Answer:
30.
Step-by-step explanation:
We can write an equation for the number of gallons of water in the bathtub using the rate of change (drainage) and the elapsed time. Let y be the number of gallons of water in the tub after t minutes. Then, the equation can be written as:
y = 42 - (drainage rate) * t
Since we know that after 2 minutes, the tub holds 30 gallons of water, we can use this information to solve for the drainage rate:
30 = 42 - (drainage rate) * 2
12 = (drainage rate) * 2
drainage rate = 6 gallons per minute
Substituting this value into the original equation, we get:
y = 42 - 6t
So, the equation that represents the number of gallons of water in the tub after 2 minutes is:
y = 42 - 6 * 2 = 42 - 12 = 30.
Answer:
The equation representing the number of gallons of water in the tub after t minutes can be represented by a linear function y = mx + b, where y is the number of gallons of water, x is the number of minutes, m is the rate of change (or the slope) and b is the y-intercept.
Since the bathtub is draining at a constant rate, the slope (m) can be found by finding the difference between the initial number of gallons of water (42) and the number of gallons after 2 minutes (30), and dividing by the difference in time (2 minutes):
m = (42 - 30) / 2 = 6 gallons per minute
The y-intercept (b) can be found using the initial conditions of the problem, when t = 0:
b = 42 - (6 * 0) = 42
Therefore, the equation representing the number of gallons of water in the tub after t minutes can be written as:
y = 6t + 42
So, after 2 minutes, y = 6 * 2 + 42 = 54 gallons of water.
why is your answer to part (a) approximately correct even though the population distribution of diameters is clearly not normal? would the same approach be equally valid for a sample of size 2 rather than 25? why or why not?
In part (a), we used the Central Limit Theorem (CLT) to approximate the sampling distribution of the sample mean. The CLT states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.
The conditions for the CLT are:
The sample is randomly drawn from the population.
The sample size is large (usually, n >= 30 is considered large enough).
The samples are independent.
In this case, we assume that the sample was randomly drawn from the population of diameters, and the sample size of 25 is large enough to satisfy the second condition. The samples are assumed to be independent, as we are sampling without replacement from a large population.
Therefore, we can apply the CLT and use the normal distribution to approximate the sampling distribution of the sample mean.
For a sample of size 2, the sample mean will still have a sampling distribution, but the CLT may not be applicable. If the population distribution is highly skewed or has heavy tails, a sample size of 2 may not be sufficient to smooth out the sampling distribution, and it may not be normal.
In this case, a normal approximation may not be appropriate, and other methods, such as bootstrapping or permutation tests, may be more appropriate for inference.
In summary, the normal approximation based on the CLT is valid for large sample sizes, regardless of the population distribution. For small sample sizes, other methods may be more appropriate, and the normal approximation may not be valid if the population distribution is highly skewed or has heavy tails.
Question: The basal diameter of a sea anemone is an indicator of its age. The density curve shown here represents the distribution of diameters in a certain large population of anemones; the population mean diameter is 4.2cm, and the standard deviation is 1.4cm.
Let Y dash represent the mean diameter of 25 anemones randomly chosen from the population.
(a) Find the approximate value of Pr{4 ≤ Ydash ≤ 5}.
(b) Why is your answer to part (a) approximately correct even though the population distribution of diameters is clearly not normal? Would the same approach be equally valid for a sample of size 2 rather than 25?Why or why not?
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ason has 4 feet of ribbon. He uses 1/3 foot of ribbon to wrap a gift. How many gifts can Jason wrap with the ribbon he has?
answer choices
1/3
1/12
4
12
The number of gifts ason can wrap with the ribbon he has is 12.
Conversions :A quantity that is multiplied or divided between one set of units and another is termed as a conversion factor. If a conversion is required, it must be carried out with the right conversion factor to generate a value that is identical.
To change a value or expression from one form to another.
Now in the given question,
ason wraps a gift using one third of a foot of ribbon.
he has total ribbon of 4 feet.
so, we have the equation,
[tex]\frac{1}{3} x=4\\\\x=12[/tex].
hence, 12 gifts can be wrapped with the ribbon ason has.
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Julius went fishing on Saturday morning. He took a cooler to store the fish that he caught. The cooler could hold less than 8 large fish. Write an inequality that represents how many fish the cooler could hold.
8 > f
8 < f
8 ≥ f
8 ≤ f
Answer:
8 < f
8 must be strictly lesser than f, not greater than or equals to.
your friend says that he will be 21 years old and seven years how old is he now?
Answer:
Step-by-step explanation:
He is now 14 years old because if you minus 21 and 7, it will be 14
Answer:
If your friend says that he will be 21 years old in seven years, then he is currently 21 - 7 = 14 years old.
Step-by-step explanation:
2. Divide R3 520 in the ratio 11:12:17.
Answer:
Rs 3520 is divided in the ratio 11:12:17 as rs 968, rs 1056, and rs 1469
Step-by-step explanation:
According to the question, we have to divide rs 3520 in the ratio 11:12:17
let the common ratio be x
so, total share= (11+12+17)x = 40 x
for the first person, share would be (11x/40x)*(Rs 3520)
=Rs 968
for the second person, share would be (12x/40x)*(Rs 3520)
=Rs 1056
for the third person, share would be (17x/40x)*(Rs 3520)
=Rs 1496
The shares are Rs 968, Rs 1056, and Rs 1469
hope this helps :)
what are the multiplicative inverses of the other elements (you may want to use trial and error for finding the inverses)?
To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element. All elements in the set have a multiplicative inverse except for 0.
To find the multiplicative inverse of an element in a set, we need to find another element in the set that, when multiplied by the first element, gives the multiplicative identity element (usually 1).
For example, in the set {1, 2, 3, 4, 5} under multiplication modulo 6, we have:
The multiplicative inverse of 1 is 1 (1 x 1 = 1 mod 6).
The multiplicative inverse of 2 is 4 (2 x 4 = 8 = 1 mod 6).
The multiplicative inverse of 3 is 5 (3 x 5 = 15 = 3 x 1 = 1 mod 6).
The multiplicative inverse of 4 is 2 (4 x 2 = 8 = 2 x 4 = 1 mod 6).
The multiplicative inverse of 5 is 3 (5 x 3 = 15 = 3 x 5 = 1 mod 6).
Note that every element in the set has a multiplicative inverse except for 0. This is because any number multiplied by 0 is 0, not 1.
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pls help asap it’s annoying me
Answer:
b. 53.1°
c. 126.9⁰
Step-by-step explanation:
These are SSA triangles; use Law of Sines to find the unknown angle:
b) sin30/15 = sinA/24
sinA(15) = sin30(24)
sinA = sin30(24)/15 = 0.80
m∠A = sin⁻1(0.80) = 53.1°
c) m∠A = 180 - 53.1 = 126.9⁰
Answer:
∠ BAC = 53.13° , ∠ BAC = 126.87°
Step-by-step explanation:
using the Sine rule in Δ ABC
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]
where a is the side opposite ∠ A and c is the side opposite ∠ C
here a = BC = 24 and c = AB = 15 , then
[tex]\frac{24}{sinA}[/tex] = [tex]\frac{15}{sin30}[/tex] ( cross- multiply )
15 sinA = 24 sin30° ( divide both sides by 15 )
sin A = [tex]\frac{24sin30}{15}[/tex] , then
A = [tex]sin^{-1}[/tex] ( [tex]\frac{24sin30}{15}[/tex] ) = 53.13°
(b)
acute angle BAC = 53.13°
(c)
the sine of an angle is positive in both the first and second quadrant , so
obtuse angle BAC = 180° - 53.13° = 126.87°
acrylamide, a possible cancer-causing substance, forms in high-carbohydrate foods cooked at high temperatures. acrylamide levels can vary widely even within the same type of food. an article appearing in a certain journal included the following acrylamide content (in nanograms/gram) for five brands of biscuits. 344 294 333 276 248 (a) calculate the mean acrylamide level (in nanograms/gram). nanograms/gram
An article appearing in a certain journal included the following acrylamide content for five brands of biscuits. 344 , 294, 333, 276, 248. The mean acrylamide level (in nanograms/gram) is 299.
In statistics, the mean is a measure of central tendency that represents the sum of all values in a dataset divided by the total number of values. It is commonly referred to as the average.
To calculate the mean, all the data values are added together, and then this sum is divided by the number of data points in the dataset. The formula for calculating the mean is:
mean = (sum of values) / (number of values)
To calculate the mean acrylamide level, we need to add up all the acrylamide levels for the five brands of biscuits and divide the sum by the total number of brands.
Sum of acrylamide levels = 344 + 294 + 333 + 276 + 248 = 1495
Total number of brands = 5
Mean acrylamide level = (Sum of acrylamide levels) / (Total number of brands) = 1495 / 5 = 299
Therefore, the mean acrylamide level is 299 nanograms/gram.
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Solve this(the best answer and explanation gets brainliest)
Answer: 5/12
Step-by-step explanation:
- For the ease of the problem, turn them into improper fractions, so it would be:
13/3 divided by 14/5 divided by 26/7
- Next, let's turn the equation from division to multiplication. This can be done by flipping the fractions of everything being divided, so:
13/3 times 5/14 times 7/26
- We can cross out some parts of the fraction, like 13 and 26, 14 and 7, which simplifies our equation to:
1/3 times 5/2 times 1/2 = 5/12
Answer:
[tex]\dfrac{5}{12}[/tex]
Step-by-step explanation:
Given equation:
[tex]4 \frac{1}{3} \div 2 \frac{4}{5} \div 3 \frac{5}{7}[/tex]
Convert the mixed numbers into improper fractions:
[tex]\dfrac{4 \times 3+1}{3} \div \dfrac{2 \times 5+4}{5} \div \dfrac{3 \times 7+5}{7}[/tex]
[tex]\dfrac{13}{3} \div \dfrac{14}{5} \div \dfrac{26}{7}[/tex]
[tex]\textsf{Apply the fraction rule:} \quad \dfrac{a}{c}\div\dfrac{b}{d}=\dfrac{a}{c}\times \dfrac{d}{b}[/tex]
[tex]\dfrac{13}{3} \times \dfrac{5}{14} \times \dfrac{7}{26}[/tex]
Multiply the fractions:
[tex]\dfrac{13\times5\times7}{3 \times14 \times 26}[/tex]
[tex]\dfrac{455}{1092}[/tex]
The greatest common factor of 455 and 1092 is 91.
Therefore, divide the numerator and denominator by the GCF:
[tex]\dfrac{455 \div 91}{1092\div 91}=\dfrac{5}{12}[/tex]
amy invested $223 in the banck and a year later has $280,98 . by what percent has changed
David and Alec are comparing the international calling plans on their cell phones. On his plan,
David pays $4 just to place a call and $1 for each minute. When Alec makes an international
call, he pays $1 to place the call and $2 for each minute. A call of a certain duration would
cost exactly the same under both plans. What is the duration?
Write a system of equations, graph them, and type the solution.
3 minutes is the cost of the call that is same for both plans
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's assume the call duration in minutes is represented by x.
For David, the cost of the call can be represented by the equation: C(d) = 4 + x
For Alec, the cost of the call can be represented by the equation: C(a) = 1 + 2x
Since the cost of the call is the same for both plans, we can set the two equations equal to each other and solve for x:
4 + x = 1 + 2x
Solve for x.
3 = x
Hence, the call duration that costs the same on both plans is 3 minutes.
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Find the value of z such that 0. 14 of the area lies to the left of z. Round your answer to two decimal places.
The value of z is -1.09.
The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data collection.
Given: P(Z<z)=0.14
To find the value of z such that 0.14 of the area lies to the left of z.
We will use z-score table to get the value of z here.
IN z-score table, we have
For P(Z<-1.09)=0.14
Hence, the value of z is -1.09.
Its approximate value is -1.09
So the final answer is z=-1.09.
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The diameter of a fountain is 9 meters. A sidewalk that is 0.7 meters will be built around it. Find the diameter
Round to the nearest tenth
An estimated Rs. 1863.40 will be needed to cement the route.
What is meant by Cost?A mathematical formula known as a cost function can be used to determine the overall cost of production for a given quantity of goods produced. We'll go into more detail about the cost function below. Representation of unit expenses in relation to the production of 1 or more units during a construction project. For instance, the most popular cost function has the formula y = a + bx, where y is the total cost, an is the total fixed cost, b is the variable cost per unit of production or sales, and x is the number of units produced or sold. This formula sums the fixed costs and the variable costs to represent the total cost.Diameter of park [tex]$=7 \mathrm{~m}$[/tex]
so, radius of park [tex]$=\mathrm{r}_1=3.5 \mathrm{~m}$[/tex]
Width of park [tex]$=0.7 \mathrm{~m}$[/tex]
Bigger radius of park [tex]$=\mathrm{r}_2=0.7+3.4=4.2 \mathrm{~m}$[/tex]
Now, Area of path = area of bigger circle -area of smaller circle
[tex]$=\pi r_2^2-\pi r_1^2=$ $\pi\left(r_2^2-\mathrm{r}_1^2\right)=\frac{22}{7}\left(4.2^2-3.5^2\right)=\frac{22}{7}(17.64-12.25)=16.94 \mathrm{~m}^2$[/tex]
Also, Cost of expenditure = rate [tex]$\times$[/tex] area [tex]$=110 \times 16.94=1863.40$[/tex]
Cost of Expenditure of cementing the path is Rs. 1863.40.
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i need help with this one?
The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.
How does the nodal point dilate the retina ?An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."
In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.
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Use the Distributive Property to figure out (z-5)(z+3)
whats the answer
Using the distributive property, we can write (z-5)(z+3) is equal to [tex]z^2[/tex] - 2z - 15.
Let us expand the expression (z-5)(z+3).
We will distribute the terms in the first set of parentheses (z-5) to the terms in the second set of parentheses (z+3) as follows -
(z-5)(z+3) = z(z+3) - 5(z+3)
Now, we will simplify the expression by distributing z to both terms inside the first set of parentheses, and then distributing -5 to both terms inside the second set of parentheses as follows -
z(z+3) - 5(z+3) = [tex]z^2[/tex] + 3z - 5z - 15
Combining the like terms, we get,
(z-5) (z+3) = [tex]z^2[/tex] - 2z - 15
Therefore, (z-5)(z+3) is equal to [tex]z^2[/tex] - 2z - 15.
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b. Isabella has a second tray that has a length of 5/3 inches and a width of 13/4 inches
and a height of 5/2 inches. What is the volume of the second tray?
Answer: approx 13.54 (full decimal : 13.416666667)
Step-by-step explanation:
Area = Base Area x Height OR Length x Width x Height
5/3 x 13/4 x 5/2
5 x 13 x 5 = 325
3 x 4 x 2 = 24
325/24 = approx 13.54
Write an inequality.
You need to buy several pencils and an eraser. You can spend no more than $7. The eraser costs $.75 and
pencils cost $.25.
Answer: .75 + .25x ≤ 7
Step-by-step explanation: The x equals the amount that you can buy for each item.
Increase 600 by 9% equal too?
Answer:
654
Step-by-step explanation:
An increase of 9% would mean 1.09 times 600 which equals 654
an equation for the line with a slope of 3 and passing through the point (5, 7).
Answer:
y – 7 = 3(x – 5)
Step-by-step explanation:
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5}) \\\\\\ y-7=3x-15\implies {\Large \begin{array}{llll} y=3x-8 \end{array}}[/tex]
The ratio of the sides of a triangle are 3:5:12. If the perimeter of the triangle is 100 units, determine the length of the shortest side.
The measure of the length of the shortest side will be 15 units.
What is a ratio?If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. How frequently one value contains or is contained within another is shown by the numerical connection between the two values.
Given that the perimeter of the triangle is 100 and the ratio of the sides of the triangle is 3:5:12.
The length of the shortest side will be calculated as:-
3x + 5x + 12x = 100
20x = 100
x = 20
Length = 3x
Length = 3 x 5 = 15 units
Hence, the shortest side will be 15 units.
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Two large charged plates of charge density ±30�C/m2±30μC/m 2 face each other at a separation of 5.0 mm. (a) Find the electric potential everywhere. (b) An electron is released from rest at the negative plate; with what speed will it strike the positive plate?
(a) Potential on the opposite sides of the positive and negative plates is 8475 V and -8475 V, respectively. (b). 772 m/s is the speed at which the positive plate will be struck.
What is the word for speed in science?A more technical or sophisticated phrase, velocity, is occasionally used interchangeably with speed to refer to extremely high rates of linear or circular speed, such as the velocity of a bullet.
a). Positivplate should be on the right and negativeplate should be on the left.
Potential equals zero at the center of the plates.
Electric field between it plates: 30e⁻⁶/8.85e⁻¹² (338 V/m) = sigma/e0
Potential is equal to 3389830x, where x is the distance in meters from the center of the plates.
Where x is the distance in meters from the center of the plates, the potential to the left of either the middle point equals -3389830x.
Potential outside of the positive plate is equal to 3389830*0.005/2, or 8475 V.
The potential is -8475 V on the contrary side of the negative plate.
Potential between it plates is equal to -8474 + 3389830x, where x is the distance in meters from the negative plates.
b). Electron energy at the positive plate is equal to [8475 - -8475]. eV = 2*8475*1.6e⁻¹⁹ = 2.712*10⁻¹⁵ J
Speed = sqrt(2E/m) = sqrt(2*2.712e-15/9.1e⁻³¹) = 772 meters per second.
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Please help!!
Solve for x
Answer: x=8
Step-by-step explanation: since we know 2 sides of both quadrilaterals and they are similar,
just put 32/40 = 24/3x+6 ,
cross multiply ( 32 x 3x+6 and 40 x 24),
they become 96x +192 = 960.
move 192 to the other side and divide both sides by 96
In August, 18% of the middle school students voted in a school election. The number of students who voted was 213. How many students are in the middle school?
If 18% of middle school student voted in a school election and number of students who voted is 213 , then the total students in the middle school is approximately 1184 students .
Let "x" be = total number of middle school students.
We know that 18 percent of the students voted = 0.18x, and is equal to 213 ;
that means , ⇒ 0.18x = 213 ;
Now we need to solve for x,
We divide both sides by 0.18 ;
⇒ x = 213/0.18 ;
Simplifying, we get:
⇒ x = 1183.33
Since the number of students cannot be in decimal ,
So , the actual number of students must be greater than or equal to 1183.33.
Therefore, the middle school has approximately 1184 students.
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not yet answered points out of 5.00 not flaggedflag question question text what is the radius of a right circular cylinder with a volume of 12 in3 if it has a minimum surface area?
The height of the cylinder is 18 cm and its volume is 450π cubic centimeters, given that the radius of its base is 5 cm and its total surface area is 165πcm².
A right circular cylinder is a three-dimensional geometric shape with a circular base and a curved surface that extends upward in a cylindrical fashion.
Let's begin by identifying the formula for the total surface area of a cylinder. It is given by:
Total surface area = 2πr(h + r)
Where r is the radius of the base, h is the height, and π is a mathematical constant (approximately 3.14). We are given that the total surface area of the cylinder is 165πcm², and the radius of its base is 5 cm. Substituting these values in the formula, we get:
165π = 2π(5 + h)5 + 2π(5)²
Simplifying this equation, we get:
165π = 10πh + 150π
Dividing both sides by 10π, we get:
h + 15 = 33
Therefore, the height of the cylinder is 18 cm (33 - 15).
Now, let's find the volume of the cylinder. The volume of a cylinder is given by:
Volume = πr²h
Substituting the values of r and h, we get:
Volume = π(5)²(18)
Simplifying this equation, we get:
Volume = 450π
Therefore, the volume of the cylinder is 450π cubic centimeters.
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Complete Question:
The total surface area of a right circular cylinder is 165πcm². If the radius of its base is 5 cm; find its height and volume.
Daniella and her 10 friends are collecting shells on the beach to make crafts. After
they have collected the shells and put them in a pile, they split them evenly among
the group. Each person gets 4 shells. How many shells did they collect as a group?
Select the correct equation and solve for s.
4+ s = 11; s = 7
s/10 = 4; s = 40
4s = 11; s = 2.75
s/11 = 4; s = 44
Daniella and her friends collected a total of 44 shells.
What is linear equation ?
Linear equation can be defined as equation in which highest degree is one.
Given ,
Daniella and her 10 friends are collecting shells on the beach to make crafts.
After they have collected the shells and put them in a pile, they split them evenly among the group. Each person gets 4 shells.
The correct equation for this problem is:
s = 11 x 4
where s is the total number of shells collected.
Simplifying this equation, we have:
s = 44
Therefore, they collected a total of 44 shells.
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how many sides does a polygon have if the sum of the interior angles is 3960
A polygon with a sum of interior angles of 3960 has 22 sides.
The sum of the interior angles of a polygon can be calculated using the formula:
(n-2) * 180
where n is the number of sides of the polygon. This formula is derived from the fact that the total degree measure of a polygon is equal to the sum of the degree measures of its interior angles. In a polygon with n sides, there are n angles, each measuring 180 degrees. So the total degree measure of a polygon with n sides is n * 180.
Now, if we subtract the degree measures of two angles, we are left with the sum of the degree measures of the remaining n-2 angles. This is why the formula for the sum of the interior angles of a polygon is given as (n-2) * 180.
To find the number of sides of a polygon given its sum of interior angles, we can rearrange the formula as follows:
n = (Sum of interior angles / 180) + 2
So, if the sum of the interior angles is given as 3960, we can plug that into the formula:
n = (3960 / 180) + 2
n = 22
Therefore, a polygon with a sum of interior angles of 3960 has 22 sides.
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How many sides does a polygon have if the sum of the interior angles is 3960?
4,400 is placed in an account with an annual interest rate of 8. 25%. How much will be in the account after 22 years to the nearest cent
If $4400 is placed in account at 8.25% for 22 years , then the final amount received after 22 years will be $26480.08 .
We use the formula for compound interest to find the final amount :
that is ⇒ A = P(1 + r)ˣ ;
where: A = the amount of money in the account after "x years" ;
P(initial amount) = $4400 ; r (interest rate) = 0.0825 ;
⇒ x(time) = 22 years
we get ;
⇒ A = 4400×(1 + 0.0825)²² ;
⇒ A = 4400×(1.0825)²² ;
⇒ A = 4400×6.018028 ;
⇒ A = 26480.08 ;
Therefore , the amount in the account after 22 years is $26480.08 .
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**EASY POINTS**
2 part question:
1. There is a circular running path in the park. The diameter of the circle is 350 m. What is the length of one lap around the path?
2. Jimmy jogs 3 laps of the circle in question #1 every morning. How long does he jog in 5 days?
Answer:
The length of one lap around the path is 2π x 350 m, which is equal to 2200 m.
Jimmy jogs 2200 m x 3 laps x 5 days, which is equal to 33000 m or 33 km.
Step-by-step explanation:
which statement about 4 √2x+4 √x+3=0 is true?
The statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.
How to find the equation that is true?To determine which statement about 4 √2x + 4 √x + 3 = 0 is true, we need to solve the equation.
However, it is not possible to solve the equation exactly because it contains square roots. We can simplify the equation by multiplying both sides by the conjugates of the square roots, which eliminates the square roots.
Multiplying both sides by (2x + x + 3) / (2x + x + 3), we get:
(4 √2x + 4 √x + 3) * (2x + x + 3) / (2x + x + 3) = 0 * (2x + x + 3) / (2x + x + 3)
Expanding the left-hand side, we get:
12x + 6 = 0
Solving for x, we get:
x = -1/2
So, the statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.
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a department store gets an average of 16 calls in a 2 hour time period. what is the probability that the department store will get at most 3 calls in a 55 minute period? round the final answer to three decimal places.
The probability that the department store will get at most 3 calls in a 55 minute period is 0.066
The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within “x” period of time.
It is given that a department store gets an average of 16 calls in a 2 hour or 161055 = 223 calls per minute
Find the probability by Poisson distribution with parameter
λ = 223
P(X = x) = λˣе - λx!
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= (223)⁰е - 223(0!) +(223)¹е - 223(1!) +(223)²е - 223(2!) +(223)³е - 223(3!)
= 0.0006 + 0.004 + 0.018 + 0.043
P(X ≤ 3) ≈ 0.066
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