An exponential function can be equal to 1, but it would have to be a special case.
To determine this:
An exponential function has the form f(x) = ab^x, where a and b are constants. For the function to be equal to 1, the output value of the function must be 1 for all values of x. Therefore, we must have:
[tex]ab^x = 1[/tex]
In order for this equation to be true for all values of x, a and b must be chosen such that:
ab = 1
This means that a and b must be reciprocals of each other. For example, if a = 2, then b = 1/2. In this case, the function [tex]f(x) = 2(1/2)^x[/tex] would be equal to 1 for all values of x.
Another example would be if a = 1 and b = 1. In this case, the function [tex]f(x) = 1(1)^x[/tex] would be equal to 1 for all values of x.
It's important to note that while an exponential function can be equal to 1, it would only be in cases where a and b are reciprocals of each other and not with any other values.
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Raj measures the height of 70 plants calculate the estimate of the mean height of the plants
The mean height of plants is 44.07cm.
Given that a raj measures the height of 70 plants which is shown in the table in the image attached below.
The mean is defined as the mean value equal to the ratio of the total number of a given set of values to the total number of values contained in that set.
Firstly, we will find the midpoint of the height by using the formula
(upper limit +lower limit)/2
When h is 10<h<20 then the midpoint is
x₁=(10+20)/2
x₁=15
When h is 20<h<0 then the midpoint is
x₂=(20+40)/2
x₂=30
When h is 40<h<50 then the midpoint is
x₃(40+50)/2
x₃=45
When h is 50<h<60 then the midpoint is
x₄=(50+60)/2
x₄=55
When h is 60<h<90 then the midpoint is
x₅=(60+90)/2
x₅=75
Now, we will find the mean height by using the formula
x=(f₁x₁+f₂x₂+f₃x₃+f₄x₄+f₅x₅)/(Σfi)
Here, f₁=7,f₂=15,f₃=27,f₄=13,f₅=8
and Σfi=7+15+27+12+8=70
Substitute these values in the formula, we get
x=(7×15+15×30+27×45+12×55+8×75)/70
x=(105+450+1215+715+600)/70
x=(3085)/70
x=44.07
Hence, the estimate of the mean height of the plants when raj measures the height of 70 plants is 44.07cm.
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The functions f(x) and g(x) are shown on the graph.
f(x) = log(x)
g(x)
6
Using fix), what is the equation that represents gix)?
A) g(x) = log5(x) - 3
B) g(x) = log5(x) + 3
C) g(x) = log5(x-3)
D) g(x) = log5(x+3)
Using translation concepts, the equation of g(x) is:
D) [tex]\log_5{x + 3}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Researching this problem on the internet, g(x) is a shift left of 3 units of [tex]f(x) = \log_5{x}[/tex], hence:
[tex]g(x) = f(x + 3) = \log_5{x + 3}[/tex], which means that option D is correct.
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Calculating Volume of a Composite Figure 2 rectangular pyramids are connected at their bases. The total height of the 2 figures if 10 units. The base edge lengths are 9 units and 1.5 units. The height of each pyramid is 5 units. Which statements about the composite figure are true? Check all that apply. The composite figure consists of two rectangular pyramids. The composite figure can be broken down into rectangular prisms. The volume of the composite figure is 1.5(9)(5) + 1.5(9)(5). The total volume is 45 units3. The total volume is 90 units3.
The answer which are true about the two rectangular pyramids are;
The composite figure consists of two rectangular pyramids.The composite figure can be broken down into rectangular prisms.The volume of the composite figure is 1.5(9)(5) + 1.5(9)(5).Which statements about the composite figure are true?It follows from the task content that the dimensions of the rectangular prisms are the same and are as given.
On this note, it follows that the volume of the composite figure is; 1.5(9)(5) + 1.5(9)(5) = 135units³.
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It takes you two and a half hours to drive 175 miles. how fast were you driving? (mph)
If one travels 175 miles in 2hour 30 mins then his speed is 70 mph .
Calculation of the speedDistance travels= 175 miles
time is taken to cover 175 miles = 2.5 hours
We have to find out the speed in mph.
We know that,
Distance = speed x time
⇒speed = distance / time
Putting the value of distance and time, we get:
speed = 175 / 2.5 = 70 mph
Hence the final answer is 70 mph.
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Explain or show how to determine if the following coordinates are a solution to the following system of linear inequalities. y<4x+8 y>x-6
The inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.
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I really need help :(((
Answer:
B solving by factoringA the quadratic formulaStep-by-step explanation:
1.The "zero product principle" or "zero product rule" tells you a product will be zero if and only if one or more of the factors is zero. This fact is used to solve quadratic equations by factoring.
Factoring the equation y = ax² +bx +c to the form y = a(x -r)(x -s) allows you to immediately identify the solutions of y=0 as x=r and x=s. These are the values of x that make the factors zero, hence making the product zero.
Finding the values of x that satisfy ax² +bx +c = 0 by rearranging it to the form a(x -r)(x -s) = 0 is called "solving by factoring."
2.When the process of "completing the square" is applied to the standard-form quadratic y = ax² +bx +c, the result is a formula for the two solutions to y = 0:
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
This quadratic formula tells you the solutions based on the coefficients of the original equation, so does not require rearranging the equation in any way.
Triangle X Y Z is shown. Angle X Z Y is 90 degrees and angle X Y Z is 41 degrees. The length of Z X is 22.
Which equation could be used to solve for the length of XY?
XY = (22)sin(41°)
XY = (22)cos(41°)
XY = StartFraction 22 Over cosine (41 degrees) EndFraction
XY = StartFraction 22 Over sine (41 degrees) EndFraction
The equation that could be used to solve for the length of XY is XY = 22/sin(41)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Sine rule is used to show the relationship between the sides and angles of a trinagles.
Using sine rule on triangle XYZ:
XY / sin(Z) = XZ / sin(Y)
XY / sin(90) = 22/sin(41)
XY = 22/sin(41)
The equation that could be used to solve for the length of XY is XY = 22/sin(41)
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Answer:
D
Step-by-step explanation:
How many different 4 digit numbers can be formed using only digits 1,2,3 and 4 given that they contain each of these digits as many times as you want?
The number of different 4 digit numbers that can be formed using only digits 1,2,3 and 4 if they are repeated is; 256 possible numbers
How to find the probability combination?Since the numbers can be used as many times as we want, then it means they can be repeated.
Thus, if we are looking at the number of 4 digit numbers we can create using the numbers 1, 2, 3, and 4, we can calculate that the following way:
For each digit (thousands, hundreds, tens, ones), we have 4 possible choices of numbers. And so we can create;
4 × 4 × 4 × 4 = 256 numbers
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Simplify:6 to the power of 5/6to the power of 2.
A.1/6 to the power of 3
B.6 ttpo 7
C.6ttpo 2
D.6ttpo 3
The value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3
How to simplify the expression?The expression is given as:
6 to the power of 5/6to the power of 2.
Rewrite properly as:
6^5/6^2
Apply the law of indices
6^(5-2)
Evaluate the difference
6^3
Hence, the value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3
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What is the slope of the line through (-1,8)(−1,8)left parenthesis, minus, 1, comma, 8, right parenthesis and (3,-4)(3,−4)left parenthesis, 3, comma, minus, 4, right parenthesis? Choose 1 answer: Choose 1 answer: (Choice A) A \dfrac13 3 1 start fraction, 1, divided by, 3, end fraction (Choice B) B 333 (Choice C) C -\dfrac13− 3 1 minus, start fraction, 1, divided by, 3, end fraction (Choice D) D -3−3
The slope of the line through the points is -3
How to determine the slope?The points are given as:
(-1, 8) and (3, -4)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
So, we have:
m = (-4 - 8)/(3 + 1)
Evaluate the expression
m = -3
Hence, the slope of the line through the points is -3
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The slope of the line that passes through (-1, 8) and (3, -4) is: -3.
How to Find the Slope of a Line?Slope of a line (m) = change in y / change in x.
Given the points, (-1, 8) and (3, -4):
Slope (m) = (-4 - 8)/(3 - (-1))
Slope (m) = (-12)/(4)
Slope (m) = -3
Thus, the slope that passes through the given points is: -3.
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Note: Figure is not drawn to scale.
The object above is symmetrical through Z. If Y = 14 inches, Z = 14 inches, and H = 10 inches, what is the area of the object?
The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The area of kite = (product of diagonals)/2
Area of kite = (10 * 14) / 2 = 70 in²
The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².
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In a sample of 16 employees randomly selected at a company, the average age is 25 years and the standard deviation is 2 years. We want to test if the average age of all employees is greater than 24. If ages are normally distributed in the population, using a significance level of 0.05, we can claim that the population mean is: Group of answer choices
If ages are normally distributed then using a significance level of 0.05 , we can claim that the population mean is greater than 24.
Given sample mean of 25 years , sample size of 16 ,standard deviation of 2 years.
We have to find whether the population average is greater than 24.
We have to use t test because n is less than 30. It is right tailed.
We have to first form Hypothesis.
[tex]H_{0}[/tex]:μ>24,
[tex]H_{1}[/tex]:μ<24.
t=X-μ/S/[tex]\sqrt{n}[/tex]
t critical at 5% significance level and degree of freedom=15 (16-1)=1.7531
t=24-25/2/[tex]\sqrt{16}[/tex]
=-1/0.5
=-2
Because 1.7531 is greater than -2 so we will accept the null hypothesis.
Hence we can say that the average of population is greater than 24.
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At birth, one puppy weighs 15/16 pounds. A second puppy weighs 1 and 1/8 pounds. How much more did the second puppy weigh?
Answer:
3/16 pounds more.
Step-by-step explanation:
It is 1 1/8 - 15/16
= 9/8 - 15/16
= 18/16 - 15/16
= 3/16.
what is 12(w-3) if w= 10
Hey there!
12(w - 3)
= 12(10 - 3)
= 12(10) + 12(-3)
= 120 - 36
= 84
OR
12(w - 3)
= 12(10 - 3)
= 12(7)
= 84
Therefore, your answer should be:
84
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
In London, the charge of a tour bus consists of a fixed rental price plus a per kilometre rate, that depends on the distance of the trip.
The per kilometre rate is $12/km. You decide to go on a 5 km trip, and it costs you $70.
a) What is the fixed rental cost? Show your work.
b) Determine the equation relating the cost, C, in dollars, and the distance, d, in km.
d) What is the cost of an 18 km trip?
e) What is the distance travelled if the total cost is $250?
PLEASEEEEEEEE
Using a linear function, we have that:
a) The fixed cost is of $10.
b) The equation is: C = 10 + 12d.
c) The cost of an 18 km trip is $226.
d) The distance traveled is of 20 km.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the slope is of m = 12. When d = 5, C(d) = 70, hence we find the fixed cost as follows:
C(d) = 12d + b
70 = 60 + b
b = 10.
Hence the equation is:
C(d) = 12d + 10.
For a trip of 18 km, d = 18, hence the cost is:
C(12) = 12 x 18 + 10 = $226.
When the cost is of $250, the distance is found as follows:
250 = 12d + 10
12d = 240
d = 240/12
d = 20 km.
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How many quarters are there in 7 1/2?
Answer: 30.
Step-by-step explanation:
[tex]7\frac{1}{2} =\frac{7*2+1}{2} \\\frac{14+1}{2}=\frac{15}{2}\\ \frac{15*2}{2*2}=\frac{30}{4} \\ \frac{30}{4}=30*\frac{1}{4} .[/tex]
There are total 30 quarters in [tex]7\frac{1}{2}[/tex].
What is one quarter?A quarter is one out of four equal parts. One quarter is the same as the fraction ¼.
What is mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction.
How to convert a mixed fraction into an improper fraction?To change a mixed fraction to an improper fraction, we multiply the whole number by the denominator and then add this product with the numerator.
According to the given question.
We have a mixed fraction [tex]7\frac{1}{2}[/tex].
So, the improper fraction of the given mixed fraction is given by
[tex]7 \frac{1}{2} = \frac{15}{2}[/tex]
To find the number of quarters in the given mixed fraction, we will divide [tex]7\frac{1}{2}[/tex] by [tex]\frac{1}{4}[/tex].
Therefore,
[tex]\frac{7\frac{1}{2} }{\frac{1}{4} }[/tex]
= [tex]\frac{\frac{15}{2} }{\frac{1}{4} }[/tex]
[tex]= \frac{15\times 4}{2}[/tex]
[tex]= 15\times 2[/tex]
[tex]= 30[/tex]
Hence, there are total 30 quarters in [tex]7\frac{1}{2}[/tex].
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The sales department has determined that the average purchase value for their catalog business is normally distributed with a mean of $30.44 and a standard deviation of $14.99. What is the purchase value at the 20th percentile
The purchase value at the 20th percentile is $17.85 for the distribution with a mean of $30.44 and a standard deviation of $14.99.
How to calculate Z-score to raw score X?The formula for the X is
X = μ + Z × σ
where,
Z- score, μ is the mean, and σ is the standard deviation
Calculation:It is given that,
μ = $30.44
σ = $14.99
x% is given as the 20th percentile
So, α = 0.20
then, the Z score from the normal distribution table is -0.84
On substituting,
X = μ + Z × σ
= 30.44 + (-0.84 × 14.99)
= 30.44 - 12.59
= 17.85
Therefore, the purchase value at the 20th percentile is $17.88.
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Given: AD is parallel to BC
Prove: DC = 6 units
Which step is missing?
To prove DC = 6 units the missing step is ΔDAC ≅ ΔBCA by ASA.
Option C is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
AD is parallel to BC
From the figure and the given information,
We have,
∠DAC ≅ ∠BCA
AC ≅ AC∠DCA ≅∠BACThis means,
Angle-Side-Angle (ASA) Congruence
ΔDAC ≅ ΔBCA
Thus,
To prove DC = 6 units the missing step is ΔDAC ≅ ΔBCA by ASA.
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Quick algebra 1 assignment for 50 points!
Experts and Geniuses please help asap, TYSM!
Oh by the way this is just a section of the real assignment, the assignment calls for you to make an app that people can play to learn inverse variation & direct variation and stuff.
Hope that helps solve this! :)
By inverse variation, the electric force between the two particles is 5 newtons when they are 20 centimeters apart.
How to use inverse variation to represent a situation
Herein we should present a statement that represents a real life situation and solve that statement. Here is an example:
In accordance with the Coulomb's law, electric force is inversely proportional to the square of the distance between the two electrically charged particles. If you know that electric force is 20 N when the two particles are 10 cm apart, what is the electric force if the distance is doubled.
Based on the statement, we have the following relationship:
F ∝ 1/r²
Where:
F - Electric charge, in newtonsr - Distance between the two electrically charged particles, in centimeters.From such relation, we can determine the resulting force by the following equation:
F/20 = 10²/20²
F = 20 × 10²/20²
F = 5 N
By inverse variation, the electric force between the two particles is 5 newtons when they are 20 centimeters apart.
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Direct materials $ 5.50 direct labor $ 3.00 variable manufacturing overhead $ 1.50 fixed manufacturing overhead $ 4.00 fixed selling expense $ 2.50 fixed administrative expense $ 2.00 sales commissions $ 1.00 variable administrative expense $ 0.50 13. if the selling price is $21.50 per unit, what is the contribution margin per unit? (do not round intermediate calculations. round your answer to 2 decimal places.)
The contribution margin per unit is $ 1.50
The contribution margin is the percentage of a product's sales revenue that isn't consumed by variable costs and goes toward paying the firm's fixed expenses.
One of the main components of break-even analysis is the idea of contribution margin.
Labor-intensive businesses with few fixed expenses tend to have low contribution margins, whereas capital-intensive, industrial businesses have more fixed costs and, thus, higher contribution margins.
According to the question,
Total expenses per unit = $(5.50+3.00+1.50+4.00+2.50+2.00+1.00+0.50)
= $ 20
Selling Price per unit = $ 21.50
Thus, contribution margin per unit = $ (21.50 - 20)
= $ 1.50
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Juan bought a sweater for $15.95 and two shirts for $9.00 each. how much did juan spend on clothes?
Answer:
Step-by-step explanation:
Well first you have:
$15.95 for one sweater
$9.00 each for two shirts
You would double the amount $9.00 which would be:
9 + 9 = 18 or Multiply 9 x 2 = 18
So this would total to 15 + 18 = $33
How do I solve this problem 34=p+19
Hello,
[tex]34 = p + 19[/tex]
[tex]34 - 19 = p + 19 - 19[/tex]
[tex]15 = p[/tex]
[tex]p = 15[/tex]
Solve for x using
cross multiplication.
3x + 6
4
=
4x - 3
5
x = [?]
Enter
Answer:
x = 42
Step-by-step explanation:
Cross multiplying is done as follows:
the denominator of the second fraction is multiplied with the numerator of the first equation and denominator of the first fraction is multiplied with the numerator of the second equation
5(3x+6) = 4(4x-3) multiply inside the parenthesis
15x + 30 = 16x - 12 transfer like terms to same side of the equation
30 + 12 = 16x - 15x
42 = x
need answered asapp!!
Answer:b
Step-by-step explanation:goooooooo
Please help me i don’t understand
The graph of the inverse of the function is shown in the image attached below.
How to graph the inverse of a function
In this question we must apply the following transformation rule to the three points to determine the points of the inverse function:
(x, y) → (y, x)
Now we proceed to find the points:
(- 7, 3) → (3, - 7)
(-3, 0) → (0, -3)
(-2, -2) → (-2, -2)
Lastly, we proceed to construct the graph of the inverse of the function.
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For the graph x = 1 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your answer with two or more sentences.
The slope of the parallel line is undefined and the slope of the perpendicular line is 0
How to determine the slope?The equation is given as:
x = 1
The above do not have any y value.
This means that the slope of the line is undefined
i.e.
m = undefined
The slope of the parallel line is:
Slope = m
This gives
Slope = undefined
The slope of the perpendicular line is:
Slope =-1/m
This gives
Slope = -1/undefined
Slope = 0
Hence, the slope of the parallel line is undefined and the slope of the perpendicular line is 0
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Which function could be a stretch of the exponential decay function shown on the graph?
f(x) = 2(6)x
f(x) = One-half(6)x
f(x) = 2(one-sixth) Superscript x
f(x) = One-half (one-sixth) Superscript x
The function that could be a stretch of the exponential decay function shown on the graph is B. f(x) = One-half(6)x.
How to illustrate the function?From the information given, it can be seen that function A is a monotonically increasing function.
Also, it can be seen that C and D don't pass through (0, 1).
Therefore, the function could be a stretch of the exponential decay function shown on the graph is B.
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Answer:
b
Step-by-step explanation:
3x-6=15 what is the value of x?
Answer:
7
Step-by-step explanation:
frist simplfying
3x-6=15
addind six to both side
3x-6+6=15+6
3x=21 dividing by 3
x=7
Mr. lee walks into the courtyard after school and wants to know the height of the tree. he measures an angle of 47* between a line of sight to the top of the tree and the ground and he is 22 feet away from the tree. how tall is the tree? *
The tree is 23.54 feet tall.
What is an angle?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean.
According to the question,
Height of tree= 22*tan [tex]47^{o}[/tex]
= 22* 1.07
= 23.54 ft.
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Josie has 16 coins. Each of her coins is either a quarter or a dime. If she has 6 more dimes than quarters, and the total value is $2.35, how many quarters does Josie have?
Josie has a total of 5 quarters.
How to find the number of quarters using equation?Josie has 16 coins. Each of her coins is either a quarter or a dime.
Let
x = number of quarters
y = number of dime
she has 6 more dimes than quarters.
Therefore,
y = 6 + x
x + y = 16
-x + y = 6
2y = 22
y = 11
11 = 6 + x
x = 11 - 6
x = 5
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