A square cannot be drawn with the same area as the parallelogram and with its vertices at the intersections of grid lines because the sides of the square would have to be diagonal to the grid lines.
What is square?
A square is a geometrical shape with four equal sides and four equal angles, each of which is a right angle (90 degrees).
A parallelogram can be drawn on a grid by connecting its vertices with line segments that are parallel to the grid lines. However, a square cannot be drawn with the same area as the parallelogram and with its vertices at the intersections of grid lines because the sides of the square would have to be diagonal to the grid lines.
This means that the sides of the square cannot be parallel to the grid lines. If the sides of the square are not parallel to the grid lines, then it cannot be drawn on the grid in a way that all of its vertices lie at the intersections of grid lines.
Therefore, a square with the same area as the parallelogram and with its vertices at the intersections of grid lines cannot be drawn.
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an aquarium holds 33.75 gallons of water. It has a lenth of 2 feet and a height of 1.5 feet what is the width of the aquarium?
The required width of the aquarium is 1.5033 feet.
To find the width of the aquarium, we can use the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
We are given the length and height of the aquarium, as well as its volume (33.75 gallons). However, the volume is in gallons, while the dimensions are in feet. We need to convert the volume to cubic feet so that we can use the formula.
1 gallon is equivalent to 0.13368 cubic feet (approximately). Therefore, we have:
Volume = 33.75 gallons x 0.13368 cubic feet/gallon
Volume = 4.51 cubic feet
Now we can substitute the given values into the formula and solve for the width:
4.51 cubic feet = 2 feet x Width x 1.5 feet
Simplifying the equation, we have:
Width = 4.51 cubic feet / (2 feet x 1.5 feet)
Width = 1.5033 feet (rounded to four decimal places)
Therefore, the width of the aquarium is approximately 1.5033 feet.
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the nth partial sum is given by
If nth partial sum of series S is given by Sₙ = n+1/n²+1, the value of S is equal to 0.7834.
To find the sum S of the series, we need to take the limit of the nth partial sum as n approaches infinity. This is because the series contains an infinite number of terms, and the sum is the value that the series approaches as we add more and more terms.
We can write the formula for the nth partial sum as:
Sₙ = 1/2 + 2/5 + 3/10 + ... + n/(n²+1)
To find the sum S, we take the limit of Sₙ as n approaches infinity:
S = [tex]\lim_{n \to \infty}[/tex] Sₙ
We can use the formula for the nth partial sum to simplify Sₙ:
Sₙ = 1/2 + 2/5 + 3/10 + ... + n/(n²+1)
= [1/(1²+1)] + [1/(2²+1)] + [1/(3²+1)] + ... + [1/(n²+1)]
= Σ[1/(k²+1)], k=1 to n
Using calculus or other advanced techniques, we can find that the limit of Σ[1/(k²+1)] as n approaches infinity is approximately 0.7834. Therefore, the sum of the series S is approximately:
S ≈ 0.7834
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This scatter plot shows the relationship between the number of years of experience at a company and the yearly
income for 12 different workers. The line of best fit is shown on the graph.
Yearly Income
(in thousands)
$60
$50
$40-
$30
$20-
$10
0
Years of Experience
vs. Yearly Income
y
TA
B
D
2 4 6 8 10 12 14 16
Years of Experience
Select True or False for each statement based on the scatter plot.
The statements regarding the scatter plot are given as follows:
Point B is an outlier because it is far away from the line of best fit: True.A good estimate of yearly income for someone with 14 years of experience is of $40,000: False.The line of best fit shows a positive linear association between years of experience and yearly income: True.What is the scatter plot?The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:
(Years of experience, yearly income).
As the line of best fit is an increasing line, there is a positive linear association between years of experience and yearly income.
For a person with 14 years of experience, we have point (14,50) on the line of best fit, meaning that a good estimate is of $50,000.
Outliers are in fact points away from the line of best fit, which is the case for item b.
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PLEASE HELP ASAP! 15 pts
The graph of y = -f(x + 2) - 1 when transformed from the graph of y = f(x) is added as an attachment
Sketching the graph of y = -f(x + 2) - 1 from the graph of y = f(x)From the question, we have the following parameters that can be used in our computation:
The graph of y = f(x)
To sketching the graph of y = -f(x + 2) - 1, we use the following steps:
Translate the graph of y = f(x) to the left by 2 units, this gives f(x + 2).Reflect the graph of y = f(x + 2) across the x-axis, this gives -f(x + 2).Translate the graph of y = -f(x + 2) down by 1 unit, this gives f(x + 2) - 1See attachment for the transformed graph
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The object is a parallelogram with a circle inside of it. The height of the parallelogram is the same as the diameter of the circle. The circle touches three sides of the parallelogram.
.
A. Object A
B. Object B
C. Obiect C
The object that matches the description is C.
Properties of a parallelogram.
A parallelogram is a four sided shape which has a pair of slant sides, though a pair of opposite sides are equal. It has some other unique properties that differentiate it from other four sided figures.
A circle is a figure that is bounded by a curved side called its circumference. Its diameter is twice of its radius.
From the information given in the question, it can be deduced that the best object that matches the description is object C.
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1.This problem refers to right triangle ABC with C = 90°. Begin the problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. If b = 7.5 mm and c = 11 mm, find B. (Round your answer to the nearest whole number.)
2.This problem refers to right triangle ABC with C = 90°. Begin the problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. If B = 17.5° and c = 9.33 cm, find b. (Round your answer to two decimal places.)
3.This problem refers to right triangle ABC with C = 90°. Begin the problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately. If A = 32° and a = 25 m, find c. (Round your answer to the nearest whole number.)
Upon answering the query As a result, triangle side C is around 13 metres long.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is a basic geometric shape. A triangle with vertices A, B, and C is referred to as Triangle ABC. In Euclidean geometry, a single plane and triangle are obtained when the three points are not collinear. If a triangle has three sides and three corners, it is a polygon. The triangle's corners are the places where its three sides intersect. Three triangle angles add up to 180 degrees.
B is given to be 7.5mm and C is given to be 11mm. The task is to determine angle B. A diagram of the triangle is shown below:
C
/|
/ |
b / | a
/ |
/__|
A c B
The sine ratio can be used to determine angle B:
[tex]sin(B) = b/c\\sin(B) = 7.5/11\\B = sin^{-1}(7.5/11)\\B =42[/tex]
As a result, angle B is around 42°.
B is stated as 17.5 degrees, and c is provided as 9.33 cm. The task is to locate b. A diagram of the triangle is shown below:
C
/|
/ |
b / | a
/ |
/____|
A c B
[tex]sin(B) = b/c\\b = c sin(B)\\b = 9.33 sin(17.5)\\b =2.65 cm\\[/tex]
As a result, side B is around 2.65 cm.
It is said that A = 32° and a = 25 m. Our task is to locate c. A diagram of the triangle is shown below:
C
/|
/ |
b / | a
/ |
/____|
A c B
[tex]sin(A) = c/a\\c = a sin(A)\\c = 25 sin(32)\\c = 13 m\\[/tex]
As a result, side C is around 13 metres long.
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What's 2(tan x -sqrt3)=2. I need it in radians or degrees, not a weird decimal like 1.2199.
Answer: Starting with 2(tan x - sqrt(3)) = 2:
First, divide both sides of the equation by 2 to simplify:
tan x - sqrt(3) = 1
Next, add sqrt(3) to both sides:
tan x = 1 + sqrt(3)
To solve for x, we need to take the arctan of both sides:
x = arctan(1 + sqrt(3))
In degrees, this is:
x = 75 degrees
In radians, this is:
x = 5π/12 radians
Step-by-step explanation:
Tiffany drew the design below that she is going to use on a stained glass window above her front door identify all the days in Tiffany’s design. See image below.
All the rays in tiffany's designs that she is going to use on a stained glass window above her front door are EA , ED , EB , GC GH
Rays are a part of a line that has a fixed starting point but no endpoint.
Rays are written in a specific form
first letter should be the fixed point and the second letter should be point with no endpoint
E is fixed point A is no end point = EA
E is fixed point D is no end point = ED
E is fixed point B is no end point = EB
G is fixed point C is no end point = GC
G is fixed point H is no end point = GH
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Suppose that the function fis defined, for all real numbers, as follows.
-2
if x≤-2
f(x)=(x+1)² if-2
-√x+1_ ifx>2
Find f(-2), f(-1), and f(3).
f(-2) = 0
f(-1) = 0
f(3) =
010
X
Ś
The function is solved for the given intervals and the values are noted
Given data ,
Let the function be represented as f ( x )
when x ≤ -2 , f ( x ) = -2
when -2 ≤ x ≤ 2 , f ( x ) = - ( x + 1 )²
And , when x > 2 , f ( x ) = - ( 1/4 )x + 1
Now , the function is defined as
a)
f ( -2 ) = -2
b)
f ( -1 ) = - ( -1 + 1 )²
f ( -1 ) = 0
c)
f ( 3 ) = ( -1/4 )(3 ) + 1
f ( 3 ) = -3/4 + 1
f ( 3 ) = 1/4
Hence , the function is solved
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What type of algebraic equation is 2x+5?
please help also explain why its the answer
Answer:
Graph B
Step-by-step explanation:
Graph B is not a function, because it fails the "vertical line test". Which means the plots that would be placed on the line intersecting the X axis would have the same X value, and X values CANNOT repeat when it comes to functions. So the Answer is B because the X Values would repeat if you were to write the coordinates of the points down.
cos²a +5 find the maximum value.
How much money should be deposited today in an account that earns 4.5% compounded monthly so that it will
accumulate to $14,000 in 3 years?
i Click the icon to view some finance formulas.
The amount of money that should be deposited is $8000
(Round up to the nearest cent as needed.)
Answer:
To solve this, we can use the following formula:
FV = PV * (1 + r/n)^nt
Where:
FV = Future Value
PV = Present Value
r = Interest Rate
n = Number of times interest is compounded per year
t = Number of years
In this case, we have the following information:
FV = $14,000
r = 4.5%
n = 12 (monthly compounding)
t = 3 years
We can solve for PV as follows:
PV = FV / (1 + r/n)^nt
PV = $14,000 / (1 + 0.045/12)^12*3
PV = $8,000.00
Therefore, the amount of money that should be deposited today in an account that earns 4.5% compounded monthly so that it will accumulate to $14,000 in 3 years is $8,000.00.
Step-by-step explanation:
Find ( f o g) for the following functions (refer to photo)
Answer:[tex]\sqrt{\frac{14}{5} }[/tex] or [tex]\frac{\sqrt{70} }{5}[/tex]
Step-by-step explanation:
(f o g )(x) means f(g(x)) so take g(x) and put it into f every time you see an x
f(g(x))[tex]=\sqrt{\frac{2(4+\sqrt{x} )}{5} }[/tex]
now plug in 9 for this answer =[tex]\sqrt{\frac{14}{5} }[/tex] or [tex]\frac{\sqrt{70} }{5}[/tex]
I need some help on this.
The actual length of roof of house is 25 feet.
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
From the given figure, model has 24 inches and roof has 15 inches and the base angle of roof is 37°.
The actual house dimension is 40 feet.
40 feet = 480 inches
a) Scale factor = 24/480
= 1/20
So, measure of actual roof is 1/20 = 15/x
x=300 inches
300 inches = 300/12 = 25 feet
b) Using cosine rule formula
25=√(40²+25²-2×40×25 cosC)
625=2225-2000cosC
-1600=-2000cosC
cosC=4/5
cosC=0.8
∠C=37°
Therefore, the actual length of roof of house is 25 feet.
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I need help with this please
Answer:
D) 4 x 3/4 = 12/4 = 3
Step-by-step explanation:
If a ball is thrown in the air with an initial
height of 4 feet, and if the ball remains in
the air for 3.8 seconds, then accurate to
the nearest foot, how high did it go?
Remember, the acceleration due to
gravity on Earth is -32 ft/sec².
[?] feet
The requried ball reached a maximum height of approximately 62 feet
Let the ball is thrown vertically upward, we can use the following formula to find the maximum height it reaches:
[tex]h(t) = -16t^2 + vt + h_0[/tex]
here, h(t) is the height of the ball at time t, v is the initial velocity of the ball (in feet per second), and h0 is the initial height of the ball (in feet). We can also use the fact that the ball remains in the air for 3.8 seconds, which means that the time it takes to reach the maximum height is half of that or 1.9 seconds.
At the highest point, the ball's velocity is zero, so we can find the initial velocity by setting v = 0 in the above formula and solving for h₀:
h₀ = h(t) + 16t²
= 4 + 16(1.9)²
≈ 4 + 57.76
≈ 61.76
Therefore, the ball reached a maximum height of approximately 62 feet
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Which expression is equal to
4/√12
the answer is
option A
Step-by-step explanation:
(2√3)/3
The school bookstore ordered three-ring notebooks. They put 75% of the order in the warehouse and sold 80% of
the rest in the first week of school. There are 25 notebooks left in the store to sell. How many three-ring notebooks
did they originally order?
The school bookstore originally ordered 500 three ring notebooks.
How to find the number of three-ring notebooks orderedInformation given in the problem:
75% of the order in the warehousesold 80% of the rest in the first week of schoolThere are 25 notebooks left in the store to sellThis helps to deduce that
25% of the order was not put in the warehouse.20% of the remaining notebooks are left to be sold.The equation set up
Assuming the original order quantity of three ring notebooks is x, then
0.20 * (0.25 * x) = 25
Solving for x
0.20 * (0.25 * x) = 25
1/20 * x = 25
x = 25 * 20
x = 500
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State the number and type of solutions
[tex]-8mx^{2} -9m+4=5[/tex]
Therefore, the expression -8mx²-9m +45 has two real solutions for any value of m.
What is expression?In mathematics, an expression is a combination of numbers, symbols, and operations that represent a value or a quantity. Expressions can be simple, such as a single number or variable, or they can be complex, consisting of multiple terms and operations. Expressions can involve a variety of mathematical operations, including addition, subtraction, multiplication, division, exponents, and roots. They can also include parentheses, brackets, and other symbols to indicate the order of operations or to group terms together. Expressions are commonly used in mathematical equations and formulas, and they are also used in programming languages and computer science to represent calculations and algorithms.
Here,
The expression -8mx²-9m +45 is a quadratic expression in the variable x, where m is a constant. When we set this expression equal to zero and try to solve for x, we get the quadratic equation:
-8mx² - 9m + 45 = 0
This is a quadratic equation in standard form, where the coefficients a = -8m, b = -9m, and c = 45. To determine the number and type of solutions, we can use the discriminant:
=b² - 4ac
= (-9m)² - 4(-8m)(45)
= 81m² + 1440m
The discriminant is positive for all values of m, so there are always two real solutions to this quadratic equation.
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Insect the numbers 1-5 in the circles so that for any particular circle the sum of the numbers in the circle connected directly to it equals the value corresponding to the number in the circle as given in the list.
* please let me know the reason, step by step solve the question. Thank you
To get the numbers and their values we must match the circles directly linked to a number with values whose summation equals the assigned number.
How to get the valuesWe can get the numbers and their reasons as follows:
1 equals 4 because the numbers directly connected to figure one in the circles are 3 and 4.
2 equals 12 because the numbers directly linked to the number two are 8 and 4.
3 equals 7 because the numbers directly linked through the circles are 3 and 4.
The number 4 is 8 because the number directly linked to it is 8.
Finally, the number 5 is 5 because 4 and 5 are directly connected.
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A recipe book shows measurement conversions for cups to pints. It shows that 3 cups converts to 1.5 pints and 5 cups converts to 2.5 pints.
Write an equation that shows the proportional relationship between pints and cups where p represents pints and n represents cups.
ANSWER PLEASE
The relationship between pints and cups where p represents pints and n represents cups is n = 2p.
We have,
3 cups converts to 1.5 pints
and 5 cups converts to 2.5 pints.
We know from constant of proportionality
y = kx
k = y/x
Put y= 2.5 and x= 5
Then, k = 5/2.5
k = 2
So, the relationship between pints and cups where p represents pints and n represents cups is
n = 2p
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A running club has three types of
members: adults, juniors and children.
The ratio of juniors to children is 3 : 5.
The ratio of children to adults is 3 : 1.
What is the ratio of juniors to adults in its
simplest form?
We can conclude that the ratio of juniors to adults is 9:5 respectively.
What are ratios?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
A proportion is an equation that sets two ratios at the same value.
For instance, you may express the ratio as 1: 3 (there are 3 girls for every boy) if there is only 1 boy.
There are 1 in 4 boys and 3 in 4 girls.
So, we know that:
Juniors to children = 3:5
Children to adults = 3:1
Now, calculate the ratio of Junoirs to adults as follows:
J:C = 3:5
C:A = 3:1
Then,
J:C:A
3:5:5
3:3:1
Add, and we get:
9:15:5
The ratio of juniors to adults is 9:5.
Therefore, we can conclude that the ratio of juniors to adults is 9:5 respectively.
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Construct a 90% confidence interval of the population proportion using the given information. x=75 n=150
We can be 90% confident that the true population proportion lies between 0.433 and 0.567.
What is proportion ?In statistics, proportion refers to the percentage or fraction of a population or sample that possesses an important trait.
If we wanted to know, for instance, what percentage of individuals in a particular city possessed cars, we would pick a sample of people from that city, count how many of them did, and express that number as a percentage of the whole sample size.
When drawing conclusions about a wider population from a sample, proportions are frequently used. Based on the sample proportion, one can estimate or evaluate the population proportion using confidence intervals and hypothesis tests.
What is interval?A range of values used to estimate or define a population parameter, such as a mean, percentage, or variance, is referred to in statistics as an interval. The lower and upper bounds of an interval estimate are determined using the sample data and a degree of confidence or probability.
For instance, a range of values near the sample mean that we may reasonably be convinced contains the true population mean would make up a confidence interval for the population mean. The margin of error reveals the accuracy of the estimate, while the confidence level shows the likelihood that the interval contains the actual population mean.
According to question,
We can apply the following formula to create a confidence interval for a population proportion:
Confidence Interval is calculated as Sample Proportion +/- Error Margin.
where the margin of error takes into account the uncertainty in calculating the population proportion from the sample proportion and the sample proportion is the portion of the sample that possesses the feature of interest.
The sample proportion in this instance is:
x/n = 75/150 = 0.5
The following formula can be used to determine the margin of error:
Error margin is equal to z*√(p(1-p)/n)).
where z is the desired level of confidence's associated z-score. Using a typical normal distribution table, the z-score is 1.645 with a 90% degree of confidence.
When we enter the values, we obtain:
1.645√(0.5(1-0.5)/150) = 0.067 is the margin of error.
the 90% confidence interval for the population proportion is:
0.5 +/- 0.067, or (0.433, 0.567)
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Find the measure of each arc.
arc AE=
arc ACE=
arc GDC=
arc BHC=
arc FD=
arc FBD=
The measure of each arc.
arc AE= 103°
arc ACE= 257°
arc GDC= 196°
arc BHC= 305°
arc FD= 79°
arc FBD= 281°
What is meant by measure?
Measure refers to the quantity or size of something, often expressed in numerical terms, such as length, weight, volume, or time. It helps to provide a standard for comparison or evaluation.
What is meant by arc?
An arc is a curved portion of a line or circle that is defined by two endpoints and the points along the curve between them. It is often used in geometry and trigonometry.
According to the given information
Here are the measures of each arc:
arc AE = (17+26+28+32)° = 103°
arc ACE = (66+55+89+47)° = 257°
arc GDC = (28+32+47+89)° = 196°
arc BHC = (66+17+26+28+32+47+89)° = 305°
arc FD = (32+47)° = 79°
arc FBD = (28+26+17+66+55+89)° = 281°
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DO THE MATH: Which coffee is the better price?
Five pounds of Kroger Dark Ground at $17.81.
Bulk Pete's Italian Roast at $3.11 per pound.
Kroger Dark Ground
Pete's Italian Roast
The are both the same unit price.
Bulk Pete's has the smaller unit price, so that coffe has the better price.
Which coffee is the better price?First, we know that five pounds of Kroger Dark Ground at $17.81, then the cost of a single pound of this cofee is given by the quotient:
$17.81/5 lb = $3.56 per lb.
That is the unit price of this coffe
While we know that Bulk Pete's Italian Roast at $3.11 per pound.
So we already can see that Bulk Pete's coffec has a smaller cost per pound, so that one has the better price.
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The equation of the line l passing through (0, 7) and perpendicular to d: 3x − 6y = 1 is l: 2x + by = c. What is the value of c? Please answer with steps.
To find the equation of a line perpendicular to d: 3x − 6y = 1, we need to determine its slope. We can rewrite d in slope-intercept form as:
y = (1/2)x - 1/6
The slope of d is then 1/2. A line perpendicular to d will have a slope that is the negative reciprocal of 1/2:
slope of perpendicular line = -2
Since the line passes through (0, 7), we know that when x = 0, y = 7. We can use this point and the slope of the line to find its equation using point-slope form:
y - 7 = -2(x - 0)
y - 7 = -2x
2x + (y - 7) = 0
2x + (y - 7) = c
where c is a constant.
To find the value of c, we need another point on the line. Since the line is perpendicular to d, we know that their intersection point will be the midpoint between (0, 7) and the x-intercept of d. To find the x-intercept of d, we let y = 0:
3x - 6(0) = 1
x = 1/3
So the midpoint between (0, 7) and (1/3, 0) is:
((0 + 1/3)/2, (7 + 0)/2) = (1/6, 7/2)
This point lies on the line, so we can substitute its coordinates into the equation 2x + (y - 7) = c:
2(1/6) + (7/2 - 7) = c
1/3 = c
Therefore, the value of c is 1/3. The equation of the line passing through (0, 7) and perpendicular to d: 3x − 6y = 1 is:
the value of c is 1/3. The equation of the line passing through (0, 7) and perpendicular to d: 3x − 6y = 1 is:2x + (y - 7) = 1/3
The value of c=7.
What is a equation of line?The equation of a straight line is given by y = mx + c where m represents the slope of the line and c is the height at which the line crosses the y-axis.
The equation of the given line is l:2x+by=c and it is perpendicular to d:3x-6y=1 and also the given line l passes through point (0,7)
The slope of two mutually perpendicular lines is related as per the following formula:
m1*m2=-1
Slope for line d = 1/2. Therefore, m*(1/2)=-1
i.e. slope of line l will be m=-2.
So, the given equation becomes [tex](y-y_1)=m(x-x_1)[/tex]
[tex](y-y_1)=-2(x-x_1)[/tex]
For point (0,7) the equation will be
[tex](y-7)=-2(x-0)[/tex]
y=-2x+7
Upon comparing the obtained values will be b=1 and c=7
Hence, the value of c will be 7 for the given equation.
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What is the area of a right triangle with a height of eighteen and one-fourth meters and a base of 42 meters?
seven hundred sixty-six and one-half m2
three hundred eighty-three and one-fourth m2
sixty and one-fourth m2
thirty and one-half m2
Answer:
A = 383 [tex]\frac{1}{4}[/tex] m²
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
= [tex]\frac{1}{2}[/tex] × 42 × 18 [tex]\frac{1}{4}[/tex] ( change mixed number to improper fraction )
= 21 × [tex]\frac{73}{4}[/tex]
= [tex]\frac{21(73)}{4}[/tex]
= [tex]\frac{1533}{4}[/tex]
= 383.25
= 383 [tex]\frac{1}{4}[/tex] m²
a city council consists of five democrats and five republicans. if a committee of four people selected find the probability of selecting two democrats and two Republicans
Therefore, the probability of selecting two Democrats and two Republicans from a committee of four people is approximately 0.476 or 47.6%.
To find the probability of selecting two Democrats and two Republicans from a committee of four people out of a city council consisting of five Democrats and five Republicans, we can use the formula for probability:
Probability = (number of ways to select two Democrats and two Republicans) / (total number of ways to select any four people)
The number of ways to select two Democrats and two Republicans can be found by multiplying the number of ways to select two Democrats from the five available Democrats and the number of ways to select two Republicans from the five available Republicans. This can be expressed as:
(Number of ways to select 2 Democrats from 5 Democrats) * (number of ways to select 2 Republicans from 5 Republicans)
= (5 choose 2) * (5 choose 2)
= 10 * 10
= 100
The total number of ways to select any four people from the city council is:
(Number of ways to select 4 people from 10 people)
= (10 choose 4)
= 210
Therefore, the probability of selecting two Democrats and two Republicans is:
Probability = (number of ways to select two Democrats and two Republicans) / (total number of ways to select any four people)
= 100 / 210
= 10 / 21
≈ 0.476 or 47.6% (rounded to the nearest tenth)
Therefore, the probability of selecting two Democrats and two Republicans from a committee of four people is approximately 0.476 or 47.6%.
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An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.
Outcome Frequency
Heads, Heads 40
Heads, Tails 75
Tails, Tails 50
Tails, Heads 35
What is the P(No Tails)?
20%
25%
50%
85%
The probability of no tails is 20% which is option A.
Probability calculation.
in order to calculate the probability of no tails in the question, al we have to do is to add the frequency of the outcome given which are the "Heads, Heads" that is two heads in a row:
Probability(No Tails) = Frequency of head, Head divide by / Total frequency
The Total frequency is 40 + 75 + 50 + 35 = 200
Therefore, we can say that P(No Tails) = 40/200 = 0.2 or 20%
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