Answer:
True
Step-by-step explanation:
If a is negative then the shape of the graph is an upside down U, which intersects the x-axis. If a is positive it will never cross the X axis.
It is true that f(x)=[tex]a^{x}[/tex]+4 will never cross the x axis if a is positive.
What is function?Function is relationship between two or more that are variables expressed in equal to form. In a function each value of x must have a corresponding value of y.
How to find x intercept?We have been given that f(x)=[tex]a^{x} +4[/tex] and we have to find whether it will cross x axis or not.
when a line crosses the x axis the value of y becomes negative. We have to first check at y=0.
[tex]a^{x}+4[/tex]=0
[tex]a^{x}[/tex]=-4
taking log both sides,
log [tex]a^{x}[/tex]=log(-4)
x log a=0.602059991+1.3437635i
x=(0.602059991+1.3437635i)/log a
when we put the value of x in f(x) the value of f(x) cannot be negative so it cannot crosses the x axis.
Hence it is true that f(x)=[tex]a^{x}[/tex]+4 will never cross the x axis if a is positive.
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Plzzz help as soon as possible
Answer:
Step-by-step explanation:
8 is not a function
9 is a function
10 is a function
A rectangular garden is to be constructed using a rock wall as one side of the garden and wire fencing for the other three sides. Given that there are 56 meters of fencing available, determine the dimensions that would create the garden of maximum area. You may enter an exact answer or round your answer to the nearest hundredth.
Answer:
x = 28 m
y = 14 m
A(max) = 392 m²
Step-by-step explanation:
Rectangular garden A (r ) = x * y
Let´s call x the side of the rectangle to be constructed with a rock wall, then only one x side of the rectangle will be fencing with wire.
the perimeter of the rectangle is p = 2*x + 2*y ( but in this particular case only one side x will be fencing with wire
56 = x + 2*y 56 - 2*y = x
A(r) = ( 56 - 2*y ) * y
A(y ) = 56*y - 2*y²
Tacking derivatives on both sides of the equation we get:
A´(y ) = 56 - 4 * y A´(y) = 0 56 - 4*y = 0 4*y = 56
y = 14 m
and x = 56 - 2*y = 56 - 28 = 28 m
Then dimensions of the garden:
x = 28 m
y = 14 m
A(max) = 392 m²
How do we know that the area we found is a local maximum??
We find the second derivative
A´´(y) = - 4 A´´(y) < 0 then the function A(y) has a local maximum at y = 14 m
another name for the positive integrets is the ___ Numbers.
Answer:
natural
Step-by-step explanation:
Rewrite 5ab showing the multiplication signs
Answer:
[tex]5ab = 5 \times a \times b[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
5a*b
If y is inversely proportional to (tan x) and y = 2
when x = 30°, find the value of y when this value
of x is doubled.
Answer:
When something is inversely proportional it can be solved by using the equation:
y = k/x
where k is the constant.
So using this we can plug in x and y to find the value of k.
3 = k/4.
Next we isolate k and find that k = 12. Now we use this to find the value of y when x = 8. Plug in x and you get y = 12/8 or y = 3/2 or 1.5.
Another way to solve this is to look at how the value of x changes. When the value of x goes up, the value of y goes down.
In other words, when x is multiplied by some number, y is divided by that number. In this equation we can see that x is multiplied by 2 to go from 4 to 8.
Thus, y must be divided by 2.
Thus, y = 3/2 or 1.5.
Answer:
Step-by-step explanation:
y is inversely proportional to tan x means
[tex]y \ \alpha \ \frac{1}{tan x}\\\\y = k \times \frac{1}{tanx}[/tex]
Given y = 2 when x =30° . So we will find k.
[tex]y =k \times \frac{1}{tanx } \\\\2 = k \times \frac{1}{tan 30}\\\\k = 2 \times tan 30 = 2 \times \frac{1}{\sqrt{3}} = \frac{2}{\sqrt{3} }[/tex]
Now x is doubled, x = 60°, find y
[tex]y = k \times \frac{1}{tanx}\\[/tex]
[tex]= \frac{2}{\sqrt{3}} \times \frac{1}{tan 60}\\\\= \frac{2}{\sqrt{3}} \times \sqrt{3}\\\\=2[/tex]
What do u multiply first?
Answer:
Order of operations tells you to perform multiplication and division first, working from left to right, before doing addition and subtraction. Continue to perform multiplication and division from left to right. Next, add and subtract from left to right.
pls Mark me as brainliest trust me..
What is 0.25% of 30?
Answer:
0.075
Step-by-step explanation:
if you were to too a dice one time what is the odds of rolling a number less than three?
Answer:
1/3 or 33.33%
Step-by-step explanation:
A regular dice has 6 sides each with a single number from 1 to 6. Therefore, there are a total of 6 possible outcomes. Out of all of these only two outcomes are actually less than three and those are the numbers 1 and 2. Meaning, that if the dice were rolled only a single time then the probability of rolling a number less than 3 would be 2/6 or 1/3 (simplified). As a percentage, this probability would be 33.33%
A watering can contained 5 1/2 quarts water. After all the plants were watered, only 4 cups remained.
How many cups of water were used to water the plants?
Answer:
4 1/2 quarts.
Step-by-step explanation:
So 5 1/2 quarts to start. 4 left over.
Theres 4 cups in a quart.
So theres be 4 1/2 quarts used.. as 4 cups left would be a quart and 1 quart taken away from 5 1/2 quarts in 4 1/2.
area
help hellllppppp
Answer:
Area = 14¹/16 yd² or 14.0625 yd²
Step-by-step explanation:
2. The figure given is a square having equal sides of 3¾ yd each.
Formula for area of the square = a²
Where,
a = 3¾ yd
Plug in the value into the equation:
Area = (3¾)²
Change to improper fraction
Area = (15/4)²
Area = 225/16
Area = 14¹/16 yd² or 14.0625 yd²
The sampling distribution describes the a. long-run behavior of a statistic. b. short-term behavior of the population. c. sample size. d. population proportion.
Answer:
Option A
Step-by-step explanation:
A probability distribution of a statistic that represents a large sample derived from a certain specific population size to determine a range of possible outcomes of statistics such as Mean, Standard deviation, mode, median etc. in a way that it represents the existing entire population is known as a sampling distribution
Hence, option A is correct
please help (i mark brainlist)
Seven hundred twenty -one thousandths as a decimal
Answer:
0.721
Step-by-step explanation:
the last digit (the number '1') must be in the thousandths place; then work backward so the '2' would be in the hundredths and the '7' would be in the 'tenths'
Find the quotient of -4 1/6 and -3 1/3
A) 13 8/9
B) -5/6
C) -7 1/2
D) 1 1/4
Answer:
B -5/6
Step-by-step explanation:
how do I find the percent of 60% of 40
Answer: turn percentages into decimals then multiply that by the initial number
Step-by-step explanation:
60%
0.60
0.60*40= 24
Kelly is using a rectangular container to fill up a bucket of water. The container is 3.8 inches long, 2.5 inches wide, and 7.2 inches tall. If the bucket holds 1,368 cubic inches of water, how many times will Kelly have to fill the cup in order to fill the bucket
Answer:
Kelly will have to fill the cup 20 times.
Step-by-step explanation:
Volume of the cube:
Rectangular cube, so the volume of the cube is the multiplication of its three dimensions(3.8 inches, 2.5 inches and 7.2 inches).
V = 3.8*2.5*7.2 = 68.4 cubic inches.
If the bucket holds 1,368 cubic inches of water, how many times will Kelly have to fill the cup in order to fill the bucket?
Solved by proportions, using a rule of three.
1 time - 68.4 cubic inches
x times - 1368 cubic inches
Applying cross multiplication:
[tex]68.4x = 1368[/tex]
[tex]x = \frac{1368}{68.4}[/tex]
[tex]x = 20[/tex]
Kelly will have to fill the cup 20 times.
20 POINTS AND I WILL MARK YOU BRAINLIEST !!!
the london ferris wheel has a maximum height of 443 ft and a diameter of 394 ft . the wheel takes 30 mins to rotate
#1. what is the minimum height of the ferris wheel ?
94 , 85 , 49 , or 40
#2. where would the midline of the graph be ?
y=246 , y=221.5 , or y=197
#3. what is the amplitude of the graph ?
246 ft , 221.5 ft , or 197 ft
#4. what is the period of the function ?
15 , 30 , or 60 minutes
Step-by-step explanation:
#1 . the minimum height =
443 - 394 = 49 ft
#2. y = (394/2) + 49 = 197+49
=> y =246
#3. the amplitude is ½× diameter
= ½×394 = 197 ft
#4. the period of function is
the time that the wheel takes
one rotation =>30 minutes
I need help
1−(−3)−5
answer is -1 you can check it on the calculator
pleaseeee mark me as the BRAINLIEST pleaseeee
Step-by-step explanation:
(-)(-)=+
1−(−3)−5
1+3-5
4-5
-1
Given P(A) = 0.3, P(B) 0.63 and P(BA) = 0.79, find the value of
P(A and B), rounding to the nearest thousandth, if necessary.
Answer:
P(A and B) = 0.14.
Step-by-step explanation:
Venn probabilities:
Suppose we have two events, A and B. The probability P(A and B) is given by:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
In which [tex]P(A \cup B)[/tex] is P(A or B).
In this question:
P(A) = 0.3, P(B) = 0.63, P(A or B) = 0.79. So
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.3 + 0.63 - 0.79 = 0.93 - 0.79 = 0.14[/tex]
So
P(A and B) = 0.14.
please help what's the exact value for x?
cos(x+pi)-sin(x-pi)=0
SHOW WORK PLEASE
Step-by-step explanation:
Recall that
[tex] \cos(x + \pi) = \cos x \cos\pi - \sin x \sin\pi[/tex]
and
[tex] \sin(x - \pi) = \sin x \cos \pi - \cos x \sin \pi[/tex]
But we also know that
[tex] \cos \pi = - 1 \\ \sin \pi = 0 \: \: \: \: [/tex]
so the above relations reduce to
[tex] \cos(x + \pi) = - \cos x \\ \sin(x - \pi) = - \sin x [/tex]
Therefore,
[tex] \cos(x + \pi) - \sin(x - \pi) = - \cos x + \sin x [/tex]
Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 77 and a standard deviation of
10. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals.
(a) Find the 28th percentile of the scores.
(b) Find the 65th percentile of the scores.
(c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score
needed to get an A?
(d) Between what two values are the middle 64% of the scores? (Enter the smaller number in the first box.)
Fat Kat's offers a special on large two topping pizzas. In how many different ways can you order a two topping pizza if you can choose from 18 toppings? NO LINKS!!!
=======================================================
Explanation:
There are 18 ways to pick the first topping and 18-1 = 17 ways to pick the next topping. Picking the same topping again doesn't make much sense (though I suppose it could mean that you just want more of that topping than usual?), so that's why we have the 18 drop to 17 when making that second selection.
If the order of toppings mattered, then we'd have 18*17 = 306 permutations. However, the order of toppings doesn't matter. All that matters is the group rather than the individual toppings. When counting out the 306 permutations, we've overcounted by a factor of 2. In other words, we've double counted.
So we must divide by 2 to fix this double count. That leads to 306/2 = 153 combinations
------------------------
The alternative method involves using the nCr combination formula
Use n = 18 and r = 2 in this formula
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
the exclamation marks indicate factorial.
The step function f(x) is graphed
What is the value of f(-1)?
0-3
O-1
ОО
0 1
The value of f(-1) in the graph is 1.
What is Function?In mathematics, a function is an expression, rule, or law that establishes a relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The graph leads to the following finding:
The values of f(-1) for x = -1 are -1 and -3.
The function does, however, have a closed circle at f(-1) = 1.
The function has an open circle at f(-1) = -3.
A closed circle represents inclusive principles.
Hence, the graph's value for f(-1) is 1.
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Here is the function for the number of zombies, N, after t years, with the negative exponent expressed using the fraction ½:
N(t) = 300 • 0.5t/8
What is the half-life for the zombie population?
Answer:
The half-life for the zombie population is of 8 years.
Step-by-step explanation:
Exponential equation:
An exponential equation has the following format:
[tex]N(t) = N(0)(1-r)^t[/tex]
In which N(0) is the initial value and the part [tex](1-r)^t[/tex] is related to the decay.
In this question:
[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]
Thus N(0) = 300, that is, initial population of 300.
What is the half-life for the zombie population?
This is t for which N(t) = 0.5*300 = 150. So
[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]
[tex]150 = 300(0.5)^{\frac{t}{8}}[/tex]
[tex](0.5)^{\frac{t}{8}} = \frac{150}{300}[/tex]
[tex](0.5)^{\frac{t}{8}} = 0.5[/tex]
[tex](0.5)^{\frac{t}{8}} = (0.5)^1[/tex]
Equal exponents, so:
[tex]\frac{t}{8} = 1[/tex]
[tex]t = 8[/tex]
The half-life for the zombie population is of 8 years.
A box is filled with 2 red carts, 3 green cards, and 8 brown cards. A card is chosen at random from the box, What is the grobability that the card is not green?
Write your answer as a fraction in simplest form.
Answer:
10/13
Step-by-step explanation:
High. Very High
The total number of cards is 8 + 3 + 2 = 13
There are 3 green ones and 10 others.
P(~G) = 10/13 = 0.769
Imagine a simple process in which 5 ticket booths are selling tickets for an opera. If customers are coming at a rate of 15 / hour, and the utilization of the 5 booths is 50%, then how long does a customer spend at a booth (each customer goes to only one booth)?
Answer: The customer spends 10 minutes at a booth.
Step-by-step explanation:
Let n= number of booths, [tex]\rho[/tex] = utilization, [tex]\lambda[/tex] = arrival rate, [tex]\mu=[/tex]Service rate
We know that
[tex]\rho=\dfrac{\lambda}{\mu\times n}[/tex]
As per given,
[tex]0.5=\dfrac{15}{\mu\times5}\\\\\Rightarrow\ \mu=\dfrac{15}{5\times0.5}\\\\\Rightarrow\ \mu=6[/tex]
Service rate = 6 customers per hour.
Time taken by each customer = [tex]\frac{1}{\mu}[/tex]
[tex]=\frac{1}{6} \ hours \ or\ \dfrac{60}{6}\ minutes\\\\=10 \ minutes[/tex]
Hence, the customer spends 10 minutes at a booth.
Help with volume all help is appreciated :)
Answer:
It would be 0.41 ft^3
Step-by-step explanation:
Alright, to start, lets get the volume of the entire cinder block and the holes within it.
1.31 * 0.66 * 0.66 ---> 0.5706...
Next with the holes, they are both 0.33 wide, 0.39 long, and just as tall at 0.66 feet.
0.33 * 0.39 * 0.66 ---> 0.0849...
Since there's two of them: 0.1698...
To finish it, subtract the hole volume from the total volume;
0.5806 - 0.1698 = 0.4108
Rounds to 0.41 ft^3
A salesman earns $250 per week PLUS a 10% commission on all sales over $5000. In one week, his sales totaled $14,000. What were his earnings that week?
A. $1,050
B. $1,150
C. $400
D. $2,150
Answer:
B. 1150
Step-by-step explanation:
14000-5000=9000 sales over 5000
9000 x .10=900 commission
250 (salary)+ 900 (commission)=1150 total
READ PIC! PLEASE HELP
Answer:
B. 0< b < 1
Step-by-step explanation:
b is a fraction that less than 1, so 0 < b < 1
Please help and thank you
( ignore the answer I clicked)
Answer:
Step-by-step explanation:
Answer:
your answer is correct. a trapezoid can be defined by it's set of parallel sides
Step-by-step explanation:
If the shape you're looking at doesn't have at least one set of parallel sides, it's not a trapezoid;