Answer:
Probability that one of the giftcards will go to a student athlete and one will go to a freshman = 26.4%
Step-by-step explanation:
At Central High School, 55% of students play a school sport. Also, 24% of the student population is in ninth grade. No ninth graders are allowed to play school sports. If two students are selected at random to receive a gift card, what is the probability that one will go to a student athlete and one will go to a freshman? Write the answer as a percent rounded to the nearest tenth of a percent.
Solution
Probability that a student plays a school sport, that is, probability that a student is a student athlete = P(S) = 55% = 0.55
Probability that a student is in the ninth grade, that is, probability that a student is a freshman = P(F) = 24% = 0.24
It was given that no freshman is allowed to play sports, hence, it translates that the event that a student is a student athlete and the event that a student is a freshman are mutually exclusive.
P(S n F) = 0
If two students are then picked at random to receive a gift card, we require the probability that one will go to a student athlete and one will go to a freshman.
Probability that the first one goes to a student athlete = P(S) = 0.55
Probability that the second one goes to a freshman ≈ 0.24
Probability that the first one goes to a freshman = P(F) = 0.24
Probability that the second one goes to a student athlete ≈ 0.55
Probability that one will go to a student athlete and one will go to a freshman
= (0.55 × 24) + (0.24 × 0.55)
= 0.132 + 0.132
= 0.264
= 26.4% in percent to the nearest tenth.
Hope this Helps!!
Lisa washes dishes at the local diner. She can wash 4 dishes every minute. What is the algebraic equation to express the function of the total number of dishes Lisa washes?
Answer:
f(x)= 4x or y=4x
Step-by-step explanation:
X represents minutes and the 4 is how many dishes she can wash.
PLZ PLZ HELP ME I NEED THIS FOR ONE OF MY FIANLE ASSIGNMENTS OF THE YEAR AND WHOEVER ANSWERS CORRECTLY WILL GET BRAINLEST
5×4=20 is closer to 24.9344.
[tex]487 \times 512=24.9344[/tex]
Let's try placing the decimals after the hundreds place.
[tex]4.87 \times 5.12=24.9344[/tex]
It works.
There is more than one possibility.
[tex].487 \times 51.2=24.9344[/tex]
[tex]48.7 \times .512=24.9344[/tex]
John works 21 hours a week and earns $157.50. How much does john earn per hour?
Answer:
D. $7.50
Step-by-step explanation:
$157.50 / 21 hours = $7.50 per hour
15=3(2x+4)-3 prove x=1
Answer:
X=1
Step-by-step explanation:
6x+12-3=15
6x+9=15
6x+9-9=15-9
6x=6
X=1
Answer:
see below
Step-by-step explanation:
15=3(2x+4)-3
Distribute
15 = 6x +12 - 3
Combine like terms
15= 6x +9
Subtract 9 from each side
15 -9 = 6x+9-9
6 = 6x
Divide each side by 6
6/6 = 6x/6
1 =x
Is the function given by f(x)equalsleft brace Start 2 By 2 Matrix 1st Row 1st Column one fourth x plus 1 comma 2nd Column for x less than or equals 4 comma 2nd Row 1st Column 4 x minus 11 comma 2nd Column for x greater than 4 comma EndMatrix continuous at xequals4? Why or why not? Choose the correct answer below. A. The given function is continuous at xequals4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist. B. The given function is not continuous at xequals4 because f(4) does not exist. C. The given function is continuous at xequals4 because the limit is 2. D. The given function is not continuous at xequals4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist.
Answer:
C. The given function is continuous at x=4 because the limit is 2.
Step-by-step explanation:
Given the function:
[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]
We are to determine if the function is continuous at x=4.
For a function to be continuous at some value c in its domain:
f(c) must be defined.[tex]Lim_{x \to c}$ f(x)[/tex] must exist. [tex]f(c)=Lim_{x \to c}$ f(x)[/tex]Now: at x=4
[tex]f(4)=\dfrac{1}{4}*4+1=2[/tex][tex]Lim_{x \to 4}f(x)=2[/tex]Since the two values are the same, we say that f(x) is continuous at x=4.
The correct option is C.
need answers to 34 35 and 36
Answer:
34) 75
35) 60
36) 210
Step-by-step explanation:
34) Area of a rectangle:
L x B
= 15 x 5
= 75
35) Area of a trapezium :
½ h (sum of || sides)
= ½ x 6 x (12+8)
= 3 x 20
= 60
36) Area of a regular hexagon:
3BH
= 3 x 7 x 10
210
Hope it helps....
Answer:
Step-by-step explanation:
35. 75
area of rectangle : A = b x h
= 15 X 5
= 75
36. 60
area of trapezoid : A = (b1 + b2) x h
2
= (8+12) x 6
2
= 60
37. 210
area of regular polygon : A = P x a (P no. of sides) (a is apothem)
2
= (6 x 10) x 7
2
= 210
11+11=4
22+22=16
33+33=
What’s the answer
Answer:
what method exactly r u using ????
How much will a person pay for 12.2 pounds of bananas at a price of $2.24 per pound
Answer:
It would be 27.328 but since it is money, we have to leave the 8 out.
So the answer is 27.32
Step-by-step explanation:
Answer:
$27.33
Step-by-step explanation:
You multiply 12.2 and 2.24 and the answer is 27.328. You then round it to the nearest tenth which is 27.33.
Analyze the diagram below and answer the question that follows.
Answer:
B. Complements of congruent angles are congruent.
Step-by-step explanation:
Angles <DCF and <FEG have angles measures that are complementary to to angles E and C.
Simplify the following:
(4x^3+2x) + (8x^3 -5x + 4)
Answer:
12x^3 - 3x + 4
Im 100% percent sure and if you are kind enough, I’d love a BRAINLIEST :)
Please help! Correct answer only, please! Consider the matrix shown below: What are the dimensions of A. A. 3 X 4 B. 4 X 3 C. 12 D. A and B
Answer: A) 3 x 4
Step-by-step explanation:
The dimensions of a matrix are ROWS x COLUMNS.
The given matrix has 3 rows and 4 columns,
therefore the dimensions are: 3 x 4
(please answer as soon as possible)If two lines intersect at a point, then vertically opposite angles are always: a)Complememtary b)Supplementary c)Unequal d)Equal
Answer:
D
Step-by-step explanation:
This is the veritcal angles theorem
arl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute? 2 feet 12 feet 720 feet 7,200 feet
Answer: 720 ft
Step-by-step explanation: He rides 720 feet.
if 120 feet are in 10 seconds then;
60 seconds are 60/10*120=720 feet
Answer:
720
Step-by-step explanation:
120/10 to find his feet per second which is 12 feet per second
12*60
since there are 60 seconds in a minute
= 720
If 5=3+2,then 3+2=5. What is the truth value
Answer:
true
Step-by-step explanation:
The area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.
Answer:
Option (2). 14 m
Step-by-step explanation:
Formula to get the area of a circle 'A' = [tex]\pi r^{2}[/tex]
where r = radius of the circle
Given in the question,
Area of the circle = 153.86 square meters
By putting the values in the formula,
153.86 = πr²
r = [tex]\sqrt{\frac{153.86}{\pi } }[/tex]
r = [tex]\sqrt{49}[/tex]
r = 7 meters
Diameter of circle = 2 × (radius of the circle)
= 2 × 7
= 14 meters
Therefore, diameter of the circle is 14 meters.
Option (2) is the answer.
Answer:
14m
Step-by-step explanation:
A hose fills a hot tub at a rate of 3.15 gallons per minute. How many hours will it take to fill a 322-gallon hot tub? It will take nothing hours to fill the hot tub. (Simplify your answer. Round to two decimal places as needed.)
Answer:
So we find how many of 3.15 units of gallons will fit into the tub.
That means we need to divide. 311/3.15 is about 98.73 minutes
That means that it takes 1 hour and 38.73 mins
Step-by-step explanation:
Shiva brought $39.00 to the state fair. She bought a burger, a souvenir, and a pass. The burger was 1/3 as much as the souvenir, and the souvenir cost 1/2 the cost of the pass. Shiva had $4.00 left over after buying these items.
Pass = $21 , Souvenir = 2x/3 = $14 , Burger = x/6 =$3.5 .
Look at the row of numbers. What number should come next?
8, 4, 2, 1, 1/2, 1/4, ?
Answer:
1/8
Step-by-step explanation
Every time the number is divided by 2 like 8 divided by 2 is 4 and 4 divided by 2 is 2 and so on so if you divide 1/4 by 2 it would be 0.125 and that in fraction would be 1/8.
Find the term that must be added to the equation x2−2x=3 to make it into a perfect square. A. 1 B. 4 C. -3 D. 2
Answer:
1
Step-by-step explanation:
x^2−2x=3
Take the coefficient of x
-2
Divide by 2
-2/2 =-1
Square it
(-1)^2 = 1
Add this to each side
What’s the correct answer for this question?
Answer:
D
Step-by-step explanation:
Answer:
V ≈ 382 inches ³
Step-by-step explanation:
V = 4/3πr³
V = 4/3(3.14)(4.5)³
V = 1145.11/3
V = 381.7
V ≈ 382 inches ³
Suppose 44% of a large sample of a population favor a tax increase. If there
are 95,000 people in the population about how many people in the population
favor a tax increase?
A. 13,300
B. 22,800
C. 41,800
D. 32,300
Answer:
C. 41,800
Step-by-step explanation:
Multiply 0.44 by 95,000.
0.44 x 95,000 = 41,800
Suppose you want to buy a new car and are trying to choose between two models: Model A: costs $16,500 and its gas mileage is 25 miles per gallon and its insurance is $250 per year. Model B: costs $24,500 and its gas mileage is 40 miles per gallon and its insurance is $450 per year. If you drive approximately 40,000 miles per year and the gas costs $3 per gallon:
1. Find a formula for the total cost of owning Model A where the number of years you own the car is represented by x.
2. Find a formula for the total cost of owning Model B where the number of years is the independent variable.
3. Find the total cost for each model for the first five years. If you plan to keep the car for 4 years, which model is more economical?
4. Find the number of years in which the total cost to keep the two cars will be the same.
5. Identify the number of months where neither car holds a cost of ownership advantage.
6. What effect would the cost of gas doubling have on cost of ownership?
7. If you can sell neither car for 40% of its value at any time, how does the analysis change?
Answer:
1. CA=16,500+5,050x
2. CB=24,500+3,450x
3. CA(x=5)=CB(x=5)=41,750
If keeped 4 years, Model A is more economical.
4. 5 years
5. From month 49 to 61.
6. The cost of ownership of Model A increases more than Model B, as it is less gas efficient. The break-even point for x is reduced from x=5 to x=2.35.
7. The fixed cost are reduced by a 40%, so the variable cost, the ones that depend on time of ownership, are increased in importance.
Step-by-step explanation:
We can express the cost of ownership as the sum of the purchase cost, gas cost and insurance cost.
1. For model A we have:
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$16,500+3 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{25\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$250\cdot x\\\\\\\text{Cost of ownership}=\$16,500+\$4,800x+\$250x\\\\\\\text{Cost of ownership}=$16,500+\$5,050x[/tex]
2. For model B we have:
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$24,500+3 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{40\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$450\cdot x\\\\\\\text{Cost of ownership}=\$24,500+\$3,000x+\$450x\\\\\\\text{Cost of ownership}=$24,500+\$3,450x[/tex]
3. If x=5, the costs for each car are:
[tex]\text{CoOwn A}=16,500+5,050\cdot(5)=16,500+25,250=41,750\\\\\\\text{CoOwn B}=24,500+3,450\cdot(5)=24,500+17,250=41,750[/tex]
5 years is the break-even point for the cost of ownership between these two cars.
If you plan to keep the car for 4 years, the costs are:
[tex]\text{CoOwn A}=16,500+5,050\cdot(4)=16,500+20,200=36,700\\\\\\\text{CoOwn B}=24,500+3,450\cdot(4)=24,500+13,800=38,300[/tex]
For a 4 year period ownership, the model A is more economical ($36,700).
4. This happens for 1 year, the fifth year, in which the two models have the same cost of ownership.
5. At the 5th year, the cost for both models are the same.
Then, this corresponds to the months 4*12+1=48+1=49 and 5*12+1=61.
6. If the cost of gas doubles, the cost of ownership would rise for both model, but more for the Model A, which is less gas efficient and hence has a higher gas cost.
Model A
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$16,500+6 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{25\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$250\cdot x\\\\\\\text{Cost of ownership}=\$16,500+\$9,600x+\$250x\\\\\\\text{Cost of ownership}=$16,500+\$9,850x[/tex]
Model B
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$24,500+6 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{40\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$450\cdot x\\\\\\\text{Cost of ownership}=\$24,500+\$6,000x+\$450x\\\\\\\text{Cost of ownership}=$24,500+\$6,450x[/tex]
The breakeven point goes from x=5 (for $3 per gallon) to x=2.35 (for $6 per gallon).
[tex]16,500+9,850x=24,500+6,450x\\\\(9,850-6,450)x=24,500-16,500\\\\x=8,000/3400=2.35[/tex]
7. If we can sell any car for 40% of its value at any time, the cost of ownership becames:
Model A:
[tex]\text{Cost of ownership}=16,500+5,050x-0.4\cdot16,500\\\\\text{Cost of ownership}=9,900+5,050x[/tex]
Model B
[tex]\text{Cost of ownership}=24,500+3,450x-0.4\cdot24,500\\\\\text{Cost of ownership}=14,700+3,450x[/tex]
The fixed costs are lowered by 40%, so the variable costs (the ones that depend on time) became more important.
Which is the graph of f(x) = 2(3)^x?
Answer: The graph is:
find the quotient of 25.5÷0.5
Answer:
[tex]51[/tex]
Step-by-step explanation:
[tex]\frac{25.5}{0.5}[/tex]
[tex]\frac{255}{5}[/tex]
[tex]=51[/tex]
Find values of a. b. and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
X + y = 6
y + z = 6
x + z = 6
ax + by + cz = 0
a) a unique solution (a. b .c)=([])
b) no solution (a. b .c)=([])
c) infinitely many solutions (a. b, c) = ([])
Answer:
Step-by-step explanation:
The given equations are
x + y = 6- - - - - - - - -1
y + z = 6- - - - - - - -2
x + z = 6- - - - - - - - - 3
From equation 2, y = 6 - z
Substituting y = 6 - z into equation 1, it becomes
x + 6 - z = 6
x - z = 6 - 6
x - z = 0
x = z
Substituting x = z into equation 3, it becomes
z + z = 6
2z = 6
z = 6/2
z = 3
x = 3
Substituting x = 3 into equation 1, it becomes
3 + y = 6
y = 6 - 3
y = 3
ax + by + cz = 0
3a + 3b + 3c = 0
3(a + b + c) = 0
Therefore, it is impossible
The sum of two consecutive integers is −19. Find the integers.
Answer:
-9 and -10
Step-by-step explanation:
x + x+1=-19
2x+1=-19
2x=-19-1
2x=-20
x=-10
x+1
-10+1=-9
Answer:
[tex]-9[/tex]
[tex]-10[/tex]
Step-by-step explanation:
[tex]x+x+1=-19[/tex]
[tex]2x+1=-19[/tex]
[tex]2x=-19-1[/tex]
[tex]2x=-20[/tex]
[tex]x=-20 \div 2[/tex]
[tex]x=-10[/tex]
[tex]x+x+1=-19[/tex]
[tex]x+1=-19-x[/tex]
[tex]-10+1=-19-(-10)[/tex]
[tex]-9=-19+10[/tex]
[tex]-9=-9[/tex]
A population has the following characteristics.(a) A total of 25% of the population survives the first year. Of that 25%, 75% survives the second year. The maximum life span is 3 years.(b) The average number of offspring for each member of the population is 3 the first year, 5 the second year, and 3 the third year.The population now consists of 144 members in each of the three age classes. How many members will there be in each age class in 1 year?0 ≤ age ≤ 1 = 1 ≤ age ≤ 2 = 2 ≤ age ≤ 3 = In 2 years?0 ≤ age ≤ 1 = 1 ≤ age ≤ 2 = 2 ≤ age ≤ 3 =
Answer:
After 1st year, the age distribution will be
[tex]x_1 = \left[\begin{array}{ccc}1584\\36\\108\end{array}\right][/tex]
After 2nd year, the age distribution will be
[tex]x_2 = \left[\begin{array}{ccc}5256\\396\\27\end{array}\right][/tex]
Step-by-step explanation:
A population has the following characteristics.
A total of 25% of the population survives the first year. Of that 25%, 75% survives the second year.
The average number of offspring for each member of the population is 3 the first year, 5 the second year, and 3 the third year.
From the above information, we can construct a transition age matrix.
[tex]A = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right][/tex]
The population now consists of 144 members in each of the three age classes.
From the above information, we can construct the current age matrix.
[tex]x = \left[\begin{array}{ccc}144\\144\\144\end{array}\right][/tex]
How many members will there be in each age class in 1 year?
After 1st year, the age distribution will be
[tex]x_1 = A \cdot x[/tex]
[tex]x_1 = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right] \times \left[\begin{array}{ccc}144\\144\\144\end{array}\right][/tex]
The matrix multiplication is possible since the number of columns of first matrix is equal to the number of rows of second matrix.
[tex]x_1 = \left[\begin{array}{ccc}1584\\36\\108\end{array}\right][/tex]
After 2nd year, the age distribution will be
[tex]x_2 = A \cdot x_1[/tex]
[tex]x_2 = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right] \times \left[\begin{array}{ccc}1584\\36\\108\end{array}\right][/tex]
[tex]x_2 = \left[\begin{array}{ccc}5256\\396\\27\end{array}\right][/tex]
What is the difference? Negative 6 minus (11)
Answer:
-17
Step-by-step explanation:
-6-11=-17
Answer:
the answer is -17
Step-by-step explanation:
please help me... I'm confused
Answer:
a=5
b=15
Step-by-step explanation:
By following the pattern on the table we can see that the x is increasing by 1 and the y is increasing by 3 each time. Therefore, the next set of numbers would be (5,15).
If A={A,15,E,17,18, B,20} and B={ X,22, F,42, Y,62,72}, then what is n(A∪B)?
Answer:
14
Step-by-step explanation:
There are 7 elements in each set, and no elements are shared. The number of elements in the union of the sets is then ...
n(A∪B) = 7+7 = 14