Answer:
a) 10/21 b) 5/21 c)1/21
Step-by-step explanation:
a) your have 7 choice and 5 or them or red, 5/7. You do not replace the red marble, so for your second draw, you now only have 6 choices and of those 6 choices only 4 of them are now red or 4/6 or 2/3. We multiple these two numbers together:
5/7(2/3) = 10/21
b) For the first draw, you have 5 red marbles available out of a total 7 marbles or 5/7. The second draw now only has 6 marbles and 2 of them or yellow to make 2/6 or 1/3 (simplified). We multiply these together.
5/7(1/3) =5/21
c) I am assuming that you are still selecting 2 marbles. The first draw would be 2/7. This time I am selecting yellow and there are only 2 choices for yellow. My next draw will only have 6 marbles and only 1 of them will be yellow, so 1/6. We multiply these together
2/7(1/6) = 2/42 or 1/21
Write the Egyptian numeral as a Hindu-Arabic numeral
Answer:
2635
Step-by-step explanation:
the first two stand for 1000
so
2000
is the first part
the second numeral stands for 100
there are 6 of them
so
600
is the second part
the third numeral stands for 10 and there are 3 of them
thus
30
is the third part
there are 5 lines so the last part is 5
so your answer is 2635
Rotate the given triangle 270° counter-clockwise about the origin.
[tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-1&[?]&[?]\\1&[?]&[?]\end{array}\right][/tex]
The rotation of the triangle [tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex] 270° counter-clockwise about the origin gives [tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point (x, y) is rotated 270° counter-clockwise about the origin, the new point is (y, -x)
The rotation of the triangle [tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex] 270° counter-clockwise about the origin gives [tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]
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3. Luke, the furniture maker, knows that he has 54 stools in stock. Some of these stools have three legs and some have four legs. Luke, however, does not know how many of each type of stool he has in stock. Since the stools are stored upside down, he only counts the number of legs to find out how many of of stool he has in stock. He counts 200 legs. each type 3.1 If the number of four-legged stools is x, write an algebraic expression for the number of three-legged stools. 3.2 Now write algebraic expressions for the number of legs that the three- legged stools have altogether as well as the number of legs that the four- legged stools have altogether. 3.3 Use your answers to Question 3.2 to write an equation in x and then determine the number of four-legged and three-legged stools in stock.
The number of number of four-legged and three-legged stools in stock is 38 and 16 respectively.
Simultaneous equationlet
number of four-legged stools = xnumber of three-legged stools = yx + y = 54
4x + 3y = 200
From equation (1)
x = 54 - y
Substitute x = 54 - y into4x + 3y = 200
4(54 - y) + 3y = 200
216 - 4y + 3y = 200
216 - y = 200
- y = 200 - 216
-y = -16
y = 16
substitute y = 16 intox + y = 54
x + 16 = 54
x = 54 - 16
x = 38
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What is the measure of angle A?
250
140
70
110
Using the angle of intersecting tangents theorem, the measure of angle A is: C. 70°
What is the Angle of Intersecting Tangents Theorem?Based on the angle of intersecting tangents theorem, measure of angle A = 1/2(the positive difference of the intercepted arcs).
Measure of one of the intercepted arcs = 250°
The second intercepted arc = 360 - 250 = 110°
Positive difference of the intercepted arcs = 250 - 110 = 140°
Measure of angle A = 1/2(140)
Measure of angle A = 70°
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Answer:
the answer is 70. hope this helps <3
Step-by-step explanation:
how tell me how you got answer 5.9 and also if you do at calculate can show me how to do pls thanks.
The steps you have are correct. I'll fill in the gap between step 2 and step 3.
[tex]0.4245 = \frac{2.5}{\text{x}}\\\\0.4245\text{x} = 2.5\\\\\text{x} = \frac{2.5}{0.4245}\\\\\text{x} = 5.8892815\\\\\text{x} = 5.9\\\\[/tex]
I multiplied both sides by x, then divided both sides by 0.4245 to isolate the variable.
With the exception of 2.5, every other decimal value mentioned is approximate.
If X-A and X-B, then…
A ZperpA
B X||Y
C A||B
From the line theorems explained below and when we apply it to the given image, we have; X║Y, A║B, Z ⊥ A
What is the transverse line theorem?The perpendicular transversal theorem states that in a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.
Now, since we are told that Line X is perpendicular to Line A, then it means that Line X is also perpendicular to line B.
The inverse of perpendicular transversal theorem states that if there are two perpendicular lines to a straight line, they're parallel to each other. Thus, it means that Line X is parallel to Line Y and similarly, line A is parallel to Line B.
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Point A is at (5, 6) on the coordinate plane. It is reflected over the y-axis to create point B. Point A is then reflected over both axes to create point C. What is the area of the triangle that results from connecting the three points?
The area of the triangle which is formed as described is; 60.
What is the area of the triangle formed?According to the task content, when Point A(5,6) is reflected over the y-axis, the point B formed is; (-5,6) and when reflected over both axis, the point C formed is; (-5,-6).
It therefore follows that the length of segments AB and BC which represents the base and height of the triangle formed are; 10 and 12 respectively.
Therefore, the area of the triangle is; (1/2) × 10 × 12 = 60.
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Given the volume is 105 inches³ for an 8 pound bowling ball, find the radius of the bowling ball,
to the nearest hundredth of an inch.
Answer:
2.92
Step-by-step explanation:
[tex]V=\frac{4}{3}\pi r^3 \\ \\ 105=\frac{4}{3}\pi r^3 \\ \\ r^3=\frac{105}{\frac{4}{3}\pi} \\ \\ r=\sqrt[3]{\frac{105}{\frac{4}{3}\pi}} \\ \\ r \approx 2.92[/tex]
A piece of wood is 5 m long. It is cut into pieces. The lengths of the pieces are in the ratio 4:3:2:1. The longest piece is then cut in the ratio 4:1 so that there are now five pieces. How long is the smallest piece?
Answer:
0.4
Step-by-step explanation:
4+3+2+1 =10
5m÷10 =0.5
(0.5×4=2, 0.5×3=1.5, 0.5×2=1, 0.5×1=0.5)
2 : 1.5 : 1 : 0.5
longest piece= 2 (2m)
4+1= 5
2÷5= 0.4
(0.4×4=1.6, 0.4×1=0.4)
1.6 : 0.4
so the shortest piece is 0.4!
Evaulate u^2-4u+2 when u=-2
You can just replace [tex]u[/tex] with 2:
[tex]2^2 - 4\times2 + 2 = 4 - 8 + 2 = \boxed{-2}[/tex]
Alternatively, you can complete the square.
[tex]u^2 - 4u + 2 = u^2 - 4u + 4 - 2 = (u-2)^2 - 2[/tex]
When [tex]u=2[/tex], the quadratic term vanishes and we again get -2.
Suppose Mai places $3500 in an account that pays 19% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
S
(b) Find the amount in the account at the end of 2 years.
Answer:
a.$4165
b.$4956.35
Step-by-step explanation:
a)19% × 3500 = 665.
3500+665 =4165
b)19% × 4165 = 791.35
4165+791.35= 4956.35
Which of the following are true?
Estimate and classify the critical points for the graph of the function
Please show work
The critical points of the function graphed are given as follows:
x = -1.5: Local maximum.x = -1: Local minimum.What are the critical points of a function?The critical points of a function are the values of x for which:
[tex]f^{\prime}(x) = 0[/tex]
In a graph, they are turning points, and are classified as follows:
Local maximum, if the functions changes from increasing to decreasing.Local minimum, if the functions changes from decreasing to increasing.Looking at the graph, the turning points are approximately:
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need help with this
Answer:
[tex]x^4-20x^3 +175x^2 -750x+1250[/tex]
Step-by-step explanation:
By the conjugate root theorem, 5+5i is also a root.
[tex]f(x)=a(x-5)^2 (x-5-5i)(x-5+5i) \\ \\
= a(x^2 - 10x+25)((x-5)^2 - (5i)^2) \\ \\
= a(x^2 - 10x+25)(x^2 - 10x+25+25) \\ \\
= a(x^2-10x+25)(x^2-10x+50) \\ \\
= a(x^4- 10x^3 + 50x^2 - 10x^3 + 100x^2 - 500x + 25x^2 - 250x+1250) \\ \\
= a(x^4-20x^3 +175x^2 -750x+1250) \\ \\ [/tex]
Select the correct answer. Which chart best represents the following information about student results from a class assignment? Frequency 10 Score Frequency Chart 1 23 2 Frequency 10 24 8 25 4 Chart 2 26 3 27 5 28 4 29 5
The chart that best represents the student results from a class assignment is B. Histogram or bar graph.
What is a histogram or bar graph?Both histograms and bar charts are graphic vertical and horizontal bars that visually display frequencies with columns plotted on a graph.
The frequencies are depicted on the Y-axis (vertical axis).
The X-axis (horizontal axis) represents the measured variable.
Question Completion with Answer Options:A. Frequency table
B. Histogram or bar graph
C. Pareto chart
D. Pictogram
E. Pie chart
Thus, the best chart to represent the student results from a class assignment is B. Histogram or bar graph.
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The point A (-5, -2) is reflected over the line y=-1, and then is reflected over the line x= 3.
The coordinates of A exist (11, 0).
How to estimate the coordinates of A?Let, the point A (-5, -2) exists reflected over the line y = -1, and then stand reflected over the line x = 3.
The distance between the y value exists -1 - (-2)= 1
We move 1 unit beyond the line y = -1
After reflection over the line y = -1 the coordinates of A becomes (-5, 1-1) is (-5, 0)
It exists reflected over the line x = 3
The distance between -5 and 3 exists 3 - (-5) = 8
We move 8 units out from the line x = 3
The Point (-5, 0) becomes (3 + 8, 0) exists (11, 0).
Therefore, the coordinates of A exist (11, 0).
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The complete question:
The point A (-5, -2) is reflected over the line y = -1, and then is reflected over the line x = 3. What are the coordinates of A.
3 to 2 if there are 120 children who like pizza, how many total
Answer:
320
Step-by-step explanation:
Is the 3 to 2 part to part? Out of every 5 people, 3 prefer pizza and 2 do not. We can us this to set up a proportion.
3/5 = 120/x The 3 represent the part that like pizza over the whole of 5. The second ratio is showing the actual number of people that liked pizza over the total number of people.
What would be multiply 3 by to get 120? 40. So, we will multiply 5 times 40 to get the total number of people. 5 x 40 = 200
The sum
of three numbers is 24. If two numbers are 16 and 22, what is the third?
Answer:
-14
Step-by-step explanation:
[tex]16+22+x=24\\38+x=24\\x=-14[/tex]
claire and martin are trying to determine the length of a slug. Claire has a mesuring stick whose markings are 1 cm apart, and Martin has a measuring stick whose markings are 0.1cm apart.
Claire's measuring stick would make a more precise measurement
How to determine the precise measurement?The given parameters are:
Claire = 1 cm
Martin = 0.1 cm
The 0.1 cm marking would make a more accurate measurement.
This is so because the length of a slug would most likely be in decimal centimeters
However, this doesn't translate to a precise measurement.
Hence, Claire's measuring stick would make a more precise measurement
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Find the sum of the first 20 arithmetic progression 2, 7, 12, 17, 22
Answer: 5
Step-by-step explanation: 2 + 5 = 7, 7 + 5 = 12, 12 + 5 = 17, 17 + 5 = 22
To calculate the area of this shape, you would identify the known figures and add their individual areas together.
However, the half circle is unlike the other known figures in this unknown shape in that it TAKES AWAY from the total area. How should you handle its area when
calculating the total area of the unknown figure?
When calculating the total area of this unknown figure, you should use (π - r²)/4 for the area of both the semicircle (half circle) and the larger square.
How to determine the total area?By critically observing this unknown figure, we can logically deduce that it comprises a semicircle, squares, a rectangle and a triangle. Thus, its total area should be calculated by adding the area of each of the geometric figures together.
Total area = A₁ + A₂ + A₃ + A₄
However, you should take note that the diameter of the semicircle (half circle) is equal to the side length of the larger square.
Area of a semicircle = πr²/4
Thus, the total area of both the semicircle (half circle) and the larger square is given by:
Area = πr²/4 - d²
Note: d = 2r
Area = πr²/4 - (2r)²
Area = πr²/4 - 4r²
Area = (π - r²)/4 sq. units.
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Determine the current through each of the LEDs in the circuits below. Which LED will be
glowing the brightest? Which LED will be the most dim?
a. [tex]I = 6. 1[/tex] × [tex]10^-4[/tex] A
b. [tex]I = 2. 6[/tex] × [tex]10^-3[/tex] A
c. [tex]I = 0. 04[/tex] A
The LED which would glow brightest is LED C with the greatest current and voltage
The LED which would be the most dim is LED B with low voltage and consequently low current.
How to determine the currentThe formula for finding current
I = V/R
Where v = voltage
R = resistance
A. V = 12V
R = 4. 7 + 15 = 19. 7 kΩ = 19700 Ω in series
[tex]I = \frac{12}{19700}[/tex]
[tex]I = 6. 1[/tex] × [tex]10^-4[/tex] A
B. V = 9V
R = 4. 7 + 1 = 4. 7 kΩ = 4700Ω in series
[tex]I = \frac{12}{4700}[/tex]
[tex]I = 2. 6[/tex] × [tex]10^-3[/tex] A
C. V= 12V
1/R = [tex]\frac{1}{750} + \frac{1}{1200} + \frac{1}{950 }[/tex] = [tex]3. 22[/tex] × [tex]10^-3[/tex]
R = [tex]\frac{1}{3. 22 * 10 ^-3}[/tex] = 310. 56 Ω
[tex]I = \frac{12}{310. 56}[/tex]
[tex]I = 0. 04[/tex] A
It is important to note that the brightness of a bulb depends on both current and voltage depending on whether the bulb it is in parallel or series.
The LED which would glow brightest is LED C with the greatest current and voltage
The LED which would be the most dim is LED B with low voltage and consequently low current.
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The board of education has decreed that a maximum student teacher ratio in a classroom be 18:1
If the current school has 235 total students then what is the minimum number if teachers that must be working in your school ?
Answer:
235÷18=
how many classes of 18 students for each teacher
Step-by-step explanation:
Graph the parabola.
y=x^2
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex.
Then click on the graph-a-function
button.
Answer:
Vertex: (0,0)
Left 2 points: (-1,1) , (-2,4)
Right 2 points: (1,1) , (2,4)
Step-by-step explanation:
Maria plots the following points on a coordinate grid. Then, she connects each plotted point to the previous one in the order shown to form a figure. What is the area, in square units, of the enclosed figure?
The area of the enclosed figure is 4 square units.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
The triangle's area can be described as,
Area = 1/2 x base x height.
To find the area of the enclosed figure, we need to first plot the given points and then determine the shape of the figure.
Plotting the points A, B, and C on a coordinate grid, we get:
The image is given below.
Connecting points A, B, and C, we can see that the figure formed is a right triangle with legs of lengths 4 and 2.
Therefore, the area of the enclosed figure is:
Area = (1/2) x base x height
= (1/2) x 4 x 2
= 4 square units
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The complete question:
Maria plots the following points on a coordinate grid. Then, she connects each plotted point to the previous one in the order shown to form a figure. What is the area, in square units, of the enclosed figure?
Point A (1, 3)
Point B (5, 7)
Point C(5, 3)
Point A (1, 3)
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and the cover extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
A. What is the area of the pool cover?
B. What is the length of the rope?
For the circular cover we have:
A) The area is 379.94 ft²
B) The length of the rope must be 68.2 ft
How to get the area of the cover?Remember that the area of a circle of radius R is given by the formula:
[tex]A = pi*R^2[/tex]
Where pi = 3.14
In this case, the diameter of the pool is 20ft, then the radius is:
R = 20ft/2 = 10ft
And it must extend 12 inches beyond, then the radius of the cover must be:
R = 10ft + 12in
Now, we know that 1ft = 12 in, then we can rewrite the radius as:
R = 10ft +1ft = 11ft
Then the area of the cover is:
[tex]A = 3.14*(11ft)^2 = 379.94 ft^2[/tex]
B) now we want to get the length of the rope, we know that the rope runs along the cover, then the length of the rope must be equal to the circumference of the cover.
Remember that the circumference of a circle of radius R is:
[tex]C = 2*pi*R[/tex]
Then the length of the rope will be:
[tex]C = 2*3.14*11ft = 68.2ft[/tex]
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Please help I don’t understand this can someone help me
Answer:
Step-by-step explanation:
Okay, so first of all, when a slope is negative, the line goes down from left to right, not up from left to right. Then, plot the Y intercept as -2. Finally, either go up 2 and left 3 or down 2 and right 3.
Answer:
Graph attached.
Step-by-step explanation:
As we have been given the slope and the y-intercept, we can create a linear equation using the slope-intercept form.
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slopeb is the y-interceptSubstitute the given values into the formula to create an equation for the line:
[tex]\implies y=-\dfrac{2}{3}x-2[/tex]
Now we have an equation for the line, find at least two points on the line by inputting values of x into the found equation:
[tex]x=0 \implies y=-\dfrac{2}{3}(0)-2=-2 \implies (0,-2)[/tex]
[tex]x=3 \implies y=-\dfrac{2}{3}(3)-2=-4 \implies (3,-4)[/tex]
[tex]x=-6 \implies y=-\dfrac{2}{3}(-6)-2=2 \implies (-6,2)[/tex]
Plot the found points and draw a straight line through them (see attachment).
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IfX+9=11,
then the value of 7 X = ......
The answer is 14.
First, we need to find X using the first statement.
X + 9 = 11X = 11 - 9X = 2Now, we have to substitute this in the required expression.
7X7(2)14Sketch the graph of y = (x-3)^2 -25, than select the graph that corresponds to your sketch.
Answer: graph c
Hope I was able to help
Which ordered pair is a solution to the inequality 3x-4y<12 ?
The ordered pair (2,-1) is a solution the inequality.
Given the inequality is 3x-4y<12.
An inequality is a statement that compares two quantities and claims that one is greater or less than the other (the equation may also be included). These inequalities are linear if the variables are only linear.
By substituting each of the given option in the given inequality we will check which ordered pair satisfy the inequality.
1. (4,0)
Here x=4 and y=0
Substitute this in the inequality 3x-4y<12, we get
3(4)-4(0)<12
12<12
This is not true
2. (0,-3)
Here x=3 and y=-3
Substitute this in the inequality 3x-4y<12, we get
3(0)-4(-3)<12
12<12
This is not true.
3. (2,-1)
Here x=2 and y=-1
Substitute this in the inequality 3x-4y<12, we get
3(2)-4(-1)<12
6+4<12
10<12
This is true.
4. (4,-3)
Here x=4 and y=-3
Substitute this in the inequality 3x-4y<12, we get
3(4)-4(-3)<12
12+12<12
24<12
This is not true.
Hence, the ordered pair that satisfy the given inequality 3x-4y<12 is (2,-1).
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