Answer:
The answer is n < 14.
Step-by-step explanation:
First, we need to distribute 6, then 3 through the parentheses.
6n - 30 < 3(n + 4)
6n - 30 < 3n + 12
We now need to move the variable to the left-hand side and change its sign.
6n - 30 - 3n < 12
Next, we have to move the constant to the right-hand side and change its sign.
6n - 3n < 12 + 30
Now we need to collect like terms.
3n < 12 + 30
Then, we need to add the numbers.
3n < 42
Last but not least, we need to divide both sides of the inequality by 3. This gets us to:
n < 14
A rectangle is constructed on a semicircle so that the length equals the diameter. The rectangle is 3 times as long as it is wide. The total area of the figure is 750 inches squared. Find the approximate dimensions of the rectangle.
A rectangle is constructed on a semicircle so that the length equals the diameter. The width of the rectangle is approximately 10.65 inches.
What are the approximate dimensions of the rectangle.?Generally, Let the width of the rectangle be x. Then the length of the rectangle is 3x.
The diameter of the semicircle is also the length of the rectangle, so it is 3x.
The area of the rectangle is x*(3x) = 3x^2. The area of the semicircle is (1/2)πr^2, where r is the radius of the semicircle. Since the diameter of the semicircle is 3x, the radius is (3x)/2. The area of the semicircle is (1/2)π((3x)/2)^2 = (9/8)πx^2.
The total area of the figure is the sum of the area of the rectangle and the area of the semicircle. We can set up the equation:
3x^2 + (9/8)πx^2 = 750
(21/8)πx^2 = 750
x^2 = 750/(21/8)*π
x = √(750/(21/8)*π)
To find the approximate dimensions of the rectangle, we can use the fact that pi is approximately 3.14. This gives us:
x = √(750/(21/8)*3.14)
= √(750/6.71)
= √(112.64)
= approximately 10.65 inches.
The width of the rectangle is approximately 10.65 inches. The length of the rectangle is 3 times the width, so it is approximately 31.95 inches.
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Is n-3^2 linear explain why please
Answer:
y=n-3^2 is linear
Step-by-step explanation:
A linear equation is an equation between two variables that give a straight line with plotted on a graph.
The two variables used are "n" and "3^2"
When graphed, it forms a diagonal, straight line.
HELP ASAP!!
A quadrilateral has 4 sides. One angle of a regular quadrilateral measures (6w+13) Determine the value of w. Round to the nearest whole number
Ow=13
Ow=23
Ow=59
Ow=90
Answer:
(a) w = 13
Step-by-step explanation:
You have a regular quadrilateral with interior angle measure (6w+13)°, and you want the value of w to the nearest integer.
Regular quadrilateralA regular quadrilateral is a square. Its interior angles are 90°, so we have ...
6w +13 = 90
6w = 77
w = 12.833...
w ≈ 13
The value of w to the nearest whole number is 13.
In a math class with 19 students, a test was given the same day that an assignment was due. There were 11 students who passed the test and 14 students who completed the assignment. There were 3 students who failed the test and also did not complete the assignment. What is the probability that a student chosen randomly from the class completed the homework?
The chance that a student is selected at random from the class who passed the exam and finished the assignment is 0.2105
Describe probability.Probability refers to potential. The occurrence of a random event is the subject. Probability values are limited to the range of 0 to 1. Its fundamental notion is that something is probable to occur. It is the proportion of favorable events to all other events.
A exam and an assignment were due on the same day in a math class with 19 pupils.
There were 14 students that finished the assignment, and 11 of them completed the test.
3 pupils both failed the exam and didn't finish the assignment.
Then the probability that a student is chosen randomly from the class passed the test and completed the homework will be
The number of the student who has done at least one assignment or passed the test is 19 - 3 = 16
n(A) = passes student
n(B) = given assignment
Then we have
n(A ∩B) = n(A) + n(B) - n (A ∪B )
n(A ∩B) = 11 + 14 - 16
n(A ∩B) = 9
Then the probability will be
P = 9C2 /19C2
P = 36/171
P = 0.2105
The probability that a student chosen randomly from the class completed the homework is 0.2105
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The figure is made up of 10 identical squares. The perimeter is y cm. What is the side
of each square in terms of y?
(answer in cm)
The side of each square in terms of y is y/16.
What is a perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.
Here, we have
The figure is made up of 10 identical squares. The perimeter is y cm.
The number of outer sides is 16
Let the side be x
then
16x = y
x = y/16
Hence, the side of each square in terms of y is y/16.
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I need help with this problem, look at image below.
Answer:
no
Step-by-step explanation:
The three angles of a triangle are 180, but the sum of the three angles in the figure is 200.so its impossible .
If Y varies directly with X and X=5 and Y=15 what would be the value of Y if X=12
Answer:
i think 3
Step-by-step explanation:
1 1/2 times 3/5 and write it as a division sentence too.
Answer:
9/10 =0.9
Step-by-step explanation:
We have been given to calculate 1 1/2 times 3/5 . First of all ,we shall convert 1 1/2 ( a mixed fraction form) to a proper fraction form .
1 1/2 is actually 1 + 1/2 =3/2
1 1/2 X 3/5 =3/2 X 3/5 =9/10
9/10 is actually 0.9
Therefore we have finally converted this into division sentence too
fully simplify3d/ac x 2ad/30
The value of the equation 3d/ac x 2ad/30 is ( d² / 5c )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
A = 3d/ac x 2ad/30 be equation (1)
On simplifying the equation , we get
A = 3d/ac x 2ad/30
A = 6ad² / 30ac
On further simplification of the equation , we get
The value of A = 1/5 ( ad² / ac )
The value of A = 1/5 ( d²/c )
Therefore , the value of A is ( d² / 5c ) or A = 1/5 ( d²/c )
Hence , The value of the equation 3d/ac x 2ad/30 is ( d² / 5c ) or
A = 1/5 ( d²/c )
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What is the 9th term of the sequence 2,8,32,128
Answer: 131072
Step-by-step explanation:
Basically the sequence is just being multiplied by 4, like 2(4)=8 and 8 is the next number in the sequence or 32(4)=128 which then again is the next number in the sequence.
If you flip a coin 300 times, how many times would you expect it to land on
tails?
If you flip a coin 300 times, 150times would you expect it to land on
tails
How many times would you expect it to land on tails?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
There are three primary categories of algebraic expressions, including:
Numeral Expression.
Binary Expression
Expression of a polynomial.
Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.
Given
flip a coin = 300
So the coin have 2 sides , one side is head and other side is tail
300/2
=150
So the 150 times the tail will come while Flip a coin.
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For the function g(x) = -2x - 5, determine g(6)
A) -10
B)-17
Answer:
-17
Step-by-step explanation:
replace x with 6
g(6)=-2(6)-5
g(6)=-12-5
g(6)= -17
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Whitch one is correct a b c or d
Answer:
Step-by-step explanation:
u got it right the first time it is D
*NOT A QUIZ QUESTION JUST REGULAR HOMEWORK*
Two figures are similar when they have some common properties. The value of PQ as required is 28 units.
Similar triangles are two or more which have a series of common properties. This may be in relations to the length of their sides or measure of their angles.
In the given triangle PQR,
ΔPQS ll ΔSTR
Given that PS = RS, and QT = RT.
Then we can say that;
[tex]\frac{RS}{ST}[/tex] = [tex]\frac{PQ}{PQ}[/tex]
But, PR = 2RS;
[tex]\frac{RS}{ST}[/tex] = [tex]\frac{2RS}{PQ}[/tex]
[tex]\frac{1}{ST}[/tex] = [tex]\frac{2}{PQ}[/tex]
2ST = PQ
2(-22 + 9x) = 9x - 8
-44 + 18x = 9x - 8
18x - 9x = -8 + 44
9x = 36
x = 4
So that,
PQ = 9x - 8
= 9(4) - 8
PQ = 36 - 8
= 28
Thus, the length of PQ is 28 units.
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a local winery bottles 14 different white wines. to help customers with their purchasing choice, the winery offers customers 5 white wine tasting samples free of charge. how many ways does a customer have to choose 5 different white wines to taste
a local winery bottles 14 different white wines. to help customers with their purchasing choice, the winery offers customers 5 white wine tasting samples free of charge 2002 many ways does a customer have to choose 5 different white wines to taste, using the concept of combination formula.
What is combination formula?The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.
The combination formula is: n! / (n-r)! r! , where n is the total number of items (14 in this case) and r is the number of items being selected at once (5 in this case),
Plugging our numbers into the formula we get:
= 14! / (14-5)! 5!
= 2002
After simplifying, we get 2002.
So, there are 2002 ways of picking 5 different white wines to taste from a group of 14 local winery bottles.
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can someone explain this to me? i have an answer key but don’t know how to do it
Check the picture below.
To make orange fizz, Noah mixe 4 coop of powder with 6 cup of water. Andre mixe 5 coop of powder with 8 cup of water. Create a double number line or a table that how different amount of powder and water that tate the ame a noah' mixture
5 scoops of powder are combined with 8 glasses of water by Noah.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
Hence, 5 scoops of powder are combined with 8 glasses of water by Noah.
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Use Pythagoras' theorem to work out the length of
the side AD in the rectangle below.
Give your answer in centimetres to 2 d.p.
B
A
6.3 cm
с
4 cm
D
The value of AD in one decimal place for the given triangle is 9.8 cm.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
As per the given by triangle ΔADE
By Pythagoras' theorem,
(AD)² = (AE)² + (ED)²
(AD)² = 4² + 9²
(AD)² = 97
AD = 9.8
Hence "The value of AD in one decimal place for the given triangle is 9.8 cm".
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The missing image is attached below,
Write two expressions for the perimeter of the figure.
2
8
4x
4
7x
Note: The figure is not drawn to scale.
(a) Use all five side lengths.
perimeter = 0+0+0+0+0
(b) Simplify the expression from part (a).
perimeter =
The perimeter can be calculated using the formulas 22x+23 and 2x+3x+17x+7+16.
How to calculate perimeter of two expression ?The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The surface of a shape's area is measured.
The total length of the four sides makes up the perimeter (P) of a rectangle. A rectangle has two equal lengths and two equal widths since its opposite sides are equal. The following is the formula for calculating a rectangle's perimeter: The formula for perimeter is length + length + width + width. P = l + l + w + w.
you want to add the variables of the same kind in this case
2x
3x 7
17x 16
_________
22x + 23
Therefore Two expressions for the perimeter would be 22x+23 and 2x+3x+17x+7+16
The complete question is : Write two expressions for the perimeter of the figure.
2x
7
3x
172
16
Note: The figure is not drawn to scale.
(a) Use all five side lengths.
perimeter - ] + + + +
(b) Simplify the expression from part (a).
perimeter =
Х
$ ?
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A sandwich store charges a $10 delivery fee, and $4.50 for each sandwich.
a. What is the total cost (sandwiches and delivery charge) if an office orders 6 sandwiches?
Type the answer in the box below.
$
b. What is the total cost for x sandwiches?
Type the answer in the box below.
Find the circumcenter of the triangle (-2,4) (-2,-1) (1,-1)
Answer:
( [tex]-\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] )
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
Coordinates of midpoint are
( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
~~~~~~~~~~~~~~~~~~~~
The figure is right triangle.
The circumcenter is the middle of the hypotenuse.
( - 2, 4 )
( 1 , - 1 )
( [tex]-\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] )
A lorry leave a factory on a journey of 195km at 08 45 , travelling at an average peed of 52 km/h. A) Find the time at which the lorry the time taken arrive at it detination. B) on the return journey, the lorry leave at 14 55 and arrive at the factory at 18 15. Calculatge the time taken and the average peed of the lorry on the return journey
The time at which the lorry the time taken arrive at it destination is 12.20.
Given :
A lorry leave a factory on a journey of 195km at 08 45 , travelling at an average speed of 52 km/h.
here,
Distance = 195 km
Speed = 52 km/h
we know that ,
speed = distance / time
on cross muliplicating
speed * time = distance
time = distance / speed
substitute the values
time = 195 / 52
= 3.75 hours
destination time = 8.45 + 3.75
= 12.20
Therefore the time at which the lorry the time taken arrive at it destination is 12.20
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a regional director responsible for business development in the state of pennsylvania is concerned about the number of small business failures. if the mean number of small business failures per month is 14, what is the probability that exactly 5 small businesses will fail during a given month? assume that the probability of a failure is the same for any two months and that the occurrence or non occurrence of a failure in any month is independent of failures in any other month. (round your answer to four decimal places.) g
The probability that exactly 5 small businesses will fail during a given month 0.0037268.
The Poisson distribution would be used to calculate the likelihood that different counts of the same event will occur within a constrained time period. It is viewed as a discrete distribution since it evaluates counts. The distribution displays identical mean and dispersion values.
The pmf of the Poisson distribution is
[tex]p(x)=\frac{e^{\lambda} \lambda^{x}}{x!}[/tex]
The mean total number of small business failures λ=14
Let x represent the number of failed small businesses in a given month.
X~P(14)
X follows the Poisson distribution since the likelihood of failure stays constant for two months and the mean number of failures per month is 14.
The likelihood that precisely four small firms would fail in a given month must be calculated.
P(X=5)
[tex]P(X=5)= \frac{e^{14} \ 14^{5}}{5!}[/tex]
P(X=5)= 0.44721/5!
P(X=5)=0.0037268.
In a month there is 0.0037 that is 3.7% probability that a small business fail.
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Which one is nonlinear
y = x + x + 3
y=x2+6
y = 4x - 5
y=1/x+3
Step-by-step explanation:
I think it's y=x² +6 because this is a quadratic equation
points a and b lie on a circle with radius 4 and arc ab has length meters. the length of arc 4pi/5 is what fraction of the circumference of the circle?
1/10 fraction of the circumference of the circle .
What is arc?
An arc is any straight line that connects two locations. The term "arc length" refers to an arc's length. An ordered pair of adjacent vertices is referred to as a graph arc in a graph.
Any section of the circle's circumference (other than the entire curve) is referred to as an arc.
C = 2πr
C - circumference of a circle
r - radius of a circle
r = 4
Then
C = 2π • 4 = 8π
Writing the fraction:
(4π/5)/8π = 1/10
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Alan travel 8 2/3 kilometer to get to chool. He ran 1 10/11 kilometer and walked the ret. How many kilometer were left to walk?
If Alan had ran 1 10/11 kilometer and walked the ret so his remaining distance from school is 6 5/11 kilometer.
What is called distance?Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
What is the formula for distance?Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=√((x_2-x_1)²+(y_2-y_1)²) to calculate the separation between any two locations.
As the total travel of alan from his school is
=8 2/3 kilometer
according to given condition;
he has traveled;
=1 10/11 kilometer
so his remaining travel from his school is;
=8 2/3 kilometer-1 10/11 kilometer
= 6 5/11 kilometer
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Convince me that -3to the second power is not equal to (-3) to the second power
Answer:
Yeah, they are not equal.
Step-by-step explanation:
Given statement,
→ -3 to the second power is not equal to (-3) to the second power.
Forming the equation,
→ -3² ≠ (-3)²
Let's check the equation,
→ -3² = (-3)²
→ -(3)² = (-3)²
→ -9 ≠ 9
→ LHS ≠ RHS
Hence, they are not equal.
Triangle JKL is similar to triangle STU. What is the length of side LK?
Using mathematical operations, we can conclude that the length of LK is 1.25 units in triangle JKL.
What are mathematical operations?
A mathematical "operation" is indeed the method by which a value utilizes operands and a math operator.
The supplied operands or numbers must conform to a set of predefined rules that are connected to the symbol of the math operator.
Parentheses, Exponents, Arithmetic, Division, and Addition Simple arithmetic is also known as PEMDAS (from left to right).
So, we know that the given triangles are similar:
Then, the length of line LK will be:
JK/ST = LK/UT
Solve this as follows:
JK/ST = LK/UT
2.5/10 = LK/5
10LK = 2.5(5)
10LK = 12.5
LK = 12.5/10
LK = 1.25
Therefore, using mathematical operations, we can conclude that the length of LK is 1.25 units in triangle JKL.
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determine whether a triangle with the given vertices is a scalene, isosceles, or equilateral triangle. check all that apply
Answer: the first one(triangle ABC) is scalene, the second one(triangle TRI) is Isosceles, and the last one(triangle PQR) is
Isosceles
Step-by-step explanation: graph each joint is Desmos online calculator
A clothing company has 4,630 shirts to ship. It can fit 130 shirts in a shipping box .How many boxes are to ship all the shirts?
Answer: 36 boxes
Step-by-step explanation:
4630 divided by 130 = 35.6 boxes
Then we ground up to 36 boxes
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