jacob needs to cover his living room, we can multiply the length and width of the room:
15 ft x 12 1/3 ft = 15 ft x (37/3) ft = 555/3 ft²
To simplify this fraction, we can divide both the numerator and denominator by 3:
555/3 ft² = 185 ft²
So the living room requires 185 square feet of carpet.
To find out how much carpet Jacob needs to cover his dining room, we can multiply the length and width of that room:
10 1/4 ft x 10 1/3 ft = (41/4) ft x (31/3) ft = 1271/12 ft²
To simplify this fraction, we can divide both the numerator and denominator by 1:
1271/12 ft² = 105.92 ft² (rounded to two decimal places)
So the dining room requires 105.92 square feet of carpet.
To find out how much carpet Jacob needs in total, we can add the amount of carpet required for each room:
185 ft² + 105.92 ft² = 290.92 ft²
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a cable company earned 125 million in one year. the next year they earned 312.5 million dollars. estimate how many times bigger their profit was the second year compared to the first year.
Answer: The difference between 125 million dollars and 312.5 million dollars is, 187.5 Million Dollars.
3. repeated-measures and matched-subjects experiments repeated-measures experiments measure the same set of research participants two or more times, while matched-subjects experiments study participants who are matched on one or more characteristics. which of the following are true for both a repeated-measures experiment and a matched-subjects experiment when used to compare two treatment conditions? check all that apply. they both use the same t statistic. the researcher computes difference scores to compute a t statistic. the researcher must compute an estimated standard error for the mean difference score to compute a t statistic. the researcher must compute a pooled variance to compute a t statistic. for a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31. how many subjects participated in this study? 64 32 62 31 a matched-subjects experiment produced a t statistic with a df of 17. how many subjects participated in this study? 34 36 18 17
A repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31. 32 subjects participated in this study.
A matched-subjects experiment produced a t statistic with a df of 17.
34 subjects participated in this study.
Both a repeated-measures experiment and a matched-subjects experiment share the following characteristics when used to compare two treatment conditions:
1. They both use the same t statistic.
2. The researcher computes difference scores to compute a t statistic.
3. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.
For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31.
The number of subjects that participated in this study is 32 because the degrees of freedom (df) for a repeated measures experiment is calculated as (number of subjects - 1),
so 31 + 1 = 32.
A matched-subjects experiment produced a t statistic with a df of 17.
In this case,
the number of subjects that participated in the study is 34 because the degrees of freedom (df) for a matched-subjects experiment is calculated as (number of pairs - 1),
since there are two subjects in each pair, 17 + 1 = 18 pairs, which means 18 * 2 = 34 subjects.
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If you start as 2,10 and move 2 units to the left. Where will you end
what is the rate at which a car's value will decrease as its mileage goes up between 20,000 miles and 40,000 miles?
y=value of car
x=mileage
The car's value will decrease at rate of 1/5.
What is the rate at which a car's value will decrease?
Rate refers to the ratio between two quantities with different units. For example, if you travel 100 miles in 2 hours, your rate of speed would be 50 miles per hour (mph).
From the graph, we have the following:
1: At mileage (x) = 20,000 miles, value of car (y) = $12000
2: At mileage (x) = 40,000 miles, value of car (y) = $8000
Rate = (y2 - y1)/(x2 - x1)
Rate = (8000 - 12000)/(40000 - 20000)
Rate = -1/5
Thus, the car's value will decrease at rate of 1/5.
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Complete Question
Check attached image
Fill in the blanks to make the equations true. (x ....)(x ....)=x^2-4x-32
If two sides of a right triangle are 20 and 25 and the sides form a Pythagorean triple, find the third side.
The third side of the given Pythagorean triple-right-angled triangle is 32.02 units.
As per the formula pertaining to the Pythagorean triple-right-angled triangle, we have the:
h = √{(a)^2+(b)^2} .........(i),
Where, (h) = Third side of a Pythagorean triple-right-angled triangle,
(a) = First side of a Pythagorean triple-right-angled triangle = 20 units
(b) = Second side of a Pythagorean triple-right-angled triangle = 25 units
Substituting the values in equation (i), we get:
h = √{(20)^2+(25)^2} units,
or, h = √(1025) units,
or, h = 32.015 units = rounded off to 32.02 units.
Hence the third side of the given Pythagorean triple-right-angled triangle is 32.02 units.
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Put the following equation of a line into slope-intercept form, simplifying all
fractions.
6x 10y=-40
Answer:
[tex]\mbox{\large y = -\dfrac{3}{5}x - 4}[/tex]
Step-by-step explanation:
The given equation is
[tex]\mbox{\large 6x + 10y = - 40}[/tex]
The slope-intercept form of the equation of a line is
[tex]y = mx +b[/tex]
where
m = slope
b = y-intercept
Subtract 4x from both sides of [tex]\mbox{\large 6x + 10y = - 40}[/tex]
[tex]6x - 6x + 10y = - 6x-40\\\\\rightarrow \quad 10y = -6x - 40\\\\\text{Divide both sides by 10}\\\rightarrow \quad \dfrac{10y}{y} = -\dfrac{6}{10}x - \dfrac{40}{10}\\\\y = -\dfrac{6}{10}x - 4\\\\\dfrac{6}{10} = \dfrac{3}{5}\\\\\text{Equation of the line in slope-intercept form is: }\\\\y = -\dfrac{3}{5}x - 4[/tex]
The first number in a pattern is 1.95.
Each number in the pattern is formed by subtracting 0.15 from the previous number.
What is the third number in this pattern?
1.5 1.65 1.8 2.25
Answer:
1.65
Step-by-step explanation:
The first number is 1.95, to find the rest we must keep subtracting 0.15 from the previous.
1.95-0.15 = 1.8 (second number)
1.8-0.15 = 1.65 (third number)
Above, we find our answer with the 3rd number.
Please help! Parallel lines with Parallel Sequences question! Thanks
Given the above parallelogram,
1) ∠ABC = 90°
2) ∠BCD = 90°
3) ∠CDA = 90°
4) ∠DAB = 90°
To find the value of the angles, we need to first find x. Given that ∠ABC = (x+35)° on the basis of opposite angles in a parallelogram, and
∠CDA = (180-(3x-75)°
since ∠ABC and ∠CDA are opposite angles.
We can state that
(180-(3x-75)° = (x+35)° since opposite sides of a parallelogram are equal.
Simplifying the above, we can find x:
180 - (3x - 75) = 180 - 3x + 75 = 255 - 3x
Now we can substitute this expression into the original equation:
255 - 3x = x + 35
To solve for x, we want to isolate the variable on one side of the equation. Let's start by adding 3x to both sides:
255 = 4x + 35
Next, we can subtract 35 from both sides:
220 = 4x
Finally, we can divide both sides by 4 to get the value of x:
x = 55
Therefore, the solution to the equation is x = 55°.
Since x = 55°
∠ABC = (x+35)°
∠ABC = 55 + 35
∠ABC = 90°
Also, since:
∠CDA = (180-(3x-75)°)
∠CDA = 180- (165-75)
∠CDA = 90°
Since ∠DAB = (3x-75)° on the basis of alternate angles,
∠DAB = (3(55) -75)°
∠DAB = 165 -75
∠DAB = 90°
Since ∠DAB is opposite ∠BCD and Opposite angles of a parallelogram are equal, thus, ∠BCD is also 90°
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-9>2x what best describes the soltuion to this inequality
The correct option is D. Inequality. The expression -9 > 2x is an inequality, meaning it shows a relationship between two values that are not necessarily equal.
In this case, it indicates that -9 is greater than 2 times x. To solve the inequality, we would need to isolate x on one side of the inequality symbol. We can start by dividing both sides by 2, which gives us -4.5 > x. This means that any value of x that is less than -4.5 would satisfy the inequality. Therefore, the solution set for this inequality is all real numbers less than -4.5.
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Full question:
Which word BEST describes 9(2x+6y)
A Constant
B. Equation
c. Expression
D. Inequality
The scatter plot shows the average monthly temperature, , and a family's monthly heating cost, , for different months.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the monthly heating cost for a month with an average temperature of .
Note that you can use the graphing tools to help you approximate the line.
y102030405060708090100x1020304050607080901000
(a) Write an approximate equation of the line of best fit.
(b) Using your equation from part (a), predict the monthly heating cost for a month with an average temperature of .
Answer:
need brainly point
Step-by-step explanation:
A cylinder has a height of 11 millimeters and a radius of 15 millimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
The volume of this cylinder is equal to 7,771.5 cubic millimeter
How to calculate the volume of a cylinder?In Mathematics, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Since the radius of the base is 15 mm and the height of this cylinder is 11 mm, the volume of the cylinder in cubic millimeter can be calculated as follows;
Volume of a cylinder, V = 3.14 × 15² × 11
Volume of a cylinder, V = 3.14 × 2,475
Volume of a cylinder, V = 7,771.5 cubic millimeters.
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Work out the area of the rectangle using a calculator and giving your anwser in as a mixed number
The area of the rectangle is 31/3 square centimeters or 10 1/3 square centimeters as a mixed number.
To find the area of the rectangle, we need to multiply its length by its width.
First, we need to convert the mixed numbers to improper fractions:
Length = 5 1/6 cm = (6 × 5 + 1)/6 = 31/6 cm
Width = 2 2/7 cm = (7 × 2 + 2)/7 = 16/7 cm
Now, we can multiply the two fractions to get the area of the rectangle:
Area = length × width
= (31/6 cm) × (16/7 cm)
= (31 × 16) / (6 × 7) cm²
= 496/42 cm²
= 248/21 cm²
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 8:
248/21 cm² = (8 × 31)/ (8 × 3) cm²
= 31/3 cm²
= 10 1/3 cm²
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susan is making a blanket. she bought 1/3 pf a yard of material to use for the border for the blanket.susant cut the material into 4 same-size strips. what part of a whole yard is each strip
The fraction of the material that each strip represents is 1/12 of a yard.
Susan bought 1/3 of a yard of material to use for the border for the blanket. She cut the material into 4 same-size strips. The problem is asking for the part of a whole yard that each strip represents.
Since Susan has 1/3 of a yard of material and she cut it into 4 same-size strips, we can use division to find the fraction of the material that each strip represents.
Therefore, the fraction of the material that each strip represents is 1/3 ÷ 4.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 4 is 1/4, so we can rewrite the expression as:
1/3 ÷ 4 = 1/3 × 1/4
Now we can multiply the fractions:
1/3 × 1/4 = 1/12
Therefore, each strip represents 1/12 of the whole yard of material.
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A grocery store charges $14 for 20 pounds of bananas. Write an equation that gives the cost, C, of x pounds of bananas
This equation tells us that the cost of x pounds of bananas is equal to the number of pounds of bananas, x, multiplied by the cost per pound
So equation becomes C = 0.70x
We can use proportional reasoning to set up an equation to represent the cost, C, of x pounds of bananas.
We know that 20 pounds of bananas cost 14, so the cost per pound can be found by dividing the total cost by the total weight:
Cost per pound = Total cost / Total weight
Cost per pound = 14 / 20 pounds
Cost per pound = 0.70 per pound
Now, we can use this cost per pound to set up an equation:
C = cost of x pounds of bananas
x = number of pounds of bananas
Cost per pound = 0.70
So, we can write the equation as:
C = 0.70x
This equation tells us that the cost of x pounds of bananas is equal to the number of pounds of bananas, x, multiplied by the cost per pound, 0.70.
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