Answer: There are 151,200 ways the members can be appointed.
Step-by-step explanation:
Since we have given that
Number of eligible candidates = 10
Number of remaining spots available = 6
Here, rank matters.
so, we will use "Fundamental theorem of counting or by Permutation":
So, Number of different ways the members can be selected is given by
[tex]^{10}P_6=10\times 9\times 8\times 7\times 6\times 5\\\\=151,200[/tex]
Hence, there are 151,200 ways the members can be appointed.
The number of different ways the president can appoint the members of the cabinet given that order matters and there are 10 eligible candidates for the remaining 6 positions is 151,200.
Explanation:The question is asking for the number of different ways the six remaining cabinet positions can be filled, given that there are ten eligible candidates and rank matters. This scenario is an example of a permutation problem in combinatorics, a subfield of mathematics. A permutation is an arrangement of objects in a specific order. If rank matters, this means that the order in which the candidates are chosen for the cabinet positions is important. In this case, the formula for permutations is applicable. The formula for permutation when there are 'n' items available (10 eligible candidates) and 'r' items are chosen (6 positions) is given by nPr = n! / (n-r)!. Substituting these values, we have 10P6 = 10! / (10-6)!. After performing the calculation, we find there are 151,200 different ways in which the president can appoint the members of the cabinet.
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A 27-foot pole casts a 25-foot shadow. At the same time, a nearby tower casts a 45-foot shadow. How tall is the tower?
Answer:
The answer to your question is: 48.6 ft
Step-by-step explanation:
See the picture below
Use the Thales's theorem to solve this exercise
x / 27 = 45 / 25
x = 45(27) / 25
x = 1215 / 25
x = 48.6 ft
Answer: 48.6
Step-by-step explanation:
((:
The perimeter of a rectangle is 66 inches. If the length is 3 less than five times the width, find the length and width.
Answer:
length: 27 incheswidth: 6 inchesStep-by-step explanation:
Let w represent the width of the rectangle. The perimeter is twice the sum of length and width so is ...
P = 2(L + w) . . . . . . equation for perimeter
66 = 2((5w-3) +w) . . . substitute the given values
33 = 6w -3 . . . . . . . divide by 2 and collect terms
36 = 6w . . . . . . . . . add 3
6 = w . . . . . . . . . . . .divide by 6
L = 33-6 = 27
The length is 27 inches; the width is 6 inches.
The area of a certain rectangle is 288 yd2. The perimeter is 68 yd. What are the dimensions of the rectangle?
A) 24 yd by 10 yd
B) 18 yd by 16 yd
C) 22 yd by 12 yd
D) 36 yd by 8 yd
Please show work-THX
Answer:
The rectangle is 16*18
Step-by-step explanation:
The area of a rectangle is length * width and the perimeter is 2 times length * width
A = l*w
P = 2(l+w)
Replacing A and P
288 = l*w
68 = 2(l+w) => 34 = l+w => 34 - w = l
replacing l in the area
288 = (34 - w) w
w^2 - 34w + 288 = 0
(w - 16)(w - 18)
w = 16
w = 18
replacing in 34 - w = l
you get that when w = 16, l = 18 and when w = 18, l = 16
The florist selects from these flowers to make arrangements for the upcoming flower show. Use the drop-down menus to complete the statements.
The greatest number of identical arrangements that can be made using only the carnations and asters with no flowers left over is ______.
The greatest number of identical arrangements that can be made using only the lilies and daffodils with no flowers left over is ______.
The greatest number of identical arrangements that can be made using only the carnations and asters with no flowers left over is 6
.
The greatest number of identical arrangements that can be made using only the lilies and daffodils with no flowers left over is
12
ANSWER:
-6
-12
STEP-BY-STEP EXPLANATION:
The greatest number of identical arrangements that can be made using only the carnations and asters with no flowers left over is 6
The greatest number of identical arrangements that can be made using only the lilies and daffodils with no flowers left over is 12
Can someone please help me with this problem? Thank you.
Answer:
HOPE IT HELPS YOU
THANKYOU
PLEASE THANK ME
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If this is calculus AP the answer will be right
=73
you add both angles 56 and 51 then you compare it with the high of the rectangle 7.9 ft to get the answer.
What is the solution to the equation 133/4+x=71/4
the answer is: b
edfvbauskygrweafvuy
State how many imaginary and real zeros the function has.
f(x) = x4 - 15x2 - 16
4 imaginary; 0 real
3 imaginary; 1 real
2 imaginary; 2 real
0 imaginary; 4 real
Answer:
2 imaginary; 2 real
Step-by-step explanation:
You can factor it as ...
f(x) = (x^2 -16)(x^2 +1) . . . . . . . . . x^2-16 is the difference of squares
= (x -4)(x +4)(x^2 +1)
The two linear factors have real zeros; the quadratic factor has two imaginary zeros. There are 2 imaginary and 2 real zeros.
A manufacturer of tennis rackets finds that the total cost of manufacturing x rackets/day is given by 0.0003x2 + 4x + 500 dollars. Each racket can be sold at a price of p dollars, where p = −0.0002x + 9 Find an expression giving the daily profit P for the manufacturer, assuming that all the rackets manufactured can be sold. Hint: The total revenue is given by the total number of rackets sold multiplied by the price of each racket. The profit is given by revenue minus cost. (Simplify your answer completely.)
Answer:
[tex]PT =-0.0005^2 +5x - 500[/tex]
Step-by-step explanation:
We have price (P) = [tex]-0.0002x + 9[/tex]
to calculate Total revenue (TR) we have to multiply Price by Production quantity.
[tex]TR=P * X[/tex] , we denote production quantity with the letter X.
[tex] TR=(-0.0002x + 9)*x[/tex]
We apply distributive law and then we have:
[tex] TR=-0.0002x^2 + 9x[/tex] , this is the Total revenue (TR) of selling X amount of production at a P price.
Now we only have to find the Profit (PT) using the formula:
[tex]PT=TR - TC[/tex] , TR is total revenue and TC is total cost
The expression of the daily profit (PT) for the manufacturer is:
[tex] PT=-0.0002x^2 + 9x - (0.0003x^2 + 4x + 500)[/tex]
[tex] PT= - 0.0002^2 + 9x -0.0003^2 -4x -500[/tex]
[tex]PT =-0.0005^2 +5x - 500[/tex]
The daily profit for the manufacturer, given by P, is equal to -0.0005x^2 + 5x - 500, where x represents the number of rackets manufactured and sold each day.
Explanation:In this example, the manufacturer's daily profit, P, is given by the difference between the total revenue and the total cost. The total revenue is found by multiplying the price of each racket, p , by the number of rackets sold daily, x. i.e, px. The total cost is given by the equation 0.0003x^2 + 4x + 500. Thus, the daily profit is P = (px) - (0.0003x^2 + 4x + 500). Substituting the expression for p gives P = [(−0.0002x + 9)x] - (0.0003x^2 + 4x + 500), which simplifies to P = - 0.0002x^2 + 9x - 0.0003x^2 - 4x - 500. Further simplification leads to P = -0.0005x^2 + 5x - 500. Therefore, the daily profit for the manufacturer is given by P = -0.0005x^2 + 5x - 500.
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Marcus purchased 80 shares of stock in a computer company at $74.19 per share and Taylor purchased 65 shares of stock in a different computer company for $85.21 per share. After holding the stock for two years, Marcus sold his for a total of $6,404.57, and Taylor sold hers for a total of $6,192.83. Which person had a higher ROI and by how much?
Answer: Taylor, by 3.9 pp ($184.81)
Step-by-step explanation:
Marcus: Invested 80 x 74.19 = 5935.20
Taylor: Invested 65 x 85.21 = 5538.65
After 2 y
Marcus: Sold for 6404.57
Taylor: Sold for 6192.83
Net profit
Marcus: 6404.57 - 5935.20 = 469.37
Taylor: 6192.83 - 5538.65 = 654.18
ROI
Marcus: 469.37/5935.20 * 100 = 7.91%
Taylor: 654.18/5538.65 * 100 = 11.81%
Taylor had a higher ROI by 3.9 percentage points (11.81 - 7.91)
Which expression is equivalent to -6 (-2/3 + 2x)
-4 - 12x
-4 + 2x
4 - 12x
4 + 12x
Answer:
c. 4 - 12x.
Step-by-step explanation:
-6(-2/3 + 2x)
Using the distributive law:
= -6*-2/3 - 6*2x
= 12/3 - 12x
= 4 - 12x.
Answer:
4-12x
Step-by-step explanation:
multiply each term by -6
-6 × (2/3)
reduce the numbers with the greatest common divisor 3
In the Pick 4game, you win a straight bet by selecting fourdigits (with repetition allowed), each one from 0 to 9, and getting the same fourdigits in the exact order they are later drawn. What is the probability of winning this game?
Answer:
Probability of winning the game: 1/10000
Step-by-step explanation:
The nominator in the only outcome possible for you to win the bet. So that would be your only selected fourdigit number.
The denominator is the total possibles outcomes. If the first posible number is 0000 and the last number is 9999. There are a total of 10000 possible outcomes that the selected number is drawn.
The general rule is [tex]\frac{p}{q}[/tex]
Where p are the draws where i win.
And q is the total population of possible numbers.
Adam bought a $1,670 custom video game/sound system on a special no interest plan. He made
$100 down payment and agreed to pay the entire purchase off in 1 and half years. The minimum monthly
payment is $10. If he makes the minimum monthly payment up until the last payment, what will be
the amount of his last payment?
Hello!
if he bought it with no interest applied, then the last payment will be $1400
1670 - 100 = 1570
if he has to pay it off in 18 months (1 and a half years), and only pays $10 per month, that means he will pay off $170 before the last payment is due.
1570 - 170 = 1400
so his last payment will have to be $1400 to pay it off completely
I hope this helps, and have a nice day!
$1,400 is the amount of his last payment.
1. First, determine the total amount Adam needs to pay after the down payment. Adam made a $100 down payment on the $1,670 system, so the remaining amount to be paid is:
[tex]\[ \text{Remaining amount} = \$1,670 - \$100 = \$1,570 \][/tex]
2. Next, calculate the total number of monthly payments Adam will make. Since he agreed to pay off the purchase in 1 and a half years, and there are 12 months in a year, the total number of payments is:
[tex]\[ \text{Total payments} = 1.5 \times 12 = 18 \text{ payments} \][/tex]
3. The minimum monthly payment is $10. To find out how much Adam will have paid after 17 payments (one less than the total number of payments), we multiply the monthly payment by the number of payments:
[tex]\[ \text{Amount paid after 17 payments} = 17 \times \$10 = \$170 \][/tex]
4. Now, subtract the amount paid after 17 payments from the remaining amount to find the last payment:
[tex]\[ \text{Last payment} = \$1,570 - \$170 = \$1,400 \][/tex]
Therefore, the amount of Adam's last payment will be $1,400.
Explain why each function is continuous or discontinuous. (a) The temperature at a specific location as a function of time (b) The temperature at a specific time as a function of the distance due west from New York City (c) The altitude above sea level as a function of the distance due west from New York City (d) The cost of a taxi ride as a function of the distance traveled (e) The current in the circuit for the lights in a room as a function of time
Answer:
(a) The temperature at a specific location as a function of time.
This is a continuous function as the temperature cannot increase in an instant like time.
(b) The temperature at a specific time as a function of the distance due west from New York City.
This is a continuous function as the temperature in one location is affected by its neighboring places.
(c) The altitude above sea level as a function of the distance due west from New York City.
The altitude above sea level can be discontinuous at a cliff, or continuous at very deep hole.
(d) The cost of a taxi ride as a function of the distance traveled.
This is a discontinuous function as the cost still raises if you make a stop.
(e) The current in the circuit for the lights in a room as a function of time.
This is a discontinuous function as the function takes the value of 0 when the switch is off and 1 when the switch is on.
The electron traveling speed makes this discontinuous.
Final answer:
a) Continuous
b) Continuous
c) Continuous
d) Discontinuous
e) Continuous
Explanation:
In examining whether a function is continuous or discontinuous, we consider if there are any interruptions in the value of the function as the input changes. Here's an analysis for each given scenario:
The temperature at a specific location as a function of time tends to be continuous because temperature normally changes gradually over time without abrupt jumps.The temperature at a specific time as a function of the distance due west from New York City could be continuous, assuming that there are no abrupt changes in the geographical factors that influence temperature.The altitude above sea level as a function of the distance due west from New York City is typically continuous, generally changing smoothly as one moves across the landscape.The cost of a taxi ride as a function of the distance traveled is often a piecewise function, with portions being continuous within certain distance intervals, but possibly discontinuous at specific points where the rate changes (e.g., base fare to metered fare).The current in the circuit for the lights in a room as a function of time is generally continuous when the lights are on, but if the light switch is flipped, this creates a discontinuity at the moment the lights turn on or off.A continuous probability function has been defined such that probability equals area under the curve of the function over an interval. For real-world phenomena like temperature and altitude, these functions tend to be continuous as they reflect gradual changes over time or distance.
Mary has a third of the money that Erin has. Erin has $8 less than John. Together they have $267. How much money does each of them have?
Mary has $37, Erin has $111, and John has $119 and together they have $267 .
1. Mary has a third of the money that Erin has. Let's represent the amount of money Mary has as "m" and the amount Erin has as "e."
Based on the information given, we can write the equation:
m = (1/3)e
2. Erin has $8 less than John. Let's represent the amount Erin has as "e" and the amount John has as "j."
Based on the information given, we can write the equation:
e = j - 8
3. Together they have $267. This means the total amount of money they have is the sum of what Mary, Erin, and John have:
m + e + j = 267
Now, let's substitute the values we know into the equations to solve for the unknowns.
From equation 1, we have m = (1/3)e. Substituting this into equation 3, we get:
(1/3)e + e + j = 267
To simplify the equation, let's multiply all terms by 3 to eliminate the fraction:
e + 3e + 3j = 801
4e + 3j = 801
From equation 2, we have e = j - 8. Substituting this into the above equation, we get:
4(j - 8) + 3j = 801
Simplify and solve for j:
4j - 32 + 3j = 801
7j - 32 = 801
7j = 801 + 32
7j = 833
j = 833 / 7
j = 119
Now that we know the value of j (which represents the amount John has), we can substitute it back into equation 2 to find the value of e (the amount Erin has):
e = j - 8
e = 119 - 8
e = 111
Finally, we can substitute the values of e and j into equation 1 to find the value of m (the amount Mary has):
m = (1/3)e
m = (1/3)111
m = 37
So, Mary has $37, Erin has $111, and John has $119.
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What is the circumference of a circle with a diameter of 5.8 inches? Use 3.14 for π and round the answer to the nearest tenth. A) 9.1 inches B) 18.2 inches C) 36.4 inches D) 105.6 inches
Answer: B) 18.2 inches
Step-by-step explanation:
We know that the circumference of a circle is given by :-
[tex]\text{Circumference}=\pi d[/tex]
Given : Diameter of a circle = 5.8 inches
Then, the circumference of the circle will be :-
[tex]\text{Circumference}=(3.14)\times5.8=18.212\approx18.2\text{inches}[/tex]
Hence, the circumference of the circle = 18.2 inches
Answer:
Option B.
Step-by-step explanation:
It is given that diameter of the circle is 5.8 inches.
[tex]d=5.8[/tex]
Radius of the circle is
[tex]r=\dfrac{d}{2}=\dfrac{5.8}{2}=2.9[/tex]
We need to find the circumference of the circle.
Circumference of a circle is
[tex]C=2\pi r[/tex]
Substitute π= 3.14 and r=2.9 in the above formula, to find the circumference of the circle.
[tex]C=2(3.14)(2.9)[/tex]
[tex]C=18.212[/tex]
Round the answer to the nearest tenth.
[tex]C=18.2[/tex]
The circumference of the circle is 18.2 inches. Therefore, the correct option is B.
IF A SUBSCRIPTION IS $499 PLUS 8% TAX FOR 30 DAYS, BUT IS BEING PRORATED FOR 7 DAYS, PLUS THERE IS A $10 OFF COUPON, WHAT'S THE FINAL COST?
Answer:
$528.12
Step-by-step explanation:
499-10
489×1.08= 528.12
Answer:
The final cost is $115.74.
Step-by-step explanation:
Total amount of 30 days with tax = [tex]499+(0.08\times499)[/tex] = 538.92 dollars
This value is for 30 days, and its prorated for 7 days, so value for 7 days is =
[tex]\frac{538.92}{30}\times7[/tex] = 125.74 dollars
And $10 is off, so final cost is [tex]125.74-10=115.74[/tex] dollars
(Suppose the discount coupon is applied at the end of billing)
The final cost is $115.74.
Plzzzz help quickly!!! Worth 20 points will mark brainliest! The data below shows cell phone bills for various numbers of minutes used.
What does the slope of the line of best fit represent?
A. There is a charge of $0.15 for each minute of use.
B. There is a charge of $0.45 for each minute of use.
C. There is a monthly fee of $15.00
D. There is a monthly fee of $45.00
Answer:
A
Step-by-step explanation:
Option: A is the correct answer.
A. There is a charge of $0.15 for each minute of use.
Step-by-step explanation:We know that the slope of the line of best fit represents the ratio of change in the dependent variable to the change in the independent variable.
Here the dependent variable is: Phone bill
and the independent variable is the number of minutes used.
Let the line of best fit passes through (100,60) and (300,90).
This means that the slope of the line of best fit is:
[tex]Slope=\dfrac{90-60}{300-100}\\\\Slope=\dfrac{30}{200}\\\\Slope=0.15[/tex]
Hence, the answer is: Option: A
PLEASE HELP 25 POINTS!
Answer:
The common ratio r = 2.
Step-by-step explanation:
Now s2 = a1r and s4 = a1r^3 where a1 = first term and r = common ratio so
s4 / s2 = a1r^3 / a1r = r^2 = 32/8
r^2 = 4
r = 2.
Hey!
--------------------------------------------------
Answer:
r = 2
--------------------------------------------------
Solution:
So we know that s2 = 8 and s4 = 32.
We need to find s1!
32 / 8 = 4
8 / 4 = 2 (ratio is 2)
8 / 2 = 4
32 / 2 = 16
s1 = 4
s3 = 16
Each number is multiplied by 2.
--------------------------------------------------
Hope This Helped! Good Luck!
Given that the average rate of change for y = f(x) over the interval [0,3] is −1, the average rate of change over the interval [2,3] is 5, and the average rate of change over the interval [2,6] is 3, determine the average rate of change over the interval [0,6].
The average rate of change over the interval [0,6] is approximately 1.1666666666666667.
Explanation:As a maths teacher, my aim is to make you understand the concept and how to solve this problem. Let's start by understanding the given information.
We know that the average rate of change, \(m\), of \(f(x)\) over an interval \([a, b]\) is given by:
\(m = \frac{f(b) - f(a)}{b - a}\)
We have been given that:
1) The average rate of change over the interval [0,3] is -1,
2) The average rate of change over the interval [2,3] is 5,
3) The average rate of change over the interval [2,6] is 3.
So we can set up the following system of equations from these:
We have:
\(f(3) - f(0) = -1 * 3 = -3\) (from 1)
\(f(3) - f(2) = 5 * 1 = 5\) (from 2)
\(f(6) - f(2) = 3 * 4 = 12\) (from 3)
From the second equation we can express \(f(3) = 5 + f(2)\).
Then, by substituting this into the first equation we get \(f(2) = -3 - 5 = -8\).
Now we substitute \(f(2) = -8\) into the third equation we get \(f(6) = 12 + f(2) = 12 - 8 = 4\).
And finally, using these we can find the average rate of change over the interval [0,6] is \((f(6) - f(0))/6 = (4 - (-3))/6\), we subtract \(f(3)\) from both sides and we get that \(f(0)\) is equal to \(f(3) - 3\).
This gives us that the average rate of change over the interval [0,6] is approximately 1.1666666666666667.
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The common denominator of
5/6-2/7
The common denominator is 42
Given,
5/6-2/7
Now,
Take LCM of 6 and 7 for obtaining the common denominator,
LCM of 6,7
As 7 is a prime number and 6 is non prime number than there LCM is obtained by multiplying the two numbers .
Hence LCM is 6* 7
LCM = 42
Now
Multiply the denominators 6 and 7
Hence the result will be,
35 - 12 /42
23/42 .
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Final answer:
To find the common denominator of 5/6 and 2/7, multiply each fraction by a factor that will give the least common denominator of 42, then subtract the resulting fractions with the same denominator.
Explanation:
To find the common denominator for the fractions 5/6 and 2/7, we need to determine a shared denominator that both original denominators can be multiplied into without changing the value of the fractions. Multiplication is the key technique to creating a common denominator. In this case, the least common denominator (LCD) is 42 because 6 and 7 have no common factors other than 1, and 6 times 7 equals 42. To transform these fractions, we multiply the numerator and denominator of each fraction by the number that will give us our LCD as the new denominator.
To calculate the difference using the LCD:
Multiply 5/6 by 7/7 to get 35/42.
Multiply 2/7 by 6/6 to get 12/42.
Now, subtract the two new fractions: 35/42 - 12/42 = 23/42.
It is essential to remember that we never add or subtract the denominators when combining fractions; we only combine the numerators after establishing a common denominator.
Please help me out!!!!!!!!!!!!!!!!
Answer:
y = 0.5x
Step-by-step explanation:
Given that x and y vary directly then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 1, y = 0.5, then
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{0.5}{1}[/tex] = 0.5, hence
y = 0.5x ← equation of variation
George picked flowers every day for three days. On the first day George picked 2 flowers. On the second day George picked 6 flowers, and on the third day he picked 10. A function can model George's sequence. What is the slope of that function? A) 2 B) 3 C) 4 D) 5
Answer:
The answer to your question is: 4
Step-by-step explanation:
first day second day third day
2 6 10
represent them considering number two
2 2 + 4 2 + 8
Here, we can notice that the increase
from day 1 to day 2 was 4 and the
increase from day 2 to three was also 4
then the slope will be 4.
Write the first five terms of the geometric sequence if the nth term is given by 36(1/3)^n-1
Answer:
G1=36,G2=12,G3=4,G4=4/3,G5=4/9
Step-by-step explanation:
Since the nth term is given by;
Gn= 36(1/3)^n-1, then, substitute the values of n as 1,2,3,4 and 5 to get the values of G1,G2,G3,G4 and G5 respectively.
G1=36(1/3)^1-1 = 36
G2= 36(1/3)^2-1= 12
G3= 36(1/3)^3-1 = 4
G4= 36(1/3)^4-1 = 4/3
G5= 36(1/3)^5-1=4/9
Answer:
36, 12, 4, 4/3, 4/9.
Step-by-step explanation:
We find each term by substituting the sequence number.
So the first term (where n = 1)
= 36(1/3)^(1-1)
= 36(1/3)^0
= 36 * 1
= 36.
The second term is 36(1/3)^(2-1) = 36 * 1/3
= 12.
We can find subsequent terms by just multiplying the previous term by 1/3 so the third term = 12 * 1/3 = 4.
So the first 5 terms are 36, 12, 4, 4/3, 4/9.
15 strips, 1 1/4" wide are to be ripped from a sheet of plywood. If 1/8" is lost with each cut, how much of the plywood sheet is used to make the 15 strips
The plywood needed for 15 strips is 20.5 inches.
Given to usNumber of strips needed = 15width of the strip = [tex]\rm 1\dfrac{1}{4}\ inches[/tex]Lost of the plywood to cut a strip = [tex]\rm{ \dfrac{1}{8}\ inches[/tex]width of the strip[tex]\rm 1\dfrac{1}{4}\ inches = \dfrac{(4 \times 1) +1 }{4} =\dfrac{5}{4}\ inches[/tex]
Number of cutsAs to cut 15 strips of plywood a total of 14 cuts will be needed.
therefore, the waste of plywood in these 14 strips will be
= Lost in each cut x Number of cuts
[tex]=\dfrac{1}{8}\times 14\\\\=\dfrac{14}{8}\\\\ = \dfrac{7}{4} inches[/tex]
Total plywood needed for all stripsTotal plywood needed for all single strip
= width of the strip x number of strips
[tex]=\dfrac{5}{4} \times 15\\\\ =\dfrac{75}{4}\\\\[/tex]
Plywood neededPlywood needed
= Total plywood needed for all strip + Total waste of plywood
[tex]=\dfrac{7}{4}+\dfrac{75}{4}\\\\=\dfrac{82}{4}\\\\=20.5\ \rm inches[/tex]
Hence, the plywood needed for 15 strips is 20.5 inches.
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Assume the readings on thermometers are normally distributed with a mean of 0degreesC and a standard deviation of 1.00degreesC. Find the probability that a randomly selected thermometer reads between negative 0.12 and 1.02
Answer:
0.2983
Step-by-step explanation:
Let X be the reading on thermometer. Given that X is N(0,1)
We are to find the probability that a randomly selected thermometer reads between negative 0.12 and 1.02
Reqd probability = [tex]P(0.12<x<1.12)[/tex].
Since this x is already normal std variable x=z
i.e. reqd prob = [tex]P(0.12<z<1.02) =0.3461 -0.0478\\=0.2983[/tex]
Hence answer is 0.2983
On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
A. 0.027
B. 0.090
C. 0.417
D. 0.657
E. 0.900
Answer: The answer is d.
Step-by-step explanation: Ok, so, we know that we have 3 radio stations, each one has a 30% chance of broadcasting a song that leo likes.
Lets see the cases:
Station A has a probability of 0.30 to broadcast a song, but let's suppose that it doesn't, then we go to station B, who has te same probability, 0.30, but for this to happen, we first must have the 0.70 prob of A to broadcasting another song, so here we have a probability of (0.30)*(0.70).
Now with a similar way of thinking, if Station B also fails, we will have a probability of 0.70*0.70*0.30 for Station C succes.
Also, there is the case were station A broadcast the nice song, which we already know that is with probability of 30%.
So, the total probability will be the sum of the 3 cases: 0.30 + 0.30*0.70 + 0.30*0.70*0.70 = 0.657.
Find the break-even point for the given cost and revenue equations. Round to the nearest whole unit.
C = 15n + 269,000
R = 95n
Answer:
[tex]n=3,587\ units[/tex]
Step-by-step explanation:
we know that
The term Break even is when the Revenue is equal to the Cost (the profit is equal to zero)
so
we have
[tex]C=15n+269,000[/tex]
[tex]R=95n[/tex]
Equate the equations
[tex]95n=15n+269,000[/tex]
Solve for n
[tex]95n-15n=269,000[/tex]
[tex]75n=269,000[/tex]
[tex]n=3,587\ units[/tex]
Answer:
It’s C, 3363
Step-by-step explanation:
You received a discount on each book you buy . The original price of each book is x dollars You buy 5 books for a total of (5x - 15 dollars factor the expression using GCF
Answer:
5(x -3)
Step-by-step explanation:
The GCF of 5 and 15 is 5, since 5 is a factor of 15. Factoring that out gives ...
5x -15 = 5(x -3)
A professor is interested in the average length of books in her library. She has divided her books into a few different categories: 235 books on mathematics, 290 books on sports, and 166 books on interior design. Rather than examining all the books, she plans to use a stratified sample of 50 books. How many of the sports books should she choose?
Answer:I would rather be playing Minecraft
Step-by-step explanation:
I like Minecraft
Answer:
21 books approximately.Step-by-step explanation:
First of all we need to find the proportion of the sample. To do that, we sum all the books and then divide by the sample we need, which is 50
[tex]\frac{50}{235+290+166} =\frac{50}{691}[/tex], because we need 50 books among 691 total.
Now, with this ratio, which is the same for all sample we would make here, we find the stratified sample of books, specifically, for sports books which are 290.
[tex]s=290 \times \frac{50}{691}\\ s \approx 21[/tex]
Thefore, she should take 21 sports books.
Remember that stratified sampling refers to a type of sampling method where the population is divided into separate groups, which in this case represented the type of books. Then, we use a "probability" sample, or a proportion of the sample to apply it.
Estimate the time juanita will arive at her aount's home 320 miles away if she leaves at 9:00 am.,drives about 60 miles per hour, and stops for a 40 minute break halfway
Final answer:
Juanita will arrive at her aunt's home around 3:00 pm after accounting for 5 hours and 20 minutes of driving time and a 40-minute break to her journey that began at 9:00 am.
Explanation:
The question is asking us to estimate the arrival time for Juanita who is traveling to her aunt's home 320 miles away. Juanita leaves at 9:00 am, drives at an average speed of 60 miles per hour, and plans to take a 40-minute break halfway through her trip.
To estimate the time it will take Juanita to reach her aunt's house, we need to calculate the driving time and add the time for the break.
The driving time is calculated by dividing the total distance by the average speed. The total driving time is 320 miles \'d'vided by' 60 miles per hour, which equals approximately 5.33 hours or 5 hours and 20 minutes of driving time.
Next, we add the 40-minute break to the driving time. Convert 40 minutes to hours by dividing by 60, which is approximately 0.67 hours or 40 minutes. Now, we sum the hours: 5 hours and 20 minutes driving + 40 minutes break = 6 hours total time spent.
Juanita left at 9:00 am, so we add the 6 hours to this time. Therefore, Juanita should arrive at her aunt's home around 3:00 pm.