The correct option is option (d).
To solve this problem, we need to find the probability that two randomly selected packages are both more than 4.5 pounds. Since the distribution is normal, we can use the standard normal distribution table to find the probability.
The first step is to standardize the weight of the packages by subtracting the mean from the weight and dividing it by the standard deviation. The weight of 4.5 pounds is the mean, so the standardized weight is (4.5 - 4.5) / 1.8 = 0.
The probability that a package weighs more than 4.5 pounds is the same as the probability that a standardized package weighs more than 0. This probability is equal to 1 - P(Z < 0) , where Z is the standardized weight.
Using a standard normal distribution table, we find that P(Z < 0) = 0.5. Therefore, the probability that a package weighs more than 4.5 pounds is 1 - 0.5 = 0.5.
Since the two packages are independent, we can find the probability that both packages are more than 4.5 pounds by multiplying the probability of one package being more than 4.5 pounds by itself. So, the probability that two randomly selected packages are both more than 4.5 pounds is 0.5 * 0.5 = 0.25.
In conclusion, the probability that two randomly selected packages are both more than 4.5 pounds is 0.25
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If you deposit $8,000 into an account paying 6% simple interest, how long until there is $13,000 in the account? Round to the nearest
tenth
• The balance of the account will be $13,000, in
years.
After 10 years the balance of the account will be $13000.
What is simple interest?
A simple interest is one that does not compound anyway. In this system, a creditor only pay interest on the initial amount and the rate of interest is not changed during the time period.
How many years needed to reach the required amount?
given, initial deposit money = initial principal amount = $8000
initial money is denoted by P
interest rate (annually), r = 6%
generally, simple interest is annual.
expected amount after t years = final amount = $13000
final amount is denoted by A.
t is the time in years.
According to the formula for simple interest, A = P (1 + rt)
$13000 = $8000(1 + 6/100×t)
$13000/ $8000 = (1 + 0.06t)
(1 + 0.06t) = 1.625
0.06t = 0.625
t = 10.417 years or t = 10 years
Therefore, after 10 years the balance of the account will be $13000.
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The double number line shows that a traffic signal allows traffic through the intersection for 363636 seconds. A double number line with 2 tick marks. The line labeled Time, seconds, reads from left to right: 0, 36. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. A double number line with 2 tick marks. The line labeled Time, seconds, reads from left to right: 0, 36. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. Complete the table to show different percentages of the time the signal allows. Time (\text{s}sstart text, s, end text) Percentage 100\%100%100, percent of 36\,\text{s}36s36, start text, s, end text 25\%25%25, percent of 36\,\text{s}36s36, start text, s, end text 125\%125%125, percent of 36\,\text{s}36s36, start text, s, end text Report a problem
The percentages for this problem are calculated as follows:
100% of 36 seconds: 36 seconds.25% of 36 seconds: 9 seconds.125% of 36 seconds: 45 seconds.How to obtain the percentages?The percentages in this problem are obtained applying proportions, multiplying the total amount by the decimal equivalent of the percentage.
Hence the amount that represents 100% of 36 seconds is obtained as follows:
1 x 36 = 36 seconds.
(as a percentage of 100% has a decimal equivalent of 1).
The amount that represents 25% of 36 seconds is obtained as follows:
0.25 x 36 = 9 seconds.
(as a percentage of 25% has a decimal equivalent of 1).
The percentage of 125% of 36 students can be obtained combining the two previous expressions as follows:
1.25 x 36 = 1 x 36 + 0.25 x 36 = 36 + 9 = 45 seconds.
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Condos in Georgetown go up in value by 10% each year. If the Sutton family's condo is now worth $120,000, what will it be worth in 8 years?
With 8 percent increase each year the Sutton family's condo's worth in 8 years will be $216000.
What is exponential function?An exponential function is a mathematical function in the form f(x) = ax, where {x} is a variable and {a} is a constant which is called the base.
Given is that Condos in Georgetown go up in value by 10% each year. Sutton family's condo's current worth is $120,000.
We can write the function to calculate the worth after {T} years as follows.
A{T, R} = A{I} {1 + RT}
A{T, R} = {120000} {1 + (10/100) x 8}
A{T, R} = {120000} {1 + 0.1 x 8}
A{T, R} = {120000} {1 + 0.8}
A{T, R} = {120000 x 1.8}
A{T, R} = 216000
Therefore, the Sutton family's condo's worth in 8 years will be $216000.
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An operator works a basic fortnight at a basic
rate of $8. 95 and earns $671. 25. Determine the
basic fortnight for the operator.
just the answer pls
To determine the basic fortnight for the operator, we need to divide the operator's earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
The basic fortnight for an operator is the number of fortnights the operator has worked at their basic rate of pay. In this case, the operator has earned $671.25 at a basic rate of $8.95 per fortnight. To determine the basic fortnight, we need to divide the operator's total earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
So, the operator has worked 75.05 basic fortnights. It means he has been working for 75.05*14=1053 days. This is the number of days the operator has worked at their basic rate of pay. It is important to note that this calculation assumes that the operator has not earned any overtime pay or other bonuses.
$671.25 ÷ $8.95 = 75.05
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Please help!!! Very confused on my homework.
The tank is completely filled with water and then drains completely into the pool. The volume of the cylindrical tank is v1=36pir2/1 where r1 is the radius of the tank in feet.
PROBLEM IS ON THE ATTACHMENT!
Step-by-step explanation:
we need to use both equations for the volumes.
the only variables in them are r1 and r2.
when we say both results (volumes) are equal, that means we can create an equation with one formula on one side and the other formula on the other side.
and then we can easily transform the equation into "r1 = ..." or "r2 = ..."
and yes, your teacher made a mistake by hinting to solve for r1 in a. and b. it is r1 in a. and r2 in b.
a.
the goal here is an equation in the form
"r1 = ..."
that means r1 is a function of r2.
36×pi×r1² = 1/2 × 4/3 × pi × r2³ = 4/6 × pi × r2³ =
= 2/3 × pi × r2³
36 × r1² = 2/3 × r2³
r1² = (2/3 / 36) × r2³ = (1/(3×18)) × r2³ = 1/54 × r2³
r1 = sqrt(1/54 × r2³) = 1/3 × sqrt(1/6 × r2³)
b.
the goal here is
"r2 = ..."
again
36×pi×r1² = 2/3 × pi × r2³
36 × r1² = 2/3 × r2³
3×36 × r1² = 2 × r2³
3×18 × r1² = r2³
54 × r1² = r2³
[tex]r2 = \sqrt[3]{54 \times {r1}^{2} } = 3 \times \sqrt[3]{2 \times {r1}^{2} } [/tex]
c.
r2 is doubled.
so, we have to go back to our equation of a.
r1 = sqrt(1/54 × r2³).
when r2 is doubled, we get
r1 = sqrt(1/54 × (2×r2)³) = sqrt(1/54 × 8 × r2³) =
= sqrt(8) × sqrt(1/54 × r2³)
so, when r2 doubles, r1 has to grow by the factor of sqrt(8) to keep the equality intact.
help help help help help
Answer:
the answer is (3,4) and (2,3)
Step-by-step explanation:
that's my answer
N(t) = 8950 times (0.7)^2t
Answer: t = 0
Step-by-step explanation:
Expand 8950×0.7²: 4385.5t
8950(0.7) ²t
8950×0.49t = 4385.5t
N(t) = 4385.5t
N(t) - 4385.5t=0
Factor N(t) - 4385.5t: t (N - 4385.5)
t (N - 4385.5) =0
t=0
Can you help me with this
Answer:
y = 3/2x - 3
Step-by-step explanation:
first find slope (m):
m = (-3/2 -(-15/2)) / (1 - (-3)) = (12/2) / 4 = 6/4 = 3/2
plug the point (1, -3/2) into the point-slope form (y-y1) = m(x-x1):
y - (-3/2) = 3/2(x-1)
y + 3/2 = 3/2x -3/2
now put it in slope-intercept form y = mx + b:
y = 3/2x -6/2
y = 3/2x - 3
Find the value of StartFraction P (t) Over A EndFraction for this problem. StartFraction P (t) Over A EndFraction
The value of StartFraction P (t) Over A EndFraction for this problem will be 20
Take the value of x that they provide you and plug it into the problem for these kinds of difficulties.
The fraction's numerator is the highest number. It stands in for the entire thing that must be divided.
A fraction's denominator is the value at the bottom. It shows how many equally sized pieces are divided up in the object.
adding 3 to the formula:
6/(3) + 2(3)^2 —> use PEMDAS. Apply the 32 exponents first, followed by left-to-right multiplication and division, and finally addition.
6/x + 2x^2,
when x = 3
=20
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The question the incomplete the full question:
What is the value of StartFraction 6 Over x EndFraction + 2x2, when x = 3?
Answer:
The second part is 0.8 and B. About 1,845 years.
Step-by-step explanation:
:)
1/2x+y=4
x+1/3=2
solve the linear system
Answer:
x = 5/3, y = 2/3
Step-by-step explanation:
x/2 +y = 4 equ 1x + 1/3 = 2 equ 2
solve for x in equation 2 and then use it to find y in equation 1Select the correct answer. A record label surveyed 150 random visitors to its website to discover whether they prefer metal, rock, hip-hop, or jazz. The survey showed that 27 visitors preferred metal, 78 preferred rock, 21 voted for hip-hop, and 24 liked jazz. If the company estimates sales of 6,000 copies a week at its online store, how many will likely be from the rock genre
The company is likely to sell 3,120 copies of rock music per week.
If the company estimates sales of 6,000 copies a week at its online store, it is likely that 78/150 x 6,000 = 3,120 copies will be from the rock genre.
To find this, we first need to calculate the proportion of visitors that preferred rock music by dividing the number of visitors who preferred rock (78) by the total number of visitors surveyed (150). This gives us 78/150 = 0.52.
Next, we multiply this proportion by the estimated number of weekly sales at the online store (6,000) to find the number of sales that are likely to be from the rock genre. 0.52 x 6,000 = 3,120.
So, the company is likely to sell 3,120 copies of rock music per week.
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Please help me I am struggling with this
Step-by-step explanation:
(1). x-intercept: Put y = 0 in the equation y = 2x - 6 and solve for x. The x-intercept is 3.
y-intercept: Put x = 0 in the equation y = 2x - 6 and solve for y. The y-intercept is -6.
(2). x-intercept: Put y = 0 in the equation y = x - 7 and solve for x. The x-intercept is 7.
y-intercept: Put x = 0 in the equation y = x - 7 and solve for y. The y-intercept is -7
(3). x-intercept: Put y = 0 in the equation y = (3/2)x - 9 and solve for x. The x-intercept is -6.
y-intercept: Put x = 0 in the equation y = (3/2)x -9 and solve for y. The y-intercept is -9.
(4). x-intercept: Put y = 0 in the equation y = (-1/4)x + 1 and solve for x. The x-intercept is -4.
y-intercept: Put x = 0 in the equation y = (-1/4)x + 1 and solve for y. The y-intercept is 1.
(5). x-intercept: Put y = 0 in the equation -x + y = -5 and solve for x. The x-intercept is 5.
y-intercept: Put x = 0 in the equation -x + y = -5 and solve for y. The y-intercept is -5.
(6). x-intercept: Put y = 0 in the equation x + 2y = -14 and solve for x. The x-intercept is -14.
y-intercept: Put x = 0 in the equation x + 2y = -14 and solve for y. The y-intercept is -7.
(7). x-intercept: Put y = 0 in the equation 3x - y = -3 and solve for x. The x-intercept is -1.
y-intercept: Put x = 0 in the equation 3x - y = -3 and solve for y. The y-intercept is 3.
(8). x-intercept: Put y = 0 in the equation 5x + 3y = 15 and solve for x. The x-intercept is 3.
y-intercept: Put x = 0 in the equation 5x + 3y = 15 and solve for y. The y-intercept is 5.
How do you do a simple random sample on a calculator?
Using the calculator there are various methods according to the calculator we used and the approach we follow, Basic answer is to select N and generate random number.
What do you mean by random sampling?Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.
What are samples?A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.
Define the population size (N) and the sample size (n) that you want to obtain.
Use the calculator's random number generator to generate a random number between 1 and N. This will be the first element of your sample.
Repeat step 2 to generate the remaining elements of the sample, making sure that each element is different from the previous ones.
Record the elements of the sample, which are the random numbers that have been generated.
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A small box can hold 94.24 g of candy. If each candy has a mass of 1.52 g, how many candies can fit into each box?
Answer:
62 candies can fit into each box
Step-by-step explanation:
We know
A small box can hold 94.24 g of candy
Each candy has a mass of 1.52 g
How many candies can fit into each box?
To find it we take
94.24 divided 1.52 = 62 candies
So, 62 candies can fit into each box
A pound of strawberries costs $3.28 and a pound of apples costs $4.63. What is the combined cost of 0.7 pound of strawberries and 1.4 pounds of apples
The combined cost of 0.7 pound of strawberries and 1.4 pounds of apples is $8.778.
What is called a pound?The Latin word "poundus," which means "weight," is whence its name originates.
Any of the many weight and mass units. especially: a measurement that is commonly used by English-speaking peoples and equals 16 ounces (about 0.454 kilograms) see measurement. the United Kingdom's fundamental monetary unit. known also as the pound sterling.
Given that A pound of strawberries costs $3.28
and a pound of apples costs $4.63
So the combined cost of 0.7 pound of strawberries and 1.4 pounds of apples is
cost = $3.28(0.7) + $1.4(4.63)
cost = $2.296 + $6.482
cost = $8.778
Therefore, the answer is $8.778.
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What is the negation of ∃?
In order to find the negation of an expression we simply put the not operator in front of them . Therefore, the negation of ∃ is that â is not ^ to f.
The term negation means opposite , that is the negation of a statement is the opposite of the given mathematical statement. If we will take the example of P , let P be a statement, then the negation of P will be represented by ~P.
There are two symbols which are used to represent the negation of a statement which are “~” or “¬”. Therefore, ~P is known as the negation of P.
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The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys.
Company A: 1/5=5 25/5=5 50/10=5 75/15=5.
These ratios are all equivalent
This relationship is proportional.
company B: 5/1=5 20/5=4 40/10=4 69/15=4.
These ratios are not all equivalent.
This relationship is not proportional.
Is the ratio constant or varying for company B? Explain
When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.
Find the equivalent ratio by what method?Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you can determine the equivalent ratio. Finding equivalent fractions follows the same procedure.
A ratio formula is what?The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.
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What is the result of adding the system of equations 2x y 4 3x y 6?
The addition of terms [tex]2x+y^4[/tex] and [tex]3x+y^6[/tex] will be [tex]5x+y^4+y^6[/tex]
A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).
Simply add the coefficients of each phrase to add polynomials.
You may remove polynomials by subtracting the coefficients.
To add polynomials, just combine any like terms.
Step 1: Arrange each polynomial in decreasing order of degree, starting with the term with the highest degree.
Step 2: Sort the words that are similar. Similar phrases have the same variables and exponents.
So, the addition of terms [tex]2x+y^4[/tex] and [tex]3x+y^6[/tex] will be (2x+3x) (As here both are only the like terms, so they will be added together)
So, the sum will be: [tex]5x+y^4+y^6[/tex]
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The correct question should be:
What is the result of adding the system of equations:
[tex]2x+y^4[/tex] and [tex]3x+y^6[/tex]
x+2y=3x+4 into y=mx+b form
x + 2y = 3x + 4
2y = 3x + 4 - x
y = (2x + 4)/2
y = x + 2
Answer: y=x+2
Step-by-step explanation:
you subtract x on the left on both sides then you'll have 2y=2x+4 we have to get y by itself so divide it by 2 on both side and when you do that on the right you divide both 2x and 4 by 2 thus giving y=x+2
help i cant solve it
Answer:
Step-by-step explanation:
We have,
x = 3y - 3 ---> x - 3y = -3 ------(1)
5x + 4y = 23 -----(2)
Multiplying eq. (1) by 5:
5x - 15y = -15 ------(3)
5x + 4y = 23
Subtracting (1) from (3):
-19y = - 38
y = 2
therefore, x - 6 = -3
x = 3
The minimum hours of daylight occur mid-year with the maximum hours of daylight occuring in December.b.The maximum hours of daylight occur in January. The amount of daylight decreases each month until the minimum is reached in December.c.The minimum hours of daylight occur in December. The amount of daylight decreases each month until the minimum is reached.d.The minimum hours of daylight occur in January and December. The amount of daylight increases each month until it reaches a maximum mid-year.
The minimum hours of daylight occur in January and December is the correct answer . The amount of daylight increases each month until it reaches a maximum mid-year. Therefore, option D is correct.
The reason behind this is the rotation and revolution of Earth around the sun. The more the sun is towards the North Pole the shorter the day will be. On the equator, daylight will last generally for 12 hours as because sunlight falls directly on the equator
Therefore the shortest duration of daylight occurs in the month of December solstice when the North Pole is at its maximum distance from the Sun .
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(2, -4) and (-3, -3) write the linear equation in slope intercept form given the following
Answer:
y = -1/5x - 3.6
Step-by-step explanation:
(2, -4) and (-3, -3)
m = -3+4/ -3-2
m = 1/-5
m = -1/5
y = -1/5x + b
-4 = -1/5(2) + b
-4 = -0.4 + b
b = -3.6
y = -1/5x - 3.6
A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest
having an altitude of 8849m. Calculate the value of ‘g’ at that point.
Answer: A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest having an altitude of 8849m. Calculate the value of 'g' at that point.
The period of this pendulum can be solved using the formula shown in the picture below. T is the period in seconds; L is the length in meters and g is the acceleration due to gravity which is equal to 9.81 m/s²near the equator.
T = 2 × π × (square root of 1.00 m / 9.81 m/s²)
T = 2 * 3.1416 * (square root of 0.101936799)
T = 6.2832 * 0.319275428
T = 2.00 seconds
The period of this pendulum correct to 3 significant figures is 2.00 seconds.
The frequency of this pendulum is solved by the formula f = 1/T
f = 1/2.00 seconds
f = 0.500 hertz
Answer: 9.76 m/s^2
Step-by-step explanation:
What are the 3 types of translation?
When the state of an object is changed from one to another it is known as translation in mathematics and they are of three types.
The three types of translation in math are
horizontal translationvertical translationcompression translationWhen the object moves either from left to right or from right to left it is known as vertical translation.
The movement in up or downward direction of the graph is known as horizontal translation.
The domain of the function remains same in both the cases.
A translation in which the size of the object decreases or is compressed is known as the compression translation.
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A 140 meter rope is cut into two pieces. One piece is four time as long as the other. How long is each piece? Solve using substitution or elimination.
Answer:
28 m, 112 m
Step-by-step explanation:
x = length of short piece
4x = length of long piece
x + 4x = 140
5x = 140
x = 140/5 = 28
4x = 4(28) = 112
The coordinates of 3 of the vertices of a parallelogram are (-3, 4), (-2, 1), and (2, 6). What is the equation for the
line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a
parallelogram are parallel.)
A.
B.
-2
y=-x
5
2
y=-x+5
52.38
C. y=-3x
D. y=-3x+12.
y = -3x + 12 is the equation for the line containing the side opposite the side containing the first two vertices.
Given coordinates:
(-3,4) ; (-2,1) ; and (2,6)
let us solve for the slope.
Since , parallel sides have the same slope.
m = y2-y1 / x2-x1
m = 1 - 4 / -2-(-3)
m = -3 / 1
m = -3
y = mx + b
Since , (2,6) is a point which passes through the line . Hence , it must satisfy the equation.
Therefore,
6 = -3(2) + b
6 = -6 + b
6 + 6 = b
12 = b
On Substituting , values of m and b in y = mx +b , we get y = -3x +12 which is the required equation of the line.
Hence, y = -3x + 12 is the equation for the line containing the side opposite the side containing the first two vertices.
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You have to pay 25% income tax on all of the money you make. If you made $3000 this month, how much did you have to pay in taxes this month?
Please answer ASAP! :{
You get 20 points! :)
Answer: 750
Step-by-step explanation:
3000/4= 750
750
express √832 in the form 4n where n is the integral
We can express √832 as 4(2√13).
What is definite integral?A definite integral of a function can be represented as the signed area of the region bounded by its graph.
Given is the root of 832 or √832.
Assume that {4n} is equal to {y}. So, we can write -
y = 4n
Squaring both sides, we get -
y² = (4n)² = (√832)²
y² = 16n² = 832
16n² = 832
n² = (832/16)
n² = 52
n = √52
n = 2√13
So, we can write (√832) as 4(2√13).
Therefore, we can express √832 as 4(2√13).
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Melee has 1/8 of her candy bar left valid has 3/8 of his candy bar left if they put their candy together which fraction of candy bar do they have
Answer:
4/8
3/8 + 1/8 = 4/8
In ΔABC, if AB = BC and
Answer: not enough to answer