Answer: 5040ways
Step-by-step explanation:
This is a circular permutation question. Arrangement of objects in a circular path is (n-1)! where n is the amount of object. Since there are 8 students sitting in a circle excluding their teacher, they can sit in (8-1)! ways i.e 7! ways
7! = 7×6×5×4×3×2×1
7! = 5040ways
This means the students can sit in a circle in 5,040 ways
Final answer:
To find out the number of ways 8 students can sit in a circle, we calculate 7! (7 factorial), as the formula for arrangements in a circle is (n-1)!, resulting in 5040 ways.
Explanation:
The question involves determining the number of ways 8 students can sit in a circle. When arranging n distinct objects in a circle, the number of arrangements is given by (n-1)! .
since one position is fixed to account for the circular arrangement's rotational symmetry. In this case, with 8 students, the calculation is as follows: 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways.
Therefore, the students can sit in a circle in 5040 different ways.
A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation 5. A e 95 percent confidence level? (A) with 100 confidence intervals, we can be95% co nfident that the sample proportion of citizens of the (B) We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the (C) We would expect about 5 of the 100 confidence intervals to not contain the sample proportion of citizens of (D) Of the 100 confidence intervals, 95 of the intervals will be identical because they were constructed from (E) The probability is 0.95 that 100 confidence intervals will yield the same information about the sample United States who are optimistic about the economy
Answer:
Correct option (B).
Step-by-step explanation:
A 95% confidence interval for a population parameter implies that there is 0.95 probability that the population parameter is contained in that interval.
Or, if 100, 95% confidence intervals are created then 95 of those intervals would contain the population parameter with probability 0.95.
In this question the 95% confidence interval was created for population proportion of all United States citizens who were optimistic about the economy.
Then this 95% confidence interval implies that if 100 such confidence intervals were created then 95 of those would consist of the true proportion of US citizens who were optimistic about the economy..
Thus, the correct option is (B).
Answer:
We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.
Step-by-step explanation:
Jerry is buying a new large screen television for his game room.He knows that the diagonal of the television measures 42.1 inches and the base is 34.3 inches.What is the area of the television (round to the nearest tenth)
Answer:
Step-by-step explanation:
The large screen television is rectangular in shape. The diagonal divides the rectangle into two equal right angle triangles. The diagonal represents the hypotenuse of the right angle triangle.
He knows that the diagonal of the television measures 42.1 inches and the base is 34.3 inches. To determine the height,h of the triangle which is also the width of the rectangle, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
42.1² = 34.3² + h²
h² = 1772.41 - 1176.49 = 595.92
h = √595.92 = 24.41 inches.
Area of rectangle = Length × width
Area of Television = 34.3 × 24.41 = 837.3 inches²
Ms Nelson will be teaching a group math lesson with counters frist she dumps out 4 bags that have 20 counters each then she divides the counter among 6 group of students
Answer:
13 r 3
Step-by-step explanation:
Marie used one bag of flour.She baked two loaves of bread.Each loaf required 2 1/4 cups of flour.Then she used the remaining 6 1/2 cups of flour to make muffins.How much flour was in the bag to begin with
Final answer:
Marie used 4 1/2 cups of flour for the bread and had 6 1/2 cups left for the muffins. By adding these amounts together, we find that the original bag of flour contained 11 cups of flour in total.
Explanation:
To determine how much flour was initially in the bag, we need to add together the amount of flour used for the bread and the muffins.
Marie baked two loaves of bread, with each loaf requiring 2 1/4 cups of flour. Therefore, the total flour used for bread is:
2 loaves × 2 1/4 cups/loaf = 4 1/2 cups
After baking the bread, she used the remaining 6 1/2 cups of flour to make muffins. To find the initial amount of flour in the bag, we add the flour used for the bread to the flour used for the muffins:
4 1/2 cups + 6 1/2 cups = 11 cups
Therefore, the bag originally had 11 cups of flour.
PLEASE HELPPP!!! QUESTION AND ANSWERS IN PICTURE !!!
A vertical pole is supported by a wire that is 26 feet long. If the wire is attached to the ground 24 feet away from the base of the pole, how many feet up the pole should the wire be attached?
The answer is in the attachment
Final answer:
Using the Pythagorean theorem, the calculation shows that the wire should be attached 10 feet up the pole to support it if the wire is 26 feet long and attached to the ground 24 feet away from the base of the pole.
Explanation:
The question asks how high up the pole a wire should be attached if the pole is supported by a wire that is 26 feet long and is attached to the ground 24 feet away from the base of the pole. This scenario forms a right triangle with the ground and the pole as the perpendicular sides, and the wire as the hypotenuse. To solve for the height of the pole where the wire should be attached (the vertical side of the triangle), we can use the Pythagorean theorem which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): [tex]a^2 + b^2 = c^2[/tex].
Given that the distance from the pole to the point where the wire is attached to the ground (b) is 24 feet and the length of the wire (c) is 26 feet, we can set up the equation as follows:
[tex]24^2 + a^2 = 26^2[/tex]
576 + [tex]a^2[/tex] = 676
[tex]a^2[/tex] = 676 - 576
[tex]a^2[/tex] = 100
a = [tex]\sqrt{100}[/tex]
a = 10
Thus, the wire should be attached 10 feet up the pole.
Davis is putting tile in his rectangular kitchen. His kitchen is 13 feet long, and 17 feet wide. The tile davis is installing is $3.75 per square foot. How much will it cost davis
Answer:
It will cost is $828.75.
Step-by-step explanation:
Given:
Davis is putting tile in his rectangular kitchen. His kitchen is 13 feet long, and 17 feet wide. The tile davis is installing is $3.75 per square foot.
Now, to find the total cost.
Davis is putting tile in his rectangular kitchen.
Length = 13 feet.
Width = 17 feet.
So, to get the area of kitchen:
Area = length × width
Area = 13 × 17
Area = 221 square foot.
As, the unit rate is given.
Cost per square foot = $3.75.
Now, to get the total cost by using unitary method:
If cost of 1 square foot = $3.75.
So, the cost of 221 square foot = $3.75 × 221
= $828.75.
Therefore, it will cost $828.75.
To find the total cost of tiling Davis' kitchen, we need to find the area of the kitchen in square feet by multiplying its length and width, then multiply the area by the cost per square foot. In this case, it will cost Davis $828.75 to tile his kitchen.
Explanation:The question is about Davis installing tiles in his rectangular kitchen and how much the cost will be at $3.75 per square foot. First, we need to determine the total area of the kitchen. In this case, the kitchen is rectangular in shape and the area of a rectangle is calculated by multiplying the length by the width. Here, length is 13 feet and the width is 17 feet, hence the area of the kitchen is 13 x 17 = 221 square feet.
Now, the cost per square foot of tile is given as $3.75. So, we multiply the total area by the cost per square foot to determine the overall cost of the tile. The calculation is as follows, 221 square feet x $3.75 = $828.75.
Therefore, it will cost Davis $828.75 to tile his kitchen.
Learn more about Area and Cost Calculation here:https://brainly.com/question/30694298
Help please
Find the area of the following figure: (Do NOT include the units in your answer...only type the numerical portion of your answer!)
Answer:
84
Step-by-step explanation:
Area of a rectangle : A = bh
5 x 6 = 30
Area of a trapezoid : A = 1/2 (b1 + b2) h
b1: 7 + 5 = 12
b2: 15
h: 10 - 6 = 4
12 + 15 = 27
27 x 4 x .5 = 54
Add the areas up:
30 + 54 = 84
{(2,4),(3,5),(4,6),(5,8)}
Step-by-step explanation:
The given four sides of quadrilateral = (2, 4), (3, 5), (4, 6) and (5,8)
To find, the area of the quadrilateral = ?
We know that,
The area of quadrilateral [tex]=\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]
[tex]=\dfrac{1}{2} [2( 5-6)+3( 6-8)+4( 8-4)+5(4-5)][/tex]
[tex]=\dfrac{1}{2} [2(-1)+3(-2)+4(4)+5(-1)][/tex]
[tex]=\dfrac{1}{2} (-2-6+16-5)[/tex]
[tex]=\dfrac{1}{2} (16-13)[/tex]
= [tex]\dfrac{3}{2}[/tex] units
Thus, the area of the quadrilateral is [tex]\dfrac{3}{2}[/tex] units.
A statistician proposed a new method for constructing a 90 percent confidence interval to estimate the median of assessed home values for homes in a large community. To test the method, the statistician will conduct a simulation by selecting 10,000 random samples of the same size from the population. For each sample, a confidence interval will be constructed using the new method. If the confidence level associated with the new method is actually 90 percent, which of the following will be captured by approximately 9,000 of the confidence intervals constructed from the simulation? a. The sample mean b. The sample median c. The sample standard deviation d. The population mean e. The population median
Answer: e. The population median
Step-by-step explanation:
If repeated intervals are taken for each sample then the 90% of the intervals would actually have the population median in them. The other options like the sample mean, the sample median and the sample standard deviation and population will not be captured as only the population median is captured and confidence intervals can be interpreted in this way.
Samuel wants to eat at least 15 grams of protein each day. Let x represent the amount of protein he should eat each day to meet his goal. Which inequality represents this situation?
Answer:
X is greater than or equal to 15
Step-by-step explanation:
Final answer:
The inequality x >= 15 represents Samuel's goal of eating at least 15 grams of protein each day. Protein-rich foods like chicken breast and Greek yogurt are good sources of protein.
Explanation:
The inequality representing the situation is: x >= 15
To meet his goal of eating at least 15 grams of protein each day, Samuel should eat at least 15 grams of protein daily.
Examples of protein-rich foods include:
3 ounces of chicken breast: about 25 grams of protein
1 cup of Greek yogurt: approximately 20 grams of protein
26 POINTS!!! BRAINLIEST TOO.
Answer:
Therefore option A.) 0 is correct.
Step-by-step explanation:
The graph is attached.
The solution of the equations as seen from the intersection of the equations in the graph is (0,2).
Therefore x = 0 is the solution which gives y = 2 for both equations.
Therefore option A.) 0 is correct.
which of the following is the product of the rational expressions shown below? 7x/x-4•x/x+7
Step-by-step explanation:
We have,
[tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex]
To find, the product of the rational expressions [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex] = ?
∴ [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex]
= [tex]\dfrac{7x.x}{(x-4)(x+7)}[/tex]
= [tex]\dfrac{7x^2}{(x(x+7)-4(x+7)}[/tex]
= [tex]\dfrac{7x^2}{x^2+7x-4x-28}[/tex]
= [tex]\dfrac{7x^2}{x^2+3x-28}[/tex]
Thus, the product of the rational expressions [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7} = \dfrac{7x^2}{x^2+3x-28}[/tex].
Which choice is equivalent to the quotient shown here when x>0?
Answer:
The answer to your question is letter C.
Step-by-step explanation:
[tex]\sqrt{50x^{3}}[/tex] Find the prime factors of 50
50 2
25 5
5 5
1
50 = 2 5²
[tex]\sqrt{5^{2} 2 x^{2} x} = 5 x\sqrt{2x}[/tex]
[tex]\sqrt{32x^{2}}[/tex] Find the prime factors of 32
32 2
16 2
8 2
4 2
2 2
1
32 = 2⁴2[tex]\sqrt{32x^{2}} = 2^{2} x\sqrt{2} = 4x\sqrt{2}[/tex]
Division [tex]5x\sqrt{2}\sqrt{x} / 4x\sqrt{2}[/tex]
Simplification [tex]\frac{5\sqrt{x}}{4}[/tex]
Answer:
C
Step-by-step explanation:
A P E x
Racheal has a board that is 1 7/12 feet long and another board that is 2 11/12 feet long. Write an expression Racheal can use to find the total length I feet of the two boards
Racheal can use the expression [tex]\(4 \frac{1}{2}\)[/tex] feet to find the total length of the two boards.
To find the total length of the two boards, Racheal needs to add the lengths of the two boards together.
The length of the first board is [tex]\(1 \frac{7}{12}\)[/tex] feet, and the length of the second board is [tex]\(2 \frac{11}{12}\)[/tex] feet.
To add these lengths together, we first need to convert them to improper fractions:
[tex]\[ 1 \frac{7}{12} = \frac{12}{12} + \frac{7}{12} = \frac{19}{12} \][/tex]
[tex]\[ 2 \frac{11}{12} = \frac{24}{12} + \frac{11}{12} = \frac{35}{12} \][/tex]
Now, to find the total length, we add the lengths of the two boards:
[tex]\[ \text{Total length} = \frac{19}{12} + \frac{35}{12} \][/tex]
To add fractions, we need a common denominator, which in this case is [tex]\(12\)[/tex].
[tex]\[ \text{Total length} = \frac{19}{12} + \frac{35}{12} = \frac{19 + 35}{12} = \frac{54}{12} \][/tex]
Now, we simplify the fraction:
[tex]\[ \text{Total length} = \frac{54}{12} = 4 \frac{1}{2} \][/tex]
So, Racheal can use the expression [tex]\(4 \frac{1}{2}\)[/tex] feet to find the total length of the two boards.
You can work a total of no more than 10 hours each week at your two jobs. Your house cleaning job pays $5. per hour and your sales job pays $8 per hours. You need to earn at least $56 each week to pay your bills.
Define your variables and write a system of inequalities that shows the number of hours you can work at each job.
System of inequalities are, [tex]x+y<10[/tex] and [tex]5x+8y\geq 56[/tex]
Let us consider, He does house cleaning job for x hours and sales job for y hours.
Since, he can work a total of not more than 10 hours each week at two jobs.
So, inequality are, [tex]x+y<10[/tex]
Since, house cleaning job pays $5. per hour and sales job pays $8 per hours.
Thus, Total earn = 5x + 8y
But he need to earn at least $56 each week
So, inequality are , [tex]5x+8y\geq 56[/tex]
Learn more:
https://brainly.com/question/15816805
Final answer:
The variables x and y represent the hours worked at the house cleaning and sales jobs, respectively. The system of inequalities x + y ≤ 10, 5x + 8y ≥ 56, and x ≥ 0, y ≥ 0 reflects the constraints on work hours and minimum earnings.
Explanation:
To solve the problem, we need to define two variables representing the hours worked at each job:
Let x be the number of hours worked at the house cleaning job.
Let y be the number of hours worked at the sales job.
Given the conditions of the problem, we can formulate the following system of inequalities:
The total working hours from both jobs cannot exceed 10 hours per week: x + y ≤ 10.
The total earnings must be at least $56 to pay bills: 5x + 8y ≥ 56.
The number of working hours cannot be negative: x ≥ 0 and y ≥ 0.
This system of inequalities represents the constraints on the number of hours you can work at each job and the minimum earnings required to pay your bills.
Grandma's bakery sells single crust apple pies for $6.99 in double crust cherry pies for $10.99. The total number of pies sold on a busy Friday was 36. If the amount collected that day was $331.64 how many of each type were sold
Answer: 16 single crust apple pies and double crust apple pies were sold.
Step-by-step explanation:
Let x represent the number of single crust apple pies sold on a Friday.
Let y represent the number of double crust apple pies sold on a Friday.
The total number of pies sold on a busy Friday was 36. This means that
x + y = 36
Grandma's bakery sells single crust apple pies for $6.99 in double crust cherry pies for $10.99. The total amount that was collected that Friday was $331.64. This means that
6.99x + 10.99y = 331.74- - - ---- - - - -1
Substituting x = 36 - y into equation 1, it becomes
6.99(36 - y) + 10.99y = 331.74
251.64 - 6.99y + 10.98y = 331. 74 - 3 31.74
251.64 - 331.74
4y = 80
y = 80/4 = 20
x = 36 - y i= 36 - 20
x = 16
Aliens have injected Ana with mathematical nanobots. These nanobots force Ana to think about math more and more. Initially, there were only five nanobots. The population of the nanobots doubles every hour. The population of the nanobots follows the equations p(t) = 5·2^t. After there are 106nanobots, Ana will cease thinking of anything other than math. How many hours will it take for math to take over Ana's brain?
Answer:
Math will take over Ana's brain at 4.4 hours
Step-by-step explanation:
Exponential Grow
The population of the nanobots follows the equation
[tex]p(t) = 5\cdot 2^t[/tex]
We must find the value of t such that the population of nanobots is 106 or more, that is
[tex]5\cdot 2^t\geq 106[/tex]
We'll solve the equation
[tex]5\cdot2^t= 106[/tex]
Dividing by 5
[tex]2^t= 106/5=21.2[/tex]
Taking logarithms
[tex]log(2^t)= log(21.2)[/tex]
By logarithms property
[tex]t\cdot log(2)= log(21.2)[/tex]
Solving for t
[tex]\displaystyle t=\frac{log21.2} {log2}[/tex]
[tex]t=4.4 \ hours[/tex]
Math will take over Ana's brain at 4.4 hours
It will take 5 hours for the nanobot population to reach 160, utilizing the equation p(t) = 5·[tex]2^t[/tex] and solving for t.
Explanation:The problem involves determining how long it will take for the population of nanobots, which doubles each hour, to reach a specific number. The equation given for the population of nanobots at any time t is p(t) = 5·[tex]2^t[/tex], where t is the time in hours. We are tasked with finding the value of t when the population reaches or exceeds 160 nanobots.
To solve this, we set the equation equal to 160 and solve for t:
p(t) = 5·[tex]2^t[/tex] = 160Dividing both sides by 5 gives:
[tex]2^t = 32[/tex]To find t, we need to determine the power of 2 that equals 32. This can be expressed as 2⁵ = 32. Therefore, t = 5. It will take 5 hours for the population of nanobots to reach 160, at which point Ana will think of nothing but math.
Let w represent Henry's weight in pounds. Eric weighs 12 pounds less then Henry. Write an algebraic expression that represents Eric's weight in pounds.
Answer:
Step-by-step explanation:
w = Henry's weight
e = Eric's weight
e = w - 12
The algebraic expression that represents Eric's weight in pounds is [tex]\( w - 12 \)[/tex].
1. We're given that [tex]\( w \)[/tex] represents Henry's weight in pounds. This means we're using the variable [tex]\( w \)[/tex] to stand for whatever Henry's weight is.
2. The problem states that Eric weighs 12 pounds less than Henry. So, if Henry weighs [tex]\( w \)[/tex] pounds, then Eric's weight would be [tex]\( w - 12 \)[/tex] pounds because he's 12 pounds lighter than Henry.
3. Therefore, the expression [tex]\( w - 12 \)[/tex] represents Eric's weight in pounds. We subtract 12 from Henry's weight [tex]\( w \)[/tex] to get Eric's weight. This expression tells us Eric's weight in terms of Henry's weight.
Suppose that the height(In centimeters) Of a candle is a linear function of time (in hours) it has been burning. After seven hours of burning, a candle has high of 22.5 Centimeters. After 26 hours of burning, it's high is 13 cm. What is the height of the candle after 10 hours
Answer: the height after 10 hours is 21 cm
Step-by-step explanation:
Assuming the rate at which the height of the candle is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
If after seven hours of burning, a candle has high of 22.5 Centimeters, the expression is
22.5 = a + (7 - 1)d
22.5 = a + 6d - - - - - - - - - -1
If after 26 hours of burning, it's height is 13 cm. The expression is
13 = a + (26 - 1)d
13 = a + 25d - - - - - - - - - - - 2
9.5 = - 19d
d = 9.5/ - 19
d = - 0.5
Substituting d = - 0.5 into equation 1, it becomes
22.5 = a + 6 × - 0.5
22.5 = a - 3
a = 22.5 + 3
a = 25.5
The linear expression becomes
Tn = 25.5 - 0.5(n - 1)
The height of the candle after 10 hours would be
25.5 - 0.5(10 - 1)
= 25.5 - 4.5
= 21 centimeters
There was 1/4 watermelon in the refrigerator. Mom brought home 1/2 watermelon from the grocery store. What fractional part of the watermelon did the family have for supper
Answer:
The family would have [tex]\frac34[/tex] of the watermelon for supper.
Step-by-step explanation:
Given:
Amount of watermelon in refrigerator = [tex]\frac14[/tex]
Amount of water melon brought form grocery store =[tex]\frac12[/tex]
We need to find the fraction of water melon family have for supper.
Solution:
Now we can say that;
the fraction of water melon family have for supper is equal to sum of Amount of watermelon in refrigerator and Amount of water melon brought form grocery store.
framing in equation form we get;
the fraction of water melon family have for supper = [tex]\frac14+\frac12[/tex]
Now taking LCM to make the denominator common we get;
the fraction of water melon family have for supper = [tex]\frac{1\times1}{4\times1}+\frac{1\times2}{2\times2}=\frac{1}{4}+\frac24[/tex]
Now denominators are common so we will solve for numerator we get;
the fraction of water melon family have for supper = [tex]\frac{1+2}{4}=\frac34[/tex]
Hence the family would have [tex]\frac34[/tex] of the watermelon for supper.
As the former chair of the planning board for 18 consecutive years and a board member for 28 years, Joan Philkill attended more than 400 meetings and reviewed more than 700 rezoning applications.
(A) As the former
(B) The former
(C) Former
(D) She was
(E) As the
Answer:
Option E is the correct answer (As the)
Step-by-step explanation:
Option A indicates that Joan, for 18 years, was the former chair; it is inappropriate to think that she would be attending meetings while she was the former chair. The sentence indicates that Joan served for 18 years as the chair lady, and during this time she attended meetings. Thus, option E is clearer and precise in its meaning than option A.
The bill for five glasses of apple juice and four salads is $9.50, but the bill for four glasses of apple juice and five salads is $10.30. What would be the bill for a glass of juice and a salad?
Answer: the bill for a glass of apple juice is $0.7 and the bill for a salad is $1.5
Step-by-step explanation:
Let x represent the bill for a glass of apple juice.
Let y represent the bill for a salad.
The bill for five glasses of apple juice and four salads is $9.50. It means that
5x + 4y = 9.5 - - - - - - - - - - - 1
The bill for four glasses of apple juice and five salads is $10.30. This means that
4x + 5y = 10.30- - - - - - - - - - - -2
Multiplying equation 1 by 4 and equation 2 by 5, it becomes
20x + 16y = 38
20x + 25y = 51.5
Subtracting, it becomes
- 9y = - 13.5
y = - 13.5/-9
y = 1.5
Substituting y = 1.5 into equation 1, it becomes
5x + 4 × 1.5 = 9.5
5x + 6 = 9.5
5x = 9.5 - 6 = 3.5
x = 3.5/5 = 0.7
The bill for a glass of juice and a salad would be $2.20.
Explanation:To find the cost of a glass of apple juice and a salad, we need to set up a system of equations using the given information. Let's assign variables to the cost of a glass of apple juice and a salad. Let x be the cost of a glass of apple juice and y be the cost of a salad.
From the first sentence, we can write the equation 5x + 4y = 9.50. From the second sentence, we can write the equation 4x + 5y = 10.30.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method. Multiply the first equation by 4 and the second equation by 5 to eliminate x:
20x + 16y = 38.00
20x + 25y = 51.50
Subtract the first equation from the second:
9y = 13.50
Divide both sides by 9:
y = 1.50
Substitute this value of y into one of the original equations (let's use the first equation):
5x + 4(1.5) = 9.50
5x + 6 = 9.50
Subtract 6 from both sides:
5x = 3.50
Divide both sides by 5:
x = 0.70
Therefore, the bill for a glass of juice and a salad would be $0.70 + $1.50 = $2.20.
The legs of a right triangle are x and 15 while the hypotenuse is 17.
Which equation can be used to determine the value of x using the Pythagorean Theorem?
Answer:
Since the Option of equation are not given. Kindly chose any of the below equation from the answer to find the value of 'x'.
[tex]x^2+15^2=17^2[/tex]
[tex]x^2=17^2-15^2[/tex]
OR
[tex]x^2+225=289[/tex]
[tex]x^2=289-225[/tex]
Step-by-step explanation:
Given:
Length of One leg = x
Length of other Leg= 15
Hypotenuse = 17
We need to find the equation used to determine the value of x.
Solution:
Assuming Triangle to right angled triangle.
So we will apply Pythagoras theorem which sates that;
"The square of sum of two legs of right angle triangle is equal to square of the length of hypotenuse."
so we can say that;
[tex]x^2+15^2=17^2[/tex]
[tex]x^2=17^2-15^2[/tex]
OR
[tex]x^2+225=289[/tex]
[tex]x^2=289-225[/tex]
Since the equation are not given. Kindly chose any of the below equation from the answer to find the value of 'x'.
[tex]x^2+15^2=17^2[/tex]
[tex]x^2=17^2-15^2[/tex]
OR
[tex]x^2+225=289[/tex]
[tex]x^2=289-225[/tex]
Answer:
b
Step-by-step explanation:
A police report shows that 82% of drivers stopped for suspected drunk driving receive a breath test, 34% receive a blood test, and 24% receive both tests. What's the probability that a randomly selected DWI suspect receives neither test
Answer:
0.08
Step-by-step explanation:
If 8% of drivers receive neither test, then the probability = 8/100 = 0.08
Final answer:
The probability that a randomly selected DWI suspect receives neither a breath test nor a blood test is 8%, determined by subtracting the combined probability of receiving at least one test (92%) from 1.
Explanation:
Calculating the Probability of Receiving Neither Test
To determine the probability that a DWI (driving while intoxicated) suspect receives neither a breath test nor a blood test, we can use the principle of inclusion-exclusion from probability theory. According to the police report, 82% receive a breath test, 34% receive a blood test, and 24% receive both tests.
Firstly, we need to find the probability of a suspect receiving at least one test. We add the probabilities of receiving each test and subtract the probability of receiving both tests to avoid double-counting:
P(Breath or Blood Test) = P(Breath) + P(Blood) - P(Both)
= 0.82 + 0.34 - 0.24
= 0.92
This means that 92% of DWI suspects receive at least one test. To find the probability that a suspect receives neither test, we subtract this value from 1 since the sum of the probabilities of all possible outcomes must equal 1:
P(Neither) = 1 - P(Breath or Blood Test)
= 1 - 0.92
= 0.08 or 8%
Hence, the probability that a randomly selected DWI suspect receives neither a breath test nor a blood test is 8%.
An airline, believing that 5% of passengers fail to show up for flights, overbooks (sells more tickets than there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 tickets. What’s the probability the airline will not have enough seats, so someone gets bumped?
Final answer:
To find the probability that the airline will not have enough seats for passengers, we need to calculate the probability that more than 265 passengers show up for the flight. The probability is 0.1525.
Explanation:
To find the probability that the airline will not have enough seats for passengers, we need to calculate the probability that more than 265 passengers show up for the flight.
First, we need to calculate the probability that a passenger shows up for the flight. Since the airline believes that 5% of passengers fail to show up, the probability that a passenger shows up is 1 - 0.05 = 0.95.
Next, we can use the binomial distribution to calculate the probability that more than 265 passengers show up. The formula for the binomial distribution is P(X > k) = 1 - P(X <= k), where X is the number of passengers who show up and k is the maximum number of passengers the plane can hold (265).
Using the binomial distribution, we can calculate the probability that more than 265 passengers show up as P(X > 265) = 1 - P(X <= 265) = 1 - binomcdf(275, 0.95, 265) = 0.1525.
Kara is sorting buttons by lengths for a craft project.The line plot shows the length of each button.If Kara lines up all the 3/4-inche buttons,what would be the total length
Answer:
[tex]2\frac{1}{4} inches.[/tex]
Step-by-step explanation:
Hi,
We see the plot line below, which shows that three crosses above [tex]\frac{3}{4} - inch[/tex] buttons, that means we have three such buttons available with us.
To find their total lengths, we have two methods:
We can add the lengths of all buttons, that means add [tex]\frac{3}{4}[/tex] thriceOr simply multiply [tex]\frac{3}{4}[/tex] by three.[tex]\frac{3}{4} \times 3\\ = \frac{3 \times 3}{4}\\= \frac{9}{4}[/tex]
changing this improper fraction into a mixed fraction: [tex]2\frac{1}{4} inches.[/tex] will be the total length of three buttons lined up.
Which interval is the solution set to 0.35x - 4.8<5.2- 0.9x
Answer:
Solution set {x|x<8}
Step-by-step explanation:
0.35x - 4.8<5.2- 0.9x
0.35x+0.9x<5.2+4.8
1.25x<10
x<10/1.25
x<8
Solution set {x|x<8}
Answer:
x < 8
Step-by-step explanation:
0.35x - 4.8 < 5.2- 0.9x
0.35x + 0.9x < 5.2 + 4.8
1.25x < 10
x < 10/1.25
x < 8
The number of pieces of popcorn in a large movie theatre popcorn bucket is normally distributed, with a mean of 1515 and a standard deviation of 15. Approximately what percentage of buckets contain between 1470 and 1560 pieces of popcorn?
Approximately 68%
Approximately 75%
Approximately 95%
99.7%
Answer:
d: 99.7
Step-by-step explanation:
We know the mean is 1515. we know the standard devation is 15. both of 1560 and 1470 are both 3 standar devations away from the mean. on a table this would show almost all of the table. hence 99.7. Now im not 100% on this as i ahve the same question on a quiz but if i get it write i will add an answer or comment to this.
Percentage of buckets contain between 1470 and 1560 pieces of popcorn= 99.7%
How is percentage mean?percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
How do you calculate percentages?The following formula is a common strategy to calculate a percentage:
Determine the total amount of what you want to find a percentage. Divide the number to determine the percentage.Multiply the value by 100To learn more about percentage, refer
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Triangle L N M is shown. Angle L N M is 90 degrees, angle N M L is 48 degrees, and angle M L N is 42 degrees. Consider △LMN. m∠L + m∠M = ° sin(L) = sin(M) =
Answer:
m∠L + m∠M = 90° sin(L) = 0.66913sin(M) = 0.74314Step-by-step explanation:
The sum of the two angles is ...
m∠L + m∠M = 42° +48° = 90°
__
A calculator can show you the sines of these angles.
sin(42°) ≈ 0.66913
sin(48°) ≈ 0.74314
_____
The two acute angles of a right triangle always have a sum of 90°.
In triangle LNM, the sum of angles L and M is 90°. The sine values for angles L and M are approximately 0.6691 and 0.7431 respectively.
The sum of the measures of angles L and M can be calculated as follows:
m∠L + m∠M = 42° + 48°
= 90°
For a right triangle, the sine of one acute angle is equal to the cosine of the other acute angle. Therefore, using trigonometry:
sin(L) = sin(42°)
≈ 0.6691
sin(M) = sin(48°)
≈ 0.7431
Thus, the sum of angles L and M is 90°, and the sine values are approximately 0.6691 and 0.7431 respectively.