State the domain, range, intercepts, and asymptotes of y=-2^(-x+2)+1
The domain, range and asymptotes of the exponential function y = -2^(-x+2)+1 are given as follows:
Domain: All real values.Range: y < 1.Horizontal asymptote: y = 1How to obtain the domain, range and asymptotes?The function in this problem is defined as follows:
y = -2^(-x+2)+1.
It is an exponential function, hence it has no restrictions, meaning that:
The domain is composed by all real values.The function has no vertical asymptotes.The range of the function is the set that is composed by all the output values of the function.
Due to the multiplication by the negative number, the function is reflected over the x-axis, and the addition by 1 means that the function is shifted up 1 unit, thus:
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Jerald is cycling for a race. He rides 3/4 of a mile in 1/20 of an hour. If he keeps going at this rate, how far would he ride in 2 hours?
If Jerald keeps going at this rate, the miles that he will ride in 2 hours is 30 miles.
How far would Jared ride in 2 hours?Rate demonstrates how many times one number can fit into another number. It should be noted that they contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, Jerald is cycling for a race and he rides 3/4 of a mile in 1/20 of an hour. The miles in an hour will be:
= 3/4 ÷ 1/20
= 3/4 × 20
= 15 miles..
The miles in 2 hours will be:
= 2 × 15
= 30 miles.
The miles is 30 miles.
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The lens of the human eye inverts images onto the retina at the back of the eye. The triangles in the diagram, △ABC and △A′B′C′ , are similar. The length of segment BC is approximately 100 cm , and its corresponding side, segment B′C′ , has an approximate length of 2.5 cm . If segment AB has been measured as 30 cm , how tall is the inverted image of the object, represented by segment A′B′ , to the nearest hundredth of a centimeter?
The height of the inverted image representing segment [is 0.75 cm.
How to calculate the height?More than one triangle are said to be similar when the corresponding sides and angles have relatable properties. The length of segment A′B′ is 0.75 cm.
it can be observed that; △ABC ≅ △A′B′C′
Given that: BC = 100cm, B′C′ = 2.5 cm; AB = 30 cm,
A′B′ = ?
Comparing the corresponding sides of the similar triangles, we have:[tex]\frac{AB}{A^{I}B^{I} }[/tex] = [tex]\frac{BC}{B^{I}C^{I} }[/tex][tex]\frac{30}{A^{I}B^{I} }[/tex] = [tex]\frac{100}{2.5}[/tex][tex]A^{I}B^{I}[/tex] = [tex]\frac{30*2.5}{100}[/tex] = 0.75[tex]
A^{I}B^{I}[/tex] = 0.75
Thus the height of the inverted image representing segment [tex]A^{I}B^{I}[/tex] is 0.75 cm.
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you are offered a free play at the following game: ten balls are numbered 1 through 10. three are selected at random (each combination equally likely). before balls are drawn, players try to guess which three numbers are drawn by filling out a ticket. neither the order that the player selects the numbers nor the order in which the balls are drawn matters. how many outcomes are in the sample space for this experiment?
The sample space for this experiment contains a total of 120 possible outcomes. This is because there are 10 possible balls to be drawn, and each of them can be chosen in 3 different ways. Thus, 10 x 10 x 10 = 1,000 possible combinations. However, since the order of the selected numbers does not matter, the number of possible outcomes is reduced to 1,000 / 6 = 120.
What is probability?Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A value between 0 and 1 represents the likelihood of an event, with 0 basically denoting impossibility and 1 generally indicating certainty.
How can I calculate probability?Subtract the total number of events from the total number of outcomes. Divide the total number of ways the event could occur by the total number of possible outcomes once the probability event has been identified and its corresponding consequences have been determined.
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if i have 5 apples and you have 6 oranges and i eat 3 and you eat 3 how many do we have left? NO CHEATING OR ELSE I WILL BEAT THE F- :) anways awnser.
A. i have 1 and you have 2?
B. i have 99 and you have 88?
C. i have 2 and you have 3?
D. i have 3 and you have 2?
Answer:
Option c) I have 2 and you have 3
5 - 3 = 2 6 - 3 = 3find the average rate of change for the following equation over the interval -4≤x≤1
y=x^2 + 4x -1
To find the average rate of change of a function over an interval, we need to calculate the slope of the secant line connecting the points on the function at the two endpoints of the interval.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. In the case of a secant line, we can calculate the slope by using the formula:
m = (y2 - y1) / (x2 - x1)
For the function y = x^2 + 4x - 1, we can plug in the values of x and y at the two endpoints of the interval, (-4 and 1), to find the slope of the secant line:
m = [(1)^2 + 4(1) - 1] - [(-4)^2 + 4(-4) - 1] / (1 - (-4))
Simplifying this expression, we get:
m = (1 + 4 - 1) - (16 + 16 - 1) / (-3)
This simplifies to:
m = -20 / -3
Therefore, the average rate of change of the function y = x^2 + 4x - 1 over the interval -4 ≤ x ≤ 1 is 6.5.
a store sells 8 colors of balloons with at least 31 of each color. how many different combinations of 31 balloons can be chosen?
12620256 different combinations of 31 balloons can be chosen
What are combinations?
Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.
From the question, we understand that; a combination of 31 is to be selected. Because the order is not important, we make use of combination.
Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.
So:
n= 31 +8-1 = 38
r=31
Selection = [tex]^{38}C_{31}[/tex]
Use the formula:
[tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex]
= > [tex]^{38}C_{31}=\frac{38!}{(38-31)! 31!}[/tex]
[tex]^{38}C_{31}=\frac{38!}{7! 31!}[/tex]
= [tex]\frac{38*37*36*35*34*33*32*31!}{7*6*5*4*3*2*1* 31!}[/tex]
= 12620256
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What are 4 pairs of congruent sides?
Rhombus is 4 pairs of congruent sides.
Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign ≅. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.
A rhombus is a parallelogram with four congruent sides.
All the characteristics of a parallelogram are present in a rhombus, plus the following: The diagonals intersect at right angles.
Square and rhombus are the only two quadrilateral shapes that consistently have four congruent sides. Note that congruent sides refer to sides that are of the same length. A quadrilateral having four equal sides and four equal angles is called a square (90 degrees). It combines a rhombus and a right-angled rectangle ( equal side ).
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Scherita invests $2300 in one account and $2400 in an account paying 3 % higher interest. At the end of one year she had earned $166 in interest. At what rates did she invest?
PLEASE PLEASE HELP!!!
The Interest Rates are 2% and 5% respectively
What is Simple Interest?
Simple interest is a quick and straightforward way to calculate the interest on a loan. Simple interest is calculated by multiplying the daily interest rate by the principle multiplied by the number of days between payments.
Solution:
Let, the lesser interest rate be x
Simple Interest = Principal*Time*Rate/100
Total Interest = $166
166 = 2300*x*1/100 + 2400*(x + 3)*1/100
166 = 2300x + 2400x + 7200 / 100
16600 = 4700x + 7200
9400 = 4700x
x = 2%
and the Higher Interest Rate = 5%
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Which statement about the value of a credit report to lenders and borrowers is NOT true?
Answer:
A credit report is not useful for lenders and borrowers because it does not provide detailed information about a person's financial history.
What image would be created by a scale factor of 1?
The image created by the scale factor of 1 will be same as the pre-image
The scale factor of the image = 1
The ratio between the new size of the figure and the original figure = 1 : 1
The scale factor is the ratio between the dimensions of the new figure and the dimensions of the original figure.
The image in the dilation is the new/final figure and the pre-image is the original figure before dilation
Here, the size of the image and pre-image will be same because the ratio is 1 : 1, image and pre-image has same dimensions
Therefore, the image and the pre-image will be same
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A person working on the roof of a two-story house drops a paintbrush. It is 35 feet to the
ground. When the brush falls, the worker on the roof shouts "Look Out!". A 6 feet tall
person is standing directly below where the brush falls.
If the reaction time needed for the person on the ground to move away is 1.85 seconds,
will they be hit by the paintbrush before they can move out of the way?
The kinematic equation of the motion of the paintbrush dropped 35 feet height from the ground and the 1.85 seconds reaction time of the 6 feet person standing directly below, indicates that they will be hit by the paintbrush before they can move out of the way.
What is the kinematic equation of motion?The kinematic equation of motion describe the motion of a body that moves under constant acceleration, without consideration of the forces causing the body to move.
The height from which the paintbrush is dropped from the roof to the ground = 35 feet
Height of the person standing directly below where the brush falls = 6 feet
The reaction time of the person = 1.85 seconds
The kinematic equation of motion of free fall of an object is presented as follows;
s = u·t + 0.5·g·t²
Where; s = The height through which the paintbrush falls
u = The initial velocity of the paintbrush = 0
g = The acceleration due to gravity ≈ 32.1741 ft/s²
The height the paintbrush falls before meeting the 6 feet tall person, s = 35 feet - 6 feet = 29 feet
Therefore, we get;
29 = 0 × t + 0.5 × 32.1741 × t²
t² = 29 ÷ (0.5 × 32.1741) ≈ 1.803
The time it takes the paintbrush to fall 29 feet, t, is therefore;
t = √(29 ÷ (0.5 × 32.1741)) ≈ 1.343
It takes the paintbrush to reach the height of the person standing directly below in just about 1.3 seconds after it is dropped, before the person can react to move away in 1.85 seconds, therefore, they will be hit by the paintbrush before they can move out of the way.
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What is the equation of a line, in slope intercept form, that is perpendicular to y=-0.25x+1 and passes through (2,5)?
Answer:
Step-by-step explanation:
Gradient of a line that is perpendicular to another line is always the negative reciprocal.
So:
the gradient perpendicular to -0.25x is 4
to find the y-intercept (c), you need to substitute x and y into the equation:
5 = 2(4) + c
5 = 8 + c
c = -3
hence:
y = 4x -3
What is a function formula?
A function formula y = f(x) defines the relation between input values and output values.
We know that the function defines relation between the input values and the output values. A relation is a function if and only of for each input there is exactly one output.
A mathematical equation which involves x and y, i.e., a function, can be written in the form y = an expression involving x
y = f (x).
The function formulas are used for calculating the x-intercept, y-intercept and slope in any function.
We can find the x-intercept of a function by substituting the value of f(x) as 0. Similarly, the y-intercept of a function by substituting the value of x is 0. We can calculate the slope of a linear function by rearranging the function to the form, f(x) = mx + c; where m is the slope and c is the y-intercept.
Therefore, the function formulas are used to determine the x-intercept, y-intercept and slope in any function.
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Use the law of sines to solve for the variable
By means of the law of cosine, the missing side of the triangle has a length of approximately 6.502 units.
How to use the law of cosine in a triangle
Herein we find the case of a triangle with two known side lengths and a known measure of an angle between the two given sides. The measure of the unknown side is determined by the law of cosine, whose definition is shown below:
x² = a² + b² - 2 · a · b · cos θ
If we know that a = 15, b = 12 and θ = 25°, then the equation for the triangle is:
x² = 12² + 15² - 2 · 12 · 15 · cos 25°
Now we proceed to simplify and find the resulting value of x by algebra properties:
x² = 369 - 360 · cos 25°
x² = 369 - 326.271
x² = 42.279
x ≈ 6.502
The length of missing side of the triangle is approximately equal to 6.502 units.
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a football team socred 80 percent of a total 500 points in the first 11 games of the season how many points did the team scored
Answer: 400 points
Step-by-step explanation:
500 x 80 = 40,000
40,000/100 = 400 points
suppose 400 different researchers all randomly select samples of 800 individuals from a population. each researcher uses his or her sample to compute a 95% confidence interval for the proportion that has blue eyes in the population. about how many of the confidence intervals will cover the population proportion?
Assuming that the population proportion of blue eyes is accurately reflected in each sample, about 380 of the 400 confidence intervals should cover the population proportion.
The confidence interval for the proportion of blue eyes in the population is calculated as follows:
Proportion of blue eyes in the population = sample mean +/- (1.96* Standard Error)
Where Standard Error = sqrt[(proportion of blue eyes in the population)*(1-proportion of blue eyes in the population)/sample size]
At a 95% confidence level, the confidence interval should cover the population proportion 95% of the time. Therefore, 95% of the 400 confidence intervals should cover the population proportion, which is approximately 380 intervals.
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A certain brand of electric bulbs has an average life of 330 hours with a standard deviation of 35. A random sample of 80 bulbs is tested. What is the probability that the sample mean will be less than 318?.
The probability that the sample mean will be less than 318 is 0.0011.
Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m or μ. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ.
We know that,
P ( x < n ) = P ( z < x - μ / ( σ / √n ) ) → 1
where, z = x - μ / ( σ / √n )
As per the given question,
The average life of the electric bulbs i.e. mean ( μ ) = 330 hoursThe standard deviation of the bulbs ( σ ) = 35A random of 80 bulbs are tested i.e. n = 80The probability of the sample mean is less than 318 i.e.P ( x < 318 ) = ?
Substitute the values in 1,
P ( x < 318 ) = P ( z < x - μ / ( σ / √n ) )
= P ( z < 318 - 330 / ( 35 / √80 )
= P ( z < -12 / ( 35 / 8.94 )
= P ( z < -12 / 3.91 )
= P ( z < -3.069 )
= P ( z < -3.07 )
P ( x < 318 ) = 0.0011
Therefore, 0.0011 is the probability that the sample mean will be less than 318. Hence Option a is correct.
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The complete question is
A certain brand of electric bulbs has an average life of 330 hours with a standard deviation of 35. A random sample of 80 bulbs is tested. What is the probability that the sample mean will be less than 318?
a.) 0.0011
b.) 0.9989
c.) 0.0006
d.) 0.0127
A cereal box says that now it contains 20% more.
Originally, it came with 185 g of cereal.
How much cereal does the box come with now?
Answer:
222 grams.
Step-by-step explanation:
If it is 20% more, then it is 1.2 times more. 1.2*185=222, so the cereal box comes with 222 g of cereal.
Determine the value of X.
Please help!!
Number 7!
Answer: x=45 degrees
Step-by-step explanation:
125+x+10=180
all triangles add up to 180 degrees
135+x=180
x=45
which one is functions and non function??
Type the letters in order
please help me!!!!!
Answer:
2, 3, and 7 are not function
The rest are
Step-by-step explanation:
In a function every X has one and only one y
2 is not a function because X=5 has 2 different y's
3 is not a function because X=2 has 2 different Y's
7 is not a function because X=b has 2 different Y's
What are the 3 types of infinitives in Spanish?
Three types of infinitives in Spanish are the word that ends with the letters -er , -ar, and -ir.
Explanation:
Infinitive : In general sense infinitive represent the action or the purpose.
They do not represent the person or the time.Infinitive in Spanish are generally non -conjugated verbs and they are ending with -er , -ar , -ir.
Basically infinitive in Spanish classified into three groups.
-er : Aprender meaning camping.
-ar : Acampar meaning Camping and so on.
Spanish infinitives are equivalent to English verbs ending with ing.Therefore, the three types of Spanish infinitives are word ends with -er , -ar, and -ir.
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Harry's mother makes cakes for a local restaurant. She buys flour and sugar in large amounts. She has 157.86 pounds of flour and 82.69 pounds of sugar. If she uses 15 pounds of flour and 8 pounds of sugar each day, for about how many days will the flour last?
The flour will last for about 11 days.
What is equation ?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.
Suppose, the flour will last for x days.
She uses 15 pounds of flour each day.
So, the total amount of flour used in x days 15x pounds.
Given that, she has 157.86 pound of flour.
So, the equation will be
15 x = 157.86
x = 157.86 / 15
= 10.524
≈ 11
Thus, the flour will last for about 11 days.
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a rectangle has a fixed area of 100 units^2 and its length l is increasing at 2 unit/sec. find the length l at the instant the width is decreasing at .5 units/sec. ap calc related rates
The width at the instant the width is decreasing at .5 units/sec is increasing 5 units per/sec.
How to find change in length or width?
The rate at which a function changes in relation to a variable Calculus and differential equations issues must be solved using derivatives.Given:
Area of triangle = 100 units²
Area of triangle = Length * Width
Length * Width = 100
dl / st = 2 unit/sec
a) Find length
when dw/dt = -0.5 unit/sec
l * w = -0.5
l dw/dt + w dl/dt = 0
100/w (-0.5) + w(2) = 0
(- 50+ 2w²) / w = 0
2w² = 50
w² = 25
w = 5
Hence, the width at the instant the width is decreasing at .5 units/sec is increasing 5 units per sec.
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What are the coordinates of the point on the directed line segment from (−3,4)(−3,4) to (3,−8)(3,−8) that partitions the segment into a ratio of 1 to 3?
The coordinates of the point on the directed line segment from (−3,4) to (3,8) partitions the segment into a ratio of 1 to 3 is given as follows:
(-1.5, 1).
How to obtain the coordinates of the point?The coordinates of the point are applied using proportions, as the fact that the point partitions the segment into a ratio of 1 to 3 means that the following equation is built:
Point - Initial Coordinate = 1/4(Final Coordinate - Initial Coordinate).
This equation is used to find both the x-coordinate and the y-coordinate of the point.
The x-coordinate of the point is obtained as follows:
x + 3 = 1/4(3 + 3)
x + 3 = 1.5
x = -1.5.
The y-coordinate of the point is obtained as follows:
y - 4 = 1/4(-8 - 4)
y - 4 = -3
y = 1.
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a teacher wants to see if a new unit on taking square roots is helping students learn. she has five randomly selected students take a pre-test and a post test on the material. the scores are out of 20. has there been improvement? (pre-post)
Using the t-distribution, it is found that the p-value is of 0.
At the null hypothesis, it is tested if there has been no improvement, that is, the scores on test 1 are at least equal to the scores on test 2, which means that the mean of the subtraction of the means is at least 0.[tex]H_{0\\}[/tex] : μ₁ - μ₂ ≥ 0
At the alternative hypothesis, it is tested if there has been improvement, that is, the grades on the second test are higher, hence the mean of the subtraction of the variables are negative.[tex]H_{1}[/tex] : μ₁ - μ₂ < 0
Using a calculator, the p-value, for a left-tailed test, as we are testing if the mean is less than a value, with 5 + 5 - 2 = 8 df and t = -14.9, is of 0.To know more about hypothesis check the below link:
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How do I write this in standard form? (give clear steps please!)
m=-4
(9,-10)
The linear function that has a slope of -4 and goes to point (9,-10) will be y = -4x - 50.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Suppose that the linear function is y = mx + c
As per the given, slope m = -4
Put (9,-10)
-10 = -4 x -10 + c
c = -50
Thus, y = -4x - 50
Hence "y = -4x - 50 is the equation for the linear function with a -4 slope that leads to point (9,-10) in the graph.".
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raise p to the 7th power, then add q to the result
DONT SIMPLIFY
The expression equivalent to the statement raise p to the 7th power, then add q to the result is p⁷ + q
How to determine the expression of the mathematical statement?From the question, we have the following mathematical statement that can be used in our computation:
raise p to the 7th power, then add q to the result
When p is raised to the power of 7, we have the following representation
p⁷, then add q to the result
When q is added to p⁷ above, we have
p⁷ + q
Hence, the expression is p⁷ + q
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Based on the model what would be Jamall salary and dollars for a month where he made no sales y=3400 + 0.05x
Jamall's salary when he made no sales is $3400
How to determine the salary?From the question, we have the following parameters that can be used in our computation:
y = 3400 + 0.05x
When he made no sales, the value of x is 0
So, we have the following representation
y = 3400 + 0.05 x 0
Evaluate
y = 3400
Hence, the salary is $3400
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how much do you pay for $55 textbook with 7.5% tax?
Answer:
4.125 rounded to 4.13 = the price of tax.
4.13 + 55 = 59.13