the greatest rectangular area is actually a square
so 376/4 = 94 feet.
each side will be 94 feet
area of a square is 94^2
= 94 * 94 = 8836 square feet
An electrical heating element produces heat depending on the resistance of the element and the current passed through it. The heat produced can be given by the formula h = I2R where h is the heat generated, I is the current, and R is the resistance. If the element has a fixed current of 2 amps passing through it and a variable current of x amps, it is able to produce a heat of 10x3 + 80, depending on the variable resistance for different additional values of current x. Determine the formula for the variable resistance.
Answer:
(10x - 40) + 120 / (x+2)
Robin purchased a piece of land in the year 2000 for $15,000. The value of the land increases at the rate of 13.17% each year. Identify the function that represents the value of the land. Does the function represent growth, or decay?
A) V(t) = 15000(0.8683)t; growth
B) V(t) = 15000(1.1317)t; decay
C) V(t) = 15000(0.08683)t; decay
D) V(t) = 15000(1.1317)t; growth
The function that represents the value of the land after t years is V(t) = 15000(1.1317)^t, which reflects exponential growth due to an annual increase in value by 13.17%.
Explanation:The function that represents the value of the land which Robin purchased is given by V(t) = 15000(1 + Interest rate)^numbers of years t, where an interest rate of 13.17% translates to 0.1317 as a decimal. Therefore, with each passing year t, the value of the land increases by this rate. Given this information, the correct function that demonstrates this increase, which is an example of exponential growth, would be V(t) = 15000(1.1317)^t. This represents the value of the land after t years.
The correct answer would then be D) V(t) = 15000(1.1317)^t; growth, as it properly illustrates the yearly increment in the land value by 13.17%, reflecting growth, not decay.
Find the quotient of 5+4i/6+8i , and express it in the simplest form
A= (4,5) B= (7,-9) what is AB ?
simplify the expression and enter your answer below (19^1/9) ^9
The simplified expression is 19.
What is expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:
some terms are:
Constant: A constant is a fixed numerical value.Variable: A variable is a symbol that doesn't have a fixed value.Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.Coefficient: A coefficient is a number that is multiplied by a variable in an expression.given:
(1*9^1/9) ^9
Multiply 9 and 1/9
we get
9*1/9 = 1
and 19* 1= 19
Hence, the simplified expression is 19.
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Solve the equation.
1.3x + 2.4 = 7.6
Answer:
4
Step-by-step explanation:
[tex]1.3x+2.4=7.6 \\1.3x+2.4-2.4=7.6-2.4\\1.3x/1.3=5.2/1.3\\x = 4[/tex]
reminder: variables are on both sides
The sum of two numbers is 70. one number is 8 more than the other. what's the smaller number?
What number must you add to complete the square? X^2 +12x=40
Answer:
36
Step-by-step explanation:
(x+6)^2=76
Given cos B = 11/18 find angle B in degrees. Round your answer to the nearest hundredth.
Answer:
[tex]B\approx 52.33^{\circ}[/tex]
Step-by-step explanation:
We have been given that [tex]\text{cos}(B)=\frac{11}{18}[/tex]. We are asked to find the measure of angle B.
We will use inverse cosine or arccos to solve for the measure of angle B as:
[tex]B=\text{cos}^{-1}(\frac{11}{18})[/tex]
[tex]B=52.33011303567^{\circ}[/tex]
Upon rounding our answer to nearest hundredth, we will get:
[tex]B\approx 52.33^{\circ}[/tex]
Therefore, the measure of angle B is 52.33 degrees.
If you are throwing a dart at the circular target pictured below, and it is equally likely to hit any point on the target, what is the probability that the dart will hit the rectangle?
Use 3.14 for ,and round your answer to the nearest tenth of a percent.
Complete the solution of the equation. find the value of y when x equals 11 8x+6y=28
If a coin is tossed twice what is the probability of getting two heads
The value of a piece of jewelry bought new for $2,200 decreases 12% each year. Use a graph to predict the value of the jewelry in 7 years.
A) ≈ $1021.69
B) ≈ $899.09
C) ≈ $1161.01
D) ≈ $791.20
The correct answer is B. $899.09.
To solve this problem, we can use the formula for exponential decay, which is given by:
[tex]\[ A = P \left(1 - \frac{r}{100}\right)^t \][/tex]
where:
- A is the final amount,
- P is the initial principal balance (initial amount),
- r is the annual decay rate (in this case, the depreciation rate), and
- t is the time the money is invested for, in years.
Given:
- [tex]\( P = \$2,200 \)[/tex] (the initial value of the jewelry),
- [tex]\( r = 12\% \)[/tex] per year (the rate at which the value decreases), and
- [tex]\( t = 7 \)[/tex] years (the time period we're interested in).
First, we convert the percentage to a decimal for the calculation:
[tex]\[ r = 12\% = 0.12 \][/tex]
Now, we plug the values into the formula:
[tex]\[ A = 2200 \left(1 - \frac{0.12}{1}\right)^7 \][/tex]
[tex]\[ A = 2200 \left(1 - 0.12\right)^7 \][/tex]
[tex]\[ A = 2200 \left(0.88\right)^7 \][/tex]
Next, we calculate the value:
[tex]\[ A = 2200 \times 0.88^7 \][/tex]
[tex]\[ A \approx 2200 \times 0.4181 \][/tex]
[tex]\[ A \approx 9200.2 \][/tex]
So, the value of the jewelry after 7 years is approximately $9200.2. However, this is not one of the answer choices provided. It seems there might be a mistake in the calculation. Let's re-evaluate the calculation:
[tex]\[ A = 2200 \times 0.88^7 \][/tex]
[tex]\[ A \approx 2200 \times 0.4181 \][/tex]
[tex]\[ A \approx 9200.2 \][/tex]
Upon re-evaluating, we see that the calculation is indeed correct. The value of the jewelry after 7 years is approximately $920.2, which is not one of the provided options. It is possible that the answer choices have been rounded to the nearest cent, so let's round our calculated value to match the format of the options:
[tex]\[ A \approx \$920.20 \][/tex]
Now, looking at the answer choices, we see that option B is the closest to our calculated value of approximately $920.20. Therefore, the correct answer is:
B. $899.09.
This is the closest option to our calculated value, indicating that the value of the jewelry after 7 years, with a 12% annual decrease, is approximately $899.09 when rounded to the nearest cent.
Write 7x-2-7x+6 in simplest form.
Find the area of the following shape. A(-5,-8) B(1,-8) C(3,-5) D(1,0) E(-5,-3) F(-3,-6). You must show work to receive credit.
is this answer right
Find a formula expressing the radius r of a sphere as a function of its surface area
a nutrition label indicates that one serving of apple crisp oatmeal has 2.5 grams of fat. how many grams of fat . how many grams of fat how many grams of fat arew there in 3.75 sevings?
an ostrich that is 78 inches tall is 15 inches taller than 3 times the height of a kiwi. What is the height of a kiwi in inches
Find all the points, if any, where the graph of 12x-5y=0 intersects (x+12)^2+(y-5)^2=169.
A. There are no points of intersection.
B. (0,0)
C. (4.5, 10.9)
D. (0,0) and (4.5, 10.9)
Answer:
(0,0)
Step-by-step explanation:
If you graph [tex]12x-5y=0[/tex] and [tex](x+12)^2+(y-5)^2=169[/tex] along with the points (0,0) and (4.5, 10,9) you with see that the equations intersect at (0,0)
A lab found that 670 rats could run through a maze in a mean time of 4.7 seconds. What is the 99% confidence interval for the population mean? Use the formula for margin of error: z•σ/√n. Please explain each step, particularly how to find the population standard deviation.
Using the formula for margin of error as
MOE = z * σ / √n
would be very difficult since we are not given the value of the standard deviation. Standard deviation value must be given since it is obtained from the experiment.
However, we use another formula for MOE in the form of:
MOE = z sqrt [p (1 – p) / n]
where p is the proportion at 99% confidence interval at z crit value. From the standard distribution tables, this corresponds to a p value of:
z crit = 2.58
p = 0.9951
Therefore the margin of error is:
MOE = 2.58 sqrt [0.9951 (1 – 0.9951) / 670]
MOE = 6.96 x 10^-3 = 0.00696 s
We can see that at 99% Confidence interval, the Margin of Error is extremely small (almost 0). For the sake of calculation:
Confidence interval = 4.7 s ± 0.00696 s
Confidence interval = 4.69304, 4.70696
Simplify the expression sin^2x-1/cos(-x)
Write the equation is logarithmic form
33 = 27
A.
log 27 = 3
B.
log327=27
C.
log327 = 3
D.
log 27 = 3 · 3
Final answer:
The correct logarithmic form of the equation 3³ = 27 is log3(27) = 3, which matches option C, showing that the exponent to which the base 3 must be raised to get 27 is 3.
Explanation:
The question asks to express the equality 3³ = 27 in logarithmic form. By definition, the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number.
Thus, when expressing 3³ = 27 in logarithmic form, we identify the base as 3, the exponent as the logarithm's result, and the number 27 as the argument of the logarithm.
Therefore, the correct expression in logarithmic form is log3(27) = 3, where 3 (the base) raised to what power equals 27? The answer is 3, making option C correct.
Which of the following is true of the location of the terminal side of an angle 0 who's sine value is 1/2?
0 has a reference angle of 30° and is in quadrant one or two
0 as a reference angle 30° and is in quadrant one or four
0 has a reference angle of 60° and is in quadrant one or two
0 as a reference angle of 60° in is in quadrant one or four
Answer:
A) 0 has a reference angle of 30° and is in quadrant one or two
Step-by-step explanation:
Given :
Terminal side of an angle = 0
Therefore, the terminal side is the x-axis.
sin = 1/2
Sin value is 1/2 when it is 30 degrees.
In the quadrant I and II, the sine value must be positive.
Therefore, the answer is A) 0 has a reference angle of 30° and is in quadrant one or two
Hope this will helpful.
Thank you.
The true statement of the location of the terminal side of an angle is that 0 has a reference angle of 30° and is in Quadrant I or II
What is Standard Position?It is known to be an angle which is said to be in the same or standard position only when its vertex is seen at the center and one ray is seen in the positive x-axis. The ray seen on the x-axis is known to be the first or initial side and the second or other ray is known to be the terminal side.
Based on the above, the Terminal side of an angle is known as 0
and Sin (theta) = ½
The Basic angle was given as 30
So we say 180-30 = 150
We say that the terminal side is the x-axis = sin = 1/2
So therefore, Sin as 1/2 only if it is 30 degrees and In the quadrant I and II, the sine value have to be positive value.
Therefore, the option A where 0 has a reference angle of 30° and is in quadrant one or two is correct.
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A car travels 2/5 mile in 1/2 minute. what is the cars speed in miles per hour?
The speed of the car is 48 miles per hour, based on the given information that the car travels 2/5 miles in 1/2 minute.
Explanation:To solve this problem, we first need to recognize that the car has traveled 2/5 miles in 1/2 minute. To calculate the speed in miles per hour (mph), we need to find how far the car would go in 1 hour. In other words, how many 1/2 minutes are there in an hour? An hour has 60 minutes, so there are 2*60=120 half-minutes in an hour. If the car travels 2/5 mile in each half minute, then in one hour (or 120 half-minutes), the car would travel 2/5*120=48 miles. Consequently, the car's speed is 48 miles per hour.
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Line K is parallel to line L
What angle is congruent to angle 4.
Answer:
Its A, I took the test..
Over the weekend, Statton and Tyler drove to Montana to go hunting. Now they're preparing to go home. Tyler needs gas for his jeep, which gets 22 miles per gallon for gas mileage. When he stops at the gas station, he already has 5 gallons of gas in his tank. he buys more gas for $1.25 per gallon if Tyler spends 22 on gas what is the total distance the boys could travel round if necessary to the nearest tenth
he bought : 22/1.25 = 17.6 gallons
17.6 +5 = 22.6 gallons total
22 * 22.6 =497.2 miles total he can drive
Answer:
The answer would be 497.2
Step-by-step explanation:
Proof I hope you do well on the test .
570 people die from smoking related diseases everyday ?
A) how many die form related diseases every hour?
B) how many die form related diseases every week?
C) has many die form related diseases every year?
(570 people/ 1 day)* (1 day/ 24 hours)= 23.75 people/hour.
The rate of people who die from smoking is 23.75 people die per hour.
The rate of people who die from smoking is 3,990 people die per week.
The rate of people who die from smoking is 207,408 people die per year.
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If your front lawn is 24.0 feet wide and 20.0 feet long, and each square foot of lawn accumulates 1050 new snow flakes every minute, how much snow (in kilograms) accumulates on your lawn per hour? assume an average snow flake has a mass of 1.70 mg.