The mean of the data set is 37.30
The mean of teachers ages are 37.30.Given that
Ages of teachers:29, 38, 39, 26, 29, 29, 39, 77, 38, 29
To find
The Mean of teachers ages ?So, according to the question
We have,
Ages of teachers: 29, 38, 39, 26, 29, 29, 39, 77, 38, 29So, we know that
The mean of any given datamean = [tex]\frac{sum\;of\;\;data}{number\;of\;data}[/tex]
So, the sum of the teachers ages∑ Ta = 29+ 38+ 39+ 26+ 29+ 29+ 39+ 77+ 38+ 29
∑ Ta = 373
The number of teachersTn = 10
Now, The Mean of teachers ages
Tm = [tex]\frac{sum\;of\;the\;teachers\;ages}{number\;of\;teachers}[/tex]
Tm = [tex]\frac{T_a}{T_n}[/tex]
= [tex]\frac{373}{10}[/tex]
Tm = 37.30
The mean of teachers ages are 37.30.
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the right triangle shown below with hypotenuse 13 inches long and vertical leg 5 inches long is rotated 360c around the vertical leg to form a right circular cone. what is the volume of this cone, in cubic inches?
The cone has a volume of (D) 288in3.
What do we mean by volume?A volume is a unit of measure of occupied three-dimensional space. It is frequently quantified numerically using SI-derived units (such as cubic meters and liters) or various imperial modules (such as the gallon, quart, and cubic inch). The definition of volume is related to the definition of length (cubed). The volume of a container is generally recognized to be its capacity; that is, the quantity of fluid (gas or liquid) that it can hold, rather than the amount of space that it occupies.To find the volume:
Given:
Radius = 6 inheight =?g = 10 inVolume =?Formula:
Volume of a cone = πr²h / 3The Pythagorean theorem is used to calculate height.
height² = 10² - 6² = 100 - 36 = 64 height = 8The volume of the cone:
Volume = π(6)²(8) Volume = π(36)(8) Volume = 288π in³Therefore, the volume of the cone is (D) 288in³.
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The complete question is given below:
Right triangle ABC, shown, has a vertical leg 6 inches long and a hypotenuse 10 inches long. If the triangle was rotated 360 degrees around the vertical leg to form a right circular cone, what would be the volume of this cone, in cubic inches?
A. 32
B. 96
C. 128
D. 288
E. 384
Derek is going to lay grass in a
rectangular space that measures
8 by 33 feet. Find the total area
that will be covered by grass.
Answer:
264 square ft
Step-by-step explanation:
8*33=264
Find the value of sin S rounded to the nearest hundredth, if necessary.
30
R
16
S
The value of sin S is = 5/13
Given a right triangle with hypotenuse BD = 13 & BC = 12, Find CD,
By, Pythagoras theorem
BD2 = BC2 + CD2
132 = 122 + CD2
CD2 = 132 - 122
CD2 = 169 – 144
CD2 = 25
CD =
CD = 5
We know that,
Sin = opposite side/hypotenuse
Sin S = 5/13
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Hence, these triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
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of relation.
Jess and Marie share money in the ratio of 3:5. If they have 64 dollars, how much does Marie have?
valve
======================================================
Explanation:
The ratio 3:5 is equivalent to 3x:5x after multiplying both parts by x.
Jess has 3x dollars and Marie has 5x dollars
3x+5x = 64
8x = 64
x = 64/8
x = 8
Therefore,
Jess has 3x = 3*8 = 24 dollarsMarie has 5x = 5*8 = 40 dollarsThe ratio 24:40 reduces to 3:5 after dividing both parts by the GCF 8.
---------------------------
Another way to solve:
m = amount Marie has
64-m = amount Jess has
3/5 = (64-m)/m
3m = 5(64-m)
3m = 320-5m
3m+5m = 320
8m = 320
m = 320/8
m = 40 dollars is the amount Marie has
consider a group of hundred students. out of them, eighty students can speak either english or spanish. suppose twenty-five students can speak only english. how many students can speak spanish?
Which is 3 groups of 5?
3 + 5
5 - 3
3 × 5
5 ÷ 3
Answer: 3 groups of 5 = 5 + 5 + 5 = 15. 5 groups of 3 = 3 + 3 + 3 + 3 + 3 = 15. 3 groups of 5 has the same answer as 5 groups of 3! So, 3 x 5 = 5 x 3. This means that when you multiply 2 numbers, the order of the numbers (which number is first and which is second) does not matter, the answer will still be the same. Multiplication Terms
Step-by-step explanation: I hopes this helps.
A linear function is shown on the graph.
a linear function beginning with closed circle at 0 comma 2 and ending with a closed circle at 4 comma 6
What is the domain of the function?
{x | 0 ≤ x ≤ 4}
{x | 0 < x < 4}
{y | 2 ≤ y ≤ 6}
{y | 2 < y < 6}
Answer:
A) {x | 0 ≤ x ≤ 4}Step-by-step explanation:
The x-coordinates form the domain.
We know the x-coordinates of the end points of the line, the first numbers in pair of coordinates:
x = 0 and x = 4Also, since both points are closed circles, the endpoints are included.
So the domain is the interval between 0 and 4, both inclusive.
This is shown as:
{x | 0 ≤ x ≤ 4}The matching answer choice is A.
The domain of the function includes all x-values from 0 to 4, including both 0 and 4.
So, the correct answer is option A: {[tex]{x | 0 \leq x \leq 4}\\[/tex]}.
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In this case, the function begins with a closed circle at (0, 2) and ends with a closed circle at (4, 6), which means that the function is defined at these specific points.
Since the function is a linear function, it represents a straight line.
A linear function is continuous, and it extends indefinitely in both directions.
Therefore, any x-value between 0 and 4 will also be defined by the linear function.
In mathematical notation, we can represent the domain as:
Domain: {x | 0 ≤ x ≤ 4}
This means that the domain of the function includes all x-values from 0 to 4, including both 0 and 4.
So, the correct answer is option A: {[tex]{x | 0 \leq x \leq 4}\\[/tex]}.
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complete question:
A linear function is shown on the graph.
a linear function that passes through the points (0, 2) and (4, 6)
What is the domain of the function?
[tex]{x | 0 \leq x \leq 4}\\{x | 0 < x < 4}\\{y | 2 \leq y \leq 6}\\{y | 2 < y < 6}[/tex]
graph is attached
If p < 0, q > 0, and p + q = r, which statement about r is true? A number line shows p to the left of 0 and q to the right of 0, with q closer to 0 than p. |r| = |q| r > 0 r < 0 |r| > |q|
The correct option is r < 0 for the given inequalities of p < 0, q > 0, and p + q = r.
What is defined by the number line?You can select any point as "0," and all positive numbers will be to the right of the "0," and all negative numbers will be to the left of the "0." A line of infinite length, the points of which correspond to real numbers based on their distance in a negative or positive position from a point randomly chosen as zero.A number line is a straight line to numbers at equal intervals or sections along its length. A number line could be extended in any direction indefinitely and is typically represented horizontally.For the given inequalities;
p < 0, q > 0, and p + q = r;
As, we know that if p < 0; then it hold the negative value.
And for q > 0, it have the positive values.
Because -negative(P) was closer to zero than Positive q, let's say p = -10 and q = 5.
p + q = r
Put the values;
r = -10 + 5 = -5,
r = -5
Therefore, r < 0 is the correct condition for the given inequalities.
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Solve equation.
3/5b=-2
To solve the equation, multiply both sides by 5/3. The solution is b = -10/3.
A linear equation is an equation of which the highest degree of its variables is 1.
Steps to solve linear equations:
Simplify the expressions. If there are parentheses, remove them by multiplying the corresponding terms.Combine the same terms.Isolate the variable on one side by using subtraction or addition.Use division or multiplication to find the value of the variable.Recall that if we subtract or add the same number to both sides of an equation, it does not change the equality.The given problem:
Solve 3/5 b = -2
Notice that the variable, b, is already isolated on the left side.
Multiply both sides by 5/3:
3/5 b . 5/3 = -2 . 5/3
b = -10/3 (solved)
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3/5evaluate the expression and name the poperty used in each step. [5/(3times1)] 3/5
Evaluate expression and Name the property used in each step.
= { [5/(3 times 1)] } 3/5
= {[5/(3.1)]} 3/5
We can write,
Multiplicate identity,
= [5/3] 3/5
Substitution,
= (5/3) (3/5)
Cancel the numerator and denominator values,
So,
We can write,
= 1 Multiplicative Inverse
Therefore,
3/5evaluate the expression and name the property used in each step. [5/(3times1)] 3/5 is = 1 Multiplicative Inverse.
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five years ago, john was twice peters age. peter is now x years old and john is now y years old.
a) write an equation to illustrate the relation between John's age and Peter's age five years age.
b) this year, the total of their ages is 28 years old. use this information to determine John's age in three years.
c) use substitution to justify that your answers to part (a) are correct.
please help
Answer:
Step-by-step explanation:
a)
Peter now = x years old
John now = y years old
Five years ago
y-5 = 2(x-5)
y-5 = 2x-10
y = 2x-5
b)
x+y=28
y=28-x
Therefore
2x-5 = 28-x
3x = 33
x = 11
y = 28 - (11)
y = 17
Therefore
In three years time John will be:
17 + 3 = 20
c)
y-5 = 2x-10
Lefthand side:
(17)-5 = 12
Righthand side:
2(11)-10=22-10=12
Therefore
Lefthand side =Righthand side
YAY!
help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Each side is 2 centimeters.
Hope this helps :)
Step-by-step explanation:
A square has sides that are all equal. So in this case the area is 4 square centimeters, and in order to find that we had to multiply 2 sides in which they are equal to each other. All the sides were 2 centimeters. We get 2 sides and multiply to get the area of the square chip.
2 cm × 2cm = 4 square centimeters
Solve for x in the diagram below.
Answer:
x = 6
Step-by-step explanation:
From the above diagram, we can deduce that:
5x + (x + 54) = 90 (Sum of Acute Angles)
Now, we can solve for x using this equation.
[tex]5x + (x + 54) = 90 \\ 6x + 54 = 90 \\ 6x + 54 - 54 = 90 - 54 \\ 6x = 36 \\ x = \frac{36}{6} \\ x = 6[/tex]
What's the answer to this question
From calculating the percentages we can say that 43 more students went on Friday than Saturday.
Percentage is defined as quantity per hundred. Percentage is calculated by dividing the given number by the total number and multiplying it by 100.
From the survey we can see that 550 students were supposed to go on Friday. But it is given that 18 percent students did not go to the festival.
Number of students who went = 550 - (18% of 550 )
Therefore students = 550 - 99 =451 students
Again from the survey we can see that 480 students were supposed to go on Saturday . But it is given that 15 percent students did not go to the festival.
Number of students who went =480 - (15% of 480 )
Therefore students = 480 - 72 = 408 students
Therefore the number of more students who went on Friday than Saturday is 451-408 = 43 students
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A runner’s times (in minutes) in three races are 6.9, 6.6, and 6.5. The runner will run two more races and wants the average time of all five races to be less than 6.8 minutes. Describe the average time needed in the two races to achieve this goal. The average time in the two races must be less than minutes.
The average time in two races must be less than 7 minutes.
Given,
Runner's times in three races = 6.9 minutes, 6.6 minutes, 6.5 minutes.
Runner will run two more races.
The average time of all five races = less than 6.8 minutes
We have to find the average time needed in the two races:
Now,
(6.9 + 6.6 + 6.5 + x + y) / 5 < 6.8
Here, x and y are the time in two races.
Let's assume the average as 6.5 which is less than 6.8.
Then,
(6.9 + 6.6 + 6.5 + x + y) / 5 = 6.5
(6.9 + 6.6 + 6.5 + x + y) = (6.5 × 5)
x + y = (6.5 × 5) - (6.9 + 6.6 + 6.5)
x + y = 32.5 - 20
x + y = 12.5
Now, we have to find the average of two races:
That is, (x + y) / 2 = 12.5 / 2 = 6.25.
Above is a solution required by an assumption. By this solution we came to know that the average of two races must be less than 7 minutes.
So, let's conclude like:
The average time in the two races must be less than 7 minutes.
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write the index notation of 3*3*3*3
Answer:
[tex]3^{4}[/tex]
Step-by-step explanation:
Because 3x3x3x3
3 multipily by 4 times as it's same number
Question 2 (1 point)
To find which number is one thousand times larger than 2.3 x 10^2, you would do the following steps.
a
Ob
Oc
Od
Change 1,000 to Scientific notation and then subtract from (2.3 x 10^6)
Change 1,000 to Scientific notation and then divide by (2.3 x 10^6)
Change 1,000 to Scientific notation and then multiply by (2.3 x 10^6)
Change 1,000 to Scientific notation and then add to (2.3x10^2)
Answer:
d
Step-by-step explanation:
bc i think it is
To find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).
The correct answer choice option C
Scientific notationThis is a method of writing or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10.
which number is one thousand times larger than 2.3 x 10²
Change 1,000 to Scientific notation and then multiply by (2.3 x 10²)1000 to scientific notation
= 10³
2.3 x 10² × 1000
= 2.3 x 10² × 10³
= 2.3 × 10^5
Furthermore, scientific notation helps us to express numbers in decimal number between 1 and 10 followed by an integer power of 10. It also help us to represent numbers in this pattern.
Therefore, to find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).
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- Find BC if B(8, -7) and C(-4, -2).
The line segment BC has a length of 13 units.
What is the length of a line segment?
In this question we know the locations of the two ends of a line segment. The procedure consists in calculating the vector behind the line segment and later determing its magnitude by Pythagorean theorem. If we know that B(x, y) = (8, - 7) and C(x, y) = (- 4, - 2), then the length of the line segment BC is:
BC = (- 4, - 2) - (8, - 7)
BC = (- 12, 5)
BC = √[(- 12)² + 5²]
BC = 13
The line segment BC has a length of 13 units.
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what is the answer for J(-3,2) and K(9,2)
The distance between points J(-3,2) and K(9,2) is 12 units.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
The given points are
J(-3,2) and K(9,2)
[tex]x_{1} =-3\\\\x_{2} =9\\\\y_{1} =2\\\\y_{2} =2[/tex]
According to given question we have
By the use of distance formula we have
[tex]\sqrt{(x_{2} -x_{1} )^{2}+ (y_{2} -y_{1} )^{2}} \\\\=\sqrt{(9 -(-3) )^{2}+ (2 -2 )^{2}}\\\\=\sqrt{(12 )^{2}}\\\\=12[/tex]
Therefore, the distance between points J(-3,2) and K(9,2) is 12 units.
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Distance between is missing in question
PLEASE HELP V=1/3a^2h solve for h
Answer: h=3V/a^2
Step-by-step explanation:
V=1/3a^2h
V=1/3 * a^2 * h
V*3=3*1/3 * a^2 * h
3V=a^2 * h
h=3V/a^2
Question 7 (5 points)
What are the coordinates of the vertices of the image after a 90-degree counter-
clockwise rotation about the origin?
Answer:
Explanation ↓
Step-by-step explanation:
The origin is the rotation’s set point unless expressed otherwise. In a coordinate plane, when the point (x, y) is revolved in a 90-degree clockwise directive, the projected vision will have a coordinate of (y, -x).
What is the approximate value of √8?
Answer:
the approximate value should be 2.83
Solve the "or" inequality
7x-14 ≥0 or 4x+5 ≤ -3
The value of the inequality is a x ≥2 or x ≤ -2.
According to the statement
We have to find that the value in the inequality.
So, For this purpose, we know that the
Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
From the given information:
7x-14 ≥0 or 4x+5 ≤ -3
The value of the inequality is a :
7x-14 ≥0 or 4x+5 ≤ -3
x ≥14/7 or x ≤ -3-5/4
x ≥2 or x ≤ -8/4
x ≥2 or x ≤ -2.
So, The value of the inequality is a x ≥2 or x ≤ -2.
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when constructing a congruent line segment does the ray needed for the construation have to be shorter than the line segment
The condition for two line segments to be congruent is that they must have equal length.
What is a line segment?
A geometrical figure which is a part of a straight line having two unique endpoints is called a line segment. Each point on the line segment lies within the two given endpoints
Explanation of the fact that for the two given line segments to be congruent, they must have the same length
The given statement is False. Because two line segments are said to be congruent if and only if they have exactly the same length. If we construct a ray shorter than the line segment, then both will never be congruent according to the properties of congruence. So, for these two to become congruent, they must have the same length.
Hence, we obtain that the two line segments are congruent if they have exactly the same length.
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If John's credit card has a balance of $1,329.64 balance and he charged $528.44 in new purchases, what
is the new balance?
Answer: 801.2
Step-by-step explanation:
Members of a lacrosse team raised $1775-50 to go to a tournament. They rented a bus
for $901.50 and budgeted $46 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Considering the definition of an equation and the way to solve it, the equation is 901.5 + 46x= 1775.50 and the number of players the team can bring to the tournament is 19.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a equation means determining the value that satisfies it and the equality must be true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the number of players the team can bring to the tournament, and knowing that:
Members of a lacrosse team raised $1775.50 to go to a tournament. They rented a bus for $901.50 and budgeted $46 per player for meals.the equation in this case is:
901.5 + 46x= 1775.50
Solving:
46x= 1775.50 - 901.5
46x= 874
x= 874 ÷ 46
x=19
Finally, the equation is 901.5 + 46x= 1775.50 and the number of players the team can bring to the tournament is 19.
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Find an equivalent fraction for the decimal number. In your final answer, include all of your work.
0. 61
61/100 is the equivalent fraction for the given decimal number.
A decimal number then has two components: a whole number part and a fractional part. The decimal place value system for the whole part of a decimal number is the same as the whole number value system. However, we get the fractional part of the decimal number as we move toward the right after the decimal point.
A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator. It shows the total number of equal parts the whole is divided into or the total number of the same objects in a collection.
for converting a decimal into a fraction we need to multiply and divide the decimal by the 10^n where n is the number of digits after the decimal.
61/100 is the equivalent fraction for the given decimal number.
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I need help with this math question ASAP. someone PLEASE help me
Answer:
[tex]xy^2+2x-4y^2[/tex][tex];-58[/tex]
Step-by-step explanation:
First, align the same terms next to each other so that combining like terms will be easier.
Remember like terms have the same variables and powers. To combine like terms, all you have to do is add/subtract the coefficients (the numbers in from of the variables).
[tex]2xy^{2} +2xy^{2} -3xy^{2} +3x-x-4y^{2}[/tex]
[tex]2xy^{2} +2xy^{2} -3xy^{2} =xy^{2}[/tex]
[tex]3x-x=2x[/tex]
And [tex]-4y^{2}[/tex] stays the same because there is no term that has [tex]y^{2}[/tex].
So, we have [tex]xy^{2} +2x-4y^{2}[/tex].
Now to evaluate for x= -2 and y= -3 you have to plug them into the simplified expression.
[tex](-2)(-3)^{2} +2(-2)-4(-3)^{2}[/tex]
According to PEMDAS we first solve the exponents: [tex](-2)(9) +2(-2)-4(9)[/tex]
Then we multiply:
[tex](-18) +(-4)-36[/tex]
Add/subtract:
-58
Which is the correct answer
Answer:
b
Step-by-step explanation:
(x-8)(x+2)= x^2 - 6x - 16
each of the following three data sets represents the iq scores of a random sample of adults. iq scores are known to have a mean and median of 100. full data set sample of size 5 sample of size 12 sample of size 30 . . . question content area right part 1 for each data set, compute the mean and median. what is the mean of the sample of size 5? enter your response here (type an integer or decimal rounded to one decimal place as needed.)
All the above data were obtained by entering them in excel format and obtaining it using standard methods.
What is the standard deviation?A low standard deviation shows that the values tend to be close to the mean (also known as the expected value) of the set, whereas a high standard deviation suggests that the values are spread out over a wider range. The standard deviation is a measure of variance or dispersion in statistics. Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lowercase Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
For sample size 5, Mean = 117.6 and Standard Deviation = 9.2
For sample size 12, Mean = 103.5 and Standard Deviation = 8.6
For sample size 30, Mean =104.6 and Standard Deviation = 8.7
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