The probability of selecting 2 cards that are consonants is 3/10 or 0.3.
What is the sample space?The sample space is the set of all possible outcomes when two cards are randomly selected without replacement from a pile of cards labeled with the letters A, E, R, S, and T. There are 5 cards in the pile, so there are 5 ways to select the first card. After the first card is selected, there are only 4 cards left, so there are 4 ways to select the second card. Therefore, the sample space has 5 x 4 = 20 possible outcomes.
Sample space: {AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
Part B: The favorable outcomes are the outcomes where both cards are consonants. The consonants in the pile are R, S, and T, so there are 3 ways to select the first consonant. After the first consonant is selected, there are only 2 consonants left, so there are 2 ways to select the second consonant. Therefore, there are 3 x 2 = 6 favorable outcomes.
Favorable outcomes: {RS, RT, SR, ST, TR, TS}
Part C: The probability of selecting 2 cards that are consonants is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 6 / 20
Probability = 3 / 10
Therefore, the probability of selecting 2 cards that are consonants is 3/10 or 0.3.
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I need help with math ASAP
Answer: angle 7 is equal
Step-by-step explanation: I help ;)
In the diagram of circle A shown below , chords CD snd EF intersect at G, and chords CE and FD and drawn
Which statements is not always true?
The incorrect statement about the intersecting triangles is A. CG ≅ FG.
Why is the statement CG ≅ FG incorrect about the intersecting triangles?With intersecting triangles, it is not always guaranteed that segments like CG and FG will be congruent. The lengths of CG and FG will depend on the specific configuration of the chords and their intersection point G.
However, CE/EG = FD/DG statement is TRUE. This is a consequence of the Intersecting Chords Theorem. When two chords intersect inside a circle, the products of their segments are equal.
Since ∠CEG ≅ ∠FDG intersect inside a circle, the corresponding intercepted arcs create equal angles at the intersection point. Therefore the statement is true.
ΔCEG ~ ΔFDG is also true because we know that the triangles share an angle and have proportional sides.
The answer above is in response to the full question below;
In the diagram of circle A shown below , chords CD and EF intersect at G, and chords CE and FD and drawn
Which statements is not always true?
a. CG ≅ FG
b. CE/EG = FD/ DG
c. ∠CEG ≅ FDG
d. ΔCEG ~ ΔFDG
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Use the information in the table to find the constant of
proportionality and write the equation.
The constant of proportionality is
5
The equation that represents this proportional
relationship is
v
10
12.5
The constant of proportionality for the given relationship is 5.
What is the value of the constant of proportionality in the given relationship and what is the equation that represents this relationship?The constant of proportionality represents the ratio between two variables in a proportional relationship. In this case, the constant of proportionality is 5, which means that one variable is 5 times greater than the other variable. To write the equation that represents this relationship, we can use the formula y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality. In this case, the equation would be y = 5x, where y represents the value of the dependent variable and x represents the value of the independent variable.
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evaluate the integral using cylindrical coordinates: ∫∫∫3sin(x2 y2)dxdydz where t: 0≤x≤1,0≤y≤1−x2−−−−−√,0≤z≤1
The value of the given triple integral is (3π)/8.
How to find the value of triple integral?To evaluate the given triple integral using cylindrical coordinates, we first need to express the integrand in terms of cylindrical coordinates. The cylindrical coordinates are given by (ρ, θ, z), where ρ is the distance from the z-axis, θ is the angle made with the x-axis (0 ≤ θ ≤ 2π), and z is the height.
Converting the Cartesian coordinates to cylindrical coordinates, we have:
x = ρ cosθy = ρ sinθz = zWe also have the limits of integration:
0 ≤ x ≤ 10 ≤ y ≤ √(1 - x²)0 ≤ z ≤ 1Substituting the cylindrical coordinates and limits of integration, we have:
∫∫∫3sin(x² y)d²xdydz = ∫₀²π ∫₀¹ ∫₀¹ 3sin(ρ² cos²θ sin²θ) ρ dz dρ dθ
Evaluating the z-integral, we get:
∫₀²π ∫₀¹ 3/ρ sin(ρ² cos²θ sin²θ) dρ dθ
Simplifying the integrand, we get:
∫₀²π ∫₀¹ 3/ρ sin(ρ²(1-ρ² sin²θ)) dρ dθ
Let u = ρ²(1-ρ² sin²θ). Then, du/dρ = 2ρ(1-3ρ² sin²θ). Solving for ρ in terms of u, we have:
ρ² = u/(1+u sin²θ)
Substituting for ρ² and du/dρ, we get:
∫₀²π ∫₀¹ 3/2 ∫₀¹ sin(u)/(1+u sin²θ) du dθ
Evaluating the u-integral using u-substitution, we get:
∫₀²π ∫₀¹ 3/2 ∫₀¹ sin(u)/(1+u sin²θ) du dθ = ∫₀²π ∫₀¹ 3/2 (1/2) ln(1+u sin²θ)∣₀¹ dθ
= ∫₀²π ∫₀¹ 3/4 ln(1+sin²θ) dθ
Solving the inner integral, we get:
∫₀¹ ln(1+sin²θ) dθ = θ - tan⁻¹(sinθ)∣₀¹ = π/2
Substituting back into the original integral, we get:
∫₀²π ∫₀¹ 3/4 ln(1+sin²θ) dθ = (3/4) π/2 = (3π)/8
Therefore, the value of the given triple integral is (3π)/8.
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Describe in words where cube root of 35 would be plotted on a number line. between 3 and 4, but closer to 3 between 3 and 4, but closer to 4 between 2 and 3, but closer to 2 between 2 and 3, but closer to 3
The ∛35 will be plotted between 3 and 4, but closer to 3 on the number line.
In basic mathematics, real numbers are shown as a fine graphic of a graduated straight line which is called a number line.
Every point on a number line is considered to correspond to a real number, and every real number is assumed to correspond to a point.The integers are typically shown as lines of specially chosen, evenly spaced dots. Even though the image only shows the integers from -3 to 3, as well as values that are in between the integers, the product contains all real numbers, going forever in both directions. When teaching the very foundations , addition and subtraction with negative numbers, it is widely used as a teaching technique.We know that 35 lies between 27 and 64 , and 27 = 3³ and 64 = 4³.
Hence the ∛35 will be plotted between 3 and 4 and since 35 is closer to 27 than 64 , therefore it will be closer to 3.
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An illinois study examined the effect of day care on behavior in toddlers. randomly selected parents who had a toddler in full-time day care were asked if their child had behavioral problems. the researchers found that among 987 parents surveyed, 212 said their child had behavioral problems. among 349 randomly selected parents with a toddler at home, 17 reported that their child had behavioral problems.
4.87% of toddlers at home had behavioral problems, according to the parents surveyed.
The Illinois study examined the effect of day care on the behavior of toddlers by surveying randomly selected parents. There were two groups of parents: those with a toddler in full-time day care and those with a toddler at home.
In the first group, 987 parents with a toddler in full-time day care were surveyed. Among these parents, 212 reported that their child had behavioral problems. To calculate the percentage of children with behavioral problems in this group, we can use the following formula:
(212/987) x 100 = 21.48%
In the second group, 349 parents with a toddler at home were surveyed. Among these parents, 17 reported that their child had behavioral problems. To calculate the percentage of children with behavioral problems in this group, we can use the following formula:
(17/349) x 100 = 4.87%
The study found that 21.48% of toddlers in full-time day care had behavioral problems, whereas 4.87% of toddlers at home had behavioral problems, according to the parents surveyed.
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Evaluate mn when m=16 and n=14.
mn=
pls need help
Answer:
The answer is 16(14)=224.
Answer:
224
Step-by-step explanation:
So I see that mn is together so that must mean multiply.
m is 16 & n is 14
16 x 14=224
Hope this helps :>
(Likelihood MC)
The teacher gave a true and false quiz where P(true) = 0.7 for each question. Interpret the likelihood that the first question will be true.
Likely.
Unlikely.
Equally likely and unlikely.
This value is not possible to represent probability of a chance event.
The likelihood that the first question will be true in a true and false quiz where P(true) = 0.7 for each question is likely.
With a probability of 0.7 assigned to each question being true, there is a higher chance that the first question will be true compared to it being false.
However, it's important to note that this does not guarantee that the first question will be true, as probability represents the likelihood of an event occurring, not certainty.
how many cups of granulated sugar in a 5 pound bag
There are approximately 11.25 cups of granulated sugar in a 5 pound bag.
To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.
First, we multiply the number of pounds (5) by the conversion factor:
5 pounds * 2.25 cups/pound = 11.25 cups
Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.
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ompare segments 1 and 2. What do they represent? What does segment 8 represent in terms of the game? That is the significance of segments 5 and 7? What does segment 6 mean?
1. They represent people entering the arena
2. They represent people leaving the arena
3. No one is entering or leaving the game
4. Few people left before the end of the game.
help pls I need help tyy!
Answer:
X=125
Step-by-step explanation:
180-50=130-5=125
the sum of two numbers is 22. three times one number increased by five is 35. what are the two numbers?
Answer:
x + y = 22
3x + 5 = 35
3x = 30, so x = 10 and y = 12.
I’m so confused does anyone know the answer
Answer:
1.5(2x5)
Step-by-step explanation:
just swap the things in the parenthases
could u vote me brainliest plz? thx :)
May I have help on this? I am confused! :(
cory ships two paperback books. one weighs 3/8 pound and the other weighs 3/4 pound. which weight is greater than 1/2 pound?
The book that weighs 3/4 pounds is greater than 1/2 pounds.
To compare the weights of the two books with 1/2 pound, we need to convert 1/2 pound into a fraction with a common denominator as the given weights. The common denominator of 8 and 4 is 8. So, we can convert 1/2 pound to 4/8 pound.
Now we can compare the weights of the two books with 4/8 pounds. The weight of the first book is 3/8 pounds, which is less than 4/8 pounds. The weight of the second book is 3/4 pounds, which is greater than 4/8 pounds.
Therefore, the book that weighs 3/4 pounds is greater than 1/2 pound.
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CAN SOMEONE HELP PLS
Look at the circle graph showing the pet ownership data.
Pet Ownership
5%
6%
30%
4%
55%
Dogs
Cats
Fish
Rabbits
Hamsters
If 35 rabbits are owned, how many hamsters are owned? Enter the answer in the box.
The number of hamsters owned according to the circle graph is 28.
What is a pie-chart?A pie chart is a visual representation of data that looks like a pie with the slices representing the size of the data. To show data as a pie chart, a list of numerical variables and category variables are required. Each slice in a pie chart has an arc that is proportionate to the quantity it depicts, and as a result, the area and center angle it generates are also proportional.
Let us suppose the total number of animals = x.
Given that, a total of 35 rabbits are owned.
Thus,
5% of x = 35
5/100 (x) = 35
x = 35(100)/5
x = 700
Now, there are 4% hamsters, thus:
4% of 700 = number of hamsters.
H = 4/100 (700)
H = 28
Hence, the number of hamsters owned according to the circle graph is 28.
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on a circle of radius 4 and center (0, 0), find the x and y coordinates at angle 180 degrees (or π in radian measure).
On a circle with a radius of 4 and center at (0, 0), to find the x and y coordinates at an angle of 180 degrees (or π in radian measure), we can use the trigonometric functions.
At 180 degrees, the x-coordinate will be 0, as it lies on the y-axis. The y-coordinate can be found by using the sine function. Using the equation y = r * sin(θ), where r is the radius and θ is the angle in radians, we can substitute the values. In this case, r is 4 and θ is π (since 180 degrees equals π radians).
Therefore, the x-coordinate is 0 and the y-coordinate is 4 * sin(π) = 0. So, the x-coordinate is 0 and the y-coordinate is also 0.
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c. What is the volume of the rectangular prism?
28cm
d
Sunnevanath
Está bien
Based on the information in the question, the volume of the rectangular prism is 48 cm³.
How to find?To find the volume of a rectangular prism, we need to multiply its length, width, and height. The formula for the volume of a rectangular prism is V = l x w x h. Let's say the length of the rectangular prism is 6 cm, the width is 4 cm, and the height is 2 cm.
To find the volume, we can simply multiply 6 x 4 x 2, which equals 48 cubic centimeters (cm3). Therefore, the volume of the rectangular prism is 48 cm3.
The unit for volume is always cubed because it is a measure of the space a three-dimensional object occupies.
It is important to remember the formula for the volume of a rectangular prism because it can be used to find the volume of other three-dimensional shapes as well.
Hence, the volume is 48 cm³.
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irst consider a public good of value to Ann and Bob with the property that the value of the good can be expressed in monetary terms. In this case, the Samuelson condition states that the efficient level of the good is determined by MV +MVP where p is the per A B unit price of the good, and, for example, MV is Ann's marginal value of the good. Now consider a public good of value to Ann and Bob, the value of which CANNOT be expressed in monetary terms. In this case A O a. The Samuleson condition continues to work as in the case where values CAN be expressed in monetary terms. O b. We need more information before we can know how to modify the Samuelson condition. O c. The Samuelson condition is of no use because we cannot compare Ann's utility to Bob's. O d. The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.
The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.
When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.
Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.
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It costs $0.50 to download an individual song and $4 to download an album jada has $15 to spend downloading music how many albums can jada download is she downloads 6 individual songs
Answer:
3 albums
Step-by-step explanation:
6 x .5 = $3
15-3=12
12÷4=3
Answer:
^^3
Step-by-step explanation: If she has $15 and she has already downloaded 6 individual songs, and they cost .50, that leaves her with $12 to spend, which is 3 albums. Hope this helps!
Evaluate. Remember Order of Operations! (PEMDAS) 10+ 16 – (8÷2)
\(\large\text{Hey there!}\)
\(\large\boxed{\mathsf{10+ 16 - (8 \div 2)}}\)
\(\large\boxed{\mathsf{10 + 16 = \bf 26}}\)
\(\large\boxed{\mathsf{\rightarrow \bold{26} - (8 \div 2)}}\)
\(\large\boxed{\mathsf{{ 8 \div 2 = \bf 4}}}\)
\(\large\boxed{\rightarrow{\mathsf{26 - \bf 4}}}\)
\(\large\boxed{\mathsf{\rightarrow \bf 22 }}\)
\(\huge\boxed{\textsf{Therefore, your answer is: 22}}\)
\(\large\text{Good luck on your assignment \& enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
Simplify the expression.
the quantity negative 1 over 8 times r minus 5 minus 1 over 6 times r end quantity minus the quantity negative 6 over 8 times r plus 3 end quantity
The expression is simplified to give -r/24 - 8
What is an algebraic expression?An algebraic expression can be described as an expression that is made up of terms, coefficients, variables, factors and constants.
These expressions are also known to consist of certain arithmetic operations, which includes;
SubtractionMultiplicationDivisionAdditionParenthesesBracket, etcFrom the information given, we have that;
negative 1 over 8 times r = -1/8(r)5 minus 1 over 6 times r = 5 - 1/6r negative 6 over 8 times r plus 3 = -6/8r + 3Substitute the values
-1/8(r) - 5 - 1/6r - (-6/8r + 3)
expand the bracket
-1/8r - 5 - 1/6r + 6/8r - 3
collect like terms
-3r - 4r + 6r /24 -8
-r/24 - 8
Hence, the value is -r/24 - 8
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if 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor
Probability that at least one of them is a universal donar is 0.5263.
What is probability ?
What is probability explain?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Have given,
Probability of getting a universal donor is 0.072.
X be the “random variable” which “describes the number of universal donors” in the “sample of 10 people”.
X follows a “binomial distribution” with n=10 and p=0.072
P(X=x) = (\({n}C^{x}\))*(\(p^{x}\))*(\(q^{n-x}\)) ; x=1(1)10 ; q=1-p
Required probability,
P(X≥1)= 1 - P(X=0)
= 1 - (10C0)*(\(0.072^{0}\))*(\(0.928^{10}\))
= 1 - 0.4737 = 0.5263
Probability that at least one of them is a universal donar is 0.5263.
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ordered pair solution to y > 3
Answer:what I don’t get it pls explain
Step-by-step explanation:
Umm pls explain well is there supposed to be a picture or something
The area of a circle is A = 625. What is the
circumference?
Identify values of coefficients in the quadratic equation x^2-2x+7=0a=b=c=7x^2=10-13xa=b=c=5x^2=4x+7a=b=c=-11x+3=-4x^2a=b=c=
a = 7
b = 13
c = -10
Explanantion:\(7x^{2}\text{ = 10 - 13x}\)Re-writing the expression above in the form: ax² + bx + c = 0
7x² = 10 - 13x
7x² + 13x - 10 = 0
From 7x² + 13x - 10 = 0
a = 7
b = 13
c = -10
Math question is in the picture please help
a binder normally costs $8.99. use this information to answer the questions below
Answer:
You are asking a question that cannot be solved by anyone outside of your school.
Step-by-step explanation:
What information is below?
what shape is the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base?
The shape of the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base is triangle.
What is meant by cross section?The non-empty intersection of a solid body in three dimensions with a plane, or its equivalent in higher dimensions, is referred to as a cross section in geometry and science. Many parallel cross-sections are produced when an object is sliced. The boundary of a cross-section in three dimensions that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line.
A triangle-shaped pyramid essentially has a triangle-shaped base. The cross section formed when an imaginary line is produced to cut through perpendicular to the base will still have a triangular orientation, but it will be smaller than it was when the pyramid's original triangular orientation or sides were there.
Therefore, the shape of the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base is triangle.
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