Answer:
[tex]\bold{\dfrac{11}{16}}[/tex]
Step-by-step explanation:
Given four tiles with numbers:
1, 4, 5 and 8
Tile chosen once and then replaced, after that another tile chosen:
All possibilities are:
{(1, 1) ,(1, 4) ,(1, 5) ,(1, 8)
(4, 1) ,(4, 4) ,(4, 5) ,(4, 8)
(5, 1) ,(5, 4) ,(5, 5) ,(5, 8)
(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }
Total number of possibilities = 16
When the sum is greater than 7, the possibilities are:
{(1, 8)
(4, 4) ,(4, 5) ,(4, 8)
(5, 4) ,(5, 5) ,(5, 8)
(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }
Number of favorable cases = 11
Formula for probability of an event E is:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Hence, the required probability is:
[tex]\Rightarrow \bold{\dfrac{11}{16}}[/tex]
Answer:11/16
Step-by-step explanation:i took the test
A certain family has a husband, wife, son, and daughter. All together they are 68 years old. The husband is 3 years older than the wife, and the son is 3 years older than the daughter. Four years ago, all together the family was 54 years old. How old is the husband now?
Answer:
32 years old
Step-by-step explanation:
The husband is 32 years old as the wife is 3 years younger than the husband. The son is 3 years older than the daughter. Their family altogether total age today is 68 years while 4 years ago their age total was 54 years. The difference is 14 years. If we divide the difference into 4 then the age can not be whole number which means daughter is born after 2 years. She is now 2 years older. Son is 3 years older than the daughter which means he is 5 years old. The husband then must be 32 years old and wife is 3 years younger which means she is 29 years old now.
32 + 29 + 5 + 2 = 68 years.
Give the domain and range of each relation using set notation
Answer:
See below.
Step-by-step explanation:
First, recall the meanings of the domain and range.
The domain is the span of x-values covered by the graph.
And the range is the span of y-values covered by the graph.
1)
So, we have here an absolute value function.
As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:
[tex]\{x|x\in\textbb{R}\}[/tex]
(You are correct!)
For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:
[tex]\{y|y\leq 7\}[/tex]
2)
We have here an ellipse.
First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:
[tex]-4\leq x\leq 6[/tex]
So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:
[tex]\{x|-4\leq x\leq 6\}[/tex]
For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:
[tex]-5\leq y\leq 1[/tex]
This represents all the y-values between -5 and 1, including -5 and 1.
In set notation, thi is:
[tex]\{y|-5\leq y\leq 1\}[/tex]
If sin∠M = cos∠N and m∠N = 30°, what is the measure of ∠M?
Step-by-step explanation:
sin∠M = cos∠N
sin∠M = cos(30°)
sin∠M = √3 / 2
m∠M = 60° or 120°
If ∠M is acute, m∠M = 60°.
Answer: The measure of ∠M is 60°
Step-by-step explanation:
The complement of 30° is 60°
sin∠M =cos∠N
sin∠60°=cos∠30°
the measure of ∠M is 60°
A collector as a set of 224 coins. Some are valued at 20 cents and others at 25 cents. If the collector has 74 25-cent coins, then what is the total value of the collection
Answer:
48.50 dollars.
Step-by-step explanation:
The collector has a total of 224 coins but 74 of them are 25 cents coins. So, in order to find the number of 20-cent coins we're going to subtract the number of 25-cent coins from the total.
Number of 20-cent coins = 224 - 74 = 150.
Thus, the collector has 150 20-cent coins and 74 25-cent coins for a total of 224 coins.
Now, to know the total value of the collection we need to multiply the value of the coins by the number of coins there are of this value (we are going to do it with the 20-cent and the 25-cent coins) and then sum up our results.
Total value = 74(25) + 150 (20) = 1850 + 3000 = 4850 cents.
So the total value is 4850 cents, we know that each dollar has 100 cents so, to express this number in dollars we are going to divide it by 100 and thus we have that the total value of the collection is 48.50 dollars.
Find the union and interesection of each of the following A={3,6,9,12}, B ={6,8,9}
Answer:
Hello,
The answer would be,
A union B = {3,6,9,12}
and A intersection B= {6,9}
Answer:
[tex]\huge\boxed{ A\ union \ B = \{3,6,8,9,12\}}[/tex]
[tex]\huge\boxed{A\ intersection \ B = \{6,9\}}[/tex]
Step-by-step explanation:
A = {3,6,9,12}
B = {6,8,9}
A∪B = {3,6,9,12} ∪ { 6,8,9} [Union means all of the elements should be included in the set of A∪B]
=> A∪B = {3,6,8,9,12}
Now,
A∩B = {3,6,9,12} ∩ {6,8,9} [Intersection means common elements of the set]
=> A∩B = {6,9}
Solve the equation 3(2x + 2) = 3x − 15.
Hi there! :)
Answer:
x = -7.
Step-by-step explanation:
Starting with:
3(2x + 2) = 3x - 15
Begin by distributing '3' with the terms inside of the parenthesis:
3(2x) + 3(2) = 3x - 15
Simplify:
6x + 6 = 3x - 15
Isolate the variable by subtracting '3x' from both sides:
6x - 3x + 6 = 3x - 3x - 15
3x + 6 = -15
Subtract 6 from both sides:
3x + 6 - 6 = -15 - 6
3x = -21
Divide both sides by 3:
3x/3 = -21/3
x = -7.
Answer:
x = -7
Step-by-step explanation:
3(2x+2) = 3x - 15
First, we should simplify on the left side.
6x + 6 = 3x - 15 ; Now we subtract six from both sides.
-6 -6
6x = 3x - 21 ; next we just subtract 3x from both sides.
-3x -3x
3x = -21
Finally, we divide 3 from both sides to separate the three from the x.
x = -7
Hope this helps!! <3 :)
If the area of the square is A(s) = s², find the formula for the area as a function of time, and then determine A(s(3)).
A(t) = 100t^2 + 500t + 625
3,025 square pixels
Answer:
A(t) equals 100t²+ 500t + 625.
The area of the square image after 3 seconds is 3,025 square pixels.
Find the intervals on which the function f(x) = ax2 + bx + c (where "a" doesn't = 0) is increasing and decreasing. Describe the reasoning behind your answer.
Answer:
Step-by-step explanation:
Given that:
[tex]\mathtt{f(x) = ax^2 + bx + c}[/tex]
The derivative of the function of x is [tex]\mathtt{f'(x) = 2ax + b}[/tex]
Thus; f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
i.e
f'(x) > 0 , when b > 0 and a < 0
∴
2ax + b < 0
2ax < - b
[tex]\mathtt{x < \dfrac{-b}{2a}}[/tex]
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
[tex]\mathtt{x > \dfrac{-b}{2a}}[/tex]
A number to be multiplied is called a?
Answer:
The number to be multiplied is the "multiplicand"
Step-by-step explanation:
a base when it is written in exponential notation
The price of a technology stock was $ 9.56 yesterday. Today, the price rose to $ 9.69 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer and Step-by-Step explanation:
% increase = 100 x [(new price) - (original price)] / (original price)] = 100 (9.67 - 9.56) / 9.56
% increase ≅ 1.2% (to the nearest tenth)
The bowling scores for six people are:
27, 142, 145, 146, 154, 162
What is the most appropriate measure of center?
O A. The standard deviation
O B. The range
O C. The median
O D. The mean
Answer: Option D. will be the answer.
Explanation: The bowling scores for six persons have been given as 27, 142, 145, 146, 154, 162.
The most appropriate measure of the center of these scores will be the median.
Here median will be mean of 146 and 146 because number of persons are 6 which is an even number.
So there are two center scores those are 145 and 146 and median =
Option D. will be the answer.
the point p(-3,4) is reflected in the line x +2=0. find the coordinate of the image x
Answer:
(- 1, 4 )
Step-by-step explanation:
The line x + 2 = 0 can be expressed as
x + 2 = 0 ( subtract 2 from both sides )
x = - 2
This is the equation of a vertical line parallel to the y- axis and passing through all points with an x- coordinate of - 2
Thus (- 3, 4 ) is 1 unit to the left of - 2
Under a reflection in the line x = - 2
The x- coordinate will be the same distance from x = - 2 but on the other side while the y- coordinate remains unchanged.
Thus
(- 3, 4 ) → (- 1, 4 )
The driveway needs to be resurfaced. what is the BEST estimate of the area of the driveway?
Answer:
125π ft²
Step-by-step explanation:
1/4π(30)² - 1/4π(20)² = 125π
Evaluate cosA/2 given cosA=-1/3 and tanA >0
Answer:
[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]
Step-by-step explanation:
Given that:
[tex]cosA=-\dfrac{1}3[/tex]
and
[tex]tanA > 0[/tex]
To find:
[tex]cos\dfrac{A}{2} = ?[/tex]
Solution:
First of all,we have cos value as negative and tan value as positive.
It is possible in the 3rd quadrant only.
[tex]\dfrac{A}{2}[/tex] will lie in the 2nd quadrant so [tex]cos\dfrac{A}{2}[/tex] will be negative again.
Because Cosine is positive in 1st and 4th quadrant.
Formula:
[tex]cos2\theta =2cos^2(\theta) - 1[/tex]
Here [tex]\theta = \frac{A}{2}[/tex]
[tex]cosA =2cos^2(\dfrac{A}{2}) - 1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =cosA+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =-\dfrac{1}3+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =\dfrac{2}3\\\Rightarrow cos(\dfrac{A}{2}) = \pm \dfrac{1}{\sqrt3}[/tex]
But as we have discussed, [tex]cos\dfrac{A}{2}[/tex] will be negative.
So, answer is:
[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]
A researcher is interested in determining whether typists are most productive in the morning, at midday, in the evening, or late at night. To answer this question, the researcher recruits 20 participants and assigns 5 participants to be measured at each time of day. To evaluate productivity, the researcher measures words typed per minute at each time of day.
Morning Midday Evening Night
99 42 80 82
80 32 83 78
99 45 94 79
98 49 70 97
79 38 79 96
Mean 91 41.2 81.2 86.4
SStotal = 9094.95
What are the degrees of freedom for the numerator of the F-ratio?
a. 2
b. 3
c. 16
d. 19
Answer:
d. 19
Step-by-step explanation:
Degrees of freedom is the number is the number of value which is used in the final calculation. It calculate as n-1, where n is the sample size. The degrees of freedom for the given scenario is 19. The sample size is 20 so the degrees of freedom is 1 less which will be 19.
Dan weighs 205 pounds but is only 5 feet 8 inches tall. Evan is 6 feet tall. How much would you expect Evan to weigh if they have the same height/weight ratio? WILL MARK BRAINLIST
Answer:
Around 217 pounds
Step-by-step explanation:
Let's convert the height into inches.
5 feet 8 = [tex]5\cdot12 + 8 = 60 + 8 = 68[/tex]
6 feet [tex]= 6\cdot12 = 72[/tex].
We can set up a proportion
[tex]\frac{205}{68} = \frac{x}{72}[/tex]
We can use the cross products property to find x.
[tex]205\cdot72=14760\\\\\\14760\div68\approx217[/tex]
Hope this helped!
Answer:
217.0588235 lbs
Step-by-step explanation:
Convert ft inches to inches
5 ft = 5*12 = 60 inches
5 ft 8 inches = 68 inches
6 ft = 6*12 = 72 inches
We can use ratios to solve
205 lbs x lbs
------------- = ----------------
68 inches 72 inches
Using cross products
205 * 72 = 68x
Divide by 68
205 *72/68 = x
217.0588235 lbs
Which is an example of a situation that is in equilibrium?
A. The amount of air in a room increases quickly when the door is
opened.
B. The amount of money in a bank account never changes
C. The amount of water in a cup decreases as it evaporates
D. A flower slowly grows taller
Answer:B the amount of money in a bank account never changes.
Step-by-step explanation:
Answer:
B. The amount of money in a bank account never changes.
Step-by-step explanation:
Equilibrium is achieved when the state of a reversible reaction of opposing forces cancel each other out. While in a state of equilibrium, the competing influences are balanced out. Imagine a cup with a hole in it being filled with water from a tap. The level of water in this cup would stay the same if the rate at which the water that flows inside is the same as the water that flows outside. Option B will be the correct answer because the amount of money going into the account is at the same rate of money coming out of the account.
In which set(s) of numbers would you find the number -832 a. whole number b. irrational number c. integer d. rational number e. real number f. natural number
Answer:
integer of course
Step-by-step explanation:
an integer can either be negative or positive.
i will rate you brainliest
Answer:
D) 3/2(X-4)
Step-by-step explanation:
Invert and multiply to get:
3(x+4)/2(x²-16)
factor the bottom
3(x+4)/2(x+4)(x-4)
The (x+4)’s cancel out, and you’re left with
3/2(X-4)
[tex]\dfrac{{x+4\over2}}{{x^2-16\over3}}[/tex]
[tex]=\dfrac{3(x+4)}{2(x+4)(x-4)}=\frac{3}{2(x-4)} [/tex]
but in original fraction, denominator can't be zero so we have to exclude x=±4
do that answer is D
Can someone please help me with this question?
Answer:
B
Step-by-step explanation:
11q + 5 ≤ 49
Subtract 5 from each side
11q + 5-5 ≤ 49-5
11q ≤44
Divide each side by 11
q ≤44/11
q≤4
There is a close circle at 4 because of the equals sign and the lines goes to the left
Answer:
B
Step 1:
To solve this, we need to isolate the variable q. To do so, we will subtract 5 from both sides of the inequality.
[tex]11q+5(-5)\leq 49(-5)\\11q\leq 44[/tex]
Step 2:
We divide both sides by 11 to get our q.
[tex]\frac{11q}{11}\leq \frac{44}{11} \\q\leq 4[/tex]
q ≤ 4
Step 3:
To find the correct graph, we need to know that a close circle means a ≤ or ≥ and an open one means a < or >. Here, we are using a ≤ so C and D are not our answers. Also remember that if the "arrow" is pointing left (<), then the arrow on the graph should be facing the left side. If the arrow is facing the right side, then that means we are using > or ≥. Here, we are using ≤ (left), so that means the arrow on the graph should be on a 4, facing left, with a closed circle.
Our answer is B.
This is the ASVAB question If 500 people are at a concert and 70% are adults. How many children are there?
Answer:
150
Step-by-step explanation:
70% of 500 people are adults and the remainder are children.
30% of 500 are children30*500/100= 150There are 150 children
Find the length of GV¯¯¯¯¯¯¯¯ A. 43.92 B. 33.1 C. 41.45 D. 68.87
Answer:
The answer is option AStep-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find GV
To find GV we use cosine
cos∅ = adjacent / hypotenuse
From the question
GV is the adjacent
GC is the hypotenuse
So we have
[tex] \cos(37) = \frac{GV}{GC} [/tex]GC = 55°
GV[tex] \cos(37) = \frac{GV}{55} [/tex]GV = 55 cos 37
GV = 43.92495
We have the final answer as
GV = 43.92Hope this helps you
Find the area of the shape shown below.
2
2
nd
2
Need help Plz hurry and answer!!!
Answer:
=6 units squared
Step-by-step explanation:
area=1/2h(a+b)
=1/2×2(4+2)
=6
Find the total surface area of the farm silo in a farmer's field. Use π = 3.14. pls help asap uwu
Answer:
A) 1236 units²
Step-by-step explanation:
Cylinder = 2[tex]\pi[/tex]h+2[tex]\pi[/tex]r²
2(3.14)(7.5)(15)+2(3.14)(7.5x7.5)
706.5+353.25=1059.75
1/2 Sphere = 1/2(4)[tex]\pi[/tex]r²
2(3.14)(7.5)(7.5)
353.25
TOTAL: 1059.75+353.25=1413
HOWEVER...you need to subtract the top of the cylinder ([tex]\pi[/tex]r²) 176.625
1413-176.625=1236.375
So the answer would be A. (Silo’s do have a bottom, or else the answer would be D)
Answer:
1,236 units²
Step-by-step explanation:
I got it correct on founders edtell and screenshot below as proof
A number is chosen at random from the set of consecutive natural numbers $\{1, 2, 3, \ldots, 24\}$. What is the probability that the number chosen is a factor of $4!$? Express your answer as a common fraction.
Answer:
[tex]Probability = \frac{1}{3}[/tex]
Step-by-step explanation:
Given
[tex]Set:\ \{1, 2, 3, \ldots, 24\}[/tex]
[tex]n(Set) = 24[/tex]
Required
Determine the probability of selecting a factor of 4!
First, we have to calculate 4!
[tex]4! = 4 * 3 * 2 * 1[/tex]
[tex]4! = 24[/tex]
Then, we list set of all factors of 24
[tex]Factors:\ \{1, 2, 3, 4, 6, 8, 12, 24\}[/tex]
[tex]n(Factors) = 8[/tex]
The probability of selecting a factor if 24 is calculated as:
[tex]Probability = \frac{n(Factor)}{n(Set)}[/tex]
Substitute values for n(Set) and n(Factors)
[tex]Probability = \frac{8}{24}[/tex]
Simplify to lowest term
[tex]Probability = \frac{1}{3}[/tex]
Fill in the blanks and explain the pattern.
4.25, 4.5,__,__,__,5.5,__,6.0
Answer:
4.25, 4.5, 4.75, 5.00, 5.25, 5.5, 5.75, 6.00
Step-by-step explanation:
it is an arithmetic sequence with common difference 0.25
Relating a Polynomial Identity to Pythagorean Triples
In this activity you'll relate polynomial identities with Pythagorean triples. Answer the following questions
based on this triangle with side lengths x^2 – 1, 2x, and x^2 + 1.
Answer:
Step-by-step explanation:
Hello, please consider the following.
For x > 1, we can apply Pythagoras theorem as below.
[tex]\text{Let's estimate this sum of two squares.} \\\\(2x)^2+(x^2-1)^2=4x^2+x^4-2x^2+1=x^4+2x^2+1\\\\\text{Let's estimate this square, now.} \\\\(x^2+1)^2=x^4+2x^2+1\\\\\text{The two expressions are equal, meaning.} \\\\(2x)^2+(x^2-1)^2=(x^2+1)^2\\\\\text{Using Pythagoras' theorem, we can say that this is a right triangle.}[/tex]
Thank you
The number of values of xx in the interval [0,5π][0,5π] satisfying the equation 3sin2x−7sinx+2=03sin2x-7sinx+2=0 is/are
Answer:
6
Step-by-step explanation:
Given, 3sin2x−7sinx+2=03sin2x-7sinx+2=0
⇒(3sinx−1)(sinx−2)=0⇒3sinx-1sinx-2=0
⇒sinx=13 or 2⇒sinx=13 or 2
⇒sinx=13 [∵sinx≠2]⇒sinx=13 [∵sinx≠2]
Let sinα=13,0<α<π2,sinα=13,0<α<π2, then sinx=sinαsinx=sinα
now x=nπ+(−1)nα(n∈I)x=nπ+(−1)nα(n∈I)
⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α Are the solution in [0,5π][0,5π]
Hence, required number of solutions are 6
It is known that 80% of all brand A external hard drives work in a satisfactory manner throughout the warranty period (are "successes"). Suppose that n= 15 drives are randomly selected. Let X = the number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. Obtain the sampling distribution of this statistic.
Answer:
P (x= 5) = 0.0001
P(x=3) = 0.008699
Step-by-step explanation:
This is a binomial distribution .
Here p = 0.8 q= 1-p = 1-0.8 = 0.2
n= 15
So we find the probability for x taking different values from 0 - 15.
The formula used will be
n Cx p^x q^n-x
Suppose we want to find the value of x= 5
P (x= 5) = 15C5*(0.2)^10*(0.8)^5 = 0.0001
P(x=3) = 15C3*(0.2)^12*(0.8)^3 = 9.54 e ^-7= 0.008699
Similarly we can find the values for all the trials from 0 -15 by substituting the values of x =0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15.
The value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.
It is given that the 80% of all brand A external hard drives work in a satisfactory manner throughout the warranty period.
It is required to find the sampling distribution if n =15 samples.
What is sampling distribution?It is defined as the probability distribution for the definite sample size the sample is the random data.
We have p =80% = 0.8 and q = 1 - p ⇒ 1 -0.8 ⇒ 0.2
n = 15
We can find the probability for the given x by taking different values from 0 to 15
the formula can be used:
[tex]\rm _{n}^{}\textrm{C}_x p^xq^{n-x}[/tex]
If we find the value for p(x = 5)
[tex]\rm _{15}^{}\textrm{C}_5 p^5q^{15-5}\\\\\rm _{15}^{}\textrm{C}_5 0.8^50.2^{10}[/tex]⇒ 0.0001
If we find the value for p(x = 3)
[tex]\rm _{15}^{}\textrm{C}_3 0.8^30.2^{12}\\[/tex] ⇒
Similarly, we can find the values for all the trials from 0 to 15 by putting the values of x = 0 to 15.
Thus, the value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.
Learn more about the sampling distribution here:
https://brainly.com/question/10554762
Can somebody help me please?
Answer:
[tex]\boxed{x \geq 353}[/tex]
Step-by-step explanation:
Hey there!
Info Given
- Dot is solid
- Line goes to the right
- Dot is at 353
So by using the given info we can conclude that the inequality is,
x ≥ 353
Hope this helps :)
Answer:
Inequality: 100 + 50w ≥ 18000
What to put on graph: w ≥ 358
