The members of set A are the integer solutions of the inequality 2x−5≤11 and the members of set B are the integer solutions of the inequality −2x+7≤−9. What is one member of the intersection of A and B?
Answers
Answer:
8
Step-by-step explanation:
\(2x-5\leq 11\\2x\leq 16\\x\leq 8\)
\(-2x+7\leq -9\\-2x\leq -16\\x\geq 8\)
Once \(x \in \mathbb{Z}\) we can conclude that
\(A=(-\infty, 8]\)
\(B=[8, \infty)\)
So \(A\cap B = 8\)
Related Questions
exercise 6.1.12. find the laplace transform of f(t) = { t if t >= 1,0 if t < 1 }
Answers
The Laplace transform of f(t) = { t if t ≥ 1, 0 if t < 1 } is F(s) = \((e^{(-S)})/S^{2} + (e^{(-S)})/S.\)
To find the Laplace transform of f(t), we can use the definition of the Laplace transform: F(s) = ∫[0,∞] \(e^{(-st)} f(t) dt\). Since f(t) is zero for t < 1, we can write the integral as: F(s) = ∫[1,∞] \(e^{(-st)} f(t) dt\)
Using integration by parts with u = t and dv/dt =\(e^{(-st)}\), we get: F(s) = \([-e^{(-st)} t/S]\)∫[1,∞] \(e^{(st)} dt\) + (1/s) ∫[1,∞] \(e^{(-st)}\) dt.
Evaluating the integrals, we obtain: F(s) = (\(e^{(-s)})/S^{2}\) + (\(e^{(-S)}\))/s, which is the Laplace transform of f(t).
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in a season there are 40 matches.
How many matches should Sachin's team expect to win in a season?
Answers
One hundred and five students see a play. Each ticket costs $45. What is the total amount the students spend for tickets? Use mental math.
Answers
Answer:
4725
Step-by-step explanation:
105 students
think of 100 students
100 × 45 = 4500
now the remaining 5 students
cost for 10 students will be
45 × 10 = 450
divide 450 by 2 to find out for 5 students
it is 225
4500 + 225 = 4725
Expedition Everest, a major thrill ride at Walt Disney World, often has a demand of over 3,000 riders an hour causing long waiting times for guests wishing to ride. The attraction averages 1,800 riders an hour. The roller coaster has a design capacity of 2,050 riders an hour and an effective capacity of 1,900 riders an hour.
a. What is the efficiency of Expedition Everest?
b. What is the utilization of Expedition Everest?
c. Is the operation overcapacity or undercapacity?
Answers
a. The efficiency of Expedition Everest is approximately 87.8%.
b. The utilization of Expedition Everest is approximately 94.7%.
c. The demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.
To calculate the efficiency and utilization of Expedition Everest, we need to compare the actual number of riders with the design capacity and effective capacity.
Given:
Demand = 3,000 riders/hour
Average riders = 1,800 riders/hour
Design capacity = 2,050 riders/hour
Effective capacity = 1,900 riders/hour
a. Efficiency:
Efficiency is calculated as the average riders divided by the design capacity, multiplied by 100%.
Efficiency = (Average riders / Design capacity) * 100%
= (1,800 / 2,050) * 100%
≈ 87.8%
Therefore, the efficiency of Expedition Everest is approximately 87.8%.
b. Utilization:
Utilization is calculated as the average riders divided by the effective capacity, multiplied by 100%.
Utilization = (Average riders / Effective capacity) * 100%
= (1,800 / 1,900) * 100%
≈ 94.7%
Therefore, the utilization of Expedition Everest is approximately 94.7%.
c. Capacity Analysis:
To determine if the operation is overcapacity or undercapacity, we compare the demand with the effective capacity.
Demand > Effective capacity
3,000 > 1,900
Since the demand is greater than the effective capacity, the operation is considered overcapacity. This means that the ride cannot accommodate all the riders who wish to ride, resulting in long waiting times for guests.
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A triangle with a height of 16 inches. The height is perpendicular to the base labeled 32 inches. The side from the top of the perpendicular side to the base is labeled 35 inches. What is the area of the triangle represented? 256 in2 280 in2 512 in2 560 in2
Answers
256 in² is the area of the triangle represented.
What is known as a triangle?
A triangle is a three-sided polygon because it has three vertices. The connection of the three sides end to end at a single point creates the angles of the triangle.
The triangle's three points amount to a sum of 180 degrees. This two-dimensional shape has three straight sides. A triangle is included as a polygon with three sides. The sum of the three angles in a triangle is 180 degrees.
Area of a triangle = 1/2 * base * height
for this triangle: base = 32 in height = 16 in
area = 1/2 ( 32)(16) = 256 in²
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WILL MARK BRAINLIEST IF GOTTEN RIGHT!!!!
Answers
Answer:
C
Step-by-step explanation:
Using Pythagoras' identity in right triangle BPO
with PB = 4 ( half of AB ) and OB = 5 ( radius of circle )
OP² + 4² = 5²
OP² + 16 = 25 ( subtract 16 from both sides )
OP² = 9 ( take the square root of both sides )
OP = \(\sqrt{9}\) = 3
420 student 25 times 3 times the number of girls 2 times the number of boys how many girls amd how many boys
Answers
Complete Question
We have a total of 420 students. 2 times 3 times the number of girls is equal to 2 times the number of boys how many girls and how many boys
Answer:
The number of boys = x = 315 boys
The number of girls = y = 105 girls
Step-by-step explanation:
Let
The number of boys = x
The number of girls = y
We have 420 students
2 times 3 times the number of girls is equal to 2 times the number of boys
x + y = 420..... Equation 1
2 × 3y = 2x
6y => 2x
x => 6y/2 = 3y
We substitute 3y for x in Equation 1
3y + y = 420
4y = 420
y =>420/4
y => 105
Solving for x
x = 3y
x = 3 × 105
x = 315
Therefore,
The number of boys = x = 315 boys
The number of girls = y = 105 girls
Which tool is used to make header 1 look like header 2?
Answers
The tools that would be used to make header 1 appear and look like header 2 is the alignment tool icon and the Bold tool icon.
What is Microsoft Excel?Microsoft Excel is a spreadsheet that can be used for a variety of features such as:
Computation of Data sets and variablesCalculation of Business DataArrangement and Analysis of Data into Tables etc.As a Microsoft software, Microsoft Excel can also be used to edit sheets. In the image attached, the required tool icons needed to change the header 1 into header 2 is the alignment tool icon and the Bold tool icon. The two tools can be seen in the image as the two lower left icons.
What Excel Is Used For?Electronic spreadsheet programs were originally based on paper spreadsheets used for accounting. As such, the basic layout of computerized spreadsheets is the same as the paper ones. Related data is stored in tables — which are a collection of small rectangular boxes or cells organized into rows and columns.
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g What is the probability of a diffusing atom jumping from one site to another at 500C and 1000 C
Answers
The probability of a diffusing atom jumping from one site to another is influenced by temperature. It is typically described by the Arrhenius equation:
P = \(Ae^{(-Q/RT)}\)
Where:
P is the probability of a jump
A is the pre-exponential factor
Q is the activation energy
R is the gas constant
T is the absolute temperature in Kelvin
To calculate the probability at 500°C and 1000°C, we need to convert these temperatures to Kelvin:
\(T_{500C}\) = 500 + 273.15
= 773.15 K
\(T_{1000C}\) = 1000 + 273.15
= 1273.15 K
Assuming we have values for the pre-exponential factor (A) and activation energy (Q), we can substitute these values into the Arrhenius equation to calculate the probabilities at the given temperatures. However, without specific values for A and Q, we cannot provide a numerical answer.
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A line passing through (p, 1/2) and (-8, q) has a slope of 3/4.
Find two possible values for each of p and q , and write the corresponding equations of the lines in slope-intercept form.
Can someone help me with this question...?
Answers
The corresponding equation is 4q + 3p = 22.
What is the slope of a line ?
The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's b in mathematics.
Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. Locate two locations along the chosen line and find their coordinates.
Find the y-coordinate difference between these two places (rise). Find the difference between the x-coordinates of these two points (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).
The slope is defined as the relationship between the rise, or vertical change, between two points and the change, or horizontal change, between the same two points and can be represented as an equation.
Given that, coordinates are (p, 1/2) and (-8, q), slope is 3/4.
m = (y2 - y1)/(x2 - x1)
34 = (q - 1/2)/-8 - p
-24 - 3p = 4q - 2
4q + 3p = 22
The corresponding equation is 4q + 3p = 22.
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When
4a- a x 3a + 7a
is simplified it is equivalent to?
Answers
Answer:
-3a^2+11a
Step-by-step explanation:
Answer:
4a-a×3a+7a
or, 3a×3a+ 7a
or,9a+7a
or,16a
:. a =16
using the law of sines to solve the triangle if ∠ a = 38 ∘ , ∠ c = 73 ∘ , b = 19 : ∠a=38∘,∠c=73∘,b=19:
Answers
To solve the triangle using the Law of Sines, we can use the following formula:
\(\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\)\)
Given that \(\(\angle A = 38^\circ\), \(\angle C = 73^\circ\), and \(b = 19\),\) we can substitute these values into the formula and solve for the remaining sides \(\(a\) and \(c\).\)
\(\(\frac{a}{\sin(38^\circ)} = \frac{19}{\sin(B)}\) (1)\)
\(\(\frac{c}{\sin(73^\circ)} = \frac{19}{\sin(B)}\) (2)\)
From equation (1), we can solve for \(\(\sin(B)\):\)
\(\(\sin(B) = \frac{19}{a} \cdot \sin(38^\circ)\)\)
Substituting this value into equation (2), we can solve for \(\(c\):\)
\(\(\frac{c}{\sin(73^\circ)} = \frac{19}{\frac{19}{a} \cdot \sin(38^\circ)}\)\)
Simplifying, we get:
\(\(c = a \cdot \frac{\sin(73^\circ)}{\sin(38^\circ)}\)\)
Now we have expressions for both \(\(a\) and \(c\).\)
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What was the temperature at sea level at 20,000 ft
Answers
Answer:
constant temperature is -56.5°C (-69.7°F), and this is also the lowest assumed temperature in respect to ISA.
Let z1 = 15(cos(90°) + i sin(90°)) and z2 = 3(cos(10°) + i sin(10°)).
From the drop-down menus, explain the transformation of z1 to form StartFraction z 1 Over z 2 EndFraction.
The quotient of StartFraction z 1 Over z 2 EndFraction is (cos(°) + i sin(°).
z1 is scaled by a factor of and then rotated degrees clockwise.
Answers
Answer:
5 (cos(80 degrees) + i sin(80 degrees)
Factor of 1/3
Rotated 10 degrees
Step-by-step explanation:
Answer:
Step-by-step explanation:
11.2=v/7
can someone tell me what v is
Answers
Answer:
11.2=v/7
11.2×7=v
78.4=v
a box contains one 2-inch rod, one 3-inch rod, one 4-inch rod, and one 5-inch rod. what is the maximum number of different triangles that can be made using these rods as sides?
Answers
On solving the provided question, we can say that we excluded example 2 above, a maximum of 3 triangles can be created with those rods.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear.
\(2-inch, 3 inch, 4-inch\)
triangle, because 2+3 > 4, 2+4 > 3, and 3+4 > 2
\(2-inch, 3 inch, 5-inch\)
This is doesn't make a triangle as \(2+5 > 3, and 3+5 > 2,\)
2+3 is not more than 5,, they cannot make triangle.
\(2-inch, 4 inch, 5-inch\)
triangle, because 2+4 > 5, 2+5 > 4, and 4+5 > 2
\(3-inch, 4 inch, 5-inch\)
a triangle, because 3+4 > 5, 3+5 > 4, and 4+5 > 3
Therefore, since we excluded example 2 above, a maximum of 3 triangles can be created with those rods.
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bhurasi got 85%marks in s.l.c. examination if the total marks was 800,how many marks did she obtain
Answers
Answer:
680
Step-by-step explanation:
total percent=85%
total marks=800
obtain marks = total percent % 100 mutiply by total marks
A fruit stand has 200 apples. They order 19 bags with 12 apple each. They sell 42 bags that have 8 apples each. The owner says they now have about 120 apples. Is the owner's estimate reasonable? The owner's answer is reasonable. They ordered about 320 apples and sold about 240 so they should have about 80 fewer apples than they started with. The owner's estimate is not reasonable. They ordered about 320 apples and sold about 240 so they should have about 80 more apples than they started with. The owner's estimate is reasonable. They ordered about 240 apples and sold about 320 so they should have about 80 fewer apples than they started with. The owner's estimate is not reasonable. They ordered about 240 apples and sold about 240 so they should have about the same number of apples as they started with.
Answers
Answer:
The owner's estimate is reasonable. They ordered about 240 apples and sold about 320 so they should have about 80 fewer apples than they started with.
Step-by-step explanation:
Given that:
Number of apples already available with Owner = 200
Number of bags of apples ordered with 12 apples each = 19
Number of apples ordered = 12 \(\times\) 19 = 228
OR
Rounding off 19 to 20:
Number of apples ordered = 12 \(\times\) 20 = 240
Around 240 apples were ordered.
Number of bags of apples with 8 apples each, sold = 42
Number of apples sold = 42 \(\times\) 8 = 336
Rounding off 42 to 40, number of apples sold = around 320
Therefore, 80 more apples were sold than that of apples bought.
So, according to the estimate, there will be 80 fewer apples left than they started with.
Correct answer is:
The owner's estimate is reasonable. They ordered about 240 apples and sold about 320 so they should have about 80 fewer apples than they started with
Can somebody who has done word problems plz help give the correct equations for each one :DD thanks!
WILL MARK BRAINLIEST WHOEVER ANSEERS THEM FIRST !!!!!!:D
Answers
Answer:
18. x + 7 = 21
19. x - 55 km = 1000 km
19) 55 > x = 1000
hopefully this helps :) have a nice day/night and good luck in your class!!
Please hurry will give brainliest
Write the inequality in slope intercept form.
2x-3y>9
Answers
Step-by-step explanation:
2x - 3y > 9
the target as slope intercept form is
y = ax + b (or any fitting inequality sign)
so, let's transform the original inequality
2x > 3y + 9
2x - 9 > 3y
2x/3 - 3 > y
or
y < 2x/3 - 3
the slope is 2/3 (always the factor of x). the y-intercept = -3.
Find the perimeter and area of the figure, rounding to the nearest tenth. Use 3. 14 for pi
Answers
The area of the figure is 248.52 sq.cm.
The figure given below is a semi-circle of diameter 12 cm and a rectangle of length 16 cm and width 12 cm:So, the total perimeter of the figure is given as follows:
Perimeter of the figure = perimeter of the semi-circle + perimeter of the rectangle+ length of the rectangle.
= 1/2 * 2 * 3.14 * 6 + 16 + 12 + 12 + 1/2 * 2 * 3.14 * 6= 18.84 + 40= 58.84 cm
So, the perimeter of the figure is 58.84 cm.The area of the semi-circle is given as:Area of the semi-circle = 1/2 * pi * r^2= 1/2 * 3.14 * 6^2= 56.52 sq.cm
Now, the area of the rectangle is given as:
Area of the rectangle = length * width= 16 * 12= 192 sq.cmSo, the total area of the figure is given as:Total area of the figure = area of the semi-circle + area of the rectangle= 56.52 + 192= 248.52 sq.cm.
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A watch was bought for Rs 1200. At what labeled price should it be sold to gain 33.33% after 20% discount find SP with 13% vat olascout
Answers
Answer:
Lebeled Price of watch = Rs. 2000
Selling price pf the watch = Rs. 1600
Step-by-step explanation:
∴ S = L - 20% L∴ S = 0.8 L ..... (1)∴ S = P + (1/3)P∴ S = (4/3) P ..... (2)As we know, P = 1200∴ S (4/3) × 1200∴ S = Rs. 16001600 = 0.8L∴ L = 1600 ÷ 0.8∴ L = Rs.2000∴ Lebeled Price of watch = Rs. 2000Selling price pf the watch = Rs. 16005/6 + 2/3 = ?
Your
answer
Answers
Answer:
1.5
Step-by-step explanation:
Answer:
Improper Fraction: \(\frac{10}{6}\)
Proper Fraction: \(1\frac{4}{6}\)
Simplified Proper Fraction: \(1\frac{2}{3}\)
Step-by-step explanation:
\(\frac{5}{6} + \frac{2}{3}\) Is our equation... first we must find a common denominator! Let's take a look...
6: 1, 6, 12
3: 1, 3, 6
We see that both numbers get to 6 so we use that as our common denominator. Now we plug that in...
\(\frac{5*1}{6*1} +\frac{2*2}{3*2}\)
We get...
\(\frac{5}{6} +\frac{4}{6} = \frac{10}{6}\)
Now if you want to leave it as an improper fraction your answer will be \(\frac{10}{6}\). However, if you want you answer to be a proper fraction your answer is \(1\frac{4}{6}\) which can be simplified further to,\(1\frac{2}{3}\).
Whew! What a toughie! We showed that math problem!
On the map, the distance between B and S is 13.25. How long it
will take to drive from B to S at an average speed of 70 mph?
Recall that distance=speedxtravel time.
Answers
The time it will take to drive from point B to point S at an average speed of 70 mph, distance = speed × travel time. Therefore, it will take approximately 11.34 minutes to drive from point B to point S at an average speed of 70 mph.
The formula to calculate travel time is given by time = distance / speed. In this case, the distance between B and S is 13.25 miles, and the average speed is 70 mph.
Using the formula, we can calculate the travel time as follows:
time = 13.25 miles / 70 mph
Dividing 13.25 by 70, we find:
time ≈ 0.189 hours
To convert hours to minutes, we multiply the time by 60:
time ≈ 0.189 hours × 60 minutes/hour ≈ 11.34 minutes
Therefore, it will take approximately 11.34 minutes to drive from point B to point S at an average speed of 70 mph.
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what is the length, in centimeters, of EF
Answers
Answer:
8
Step-by-step explanation:
1. Use the Pythagorean theorem: a^2+b^2=c^2.
You are already given c (which is always the longest side of the triangle) and one of the legs, which can be either a or b.
2. Put the numbers into the equation and square them.
6^2+b^2=10^2
When you square the numbers, it becomes 36 + b^2 = 100.
3. Subtract 36 from both sides and take the square root of the difference.
b^2 = 64
\(\sqrt{64}\) = 8
Answer: 8cm
Step-by-step explanation: Let’s use the Pythagorean Theorem! 6^2+x^2=10^2
36+x^2=100
x^2=64
X=8
A newspaper provided a​ snapshot illustrating poll results from 1910 professionals who interview job applicants. The illustration showed that​ 26% of them said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company. The margin of error was given as percentage points. What important feature of the poll was​ omitted?.
Answers
Confidence level feature of the poll was ​ omitted
To find the what important feature of the poll was ​ omitted?.
The illustration showed that 26% of applicants said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company.
The margin of error was given as plus or minus 3 percentage points.
The important feature of the poll that was omitted was - confidence level.
The percent of all samples that are included in the true population parameter is given by a confidence level.
Confidence interval defines the probability that the given population parameter will fall within a specific range of values.
Mathematically we can express the scenario as :
Sample size is given as 1910 professionals
Point estimate is 26%
Confidence level is not given.
Confidence interval is plus or minus 3 percent around 26%.
Hence, Confidence level feature of the poll was ​ omitted.
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Numbers: 4 and 6 it’s asking what the right triangle area is in square inches
Answers
This table shows the ratio of cups of white paint to cups of blue paint.
A 2-column table has 3 rows. Column 1 is labeled White paint (cups) with entries 1, 3, 5. Column 2 is labeled Blue paint (cups) with entries 8, 24, 40.
Answers
Answer:
6 to 48
Step-by-step explanation:
i just did that question in a test
Answer:
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Step-by-step explanation:
how do you solve for u?
Answers
Answer:
u=9.8
Step-by-step explanation:
the minus sign on u and the minus sign on 9.8 cancel out so you get u=9.8.
consider the following random sample of income and education: income(y) education(x) 100 18 65 14 47 14 112 16 34 12 85 16 92 18 83 14 67 16 29 12 a. find sample means, variances, and standard deviations of x and y. b. find sample covariance, cov(y,x), and correlation corr(y,x). c. find cov(2y,3x), and correlation corr(2y,3x) d. find covariance of y and y and corr
Answers
The sample means are Mean(Y) = 61.4 and Mean(X) = 15, the sample variances are Variance(Y) ≈ 1124.89 and Variance(X) ≈ 2.67, the sample standard deviations are Standard deviation(Y) ≈ 33.56 and Standard deviation(X) ≈ 1.63, the sample covariance is Covariance(X, Y) ≈ -131.69, and the sample correlation is Correlation(X, Y) ≈ -0.77.
a. To find the sample means, variances, and standard deviation, we can use the following formulas:
Sample mean of income (Y):
Mean(Y) = (100 + 65 + 47 + 112 + 34 + 85 + 92 + 83 + 67 + 29) / 10 = 614 / 10 = 61.4
Sample mean of education (X):
Mean(X) = (18 + 14 + 14 + 16 + 12 + 16 + 18 + 14 + 16 + 12) / 10 = 150 / 10 = 15
Sample variance of income (Y):
Variance(Y) = [(100 - 61.4)^2 + (65 - 61.4)^2 + (47 - 61.4)^2 + (112 - 61.4)^2 + (34 - 61.4)^2 + (85 - 61.4)^2 + (92 - 61.4)^2 + (83 - 61.4)^2 + (67 - 61.4)^2 + (29 - 61.4)^2] / 9 ≈ 1124.89
Sample variance of education (X):
Variance(X) = [(18 - 15)^2 + (14 - 15)^2 + (14 - 15)^2 + (16 - 15)^2 + (12 - 15)^2 + (16 - 15)^2 + (18 - 15)^2 + (14 - 15)^2 + (16 - 15)^2 + (12 - 15)^2] / 9 ≈ 2.67
Sample standard deviation of income (Y):
Standard deviation(Y) = √Variance(Y) ≈ √1124.89 ≈ 33.56
Sample standard deviation of education (X):
Standard deviation(X) = √Variance(X) ≈ √2.67 ≈ 1.63
b. To find the sample covariance and correlation, we can use the following formulas:
Sample covariance:
Covariance(X, Y) = [(18 - 15)(100 - 61.4) + (14 - 15)(65 - 61.4) + (14 - 15)(47 - 61.4) + (16 - 15)(112 - 61.4) + (12 - 15)(34 - 61.4) + (16 - 15)(85 - 61.4) + (18 - 15)(92 - 61.4) + (14 - 15)(83 - 61.4) + (16 - 15)(67 - 61.4) + (12 - 15)(29 - 61.4)] / 9 ≈ -131.69
Sample correlation:
Correlation(X, Y) = Covariance(X, Y) / (Standard deviation(X) * Standard deviation(Y)) ≈ -131.69 / (1.63 * 33.56) ≈ -0.77
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Correct question-
Consider the following random sample of income and education: Income(Y) Education(X) 100 18 65 14 47 14 112 16 34 12 85 16 92 18 83 14 67 16 29 12 a. Find sample means, variances and standard deviation. b. Find sample covariance and correlation.