Answer:
Amount deposited into Lou's 401(k) each payday is $119.665
Step-by-step explanation:
Here we have gross income annual $41028
Payment frequency = Every two weeks
Number of payments (Pay days per annum) = 12 × 2 = 24 payments annually
Amount payed on pay day = $41028/24 = $1709.5
Amount deducted from Lou's paycheck on payday = 4% of Pay = 0.04×$1709.5
∴ Amount deducted from Lou's paycheck on payday = $68.38
Amount employer matches = 3% of pay = 0.03 × $1709.5 = $51.285
Therefore, amount deposited into Lou's 401(k) each payday = $68.38 + $51.285
Amount deposited into Lou's 401(k) each payday = $119.665.
Answer:
$110.46
Step-by-step explanation:
The measures of two angles have a a sum of 180°. The measures if the angles are in a ratio of 5:1. Determine the measures of both angles by setting up and solving an equation.
Answer:
one angle is 150 degrees and the other is 30 degrees.
Step-by-step explanation:
please kindly check the attached file for explanation.
Answer:
I think, one angle is 150 and the other 30.
Step-by-step explanation:
First, you can make a table of 3 columns: Angle 1, Angle 2 and Total
Then, you will work with the ratio 5:1 and say
Angle 1 Angle 2 Total
5 1 6
Then you do a little algebra process like this:
6a=180
6 x a /6= 180 / 2
a=30
6a=180
6 x a / 6=180/2 This means 6 times a divided by 6= 180 divided by 2. We insolate the variable, and we cross out the two six
a=30 And our answer is 30.
You can choose any variable. In this case I did with the variable a since we are talking about angles.
Returning to the table, the thing we need to do is this:
Angle 1 Angle 2 Total
5 1 6
150 30 180
We need to multiply 5x30 and 1x30
Then we add 150 plus 30 is 180.
So one angle is 150 and the other 30.
Hope this helps.
A population is a group of a single species living in a certain area at a certain time. A community is all combination of all of the populations in an area
Answer:
The above definition of Population & Community of species is correct.
Step-by-step explanation:
Population is the group of organisms living together in same geographical area, at a point of time. Community is the group of all organisms living together in same geographical area, at a point of time.
Population is the smaller group of interbreeding individuals of same species, Community is a bigger group of different species sharing same geographical area.
Eg : Lions in a particular forest can be defined as 'population' ; & all the organisms in a particular forest can be defined as 'community'.
Two thirds of a number is negative Twenty
The unknown number was found from the equation to be -30.
EquationAn equation is an expression used to show the relationship between two or more variables and numbers.
Let x represent the unknown number. Two thirds of a number is negative Twenty, hence:
(2/3)x = -20
Multiply both sides of the equation by 3/2, hence:
(2/3)x * 3/2 = -20 * 3/2
x = -30
The unknown number was found from the equation to be -30.
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Solve for m.
12.6 + 4m = 9.6 + 8m
m
=
Answer:
m = 3/4
Step-by-step explanation:
12.6 + 4m = 9.6 + 8m
4m - 8m = 9.6 - 12.6
- 4m = - 3
- m = - 3/4
m = 3/4
Suppose that 40% of a population has brown hair. You want to estimate the probability that it will take at least a sample of four to find one person with brown hair. You set up a random digit simulation where 0, 1, 2, 3 represents a person with brown hair and 4, 5, 6, 7, 8, 9 represents a person that does not have brown hair. Which would constitute a trial for this simulation?
Answer:
A
Step-by-step explanation:
A trail would consist of three random digits.
The problem asks for the probability that it will take at least a sample of four to find one person with brown hair. This implies that the first three people do not have brown hair. Therefore, a trial would consist of three random digits. A success is none of the three digits are 0, 1, 2, or 3. For example, 675 would be a success and a failure would be 792.
Answer:
A
Step-by-step explanation:
USA testprep said...
A trail would consist of three random digits.
The problem asks for the probability that it will take at least a sample of four to find one person with brown hair. This implies that the first three people do not have brown hair. Therefore, a trial would consist of three random digits. A success is none of the three digits are 0, 1, 2, or 3. For example, 675 would be a success and a failure would be 792.
Subtract 6 from me. Then multiply by 2. If you subtract 49 and then divide by 4, you get 8. What number am I?
Answer:
46.5
Step-by-step explanation:
Which statement best describes a physical change?
O Changes can occur to certain chemical properties of the substance, but the overall shape of the substance will remain the
same.
O Changes can occur to certain physical properties of the substance, but the overall shape of the substance will remain the
same.
Changes can occur to physical properties of a substance, but the chemical composition of the substance remains the
same.
Changes can occur to chemical properties of a substance, but the chemical composition of the substance remains the
same.
Joan has 2 dozen golf balls how many golf balls does she have
Anwer:12
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
1 dozen= 12
12x2=24
Javier solved this system of equations. y = 3x – 4, y = 3x – 4 6x – 8 = 6x – 8 –8 = –8 What can you conclude about the number of solutions to this system of equations? There is one solution, (–8, –8). There is one solution, (–8, 0). There is no solution. There are infinitely many solutions.
Answer:
there are infinite many solutions.
Step-by-step explanation:
i have taken this before
Answer:
D
Step-by-step explanation:
A teacher bought 15 boxes of markers. Each box contained 8 markers. Estimate how many markers she bought by rounding the number of markers in a box to the nearest ten.
Answer: She bought about 150 markers.
Step-by-step explanation:
Given : A teacher bought 15 boxes of markers.
i.e. Total boxes of markers = 15
Each box contained 8 markers.
That is , the estimated number of markers in each box = 10 [∵ 8≈10 [Round to the nearest tens]]
Now , the total number of markers in all 15 boxes of markers = (15) x (10)
= 150
Hence, she bought about 150 markers.
10, 4, 1.6, 0.64.. what’s next
Answer:
0.256 or 0.26
Step-by-step explanation:
The common ration is being multiply by 0.4
Please help me idk this
Answer:
37.68
Step-by-step explanation:
C=2[tex]\pi[/tex]r
C=2*6*3.14
C=12*3.14
C=37.68
Answer:
C = 2 π r
Step-by-step explanation:
2*3.14*6=37.69911=37.7
the answer is 37.7
The radius of a cylindrical construction pipes is 2ft if the pipe is 24 ft long what is its volume
V= (3.14)x(2²)x(24)= 301.592 ft³
Answer:
96π ft^3 or 301.59 ft^3 to the nearest hundredth.
Step-by-step explanation:
Volume = π r^2 L (r = radius L = length).
= π * 2^2 * 24
= 96π ft^3.
Find the slope to Y = 5/2x-3
Answer:
slope = 5/2
Step-by-step explanation:
This equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 5/2x -3
The slope is 5/2 and the y intercept is -3
Answer:
Slope: 5/2
Y Intercept: -3
Step-by-step explanation:
use the venom diagram to calculate probabilities. which probability is correct?
Answer:
Wheres the diagram?
Step-by-step explanation:
A Venn Diagram is commonly used in probability theory to visualize and calculate probabilities. The probability of two conditions being met can be found by taking a sum of the probabilities of both conditions and their intersection, and subtracting the probabilities of each condition occurring separately. A Tree Diagram is another tool used to easily represent and calculate probabilities of multiple outcomes.
Explanation:The use of a Venn Diagram is a common strategy in probability theory to help visualize and calculate probabilities effectively. To begin solving these problems, label each piece of the Venn Diagram clearly and note the probability or frequency of each part. Start by labeling the overlapping section first.
In the case of calculating the probability that a student belongs to a club and works part-time, identify the overlapping section of the Venn Diagram that represents both these conditions. The probability of this will be the sum of the probabilities of the student belonging to a club, working part-time, and both these conditions minus the probabilities of each of these conditions occurring separately.
Another tool that can be useful for visualizing and calculating probabilities is a Tree Diagram. A tree diagram uses branches to represent the possible outcomes of a scenario, which makes it easier to visually work through and solve probability problems. For instance, to visualize the probability of a man developing cancer in his lifetime and having at least one false-positive test, a tree diagram could be used where one branch represents the man developing cancer and the other branch represents the man having a false-positive.
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A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (half a sphere). Complete parts (a) through (e) below. a. Write and simplify an expression for the ratio of the volume of the hemispherical tank to its surface area (including the base). For a sphere, Vequals four thirds pi r cubed and SAequals 4 pi r squared . What is the volume of the hemispherical tank (including the base)? Vequals nothing (Simplify your answer. Type an exact answer in terms of pi .)
Answer:
Volume: [tex]\frac{2}{3}\pi r^3[/tex]
Ratio: [tex]\frac{2}{9}r[/tex]
Step-by-step explanation:
First of all, we need to find the volume of the hemispherical tank.
The volume of a sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]
where
r is the radius of the sphere
V is the volume
Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:
[tex]V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3[/tex]
Now we want to find the ratio between the volume of the hemisphere and its surface area.
The surface area of a sphere is
[tex]A=4 \pi r^2[/tex]
For a hemisphere, the area of the curved part of the surface is therefore half of this value, so [tex]2\pi r^2[/tex]. Moreover, we have to add the surface of the base, which is [tex]\pi r^2[/tex]. So the total surface area of the hemispherical tank is
[tex]A'=2\pi r^2 + \pi r^2 = 3 \pi r^2[/tex]
Therefore, the ratio betwen the volume and the surface area of the hemisphere is
[tex]\frac{V'}{A'}=\frac{\frac{2}{3}\pi r^3}{3\pi r^2}=\frac{2}{9}r[/tex]
A recent study found that the life expectancy of a people living in Africa is normally distributed with an average of 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at random, what is the probability that the person will die before the age of 65?
Answer:
P(X<65)=0.9452
Step-by-step explanation:
This is a normal distribution problem.
-Given the mean age is 53 years and the standard deviation is 75, the probability of dying before age 65 is calculated as:
[tex]z=\frac{\bar x-\mu}{\sigma}\\\\\\=\frac{65-53}{7.5}\\\\=1.60[/tex]
#We check the value of z=1.60 on the z table:
[tex]P(X<65)=0.5+0.4452\\\\=0.9452[/tex]
Hence, the probability of dying before 65 is 0.9452
the probability that the person will die before the age of 65 is 0.9452.
The calculation is as follows:[tex]P(X<65 ) = P[(X- \mu ) \div \sigma < (65 -53) \div 7.5][/tex]
= P(z <1.6 )
Now here we Using z table
So,
= 0.9452
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A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 2% of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed. b) Find the minimum sample size needed, using a prior study that found that 38% of the respondents said they think their president can control the price of gasoline. c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available?
To determine the minimum sample size needed to estimate the population proportion, and the minimum sample size needed, assuming no prior information is available, is approximately 6636.
Explanation:To determine the minimum sample size needed to estimate the population proportion, we can use this formula: [tex]n = (Z^2 * p * (1-p)) / E^2.[/tex]
Where:
n is the minimum sample sizeZ is the z-value corresponding to the desired confidence level (in this case, 99% confidence corresponds to Z = 2.58)p is the estimated proportion (0.5 is typically used when there is no preliminary estimate available)E is the margin of error (0.02 in this case)By plugging in the values into the formula, we get:
[tex]n = (2.58^2 * 0.5 * (1-0.5)) / 0.02^2[/tex]
= 6635.44
Similarly, a prior study found that 38% of the respondents think the president can control the price of gasoline, which is 9448.7 The sample size needed when using the prior estimate (9449) is larger than when assuming no prior information (6636). This is because having a prior estimate reduces the uncertainty, which allows for a smaller sample size to achieve the same level of confidence and margin of error.
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Final answer:
The minimum sample size needed for estimating the population proportion depends on the desired confidence level, margin of error, and estimated proportion. The formula used is n = (Z^2 * p * (1-p)) / E^2, and without prior estimate, p is taken as 0.5, whereas using a prior study, the actual estimate from the study is used.
Explanation:
To calculate the minimum sample size needed to estimate the population proportion with certain confidence and precision, we use the following formula for sample size calculation:
n = (Z^2 * p * (1-p)) / E^2
Where:
n is the sample size
Z is the Z-score corresponding to the desired confidence level
p is the estimated proportion of the population (p-hat)
E is the margin of error
(a) Without preliminary estimate: Assuming that no prior information is available, we use p = 0.5 for the most conservative sample size estimate. For a 99% confidence level, the Z-score is approximately 2.576. With a margin of error E of 0.02, the formula becomes:
n = (2.576^2 * 0.5 * (1-0.5)) / 0.02^2
(b) Using a prior study: If a prior study found p = 0.38, the calculation uses this value. The formula with Z = 2.576 and E = 0.02 becomes:
n = (2.576^2 * 0.38 * (1-0.38)) / 0.02^2
(c) Comparing results: Using p = 0.5 in (a) will result in a larger sample size than using p = 0.38 in (b) because the variance (p * (1-p)) is maximized when p = 0.5.
Four circles, each with a radius of 2 inches, are removed
from a square. What is the remaining area of the square?
Exact answer = 64 - 16pi
Approximate answer = 13.7345175425633
Units for the area are in square inches.
==============================================================
Work Shown:
The radius of each circle is 2 inches. Double this value to get the diameter to be 4 inches.
Two circles along the top have their diameters combine to 8 inches total, which is the side length of the square.
The area of the entire square, before we subtract off the circles, is 8^2 = 64 square inches.
Let A = 64
The area of one circle is pi*r^2 = pi*2^2 = 4pi square inches. Four circles combine to an area of 4*4pi = 16pi square inches.
Let B = 16pi
Subtract A and B to get the area of the shaded region, which is the leftover area after subtracting off the four circles
A-B = 64-16pi
To get the approximate answer, use a calculator
64-16pi = 13.7345175425633
What do I dots solve this
[tex]8y - 72 = 8 \times y - 8 \times 9 = \\ = 8 \times (y - 9) = 8(y - 9)[/tex]
The circumference of a circle is 3 pi miles. What is the diameter?
Answer:
3 miles
Step-by-step explanation:
The circumference of a circle can be found using:
c=[tex]\pi d[/tex]
We know the circumference is [tex]3\pi[/tex], so we can substitute that in for c
[tex]3\pi[/tex]=[tex]\pi d[/tex]
We want to find the diameter. To do this, we need to get d by itself. It is being multiplied by pi. To undo this, divide both sides by pi. This will cancel pi, and leave d by itself.
[tex]3\pi /\pi =\pi d/ \pi[/tex]
3=d
So, the diameter is 3 miles
Answer:
Diameter is 3
Step-by-step explanation:
C=2πr
3π = 2πr
3π / 2π = r (Divide each side by 2π)
3/2 = r (Simplify π)
3/2 *2 = d (d = 2r)
d = 6/2 = 3
Solve the equation -3/13 - 2/5 =
To solve the equation -3/13 - 2/5, find the common denominator, convert both fractions and then subtract them. The answer is -41/65.
Explanation:The question asks to solve the equation -3/13 - 2/5. To solve this, we need to find a common denominator for the fractions, which in this case is 65. We then convert each fraction to have this common denominator and subtract them.
Here is the step-by-step solution:
Find the Least Common Denominator (LCD) of 13 and 5, which is 65.Convert -3/13 to a fraction with a denominator of 65: (-3/13) imes (5/5) = -15/65.Convert 2/5 to a fraction with a denominator of 65: (2/5) imes (13/13) = 26/65.Now subtract the two fractions: -15/65 - 26/65 = -41/65.The answer to the equation is -41/65.
10, 15, 22.5, 33.75.... what’s next?
.
Answer:
50.625
Step-by-step explanation:
1) 10/2=5
10+5= 15
2) 15/2 = 7.5
15+7.5 = 22.5
3) 22.5/2 = 11.25
22.5+11.25= 33.75
4) Answer: 33.75/2 = 16.875
33.75+16.875 = 50.625
Which sequence below represents an exponential sequence? A) {2, 6, 10, 14, 18,...} B) {3, 5, 9, 16, 24,...} C) {4, 8, 24, 96,....} D) {256, 64, 16, 4,....}
Answer:d
Step-by-step explanation:
Clearly from observation option D is the exponential sequence
256,64,16,4 is decreasing exponential function
[tex]\Rightarrow \frac{256}{64}=\frac{4^4}{4^3}=4[/tex]
[tex]\Rightarrow \frac{64}{16}=4[/tex]
for other option they simply follow an AP
2,6,10,14,18
common difference d=4
Una piscina portátil ha tardado en llenarse seis horas utilizando cuatro grifos iguales. ¿Cuántos grifos, iguales a
los anteriores, serían necesarios para llenarla en 3 horas?
Para llenar la piscina en 3 horas, serían necesarios 8 grifos. Se aplica la regla de tres inversa: si aumentamos los grifos, disminuirá el tiempo requerido.
Explanation:Esta pregunta se resuelve aplicando la regla de tres inversa. Si cuatro grifos tardan seis horas en llenar la piscina, para llenarla en la mitad de tiempo (3 horas), serán necesarios el doble de grifos.
La regla de tres inversa señala que si aumentamos la cantidad de grifos, disminuirá el tiempo requerido para llenar la piscina y viceversa. En este caso, como queremos reducir el tiempo a la mitad, necesitaremos el doble de grifos. Entonces, necesitaremos 4 * 2 = 8 grifos para llenar la piscina en 3 horas.
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When bands play at the arena the money made from ticket sales is split in an agreed ratio. When Phillip Cage played, £21,000 was split at a ratio of 2:5 between the arena and Phillip Cage. How much money did the arena make from Phillip Cage's concert?
Answer:
£6000
Step-by-step explanation:
Given:
Phillip Cage played, £21,000 was split at a ratio of 2:5 between the arena and Phillip Cage.
Question asked:
How much money did the arena make from Phillip Cage's concert?
Solution:
Ratio Arena and Philip cage in which money distributed = 2 : 5
Let ratio be [tex]x[/tex]
Money earned by Arena = [tex]2x[/tex]
Money earned by Phillip Cage = [tex]5x[/tex]
Phillip Cage played total for = £21,000
Money earned by Arena + Money earned by Phillip Cage = £21,000
[tex]2x+5x=21000\\7x=21000\\[/tex]
Dividing both sides by 7
[tex]x=3000[/tex]
Money earned by Arena = [tex]2x[/tex] = [tex]2\times3000=6000[/tex]
Thus, Arena made £6000 from Phillip Cage's concert.
find x. round our answer to the nearest tenth of a degree.
Answer:
Step-by-step explanation:
From the given right angle triangle,
the hypotenuse of the right angle triangle is 6
With m∠x as the reference angle,
the adjacent side of the right angle triangle is the unknown side.
the opposite side of the right angle triangle is 4
To determine m∠x, we would apply
the sine trigonometric ratio.
Sin θ = opposite side/hypotenuse. Therefore,
Sin x = 4/6 = 0.67
x = Sin^-1(0.67)
x = 42.1° to the nearest tenth.
Solve for x: −2x − 4 > 8
Answer:
x < -6
Step-by-step explanation:
-2x -4 > 8
-2x +4 >+4
-2x >12
/-2 > /-2
x < -6
remember to flip the inequality sign whenever you divide by a negative number :)
If the parabola shifts 3 units to the left, which equation represents the translated parabola?
A) f(x)=x^2-8x-14
B) f(x)=x^2+9x+14
C) f(x)=x^2+4x-21
D) f(x)=x^2+5x-14
The table shows the distance, y, a cheetah can travel in feet in x seconds.
Speed of a Cheetah
Time, x
(seconds)
5
10
Distance, y
(feet)
470
940
1,410
1,880
2,350
15
|
20
25
Based on the information in the table, which equation can be used to model the relationship between x and y?
a
Ob
OC
O d
y = 5x
y = x + 5
y = x + 470
y = 94x
what is the answer
Answer:D.y=94x
Step-by-step explanation:
Final answer:
The relationship between time and distance for the cheetah can be modeled by y = 94x.
Explanation:
The relationship between the time, x, and distance, y, for the cheetah can be modeled by the equation y = 94x. This equation corresponds to the pattern shown in the table where the distance traveled increases by 470 feet as the time increases by 5 seconds.