Which logarithmic equation is equivalent to 3^2 = 9?
Answer:
[tex]log_3(9)=2[/tex]
Step-by-step explanation:
[tex]3^2 = 9[/tex]
Logarithmic form is the reverse of exponential form
To convert exponential form in to log form we use a rule
[tex]b^x=a[/tex] can be written as [tex]log_b(a)=x[/tex]
WE apply the same rule in our exponential equation to convert it into log form
[tex]3^2 = 9[/tex]
The base of exponent is the base of log
[tex]log_3(9)=2[/tex]
Trigonometric Identities and Applications plz help
Gavin's mean score on 3 math tests is 87. What equation can be solved to find x, the score he needs on his next test to bring his mean score up to 90?
To find the score Gavin needs on his next test to have an average of 90, we understand that the sum of his first three tests and the fourth test, divided by four, must equal 90. Translating this understanding to an equation gives: (261 + x4) / 4 = 90, which can be solved for x4.
Explanation:The subject posed deals with the understanding of mean averages and algebra. The mean, or average, is calculated by adding up all the values and dividing by the total number of values. In Gavin's case, his mean score of 87 over three tests can be represented algebraically as (x1 + x2 + x3) / 3 = 87. The challenge is to find out what Gavin needs to score in his next test (let's call this x4) to have a new mean score of 90.
To set up the equation we need to understand that now the average is calculated over four tests, and it must equal 90. Thus, the equation to solve is ((x1 + x2 + x3) + x4) / 4 = 90. As we know that the sum of his first three test scores is 87 * 3 (because (x1 + x2 + x3) / 3 = 87), we substitute that sum (261) into the equation:
(261 + x4) / 4 = 90. Solving this equation for x4 will give the score Gavin needs on his next test to achieve an average of 90.
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2) Suppose 3x + 4y = 52 and 5x + y = 30. What is the value of 8x − 2y?
Answer:
c
Step-by-step explanation:
Bella Sandino failed to pay her cell phone bill in the amount of $85.14 by the due date of March 4. Calculate the amount Bella must pay on March 20 if the company charges 20% interest on late payments. Assume a 365-day year.
How to find A? help please and thanks
During the two hours of the morning rush from 8
a.m. to 10
a.m., 100 customers per hour arrive at the coffee shop. the coffee shop has a capacity of 80 customers per hour. what is the number of customers waiting at 10
a.m.
A rectangular prism has a length of 5 centimeters, a width of 5 centimeters, and a height of 10 centimeters. The surface area of this prism is 250 square centimeters.
True or False
Let j and k stand for two different rational numbers. If ∣j∣>∣k∣, then what else must be true?
A) j is farther from 0 than k is. B) j is less than k. C) On a number line, j is to the right of k.
D) the opposite of j is less than the opposite of k
A is the correct answer trust me
Answer:
A) j is farther from 0 than k is
Step-by-step explanation:
A light bulb consumers 1800 watt-hours per day. How long does it take to consume 9450 watt-hours?
To find out how long it takes for a light bulb to consume 9450 watt-hours, when it uses 1800 watt-hours per day, divide 9450 watt-hours by 1800 watt-hours per day, which equals 5.25 days.
Explanation:The question involves calculating how long it takes for a light bulb to consume a certain amount of energy (9450 watt-hours) given its daily consumption rate (1800 watt-hours per day).
To find the duration, you simply divide the total energy by the daily consumption rate:
Total energy to be consumed = 9450 watt-hours
Daily energy consumption = 1800 watt-hours per day
Duration = Total energy ÷ Daily energy consumption
Duration = 9450 watt-hours ÷ 1800 watt-hours/day = 5.25 days
Therefore, it will take 5.25 days for the light bulb to consume 9450 watt-hours of energy.
In △ABC, AB = 7 and AC = 17. Find m∠B to the nearest degree
68
38
21
87
Answer:
The m∠B is 68°
Step-by-step explanation:
Given the right angled triangle ABC in which right angled is at A.
AB = 7 units and AC = 17 units
we have to find the measure of ∠B.
By trigonometric ratios,
[tex]cot \angle B=\frac{AB}{AC}[/tex]
[tex]cot \angle=\frac{7}{17}[/tex]
[tex]\angle B=cot^{-1}(\frac{7}{17})[/tex]
[tex]\angle B=67.619864948\sim 68^{\circ}[/tex]
Hence, the m∠B is 68°
Option 1 is correct
Johnson Certified bought a fiber optic cable for $975,000. The estimated life of the cable is 20 years, after which its salvage value is estimated to be $5,000. Using the straight-line method, what is the annual depreciation to the nearest cent?
an automobile radiator contains 20 L of antifreeze and water. this mixture is 20% antifreeze. how much of this mixture should be drained and replaced with pure antifreeze so that the mixture will be 50% antifreeze.
Final answer:
To make a 20L mixture 50% antifreeze, 7.5L of the mixture should be drained and replaced with pure antifreeze. This calculation is based on the original 20% antifreeze concentration and the goal of reaching a 50% concentration without changing the total volume.
Explanation:
The question asks how much of a 20L mixture, which is 20% antifreeze, needs to be drained and replaced with pure antifreeze so the mixture will be 50% antifreeze. To solve this, first calculate the current amount of antifreeze in the mixture: 20L * 20% = 4L. Let's say x liters are drained and replaced with pure antifreeze. The volume of the solution does not change, the remaining 20L. After replacement, the quantity of antifreeze is (4 - 0.2x + x) liters (since we subtract the antifreeze drained, which is 20% of x, and add back x liters of pure antifreeze), and we require this to be 50% of the total, which is 10L (50% of 20L).
Setting up the equation: 4 - 0.2x + x = 10. Simplifying gives 0.8x = 6, so x = 7.5. Therefore, 7.5L of the mixture should be drained and replaced with pure antifreeze to achieve a 50% concentration.
Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of vector PQ.
Patricia pays $1.19 each to download songs to her MP3 players. If n is the number of downloaded songs, which equation represents the cost C in dollar?
A recipe for bread calls for 4 1/4 cups of flour. Which expression gives the number of cups of flour needed if you want to make 3 1/2 batches of this recipe?
A. 3 1/2 + 4 1/4
B. 3 1/2 x 4 1/4
C. 4 1/4 ÷ 3 1/2
D. 4 + 1/2 + 3 + 1/2
i dont get this. can you explain
Edgar has a bird bath that holds 2 gallons of water. He only want to fill it 3/4 full. How much water in gallons should Edgar put in the bird bath?
Suppose 60% of the people in a town will get exposed to flu in the next month. if you are exposed and not inoculated then the probability of your getting the flu is 80%, but if you are inoculated that probability drops to 15%. of two executives at beta company, one is inoculated and one is not. what is the probability at least one will not get the flu? assume that the events that determine whether or not they get the flu are independent.
Use the zero product property to find the solutions to the equation 6x^2-5x=56
6x² -5x -56 = 0 . . . . . subtract the constant
(3x +8)(2x -7) = 0 . . . .factor*
The zero product property says the product will be zero only when one (or both) of the factors is zero.
First Factor
... 3x +8 = 0
... x + 8/3 = 0 . . . . divide by the coefficient of x
... x = -8/3 . . . . . . subtract 8/3
Second Factor
... 2x -7 = 0 . . . . . . set the factor to zero
... x -7/2 = 0 . . . . . divide by the coefficient of x
... x = 7/2 . . . . . . . add 7/2
_____
*Comment on factoring
There are various ways to do this. In basic terms, we want to find numbers that are factors of the product 6·(-56) whose sum is -5. We found those numbers to be -21 and 16. Then we can rewrite the -5x term using these numbers and factor by grouping.
... 6x² -5x -56 = (6x² -21x) +(16x -56) = 3x(2x -7) +8(2x -7) = (3x +8)(2x -7)
Answer:
B. x = -8/3, or x= 7/2
Step-by-step explanation:
Rachel jogged along a trail that was 1/4 (fraction) of a mile long. She jogged along the trail 8 times. How many miles did Rachel jog in all??
At a grocery store a four-pack of yogurt costs $3.95. How much does each container of yogurt cost
Each term in a binomial expansion has degree n; therefore, the product of the exponents of each term is n.
true
or
false
Answer:
False
Step-by-step explanation:
In any binomial expansion of the form
[tex](x+a)^n = \Sigma_0^n nCr x^{n-r} a^{r}[/tex]
We find that each term has decreasing powers of x by 1 and increasing powers of a by 1, such that the sum of exponents is always n
Hence product of exponents of each term cannot be n.
The given statement is false.
Only the sum of the exponents of each term in a binomial expansion has degree n
On a standardized test raw answer the first 22 questions in 5 minutes there are 77 questions on the test if he continues to answer questions at the same rate how long will it take him to complete the test from start to finish
Answer:
Step-by-step explanation:
17.5
How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number. The large tire has a diameter of 60 inches. The small tire has a radius of 9 inches.
For the large tire with a diameter of 60 inches, it would make 38 rotations after traveling 600 feet. The small tire with a radius of 9 inches would make 127 rotations in the same distance.
Explanation:First, let's convert the feet into inches since the tire measurements are given in inches. There are 12 inches in a foot, so 600 feet is equal to 7200 inches. Now, we need to determine the circumference of each tire, which we can find using the formula for the circumference of a circle which is 2πr (twice the product of pi and the radius).
For the large tire, the diameter is 60 inches, so the radius (r) is half the diameter, which is 30 inches. Thus, the circumference of the large tire would be 2π*30, which is about 188.5 inches. The large tire would therefore make about 7200/188.5 = 38 rotations.
The small tire has a radius (r) of 9 inches, so its circumference is 2π*9, which is about 56.55 inches. The small tire would hence make about 7200/56.55 = 127 rotations.
Please note that the numbers are rounded off to the nearest whole number as requested.
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The large tire makes approximately 38 rotations, and the small tire makes approximately 128 rotations when each travels a distance of 600 feet.
Explanation:To find the number of rotations a tire makes, you first need to know the circumference of the tire, which represents the distance the tire would cover in one full rotation. The circumference of a circle (or tire, in this case) is calculated as 2πr, where r is the radius of the circle.
For the large tire with a diameter of 60 inches (which makes the radius 30 inches because the radius is half the diameter): The circumference is 2π × 30 = 188.5 inches. Convert this to feet because the distance given is in feet. So, 188.5 inches is about 15.7 feet. Divide the total distance by the circumference to find the number of rotations: 600 feet / 15.7 feet = approximately 38 rotations.
For the small tire with a radius of 9 inches: The circumference is 2π × 9 = 56.5 inches, which is about 4.7 feet. Divide the total distance by the circumference to find the number of rotations: 600 feet / 4.7 feet = approximately 128 rotations.
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There were three trains made of the cars with exactly the same number of passenger's seats. The first train had 418 seats, the second 456, and the third 494. How many cars were in each train, if it is known that each train had not more than 50 cars?
1 train=?
2 train=?
3 train=?
The city transportation commission surveys a random sample of licensed drivers, asking the question, "Do you favor increasing the number of bus routes within the city limits?" Which shows how bias might have affected the results of the survey? A. The question is biased in favor of bus riders. B. The question is biased against bus riders. C. Surveying only licensed drivers creates a bias against people who don't have driver's licenses. D. Since the survey used random sampling, it is unlikely to be biased.
The lifetimes of batteries produced by the juicy battery company are normally distributed with a mean of 100 hours and a standard deviation of 10 hours. find the number of hours where at least 90% of the batteries will continue to operate at.
How many ways can Hannah give three of her eight T-shirts to her younger sister?
A snail traveled 3 over 8, of an inch in 3 minutes. How many inches can the snail travel in 9 minutes? Express the answer as a decimal