NO LINKS!! URGENT HELP PLEASE!!!!
y = 3*2^x - 6
Name the "family" and state the parent function.
Answer:
Family: exponential functions
Step-by-step explanation:
The given function is:
[tex]y = 3*2^x - 6[/tex]
It is in the form of exponential function:
[tex]y = a*b^x + c[/tex]
where "a", "b", and "c" are constants.
The parent function of an exponential function is:
[tex]y = b^x[/tex]
where "b" is the base of the exponential function. In this case, the parent function would be:
The given function is a member of the family of exponential functions with base 2 and with a vertical shift of -6 units and a vertical stretch by a factor of 3.
Answer:
Exponential function family with base 2.
[tex]\textsf{Parent function:} \quad y=2^x[/tex]
Step-by-step explanation:
The given equation is in the form of an exponential function with a vertical stretch and vertical shift.
The standard form of this type of exponential function is:
[tex]y=ab^x+c[/tex]
where:
a is the vertical stretch factor.b is the base (growth/decay factor) in decimal form.c is the vertical shift.y = c is the equation of the horizontal asymptote.If |a| > 1 then it is a vertical stretch, and if 0 < |a| < 1 it is a vertical "compression".
The parent function of this type of exponential function is y = bˣ, where b is the base.
Given function:
[tex]y=3 \cdot 2^x-6[/tex]
Therefore, the parent function of the given function is:
[tex]\boxed{f(x)=2^x}[/tex]
The given function is a vertical stretch by a factor of 3, followed by a vertical shift downwards by 6 units, from the parent exponential function with base 2.
Hence, the family of functions that this equation belongs to is the exponential function family with base 2, and the parent function is [tex]y = 2^x[/tex].
Correct answer gets brainliest!!!!
Answer:is b
A line segment has both of its end-points fixed and so it has a definite length.
Step-by-step explanation:
pl z give me brianlieyst and have a good day
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Which expression is equivalent to 2^3 . 5^-2 ?
15 POINTS! HELP PLEASE ASAP!!
Answer:
C
Step-by-step explanation:
The equation is:
y = [tex]\frac{1}{4}[/tex]x - 8
If you plug in the x and y value from the table, you find they are solutions to the equation.
(36,1)
y = [tex]\frac{1}{4}[/tex]x - 8 Substitute in 36 for x and 1 for y
1 = [tex]\frac{1}{4}[/tex](36) - 8
1 = 9 - 8
1 = 1
You can do the same thing for all of the other points on the table.
Helping in the name of Jesus.
For the right triangle below, find the measure of the angle.
Figure is not to scale.
For the given right-angled triangle the measure of the angle is 11.30°.
Given adjacent base of the triangle = 10
given opposite side of the triangle = 2
To find out the angle we can use a little bit of trigonometry. By trigonometry, we know that tan ∠ = opposite side / adjacent side.
So, we can use the above tan ∠ relation to find the angle.
Tan ∠ = opposite side / adjacent side
Tan ∠ = 2/10
Tan ∠ = 1/5
∠ = Tan⁻¹(1/5)
∠ = 11.30°.
From the above explanation, we can conclude that the measure of the angle for the given right triangle is 11.30°.
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The estimated population of a certain city over time is given in the table below. Answer the questions below to explain what kind of function would better model the data, linear or exponential.
Number of Years Since Last Census, x
1
2
3
4
Estimated Population, f(x)
66,118
77,212
88,340
99,535
function would better model the data because as x increases, the y values change
. The
of this function is approximately
.
The linear function is the more appropriate function that has to be used here.
How to use the linear functionTo determine which type of function better models the data, we can analyze the difference in the y values (Estimated Population) as x increases.
Differences between consecutive y values:
77,212 - 66,118 = 11,094
88,340 - 77,212 = 11,128
99,535 - 88,340 = 11,195
The differences between consecutive y values are relatively constant as x increases.
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Suppose you are 5 feet 2 inches tall. Give your height in meters and centimeters
A triangle with area 184 square inches has a height that is two less than six times the width. Find the height and the width of the triangle.
The height of the triangle is √(115) - 1 inches and the width is (1 + √(115)) / 6 inches.
Let's begin by assigning variables to the height and width of the triangle. We'll use h for height and w for width.
From the problem statement, we know that the area of the triangle is 184 square inches:
Area = (1/2) * base * height
where the base is equal to the width. We can rearrange this formula to solve for the height:
height = 2 * Area / base
Since the area is given as 184 square inches and the base is equal to the width, we can write:
h = 2 * 184 / w
We also know that the height is two less than six times the width. Writing this as an equation, we have:
h = 6w - 2
Now we can substitute the expression for h from the second equation into the first equation:
2 * 184 / w = 6w - 2
Multiplying both sides by w gives:
2 * 184 = w * (6w - 2)
Expanding the right side gives:
2 * 184 = 6w² - 2w
Simplifying further gives:
6w² - 2w - 368 = 0
This is a quadratic equation that we can solve using the quadratic formula:
w = (-b ± √(b² - 4ac)) / 2a
where a = 6, b = -2, and c = -368. Plugging in these values gives:
w = (2 ± √(2² - 4 * 6 * (-368))) / 2(6)
Simplifying further gives:
w = (1 ± √(115)) / 6
Taking the positive value gives:
w = (1 + √(115)) / 6
Plugging this value back into either equation for h gives:
h = 6w - 2 = 6((1 + √(115)) / 6) - 2 = 1 + √(115) - 2 = √(115) - 1
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Non mutually exclusive events !
The missing probability is P(A or B) = 131/200
How to calculate the probabilityIt should be noted that in order to find the probability of the union of two events A and B, i.e., P(A or B), we can use the following formula:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = P(A) + P(B) - P(A and B) = (9/20) + (1/4) - (9/200)
Simplifying the expression, we get:
P(A or B) = 45/100 + 25/100 - 9/200 = (90+50-9)/200 = 131/200
The probability is 131 / 200.
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Bree is replacing the wire on her farm paddock fences. She has measured a couple of the sides and drawn a sketch of the paddock shape. (pic below)
a. Find the two missing sides and calculate the perimeter of the paddocks
Perimeter?
b. The cost of fencing wire is $5 per meter. How much will the wire cost
Cost?
a. The perimeter of the paddock is 120 meters
b. The cost of the wire will be $600
a. To find the missing sides and calculate the perimeter of the paddock, let's analyze the given sketch.
The length of the missing side on the left can be determined by subtracting the known length of 10m from the total height of 20m. Therefore, the left side has a length:
20m - 10m = 10m.
The missing side on the right is equal in length to the known side of 40m.
Now we can calculate the perimeter by adding up all the side lengths:
Perimeter = 10m + 40m + 20m + 10m + 40m
= 120m.
b. To calculate the cost of the wire, we need to multiply the perimeter of the paddock by the cost per meter of fencing wire, which is $5/m.
Wire Cost = Perimeter × Cost per meter
= 120m × $5/m
= $600.
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The following table shows students’ test scores on the first two tests in an introductory calculus class.
Calculus Test Scores
First test, x 64
59
45
73
73
76
40
56
68
55
78
83
Second test, y 68
63
55
74
68
75
43
64
61
64
77
84
Step 2 of 2 : If a student scored a 69
on his first test, make a prediction for his score on the second test. Assume the regression equation is appropriate for prediction. Round your answer to two decimal places, if necessary.
if a student scored a 69 on his first test, predict that his score on the second test will be approximately 64.57.
Students’ test scores on the first two tests in an introductory calculus class.
To make a prediction for the student's score on the second test based on their score of 69 on the first test, we need to find the regression equation for the data set.
The regression equation for these data is
y = 0.6443x + 19.943
Where y is the predicted score on the second test and x is the actual score on the first test.
Substituting x = 69 into this equation, we get
y = 0.6443(69) + 19.943 ≈ 64.57
Therefore, if a student scored a 69 on his first test, we predict that his score on the second test will be approximately 64.57.
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FIND THE AREA PLEASE
Answer:
the area of the shape is 48m
Step-by-step explanation:
10*4=40
2*4=8
40+8=48
brake it up into two triangles. one is a triangle that is 10m tall and 8m wide at the top. you can solve that by doing 4*10=40. the other triangle is 4m wide at the bottom and 2m tall. you can solve that by doing 2*4=8. and 40+8=48.
Use mathematical induction to prove 2^n>=2n is true for all positive integers.
By the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.
The given inequality is 2ⁿ≥2n.
Let n = 1
2^1 ≥ 2^1
2 ≥ 2 which is true
Inductive Step: Assume 2ⁿ≥2n is true for some arbitrary positive integer k.
We need to prove that 2^(k+1) ≥ 2^(k+1)
2^(k+1) ≥ 2*2^k (by the inductive hypothesis)
2^(k+1) ≥ 2*2^(k+1)
2^(k+1) ≥ 2^(k+1) which is true
Therefore, by the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.
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what number is 8% larger than 230
Answer:
That number is 230 × 1.08 = 248.4.
To find this number, we calculated 8% of 230, which is 18.4 , and then added it to 230, Hence The number that is 8% larger than 230 is 248.4.
How to solve for the numberTo find a number that is 8% larger than 230, we can calculate the 8% increase of 230 and add it to the original number.
Step 1: Calculate the 8% increase of 230:
8% of 230 = (8/100) * 230 = 0.08 * 230 = 18.4
Step 2: Add the 8% increase to 230:
230 + 18.4 = 248.4
Therefore, a number that is 8% larger than 230 is 248.4.
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How many games did the team play last season?
The number of games that the team did play in the last season is 23.
What is the frequency?The frequency is the number of times an event happens. Therefore, frequency is the number of repetitions of a digit or an event.
The given frequency table represents the frequency of different runs scored by the team in the entire season.
The frequency is written in tally form, which means that each of the vertical lines represents the count of 1, while a group of fours lines such that the four lines are vertical while the fifth line cuts the other four represents a count of 5 as shown in the second column of the second row.
Therefore, the frequency table can be made as:
Number of runs Frequency
0 8
1 5
2 3
3 6
4 1
Total: 23
Hence, the team played 23 games.
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What is the value of "x", when 1/3x = 9 1/3?
Answer:
x=28
Step-by-step explanation:
solve for x by simplifying both sides of the equation, then isolating the variable.
have a good day :)
Answer
x=3 1/9
Step-by-step explanation:
In the quadratic formula, the number for a is filled in with the coefficient of x
In the quadratic formula, the number for "a" is filled in with the coefficient of x².
What is a quadratic equation?In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Mathematically, the quadratic formula is represented by this mathematical equation:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
For instance, given the quadratic equation 2x² - 3x - 1 = 0, we have:
a = 2
b = -3
c = -1
[tex]x = \frac{-(-3)\; \pm \;\sqrt{(-3)^2 - 4(2)(-1)}}{2(2)}\\\\x = \frac{3\; \pm \;\sqrt{9 + 8}}{4}\\\\x = \frac{3\; \pm \;\sqrt{17}}{4}[/tex]
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$800000 into a 25:17 ratio. How much do each get
Answer: Therefore, the first person gets $476,190.48 and the second person gets $323,809.52.
Step-by-step explanation: To divide $800,000 into a 25:17 ratio, we first need to add the ratio terms (25 + 17 = 42) to determine the total number of parts. Then, we divide the total amount by the total number of parts to determine the value of each part. Finally, we multiply the value of each part by the respective ratio term to determine the amount that each person gets.
The calculation steps are as follows:
Determine the total number of parts: 25 + 17 = 42
Determine the value of each part:
Value of each part = Total amount / Total number of parts
= $800,000 / 42
= $19,047.62 (rounded to two decimal places)
Determine the amount that each person gets by multiplying the value of each part by the respective ratio term:
First person gets: 25 parts * $19,047.62 per part = $476,190.48
Second person gets: 17 parts * $19,047.62 per part = $323,809.52
pleaseeeeeeeeeeeeeeeeeeeeeeee
Answer:
congruent to each other cause their measurements are same.
congruent means if 2 shapes have same measurements they are called congruent
Someone help i really need help with this
The equation which can be used to find the amount the admission tickets cost would be 4x + 25 = 175. The cost of the admission tickets would therefore be $ 37.50.
How to find the equation ?The total spent by Ms. Boi was $ 175.00 so this is what the entire equation would be equal to. The cost of admission tickets will be denoted as x because they are the unknown figure.
There are 4 tickets purchased so the equation would be:
4 x Cost of tickets - Parking cost = Total spent
4 x - 25 = 175
The cost of each admission ticket is:
4 x - 25 = 175
x = 150 / 4
x = $ 37.50
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Compare these distributions.
Both distributions of exam scores are and there are clear outlier(s) in each distribution of exam scores.
The center of the distribution of exam scores earned by students who completed homework is the center of the distribution of exam scores earned by students who did not complete homework.
The variability in scores of those who completed homework is that of the students who did not complete homework.
The comparison data is shown below.
Based on the information provided, we can infer that:
Both distributions have outliers.The center of the distribution of exam scores is the same for both groups, meaning that the average score of students who completed homework is the same as the average score of students who did not complete homework.The variability (spread) of exam scores of those who completed homework is the same as the variability of exam scores of those who did not complete homework.Without more information about the specific data and the context of the study, it is difficult to make further comparisons or draw any conclusions about the relationship between completing homework and exam scores. However, it is interesting to note that completing homework did not seem to have an impact on the average exam score or the variability of exam scores.
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Expand the expression below. Express each answers in terms of log or log y to log8x^2
Expressing the expansion of the logarithm in terms of log y, we can write: log(8x^2) = log(8) + 2*log(y), where y = x
What is the value of the expansion of the logarithm?Using the logarithmic identity that states log(a^b) = b*log(a), we can expand log(8x^2) as:
log(8x^2) = log(8) + log(x^2)
Note that a logarithmic identity is a mathematical relationship or equation that involves logarithms.
We can further simplify log(x^2) as:
log(x^2) = 2*log(x)
Therefore, we can write:
log(8x^2) = log(8) + 2*log(x)
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what does scaled version mean in this case its 3:5 scaled version but i just want to know what it means i dont care about answers il give brainliest !
A 3:5 scaled version means that the dimensions of the new version are proportional to the original dimensions in a ratio of 3:5.
What does a scaled version mean?A scaled version is a version of a shape where every size in the original shape is multiplied by the same number.
In this situation, a 3:5 scaled version means that the dimensions (or sizes) of the new version are proportional to the original dimensions in a ratio of 3:5.
For example, if we have a circle with radius 20 cm, we can create a 3:5 scaled version by multiplying the radius by the ratio 3/5. That is:
scaled version radius = 3/5 * 20 = 12 cm
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Malik opens a savings account with an initial deposit of $2500. The account earns 2.1% annual interest compounded quarterly? Round to the nearest cent.
Answer:
Step-by-step explanation:
Three fourths of the girls in the eighth grade have long hair. One half of the girls are wearing dresses today. What is the probability that an eighth grade girl will have long hair and be wearing a dress?
The probability that an eighth-grade girl will have long hair and be wearing a dress is 3/8 or 0.375, which is the same thing expressed as a decimal.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To solve the problem, we need to find the intersection of the events "having long hair" and "wearing a dress" and calculate the probability of that intersection.
Let L be the event "having long hair" and D be the event "wearing a dress". Then we know:
P(L) = 3/4, since three-fourths of the girls have long hair.
P(D) = 1/2, since half of the girls are wearing dresses.
To find P(L ∩ D), we need to multiply the probabilities of the two events:
P(L ∩ D) = P(L) × P(D) = (3/4) × (1/2) = 3/8
Therefore, the probability that an eighth grade girl will have long hair and be wearing a dress is 3/8 or 0.375, which is the same thing expressed as a decimal.
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PLS HELP ASAP PLSSSSSS
Answer:
a) |x -8| = 6
b) |x -15| = 0
Step-by-step explanation:
You want the values of 'b' and 'c' for the cases where the solutions to the equation |x -b| = c are ...
2 and 1415SolutionsThe solutions to |x -b| = c are the solutions to ...
x -b = c ⇒ x = b +c
x -b = -c ⇒ x = b -c
ParametersGiven the two solutions P and Q, the values of 'b' and 'c' can be found from ...
P = b +c
Q = b -c
Adding these two equations gives ...
P +Q = 2b ⇒ b = (P +Q)/2
Subtracting the second equation from the first gives ...
P -Q = 2c ⇒ c = (P -Q)/2
a) Solutions 2 and 14b = (2 +14)/2 = 8
c = (14 -2)/2 = 6
The equation is ...
|x -8| = 6
b) Solutions 15 and 15b = (15 +15)/2 = 15
c = (15 -15)/2 = 0
The equation is ...
|x -15| = 0
Can someone please help me with this? I'll mark anyone who answers for helping
There are two spinners. The first spinner has three same-sized sectors labeled 1, 2, and 3. The second spinner has four same-sized sectors labeled 3, 4, 5, and 6. The spinners are spun once. How many outcomes do not show an odd number on the first spinner and show a 3 on the second spinner?
Answer:
The first spinner has a 1/3 chance of not showing an odd number, and the second spinner has a 1/4 chance of showing a 3. The probability of both events happening is:
1/3 x 1/4 = 1/12
Therefore, there is a 1/12 chance of an outcome showing a 3 on the second spinner and not showing an odd number on the first spinner. Since there are a total of 3 x 4 = 12 possible outcomes, the number of outcomes that meet the criteria is:
12 x 1/12 = 1
So there is only one outcome that meets the criteria.
A list 7 members at the gym 10, 64, 52, 46,54,67,54. find the median
The calculated value of the median of the A-list 7 members at the gym is 54
Finding the median of the A-list 7 members at the gymFrom the question, we have the following parameters that can be used in our computation:
10, 64, 52, 46,54,67,54.
When the numbers are sorted in ascending order, we have
Sorted list = 10, 46, 52, 54, 54, 64, 67
The median is the middle number of the sorted list
So, we have
Middle number = 54
Thsis means that
Memdian = 54
Hence. the median of the A-list 7 members at the gym is 54
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Can someone help with this and give the right answer I am on a time limit
The constant of variation, k, is defined as the ratio between the two variables' values, multiplied by their respective powers: [tex]k = y/x^a \times z/x^b,[/tex] where a and b are the powers of x in the expressions for y and z, respectively. when [tex]x = -3[/tex] and [tex]y = 4[/tex] , z is equal to -81/16.
What is the constant of variation?In this case, we have x = 8, y = 54, and z = 144, so we need to determine the powers of x in the expressions for y and z:
[tex]y = 54 = (8^a) \times k = > a = 3[/tex]
[tex]z = 144 = (8^b) \times k = > b = 2[/tex]
Substituting these values into the formula for k, we get:
[tex]k = y/x^a \times z/x^b = 54/8^3 \times 144/8^2 = 27/64[/tex]
Therefore, the constant of variation is 27/64.
Using the same formula as above, we can solve for z when x = -3 and y = 4:
[tex]k = y/x^a \times z/x^b[/tex]
We need to determine the powers of x in the expressions for y and z:
[tex]y = 4 = (-3)^a * k = > a = -1[/tex]
[tex]z = ? = (-3)^b * k = >[/tex] we don't know b or z yet
Substituting these values into the formula for k, we get:
[tex]k = y/x^a * z/x^b = 4/(-3)^(-1) * z/(-3)^b = -12z/(-3)^2[/tex]
Simplifying this expression, we get:
[tex]k = -12z/9 = -4z/3[/tex]
Now we can solve for z:
[tex]-4z/3 = 27/64[/tex]
Multiplying both sides by 3/(-4), we get:
[tex]z = -81/16[/tex]
Therefore, when [tex]x = -3[/tex] and [tex]y = 4, z[/tex] is equal to [tex]-81/16.[/tex]
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