Answer:
option D.
Step-by-step explanation:
Data given in the table is
x 2 3 4
f(x) -3 0 12
Now we will plug in the values of x in the given functions to find the correct exponential function.
For x =2
A). f(x) = 4(4)[tex]^{(x-1)}[/tex] + 4
f(2) = 4(4)[tex]^{2-1}[/tex] + 4 = 4 × 4 + 4 = 20
B). f(x) = 4(4)[tex]^{(2-1)}[/tex] - 4
f(2) = 4(4)[tex]^{2-1}[/tex] - 4 = (4)(4) - 4 = 16 - 4 = 12
C). f(x) = 1/4(4)[tex]^{x-1}[/tex] +4
1/4(4)[tex]^{2-1}[/tex] + 4 = [tex]\frac{1}{4}[/tex] × 4 + 4
= 1 + 4 = 5
D). f(x) = [tex]\frac{1}{4}(4)^{x-1}-4[/tex]
f(2) = [tex]\frac{1}{4} (4)^{2-1}-4=\frac{1}{4}(4)-4[/tex]
= 1 - 4 = -3
We find option D in which f(2) = (-3). so the answer would be option D.
Anybody know the answer?
Which is the best estimate for (8.9x10^8)/(3.3x10^4) written in scientific notation? A. 3x10^2 B. 6x10^2 C. 3x10^4 D. 6x10^4
Answer:
Option C
Step-by-step explanation:
The given expression is[tex]\frac{8.9\times 10^{8}}{3.3\times 10^{4}}[/tex]
Now we have to solve this.
[tex]\frac{8.9\times 10^{8}}{3.3\times 10^{4}}[/tex]
[tex]=\frac{8.9}{3.3}\times \frac{10^{8}}{10^{4}}[/tex]
= 2.70 × 10⁽⁸⁻⁴⁾
= 2.70 × 10⁴
≈ 3 × 10⁴
Therefore, Option C is the answer.
What is the first step in solving the equation x2 – 16/25 = 0?
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2-(16/25)=0
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 25 as the denominator :
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2.3 Factoring: 25x2 - 16
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 25 is the square of 5
Check : 16 is the square of 4
Check : x2 is the square of x1
Factorization is : (5x + 4) • (5x - 4)
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
Now, on the left hand side, the 25 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
(5x+4) • (5x-4) = 0
3.2 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
3.3 Solve : 5x+4 = 0
Subtract 4 from both sides of the equation :
5x = -4
Divide both sides of the equation by 5:
x = -4/5 = -0.800
3.4 Solve : 5x-4 = 0
Add 4 to both sides of the equation :
5x = 4
Divide both sides of the equation by 5:
x = 4/5 = 0.800
The first step in solving the equation [tex]\rm x^2-\dfrac{16}{25}=0[/tex] is adding and subtracting 4\5x in the equation.
What is a quadratic equation?The quadratic formula helps to evaluate the solution of quadratic equations by replacing the factorization method.
The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are real numbers, also called “numeric coefficients”.
The given quadratic equation is;
[tex]\rm x^2-\dfrac{16}{25}=0\\\\x^2-\dfrac{4^2}{5^2}=0\\\\ x^2+ \dfrac{4}{5}x-\dfrac{4}{5}x - \dfrac{4^2}{5^2}=0\\\\\left (x-\dfrac{4}{5} \right ) \left (x+\dfrac{4}{5} \right )=0[/tex]
Hence, the first step in solving the equation [tex]\rm x^2-\dfrac{16}{25}=0[/tex] is adding and subtracting 4\5x in the equation.
Learn more quadratic equations here;
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1. Most credit card incentive programs give----
a. cash
b. cash back
c. discounts
d. set dollar savings
2. To calculate a rewards program incentive, you---
a. use the simple interest formula
b. use the percentage of a number
c. multiply the whole numbers
d. divide by the percentage offered
3. A credit card gives 2% cash back on purchases. You purchase $1,685.90 in items with that card. What is your reward amount?
a. $33.72
b. $337.18
c. $280.98
d. $2.81
Help please i don't have a graphing calculator and don't know how to use one.
Use the table feature on a graphing calculator to evaluate e^1.6 to four decimal places.
A. 4.953
B. 0.2019
C. 2.7183
D. 4.3493
Part A
Read the following sentences from the passage.
John James lived in Nantes, France, when he was a small boy, although he was born in Louisiana. His father was a wealthy French gentleman, an officer in the French navy, and was much in America, so that John James was first in France and then in America until he was about twenty - five, at which time he settled in his native country for good.
Which explains the meaning of the word native ?
Question 1 options:
a person from another country
a person who moves from country to country
a person who loves his/her country
a person born in a certain place or country
Answer : a person born in a certain place or country
the word 'native' means "of indigenous origin or growth".
John James was of French origin although he was born in America.So, his native country would be France to which he finally shifted when he was 25 years old.
1.ADD (5x4 + 3x3 -x2 +16x)+(2x3 -3x2 -10x4 +x -1)
Ihave tried every possible correct answer and none of them seem to be right on any of these 3 questions please help
2.Subtract the following polynomials correctly.... (5x4 + 3x3 -x2 +16x) - (2x3 -3x2 -10x4 +x -1)
3.Multiply (5x4 + 3x3 -x2 +16x)(x5+2x-1)
A runner burned 120 calories on a 1.6 km run. How many calories would they burn on a 5 km run
Final answer:
The number of calories burned on a 5 km run are 375 calories burned.
Explanation:
The question involves burning calories relative to the distance run by a runner. To find out how many calories would be burned on a 5 km run, we need to set up a proportion since the relationship is assumed to be linear.
Let's start by examining the given data: a runner burns 120 calories for a 1.6 km distance. If we divide the number of calories burned by the distance, we get the rate of calories burned per kilometer:
120 calories / 1.6 km = 75 calories/km.
Now, we can find the total calories burned for a 5 km run:
75 calories/km x 5 km = 375 calories.
Therefore, the runner would burn 375 calories on a 5 km run.
Suppose that there are 67 butterfly species for every 22,000 insect species and there are 15,000 to 22,000 species of butterflies worldwide. how many insect species are there
Answer:
There are 4,925,250 to 7,223,700 insect species worldwide.
Step-by-step explanation:
Supposing that there are 67 butterfly species for every 22,000 insect species and there are 15,000 to 22,000 species of butterflies worldwide, in order to know how many insect species are there we have to do the following calculation:
22,000 (insect species) / 67 (butterfly species) = X (relation of butterfly and insect species)
22,000 / 67 = X
328.35 = X
There are 328.35 insect species for every butterfly species.
So, as there are 15,000 to 22,000 species worlwide, we have to multiply those numbers by 328.35 to know the total amount of insect species:
15,000 x 328.35 = 4,925,250
22,000 x 328.35 = 7,223,700
There are 4,925,250 to 7,223,700 insect species worldwide.
What is the measure of angle C?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
°
A basketball player makes 160 out of 200 free throws. we would estimate the probability that the player makes his next free throw to be
The estimated probability of the basketball player making the next free throw is 0.8 or 80%, calculated by dividing the number of successful throws by total attempts (160/200).
Explanation:The student's question involves estimating the probability of a basketball player making the next free throw based on past performance. Given the player made 160 out of 200 free throws, the estimated probability is calculated by dividing the number of successful throws by the total number of throws attempted. Therefore, the estimated probability is:
P(successful free throw) = Number of successful free throws / Total free throws attempted
P(successful free throw) = 160 / 200 = 0.8 or 80%
Probability lessons often use sports examples to explain concepts because they provide clear, real-world instances of chance and outcomes. To further understand the concept, one can look at various situations, such as Helen's basketball free throw practice where P(C) = 0.75 and P(D) = 0.75 for her making each shot, or Carlos's soccer goal shooting with a probability of 0.65 for each shot, and special situations like streak shooting where probabilities may change after a successful event.
Anybody have the answer?
BRAINLIEST FOR BEST ANSWER
Describe what is meant by the statement “Renting can restrict ones lifestyle.”
Answer:
You have to follow the landlord/owner's rules. For example, if you are renting an apartment and want to have a pet, but your landlord says no then you can't get a pet, or you'll be kicked out.
let g(x) = 2x and h(x)= x^2 -4. find (g o h)(0)
To find (g o h)(0), first calculate h(0) which is -4, then apply this result to g(x), leading to a final result of -8.
Explanation:The student's question asks to find (g o h)(0), which means to find the value of g(h(0)). This involves two functions, g(x) = 2x and h(x) = x2 - 4. First, we need to find h(0), which is 02 - 4 = -4. Then, we use this result as the input for g(x), resulting in g(-4) = 2*(-4) = -8. Therefore, (g o h)(0) = -8.
Find the mean, median, mode, and range of the following values: 6, 12, 13, 17, 3, 7, 12. a. Mean = 10 Median = 13 Mode = 12 Range = 18 c. Mean = 10 Median = 13 Mode = 13 Range = 18 b. Mean = 8.6 Median = 12 Mode = 13 Range = 14 d. Mean = 10 Median = 12 Mode = 12 Range = 14 "
Answer:
D. Mean: 10, Median: 12, Mode: 12, Range: 14
Step-by-step explanation:
3, 6, 7, 12, 12, 13, 17
Mean: 3 + 6 + 7 + 12 + 12 + 13 + 17 = 70/7 = 10
Median: 12
Mode: 12
Range: 17 - 3 = 14
what is the value of y
In a raffle, the winners of the first and second prizes each receive one ticket to an upcoming concert. You and a friend each buy a raffle ticket along with 16 other people. What is the exact probability that you win the first prize and your friend wins the second prize?
Final answer:
The exact probability that you win the first prize and your friend wins the second prize in a raffle with 18 participants is 1/306.
Explanation:
To calculate the exact probability that you win the first prize and your friend wins the second prize in a raffle, we need to look at the total number of possible outcomes and the number of favorable outcomes. Assuming that there are 18 tickets in total (yours, your friend's, and 16 others), the chance that you win the first prize is 1 in 18. After you win, there are 17 tickets left, so your friend's chance of winning the second prize is 1 in 17. To find the combined probability, we multiply these individual probabilities:
The probability that you win first prize = 1/18
The probability that your friend wins second prize given you've won first = 1/17
Combined probability = (1/18) x (1/17) = 1/306
The exact probability that you win the first prize and your friend wins the second prize is 1/306.
The exact probability that you win the first prize and your friend wins the second prize is[tex]\( \frac{1}{306} \).[/tex]
To determine the probability that you win the first prize and your friend wins the second prize in the raffle, we need to calculate the total number of possible outcomes and the number of favorable outcomes where this specific event occurs.
Total number of participants: You and your friend are among 18 people who bought raffle tickets.
Total number of outcomes: There are 18 people in total, so there are
( 18 ) possible winners for the first prize and ( 17 ) remaining people eligible for the second prize after the first winner is chosen.
Therefore, the total number of outcomes where one person wins the first prize and another wins the second prize is:
[tex]\[ 18 \times 17 = 306 \][/tex]
This represents all possible ways the first and second prize can be awarded to two different individuals.
Favorable outcomes (desired event): There is exactly ( 1 ) way for you to win the first prize and ( 1 ) way for your friend to win the second prize.
So, the number of favorable outcomes where you win the first prize and your friend wins the second prize is:
[tex]\[ 1 \times 1 = 1 \][/tex]
Probability calculation: The probability ( P ) that you win the first prize and your friend wins the second prize is given by the ratio of the number of favorable outcomes to the total number of outcomes:
[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{306} \][/tex]
Therefore, the exact probability that you win the first prize and your friend wins the second prize is [tex]\( \frac{1}{306} \).[/tex]
A 10-foot ramp must make an angle of 30degrees with the ground if it is to reach a certain window. What angle must a 15-foot ramp make with the ground to reach the same window?,
PLEASE HELP ME!! I HAVE TO WRITE EXPRESSIONS FOR THESE PROBLEMS BUT I DO NOT KNOW HOW TO....
Writing Expressions. Write expressions to describe each situation. Do NOT solve.
a) Lenny budgeted $55 to buy lunch for the next 7 days. If he buys a soda each day for $1.75, how much of his budget does he have left?
b) Mandy makes a monthly mortgage payment of $850. If she budgeted $11,000 of her salary for mortgage payments this year, what amount of this budget will remain after 12 months?
c) Tim is washing his car. He has $8.45 in his pocket when he starts washing his car. If he spends 18 quarters to wash his car, how much money does he have left?
Geometry proofs! 100+ points!
1. BC/CD = AC/CE 1. Given
2. <BCA is congruent to <ECD 2. Vertical angles are congruent
3. Tr.ACB is congr to Tr.ECD 3. SAS Similarity
Solve for X please
Need help
which of the following is the solution
Solve Q-7/ 1/2= 6/ 1/2
Express as a fraction or mixed number.
30 ÷ 19
What is equivalent fraction of 2/3
Find the center, vertices, and foci of the ellipse with equation 4x2 + 6y2 = 24.
helpppppppppppppppppppppppppppppppppppppppp
An open box is formed from a rectangular piece of cardboard, whose length is 3 inches more than it's width, by cutting 3 inch squares from each corner and folding up the sides. if the volume of the box is to be 264 in^2, find the size of the original piece of cardboard. what are the original dimensions of the piece of cardboard
hello
could anyone please help on this question?
thx