Charlie, who is 6 feet tall, walks away from a streetlight that is 16 feet high at a rate of 6 feet per second, as shown in the figure. Express the length s of Charlie's shadow as a function of time.
The detailed answer provides a step-by-step explanation of how to express the length of Charlie's shadow as a function of time based on his movement away from a streetlight.
Explanation:Length of Shadow as a Function of Time:
Define the variables:Express s as a function of time: s(t) = (h * d) / (d + rt), where r is Charlie's rate of movement away from the streetlight.
Calculate the specific function: In this case, s(t) = (16 * 6) / (d + 6t), where s is the length of the shadow at time t.
the graph of g(x) is the graph of f(x)=8x+20 stretched horizontally by a factor of 4.
Which equation describes the function g?
1. g(x)= 8x+5
2. g(x)= 2x+5
3. g(x)= 32x+20
4. g(x)= 2x+20
how do I answer this?
4th grade homework.
Write an equation that represents this comparison sentence..
32 is 8 times as many as 4
An ounce is 1/16 of a pound. How many ounces are in 8 3/4 pounds?
There are 140 ounces are in 8 3/4 pounds.
Given that,
1 ounce = 1/16 pound
We can also write it as
1/16 pound = 1 ounce
Multiply 16 both sides we get,
1 pound = 16 ounces ......(i)
Therefore,
There are 16 ounces in 1 pound.
Now we can write [tex]8\frac{3}{4}[/tex] in simple fraction as,
= (8x4+3)/4
= 35/4
Now we can say that [tex]8\frac{3}{4}[/tex] pounds as 35/4 pound as both are same quantity
Now, multiply 35/4 both sides in equation (i) we get,
35/4 pound = (35/4)x16 ounces
= 140 ounces.
Hence,
[tex]8\frac{3}{4}[/tex] pounds = 140 ounces.
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A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 48 states. What is the probability that she selects the route of three specific capitals?
The probability that the candidate selects the route of three specific capitals out of 48 states is [tex]\( \frac{1}{17296} \)[/tex].
To calculate the probability of the candidate selecting the route of three specific capitals out of 48 states, we need to consider the total number of possible routes and the number of routes that include the specific capitals.
Calculate the total number of possible routes.
Since the candidate plans to visit 3 out of 48 states, the total number of possible routes is the number of ways to choose 3 states out of 48, which can be calculated using combinations:
[tex]\[ \text{Total number of routes} = \binom{48}{3} \][/tex]
Calculate the number of routes including the specific capitals.
Since the candidate plans to visit the capitals of three specific states, there is only one way to choose each of those specific states. So, the number of routes including the specific capitals is 1.
Calculate the probability.
[tex]\[ \text{Probability} = \frac{\text{Number of routes including specific capitals}}{\text{Total number of possible routes}} \][/tex]
[tex]\[ = \frac{1}{\binom{48}{3}} \][/tex]
Now, let's compute this.
[tex]\[ \binom{48}{3} = \frac{48!}{3!(48-3)!} = \frac{48 \times 47 \times 46}{3 \times 2 \times 1} = 17296 \][/tex]
So, the probability is:
[tex]\[ \text{Probability} = \frac{1}{17296} \][/tex]
Therefore, the probability that the candidate selects the route of three specific capitals out of 48 states is [tex]\( \frac{1}{17296} \)[/tex].
G find the probability that (a) more than 5, (b) between 1 and 3, (c) less than or equal to 2, bulbs will be defective
How to convert pounds to ounces
Step-by-step explanation: To convert pounds into ounces, we need to start with a conversion factor for pounds and ounces which is 16 ounces = 1 pound.
Next, since we are going from a larger unit "pounds" to a smaller unit "ounces" we will multiply the pounds by our conversion factor.
Finally, our product will be our answer.
DBE is obtained by enlarging ABC. If the area of ABC is 3 square units, what is the area of DBE?
A. 27 square units
B. 24 square units
C. 12 square units
D. 9 square units
Answer:
A. 27 square units
Step-by-step explanation:
PLATO 2022 Lnhs
12^10·75^15/15^25·80^5
To solve this expression, apply the rules of exponents and convert the fractions to decimal values. Simplify the expression and use a calculator to find the decimal values of the powers. Divide the values and express the final result in scientific notation.
Explanation:To solve this expression, we can first look at the different components. 12^10 means 12 raised to the power of 10. 75^15 means 75 raised to the power of 15. 15^25 means 15 raised to the power of 25. And finally, 80^5 means 80 raised to the power of 5.
Now, we can substitute these values back into the original expression: (12^10 · 75^15)/(15^25 · 80^5).
By using the rules of exponents, we can simplify this expression. For example, when you multiply two powers with the same base, you add the exponents. When you divide two powers with the same base, you subtract the exponents. Applying these rules, we get:
12^10 · 75^15/15^25 · 80^5 = (12/15)^10 · (75/80)^15/15^25 · 80^5 = (4/5)^10 · (3/4)^15/15^25 · 80^5.
To further simplify, we can convert the fractions into decimal values: 4/5 is equal to 0.8 and 3/4 is equal to 0.75. Substituting these values, we get:
(0.8)^10 · (0.75)^15/15^25 · 80^5 = 0.8^10 · 0.75^15/15^25 · 80^5.
We can use a calculator to find the decimal values of 0.8^10 and 0.75^15. After calculating the values and substituting them back into the expression, we get:
0.4 × 10^2 · 1.99 × 10^4/3.12 × 10^4 · 2.32 × 10^6 = 0.4 × 1.99/3.12 × 2.32 × 10^2 × 10^4 × 10^6 = 0.796/7.244 × 10^2 × 10^4 × 10^6.
Simplifying further, we get:
0.796/7.244 × 10^(2+4+6) = 0.796/7.244 × 10^12.
Dividing 0.796 by 7.244, we get approximately 0.1099373. So, the simplified expression is approximately 0.1099373 × 10^12.
If a(x) = 3x + 1 and b(x)=square root of x-4 , what is the domain of (b*a)(x)?
A.(-infinity ,+infinity)
B.(0 , +infinity)
C.(1 , +infinity)
D.(4 , +infinity)
What is the slope of this line?
a. −15
b. −5
c. 5
d. 15
Answer:
C. 5
Step-by-step explanation:
I did the test
What is green and famous for running away from jail?
Escape peas. It is a joke (cause someone to laugh/cause amusement), an example of a joke in English. Jokes are popular because children learn them. Jokes can be an element of mood change for adults. The peas mean the "green" and the escape is related to the "famous for running away from jail" part.
Prove or disprove each of these statements about the floor and ceiling functions.
Your high school freshman class consists of 760 students. In recent years only 4 out 7 students actually graduated in four years. Approximately how many of your classmates are expected to graduate in four years
To find out how many of the 760 students in the freshman class are expected to graduate in four years, we use the rate of 4 out of 7 students graduating. This calculation yields approximately 434 students expected to graduate.
To calculate the approximate number of students expected to graduate in four years from a freshman class of 760 students, given a historical graduation rate of 4 out of 7, we use a simple proportion calculation. We set up a proportion where 4 out of 7 students graduate, which can be written as 4/7 = x/760, where x represents the number of graduating students.
Calculating this, we get x = (4/7) times 760. To solve for x, multiply both sides of the equation by 760 to isolate x.
x = 760 imes (4/7) = 760 imes 0.57142857
Approximately x = 434
Therefore, we can expect that approximately 434 students in the freshman class will graduate in four years, based on the provided rate.
how many 1/3 pounds serving in 4 2/3 pound of cheese
An airliner carries 100 passengers and has doors with a height of 76 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8in.
a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
(Round to four decimal places as needed.)
First let us calculate for the z score using the formula:
z = (x – u) / s
where u is the mean height of men = 69 in, x is the height of the door = 76, and s is the standard deviation = 2.8 in
z = (76 – 69) / 2.8
z = 2.5
From the standard probability table, at z = -2.5 the probability P is:
P = 0.9938 = 99.38%
2767545 to the nearest ten
Which ordered pair is in the solution set of the following system of inequalities? y>0.5x+4 y≥‒3x+10 A. (2, 6) B. (1, 5) C. (3, 2) D. (4, 5)
completely factor the expression 16t^3 - 50t^2 + 36t
use the fundamental theorem of algebra to determine the number of roots for 2x^2+4x+7
G verify that the divergence theorem is true for the vector field f on the region
e. f(x, y, z) = z, y, x , e is the solid ball x2 + y2 + z2 ≤ 36
A 3-foot piece of wire costs $0.76. What is the unit price, rounded to the nearest cent?
divide total cost by length:
0.76 / 3ft = 0.2533 cents per foot
rounded to nearest cent = 0.25 cents per foot
what is the sale tax on a 17500 truck if the tax rate is 6%
Answer: the sales tax is 1050
A researcher sends out a survey to 740 subjects by mail and receives completed surveys from 65% of the subjects. How many surveys did the researcher receive?
NEED HELP FAST!!!!
Solve the equation.
3x/5 - 0.5 = 1.9
A. 2.3
B. 0.16
C. 4
D. 16
Please explain your answer.
Carlos wants to add two more bags of apples to his order. What is the new total?
Answer:
Hi! The answer to this question is 9.10
Step-by-step explanation:
All of the Items added up equals 9.10
Answer:I thought it was 4.34 but its 9.10
Step-by-step explanation:
Describe t-test and explain how to interpret its results ?
The t-test is a statistical test used to compare the means of two samples. The t-score, which represents the standardised difference between group means, and the p-value, which gives the probability of observing the data given the null hypothesis, are key components of the t-test result interpretation. A small p-value (typically less than 0.05) typically leads to rejection of the null hypothesis.
Explanation:The t-test is a statistical measure used in hypothesis testing to analyze the difference between two sample means. Key to proper interpretation of its results is understanding the test statistic, otherwise known as the t-score, and the p-value.
The t-score is calculated by subtracting one measure from the other and dividing by the standard error to standardize the difference. A large absolute value of the t-score indicates a larger difference between the groups being compared. The t-distribution, which the t-score follows, depends on the sample size (n) and has n - 1 degrees of freedom.
The p-value, usually calculated using technology, is the probability that you would observe the given t-score (or one more extreme) if the null hypothesis was true. It corresponds to the combined area in both tails of the t-distribution. If the p-value is small (typically less than 0.05), this suggests the differences you observed are statistically significant, and you would reject the null hypothesis.
When comparing the results, note that 95 percent of all confidence intervals constructed in this way contain the true value of the population mean statistic.
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Gary is buying a $1,250 computer on the installment plan you makes a down payment on of $150 she has to make monthly payments of $48.25 for two and a half years what is the finance change
Answer:
$347.6
Step-by-step explanation:
The computer cost $1250. If Gary made a down paymnet of $150, $1100 is left to be paid. The financial cost per month is $48.25. For two and a half years this amount must be multiplied by the number of months. In two and a half years there is:
[tex]=12+12g+6=30[/tex]
30 months. Gary pays
[tex]=30\cdot{48.25}=1447.5[/tex]
$1447.5 for 30 months. The original amount was $1250. Cary pays a total of:
[tex]=150+1447.6=1597.6[/tex]
The financial change is:
[tex]1597.6-1250=347.6[/tex]
When "P" Dollars is invested at interest rate "i", compounded annually, for "t" tears, the investment grows to "A" dollars, where A=P(1+i)^t. When Sara enters 11th grade, her grandparents deposit $10,000 in a college savings account. Find the interest rate "i", if the $10,000 grows to $11,193.64 in two years.
Final answer:
The annual interest rate compounded annually that grows $10,000 to $11,193.64 in two years is approximately 5.882%.
Explanation:
To find the interest rate i if the $10,000 grows to $11,193.64 in two years, we can rearrange the compound interest formula to solve for i:
[tex]A = P(1 + i)^t[/tex]
Given:
A = $11,193.64
P = $10,000
t = 2
Rearranging the formula to solve for i, we get:
[tex](A / P) = (1 + i)^t[/tex] → (11,193.64 / 10,000) = (1 + i)²
Now we must solve for i:
1.119364 = (1 + i)² → i = [tex]\sqrt{(1.119364)}[/tex] - 1
Calculating the square root of 1.119364 and subtracting 1 gives us:
i ≈ 0.05882 or 5.882%
Therefore, the annual interest rate compounded is approximately 5.882%.