Answer:
The student's z-score for mathematics is 0.75, which means that his score is 0.75 standard deviations above the mean. This puts him in the upper quartile of the class, indicating that he performed better than 75% of the class.
The student's z-score for economics is 1.5, which means that his score is 1.5 standard deviations above the mean. This puts him in the upper quintile of the class, indicating that he performed better than 80% of the class.
The student performed better in economics than in mathematics.
tapas and paella that originated in what country
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -0.08°C and 1.68°C.
The probability of obtaining a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.
What are the four types of probability?Probability is the branch of mathematics concerned with the occurrence of a random event, and there are four types of probability: classical, empirical, subjective, and axiomatic.
The readings at freezing on a set of thermometers are normally distributed, with a mean () of 0°C and a standard deviation () of 1.00°C. We want to know how likely it is that we will get a reading between -0.08°C and 1.68°C.
To solve this problem, we must use the z-score formula to standardise the values:
z = (x - μ) / σ
where x is the value for which we want to calculate the probability, is the mean, and is the standard deviation.
The lower bound is -0.08°C:
z1 = (-0.08 - 0) / 1.00 = -0.08
1.68°C is the upper bound:
z2 = (1.68 - 0) / 1.00 = 1.68
We can now use a standard normal distribution table or calculator to calculate the probabilities for each z-score.
The probability of obtaining a z-score of -0.08 or less is 0.4681, and the probability of obtaining a z-score of 1.68 or less is 0.9535, according to the table. We subtract the probability associated with the lower bound from the probability associated with the upper bound to find the probability of obtaining a reading between -0.08°C and 1.68°C:
P(-0.08°C x 1.68°C) = P(z1 z z2) = P(z 1.68) minus P(z -0.08) = 0.9535 - 0.4681 = 0.4854
As a result, the chance of getting a reading between -0.08°C and 1.68°C is approximately 0.4854 or 48.54%.
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TERM 1 ASSIGNMENT GRADE 7 Question 3 3.1. Calculate the following WITHOUT using a calculator; 3.1.1 6234 ×32
Answer: 6234 × 32 = 199488.
Step by step:
To calculate 6234 × 32 without using a calculator, you can use the traditional multiplication method as follows:
6234
x 32
-------
12468 (2 x 6234)
+ 62340 (3 x 6234 with a zero added)
--------
199488
Find the measure of ACD
A - 36 degrees
B - 126 degrees
C - 162 degrees
D - 216 degrees
Answer:
C
Step-by-step explanation:
i assume its
C.
PLEASE HELP!
whoever answers right get brainliest!!!
Answer:
FIRST ONE "Deb sold vases for two years, neither sold nor bought the next year and then sold bases for two more years"
Step-by-step explanation:
Notice the number of bases in debs collection is DECREASING as the years passes for the first and third period. This is she is selling her vases but in the middle the number is the same (two point in the same horizontal line) this means she neither sold nor bought any vase in that period.
Determine the relationship between the two triangles and whether or
not they can be proven to be congruent.
The two triangles are related by_____, so the triangles______
The two triangles are related by SAS criteria, so the triangles are congruent.
What are congruent triangles?Congruent triangles are triangles that are precisely the same size and form. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent. Corresponding portions are those areas of the two triangles that share the same dimensions (are congruent). This indicates that corresponding triangle parts are congruent (CPCTC).
From the given figure we observe for that the two triangles two sides and the corresponding angle of 90 degree is similar.
Thus, using the SAS criteria we see that the two triangles are equal.
Hence, the two triangles are related by SAS criteria, so the triangles are congruent.
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Given the equation x² + 4x + y²-2y = 20: (HINT: Type in the equation is the desmos calculator and get the answers from the graph.)
What is the radius of the circle?
What is the center of the circle?
Answer:
The radius of the circle is 3.
The center of the circle is (-2, 1).
Step-by-step explanation:
Rewrite the equation in standard form:
We need to rewrite the given equation in standard form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. To do this, we complete the square for both the x and y terms.
x² + 4x + y²-2y = 20
(x² + 4x + 4) + (y² - 2y + 1) = 20 + 4 + 1
(x + 2)² + (y - 1)² = 25
Identify the center and radius:
Now that we have the equation in standard form, we can identify the center and radius of the circle.
The center is the point (-2, 1), which we can read directly from the equation.
The radius is the square root of the number on the right side of the equation, which is 5. Therefore, the radius is sqrt(5) or approximately 2.236.
Alternatively, we can also use the Desmos graphing calculator to plot the equation and visually determine the center and radius. When we plot the equation, we see that it forms a circle with center (-2, 1) and radius 3.
Give an example to show that if d is not prime and n2 is divisible by d, then n need not be divisible by d.
If d is not a prime number and n^2 is divisible by d, it does not necessarily mean that n is also divisible by d, example is d = 6 and n = 3, where n^2 = 9 is divisible by 6, but n = 3 is not divisible by 6.
A prime number is a positive integer greater than 1 that has exactly two distinct factors: 1 and itself. For example, 2, 3, 5, 7, 11, 13, and 17 are all prime numbers.
If a number d is not prime, then it has at least one factor other than 1 and itself. Let's assume that d is not prime, and let p be a factor of d such that p is not equal to 1 or d. Then, by definition, p divides d evenly with no remainder.
Consider the case where d = 6 and n = 3.
Here, d is not a prime number, and n^2 = 9, which is divisible by d since 9 is a multiple of 6. However, n = 3 is not divisible by d = 6, as 6 does not divide 3 evenly.
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when a certain number is doubled and then decreased by 9, the result is not more than 19. Find the range of values of the number
Answer:
The number must be at most 10.
If the number is doubled and then decreased by 9, the result is 2x - 9.
2x - 9 ≤ 19
2x ≤ 28
x ≤ 14
Therefore, the range of values of the number is 0 to 10.
! 100 POINTS !
What is this question asking? What does it mean by floor plan? A step-by-step explanation would be very much appreciated.
Brainliest, ratings and thanks are promised if a helpful answer is received.
Step-by-step explanation:
So first of all u have to convert the metres into centimetres. After the conversation draw the map of both in centimetres and your map is done. The question is answered
Answer:
Determine the dimensions of the room: Measure the length and width of the room you want to draw a floor plan for using a tape measure. Record these measurements in meters.
Choose a scale: Since you want to use a scale of 1cm to 0.5m, you need to convert your measurements from meters to centimeters. For example, if your room measures 6 meters by 4 meters, you need to multiply each measurement by 100 to get 600cm by 400cm. Then, divide each measurement by 2 to get your scale measurement. In this case, your floor plan will be 300cm by 200cm.
Draw a rough sketch: Using a pencil and graph paper, draw a rough sketch of the room's shape based on the dimensions you have recorded.
Add doors and windows: Using the same scale, add doors and windows to your floor plan. Doors are typically represented by a straight line with an arc on top, while windows are represented by a straight line with a horizontal line through the middle.
Add fixtures and appliances: Add any fixtures and appliances that are permanent to the room, such as sinks, cabinets, and appliances. You can use symbols to represent these items, such as a rectangle for a refrigerator or a triangle for a sink.
Label everything: Finally, label everything on your floor plan using a legible font. This includes the dimensions of the room, the location of doors and windows, and the names of fixtures and appliances.
Step-by-step explanation:
the c on the left has blank1 - word answer please type your answer to submit electron geometry and a bond angle of
The CH3-CIOI-CNI molecule contains three carbon atoms with different electron geometries and bond angles. The CH3 and CIOI carbon atoms have tetrahedral geometry with a bond angle of approximately 109.5 degrees, while the CNI carbon atom has a trigonal planar geometry with a bond angle of approximately 120 degrees.
Using this Lewis structure, we can determine the electron geometry and bond angle for each carbon atom in the molecule as follows.
The carbon atom in the CH3 group has four electron domains (three bonding pairs and one non-bonding pair). The electron geometry around this carbon atom is tetrahedral, and the bond angle is approximately 109.5 degrees.
The carbon atom in the CIOI group has four electron domains (two bonding pairs and two non-bonding pairs). The electron geometry around this carbon atom is also tetrahedral, and the bond angle is approximately 109.5 degrees.
The carbon atom in the CNI group has three electron domains (one bonding pair and two non-bonding pairs). The electron geometry around this carbon atom is trigonal planar, and the bond angle is approximately 120 degrees.
Therefore, the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI are:
CH3 carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees
CIOI carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees
CNI carbon atom trigonal planar geometry, bond angle of approximately 120 degrees
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_____The given question is incomplete, the complete question is given below:
Determine the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI
Participant A did 120 jumping jacks in 10 minutes. Participant B did 140 jumping jacks in 14 minutes. Which participant had the greater jumping jack rate?
Answer: Participant A
Step-by-step explanation:
if you divide 120 by 10 you would get 12 jumping jacks per minute and if you divide 140 by 14 you would get 10 jumping jacks per minute
can someone help?
solve for x, using the secant lines
10cm, 7cm, 7cm. round to the nearest tenth
x = 4.9
Solution:
We can use the intersecting chords formula:
[tex]\text{(segment piece) x (segment piece) = (segment piece) x (segment piece)}[/tex][tex]7\times7 = 10x[/tex]
[tex]49 = 10x[/tex]
Divide each side by 10[tex]49\div10=10x\div10[/tex]
[tex]4.9 = x[/tex]
Therefore, x = 4.9.
Explain the Pythagorean identity in terms of the unit circle.
The three Pythagorean trigonometric identities, which I’m sure one can find in any Algebra-Trigonometry textbook, are as follows:
sin² θ + cos² θ = 1
tan² θ + 1 = sec² θ
1 + cot² θ = csc² θ
where angle θ is any angle in standard position in the xy-plane.
Consistent with the definition of an identity, the above identities are true for all values of the variable, in this case angle θ, for which the functions involved are defined.
The Pythagorean Identities are so named because they are ultimately derived from a utilization of the Pythagorean Theorem, i.e., c² = a² + b², where c is the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides.
This derivation can be easily seen when considering the special case of the unit circle (r = 1). For any angle θ in standard position in the xy-plane and whose terminal side intersects the unit circle at the point (x, y), that is a distance r = 1 from the origin, we can construct a right triangle with hypotenuse c = r, with height a = y and with base b = x so that:
c² = a² + b² becomes:
r² = y² + x² = 1²
y² + x² = 1
We also know from our study of the unit circle that x = r(cos θ) = (1)(cos θ) = cos θ and y = r(sin θ) = (1)(sin θ) = sin θ; therefore, substituting, we get:
(sin θ)² + (cos θ)² = 1
1.) sin² θ + cos² θ = 1 which is the first Pythagorean Identity.
Now, if we divide through equation 1.) by cos² θ, we get the second Pythagorean Identity as follows:
(sin² θ + cos² θ)/cos² θ = 1/cos² θ
(sin² θ/cos² θ) + (cos² θ/cos² θ) = 1/cos² θ
(sin θ/cos θ)² + 1 = (1/cos θ)²
(tan θ)² + 1 = (sec θ)²
2.) tan² θ + 1 = sec² θ
Now, if we divide through equation 1.) by sin² θ, we get the third Pythagorean Identity as follows:
(sin² θ + cos² θ)/sin² θ = 1/sin² θ
(sin² θ/sin² θ) + (cos² θ/sin² θ) = 1/sin² θ
1 + (cos θ/sin θ)² = (1/sin θ)²
1 + (cot θ)² = (csc θ)²
3.) 1 + cot² θ = csc² θ
Find the probability of landing on yellow, the probability of the complement, and the sum of the event and the complement. Type your answers without any spaces.
The probability of landing on yellow is 0.2, probability of component is 0.8, and sum of event and complement is 1.
On assuming that the pie is evenly divided into 5 parts,
So, the probability of landing on yellow is = 1/5 = 0.2,
The complement of landing on yellow is the probability of not landing on yellow, which is the probability of landing on any of the other 4 parts of the pie.
So, the probability of the complement is = 4/5 = 0.8,
The sum of the event (landing on yellow) and the complement (not landing on yellow) is equal to the probability of the entire sample space, which is 1.
⇒ P(Yellow) + P(Not Yellow) = 1
⇒ 0.2 + 0.8 = 1
So, the sum of the event and the complement is 1 or 100%.
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The given question is incomplete, the complete question is
A circular pie is divided in 5 parts , Green , Yellow, Blue Black and Red.
Find the probability of landing on yellow, the probability of complement, and the sum of the event and the complement.
the function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0. g
The required value of the function (f + g)(x) for given f(x) and g(x) as ( 3 / √x ) - ( 2 / x³ ) and √(5x - 7) is equals to ( 3 / √x ) - ( 2 / x³ ) + √(5x - 7).
Function f(x) is equals to,
( 3 / √x ) - ( 2 / x³ ) for all x > 0
Function g(x) is equals to,
g(x) = √(5x - 7)
To get the value of (f + g)(x),
Substitute the value of f(x) and g(x) and add the functions f(x) and g(x) together,
Sum of f(x) and g(x) is equals to,
(f + g)(x)
= f(x) + g(x)
= ( 3 / √x ) - ( 2 / x³ ) + √(5x - 7)
Therefore, value of the function (f + g)(x) is equals to ( 3 / √x ) - ( 2 / x³ ) + √(5x - 7).
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The above question is incomplete, the complete question is:
The function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0, g as a function of x is equal to the square root of quantity 5 x minus 7 Find (f + g)(x).
What is the measure of angle ABC?
After y - 4x = 12 is put in slope-intercept form, what is the slope?
-4
-1/4
-3
4
The Nutty Professor sells cashews for $6.80 per pound and Brazil nuts for $4.20 per pound. How much of each type should be used to make a 35 pound mixture that sells for $5.31 per pound?
The Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts tο make a 35 pοund mixture that sells fοr $5.31 per pοund.
Assume the Nutty Prοfessοr makes a 35-pοund mixture with x pοunds οf cashews and (35 - x) pοunds οf Brazil nuts.
The cashews cοst $6.80 per pοund, sο the tοtal cοst οf x pοunds οf cashews is $6.8x dοllars.
Similarly, Brazil nuts cοst $4.20 per pοund, sο (35 - x) pοunds οf Brazil nuts cοst 4.2(35 - x) dοllars.
The tοtal cοst οf the mixture equals the sum οf the cashew and Brazil nut cοsts, which is:
6.8x + 4.2(35 - x) (35 - x)
When we simplify, we get:
6.8x + 147 - 4.2x
2.6x + 147
The mixture sells fοr $5.31 per pοund, sο the tοtal revenue frοm selling 35 pοunds οf the mixture is:
35(5.31) = 185.85
When we divide the tοtal cοst οf the mixture by the tοtal revenue, we get:
2.6x + 147 = 185.85
Subtractiοn οf 147 frοm bοth sides yields:
2.6x = 38.85
When we divide by 2.6, we get:
x ≈ 14.94
Tο make a 35-pοund mixture that sells fοr $5.31 per pοund, the Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts.
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find the following answer
Cardinality of given set is 10.
Describe Cardinality.The cardinality of a mathematical set refers to the number of entries in the set. It may be limited or limitless. For instance, if set A has six items, its cardinality is equivalent to 6: 1, 2, 3, 4, 5, and 6. A set's size is often referred to as the set's cardinality. The modulus sign is used to indicate it on either side of the set name, |A|.
a Set's CardinalityA set that can be counted and has a finite number of items is said to be finite. On the other hand, an infinite set is one that has an unlimited number of components and can either be countable or uncountable.
Possible set of A=14+4+1+9=28
Possible set of C=1 +6+9+9=25
n(A∩ C)=10
Hence, Cardinality of given set is 10.
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Earnings per Share, Price-Earnings Ratio, Dividend Yield
The following information was taken from the financial statements of Zeil Inc. for December 31 of the current fiscal year:
Common stock, $25 par value (no change during the year) $3,500,000
Preferred $10 stock, $100 par (no change during the year) 2,000,000
The net income was $424,000 and the declared dividends on the common stock were $35,000 for the current year. The market price of the common stock is $11.20 per share.
For the common stock, determine (a) the earnings per share, (b) the price-earnings ratio, (c) the dividends per share, and (d) the dividend yield. If required, round your answers to two decimal places.
a. Earnings per Share $fill in the blank 1
b. Price-Earnings Ratio fill in the blank 2
c. Dividends per Share $fill in the blank 3
d. Dividend Yield fill in the blank 4
%
Therefore , the solution of the given problem of unitary method comes out to be common shares of Zeil Inc. is 2.23%.
An unitary method is what?This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.
Here,
Earnings per Share are calculated as (Net Income – Preferred Dividends) / the average number of outstanding Common Shares.
=> Market price per share / earnings per share is the Price-Earnings Ratio.
=> Dividends per Share are calculated as follows: Common Stock Dividends / Average Common Shares Outstanding
=> Dividend Yield is the product of dividends per share and the share price.
=> (Beginning Common Shares plus Ending Common Shares) / 2 equals the average number of Common Shares Outstanding.
=> Starting common shares equals ending common shares, which is
=> $3,500,000 / $25, or 140,000.
(a) The earnings per share are ($424,000 - $0) / 140,000, which equals $3.03.
The ordinary stock price of Zeil Inc.
(b) The price-earnings ratio for Zeil Inc.'s common shares is 11.20 divided by 3.03, or 3.69.
(c) Dividends per Share: $35,000./140,000. = $0.25
Therefore, $0.25 in dividends are paid per unit of Zeil Inc. common stock.
(d) Dividend Yield: $0.25 divided by $11.20 equals 0.0223, or 2.23%.
The common shares of Zeil Inc. is 2.23%.
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Need Help!
A commuter railway has 800 passengers per day and charges each one two dollars per day. For each 4 cents that the fare is increased, 5 fewer people will go by train.
What is the greatest profit that can be earned?
Greatest profit = $_____
Answer:
Step-by-step explanation:
To find the greatest profit, we need to determine the fare that will maximize revenue, while also considering the decrease in ridership due to the fare increase.
Let's assume the initial fare is $2, and the number of passengers is 800 per day. So, the initial revenue is:
$2 x 800 = $1600 per day
Now, let's say we increase the fare by 4 cents to $2.04. According to the problem, for each 4 cents increase in fare, there will be 5 fewer passengers. So, the number of passengers will decrease to:
800 - (5 x 4) = 780 passengers per day
The new revenue at this fare will be:
$2.04 x 780 = $1591.20 per day
By increasing the fare, the revenue decreased. This means that we may have increased the fare too much. Let's try another fare.
If we increase the fare by 2 cents to $2.02, the number of passengers will decrease by:
800 - (5 x 2) = 790 passengers per day
The new revenue at this fare will be:
$2.02 x 790 = $1595.80 per day
This is more revenue than the initial fare of $2 per person. Let's continue this process:
If we increase the fare by another 2 cents to $2.04, the number of passengers will decrease by:
790 - (5 x 2) = 780 passengers per day
The new revenue at this fare will be:
$2.04 x 780 = $1591.20 per day
This is less revenue than the $2.02 fare, so we can stop here.
Therefore, the greatest profit can be earned by charging $2.02 per person per day, and the maximum revenue will be:
$2.02 x 790 = $1595.80 per day
This is a bit less than the initial daily revenue of $1600, but it is the most revenue we can get by increasing the fare without causing a significant reduction in ridership.
Answer:
$2205
Step-by-step explanation:
You want the greatest profit that can be earned by a commuter railway that has 800 passengers per day at a fare of $2, and 5 fewer for each 4¢ increase in the fare.
Ridership functionThe number of riders (q) as a function of price (p) can be described by ...
q = 800 -5(p -2)/0.04
q = 1050 -125p . . . . . . . simplified
Revenue functionThe daily revenue is the product of price and the number of riders who pay that price.
r = pq
r = p(1050 -125p)
r = 125p(8.40 -p)
Maximum revenueThis function describes a parabola that opens downward. It has zeros at p=0 and p=8.40. The vertex of the parabola is on the line of symmetry, halfway between the zeros:
pmax = (0 +8.40)/2 = 4.20
The maximum revenue is ...
r(4.20) = 125·4.20(8.40 -4.20) = 125(4.20²) = 2205
The maximum revenue that can be earned is $2205.
__
Additional comment
The ridership at that fare is 125(4.20) = 525.
Profit is the difference between revenue and cost. Here, we have no information about the cost function, so we cannot predict the maximum profit. The question seems to assume that profit is equal to revenue.
6TH GRADE MATH, WRITE THE EQUATION FOR THIS GRAPH IN THE FORM OF Y=MX+B, TYSM
Answer:
m = 0
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0,2) (1,2)
We see the y stay the same and the x increase by 1, so the slope is
m = 0/1 = 0
So, the slope is 0
State whether the triangles could be proven congruent as SSS or SAS Theorem.
Using SSS theorem of congruency in triangles, we can prove that in all the cases, each triangle is congruent to the other.
What do you mean by congruent triangles?Whether two or more triangles are congruent depends on the size of the sides and angles. A triangle's size and shape are consequently determined by its three sides and three angles. If the pairings of the respective sides and accompanying angles are equal, two triangles are said to be congruent. Both of these are the exact same size and shape. Triangles may satisfy a number of distinct congruence requirements.
The SSS criterion is also known as the Side-Side-Side criterion. This standard states that two triangles are congruent if the sum of the three sides of each triangle is the same.
Here in the question,
It is given that the two sides of each triangle are equal to the corresponding sides of the other triangle.
Now as two sides of a triangle is equal to the two sides of another triangle, it is obvious that he third side will be equal to the corresponding sides of the other triangle.
Now as per the SSS criteria, as all the sides are equal to the corresponding sides of the other triangle, the triangle are congruent.
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true/false. The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed, given that the null hypothesis is true.
True. The p-value is a probability value that measures the power of evidence in against to the null hypothesis in a statistical test.
Mainly, it represents the possibility of staring at a test statistic as a minimum as extreme as the one computed, assuming that the null hypothesis is genuine.
If the p-value is small, commonly less than a chosen significance stage (e.g., 0.05), it shows that the determined data is unlikely to have took place by danger alone and provides proof against the null hypothesis. alternatively, a large p-value suggests that the determined information is consistent with the null speculation, and the evidence isn't sturdy enough to reject it.
Consequently, the p-value is an critical tool in statistical inference, permitting researchers to draw conclusions about the population based totally on pattern information and degree the extent of uncertainty in their outcomes.
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Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us?
92 19 41 24 75 53 70 3 67 64 9
Step-by-step explanation:
To find the range, we need to subtract the smallest value from the largest value in the dataset:
Range = Largest value - Smallest value
Range = 92 - 3
Range = 89
To find the variance and standard deviation, we need to calculate the mean first:
Mean = (Sum of all values) / (Number of values)
Mean = (92+19+41+24+75+53+70+3+67+64+9) / 11
Mean = 45.09 (rounded to two decimal places)
Next, we need to calculate the variance:
Variance = (Sum of squared differences from the mean) / (Number of values - 1)
Variance = [(92-45.09)^2 + (19-45.09)^2 + (41-45.09)^2 + (24-45.09)^2 + (75-45.09)^2 + (53-45.09)^2 + (70-45.09)^2 + (3-45.09)^2 + (67-45.09)^2 + (64-45.09)^2 + (9-45.09)^2] / (11-1)
Variance = 1071.45 (rounded to two decimal places)
Finally, we can calculate the standard deviation by taking the square root of the variance:
Standard deviation = Square root of variance
Standard deviation = Square root of 1071.45
Standard deviation = 32.74 (rounded to two decimal places)
The range tells us the difference between the highest and lowest values in the dataset, which in this case is 89. The variance and standard deviation tell us how spread out the data is from the mean. The higher the variance and standard deviation, the more spread out the data is. In this case, the variance and standard deviation are both relatively high, indicating that the data is fairly spread out.
please help asap!!!!!!!
To remove the y-term in the given linear equation in two Variable multiply the equation by 4 then add these two equations.
What is linear equation in two Variable;
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. Yet, there are two solutions to a linear equation with two variables.
According to given question;
5X+8y=5 ……..eqn 1.
3x-2y=3 ………eqn 2.
Multiply by 4 in the eqn 2.
We get
12x-8y=12 ……..eqn 3 .
When we add eqn 1 and eqn 3 we get ;
17x =17
X =1
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After eliminating the y-term in the given equations i.e 5x+8y=5 and
3x-2y=3, The solution to the system of equations is x = 1, y = 0.
What is elimination method?The elimination method is the technique used to solve systems of linear equations. It involves adding or subtracting equations in a system to eliminate one variable and find the value of the other variable.
To eliminate the y-term in these equations, you can multiply the second equation by 4, which will give you:
12x - 8y = 12
Now, you can add this equation to the first equation:
5x + 12x + 0y = 5 + 12
Simplifying the left side gives you 17x, and simplifying the right side gives you 17. So, you have the equation:
17x = 17
Solving for x gives you x = 1.
Now that you have found the value of x, you can substitute it into one of the original equations to solve for y. Using the first equation, you get:
5(1) + 8y = 5
Simplifying this equation gives you:
8y = 0
Solving for y gives you y = 0.
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Sara is a salesperson for Camera's Etc., which is a retailer for high-end digital cameras. Historically. Sara has averaged selling 2.7 extended warranties per day for cameras that she sells. Assume the number of camera warranties that Sara
sells per day follows the Poisson distribution. Complete part A
a. What is the probability that Sara will sell four extended warranties tomorrow?
The probability that Sara whassell four extended warranties tomorrow is___
(Round to four decimal places as needed.)
Answer:
The probability that Sara whassell four extended warranties tomorrow is 0.1046
Step-by-step explanation:
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We can use the Poisson probability formula to calculate the probability of selling 4 extended warranties tomorrow:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the average number of extended warranties sold per day and k is the number of extended warranties sold.
In this case, λ = 2.7 and k = 4. So, plugging in the values, we get:
P(X = 4) = (e^(-2.7) * 2.7^4) / 4!
P(X = 4) ≈ 0.1046
Therefore, the probability that Sara will sell four extended warranties tomorrow is approximately 0.1046, rounded to four decimal places.
Please help fast!! Find the slope of a line parallel to the line whose equation is 3x+18y=−486.
Fully simplify your answer.
Answer: -1/6
Step-by-step explanation:
Put the equation into y = mx + b (slope) form.
3x + 18y = -486
18y = -3x - 486
y = -1/6x - 27
If the line is parallel to this line, the slope must be the same.
Use the slope and y-intercept to identify the equation of this line.
The equation of the line is y = -2x. The correct option is the last option y = -2x
Writing the equation of the line in the given graphFrom the question, we are to write the equation of the line in the given graph using the slope and y-intercept from the graph
First, we will determine the slope of the graph
The slope of the graph calculated from the formula
Slope = Change in y / Change in x
Slope = (y₂ - y₁) / (x₂ - x₁)
Picking the points (-1, 2) and (0, 0)
Slope = (0 - 2) / (0 - (-1))
Slope = -2/(0 + 1)
Slope = -2/1
Thus,
Slope = -2
From the graph, the y-intercept of the graph is 0
Then,
From the slope-intercept form of the equation of a line,
y = mx + c
Where m is the slope
and c is the y-intercepts
The equation of the line is
y = -2x + 0
y = -2x
Hence, the equation is y = -2x
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