Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.
To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.
So, let's assume that g(x1) = g(x2). Then, we have:
f(x1) = f(x2)
x1(x1-1) = x2(x2-1)
x1^2 - x1 = x2^2 - x2
x1^2 - x2^2 - x1 + x2 = 0
(x1 - x2)(x1 + x2 - 1) = 0
Since x1 and x2 are distinct, we must have x1 + x2 = 1.
But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.
To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.
So, let's solve the equation f(x) = y for x:
x(x-1) = y
x^2 - x - y = 0
Using the quadratic formula, we get:
x = (1 ± √(1 + 4y))/2
Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.
Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.
Identify the parts of the expression. Then write a word expression for the numerical or algebraic expression 1.5×6+8.3
The numerical value of the algebraic expression 1.5 × 6 + 8.3 is 17.3; The factors are 1.5 and 6 & the terms: 1.5 * 6 and 8.3
Identifying and solving the parts of the expressionFrom the question, we have the following parameters that can be used in our computation:
1.5 × 6 + 8.3
The above expression is an algebraic expression and as such the parts of the expressions are
Factors: 1.5 and 6Terms: 1.5 * 6 and 8.3When the expression is evaluated, we have
1.5 × 6 + 8.3 = 17.3
This means that the result of evaluating the expression 1.5 × 6 + 8.3 is 17.3
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what is the radius of the sphere with volume of 10000
The radius of the sphere with a volume of 10000 m³ is approximately 13.4 meters.
What is the radius sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The volume of a sphere is expressed as:
Volume = (4/3)πr³
Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).
Given that the volume of the sphere is 10000 m³, we can set up the equation:
Volume = (4/3)πr³
r³ = Volume / (4/3)π
r = ∛( Volume / (4/3)π )
r = ∛( 10000/ ( (4/3) × 3.14) )
r = 13.4 m
Therefore, the radius is 13.4 m.
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Which line has the slope with the greatest value?
A blue B purple C red D green
Answer:
A. The blue line has the slope with the greatest value. The blue line is the steepest of the lines.
An oil company has a cylindrical drum with a capacity of 806 cubic yards. To construct this drum, the
cost of material for the top of the drum is $2 per square yard, $2 per square yard for the bottom of
the drum, and $17 per square yard for the side wall of the drum. What dimensions must this
cylindrical drum have to be constructed at minimum cost?
The measurements of the cylindrical (round and hollow) drum that minimize the fetched of development are roughly 10.19 yards by 2.46 yards.
How to Solve the Problem?Let's expect that the round and hollow drum includes a stature of h and a span of r.
The volume of a barrel is given by: V = πr^2h.
We know that the drum includes a capacity of 806 cubic yards, so able to compose:
πr^2h = 806
We need to play down the taken a toll of building the drum, which is given by the entirety of the fetched of the beat, foot, and side divider.
The zone of the beat and foot of the drum is given by: A = πr^2.
The fetched of fabric for the beat and foot is $2 per square yard, so the taken a toll of the best and foot is:
C_topbottom = 2A = 2πr^2
The cost of fabric for the side divider is $17 per square yard, and the region of the side divider is given by:
A_side = 2πrh
The whole fetched of building the drum is in this manner:
C = C_topbottom + C_side = 2πr^2 + 17(2πrh) = 2πr^2 + 34πrh
Presently we are able utilize the condition for the volume of the drum to kill h from the fetched condition:
h = 806/(πr^2)
Substituting this expression for h into the taken a toll condition, we get:
C = 2πr^2 + 34πr(806/(πr^2)) = 2πr^2 + 27404/r
To discover the least fetched, we got to take the subordinate of the fetched condition with regard to r and set it rise to to zero:
dC/dr = 4πr - 27404/r^2 =
Fathoming for r, we get:
r = (27404/(4π))^(1/3) ≈ 10.19 yards
Substituting this esteem of r back into the expression for h, we get:
h = 806/(π(10.19)^2) ≈ 2.46 yards
Hence, the measurements of the round and hollow drum that minimize the fetched of development are roughly:
Span: 10.19 yards
Stature: 2.46 yards
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HELP ASAP ASAP PLS PLS ALSO BRAINLIEST
A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.
Servings Sauce (cups) Oregano (tsp)
4 8 one half
6
At this rate, how much sauce and oregano will be needed to make 6 servings?
The recipe will need 12 cups of sauce and three fourths teaspoons of oregano for 8 servings.
The recipe will need 12 cups of sauce and 1 teaspoon of oregano for 8 servings.
The recipe will need 10 cups of sauce and 1 teaspoon of oregano for 8 servings.
The recipe will need 10 cups of sauce and three fourths teaspoons of oregano for 8 servings.
For 6 servings, the recipe will need 12 cups of sauce and 3/4 teaspoon of oregano. So, the answer is option A: The recipe will need 12 cups of sauce and three-fourths teaspoons of oregano for 8 servings.
To find how much sauce and oregano will be needed to make 6 servings, we can use the ratio of sauce to oregano in the recipe.
For 4 servings, the recipe calls for 8 cups of sauce and 1/2 teaspoon of oregano. To find how much sauce and oregano are needed for 6 servings, we can set up a proportion:
sauce : oregano = 8 cups : 1/2 teaspoon = 16 cups : 1 teaspoon
So, for 6 servings, we need:
sauce : oregano = 16 cups : 1 teaspoon
To convert this to cups and tablespoons, we can multiply both sides of the proportion by 3/4:
sauce : oregano = (16 x 3/4) cups : (1 x 3/4) teaspoons
sauce : oregano = 12 cups : 3/4 teaspoon
sauce : oregano = 48 cups : 3 teaspoons
Therefore, for 6 servings, the recipe will need 12 cups of sauce and 3/4 teaspoon of oregano. So, the answer is option A: The recipe will need 12 cups of sauce and three-fourths teaspoons of oregano for 8 servings.
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please HELPP! Graphing Linear Equations
Answer: 2 2/3+ 8
Step-by-step explanation: it goes 2 under the ten
Answer:
See provided explanation
Step-by-step explanation:
Slope=change in y/change in x
General equation for a line: y=mx+b
You know that the slope(m) is 8/3, and the y-intercept is 8. So your graph will intersect the y axis at the point (0,8). from there, use slope=rise/run to graph the remaining points. Starting at (0,8), move 8 up and 3 right, this is your next point. Do the same in the other direction, starting at (0,8) move down 8 and left 3 points. Doing this will get you the points (-3,0) and (3,16). repeat this process until you have enough points to form a line. I attatched a picture of what the graph should look like.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The correct statements about the circle equation are:
The radius of the circle is 3 units. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.Which statements are true?Remember that the general circle equation is:
(x - a)² + (y - b)² = R²
Where (a, b) is the center and R is the radius.
Here the given equation is.
x² + y² - 2x - 8 = 0
We can complete squares in x to get:
(x - 1)² - 1 + y² - 8 = 0
(x - 1)² + y² = 9
(x - 1)² + y² = 3
So, the center is (1, 0) and the radius is 3.
The correct statements are:
The radius of the circle is 3 units.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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Jenny has recently begun keeping her spending under better control, but she
still can't fully pay off her credit card. She maintains an average monthly
balance of about $1100, and her card charges a 24% annual interest rate,
which it bills at a rate of 2% per month.
How much is she spending on credit card interest per year?
Answer:
$264
Step-by-step explanation:
You want to know Jenny's annual finance charges if her credit card balance averages $1100 and her interest rate is 24%.
Annual interest chargeThe annual interest charge will be the product of the annual interest rate and the average balance over the course of the year.
24% × $1100 = $264
Jenny spends about $264 per year on credit card interest.
A rectangular room is 28 feet by 32 feet.
A scale drawing of the room has a perimeter is 12 inches.
What is the length of the shorter side of the room on the scale drawing?
The length of the shorter side of the room is 3.2 inches
What is the length of the shorter side of the roomFrom the question, we have the following parameters that can be used in our computation:
A rectangular room is 28 feet by 32 feet.
So, the perimeter is
P = 2 * (28 + 32)
Evaluate
P = 120
So, the scale factor from the room to the drawing is
Scale factor = 12/120 i.e. division of perimeters
So, we have
Scale factor = 1/10
The small length of the room is 32 feet
So, we have
Smaller length = 1/10 * 32
Smaller length = 3.2 inches
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Construct a 96% confidence interval about u if the sample size, n, is 57.
s=4.8
x=19.3
lower bound =
upper bound=
The 96% confidence interval for the population mean μ is approximately (18.06, 20.54).
We have,
To construct a 96% confidence interval about the population mean(μ) with a sample size of n = 57,
we can use the following formula:
CI = x ± z (s/√n)
where x is the sample mean, s is the sample standard deviation, n is the sample size, z is the z-score associated with the desired confidence level (96% in this case), and √n is the square root of the sample size.
The z-score corresponding to a 96% confidence level can be found using a standard normal distribution table or calculator.
For a two-tailed test, the z-score is 1.96.
Substituting the given values, we have:
CI = 19.3 ± 1.96 (4.8/√57)
Calculating the standard error of the mean (s/√n):
s/√n = 4.8/√57 ≈ 0.634
Substituting this value into the formula:
CI = 19.3 ± 1.96*0.634
Calculating the upper and lower bounds of the confidence interval:
lower bound = 19.3 - 1.96*0.634 ≈ 18.06
upper bound = 19.3 + 1.96*0.634 ≈ 20.54
Therefore,
The 96% confidence interval for the population mean μ is approximately (18.06, 20.54).
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To construct a 96% confidence interval for the population mean, use the formula x ± z*(s/√n) with z being the z-score for the 96% level, x being the sample mean, s being the sample standard deviation, and n being the sample size. Substituting the given values will give the lower and upper bound of the confidence interval.
Explanation:The question is asking for the construction of a 96% confidence interval for a population mean u, given a sample size (n) of 57, a sample mean (x) of 19.3 and a sample standard deviation (s) of 4.8.
To find the confidence interval, we need to use the formula: x ± z*(s/√n) where z is the z-score associated with our confidence level. For a 96% confidence interval, the z-score is approximately 2.05 (you can find this from a standard z-table).
Substituting the given values into the formula gives: 19.3 ± 2.05*(4.8/√57)
Calculating the above expression will give the lower and upper bound of the 96% confidence interval.
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Given:
m∠M=m∠J and MJ bisects LN
What triangle congruence criteria can be used to prove that ΔLKM≅ΔNKJ?
Selected Answer:
C. ASA
Answers:
A. SSS
B. SAS
C. ASA
D. AAS
The triangles Δ MNO and ΔXYZ are congruent to each other by AAS postulate as two corresponding angles and a corresponding side are equal to each other.
We have,
Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Given that YO = NZ.
Consider YO = NZ
Now Add OZ on both sides
YO + OZ = NZ + OZ
YZ = NO
Consider triangles Δ MNO and ΔXYZ.
M ≅ X
N ≅ Y
YO ≅ NZ
Δ MNO ≅ ΔXYZ by AAS postulate.
Therefore, the triangles Δ MNO and ΔXYZ are congruent to each other by AAS postulate as two corresponding angles and a corresponding side are equal to each other.
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complete question:
The congruency of △MNO and △XYZ can be proven using a reflection across the line bisecting OZ. However, this congruency can also be proven using geometric postulates, theorems, and definitions. Prove that the triangles are congruent using a two-column proof and triangle congruency theorems.
Given: M ≅ X
N ≅ Y
YO ≅ NZ
Prove: △MNO ≅ △XYZ
True or false there are 3 ways to write a ratio the word to a colon and a fraction bar
The requried it's true, that there are 3 ways to write a ratio the word to a colon and a fraction bar.
There are three ways to write a ratio:
Using the word "to", as in "the ratio of apples to oranges is 2 to 1".Using a colon ":", as in "the ratio of apples to oranges is 2:1".Using a fraction bar "/", as in "the ratio of apples to oranges is 2/1".Thus, the requried it's true, that there are 3 ways to write a ratio the word to a colon and a fraction bar.
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The base of a rectangular prism is 20 cm 2 . If the height of the prism is 5 cm, what is its volume
The volume of a rectangular prism would be 100 cubic cm.
Since we know that rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
The volume of a rectangular prism=Length X Width X Height
We are given that base of a rectangular prism is 20 cm sq. . If the height of the prism is 5 cm, then;
Base area = 20 cm sq.
Height = 5 cm
Volume of a rectangular prism=Length X Width X Height
Volume of a rectangular prism= Base area X Height
Volume of a rectangular prism= 20 x 5
= 100
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Nemo can make a monthly payment of $565 for a car. If the annual interest rate he
qualifies for is 9% for 4 years, what price could he afford for the car?
Answer:$ 24,679.20 or 514.15 a month
Step-by-step explanation: 565(.09) is 50.85 which needs to be deducted from the payment of 565 because he needs to be able to pay for interest. 514.15 is then multiplied by 48 months which will bring you to 24,679.20
20 Per Question, Algebra 2, Thanks :)
The product of the expression is given as 1/4x²y²
What is an algebraic expression?Remember that an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). It can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient
The given expression is (3x⁵y²)/(xy) * (6xy²) / (9x³y)
Multiply through to have
{(3x⁵y²)(6xy²)} / {(xy)(xy)}
⇒( 18x⁶y⁴) / (72x⁴y²)
Simplify to get
Therefore the value of the expression is 1/4x²y²
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A rectangular prism has a length of 8in., a width of 4in., and a height of 2 1/4in. The prism is filled with cubes that have edge lengths of 1/4 in. How many cubes are needed to fill the rectangular prism?
We need 4608 cubes to fill the rectangular prism.
We have,
The rectangular prism has a volume of:
Volume = length x width x height
Volume = 8 in. x 4 in. x 2 1/4 in.
Volume = 72 in³
Each cube has a volume of:
Volume of cube = edge length³
Volume of cube = (1/4 in.)³
Volume of cube = 1/64 in³
To find the number of cubes needed to fill the rectangular prism, we can divide the volume of the prism by the volume of each cube:
Number of cubes = Volume of prism / Volume of a cube
Number of cubes = 72 in³ / (1/64 in³)
Number of cubes = 72 in³ x 64 / 1
Number of cubes = 4608 cubes
Therefore,
We need 4608 cubes to fill the rectangular prism.
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How many more children have an age of 6 1/2 years than 7 1/4 years?
Result:
The number of children having an age of 6 1/2 years more than 7 1/4 years = 3/4.
How to calculate the number of children having an age of 6 1/2 years more than 7 1/4 years?To do this, we would subtract the number of children who are 7 1/4 years old from the number of children who are 6 1/2 years old: x - y
Let x = number of children 6 1/2 years old
Let y = number of children 7 1/4 years old
x = 6 1/2 years or 13/2 years
y= 7 1/4 years or 29/4 years
= 13/2 - 29/4
= (26/4) - (29/4)
= -3/4
Coverting to the absolute value, we get:
|-3/4| = 3/4
Thus, 3/4 more children are 6 1/2 years old than 7 1/4 years old.
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is this a rigid motion
The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.
The transformation for this problem has the rule defined as follows:
(x,y) -> (x + 2, -y).
The transformations are defined as follows:
x -> x + 2 is a translation right two units.y -> -y is a reflection over the x-axis.Neither transformation is a dilation, hence it is a rigid motion.
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A rectangle has side lengths (x+4) feet and (2x+1) feet for x > 0. Write a function that describes the area A, in square feet, in terms of x.
A.) A(x) = 3x+5
B.) A(x) =6x+10
C.) A(x) =2x(squared by 2) +9x+4
D.) A(x)= 2x(squared by 2) +7x-4
C. The function that describes the area A, in square feet, in terms of x is A(x) = 2x^2 + 9x + 4
How to solve for the functionTo find the area A of a rectangle, you multiply its length by its width. In this case, the side lengths of the rectangle are (x+4) feet and (2x+1) feet. So, we can write the area function A(x) as follows:
A(x) = (x+4)(2x+1)
Now, we'll expand the expression:
A(x) = x(2x+1) + 4(2x+1)
A(x) = 2x2 + x + 8x + 4
Now, combine like terms:
A(x) = 2x^2 + 9x + 4
So, the correct answer is:
C.) A(x) = 2x^2 + 9x + 4
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Ronnie records the number of chirps per minute (x) that crickets make at
different temperatures (y) in degrees Fahrenheit.
He determines that the association is linear and that the line of best fit is
y = x + 60.
What is the interpretation of the slope and y-intercept of this equation?
Temperature (°F)
8888888888
100
90
80
70
60
50
40
30
20
10
•
1
=x+
y=
X+60
5 10 15 20 25 30 35 40 45 50
Chirps per minute
The interpretation of the slope and y-intercept of this equation is that: C. The slope predicts a temperature increases of about 1/6 for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x = 0), the temperature is 60 degrees.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Since Ronnie determined that the association between the number of chirps per minute (x) that crickets make at different temperatures (y) in degrees Fahrenheit is linear and that the line of best fit is given by;
y = 1/6(x) + 60
By comparison, we have the following:
Slope, m = 1/6.
y-intercept = 60.
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Stephan is 46 inches tall. His sister is 6 inches taller than he is how tall is may
Answer:
May is 52 inches tall
Step-by-step explanation:
stephan=46in
sister=6+stephan(in inches)=6+46=52
To receive monthly payments of $1500 for 20 years, how much would a person have to invest now in an annuity with an annual interest rate of 3.1% to achieve this goal? Round the answer to the nearest dollar.
The person would have to invest approximately $461,044.94 now in an annuity with an annual interest rate of 3.1% to receive monthly payments of $1500 for 20 years.
To calculate the present value of an annuity, we can use the following formula:
[tex]PV = PMT \times \dfrac{(1 - (\dfrac{1}{(1 + r)^n})) }{ r}[/tex]
Where:
PV = present value of the annuity
PMT = monthly payment
r = annual interest rate
n = total number of payments
In this case, the PMT is $1500, the annual interest rate is 3.1%, and the number of payments is 20 years x 12 months per year = 240 payments.
First, we need to convert the annual interest rate to a monthly interest rate by dividing it by 12:
r = 3.1% / 12 = 0.2583%
Next, we can plug in the values and solve for PV:
PV = $1500 x [(1 - (1 / (1 + 0.2583%)²⁴⁰)) / 0.2583%]
PV = $1500 x [(1 - (1 / 1.002152²⁴⁰)) / 0.002583]
PV = $1500 x [(1 - (1 / 4.818681)) / 0.002583]
PV = $1500 x (0.7915 / 0.002583)
PV = $461,044.94
Therefore, the person would have to invest approximately $461,044.94 now in an annuity with an annual interest rate of 3.1% to receive monthly payments of $1500 for 20 years.
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Trapezoid ABCD is transformed according to the rule . What is the x-coordinate of A”? -3 -2 2 3
The x-coordinate of A” is 2
Here, we want to know;
the x-coordinate of the rotation about the origin of a point 90 degrees clockwise.
A rotation of 90 degrees clockwise about the origin will turn the coordinates (x, y) to (-y, x)
Here, The coordinates of A is (3,-2)
So, upon the assigned rotation, it becomes;
A'' = (2,-3)
So, the x-coordinate of A” is 2
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On your w-2 it states that you paid $12,042 in federal taxes. When filing your taxes and after all deductions, it says you should have paid $10,628 in federal taxes. How much is your tax refund? Please round to the nearest cent and do not put a dollar sign or spaces in your answer.
The amount of your tax refund is $1,414
how to determine how much is your tax refundTo find the tax refund, we need to subtract the amount of federal taxes owed after deductions from the amount of federal taxes already paid.
Tax refund = Federal taxes paid - Federal taxes owed after deductions
Tax refund = $12,042 - $10,628
Tax refund = $1,414
Rounding to the nearest cent, the tax refund is $1,414.00.
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Based on lofftings research the probability a tp ranked baseball player is left handed is 1 in 3How many lefties would you expect in a group of 15 top ranked baseball players.
The expected number of lefties top ranked baseball players in a sample of 15 top ranked baseball players, obtained from the 1 to 3 ratio of lefties to righties top ranked baseball players is 5 top ranked baseball players
What is a ratio?A ratio is a quantitative comparison between two values that indicates the number of times one quantity is contained in or can contain the other value or quantity.
The ratio or proportion of left handed top ranked baseball players = 1 in 3
Therefore, the ratio of lefties to righties top ranked baseball players = 1 : 3
The number of top ranked baseball players in the sample = 15
The number of the top ranked baseball players in the sample that are left handed is therefore;
Number of left handed baseball players in the sample = (1/3) × 15 = 5
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The radius of Mercury is approximately 2 × 103 kilometers, and the radius of Uranus is approximately 2 × 104 kilometers. To determine approximately how many times bigger the radius of Uranus is than the radius of Mercury, Ken performs the following operation. Approximately how many kilometers bigger is the radius of Uranus than the radius of Mercury?
The diameter of Earth is about 2.7 times greater than the diameter of Mercury.
We have,
to determine the scale factor
Given the following values
Diameter of Mercury = 4.9×10^3km
Diameter of Earth = 1.3×10^4km
Taking the ratio of the diameters:
Ratio = 1.3×10^3/4.9×10^4
Ratio = 2.7
This shows that the diameter of Earth is about 2.7 times greater than the diameter of Mercury.
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complete question:
The diameter of Mercury is approximately 4.9×103 kilometers. The diameter of Earth is approximately 1.3×104 kilometers. About how many times greater is the diameter of Earth than the diameter of Mercury? 2.7 27 270 2700
Find the mean number of hrs for these students if necessary round your answer to the nearest tenth
Answer:
[tex]\huge\boxed{\sf Mean = 11.1 \ hours}[/tex]
Step-by-step explanation:
Given data:18, 7, 6, 13, 8, 17, 9
Mean:[tex]\displaystyle Mean = \frac{Sum \ of \ data}{No. \ of \ data} \\\\Mean = \frac{18+7+6+13+8+17+9}{7} \\\\Mean = \frac{78}{7} \\\\Mean = 11.1 \ hours\\\\\rule[225]{225}{2}[/tex]
Answer:
11.1
Step-by-step explanation:
What is mean?The mean is simply the average of a given set of numbers
To find the mean we find the sum of the given numbers and divide that by the number of given values.
Finding the mean.Given set of values:
18, 7, 6, 13, 8, 17, 9Mean:
Sum of values/Number of values (18 + 7 + 6 + 13 + 8 + 17 + 9)/778/711.1 (rounded to the nearest tenth)The mean of the number of hours the students watched of tv is 11.1 hours
Explain how decimal place value is like place value with whole numbers. Use pictures or words to explain your thinking.
The Explanation of decimal place value is like place value with whole numbers is shown below.
We know,
Each place value to the left of a whole number is multiplied by ten, but a place value to the right of a decimal number is divided by ten.
For example,
We take whole number 254 where place values are
2- Hundred, 5- Tens and 4- Ones
and, take the decimal 2.369 where the place values are
3- Tenth, 6- hundredth and 9- thousandth
So, both decimal and whole number have similar concept of place value but one is multiplied by 10 and other is divided by 10.
Learn more about Place value here:
https://brainly.com/question/27734142
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f(1)=0
f(n)=f(n−1)+2
Answer: f(n) = 2n - 2
Therefore, we can use this formula to find the value of f(n) for any positive integer n.
Step-by-step explanation: Using the given recursive formula:
f(1) = 0
f(n) = f(n-1) + 2
We can find the values of f(n) for different values of n:
f(1) = 0
f(2) = f(1) + 2 = 0 + 2 = 2
f(3) = f(2) + 2 = 2 + 2 = 4
f(4) = f(3) + 2 = 4 + 2 = 6
f(5) = f(4) + 2 = 6 + 2 = 8
And so on.
We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:
f(n) = 2n - 2
Therefore, we can use this formula to find the value of f(n) for any positive integer n.
I need help with his question it’s not 156 that’s all I know
Answer: B. 78
Step-by-step explanation:
Given:
BC=CD
all the other sides of each triangle are radii, so they are all equal the 2 triangles are congruent.
>Both angles A =78
An angle from the radius is the same as the arc angle it creates.
The arc angle is double only if the angle touches the end of the circle not the radius. that's why it's not 156
So, <BAC =78 so arc angle BC=78