If the range of the function is F(X)=x/4 {28, 30, 32, 34, 36}, what is its domain?
28 x 4 = 112
30 x 4 = 120
32 x 4 = 128
34 x 4 = 136
36 x 4 = 144
domain = {112,120,128,136,144}
Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she had 38 coins all of the dimes and quarters.When she added them up she had a total of $6.95
d = dimes
q = quarters
d+q = 38 coins
q=38-d
0.25q + 0.10d=6.95
0.25(38-d)+0.10d=6.95
9.5-0.25d+0.10d=6.95
-015d=-2.55
d=-2.55/-0.15 = 17
q=38-17 =21
21*0.25 =5.25
17*0.10 = 1.70
5.25+1.70 = 6.95
she had 21 quarters and 17 dimes
Karen bought 4⁄5 pound of broccoli and 2⁄10 pound of cauliflower. How many more pounds of broccoli did she buy?
If 2/3p+6=7/6p what is the value of p?
G the base of a solid is the circle x2 + y2 = 9. cross sections of the solid perpendicular to the x-axis are equilateral triangles. what is the volume, in cubic units, of the solid
Final answer:
To find the volume of the solid, we can use the formula V = A * h, where A is the area of the base and h is the perpendicular height. Given that the base is a circle and the cross sections of the solid are equilateral triangles, we can calculate the volume by integrating the expression for the area of the cross section from -3 to 3.
Explanation:
To find the volume of the solid, we can use the formula V = A * h, where A is the area of the base and h is the perpendicular height.
Given that the base is a circle with equation x^2 + y^2 = 9, we can determine the radius of the circle to be 3 units.
The cross sections of the solid perpendicular to the x-axis form equilateral triangles. The side length of an equilateral triangle is equal to the radius of the circle, which is 3 units. Since the height of each elemental cylinder is 2y, and the height of an equilateral triangle is h = √(3^2 - (3/2)^2) = √(9 - 9/4) = √(36/4 - 9/4) = √(27/4), the volume of each elemental cylinder is 4π(3^2 - x^2)^(1/2) dx = 4π(27 - 4x^2)^(1/2) dx.
To find the total volume of the solid, we integrate the expression 4π(27 - 4x^2)^(1/2)dx from x = -3 to x = 3.
∫(4π(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π∫(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π∫(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π∫(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π(3^3/3 - (-3)^3/3) = 36π units^3.
Riverside bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. the loan (principal plus interest) must be repaid at the end of the year. midwest bank also offers to lend you the $50,000, but it will charge an annual rate of 6.2%, with no interest due until the end of the year. how much higher or lower is the effective annual rate charged by midwest versus the rate charged by riverside
The effective annual rate of Midwest is 0.2% lower than the rate charged by Riverside.
Further Explanation:
Riverside Bank:
Principal = $50,000
Duration = 1 year
APR = 6.5%
The amount paid after 1 year is
A = 50000(1 + 0.065/12)¹² = $53,348.59
Midwest Bank:
Principal = $50,000
APR = 6.2%
Duration = 1 year
The amount paid after 1 year is
A = 50000*(1 + 0.062) = $53,100.00
The amount charged by Midwest is lower:
Let r = the effective annual rate of Riverside Bank.
Then
50000*(1 + r) = 53348.59
1 + r = 53348.59/50000 = 1.067
r = 0.067 = 6.7%
Effective annual rate:
The viable yearly financing cost is the loan fee that is really earned or paid on a venture, advance or other money related item because of the aftereffect of intensifying over a given timeframe. It is additionally called the powerful loan cost, the viable rate or the yearly comparable rate.
Instructions to Calculate the Effective annual Rate:
1. Determine the expressed loan fee. The expressed financing cost (additionally called yearly rate or ostensible rate) is generally found in the features of the credit or store understanding.
2. Determine the quantity of aggravating periods.
3. Apply the EAR Formula: EAR = (1+ I/n)n – 1.
Subject: mathematics
Level: college
Keywords: Riverside Bank, Midwest Bank, The amount charged by Midwest is lower, Effective annual rate, Instructions to Calculate the Effective annual Rate.
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How will the solution of the system y>2x+2/3 and y<2x+1/3 change if the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?
Sample Response: There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions.
The CBS’ television show 60 Minutes has been successful for many years. That show recently had a share of 20, which means that among the TV sets in use at the time the show aired, 20% were tuned to 60 Minutes. Assume that this is based on a sample size of 5000 – which is a typical sample size for this kind of experiments. Construct a 95% confidence interval for the true proportion of TV sets that are tuned to 60 Minutes..
How many 3 person group can be formed in a club with 8 people?
The number of three person group that can be formed in a club of 8 people would be = 56.
How to calculate the number of three person groups?To calculate the number of three person groups when 8 people are involved, the following steps needs to be taken as follows;
The combination formula should be used = n!/(n-r)!r!
Where:
n= 8
r= 3
Combination=8!/(8-3)!×3!
= 8×7×6×5!/5!×3!
= 8×7×6/3×2×1
= 336/6
= 56
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h(t)=15-10t-16t^2 if a snowboarders horizontal velocity is 10feet per second, how far from the base of the overhang will she land? 15 equals initial height of overhang, -10 is the initial vertical velocity and t is the time.
To convert 2.7 hours into seconds, which two ratios could you multiply by?
Is the GCF of any two odd numbers is always odd?
You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. you will deposit your savings in an account that pays 5.2% interest. how much will you have just after you make the 3rd deposit, 3 years from now?
Chase makes 2 gallons of soup for a dinner party. He serves 10 cups of soups to his guests. How many cups of soup will he have left over?
1 gallon = 16 cups
2 gallons = 16 x 2 = 32
32-10=22
there will be 22 cups left over
Answer:
Step-by-step explanation:
1 gallon = 16 cups
2 gallons = 16 x 2 = 32
32-10=22
there will be 22 cups left over
Please help me with this question please !!!!!!!!!!!!
what is the volume of tue box pictured below 5/6, 1 1/8,4/5
Answer:
The answer is 3/4
Step-by-step explanation:
Palmers average running speed is 3 kilometers per hour faster than his walking speed. If Palmer can run around a 40-kilometer course in 4 hours, how many hours would it take for Palmer to walk the same course?
when a number is multiplied by 9 the result is 35 what is the value of x.
x *9 =35
x =35/9
if you need it in decimal format it would be 3.888888889
52.85 rounded to nearest tenth
Answer:
The required number is 52.9.
Step-by-step explanation:
Given : Number 52.85
To find : The number rounded to nearest tenth?
Solution :
Rounded to the tenth means round the number so that only one number left after the decimal.
Rules of rounding :
1) If the hundredth place value is >5 or =5 then add 1 to first digit and remove second.
2) If the hundredth place value is <5 ,then hundredth place number is removed.
Now, In the number 52.85
The hundredth place value is 5 so, 1 is added to the 8
Then the required number is 52.9.
When no unit is given for an angle, what unit must be used?
Use the table.
Style Color
regular light blue
loose fit indigo
boot cut washed
slim fit black
blue
a. How many possible pairs of jeans are there if each pair has one style and one color?
b. Suppose you have one pair of jeans of each possible style and color in the table. What is the probability of choosing a pair of black jeans at random?
Solution:
The table which is about kind of jeans and it's color is
Style Color
regular light blue
loose fit indigo
boot cut washed
slim fit black
slim fit blue
(a) A regular can be chosen out of five colors, A loose fit can also be chosen in five colors,Similarly a boot cut as well as slim fit can also be chosen out of five colors.
If you consider this as a relation , total number of relation that is total jeans = 1×5 + 1×5 +1×5+1×5= 20 Jeans = 10 Pairs of jeans(Possible)
(b) Total number of jeans , if i have one pair of jeans of each possible style and color = As there are 5 colors and 4 styles , the jeans are in pair = 5×4×2=40
Number of Black color jeans = 2× black color in 4 styles= 2×4=8
Probability of an event = [tex]\frac{\text{Total possible outcome}}{\text{Total favorable outcome}}[/tex]
Probability of choosing a pair of black jeans at random=[tex]\frac{8}{40}=\frac{1}{5}[/tex]
The following statistics represent weekly salaries at a construction company.
Mean $550. First quartile $480
Median $630 third quartile $700
Mode $605. 91st percentile $891
The most common salary is ?
The salary that half the employees salaries surpass is ?
The percent of employees salary that serve because $700 is ?
Percent of employees salaries that were less than $480 is
The percent of employees salaries this surpass $891 years
if the company has 104 is the total weekly salary of all employees he is $?
I don't know how to solve the questions
Answer:
The most common salary is $605. The salary that half the employees salaries surpass is $630. The percent of employees salary that serve because $700 is 75%. Percent of employees salaries that were less than $480 is 25%. The 9% percent of employees salaries this surpass $891 years. The total weekly salary of 104 employees is 57200.
Step-by-step explanation:
It is given that mean is $550, first quartile is $480, median is $630, third quartile is $700, mode is $605 and 91st percentile is $891.
First quartile is at 25% of the data, median is at 50% of the data, third quartile is at 75% of the data.
The mode of a set of data values is the value that occurs most often.
The most common salary is mode, therefore the most common salary is $605.
The salary that half the employees salaries surpass is $630. Because median is the half of the data.
The percent of employees salary that serve because $700 is 75%. Because $700 is third quartile.
Percent of employees salaries that were less than $480 is 25%. Because $480 is first quartile.
The percent of employees salaries this surpass $891 years is 9%. Because $891 is 91 percentile. Therefore 9% employees get more than $891.
If the company has 104 employees than the total salary of employees is
[tex]104\times 550=57200[/tex]
because means is $550, therefore the total weekly salary of 104 employees is 57200.
The most common salary is [tex]605USD[/tex].
The salary that half the employees' salaries surpass is [tex]630USD[/tex].
The percent of employees salary that serves because [tex]700USD[/tex] is [tex]75[/tex]%.
The percent of employees' salaries that were less than [tex]480USD[/tex] is [tex]25[/tex]%.
The [tex]9[/tex]% percent of employees' salaries surpass [tex]891USD[/tex] years.
The total weekly salary of [tex]104[/tex] employees is [tex]57200[/tex].
Given Mean is [tex]550USD[/tex], the first quartile is [tex]480USD[/tex].
The Median is [tex]630USD[/tex], the third quartile is [tex]700USD[/tex], the Mode is [tex]605 USD[/tex] and the [tex]91st[/tex] percentile is [tex]891USD[/tex].
The first quartile is at [tex]25[/tex]% of the data, the median is at [tex]50[/tex]% of the data, the third quartile is at [tex]75[/tex]% of the data.
The mode of a set of data values is the value that occurs most often, So the most common salary is a mode, therefore the most common salary is [tex]605USD[/tex].
As the median is half of the data, the salary that half of the employees' salaries surpass is [tex]630USD[/tex].
Given that [tex]700USD[/tex] is the third quartile, so the percent of employees ' salary that serves
The Percent of employees' salaries that were less than is % as first quartile.
The percent of employees salaries this surpass $891 years is [tex]9[/tex] %. Because [tex]891USD[/tex] is [tex]91[/tex] percentile. Therefore more than [tex]891USD[/tex].
If the company has [tex]104[/tex] employees then the total salary of employees is
[tex]104\times550=57200[/tex] because means is [tex]550USD[/tex], therefore the total weekly salary of [tex]104[/tex] employees is [tex]57200 USD[/tex].
Therefore, the most common salary is [tex]605USD[/tex]. The salary that half the employees' salaries surpass is [tex]630USD[/tex]. The percent of employees salary that serves because [tex]700USD[/tex] is [tex]75[/tex]%. The percent of employees' salaries that were less than [tex]480USD[/tex] is [tex]25[/tex]%.The [tex]9[/tex]% percent of employees' salaries surpass [tex]891USD[/tex] years and the total weekly salary of [tex]104[/tex] employees is [tex]57200[/tex][tex]USD[/tex].
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Suppose a certain population of observations is normally distributed. What percentage of the observations in the population.
(a) are within + 1.5 standard deviations of the mean?
(b) are more that 2.5 standard deviations above the mean?
(c) are more that 3.5 standard deviations away from ( above or below) the mean?
The required percentages are:
(a) 86.64%
(b) 0.62%
(c) 0.04%
With the use of standard normal table, we can find the required percentage, such as:
(a)
→ [tex]P( -1.5<z<1.5)= P( z <1.5)- p( z < -1.5)[/tex]
[tex]= 0.9332-0.0668[/tex]
[tex]= 0.8664[/tex]
[tex]= 86.64[/tex] (%)
(b)
→ [tex]P( z >2.5)=0.0062[/tex]
[tex]= 0.62[/tex] (%)
(c)
→ [tex]P( z < -3.5) + p( z > 3.5) = 0.0002+0.0002[/tex]
[tex]= 0.0004[/tex]
[tex]=0.04[/tex] (%)
Thus the above approach is right.
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Now suppose the roster has 3 guards, 5 forwards, 3 centers, and 2 "swing players" (x and y) who can play either guard or forward. if 5 of the 13 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (round your answer to three decimal places.)
The problem calculates the probability of forming a legitimate basketball starting lineup from a given roster, using combinatorial methods to determine the ratio of favorable outcomes to total outcomes.
Explanation:The question asks for the probability of selecting a legitimate starting lineup for a basketball team, given a roster with specific numbers of guards, forwards, centers, and swing players. A standard basketball starting lineup consists of 2 guards, 2 forwards, and 1 center. Given the roster has 3 guards, 5 forwards, 3 centers, and 2 swing players (who can play either guard or forward), we calculate the probability of forming a legitimate lineup through combinatorial methods.
To calculate the total number of ways to form a starting lineup, we consider the swing players as forwards when calculating combinations since they can play either role. The total number of ways to choose 2 guards out of 5 possible options (3 guards + 2 swing players), 2 forwards out of 7 possible options (5 forwards + 2 swing players treated as forwards), and 1 center out of 3 options is given by the product of combinations: C(5,2) * C(7,2) * C(3,1).
The total number of ways to select any 5 players out of the 13 (without regard for position) is C(13,5). Therefore, the probability is the ratio of these two numbers, rounded to three decimal places.
When you convert 0.63 to a fraction, which of the following could be the first step of the process
If f(x) = sqrt x-3, which inequality can be used to find the domain of f(x)?
sqrt x-3 >/= 0
x - 3 >/= 0
sqrt x - 3 = 0
x - 3 = 0
Answer: B: x-3 >_ 0
Step-by-step explanation:
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FIND X. THE UNITS ARE IN FEET....pLEASE HELP ME ASAP!!!!
10 times as many as 1 hundred is
Pamela is 11 years older than Jiri. The sum of their ages is 77 . What is Jiri's age?
f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f – g)(x).
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