The equation y = 3/8x can be used to compare the number of marbles Molly uses, x, to the number of blue marbles, y, in each bag.
To calculate the number of blue marbles Molly uses, we can use the equation y = 3/8x.
To start, we need to identify the variables in the equation. In this case, x represents the number of marbles Molly uses and y represents the number of blue marbles.
Next, we can substitute in the given information. In this case, we know that 3 out of every 8 marbles are blue, so we can set y equal to 3 and x equal to 8.
This gives us the equation 3 = 3/8x. We can then solve for x by dividing both sides by 3/8 to get x = 8.
This tells us that for every 8 marbles Molly uses, 3 of them are blue.
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Who invented the number zero?
Aryabhata, the famous Indian mathematician discovered 0.
What is an Integer?Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.
The concept of zero was first developed by ancient Indian mathematicians as early as the 5th or 6th century CE. However, the actual symbol for zero (a small circle) was invented by the Indian astronomer and mathematician Brahmagupta in 628 CE.
Aryabhatta, the famous Indian mathematician discovered 'zero'. Grutsamad discovered the process of writing zeroes after figures.
Hence, Aryabhata, the famous Indian mathematician discovered 0.
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Write a recursive sequence that represents the sequence defined by the following
explicit formula:
an = -2-4(n − 1)
find the circumference of 80 cm using π ² = 3.14
Answer:
....
Step-by-step explanation:
can you provide an image if the question instead...
A water sample shows 0.03 grams of some trace element for every cubic centimeter
of water. Brianna uses a container in the shape of a right cylinder with a radius of 9.6
em and a height of 11.6 cm to collect a second sample, filling the container all the
way. Assuming the sample contains the same proportion of the trace element,
approximately how much trace element has Brianna collected? Round your answer to
the nearest tenth.
According to the solving volume of the cylinder where the Brianna has collected approximately 99.1 grams of trace element (rounded to one decimal place).
Define volume of cylinder?The cylinder has a circular base and is a three-dimensional shape. A group of circular discs placed on top of one another might be thought of as a cylinder. Consider a situation where we need to figure out how much sugar can fit inside a cylindrical box.
In other words, we want to figure out the volume or capacity of this box. A cylindrical box's capacity is essentially equal to the volume of the cylinder inside. As a result, the volume of a three-dimensional shape is determined by how much space it takes up.
The volume of the cylinder is given by the formula V = πr²h
where r is the radius and h is the height.
Substituting the given values,
we get V = π(9.6 cm)²(11.6 cm) = 3,301.57 cm³ (rounded to two decimal places).
Since the sample contains 0.03 grams of trace element for every cubic centimeter of water,
Brianna has collected approximately 0.03 × 3,301.57 = 99.05 grams of trace element (rounded to two decimal places).
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Graph the function y = 2/x-2 +1
**Please use dotted lines to indicate the vertical and horizontal asymptotes. **Please clearly indicate at least 3 (three) points on your graph. **No computer-generated graphs will be accepted
Answer:
Step-by-step explanation:
Domain: D=R-{2}
Asymptote vertical: x=2
Asymptote horizontal: y=1
Hey, I tried to graph this function, I hope you understand something here...
if i'm given a list of values and asked to graph the average and standard deviation, what kind of graph should i use
To graph the average and standard deviation of a given list of values, you should use a bar graph or a histogram.
1. Calculate the average (mean) of the given list of values.
2. Calculate the standard deviation of the given list of values.
3. Create a bar graph or histogram with two bars.
4. Label the first bar as "Average" and set its height to the calculated average value.
5. Label the second bar as "Standard Deviation" and set its height to the calculated standard deviation value.
This graph will visually represent the average and standard deviation of the given list of values.
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your recipe calls for 7 ounces of granulated sugar, but your kitchen scale only measures weight in grams. how many grams of granulated sugar will you need to measure to equal 7 ounces?
Answer:198.447
Step-by-step explanation:
just search 7 ounces to grams
c) (-1,2) m = -4
What is the equation of the line?
Answer:
Point-slope form:
[tex]y - 2 = - 4(x + 1)[/tex]
Slope-intercept form:
[tex]y = - 4x - 2[/tex]
Standard form:
[tex]4x + y = - 2[/tex]
Step-by-step explanation:
[tex]y - 2 = - 4(x + 1)[/tex]
[tex]y - 2 = - 4x - 4[/tex]
[tex]y = - 4x - 2[/tex]
[tex]4x + y = - 2[/tex]
Question
Solve the equation. Check your solutions.
∣x−7∣=∣2x−8∣
Answer:
x = 1, x = 5
Step-by-step explanation:
You want the solutions to the absolute value equation ...
|x -7| = |2x -8|
Piecewise equationEach of the absolute value functions is equivalent to a piecewise-defined function. The boundary for the pieces is the turning point of the absolute value function, where its argument is zero.
The turning points are ...
x -7 = 0 ⇒ x = 7
2x -8 = 0 ⇒ x = 8/2 = 4
This means the equivalent piecewise equation will have 3 pieces. We know the absolute value function is defined as ...
[tex]|x|=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge0\end{cases}[/tex]
If we write the equation in the form |x -7| - |2x -8| = 0, we have ...
[tex]0=\begin{cases}-(x-7)-(-(2x-8))&\text{for }x < 4\\-(x-7)-(2x-8)&\text{for }4\le x < 7\\(x-7)-(2x-8)&\text{for }7\le x\end{cases}[/tex]
x < 4The equation simplifies to ...
-x +7 +2x -8 = 0
x -1 = 0 . . . . collect terms
x = 1 . . . . . . a value in the domain. This is one solution.
4 ≤ x < 7The equation simplifies to ...
-x +7 -2x +8 = 0
15 = 3x . . . . . . . . . . add 3x
5 = x . . . . . . . . a value in the domain. This is another solution
7 ≤ xThe equation simplifies to
x -7 -2x +8 = 0
-x +1 = 0
x = 1 . . . . . . . . . not in the domain 7 ≤ x, so not a solution
The solutions are x = 1 and x = 5.
__
Check
|1 -7| = |2·1 -8| ⇒ |-6| = |-6| . . . . true
|5 -7| = |2·5 -8| ⇒ |-2| = |2| . . . . true
Both solutions check in the original equation.
Mr. Hesch has 4 stations set up in his classroom. Each station is labeled with a color: blue, purple, green, or yellow. As each student enters the classroom, they spin the spinner to decide at which station they will start. What is the probability a student spins purple?
The probability of spinning purple on the spinner is 1/4 or 25%.
What is permutation and combination?Calculating the variety of ways to select or arrange a collection of items is a key component of the probability theory concepts of permutation and combination. The key distinction between combination and permutation is whether or not order matters. Contrarily, combination refers to the variety of ways to choose a smaller subset of items from a larger collection, where the order of the items is irrelevant. For instance, there are three potential two-letter combinations if you have the letters A, B, and C: AB, AC, and BC.
Given there are 4 stations, thus he spinner is equally likely to land on any of the four colors.
The probability of spinning purple is 1/4 or 25%.
Hence, the probability of spinning purple on the spinner is 1/4 or 25%.
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a sphere has a radius of 2.7cm what is its volume to the nearest cubic centimeter
Answer:
around 82.45 cubic cm
Step-by-step explanation:
The formula for the volume of a sphere is (4/3) * pi * r^3.
Since the radius is 2.7, we can plug this into the formula to get (4/3) * pi * 19.683.
This simplifies to 26.244pi, which is around 82.45 cubic cm.
Using v^2 - u^2 =2as, find " v " when s = 21, u = 4 and a = 2.
Answer:
v = 10
Step-by-step explanation:
[tex] \dashrightarrow \: { \sf{ {v}^{2} - {u}^{2} = 2as}} \: \: \: \\ \\ \dashrightarrow \: { \sf{ {v}^{2} = {u}^{2} + 2as }} \: \: \: \\ \\ \dashrightarrow \: { \sf{v = \sqrt{ {u}^{2} + 2as} }} \\ \\ \: \: \: \: \: \: \: { \colorbox{lightblue}{substitute \: variables}} \\ \\ \dashrightarrow \: { \sf{v = \sqrt{ {4}^{2} + 2(2 \times 21) } }} \\ \\ \dashrightarrow \: { \sf{v = \sqrt{16 + 84} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\dashrightarrow \: { \sf{v = \sqrt{100} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow \: { \sf{v = 10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Round 453, 605 to the nearest 10,000
Answer:450,000
Step-by-step explanation:It becomes 450,000 thousand because anything under 5 in the ten thousands place becomes a zero and anything in front of it which is the 4 will stay the same.
6. Workers A and B, doing the same job, show the following results over a long period: A B mean time of completing job (in hours) 5 4 standard deviation (in hours) 1. 5 1. 5 a) Who appears to be more consistent in performance? b) Who is more efficient from an overall point of view?
Worker B appears to be more consistent in performance, while Worker B is more efficient from an overall point of view.
To determine who appears to be more consistent in performance, we need to compare the standard deviations of A and B. Both A and B have a standard deviation of 1.5 hours, which means that they have the same level of consistency in their performance.
To determine who is more efficient from an overall point of view, we need to compare the mean times of A and B. Worker B has a mean time of 4 hours, which is less than the mean time of Worker A (5 hours). This means that Worker B is more efficient than Worker A in completing the job from an overall point of view.
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In the figure, BC=26, EF=22. Find OD. Round to the nearest hundredth.
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{OD}\\ o=\stackrel{opposite}{11} \end{cases} \\\\\\ (13)^2= (OD)^2 + (11)^2\implies 13^2-11^2=OD^2\implies 48=OD^2 \\\\\\ \sqrt{48}=OD\implies 6.93\approx OD[/tex]
using diagonals from a common vertex, how many triangles could be formed from a 14-gon?
Using diagonals from a common vertex of a 14-gon, a total of 11 triangles can be formed.
To see why, we can apply the formula for the number of triangles formed by drawing all the diagonals from a single vertex of a polygon, which is (number of sides - 2). For a 14-gon, the formula gives us:
number of triangles = (14 - 2) = 12
However, we need to subtract one from the total because the vertex where the diagonals are drawn from is not included in any of the triangles. Therefore, the number of triangles formed by drawing diagonals from a common vertex of a 14-gon is:
number of triangles = 12 - 1 = 11
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Answer: 14-2=12
Step-by-step explanation:
The owner of the Jazz has given out 10 signed basketballs at a pre-season event. Their goal is to give out 3 basketballs each week during the season. Function b gives the total number of basketballs as a function of the number of weeks since the pre-season event.
describe four right that individuals in relationships have when they stay together
Differentiate y = 7x^4.
Therefore, the derivative of y = 7x⁴ with respect to x is dy/dx = 28x³.
What is differentiation?Differentiation is a mathematical concept that refers to the process of finding the derivative of a function. The derivative of a function is the rate at which the function changes with respect to its independent variable. In other words, it measures how quickly the output of the function is changing as the input value is changing.
The derivative of a function can be used to determine many properties of the function, such as its slope, maximum and minimum values, and whether it is increasing or decreasing. It is an important tool in calculus and is used in many fields, including physics, engineering, economics, and finance.
The process of differentiation involves applying specific rules to a given function to determine its derivative. The most common method of differentiation is using the power rule, which states that the derivative of a function raised to a power is equal to the product of the power and the function raised to the power minus one. Other rules include the product rule, the quotient rule, and the chain rule, which are used to differentiate more complex functions.
by the question.
To differentiate y = 7x⁴, we need to use the power rule of differentiation, which states that if [tex]y = kx^{n}[/tex], where k is a constant and n is a non-negative integer, then the derivative of y with respect to x is dy/dx = [tex]\frac{dy}{dx} = nkx^{(n-1)}[/tex].
Using this rule, we can differentiate y = 7x⁴ as follows:
dy/dx = 47[tex]x^{4-1}[/tex] [applying the power rule]
dy/dx = 28x³
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Which postulate proves the two triangles are congruent?
A. none
B. HL
C. SAS
D. AAS
Answer:
AAS
Step-by-step explanation:
They share the same side, and the 2 angles are the same as well and match
I need some help please
Answer:
Step-by-step explanation:
1. What is the vertex of the parabola?
Answer:
Step-by-step explanation: frost add the vertical and horizontal axis to find your nearest angle
Consider the following square pyramid:
Calculate the Volume of the pyramid.
Volume = _____ m3
The Volume of the pyramid.
Volume = 288.67 m³
As the volume of the pyramid is the amount of space enclosed inside the pyramid, the formula to find the volume of a square pyramid is given as;
Volume = (1/3) × base area × height.
Where: Base area (B) = s²
Where; s = length of the square pyramid side
And, Height (h) = perpendicular height to the base.
Substituting the given values in the formula we get;
Volume = (1/3) × s² × h
Given, s = 8.5m and h = 12m
Therefore, Volume = (1/3) × 8.5² × 12
= (1/3) × 72.25 × 12
= 288.67 m³
Thus, the volume of the given square pyramid is 288.67 m³, to the nearest hundredth of a cubic meter.
The volume of any pyramid is a measure of the total amount of space enclosed within the pyramid. If you have a pyramid of a specific shape and size, you can calculate its volume by using an appropriate formula. In this case, we have been given the length of the square pyramid side (s) and the perpendicular height (h) of the pyramid to the base. We can use the formula to calculate the volume of the pyramid.
The formula is Volume = (1/3) × base area × height.
For a square pyramid, the base area is the area of the square that forms the base. Since all four sides of the square are of equal length, the area is given as the square of the length of one of the sides. Thus, Base area (B) = s².
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Angela, the head of the office party planning committee, sent two coworkers, Kevin and Dwight, to the party store to purchase party hats and party whistles. Kevin purchased four packs of party hats and three packs of party whistles, and paid a total of $15.53. Dwight purchased three packs of party hats and four packs of party whistles, and paid a total of $13.73. When they returned to the office, Angela informed them that they were supposed to buy a total of four packs of party hats and four packs of party whistles and sent them back to the store to straighten things out. How much should they be refunded?
In T-ball, batters hit a ball that is placed on a T-shaped stand. Batter A hits the ball by swinging the bat from a resting position on his shoulder. Batter B hits the ball with the bat directly behind it. In one or two sentences, create and justify a claim about which batter will likely hit the ball the greater distance.
It is likely that Batter A, who swings the bat from a resting position on his shoulder, will hit the ball a greater distance than Batter B, who hits the ball with the bat directly behind it. This is because Batter A is able to generate more power and momentum with his swing, whereas Batter B's swing may be more limited in its range of motion and force.
4. The local grocery store wants to stock another brand of cereal that has 20% less grams of carbohydrates per serving than Tasty Oats 75% more grams of protein per serving than Cornbits. A serving size of 100 grams • How many grams per serving are not carbohydrates or protein in the new cereal? Show how you determined your answer.
The amount of grams per serving that are not carbohydrates or protein in the new cereal is 24.05 grams.
What is the amount of grams?In the preceding question, we were told that the amount of carbohydrates in both Cornbits and Tasty Oats is 700% of the amount of protein. The amount of protein is 12 grams. So, we can conclude that the amount of carbohydrates is 700% 0f 12 grams which equal 84 grams. Also, we know that there are 5 grams of protein in 45 grams of Cornbits cereal.
Now 20% less grams of carbohydrates gives us 0.8 × 84 = 67.2
while 75% more grams of protein per serving than Cornbits gives us 175% × 5 = 8.75
The number of grams per serving that are not carbohydrates or protein in the new cereal will be:
100 - 67.2 - 8.75 = 24.05.
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One angle of an isosceles triangle measures 130°. What measures are possible for the other two angles? Choose all that apply.
75 65 25 50
Answer:
25
Step-by-step explanation:
Isosceles triangle has two congruent angles.
∠ + ∠ + 130 = 180
2∠ = 50
∠ = 25
Answer:
25°
Step-by-step explanation:
In an isosceles triangle, 2 angles are equal.
The sum total of all angles in a triangle = 180
Assume unknown angle as x.
As 1 angle is already given, the equation is
130 + x + x = 180
130 + 2x = 180
2x = 50
x = 25°
How to solve a system of equations by graphing
According to the solution we have come to find that, Write the two equations in the form y = mx + b, where m is the slope and b is the y-intercept.
What is graph?In mathematics, a graph is a collection of vertices or nodes and edges, where each edge connects a pair of nodes.
To solve a system of equations by graphing, follow these steps:
Write the two equations in the form y = mx + b, where m is the slope and b is the y-intercept.
Plot the y-intercept of each equation on the y-axis.
Use the slope of each equation to find one or two more points on the line, and plot these points.
Draw a line through the plotted points for each equation.
Look for the point where the two lines intersect. This point represents the solution to the system of equations.
Check the solution by plugging in the coordinates of the intersection point into both equations. If the coordinates satisfy both equations, then the point is the correct solution.
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!NEED HELP NOW!
Triangle ABC
maps to triangle XYZ
by a rotation of 90∘
counterclockwise about the origin followed by a reflection across the line y=x.
In triangle ABC,
m∠A=45∘,
m∠B=55∘,
and m∠C=80∘.
What is the measure of ∠Y?
i have tried 350, 76, 35,14, and none of them have been right
Answer:
Hopes this helps
Step-by-step explanation:
Therefore , the solution of the given problem of triangle comes out to be the angle Y has a value of roughly 76.4 degrees.
What precisely is a triangle?
Because a triangle has four or more extra parts, it is a polygon. Its form is a straightforward rectangle. A triangle is a rectangle with the edges A, B, and C. A singular plane but instead cube are produced by Euclidean geometry when the sides aren't truly collinear. A triangular is a shape if it has three sides and three angles. Angles are the points where a quadrilateral three sides meet. A triangle's sides add up to 180 degrees.
Here,
We can determine the images of locations A, B, and C using the following method:
=> A': (-yA, xA)
=> B': (-yB, xB)
=> C": (-yC', xC')
where C' is the rotated version of location C.
We can determine the side lengths of triangular ABC using the Law of Cosines:
Assume that
=> a = BC = 2R sin(A/2) = 2R sin(45/2) 1.441R,
=> b = AC = 2R sin(B/2) = 2R sin(55/2) 1.663R, and
=> c = AB = 2R sin(C/2) = 2R sin(80/2) 2.219R.
where R represents the triangular ABC's circumradius.
Now, by turning point C 90 degrees anticlockwise with respect to the origin, we can determine the coordinates of point C':
xC' = -yC
yC' = xC
Then, to obtain the picture of point C, we can reflect point C' across the line y = x:
xC"=yC' and yC"=xC'
Again employing the Law of Cosines, we can determine the triangular XYZ's side lengths:
=> x = YZ = 2R sin(A'/2) = 2R sin(35) ≈ 1.189R
=> y = XZ = 2R sin(B'/2) = 2R sin(45) ≈ 1.414R
=> z = XY = 2R sin(C'/2) = 2R sin(55) ≈ 1.630R
where the picture angles of angles A, B, and C are A', B', and C', respectively.
Last but not least, we can apply the Law of Cosines once more to determine the size of angle Y:
cos(Y) i= t (x2 + z2 - y2)/ (2xz)
cos(Y) = 0.224 Y = 76.4 °
As a result, the angle Y has a value of roughly 76.4 degree
On a map, the distance between two towns is 4.25 inches. The map scale is 1 inch = 16 miles. What is the actual distance between the towns?
Step-by-step explanation:
4.25 inches * 16 miles / 1 inch = 68 miles
The area of a rectangle is 6x^2 + 9x, and its width is 3x. What is the length of the rectangle?
Answer:
L=2x-3
Step-by-step explanation:
A =L×W
Given,
A=6x²-9x
W=3x
Substituting into the main equation
6x²-9x=L×(3x)
3x(2x-3)=L×(3x)
divide both sides by 3x
2x-3=L
L=2x-3