The correct compound inequality is:
x - 4 < 9 or x - 4 > -9
Which inequality is equivelnt to |x - 4| < 9?We want to find a compound inequality equal to the absolute value one below:
|x - 4| < 9
We can break it into two ones, these are:
x - 4 < 9
x - 4 > -9
Solving these two we will get:
x < 9 + 4 = 13
x > -9 + 4 = -5
Then the compound inequality is:
x < 13
x > -5
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6. Use summary statistics (mean, median, range, interquartile range, mean absolute deviation) to compare Bob and Alan's points per game.
7.What is the best measure of central tendency to compare the two players? Why?
a. Compare each person's data in terms of center.
8. What is the best measure of spread to compare the two plavers? Why?
a. Compare each person's data in terms of spread.
9. Based on your representations and your calculations, is either friend a basketball star?
Justify your answer, based on your graphical representations (#1-3), your summary statistics (#4), and the interpretations (#7-8).
Answer:
To compare Bob and Alan's points per game, we can use the following summary statistics:
Mean: This is the average of the data set. It can be calculated by adding up all the values and dividing by the number of values.
Median: This is the middle value of the data set when it is arranged in order.
Range: This is the difference between the largest and smallest value in the data set.
Interquartile range (IQR): This is the range of the middle 50% of the data set, calculated as the difference between the 75th and 25th percentiles.
Mean absolute deviation (MAD): This is the average of the absolute differences between each value and the mean.
To compare the center of each player's data, the best measure of central tendency would be the mean. This is because it takes into account all the values in the data set and gives an overall average. The median can also be used, but it only considers the middle value and may not accurately represent the center if there are outliers in the data set.
To compare the spread of each player's data, the best measure of spread would be the range or IQR. This is because they give an idea of the range of values in the data set and how spread out the data is. The MAD can also be used, but it is a more complex calculation and may not provide as clear of an understanding of the spread of the data.
Based on the representations, summary statistics, and interpretations, it is not possible to determine if either friend is a basketball star without more context. A basketball star could have a high average points per game, a narrow range, and a small spread, but this would depend on the level of competition and the type of game being played. A player who consistently scores a high number of points and performs well under pressure could be considered a basketball star, but this cannot be determined solely based on the data presented.
Use the equation to answer the question.
8-3=9
What is the value of g in the equation?
OA. -12
OB. -6
OC. 6
OD. 12
OE. 27
Therefore , the solution of the given problem of equation comes out to be value of g is 12 .
Equation : What is it?In a math equation, the comparable symbol (=) is used to denote equality between two propositions. It is demonstrated that by using mathematical formulas, which have been expressions of reality, different numerical factors can be compared. The equal sign, for instance, splits the integer 12 or the equation y + 6 = 12 to 2 different halves. It is possible to determine how many characters each side of such a symbol has. It's common for symbols to have conflicting meanings.
Here,
Given :
=> g -3 = 9
To find the value of g :
=> g = 9 + 3
=> g = 12
Thus , value of g is 12.
Therefore , the solution of the given problem of equation comes out to be value of g is 12 .
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How long would Joey need to invest his $300 at 4% annual interest if he wants to end up with $400? Assume simple interest, I = PRT and round to the nearest tenth of a year.
Answer:
1 year
Step-by-step explanation:
the equation to find simple interest
A = P (1 + rt)
so plug in yore numbers
400=300(1+0.4*t)
400=300+120t
120=120t
1=t
You and your sister are saving money from your allowances. You have $25 and you save $3 each week. Your sister has $40 and she saves $2 each week.
In
weeks, you and your sister will have the same amount of money; and at the time, you both will have
Answer:
c below
Step-by-step explanation:
you: 25 +$3 /week * x weeks
sis: 40 + 2/week * x weeks
they have to equal to each other
so 25 + 3x = 40 +2x
move x around & simplify
so x = 15
total 25+3*15 = 25+45 = 70
Elisa and her friend are dividing a 34-ounce bag of pretzels. Elisa
shares her portion equally with her two sisters. Which fraction
represents the amount of pretzels, in pounds, each person receives?
A. 17/48 lb
B. 2 1/8 lb.
c. 11 1/3 lb.
D. 1/2 lb.
Amount of pretzel each person receives is 17/16 lb.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Total weight of the bag of pretzels = 34 ounce
Elisa shares this among her two sisters equally.
Share of pretzels each sister gets = 34 / 2 = 17 ounces
We need this amount in pounds.
We know that,
16 ounce = 1 lb.
17 ounces = 17/16 lb.
Hence the amount of pretzels each get is 17/16 lb.
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PLS HELP ME WITH THIS
Answer:
the drawing is attachedcomponent form: -9i -12jmagnitude∠direction = 15∠233.13°unit vector: -0.6i -0.8j = 1∠233.13°Step-by-step explanation:
You want a drawing of the vector between (1, 3) and (-8, -9), along with its component form as sum of unit vectors i and j, its magnitude and direction, and the corresponding unit vector.
DrawingSee the attachment for the drawing.
Component formThe difference between the head and tail coordinates is ...
(-8, -9) -(1, 3) = (-9, -12)
That is, the vector extends -9 units in the +x direction, and -12 units in the +y direction, so its component form is ...
-9i -12j
Polar form
The magnitude of a vector is the root of the sum of squares of its components:
|v| = √((-9)² +(-12)²) = √(81+144) = √225
|v| = 15
The direction can be found using the arctangent function:
∠v = arctan(-12/-9) = 180° +51.13° . . . . . accounting for quadrant
∠v = = 233.13°
Unit vectorThe unit vector in the same direction is found by replacing the magnitude in polar form by 1.
u = 1∠233.13°
The component form is found by dividing the vector by its magnitude:
u = v/|v| = (-9i -12j)/15
u = -0.6i -0.8j
__
Additional comment
The attached calculator output shows the polar form angle as negative. That is another way the direction can be expressed. The positive angle value is found by adding 360° to that negative value.
In a random sample survey of employees, 4/5 start fraction of the survey respondents are in favor of stocking healthier snacks in the break room. If the employees surveyed are representative of all 240 employees, how many employees are in favor of stocking healthier snacks in the break room? Choose 1 answer:
A:48
B:80
C:192
D:200
Number of employees that are in favor of stocking healthier snacks in the break room are 192.
What is the ratio?Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
Given;
4/5 start fraction of the survey respondents are in favor of stocking healthier snacks in the break room
The employees surveyed are representative of all 240 employees
Now, the number of employees in favor;
=4/5 * 240
=4*48
=192
Therefore, the answer according to the given ratio will be 192.
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assume the number of u.s. households with land-line phones stood at 35 million at the beginning of 2014 and was projected to decline at the rate of 2 million households per year for the next 8 years. find a linear function giving the projected u.s. land-line phone households (in millions in year ), where corresponds to the beginning of 2014.
The linear function giving U.S. land-line phone households(in millions in year) is f(t) = 35 - 2t
The number of U.S. households with land-line phones stood at 35 million at the beginning of 2014 and was projected to decline at the rate of 2 million households per year for the next 8 years.
let t = 0 corresponds to the beginning of 2004.
so the linear function formed by this information.
f(t) = 35 - 2t
where t is number of years since 2014 and f(t) will be the number of land-line phone households (in millions in years) in that particular year.
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Solve for x. Round to the nearest hundredth.
A.) 3.76
B.) 3.75
C.) 2.76
D.) 2.50
E.) 3.50
Answer:
C) 2.76
-------------------
Given:
Inscribed angle 34x + 4 with arc measure of 196°.We know that inscribed angle is half the arc measure. Set up equation and solve for x:
34x + 4 = 196/234x + 4 = 9834x = 94x = 94/34x = 2.76 (rounded)What is the value of x? responses x = 4.8 cm x, = 4.8 cm x = 30 cm x, = 30 cm x = 93 cm x, = 93 cm x = 187.5 cm
The value for x is 30 cm.
equivalent triangles
According to the following equation is valid:
x/75 = 12/30
30x = 900 is obtained by dividing by 12 * 75.
Divide both sides of 30x/30 to get 900/30x = 30.
As a result, the value of x is 30 cm.
What are some similar triangles?Two rectangles are said to be comparable if the ratio of one triangle's two sides to the two sides of that other triangle is the same, and the angles that the two sides of both triangles inscribe are equal. This means that if A = X and Acceptor = AC/XZ, then ABC XYZ.
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I understand the question looking for is :
What is the value of x?
X= 4.8 cm
X= 30 cm
X= 93 cm
X= 187.5 cm
The value for x is 30 cm.
equivalent triangles
According to the following equation is valid:x/75 = 12/30
30x = 900 is obtained by dividing by 12 * 75.Divide both sides of 30x/30 to get 900/30x = 30.
As a result, the value of x is 30 cm.
What are some similar triangles?
Two rectangles are said to be comparable if the ratio of one triangle's two sides to the two sides of that other triangle is the same, and the angles that the two sides of both triangles inscribe are equal. This means that if A = X and Acceptor = AC/XZ, then ABC XYZ.
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I understand the question looking for is :
What is the value of x?
X= 4.8 cm
X= 30 cm
X= 93 cm
X= 187.5 cm
Find the slope of the line represented by the data below
The slope of the line represented by the given data is; 1
How to find the slope between two coordinates?
The slope of a line is defined as the rate of change of y divided by the rate of change of x.
Thus, the formula to find the slope between two coordinates is;
m = (y2 - y1)/(x2 - x1)
Taking the last two coordinates gives us;
m = (16 - 13)/(7 - 3)
m = 3/3
m = 1
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Points X and Y are on AB.if AX>BY,then which statement must be true
If x > y and a > b, the option that must be true is D. x + a > y + b.
How to solve the inequalityInequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
If two inequalities have inequality symbols facing the same direction, we can add the inequalities
For example: 4 < 7 and 1 < 10
So, we can add them to get: 4 + 1 < 7 + 10
Since x > y and a > b have inequality symbols facing the same direction, we can add the inequalities to get: x + a > y + b
The correct option is D.
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If x > y and a > b, which of the following must be true?
A. x > a
B. y > b
C. x + b > y + a
D. x + a > y + b
E. a + b > x + y
Question
What division problem does this area model represent?
Enter your answer in the boxes.
[ ] ÷ 45 = [ ] R [ ]
The division problem that the area model represents is; 0 remainder 32
How to divide numbers with remainders?We are given that the accurate division;
3600/45 = 80
We are also given that the accurate division as;
315/45 = 7
Now, we want to find 32/45 which would lead to a remainder. Thus, we have;
45 cannot go into 32 at all and as such, we will have the result as 0 remainder 32
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The two equations shown below represent different functions. Function P: y = + 2 Function Q: y = + 2 Identify each function as linear or nonlinear. State a reason why each function is linear or nonlinear
The functions are classified as follows:
Function P: nonlinear, as the variable x is in the denominator.Function Q: linear, as the variable x has an exponent of 1 in the numerator.How to model a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
Hence the conditions needed for a function to be a linear function are given as follows:
Variable x is present only on the numerator.The highest exponent of assumed by the variable x is of 1.Missing InformationThe functions are given as follows:
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T/F of the range, the interquartile range, and the variance, the interquartile range is least influenced by an outlying value in the data set.
false :) thats ur answer
The sides of a regular hexagon are equal in length. The perimeter of the hexagon is at most 24 inches. Find the possible side lengths of the hexagon. Let the lengths of the sides be x.
Answer:
[tex]0 < \text{x} \le 4[/tex]
If x is an integer, then x is any value in the set {1,2,3,4}
======================================================
Work Shown:
x = length of each side
6x = perimeter of the regular hexagon
The perimeter must be greater than 0.
Also, the perimeter must be less than or equal to 24. This is because of the phrasing "perimeter is at most 24 inches".
In other words, the perimeter is between 0 and 24, excluding 0 and including 24.
[tex]0 < \text{ perimeter } \le 24\\\\0 < 6\text{x} \le 24\\\\0/6 < 6\text{x}/6 \le 24/6\\\\0 < \text{x} \le 4\\\\[/tex]
If x is an integer, then x can be any value in the set {1,2,3,4}
Examples:
The side length x = 2 leads to a perimeter 6x = 6*2 = 12 inches. This shows why x = 2 is in the set shown above.The side length x = 5 leads to a perimeter 6x = 6*5 = 30 inches. This shows why x = 5 (and larger) is not in the set shown above.Find the volume of this object.
Use 3 for T.
Sphere 7.ft. Radius
Sphere 12 ft by
12 ft by
12 ft
Volume of a Cube
V = lwh
Volume of a Sphere
V=
Прз
πr²³
ㅠ
V≈ [?] ft³
The volume of the sphere of radius 7 feet is given as follows:
1372 ft³.
The volume of the cube of sides 12 ft is given as follows:
1728 ft³.
How to obtain the volumes?The volume of a sphere of radius r is given by the multiplication of 4 by pi = 3 by the cubed radius, and the multiplication is then divided by 3, hence:
V = 4 x 3 x 7³/3
V = 1372 ft³.
The volume of a cube of side length s is given by the side length cubed, hence:
V = 12³
V = 1728 ft³.
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completa las siguientes tablas de proporcionalidad
To find the proportionality of a table, you need to determine if the relationship between two variables in the table is proportional or not.
How do you find the proportionality of a table?Calculating the ratio between each pair of data in a table allows you to determine whether a proportional relationship is there. The table depicts a proportionate relationship if all of those ratios are the same.
This can be done by dividing one variable by the other and checking if the ratio is equal for all data points in the table. If the ratio is constant, then the variables are proportional and the table is considered proportional.
Given that the question is incomplete and does not show the proportionality table, it is worth it to show how to find the proportionality of a table which would help solve the solution and gain knowledge.
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The question translated in English is:
Complete the following proportionality tables
Multiple Choice Which expression represents the area of the square?
0
A 10₂³
B. 526
C. 2525
D 2526
T
√
8
The area of the square with side measuring 10 cm and 10 cm is 100 cm²
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
The area of a figure is the amount of space that is occupied by the two dimensional shape. The area of a square is the product of its length . It is given by:
Area = length * length
Let us assume that each side of the square is 10 cm, hence:
Area = 10 cm * 10 cm = 100 cm²
The area of the square is 100 cm²
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a polygon that is both equilateral and equiangular it is called___
Answer:
REGULAR
Step-by-step explanation:
Directions: Based on the information given in the following problem, compute the gross pay.
Hours worked: 51
Overtime hours worked: 11
Regular rate of pay: $7.35 per hour
Round your answers to two decimal places.
gross pay: $
The gross pay is $496.68.
SolutionTo calculate the gross pay, you need to calculate the total pay for the regular hours worked and the overtime hours worked separately, and then add them together.
Regular hours worked: 51 hoursRegular rate of pay: $7.35 per hourTotal pay for regular hours: 51 hours x $7.35/hour = $375.35
Overtime hours worked: 11 hours
Overtime rate of pay: 1.5 times the regular rate of pay, or $7.35 x 1.5 = $11.03
Total pay for overtime hours: 11 hours x $11.03/hour = $121.33
Gross pay: $375.35 + $121.33 = $496.68
So the gross pay is $496.68.
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it 6-2: MathXL for School: Additional Practice
Find the values of x and y in parallelogram PQRS.
PT=y, TR=2x+1, QT=5y, TS=7x+11
x=and y=
P
T
R
S
The value of x and y for the parallelogram PQRS is 2 and 5 respectively.
What is parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.
The qualities of a parallelogram are shared by the shapes of a square and a rectangle.
PT=y, TR=2x+1, QT=45y, TS=7x+11
The diagonals of a parallelogram bisect each other:
So, PT = TR and QT = TS
Thus, the system of equation is:
y = 2x+1
5y = 7x+11
Multiply the first equation by 5:
5y = 10x+5
Set the two equations as equal:
10x + 5 = 7x + 11
Subtract 7x from each side.
10x + 5 -7x = 7x + 11 -7x
3x + 5 = 11
Subtract 5 from both sides:
3x + 5 - 5 = 11 - 5
3x = 6
x = 2
Now solve for y:
y = 2x+1
y =2(2)+1
y =5
Hence, the value of x and y for the parallelogram PQRS is 2 and 5 respectively.
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what is the area of a circle with a diameter of 15.8 cm? use 3.14 for pi and round your final answer to the nearest hundredth. enter your answer in the box.
Answer:
196.1 cm^2
Step-by-step explanation:
The area of a circle is given by Area = πr^2
R is (15.8 cm)/2 = 7.9 cm
Area = (3.14)*(7.0cm)^2
Area = 196.1 cm^2
Answer:
The formula to calculate the area of a circle is given by: A = π * r^2, where r is the radius of the circle.
Given the diameter of 15.8 cm, we can calculate the radius by dividing the diameter by 2: r = 15.8 cm / 2 = 7.9 cm
Plugging the value of the radius into the formula: A = π * 7.9^2 = 3.14 * 62.41 = 196.0794 cm^2
Rounding the answer to the nearest hundredth, the area of the circle with a diameter of 15.8 cm is approximately 196.08 cm^2.
Manny says he should multiply the first equation in the system of equations below by 3 and the second equation by 2, then add to eliminate x. Is there a more efficient way to solve this system? Explain your answer.
−2x+y=15
3x+4y=−12
A. No, there isn't a more efficient way to solve this system.
B. Yes, a more efficient way is to multiply the first equation by −4
add to eliminate y, then solve for x.
C. Yes, a more efficient way is to multiply the first equation by −4
add to eliminate x, then solve for y.
D. Yes, a more efficient way is to multiply the first equation by 4
add to eliminate y, then solve for x.
Step-by-step explanation:
A,No, there isn't a more efficient way to solve this system.
B.Yes, a more efficient way is to multiply the first equation by 4, add to eliminate y, then solve for x.
C.Yes, a more efficient way is to multiply the first equation by −4, add to eliminate y, then solve for x.
D.Yes, a more efficient way is to multiply the first equation by −4, add to eliminate x, then solve for y.
Complete the equation so that it has no solution. 5(2x−3)−7x= x− 10
Answer:
5(2x-3)-7x=x-10
or, 10x -15 -7x = x-10
or, 3x-15=x-10
or, 3x- x = 15-10
or, 2x = 5
or, x= 5/2
I need help understanding how to do this with a step by step please
The required value of the cos(θ) for the interval 0 < θ < π/2 is given as 0.857.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
The value of cos(θ) can be found using the Pythagorean identity:
cos²(θ) + sin²(θ) = 1
Substituting the given value of sin(θ) = 0.515, we have:
cos²(θ) + 0.515² = 1
cos²(θ) = 1 - 0.515²
cos(θ) = √(1 - 0.515²)
= √(1 - 0.265)
= √(0.735) ≈ 0.857
So, cos(θ) = 0.857.
Thus, the required value of the cos(θ) for the interval 0 < θ < π/2 is given as 0.857.
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4z-10-9z please help me i need these
Answer:
-5z - 10
Step-by-step explanation:
Subtract 9z from 4z.
If 5 sweaters cost 47.45$, how much would 7 sweaters cost?
Answer:
$66.43
Step-by-step explanation:
In order to see how much one sweater cost you need to divide 47.45 by 5 and you will get 9.49 then after that you will multiply 9.49 by 7 and get 66.43
[tex]\begin{array}{ccll} sweaters&\$\\ \cline{1-2} 5 & 47.45\\ 7& x \end{array} \implies \cfrac{5}{7}~~=~~\cfrac{47.45}{x} \\\\\\ 5x=7(47.45)\implies x=\cfrac{7(47.45)}{5}\implies x=66.43[/tex]
from a to b a private plane flies 1.6 hours at 110 mph on a bearing of 22o. it turns at point b and continues another 2.9 hours at the same speed, but on a bearing of 112o to point c. round each answer to three decimal places. at the end of this time, how far is the plane from its starting point? incorrect miles on what bearing (from due north) is the plane from its original location?
The plane is 361.99 miles from its starting point on a bearing of 147.72 degrees from due north.
To calculate the distance travelled by plane, we can use the formula:
distance = speed x time
First, let's calculate the distance travelled from point A to B:
distance = 110 mph x 1.6 hours = 176 miles
Next, let's calculate the distance travelled from point B to C:
distance = 110 mph x 2.9 hours = 319 miles
To calculate the total distance from the starting point, we need to find the hypotenuse of the triangle formed by points A, B, and C. To do this, we need to utilise the Pythagorean theorem:
c² = a² + b²
Where c is the distance between the two points and a and b are the distances travelled in each direction. In this case, a is the distance from A to B (176 miles), and b is the distance from B to C (319 miles).
c² = 176² + 319²
c = √(176² + 319²)
c = √(31,521 + 100,761)
c = √(132,282)
c = 361.99 miles (rounded to three decimal places)
So, the plane is 361.99 miles from its starting point.
To find the bearing of the plane from its original location, we need to use the arctangent formula:
θ = arctan(b/a)
Where θ is the bearing, and a and b are the distances travelled in each direction. In this case, a is the distance from A to B (176 miles) and b is the distance from B to C (319 miles).
θ = arctan(319/176)
θ = 57.72 degrees (rounded to three decimal places)
This means the plane is 57.72 degrees from due north. To find the actual bearing from due north, we need to add 90 degrees since the plane is travelling in the northeasterly direction:
Bearing = 90 + 57.72 = 147.72 degrees (rounded to three decimal places)
In conclusion, the plane is 361.99 miles from its starting point on a bearing of 147.72 degrees from due north.
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2x-7/4 - (1-x/6)=17
Find the value of x in this given problem