answer:
178.5398mm²
explanation:
attached
--
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Check My Work Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of ounces. a. The process standard deviation is , and the process control is set at plus or minus standard deviations. Units with weights less than or greater than ounces will be classified as defects. What is the probability of a defect (to 4 decimals)
Answer:
0.0026 x 1000 = 2.6
Step-by-step explanation:
Looked it up
What is the slope of the line through (- 3, 2) and (0, 1) ?
Answer:
-1/3
Step-by-step explanation:
Slope Formula = (y2-y1) over (x2-x1)
(1-2) over (0- -3)
(-1) over (0+3)
-1 over 3
-1/3
Hope this helps. Have a nice day you amazing bean child.
at a university, 75%, or 1,014, of first-year students take a maths course. How many first-year students are there at the university?
A. s/1,014 = 75/100 ; 76 students
B. s/1,014 = 75/100 ; 761 students
C. 1,014/s = 75/100 ; 1,352
D. 1,014/s = 75/100 ; 714
help me pls!?
Answer:
C
Step-by-step explanation:
1014=0.75s
1014/0.75=s is the same as 1014/s=0.75
a) In GeoGebra Links to an external site., construct a triangle (e.g. ABC), find the measure of all angles and all sides. Identify the type of your triangle (acute, right, obtuse/ scalene, isosceles, equilateral). Then construct a quadrilateral (e.g. DEFG), measure all angles and all sides. Identify the type of your quadrilateral (irregular, square, rectangle, etc.) Use the text command available in GeoGebra to describe the type.
b) Make a screenshot of your work in Geogebra and insert in the space provided below.
All angles are 90 degrees.Rhombus: All sides are of equal length.Square: All angles are 90 degrees and all sides are of equal length
a) To construct a triangle in GeoGebra, we can follow the steps below:
Step 1: Open GeoGebra and select the ‘Polygon’ tool.
Step 2: Select the ‘Triangle’ option.
Step 3: Click three points anywhere on the graph.
Step 4: Once you have drawn the triangle, you can use the ‘Angle’ tool to measure all the angles in the triangle. Similarly, use the ‘Length’ tool to measure the length of each side of the triangle.To identify the type of triangle, we can use the following properties:Acute Triangle: All angles of the triangle are less than 90 degrees.Right Triangle: One of the angles in the triangle is 90 degrees.Obtuse Triangle: One of the angles of the triangle is greater than 90 degrees.Scalene Triangle: All sides of the triangle are of different lengths.Isosceles Triangle: Two sides of the triangle are of the same length.Equilateral Triangle: All sides of the triangle are of the same length.To construct a quadrilateral in GeoGebra, we can follow the steps below:
Step 1: Open GeoGebra and select the ‘Polygon’ tool.
Step 2: Select the ‘Quadrilateral’ option.
Step 3: Click four points anywhere on the graph.
Step 4: Once you have drawn the quadrilateral, you can use the ‘Angle’ tool to measure all the angles in the quadrilateral. Similarly, use the ‘Length’ tool to measure the length of each side of the quadrilateral.To identify the type of quadrilateral, we can use the following properties:Irregular Quadrilateral: All sides and angles of the quadrilateral are of different lengths and measures.Trapezium: Only one pair of opposite sides is parallel.Parallelogram: Opposite sides are parallel.Rectangle:.b) Since we need to add a screenshot of the work done in GeoGebra, we cannot add it here. However, while you construct the triangle and the quadrilateral, you can keep adding the measure of angles and sides to find the properties of the figure. You can then use the Text command available in GeoGebra to describe the type of triangle or quadrilateral that you have constructed. To use the Text command in GeoGebra, follow the steps below:
Step 1: Select the ‘Text’ tool from the toolbar
.Step 2: Click anywhere on the graph to add the text box.
Step 3: Type the text in the text box.
Step 4: Customize the font, color, and size of the text as required.
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If the mean of five values is 41, find the sum of the values.The sum of the values is
The mean is determined by dividing the sum by the number of values. Let s be the sum, we can expressed it as
\(\frac{s}{5}=41\)Solve for s by multiplying both sides by 5
\(\begin{gathered} \frac{s}{5}\cdot5=41\cdot5 \\ \frac{s}{\cancel{5}}\cdot\cancel{5}=41\cdot5 \\ s=205 \end{gathered}\)Therefore, the sum of values is 205.
The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 16 years; the standard deviation is 1.7 years. Use the empirical rule (68−95−99.7%) to estimate the probability of a gorilla living between 14.3 and 19.4 years.
The probability that a gorilla in this particular zoo will live between 14.3 and 19.4 years is 86% (or 0.86)
Understanding Normal DistributionFrom the Empirical Rule, for a Normal Distribution, approximately:
68% of the data falls within one standard deviation of the mean
95% of the data falls within two standard deviations of the mean
99.7% of the data falls within three standard deviations of the mean
To estimate the probability of a gorilla living between 14.3 and 19.4 years, we first need to standardize these values by subtracting the mean and dividing by the standard deviation:
For 14.3 years: (14.3 - 16) / 1.7 = -1.18
For 19.4 years: (19.4 - 16) / 1.7 = 2
Now we can use a standard normal distribution table to find the probabilities associated with these z-scores:
The probability of a gorilla living less than 14.3 years is approximately the same as the probability of a standard normal variable being less than -1.18, which is about 0.12.
The probability of a gorilla living less than 19.4 years is approximately the same as the probability of a standard normal variable being less than 2, which is about 0.98.
Therefore, the probability of a gorilla living between 14.3 and 19.4 years is approximately the difference between these two probabilities: 0.98 - 0.12 = 0.86.
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ASAP Which graph has a correlation coefficient, r, closest to 0.75?
Answer:
C. Graph C
Step-by-step explanation:
In a scatter plot, a positive correlation coefficient suggests that as one variable increases the other increases as well, or as one decreases, the other decreases.
Also, the more clustered the data points are along the line of best fit, the higher the value of the coefficient, whether positive or negative.
Graph C shows a positive correlation because as the variable on the x-axis increases, the variable on the y-axis also increases. The data points are more clustered along the line if best fit, if we draw one. This suggest a positive correlation coefficient (r) as strong as 0.75.
Graph C has a correlation coefficient, r, that is closer to 0.75.
Answer: graph A ‼️
Step-by-step explanation:
a boat is going 144 miles upstream on a river. the speed of the boat in still water is 60 miles per hour. the speed of the river current is 80% less than the speed of the boat in still water. how long does the journey take?
Answer:
45
Step-by-step explanation:
Answer:
3 hours
Step-by-step explanation:
the speed of the river current is 80% less
80% of 60 is 48
so the speed is now 48 mph, because the river is pushing the boat back (duh)
144 miles/ 48 mph is 3 hours.
Please help been stuck on this for hours
The size of angle ACB to the nearest degree is 88 degree.
How is a triangle ABC put together?
Construction Steps:
Create a line segment BC with the property AC = 4 cm.
Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.
Join AB and AC now. Consequently, the necessary triangle is ABC.
With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.
Cut an arc of 3 cm from point B.
Embrace BC and AC
Triangle with angle ABC is necessary.
< ACB = 88 degree
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What is the value of 0.8–0.6? Write your answer as a fraction in lowest terms
Given expression:
\(0.8 - 0.6\)To simplify the expression as a fraction in simplest form, let us multiply both terms by 10. Then, both terms must also be divided by 10.
\(\implies \dfrac{[10(0.8) - 10(0.6)]}{10}\)
\(\implies \dfrac{[8 - 6]}{10}\)
\(\implies \dfrac{[2]}{10} = \dfrac{2}{10}\)
When 2/10 is simplified in lowest terms, we get;
\(\implies \dfrac{2}{10} \implies \dfrac{1 \times 2}{5 \times 2} \implies \dfrac{1}{5}\)
Therefore, 0.8 - 0.6 in fraction form is 1/5.
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
x = 1 + (y â 4)2, x = 2
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis.
y = x3, y = 8, x = 0; about x = 7
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis.
y = 6x â x2, y = 5; about x = 1
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the graphs of the given equations about the x-axis.
y = x3â2, y = 8, x = 0
The volume of the solid obtained by rotating the region bounded by the given curves about the X-axis is 340978 vu.
Given curve is,
y = \(x^{3}\) , y = 8, x = 0 about x = 7
we know the formula for cylindrical shell is
V = πR²h
where R² = f(x)₂-f(x)₁ ,
h = dx
here f(x)₂ = 8 and f(x)₁ = x³
⇒ V = π(8 - x³)²h
V = π(64 - 16x³+x⁶)dx
integrating on both sides,
\(\int dV\) =π \(\int ({64 - 16 x^{2} + x^{6} }) \, dx\)
= \(64 \int dx - 16 \int {x^{3} } \, dx + \int\ {x^{6} } \, dx\)
V = π(64x - 4x⁴+\(\frac{x^{7} }{7}\))
V = π(64 × 7 - 4(7)⁴ + \(\frac{7^{7} }{7}\))
= π(448 - 9604 + 117649 )
= \(\frac{22}{7}\)(108493)
V = 340978 vu
Therefore volume of the cylindrical shells to the region y = x³, y = 8, x = 0 about x = 7 is 340978 vu.
Cylindrical shells are essential structural elements in offshore structures, submarines, and airspace crafts. They are often subjected to combined compressive stress and external pressure, and therefore must be designed to meet strength requirements.
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Benchmark 2 - Item 206328
Jeff sells popcorn for $3 per bag. To make a profit each day, he needs to sell at
least $120 worth of popcorn. He has sold $36 worth of popcorn today. Which
inequality can be used to find the number of bags of popcorn, p, Jeff still needs
to sell today to make a profit?
Answer:
I think its option 2.
Step-by-step explanation:
Angle ADB and CD are straight lines. angle ADC = 5 x angle CDB Work out the size of angle ADC.
Answer:
Step-by-step explanation:
The first shelf on Hannah’s bookshelf hoods an equal number of fiction and nonfiction. If Hannah’s selects 5 books randomly, what is the probability that 3 of the books will be fiction and 2 will be nonfiction
Answer:
The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
Step-by-step explanation:
What is probability?
Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.
To find which 2 books describe a pair of dependent events:
A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change.
Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance.
Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is.
Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.
Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
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Find the midpoint of the segment with the given endpoints. (-8,6) and (1,1)
Answer:
you just have to position them on a Cartesian plane.
-8 is x and 6 is y same goes for 1 x and 1 y
factor the following expression 14x + 49
Answer:
7(2x +7)
Step-by-step explanation:
Find x
14.2
18.5
find correct answer
From the circle the value of angle x is 90 degrees
We have to find the value of x
The radius of the circle is 18.5
As we observe the figure the angle x is opposite to the 90 degrees
The angle x and angle 90 degrees are vertical angles
We know that the vertical angles are equal or same
∠x = 90 degrees
Hence, the value of angle x is 90 degrees from the circle
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Identify the domain of the function shown in the graph.
A. X≥ 0
B. x < 0
C. 0
-8-84-2
D. x is all numbers.
10-
8
8.
4+
2+
y
-2-
4.
-8-
-10+
2
4 6 8 10 12
Answer:
A. \( x \geq 0\)
Step-by-step explanation:
The domain of a function is the set of \(x\)-values.
This is the problem I am having.
Answer:
Can you send a better picture please thanks.
Step-by-step explanation:
two points on a line are (4,-1) and (1,5) what is the slope of the line
Answer: -2
I hope this helps and may God bless you! Have a nice day, bye! :)
slove for x: 3x+4=9x+3
Answer:
x = 1/6
Step-by-step explanation:
move the letters to one side and the numbers to the other:
-6x=-1
divide by minus 1
6x=1
divide by 6
x=1/6
hope this works :)
Answer:
1/6
Step-by-step explanation:
3x + 4 = 9x + 3
9x - 3x = 4-3
6x = 1
x = 1/6
If I = prt, which equation is solved for t?
O 1-pr=t
O
1-P-1
I
pr
O 1+pr=t
The solution of the equation for t is t = i/pr
How to determine the equation for t?The equation is given as
i = prt
Divide both sides of the equation by p
So, we have the following equation
i/p = prt/p
Divide both sides of the equation by r
So, we have the following equation
i/pr = prt/pr
Evaluate the quotients
i/pr = t
Rewrite as
t = i/pr
By the above computation, we changed the subject of the formula in i = prt from i to t.
This implies that solving for t is a concept of subject of formula
Hence, the solution is t = i/pr
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Camille is comparing different apartment complexes. Here is the data she collected. Complex name Bedrooms Bathrooms Rent Rent includes heat Amenities Grand Vistas 2 br 2 bath $990 no fitness center, pool ; Maple Ridge 2br 1.5 bath , $685 yes fitness center, pool; Old Mill 2 1.5, 790 no pool; Willow Brook 2br 2bath $885 no jacuzzi. The individuals in this data set are:
The individuals in this data set are the different apartment complexes: Grand Vistas, Maple Ridge, Old Mill, and Willow Brook.
The individuals in this data set are the different apartment complexes that Camille is comparing. The data provides information on the complex name, number of bedrooms and bathrooms, rent amount, whether rent includes heat, and the amenities offered.
Grand Vistas:
Bedrooms: 2
Bathrooms: 2
Rent: $990
Rent includes heat: No
Amenities: Fitness center, pool
Maple Ridge:
Bedrooms: 2
Bathrooms: 1.5
Rent: $685
Rent includes heat: Yes
Amenities: Fitness center, pool
Old Mill:
Bedrooms: 2
Bathrooms: 1.5
Rent: $790
Rent includes heat: No
Amenities: Pool
Willow Brook:
Bedrooms: 2
Bathrooms: 2
Rent: $885
Rent includes heat: No
Amenities: Jacuzzi
Each apartment complex is represented as an individual in the data set. Camille has collected specific details for each complex, including the number of bedrooms and bathrooms, the rent amount, whether heat is included in the rent, and the amenities provided.
This data set allows Camille to compare different apartment complexes based on these attributes. She can evaluate factors such as rent prices, included amenities, and the presence of heat in the rent. This information will assist Camille in making an informed decision about which apartment complex may be the most suitable for her needs and preferences.
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plz help multiply/divide one step
Answer:
The answer is x=7
Step-by-step explanation:
You divide both sides by 5 where you put the squares below the values then you get 5.
1. The population of a town was 112 in 2014. The population doubles every year.
(a) Use the exponential growth model to write an equation that estimates the population t years after 2014.
(b) Estimate the population of the town in 2023.
Show your work.
Answer:
Answer: 2048
Step-by-step explanation: 1. Write the exponential growth model.
The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.
2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048
Therefore, the estimated population of the town in 2023 is 2048.
What rigid motion maps the solid-line figure onto the dotted-line figure?
A. reflection
Brotation
Ctranslation
The rigid motion of the solid line figure is translated to the dotted line figure.
How to find the rigid motion maps a solid line?Translation describe a function that moves an object a certain distance.
In a translation, every point of the object must be moved in the same direction and for the same distance.
In translation, the object is not resized, rotated or reflected. The object usually remains the same but it moves a certain distance.
Therefore, the rigid motion maps the solid-line figure onto the dotted-line figure by translation
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The length of a rectangular field is represented by the expression 14x-3x^2+2y . The width of the field is represented by the expression 5x-7x^2+7y . How much greater is the length of the field than the width?
The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)
1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)
2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).
3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).
4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)
5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)
6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)
7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)
8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the Binomial Theorem to find the binomial expansion of the given expression. Show your work.
\((2x-3y)^5\)
The binomial theorem states that: \((x + y)^n = \sum_{k=0}^n{n\choose k} x^{n-k}y^k\). So, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).
Now, let's use the Binomial Theorem to find the binomial expansion of (2x - 3y)⁵. We will have to find the coefficients for each term. So, let's get started. n = 5x = 2xy = -3[nCr = n! / (r! * (n-r)!)]
Term k = 0: \( {5 \choose 0} (2x)^5 (-3y)^0\) = 32x⁵
Term k = 1: \({5 \choose 1} (2x)^4 (-3y)^1\) = -240x⁴y
Term k = 2: \({5 \choose 2} (2x)^3 (-3y)^2\) = 720x³y²
Term k = 3: \({5 \choose 3} (2x)^2 (-3y)^3\) = -1080x²y³
Term k = 4: \({5 \choose 4} (2x)^1 (-3y)^4\) = 810xy⁴
Term k = 5: \({5 \choose 5} (2x)^0 (-3y)^5\) = -243y⁵
Now we can combine all of these terms to form the binomial expansion of (2x - 3y)⁵:\((2x - 3y)^5 = 32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\)
Therefore, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).
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Three friends, Billy, Joe and Paul plan to go on go on holiday.
Billy pays 1/2of the holiday cost.
Joe pays 2/5 of the holiday cost.
What fraction of the holiday cost does Paul pay.
Paul pays 1/10 of the holiday cost, while Billy pays 1/2 and Joe pays 2/5.
To determine the fraction of the holiday cost that Paul pays, we need to find the remaining portion after Billy and Joe have paid their shares.
Let's start by calculating the sum of the fractions Billy and Joe have paid:
Billy's share = 1/2
Joe's share = 2/5
To find the combined share of Billy and Joe, we add their fractions:
1/2 + 2/5
To add these fractions, we need a common denominator. The least common multiple of 2 and 5 is 10. So, we can convert the fractions to have a common denominator of 10:
1/2 = 5/10
2/5 = 4/10
Now, we can add the fractions:
5/10 + 4/10 = 9/10
Billy and Joe have paid a combined fraction of 9/10 of the holiday cost. To find the fraction that Paul pays, we need to determine the remaining portion, which can be calculated by subtracting the combined fraction from 1 (since 1 represents the whole).
Remaining fraction = 1 - 9/10
= 10/10 - 9/10
= 1/10
Therefore, Paul pays 1/10 of the holiday cost.
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Johanna graphed the number of calls she made during one day. How many calls were made before 6 pm?
Cell Phone Calls
12
10
00
Number of calls
6
4
2
0
10 am.- 12 p.m.- 2 p.m. - 4 p.m.- 6 p.m. - 8 p.m.-
11:59 am 1:59 p.m. 3:59 p.m. 5:59 p.m. 7:59 p.m. 9:59 pm
Time of Day
Answer:
im pretty sure its 4! if not 6!