[tex] 4*e^{2x} -3 = 12 [/tex]
Step 1:
Here we have -3 in subtraction on the left side, so when we take it to the right we apply opposite operation of subtraction that is addition.
[tex] 4*e^{2x} = 12+3 [/tex]
[tex] 4*e^{2x} = 15 [/tex]
Step 2:
Next we have 4 in multiplication on left side, so dividing right side by 4,
[tex] e^{2x} = 15/4 [/tex]
[tex] e^{2x} = 3.75 [/tex]
Step 3:
taking log on both sides
[tex] ln ( e^{2x}) = ln(3.75) [/tex]
[tex] {2x} =ln 3.75 [/tex]
Step 4:
Dividing right side by 2,
x= ln (3.75) /2 = 0.66088
Answer : x = 0.66088..
Does 6(x+2)>x-3 have a solution
In a statistics class there are 11 juniors and 6 seniors; 2 of the seniors are females; 6 of the juniors are males. if a student is selected at random, what is the probability that the student is either a junior or a female?
enter your answer as a fully reduced fraction.
Answer: [tex]\dfrac{13}{17}[/tex]
Step-by-step explanation:
Given: Number of juniors = n(J)= 11
Number of seniors = 6
Total students n(S)=[tex]11+6=17[/tex]
Number of seniors are which are females =2
Number of juniors are which are males =6
Then, number of juniors which are females = [tex]11-6=5[/tex]
Now, total females n(F)=[tex]2+5=7[/tex]
such that number of juniors which are females n(J∩F) = [tex]5[/tex]
Now, the number of students either a junior or a female is given by :_
[tex]n(J\cup F)=n(J)+n(F)-n(J\cap F)\\\\\Rightarrow n(J\cup F)=11+7-5=13[/tex]
Now, the probability that the student is either a junior or a female is given by :-
[tex]P(J\cup F)=\dfrac{n(J\cup F)}{n(S)}=\dfrac{13}{17}[/tex]
Solve by factoring 4x^2+16x+12=0
How many different towers can you make using one red, one blue and one yellow block?
Final answer:
Using permutation principles, one can determine that six different towers can be made from one red, one blue, and one yellow block, by multiplying the number of choices for each position (3 x 2 x 1).
Explanation:
The question is about determining the number of different towers that can be made using one red, one blue, and one yellow block. This type of problem involves understanding permutations, as each block can be placed in any order.
To calculate the permutations of the three blocks, we consider how many choices we have for each position in our tower. For the top position, there are three choices (red, blue, yellow), for the second position, there are two remaining choices, and for the last position, there is only one choice left. This gives us a total of 3 x 2 x 1 = 6 different towers. Each tower is a unique combination of the colors in a specific order.
Name at least two pieces of information that might be found in stock listings.
The value of the investment is expected to grow by 3% per year.
How long will it take to double?
A. About 4 years
B. About 6 years
C. About 12 years
D. About 24 years
Answer:
D. About 24 years
Step-by-step explanation:
Compounding is the means the future value of an amount saved today while discounting means the present value of a future amount.
In other words, we discount to know the present value of $1 in the future while we compound to know the future worth of $1 saved today.
Let the value of the investment be x. if it is expected to double in n years then using the compound interest formula
fv = pv(1 + r)^n
where fv and pv are the future and present values respectively and n is the time, r is the growth rate
2x = x(1 + 0.03)^n
2 = (1.03)^n
log 2 = log (1.03)^n
= n log 1.03
n = log 2/ log 1.03
n = 23.44
This is approximately 24 years hence option D is right
If 1 Chinese yuan equals 0.1558 U.S. dollars, then 1 U.S. dollar equals approximately how many Chinese yuan?
A. 0.4185
B. 0.1558
C. 6.1558
D. 6.4185
Answer:
1 U.S. dollar equals 6.4185 Chinese yuans. The correct answer is D.
Step-by-step explanation:
- The first step is to get a fraction between the currencies. The fraction is obtained by dividing the 1 yuan by 0.1558 U.S. dollars.
[tex]fraction=\frac{1\, \, yuan}{0.1558\, \, U.S.\, \, dollars.}[/tex]
- The second step is to multiply the previous fraction by 1 U.S. dollar.
[tex]\frac{1\, \, yuan}{0.1558\, \, U.S.\, \, dollars}\times 1\, \, U.S.\, \, dollars[/tex]
As you can see, the U.S. dollar units can be cancelled and yuan remains.
[tex]\frac{1\, \, yuan}{0.1558}\times 1[/tex]
- The last step is to perform the division.
[tex]1\, \, U.S.\, \, dollars=6.4185\, \, yuans[/tex]
Thus, 1 U.S. dollar equals 6.4185 Chinese yuans. The correct answer is D.
Hey
PLEASE HELP ME
Limited time!!!!
Blank 1: 38,35,65,15
Blank 2: purchasing 12 apps, purchasing 35 apps, spending $35, spending $12
Blank 3: Has 12 new on her phone , Has $35 remaining on her card , Has 35 new apps , Has $12 remaining on her card.
CHOOSE ONE ONLY FOR EACH BLANK.
THX
Side ab in triangle abd corresponds to which side of triangle abc? ab bc ac
Answer:
The correct answer to this question going by the reference photo is AC (answer) that corresponds to AB.
Step-by-step explanation:
Answer:
it is AC
Step-by-step explanation:
option c
Probabilities are between 0 and 1. A probability of 0 means that an event occur or that it is for the event to occur. If it is unlikely that the event will occur, then the probability of that event is . If it is equally likely that the event will occur or that the event will not occur, then the probability is . If it is very likely that the event will occur, then the probability of that event is . If the event will definitely occur, then the probability of that event is . A sample space has probability when all of the possible outcomes of the sample space have probabilities.
closer to zero equal to one impossible real numbers one-half will not closer to one uniform equal
Final answer:
Probability measures the likelihood of an event occurring, with values between 0 (impossible) to 1 (certain). A probability closer to 0 implies unlikeliness, one-half means equal likelihood, and closer to 1 suggests high likelihood. The probabilities in a uniform sample space are equal for all outcomes.
Explanation:
Probabilities are mathematical measures between 0 and 1. A probability of 0 means an event will not occur, or it is impossible for the event to happen. Conversely, if the probability is equal to one, it means the event will definitely happen. When it's unlikely that the event will occur, the probability is closer to zero. If there's an equal chance the event will occur or not, the probability is one-half (0.5). For events that are very likely to occur, the probability is closer to one. A sample space is considered uniform when all the possible outcomes have equal probabilities.
To calculate the probability of an event A in a uniform sample space, count the number of outcomes for event A and divide by the total number of outcomes in the sample space. This is the theoretical probability of A. For example, when tossing a fair coin, there is an equal likelihood of landing on heads or tails, which are mutually exclusive events, each with a probability of 0.5, and together they form the sample space with a total probability of 1.
find the inverse of the following function:
[tex]f(x)=-2 \sqrt{3x-1} -5 [/tex]
if x \geq 1/3[/tex]
Trayvon sells candy bars at a price of $3 each. He purchases every order of 200 candy bars for $350. If the cost of shipping is $0.15 per bar, what is Trayvon’s profit function?
Someone please help me find x and y for problems #19 and 20!!! Please explain if you can
The Smiths want to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room.
Which of the following would be an appropriate scale to use on an 8 1/2 by 11 sheet of paper for a sketch of the room and carpet?
1 inch = 1 foot
1 inches = 1 foot
1/2 inch = 1 foot
2 inches = 1 foot,
The room scale will only fit on an 8 1/2" X 11" page if 1/2 iinch = 1 foot is used. If we take the largest measurement 15 X 20......the 15 would hang over the edge of the paper no matter which way we turn it. With the 1/2" we can get 17 feet on the 8 1/2 side and and 22 on the 11" side.
1/2 inch = 1 foot is the correct answer
During a basketball game, the East Middle School Tigers scored 42 points from two-point baskets. How many two-point baskets did they make?
84
14
21
42
Answer:
21 two point basket.
Step-by-step explanation:
It is given that During a basketball game, the East Middle School Tigers scored 42 points from two-point baskets. It means
Total score = 42 points
Score for each basket = 2 point
Let total number of two-point baskets be x. So,
Total score = 2x points.
[tex]2x=42[/tex]
Divide both sides by 2.
[tex]\dfrac{2x}{2}=\dfrac{42}{2}[/tex]
[tex]x=21[/tex]
Hence, they make 21 two point basket.
−2x+5y=13
16x+3y=25
Your weekly allowance is $25.you spent 6% of the budget on a new video game . how much did you spend on the video game ?\
Which statement best describes how to determine whether f(x) = x3 + 5x + 1 is an even function?
The answer is B) Determine whether (–x)^3 + 5(–x) + 1 is equivalent to x^3 + 5x + 1
Plutonium -25 has a half live of 6 hours . George has 5000 grams of plutonium -25 . How much plutonium-25 will hearse have after 4 days
Use the Law of Sines to find the missing angle in the triangle. Find m
Which equation could have been used to create this graph?
A.
y = 5x
B.
y = x + 0
C.
y = x + 1
D.
y = x + 5
Answer:
Its b :)
Step-by-step explanation:
Suppose the number of gallons of gasoline per day used by a car is normally distributed with a mean of 2.2 gallons and a standard deviation of 1.2 gallons.
What is the difference in gallons per day used by a car with a z-score of 3 and another car that has a z-score of 0?
A. 1.2
B. 2.6
C. 3.6
D. 4.6
PLZ HELP QUICKLY AND CORRECT GETS BRAINLY!
Solve for x: −3|x − 3| = −6
Explain how you can tell without calculating whether the sum of a positive number and a negative number will be positive, negative, or zero.
Based on the given information, choose the abbreviation of the postulate that supports the conclusion that ΔWAS ΔNOT.
AHH! HELP!!
If the conclusion cannot be drawn from the given information, then choose "not possible."
Given:
WS = NT, AS = OT, S = T.
HELP!!!
Draw a tree diagram illustrating the events, two cards are drawn in succession with replacement from a standard deck of 52 and its suit is observed.
I got 50 branches but it's wrong and I'm not sure what I'm doing incorrectly.,
What is the length of bc?
Lexi bought 1 2/5 of green grapes and 2 3/10 of red grapes. Grapes are 2.99 a pound.Did lexi spend more or less then $12?
The perimeter of square A is 28 feet less than the perimeter of square B. The area of square A is 161 square feet less than the area of square B. If x and y are the side lengths of square A and square B, respectively, what is the value of x + y?
factor each polynomial 9x-6 a.9(x-6) b.3(3x-2) c.6(3x-1) d.3x
The correct answer is b) 3(3x - 2)
In order to factor this, you have to find the greatest common factor of 9x and 6. Since 6 does not have an x in it, we cannot pull out an x. Instead we have to look for the biggest whole number that goes into 9 and 6, which is 3.
Next, to take the 3 out, we need to divide each term by 3.
9x/3 = 3x
-6/3 = -2
So the 3 comes out and the results above go together in the parenthesis.
3(3x - 2)
[tex] 9x-6=3(3x-2)\implies\text{B} [/tex]