Answer:
310cm
Step-by-step explanation:
The Total surface of cuboid is S=2(lb+bh+lh)
l=length
b=breadth b means w (width)
h=height
S=2(50+70+35)
S=2(155)
=310cm
Answer:
260 cm²
Step-by-step explanation:
Bottom surface area = 5 x 10 = 50
Surface area of the 2 long sides = 2(10 x 7) = 140
Surface area of the 2 short sides = 2(5 x 7) = 70
Total surface area = bottom + 4 sides = 50 + 140 + 70 = 260 cm²
Precision Engineering Factory consumes 12,500 units of a component in every three- month period. The ordering, receiving and handling costs are TZS 3 per order while the trucking costs are TZS 12 per order. Further details are as follows: deterioration and obsolescence cost TZS 0.04 per unit per year, interest cost, TZs 0.06 per unit per year, storage cost TZS 1,000 per year for 50.000 units, a) Calculate the total cost of matenal (ignore decimals and show working clearly).
If Precision Engineering Factory consumes 12,500 units of a component in every three- month period. the total cost of material is TZS 6,060 per year.
How to find the total cost of material?The annual demand for the material can be calculated as follows:
Annual demand = (12,500 units/3 months) x (4 quarters/year) = 50,000 units/year
Ordering cost = TZS 3 per order
Number of orders = (50,000 units/year) / (12,500 units/order) = 4 orders/year
Ordering cost per year = (4 orders/year) x (TZS 3/order) = TZS 12/year
Trucking cost = TZS 12 per order
Trucking cost per year = (4 orders/year) x (TZS 12/order) = TZS 48/year
Deterioration and obsolescence cost = TZS 0.04 per unit per year
Deterioration and obsolescence cost per year = (50,000 units/year) x (TZS 0.04/unit/year) = TZS 2,000/year
Interest cost = TZS 0.06 per unit per year
Interest cost per year = (50,000 units/year) x (TZS 0.06/unit/year) = TZS 3,000/year
Storage cost = TZS 1,000 per year for 50,000 units
Storage cost per unit per year = (TZS 1,000/year) / (50,000 units) = TZS 0.02/unit/year
Storage cost per year = (50,000 units/year) x (TZS 0.02/unit/year) = TZS 1,000/year
Total cost of material = Ordering cost + Trucking cost + Deterioration and obsolescence cost + Interest cost + Storage cost
Total cost of material = TZS 12/year + TZS 48/year + TZS 2,000/year + TZS 3,000/year + TZS 1,000/year
Total cost of material = TZS 6,060/year
Therefore, the total cost of material is TZS 6,060 per year.
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
Answer:
(3/5) (30x - 15) = 72 ⇔ 18x - 9 = 72
(3/5) (30x - 15) = 72 ⇔ 3(6x - 3) = 72
(3/5) (30x - 15) = 72 ⇒ x = 4.5
Equation 1 and 2 have the same value.
Equations C and D have the same value.
A formula is given to us: 3/5 (30x -15) = 72. The equations with the same value of x are the ones we are to choose.
Let's tackle the issue at hand.
3/5 . 30x - 3/5 . 15=72
3.6x - 3.3= 72
18x - 9 = 72
As a result, option C is the best one.
As we factor 3 out of the equation above, we get:
3 . 6x - 3 . 3 = 72
3(6x-3)=72
As a result, option D is also a good decision.
Let's figure out what x is: 3(6x-3) / 3 = 72/3
6x-3=24
x = 4.5
As a result, the final choice is also right.
(3/5) (30x - 15) = 72⇔ 18x - 9 = 72
(3/5) (30x - 15) = 72 ⇔ 3(6x - 3) = 72
(3/5) (30x - 15) = 72 ⇒ x = 4.5
Equations C and D have the same value.
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[7] Which country is known as the ‘Land of Thunderbolts’?
(A) China
(B) Bhutan
(C) Mongolia
(D) Thailand
IAS CHINADU KUMAR KHAN
Answer: CHINA
Step-by-step explanation:
IAS CHINADU
Answer:
Bhutan is the answer.
Some values of f(x) are given in the table. Find the value of f-¹ (6).
Using the table and definition of inverse functions we will get:
f ⁻¹ (6) = 10.
How to find the value of f ⁻¹ (6)?Remember how inverse functions work, we know that for two inverse functions f(x) and f ⁻¹ (x)?
if f(x) =y
Then:
f ⁻¹ (y) = x
So now we want to find f ⁻¹ (6), then if:
f ⁻¹ (6) = k
f(k) = 6
Looking at the table we can see that f(10) = 6, then f ⁻¹ (6) = 10.
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I need help please!!
Equation of line of reflection:
Will award brainliest need help on a few questions.
Answer:
32 degrees
Step-by-step explanation:
We know that the two opposite angles are equivalent so we need to figure out what each one equals.
First we find what x equals so:
9x - 55 = 5x + 21
When we solve for x we get 19 so we can put this back into the expression to find out the first angle
5(19) + 21 = 116
Since we know both sides are 116 we can add them and get 232
We know now that since all sides all add to 360 we can do
360-232= 128
then split 128 in two for the left and right sides we get 64 degrees
Since the line VU bisects the left angle we know the angle WOV is half of 64 which is:
32 degrees
Determine whether the study depicts an observational study or an experiment. Thirty university students are divided into two groups. One group receives free tutoring in mathematics, the other doesn't. After one semester, scores on final mathematical examinations are compared. Does the description correspond to an observational study or an experiment?
The description corresponds to an experiment.
What is mathematics?Mathematics is the sciences and study of quality, structure, space, and change. Mathematician's are seek out patterns, formulate new conjectured, and establish truth by the rigorous seduction from appropriately choden axioms and definitions.
An experiment is a type of scientific research method in which a researcher manipulates one or more variables and measures the effects of the manipulation on other variables. In this example, the researcher divided the thirty university students into two groups and manipulated one variable (free tutoring in mathematics) to measure the effects on another variable (final mathematical examination scores). Therefore, this is an experiment.
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38.8% of Canada's population lives in Ontario. The population of Ontario is 12.9 million. What is the population of Canada?
let the total population be x
Step-by-step explanation:
38.8%of x=12,900,000
x=12,900,000*100/38.8
x=12,900,000*100*10/388
x=33,247,422.680412A restaurant has 8 quarts of pudding. They serve the pudding in cups that hold 1/6 of a quart. How many cups of pudding could be made?
Therefore , the solution of the given problem of fraction comes out to be the restaurant could make 48 cups of pudding from the 8 quarts they have.
Fraction : What is it ?An whole can be represented by any set of related sums or fractions. In standard English, a percentage is used to represent the quantity of a specific size. 8, 3/4. Also wholes are fractions. Numbers are expressed in mathematics using the ratio of it's own portion to the bottom. These fractions are all made up of basic numbers. Due to variances in actual percentage calculations, numerators, and numerators, a difficult fraction contains a fraction. A measurement that reflects a portion of the whole is a percentage.
Here,
There are different ways to approach this problem, but one possible method is to use unit conversions to find how many cups are in 8 quarts, and then divide by 1/6 of a quart per cup.
1 quart = 4 cups (by definition of quart)
Therefore, 8 quarts = 8 x 4 cups = 32 cups
1/6 of a quart = 1/6 x 4 cups = 2/3 cups
Therefore, the number of cups of pudding that could be made is:
32 cups / (2/3 cups) = 48 cups
Therefore, the restaurant could make 48 cups of pudding from the 8 quarts they have.
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What is the coordinate of A’ after Triangle ABC is reflected across the y-axis?
Answer:
The rule for a reflection over the y -axis is (x,y)→(−x,y) .
A'(-(x) ; y)
A'(-(-5) ; 3)
A'(5 ; 3)
What is the area of the figure?
6 ft
5 ft/
4 ft
3 ft
The area of the sector is 16.1 ft².
What is the area of a sector?The formula for the area of a sector of a circle is given as;
A = θ/360⁰ x ( r² )
where;
r is the radius of the circle andθ is the angle of the sectorThe angle of the sector is calculated as follows;
sin (θ/2) = 3 / 5
sin (θ/2) = 0.6
θ/2 = sin⁻¹ ( 0.6 )
θ/2 = 36.87⁰
θ = 2 x 36.87⁰
θ = 73.74⁰
The area of the sector is calculated as;
A = (73.74 / 360 ) x π (5²)
A = 16.1 ft²
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I'll give brainliest
The system of equations that shows the situation is option 1. L+J=29 L=2J-10
How to get the equationsThe question tells us that the summation of the age of Latifa and Jameel is 29
Let J = Jameel
L = Latifa
L + J = 29
The question says that Latifa's age is 2 time of Jameels age = 2J with 10 years subracted
L = 2J - 10
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Find the solution to the system of equations: x + 3y = 7 and 2x + 4y = 8 1. Isolate x in the first equation: 2. Substitute the value for x into the second equation: 3. Solve for y: 4. Substitute y into either original equation: 5. Write the solution as an ordered pair:.
The solution to the system of equations: x + 3y = 7 and 2x + 4y = 8 is (-2, 3)
Isolate x in the first equation:
x + 3y = 7
x = 7 - 3y
Use the substitution method, Substitute the value for x into the second equation:
2x + 4y = 8
2(7 - 3y) + 4y = 8
Solve for y:
14 - 6y + 4y = 8
-2y = -6
y = 3
Substitute y into either original equation:
x + 3y = 7
x + 3(3) = 7
x + 9 = 7
x = -2
Write the solution as an ordered pair:
The solution is (-2, 3).
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13. In a football game, the Tigers scored 9 touchdowns and the Leopards scored 5 touchdowns.
Each touchdown is worth 6 points. What equation can be used to find how many more points
the Tigers scored than the Leopards? Use p to represent the number of points.
Write your equation and answer to the problem in the box.
and p =
O
14. Last month, Mr. Foreman spent $105 on landscaping, $448 on utility bills, $115 on his cell-
phone bill, and $143 on his cable-Internet bill. He received a credit of $21 on his cell-phone bill.
He estimated his total expenses for these bills for last month to be about $780. Use estimation
strategies to see if Mr. Foreman's estimate is correct.
So, in response to the above question, we can state that The projected sum is $800, or around $780. Hence, equation of Mr. Foreman's estimation is accurate.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Nine touchdowns by the Tigers, each earning six points, for a total of nine times six or 54 points.
The Leopards scored 5 touchdowns for a total of 5 x 6 = 30 points, each of which was worth 6.
We may deduct the total points scored by the Leopards from the total points scored by the Tigers to see how many more points the Tigers scored than the Leopards:
Leopards' points minus Tigers' points equals 54 - 30 = 24.
As a result, the formula is p, where p = 24, where Tigers' points Equal Leopards' points.
Hence, the Tigers outscored the Leopards by 24 points.
$105 + $448 + $115 + $143 - $21 = $790
We have the following by rounding the numbers to the closest tens:
$110 + $450 + $120 + $140 - $20 = $800
The projected sum is $800, or around $780. Hence, Mr. Foreman's estimation is accurate.
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Please help me. The point P(4, 28) lies on the curve y = x² + x + 8.
The slope of the line tangent to the quadratic equation f(x) = x² + x + 8 is approximately equal to 27.996.
How to calculate the slope of the secant line and estimate the slope of the tangent line
In this case we need to estimate the slope of a line tangent to a quadratic equation based on behavior exhibited by a set of secant lines. A secant line is a line that passes through only two points of the curve and a tangent line is a line that passes through only one point of the curve. The slope of the secant line can be determined by the following expression:
m = Δf(x) / Δx
Now we proceed to determine the slopes associated with each secant line:
x = 4
f(4) = 4² + 4 + 8
f(4) = 28
x = 4.1
f(4.1) = 4.1² + 4.1 + 8
f(4.1) = 28.91
x = 4.01
f(4.01) = 4.01² + 4.01 + 8
f(4.01) = 28.091
x = 3.9
f(3.9) = 3.9² + 3.9 + 8
f(3.9) = 27.110
x = 3.99
f(3.99) = 3.99² + 3.99 + 8
f(3.99) = 27.910
And the slope of the tangent line can be estimated by average:
m = 0.5 · [f(3.99) + f(4.01)]
m = 0.5 · (27.910 + 28.091)
m = 27.996
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A theatre contains 487 seats and the ticket prices for a recent play were $47 for adults and $ for29 children. If the total proceeds were $17,525 for a sold-out matinee, how many of each type of ticket were sold?
Answer:
40x + 17(468-x) = 11912
23x = 11912 - 17*468 |Solve for x and then find (468-x) as well
In the year 2020, there were 14.02 billion cell phones in use worldwide. In 2022, the number
increased to 15.96 billion worldwide.
a. What is the average rate of change in the number of worldwide cell phones?
b. Using 14.02 as the initial amount, write a linear equation that models the number of
worldwide cell phones. Make sure to define the variables.
C.If the rate stays the same, predict the number of cell phones that will be in use worldwide
in the year 2027.
Answer:
Step-by-step explanation:
a. The average rate of change in the number of worldwide cell phones can be calculated as:
Average rate of change = (change in number of cell phones) / (change in time)
The change in number of cell phones is 15.96 billion - 14.02 billion = 1.94 billion, and the change in time is 2 years. Therefore,
Average rate of change = 1.94 billion / 2 years = 0.97 billion/year
So, the average rate of change in the number of worldwide cell phones is 0.97 billion per year.
b. We can use the point-slope form of a linear equation to model the number of worldwide cell phones. Let t be the time in years since 2020, and C(t) be the number of worldwide cell phones in billions. Then the equation can be written as:
C(t) - 14.02 = 0.97t
Simplifying, we get:
C(t) = 0.97t + 14.02
So, the linear equation that models the number of worldwide cell phones is C(t) = 0.97t + 14.02.
c. To predict the number of cell phones that will be in use worldwide in the year 2027, we need to find the value of C(2027 - 2020) = C(7) using the linear equation we derived in part (b).
C(7) = 0.97(7) + 14.02 = 20.83 billion
Therefore, if the rate stays the same, we can predict that there will be 20.83 billion cell phones in use worldwide in the year 2027.
The winner of the 1998 Peoria 500 (mile) race was Serge Bologna, with an average rate
of 123.362 mi per hr. What was his time (to the nearest thousandth of an hour)?
Time is 4.053 hours (to the nearest thousandth of an hour).
What is average rate?
This refers to the change in speed over a selected period of time. It depends on when you take the measurements. •
Solving for average rate:
Average Rate = 123.362 mi per hr
Distance = 500 (mile)
Time =?
Average Rate = Distance
Time
123.362 mi per hr = 500 (mile)
Time
Making time subject of the formular we have:
Time = 500 (mile)
123.362 mi per hr
Time = 4.053 hrs
Time is 4.053 hours (to the nearest thousandth of an hour).
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D is partly constant and partly varies with V. When V = 40, D = 150, and when V = 54, D = 192. a Find the formula connecting D and V. b Hence find D when V = 73.
[tex]\textit{Partial Variation} \\\\ y = k_ox+k_1\hspace{5em}\textit{"y" varies partly with a constant and directly with "x"} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{"D" varies partly with a constant and directly with "V"}}{D=k_oV+k_1}\qquad \textit{we know that} \begin{cases} V=40\\ D=150\\[-0.5em] \hrulefill\\ V=54\\ D=192 \end{cases}[/tex]
[tex]\boxed{\begin{array}{llll} 150=40k_o+k_1\\\\ 192=54k_o+k_1 \end{array}}\qquad \stackrel{ \textit{using elimination method} }{\begin{array}{llll} -150=-40k_o-k_1\\\\ ~~ 192= ~~ 54k_o+k_1\\\cline{1-1} ~~ 42~= ~~ 14k_o+0 \end{array} }\qquad \implies 42=14k_o \\\\\\ \cfrac{42}{14}=k_o\implies \boxed{3=k_o}\hspace{5em}\stackrel{\textit{substituting on the 1st equation}}{150=40(3)+k_1}[/tex]
[tex]\cfrac{150}{40(3)}=k_1\implies \boxed{\cfrac{5}{4}=k_1}\hspace{5em} {\Large \begin{array}{llll} D=3V+\cfrac{5}{4} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \textit{when V=73, what is "D"?}\qquad D=3(73)+\cfrac{5}{4}\implies D=\cfrac{881}{4}\implies D=220\frac{1}{4}[/tex]
please help me, due toromow!! (ignore the numbers i put)
The Area of Trapezoid of figures given below.
What is Area of Trapezoid?The area of a trapezoid is found using the formula, A = ½ (a + b) h,
where 'a' and 'b' are the bases (parallel sides) and 'h' is the height (the perpendicular distance between the bases) of the trapezoid.
Given:
1. Area of Trapezoid
= 1/2 ( a+ b) x h
= 1/2 (22+ 11) x 12
= 33 x 6
= 198 m²
2. Area of Trapezoid
= 1/2 ( a+ b) x h
= 1/2 (38+ 24) x 26
= 806 mm²
3. Area of Trapezoid
= 1/2 ( a+ b) x h
= 1/2 (105 + 212) x 78
= 12363 Km²
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How much will be charged in prepaid interest on a $250,000 loan with an APR of 5.25% that was closed on April 12th
The amount that will be charged in prepaid interest on a $250,000 loan with an APR of 5.25% closed on April 12th is $9,457.19.
What is the APR?The APR represents the annual percentage rate.
The annual percentage rate is the interest rate for the year, including other finance charges.
To compute the interest, the annual percentage rate is multiplied by the loan amount and the period divided by 365 days.
Loan amount = $250,000
Annual percentage rate (APR) = 5.25%
Loan closing date = April 12th
April 12th to December 31st = 263 days
Interest for the year = $9,457.19 ($250,000 x 5.25% x 263/365)
Thus, for the year, the interest is $9,457.19.
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A circle is inscribed in a square
as shown. The area of the circle
is 153.94 square inches. What is
the area of the square?
The area of the square is 196.1019 square inches
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.
area of the circle = 3.14r² , r =radius
=> 153.94 = 3.14r²
=> r² = 153.94/3.14 = 49.0254
=> r= ± √ 49.0254 =± 7.0018
=> r= + 7.0018, r= - 7.0018
Consider positive value
r= + 7.0018
Diameter, d= 2r = 2*7.0018 = 14.0036 inches
Side (a) of square = Diameter = 14.0036 inches
The area of the square
= a²
= 14.0036² square inches
= 196.1019 square inches
The area of the square is 196.1019 square inches
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Solve the compound inequality, and write the solution in interval notation:
The solution of the given compound inequality in the interval notation is (∅).
What is compound inequality?
Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols. Typically, we use the not equal symbol to indicate that two values are not equal. But to compare the values, whether it is less than or greater than, different inequalities are used.
Given a compound inequality,
1/4 x - 3 ≥ 1 and -3(x - 2) ≥ 2
To solve this we take the first inequality.
1/4 x - 3 ≥ 1
1/4 x ≥ 4
x ≥ 16
Now solve the second inequality.
-3(x - 2) ≥ 2
-3x +6 ≥ 2
-3x ≥ -4
x ≤ 4/3 (The inequality sign reverses because we are dividing by a negative number, -3)
Now from both solved inequalities, we can see that x should be greater than 16 as well as it should be less than 4/3.
There exists no such number.
Therefore the solution of the given compound inequality in the interval notation is (∅).
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At a sports event, a fair coin is flipped to determine which team has possession of the ball to start. The coin has two sides, heads, (H), and tails, (T). Identify the correct experiment, trial, and outcome below: Select all that apply: a. The experiment is identifying whether a heads or tails is flipped. b. The experiment is flipping the coin c. A trial is flipping a heads. d. A trial is one flip of the coin. e. An outcome is flipping a tails. f. An outcome is flipping a coin once.
The correct answer about experiment, trial, and outcome is
a. The experiment identifies whether a head or tail
b. The experiment is flipping the coin
d. A trial is one flip of the coin
Experiment:
An experiment in probability is a process or activity that involves observing or measuring an outcome or event, in order to determine the likelihood or probability of certain outcomes.
Outcome:In probability, an outcome refers to a possible result that can occur from an experiment or event. It is one of the possible outcomes that can happen, and it may be a single result or a set of results.
TrialIn probability, a trial is a single repetition of an experiment or event. It is the process of observing or measuring the outcome of an event or experiment once.
Here we have
At a sports event, a fair coin is flipped to determine which team has possession of the ball.
The coin has two sides, heads, (H), and tails, (T).
From the given options correct answers are
a. The experiment identifying whether a head or tail is flipped is correct because the experiment is to determine which side of the coin will be facing up after the coin is flipped, either heads (H) or tails (T).
b. The experiment is flipping the coin is correct because the experiment involves physically flipping the coin.
d. A trial is one flip of the coin is correct as a trial is defined as a single performance of an experiment, in this case, flipping the coin once.
Therefore,
The correct answer about experiment, trial, and outcome is
a. The experiment identifies whether a head or tail
b. The experiment is flipping the coin
d. A trial is one flip of the coin
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If a circular garden with a radius of 3 ft. Is bordered by a circular sidewalk that is 2 ft. Wide, what is the area of the sidewalk?.
If a circular garden with a radius of 3 ft. Is bordered by a circular sidewalk that is 2 ft. Wide, then The area of the sidewalk is 28.26 ft².
To calculate this, first calculate the area of the garden, which is 28.27 ft² (A=πr²). After that subtract this from the area of the sidewalk, which is 56.54 ft² (A=π(r+2)²). The area of the sidewalk is the difference between these two values, which is 28.26 ft².
To calculate the area of the garden, we use the formula A=πr², where r is the radius of the garden. In this case, the radius is 3 ft., so the area is 28.27 ft². To calculate the area of the sidewalk, we use the formula
A=π(r+2)²where r is the radius of the garden and 2 is the width of the sidewalk. In this case, the radius is 3 ft. and the width is 2 ft., so the area is 56.54 ft². The area of the sidewalk is then the difference between these two values, which is 28.26 ft².
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PLEASE HELPPP DUE IN 2 HOURS!!!!!!!
Answer:
1.15%
Step-by-step explanation:
Why is the numerator greater than the denominator in a fraction that is equivalent to a percent greater than 100?
When a fraction is equivalent to a percentage greater than 100, it means that the numerator represents a value that is greater than the denominator.
What is the percentage?A percentage is a way to express a number as a fraction of 100. For example, 50% is the same as 50/100, which simplifies to 1/2.
Suppose we have a fraction that is equivalent to a percentage greater than 100, such as 125%. This means that the fraction represents 125 parts out of 100, or 125/100.
To simplify this fraction, we can divide both the numerator and denominator by the greatest common factor(GCF), which is 25 in this case. This gives us:
125/100 = (125 ÷ 25)/(100 ÷ 25) = 5/4
As we can see, the numerator (5) is greater than the denominator (4). This is because the original percentage value (125%) is greater than 100%, which means the fraction must have a numerator that is greater than the denominator to reflect this increase.
In general, if a fraction is equivalent to a percentage greater than 100, its numerator will be greater than its denominator because the percentage value represents a quantity that is greater than the whole (100%).
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Defective rate. A machine that produces a special type of transistor (a component of computers) has a 2% defective rate. The production is considered a random process where each transistor is independent of the others.
(a) What is the probability that the 10th transistor produced is the first with a defect?
(b) What is the probability that the machine produces no defective transistors in a batch of 100?
(c) On average, how many transistors would you expect to be produced before the first with a defect? What is the standard deviation?
(d) Another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. On average how many transistors would you expect to be produced with this machine before the first with a defect? What is the standard deviation?
(e) Based on your answers to parts (c) and (d), how does increasing the probability of an event a?ect the mean and standard deviation of the wait time until success?
a) Note that the probability that the 10th transistor produced is the first with a defect is: ≈ 0.0171
b) The probability that the machine produces no defective transistors in a batch of 100 is: ≈ 0.1338
c) The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is: = 50
d) The expected value and standard deviation for the number of transistors produced before the first with a defect is ≈ 18.71
e) Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.
What is the rationale for the above responses?(a) Since each transistor is independent, the probability that the 10th transistor produced is the first with a defect is the same as the probability that the first 9 transistors are not defective and the 10th one is defective. The probability that a transistor is not defective is 1 - 0.02 = 0.98. Therefore, the probability is:
P(1st defective on 10th) = (0.98)⁹ x 0.02 ≈ 0.0171
(b) The probability that the machine produces no defective transistors in a batch of 100 is:
P(no defects in 100) = (0.98)¹⁰⁰ ≈ 0.1338
(c) The number of transistors produced before the first with a defect follows a geometric distribution with parameter p = 0.02. The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is:
E(X) = 1/p = 1/0.02 = 50
The variance of a geometric distribution is (1-p)/p², so the standard deviation is:
σ = √((1-p)/p²)
= √(0.98/0.0004)
≈ 22.36
(d) The expected value and standard deviation for the number of transistors produced before the first with a defect are calculated in the same way as in (c), but with a different value of p:
E(X) = 1/p = 1/0.05 = 20
σ = √((1-p)/p₂)
= √(0.95/0.0025)
≈ 18.71
(e) Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.
As the probability of an event increases, the expected wait time until success decreases. In other words, the mean becomes smaller. However, as the probability of an event increases, the variability in the wait time until success also increases.
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Answer:
(a) 0.0167
(b) 0.1326
(c) The expected value, mean, μ = 50 SD, σ = 49.4975
(d) The expected value, mean, μ = 20 SD, σ = 19.4936
(e) Increasing the probability of an event decreases the mean and standard deviation of the wait time until success.
Step-by-step explanation:
Which transformations can be used to show that circle P is similar to circle Q? Circle P: center (2, −3) and radius 4 Circle Q: center (2, 3) and radius 28 Select each correct answer. Responses Circle Q is a translation of circle P, 6 units left. Circle , Q, is a translation of circle , P, , 6 units left. Circle Q is a dilation of circle P with a scale factor of 7. Circle , Q, is a dilation of circle , P, with a scale factor of 7. Circle P is a dilation of circle Q with a scale factor of 24. Circle , P, is a dilation of circle , Q, with a scale factor of 24. Circle Q is a translation of circle P, 6 units up.
The correct statements of the given ones are -
Circle Q is a dilation of circle P with a scale factor of 7.Circle Q is a translation of circle P (6 units up).What are similar circles?Two circles are said to be similar if the ratio of their corresponding radius, circumferance and areas are proportionally constant.
Given are the two circles such that circle P is similar to circle Q.
{ 1 } -
Circle Q is a dilation of circle P with a scale factor of 7.
Proof :
r{Q}/r{P} = 28/4 = 7
{ 2 } -
Circle Q is a translation of circle P, 6 units up.
Proof :
Apply the rule (x, y + 6) to the coordinate (2, -3), we get (2, 3).
Therefore, the correct statements of the given ones are -
Circle Q is a dilation of circle P with a scale factor of 7.Circle Q is a translation of circle P (6 units up).To solve more questions on dilations, visit the link below -
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subtract the polynomials (6x^7-x+8)-(x^7+2)
Answer:
[tex]5x^{7} -x+2[/tex]
Step-by-step explanation:
[tex]6x^{7} -x+8[/tex] minus [tex]x^{7} +2[/tex] equals to [tex]5x^{7} -x+2[/tex].
We can solve this by subtracting [tex]x^{7}[/tex] from [tex]6x^7[/tex]. This will make it [tex]5x^7[/tex].
x cannot be subtracted, so it becomes [tex]5x^7 -x[/tex].
8-6 is 2, so it becomes [tex]5x^7-x+2[/tex]