Answer:
1. The median is a much more precise measure of the team's perfomance & it showcases the true picture of the team's average performance
2. This implies that Armand needs to train for 23 minutes on Sunday
Step-by-step explanation:
The mean (also called arithmetic mean) is the central value of a given set of data; gotten by dividing the sum of the values in the data set by the number of items in the data set.
Mathematically,
Mean (m) = ∑ [tex]\frac{x_i}{n}[/tex]
where [tex]x_{i}[/tex] = the sample
n = the number of items in the sample
The median is the central value in a distribution or given set of data after the data has been arranged sequentially either in ascending or descending degree. In simpler terms, it is regarded as the 'middle number'. The basic advantage of the median over the mean is that unlike the mean which can be skewed by outliers (extremely high or low values) in a data set, the median stays close to presenting a true value
1.
Data for the basketball team in its last 5 games = 73, 70, 72, 71, 130
Mean (m) = (73 + 70 + 72 + 71 + 130) ÷ 5
Mean (m) = 416 ÷ 5 = 83.2
Arranging the data sequentqially, we have: 70, 71, 72, 73, 130
Median ([tex]{\displaystyle a}[/tex]) = 72
The median is a much more precise measure of the team's perfomance & it showcases the true picture of the team's average performance. The mean was skewed by the result of the team's last game where the team scored 130 points (an outlier)
2.
Armand's training data (the week begins on Monday & ends on Sunday):
Monday = 53 minutes, Tuesday = 24 minutes, Wednesday = 35 minutes,
Thursday = 60 minutes, Friday = 20 minutes, Saturday = 65 minutes,
Sunday = ?
Since Armand intends to practise an average of 40 minutes for the week (7 days), we calculate thus
Mean (m) = sum of time Armand spends training ÷ number of days Armand spends training
Target Mean = 40 minutes, sum of time = 53 + 24 + 35 + 60 + 20 + 65 + x = 257 + x
where x = minutes Armand needs to practice on Sunday to meet his goal
number of days = 7
40 = (257 + x) ÷ 7
Make x the subject of the formula, we have:
257 + x = 40 * 7
x = 280 - 257 = 23
x = 23 minutes
This implies that Armand needs to train for 23 minutes on Sunday if he is to make his targeted weekly average of 40 minutes
Which of the following is the solution of One-fourth x + 5 = 7?
Answer:
x/4 + 5 = 7
-5 -5
x/4 = 2
*4 *4
x=8
Step-by-step explanation:
Answer:
its 8
Step-by-step explanation:
i know so big brains
Plot the coordinates
A (1, 2), B (4, 5), C (4, –3), and D (1, –1).
If the points are connected, what polygon is formed?
Triangle
Quadrilateral
Pentagon
Hexagon
Answer:
Quadrilateral
Explanation:
there are only for points,
triangle= three points
hexagon= 6 points
pentagon= 5 points
The A(1, 2), B(4, 5), C(4, -3), and D(1, -1) forms a quadrilateral.
What is a quadrilateral?A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.
The points A (1, 2), B (4, 5), C (4, -3), and D (1, -1) form a quadrilateral
as all four points are noncolinear.
These four points represent four vertices of a quadrilateral.
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Please help me with this question.
Answer:
y = 6
Step-by-step explanation:
if the triangles are congruent then the corresponding sides are equal.
so
4x + 1 = 13
4x = 13 -1
4x = 12
Therefore x = 3
Now
8x - 2y = 2x + y
y + 2y = 8x - 2x
3y = 6x
3y = 6 * 3
3y =18
Therefore y = 6
Answer:
y = 6
Step-by-step explanation:
Since the triangles are congruent then corresponding sides are congruent
4x + 1 = 13 ( hypotenuse are congruent )
Subtract 1 from both sides
4x = 12 ( divide both sides by 4 )
x = 3
Thus
8x - 2y = 2x + y ( substitute x = 3 )
8(3) - 2y = 2(3) + y, that is
24 - 2y = 6 + y ( subtract y from both sides )
24 - 3y = 6 ( subtract 24 from both sides )
- 3y = - 18 ( divide both sides by - 3 )
y = 6
A bus travels 120 km in 2 hours. What is the speed of the bus?
Answer:
60 km/hour
Step-by-step explanation:
To find the speed, divide the number of kilometers by the number of hours
kilometers/hours
120 km/ 2 hours
120/2=60
60 km/hour
The speed of the bus is 60 kilometers per hour
Answer:
60km/hr
Step-by-step explanation:
120 divided by 2 equals 60
Add 6x+2y=-2 and 3x-2y=-5
Answer:
[tex]6x+2y=-2\\3x-2y=-5\\-------\\9x=-7[/tex]
Which statements best describe the motion of Car A and Car B? Check all that apply.
Answer:
Car A and Car B are moving in opposite directions.
Car A is moving faster than Car B.
Car A and Car B pass each other at the crossover point on the graph.
Step-by-step explanation:
Hope that helps!
You deposit $1800 into a bank account that pays 5% annual interest. Find the balance after 7 years if the interest is compounded quarterly. Round to the nearest cent
Answer:
The balance after 7 years would be $2,548.79
Step-by-step explanation:
We are given the following in the question:
P = $1800
r = 5% = 0.05
t = 7 years
The compound interest is given by:
[tex]A = p\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]
where A is the amount, p is the principal, r is the interest rate, t is the time in years and n is the nature of compound interest.
When compounded quarterly, n = 4
Putting values, we get,
[tex]A = 1800\bigg(1+\dfrac{0.05}{4}\bigg)^{28}\\\\A = \$2,548.79[/tex]
Thus, the balance after 7 years would be $2,548.79
Pleaseee, I really need help with this❤️
Answer:
(4x + 5)(4x - 3)
Step-by-step explanation:
Given
16x² + 8x - 15
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 16 × - 15 = - 240 and sum = + 8
The factors are + 20 and - 12
Use these factors to split the x- term
16x² + 20x - 12x - 15 ( factor the first/second and third/fourth terms )
= 4x(4x + 5) - 3(4x + 5) ← factor out (4x + 5) from each term
= (4x + 5)(4x - 3) ← in factored form
Complete each equivalent rate.
20 miles
1 gallon
180 miles
gallons
Answer:
20 gallons per 180 miles
Step-by-step explanation:
If a part represents 24% of a total then which of the following is the fraction of the total part this represents ?
A. 7/20
B.1/24
C. 3/5
D.6/25
A scale drawing of an office space uses a scale of 2 inches in 3 yards the scale drawing has an area of 16 in.² what is the area of the actual office space
Answer:
36 Square Yards
Step-by-step explanation:
The Scale Drawing uses a ratio
2 Inches : 3 Yards
Therefore,
1 Inch = 3/2 Yards
If the area of the scale drawing is 16 Inch²
To get the area of the actual office, we multiply by the square of the scale factor.
Scale Factor=3/2
Therefore:
The area of the actual office space
=16X(3/2)² Square Yards
=36 Square Yards
Answer:
36 square yards.
Step-by-step explanation:
This question is solved with rule of three and ratios
We know that 2 inches is equivalent to 3 yards, and the area in the drawing is 16 square inches.
so if
2 inches ---- 3 yards then 1 inch is 3/2 yards.
Let's say that the office is 8 inches x 2 inches = 16 squared inches
Then, if we convert it to yards,
8 inches would be: [tex]8(\frac{3}{2})=12[/tex] yards
and 2 inches would be: [tex]2(\frac{3}{2})=3[/tex] yards
Then, the area of the office would be 12 x 3 = 36 squared yards.
simplify 5/12+-5/18-7/24
Answer:
-11/72
Step-by-step explanation:
5/12+-5/18-7/24
We need to get a common denominator of 72
5/12 *6/6 =30/72
5/18 * 4/4 = 20/72
7/24 *3/3 = 21/72
30/72 -20/72 - 21/72
10/72 -21/72
-11/72
Solving Square Root Worksheet (x - k)^2 Part 3
7. 4(x + 2)^2 + 320 = 0
8. 7(x - 4)^2 - 18 = 10
9. -2(x + 2)^2 - 5 = 8
10. 1/5(t + 3)^2 = 7
Answer:
7. x = -2 +/- [tex]4i\sqrt{5}[/tex]
8. x = 2 or x = 6
9. x = -2 +/- [tex]\frac{\sqrt{26} }{2} i[/tex]
10. t = -3 +/- [tex]\sqrt{35}[/tex]
Step-by-step explanation:
7. Subtract 320 from both sides: 4(x + 2)^2 = -320
Divide by 4: (x + 2)^2 = -80
Square root both sides: x + 2 = +/- [tex]\sqrt{-80}[/tex]. We need to add the imaginary i to this: +/- [tex]\sqrt{-80}[/tex] = +/- [tex]i\sqrt{80}[/tex] = +/- [tex]4i\sqrt{5}[/tex]
Subtract 2 from both sides: x = -2 +/- [tex]4i\sqrt{5}[/tex]
8. Add 18 to both sides: 7(x - 4)^2 = 28
Divide by 7: (x - 4)^2 = 4
Square root both sides: x - 4 = +/- 2
Add 4 to both sides: x = 4 +/- 2 ⇒ x = 2 or x = 6
9. Add 5 to both sides: -2(x + 2)^2 = 13
Divide by -2: (x + 2)^2 = -13/2
Square root both sides: x + 2 = +/- [tex]\sqrt{-13/2}[/tex]. We again need i: +/- [tex]\sqrt{-13/2}[/tex] = +/- [tex]i\sqrt{13/2} =[/tex] +/- [tex]\frac{\sqrt{26} }{2} i[/tex]
Subtract 2 from both sides: x = -2 +/- [tex]\frac{\sqrt{26} }{2} i[/tex]
10. Multiply by 5 on both sides: (t + 3)^2 = 35
Square root both sides: t + 3 = +/- [tex]\sqrt{35}[/tex]
Subtract 3: t = -3 +/- [tex]\sqrt{35}[/tex]
Hope this helps!
Answer:
7. -2 + 4sqrt(5) i, -2 - 4sqrt(5) i
8. x = 2, 6
9. x = -2 + sqrt(13/2) i, -2 - sqrt(13/2) i
10. t = -3 + sqrt(35), -3 - sqrt(35)
Step-by-step explanation:
7. 4(x + 2)² + 320 = 0
(x + 2)² = -80
x + 2 = +/- i × sqrt(80)
x + 2 = +/- i × 4sqrt(5)
x = -2 +/- i × 4sqrt(5)
8. 7(x - 4)² - 18 = 10
(x - 4)² = 4
x - 4 = +/- 2
x = 2, 6
9. -2(x + 2)² - 5 = 8
(x + 2)² = -13/2
(x + 2) = +/- i × sqrt(13/2)
x = -2 +/- i × sqrt(13/2)
10. 1/5(t + 3)² = 7
(t + 3)² = 35
t + 3 = +/- sqrt(35)
t = -3 +/- sqrt(35)
In order to answer the question correctly, please use the following image below:
Find the value of x.
X=(Blank)
Please show all the work on how you got your answer.
Answer:
106°
Step-by-step explanation:
(152 + 60)/2
212/2
106°
Which of the following is an irrational number? A. 16 B. 0.4 C. 4 D. 16
PLEASE HELP!!!!
Ms. Calcutta, the owner of a business park is adding a recycling station for every three office buildings. To make it easier for the tenants, she is going to to use the circumcenter of the three office buildings to place the recycling stations. By doing this, it will be easier to get to the station, because it is equidistant from the three office buildings.
Complete Question:
Justify the rationale behind Ms Calcutta's decision to use the circumcenter
Answer:
Check below for the answer and explanations.
Step-by-step explanation:
Ms Calcutta wants every occupant of the three office buildings to have equal easy access to the recycling station. The circumcenter of the three three office buildings, where the recycling station is located, has equal distance from the three offices, this means that all of Ms. Calcutta's workers in the three buildings can have to the recycling station equally without causing unnecessary inconvenience for occupants of any of the buildings.
A bonsai tree is 18 inches wide and stands 2 feet tall. What is the ratio of the width of the bonsai to its height?
Answer:
3:4
Step-by-step explanation:
Before we start to deal with the ratio, we need all lengths in the same units.
The width is 18 inches.
The height is 2 feet.
Let's convert the height to inches. Then we will have both dimensions in the same units, inches.
2 ft * (12 in.)/ft = 24 in.
Now we have:
width = 18 in.
height = 24 in.
ratio of width to height = 18 in. to 24 in. = 18/24 = 3/4 = 3:4
Final answer:
The ratio of the width to the height of the bonsai tree is 3:4 after converting both measurements to inches and simplifying. For the scale of a flower garden with a 1:12 scale and a plan width of 6 inches, the actual width of the garden is 6 feet.
Explanation:
The student asked about the ratio of the width to the height of a bonsai tree. First, it's important to have both measurements in the same units. Since the height is given in feet and the width in inches, we need to convert the height from feet to inches. There are 12 inches in a foot, so the height is 2 feet x 12 inches/foot = 24 inches. The resulting ratio of the width to the height is therefore 18 inches (width) to 24 inches (height). To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 6 in this case. This gives us a simplified ratio of 3 to 4.
When calculating a scale for a flower garden, based on the available information where the plan shows 6 inches wide and the scale is 1:12, setting up the proportion would look like this: 1 inch on the plan equals to 12 inches in the actual garden. Therefore, to find the actual width of the flower garden, we multiply 6 inches (on the plan) by 12, resulting in an actual width of 72 inches or 6 feet.
Seraphina says that △KLM is a right
triangle. Is she correct? Explain.
J K
N M 16 cm L
Without additional details about the triangle's angles or side lengths, it cannot be determined whether △KLM is a right triangle.
Explanation:Based on the information given in your question, it is impossible to definitively state whether Seraphina is correct in her assertion that △KLM is a right triangle. Checking if a triangle is a right triangle typically involves measuring its angles or applying the Pythagorean theorem to its sides. However, there is insufficient information in your question to do either. For instance, you mentioned a '16 cm' measurement but did not specify to which side it corresponds. Similarly, no angles are provided. Thus, without additional information, the claim that △KLM is a right triangle cannot be confirmed or refuted.
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You are trying to improve communication with your staff by posting graphs of significant statistics on the employee bulletin board. You recently calculated the percentage of time employees spend on each of six major tasks. Because you would like the employees to appreciate each task as a percentage of their whole day, you will post these figures using a pie graph.
Answer:
Yes, the Pie Graph is the right choice.
Step-by-step explanation:
A Pie Graph, or Sector Graph is one of the good options to display, usually relative frequencies, proportionally.
In a Pie Graph the focus is to show the importance of each observation, or category in comparison with the whole.
You need to be careful with the angles, since 180º is equal to 50%, 90º to 25% and 360º is equal to 100% so each "slice" each portion must directly proportional to the angles of one circle.
Since the goal is to show the importance of each work to the whole team, definitely a Pie Graph is one the appropriate one to pick.
The function f(x)= 9√x gives the speed in feet per second (ft/s) of a free-falling object after it has fallen x feet (ignoring air resistance). FInd the speed of the object after it has fallen 26 feet. If necessary, round your answer to the nearest tenth.
Answer:
45.9ft/s
Step-by-step explanation:
Simply plug your given value into the function
[tex]f(26)=9\sqrt{26} = 45.9 (1.d.p.)[/tex]
A sporting goods company has observed a decline in sales following the end of each of its advertising campaigns. The decline in
sales follows the formula S=42e -0.16t, where is the monthly sales in millions of dollars and is the number of months after the end
of the advertising campaign. What will the monthly sales be three months after the end of the current campaign, rounded to the
nearest hundred thousand dollars?
Answer:
$26.0 million
Step-by-step explanation:
Use t=3 and do the arithmetic.
S = 42e^(-0.16·3) = 42e^-0.48 ≈ 26.0
Three months after the end of the campaign, monthly sales are predicted to be $26.0 million.
Answer:
$26.0 million
Step-by-step explanation:
If I have 196 points and then loose 227 points how many points do I have in total
Answer:
You would have -31 points left. :)
196 - 227 = -31
Hope this helped!!
Answer:
-31
Step-by-step explanation:
196 - 227 = -31
The Pew Research Center interviewed a random sample of 1,546 adult Americans to determine the average time they spent sleeping per night. The sample mean was found to be 7.2 hours of sleep, with a sample standard deviation of 1.4 hours. Construct a 95% confidence interval for the true mean. Interpret your confidence interval in words.
Answer:
CI=[ 7.1302,7.2698]
we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]
Step-by-step explanation:
-Given that the sample size, n=1546 the mean is 7.2 hrs and the standard deviation, [tex]\sigma=1.4[/tex]
-The 95% confidence interval can be calculated using the formula:
[tex]CI=\mu\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\\\=\mu\pm z_{0.025}\times \frac{\sigma}{\sqrt{n}}\\\\=7.2\pm1.96\times \frac{1.4}{\sqrt{1546}}\\\\=7.2\pm 0.0698\\\\CI=[7.1302, \ 7.2698][/tex]
The confidence intervals is therefore 7.1302,7.2698]
Hence, we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]
A water tank is in the shape of a cylinder with a diameter of 20 feet and a height of 20 feet. The tank is 70% full. About how many gallons of water are in the tank? Round your answer to the nearest whole number.
Answer:
32901 gallons
Step-by-step explanation:
First, we find the volume of the cylindrical water tank when it is full.
The volume of a cylinder is given as:
V = [tex]\pi r^2h[/tex]
where r = radius and h = height of the cylinder
The diameter of the tank is 20 feet, hence, its radius is 10 feet.
Volume, V, is therefore:
V = [tex]\pi * 10^2*20 = 6283.19 ft^3[/tex]
This is the volume of the tank, when it is full.
When it is 70% full, the volume will be:
[tex]\frac{70}{100} * 6283.19 = 4398.23 ft^3[/tex]
1 cubic foot ([tex]ft^3[/tex]) is 7.48 gallons.
Therefore, the volume of the 70% full tank in gallons will be:
4398.23 * 7.48 = 32901.05 gallons ≅ 32901 gallons
The tank contains 32901 gallons of water.
Answer:
32886.476 gal
Step-by-step explanation:
Given:
Diameter of tank 'd'= 20 ft
∴radius 'r'= d/2=> 20/2=> 10ft
Height 'h' = 20 ft
Volume of cylinder can be determined by
V= π r² h
Substituting the values in above equation
V= π (10)² (20) =>π(100)(20)
V=2000π ft³
When the tank is 70% full.
70% of 2000π =>0.7 x 2000π
1400π ft³
As we know that, 1ft³ = 7.481 gal
1400π ft³= 1400π x 7.481 gal
1400π ft³= 32886.476 gal
Therefore, if the tank is 70% full then 32886.476 gallons of water are in the tank
whcih point on the number line represents the problem. point a point b point c or point d
Answer:
its D 100%
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
For the following set of data, find the sample standard deviation,
to the nearest hundredth.
34, 47, 16, 43, 73, 17, 56
Summary:
The sample standard deviation of the given data set is approximately 20.72.
Explanation:To find the sample standard deviation, we can use the following steps:
Calculate the mean of the data set by adding up all the numbers and dividing by the total number of values. In this case, (34+47+16+43+73+17+56) / 7 = 38.57.Subtract the mean from each value to get the deviations from the mean: 34-38.57 = -4.57, 47-38.57 = 8.43, 16-38.57 = -22.57, 43-38.57 = 4.43, 73-38.57 = 34.43, 17-38.57 = -21.57, 56-38.57 = 17.43.Square each deviation: (-4.57)^2 = 20.89, (8.43)^2 = 70.92, (-22.57)^2 = 509.94, (4.43)^2 = 19.60, (34.43)^2 = 1185.37, (-21.57)^2 = 465.28, (17.43)^2 = 303.88.Add up all the squared deviations: 20.89 + 70.92 + 509.94 + 19.60 + 1185.37 + 465.28 + 303.88 = 2576.88.Divide the sum of squared deviations by the sample size minus 1: 2576.88 / (7-1) = 429.48.Take the square root of the result from step 5 to get the sample standard deviation: sqrt(429.48) ≈ 20.72.What is the slope of the line through the points (-4, 6) and (-3, -1)?
Answer:
m= -7
Step-by-step explanation:
using the slope formula, plug in the variables and solve
m=rise/run
m=y2-y1 / x2-x1
(x1, y1) = coordinates of first point in the line
(x2, y2) = coordinates of second point in the line
Answer:
[tex]slope=-7[/tex]
Step-by-step explanation:
Use the slope formula for when you have two points:
[tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
It is y over x because slope is rise over run : the change in the y-axis over the change in the x-axis. Plug in values:
(-4,6) (-3,-1)
[tex]\frac{-1-6}{-3-(-4)}[/tex]
Simplify
[tex]\frac{-1-6}{-3+4}=\frac{-7}{1}[/tex]
Simplify
[tex]\frac{-7}{1}=-7[/tex]
Done.
Upper bound perimeter of rectangle 15.8 m x5.2 m
Answer:
82.16 m²
Step-by-step explanation:
15.8 m x 5.2 m
HELP QUICK PLEASE!!
A cell phone costs $168, a battery charger costs $10, and batteries cost $5. What is the sales tax and total price for purchasing these items if the sales tax rate is 6%?
Whats the total sales tax?
Answer: $193.98
Step-by-step explanation:
$168 + $10 + $5 = $183
$183 x 6% = $10.98
$183 + $10.98 = $193.98
To find the sales tax and total price for purchasing these items, calculate the sales tax by multiplying the total cost of the items by the sales tax rate, and then add the sales tax to the total cost of the items.
Explanation:To find the sales tax and total price for purchasing these items, we need to calculate the amount of sales tax and then add it to the total cost of the items.
First, calculate the sales tax by multiplying the total cost of the items ($168 + $10 + $5 = $183) by the sales tax rate (6% or 0.06): $183 * 0.06 = $11. Therefore, the sales tax is $11.To find the total price, add the sales tax to the total cost of the items: $183 + $11 = $194.Therefore, the sales tax is $11 and the total price for purchasing these items is $194.
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(5w7)2
What is the simplified power of the product?
A. 5w9
B. 10w14
C. 25w9
D. 25w14
Answer:
Its D i did the question
Step-by-step explanation: