Answer: Since the spinners have 5 and 6 numbers respectively, the total number of outcomes is 5 x 6 = 30.
If we get the same number as a previous spin, it means that the first spin is irrelevant, and we only care about the second spin. Therefore, the probability of getting the same number as a previous spin is the same as the probability of getting any specific number on the second spin, which is 1 out of 6.
Therefore, the probability of getting the same number as a previous spin is 1/6, or approximately 0.17 to two decimal places.
Step-by-step explanation:
If the 8th term of an A.P is twice the 4th term and the sum of the first terms is 47. find the five common difference
If the 8th term of an A.P is twice the 4th term and the sum of the first terms is 47. the five common difference is 3.
How to find the five common difference?Let the first term be "a" and the common difference be "d".
The 4th term of the AP is: a + 3d
The 8th term of the AP is: a + 7d
We know that the 8th term is twice the 4th term, so:
a + 7d = 2(a + 3d)
Simplifying and solving for "a", we get:
a = d
Substituting this value of "a" in the sum of the first terms, we get:
47 = (5/2)(2a + 4d)
47 = 5(a + 2d)
9.4 = a + 2d
Substituting the value of "a" from above, we get:
9.4 = 3d
d = 3.13333
d = 3 (approximately )
Therefore, the common difference (d) is approximately 3.
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Please help ASPA
Graph the functions on the same coordinate axis.
f(x)=-2x+1
g(x)=x²-2x-3
What are the solutions to the system of equations?
Select each correct answer.
(-2, -3)
(-2,5)
(2, -3)
(2,5)
(2, 3)
Answer: (2,-3) and (-2,5)
Step-by-step explanation:
Let us graph the two equations one by one.
If we compare this equation with the slope intercept form of a line which is given as we see that m = -1 and c =1
Hence the slope of the line is -2 and the y intercept is 1.
Hence one point through which it is passing is (0,1) .
Let us find another point by putting x = 1 and solving it for y Let us find another point by putting x = 2 and solving it for y Hence the another point will be (2,-3)Let us find another point by putting x = -2 and solving it for y Hence the another point will be (-2,5)Now we have two points (0,1) ,(1,-1) , (2,-3) and (-2,5) we joint them on line to obtain our line 2.
It represents the parabola opening upward with vertices (1,-4)Let us mark few coordinates so that we may graph the parabola.i) x=0 ; ; (0,-3)ii)x=-1 ; ; (-1,0)iii) x=2 ; ;(2,-3)iii) x=1 ; ;(1,-4)iii) x=-2 ; ;(-2,5)Now we plot them on coordinate axis and line them to form our parabolaWhen we plot them we see that we have two coordinates (2,-3) and (-2,5) are common , on which our graphs are intersecting. These coordinates are solution to the two graphs.
fill in the sentence below with the description that most specially applies to the quadrilateral below
The quadrilateral is most specifically a parallelogram because the opposite sides are parallel to each other
What is a parallelogram?
A parallelogram is a geometric shape with four sides, where opposite sides are parallel and congruent (having the same length), and opposite angles are also congruent (having the same measure).
In other words, a parallelogram is a quadrilateral (a polygon with four sides) where both pairs of opposite sides are parallel.
The opposite sides of a parallelogram are equal in length, and its diagonals bisect each other. The area of a parallelogram is equal to the product of its base (one of its sides) and its height (the perpendicular distance between the base and the opposite side).
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y=2/5+2 how to get the x intercept
Answer:
Step-by-step explanation:
The equation you provided, y = 2/5 + 2, appears to be missing the variable x. Assuming you meant y = 2/5x + 2, here's how you can find the x-intercept:
To find the x-intercept, we need to find the value of x when y = 0. This is because the x-intercept is the point on the graph where the line crosses the x-axis, and at that point, the y-coordinate is always 0.
So, we can set y = 0 in the equation:
0 = 2/5x + 2
Subtracting 2 from both sides:
-2 = 2/5x
Multiplying both sides by 5/2:
-5/2 = x
Therefore, the x-intercept is at the point (-5/2, 0).
MATHEMATICS
1. If each interior angle of a regular polygon is five times the exterior angle, how many sides has the polygon? x° зх°6x° 4xº 4x° 2x⁰ 2. Find the value of X in the polygon drawn above.
1. The number of sides of the polygon is 8
2. The value of x is 36
What is a polygon?A polygon can be defined as a flat or plane. The sum of a regular polygon is expressed as (n-2)180. The sum of exterior angle of a polygon is 360.
Therefore the sum of the interior is 5 times the exterior.
(n-2)180 = 5×360
180n - 360 = 1800
180n = 1800-360
180n = 1440
divide both sides by 180
n = 1440/180
n = 8
therefore the number of sides of the polygon is 8
2. The number of sides of the polygon is 6
Therefore the sum of angle in the polygon = 6-2)180 = 4× 180
= 720°
x+3x+6x+4x+4x+2x = 720
20x = 720
x = 720/20
x = 36
therefore the value of x is 36
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Jayden throws a ball up in the air. The graph below shows the height of the ball h in feet after t seconds. Find the interval for which the ball's height is increasing.
The intervals during which the ball's height is increasing are: [0, 2.5] and
[5, 7.5]
What is an intervals?In a graph, an interval represents a range of values along the x-axis or y-axis. It is a continuous segment of the axis between two points, often used to indicate a particular range of values or a specific time period.
Since the graph represents the height of the ball h in feet after t seconds, we can find the interval during which the ball's height is increasing by examining the slope of the graph.
If the slope of the graph is positive, the height of the ball is increasing. If the slope is negative, the height of the ball is decreasing.
Looking at the graph, we can see that the slope of the graph is positive between approximately 0 and 2.5 seconds, and between approximately 5 and 7.5 seconds.
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Help me! I need help with my homewor!
Answer:
Area of shaded region= 1142.96mm²
Step-by-step explanation:
•First calculate the Area covered by the interior circle.
•To calculate the Area of the exterior circle first add the two radii to get the radius from the centre of the interior circle to the circumference of the exterior circle.
•Use the calculated radius to calculate the Area covered from the centre to the circumference of the exterior circle.
•Now subtract the Area of the interior circle from the area covered by the bigger circle to get the Area of the shaded region.
Answer:
1141.76
Step-by-step explanation:
To solve for the area of the entire circle, we must first solve for the radius. Adding 6 and 14 will get us the total radius of the circle.
6 + 14 = 20Therefore, the radius of the entire circle is 20.
The expression you can use to solve for the area of a circle is:
Area = π × radius²Inserting the radius into the expression:
Area = π × 20²Therefore, the area of the entire circle is 400π.
If there is a hole in the circle in the shape of a circle, we must subtract the area of that hole to find the area of the shaded region.
Inserting 6 into the expression to solve for area:
Area = π × 6²Therefore, the area of the hole is 36π.
Now, we need to subtract the area of the gap from the area of the entire circle.
400π - 36π = 364πBecause π is approximately equal to 3.14, we can calculate an approximate value for 364π by multiplying 364 by 3.14. This gives us:
364 × 3.14 = 1141.76.Therefore, the area of the shaded region is [tex]1141.76^{2}[/tex]
This table shows the amount of money that Bradford saved in his savings account after different amounts of time.
Number of Months 4 8 18
Amount Saved ($) 50 100 225
What is the constant of proportionality?
Responses
0.08
0.08
12.5
12.5
25
25
50
Answer:
Number of Months 4 8 18
Amount Saved ($) 50 100 225
What is the constant of proportionality?
The constant of proportionality is 25.
Step-by-step explanation:
Fill the missing number: 0, 3, 8, 15, …….
Answer:
The next number is 24
Step by step explanation:
Write all the numbers down and make sure they are separated from each other. Example, 0 3 8 15.Find the difference between the numbers.0 3 8 15
+3 +5 +7(the difference here is 2) so the next one will be +9. 15+9=24.
Critical Thinking Question (5 pts.)
(You may use the back of the page to write your answer if needed). Here is a case-study for you to solve. Use what you learned
about blood types and Rhesus factor to solve this situation.
Two friends, Mike and Jake were returning late at night from a club in the same car. Suddenly, Mike, who was driving, lost control of
the car and they crashed into a big tree. Mike ended up with only a few bruises and scratches, but Jake got hurt.
Jake had internal bleeding and was taken to a hospital, but he lost a lot of blood and needed a blood transfusion. Mike, feeling
responsible for his friend's condition, wanted to donate blood to his friend. Both Mike and Jake had blood type O. So, in the ER, Mike
gave 2 pints of blood to Jake.
Two weeks later, Jake became anemic. So, Mike, being a good friend, decided to give blood again. However, after the second
transfusion, Jake went into an anaphylactic shock (severe immune response) and almost died.
What, do you think, was the problem here? Your answer should have two parts:
1. Explain, what happened in Jake's body after the first blood transfusion - why did he become anemic so soon after the transfusion?
(hint: it's not from bleeding)
2. Explain, what happened after the second blood transfusion - why did Jake go into an anaphylactic shock?
1.Jake became anemic after the first blood transfusion because his body reacted to the foreign antigens.
2.He went into an anaphylactic shock after the second transfusion due to an even stronger allergic reaction.
1. After the first blood transfusion, Jake became anemic because he was given type O blood, which is not compatible with his own blood type. Incompatible blood transfusions occur when a person is given blood that carries a different antigen than the one they have. In this case, Jake was given type O blood, which carries both the A and B antigens, while Jake’s own blood carries the Rh antigen. Therefore, Jake’s body reacted to the foreign antigens and created antibodies to fight against them. This reaction caused Jake to become equation anemic, as his body was not able to absorb the oxygen from the transfused blood.
2. After the second blood transfusion, Jake went into an anaphylactic shock because he was given type O blood, which carries both the A and B antigens, while Jake’s own blood carries the Rh antigen. Since Jake’s body had already created antibodies to fight against the foreign antigens, when it was exposed to the same foreign antigens a second time, his body reacted with an even stronger immune response. This reaction caused Jake to go into an anaphylactic shock. In other words, the second transfusion caused an allergic reaction in Jake’s body, which was much more severe than the allergic reaction caused by the first transfusion.
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You are conducting a study testing whether depression symptoms are lower after participating in therapy compared to before. Given this information, complete the hypotheses in symbols:
Given this information, the complete hypotheses in symbols for the study is:
H0:μ_Post-μ_pre ≥ 0H0:μ_Post-μ_pre < 0What are the hypotheses symbol?In statistics, the null hypothesis is usually represented by the letter H with the subscript '0' (zero), as in H0. It's spelled H-null, H-zero, or H-nought. Simultaneously, the alternative hypothesis expresses the observations caused by the non-random cause. It is represented by the letters H1 or Ha.
The null and alternative hypotheses in symbols would be:
H0: μafter ≤ μbeforeHa: μafter < μbeforeNote: Where: H0 = null hypothesis, Ha = alternative hypothesis, μafter = population mean of depression symptoms after therapy and μbefore = population mean of depression symptoms before therapy
The null hypothesis states that the mean depression symptoms after therapy is less than or equal to the mean depression symptoms before therapy. The alternative hypothesis states that the mean depression symptoms after therapy is less than the mean depression symptoms before therapy.
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I will mark you brainiest!
In completing the following proof, which of the following statements should be included?
Given: regular ΔDAF; midpoints B, C, E; ∠DBE ≅ ∠FCE
Prove: DB ≅ FC
A) CCPTC
B) CPCTC
C) CSATC
D) CASTC
Answer:
B) CPCTC (stands for Corresponding Parts of Congruent Triangles are Congruent) should be included in the proof. This statement is necessary to show that ΔDBE ≅ ΔFCE, which then allows us to conclude that DB ≅ FC.
Step-by-step explanation:
What are the coordinates of the point that is of the way from G to F?
OA. (3,2)
OB. (5,-2)
O C. (1.5, 3)
OD. (4.5, -3)
4
6
2
-6 -4-2 0
ON
-2
-4
-6
Ty
F
2
4
6
G
X
The coordinates of the point that is halfway between G (2,4) and F (6,-6) is (4, -2).
What is coordinate?Coordinate is a pair of numbers that represents a position on a two-dimensional plane. Coordinates are usually written in the form (x, y), with the x-coordinate representing a position along the horizontal axis, and the y-coordinate representing a position along the vertical axis. Coordinates can also be used to represent positions on a three-dimensional plane in the form (x, y, z). These coordinates can be used to pinpoint a specific location or to describe the shape of a figure on a graph.
This can be calculated by taking the average of the x coordinates (2 + 6 = 8/2 = 4) and the average of the y coordinates (4 - 6 = -2/2 = -2).
Therefore, the point is (4, -2).
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How much money should be deposited today in an account that earns 3.5% compounded monthly so that it will
accumulate to $12,000 in 3 years?
Click the icon to view some finance formulas.
The amount of money that should be deposited is
(Round up to the nearest cent as needed.)
orre
The amοunt οf mοney that shοuld be depοsited tοday is apprοximately $9,786.04 (rοunded up tο the nearest cent).
What dοes the mathematical term "cοmpοund" mean?The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest.
It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest. Cοmpοund interest is cοmmοnly abbreviated C.I. in mathematics.
The amοunt that has tο be depοsited tοday can be determined using the calculatiοn fοr the future value οf an annuity.
FV is equal tο P * [(1 + r/n)(nt) - 1] / (r/n)
where:
$12k in future value P = principle (the amοunt tο be depοsited tοday)
3.5% as the annual interest rate
12 times every year are added tο the number n. (cοmpοunded mοnthly)
If t Equals time in years, then 3
When we enter the values, we οbtain:
[tex]12,000 = P * [(1 + 0.035/12)^{(12*3)} - 1] / (0.035/12)[/tex]
Simplifying:
[tex]12,000 = P * (1.035^{36} - 1) / (0.00291667) (0.00291667)[/tex]
[tex]P = 12,000 * (0.00291667) / (1.035^{36 }- 1)[/tex]
P ≈ $9,786.04
The sum that shοuld be depοsited as a result is abοut $9,786.04 tοday (rοunded up tο the nearest cent).
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144 is 90% what is the other 10 percent
Answer:
the missing 10% of 144 is 16. The whole amount would be 144 + 16 = 160.
Step-by-step explanation:
To find the missing 10%, you can use the fact that 100% is equal to the whole amount, and set up a proportion:
90/100 = 144/x
Simplifying this proportion, you can cross-multiply:
90x = 100 * 144
Then, you can solve for x:
x = (100 * 144) / 90
x = 160
Therefore, the missing 10% of 144 is 16. The whole amount would be 144 + 16 = 160.
Question 1 1.1. Express each of the ratios below in the simplest form. Show all you steps and calculations. 1.1.1. 75: 125 1.1.2. 3mm: 3m 1.1.3. 7500g: 2 Kg 1.1.4.250ml: 21 1.1.5. 250 kg: 2 tonnes bank fo
The ratio of 75:125 is 3:5.
The ratio 3 mm : 3000 mm is 1:1000.
The ratio of 7500g:2 Kg is 3.75:1.
The ratio of 250ml:2l is 1:8.
How to calculate the ratioTo simplify this ratio, we need to find the greatest common factor (GCF) of 75 and 125, and divide both terms by it.
The factors of 75 are: 1, 3, 5, 15, 25, 75.
The factors of 125 are: 1, 5, 25, 125.
The GCF is 25.
Dividing both terms by 25, we get:
75 ÷ 25 = 3
125 ÷ 25 = 5
Therefore, the simplified ratio is 3:5.
1.1.2. 3mm:3m
To simplify this ratio, we need to convert the units so that they are the same.
1 m = 1000 mm
So, 3 m = 3000 mm
Now, the ratio is 3 mm : 3000 mm.
We can simplify this ratio by dividing both terms by 3:
3 mm ÷ 3 = 1 mm
3000 mm ÷ 3 = 1000 mm
Therefore, the simplified ratio is 1:1000.
1.1.3. 7500g:2 Kg
To simplify this ratio, we need to convert either grams to kilograms or kilograms to grams so that both terms have the same unit.
7500 g = 7.5 kg (since 1 kg = 1000 g)
Now, the ratio is 7.5 kg : 2 kg.
We can simplify this ratio by dividing both terms by 2:
7.5 kg ÷ 2 = 3.75 kg
2 kg ÷ 2 = 1 kg
Therefore, the simplified ratio is 3.75:1.
1.1.4. 250ml:21
To simplify this ratio, we need to convert milliliters to a whole number.
We can convert 250 ml to 250/21 ml by dividing both terms by 21:
250 ml ÷ 21 = 11.9 ml (rounded to one decimal place)
Now, the ratio is 11.9 ml : 21.
We can simplify this ratio by dividing both terms by 0.1:
11.9 ml ÷ 0.1 = 119 ml
21 ÷ 0.1 = 210
Therefore, the simplified ratio is 119:210.
1.1.5. 250 kg:2 tonnes
To simplify this ratio, we need to convert either kilograms to tonnes or tonnes to kilograms so that both terms have the same unit.
1 tonne = 1000 kg
So, 2 tonnes = 2000 kg
Now, the ratio is 250 kg : 2000 kg.
We can simplify this ratio by dividing both terms by 250:
250 kg ÷ 250 = 1 kg
2000 kg ÷ 250 = 8 kg
Therefore, the simplified ratio is 1:8.
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what is the anwser to finding the radius
The radius of the circle is r = 3.75
What is the radius of a circle?The radius of a circle is the distance from its center to its circumference.
To find the radius of the circle, we see that there is a right-angle triangle there. So, using Pythagoras' theorem, we have that
AC² = AB² + BC²
(6 + r)² = 9² + r²
Expanding the brackets, we have that
36 + 12r + r² = 81 + r²
Cancelling out r², we have that
36 + 12r = 81
Subtracting 36 from both sides, we have that
12r = 81 - 36
12r = 45
r = 45/12
r = 15/4
r = 3.75
So, the radius is r = 3.75
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If Haechan has 1 apple and Mark has 2 and Jungwoo has 7 how much apples are there combined?
Answer:
9 apples
Step-by-step explanation:
1 apple + 2 apples + 7 apples= 9 apples
Answer:
1+7+2= 10
Step-by-step explanation:
1 apple + 7 apples + 2 apples = 10 apples
Plot the following points and join them together and describe what you get, (1₁-1), (2,1), (3, 3), (4.5) (5.7)
Answer:
A positive line
Step-by-step explanation:
Answer:
Step-by-step explanation:
you get a straight line with a slope = 2
the line slants up and to the right
it passes through the y axis at the point (0, -3)
Find the length of QS
Answer:
112
Step-by-step explanation:
you have to find the length of QT and ST, then QS will be the hypotenuse (opposite of the right angle) of the triangle QTS.
use the formula:
c²=a²+b²
a²=c²-b²
1. to find QT:
QT²=53²-45²
QT²=2,809-2,025
QT²=784
QT=28
2.to find ST:
ST²=117²-45²
ST²=13,689-2,025
ST²=11,664
ST=108
3. find QS:
QS²=28²+108²
QS²=784+11,664
QS²=12,448
QS=111.570605
QS≈112
Use the image to determine the line of reflection. Graph of polygon ABCDE with point E at negative 3 comma 1. A second polygon A prime B prime C prime D prime E prime with E prime at negative 3 comma negative 3. Reflection across the x-axis Reflection across the y-axis Reflection across y = −1 Reflection across x = −3
The line of reflection is y = -1, which is the equation of the horizontal line passing through the midpoint of the line segment joining E and E'.
A line section is what?Two different points on a line define the boundaries of a line segment in geometry. Or, a line segment is a section of the line that links two points, as another alternative. In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are set or identifiable.
According to the given information:From the given image, we can see that the original polygon ABCDE has point E at (-3, 1), and the reflected polygon A'B'C'D'E' has point E' at (-3, -3). This means that the reflection must have occurred across the horizontal line passing through the point (-3, -1), which is the midpoint of the line segment joining E and E'.
Therefore, the line of reflection is y = -1, which is the equation of the horizontal line passing through the midpoint of the line segment joining E and E'.
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Solve the system of equations using substitution. y = 4x y = 8x + 8 (−3, −12) (−2, −8) (2, 8) (3, 12)
Answer:
(- 2, - 8 )
Step-by-step explanation:
y = 4x → (1)
y = 8x + 8 → (2)
substitute y = 8x + 8 into (1)
8x + 8 = 4x ( subtract 4x from both sides )
4x + 8 = 0 ( subtract 8 from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
substitute x = - 2 into (1)
y = 4x = 4(- 2) = - 8
solution is (- 2, - 8 )
Answer:(-2,-8)
Step-by-step explanation:
if you use a graph and find where they intercept that will give you the answer use desmos graphing
I need help with this IXL special right triangles
Answer:
Step-by-step explanation:
m = 30
10√3 · √3 = 10·3 = 30
ngozi is twice as old as Ada and Agnes 13 1/3 of ada if sum of their age is 30 how old is ngozi
The age of Ngozi if ngozi is twice as old as Ada and Agnes 13 1/3 of ada if sum of their age is 30 is 3.68 years.
How old is Ngozi?Let
Ada age = x
Agnes age = 13 1/3x
Ngozi age = 2x
30 = x + 13 1/3x + 2x
30 = 3x + 40/3x
30 = 49/3x
divide both sides by 49/3
x = 30 ÷ 49/3
multiply by the reciprocal of 49/3
x = 30 × 3/49
x = 1.84 years
Ngozi age = 2x
= 2(1.84)
= 3.68 years
Therefore, Ngozi is 3.68 years old
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x/15 = h make x the subject
Answer:
To make "x" the subject of the equation, we can isolate it on one side of the equation by multiplying both sides by 15:
x/15 = h
Multiplying both sides by 15 gives:
x = 15h
The equation in terms of "x" is x = 15h.
Step-by-step explanation:
state of each triangle is acute, obtuse, or right show work
The triangle can be classified as follow:
15: obtuse
16: right
How to know if a triangle is acute based on side lengths?To classify the triangle as acute, obtuse, or right, follow the following steps:
1. Calculate the sum of squares of the two smaller sides.
2. Compare it to the square of the longest side.
3. If the sum is greater, your triangle is acute. If they are equal, your triangle is right. If the sum is less, your triangle is obtuse.
No. 15
10² + (2√39)² = 256
18² = 324
256 < 324 (obtuse)
No. 16
11² + (2√19)² = 197
(√197)² = 197
197 = 197 (right)
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24. A bag of candy contained a total of 1,000 candies before it was opened. Four students each pulled out 20 candies at random and recorded the color of the candies in this table.
According to this data, which was the most likely distribution of the colors of candies in the bag before it was opened?
A. 250 red, 250 blue, 250 green, 125 yellow, and 125 orange
B. 300 red, 250 blue, 200 green, 100 yellow, and 150 orange
C. 200 red, 200 blue, 200 green, 200 yellow, and 200 orange
D. 200 red, 200 blue, 200 green, 100 yellow, and 100 orange
A. 250 red, 250 blue, 250 green, 125 yellοw, and 125 οrange is the mοst likely distributiοn οf the cοlοrs οf candies in the bag befοre it was οpened
What is equatiοn?A mathematical equatiοn links twο statements and utilises the equals sign (=) tο indicate equality. In algebra, an equatiοn is a mathematical assertiοn that prοves the equality οf twο mathematical expressiοns. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical fοrmula may be used tο determine hοw the twο sentences οn either side οf a letter relate tο οne anοther. The lοgο and the particular piece οf sοftware are usually identical. like, fοr instance, 2x - 4 = 2.
We must make use οf the data the students cοllected in οrder tο calculate the mοst likely distributiοn οf the candy cοlοurs in the bag befοre it was οpened. Nοw, let's determine the tοtal amοunt οf sweets the pupils pulled οut:
40 sweets divided by 4 pupils is 80 candies.
We may assume that there were twice as many red candies in the bag befοre it was οpened if the kids tοοk οut 40 οf them:
4 x 250 = 1,000
By emplοying this technique, we may determine hοw many candies οf each hue were included in the bag priοr tο its οpening.
Thus, A. 250 red, 250 blue, 250 green, 125 yellοw, and 125 οrange is the mοst likely distributiοn οf the cοlοrs οf candies in the bag befοre it was οpened
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a retailer sold bat at 25% profit
Answer:
25% Profit = CP of 5 bats = 5x W
Step-by-step explanation:
HELP HELP FAST FAST QUICK BRAINLIEST
Answer:
the answer is 2 pls mark me brainliest
QUESTION 1 The number of elements in sets A and B are shown in Figure 1.0. If n(A) = n(B) find: (a) x (b) n(A) (c) n(B) (d) n(AUB) 2x 4xx+5 Figure 1.0 10 marks
Answer:
From the given figure, we can write the following equations:
n(A) = 2x + 4
n(B) = x + 5
n(A∪B) = n(A) + n(B) - n(A∩B)
Since we are given that n(A) = n(B), we can substitute the expressions for n(A) and n(B) to get:
2x + 4 = x + 5
x = 1
(a) x = 1
(b) n(A) = 2x + 4 = 2(1) + 4 = 6
(c) n(B) = x + 5 = 1 + 5 = 6
(d) n(A∪B) = n(A) + n(B) - n(A∩B)
We still need to find n(A∩B) to calculate n(A∪B). Looking at the figure, we can see that there are 2 elements that are common to both A and B. Therefore,
n(A∩B) = 2
Substituting this value, we get:
n(A∪B) = n(A) + n(B) - n(A∩B) = 6 + 6 - 2 = 10
Therefore, (d) n(A∪B) = 10.
Step-by-step explanation: