What is the area of the shaded region in the figure below ? Leave answer in terms of pi and in simplest radical form
Answers
Answer:
Step-by-step explanation:
That shaded area is called a segment. To find the area of a segment within a circle, you first have to find the area of the pizza-shaped portion (called the sector), then subtract from it the area of the triangle (the sector without the shaded area forms a triangle as you can see). This difference will be the area of the segment.
The formula for the area of a sector of a circle is:
\(A_s=\frac{\theta}{360}*\pi r^2\) where our theta is the central angle of the circle (60 degrees) and r is the radius (the square root of 3).
Filling in:
\(A_s=\frac{60}{360}*\pi (\sqrt{3})^2\) which simplifies a bit to
\(A_s=\frac{1}{6}*\pi(3)\) which simplifies a bit further to
\(A_s=\frac{1}{2}\pi\) which of course is the same as
\(A_s=\frac{\pi}{2}\)
Now for tricky part...the area of the triangle.
We see that the central angle is 60 degrees. We also know, by the definition of a radius of a circle, that 2 of the sides of the triangle (formed by 2 radii of the circle) measure √3. If we pull that triangle out and set it to the side to work on it with the central angle at the top, we have an equilateral triangle. This is because of the Isosceles Triangle Theorem that says that if 2 sides of a triangle are congruent then the angles opposite those sides are also congruent. If the vertex angle (the angle at the top) is 60, then by the Triangle Angle-Sum theorem,
180 - 60 = 120, AND since the 2 other angles in the triangle are congruent by the Isosceles Triangle Theorem, they have to split that 120 evenly in order to be congruent. 120 / 2 = 60. This is a 60-60-60 triangle.
If we take that extracted equilateral triangle and split it straight down the middle from the vertex angle, we get a right triangle with the vertex angle half of what it was. It was 60, now it's 30. The base angles are now 90 and 60. The hypotenuse of this right triangle is the same as the radius of the circle, and the base of this right triangle is \(\frac{\sqrt{3} }{2}\). Remember that when we split that 60-60-60 triangle down the center we split the vertex angle in half but we also split the base in half.
Using Pythagorean's Theorem we can find the height of the triangle to fill in the area formula for a triangle which is
\(A=\frac{1}{2}bh\). There are other triangle area formulas but this is the only one that gives us the correct notation of the area so it matches one of your choices.
Finding the height value using Pythagorean's Theorem:
\((\sqrt{3})^2=h^2+(\frac{\sqrt{3} }{2})^2\) which simplifies to
\(3=h^2+\frac{3}{4}\) and
\(3-\frac{3}{4}=h^2\) and
\(\frac{12}{4} -\frac{3}{4} =h^2\) and
\(\frac{9}{4} =h^2\)
Taking the square root of both the 9 and the 4 (which are both perfect squares, thankfully!), we get that the height is 3/2. Now we can finally fill in the area formula for the triangle!
\(A=\frac{1}{2}(\sqrt{3})(\frac{3}{2})\) which simplifies to
\(A=\frac{3\sqrt{3} }{4}\)
Therefore, the area in terms of pi for that little segment is
\(A_{seg}=\frac{\pi}{2}-\frac{3\sqrt{3} }{4}\), choice A.
Related Questions
The purchased cost of a 5-m3 stainless steel tank in 1995 was $10,900. The 2-m-diameter tank is cylindrical with a flat top and bottom. If the entire outer surface of the tank is to be covered with 0.05-m-thickness of magnesia block, estimate the current total cost for the installed and insulated tank. The 1995 cost for the 0.05-m-thick magnesia block was $40 per square meter while the labor for installing the insulation was $95 per square meter.
Answers
The estimated current total cost for the installed and insulated tank is $12,065.73.
The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:
surface_area = 2 * pi * r * h + 2 * pi * r^2
where:
r is the radius of the cylinder
h is the height of the cylinder
In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:
surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586
The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:
surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293
The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:
cost = 6.806032934459293 * (40 + 95) = $1,165.73
The original cost of the tank was $10,900, so the total cost of the insulated tank is:
cost = 10900 + 1165.73 = $12,065.73
Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.
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a data set has its first and third quartiles as 9 and 17 respectively. Which of the following data points would be considered an outlier for the data set
A. 27
B. 17
C. 3
D. 41
In which of these cases should the mean be used?
A. When the data is left-skewed
B. When the data is symmetric
C. When the data is right-skewed
D. When the data has extreme values
Answers
To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).
We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:
IQR = Q3 - Q1 = 17 - 9 = 8
To identify outliers, we can use the following rule:
- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.
Using this rule, we can evaluate each data point:
A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.
B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).
C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.
D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.
Therefore, the outliers in the data set are A (27) and D (41).
As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.
Therefore, the correct option would be B. When the data is symmetric.
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Researchers interested in the perception of three-dimensional shapes on computer screens decide to investigate what components of a square figure or cube are necessary for viewers to perceive details of the shape. They vary the stimuli to include: fully rendered cubes, cubes drawn with corners but incomplete sides, and cubes with missing corner information. The viewers are trained on how to detect subtle deformations in the shapes, and then their accuracy rate is measured across the three figure conditions. Accuracy is reported as a percent correct. Four participants are recruited for an intense study during which a large number of trials are required. The trials are presented in different orders for each participant using a random-numbers table to determine unique sequences.
The sample means are provided below:
Answers
The researchers are investigating the perception of three-dimensional shapes on computer screens and specifically examining the components of a square figure or cube necessary for viewers to perceive details of the shape. They vary the stimuli to include fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. Four participants are recruited for an intense study, and their accuracy rates are measured across the three figure conditions. The trials are presented in different orders for each participant using a random-numbers table to determine unique sequences.
In this study, the researchers are interested in understanding how viewers perceive details of three-dimensional shapes on computer screens. They manipulate the stimuli by presenting fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. By varying these components, the researchers aim to identify which elements are necessary for viewers to accurately perceive the shape.
Four participants are recruited for an intense study, indicating a small sample size. While a larger sample size would generally be preferred for generalizability, intense studies often involve fewer participants due to the time and resource constraints associated with conducting a large number of trials. This approach allows for in-depth analysis of individual participant performance.
The participants are trained on how to detect subtle deformations in the shapes, which suggests that the study aims to assess their ability to perceive and discriminate fine details. After the training, the participants' accuracy rates are measured across the three different figure conditions, likely reported as a percentage of correctly identified shape details.
To minimize potential biases, the trials are presented in different orders for each participant, using a random-numbers table to determine unique sequences. This randomization helps control for order effects, where the order of presenting stimuli can influence participants' responses.
The researchers in this study are investigating the perception of three-dimensional shapes on computer screens. By manipulating the components of square figures or cubes, they aim to determine which elements are necessary for viewers to perceive shape details accurately. The study involves four participants, an intense study design, and measures accuracy rates across different figure conditions. The use of randomization in trial presentation helps mitigate potential order effects.
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how many integers between 1 and 1,000,000 have the sum of the digits equal to 15
Answers
There are 13,992 integers between 1 and 1,000,000 with a sum of digits equal to 15.
To find the number of integers between 1 and 1,000,000 with a sum of digits equal to 15, we can use a combinatorial approach.
We need to distribute the sum of 15 among the digits of the number. We can think of this as placing 15 indistinguishable balls into 6 distinct boxes (corresponding to the digits).
Using the stars and bars method, the number of ways to distribute the sum of 15 among 6 boxes is given by the combination formula:
C(n + r - 1, r - 1)
where n is the sum (15) and r is the number of boxes (6).
Plugging in the values, we have:
C(15 + 6 - 1, 6 - 1) = C(20, 5)
Calculating this combination, we find:
C(20, 5) = 13,992
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Xyz corporatio nis selling 100000 shares of common stock through an underwriter at $15 per share, xyz corporation will receive?
Answers
The XYZ corporation will receive $1500000 for all the shares sold.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Now,
Given: Cost of 1 share = $15
To find: Money received on selling 100000 shares.
Finding:
By unitary method,
Money received on selling 1 share = $15
Money received on selling 100000 shares = 15(100000) = $1500000
Hence, The XYZ corporation will receive $1500000 for all the shares sold.
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Given RS and TS are tangent to v at Rand T, respectively, and intersectat
the extenorpoints
Prove: méRST = (MTQR-MTR)
Proof
Proof
Statement
ASVR ASVT
MZRVS + m RSV = 90 and
MZTVS + TSV = 90
Proven)
1.
Angle Addition Postulate
Substitution
4.
MTR = 180 - 2x
5.
The degree measure of a circle is 360
MTQR = 180 + 2x
Substitution and Addition Property al
Equality
Angle Addition Postulate
mZRSV +mZTSV = x+*
TIL RST - 2x
MTOR-FR = (180 + 2x) - (180 - 2x)
10
By Substitution
Multiplication Property
meRST – IMICR-FR
Answers
The given proof demonstrates that the measure of angle RST is equal to the difference between the measures of angles MTQR and MTR. It begins by establishing the tangency of RS and TS to arc v at points R and T, respectively.
Using the Angle Addition Postulate and substitution, the proof shows that angles MZRSV and MZTSV are both equal to x. By substituting the values for MTR and MTQR and applying the Angle Addition Postulate, it is concluded that the measure of angle RST is equal to the difference between the measures of angles MTQR and MTR.
The given proof utilizes various geometric properties and postulates to establish the relationship between angles RST, MTQR, and MTR. It starts by stating that RS and TS are tangent to arc v at points R and T, respectively. Then, it applies the Angle Addition Postulate to establish that the sum of angles MZRSV and RSV is equal to 90 degrees, and the sum of angles MZTSV and TSV is also equal to 90 degrees. These steps are proven using substitution and the properties of tangent lines.
Next, the proof substitutes the given information that MTR equals 180 degrees minus 2x. By using the Angle Addition Postulate again, it determines that MTQR is equal to 180 degrees plus 2x. Substituting these values into the equation, the proof concludes that the measure of angle RST is equal to the difference between the measures of angles MTQR and MTR, which is (MTQR - MTR). This conclusion is reached by applying the Substitution and Addition Property of Equality, as well as the Multiplication Property.
In summary, the proof provides a logical and step-by-step demonstration of how the measure of angle RST can be derived as the difference between the measures of angles MTQR and MTR, based on the given information about the tangency of RS and TS to arc v.
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One of the factors of x2 + 3x – 10 is
Answers
Answer:
(x - 2) or (x + 5)
Step-by-step explanation:
Step 1: Write quadratic
x² + 3x - 10
Step 2: Factor
(x - 2)(x + 5)
Answer: x2 + 3x – 10= (x+5)⋅(x−2)= -6
so x=-6
Step-by-step explanation: "x2" was replaced by "x^2".
Factoring x2+3x-10
The first term is, x2 its coefficient is 1 .
The middle term is, +3x its coefficient is 3 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 1 • -10 = -10
Step-2 : Find two factors of -10 whose sum equals the coefficient of the middle term, which is 3 .
-10 + 1 = -9
-5 + 2 = -3
-2 + 5 = 3
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 5
x2 - 2x + 5x - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-2)
Add up the last 2 terms, pulling out common factors :
5 • (x-2)
Step-5 : Add up the four terms of step 4 :
(x+5) • (x-2)
Which is the desired factorization
so (x + 5) • (x - 2)= x=-6
The differential equation (x + 2y)dx +ydy = 0 can be solved using the substitution. Select the correct answer. a. U=x+2yb. U=yc. U=xyd. U=y/xe. It cannot be solved using a substitution
Answers
The solution of the differential equation is U=x+2y. (A)
To solve the differential equation (x + 2y)dx + ydy = 0 using substitution, you can use the substitution U = x + 2y.
1. Substitute U for x+2y: dU = (dx + 2dy)
2. Replace (x + 2y)dx + ydy with dU - 2ydy + ydy: dU - ydy = 0
3. Factor out dy: dU - ydy = dy(U - y) = 0
4. Separate variables: (1/dU) dU = dy/y
5. Integrate both sides: ∫(1/dU) dU = ∫(dy/y)
6. Obtain the solution: ln|U| = ln|y| + C
7. Replace U with x+2y: ln|x+2y| = ln|y| + C
8. Exponentiate both sides: x+2y = k*y, where k = e^C
Thus, the differential equation (x + 2y)dx + ydy = 0 can be solved using the substitution U = x + 2y.(A)
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Identify the expression that is not equivalent to 6x + 3.
Answers
The resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.
What are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.
Expressions in writing are made using mathematical operators such as addition, subtraction, multiplication, and division.
For instance, "4 added to 2" will have the mathematical formula 2+4.
So, we have the expression:
= x² + 10x + 24
Now, solve when x = 3 as follows:
= x² + 10x + 24
= 3² + 10(3) + 24
= 9 + 30 + 24
= 63
Therefore, the resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.
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Correct question:
Evaluate the expression when x = 3.
x² + 10x + 24
a. 81
b. 86
c. 63
d. 60
Which of the following is not included in the cost of merchandise inventory? O Purchase discounts. O Purchase returns and allowances. O Purchase price of the inventory. O Freight costs paid by the seller. O Freight costs paid by the buyer. 4 pts 0 Question 2 Sunshine Cleaning purchased $3,500 worth of merchandise. The seller offered a 2% cash discount. Transportation costs for the buyer were an additional $310. The company returned $240 worth of merchandise and then paid the invoice within the discount period. The total cost of this merchandise is: O $3.570.00. O $3,500.00 O $3,332.00 O $3,430.00. $3,504.80 Question 5 A company has not sales of $759.300 and cost of goods sold of $548.300. Its not income is $10.280. The company's gross margin and operating expenses, respectively, are: O $211.000 and $230,750 $739.550 and $191,720 O $529,020 and $230.750 O $211.000 and $191,720 $230,750 and $529,020 4 pts D D Question 5 A company has not sales of $750,300 and cost of goods sold of $548,300. Its not income is $10.280 The company's groas margin and operating expenses, respectively, arm O $211,000 and $230,750 O $739,550 and $191,720 $529,020 and $230,750 O $211.000 and $191,720 O $230.750 and $529,020 Question 6 Sales less sales discounts, less sales returns and allowances equals: Cost of Goods Sold Net Income O Net Sales O Gross Profit 4 pts 4 pts Goods in transit are included in a purchaser's inventory: O At any time during transit. O After the half-way point between the buyer and seller, When the supplier is responsible for freight charges. When the goods are shipped FOB shipping point. OIf the goods are shipped FOB destination. Question 11 The inventory costing method that smooths out erratic changes in costs is: O LCM. O FIFO. OLIFO. O Specific Identification. O Weighted average. 4 t ne 0 Question 12 Krusty Krab has the following products in its ending inventory Compute lower of cost or market for inventory. applied separately to each product Inventory by Product Product Quantity Cost per Unit 500 $ 500 $ 30 600 Scuba Masks Scuba Sults O $265,000 O $290,000. O $250,000 $268,000 O $275,000. Question 13 Market per Unit $ 550 $ 25 If equity is $368,000 and liabilities are $186,000, then assets equal: O $554,000. $922,000. $368,000. $186,000. O $182,000. 2 pts
Answers
Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."
2: The total cost of the merchandise is $3,332.00.
5: The company's gross margin and operating expenses, are $211,000 and $191,720.
What is the cost of merchandise inventory?Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.
Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.
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By selling a book for $16.50, a bookseller loses 12%. What is the cost price of the book?
Answers
Answer: 18. 75
Step-by-step explanation:
plz follow my table format here i will be delighted to share
cp percent fraction sp
-12 88/100 16. 50
100*16.50 /88= 18.75
There are 3g of flour for every 2g of butter . Write the ratio of flour to butter
Answers
The ratio of flour to butter in this scenario is 3:2.
1. Rudy paid for 5 trees to be delivered.
Each tree cost $119.95.
Rudy paid $86.20 for delivery.
What is the total amount Rudy paid for mulch and delivery?
Answers
A kilogram of potatoes cost $25.A dozen bananas cost $40.
a) Write an algebraic expression for the total cost of n kilograms of potatoes and one dozen bananas.
b) Evaluate your expression to determine the cost of 15kg of potatoes and one dozen bananas
Answers
Answer:
a) T = 25n + 40
b) T = $415
Step-by-step explanation:
The total cost of 'n' kilograms of something can be expressed as 'n' multiplied by the cost, since it is a constant cost per unit. Therefore the price for n kg of potatoes can be expressed as 25n. We are also told that a dozen bananas cost $40, so our expression is the cost of potatoes added to the cost of bananas. So, is we use 'T' for total cost, our expression will look like this:
T = 25n + 40
Now we can use this expression to find the cost of 15kg of potatoes and the same amount of bananas. We can do this by simply substituting the given amount for n:
T = 25(15) + 40
T = 375 + 40
T = $415
The cost of 15kg of potatoes and one dozen bananas is $415.
Hope this helped!
What is the value of arc EDG°?
Answers
Answer:
210°
Step-by-step explanation:
By inscribed angle theorem:
\( m\angle DFG = \frac{1}{2} \times m\widehat{(EDG)} \\\\
105\degree = \frac{1}{2} \times m\widehat{(EDG)} \\\\
105\degree\times 2= m\widehat{(EDG)} \\\\
\huge \red {\boxed {\therefore m\widehat{(EDG)} = 210\degree}} \)
The library sponsors a chess club for members of all ages and skill levels. Currently, the ages of the members are 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, and 22. The librarian uses a histogram to track the number of members in different age groups. For this situation, which is the appropriate way to label the age intervals on the x-axis?
Answers
Answer:
B. 7−10; 11−14; 15−18; 19−22
Step-by-step explanation:
The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals 10 6400 4096 Question 15 (1 point) The interquartile range is the 50th percentile the difference between the third quartile and the first quartile another name for variance the difference between the largest and smallest values
Answers
The variance of a sample is 4,096. And for interquartile, the difference between the largest and smallest values. The correct answer is option D
To calculate the variance we have a small formula:
v=s^2-----(1)
v=variance
s=Standard deviation
so, given that s=64
substitute in equation(1)
v=64*64
v=4096.
variance: The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean.
Variance is denoted by a symbol: σ2.
Interquartile range (IQR) is a measure of statistical dispersion, which is used to spread the data. The IQR is also called midspread.
To calculate the IQR, the data set is divided into quartiles. These quartiles are denoted by Q1 (another name is the lower quartile), Q2 (the median), and Q3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q3 − Q1
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Rita baked pies at the corner bakery the number Of pies she can bake x is limited by the ingredients they have in stock situation is represented by the compound inequality 2c-3<7 and 5-x<8 Solve the compound any quality inn select all the value solutions
Answers
Answer:
-3<x<5
Step-by-step explanation:
Given the inequality 2x-3<7 and 5-x<8
Solve 2x-3<7
Add 3 to both sides
2x-3+3 < 7+3
2x < 10
2x/2 < 10/2
x < 5
Solve 5-x<8
subtract 5 from both sides:
5-x-5<8-5
-x < 3
multiply both sides by -1
-(-x) > -3
x > -3
-3<x
Combine both solutions x < 5 and -3<x
-3<x<5
The solution to the compound inequality is -3<x<5
You read about an issue that was the subject of an observational study when clearly is should have been studied with a double-blind experiment.
How can the results from the observational study be classified?
Answers
The results from the observational study can only be classified as correlational or associative, but not causal.
This is because an observational study does not have the same level of control over variables as a double-blind experiment, making it difficult to establish a cause-and-effect relationship between the variables being studied. A double-blind experiment, on the other hand, allows for more rigorous control over variables and can establish a causal relationship between them. Therefore, the results from the observational study should be interpreted with caution and may require further investigation using a double-blind experiment to confirm any causal relationship.
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$1000 into savings account earning %1 annual compound interest for 10 years
Answers
After 10 years, the savings account will have approximately $1104.62.
If you deposit $1000 into a savings account earning an annual compound interest rate of 1% for 10 years, your money will grow over time due to the power of compounding. Compound interest means that the interest earned is added to the principal, and subsequent interest is calculated based on the new total.
In this case, with an interest rate of 1%, the amount will grow steadily over the 10-year period. The formula for calculating the future value of compound interest is FV = PV × (1 + r)ⁿ, where FV is the future value, PV is the principal amount, r is the interest rate, and n is the number of periods.
Plugging in the values, we get FV = $1000 × (1 + 0.01)¹⁰. Evaluating this equation, we find that the future value is approximately $1104.62.
This means that after 10 years, your initial $1000 investment will have grown to approximately $1104.62 due to the compounded interest. It demonstrates the benefit of saving money and allowing it to accumulate over time with compound interest.
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WILL MAKE BRAINLIEST!!Determine if two triangles are congruent if they are state the triangle congruence statement.
Answers
Answer:
Yes they are congruent by SSS criterion Explanation:AC=DC. (Given in figure)
AB=BD. (Given in figure
BC=BC. (Common)
that means triangle BAC is congruent to triangle BDC by SSS criterion
A soccer team orders 15 wooden pedestals to mount their brass trophies on. The design of each pedestal is shown below. The team is charged $0.12 per cubic inch of wood. What is the total cost of the order, rounded to the nearest dollar?
Answers
Answer:
$1193
Step-by-step explanation:
First we need to find the volume of one pedestal, that has a cylindrical part and a cubic part.
The volume of the cylindrical part is:
V1 = pi * r^2 * h
The radius is half the diameter, so r = 8/2 = 4 in. So the volume is:
V1 = pi * 4^2 * 3 = 48pi in3
The volume of the cubic part is:
V2 = side^3 = 8^3 = 512 in3
So the total volume of the pedestal is:
V = V1 + V2 = 512 + 48pi in3
If we want 15 pedestals, we have a total volume of:
15 * V = 15 * (512 + 48pi) = 9941.9467 in3
As each cubic inch costs $0.12, we just need to multiply the volume by the price to find the total cost:
Cost = 9941.9467 * 0.12 = $1193.03
Rounding to the nearest dollar, we have a cost of $1193
00 which statement best describes the
solutions to the scenario above?
A) Potrick con eat out only 1 time per week.
B Potick can eat out e'ther 1 or 2 times per week.
© Patrick con eat out 1, 2 or 3 times per week.
D) Potrick con cot Out 1, 2, 3, or times per week.
a 20/20 The Marn Cafe
Answers
Answer: D) Potrick con cot Out 1, 2, 3, or times per week.
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What is 12 1/2 X 4? I rlly need to know
Answers
SOLUTION
We want to solve
\(12\frac{1}{2}\times4\)To do this, change the mixed fraction into improper fraction.
We say, 2 multiplied by 12, then plus 1. We write the result as the numerator over the denominator which is 2. That is
\(\begin{gathered} 12\frac{1}{2}\text{ to improper fraction becomes } \\ 2\times12=24 \\ 24=1=25.\text{ this becomes } \\ \frac{25}{2} \end{gathered}\)We then multiply by 4, we have
\(\begin{gathered} \frac{25}{2}\times4 \\ This\text{ becomes } \\ \frac{25}{2}\times\frac{4}{1} \\ 2\text{ cancels itself is 1, and into 4, it is 2. So we have } \\ \frac{25}{1}\times\frac{2}{1} \\ =\frac{25\times2}{1\times1} \\ =\frac{50}{1} \\ =50 \end{gathered}\)Hence the answer is 50
volume of a cube that measeure 4.6 by 4.6 by 4.6
Answers
Answer:
97.336 (unit)³
Step-by-step explanation:
V=a³=(4.6)³=97.336 (unit)³
in a large western university, 15% of the students are graduate students. if a random sample of 5 students is selected, what is the probability that the sample contains exactly three graduate students?
Answers
There is a 0.2428 percent chance that the sample comprises exactly three graduate students.
Given That,
15% of the students at a big western university are graduate students. If five students are chosen at random as a sample
What is Binomial Distribution ?
The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.
This is a binomial distribution, the probability distribution function is
P(X =x) = C^320 (0.15)^3(1-0.15)^20-3
= [(20x19x18)/2x3](0.15)^3(1-0.15)^20-3
= 0.2428
As a result, 0.2428 is the likelihood that the sample contains exactly three graduate students.
To learn more about binomial distribution speed click here:
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Use the distributive property to remove the parentheses.
(-2+6y+w)(-5)
Answers
Answer: 10 - 30y - 5w
Step-by-step explanation:
Multiply each value of the first parenthesis to -5. Start with -2 (10), then 6y (-30y), and lastly w (-5w). Combine all the terms in order.
help pls Ix would really appreciate
Answers
Answer:
B
Step-by-step explanation:
g(2)=-7 because -(2)-5=-7
f(-7)=-18 because 2(-7)-4=-18
What is the solution to 3/2b + 5 < 17? Explain how.
(1) b < 8
(2) b > 8
(3) b < 18
(3) b > 18
Answers
Answer:
\( \blue{b < 8}\)
Answer 1 is correct
Step-by-step explanation:
\( \frac{3}{2} b + 5 < 17\)
Take 5 to the right side.
\( \frac{3}{2} b < 17 - 5 \)
\(\frac{3b}{2} < 12 \)
Multiply both sides by 2.
\(3b <12 \times 2\)
\(3b < 24\)
Divide both sides by 3.
\(b < 8\)
f(x) = 2x^2 Find f (-6)
Answers
Answer:
\(72\)
Step-by-step explanation:
\(f(x)=2x^2\)
replace x with -6
\(f(-6)=2(-6)^2\)
exponent
\(f(-6)=2(36)\)
multiply
\(f(-6)=72\)