The required probability that a household in Maryland with annual income of ,
$90,000 or more is equal to 0.3377.
$50,000 or less is equal to 0.2218.
Annual household income in Maryland follows a normal distribution ,
Median = $75,847
Standard deviation = $33,800
Probability of household in Maryland has an annual income of $90,000 or more.
Let X be the random variable representing the annual household income in Maryland.
Then,
find P(X ≥ $90,000).
Standardize the variable X using the formula,
Z = (X - μ) / σ
where μ is the mean (or median, in this case)
And σ is the standard deviation.
Substituting the given values, we get,
Z = (90,000 - 75,847) / 33,800
⇒ Z = 0.4187
Using a standard normal distribution table
greater than 0.4187 as 0.3377.
P(X ≥ $90,000)
= P(Z ≥ 0.4187)
= 0.3377
Probability that a household in Maryland has an annual income of $90,000 or more is 0.3377(rounded to four decimal places).
Probability that a household in Maryland has an annual income of $50,000 or less.
P(X ≤ $50,000).
Standardizing X, we get,
Z = (50,000 - 75,847) / 33,800
⇒ Z = -0.7674
Using a standard normal distribution table
Probability that a standard normal variable is less than -0.7674 as 0.2218. This implies,
P(X ≤ $50,000)
= P(Z ≤ -0.7674)
= 0.2218
Probability that a household in Maryland has an annual income of $50,000 or less is 0.2218.
Therefore, the probability with annual income of $90,000 or more and $50,000 or less is equal to 0.3377 and 0.2218 respectively.
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For a standard normal distribution, find:
P(-2.11 < z < -0.85)
Answer:
Step-by-step explanation:
Using a standard normal table, we can find the area under the curve between -2.11 and -0.85.
P(-2.11 < z < -0.85) = P(z < -0.85) - P(z < -2.11)
Using the table, we find:
P(z < -0.85) = 0.1977
P(z < -2.11) = 0.0174
Therefore,
P(-2.11 < z < -0.85) = 0.1977 - 0.0174 = 0.1803
So the probability that a standard normal random variable falls between -2.11 and -0.85 is 0.1803.
PLEASE HELP 30 POINTS!
Answer:
57
57
123
123
57
57
123
that's all.
Answer:
m<1 = 57°
m<2 = m<1 = 57°
m<3 = x = 123°
m<4 = x = 123°
m<5 = m<1 = 57°
m<6 = m<5 = 57°
m<7 = m<4 = 123°
Step-by-step explanation:
[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]
The roots of a quadratic equation a x +b x +c =0 are (2+i √2)/3 and (2−i √2)/3 . Find the values of b and c if a = −1.
[tex]\begin{cases} x=\frac{2+i\sqrt{2}}{3}\implies 3x=2+i\sqrt{2}\implies 3x-2-i\sqrt{2}=0\\\\ x=\frac{2-i\sqrt{2}}{3}\implies 3x=2-i\sqrt{2}\implies 3x-2+i\sqrt{2}=0 \end{cases} \\\\\\ \stackrel{ \textit{original polynomial} }{a(3x-2-i\sqrt{2})(3x-2+i\sqrt{2})=\stackrel{ 0 }{y}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \textit{difference of squares} }{[(3x-2)-(i\sqrt{2})][(3x-2)+(i\sqrt{2})]}\implies (3x-2)^2-(i\sqrt{2})^2 \\\\\\ (9x^2-12x+4)-(2i^2)\implies 9x^2-12x+4-(2(-1)) \\\\\\ 9x^2-12x+4+2\implies 9x^2-12x+6 \\\\[-0.35em] ~\dotfill\\\\ a(9x^2-12x+6)=y\hspace{5em}\stackrel{\textit{now let's make}}{a=-\frac{1}{9}} \\\\\\ -\cfrac{1}{9}(9x^2-12x+6)=y\implies \boxed{-x^2+\cfrac{4}{3}x-\cfrac{2}{3}=y}[/tex]
what is the Taylor's series for 1+3e^(x)+x^2 at x=0
The Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] is :
[tex]1 + 3e^x+ x^2 = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]
What do you mean by Taylor's series ?
The Taylor's series is a way to represent a function as a power series, which is a sum of terms involving the variable raised to increasing powers. The series is centered around a specific point, called the center of the series. The Taylor's series approximates the function within a certain interval around the center point.
The general formula for the Taylor's series of a function f(x) centered at [tex]x = a[/tex] is:
[tex]f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...[/tex]
where [tex]f'(a), f''(a), f'''(a),[/tex] etc. are the derivatives of f(x) evaluated at [tex]x = a[/tex].
Finding the Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] :
We need to find the derivatives of the function at [tex]x=0[/tex]. We have:
[tex]f(x) = 1 + 3e^x + x^2[/tex]
[tex]f(0) = 1 + 3e^0 + 0^2 = 4[/tex]
[tex]f'(x) = 3e^x+ 2x[/tex]
[tex]f'(0) = 3e^0 + 2(0) = 3[/tex]
[tex]f''(x) = 3e^x + 2[/tex]
[tex]f''(0) = 3e^0 + 2 = 5[/tex]
[tex]f'''(x) = 3e^x[/tex]
[tex]f'''(0) = 3e^0 = 3[/tex]
Substituting these values into the general formula for the Taylor's series, we get:
[tex]f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...[/tex]
[tex]f(x) = 4 + 3x + 5x^2/2 + 3x^3/6 + ...[/tex]
Simplifying, we get:
[tex]f(x) = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]
Therefore, the Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] is :
[tex]1 + 3e^x+ x^2 = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]
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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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Which expressions are equivalent to 8(3/4y -2)+6(-1/2+4)+1
Answer: 6y + 6
Step-by-step explanation:
To simplify the expression 8(3/4y -2) + 6(-1/2+4) + 1, we can follow the order of operations (PEMDAS):
First, we simplify the expression within parentheses, working from the inside out:
6(-1/2+4) = 6(7/2) = 21
Next, we distribute the coefficient of 8 to the terms within the first set of parentheses:
8(3/4y -2) = 6y - 16
Finally, we combine the simplified terms:
8(3/4y -2) + 6(-1/2+4) + 1 = 6y - 16 + 21 + 1 = 6y + 6
Therefore, the expression 8(3/4y -2) + 6(-1/2+4) + 1 is equivalent to 6y + 6.
Find the distance from Link to the Octorok so Link can attack
The distance from Link to the Octorok is 10.63 units.
How to find the distance?We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below:
distance = √( (x₂ - x₁)² + (y₂ - y₁)²)
Here we want to find the distance from Link to the Octorok so Link can attack, so we need to get the distance between the points (-4, -5) and (3, 3).
The distance will be:
distance = √( (3 + 4)² + (3 + 5)²)
distance = √( (7)² + (8)²)
distance = √113
distance = 10.63
The distance is 10.63 units.
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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 less than 0.35°C.
Round your answer to 4 decimal places
The probability of obtaining a reading less than 0.35° C is approximately 35%.
What exactly is probability, and what is its formula?Accοrding tο the prοbability fοrmula, the likelihοοd οf an event οccurring is equal tο the ratiο οf the number οf favοurable οutcοmes tο the tοtal number οf οutcοmes. Prοbability οf an event οccurring P(E) = The number οf favοurable οutcοmes divided by the tοtal number οf οutcοmes.
The readings at freezing οn a set οf thermοmeters are nοrmally distributed, with a mean (x) οf 0°C and a standard deviatiοn (μ) οf 1.00°C. We want tο knοw hοw likely it is that we will get a reading that is less than 0.35°C.
To solve this problem, we must use the z-score formula to standardise the value:
[tex]$Z = \frac{x - \mu}{\sigma}[/tex]
Z = standard score
x = observed value
[tex]\mu[/tex] = mean of the sample
[tex]\sigma[/tex] = standard deviation of the sample
Here
x = 0.35° C
[tex]\mu[/tex] = 0° C
[tex]\sigma[/tex] = 1.00°C
Using the values on the formula:
[tex]$Z = \frac{0.35 - 0}{1}[/tex]
Z = 0.35
The probability of obtaining a reading less than 0.35° C is approximately 35%.
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(b) Write 5 as a percentage.
Answer:
5 as a percentage of 100 is 5/100 which is 5%
Solve each proportion round to the nearest tenth
Answer:
[tex]v = \frac{7}{2}[/tex]
Step-by-step explanation:
P, Q, R, S, T and U are different digits.
PQR + STU = 407
Step-by-step explanation:
There are many possible solutions to this problem, but one possible set of values for P, Q, R, S, T, and U is:
P = 2
Q = 5
R = 1
S = 8
T = 9
U = 9
With these values, we have:
PQR = 251
STU = 156
And the sum of PQR and STU is indeed 407.
T
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View Instructions
Interpreting a Dot Plot
DAR
3 4 5
1 2
Number of pets at home
6
How many people have 2 pets at home?
How many people have at least 3 pets at home?
How many more people have 2 pets than 5 pets?
How many people have less than 3 pets at home?
11
10 HELP MEEE
If we total up the dots plot for 3, 4, and 5 pets, we find that 3 people have 2 pets at home, 10 individuals have at least 3 pets at home.
What is the 1 pet in the world?The fact that dogs are the most common pet in the world shouldn't be shocking. There is a reason why there are tens of millions of dogs living in the United States alone, which is why some people say that dogs are a man's greatest friend. Around the world, at least one dog is kept in one-third of all households.
What exactly is a house pet?A fully domesticated animal kept constitutes a "household pet." a pet kept by you for personal company, like a dog, cat, reptile, bird, or mouse. Any kind of horse, cow, pig, sheep, goat, chicken, turkey, other captive fur-bearing animal is not considered a household pet, nor is any animal that is typically kept for food or profit.
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The total number of people with pets at home is 11, which is the sum of the heights of the columns.
What is equation?
A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra.
Based on the given dot plot, we can answer the following questions:
How many people have 2 pets at home?
Answer: Two people have 2 pets at home, as indicated by the two dots in the second column.
How many people have at least 3 pets at home?
Answer: Six people have at least 3 pets at home, as indicated by the dots in the third column and beyond.
How many more people have 2 pets than 5 pets?
Answer: There are no dots in the last column, which represents 5 pets. Therefore, the difference between the number of people with 2 pets and those with 5 pets is 2 - 0 = 2.
How many people have less than 3 pets at home?
Answer: Three people have less than 3 pets at home, as indicated by the dots in the first two columns.
Therefore, the total number of people with pets at home is 11, which is the sum of the heights of the columns.
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During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 131°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T=-0.005x^2+0.45x+125. Will the temperature of the part ever reach or exceed 131°F? Use the discriminant of a quadratic equation to decide.
answer options
1. No
2. Yes
From the discriminant of the give quadratic equation, the temperature of the machine will part after 50 minutes of operation.
Will the temperature of the part ever reach or exceed 135°F?The given equation that models the temperature of the machine is;
T = -0.005x² + 0.45x + 125
Let check if there's a value that exists for T = 135
Putting T = 135 in the given equation,
135 = -0.005x² + 0.45x + 125
We can simplify this to;
0.005x² - 0.45x + 10 = 0
From the general form of quadratic equation which is ax² + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.
The discriminant of this quadratic equation is given by:
D = b² - 4ac
= (-0.45)² - 4(0.005)(10)
= 0.2025 - 0.2
= 0.0025
The discriminant of the equation is positive which indicates we have two roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.
We can also find the roots of the quadratic equation using the formula:
[tex]x = (-b \± \sqrt(D)) / 2a[/tex]
Substituting the values of a, b, and D, we get:
[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]
Taking the positive value, we get:
x = 50
Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.
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Solve please geometry, solve for x
Answer: The answer is D
Step-by-step explanation:
Pythagorean theorem: a²+b²=c²
x²+x²=14²
2x²=196
Evaluate...
x=7√2
-51+((-5+(-4)) all calculation
Answer:
the answer to that is -31
The population of a certain city was 3,846 in 1996. It is expected to decrease by about 0.27% per year. Write an exponential decay function, and use it to approximate the population in 2022.
Answer:
To write an exponential decay function for this situation, we can use the formula:
P(t) = P₀e^(rt)
where:
P(t) = the population at time t
P₀ = the initial population
r = the annual rate of decrease (as a decimal)
t = time in years
We are given P₀ = 3,846 and r = -0.0027 (since the population is decreasing).
To approximate the population in 2022, we need to find t, the number of years from 1996 to 2022. That is:
t = 2022 - 1996 = 26 years
Now we can plug in the values we have:
P(t) = 3,846 e^(-0.0027t)
To find P(2022), we plug in t = 26:
P(26) = 3,846 e^(-0.0027(26))
≈ 3,200.62
Therefore, we can approximate the population of the city in 2022 to be about 3,201 people.
Answer:
3,101
Step-by-step explanation:
Please hit brainliest if this helped!
To write an exponential decay function for the population of the city, we can use the formula:
P(t) = P₀e^(-rt)
where P(t) is the population at time t, P₀ is the initial population, r is the decay rate, and e is the base of the natural logarithm.
In this problem, P₀ = 3,846 and r = 0.0027 (0.27% expressed as a decimal). We want to find the population in 2022, which is 26 years after 1996.To use the formula, we need to convert 26 years to the same time units as the decay rate. Since the decay rate is per year, we can use 26 years directly. Therefore, the exponential decay function for the population is:
P(t) = 3,846e^(-0.0027t)
To find the population in 2022 (t = 26), we substitute t = 26 into the function:
P(26) = 3,846e^(-0.0027*26) ≈ 3,101
Therefore, the population in 2022 is approximately 3,101.
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generally, cold fronts move fast er than warm fronts generally, cold fronts have steeper slopes generally, precipitation cover s a much broader area with a cold front especially in winter, cumuliform clouds are more often associated with cold fronts
Cold fronts generally move faster than warm fronts because cold air is denser and thus, moves more quickly. Precipitation with a cold front typically covers a broader area, especially during the winter.
On the other hand, warm fronts move more slowly as they are characterized by the gradual lifting of warm air over colder air. Cold fronts also typically have steeper slopes than warm fronts. This is because the leading edge of a cold front is more abrupt.
With a steep rise in the cold air mass. In contrast, the leading edge of a warm front has a gentler slope as the warm air gradually rises over the colder air.
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Uri paid a landscaping company to mow his lawn. The company charged $74 for the service plus
5% tax. After tax, Uri also included a 10% tip with his payment. How much did he pay in all?
Uri paid a total of $85.47 for the landscaping service including tax and tip.
What is tax?Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.
Given that company charged $74 for the service plus 5% tax.
The tax is 5%, that is:
Tax = 5% of $74 = 0.05 x $74 = $3.70
Cost after tax = $74 + $3.70 = $77.70
Now, tip is 10%:
Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77
Total cost = $77.70 + $7.77 = $85.47
Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.
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.2 In the diagram below, given that XY = 3cm, XZY = 30° and YZ = x, is it possible to solve for x using the theorem of Pythagoras? Motivate your answer. Show Calculations
Sin 30 =3/x
1/2=3/x
x=6
I will mark you brainiest!
If the triangles above are reflections of each other, then ∠D ≅ to:
A) ∠F.
B) ∠E.
C) ∠C.
D) ∠A.
E) ∠B.
Answer:
D I believe
Step-by-step explanation:
se spherical coordinates to evaluate the triple integral where is the region bounded by the spheres and .
The value of the triple integral[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex] by using spherical coordinates [tex]2\pi(e^{-1}-e^{-9})[/tex].
Given that the triple integral is-
[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]
E is the region bounded by the spheres which are,
[tex]x^2+y^2+z^2=1\\\\x^2+y^2+z^2=9[/tex]
In spherical coordinates we have,
x = r cosθ sin ∅
y = r sinθ sin∅
z = r cos∅
dV = r²sin∅ dr dθ d∅
E contains two spheres of radius 1 and 3 () respectively, the bounds will be like this,
1 ≤ r ≤ 3
0 ≤ θ ≤ 2π
0 ≤ ∅ ≤ π
Then
[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]
[tex]\int\int\int _{E} \frac{e^{-r^2}}{r}r^2Sin\phi drd\phi d\theta\\\\2\pi \int_{0}^{\pi} \int_1^3 re^{-r^2} dr d\phi\\\\2\pi \int_1^3 re^{-r^2} dr\\\\2\pi(e^{-1}-e^{-9})[/tex]
The complete question is-
Use spherical coordinates to evaluate the triple integral ∭ee−(x2 y2 z2)x2 y2 z2−−−−−−−−−−√dv, where e is the region bounded by the spheres x2 y2 z2=1 and x2 y2 z2=9.
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Use the power of a power property to simplify the numeric expression.
(91/4)^7/2
Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8
Given the expression
(9¹⁺⁴)⁷⁺²
To simplify this expression using the power of a power property, we need to multiply the exponents:
(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)
Simplifying the exponents in the parentheses:
(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8
Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).
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WILL MARK AS BRAINLIEST!!!!!!!!!!!!!!!!!!
The point on the parabola y=x^2 that is closest to the point (1,0) is (_______,_______). The distance between the two points is ________.
you can use Newtons's Method or Bisection to help but you don't have to.
Answer:Approximately
(0.58975,0.34781)
Step-by-step explanation:
If (x,y) is a point on the parabola, then the distance between (x,y) and (1,0) is:
√(x−1)2+(y−0)2=√x4+x2−2x+1
To minimize this, we want to minimize
f(x)=x4+x2−2x+1
The minimum will occur at a zero of:
f'(x)=4x3+2x−2=2(2x3+x−1)
graph{2x^3+x-1 [-10, 10, -5, 5]}
Using Cardano's method, find
x=3√14+√8736+3√14−√8736≅0.58975
y=x2≅0.34781
Elizabeth works as a server in coffee shop, where she can earn a tip (extra money) from each customer she serves. The histogram below shows the distribution of her 60 tip amounts for one day of work. 25 g 20 15 10 6 0 0 l0 15 20 Tip Amounts (dollars a. Write a few sentences to describe the distribution of tip amounts for the day shown. b. One of the tip amounts was S8. If the S8 tip had been S18, what effect would the increase have had on the following statistics? Justify your answers. i. The mean: ii. The median:
a. Histogram shows tip amounts ranging between $6 and $25, skewed to the right with a longer tail of higher tips.
b. Increasing the $8 tip to $18 would increase the mean since total tip amount increases by $10 spread out over 60 customers. Median won't be affected since changing one value does not alter the middle value.
a. The histogram shows that Elizabeth received a range of tip amounts, with the majority of tips falling between $6 and $25. The distribution is skewed to the right, with a longer tail of higher tip amounts.
b. i. The mean would increase because the total tip amount would increase by $10, and this increase would be spread out over the 60 customers.
ii. The median would not be affected because it is the middle value when the data is ordered, and changing one value does not change the middle value.
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type the correct words in the blanks. two radicals are said to be radicals if they have the same and the radicand.
Two radicals are said to be radicals if they have the same indices and the radicand.
In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:
3√(pq) → pq is the radicand
√(a+b) → a + b is the radicand
4√15 → 15 is the radicand
A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.
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Complete question:
Type the correct words in the blanks:
Two radicals are said to be radicals if they have the same and the radicand.
To the nearest hundredth, what is the volume of the sphere? (Use 3.14 for pie.)
Therefore, the volume of the sphere to the nearest hundredth is 724,775.70 cubic millimeters.
What is volume?Volume is a measurement of the amount of space occupied by a three-dimensional object. It is often expressed in units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or gallons (gal), depending on the context. The volume of a solid object can be calculated by multiplying its length, width, and height or using a specific formula depending on the shape of the object. For example, the volume of a rectangular box can be calculated as length x width x height, while the volume of a cylinder can be calculated as π x radius² x height. In general, volume is an important concept in many fields, including physics, chemistry, engineering, and architecture. It is often used to describe the capacity of containers, the displacement of fluids, and the amount of material used in construction or manufacturing.
Here,
The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is approximately 3.14.
Substituting the given value of the radius, we get:
V = (4/3) x 3.14 x 48³
V ≈ 724,775.68 cubic millimeters
Rounding this value to the nearest hundredth, we get:
V ≈ 724,775.68 ≈ 724,775.70 cubic millimeters (rounded to two decimal places)
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Find the 66th derivative of the function f(x) = 4 sin (x)…..
In response to the stated question, we may state that As a result, the 66th derivative of f(x) = 4 sin(x) is 4 sin(x) (x).
what is derivative?In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.
Using the chain rule and the derivative of the sine function repeatedly yields the 66th derivative of the function [tex]f(x) = 4 sin (x).[/tex]
The derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x), and this pattern repeats itself every two derivatives.
As a result, the first derivative of f(x) is:
[tex]f'(x) = 4 cos (x)[/tex]
The second derivative is as follows:
[tex]f"(x) = -4 sin (x)[/tex]
The third derivative is as follows:
[tex]f"'(x) = -4 cos (x)[/tex]
The fourth derivative is as follows:
[tex]f""(x) = 4 sin (x)[/tex]
And so forth.
[tex]f^{(66)(x)} = 4 sin (x)[/tex]
Because the pattern repeats every four derivatives, the 66th derivative is the same as the second, sixth, tenth, fourteenth, and so on.
As a result, the 66th derivative of f(x) = 4 sin(x) is 4 sin(x) (x).
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please help me with math quiz i’ll give you brainlist
Answer:
Answer: B. Symmetric.
Explanation:
In a symmetric distribution, the data is evenly distributed around the mean or median, creating a mirror image on both sides of the center. In this histogram, the median and mean are very close together at 55 and the bars on both sides of the center are roughly equal in height, indicating a fairly even distribution. Therefore, the histogram is symmetric.
Without an appointment, the average waiting time in minutes at the doctor's office has the probability density function f(t)=1/38, where 0≤t≤38
Step 1 of 2:
What is the probability that you will wait at least 26 minutes? Enter your answer as an exact expression or rounded to 3 decimal places.
Step 2 of 2:
What is the average waiting time?
The probability of waiting at least 26 minutes is 0.316. The average waiting time is 19 minutes.
Step 1:
The probability of waiting at least 26 minutes can be calculated by finding the area under the probability density function from 26 to 38:
P(waiting at least 26 minutes) = ∫26^38 (1/38) dt = [t/38] from 26 to 38
= (38/38) - (26/38) = 12/38 = 0.316
So the probability of waiting at least 26 minutes is 0.316 or approximately 0.316 rounded to 3 decimal places.
Step 2:
The average waiting time can be calculated by finding the expected value of the probability density function:
E(waiting time) = ∫0³⁸ t f(t) dt = ∫0³⁸ (t/38) dt
= [(t²)/(238)] from 0 to 38
= (38²)/(238) = 19
Therefore, the average waiting time is 19 minutes.
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