Answer:
i. E ∩ A = { a , c }ii. E ∪ A = { a , c , f , j }Step-by-step explanation:
Given
E = { a , c , f }
A = { a , c , j }
i) Let's find the intersection of E and A
E ∩ A = { a , c , f } ∩ { a , c , j }
In the case of intersection , we have to list the elements which are common in both sets:
E ∩ A = { a , c }
ii) Let's find the union of E and A
E ∪ A = ( a , c , f } { a , c , j }
In the case of Union, we have to list all the elements which are present in both sets.
E ∪ A = { a , c , f , j }
Hope this helps..
Best regards!!
Write an inequality to model the situation.
A number exceeds 21.
n ≤ 21
n < 21
n > 21
n ≥ 21
Answer:
[tex]n >21[/tex]
Step-by-step explanation:
The number exceeds 21 or is greater than 21.
‘[tex]>[/tex]’ represents greater than.
Let the number be [tex]n[/tex].
[tex]n >21[/tex]
One leg in a right triangle is 11 m, and the hypotenuse measures 11√2 m. Find the length of the other leg.
Answer:
[tex]\boxed{11m}[/tex]
Step-by-step explanation:
Method #1: 45-45-90 Triangle
You can use the rules for a 45-45-90 triangle. These are:
→ Each 45-45-90 triangle is a right triangle with two additional 45° angles.
→ The triangle will have 2 legs, x, and one hypotenuse, x√2.
Therefore, because the problem gives values for one leg and the hypotenuse, the value for the one leg is equal to the value for the unsolved leg.
Method #2: Pythagorean Theorem
You can use the Pythagorean Theorem to solve for a missing side in a triangle. Please note, however, that the Pythagorean Theorem only works on right triangles.
The Pythagorean Theorem is defined as [tex]a^{2} + b^{2} = c^{2},[/tex] where a and b are both legs of the triangle and c is the hypotenuse.
Therefore, substitute the known value for a, 11, and the known value for c, 11√2. Then, evaluate each value to its power (except for b - it is unsolved) and simplify the equation with basic algebraic methods. Once your equation is down to [tex]b^{2}= ?[/tex], you should take the square root of both sides of the equation to get the value for b.
[tex]11^{2} +b^{2} =(11\sqrt{2} )^{2}\\121 + b^{2} = 242\\b^{2}=121\\b=11[/tex]
What are the solutions to the system of equations graphed below?
Answer:
Its B and D
Step-by-step explanation:
Because thats where the points intersects/meet.
CAN I GET SOME HELP OVER HERE? Ina Crespo rowed 12 miles down the Habashabee River in 2 hours, but the return trip took her 3 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current. Ina can row ? mph in still water
Answer: The speed of Ina in still water is 5mph
Step-by-step explanation:
If the speed of Ina on still water is x, and the speed of the river is y:
The total speed of Ina when she goes along with the current is:
S = x + y
when she goes against the current we have:
St = x - y.
Now we can use the relation:
speed = time/velocity.
along with the current, we have:
x + y = 12mi/2h = 6mi/h
against the current we have:
x - y = 12mi/3h = 4mi/h
So we have the equations
x + y = 6mi/h
x - y = 4mi/h
in the first equation we can isolate x
x = 6mi/h - y
now we replace this in the second equation:
(6mi/h - y) - y = 4mi/h
6mi/h - 2y = 4mi/h
-2*y = 4mi/h - 6mi/h = -2mi/h
y = 1mi/h
now we replace this in the first equation:
x + 1mi/h = 6mi/h
x = 5mi/h.
The speed of Ina in still water is 5mph
Solve by using logarithms, not the same base. I have absolutely no clue how to solve so any help would be amazing, thanks
Answer:
-5/48
Step-by-step explanation:
(8 · 2⁷ˣ)⁴ = (1/16)⁵ˣ · 128
Take log of both sides.
log (8 · 2⁷ˣ)⁴ = log ((1/16)⁵ˣ · 128)
Use log exponent/product rules.
4 log (8 · 2⁷ˣ) = log (1/16)⁵ˣ + log 128
Use log exponent/product rules.
4 (log 8 + log (2⁷ˣ)) = 5x log (1/16) + log 128
Use log exponent rule.
4 (log 8 + 7x log 2) = 5x log (1/16) + log 128
Distribute.
4 log 8 + 28x log 2 = 5x log (1/16) + log 128
Write as powers of 2.
4 log 2³ + 28x log 2 = 5x log (2⁻⁴) + log 2⁷
Use log exponent rule.
12 log 2 + 28x log 2 = -20x log 2 + 7 log 2
Combine like terms.
5 log 2 + 48x log 2 = 0
Divide by log 2.
5 + 48x = 0
Solve for x.
x = -5/48
"An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.1 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 260 engines and the mean pressure was 4.2 pounds/square inch. Assume the standard deviation is known to be 0.9. A level of significance of 0.02 will be used. Determine the decision rule. Enter the decision rule."
Answer:
H₀ is accepted, we don´t have evidence to claim valves produces more than 4,1 pounds/square inch
Step-by-step explanation:
Normal Distribution
Population mean μ₀ = 4.1
Population standard deviation σ = 0,9
Sample size n = 260
Sample mean μ = 4,2
Level of significance 0,02 α = 0,02 form z-table we find z score
z(c) = 2,05 (critical value)
Test hypothesis
Null hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ > μ₀
Is a one tail-test ( to the right. Values have a mean over the population mean)
z(s) = ( μ - μ₀ )/ σ /√n
z(s) = 4,2 - 4,1 / 0,9/√260
z(s) = 0,1 *16,1245 / 0,9
z(s) = 1,7916
To compare z(s) and z(c)
z(s) < z(c)
Then z(s) is in the acceptance region, we accept H₀
You may assume the conditions for regression inference are satisfied. A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are given below.
Seed Density Lawn Quality
1 30
1 40
2 40
3 40
3 50
3 65
4 50
5 50
At the 1% level of significance, is there evidence of an association between seed density and lawn quality?
a) yes
b) no
Answer:
b) no
Step-by-step explanation:
The regression analysis is a statistical technique which is used for forecasting. It determines the relationship between two variables. It determines the relationship of two or more dependent and independent variables. It is widely used in stats to find trend in the data. It helps to predict the values of dependent and independent variables. In the given question, the relationship is determined to identify the relationship between density of seed planted and quality of lawn. The significance level is 1% which means strength of evidence is not strong enough to support the test.
write and equation to represent the following statement 28 is 12 less thank K. solve for K K =
Answer:
K = 40
Step-by-step explanation:
As they said that 28 is 12 less than K , it means that you've to add them to get the answer. So , 28 + 12 = 40 which is represented by the variable "K"
Hope it helps and pls mark as brainliest : )
Answer:
Equation : 28 = k - 12K = 40Step-by-step explanation:
28 is 12 less than k
Let's create an equation:
[tex]28 = k - 12[/tex]
Now, let's solve:
[tex]28 = k - 12[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] - k = - 12 - 28[/tex]
Calculate the difference
[tex] - k = - 40[/tex]
Change the signs on both sides of the equation
[tex]k = 40[/tex]
Hope this helps...
Best regards!!
Which system of equations represent the matrix shown below?
1 2 -1| 8
-1 0 3| 15
1 -2 4| 18
A. x + 2y + z =8
x + y + 3z =15
x + 2y + 4z =18
B. x + 2y + z =8
x + 3z =15
x + 2y + 4z =18
C. x + 2y - z =8
-x + y + 3z =15
x - 2y + 4z =18
D. x + 2y - z =8
-x + 3z =15
x - 2y + 4z =18
Answer:
the solution to the problem is D
A consumer magazine wants to compare lifetimes of ballpoint pens of three different types. The magazine takes a random sample of pens of each time and records the lifetimes (in minutes) in the table below. Do the data indicate that there is a difference in the mean lifetime for the three brands of ballpoint pens?
Answer:
The first step would be to look at the average for each brand.
The average can be calculated as:
A = (a1 + a2 + .... + an)/N
where a1 is the first lifetime, a2 is the second one, etc. And N is the total number of data points.
So, for Brand 1 we have:
A1 = (260 + 218 + 184 + 219)/4 = 220.25
Brand 2:
A2 = (181 + 240 + 162 + 218)/4 = 200.25
Brand 3:
A3 = (238 + 257 + 241 + 213)/4 = 237.25
So only from this, we can see that Brand 3 has the larger lifetime, then comes Brand 1 and last comes Brand 2.
You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you decide to swim 151515 minutes longer than she does one day at practice. Write an equation for the number of minutes you swim, yyy, when your friend swims xxx number of minutes. Y
Answer:
yyy = xxx + 151515
Step-by-step explanation:
Since you want to swim 151515 minutes longer one day at practice (note this time is actually 105 days), you simply need to swim the same amount of time as your friend, plus the extra time. Hence, your time will be equal to your friends time plus the extra time you plan to swim.
In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find the energy consumption level for the 45th percentile. Group of answer choices
Answer: 1022.75 kWh.
Step-by-step explanation:
Given: In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh.
i.e. [tex]\mu=1050\ kWh[/tex] and [tex]\sigma=218\ kWh[/tex]
Let X denote energy consumption levels for random single-family homes and x be the energy consumption level for the 45th percentile.
Then, [tex]P(X<x)=0.45[/tex]
From z-table, [tex]P(z<-0.125)=0.45[/tex]
Also, [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]\Rightarrow\ -0.125=\dfrac{x-1050}{218}\\\\\Rightarrow\ x=-0.125\times218+1050=1022.75[/tex]
Hence, the energy consumption level for the 45th percentile is 1022.75 kWh.
Need Assistance With This
*Please Show Work*
Answer:
a =7.5
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+ b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 + 10 ^2 = 12.5^2
a^2 + 100 =156.25
Subtract 100 from each side
a^2 = 56.25
Take the square root of each side
sqrt(a^2) = sqrt( 56.25)
a =7.5
What are the solutions to the system of equations graphed attached pic
Answer: C
Step-by-step explanation:
For system of equations, the solution is the point or points where the equations intersect. The point they meet signifies that they are the same at the x and y point.
Looking at the graph, we see 2 intersection points. They are (0,-8) and (4,8). Therefore, C is the correct answer.
A triangle has an area of 900m^2 . If a parallelogram has the same height and base as the triangle, what is the area of the parallelogram?
Answer:
area = 1800 m²
Step-by-step explanation:
area of one triangle = 900 m²
if a parallelogram has the same height and base as the triangle, then that means the area or the two triangle and shaped as a parallelogram
is twice the area given.
area = 900 * 2
area = 1800 m²
What is the answer? I'm stuck
Answer:
[tex]g(2)=1[/tex]
Step-by-step explanation:
So first, we know that:
[tex]f(1)=g(1)+1[/tex]
And:
[tex]f(2)=2[/tex]
This means that instead of 1, if we put two in like so:
[tex]f(2)=g(2)+1[/tex]
Then we can substitute the f(2):
[tex]2=g(2)+1\\g(2)=1[/tex]
Therefore, g(2)=1.
Someone help me with this, please!
Answer:
B = 26.4
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin B = 4/9
Take the inverse sin of each side
sin ^-1 sin ( B) = sin ^-1 ( 4/9)
B = 26.38779996
B = 26.4
Answer:
[tex]26.4\º[/tex]
Step-by-step explanation:
[tex]\theta=?[/tex]
[tex]$\sin(\theta)=\frac{opp}{hyp} = \frac{4}{9} $[/tex]
[tex]$\theta=\sin^{-1}\frac{4}{9} =\arcsin\frac{4}{9} \approx 26.4\º$[/tex]
Segments AC and BD are diameters of circle O. Circle O is shown. Line segments A C and B D are diameters. Angle A O D is 73 degrees. What is the measure of Arc A D B? 107° 146° 253° 287°
Answer:
253°
Step-by-step explanation:
The central angle whose rays intercept a diameter of the circle has measure 180 deg.
m<AOD = 73 deg
m<DOB = 180 deg
m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg
The measure of an arc of a circle is equal to the measure of the central angle that subtends it.
m(arc)AOD = m<AOD = 253 deg
Answer: 253°
The solution is, the measure of Arc A D B is 253°.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
Here, we have,
given that AC and BD are diameters of circle O.
AC and BD intersect at point C the centre of the circle.
The central angle of a circle is the angle based at the circle's center. In other words, the vertex of the angle must be at the center of the circle. A central angle is formed by two radii that start at the center and intersect the circle itself.
The central angle whose rays intercept a diameter of the circle has measure 180 deg.
m<AOD = 73 deg
m<DOB = 180 deg
m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg
The measure of an arc of a circle is equal to the measure of the central angle that subtends it.
m(arc)AOD = m<AOD = 253 deg
Answer: the measure of Arc A D B is 253°.
To learn more on angle click:
brainly.com/question/28451077
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What is the solution to the equation below? Round your answer to two decimal places. In x=0.3
Step-by-step explanation:
Since you are given the values there is no need to try another method then replacing x by the values
We can eliminate the negative values since you'll face math errors We have two remaining values 2 and 1.35㏑(2)= 0.69
㏑(1.35) = 0.3
so the right answer is D
A patrolmen spend 25% of every day completing paperwork. The patrol and shift each day is 8 hourZ how much of his time does he spend doing paperwork each day
Answer:
25 percent of 8 is 2 so 2 hours
Step-by-step explanation:
Please tell me if I'm right or wrong! No work needed! Brainliest will be given!
Answer:
The first one is correct
The second one is also correct
The third is also correct
Congrats!
Answer:
1) [tex]\boxed{Option \ B}[/tex]
2) [tex]\boxed{Option \ B}[/tex]
3) [tex]\boxed{Option \ B}[/tex]
You're totally correct, Man! :)
Step-by-step explanation:
Question 1:
[tex](6b^2-4b+3)-(9b^2-3b+6)\\Resolving \ the\ brackets\\6b^2-4b+3-9b^2+3b-6\\Combining \ like \ terms\\6b^2-9b^2-4b+3b+3-6\\-3b^3-b-3[/tex]
Question 2:
[tex](b+6)(b-3)\\Using \ FOIL\\b^2-3b+6b-18\\b^2+3b-18[/tex]
Question 3:
[tex](4x-3)(6x-1)\\Using \ FOIL\\24x^2-4x-18x+3\\24x^2-22x+3[/tex]
Determine the measure of the unknown variables
Answer:
27°Step-by-step explanation:
Let's create an equation:
[tex]5y = 135[/tex]
( Being vertically opposite angles)
Now, let's solve
Divide both sides of the equation by 5
[tex] \frac{5y}{5} = \frac{135}{5} [/tex]
Calculate
[tex] y = 27[/tex]
Hope this helps...
Best regards!!
Which expression is equivalent to 6 cubed? 6 times 3 6 times 6 times 6 6 times 6 times 6 times 6 3 times 3 times 3 times 3 times 3 times 3
The expression that is equivalent to 6 cubed is: 6 times 6 times 6.
This is true since cubed indicates that the base number is multiplied by itself 3 times.
So, 6^3 equates to 6 x 6 x 6.
Answer:
The expression that is equivalent to 6 cubed is: 6 times 6 times 6.
This is true since cubed indicates that the base number is multiplied by itself 3 times.
So, 6^3 equates to 6 x 6 x 6.
Step-by-step explanation:
Cirlce B is given the equation, (x-2)^2 + (y-9)^2 = 25. What are the coordinates of the center and the length of the radius?
Answer:
The answer to your question is Center = (2, 9) Radius = 5 units
Step-by-step explanation:
Data
(x - 2)² + (y - 9)² = 25
Process
1.- Determine the coordinates of the circle.
The coordinates are the numbers after the x and y just change the signs.
h = 2 and k = 9
Then the coordinates are (2, 9)
2.- The length of the radius is the square root of the number after the equal sign.
radius = [tex]\sqrt{25}[/tex]
radius = 5 units
The value of y varies inversely as the square of x, and y = 9, when x = 4.
Find the value of x when y = 1. Do not include "=" in your answer.
Answer:
The answer is
12Step-by-step explanation:
The above variation is written as
[tex]y = \frac{k}{ {x}^{2} } [/tex]
where k is the constant of variation
when y = 9
x = 4
We have
k = yx²
k = 9(4)²
k = 9 × 16
k = 144
So the formula for the variation is
[tex]y = \frac{144}{ {x}^{2} } [/tex]
when y = 1
[tex]1 = \frac{144}{ {x}^{2} } [/tex]
Cross multiply
x² = 144
Find the square root of both sides
x = √144
x = 12
Hope this helps you.
±2
Step-by-step explanation:
Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1
Answer:
5
Step-by-step explanation:
The limit of f(x) at x=-1 is 5 when approached from the left or right. Since those limits are the same, the limit exists and is ...
[tex]\boxed{\lim\limits_{x\to-1}f(x)=5}[/tex]
In a study of the progeny of rabbits, Fibonacci (ca. 1170-ca. 1240) encountered the sequence now bearing his name. The sequence is defined recursively as follows.
an + 2 = an + an + 1, where a1 = 1 and a2 = 1.
(a) Write the first 12 terms of the sequence.
(b) Write the first 10 terms of the sequence defined below. (Round your answers to four decimal places.)
bn =
an + 1/
an, n ? 1.
(c) The golden ratio ? can be defined by
limn ? In a study of the progeny of rabbits, Fibonacci (cbn = ?
, where
? = 1 + 1/?. Solve this equation for ?. (Round your answer to four decimal places.)
The question in part c is not clear, nevertheless, part a and part b would be solved.
Answer:
a. The first twelve terms are:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
b. The first ten terms are:
1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.
Step-by-step explanation:
a. Given
an + 2 = an + an + 1
where a1 = 1 and a2 = 1.
a3 = a1 + a2
= 2
a4 = a2 + a3
= 3
a5 = a3 + a4
= 5
a6 = a5 + a4
= 8
a7 = a6 + a5
= 13
a8 = a7 + a6
= 21
a9 = a8 + a7
= 34
a10 = a9 + a8
= 55
a11 = a10 + a9
= 89
a12 = a11 + a10
= 144
The first twelve terms are:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
(b)
Given
bn = an+1/an
b1 = a2/a1
= 1/1 = 1.000
b2 = a3/a2
= 2/1 = 1.000
b3 = a4/a3
= 3/2 = 1.500
b4 = a5/a4
= 5/3 = 1.667
b5 = a6/a5
= 8/5 = 1.600
b6 = a7/a6
= 13/8 = 1.625
b7 = a8/a7
= 21/13 = 1.615
b8 = a9/a8
= 34/21 = 1.619
b9 = a10/a9
= 55/34 = 1.618
b10 = a11/a10
= 89/55 = 1.618
The first ten terms are:
1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. A quality control analyst wants to examine thermometers that give readings in the bottom 4%. Find the temperature reading that separates the bottom 4% from the others. Round to two decimal places.
Answer:
the temperature reading that separates the bottom 4% from the others is -1.75°
Step-by-step explanation:
The summary of the given statistics data set are:
Mean [tex]\mu[/tex] : 0
Standard deviation [tex]\sigma[/tex] = 1
Probability of the thermometer readings = 4% = 0.04
The objective is to determine the temperature reading that separates the bottom 4% from the others
From the standard normal table,
Z score for the Probability P(Z < z) = 0.04
P(Z < -1.75) = 0.04
z = -1.75
Now, the z- score formula can be expressed as :
[tex]z = \dfrac{X-\mu}{\sigma}[/tex]
[tex]-1.75 = \dfrac{X-0}{1}[/tex]
-1.75 × 1 = X - 0
X = -1.75 × 1 - 0
X = -1.75
Therefore, the temperature reading that separates the bottom 4% from the others is -1.75°
Can anyone help? I am stuck. Find m∠G.
Answer:
80
Step-by-step explanation:
The quadrilateral is a kite.
The angle opposite to angle H is equal to angle H.
Angle F = 110 degrees
Angles in a quadrilateral add up to 360 degrees.
60 + 110 + 110 + G = 360
280 + G = 360
G = 360 - 280
G = 80
The measure of angle G is 80 degrees.
Answer: 80 degrees.
Step-by-step explanation:
In a kite, the angles formed by noncongruent sides are congruent. Thus, <EFG is 110 degrees. Then, because a kite is a quadrilateral, all of the angles in it add up to 360. Thus, is <FGH = x, then 110+110+60+x=360. Thus, x = 80.
Hope it helps <3
If $y^2= 36$, what is the greatest possible value of $y^3$?
Answer:
216
Step-by-step explanation:
y = ±√36 = ±6
y³ = (±6)³ = ±216
The largest of these values is 216, the greatest possible value of y.