Answer:
a. The distribution is bell-shaped and symmetric: True.
b. The distribution is bell-shaped and symmetric: True.
c. The probability to the left of the mean is 0: False.
d. The standard deviation of the distribution is 1: True.
Step-by-step explanation:
The Standard Normal distribution is a normal distribution with mean, [tex] \\ \mu = 0[/tex], and standard deviation, [tex] \\ \sigma = 1[/tex].
It is important to recall that the parameters of the Normal distributions, namely, [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex] characterized them.
We can use the Standard Normal distribution to find probabilities for any normally distributed data. All we have to do is normalized them through z-scores:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where [tex] \\ x[/tex] is the raw score that we want to standardize.
Therefore, taking into account all this information, we can answer the following questions about the Standard Normal distribution:
(a) True or False: The distribution is bell-shaped and symmetric
Answer: True. As the normal distribution, the standard normal distribution is also bell-shape and it is symmetrical around the mean. The standardized values or z-scores, which represent the distance from the mean in standard deviations units, are the same but when it is above the mean, the z-score is positive, and negative when it is below the mean. This result is a consequence of the symmetry of this distribution respect to the mean of the distribution.
(b) True or False: The mean of the distribution is 0.
Answer: True. Since the Standard Normal uses standardized values, if we use [1], we have:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
If [tex] \\ x = \mu[/tex]
[tex] \\ z = \frac{\mu - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{0}{\sigma}[/tex]
[tex] \\ z = 0[/tex]
Then, the value for the mean is where z = 0. A z-score is a linear transformation of the original data. For this reason, the transformed mean is equivalent to 0 in the standard normal distribution. We only need to find distances from this zero in standard normal deviations or z-scores to find probabilities.
(c) True or False: The probability to the left of the mean is 0.
Answer: False. The probability to the left of the mean is not 0. The cumulative probability from [tex] \\ -\infty[/tex] until the mean is 0.5000 or [tex] \\ P(-\infty < z < 0) = 0.5[/tex].
(d) True or False: The standard deviation of the distribution is 1.
Answer: True. The standard normal distribution is a convenient way of calculate probabilities for any normal distribution. The standardized variable, represented by [1], permits us to use one table (the standard normal table) for all normal distributions.
In this distribution, the z-score is always divided by the standard deviation of the population. Then, the standard deviation for the standard normal distribution are times or fractions of the standard deviation of the population, since we divide the distance of a raw score from the mean of the population, [tex] \\ x - \mu[/tex], by it. As a result, the standard deviation for the standard normal distribution will be times (1, 2, 3, 0.96, -1, -2, etc) the standard deviation of any normal distribution, [tex] \\ \sigma[/tex].
In this case, the linear transformation of the original data for one standard deviation from the mean is z = 1. Therefore, the standard deviation for the standard normal distribution is the unit.
Answer:
A: true
B: true
C: false
D: true
P(AB) can be read as "the probability that A occurs given that Bhas
occurred."
A. True
B. False
Answer:
False
Step-by-step explanation:
from *millermoldwarp*
"Events are called dependent when the probability of an event depends on the occurrence of another. When event A depends on event B, the probability that A occurs, given that B has occurred, is different from the probability that A occurs only ."
hopes this helps
Answer:false
Step-by-step explanation:
Consider the differential equation4y'' − 4y' + y = 0; ex/2, xex/2.Verify that the functions ex/2 and xex/2 form a fundamental set of solutions of the differential equation on the interval (−[infinity], [infinity]).The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2) =
Step-by-step explanation:
Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.
The Wronskian of them functions be
W = (y1y2' - y1'y2)
y1 = (e^x)/2 = y1'
y2 = (xe^x)/2
y2' = (1/2)(x + 1)e^x
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.
Answer:
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Step-by-step explanation:
Which statements are true? Check all that apply. All rectangles are squares. All rhombi are parallelograms. All squares are rhombi. All trapezoids are parallelograms. No trapezoid is a rectangle.
Answer:
All rhombi are parallelograms.
All squares are rhombi.
No trapezoid is a rectangle.
Help needed ASAP please !!!!
Answer:I believe that it is A but i am not fully sure
Step-by-step explanation:
A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.a. P(A ∩ B).b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.
Complete question is;
A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.
a. P(A ∩ B).
b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.
Answer:
A) 0.4
B) 0.4
Step-by-step explanation:
We are given;
P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8
A) To solve this question, we will use the the general probability addition rule for the union of two events which is;
P(A∪B) = P(A) + P(B) − P(A∩B)
Making P(A∩B) the subject of the equation, we have;
P(A∩B) = P(A) + P(B) − P(A∪B)
Thus, plugging in the relevant values, we have;
P(A∩B) = 0.7 + 0.5 - 0.8
P(A∩B) = 0.4
B)The probability that the lifeline usage amount is exceeded in exactly one of the two months can be described in terms of A and B as:
P(A but not B) + P(B but not A) = P(A∩B') + P(B∩A')
where;
A' is compliment of set A
B' is compliment of set B
Now,
P(A∩B') = 0.7 − 0.4 = 0.3
P(B∩A') = 0.5 − 0.4 = 0.1
Thus;
P(A but not B) + P(B but not A) = 0.1 + 0.3 = 0.4
Approximately 10% of all people are left-handed. If 200 people are randomly selected, what is the expected number of left-handed people? Round to the whole number. Do not use decimals. Answer:
Answer:
N(L) = 20
The expected number of left handed people is 20.
Step-by-step explanation:
Given;
Percentage of left handed people P(L) = 10%
Total number of selected people N(T) = 200
The Expected number of left handed people N(L) is;
N(L) = Total number of selected people × Percentage of left handed people/100%
N(L) = N(T) × P(L)/100%
Substituting the given values;
N(L) = 200 × 10%/100%
N(L) = 200 × 0.1
N(L) = 20
The expected number of left handed people is 20.
if 3x+2y=72 and y=3x, then x whoever solve I give them all my points
Answer:
[tex]x=8[/tex]
[tex]y=24[/tex]
Step-by-step explanation:
3x+2y=72
If y=3x, we plug it into our equation and get:
3x+2×3x=72
3x+6x=72
9x=72
Divide both sides by 9
x=8
Answer:
x = 8
Step-by-step explanation:
3x + 2y = 72
Put y as (3x), and solve for x.
3x + 2(3x) = 72
Multiply 2(3x).
3x + 6x = 72
Add like terms 3x and 6x.
9x = 72
Divide 9 into both sides and isolate x.
x = 72/9
x = 8
The value of x is 8.
For every 1% increase in
unemployment, there is a 2%
decrease in potential GDP. This
creates a GDP gap. What is the GDP
gap when there is 4.5%
unemployment?
Answer:
The GDP gap is 9 % when there is 4.5 % unemployment.
Step-by-step explanation:
The statement shows a reverse relationship, where an increase in unemployment is following by decrease in potential GDP and can be translated into the following rate:
[tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex]
The GDP gap at a given increase in unemployment can be estimated by the following expression:
[tex]\frac{g}{u} = r[/tex]
[tex]g = r\cdot u[/tex]
Where:
[tex]r[/tex] - GDP gap-unemployment increase rate, dimensionless.
[tex]u[/tex] - Increase in unemployment rate, measured in percentage.
[tex]g[/tex] - GDP gap, measured in percentage.
If [tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex] and [tex]u = 4.5\,\%\,unemp.[/tex], the GDP gap is:
[tex]g = \left(\frac{2\,\%\,GDP}{1\,\%\,unemp.} \right)\cdot (4.5\,\%\,unemp.)[/tex]
[tex]g = 9\,\%\,GDP[/tex]
The GDP gap is 9 % when there is 4.5 % unemployment.
The population of a city has increased by 35% since it was last measured. If the current population is 29,700 , what was the previous population?
Answer:
19305
Step-by-step explanation:
We simply take the percentage of 29700 to find how many people were added.
29700(0.35) = 10395 <== so 10395 people have been added
Subtract it from the current:
28700 - 10395 = 19305 people before.
Un importante grupo de inversionistas, asociado a una línea de buses interurbanos, está considerando instalar un centro logístico de mantención, a usted le ha encargado la evaluación de este proyecto, considerando un horizonte de 5 años. el estudio técnico del proyecto indica que se requiere disponer de un galpón 1000 m2 dentro de las instalaciones que la empresa ya cuenta, además de un acceso pavimentado con cimientos especiales de 6000 m2. el costo de construcción del galpón es de $ 42 por m2, y el costo de construcción del acceso pavimentado es de $ 32 por cada m2. adicionalmente, se requiere adquirir servidores de punta para realizar el check de los buses antes de comenzar sus recorridos, su costo se estima en $ 630.000, además se necesitan equipos especiales para la revisión de los neumáticos, con un costo de $ 400.000. finalmente, se deberá conseguir un terreno al interior del terminal de buses, con una superficie de 1 m2, con un costo de $50 por m2.
Answer:
Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = $ 1,264,000
Total start-up amount required, according to the details provided in the question = $1,264,000
Step-by-step explanation:
- Hay 1000 m² de espacio de almacén para construir a $ 42 por m². Dinero total requerido = 1000 × 42 = $ 42,000.
- Hay 6000 m² de espacio de acceso pavimentado para construir a $ 32 por m². Dinero total requerido = 6000 × 32 = $ 192,000.
- Compra de servidores de última generación para revisar los autobuses antes de comenzar sus recorridos. Costo total = $ 630,000.
- Se necesita comprar equipo especial para revisar los neumáticos. Costo = $ 400,000.
Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = 42000 + 192000 + 630000 + 400000 = $ 1,264,000
¡¡¡Espero que esto ayude!!!
English Translation
- There is 1000 m² of warehouse space to construct at $42 per m². Total required money = 1000 × 42 = $42,000
- There is 6000 m² of paved access space to construct at $32 per m². Total money required = 6000 × 32 = $192,000
- Purchase of state-of-the-art servers to check the buses before starting their tours. Total Cost = $630,000
- Purchase of special equipment is needed to check the tires. Cost = $400,000
Total start-up amount required, according to the details provided in the question = 42000 + 192000 + 630000 + 400000 = $1,264,000
Hope this Helps!!!
∠A and ∠B are supplementary, and ∠A and ∠C are supplementary. Which conclusion is valid? Select one: A. ∠B and ∠C are supplementary. B. ∠B and ∠C are acute. C. ∠B and ∠C are complementary. D. ∠B and ∠C are congruent.
Option D is the correct answer.
Answer:
D. ∠B and ∠C are congruent.
Step-by-step explanation:
Since, ∠A and ∠B are supplementary.
Therefore,
∠A + ∠B = 180°.....(1)
Since, ∠A and ∠C are supplementary.
Therefore,
∠A + ∠C = 180°.....(2)
From equations (1) & (2)
∠A + ∠B = ∠A + ∠C
=> ∠B = ∠C
Hence, ∠B and ∠C are congruent.
) Let an denote number of n-digit ternary sequences (sequences of 0,1 and 2) which have no consecutive 0’s in them. Find a recurrence relation for an. (Do not solve the recurrence. However, depending on the order of the recurrence, provide a sufficient number of initial conditions. )
Answer:
The recurrence relation for aₙ is aₙ = 2aₙ - 1 + 2aₙ -2 ; is n≥ 3 with the initial conditions as a₁ =3; a₂ = 8
Step-by-step explanation:
Solution
Recurrence relation for n - digit ternary sequence with no occurrence of consecutive 0's in them.
Ternary sequence is sequence with each of digits either 0, 1 or 2.
Now
Let aₙ = denote the number of n - digit ternary sequence with no occurrence of consecutive 0's in them.
Let us first find few initial values of aₙ
For n = 1
a₁ represent the number of 1- digit ternary sequence with no occurrence of consecutive 0's in them.
This 1-digit sequence can be either 0 or 1 or 2.
Thus,
a₁ = 3
For n =2
a₂ represent the number of 2- digit ternary sequence with no occurrence of consecutive 0's in them.
This 2-digit sequence can have either 0 or 1 or 2 as each of its two digit, but making sure that there are no two consecutive 0 in the sequence.
here are " 9 " 2-digit ternary sequence ........... (three choices for 1st digit and three choices for 2nd digit)
But one of these 9 sequence there are consecutive 0's .... (00)
So we eliminate this one sequence.
So, a₂ = 8
Now
let us find the recurrence relation
Fir n ≥ 3
aₙ s the number of n - digit ternary sequence with no occurrence of the consecutive 0's in them.
For the first case: if 1st digit of this n - digit ternary sequence is 1 or 2
Let assume the 1st digit of this n - digit ternary sequence is 1.
Then for remaining n - 1 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them.
For example, we have to form a n-1-digit ternary sequence with no occurrence of consecutive 0's in them which is by definition aₙ -1
So,
The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 1 is aₙ -1.
Likewise, the number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 2 is aₙ -1.
So
If 1st digit of this n - digit ternary sequence is 1 or 2, then the number of n - digit ternary sequence with no occurrence of consecutive 0's in them is shown as:
aₙ-1 + aₙ -1 = 2aₙ -1
For the second case: if 1st digit of this n - digit ternary sequence is 0
If 1st digit of this n - digit ternary sequence is 0, then the next digit cannot be 0 as well because that would make two consecutive 0's in the sequence Thus,
If 1st digit of this n - digit ternary sequence is 0, the next term can be either 1 or 2.
So there are 2 choices for 2nd digit.
After this there are more n-2 digits.
Then
For remaining n - 2 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them
For example, we have to form a n-2-digit ternary sequence with no occurrence of consecutive 0's in them. which is by definition aₙ - 2.
Now,
The total number of sequence in this case is given as:
2aₙ -2........... (2 choices for 2nd digit and aₙ - 2 choices for remaining n-2 digit)
Hence
The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 0 is aₙ = 2aₙ - 1 + 2aₙ -2 which is n≥ 3
Now,
The recurrence relation for aₙ is shown below:
aₙ = 2aₙ - 1 + 2aₙ -2; is n≥ 3
With the initial conditions as a₁ =3; a₂ = 8
What type of error is present in the underlined
sentence?
Which is the best revision to fix the error?
Answer:
Type of error: Run-on(comma splice).
Best revision to fix it: Adding a semicolon after beginners .
Explanation:
A run-on sentence is described as a sentence in which two independent clauses are joined inappropriately. It could be either comma splice where the two independent clauses are incorrectly linked using a comma or fused sentence when the two clauses run-on without employing appropriate coordinating conjunction or punctuation marks to separate the two ideas.
In the given sentence, it exemplifies a comma splice type of run-on sentence error. To fix this error, a semicolon after 'beginners' can be employed instead of a comma. This will help in connecting the two ideas appropriately where the first idea leads the second. Thus, the final sentence reads as:
'The guitar is another excellent instrument for beginners; however, it takes more practice than a recorder.'
Answer:
Many people play a musical instrument music can be soothing. A lot of schools teach the recorder; it is inexpensive and easy to play. The guitar is another excellent instrument for beginners, it takes more practice than a recorder.
What type of error is present in the underlined sentence?
✔ run-on
Which is the best revision to fix the error?
✔ adding a semicolon after instrument
Step-by-step explanation:
The management of a chain of frozen yogurt stores believes that t days after the end of an advertising campaign, the rate at which the volume V (in dollars) of sales is changing is approximated by V ' ( t ) = − 26400 e − 0.49 t . On the day the advertising campaign ends ( t = 0 ), the sales volume is $ 170 , 000 . Find both V ' ( 6 ) and its integral V ( 6 ) . Round your answers to the nearest cent.
Answer:
Step-by-step explanation:
Given the rate at which the volume V (in dollars) of sales is changing is approximated by the equation
V ' ( t ) = − 26400 e^− 0.49 t .
t = time (in days)
.v'(6) can be derived by simply substituting t = 6 into the modelled equation as shown:
V'(6) = − 26400 e− 0.49 (6)
V'(6) = -26400e-2.94
V'(6) = -26400×-0.2217
V'(6) = $5852.88
V'(6) = $5,853 to nearest dollars
V'(6) = 585300cents to nearest cent
To get v(6), we need to get v(t) first by integrating the given function as shown:
V(t) = ∫−26400 e− 0.49 t dt
V(t) = -26,400e-0.49t/-0.49
V(t) = 53,877.55e-0.49t + C.
When t = 0, V(t) = $170,000
170,000 = 53,877.55e-0 +C
170000 = 53,877.55(2.7183)+C
170,000 = 146,454.37+C
C = 170,000-146,454.37
C = 23545.64
V(6) = 53,877.55e-0.49(6)+ 23545.64
V(6) = -11,945.63+23545.64
V(6) = $11,600 (to the nearest dollars)
Since $1 = 100cents
$11,600 = 1,160,000cents
A test consists of 580 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers? Round the answer to the nearest hundredth.
Answer:
12.04
Step-by-step explanation:
Because the questions are true and false, that is, there are only two answer options, therefore, you have a success probability = 1/2 = 0.5
The standard deviation can be calculated as follows:
Standard Deviation = (n*p* (1-p)] ^ (1/2)
replacing we have:
SD = (290 * (1-0.5)] ^ (1/2) = 12.04
That is, the standard deviation is 12.04
Solve the linear equality 4x-7 <5
Answer:
X<3
Step-by-step explanation:
4x-7 <5
4x < 5+7
4x < 12
X < 12/4
X < 3
Hope this helps..
Good Luck!
Engineers want to design passenger seats in commercial aircraft so that they are wide enough to fit 95 percent of adult men. Assume that adult men have hip breadths that are normally distributed with a mean of 14.4 inches and a standard deviation of 1.1 inches. Find the 95th percentile of the hip breadth of adult men. Round your answer to one decimal place; add a trailing zero as needed. The 95th percentile of the hip breadth of adult men is [HipBreadth] inches.
Answer:
[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]
And if we solve for a we got
[tex]a=14.4 +1.64*1.1=16.204[/tex]
The 95th percentile of the hip breadth of adult men is 16.2 inches.
Step-by-step explanation:
Let X the random variable that represent the hips breadths of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(14.4,1.1)[/tex]
Where [tex]\mu=14.4[/tex] and [tex]\sigma=1.1[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.05[/tex] (a)
[tex]P(X<a)=0.95[/tex] (b)
We can find a quantile in the normal standard distribution who accumulates 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64
Using this value we can set up the following equation:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.95[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.95[/tex]
And we have:
[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]
And if we solve for a we got
[tex]a=14.4 +1.64*1.1=16.204[/tex]
The 95th percentile of the hip breadth of adult men is 16.2 inches.
Edwin has 3 1 2 gallons of green paint. He uses 2 3 of the paint to paint his bedroom. He uses the rest of the paint for a mural in his garage. How much paint does Edwin use for the mural?
Answer:
1 1/6
Step-by-step explanation:
Edwin used a quantity of 2.833 gallons of paint for the mural which is the difference between the quantity of paint at the beginning and the used for the bedroom.
We have been given that Edwin has 3 1/2 gallons of green paint. He uses 2/3 of the paint to paint his bedroom. He uses the rest of the paint for a mural in his garage.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
To determine the quantity of paint Edwin used for the mural.
The quantity of paint Edwin used for the mural is the difference between the quantity of paint at the beginning and the used for the bedroom.
The quantity of paint used for the mural = 3 1/2 gallons - 2/3 gallons
The quantity of paint used for the mural = 3.5 - 0.66
The quantity of paint used for the mural = 2.833
Thus, Edwin used a quantity of 2.833 gallons of paint for the mural.
Learn more about the fractions here:
brainly.com/question/10354322
#SPJ2
Brian invests £8300 into his bank account. He receives 1.4% per year compound interest. How much will Brian have after 7 years? Give your answer to the nearest penny where appropriate.
Answer:
The nearest penny will be £9146.6
Step-by-step explanation:
A = P[1 + (r/n)]^(nt)
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
A = 8300 [ 1 + {1.4 / (7*100)}]^(7*7)
A = 8300 [ 1 + {0.002}]^(49)
A= 8300 [ 1.002 ]^(49)
A = 8300 [ 1.102 ]
A = £9146.6
What is Compound Interest (CI) ?
Compound Interest is all about adding interest to principal amount of loan , deposit .
A group of campers is going to occupy 4 campsites at a campground. There are 14 campsites from which to choose. In how many ways can the campsites be chosen?
There are
possible ways to choose the campsites.
Check
Enter your answer in the answer box and then click Check Answer.
Clear All
All parts showing
Answer:
24024 are the total number of ways of choosing 4 campsites out of 14.
Step-by-step explanation:
We are given that there are a total of 14 campsite out of which 4 campsites are to be chosen.
It is a simple example of selection problem.
Number of ways to choose the first campsite = 14
Now, one campsite is chosen, 13 campsites are left.
Therefore,
Number of ways to choose the second campsite = 13
Now, one more campsite is chosen, 12 campsites are left.
Therefore,
Number of ways to choose the third campsite = 12
Now, one more campsite is chosen, 11 campsites are left.
Therefore,
Number of ways to choose the fourth campsite = 11
So, total number of ways for choosing 4 campsites out of 14:
14 [tex]\times[/tex] 13 [tex]\times[/tex] 12 [tex]\times[/tex] 11 = 24024
Hence, answer is 24024.
Which leader was a member of the Kikuyu tribe?
A. Kwame Nkrumah
B. Marcus Garvey
C. Mohandas Gandhi
D. Jomo Kenyatta
Answer:
Jomo Kenyatta
Step-by-step explanation:
Jomo Kenyatta was a Kenyan politician, who was one of the first African anti-colonial figures. He became the prime minister of Kenya from 1963 to 1964, and after Kenyan independence in 1964, he became president of Kenya. Jomo Kenyatta was born into a family of Kikuyu farmers in Kiambu, present day Kenya which was then, British East Africa. He had his basic schooling in a missionary school before proceeding to study at Moscow's Communist University of the Toilers of the East, University College London, and the London School of Economics.
Answer:
Jomo Kenyatta
Step-by-step explanation:
took the test
Deanna's Quiz Scores
Use the dot plots to answer the question
has quiz scores that are less variable and
typically higher
80 82 84 86 88 90 92 94 96 98 100
Amy's Quiz Scores
.
.
.
..
80 82 84 86 88 90 92 94 96 98 100
Answer:
1.90.93
2.90.27
Step-by-step explanation:
Answer:
one above correct
Step-by-step explanation:
1st - 90.93
2nd-90.27
⅝ of a school's population are girls. There are 129 boys. If each classroom can hold 25 students. How many classroom does the school have ?
Answer:
AT least 14 classrooms to hold the total number of students
Step-by-step explanation:
Since we don't know the numer of girls in the school, let's call it "x".
What we know is that the number of girls plus the number of boys gives the total number of students. This is:
x + 129 = Total number of students
Now, since 5/8 of the total number of students are girls, and understanding that 5/8 = 0.625 in decimal form, then we write the equation that states:
"5/8 of the school's population are girls" as:
0.625 (x + 129) = x
then we solve for "x":
0.625 x + 0.625 * 129 = x
0.625 * 129 = x - 0.625 x
80.625 = x (1 - 0.625)
80.625 = 0.375 x
x = 80.625/0.375
x = 215
So now we know that the total number of students is: 215 + 129 = 344
and if each classroom can hold 25 students, the number of classroom needed for 344 students is:
344/25 = 13.76
so at least 14 classrooms to hold all those students
AC =
Round your answer to the nearest hundredth.
A
5
35
B
C
Answer:
2.87 = AC
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opp / hyp
sin 35 = AC /5
5 sin 35 = AC
2.867882182= AC
To the nearest hundredth
2.87 = AC
Any help would be appreciated
What number should go in the space? Multiplying by 0.65 is the same as decreasing by _____%
Answer: 35%
Step-by-step explanation:
If no is 10, 10 x 0.65 = 6.5. OR
10 - 35% of 10 = 6.5
Multiplying by 0.65 is the same as decreasing by 35%
Conversion of statements into algebraic expression:To convert the statement into algebraic expression choose the variables first.Then form the expression or equation as per given statements.
Let the number is 'a' and percentage decrease is 'b',
Expression for the given statement will be,
a × 0.65 = a - (b% of a)
[tex]0.65a=a(1-\frac{b}{100})[/tex]
[tex]0.65=1-\frac{b}{100}[/tex]
[tex]\frac{b}{100}=1-0.65[/tex]
[tex]b=100(0.35)[/tex]
[tex]b=35[/tex]
Therefore, Multiplying by 0.65 is the same as decreasing by 35%.
Learn more about the Algebraic expressions for the statements here,
https://brainly.com/question/2043566?referrer=searchResults
Tyler drew a figure that has two pairs of equal sides, four angles formed by perpendicular lines, and two pairs of parallel sides. What geometric term best describes the figure Tyler drew? What geometric term best describes the figure Tyler drew?
Answer:
A shape with two pairs of parallel lines, perpendicular lines, and two pairs of equal sides can be best described as a rectangle.
Suppose that, in an experimental setting, 100 students are asked to choose between Gamble A and Gamble B, where: Gamble A: The student will receive $5,100 with a 70 percent probability and $200 with a 30 percent probability. Gamble B: The student will receive $5,100 with a 50 percent probability, $200 with a 25 percent probability, and $0 (nothing) with a 25 percent probability. What is the expected value (EV) of Gamble B
Focus on Gamble B only. Multiply each winnings with their corresponding probabilities.
5100*0.50 = 2550
200*0.25 = 50
0*0.25 = 0
Add up those results: 2550+50+0 = 2600
The expected value of gamble B is $2600
What is the area of the triangle below?
18
Answer:
D. 32 sq. unit s
Step-by-step explanation:
4×18/2=32
A product is introduced to the market. The weekly profit (in dollars) of that product decays exponentially as function of the price that is charged (in dollars) and is given by P ( x ) = 95000 ⋅ e − 0.05 ⋅ x Suppose the price in dollars of that product, x ( t ) , changes over time t (in weeks) as given by x ( t ) = 53 + 0.95 ⋅ t 2 Find the rate that profit changes as a function of time, P ' ( t ) dollars/week How fast is profit changing with respect to time 7 weeks after the introduction. dollars/week
Answer:
1). [tex]P'(t) = (-9025t).e^{-0.05(53+0.95t^2)}[/tex]
2). (-435.36) dollars per week
Step-by-step explanation:
Weekly price decay of the product is represented by the function,
P(x) = [tex]95000.e^{-0.05x}[/tex]
And the price of the product changes over the period of 't' weeks is represented by,
x(t) = [tex]53+0.95t^2[/tex]
Function representing the rate of change in the profit with respect to the time will be represented by,
1). P'(t) = [tex]\frac{dP}{dx}.\frac{dx}{dt}[/tex]
Since, P(x) = [tex]95000.e^{-0.05x}[/tex]
P'(x) = [tex]95000\times (-0.05).e^{-0.05x}[/tex]
= [tex](-4750).e^{-0.05x}[/tex]
Since, x(t) = 53 + 0.95t²
x'(t) = 1.9t
[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05x}\times (1.9t)[/tex]
By substituting x = 53 + 0.95t²
[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05(53+0.95t^2)}\times (1.9t)[/tex]
P'(t) = [tex](-9025t).e^{-0.05(53+0.95t^2)}[/tex]
2). For t = 7 weeks,
P'(7) = [tex](-9025\times 7).e^{-0.05(53+0.95(7)^2)}[/tex]
= [tex](-63175).e^{-4.9775}[/tex]
= (-63175)(0.006891)
= (-435.356) dollars per week
≈ (-435.36) dollars per week