[tex]\(1138368400\)[/tex] different outcomes possible when considering all the events together.
Coin Toss: Since each toss is independent of the others, the total number of outcomes for 4 tosses is:
[tex]\(2 \times 2 \times 2 \times 2 = 2^4 = 16\)[/tex].
Die Roll: A standard six-sided die has 6 faces, each with a different number from 1 to 6. When the die is rolled once, there are 6 possible outcomes. If the die is rolled 2 times, the number of different outcomes is:
[tex]\(6 \times 6 = 6^2 = 36\)[/tex]
Card Draw: When drawing a card from the deck, there are 52 possible outcomes. If a second card is drawn without replacing the first, there are now 51 possible outcomes for the second card (since one card has already been drawn). Continuing this pattern, for the third card, there are 50 possible outcomes, and for the fourth card, there are 49 possible outcomes.
The number of different outcomes for drawing 4 cards without replacement is: [tex]\(52 \times 51 \times 50 \times 49\)[/tex].
[tex]\[ \text{Total Outcomes} = (\text{Coin Toss Outcomes}) \times (\text{Die Roll Outcomes}) \times (\text{Card Draw Outcomes}) \][/tex]
[tex]\[ \text{Total Outcomes} = 16 \times 36 \times (52 \times 51 \times 50 \times 49) \][/tex]
[tex]\[ \text{Total Outcomes} = 6^2 \times 52 \times 51 \times 50 \times 49 \][/tex]
[tex]\[ \text{Total Outcomes} = 36 \times 52 \times 51 \times 50 \times 49 \][/tex]
[tex]\[ \text{Total Outcomes} = 36 \times 31625400 \][/tex]
[tex]\[ \text{Total Outcomes} = 1138368400 \][/tex]
The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month? 0.2158 0.8750 0.0362 0.1151
Answer:
0.1151
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 500, \sigma = 75[/tex].
What is the probability that a family spends less than $410 per month?
This probability is the pvalue of Z when X = 410. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{410 - 500}{75}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151. This is the answer.
The Sears tower in Chicago is 1,454 feet tall. Write the height as an integer
Juan's baseball card collection was worth 800$. Over the last 5 years,thw collection decreased $300 in value. What integer representa the average decrease in value each year.
Final answer:
The average yearly decrease in the value of Juan's baseball card collection, which decreased by $300 over 5 years, is $60. This integer represents the yearly reduction in value.
Explanation:
Juan's baseball card collection was worth $800. Over the last 5 years, the collection decreased by $300 in value. To find the average decrease in value each year, we can use the formula: Average decrease per year = Total decrease / Number of years.
Given that the total decrease is $300 and the time period is 5 years, the calculation would be:
Average decrease per year = $300 / 5 = $60.
Therefore, the integer that represents the average decrease in value each year for Juan's baseball card collection is $60.
Jonathan can jog 3 2/5 miles in 7/8 hour.Find his average speed in miles per hour
1 penny has a mass of 4 grams and is 1.55 millimeters thick. How much mass will a stack of 20 pennies tall have?
To find the mass of a stack of 20 pennies, multiply the mass of a single penny by 20.
Mass of a single penny: A single penny weighs around 3 grams on average.
Calculate the total mass: Multiply the mass of a single penny by the number of pennies in the stack (4 grams/penny * 20 pennies).Answer: A stack of 20 pennies will have a mass of 80 grams.A sample of n = 8 scores has ss = 50. if these same scores were a population, then the ss value for the population would be ____.
Answer:
5.69999
Step-by-step explanation:
Which of the various ways of orienting the definitional triangle must be used to resolve n⃗ into components in the tilted coordinate system shown? (in the figures, the hypotenuse is blue (long dashes), the side adjacent to θ is red (short dashes), and the side opposite is yellow (solid).)?
Write 24.652 as a mixed number.
what is length of DE
The population of a town grew from 20,000 to 28,000. The continuous growth rate is 15%. The equation 20,000e^0.15t=28,000 represents the situation, where t is the number of years the population has been growing. About how many years has the population of the town been growing? Use a calculator and round your answer to the nearest whole number.
A. 2 years
B.9 years
C. 17 years
D. 22 years
The correct option is: A. 2 years
Explanation
The given growth equation is: [tex]20000e^0^.^1^5^t = 28000[/tex], where [tex]t[/tex] is the number of years the population has been growing.
For finding the number of years, we will solve the above equation for [tex]t[/tex].
First, dividing both sides by 20000, we will get........
[tex]\frac{20000e^0^.^1^5^t}{20000}=\frac{28000}{20000}\\ \\ e^0^.^1^5^t = 1.4[/tex]
Now taking 'natural log' on both sides, we will get........
[tex]ln(e^0^.^1^5^t)=ln(1.4)\\ \\ 0.15t*ln(e)= ln(1.4)\\ \\ 0.15t*1=ln(1.4)\\ \\ t=\frac{ln(1.4)}{0.15}=2.243..... \approx 2[/tex]
So, the population of the town has been growing about 2 years.
The town has been growing for 17 years
Exponential functionsGiven the exponential function
Given the expressions 20,000e^0.15t=28,000
We are to find the value of "t" which is the time.
e^0.15t = 28000/20000
e^0.15t = 7/5
e^0.15t = 1.4
Take the ln of both sides
lne^0.15t = ln 1.4
0.15t = 2.639
t = 2.639/0.15
t = 17years
Hence the town has been growing for 17 years
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Write the quadratic equation whose roots are -2 and 3, and whose leading coefficient is 3
You need to fill a football with air to play with it. You know that your pump expels air at speed of 8.2 ft/s. The needle of your pump has a radius of 4.5 millimeters. What is the volume flow rate of the air being pumped into the football?
Answer:
The volume flow rate of the air being pumped into the football is approximately [tex]\( 5.261 \times 10^{-7} \)[/tex] cubic feet per second.
Explanation:
To find the volume flow rate of the air being pumped into the football, we first need to calculate the cross-sectional area of the needle of the pump.
Given:
- The radius of the needle, [tex]\( r = 4.5 \)[/tex] millimeters.
The cross-sectional area, [tex]\( A \)[/tex], of the needle can be calculated using the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
Converting the radius from millimeters to feet:
[tex]\[ r = \frac{4.5}{1000} \text{ feet} \][/tex]
Now, let's calculate the cross-sectional area:
[tex]\[ A = \pi \left( \frac{4.5}{1000} \right)^2 \][/tex]
[tex]\[ A \approx \pi \left( \frac{0.0045}{1000} \right)^2 \][/tex]
[tex]\[ A \approx \pi \times 2.025 \times 10^{-8} \text{ square feet} \][/tex]
Now, we can find the volume flow rate, [tex]\( Q \)[/tex], of the air being pumped into the football. The volume flow rate is the product of the cross-sectional area of the needle and the speed of the air:
[tex]\[ Q = A \times \text{Speed} \][/tex]
Given:
- Speed of the air, [tex]\( \text{Speed} = 8.2 \)[/tex] ft/s
Now, let's calculate the volume flow rate:
[tex]\[ Q = \pi \times 2.025 \times 10^{-8} \text{ square feet} \times 8.2 \text{ ft/s} \][/tex]
[tex]\[ Q \approx 5.261 \times 10^{-7} \text{ cubic feet/s} \][/tex]
Each U.S. penny weighs 2.5 grams. How many pennies,x is how many pennies it an equation, are on scale if their total weight is 37.5 grams:A. 2.5+x=37.5 x=12,B. 2.5x=37.5 x=15, C. x-2.5=37.5 x=40,D. 2.5x=37.5 x=18???? please answer quick.
Solve your formula from problem 12 for m. Then find the taxi driver’s hourly rate of his pickup rate is $2 and he charges $19.50 for a 7 - mile trip
Answer: Cost per mile m = $4.78.
Step-by-step explanation:
Since we have given that
Pick up rate = $2
Charges for a 7 mile trip = $19.50
Charges for a mile trip would be
[tex]\dfrac{19.50}{7}\\\\=2.78[/tex]
So, amount of taxi's drivers is given by
[tex]\$2.78+\$2\\\\=\$4.78[/tex]
Hence, cost per mile m = $4.78.
Andrew is planning a tailgate party before the big football game. He has budgeted a maximum of $60 for hamburgers and hot dogs. Hamburgers cost $3 per pound, and hot dogs cost $2 per pound. Write an inequality to describe the possible number of pounds of hamburgers and of hot dogs he can purchase.
The inequality that describes the the possible number of pounds of hamburgers and of hot dogs he can purchase is 3x + 2y ≤ 60.
We have,
Let x be the number of pounds of hamburgers that Andrew purchases, and let y be the number of pounds of hot dogs that he purchases.
The cost of x pounds of hamburgers is 3x dollars, and the cost of y pounds of hot dogs is 2y dollars.
According to the problem, Andrew has budgeted a maximum of $60 for hamburgers and hot dogs.
Therefore, we can write the following inequality:
3x + 2y ≤ 60
This inequality describes the possible combinations of x and y that Andrew can purchase, such that the total cost of hamburgers and hot dogs does not exceed his budget of $60.
Thus,
The inequality that describes the the possible number of pounds of hamburgers and of hot dogs he can purchase is 3x + 2y ≤ 60.
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In the parabola y = (x + 1)2 + 2, what is the vertex?
The vertex form of a quadratic equation is expressed as y = a(x - h)^2 + k. The vertex of the parabola is (-1, 2)
Vertex form of an equationThe vertex form of a quadratic equation is expressed as:
y = a(x - h)^2 + k
where (h, k) is the vertex of the equation
Given the equation of the parabola as y = (x - 1)^2 + 2, On comparing;
h = -1
k =2
Hence the vertex of the parabola is (-1, 2)
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URGENT
The depth of water in the port at hinchinbrook is given by: d(t)= 2.6 sin (Pi over 6 t) + 13.1, where d is in meters and t is the number of hours since high tide.
Use the model to determine how many hours are there between high tides.
If high tide was at midnight, draw a graph to determine during which hours should it be safe for the boats to be in the port and between which hours they would have to stay away from the port. Justify answers mathematically
The sum of three consecutive integers is −261−261. Find the three integers.
a 26 inch piece of Steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 2 in more than three times the length of the first piece find the links of the pieces
What is the fourth term in the arithmetic sequence 13,10,7
The fourth term in the arithmetic sequence 13, 10, 7 is 4.
Explanation:The arithmetic sequence 13, 10, 7 has a common difference of -3. To find the fourth term, we can start with the first term and keep subtracting the common difference. So, 13 - 3 = 10, 10 - 3 = 7, and 7 - 3 = 4. Therefore, the fourth term in the arithmetic sequence 13, 10, 7 is 4.
The cost of a new house can be represented by the regression equation c = 120f + 90,000, where $120 is the cost per square foot and $90,000 is the cost of the lot. A new house on a lot costs $438,000. How many square feet does it have?
Answer: 2900 Square Feet
Step-by-step explanation: i took the test
Write forty and eight tenths as a decimal
i need help to evaluate this p + (-q) - 2 where p = -3 and q =5
how can you use absolute value to represent a negative number in a real world situation
What is the range of f(x) = 4x?
Answer:
D. All positive real numbers
Step-by-step explanation:
The range of a function f(x) are all the possibles values that f(x) can take. So in the function of the question it doesn't matter what value takes x, f(x) is always going to be a positive number. For example:
f(0)=[tex]4^{0}[/tex]=1
f(-1)=[tex]4^{-1}[/tex]=1/4
f(2)=[tex]4^{2}[/tex]=16
Then, the range of f(x) is all positive real numbers.
What is the expression for the calculation double 5 and then multiply by 3?
evaluate the expression 4(2x + 3) + 2(x + 1)-7
Joe practiced his trumpet 3/4 hour on Monday and 7/12 hour on Tuesday. How long did he practice altogether
Find the exact circumference of a circle with the given radius. 36 inches C = 72 in. 36 in. 18 in. IN PIE TERMS PLEASE!!!!!:)
Answer:
The circumference of a circle is [tex]72\pi [/tex] .
Step-by-step explanation:
Forrmula
[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]
Where r is the radius of the circle .
As given in the question
The radius of the circle is 36 inches .
Put all the values in the formula
[tex]Circumference\ of\ a\ circle = 2\times 36\pi [/tex]
[tex]Circumference\ of\ a\ circle = 72\pi [/tex]
Therefore the circumference of a circle is [tex]72\pi [/tex] .
What number is 2 hundred 15 tens and 6 one