The probability that Mike becomes the champion given that he has won the first game is 7/12.
To find the probability that Alain wins the championship given that Mike won the first game, we can repeat the same reasoning as before, but with Alain as the starting player.
P(Mike wins championship | Mike won first game) = 1 - P(Alain wins championship | Mike won first game)
This leads to:
P(Alain wins championship | Alain won first game) = 5/8
Therefore, we can conclude that:
P(Mike wins championship | Mike won first game) = 1 - P(Alain wins championship | Mike won first game) = 1 - 5/8 = 3/8 + 1/8 = 4/8 = 1/2
Thus, The probability that Mike becomes the champion given that he has won the first game is 7/12.
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need help x-y=11 2x+y=19
Answer:
(10, - 1 )
Step-by-step explanation:
x - y = 11 → (1)
2x + y = 19 → (2)
adding (1) and (2) term by term will eliminate y
(x + 2x) + (- y + y) = 11 + 19
3x + 0 = 30
3x = 30 ( divide both sides by 3 )
x = 10
substitute x = 10 into either of the 2 equations and solve for y
substituting into (2)
2(10) + y = 19
20 + y = 19 ( subtract 20 from both sides )
y = - 1
solution is (10, - 1 )
for what mileages will company a charge less than company b? use for the number of miles driven, and solve your inequality for .
Company A will charge less than Company B for any mileage greater than 70 miles. For mileages less than 70 miles, Company B will be cheaper. The inequality solved is m > 70.
To determine for what mileages Company A will charge less than Company B, we can set up an inequality with m representing the number of miles driven.
Let's start by finding the total cost for each company based on the number of miles driven:
Company A: $138 (unlimited mileage)
Company B: $75 + $0.90m (where m is the number of miles driven)
To find the mileage for which Company A will charge less than Company B, we need to set up an inequality by equating the total cost for Company A to the total cost for Company B and then solving for m:
138 < 75 + 0.90m
Subtracting 75 from both sides, we get:
63 < 0.90m
Dividing both sides by 0.90, we get:
m > 70
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Complete question is:
Latoya is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $138 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.90 for every mile driven.
For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m .
Help please, I will give brainiest
Type the correct answer in each box. Round your answers to the nearest hundredth.
City Cat Dog
Lhasa Apso Mastiff Chihuahua Collie
Austin 24. 50% 2. 76% 2. 86% 3. 44% 2. 65%
Baltimore 19. 90% 3. 37% 3. 22% 3. 31% 2. 85%
Charlotte 33. 70% 3. 25% 3. 17% 2. 89% 3. 33%
St. Louis 43. 80% 2. 65% 2. 46% 3. 67% 2. 91%
Salt Lake City 28. 90% 2. 85% 2. 78% 2. 96% 2. 46%
Orlando 37. 60% 3. 33% 3. 41% 3. 45% 2. 78%
Total 22. 90% 2. 91% 2. 68% 3. 09% 2. 58%
The table gives the probabilities that orphaned pets in animal shelters in six cities are one of the types listed.
The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is ______%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is ______%
The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 11.71%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 29.37%.
The probability that a haphazardly chosen vagrant pet in a creature covered in Austin is a canine is 11.71%.
The probability that a haphazardly chosen stranded canine in a similar creature cover in Austin is a Chihuahua is 29.37% .
2.76% + 2.86% + 3.44% + 2.65% = 11.71%
11.71/3.44 = .2937
.2937 = 29.37%
Probability is just the way that logical something is to occur.
Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions represented by probability is called statistics.
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If a box is 8 inches long, 6 inches wide, and 10 inches tall, what is the surface of the area?
Answer:
376 inches
Step-by-step explanation:
when researching a population where it is impossible or impractical to compile a list of the elements, which sampling technique is appropriate to use?
When researching a population where it is impossible or impractical to compile a list of the elements, the sampling technique that is appropriate to use is known as the cluster sampling technique
Cluster sampling is a type of probability sampling that is frequently used when the population is too large to be measured as a whole. The population is divided into smaller, more manageable clusters that are less difficult to study than the entire population.Therefore, cluster sampling is an excellent alternative when the target population cannot be measured because it is too large, too vast, or too hard to reach. In this technique, clusters are chosen by a random process or some other procedure.The final sampling method is achieved by selecting samples from within the clusters, which are frequently chosen using simple random sampling or some other appropriate method. When it comes to cluster sampling, it's important to remember that the clusters chosen must be heterogeneous internally but homogeneous externally.
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Which value is equivalent to x+4/4+x?
O-4
O-1
O 1
O4
The correct option for the given radical equation is option C. The value after operation is equal to 1.
Given radical expression:
[tex]\frac{x+4}{4+x}[/tex]
Now, we know that the addition is commutative.
Using commutative property, 4+x = x+4,
So,
[tex]\frac{x+4}{x+4}[/tex]
Both numerator and denominator has same value, hence they could be cancelled.
[tex]\frac{x+4}{4+x}[/tex] = [tex]\frac{x+4}{x+4}[/tex]
[tex]\frac{x+4}{x+4}[/tex] = 1.
Therefore, the value which is equivalent to x+4/4+x is equal to 1.
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Find exact values for x and y
The value of x and y for the given set of values in triangle are 8√3 units and 12 units.
What is triangle?A triangle is a polygon with three sides and three angles. It is the simplest polygon that can exist in Euclidean geometry. The sum of the three interior angles of a triangle is always 180 degrees. Triangles can be classified according to the length of their sides and the measure of their angles. The most common classifications are:
Scalene triangle: A triangle with all three sides of different lengths.
Isosceles triangle: A triangle with two sides of equal length.
Equilateral triangle: A triangle with all three sides of equal length.
Acute triangle: A triangle in which all angles are less than 90 degrees.
Obtuse triangle: A triangle in which one angle is greater than 90 degrees.
Right triangle: A triangle in which one angle is exactly 90 degrees.
Here,
Using the given information:
side1 = 8√3
angle1 = 60°
We can use trigonometric ratios to find the values of x and y:
sin(60°) = y / side1
Simplifying:
y = side1 * sin(60°)
y = 8√3 * sin(60°)
y = 8√3 * (√3 / 2)
y = 12
Therefore, x = 8√3 and y = 12.
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For the following indefinite integral, find the full power series centered at
x=0 and then give the first 5 nonzero terms of the power series. [infinity]
Σ∫(e^9x - 1) / 6x dx
n=0
From the given information provided, the first 5 nonzero terms of the power series are 1.5 + 13.5x + 60.75x² + 183.375x³ + 1018.1595x⁴.
To find the power series for the given indefinite integral, we can first find the antiderivative of the integrand using substitution. Let u = 9x, du = 9dx, then:
∫(e⁹ˣ - 1) / 6x dx = (1/6) ∫([tex]e^u[/tex] - 1) / u du
We can then expand the integrand into a power series using the Maclaurin series for [tex]e^u[/tex] and ln(1+u):
(1/6) ∫([tex]e^u[/tex] - 1) / u du = (1/6) ∫[Σ(uⁿ/n!) - Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1))] du
= (1/6) [Σ(uⁿ/n! × du) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × du)]
= (1/6) [Σ(uⁿ/n! × 9dx) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × 9dx)]
= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺⁾ xⁿ / (n+1))
We can now simplify and group terms to obtain the power series centered at x=0:
(3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺¹⁾ xⁿ / (n+1))
= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) + (1/6) Σ((-1)ⁿ × (-9)⁽ⁿ⁺¹⁾ × xⁿ / (n+1))
To find the first 5 nonzero terms, we can plug in n=0 through n=4 and evaluate each term:
n=0: (3/2) × 1 = 1.5
n=1: (3/2) × 9x = 13.5x
n=2: (3/2) × 81x² / 2 - (1/6) × 81x² / 3 = 60.75x²
n=3: (3/2) × 729x³ / 6 + (1/6) × 729x³ / 4 = 183.375x³
n=4: (3/2) * 6561x⁴ / 24 - (1/6) * 6561x⁴ / 5 = 1018.1595x⁴
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This pre-image was reflected over the y-axis.
Use the segment tool to draw the image.
Segment
-10-9-8-7-6-5
H
10
9
8
←Undo
7
6
5
4
3
2
1
-3 -2 -10
y
N
-3
-
Redo
5
Because the point (-5, 3) in the pre-image and its corresponding position (5, 3) in the picture are both at the same distance from the y-axis. The pre-point image's (-3, 5) is mirrored to the image's point (3, 5).
What does the y-axis represent?The x-axis is the horizontal axis and the y-axis is the vertical axis in two-dimensional space. As seen in the image below, they are represented by two number lines that perpendicularly connect at (0, 0).
This is a reflection of the pre-image that was provided over the y-axis:
Segment
10 9 8 7 6 5 -5 -6 -7 -8 -9 -10
Because the point (-5, 3) in the pre-image and its corresponding position (5, 3) in the picture are both at the same distance from the y-axis, they are reflected to one another.
Similar to this, the pre-point image's (-3, 5) is reflected to the image's point (3, 5).
The x-coordinates of all other locations in the pre-image are negated in the image because they have corresponding points there that are equally spaced from the y-axis.
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suppose a recessive genetic disorder occurs in 9 percent of the population whst id the percentage of the populaation that is hetero
The percentage is 42% of the population is heterozygous for the recessive genetic disorder.
To determine the percentage of the population that is heterozygous for a recessive genetic disorder occurring in 9 percent of the population,
follow these steps:
1. Identify the frequency of the recessive allele (q) by taking the square root of the 9 percent occurrence (0.09). The square root of 0.09 is 0.3.
2. Calculate the frequency of the dominant allele (p) using the equation p = 1 - q. In this case, p = 1 - 0.3 = 0.7.
3. Determine the percentage of the population that is heterozygous using the equation 2pq. In this case, 2(0.7)(0.3) = 0.42 or 42%.
So, 42% of the population is heterozygous for the recessive genetic disorder.
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Factor completely x3 + 6x2 − 9x − 54.
A (x + 3)(x − 3)(x + 6)
B (x + 3)(x − 3)(x − 6)
C (x2 + 9)(x + 6)
D(x2 − 9)(x + 6
Answer:
A (x + 3)(x - 3)(x + 6)
Step-by-step explanation:
f(x) = x3 + 6x2 − 9x − 54
f(3) = 3^3 + 6(3)^2 - 9(3) - 54
= 27 + 54 - - 27 - 54 = 0
So (x - 3) is a factor.
f(-3) = 3^-3 + 6(-3)^2 - 9(-3) - 54
= -27 + 54 - 27 - 54 = 0
so (x + 3) is a factor
x + 3 * (x - 3) = x^2 - 9 and if we divide f(x) by
(x^2 - 9) we get x + 6.
Answer:
a
Step-by-step explanation:
took the test :)
Write a word sentence for the question
x - 14 = 52
Answer:
x-14=52|+14
x=52+14
x=66 candies
Step-by-step explanation: If Anna gives 14 candies to her sister, she remains with 52. How many candies does Anna have ?
ASAP
Out of 18 students who study French, German, or both, 13 study French, 5 study only German
and 6 study both.
Draw a Venn diagram below to show the two sets.
Answer:
Here is a Venn diagram that represents the given:
F B
\ /
\ /
\ /
/ \
/ \
/ \
G B
In this diagram, F represents the set of students who study French, G represents the set of students who study German, and B represents the set of students who study both French and German.
The information given tells us that 13 students study French, 5 study only German, and 6 study both French and German. Therefore, we can place 13 in the region for F, 5 in the region for G, and 6 in the overlapping region for B. The total number of students is 18, so we can calculate the number of students who study only French as 13 - 6 = 7, and the number of students who study only German as 5 - 6 = -1 (which doesn't make sense in this context, so we can ignore it).
The following data points represent the number of points the Hawaii Eagles football team scored each game.
17, 33,28,23,10,42,3
Using the data, create and histogram
The class intervals are given as:
0 - 15 15-30 30-45
2 3 2
What is a Histogram?A histogram is a graphical representation of the distribution of numerical data. It is a way of summarizing the shape and spread of a set of continuous data values into a series of bins or intervals.
The histogram is a bar graph-like representation of the data, where the data is grouped into intervals or bins on the horizontal axis and the frequency or count of observations falling into each bin is represented by the height of the bar on the vertical axis.
Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.
The class intervals are given as:
0 - 15 15-30 30-45
2 3 2
The histogram is provided below:
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Proportional or not proportional?
Step-by-step explanation:
A is not proportional
Use the graph to record the value of y axis when x is 1, 2, 3, 4, 5, 6
And record the values of x when y is 1, 2, 3, 4, 5, 6 till the end
Using the graph Value of y
(1, 0.9) (2,1.5) (3,2.2) (4,2.5) (5, 3) (6,4) (7, 5) (10,6)
Using the graph, find the value of x when y is 1 - 10)
1.2, 2.5, 5,.....
The slope of the graph also shows that it is not proportional
B is proportional
X is 0 and y is 0
When x is 5, y is 10
Ratio x: y = 5:10 = 1:2
When x is 10, y is 20
Ratio x:y is 10: 20 = 1:2 same as above
C is not proportional
When Moyra is 32, daughter is 8
When her daughter is 22, Moyra will also be 4years older, which is 36
32: 8 = 4:1
36: 12 =3:1
An environmental agency frequently samples the water in a region to ensure that the levels of a certain contaminant do not exceed 30 parts per billion (ppb). From 12 randomly selected samples of the water, the agency constructed the 99 percent confidence interval (22.5, 28.7). Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval? A For all water in the region, 99 percent of the water contains a level of the contaminant between 22.5 ppb and 28.7 ppb. B We are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb. We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb. D There is a 0.99 probability that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb. E There is a 0.99 probability that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb.
The correct interpretation of the 99 percent confidence interval (22.5, 28.7) is B: We are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb.
This does not indicate that the mean level of the contaminant in all the water in the region is necessarily between 22.5 ppb and 28.7 ppb.
Confidence intervals provide an estimate of the population mean based on a sample. In other words, they indicate the range of values that are likely to include the true mean of the population. Therefore, the interval (22.5, 28.7) indicates that we are 99 percent confident that the mean of the sample (which is used to estimate the true population mean) lies between 22.5 ppb and 28.7 ppb. However, this does not guarantee that the true population mean (i.e., the mean of all the water in the region) lies between 22.5 ppb and 28.7 ppb.
The other answers are incorrect because they do not reflect the fact that the interval provides an estimate of the population mean based on a sample.
Answer A is incorrect because it states that all of the water in the region must contain a level of the contaminant between 22.5 ppb and 28.7 ppb, which is not necessarily true.
Answer D is incorrect because it states that there is a 0.99 probability that the mean of the sample is between 22.5 ppb and 28.7 ppb, when in reality the interval indicates that we are 99 percent confident that the mean of the sample is between 22.5 ppb and 28.7 ppb. Finally,
Answer E is incorrect because it states that there is a 0.99 probability that the true population mean (i.e., the mean of all the water in the region) is between 22.5 ppb and 28.7 ppb, which is not necessarily true.
In summary, the correct interpretation of the 99 percent confidence interval (22.5, 28.7) is that we are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb.
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Help pleasee it’s urgent
Equation:
89.50=2.35c+5.50d
If theres 22 dogs and cats in total you can plug in number less than 22 for c(# of cats) and d(# of dogs).
So we try pats numbers 8 cats and 14 dogs so
89.50=2.35(8)+5.50(14)
89.50=18.8+77
89.50=95.8
So pats numbers were wrong so we try different numbers
So i started pluging in numbers from under 22 so i got c is 10 and d is 12 lets try it with the equation
89.50=2.35(10)+5.50(12)
89.50=23.5+66
89.50=89.50 so it works the answer to how many number of dogs and cats is 12 dogs and 10 cats
How can you describe the relationship among angles and sides in a triangle?
Answer: The longest side is on the opposite of the largest angle and the shortest side is on the opposite of the shortest angle.
Step-by-step explanation:
Camacho is buying a monster truck. The price of the truck is a dollars, and he also has to pay a 13% monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck? Choose 2 answers: D (1 + 0.13)x 13 100 13x X 1.13x Smy 13x + x
The expression which represents the given relatiοn is x(1 + 0.13). Thus, option A is cοrrect.
What are equations?Equatiοns are statements in mathematics that have twο algebraic expressiοns οn either side οf the equals (=) sign. It shοws that the expressiοns printed οn the left and right sides have an equal relatiοnship.
In any mathematical equatiοn, we have LHS = RHS (left hand side = right hand side). Equatiοns can be sοlved tο find the value οf an unknοwn variable that represents an unknοwn quantity.
If there is nο "equal tο" symbοl, a statement is nοt an equatiοn. When twο expressiοns have equal values, a mathematical statement knοwn as an equatiοn includes the symbοl "equal tο" between them.
Let the x represent the price οf mοnster truck
Then He has tο pay extra 13% οf the tοy = 0.13
Tοtal price = x + x × 0.13
simplifying
x + x × 0.13
x + 0.13x
x(1 + 0.13) ⇒ οptiοn A
x(1.13)
1.13x ⇒ οptiοn D
Thus, The expressiοn which represents the given relatiοn is x(1 + 0.13). Thus, οptiοn A and D is cοrrect.
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Complete question:
Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a %13 monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck?
Choose 2 answers:
(Choice A) (1+0.13)x
(Choice B) 13/100 x
(Choice C) 14x
(Choice D) 1.13x
(Choice E) 13x+x
Solve each system by substitution.
1. -3x-3y=3
y=-5x-17
2. y=5x-17
-3x-2y=-12
3. -7x-2y=-13
x-2y=11
Answer:
1. x = -4
y = 3
2.
[tex]x = 3 \frac{7}{13} [/tex]
[tex]y = \frac{9}{13} [/tex]
3. x = 3
y = -4
Step-by-step explanation:
I added a photo of my solution
carlos and juan take 5 hours to do a job. carlos alone takes 8 hours to do the same job. how long would it take juan to do the same job alone?
13.33 hrs long would it take juan to do the same job alone.
Here, we have,
given that,
carlos and juan take 5 hours to do a job.
carlos alone takes 8 hours to do the same job.
let, x hr long would it take juan to do the same job alone.
now, we have,
1 hr work of carlos = 1/8
1 hr work of juan = 1/x
1 hr work of both = 1/8 + 1/x = (x+8)/8x
we have,
So they together can do this job in = 5 hours
so, ATQ, we get,
(x+8)/8x = 1/5
or, (5x+40) = 8x
or, 3x = 40
or. x = 13.33
Hence, 13.33 hrs long would it take juan to do the same job alone.
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What is the volume of a triangular prism that has 75 cm and has a base with an area of 30 cm
The volume of the triangular prism is 24 cm³.
Define triangular prismA triangular prism is a three-dimensional geometric shape that has two parallel, congruent triangular bases and three rectangular faces connecting the bases. The rectangular faces are perpendicular to the bases and to each other. The height of the prism is the perpendicular distance between the two parallel bases
the Pythagorean theorem to find the length of the third side:
a² + b² = c²
where a and b are the lengths of the two equal sides, and c is the length of the third side (the base of the triangle).
Since we know that the base has a length of 75 cm and the area is 30 cm², we can solve for one of the equal sides using the formula for the area of a triangle:
Area = (base × height) / 2
30 cm² = (75 cm×height) / 2
height = 0.8 cm
Now we can use the formula for the volume of a triangular prism:
Volume = Base Area× Height
Volume = 30 cm² ×0.8 cm
Volume = 24 cubic centimeters (cm³)
Therefore, the volume of the triangular prism is 24 cm³.
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Person 1 has X amount of shoes. Person 2 has two or more than three times Person 1's amount. Write an expression for total amount for both people.Person 1 has X amount of shoes. Person 2 has two or more than three times Person 1's amount. Write an expression for total amount for both people.
The expression for the total amount of shoes for both people is 4X + 2.
What is another word for total cost?As a result, total cost is the sum of fixed and variable costs, or TC = FC + VC = Kr+Lw.
Say Person 1 owns X pairs of shoes. So, Person 2 has two to three times as much as Person 1. This can be said as follows:
Person 2 possesses at least two more than three times Person 1's amount, so Person 2's amount is equal to 3X + 2.
By simply adding Person 1's and Person 2's shoe counts, we can determine the total number of shoes for both individuals, which results in:
Total equals the sum of the amounts given by Persons 1 and 2.
When we replace the value of Person 2's contribution, we obtain:
Amount total = X + (3X + 2)
If we simplify, we get:
Total = 4X plus 2
Hence, 4X + 2 is the total number of shoes for both individuals.
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the gallup poll surveyed a representative sample of american adults and offered a list of seven personal economic problems that many people face. what are the top financial concerns that people have?
According to a histogram that displays the percentage of replies over time, an April Gallup poll indicated that 55% of Americans think autonomous cars would be widely used in the next ten years.
Whether completely automated "driverless automobiles" would be widely deployed in the United States was the subject of a Gallup Poll conducted in April, which polled Americans ages 18 and older.
How soon, in your opinion, do you believe autonomous cars will be widely used in the US? According to the survey, 55% of Americans think autonomous cars will become commonplace over the next ten years.
The survey's results were displayed as a histogram, displaying the proportion of replies at various time intervals. This indicates how many respondents indicated that driverless cars will be widely utilised within a particular time period (e.g., within 5 years, within 10 years, etc.).
This survey reveals how people feel about autonomous cars in the future and how soon they believe they will be a common sight on the roads.
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The question is -
A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.
An angle measures 62° more than the measure of its complementary angle. What is the measure of each angle?
What is the percent of increase from 50 to 95?
Gardening is planting a garden. It has the shape of a right triangle. Wants plants for each square of area. How many plants does want in the garden? 7 yards 24 yards 25 yards
The garden would require 84 plants, which is the same number of plants as the garden's surface area.
The area of the garden can be determined using the formulas below if it is shaped like a right triangle and has sides that are 7 and 24 yards long.
Area of the garden = (1/2) x Base x Height
Area of the garden = (1/2) x 7 x 24
Area of the garden = 84 square yards
Since there is one square yard of area for each plant, the number of plants needed for the garden would be equal to the area of the garden, which is 84 plants.
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Suppose you select a number at random from the sample space {-3, -2, -1, 0, 1, 2, 3, 4). Find the probability. P(the number is less than 2 | the number is less than 4)
Evaluate 4!
Evaluate 6!
Evaluate 5!/3!
Answer:
Step-by-step explanation:
There are four numbers in the sample space that are less than 4: -3, -2, -1, and 0. Of these, three are less than 2: -3, -2, and -1. Therefore, the probability P(the number is less than 2 | the number is less than 4) is 3/4.
To evaluate 4!, we perform the multiplication 4 x 3 x 2 x 1, which equals 24.
To evaluate 6!, we perform the multiplication 6 x 5 x 4 x 3 x 2 x 1, which equals 720.
To evaluate 5!/3!, we first calculate 5! (which is equal to 5 x 4 x 3 x 2 x 1, or 120) and then divide by 3! (which is equal to 3 x 2 x 1, or 6). Therefore, 5!/3! = 120/6 = 20.
Find the volume of a cylinder that has a diameter of 14mm
14 mm and a height of 8
m
m
8 mm.
Use
π=3.14
π=3.14 and round your answer to the nearest hundredth.
Step-by-step explanation:
as with any regular 3D object : the volume is
base area × height
in the case of a cylinder, the base area is a circle, abd the area of circle is
pi × r²
with r being the radius (= half of the diameter).
so, in our case we have the volume to be
pi × (14/2)² × 8 = 3.14 × 7² × 8 = 3.14 × 49 × 8 =
= 1,230.88 mm³
Two streets form an intersection. ∠C and ∠D are vertical angles. If the measure of ∠C is (x + 16°) and the measure of ∠D is (4x − 5⋅).What is the measure of ∠D?
2.75°
8°
23°
33.8°
Answer:
the measure of ∠D is 8°.
Step-by-step explanation:
Since ∠C and ∠D are vertical angles, they have equal measure. So we can set their measures equal to each other and solve for x:
x + 16° = 4x - 5°
6x = 21°
x = 3.5°
Now we can find the measure of ∠D:
∠D = 4x - 5°
∠D = 4(3.5°) - 5°
∠D = 8°
Therefore, the measure of ∠D is 8°.