The exponential function always exceeds the linear function
A mathematical function of form f (x) = an x is an exponential function. where x is a variable and an is the function's base constant The transcendental number e, which is approximately 2.71828, is the most commonly encountered exponential-function base.
An exponential function is distinguished from linear and quadratic functions in that the variable to be solved for is contained within the function's exponent rather than (necessarily) within the base of some exponential expression. Here are some examples:
Linear function: f(x) = 3x - 7: The exponents 1 and 0 are implied here, so f(x) is 3(x^1) - 7(x^0). It is worth noting that x is not a component of either exponent; rather, it is a component of the base of each exponent.
h(x) = 4^(3x + 7):This is an exponential function because the variable x is contained within the exponent in this expression.
As a result, the exponential function always outperforms the linear function.
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A 16-ounce bottle of water from Store A costs $1.28. The cost in dollars, y, of a bottle of water from Store B is represented by the equation y=0.07x, where x is the number of ounces. What is the cost per ounce of water at each store? Which store's bottle of water costs less per ounce?
The cost of per ounce of water at store A is $0.08 and at store B is $0.07 , the water in the store B will cost less per ounce .
In the question ,
it is given that
in store A the cost of 16 ounce of water is $1.28 ,
so the cost of 1 ounce of water in store A is = 1.28/16
= $0.08
in store B the cost of water is represented by the equation
y = 0.07x
where "x" is the number of ounces of water ,
which means
the cost of 1 ounce of water in store B is = $0.07
hence , the water in store B will cost less .
Therefore , The cost of per ounce of water at store A is $0.08 and at store B is $0.07 , the water in the store B will cost less per ounce .
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Solve inequality 2(5-x)-6<15-4x-9
Answer:
x<1
Step-by-step explanation:
10-2x-6<15-4x-9 (distributive property)
4-2x<6-4x (simplified both sides)
-2x<2-4x (1st step to get x isolated)
2x<2 (2nd step to get x isolated)
x<1 (divide 2 from each side)
and that's how! :)
tiffany walks x miles in 90 minutes. How many miles can she walk in 120 minutes?
A. 4/3 x
B. 30x
C. 3/4
D. 0.75x
Answer: A. 4/3 x
Step-by-step explanation:
x miles in 90 minutes to ? miles in 120 minutes
90 miles to 120 miles is 1.3333 which is equal to 4/3.
Multiply it to x and you have A. 4/3x
you have 3 bags of candy each with 4 pieces of candy in them. How many pieces of candy do you have?
Answer:
12
Step-by-step explanation:
3x4
It took an ice cream truck 28 minutes to drive through one neighborhood. The truck stopped
driving through the neighborhood at 2:05 p.m.
What time did the clock show when the truck start driving through the neighborhood?
Answer:
1:38
Step-by-step explanation:
i think that is the answer
Answer: Its started driving through the neighborhood at 1:37
Step-by-step explanation:
2- Which equations have no solution? Select all
that apply.
x + 3 = 2x + 3
8 = 2(x+4) − 2x.
5x-2x = -7x+1
2x-3 = 5x - 3-3x
4xx+6= 2(x+1)+x
Answer: E has no solution
Step-by-step explanation: It is a contradiction
keisha is catering a luncheon. She has $30 to spend on a mixture of Cheddar cheese and Swiss cheese. How many pounds of cheese can Keisha get if she buys only Cheddar cheese? Only Swiss cheese? A mixture of both cheeses? What linear equation in STANDARD FORM can she use to model the situration?
Cheddar Cheese: $3/lb
Swiss Cheese: $5/lb
Answer:
Only cheddar 10 pounds
Only swiss 6 pounds
Use the equation to find out different combinations.
3x + 5y = 30
For example, 1 pound of cheddar and 5.4 pounds of swiss.
Step-by-step explanation:
Let x = cheddar
Let y = swiss
3x + 5y = 30
If we only wanted cheddar let y be 0
3x =30 Divide both sides by 3
x = 10
You can buy 10 pounds of cheddar.
If we only wanted swiss let x be 0
5y = 30 Divide both sides by 5
y = 6
You can buy 6 pounds of swiss.
1 pound of cheddar:
3(1) + 5y = 30 Subtract 3 from both sides
5y = 27 Divide both sides by 5
y = 5.4
A pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%, what is the total amount paid for the jeans?
The total amount that a customer will pay for the jeans is $33.696.
How to calculate the value?From the information given, pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%,
The value of the sales tax will be:
= Sales percentage × Amount
= 5.3% × $32
= $1.696
The total amount paid will be:
= Cost + Tax
= $32 + $1.696
= $33.696
The amount is $33.696.
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Write 5/3 as a mixed number.
Answer:
Step-by-step explanation:
the answer would be 1 and 2/3
3 goes into 5 one time and you have 2 left
A right triangle has coordinates (-3, 4), (3,6), and (-1,-2). What is the area of the right triangle?
help
Answer:
2728
Step-by-step explanation:
Answer:
20 sq units
Step-by-step explanation:
A quick sketch graph will show the right angle is at (-3 ,4)
The lengths of the shorter sides are both sqrt(2^2 + 6^2) = sqrt(40)
Area = 1/2 x (sqrt(40))^2 = 20
If you didn’t have a right angle you could find the lengths of all sides a, b and c
Calculate the semi perimeter s = (a+b+c) / 2
And the area = sqrt(s(s-a)(s-b)(s-c))
Try and use this method to check the first one
suppose you have 6 pairs of sock in your sock drawer and every pair has a unique color. it is still dark out in the morning when you get dressed, so you just pull socks out of the drawer at random, one at a time, until you have removed two matching socks. what is the probability that you pull out exactly 5 socks from your sock drawer in the morning before you get a matching pair of socks?
The probability there is at least one pair is therefore 1−p.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
It is little known, but socks have individual identities. There are (166) equally likely ways to choose 6 socks from the 16.Now we find the number of ways to choose 6 socks, so that there is no pair among them. There are (86) ways to choose the "types" of sock we will have. For each choice of 6 types, there are 26 ways to choose the actual socks. For at each chosen "type" of sock, we have 2 choices as to which of the two socks of that type to take.hence,The probability there is at least one pair is therefore 1−p.
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PLEASE HELP I WILL GIVE OUT BRAINLIST!!!!!
We list the operations done between two functions below:
g(x) / h(x) = (4 · x² + 2 · x - 1) / (2 · x - 3) h(x) - g(x) = - 4 · x² - 2 h(f (x)) = 6 · x² + 1 f(x) + g(x) = 7 · x² + 2 · x + 1 h(f(2)) = 25 f(h(3)) = 29 g(2) + h(2) = 2 2 · f(0) - g(2) = - 15How to make operations between two functions
In this problem we find three functions, two of them defined by quadratic equations (f(x), g(x)) and the other defined by a linear equation (h(x)). There are five operations that can be used b two functions:
Addition: (f + g) (x) = f(x) + g(x)Subtraction: (f - g) (x) = f(x) - g(x)Multiplication: (f · g) (x) = f(x) · g(x)Division: (f / g) (x) = f(x) / g(x)Composition: (f ° g) (x) = f (g (x))Now we proceed to determine the result of each operation:
Case 1:
g(x) / h(x) = (4 · x² + 2 · x - 1) / (2 · x - 3)
Case 2:
h(x) - g(x) = (2 · x - 3) - (4 · x² + 2 · x - 1)
h(x) - g(x) = - 4 · x² - 2
Case 3:
h(f (x)) = 2 · (3 · x² + 2) - 3
h(f (x)) = 6 · x² + 1
Case 4:
f(x) + g(x) = (3 · x² + 2) + (4 · x² + 2 · x - 1)
f(x) + g(x) = 7 · x² + 2 · x + 1
Case 5:
h(f(x)) = 6 · x² + 1
h(f(2)) = 6 · 2² + 1
h(f(2)) = 25
Case 6:
f(h(x)) = 3 · (2 · x - 3)² + 2
f(h(x)) = 3 · (4 · x² - 12 · x + 9) + 2
f(h(x)) = 12 · x² - 36 · x + 29
f(h(3)) = 12 · 3² - 36 · 3 + 29
f(h(3)) = 29
Case 7:
g(x) + h(x) = (4 · x² - 12 · x + 9) + (2 · x - 3)
g(x) + h(x) = 4 · x² - 10 · x + 6
g(2) + h(2) = 4 · 2² - 10 · 2 + 6
g(2) + h(2) = 2
Case 8:
2 · f(x) - g(x) = 2 · (3 · x² + 2) - (4 · x² + 2 · x - 1)
2 · f(0) - g(2) = 2 · (3 · 0² + 2) - (4 · 2² + 2 · 2 - 1)
2 · f(0) - g(2) = 4 - 19
2 · f(0) - g(2) = - 15
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How many students catch the train?
Thank you for helping.
Answer:
35
Step-by-step explanation:
18+17=35
?
Answer the question below. Type your response in the
space provided.
Does your state have a sales tax?
OBFW Publishers
The Graduate Record Examinations (GRES) are widely used to help predict the performance of applicants to graduate schools.
The scores on the GRE Chemistry test are approximately normal with mean 694 and standard deviation 112.
(a) About what percent of test takers earn a score less than 500 on the GRE Chemistry test?
(b) What proportion of test takers earn a score greater than or equal to 900 on this test?
(c) Estimate the score at the 99th percentile on the GRE Chemistry test.
a) About 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.
b) About 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.
c) The estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.
To answer these questions, we'll use the properties of the normal distribution and the given mean and standard deviation.
(a) To find the percentage of test takers who earn a score less than 500 on the GRE Chemistry test, we need to calculate the cumulative probability up to the score 500.
z-score = (X - mean) / standard deviation
where X is the score we are interested in.
z-score = (500 - 694) / 112
z-score ≈ -1.732
Now, we look up the cumulative probability for a z-score of -1.732 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.0416 or 4.16%.
So, about 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.
(b) To find the proportion of test takers who earn a score greater than or equal to 900, we need to calculate the cumulative probability from 900 to positive infinity.
z-score = (X - mean) / standard deviation
where X is the score we are interested in.
z-score = (900 - 694) / 112
z-score ≈ 1.839
Now, we look up the cumulative probability for a z-score of 1.839 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.9664 or 96.64%.
So, about 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.
(c) To estimate the score at the 99th percentile on the GRE Chemistry test, we need to find the value that separates the lowest 99% of the scores from the highest 1%.
We use the z-score formula to find the z-score corresponding to the 99th percentile:
z-score = invNorm(0.99)
z-score ≈ 2.326
Now, we use the z-score to find the score corresponding to the 99th percentile:
X = mean + (z-score * standard deviation)
X = 694 + (2.326 * 112)
X ≈ 694 + 260.512
X ≈ 954.512
So, the estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.
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there is a 40% chance of getting stuck in traffic when leaving the city. on two separate days, what is the probability that you get stuck in traffic both days? a. 0.16 b. 0.40 c. 0.20 d. 0.80
Answer:
A
Step-by-step explanation:
40% = 40/100 = 4/10 = 2/5
2/5 * 2/5 = 4/25 = 0.16
Y=4/5x-5
Slope:
Y-intercept:
Find the value of the specified trig ratio. Be sure to reduce when possible.
The value of cosC is 8/17.
What is the trigonometric ratio?
Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.
In the figure,
Adjacent=CB=16
hypotenuse=AC=34
The formula for the cos function:
cos[tex]\theta[/tex]=adjacent/hypotenuse
cosC=16/34
divide 16 and 34 by 2 to simplify further
cosC=8/17
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f(x) = 0.75(10-x)+1
Someone help please
The solution for f(3) in the function when the function f(x) = 0.75(10 - x) + 1 is 6.25
How to determine the solution for f(x) in the function?From the question, we have the following equation that can be used in our computation:
f(x) = 0.75(10-x)+1
To make the equation legible, we need to rewrite it
So, we have the following representation
f(x) = 0.75(10 - x) + 1
Also from the question, we have
f(3)
This means that the value of x is 3, and we calculate f(x) when x = 3
Substitute the known values in the above equation, so, we have the following representation
f(3) = 0.75(10 - x) + 1
So, we have the following equation
f(3) = 0.75(10 - 3) + 1
There are constants to add or subtract to both sides of the equation
Also, there are factors to multiply or divide from both sides of the equation
So, we have the following representation
f(3) = 0.75 * 7 + 1
Solving further, we have
f(3) = 5.25 + 1
Evaluate the sum
f(3) = 6.25
Hence, the solution is 6.25
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Possible question
Given f(x) = 0.75(10-x)+1, find f(3).
gentle ben is a horse at a colorado dude ranch. over the past 8 weeks, a veterinarian took random weekly glucose readings from gentle ben. the sample mean of the 8 blood tests was we may assume that x has a normal distribution, and the population values are . does the sample data indicate that gentle ben has a glucose rate higher than 85? (use
At the 0.05 level of confidence, there is enough data to say that Gentle Ben's blood glucose is higher than 85 mg/100 ml.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, also referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph. Data are symmetrically distributed and skew-free in a normal distribution. As one moves away from the center, values start to taper off and the majority of values are concentrated in this area. In a normal distribution, the mean, mode, and median are identical measures of central tendency.
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Clarence' Ice Cream Shop old 6 undae. 4 of the undae had nut on top. What i the ratio of the number of undae with nut to the total number of undae? Write your anwer a two number eparated by a colon (for example, 2:3)
Ratio of the sundae with nut to total number is 2:3.
The ratio will be written as numerator and denominator seperated by colon. The numerator will be number of sundae with nut and denominator will be total number of sundae. So, writing the numbers in mentioned description of ratio.
Ratio of the number of sundae with nut to the total number of sundae = 4 : 6
The ratio can be further simplified by dividing both numerator and denominator by 2.
Ratio of the number of sundae with nut to the total number of sundae = 2 : 3
Thus, the required ratio fo sundae is 2:3.
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what is the t-multiplier for a 95% confidence interval for a population mean, using a well-behaved sample of size 14? r lab
The appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.
Given:
The t-multiplier for a 95% confidence interval for a population mean, using a well-behaved sample of size 14.
It is the 97.5%-quantile of the t-distribution with 14 degrees of freedom.
In the figure the dashed line shows the value such that the yellow shaded area has size 0.975: the 97.5%-quantile is the value such that 97.5% of the probability mass is to the left of it and the rest to the right.
so t - multiplier = 2.15.
Therefore the appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.
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PQR is an isosceles triangle in which PQ= PR Mand N are points on PQ and PR such that angle MRQ= angle NQR. Prove that triangles QNR and RMQ are congruent.
We have proved that triangles QNR and RMQ are congruent.
What is an isosceles triangle?
An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.
∠MRQ ≅ ∠NQR . . . . given
QR ≅ RQ . . . . reflexive property
∠PQR ≅ ∠PRQ . . . . property of isosceles triangle PQR
ΔQNR ≅ Δ RMQ . . . . ASA postulate
Hence, we have proved that triangles QNR and RMQ are congruent.
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my last question for marth
The equation of linear function is y=x-1.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
The given values are
x=1, y=0
x=2, y=1
x=3, y=2
x=4, y=3
The table represents that for the value of x the value of y is x-1,
Since for any two points from the table, let (1,0) and (2,1)
The slope = 2-1/1-0 = 1
And the interception of y is 0 when x=1
Therefore, the equation of the function can be written as,
y=x-1
Y=x-1 is the required equation.
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Find the area of a rectangle whose side lengths are 8x² feet and 8x³ feet.
A.The area of the rectangle is 16x² feet squared.
B. The area of the rectangle is 64x5 feet squared.
C.The area of the rectangle is 16x² + 16x³ feet squared.
D.The area of the rectangle is 16x5 feet squared.
Answer:
ccccccccc
Step-by-step explanation:
Select the correct answer. The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system? x + 3y = 42 2x − y = 14 A. Multiply the second equation by -3. The solution is x = 12, y = 9. B. Multiply the second equation by -2. The solution is x = 12, y = 10. C. Multiply the second equation by 2. The solution is x = 15, y = 9. D. Multiply the second equation by 3. The solution is x = 12, y = 10.
Answer:
x is 13 and y is 10
Step-by-step explanation:
Multiply the second equation by 3
Answer:
D. Multiply the second equation by 3. The solution is x = 12, y = 10.
Step-by-step explanation:
You want the multiplier for the elimination of the y-variable in the system of equations x +3y = 42; 2x -y = 14.
MultiplierThe coefficients of y are +3 and -1, so multiplying the second equation by 3 will make it the opposite of the former. Then their sum is zero, which is what you want when eliminating the y-variable.
ApplicationMultiplying the second equation by 3 and adding the first gives ...
3(2x -y) +(x +3y) = 3(14) +(42)
7x = 84 . . . . . . . . . simplify. Note the y-variable has been eliminated.
x = 12 . . . . . . . . . divide by 7
2(12) -y = 14 . . . . substitute for x in the second equation
24 -14 = y = 10 . . . . add y-14
The solution is (x, y) = (12, 10).
What is the domain of F(x) = 1 ?
O A. x = 0
O B. F(x) *0
C. all real numbers
D. all real numbers except 0
Answer:
C. all real numbers
Step-by-step explanation:
You want the domain of the function F(x) = 1.
DomainThe domain of a function is the set of values of the independent variable for which the function is defined. The function F(x) is defined for all possible values of x, so its domain is all real numbers.
If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X.
A. 12X
B. X-14
C. X-13
D. X-12
Answer:
Step-by-step explanation:
Find the area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees.
To find the area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees.
Area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.
A triangle's feature known as SAS, or "Side, Angle, Side," has two sides and an angle that are both known.
The space occupied between the sides of the SAS triangle in a plane can thus be calculated with the use of the SAS triangle area formula.
The formula to find area of SAS triangle is:
Area = ½ ab Sin C = ½ × 29 × 36 × sin 62
Thus, Area = 522 × sin 62 = 522 × 0.88 = 459.36
Hence the answer is, Area of SAS triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.
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x-4/5 - x+1/6 = 1/3 ill be very happy if answered
