The probability that the sample proportion of households spending more than $125 a week is less than 0.27 is approximately 0.35.
To find the probability that the sample proportion of households spending more than $125 a week is less than 0.27, we can use the sampling distribution of sample proportions and the Central Limit Theorem.
Given:
Population proportion (p) = 0.28
Sample size (n) = 273
First, we need to calculate the standard deviation of the sampling distribution, which is known as the standard error. The formula for the standard error is:
Standard Error = sqrt((p * (1 - p)) / n)
Substituting the given values:
Standard Error = sqrt((0.28 * (1 - 0.28)) / 273)
Standard Error ≈ 0.0258
Next, we can standardize the sample proportion using the formula:
Z = (sample proportion - population proportion) / standard error
Z = (0.27 - 0.28) / 0.0258
Z ≈ -0.3886
Now, we need to find the probability that the sample proportion is less than 0.27. This is equivalent to finding the area under the standard normal distribution curve to the left of Z = -0.3886. We can use a standard normal distribution table or a statistical software to find this probability.
The probability can be rounded to 4 decimal places:
Probability = 0.35 (approximately)
Therefore, the probability that the sample proportion of households spending more than $125 a week is less than 0.27 is approximately 0.35.
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The table below gives the percent of children under five considered to be underweight.
Percent of Underweight Children Number of Countries
16–21.45 23
21.45–26.9 3
26.9–32.35 9
32.35–37.8 6
37.8–43.25 6
43.25–48.7 2
What is the best estimate for the mean percentage of underweight children? (Round your answer to two decimal places.)
The required answer is: 9.61
Rounding the answer to two decimal places gives the best estimate for the mean percentage of underweight children as 9.61%.
To find the best estimate for the mean percentage of underweight children,
we need to calculate the midpoint of each interval and multiply it by the number of countries in that interval, then add the products and divide by the total number of countries.Below is the table that shows the midpoint of each interval and the corresponding calculations.
MidpointNumber of CountriesProducts16.73 (16 + 21.45) / 22383.29 (21.45 + 26.9) / 33253.13 (26.9 + 32.35) / 97194.08 (32.35 + 37.8) / 61411.025 (37.8 + 43.25) / 6 246.3 (43.25 + 48.7) / 2.
Total471Calculating the average of the above data giv
es:\[\frac{471}{23 + 3 + 9 + 6 + 6 + 2} = 471 / 49 = 9.6122\].
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A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 42 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 6000 aspirin tablets actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
a. The probability that this whole shipment will be accepted is ??.
b. The company will accept ??% of the shipments and will reject ??% of the shipments, ??.
Answer:
a. The probability that this whole shipment will be accepted is the probability that none or only one of the 42 randomly selected tablets is defective.
b. The company will accept approximately 36.8% of the shipments and will reject approximately 63.2% of the shipments, so many shipments will be rejected.
Step-by-step explanation:
it costs $80.50 to buy 7 skirts. how much does it cost to by 10 skirts?
Answer:
To get the price of 1 each
$80.50÷7=
$11.50
To get the price of 10
$11.50×10
=$115
Find the sum of the following finite geometric series.
The sum of the geometric sequence in this problem is given as follows:
5.77.
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.
The first term, the common ratio and the number of terms for this problem are given as follows:
[tex]a_1 = 10, q = -\frac{2}{3}, k = 8[/tex]
The formula for the sum of the first n terms is given as follows:
[tex]S_n = a_1\frac{1 - r^n}{1 - r}[/tex]
Hence the sum for this problem is given as follows:
[tex]S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}[/tex]
[tex]S_8 = 5.77[/tex]
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Which equation represents the line that is perpendicular to y=4/5x + 23 and passes through (-40,20)?
Answer:
y = [tex]\frac{-5}{4}[/tex]x - 30
Step-by-step explanation:
we will use the x = -40 and the y = 20 from the point given (-40,20). The perpendicular slope would be the opposite reciprocal from the slope given. The slope given is 4/5. The reciprocal is 5/4 and the opposite would be -5/4
y = mx + b Plug in what we know and solve for b
20 = [tex]\frac{-5}{4}[/tex] ( -40) + b
20 = [tex]\frac{-5}{4}[/tex] ·[tex]\frac{-40}{1}[/tex] + b
20 = [tex]\frac{200}{4}[/tex] + b
20 = 50 + b Subtract 50 from both sides
20 - 50 = 50 - 50 + b
-30 = b
To write the equation we need the slope (m) ([tex]\frac{-5}{4}[/tex]) and the y-intercept (b) (-30)
y = mx + b
y = [tex]\frac{-5}{4}[/tex]x - 30
Helping in the name of Jesus.
[tex]x - \dfrac{x-1}{2} = 1 - \dfrac{x-2}{3}[/tex]Solve
No spamming
Don't ignore my questions
[tex]\begin{gathered} \; \color{pink}{\frak{\qquad \: x - \dfrac{x - 1}{2} = 1 - \dfrac{x - 2}{3}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{(2 \times x) - x - 1}{2} = \dfrac{(3 \times 1) - x - 2}{3}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{2x - x - 1}{2} = \dfrac{3 - x - 2}{3}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{x - 1}{2} = \dfrac{1 - x}{3}}} \\ \end{gathered}[/tex]
Cross Multiplying,,
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3(x - 1) = 2(1 - x)}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x - 3 = 2 - 2x}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x + 2x = 2 + 3}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{5x = 5}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{x = \dfrac{\cancel{ \: 5}}{\cancel{ \: 5}}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{cyan}{\hookrightarrow \: \underline{\boxed{\frak{x = 1}}}} \: \pmb{\bigstar} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \qquad{\qquad{\pmb{━━━━━ღ◆ღ━━━━━}}} \end{gathered}[/tex]
Find the value of Y using the given diagram below
Answer:
i dont know
Step-by-step explanation:
give proper diagram please
I need all the roots of the graph
Answer:
It looks to be -4, -2, 1, and 3
A living room is two times as long and one and one-half times as wide as a bedroom. The amount of carpet needed for the living room is how many times greater than the amount of carpet needed for the bedroom?
The amount of carpet needed for the living room is three times greater than the amount of carpet needed for the bedroom.
To calculate the amount of carpet needed for each room, we need to consider the dimensions of the rooms. Let's assume the length of the bedroom is x units.
Since the living room is two times as long as the bedroom, its length will be 2x units.
Similarly, the width of the living room is one and a half times as wide as the bedroom. So, the width of the living room will be 1.5x units.
To find the area of each room, we multiply the length by the width.
The area of the bedroom is x units * x units = x^2 square units.
The area of the living room is 2x units * 1.5x units = 3x^2 square units.
The amount of carpet needed is directly proportional to the area of the room. Therefore, the amount of carpet needed for the living room is 3x^2 square units, while the amount needed for the bedroom is x^2 square units.
To find the difference, we divide the area of the living room by the area of the bedroom: 3x^2 / x^2 = 3.
Thus, the amount of carpet needed for the living room is three times greater than the amount needed for the bedroom.
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Write each fraction in terms of the LCD.
X-2
x2
X + 3x - 28
X
x + 9x + 14
Answer:
a) [tex]\frac{x^2-4}{(x + 7)(x - 4)(x+2)}[/tex]
b)[tex]\frac{x^2-4x}{(x + 7)(x + 2)(x-4)}[/tex]
Step-by-step explanation:
x² + 3x - 28
= x² + 7x - 4x -28
= x(x + 7) - 4(x + 7)
=
= x² + 7x + 2x + 14
= x(x + 7) + 2(x + 7)
= (x + 7)(x + 2)
LCM of x² + 3x - 28 and x² + 9x + 14 is
(x + 7)(x - 4)(x + 2)
We can write:
[tex]\frac{x-2}{x^2 + 3x - 28}\\ \\= \frac{x-2}{(x + 7)(x - 4)}\\\\= \frac{x-2}{(x + 7)(x - 4)} *\frac{x+2}{x+2} \\\\=\frac{(x-2)(x+2)}{(x + 7)(x - 4)(x+2)} \\\\=\frac{x^2-2^2}{(x + 7)(x - 4)(x+2)} \\\\=\frac{x^2-4}{(x + 7)(x - 4)(x+2)}[/tex]
and
[tex]\frac{x}{x^2 + 9x + 14 }\\ \\= \frac{x}{(x + 7)(x + 2)}\\\\= \frac{x}{(x + 7)(x + 2)} *\frac{x-4}{x-4} \\\\= \frac{x(x-4)}{(x + 7)(x + 2)(x-4)} \\\\= \frac{x^2-4x}{(x + 7)(x + 2)(x-4)}[/tex]
Select the correct answer.
Answer:
A
Step-by-step explanation:
the x- axis is a horizontal line. A line perpendicular to it will be a vertical line, parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the only equation fitting this description from the list is
x = 3
Suppose you got 95% of the questions on your last test correct. If there were 140 equally weighted questions on the test, what was your ratio of correct to incorrect answers on the test? Write your answer in lowest terms.
Answer:
Step-by-step explanation:
To find the ratio of correct to incorrect answers on the test, we need to determine the number of correct and incorrect answers.
If you got 95% of the questions correct, it means you got 95% of 140 questions correct.
Number of correct answers = 95% of 140 = (95/100) * 140 = 133
To find the number of incorrect answers, subtract the number of correct answers from the total number of questions:
Number of incorrect answers = Total number of questions - Number of correct answers = 140 - 133 = 7
Therefore, the ratio of correct to incorrect answers on the test is 133:7, which is already in its lowest terms and cannot be simplified further.
Final result:
Of the 140 questions, you properly answered 133 of them, while 7 of them were incorrect. You have a 133:7 chance of winning because you provided the right answers.
Explanation:
We need to know how many questions were correctly and wrongly answered before we can fix this issue. You correctly answered 140 out of 140 questions, or 95 percent of them, giving you a total of 133 valid answers.
Thus, 133 correct answers out of 140 total questions equals 7 incorrect answers. As a result, the ratio of correct to incorrect answers is already very low at 133:7.
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Simplify three fifths times the quantity 1 plus the square root of 16 end quantity squared minus the quantity five minus two end quantity cubed.
PLS HURRRYYYY
Answer:
-12
Step-by-step explanation:
3/5 * (1 + sqrt(16))^2 - (5 - 2)^3 =
= 3/5 * (1 + 4)^2 - (3)^3
= 3/5 * (5)^2 - 27
= 3/5 * 25 - 27
= 15 - 27
= -12
Solve the problem bellow and reduce to lowest terms:
Find 4/7 of 1/8
A: 4/8
B: 4/56
C: 4/7
D: 1/14
Pls I need your help
Answer: D
Step-by-step explanation:
we will multiply
4/7* 1/8
we will get 1/14
Answer:
Step-by-step explanation:
After reducing 4/7 of 1/8 to the lowest terms we get 1/14. Thus, option C is the answer.
For reducing a number to its lowest terms, first, we need to simplify the numbers to a more significant number, i.e. 4/7 of 1/8 means 4/7*1/8=4/56.
Now we know that 56 is a multiple of 4 when multiplied by 14. Hence, when we get it in the lowest term we would get 1/14
2
1
-1
-2
Determine the period.
2 4
6 8 10 12 14
Acellus
According to the information we can infer that the period of the graph is 8.
How to determine the period of the graph?To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.
In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.
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Determine the period.
MAY
4 8 12 16
20 24 28
SAMLAYA
3
2
-1
-2
-3
-4
-5
Enter
The period of oscillation of the wave is 8 seconds
What is period of oscillation ?The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle.
Period is measured in seconds and it is the inverse of frequency of the oscillation. This means that T = 1/f
where f is the frequency and T is the period.
An oscillation can also be called cycle or Revolution or vibration.
From the graph, the oscillating wave made a complete oscillation at 8 seconds.
Therefore the period of oscillation of the wave is 8 seconds.
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Which expression correctly represents “three less than the product of a number and two, increased by five”?
2 n minus 3 + 5
Answer:
(2n - 3) + 5 is a correct expression.
Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences. Graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one. The graphs intersect at the point 0 comma 2.
By finding the point where the graphs intercept, we will see that the solution of the system of equations is the point (0, 2).
How to find the solutions of a system of equations graphically?The solutions of a system of equations are the points where the graphs of the different equations intercept when graphed.
Below you can see the graph of the system:
[tex]g(\text{x}) = 3x + 2 \ \ \ \ \text{(green)}[/tex] [tex]f(\text{x}) = |\text{x} - 1| + 1 \ \ \ \ \text{(blue)}[/tex]There you can see that we have only one intersection point at x = 0, y = 2, then we can conclude that our system has only one solution, and the solution is the point (0, 2).
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Find f′(x)
1. f(x) = x + 2
2. f(x) =2/x2
f'(x) = 0 * x^(-2) + (-2/x^3) = -2/x^3.
So, the derivative of f(x) = 2/x^2 is f'(x) = -2/x^3.
To find f'(x) for the function f(x) = x + 2, we can use the power rule for derivatives.
The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).
In this case, the function f(x) = x + 2 can be written as f(x) = x^1 + 2.
Applying the power rule, we differentiate each term separately:
f'(x) = d/dx (x^1) + d/dx (2)
The derivative of x^1 is 1x^(1-1) = 1x^0 = 1.
The derivative of a constant term like 2 is 0, as the derivative of a constant is always 0.
Therefore, f'(x) = 1 + 0 = 1.
So, the derivative of f(x) = x + 2 is f'(x) = 1.
To find f'(x) for the function f(x) = 2/x^2, we can use the power rule and the constant multiple rule.
The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).
The constant multiple rule states that if we have a function of the form f(x) = cg(x), where c is a constant, then the derivative is given by f'(x) = cg'(x), where g'(x) is the derivative of g(x).
In this case, the function f(x) = 2/x^2 can be written as f(x) = 2 * x^(-2).
Applying the power rule and the constant multiple rule, we differentiate each term separately:
f'(x) = d/dx (2 * x^(-2))
Applying the constant multiple rule, the derivative of 2 is 0, as it is a constant term.
Applying the power rule, the derivative of x^(-2) is (-2) * x^(-2-1) = (-2) * x^(-3) = -2/x^3.
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you are sent to the local tea shop to pick up 9 drinks. You purchase 3 sweet teas and 6 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.
The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21
The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:
Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84
Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14
Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28
Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21
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F i n d space t h e space n u m e r i c a l space v a l u e space o f space
left parenthesis 3 cross times 4 plus 4 ² plus 15 minus 4 right parenthesis cross times 2 plus open parentheses 4.5 plus 5 over 10 close parentheses
Answer:the space is 7 in the text below
Step-by-step explanation:
Please Solve, Thank you!
Answer:
1711
Step-by-step explanation:
[tex]4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711[/tex]
Make sure to follow order of operations!
n quadrilateral ABCD, AD ∥ BC. Quadrilateral A B C D is shown. Sides A D and B C are parallel. The length of A D is 3 x + 7 and the length of B C is 5 x minus 9. What must the length of segment AD be for the quadrilateral to be a parallelogram? 8 units 16 units 31 units 62 units
Answer:
(c) 31 units
Step-by-step explanation:
Given quadrilateral ABCD has AD║BC, with AD=3x+7 and BC=5x-9, you want to know the length of AD for the quadrilateral to be a parallelogram.
Congruent sidesOpposite sides of a parallelogram are congruent, so for ABCD to be a parallelogram, we must have ...
BC = AD
5x -9 = 3x +7
2x = 16
x = 8
AD = 3x +7 = 3(8) +7 = 31
The length of AD must be 31 units if ABCD is to be a parallelogram.
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f(g(x)) g(f(x)) ANSWER QUESTION BELOW BRIEF RESPONSE
Given statement solution is :- "F(g(x)) g(f(x))": The function F(x) is composed with g(x), and the result is further composed with g(f(x)).
"f(g(x)) g(f(x))": The function g(x) is composed with f(x), and the result is further composed with g(f(x)).
The expressions "F(g(x)) g(f(x))" and "f(g(x)) g(f(x))" are compositions of functions. The answer to the question posed would depend on the specific functions F(x) and g(x), as well as f(x) and g(x) in the second expression.
To provide a brief response:
For the expression "F(g(x)) g(f(x))": The function F(x) is composed with g(x), and the result is further composed with g(f(x)). The order of composition is F(g(x)) first, followed by g(f(x)).
For the expression "f(g(x)) g(f(x))": The function g(x) is composed with f(x), and the result is further composed with g(f(x)). The order of composition is f(g(x)) first, followed by g(f(x)).
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The diameter of a circle is 3 miles. What is the area?
Answer:
Area = 7.065 square miles
Step-by-step explanation:
The diameter of a circle is the distance across the circle passing through its centre, and it is equal to twice the radius. Therefore, if the diameter of a circle is 3 miles, then the radius is 1.5 miles.
The formula for the area of a circle is [tex]A = \pi r^2[/tex] ([tex]A = \pi \times r^{2}[/tex])
[tex]A[/tex] is the area [tex]r[/tex] is the radius. The value of pi ([tex]\pi[/tex]) is approximately 3.14, so we will use that value.Substituting the value of the radius into this formula, we get:
[tex]A = 3.14 \times 1.5^2[/tex][tex]A = 3.14 \times 2.25[/tex][tex]A = 7.065[/tex]Therefore, the area of the circle is approximately 7.065 square miles.
________________________________________________________
The answer is:
A = 7.069 miles²
Work/explanation:
We have the diameter, but we need to find the radius. We can do that by diving the diameter by 2:
radius = diameter ÷ 2 = 3 ÷ 2 = 1.5 miles
Now we move on to the next step - the formula.
The formula is:
[tex]\sf{A=\pi r^2}[/tex]
where:
A = areaπ = pir = radiusdiagram
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\small 1.5\ miles}\end{picture}[/tex]
Plug in the data
[tex]\sf{A=\pi \times 1.5^2}[/tex]
[tex]\sf{A=\pi\times2.25}[/tex]
[tex]\sf{A=7.069~miles^2}[/tex]
Hence, this is the areawrite equation line passing through (3,7) (-5,-1)
Answer:
Step-by-step explanation:
First find the slope using m = (y2-y1)/(x2-x1)
m = (-1-7)/(-5-3)
= -8/-8
= 1
y = mx + b
find the y-intercept
use 1 of the 2 points
Let's try (3,7)
7 = 1(3) + b
b = 4
Equation of the line is y = x + 4
The equation is:
y = x + 4Work/explanation:
First, we will use the slope formula and determine the slope:
[tex]\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where m = slope.
Plug in the data
[tex]\sf{m=\dfrac{-1-7}{-5-3}}\\\\\\\sf{m=\dfrac{-8}{-8}}\\\\\\\sf{m=1}[/tex]
The slope is 1; the equation so far is y = 1x + b or y = x + b.
Plug in the point:
[tex]\sf{7=3+b}[/tex]
[tex]\sf{3+b=7}[/tex]
Solve for b
[tex]\sf{b+3=7}[/tex]
[tex]\sf{b=4}[/tex]
So the y-intercept is 4; we plug that in and see that the equation is y = x + 4.
Hence, the equation is y = x + 4.Please help me. i need urgent help
Answer:
Step-by-step explanation:
I think there is a typo in the question
Qn : let p(n) be [tex]\sum\limits^n_{i = 1}{i2^i} = 2 + (n-1)2^{n+1} \;\;\;\;\;\;:n\geq 1[/tex]
When n = 1:
LHS: 1(2¹) = 2
RHS: 2 + (1 - 1)(2¹ ⁺ ¹) = 2
LHS = RHS
⇒ p(n) holds for n = 1
Let us assume that the proof holds for p(n): n = x
ie.
[tex]p(x): \sum\limits^x_{i = 1}{i2^i} = 2 + (x-1)2^{x+1}[/tex]
To prove that the proof holds for n = x+1
ie [tex]p(x+1): \sum\limits^{x+1}_{i = 1}{i2^i} = 2 + (x)2^{x+2}[/tex]
Consider LHS
[tex]\sum\limits^{x+1}_{i = 1}{i2^i}\\\\= \sum\limits^{x}_{i = 1}{i2^i}+\sum\limits^{x+1}_{i = x+1}{i2^i}\\\\= p(x) + (x+1)2^{x+1}\\\\= 2 + (x-1)2^{x+1} + (x+1)2^{x+1}\\\\= 2 + 2^{x+1} (x-1 + x+1)\\\\= 2 + 2^{x+1} (2x)\\\\= 2 + (x)2^{x+2}\\\\= RHS[/tex]
Pamela is 3 times older than Jakob. In 10 years from now, Pamela’s age will be twice as Jakob’s age.
How old is Pamela?
Answer:
Pamela is 30 years old.
Step-by-step explanation:
We can find Pamela's age using a system of equations where P represents Pamela's age and J represents Jakob's.First equation:
Since Pamela is 3 times older than Jakob, our first equation is given by:
P = 3J
Second Equation:
Since Pamela will be twice as old as Jakob in 10 years, our second equation is given by:
P = 2J + 10
Method to solve: Substitution:
We can solve with substitution by isolating J in the second equation. This will allow us to substitute it for J in the second equation and find P, Pamela's age:
Isolating J:
Step 1: Divide both sides by 3
(P = 3J) / 3
P/3 = J
Substituting P/3 = J for J in P = 2J + 10:
P = 2(P/3) + 10
Step 1: Distribute the 2 to P/3:
P = 2/3P + 10
Step 2: Multiply both sides by 3 to clear the fraction:
(P = 2/3P + 10) * 3
3P = 2P + 30
Step 3: Subtract 2P from both sides:
(3P = 2P + 30) - 2P
P = 30
Step 4: Divide both sides by 2 to find P, Pamela's age:
(2P = 30) / 2
P = 30
Thus, Pamela is 30 years old.
Optional Steps to check the validity of our answer:
In order to check that our answers for Pamela's age is correct, we will first need to find Jakob's age by plugging in 30 for P in any of the two equations in our system. Let's use the first one:Plugging in 30 for P in P = 3J:
Step 1: Divide both sides by 3:
(30 = 3J) / 3
10 = J
Thus, Jakob is 10 years old.
Checking the validity of answers with verbal statements:
Since 30 (i.e., Pamela's age) is indeed 3 times 10 (i.e., Jakob's age), this satisfies the first statement.
In 10 years, Pamela will be 40 as 30 + 10 = 40.
In 10 years, Jacob will be 20 as 10 + 10 = 20.
Since 40 (i.e., Pamela's age in 10 years) is indeed twice 20 (i.e., Jakob's age in 10 years), this satisfies the second statement.
Thus, our answer for Pamela's age is correct.
what is (45 )(4−3 ) =
Answer:
45
Step-by-step explanation:
Do the operation in parentheses first.
(45)(4 - 3) = (45)(1) = 45
Answer:
Step-by-step explanation:
The answer is 45.
Given,
[tex](45)(4-3)\\=(45)(1)\\=45[/tex]Using subtraction and multiplication rule.
To learn more subtraction and multiplication:
https://brainly.com/question/723406
https://brainly.ph/question/4542362
What are the domain and range of the inequality y <= sqrt(x - 1) - 4 ?
Answer:To determine the range is the same as to determine which numbers appear as the second number (the y-value) in an ordered pair that is part of the graph. Here are some examples: y ≥ x2 + 3. graph {y >= x^2+3 [-11.6, 13.72, 0.15, 12.81]} Although it is not 100% certain from just the graph, this graph does get wider and wider.
Step-by-step explanation:
