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?
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..
Karen bought 4⁄5 pound of broccoli and 2⁄10 pound of cauliflower. How many more pounds of broccoli did she buy?
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.
FIND X. THE UNITS ARE IN FEET....pLEASE HELP ME ASAP!!!!
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 no unit is given for an angle, what unit must be used?
If 2/3p+6=7/6p what is the value of p?
(a) find the position vector of a particle that has the given acceleration and the specified initial velocity and position. a(t) = 8t i + sin t j + cos 2t k, v(0) = i, r(0) = j
Final answer:
To find the position vector given the acceleration, initial velocity, and initial position, we integrate the acceleration vector to find the velocity vector, and then integrate the velocity vector to find the position vector. The resulting position vector is r(t) = (⅔t³ + t)i - sin t j - ¼ cos 2t k.
Explanation:
Finding the Position Vector
The question asks us to find the position vector of a particle given its acceleration vector a(t) = 8t i + sin t j + cos 2t k, initial velocity v(0) = i, and initial position r(0) = j. To find the position vector, we first need to integrate the acceleration vector to find the velocity vector, and then integrate the velocity vector to find the position vector.
Step 1: Find the Velocity Vector
Integrate the acceleration vector for time to get the velocity vector. The indefinite integral of the acceleration vector gives:
Vx = ½8t² + C1Vy = -cos t + C2Vz = ½sin 2t + C3Using the initial velocity v(0) = i, we find C1 = 1, C2 = 0, and C3 = 0. Therefore, the velocity vector is v(t) = (4t² + 1)i - cos t j + ½sin 2t k.
Step 2: Find the Position Vector
Integrate the velocity vector concerning time to get the position vector. The indefinite integral of the velocity vector gives:
Rx = ⅔t³ + t + C4Ry = -sin t + C5Rz = -¼ cos 2t + C6Using the initial position r(0) = j, we find C4 = 0, C5 = 1, and C6 = 0. Thus, the position vector is r(t) = (⅔t³ + t)i - sin t j - ¼ cos 2t k.
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
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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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.
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:
Isaiah spent $19.60 on a gift for his mother. The amount that he spent on the gift was 5/7 of the total amount that he spent at the store. Which statements can be used to find x, the total amount that Isaiah spent at the store? Check all that apply
The total amount that Isaiah spent at the store will be equal to $27.44.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Amount spent by Isaiah on gift = $19.60
Let the total amount spent at the store be x.
The amount that he spent on the gift was 5/7 of the total amount that he spent at the store.
So, the equation according to the statement will be,
5/7 of x = $19.60
x = (19.60 × 7)/5
x = 137.2/5
x = $27.44
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Isaiah spent 5/7 of the total amount at the store on a gift. To find the total amount spent, represented by x, we use the equation (5/7) * x = $19.60 and solve for x by multiplying $19.60 by 7/5, which yields $27.44.
Explanation:The question involves finding the total amount spent by Isaiah at the store. Since it is given that $19.60 is 5/7 of the total amount, we can set up the following equation to represent this information: (5/7) * x = $19.60. To find x, we need to perform the inverse operation, which is to divide $19.60 by 5/7, or equivalently to multiply $19.60 by the reciprocal of 5/7, which is 7/5.
Here is the step-by-step solution:
Write down the equation that represents the relationship between the part of the total amount spent on the gift and the whole amount spent: (5/7) * x = $19.60.Multiply both sides of the equation by the reciprocal of 5/7 to solve for x: x = $19.60 * (7/5).Calculate the total amount spent by Isaiah: x = 7 * $19.60 / 5.Complete the computation: x = 7 * 3.92, which gives us x = $27.44.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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The following set of coordinates represents which figure? (7, 10), (4, 7), (6, 5), (9, 8) Parallelogram Rectangle Rhombus Square
Answer:
The figure is a rectangle
Step-by-step explanation:
* Lets explain how to solve the problem
- To prove the following set of coordinates represents which figure
lets find the distance between each two points and the slopes of
the lines joining these points
- The rule of the distance between two point is
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
- The rule of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- Remember:
* Parallel lines have same slopes
* The product of the slopes of the perpendicular lines is -1
# points (7 , 10) and (4 , 7)
∵ [tex]d1=\sqrt{(4-7)^{2}+(7-10)^{2}}=\sqrt{18}[/tex]
∵ [tex]m1=\frac{7-10}{4-7}=\frac{-3}{-3}=1[/tex]
# points (4 , 7) and (6 , 5)
∵ [tex]d2=\sqrt{(6-4)^{2}+(5-7)^{2}}=\sqrt{8}[/tex]
∵ [tex]m2=\frac{5-7}{6-4}=\frac{-2}{2}=-1[/tex]
# points (6 , 5) and (9 , 8)
∵ [tex]d3=\sqrt{(9-6)^{2}+(8-5)^{2}}=\sqrt{18}[/tex]
∵ [tex]m3=\frac{8-5}{9-6}=\frac{3}{3}=1[/tex]
# points (9 , 8) and (7 , 10)
∵ [tex]d4=\sqrt{(7-9)^{2}+(10-8)^{2}}=\sqrt{8}[/tex]
∵ [tex]m4=\frac{10-8}{7-9}=\frac{2}{-2}=-1[/tex]
∵ d1 = d3 = √18 and d2 = d4 = √8
∴ Each two opposite sides are equal
∵ m1 = m3 = 1 and m2 = m4 = -1
∴ Each two opposite sides are parallel
∵ m1 × m2 = 1 × -1 = -1
∵ m2 × m3 = 1 × -1 = -1
∵ m3 × m4 = 1 × -1 = -1
∵ m4 × m1 = 1 × -1 = -1
∴ Each two adjacent sides are perpendicular
- The set of coordinates represents a figure has these properties:
1. Each two opposite sides are equal
2. Each two opposite sides are parallel
3. Each two adjacent sides are perpendicular
∴ The figure is a rectangle
A profit function is derived from the production cost and revenue function for a given item. The monthly profit function for a certain item is given by P(x)=−0.05x^2+500x−100,000, where P is in dollars and x is the number of units sold. How many units maximize the profit? FInd the maximum profit
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:
Took test
f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f – g)(x).
EASY 20 POINTS
Pamela is 11 years older than Jiri. The sum of their ages is 77 . What is Jiri's age?
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
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]
When no unit is given for an angle, what unit must be used?
Please help me with this question please !!!!!!!!!!!!
Abed says he has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is y = 3x – 1. Which could be the other equation? y = 3x + 2 3x – y = 2 3x – y = 1 3x + y = 1
Answer:
3rd Option is correct.
Step-by-step explanation:
Given: Equation is y = 3x - 1
We need to find another equation such that system of equation has infinitely solutions.
We know that System of Equations having infinitely many solution has ratio as following,
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
where a is coefficient of x and b is coefficient of y while c is constant term.
Clearly from Given Options Second equation is not a line with different coefficients. Its actually same with some changes.
Consider,
y = 3x - 1
transpose 3x to LHS
y - 3x = -1
Multiply both sides with -1
-y + 3x = 1
3x - y = 1
Therefore, 3rd Option is correct.
(APEX) Factor a number, variable, or expression out of the trinomial shown below:
4x2 – 16x + 8
A.2(x2 – 8x + 4)
B.4(x2 – 4x)
C.8(x2 – 2x + 1)
D.4(x2 – 4x + 2)
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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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}
Anne plans to save $40 a week for the next five years. she expects to earn 3 percent for the first two years and 5 percent for the last three years. how much will her savings be worth at the end of the five years
Anne's savings will be worth $11,636.924 at the end of the five years.
We have,
PV= $40
Future Value = Present Value (1 + Interest Rate[tex])^{Time[/tex]
For the first two years:
Present Value = $40 per week * 52 weeks/year * 2 years = $4,160
Interest Rate = 3% = 0.03
Time = 2 years
Future Value (first two years) = $4,160 (1 + 0.03)²= $ 4,413.344
For the last three years:
Present Value = $40 per week * 52 weeks/year * 3 years = $6,240
Interest Rate = 5% = 0.05
Time = 3 years
Future Value (last three years) = $6,240 (1 + 0.05)³ = $ 7,223.58
Then, Total Future Value = Future Value (first two years) + Future Value (last three years)
= 4413.344 + 7223.58
= $ 11,636.924
Therefore, Anne's savings will be worth $11,636.924 at the end of the five years.
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Help me please because I can't finish it