Answer:
The value is [tex]P(A) = 0.133617[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 7.5[/tex]
The standard deviation is [tex]\sigma = 0.2[/tex]
The safest water level is between 7.2 and 7.8
Generally the probability that the selected pool has a pH level that is not considered safe is mathematically represented as
[tex]P(A) = 1 - P(7.2 \le X \le 7.8 )[/tex]
Here
[tex]P(7.2 < X < 7.8 ) = P(\frac{ 7.2 - \mu }{\sigma } < \frac{X - \mu }{ \sigma } <\frac{ 7.8 - \mu }{\sigma } )[/tex]
Generally [tex]\frac{X - \mu }{ \sigma } = Z (The \ standardized \ value \ of X )[/tex]
So
[tex]P(7.2 < X < 7.8 ) = P(\frac{ 7.2 - 7.5 }{0.2 } < Z <\frac{ 7.8 - 7.5 }{0.2 } )[/tex]
[tex]P(7.2 < X < 7.8 ) = P(-1.5 < Z <1.5)[/tex]
=> [tex]P(7.2 < X < 7.8 ) = P(Z < 1.5) - P( Z < - 1.5) [/tex]
From the z-table the probability of (Z < -1.5) and ( Z <1.5) are
[tex]P(Z < 1.5) = 0.93319[/tex]
and
[tex]P(Z < -1.5) = 0.066807[/tex]
So
[tex]P(7.2 < X < 7.8 ) =0.93319 - 0.066807 [/tex]
[tex]P(7.2 < X < 7.8 ) =0.0866383[/tex]
So
[tex]P(A) = 1 - 0.0866383[/tex]
=> [tex]P(A) = 0.133617[/tex]
The probability that the selected pool has a pH level that is not considered safe pool is 0.1336
The given parameters are:
[tex]\mathbf{\mu = 7.5}[/tex]
[tex]\mathbf{\sigma = 0.2}[/tex]
Start by calculating the probability that a pool is safe.
This is represented as: P(7.2 < x < 7.8)
Calculate the z-scores for x =7.2 and 7.8 using:
[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]
So, we have:
[tex]\mathbf{z = \frac{7.2 - 7.5}{0.2} = -1.5}[/tex]
[tex]\mathbf{z = \frac{7.8 - 7.5}{0.2} = 1.5}[/tex]
So, we have:
[tex]\mathbf{P(7.2 < x < 7.8) = P(-1.5 < z < 1.5)}[/tex]
This gives
[tex]\mathbf{P(7.2 < x < 7.8) = P(z < 1.5) - P(z < -1.5)}[/tex]
Using z table of probabilities, we have:
[tex]\mathbf{P(7.2 < x < 7.8) =0.9332 - 0.0668}[/tex]
[tex]\mathbf{P(7.2 < x < 7.8) =0.8664}[/tex]
The probability that the pool is not safe is calculated using the following complement formula
[tex]\mathbf{P(Not\ Safe) = 1 - P(Safe)}[/tex]
So, we have:
[tex]\mathbf{P(Not\ Safe) = 1 -0.8664}[/tex]
[tex]\mathbf{P(Not\ Safe) = 0.1336}[/tex]
Hence, the probability that the pool is not safe is 0.1336
Read more about probabilities at:
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if caramel is put onto a sphere-shaped apple such that the surface area increase at a rate of 10 cm2/min, find the rate at which the diameter increases when the diameter is 15cm
Answer:
The diameter will increase at a rate of 1/30π cm/min
Step-by-step explanation:
Here we want to calculate the rate at which the diameter will increase
Mathematically, the area of a sphere is given as;
A = 4πr^2
But r = d/2
so A = 4 * π * d/2 * d/2 = πd^2
dA/d(d) = 2πd
Thus dd/dA = 1/2πd = 1/2 * π * 15 = 1/30π
Given dA/dt = 10
Mathematically;
d(d)/dt = d(d)/dA * dA/dt
dd/dt = 1/30π * 10 = 10/30π = 1/3π cm/min
0.079times what equals 7.9
Answer:
100
Step-by-step explanation:
Use the figure to find the measures of the numbered angles.
Answer: 5=49, 6= 131
Step-by-step explanation:
what is 3,108 rounded to the nearest thousand
Answer:
3100
Step-by-step explanation:
Answer:
3,000
Step-by-step explanation:
If the question was about 3,500 it would be rounded to 4,000
If the question was about 2,499 it would be rounded to 2,000
If it is in between 3,449 and 2,500 then it would be rounded to 3,000 which 3,108 is
compare the price per dozen eggs at the local grocery store and at the supermarket Edward bought 8 dozen eggs in the supermarket how much did he save by buying eggs at the supermarket instead of the local store
Answer:
8
Step-by-step explanation:
i'm a 12 year old girl and i get it so you have to think about the local store would be half witch would be 4 so the answer is 8Solve 6x+89(9)^2
3(2x+2403)
3(2x+234)
6x+7209
which one would it be
Answer:
It would be the last one 6x+7209
Step-by-step explanation:
because it will be simplify not factor by
Answer: The answer would be c
6x+7209
Step-by-step explanation:
since it would be like Isale said symplified and not factor by. In fact the deal of this question is that simplifying and factoring expressions are opposite processes so How do you know when to simplify? Well, you will removing the pair of the parentheses.
17. The hourly temperature at Portland, Oregon, on a particular day is recorded below.
1 A.M. 2 3 4 5 6 7 8 9 10 11 12 Noon
46° 44° 43° 41° 40° 40° 41° 43° 46° 52° 65° 69°
1 P.M. 2 3 4 5 6 7 8 9 10 11 12 Midnight
72° 74° 75° 75° 77° 75° 74° 70° 62° 55° 51° 48°
a. Find the amplitude of a sinusoidal function that models this temperature variation.
b. Find the vertical shift of a sinusoidal function that models this temperature variation.
c. What is the period of a sinusoidal function that models this temperature variation?
d. Use t = 0 at 5 P.M. to write a sinusoidal function that models this temp. variation.
e. What is the model’s temperature at 10 A.M.? Compare this to the actual value?
Answer:
a. Amplitude: 19.65446
b. Vertical Shift: 58.00713
c. Period: 2/0.22797 = 27.56146
d. 19.65446 * sin(0.22797x + 1.79552) + 58.00713
e. Model's Temperature at 10 A.M.: f(-7) = 61.91
This value is 9.91 degrees higher than the actual value.
Step-by-step explanation:
With 1 am being timed as t = 1, we fitted the temperature data collected at different points during the day in Portland, Oregon using sine regression. After receiving the sine function, we respond to the many questions connected to the sine function's properties.
What is sinusoidal Function?A smooth, repeating oscillation characterizes a sinusoidal function. Sine is an oscillation that is smooth and repeated, thus the name "sinusoidal." A pendulum swinging, a spring bouncing, or a guitar string vibrating are a few examples of commonplace objects that may be described by sinusoidal functions.
Given, The hourly temperature at Portland, Oregon, on a particular day is recorded.
Using sine regression on the given data with t = 1 being the hour 1 am etc, we get the following sine regression formula using the TI-83 Graphing Calculator where T is the temperature:
T = a sin(bt + c) + d
Where a = 19.65, b = 0.28, c = -2.93, d = 58.01
From the sine regression function above:
a. The amplitude of the sinusoidal function is a = 19.65.
b. The vertical shift is d = 58.01.
c. The period is 2*pi /b = 2*pi/ 0.28 = 22.44
d. At 5 PM, the time value is t = 17. Hence the temperature distribution with 5 PM being t = 0 will be
t = asin[b(t - 17) + c] +d.
e. From the table, at 10 AM, the actual value of the temperature is 52 degrees.
Using the model in part a., at 10 AM, with t = 10, the temperature will be
T = a sin(10b + c) + d
T = 55.46 degrees
Learn more about sinusoidal functions here:c. The period is
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Complete question:
Find the next number in the pattern given below
-10, -2, 6, ____
Round 24,837,618 to the ten thousands place. I’m on math college so I need help on this problem!
Answer:
24,840,000
Step-by-step explanation:
Round up of numbers includes rounding them up to a given place value.
We are asked to round 24,837,618 to the ten thousands place.
The ten thousands place is the place where the number 3 in the number is located.
The number after 3 = 7 is a number above 5. Hence, we add 1 to 3, making it 4
Therefore, 24,837,618 to the ten thousands place is 24,840,000
What do you think about raising the minimum wage? What do you think would be some negative outcomes of raising the minimum wage? What are some positive outcomes of raising the minimum wage
How do you find the whole in percent problems
Answer:
So essentially, you are trying to find what the overall whole is based off of a number that is the percent of the number. In order to do this, you must turn your percentage into a fraction over 100. You are going to then create the number that is a percentage of another number into a fraction over "x". Cross multiply the two fractions. Since there is an "x", count is as a zero. Now, create a fraction with the numerator as the number you just got from multiplying, and the denominator as the number you have to refer to as the percent of the whole. Since fraction is division, divide the two numbers and you get your answer. Sorry if this is so complex I tried to simplify it as best as I could
Step-by-step explanation:
Example: 8 is 80% of what number?
80% to 80/100
8 to 8/x
*cross multiply*
80x/80 = 800/80
800 divided by 80 is 10.
so, 8 is 80% percent of 10.
PLEASE QUICK BRAINLISET
Answer: the answer is f
Answer:
F
Step-by-step explanation:
the measure of angle one must be equal to the measure of angle five and when doing the math I got x=34 plug that into the equation for angle five i got 48 and the same for plugging it into the equation for angle one.
Suppose an internet marketing company wants to determine the current percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 90% confident that the estimated proportion is within five percentage points of the true population proportion of customers who click on ads on their smartphones
Answer:
The value is [tex]n =271[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 5\% = 0.05[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally we will assume that the sample proportion is [tex]\^ p = 0.5[/tex] since we have no information on the proportion of of customers who click on ads on their smartphones
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.645 }}{0.05} ]^2 * 0.5 (1 - 0.5 ) [/tex]
=> [tex]n =271[/tex]
Using the z-distribution, as we are working with a proportion, it is found that 271 customers should be sampled.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
90% confidence level, hence the critical value is z = 1.645.No prior estimate, hence p = 0.5.Within five percentage points, hence M = 0.05.Then:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.05\sqrt{n} = 0.5 \times 1.645[/tex]
[tex]\sqrt{n} = [10(1.645)][/tex]
[tex](\sqrt{n})^2 = [10(1.645)]^2[/tex]
[tex]n = 270.6[/tex]
Rounding up, 271 customers should be sampled.
More can be learned about the z-distribution at https://brainly.com/question/25890103
Evaluate the expression when y=-2.
y2 +6y-4
Answer:-12
Step-by-step explanation:
hello I need help on it pls
Answer:
19.5
Step-by-step explanation:
Last year, 450 people attended the Booster Club Breakfast. This year the number of people attending increased by 6%. Find the number of people who attended the breakfast this year.
Answer:
I'm pretty sure it's 477
Step-by-step explanation:
1.-Responde la pregunta: ¿para qué
me sirve el teorema de Pitágoras en la.
vida cotidiana?
Answer:
Respuesta. Respuesta: El Teorema de Pitágoras sirve para resolver una multitud de problemas; por ejemplo de, cálculo de distancias en el plano, en los mapas, en la realidad. ... En general, el Teorema de Pitágoras se puede utilizar para hallar longitudes en donde intervienen triángulos rectángulos.
Perform the indicated operation.
Answer:
[tex] g(3) - h(3) = -16 [/tex]
Step-by-step explanation:
Given:
[tex] g(x) = 2x - 5 [/tex]
[tex] h(x) = 4x + 5 [/tex]
Required:
[tex] g(3) - h(3) [/tex]
SOLUTION:
Substitute x = 3 into [tex] g(x) = 2x - 5 [/tex]
[tex] g(3) = 2(3) - 5 [/tex]
[tex] g(3) = 6 - 5 [/tex]
[tex] g(3) = 1 [/tex]
Substitute x = 3 into [tex] h(x) = 4x + 5 [/tex]
[tex] h(3) = 4(3) + 5 [/tex]
[tex] h(3) = 12 + 5 [/tex]
[tex] h(3) = 17 [/tex]
Therefore:
[tex] g(3) - h(3) = 1 - 17 = -16 [/tex]
Evaluate 12x−3y when x=−14 and y=3.
Answer:
-177
Step-by-step explanation:
12(-14) -3(3)
-168-9
-177
Answer:
-177
Step-by-step explanation:
Plug in -14 for x and 3 for y:
12(-14) - 3(3)
Note that when you multiply a positive and a negative number, your answer will be negative.
Multiply:
12 * -14 = -168
-3 * 3 = -9
Combine the terms:
-168 + (-9) = -168 - 9 = -177
-177 is your answer.
~
The price of a pack of steaks increased from $15 to $21. By what percentage did the price of the pack of steaks increase?
Step-by-step explanation:
21 - 15 = 6$
you have to find how many percent is 6$ in 15$
6 ÷ 15 = 0.4
15 × 0.4 (40/100)
= 6
40 percent
A backpack costs $18 and has a 7 percent tax. How much will Sheila have to pay for the backpack after tax?
O $1.26
O $5.40
O $19.26
O $30.60
Answer:
1
Step-by-step explanation:
1.26
13(6x – 5) – x = 13 – 2(x + 1)
Answer:
x= 76/79
Step-by-step explanation:
isolate the variable by dividing each side by factors that don't contain a variable (x).
Factor out the coefficient of the variable term. The expression 1/7a + 1/7 factored is___
Answer:
17 and [a+1] is the factor
Step-by-step explanation:
Given:
1/7a + 1/7
Find:
Factor
Computation:
1/7a + 1/7
By taking 1/7 as a common
1/7[a+1]
So,
17 and [a+1] is the factor
The coefficient of the variable term in factored form is; 1
The given expression is;
(1/7)a + 1/7
Now, we want to factorize this and this means that we will bring out the common factor of both terms.
The common factor of both terms is 1/7. Thus, we have;
(1/7)(a + 1)
The variable term is a and as such we see that it's coefficient inside the bracket is 1.
Read more at; https://brainly.com/question/2764126
Find the Sum:
(20 - 6) + 3(c + 8)
Answer:
38 + 3c
Step-by-step explanation:
Apply the distributed property: (20 - 6) + 3c + 2420 - 6 = 14Plug 14 in: 14 + 3c + 24Combine like terms: 38 + 3cI hope this helps!
In the accompanying diagram, line a intersects line b.
Answer:
C. 10
Step-by-step explanation:
[tex] (x + 5) = (2x - 5) [/tex] (vertical angles are congruent)
[tex] x + 5 = 2x - 5 [/tex]
Add 5 to both sides
[tex] x + 5 + 5 = 2x [/tex]
[tex] x + 10 = 2x [/tex]
Subtract x from both sides
[tex] 10 = 2x - x [/tex]
[tex] 10 = x [/tex]
[tex] x = 10 [/tex]
HELP FAST. I NEED THIS ANSWER FAST
Answer:
abunda la caca
( its 10m*9y)
Step-by-step explanation:
Answer:
First find the cubes and squares of the 1st and 2nd expression.
1st expression ⇒ [tex](-\frac{2}{3} x^2y)^3 = -\frac{8}{27}x^6y^3[/tex]
2nd expression ⇒ [tex](-\frac{3}{4}xy^2)^2 = -\frac{9}{16}xy^4[/tex]
Now you all you need to do is multiply the 1st expression to 2nd expression.
[tex]-\frac{8}{27}x^6y^3*-\frac{9}{16}xy^4\\\\= \frac{72}{432} x^7y^7[/tex]
8. The 2003 Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 top-ranking restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving for a business trip to Boston and will cat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner. a) What is the probability that none of the meals will exceed the cost covered by your company
Answer:
0.2637
Step-by-step explanation:
Population size is top 15 ranking restaurants.
Number of draws = 3
Number of observed successes = 5
Probability formula : [r . x } { n -r] [n - x]
solving the equation we get 24 / 91 which is approximately 0.2637
if you subtract 19 from my number and multiply the difference by -2, the result is -8
Answer:cool
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
let the number be 'a'
-2(a - 19)= -8
open the brackets
-2a + 38 = -8
collect like terms
38 + 8 = 2a
46 = 2a
a = 23
Pls help for Algebra 11b = 143
Answer:
b = 13
Step-by-step explanation:
Divide 143 by 11
A train travelled 275 km in 2.5 hours how fast will the train go in an hour?
!!!!!!!!!
Answer: 110 mph
Step-by-step explanation: 275 / 2.5 = 110 mph
