In every 10 minutes an average of 3 customers will arrive to the pizza station
Given,
The number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour.
We have to find the average number of customers arrives in each 10 minutes.
Here,
The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:
P (X = x) = (e^-μ × μ^x) / x!
Where,
The number of successes is x.
The Euler number is e = 2.71828.
μ is the average over the specified range.
Now,
Rate of 18 customers per hour;
μ = 18 n
n is the number of hours.
Number of customers arrive in each 10 minutes
10 minutes = 10/60 = 1/6
Then,
μ = 18 x 1/6 = 3
That is,
In every 10 minutes an average of 3 customers will arrive to the pizza station.
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A study determined that 9% of children under 18 years of age live with their father only. Find the probability that at most 2 persons selected at random from 12 children under18 years of age lived with their father onlyThe probability that at most 2 children live with their father only is(Do not round until the final answer. Then round to the nearest thousandth as needed)
Step 1: Write out the formula for binomial distribution
[tex]P(x)=^nC_x\times p^x\times q^{n-x}[/tex]Where
[tex]\begin{gathered} p\Rightarrow\text{probability of success} \\ q\Rightarrow\text{probability of failure} \\ n\Rightarrow\text{ number of trails } \\ x\Rightarrow\text{ number of success required} \end{gathered}[/tex]Step 2: State out the parameters needed in the formula to find the probabilty
[tex]\begin{gathered} p=9\text{ \%=}\frac{9}{100}=0.09 \\ q=1-p=1-0.09=0.91 \\ n=12 \\ x\Rightarrow\le2\Rightarrow0,1,2 \end{gathered}[/tex]Step 3: The probability that at most 2 children live with their father only can be described as;
[tex]P(x\le2)=P(0)+P(1)+P(2)[/tex]Step 4: Find the probability of each number of successes required
[tex]\begin{gathered} P(0)=^{12}C_0\times(0.09)^0\times(0.91)^{12-0} \\ P(0)=1\times1\times0.322475487=0.322475487 \end{gathered}[/tex][tex]\begin{gathered} P(1)=^{12}C_1\times(0.09)^1\times(0.91)^{12-1} \\ =^{12}C_1\times(0.09)^1\times(0.91)^{11} \\ =12\times0.09\times0.354368667=0.38271816 \end{gathered}[/tex][tex]\begin{gathered} P(2)=^{12}C_2\times(0.09)^2\times(0.91)^{12-2} \\ =^{12}C_2\times(0.09)^2\times(0.91)^{10} \\ =66\times0.0081\times0.389416118=0.208181856 \end{gathered}[/tex]Step 5: Add all the number of successess required
[tex]\begin{gathered} P(x\le2)=0.322475487+0.38271816+0.208181856 \\ =0.913375503 \\ \approx0.913 \end{gathered}[/tex]Hence, the probability that at most 2 children live with their father only is 0.913
A recent study conducted by a health statistics center found that 27% of households in a certain country had no landline service. This raised concerns about the accuracy of certain surveys, as they depend on random-digit dialing to households via landlines. Pick five households from this country at random. What is the probability that at least one of them does not have a landline _________
We are going to use Binomial Probability Distribution
Probability that they have no landline = q = 27/100 = 0.27
Probability that they have landline = p = 1 - 0.27 = 0.73
Now, to find the probability that at least one of them does not have a landline, we have to find the probability that all the five have a landline first.
So let's find the probability that all the five have a landline:
[tex]\begin{gathered} P(X=x)=^nC_xp^xq^{n-x} \\ ^5C_5(0.73)^5(0.27)^{5-5} \\ P(X\text{ = 5) = }0.2073 \end{gathered}[/tex]So the probability that all the five have a landline = 20.73%
Now is the time to find the probability that at least one of them does not have a landline:
P(at least one has no landline) = 1 - P(All have landline)
= 1 - 0.2073
= 0.7927
So the probability that at least one of them does not have a landline = 79.27%
That's all Please
had a question about this and i cant find a answer
A line is given by the expression:
y=mx+b
where, m is the slope of the line and since we have to write an equation that is parallel to the given line, both lines have the same slope:
We can find the equation of the line by the slope-point form of a line, with the given point (-8, -7) and the slope of -4
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y+7=-4(x+8) \\ y+7=-4x-32 \\ y=-4x-32-7 \\ y=-4x-39 \end{gathered}[/tex]3 1/2 ÷ 47/815/88/73/4
the given expression is,
[tex]\begin{gathered} 3\frac{1}{2}\div4=\frac{7}{2}\div4 \\ =\frac{\frac{7}{2}}{4}=\frac{7}{8} \end{gathered}[/tex]so the answer is option A
A baker paid $15.05 for flour at a store that sells flour for $0.86 per pound.
Solution:
Given that a store sells flour for $0.86 per pound, this implies that
[tex]1\text{ lb}\Rightarrow\$0.86[/tex]Given that a baker paid $15.05, let y represent the amount of flour the baker bought.
Thus,
[tex]y\text{ lb}\Rightarrow\$15.05[/tex]To solve for y,
[tex]\begin{gathered} 1\text{lb}\operatorname{\Rightarrow}\operatorname{\$}0.86 \\ y\text{ lb}\Rightarrow\$15.05 \\ cross-multiply, \\ y\text{ lb = }\frac{\$\text{15.05}}{\$0.86}\times1\text{ lb} \\ =17.5\text{ lb} \end{gathered}[/tex]Hence, the baker bought 17.5 lb of flour.
A loan is paid off in 15 years with a total of $192,000. It had a 4% interest rate that compounded monthly.
What was the principal?
Round your answer to the nearest cent and do not include the dollar sign. Do not round at any other point in the solving process; only round your answer.
The principal amount with the given parameters if $165.
Given that, Amount = $192,000, Time period = 15 years and Rate of interest = 4%.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100} )^{nt}[/tex]
Now, [tex]192,000=P(1+\frac{4}{100} )^{15\times 12}[/tex]
⇒ [tex]P=\frac{192,000}{(1.04)^{180}}[/tex]
⇒ P = $164.93
≈ $165
Therefore, the principal amount with the given parameters if $165.
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Answer:
Step-by-step explanation:
Use the compound interest formula and substitute the values given: $192,000=P(1+.0412)12(15). Simplify using order of operations: $192,000=P(1+.0412)180
P=192,000(1+.0412)180
P≈$105477.02
Hello. I think I have this one correct but I'm not 100% sure. Would you mind helping me work this through?
1) To better set the measurements in that picture, we need to consider that parallel line segments in this picture have the same measurements.
2) Based on that, we can look at that picture this way:
And set the following equation, given that Perimeter is the sum of all lengths of a polygon:
[tex]\begin{gathered} P=2+2+1+2+3+3+1+1+1+1+4+3 \\ P=24\:cm \end{gathered}[/tex]White the inequality shows by the shaded region in the graph with the boundary line y=x/3-5
From the given figure
Since the line is a dashed line, then
The sign of inequality does not have equal (< OR > )
Since the shading area is down the line, then
The sign of inequality should be smaller than (<)
Then the inequality is
[tex]y<\frac{x}{3}-5[/tex]Had someone explain it and I didn’t get it still
From the question:
Let f(x) = 2x² + 2x - 8
g(x) = √x - 2
We are aske to write f(g(x))
f(x) = 2x² + 2x - 8, g(x) = √x - 2
g(x) = √x - 2
= f(√x - 2)
f(√x - 2): 2x + 2√x - 2 - 12
f(g(x)) = 2x - 12 + 2√x - 2.
Perform the following matrix row operation and write the new one.
Given: A matrix
[tex]\begin{bmatrix}{1} & {-3} & {2} \\ {3} & {9} & {5} \\ {} & & {}\end{bmatrix}[/tex]Required: To perform the following matrix row operation
[tex]-3R_1+R_2[/tex]Explanation: The operation is to be applied on the first row of the given matrix. Hence the second row will be same as that of the initial matrix.
The elements of the first row are first multiplied by 3 and then added with second row to give the required matrix.
Hence,
[tex]\begin{bmatrix}{-3+3} & {9+9} & {-6+5} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]which gives
[tex]\begin{bmatrix}{0} & {18} & {-1} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Final Answer: The required matrix is
[tex]\begin{bmatrix}{0} & {18} & {-1} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]1) A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels at this speed in t hours. a) What does the 65 tell us in this situation? b) How many miles does the car travel in 1.5 hours? Show your work. c) How long does it take the car to travel 26 miles at this speed? Show you
The equation d = 65t
represents the distance (d) the car travels at a 65 mile speed in t hours
a. 65 tells us the speed at which the car travels
b. If the car travels in 1.5 hrs, then
d = 65(1.5)
= 97.5 milestone.
c. To travel 26 miles, we have d = 26
26 = 65t
t = 26/65
= 0.35 (approximately)
HELP!! My question isUsing the formula below, solve when s is 3The formula is A = 6s² and I need to know the steps on how to solve it please help! I really dont understand and my teacher is not at school to help me
The given expression : A = 6s²
Substitute s = 3 in the given expression
A = 6s²
A = 6(3)²
as : 3² = 3 x 3
3² = 9
A = 6 x 9
A = 54
Answer : A = 54
Find the links of the sides of these special triangles
From the triangle, we express the tangent of 60° as:
[tex]\tan 60\degree=\frac{Z}{7}[/tex]But tan(60°) = √(3), then:
[tex]\begin{gathered} \frac{Z}{7}=\sqrt[]{3} \\ \Rightarrow Z=7\sqrt[]{3}\text{ ft} \end{gathered}[/tex]Given Hx)= vx and g(x) = \» ,which is the graph of (fºg)(x)?-2-222&DONE
Answer:
Step-by-step explanation:
A composite function is created when one functions is substituted into another function.
Given:
[tex]\begin{gathered} f(x)=\sqrt[]{x}\text{ and g(x)=}\lvert x\rvert \\ \text{Then, (f }\circ g)(x)\text{ would be f(g(x))} \end{gathered}[/tex]Therefore,
[tex](f\circ g)(x)=\sqrt[]{\lvert x\rvert}[/tex]Now, graphing this function...
Which of the following tables shows a uniform probability model?
The answer is the third choice
Where all probability are equal
Triangle HFG is similar to triangle RPQ. Find the value of x. Find the length of HG.
Answer:
• x=1
,• HG=8 units
Explanation:
If triangles HFG and RPQ are similar, the ratios of their corresponding sides are:
[tex]\frac{HF}{RP}=\frac{HG}{RQ}=\frac{FG}{PQ}[/tex]Substitute the given values:
[tex]\frac{4}{2}=\frac{6x+2}{x+3}=\frac{6}{3}[/tex]First, we solve for x:
[tex]\begin{gathered} \frac{4}{2}=\frac{6x+2}{x+3} \\ 2=\frac{6x+2}{x+3} \\ 2(x+3)=6x+2 \\ 2x+6=6x+2 \\ 6-2=6x-2x \\ 4=4x \\ x=1 \end{gathered}[/tex]Finally, calculate the length of HG.
[tex]\begin{gathered} HG=6x+2 \\ =6(1)+2 \\ =8\text{ units} \end{gathered}[/tex]Which equation has at least one solution? Mark all that app A. 2x-1= 2 B. 3 y + 1) = 3y 1 C. 5p - (3 + p) = 6p + 1 D. 4/5m=1-1/5m E. 10 +0.5w =1/2w - 10 F. 4a + 3(a - 2) = 8a - (6 + a) Answer Choices:
Let's check the options
A.
2x - 1 = 2
2x= 3
x= 3/2=1.5
option A has atleast one solution
B
3y+ 1 = 3y
option B has no solution
C.
5p - (3 + p) = 6p + 1
5p - 3 - p = 6p + 1
4p - 6p = 1 + 3
-2p = 4
p =-2
option C has atleast one solution
D.
4/5 m = 1- 1/5 m
4/5 m + 1/5m = 1
1m = 1
m = 1
Option D has atleast one solution
E.
10 + 0.5w = 1/2w - 10
0.5 w - 1/2 w = -10 - 10
option E has no solution
F.
4a + 3(a-2) = 8a - (6+a)
4a +3a - 6 = 8a -6 - a
7a -6 = 7a - 6
option F has many solution. Hence it also has atleast one solution
Therefore;
option A, C, D and F has atleast one solution
a1. The amount of milk in a one-gallon milk container has a normal distribution with a meanof 1.07 gallons and a standard deviation of 0.12 gallons.Calculate and interpret the z-score for exactly one gallon of milk.
The z-score formula is given to be:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
[tex]\begin{gathered} x=score \\ \mu=mean \\ \sigma=standard\text{ }deviation \end{gathered}[/tex]From the question given, the mean and standard deviations are provided as:
[tex]\begin{gathered} \mu=1.07 \\ \sigma=0.12 \end{gathered}[/tex]Therefore, the z-score of exactly 1 gallon is calculated to be:
[tex]\begin{gathered} x=1 \\ \therefore \\ z=\frac{1-1.07}{0.12}=\frac{-0.07}{0.12} \\ z=-0.583 \end{gathered}[/tex]Therefore, the z-score is -0.583.
This tells us that a container with exactly one gallon of milk lies 0.583 standard deviations below the mean.
f(x) = square root of x - 5. find f^-1 (x) and it’s domain
Given:
f(x) = root x - 5
Rewrite the function using y,
[tex]y=\sqrt[]{x}-5[/tex]Now, interchange the position of x and y in the function,
[tex]x=\sqrt[]{y}-5[/tex]Isolate the dependent variable
[tex]\begin{gathered} \sqrt[]{y}=x+5 \\ y=(x+5)^2 \end{gathered}[/tex]Therefore,
[tex]f^{-1}(x)=(x+5)^2[/tex]And the domain is minus infinity to infinity
[tex]\begin{gathered} f^{-1}(x)=(x+5)^2 \\ \text{Domain}=(-\infty,\infty) \end{gathered}[/tex]5. Graph the function f (x) = 3sin (2x) + 1 Be sure to identify the midline, period, and amplitude.
Given that f(x) = 3 sin (2x) + 1
Given that : a sin (bx + c ) + d
let a = amplitude,
Midline is the that runs between the maximum and minimum value
[tex]\begin{gathered} \text{ Since, amplitude = 3} \\ \text{the graph is shifted 1 unit in positive y - coordinate} \\ \text{Maximum value = 3 - 1 = 2} \\ \text{ minimum value = -3 - 1 = -4} \\ \text{Midline is the center of (2, - 4)} \\ \text{Midline = }\frac{\text{2 - 4}}{2} \\ \text{midline = -1} \end{gathered}[/tex]Period is calculated as
[tex]\begin{gathered} \text{period = }\frac{2\pi}{|b|} \\ \\ \text{b = 2} \\ \text{Period = }\frac{2\pi}{2} \\ \text{Period = }\pi\text{second} \end{gathered}[/tex]Frequency = 1 / period
[tex]\text{frequency = }\frac{1}{\pi}\text{ Hz}[/tex]4 boxes of crayons cost $12.50 How much would 16 boxes cost? (Show work) Thank you!
Answer:
$50.08
Step-by-step explanation:
Find the unit rate.
[tex]\frac{12.50}{4}[/tex] Each box cost $3.125. We cannot have .125 cents, so round up to 3.13
3.13 x 16 = $50.08
Illustrate the ratio 7:3 using 'X' for 7 and 'y for 3
Given the ratio:
7:3
To illustrate the ratio above using x for 7 and y for 3, we have:
All you need to do is to replace 7 with x and replace 3 with y
7 : 3 ==> x : y
ANSWER:
x : y
If f (x) = 3x2 - 2x + 1, select all of the following that are TRUE?f(-1) = 6f(1) = 0f (2) = 9f(0) = 1Previous
The function is:
[tex]f(x)=3x^2-2x+1[/tex]to check witch is true we have to evaluate the function in -1, 1, 1 and 0 so:
for
you randomly select one card from a 52 card deck. find the probability of selecting a black three or a red jack
Probability of selecting a black three or a red jack = 1/13
Explanations:There are a total of 52 cards in a deck of cards
Total number of ways of selecting one card from 52 cards = 52C1 = 52 ways
There are two red jacks in a deck of cards
Number of ways of selecting a red jack = 2C1 = 2 ways
There are two blacks 3s in a deck of cards
Number of ways of selecting a black three = 2C1 = 2 ways
[tex]\begin{gathered} \text{Probablity of selecting a black 3 = }\frac{2}{52}=\text{ }\frac{1}{26} \\ \text{Probability of selecting a red jack = }\frac{2}{52}=\frac{1}{26} \end{gathered}[/tex]Probability of selecting a black three or a red jack = (1/26) + (1/26)
Probability of selecting a black three or a red jack = 2/26 = 1/13
4y - 6 = 2y + 8how to solve this equation
To solve this equation, we need to collect like terms
To collect like terms, we bring the terms similar to each other to the same side
In this case, the value having y will be brought to same side of the equation
Kindly note that if we are bringing a particular value over the equality sign, then the sign of the value has to change
This means if negative, it becomes positive and if positive, it becomes negative
Proceeding, we have
4y - 2y = 8 + 6
2y = 14
divide both sides by 2
2y/2 = 14/2
y = 7
The value of y in this equation is 7
At 3:00 PM a man 138 cm tall casts a shadow 145 cm long. At the same time, a tall building nearby casts a shadow 188 m long. How tall is the building? Give your answer in meters. (You may need the fact that 100 cm = 1 m.)
A tall man(138cm) casts a shadow of 145cm
A building nearby casts a shadow of 188m
Using the information you have to determine the height of the building.
First step is to convert the units of the height of the man and the length of his shadow from cm to meters:
100cm=1m
So 145cm=1.45m
And 138co=1.38m
Now that the measurements are expressed in the same units you can determine the height shadow ratio of the man and use it to calculate the height of the bulding.
[tex]\frac{\text{height}}{\text{shadow}}=\frac{1.38}{1.45}[/tex]Compare this ratio with the ratio between the heigth/shadow ratio of the building to determine the heigth of the building.
Said height will be symbolized as "x"
[tex]\begin{gathered} \frac{1.38}{1.45}=\frac{x}{188} \\ x=(\frac{1.38}{1.45})188 \\ x=178.92m \end{gathered}[/tex]The building is 178.92m
Give me a rhombus ABCD with BC =25 and BD= 30 find AC and the area of ABCD
300 u²
1) Let's start by sketching out this:
2) Since a Rhombus have 4 congruent sides, then we can state that 4 sides are 25 units, and we need to find out the other Diagonal (AC)
Applying the Pythagorean Theorem, to Triangle COD
a² =b² +c²
25² = 15² +c²
625 = 225 + c² subtract 225 from both sides
625-225 = c²
400 = c²
√c² =√400
c =20
2.2) Now, we can calculate the area, applying the formula for the area of a rhombus (the product of its diagonals).
[tex]\begin{gathered} A=\frac{D\cdot d}{2} \\ A=\frac{40\cdot30}{2} \\ A=\frac{1200}{2} \\ A\text{ = 600} \end{gathered}[/tex]3) Hence, the answer is 300 u²
The polynomial expression x(3x^2+25)(10x^2+4x+6), where x is in inches, can be used to mod the number of cubic inches of cement that will be needed for a new porch. The cement contractor used 2 for the value of x.
Since x is given in cubic inches, let's split the expression like this:
[tex]\begin{gathered} h=height=x \\ w=width=(3x^2+25) \\ l=length=(10x^2+4x+6) \end{gathered}[/tex]For x = 2:
[tex]\begin{gathered} h=2in \\ w=3(2)^2+25=37in \\ l=10(2)^2+4(2)+6=54in \end{gathered}[/tex]Y + 41 = 67 solve y using one step equation
Answer:
Y = 26
Step by step explanation:
[tex]y\text{ + 41 = 67}[/tex]
Then we pass the 41 to substract.
[tex]y\text{ = 67 - 41 = 26}[/tex]Write and solve the equation that has been modeled below.
Solution
[tex]\begin{gathered} x+x+1+1+1+1+1+1+1=1+1+1+1+1+1+1+1+1 \\ 2x+7=9 \\ \text{Separate similar terms} \\ 2x=9-7 \\ 2x=2 \\ \text{Divide both sides by 2} \\ \frac{2x}{2}=\frac{2}{2} \\ \\ x=1 \end{gathered}[/tex]The final answer
[tex]x=1[/tex]