Answer:
Thank you for the statement. Is there a question or additional information you would like me to respond to?
Step-by-step explanation:
A committee of 8 people is to be chosen from 7 men and 5 women. What is the number of committee if a) the committee contains at least 3 men and at least 3 women, b) the oldest man or the oldest woman, but not both, must be included in the committee?
Answer:196 possible committees
Step-by-step explanation:
Part (a): Three cases:
Case 1: 3 men and 5 women: (7 C 3) * (5 C 5) = 35 * 1 = 35; or
Case 2: 4 men and 4 women: (7 C 4) * (5 C 4) = 35 * 5 = 175; or
Case 3: 5 men and 3 women: (7 C 5) * (5 C 3) = 21 * 10 = 210
35 + 175 + 210 = 420 possible committees
Part (b): Six cases:
Cases 1–3: Oldest man included (but not oldest woman):
Case 1: 3 men and 5 women: Not possible**; therefore, 0; or
Case 2: 4 men and 4 women: 1 * (6 C 3) * (4 C 4) = 20 * 1 = 20; or
Case 3: 5 men and 3 women: 1 * (6 C 4) * (4 C 3) = 15 * 4 = 60; or
Cases 4–6: Oldest woman included (but not oldest man):
Case 4: 3 men and 5 women: (6 C 3) * (5 C 5) = 20 * 1 = 20; or
Case 5: 4 men and 4 women: (6 C 4) * 1 * (4 C 3) = 15 * 4 = 60; or
Case 6: 5 men and 3 women: (6 C 5) * 1 * (4 C 2) = 6 * 6 = 36
0 + 20 + 60 + 20 + 60 + 36 = 196 possible committees
Trey has plastic cubes stored in box that measures 4 ft long, 2 1/2 ft wide, and 2 ft tall.
The edge length of each plastic cube is 1/2 ft.
How many plastic cubes can fit into the box?
Based on the given information, Trey can fit 160 plastic cubes inside the box.
What is volume of cube?
The volume of a cube is calculated by cubing the length of any one side of the cube. In other words, if a cube has sides of length "s", then its volume "V" is V = s³
To calculate the number of plastic cubes that can fit inside the box, we need to first calculate the volume of the box and the volume of each plastic cube. Then, we can divide the volume of the box by the volume of each plastic cube to get the total number of cubes that can fit inside.
The volume of the box is:
4 ft x 2.5 ft x 2 ft = 20 cubic feet
The volume of each plastic cube is:
(1/2 ft) x (1/2 ft) x (1/2 ft) = 1/8 cubic feet
To find out how many plastic cubes can fit inside the box, we can divide the volume of the box by the volume of each plastic cube:
20 cubic feet ÷ (1/8 cubic feet) = 160
Therefore, Trey can fit 160 plastic cubes inside the box.
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Each time Caroline goes shopping she decides whether or not to buy fruit. The probability that she does buy fruit is 0.4. Independently, she then decides whether or not to buy a CD, with a probability of 0.6 that she does buy a CD. Work out the probability that she buys fruit or buys a CD or both.
Answer:
To work out the probability that Caroline buys fruit or buys a CD or both, you can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are events.
In this case, A is the event that Caroline buys fruit and B is the event that Caroline buys a CD.
The probability that Caroline buys fruit is 0.4 and the probability that Caroline buys a CD is 0.6.
To find the probability that Caroline buys fruit and a CD, you can multiply the probabilities of the two events:
P(A and B) = P(A) x P(B) = 0.4 x 0.6 = 0.24
Therefore, the probability that Caroline buys fruit or buys a CD or both is:
P(A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.6 - 0.24 = 0.76
So, the probability that Caroline buys fruit or buys a CD or both is 0.76 .
cart a with mass m travels in the x direction with a speed of 4 m/s. it collides with car t b, which has mass 3m and is initially at rest. after the collision, cart a moves in the -x direction and cart b moves in the x direction. assume that the collision was perfectly elastic
After the collision, cart a moves in the negative x direction with a speed of 4 m/s, and cart b moves in the positive x direction with a speed of 2 m/s.
In a perfectly elastic collision, the total momentum of the system is conserved, as well as the total kinetic energy. This means that the sum of the momenta of the carts before the collision is equal to the sum of the momenta after the collision. In this case, since cart b is initially at rest, its initial momentum is zero.
We can use conservation of momentum to determine the final velocities of the carts. Let the velocity of cart b after the collision be v, then the velocity of cart a after the collision is -4 m/s. The momentum of cart a before the collision is m(4 m/s) = 4m, and the momentum of cart b after the collision is 3mv.
Using conservation of momentum, we have:
m(4 m/s) + 0 = m(-4 m/s) + 3mv
Simplifying this equation, we get:
8m = 3mv + 4m
Dividing both sides by 3m, we get:
v = (8/3) - (4/3)v
Solving for v, we get:
v = 2 m/s
So after the collision, cart a moves in the negative x direction with a speed of 4 m/s, and cart b moves in the positive x direction with a speed of 2 m/s. We can verify that this satisfies conservation of momentum:
m(4 m/s) + 0 = m(-4 m/s) + 3m(2 m/s)
4m = 4m
This result shows that in a perfectly elastic collision, even though the carts exchange momentum, the total momentum of the system is conserved.
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HELLLPPP
Use addition to rewrite the subtraction expression below without changing the
digits. Do not solve.
6-(-20)
Answer:
6+20
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
44°+107°+x°=180
151°+x°=180°
x°=180°-151°
x°=29°
2. In March, Sunshine Kindergarten was given a sum of $2000. It spent 10% of the sum given on books, 70% on food and the rest on cleaning services. In April the sum given was reduced. The kindergarten spent the same amount of money on books and reduced its spending of food by $240. It spent the remaining 20% of the sum given in April on cleaning services. By what percentage was the sum given to the kindergarten reduced?
The sum given to the kindergarten was reduced by 15%.
How to solve this problemLet's first find out how much money the kindergarten spent in March:
Books: 10% of $2000 = 0.1 x $2000 = $200Food: 70% of $2000 = 0.7 x $2000 = $1400Cleaning services: $2000 - $200 - $1400 = $400So, in April, the kindergarten spent the same amount on books, which was $200. It also reduced its spending on food by $240, which means it spent:
Food: $1400 - $240 = $1160
The remaining 20% of the sum given in April was spent on cleaning services, which means:
Cleaning services: 20% of sum given in April = 0.2 x $x (where x is the sum given in April)
We can set up an equation based on the above information:
$200 + $1160 + 0.2x = x
Simplifying and solving for "x":
$1360 + 0.2x = x
0.8x = $1360
x = $1700
Therefore, the sum given to the kindergarten in April was $1700, which means it was reduced by:
($2000 - $1700) / $2000 x 100% = 15%
So, the sum given to the kindergarten was reduced by 15%.
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As an experiment, a charity decides to use SMART to determine a shortlist from the seven applicants who have
applied for the post of Regional Officer for the Western Region. The main criteria which will be used to
compare candidates are: salary they would expect (SALARY), their experience of charity work (CHARITY EXP),
their managerial experience (MANAGEMENT EXP), their educational qualifications (EDUCATION), their
apparent commitment to the charity's work (COMMITMENT) and the quality of the ideas they put forward on
the form (IDEAS).
(a) Discuss if the weights of the attributes are appropriate. If so, why do you think so? If not, why do you
think the weights are not appropriate? (You don't need to discuss whether the attributes are
appropriate. Only focus on the "weights". This is your own opinion and subjective. You don't need
references for this.)
The personnel manager ranked all the criteria, except salary, in order of importance and then assigned weights
as follows:
COMMITMENT
MANAGEMENT EXP
IDEAS
CHARITY EXP
EDUCATION
Candidate A's aggregated score is 50.
(You don't need to worry about how 50 was calculated.)
The other candidates' aggregated scores are found below.
100
70
65
55
10
b) Scatter plot chart would indicate a positive correlation
c) Candidate D would be the most cost-effective choice, as their expected salary would increase the most. Candidate F would also be a good choice, as their expected salary would increase by £1,000.
What is a Scatter plot chart?A scatter plot chart can be used to plot the data of the two variables on a two-dimensional graph, and the data points can be connected with a line or a curve.
a) The weights of the attributes in this case seem to be appropriate for the purpose of selecting a Regional Officer for the Western Region.
This data shows that the charity is placing a greater emphasis on the candidate's commitment, managerial experience and ideas, as these are likely to be the most important factors in selecting a successful Regional Officer.
Additionally, Education has the lowest weight at 10, indicating that this is not a major factor in consideration.
Overall, the weight of each criteria reflects the importance of the criteria to the charity and is appropriate for this case.
b) The scatter plot chart would indicate a positive correlation between the two variables, with the higher aggregate score corresponding to the higher expected salary.
Based on this chart, candidates A, D and F would be the best 2-3 candidates, with the highest aggregate scores of 50, 90 and 62 respectively.
c) If the charity is prepared to pay £1,000 for each additional aggregate score, then candidate D would be the most cost-effective choice, as their expected salary would increase the most (from £60,000 to £61,000). Candidate F would also be a good choice, as their expected salary would increase by £1,000 (from £52,000 to £53,000).
Candidate A would not be recommended, as their expected salary would increase by only £500 (from £46,000 to £46,500).
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PLEASE HELP!!! i am failing and im going to be held back if i dont get my grade up!!!!
Emma spent $45.20 on 5 dozen bagels and a gallon of iced tea. The price of the gallon of iced tea was $5.25. The following equation can be used to find d, the price of each dozen of bagels.
5d + 5.25 = 45.2
What was the price of each dozen of bagels?
A.
$6.99
B.
$7.99
C.
$9.04
D.
$3.79
Answer:
the answer to the question is B
Step-by-step explanation:
no need for explanation just trust the source
Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.
We want to copy the original triangle using only two of its sides and the included angle. To do this, we'll create a new triangle with the same side lengths and angle measures as the original triangle.
To copy a triangle using two of its sides and the included angle, follow these steps:
Using point E as the center, draw a circle with a radius equal to the length of side DE.Using point E as the vertex and side DE as one side of the angle, create an angle that is equal to the measure of angle D.Draw ray EF that extends from point E through the angle you created in step 2.Locate the intersection of ray EF and the circle you drew in step 1, and label the point of intersection F.Complete the triangle DEF by drawing a line segment that connects points D, E, and F.Learn more about vertex :
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Can you solve this question?
m=?
b=?
The equation of the tangent line is y = -x/3 + 1/3 where
m = -1/3 and b = 1/3What is the equation of a tangent line to a curve?The equation of a tangent line to a curve is the equation of the line that touches the curve at that point and tangent to it.
To find the equation of the tangent line to the curve y = 1/(3sinx + 3cosx) at (0, 1/3), we know that the value of the tangent at that point is the derivative of the curve at that point.
so, differentiating y wiith respect to x, we have
y = 1/(3sinx + 3cosx)
= (3sinx + 3cosx)⁻¹
Let u = 3sinx + 3cosx
y = u⁻¹
dy/dx = du⁻¹/du du/dx
= -u⁻² du/dx
Now du/dx = d(3sinx + 3cosx)/dx
= d3sinx/dx + d3cosx/dx
= 3cosx - 3sinx
So, dy/dx = -u⁻² du/dx
= -(3sinx + 3cosx)⁻²(3cosx - 3sinx)
= -(3cosx - 3sinx)/3sinx + 3cosx)²
Now, at (0, 1/3)
dy/dx = -(3cosx - 3sinx)/3sinx + 3cosx)²
= -(3cos0 - 3sin0)/3sin0 + 3cos0)²
= -[3(1) - 3(0)]/[3(0) + 3(1))²
= -[3 - 0]/[0 + 3)²
= -3/3²
= -1/3
Now, the equation of a line in slope form passing through the point (x', y') is
(y - y')/(x - x') = m where m = slope
For the tangent line
m = dy/dx = -1/3, x = 0 and y = 1/3So, substituting the values of the variables into the equation we have
(y - y')/(x - x') = m
(y - 1/3)/(x - 0) = -1/3
(y - 1/3)/x = -1/3
y - 1/3 = -x/3
y = -x/3 + 1/3
Comparing this with the equation of a line in slope-intercept form y = mx + b where m = slope and b = y-intercept
m = -1/3 and b = 1/3So, the equation of the tangent line is y = -x/3 + 1/3 where
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Tanya buys 12 water bottles.
Of those bottles, 5 hold 300 milliliters each and 7 hold 1.5 liters each.
How much water, in liters, does Tanya buy?
Answer:
12 L 500 mL
Step-by-step explanation:
Eric is planning an event at a hotel. Let g stand for the number of Eric’s guests. The two expressions represent the difference the cost of the rooms. Expression 1: (326 + 37g) - (287+ 23g). Expression 2: 38+ 14g. What can you tell about expression 2 and expression 1?
Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for all g guests, while Expression 2 represents the difference in cost between the hotel room and the cost of food and beverage for a single guest.
Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for Eric's guests. The first part of the expression (326 + 37g) represents the cost of the hotel room for all g guests, while the second part of the expression (287 + 23g) represents the cost of food and beverage for all g guests. To calculate the total cost of the hotel room and food and beverage, we can use the following formula: (326 + 37g) - (287 + 23g) = 39 + 14g.Expression 2, on the other hand, represents the difference in cost between the hotel room and the cost of food and beverage for a single guest. The first part of the expression (38 + 14g) represents the cost of the hotel room for one guest, while the second part of the expression (287 + 23g) represents the cost of food and beverage for one guest. To calculate the total cost of the hotel room and food and beverage for one guest, we can use the following formula: 38 + 14g.In conclusion, Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for all g guests, while Expression 2 represents the difference in cost between the hotel room and the cost of food and beverage for a single guest.
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i need help finding x
Answer:
Step-by-step explanation:
Formula for the sum of interior angle of an n-gon is S = (n-2)x180°.
So for our 5 sided polygon we get:
S = (5-2)x180° = 540°
Now we can solve:
[tex]100+4x+(3x+3)+(5x-2)+103=540[/tex]
[tex]12x+204=540[/tex]
[tex]12x=336[/tex]
[tex]x=28[/tex]°
Solution: [tex]x=28[/tex]°
Answer: x=43
Step-by-step explanation:
We know The interior angles in a hexagon sum to 720°.
so we can add all the angles and equal them to 720
100 + 4x + (3x + 3) + (5x-2) + 103 = 720
Simplify by combining like terms
(100 + 3 -2 + 103) and (4x + 3x +5x)
204 + 12x = 720
Subtract 204 from both sides to isolate x
204 - 204 + 12x = 720 - 204
12x = 516
Divide both sides by 12 to solve for x
12/12 x = 516/12
Simplify
x = 43
to check your work, substitute the value of x into your equation and solve
100 + 4x + 3x + 3 + 5x-2 + 103 = 720
100 + 4(43) + (3)(43) + 3 + (5)(43) -2 + 103 = 720
100 + 172 + 129 + 3 + 215 -2 + 103 = 720
720 = 720
They equal so your solution is correct
If you roll a six sided die 300 times how many times would you expect to get a five
Answer:
50, because yes
A die is rolled 2 times. What is the probability of getting a 1 on the first roll and a 2 on the second roll.
The probability of getting a '1' on the first roll and '2' on the second roll for the given expression is [tex]\frac{1}{18}[/tex] .
What about probability?
In mathematics and statistics, probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
The probability of an event A is denoted by P(A) and is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In other words, it is the number of ways that event A can occur divided by the total number of possible outcomes.
For example, if you roll a fair six-sided die, the probability of rolling a 4 is 1/6, since there is only one favorable outcome (rolling a 4) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).
Probability is used in many different fields, such as gambling, statistics, and science, to make predictions about the likelihood of different outcomes. It is also used to model complex systems and to test hypotheses in scientific experiments.
According to the given information:
When a die is rolled 2 times, the output we get
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
Total no of getting '1' on first roll and '2' on second roll = 2
Total outcomes = 36
⇒ [tex]\frac{2}{36}[/tex]
⇒ [tex]\frac{1}{18}[/tex]
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Find thenonpermissible replacment for x in this expression b^2/-7b+7
We can conclude by answering the provided question that expression As a result, b = 1 is not a valid substitute for b in the equation because it would set the denominator to zero and render the expression undefined.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical association or routine. A real integer, a mutable, or a mix of the two can be used as an equation. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and geometry. They are used in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
The expression is as follows:
[tex]b^2 / (-7b + 7)\\-7b + 7 = 0\\b = 1\\[/tex]
As a result, b = 1 is not a valid substitute for b in the equation because it would set the denominator to zero and render the expression undefined.
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100 POINTS + BRAINLIEST!!
a is 15 days
b is 20%
hope this helps you
Answer:
a is 15 daysb is 20%
Step-by-step explanation:
A company performs $3,200 of services during the month and bills customers. The customers are expected to pay next month.
Record the customer billing using (a) accrual-basis accounting and (b) cash-basis accounting.
Recording the customer billing using (a) accrual-basis accounting and (b) cash-basis accounting is as follows:
a) Accrual Method:Customer Billing:
Debit Accounts Receivable $3,200
Credit Service Revenue $3,200
(To record the performance of services for customers during the month.)
b) Cash Method:Customer Billing:
No Record during the current month.
What differentiates cash-basis accounting from accrual-basis accounting?Cash-basis accounting recognizes expenses and revenues when cash exchange takes place.
Accrual-basis accounting matches expenses and revenues to the month or period when the transaction occurs, whether there is a cash exchange or not.
For instance, the accrual-basis will recognize the receipt of cash as follows:
Next Month:
Debit Cash $3,200
Credit Accounts Receivable $3,200
On the other hand, the cash-basis will recognize revenue with the receipt of cash as follows:
Next Month:
Debit Cash $3,200
Credit Service Revenue $3,200
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Solve the following system of equations by linear combination:
3x – y = 7
x + y = 5
Answer:
x=3, y=2
Step-by-step explanation:
First Add both equations
3x-y=7 ---1
x+y=5 ---2
----------
so we get, 4x=12
so x=3
Now plug x back into equation 2 so we get y=2
Step-by-step explanation:
that means we optionally multiply one or both equations with some factors, so that one variable term has the same coefficient in both equations but with different signs.
and then we add both equations giving us one equation in the other variable, which we can solve.
and then we use that with any of the original equations to solve for the first variable.
in this case we don't need the multiplication step, as the terms in y have already the same coefficient (1) with different signs.
so, we add both equations
3x - y = 7
+ x + y = 5
------------------
4x 0 = 12
4x = 12
x = 12/4 = 3
x + y = 5
3 + y = 5
y = 5 - 3 = 2
According to komonews.com, the chances it will rain on any day in the 1st week of January in Seattle is about 0.614.
a) What is the probability that it will rain on January 1st?
b) What is the probability that it will rain for the first time in the New Year on January 3rd?
c) What is the probability that the people of Seattle get to wait at least 3 days until it rains for the first time in the New Year?
d) How many days, on average, do they wait for the first day of rain in the New Year?
e) If X = the number of days until it rains for the first time, is X binomial or geometric or neither? Explain.
(a) The probability of rain on January 1st is 0.614. (b) The probability of rain for the first time in the New Year on January 3rd is 0.136*0.614 = 0.083. (c) the probability that people of Seattle get to wait at least 3 days until it rains for the first time in the New Year is 0.053. (d) They wait for the first day of rain in the New Year is 1/0.614 ≈ 1.63 days. (e) The distribution of X is a geometric distribution.
a) The probability that it will rain on January 1st can be estimated using the information provided by komonews.com, which states that the chances of rain on any day in the first week of January in Seattle is about 0.614. Assuming that the probability of rain is constant across all days of the week, the probability of rain on January 1st is also 0.614.
b) The probability that it will rain for the first time in the New Year on January 3rd can be calculated by considering the probability of no rain for the first two days, followed by rain on the third day. The probability of no rain for the first two days is [tex](1-0.614)^2[/tex] = 0.136, and the probability of rain on the third day is 0.614. Therefore, the probability of rain for the first time in the New Year on January 3rd is 0.136*0.614 = 0.083.
c) The probability that the people of Seattle get to wait at least 3 days until it rains for the first time in the New Year can be calculated by considering the probability of no rain for the first three days. The probability of no rain for the first three days is [tex](1-0.614)^3[/tex] = 0.053. Therefore, the probability that people of Seattle get to wait at least 3 days until it rains for the first time in the New Year is 0.053.
d) The expected value or average of the number of days people in Seattle wait for the first day of rain in the New Year can be calculated by using the formula E(X) = 1/p, where p is the probability of rain on any given day. Therefore, the expected value or average number of days people in Seattle wait for the first day of rain in the New Year is 1/0.614 ≈ 1.63 days.
e) The number of days until it rains for the first time in the New Year, X, is a geometric random variable since it represents the number of trials until the first success (rain). The probability of success (rain) remains constant over time, and the trials (days) are independent of each other. Therefore, the distribution of X is a geometric distribution.
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The daily high temperatures, in degrees Fahrenheit, of Des Moines for one week were: Day Temperature (in Fahrenheit) Monday 64.5 Tuesday 64 Wednesday 66.5 Thursday 64 Friday 62.5 Saturday 61 Sunday 63 Using the data above, what is the standard error of the sample mean? Answer choices are rounded to the hundredths place.
Answer:0.65
Step-by-step explanation:
The standard error of the sample mean is approximately 0.682, rounded to the hundredths place.
To calculate the standard error of the sample mean, we need to find the sample mean and the standard deviation of the data. Then we can divide the standard deviation by the square root of the sample size.
First, let's calculate the sample mean:
Mean = (64.5 + 64 + 66.5 + 64 + 62.5 + 61 + 63) / 7 = 64.14
Next, let's calculate the standard deviation. We will use the sample formula for standard deviation (Bessel's correction):
Calculate the squared differences from the mean for each temperature:
(64.5 - 64.14)² = 0.1904
(64 - 64.14)² = 0.0204
(66.5 - 64.14)² = 5.5376
(64 - 64.14)² = 0.0204
(62.5 - 64.14)² = 2.6836
(61 - 64.14)² = 9.8324
(63 - 64.14)² = 1.2696
Calculate the sum of the squared differences:
Sum = 0.1904 + 0.0204 + 5.5376 + 0.0204 + 2.6836 + 9.8324 + 1.2696 = 19.5544
Calculate the variance:
Variance = Sum / (n - 1) = 19.5544 / (7 - 1) = 3.25907
Calculate the standard deviation:
Standard Deviation = sqrt(Variance) = sqrt(3.25907) = 1.80597
Finally, let's calculate the standard error of the sample mean:
Standard Error = Standard Deviation / sqrt(n) = 1.80597 / sqrt(7) ≈ 0.682
Therefore, the standard error of the sample mean is approximately 0.682, rounded to the hundredths place.
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What is the length of the unknown leg of the right triangle?
The length of the unknown leg of the right triangle is 6.2 ft rounded to one decimal place, using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
we shall represent the unknown leg of the right triangle with the letter "x" so that by Pythagoras rule we can evaluate for x as follows:
8² = 5² + x²
x = √(8² - 5²) {make TV the subject}
x = √(64 - 25)
x = √39
x = 6.2450
Therefore, the length of the unknown leg of the right triangle is 6.2 ft rounded to one decimal place, using the Pythagoras rule.
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A family has two cars. During one particular week, the first car consumed 25 gallons of gas and the second consumed 20 gallons of gas. The two cars drove a
combined total of 1075 miles, and the sum of their fuel efficiencies was 50 miles per gallon. What were the fuel efficiencies of each of the cars that week?
First car: miles per gallon
Second car: miles per gallon
We can conclude after answering the presented question that As a equation result, the first car's fuel efficiency was 15 miles per gallon, whereas the second car's fuel economy was 35 miles per gallon.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Let's name the first car's fuel efficiency (miles per gallon) x and the second car's fuel efficiency y. We are aware of the following:
The first automobile used 25 gallons of gas and covered 25 miles.
The second automobile used 20 gallons of petrol and drove 20 miles.
The two automobiles went a total of 1075 miles, thus 25x + 20y = 1075.
Their combined fuel economy was 50 miles per gallon, thus x + y = 50/1 = 50.
[tex]25x + 20y = 1075\\x + y = 50\\25x + 20y = 1075\\-20x - 20y = -1000\\5x = 75x = 15\\x + y = 50\\15 + y = 50\\y = 35\\[/tex]
As a result, the first car's fuel efficiency was 15 miles per gallon, whereas the second car's fuel economy was 35 miles per gallon.
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The diameter of a cone's circular base is 6 inches. The height of the cone is 12 inches.
What is the exact volume of the cone?
Enter your answer in the box.
Answer:
The correct answer is 36π
Step-by-step explanation:
The equation 24b = t is used to find b, the cost of 1 bottle of water when sold in a 24‐pack case with a case price of t dollars. What is the cost of 1 bottle of water when the case price is $7.50?
The cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents.
The given equation is 24b = t, where b is the cost of one bottle of water and t is the price of a case of 24 bottles.
We are given that the price of the case is $7.50. Substituting this value in the equation, we get:
24b = 7.50
To solve for b, we need to isolate it on one side of the equation. We can do this by dividing both sides by 24:
b = 7.50/24
Simplifying this expression, we get:
b = 0.3125
Therefore, the cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents. In other words, if you were to buy a case of 24 bottles of water for $7.50, each bottle of water would cost you about 31.25 cents.
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the table shows the heights and masses of a male gorrila and a female gorilla at zoo.Based on the table, wich statement is true?
Using mensuration, we can find that the mass of male is greater than that of the female's by 63.507kg.
Define mensuration?Mensuration can be defined as a measurement action. Our world is three dimensional. Both elementary school mathematics and secondary school mathematics heavily rely on the idea of measurement. Also, measuring is directly related to our daily life. When we learn to measure items, we practise measuring both 2D and 3D shapes. Both conventional and nonconventional units of measurement can be used to determine the size of objects or quantities.
In the given table,
Height of male = 1.68m.
Mass of male = 158.757kg.
Height of female = 1.448m.
Mass of female = 95.25kg.
Difference between mass of male and female,
= 158.757 - 95.25
= 63.507kg.
The mass of male is greater than that of the female's by 63.507kg.
So, 2nd statement is true.
Rest of the statements are not true.
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Help me out please and thank you
As a result, whereas the latter two expressions are not polynomials, the first two and last one are polynomial.
Define coefficientA coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or any expression . For instance, the first two terms of the polynomial with the variables x and y have coefficients of 7 and -3, respectively. The constant coefficient is the third term of 1.5.
Define polynomial?An expression made up of variables and coefficients and utilizing solely the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables is referred to as a polynomial.
Let's examine each phrase separately:
Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "3X² -5x⁴+2x-12" is a polynomial.
Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "x⁵-5x⁴+4x³-3x²+2x-1" is a polynomial.
- Since it contains negative exponents of variables, which are not permitted in polynomials, "x⁻⁵-5x⁻⁴+4x⁻³+2x⁻¹ - 1" is not a polynomial.
- Because it contains division, which is not permitted in polynomials, "4/x⁴+3/x³-2/x²-1" is not a polynomial.
-Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "x³-7x²+9x-5x⁴-20" is a polynomial.
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Charlie's net worth is $-35,354. Which of the following is true?
Responses
He has a negative net worth which means his liabilities are greater than his assets.
He has a negative net worth which means his liabilities are greater than his assets., EndFragment,
He has a negative net worth which means his assets are greater than his liabilities
He has a negative net worth which means his assets are greater than his liabilities , EndFragment,
He has a positive net worth which means his assets are greater than his liabilities.
He has a positive net worth which means his assets are greater than his liabilities. , EndFragment,
He has a positive net worth which means his liabilities are greater than his assets
Answer:
if the mass of 16cm3 of a metal is 20g what is the mass of 30cm3
Please help asap. i am very confused
Statement (A) is true, Statement (B) is false, Statement (C) is true, Statement (D) is true and Statement (E) is false.
The given information is that P(odd) = 1/3
where odd numbers are 3 and 5, and there are two odd-numbered sections out of six equal sections.
(A) The probability of landing on an odd-numbered section is not exactly 33.33%, but approximately equal to 33.33% or 1/3.
So, statement (A) is true.
(B) The probability of landing on an even-numbered section is not exactly 66.67%, but approximately equal to 66.67% or 2/3.
So, statement (B) is false.
(C) The probability of landing on an odd-numbered section is given as 1/3, which is less than the probability of landing on an even-numbered section, which is 2/3. Therefore, statement (C) is true.
(D) It is given that one of the sections is numbered 6. So, it is not impossible to land on 6. Therefore, statement (D) is false.
(E) To determine if the spinner is fair, we need to know the probability of each outcome, which is not provided in the given information. Therefore, we cannot determine if the spinner is fair or not based on the information given. So, statement (E) is uncertain.
Therefore, the true statements about this game are (A), (C), and (D).
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