The mean of the integers -16, -27, 21, -19, 14, -3 is found by adding together all the numbers to get -30, and then dividing by the total number of values, which in this case is 6. This results in a mean of -5.
Explanation:The solution to this problem falls under the branch of Mathematics known as Statistics, which is the study of collecting, analyzing, interpreting, presenting, and organizing data. The term mean is frequently used in statistics, and it refers to the average of a set of numbers. In this case, you are required to find the mean of the set of integers -16, -27, 21, -19, 14, -3.
To compute the mean, you need to follow a simple two-step process: Add together all the numbers in the set, and then divide the total by the number of items in the set. For the numbers given in your case (-16, -27, 21, -19, 14, -3), you add these together which gives you a total of -30. There are 6 numbers in the set, so the mean would be -30 divided by 6, which equals -5.
Therefore, the mean of the integers -16, -27, 21, -19, 14, -3 is -5.
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please help asap need for test
What is the m∠ABC?
m∠ABC = 15°
m∠ABC = 45°
m∠ABC = 60°
m∠ABC = 75°
Answer:
60 my vros
Step-by-step explanation:
A rectangle has a length of 6cm by 8cm. Which is the length of a diagonal of the rectangle?
A.10cm
B.14cm
C.24cm
D.28cm
E.48cm
Answer:
Your answer would be A 10cm
What is the solution to the equation 5(x - 3) + 7 = 5x - 8?
A.-8
B.0
C.All real numbers
D.No solution
please round to the nearest tenth if possible.
What value of c makes the statement true? -2x3(cx3 + x2) = -10x6 - 2x5
Answer: The required value of c that makes the given statement true is 5.
Step-by-step explanation: We are given to find the value of c that makes the following statement TRUE :
[tex]-2x^3(cx^3+x^2)=-10x^6-2x^5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the value of c, we need to equate the coefficients of the same powers of the unknown variable x.
From equation (i), we have
[tex]-2x^3(cx^3+x^2)=-10x^6-2x^5\\\\\Rightarrow -2cx^{3+3}-2x^{3+2}=-10x^6-2x^5\\\\\Rightarrow -2cx^6-2x^5=-10x^6-2x^5.[/tex]
Equating the coefficients of [tex]x^6[/tex] on both sides of the above equation, we get
[tex]-2c=-10\\\\\Rightarrow c=\dfrac{-10}{-2}\\\\\Rightarrow c=5.[/tex]
Thus, the required value of c that makes the given statement true is 5.
Andy is scuba diving.He starts at sea level and then descends 10 feet in 2 1/2 minutes.
a. how would you represent Andy's descend as a unit rate? Express your answer as an integer.
b. How much feet can he descend in 6 minutes?
find the circular cylinder of largest lateral area which can be inscribed in a sphere of radius R=4 feet
In march 1989 the exxon valdez ran aground and spilled 240,000 barrels of crude petroleum off the coast of alaska. one barrel of petroleum is equal to 42 gal. how many liters of petroleum were spilled?
I need help with the functions and graphing
What is 1/12 (12-v)=1/6(v-6)
What is the simplified form of the following expression? (y8)(y2) y10 y6 y16 y64
The simplified form of the expression (y^8)(y^2) is y^10, found by applying the laws of exponents that dictate adding the exponents when multiplying with the same base.
Explanation:The simplified form of the expression (y8)(y2) can be found using the laws of exponents which state that when multiplying two powers with the same base, you add the exponents. Here, since the base is y, and we have exponents 8 and 2, we add them together:
y8 × y2 = y8+2
This simplifies to y10, which is the compressed form of the given expression.
Final answer:
To simplify the expression (y⁸)(y²), use the rule of exponents which says that you add the exponents when multiplying powers with the same base, resulting in y¹⁰.
Explanation:
The question requires simplifying an algebraic expression with exponents. The given expression is (y⁸)(y²). To simplify this, we use the rule of exponents which states that when multiplying two powers with the same base, you add the exponents. Therefore, y⁸ × y² = y⁸₊²} = y¹⁰
Write and solve an equation to solve the problem. Lisa is 4 centimeters taller than her friend Ian. Ian is 8 centimeters taller than Jim. Every month, their heights increase by 2 centimeters. In 4 months, the sum of Ian's and Jim's heights will be 140 centimeters more than Lisa's height. How tall is Ian now? Let h be Ian's height today in centimeters.
(h + 8) + (__) + 8 = ( __) + 8 + 140
Ian is __ centimeters tall now.
You are timing a kitchen floor that is 10 ft wide and 4 yd long. How many square yards of tile do you need?
1 yard = 3 ft
10/3 = 3 1/3 yards
3 1/3 x 4 = 13 1/3 square yards
Write the equation of the line that passes through (2, 4) and has a slope of –1 in point-slope form.
x – 4 = –1(y – 2)
x – 2 = –1(y – 4)
y – 2 = –1(x – 4)
y – 4 = –1(x – 2)
y -
y1 = m (x - x1)
where m is the slope and (x1 , y1) is the point given
We are given:
m= -1
the point is (2, 4)
Then:
y - y1 = m (x - x1)Write the equation of the sphere in standard form. x2 + y2 + z2 + 4x − 6y − 6z = −6
To put the given equation of a sphere in standard form, complete the square for x, y, and z, and combine constant terms on the right side. The standard form of the sphere's equation is (x + 2)2 + (y - 3)2 + (z - 3)2 = 28, with a center at (-2, 3, 3) and a radius of √28.
Explanation:To write the equation of the sphere in standard form, we will complete the square for the x, y, and z terms in the given equation x2 + y2 + z2 + 4x − 6y − 6z = −6.
First, we organize the variables and separate the constants:
x2 + 4x + y2 - 6y + z2 - 6z = -6
We then complete the square for each variable by adding and subtracting the square of half the coefficient of the linear term:
x2 + 4x + 4 - 4 + y2 - 6y + 9 - 9 + z2 - 6z + 9 - 9 = -6
Now we can rewrite this as:
(x + 2)2 - 4 + (y - 3)2 - 9 + (z - 3)2 - 9 = -6
Combining the constant terms on the right side we get:
(x + 2)2 + (y - 3)2 + (z - 3)2 = 4 + 9 + 9 + 6
Which simplifies to:
(x + 2)2 + (y - 3)2 + (z - 3)2 = 28
The sphere's center is located at (-2, 3, 3) and has a radius of √28. In standard form, the equation of the sphere is:
(x + 2)2 + (y - 3)2 + (z - 3)2 = 28
express 3.01 as a mixed number
Answer:
3 1/100
hope this is helpful!
A bank's monthly charge for maintaining an account is $.45 for each check written plus a service charge of $12.50. If x represents the number of checks written during the month, which function models this situation?
Answer:
0.45x + 12.50
Step-by-step explanation:
jackson wants to divide 3\4 pound box of trail mix into small bags each of the bags will hold 1/12 pound of trail mix how many bags of trail mix can jackson fill
jennifer earns $39 for 6 hours of babysitting.how much will she earn for 10 hours
Two complementary angles are expressed as 4x - 16 and 2x 10. find the number of degrees in each angle.
Two complementary angles are given as 4x - 16 and 2x + 10. Solving for x we find x = 16. Substituting x into the expressions for the angles, we find the angles to be 48 and 42 degrees.
Explanation:The task here is to find the value of two angles that are complementary. Given the expressions for the angles are 4x - 16 and 2x + 10. As complementary angles, they sum up to 90 degrees. Hence, mathematically, we can express this as (4x - 16) + (2x + 10) = 90.
Solving the equation, combine like terms to get 6x - 6 = 90. Then, add 6 to both sides to get 6x = 96. Divide each side by 6 to find x, hence x = 16.
Substitute x = 16 into 4x - 16, therefore the first angle is 4×16 - 16 = 48 degrees. Similarly, substitute x = 16 into 2x + 10, hence the second angle is 2×16 + 10 = 42 degrees. The angles are thus 48 and 42 degrees, which adds up to 90).
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What is the square root of 112 simplified?
Toss a fair coin 10 times what is the probability of getting 7 heads
Which algebraic expression has no like terms?a.-x+4y-6x+9 B.-4x+y+4y C.-3xy-8+xy+y^2 D.-x+7+3xy-4y
Answer:D
Step-by-step explanation:
Find the middle term of ([tex]( x^{2}+2) ^{20}
[/tex]
Please help with this! Thanks!
B: measure of BCD=45; acute
C: measure of BCD=90; right
D: measure of BCD=42; acute
E: measure of BCD=17; acute
3x-6 = 2x+11
3x = 2x+17
x = 17
3(17)-6 = 45
2(17)+11 = 45
45+45 = 90
answer is C 90 degrees:right
Matt is five years older than twice his cousin Andy’s age. The sum of their ages is less than 35. Let x represent Andy's age.
Final answer:
To represent the relationship between Matt and Andy's ages mathematically, let x be Andy's age, and express Matt's age as 2x + 5. The inequality x + (2x + 5) < 35 simplifies to x < 10, indicating Andy's age must be less than 10.
Explanation:
The question involves creating an inequality to represent the relationship between Matt and Andy's ages, where Matt is five years older than twice Andy's age, and the sum of their ages is less than 35.
Let x represent Andy's age. The formula for Matt's age would be 2x + 5. To find the range of possible values for Andy's age, you would write the inequality x + (2x + 5) < 35.
Solving this inequality involves combining like terms and isolating the variable x.
Step 1: Combine like terms.
x + 2x + 5 < 35
Step 2: Simplify the inequality.
3x + 5 < 35
Step 3: Subtract 5 from both sides to isolate the term with x.
3x < 30
Step 4: Divide both sides by 3 to solve for x.
x < 10
This tells us that Andy's age must be less than 10 for the conditions to be met.
A(n) _______________ force can cause an object to change its speed and/or direction.
Write -38.375 as a mixed number in simplest form.
Josh wants to make a set of 12 ceramic cups. He figures he'll need 0.75 of a pound of clay for each cup. How many pounds of clay does Josh need in all?
A.) 8.4 pounds
B.) 9 pounds
C.) 12.75 pounds
D.) 16 pounds
multiply 12 x 0.75
12 x 0.75 = 9
answer is B. 9 pounds
Answer:
Josh will need 9 pounds Option B.
Step-by-step explanation:
Josh wants to make a set of 12 ceramic cups.
For each cup he will need 0.75 pound of clay
We have to calculate how many pounds of clay does Josh need for 12 ceramic cups. So we have to multiply 12 cups by 0.75.
for 12 cups he will need = 12 × 0.75 = 9 pounds.
Josh will need 9 pounds to make a set of 12 ceramic cups.
If 3 is added to twice a number and this sum is multiplied by 2, the result is the same as if the number is multiplied by 3 and 4 is added to the product. what is the number?
The unknown number(n) is equal to - 2 satisfying asked statement.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let the unknown number be 'n'.
Given, If 3 is added to twice a number,
and this sum is multiplied by 2,
the result is the same as if the number is multiplied by 3
and 4 is added to the product.
∴ (2n + 3)×2 = n×3 + 4.
4n + 6 = 3n + 4.
4n - 3n = 4 - 6.
n = - 2.
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