Answer:
Approximate solution of the system is:
B. (5/2, -13/4)
Step-by-step explanation:
To approximate the solution of the given system of equations using the graph, we need to find the point where the two lines intersect. Let's analyze the equations and the graph to determine the approximate solution.
The given system of equations is:
-2x + 5y = 19 ...(1)
y = (-5/6)x - (1/6) ...(2)
Looking at equation (2), we can see that it represents a diagonal line with a negative slope, passing through the points (-5, 1) and (6, 6).
Now let's plot this line on the graph:
|
6 | x
|
| x
5 | x
|
| x
4 |
|
3 |
|
2 |
|
1 | x
|
0 |____________________
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
The line rises from (-5, 1) to (6, 6).
Next, let's analyze equation (1), which can be rearranged as:
5y = 2x + 19
y = (2/5)x + (19/5)
Comparing equation (1) with equation (2), we can see that the slope of the line in equation (1) is positive, and it intersects the other line at a point. Therefore, we are looking for the point where the rising diagonal line intersects the line with a positive slope.
By visually examining the graph, we can approximate the intersection point to be around (5/2, -13/4).
Hence, the approximate solution of the system is:
B. (5/2, -13/4)
Select the number property that will justify the following expression.
If cba represents three numbers multiplied together, what property allows you to rearrange the factors to read abc?
Answer: The Commutative law. It states a * b = b * a.
So, cba is the same as abc.
Step-by-step explanation:
Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba. From these laws it follows that any finite sum or product is unaltered by reordering its terms or factors.
Answer and Explanation:
The number property that allows the re-ordering of multiplication:
[tex]c\cdot b \cdot a[/tex] to [tex]a\cdot b\cdot c[/tex]
is the Commutative Property of Multiplication.
This property states that [tex]A\cdot B = B\cdot A[/tex].
We can test this property by plugging in numbers for A and B.
For example, if [tex]A = 2[/tex] and [tex]B=3[/tex]:
[tex]A\cdot B = 2 \cdot 3[/tex]
[tex]\implies \text{ this is an array of 2 rows and 3 columns:}\\\\\text{ } \ \ \ \ \ \ \begin{array}{c c c} \square \ \ \square\ \ \square \\ \square \ \ \square\ \ \square \end{array} \\ \\ \text{ } \ \ \ \ \ \ \implies 6 \text{ items}[/tex]
__________________________________
[tex]B\cdot A = 3 \cdot 2[/tex]
[tex]\implies \text{ this is an array of 3 rows and 2 columns:}\\\\\text{ } \ \ \ \ \ \ \begin{array}{c c c} \square\ \ \square \\ \square\ \ \square \\ \square \ \ \square \end{array} \\ \\ \text{ } \ \ \ \ \ \ \implies 6 \text{ items}[/tex]
__________________________________
From this example, we can figure out that:
[tex]A \cdot B = B \cdot A = 6[/tex]
Which transformations could have occurred to map ДВС to AA'B"C"? O a rotation and a dilation O a rotation and a reflection O a reflection and a dilation O a translation and a dilation
A reflection and a dilation occurred to map △ABC to △A"B"C" (option C)
What is reflection and dilation transformation?Geometry is all about understanding shapes and their various attributes, whether its symmetry, area, volume, or something else entirely. Two common operations that can significantly alter our perception of shapes are reflections and dilations.
A reflection involves transforming a shape by flipping it over an imaginary "mirror" - called the line of reflection - while preserving certain key features such as distance between points on either side of this mirror axis.
Alternatively dilation allows us to increase or decrease the size of shapes based on some scaling factor; this can also affect other key attributes like perimeter or surface area.
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Somebody please help me with this I literally cannot understand piece wise functions and does anybody know any sites that can help or do piecewise functions?
Step-by-step explanation:
It is looking for the value of the function when x is equal to 4
f(4)
FOUR is GREATER than 1 so you use the bottom portion of the function definition : -x +2 when x is equal to 4 this is equal to -2
so f(4) = -2
If the demand equation is
Q + 4 P = 60
fi nd a general expression for the price elasticity of demand in terms of P . For what value
of P is demand unit elastic?
The general expression for the price elasticity of demand in terms of P is E = - (P / (15 - P)).
The value of P that makes the demand to be unit elastic would be 7.5.
Price elasticity of demandThe price elasticity of demand is given by the formula:
E = (%ΔQ / %ΔP) * (P/Q)
We can solve the demand equation for Q in terms of P as:
Q = 60 - 4P
Taking the derivative of Q with respect to P, we get:
dQ/dP = -4
We can now express the percentage change in Q as a function of the percentage change in P:
%ΔQ / %ΔP = (ΔQ / Q) / (ΔP / P) = (-4P/Q) / (P/Q) = -4
Substituting this expression into the formula for price elasticity of demand, we get:
E = (%ΔQ / %ΔP) * (P/Q) = -4 * (P / (60 - 4P))E = - (P / (15 - P))To find the value of P for which demand is unit elastic, we need to set the absolute value of the price elasticity of demand equal to 1. So we have:
|E| = 1(P / (15 - P)) = 1P = 7.5In other words, the value of P for which demand is unit elastic is 7.5.
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30. Which of these sentences uses active voice?
The winning homerun was hit by the worst player on the baseball
team.
My friend invited his whole class to Saturday's soccer championship.
The children were taken to the circus by their doting grandfather.
At noon, some cookies were going to be baked by the baker.
The option that represents the active voice is:
B: My friend invited his whole class to Saturday's soccer championship.
What is the difference between active and passive voice?The active voice is one that asserts that the person or thing represented by the grammatical subject performs the action represented by the verb. The passive voice is one that makes the subject the person or thing acted on or affected by the action represented by the verb.
Looking at the given options and applying the definitions above, we can see that options A, C and D are passive voice because the subject is the recipient of the action.
Thus, the statement "My friend invited his whole class to Saturday's soccer championship." represents the active voice.
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PLS HELP ME ASAP
FOR THE THIRD PICTURE, I JUST NEED THAT ANSWER FOR THE SECOND ONE
The following bar chart shows the distances run by Jay's family in a race.
Find the median distance in km.
The median of the distances is M = 6.5 kilometers
Given data ,
To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
Arranging the given set of numbers in ascending order: {4, 5, 8, 11}
Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:
(5 + 8) / 2 = 13 / 2 = 6.5
Hence , the median of the given set {4, 5, 8, 11} is 6.5
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Find x for the image attached
Answer:
x = 72 degrees
Step-by-step explanation:
By the Vertical Angles Theorem, the angle opposite the angle (let's call it angle z, the red text in the image I sent) with 108 degrees is also equal to 108 degrees.
By the Linear Pair Theorem, angle z degrees + angle x degrees = 180 degrees.
108 + x = 180, x = 72 degrees
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of pi (no approximations).
The area of the shaded regions is [tex]\sf 13\frac{1}{3}\pi[/tex] square cm.
What is area of a circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, [tex]\sf A=\pi r^2[/tex], where r is the radius of the circle. The unit of area is the square unit, such as square meter, square centimeter, etc.
We have
Inner circle radius = 3cmOuter circle radius = 4 + 3 cm = 7cmFormula to find the area of circle[tex]\sf A=\pi r^2[/tex]Area of inner circle
[tex]\sf A=\pi \times3^2[/tex]
[tex]\sf \rightarrow A=9\pi[/tex]
Since, 120° is [tex]\sf \frac{1}{3}[/tex] of 360°
Thus, it means the shaded area of the figure is of [tex]\sf \frac{1}{3}[/tex] of the circle.
[tex]\sf \therefore A = \frac{9\pi }{3}[/tex]
[tex]\sf \rightarrow A = 3\pi \ square \ cm[/tex]
Area of outer circle
[tex]\sf A=\pi \times7^2[/tex]
[tex]\sf \rightarrow A=49\pi[/tex]
Since, it means the shaded area of the figure is of [tex]\sf \frac{1}{3}[/tex] of the circle.
[tex]\sf \therefore A = \frac{49\pi }{3} \ square \ cm[/tex]
Area of the shaded regions = Area of outer circle - Area of inner circle
[tex]\sf A = \dfrac{49\pi }{3} -3\pi[/tex]
[tex]\sf \rightarrow A = \dfrac{49\pi -9\pi }{3}[/tex]
[tex]\sf \rightarrow A = \dfrac{40\pi }{3}[/tex]
[tex]\sf \rightarrow A = 13\dfrac{1}{3}\pi \ square \ cm[/tex]
Hence, The area of the shaded regions is [tex]\sf 13\frac{1}{3}\pi[/tex] square cm.
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Find the area of the figure. Type your answer as just a number, without units.
The total area of the composite figure is 704 sq cm
Calculating the area of the figureFrom the question, we have the following parameters that can be used in our computation:
The composite figure
The total area of the composite figure is the sum of the areas of the individual shapes
So, we have
Area = Area of Square + Area of Triangle
Using the above as a guide, we have the following equation
Area = 22 * 22 + 1/2 * 22 * (42 - 22)
Evaluate the products
Area = 484 + 220
Evaluate the sum
Area = 704
Hence. the total area of the figure is 704 sq cm
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A stock lost 7 1/8 points on Monday and then another 1 7/8
points on Tuesday. On Wednesday, it gained 13 points. What was the net gain or loss of the stock for these three days?
•a gain of 4 points
•a gain of 7 3/4 points
•a gain of 18 1/4 points
•a loss of 22 points
The net gain of 4 points for these three days.
To find the net gain or loss of the stock for these three days, we need to add up the changes in value for each day.
On Monday,
the stock lost 7 1/8 points. This is the same as -7 1/8.
On Tuesday,
the stock lost another 1 7/8 points. This is the same as -1 7/8.
So the total change in value for Monday and Tuesday is:
= -7 1/8 - 1 7/8
= -9
On Wednesday,
the stock gained 13 points. This is the same as +13.
So the net change in value for the three days is:
= -9 + 13 = +4
Therefore, the net gain of 4 points for these three days.
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I’m am really confused on this question
Answer:
2x^7
Step-by-step explanation:
add the exponents because they both are x
2x^4*x^3=2x^7
Find a linear function h, given h(7)=-27 and h(-4)=28. Then find h(5)?
The linear function h(x) is given by h(x) = -5x + 8.
The value of h(5) is -17.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (28 + 27)/(-4 - 7)
Slope (m) = 55/-11
Slope (m) = -5.
At data point (7, -27) and a slope of -5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-27) = -5(x - 7)
y = -5x + 35 - 27
y = h(x) = -5x + 8
h(5) = -5(5) + 8
h(5) = -25 + 8 = -17
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calculate the geometric average return for the returns in the following table:
The geometric average return for the returns in the table is 20.284
Geometric Average returnMultiply all the returns together and take the nth root, n = number of returns
The geometric average return for the given returns:
Return 1 = 10.25
Return 2 = 37.80
Return 3 = 45.07
Return 4 = 8.10
Return 5 = 20.16
Geometric average return =
[tex]( {(Return 1 * Return 2 * Return 3 * Return 4 * Return 5)}^{ \frac{1}{5} } [/tex]
Geometric average return =
[tex]( {10.25 * 37.80 * 45.07 * 8.10 * 20.16})^{0.2} [/tex]
Geometric average return = 19.6
Therefore, the geometric average return for the returns given is approximately 19.6
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.
Average Rate of Change Function Comparison
The option that represents the ordering of the functions according to their average rates of change on the interval -1<=x<=1 goes least to greatest is f(x), h(x), g(x). Therefore, option A is the correct answer.
From the given graph, zeros are x=-3 and x=7.
(x+3)=0 and (x-7)=0
So, the equation is (x+3)(x-7)=0
x(x-7)+3(x-7)=0
x²-7x+3x-21=0
x²-4x-21=0
So, f(x)=x²-4x-21
From the table, the coordinates (-2, 27) and (-1, 18), we get
Slope(m) = (27-18)/(-1+2)
m=9
Substitute m=9 and (x, y)=(-2, 27) in y=mx+c, we get
27=9(-2)+c
c=27+18
c=45
So, the equation is g(x)=9x+45
Given that, h(x)=-x²+x+49
Therefore, option A is the correct answer.
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The weights of bags of chips are normally distributed with a mean of 180 grams and a standard deviation of 4 grams.
What percent of the bags of chips weigh less than 176 grams?
2.5%
16%
32%
34%
The percent of the bags of chips weigh less than 176 grams is b 16%
What percent of the bags of chips weigh less than 176 grams?From the question, we have the following parameters that can be used in our computation:
Mean = 180
Standard deviation = 4
Bags of chips weigh less than 176 grams
This means that
x = 176
So, the z-score is
z = (176 - 180)/4
Evaluate
z = -1
The percent of the bags of chips weigh less than 176 grams is represented as
P = P(z < -1)
Using a graphing calculator, we have
Percentage = 0.15866
So, we have
Percentage = 16%
Hence , the percentage is 16%
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Last month, sales were £180 000.
This month, sales reached £196 200.
What percentage increase is this?
The percentage of increase in sales from last month to this month is 9%.
Given,
Sales for last month = £180 000.
Sales for this month = £196 200.
To calculate the percentage increase, we must first find the difference in sales between the two months:-
Difference between the two months = £180,000 - £196,200 = £16,200
Percentage of this difference = (16,200 ÷ 180,000) * 100 = 9
Thus, the percentage of increase is 9% from the last month to this month.
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Savings account A and savings account B both offer APRS of 2%, but savings
account A compounds interest quarterly, while savings account B
compounds interest annually. Which savings account offers the higher APY?
A. Savings account A, because it has more compounding periods per
year
B. Savings account B, because it has fewer compounding periods per
year
C. Savings account A, because it has fewer compounding periods per
year
D. Savings account B, because it has more compounding periods per
year
Answer:
The answer is A
Step-by-step explanation:
The formula for annual percentage yield (APY) is:
APY = (1 + APR/n)^n - 1
where APR is the annual percentage rate, and n is the number of compounding periods per year.
For savings account A, APR = 2%, and it compounds interest quarterly, so n = 4. Therefore, its APY is:
APY_A = (1 + 0.02/4)^4 - 1 ≈ 0.0202 or 2.02%
For savings account B, APR = 2%, and it compounds interest annually, so n = 1. Therefore, its APY is:
APY_B = (1 + 0.02/1)^1 - 1 = 0.02 or 2%
Comparing the two APYs, we can see that savings account A has a slightly higher APY than savings account B. Therefore, the correct answer is:
A. Savings account A, because it has more compounding periods per year
Find the area of the figure. Type your answer as just a number, without units.
After considering all the given data we conclude that the area of the given figure is 80, under the condition that the given figure is a rhombus.
Let us name the rhombus as ABCD, now looking at the figure we can detect that there are two diagonals crossing each other making a point E, this allows the two diagonals to split in four smaller lines that are congruent in value
Then
Line AE = 5ft and Line ED = 5ft (because of congruency)
Line CE = 8ft and Line EB = 8ft(because of congruency)
Therefore,
Now we know that the diagonals
AD = 10ft
CB = 18 ft
The area of a rhombus can be evaluated applying the formula
Area = (d1 × d2) / 2,
Here,
d1 and d2 = lengths of the diagonals.
For this case, the diagonals are 10 ft and 16 ft.
Then, the area of the rhombus is
(10 × 16) / 2
= 80
Then, the area of the given figure is 80.
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A trough is 6 feet long and 1
foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of =6
from =−1
to =1
. The trough is full of water. Find the amount of work required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot.
Answer:375
Step-by-step explanation:
1
Draw a vertical cross-section of the trough parallel to one end. So we draw the segment of the curve y=x2
from x=−1
to x=1
.
Draw a thin horizontal strip at height y
, of thickness "dy
."
This strip will have to be lifted, as you pointed out, through a distance 1−y
.
The strip in essence has thickness dy
, and "width" 2x
, where x2=y
. If we take into account the length of the trough, the volume of the thin layer of water is (8)(2x)dy
, so has weight (62)(8)(2x)dy
, which is (62)(8)(2y√)dy
.
Lifting this through a distance 1−y
means work done is (62)(8)(2y√)(1−y)dy
.
"Add up" (integrate) from y=0
to y=1
.
The amount of work required to empty the trough by pumping the water over the top is 744 foot-pounds.
To find the amount of work required to empty the trough by pumping the water over the top, we need to calculate the weight of the water in the trough and then convert it into work using the formula:
Work (in foot-pounds) = Force (in pounds) × Distance (in feet)
First, let's calculate the volume of water in the trough. Since the cross-section of the trough is shaped like the graph of y = 6 from x = -1 to x = 1, the width of the trough is 2 feet (from -1 to 1), the length is 6 feet, and the height is 1 foot.
The volume of the trough can be calculated as follows:
Volume = Length × Width × Height
Volume = 6 feet × 2 feet × 1 foot
Volume = 12 cubic feet
Now, we need to find the weight of the water in the trough. Given that the weight of water is 62 pounds per cubic foot, we can calculate the weight as:
Weight = Volume × Weight per cubic foot
Weight = 12 cubic feet × 62 pounds/cubic foot
Weight = 744 pounds
Now, we have the weight of the water in the trough, which is 744 pounds.
To empty the trough by pumping the water over the top, we need to raise the water to a certain height. Since the trough is 1 foot high, we need to lift the water 1 foot above the trough's top.
Now, we can calculate the work required:
Work = Force × Distance
Work = 744 pounds × 1 foot
Work = 744 foot-pounds
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The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide occurs at 9:15 a.m. and high tide occurs at 3:00 p.m. What is a cosine function that models the variation in inches above and below the water level as a function of time in hours since 9:15 a.m.?
Answer:
Answer
Step-by-step explanation:
To model the variation in inches above and below the water level as a function of time in hours, we can use a cosine function.
First, we need to determine the amplitude and period of the function. The amplitude is half the difference between the high and low tides, which is (52 - 12)/2 = 20 inches. The period is the time it takes for one complete cycle, which is the time between consecutive high tides or low tides. In this case, the period is 6 hours, since high tide occurs every 6 hours.
The general form of a cosine function is:
y = A cos (Bx - C) + D
where A is the amplitude, B is the frequency (in radians per unit time), C is the phase shift (in radians), and D is the vertical shift.
Substituting the values we found, we get:
y = 20 cos ((2π/6)(x - 1.75)) + 32
where x is the time in hours since 9:15 a.m., and 1.75 is the phase shift (since high tide occurs at 3:00 p.m., which is 5 hours and 45 minutes after 9:15 a.m.). The vertical shift D is 32 inches, which is the average of the low and high tides.
Therefore, the cosine function that models the variation in inches above and below the water level as a function of time in hours since 9:15 a.m. is:
y = 20 cos ((2π/6)(x - 1.75)) + 32
the graph of a certain quadratic function has no x-intercepts. Which of the following are possible values or the disriminant?
The possible values for the discriminant include the following:
A. -1
D. -18
What is the x-intercept?In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.
Discriminant, D = b² - 4ac
In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.
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Complete Question:
The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.
A. -1
B. 3
C. 0
D. -18
Select the correct answer. What is the solution to this equation? 9^x-1=2
Answer: 1/2
Step-by-step explanation:
Construct triangle ABC, where :
AB = 8cm
angle BAC = 40°
angle ABC = 50°
Measure the length of BC
The solution is: Measure of the length of BC is: BC = 7.9 cm
Here, we have,
To construct triangle ABC:
Draw a line 6 cm long. Label one endpoint A and the other endpoint B.
Measure an angle of 96° from point A of AB in an anticlockwise direction. Draw a line.
Measure an angle of 35° from point B of AB in a clockwise direction. Draw a line.
The point of intersection of the two lines is point C of the triangle.
Measure the length of BC. BC = 7.9 cm.
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complete question:
Construct triangle ABC, in which AB = 6cm, angle BAC = 96° and angle ABC = 35°.
Measure the length of BC.
Give your answer to 1 d.p.
Wanda has $970 to invest. She deposits $370 at a 2.25% interest rate compounded annually at Bank A, and $600 at a 2.5% simple interest rate at Bank B.
If Wanda makes no additional deposits or withdrawals, which amount is closest to the combined balance of both bank accounts at the end of 3 years?
The combined balance of both bank accounts at the end of 3 years is closest to $1039.76.
To calculate the combined balance of both bank accounts after 3 years, we'll calculate the balance for each account separately and then add them together.
For Bank A, we can use the compound interest formula:
A =[tex]P(1 + r/n)^(nt)[/tex]
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, Wanda deposited $370 at a 2.25% interest rate compounded annually, so we have:
P = $370
r = 2.25% = 0.0225 (as a decimal)
n = 1 (compounded annually)
t = 3 years
Using the formula, we can calculate the balance for Bank A:
A_A = [tex]370(1 + 0.0225/1)^(1*3)[/tex]
=[tex]370(1.0225)^3[/tex]
= 370(1.0678450625)
= $394.76
For Bank B, we can use the simple interest formula:
A = P(1 + rt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount
r = annual interest rate (as a decimal)
t = number of years
In this case, Wanda deposited $600 at a 2.5% simple interest rate, so we have:
P = $600
r = 2.5% = 0.025 (as a decimal)
t = 3 years
Using the formula, we can calculate the balance for Bank B:
A_B = 600(1 + 0.025*3)
= 600(1.075)
= $645
Finally, we can calculate the combined balance of both bank accounts:
Combined Balance = A_A + A_B
= $394.76 + $645
= $1039.76
Therefore, the combined balance of both bank accounts at the end of 3 years is closest to $1039.76.
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given triangle ABC below. Side lengths of the triangle and a = 12, b = 7₁ c = 8. What
is the area of triangle (round to nearest tenth)
Answer: 28
Step-by-step explanation:
Triangle area formula is (bh)/2. Base is 7, height is 8. So those multiplied will be 56, and then divide by 2 to get 28. hope this helps!
20 POINTS TO WHOEVER ANSWERS
DHL makes deliveries of a large number of products to its customers. Suppose it is known that 85% of all the orders it receives from its customers are delivered on time. Suppose a random sample of 100 orders are selected;
A. What is the mean and standard error of the sampling distributions of sample proportions in this example?
B. What is the shape of the sampling distribution of the sample proportions?
C. What is the likelihood the sample proportion of orders delivered on time will be less than 0.87?
D. The central 68.26% of the sample proportions are between which two sample proportions?
A. The mean of the sampling distribution is 0.85 (85%), and the standard error is approximately 0.085.
B. Since the sample size is 100, we can assume that the shape of the sampling distribution of the sample proportions is approximately normal.
C. The likelihood that the sample proportion of orders delivered on time will be less than 0.87 is approximately 59.07%.
D, The central 68.26% of the sample proportions are between 0.765 and 0.935.
To calculate the mean and standard error of the sampling distribution of sample proportions, we can use the following formulas:
Mean (μ) = p
= 85%
= 0.85
Standard Error (SE) = √[(p × (1 - p)) / n]
Where p is the population proportion (0.85) and n is the sample size (100).
Calculating the standard error:
SE = √[(0.85 × (1 - 0.85)) / 100]
SE = √[(0.7225) / 100]
SE = √[0.007225]
SE ≈ 0.085
The sampling distribution of sample proportions can be approximated by a normal distribution when the sample size is sufficiently large (central limit theorem).
To find the likelihood that the sample proportion of orders delivered on time will be less than 0.87, we need to calculate the z-score and refer to the standard normal distribution table.
First, we calculate the z-score:
z = (sample proportion - population proportion) / standard error
z = (0.87 - 0.85) / 0.085
z ≈ 0.02 / 0.085
z ≈ 0.235
Next, we look up the probability associated with the z-score of 0.235 in the standard normal distribution table.
The probability corresponds to the area to the left of the z-score.
Using the table, the probability is approximately 0.5907 or 59.07%.
The central 68.26% of the sample proportions are located within one standard deviation from the mean in a normal distribution.
To find the sample proportions that correspond to the central 68.26%, we can calculate the boundaries as follows:
Lower boundary: mean - standard deviation
Lower boundary = 0.85 - 0.085
Lower boundary = 0.765
Upper boundary: mean + standard deviation
Upper boundary = 0.85 + 0.085
Upper boundary = 0.935
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Please read the picture of the problem
Teddy can make 26 ornaments with 37/53 of clay left over
How to correct the correction?You should recall that Proportion is a mathematical comparison between two numbers, denoted using the symbol "::" or "=". It is an equation in which two ratios are set equal to each other
(20/1 ÷ 3/8)
Simplifying the fraction
20/1 * 8/3
Multiplying through to have
= 80/3
The correct solution is 26.66666
Covert the decimal to a mixed fraction to get 26 37/53
Therefore Teddy can make 26 ornaments with 37/53 of clay left over
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PLEASE HELP
If f(x) = 3x² - 5√2x - 1, find the value of f(√2).
a.-5
b.-2
d. -8
c. 0
Answer:
A
Step-by-step explanation:
Let's find the value of the function f(x) for x = √2. We'll substitute x by √2 in the equation:
f(√2) = 3(√2)² - 5√2√2 - 1
First, let's simplify the terms:
(√2)² = 2 ⇒ 3(2) = 6
5√2√2 = 5*2 = 10
Now, substitute these in the equation:
f(√2) = 6 - 10 - 1
f(√2) = -4 - 1
f(√2) = -5
Thus, the value of f(√2) is -5. The correct answer is (a).
