The height of the tallest model is 81 cm and the model is [tex]y ( x ) = 3^x[/tex].
Given data:
Let x be the height of the tallest model.
According to the information given, the height of each model is three times the height of the previous model.
So, represent the heights of the models as and exponential model where [tex]y ( x ) = 3^x[/tex].
1st model: 3 centimeters (3 cm)
2nd model: 3 times the height of the 1st model = 3 * 3 cm = 9 centimeters (9 cm)
3rd model: 3 times the height of the 2nd model = 3 * 9 cm = 27 centimeters (27 cm)
4th model: 3 times the height of the 3rd model = 3 * 27 cm = 81 centimeters (81 cm)
So, the height of the tallest model can be represented as:
x = 81 centimeters
Hence, the height of the tallest model is 81 centimeters.
To learn more about exponential form, refer:
https://brainly.com/question/29337692
#SPJ5
State your first and last name. use the letters in your first name and last name to write an equation of a line in slope-intercept form, y=mx + b as follows:
The expression 4.95+0.07x models A household monthly long distance charges where x represents the number of minutes of long-distance calls during the month what are the monthly charges for each number of long distance minutes
The expression provided models the monthly long distance telephone charges, with a fixed fee of $4.95 plus $0.07 per minute of call time. To determine the monthly charge, multiply the number of minutes by $0.07 and add the result to the base charge of $4.95.
The given expression 4.95 + 0.07x represents a model for calculating a household's monthly long distance telephone charges, where x is the number of minutes of long-distance calls. To find the monthly charges for any number of minutes (x), we simply plug in the value of x and calculate the total cost.
If a household uses 0 minutes, the cost would be $4.95 (since 4.95 + 0.07(0) = 4.95).For 100 minutes of use, the cost would be $4.95 + (0.07 x 100) = $4.95 + $7.00 = $11.95.The formula incorporates a fixed fee of $4.95, which we can see as the base charge regardless of usage, plus a variable component that depends on the number of minutes used (0.07 times the number of minutes).
Write words to match the expression 36÷4
when 15 minus 3 is multiplied by a number the product is 2.
Based on the provided information, you can find the value of the unknown by performing the operation (15-3), which is 12, and then dividing the product by this number. The result is 1/6, which is the number that fulfills the conditions stated in the problem.
Explanation:The subject of this problem is middle school math, specifically dealing with equations and unknowns. The problem states that 'when 15 minus 3 is multiplied by a number the product is 2'. To solve this, we use basic algebraic manipulation.
First, perform the operation 15 minus 3, which equals 12. Then, we state the problem algebraically: 12 times a certain number (let's call it 'x') equals 2. Stated as an equation, it would be 12x = 2.
To find the value of 'x', we need to isolate 'x' on one side of the equation, so we divide both sides of the equation by 12. This leaves us with x = 2/12. Simplifying the fraction gives x = 1/6.
In conclusion, the number that when multiplied by 12 (resulting from 15 minus 3), gives us a product of 2 is 1/6.
Learn more about Solving Equations here:https://brainly.com/question/29050831
#SPJ2
Find f'(a) f(t)=2t+1/t+3
Can somebody solve please?
a diver is swimming 11 meters below the surface. The diver sees a shark 19 meters below him. how many meters from the surface is the shark?
Is (1,5) a solution to the equation y=x-2
find the missing coefficients
y=ax^2-10x+c
vertex :(-5,20)
When dividing 592 by 9.25, how many zeros will be placed in the dividend?
No doubt, the expeced answer is 2. This is because you would ordinarily change the problem to 59200/925 for long division by hand.
For this quotient, you don't need any, because the quotient is 64, a multiple of 4, so the numbers being subtracted are always integers.
_____
If you were dividing 591 by 9.25, you would need an infinite number of zeros—because the decimal portion of the quotient is a repeating decimal with a period of 3 digits.
Answer:
it is b 100 on quiz
Step-by-step explanation:
if h(x)=(fog)(x) and h(x) = x+5, find g(x) if f(x) = x+2
Please help quickly first to answer gets bainliest
Which expression uses the greatest common factor and the distributive property to rewrite the sum 32 + 80?
A.16(2) + 80
B. 2(16 + 80)
C.16(2 + 5)
D.8(4 + 10)
Jared has a novel to read for Language Arts class. The novel has a total of 650 pages that he must read in 10 days. He estimates that he can read 25 pages in 1 hour. He plans to read for 3 hours each day. Which number below represents the coefficient of the term that represents the number of pages he can read in one day.
When a polygon reflects across the y axis ,how do the coordinates of the points change
If you stand on a ship in a calm sea, then your height x (in feet) above sea level is related to the farthest distance y (in miles) that you can see by the equation: y=sqrt (1.5x+(x/5280)^2) how high up do you have to be to be able to see 10mi?
Final answer:
To see 10 miles into the distance, one must be approximately 593.4 feet above sea level. This is calculated by substituting y = 10 into the given formula and solving for x.
Explanation:
The student's question involves finding how high above sea level they must be to see a distance of 10 miles. We begin with the equation given:
y = sqrt(1.5x + (x/5280)^2)
We need to solve this equation for x when y is 10 miles. First, we substitute 10 for y and square both sides of the equation to eliminate the square root:
10^2 = 1.5x + (x/5280)^2100 = 1.5x + x^2/(5280^2)Multiply through by 5280^2 to simplify:
100(5280^2) = 1.5x(5280^2) + x^2100(5280^2) = 7920x^2 + x^2100(5280^2) = 7921x^2Now, we solve for x:
x^2 = 100(5280^2) / 7921x = sqrt(100(5280^2) / 7921)x ≈ sqrt(2787840000 / 7921)x ≈ sqrt(352000)x ≈ 593.4 feetTherefore, a person needs to be approximately 593.4 feet above sea level to see 10 miles into the distance.
Ed Callahan Is an executive at a local bank his annual salary is $75,530 if he receive a paycheck every two weeks what is his biweekly salary
His annual salary is $75,530. If Ed receives a paycheck every two weeks, his biweekly salary is $2905.
You will be paid every 2 weeks so is beginning on Sunday and ending on the second Saturday of the pay period. So you will be paid every two weeks, giving you a total 26 .
First you divide 75530 by 26 since its biweekly and that is how you get your answer.
A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. if the service life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours? 95% 68% 34% 99.7%
Approximately 99.7% of the light bulbs are expected to last between 600 and 900 hours, according to the empirical rule of normal distributions, as these values fall within +/- 3 standard deviations from the mean.
To determine what percent of the distribution of light bulbs will have a service life between 600 and 900 hours, we employ the empirical rule for normal distributions. If we know the mean (750 hours) and standard deviation (50 hours), we can calculate the number of standard deviations each of these values are from the mean:
(600 - 750) / 50 = -3 standard deviations (SD)
(900 - 750) / 50 = 3 standard deviations (SD)
According to the empirical rule (68-95-99.7 rule), approximately:
68% of the data falls within "+/- 1 SD"
95% of the data falls within "+/- 2 SD"
99.7% of the data falls within "+/- 3 SD"
Since 600 hours and 900 hours are three standard deviations away from the mean on either side, the percentage of light bulbs expected to last between these two values would be approximately 99.7%.
In this problem, y = 1/(1 + c1e−x) is a one-parameter family of solutions of the first-order de y' = y − y2. find a solution of the first-order ivp consisting of this differential equation and the given initial condition. y(0) = − 1 8
Saeed bought 21 1/2 lb. of ground beef. he used 1/4 of the beef to make tacos and the remaining 2/3 of the remainder to make quarter pound burgers. how many burgers did he make?
Saeed made 42 2/3 burgers.
Explanation:To solve this problem, we need to find out how much ground beef Saeed used to make tacos and how much he used to make quarter-pound burgers. Let's break it down step-by-step:
1. Saeed bought 21 1/2 lb of ground beef.
2. He used 1/4 of the beef to make tacos. So, 1/4 of 21 1/2 lb is (1/4) * 21 1/2 lb = 5 3/8 lb.
3. The remaining beef is 21 1/2 lb - 5 3/8 lb = 16 1/8 lb.
4. Saeed used 2/3 of the remaining beef to make quarter-pound burgers. So, 2/3 of 16 1/8 lb is (2/3) * 16 1/8 lb = 32/3 lb = 10 2/3 lb.
5. To find the number of quarter-pound burgers, we divide the weight of the beef used for burgers by the weight of each burger. Since each burger weighs 1/4 lb, we divide 10 2/3 lb by 1/4 lb to get:
10 2/3 lb ÷ 1/4 lb = 10 2/3 lb * 4 lb/1 = 42 2/3 burgers.
Therefore, Saeed made 42 2/3 burgers.
Final answer:
Saeed used 1/4 of the ground beef for tacos and the remaining 2/3 for quarter pound burgers. After calculating, we determined that he was able to make 43 quarter pound burgers.
Explanation:
To solve Saeed's ground beef problem, we need to perform sequenced calculations to determine how much beef was used for tacos, and how many quarter pound burgers were made with the remaining beef.
First, Saeed used 1/4 of the 21 1/2 lb of beef for tacos. To find out how much that is, multiply 21.5 lb by 1/4:
21.5 lb × 1/4 = 5.375 lb for tacos
Next, we subtract this amount from the original to find the remainder:
21.5 lb - 5.375 lb = 16.125 lb remaining
Now, Saeed uses 2/3 of the remaining beef for burgers. So, we calculate:
16.125 lb × 2/3 = 10.75 lb for burgers
Since each burger is a quarter pound, we divide the weight used for burgers by 1/4 to find out how many burgers he made:
10.75 lb ÷ 1/4 lb per burger = 43 burgers
Therefore, Saeed made 43 quarter pound burgers.
Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value $10.90. How many dimes and how many quarters does she have? [hint: use the decimal values of the c coins to write an equation.]
What is the factorization of 49b2 − 81
on the quiz, i got
B. (7b – 9)(7b +9)
I just finished the edge quiz for my algebra class.
I got a 100, so this is the correct answer.
A container holds 7 quarts of water. How much is this in gallons? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
what are the domain and range of the exponential function below f(x)=4^x+3
Answer:
Step-by-step explanation: Domain are the set of x -values. Here x values from negative to positive.
Range is the set of y values. The graph clearly shows that the values never dip below 3.
Hence the answer is ;
Domain : All x values
Range: never dips below 3.
Misty took a multiple choice test in science that had 50 questions. If the relationship between the number she got correct and the number she got incorrect is 7:3, and she got 9 incorrect, how many did she get correct?
the sum of two numbers is 101. if there times the smaller number is subtracted from the larger number the result is 9. find the two numbers
Need help with math problem
The temperature of a lake drops by the same amount each day for 10 days. The temperature drops by a total of 5 degrees.
Drag the numbers to form the equation that represents the change in the lake's temperature each day.
( ? ) ( ? ) = ( ? )
5, -5, 10, -10, 1/2, -1/2, 1/10, -1/10
Thanks
HINT: THE ANSWER IS NOT (10), (-1/2)= (-5)
Find the values of x on the curve y = cos x 2 + sin x at which the tangent is horizontal. (let n be an integer. enter your answers as a comma-separated list.)
To find the values of x on the given curve at which the tangent is horizontal, we need to find the points where the derivative of y with respect to x is equal to 0.
Explanation:To find the values of x on the curve y = cos x^2 + sin x at which the tangent is horizontal, we need to find the points where the derivative of y with respect to x is equal to 0. The derivative of y is -2x sin x + cos x.
Setting the derivative equal to 0, we have -2x sin x + cos x = 0. Solving this equation will give us the values of x at which the tangent is horizontal.
Unfortunately, it is not possible to find exact solutions to this equation analytically. We can, however, solve it numerically using methods such as Newton's method or the bisection method.
A square acre of land is 4840 square yards. Between which two integers is the length of one side? Pls show the steps or work.
beth has a total of $6000 to invest, part at 6% simple interest and part at 8% simple interest. Her return for one year is $410. How much did she invest at each rate?
Determine which statement is true about the graph of a function