Answer:
8p - 9
Step-by-step explanation:
→ Expand brackets
6p - 15 + 2p + 6
→ Collect like terms
8p - 9
please help me with this math problem
Answer:
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]
Step-by-step explanation:
When adding or subtracting fractions that have different denominators, first rewrite the fractions as equivalent fractions with the same denominator. To do this, find the lowest common multiple (LCM) of the denominators.
The given subtraction is:
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}[/tex]
The LCM of the denominators 2 and 8 is 8. Therefore, we need to rewrite the first fraction as an equivalent fraction with 8 as its denominator. To do this, multiply its numerator and denominator by 4:
[tex]\implies \sf \dfrac{1}{2} \times\dfrac{4}{4}=\dfrac{4}{8}[/tex]
Therefore:
[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}[/tex]
To subtract fractions with the same denominator, simply subtract the numerators. (The denominator stays the same).
[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}=\dfrac{4-1}{8}=\dfrac{3}{8}[/tex]
Final solution
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]
In this figure, lines L and M are parallel.
What is the measure of angle w?
60\degree60°
100\degree100°
120\degree120°
128\degree128°
which is the name for the level of the independent variable intended to represent a neutral condition?
The level of a independent variable known to as the "Control group" is designed to portray a neutral state.
Define the term independent variable?The cause is the independent variable. Its value is unaffected by the other study variables.
You plan a study out whether variations in the room's temperature have an impact on students' math test results.
The interior temperature of the space is your independent variable. By making the room cooler for 1⁄2 the participants and warmer for other half, you can change the temperature.Experimental findings in mathematics are your dependent variable. Using a standardized test, you measure each participant's math prowess to see if there are significant temperature-related differences.Consequently, "control group" refers to a level of such an independent variable that is meant to stand in for "no treatment" or a neutral circumstance.
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algebra 2 help needed!
As per the given equation of the parabola, the directrix of the parabola is equal to y = -2.5.
What is directrix?
A directrix in mathematics is a curve which is associated with the process generating a geometric object, such as:
Directrix - conic section
Directrix - generatrix
Directrix - rational normal scroll
The equation of a quadratic function, with vertex (h,k), is:
y = (a)(x - h)² + k
In which, a is the leading coefficient.
The directrix is: y = k + 4a.
In this problem, the equation of parabola is given as:
y = (1/8)(x-2)² - 3
The coefficients in the given equation are a = 1/8 = 0.125,
h = 2, k = -3,
Hence the directrix is given by:
y = -3 + 4 x 0.125
y = -3 + 0.5
y = -2.5.
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I NEED HELP PLS I GIVE YOU POINTS
Answer:
Option D: 160 square feet
Step-by-step explanation:
Area of the lawn
= (7 feet × 8 feet) + (13 feet × 8 feet)
= 56 square feet + 104 square feet
= 160 square feet
help me please please please triangle 2222
The surface area of the triangular prism is 936 cm².
How to find the surface area of a triangular prism?In geometry, a triangular prism is a three-sided prism.
Therefore, the surface area of the triangular prism can be calculated as follows:
surface area of triangular prism = bh + L(x + y + z)
where
b and h are the base and height of the triangular baseL is the height of the prism.x, y and z is the side of the triangle.Therefore,
surface area of triangular prism = 24 × 18 + 7(18 + 30 + 24)
surface area of triangular prism = 432 + 7(72)
surface area of triangular prism = 432 + 504
surface area of triangular prism = 936 cm²
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Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
The formula for nth term in the given arithmetic sequence is 10 - 3n
For an nth term in an arithmetic sequence
U(n) = a + (n - 1)d
Where n is the number of terms
a is the first term
d is the common difference
From the sequence above
a = 7
d = 4 - 7 = - 3
The formula for an nth term is
U(n) = 7 + (n - 1)-3
= 7 - 3n + 3
Hence, the formula for nth term is 10-3n
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Tanisha and her children went into a restaurant that sells hamburgers for
$7.50 each and drinks for $1.75 each. Tanisha has $70 to spend and must buy
no less than 18 hamburgers and drinks altogether. If a represents the number
of hamburgers purchased and y represents the number of drinks purchased,
write and solve a system of inequalities graphically and determine one
possible solution.
HELP PLEASE QUICKLY THANKS
Graph will shift in both horizontal and vertical direction by 4 units.
What is straight line?
An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal.
What is general equation of a Straight Line?
The general equation of a straight line can be given as ax + by + c = 0, where
a, b, c are constants, andx, y are variables.The slope is -a/bWhat do you mean by function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain. The usual way to refer to a function is as fn(x), where x is the input.
We have function,
fn(x) = x + 5
when the graph is translated by 4 units, we can write it as;
g(x) = fn(x) + 4
the graph will shift in both horizontal and vertical direction by 4 units as it can be seen in the graph.
Therefore, graph will shift in both horizontal and vertical direction by 4 units.
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Jade ha 28 triangle card. He ha 4 time a many trading card a jordan. How many trading card do they have altogether
Jade and Jordan both have a total of 35 trading cards altogether.
Given, Jade has 28 trading cards. He has 4 times as many trading cards as Jordan.
As, Jade has 28 trading cards
Let Jordan has 'x' trading cards.
Now, as Jade has 4 times as many trading cards as Jordan.
So, 28 = 4x
4x = 28
x = 7
So, Jordan has 7 trading cards.
Now, they both have a total of 35 trading cards altogether.
Hence, Jade and Jordan both have a total of 35 trading cards altogether.
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A Pre-K teacher has a total of 4/5 ounces of paint. Th teacher puts 1/30 ounces of paint at each table. If the teacher sets up an equal number of tables in the 2 Pre-K classrooms, how many tables does he set up in each classroom?
Answer:
12 tables per classroom.
Step-by-step explanation:
We will assume that the teacher uses all of the 4/5 oz of paint. We can find how many samples of 1/30 oz are contained in the 4/5 oz by dividing:
(4/5)÷(1/30) = (4/5)*(30/1)
(4/5)*(30/1) = (120/5)
(120/5) = 24 samples of 1/30 oz paint in (4/5) oz total paint.
Each of the 2 Pre-K classrooms have the same number of tables, so we can divide 24 samples by 2 to find the number of tables in each classroom,
*24 samples/2 classrooms) = 12 tables/classroom
The age distribution of a population is shown. a. The probability that a person chosen at random is at least 15 years old is %. b. The probability that a person chosen at random is 25−44 years old is %.
Answer is :
The chosen at random is 25 - 44 years old is = 26 %.
Probability determines how likely it is that a stated event would
occur. This event would occur. This probability lies between 0 and 1.
The probability that a person chosen at random is at least
15 years = sum of percentages of people at least 15 years old :
14 + 13 + 13 + 15 + 12 + 13 = 80%
the probability that a person chosen at random is 25 - 44 years old :
13% + 13% = 26%
Therefore The probability is 26%.
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Three consecutive even integers have the property that when the product of the first two is taken, the result is four less than the square of the third one. What are the integers?
The three consecutive even integers are -2, 0 and 2.
How to calculate the value?Let the three consecutive even integers be x, x+2 and x+4.
Since the product of the first two is taken, the result is four less than the square of the third one. This will be:
x(x + 2) = (x + 4)² - 4
x² + 2x = x² + 8x + 16 - 4
x² + 2x = x² + 8x + 12
Collect like terms
x² - x² + 2x - 8x - 12
-6x - 12 = 0
-6x = 12.
Divide
x = -12/6
x = -2
x + 2 = -2 + 2 = 0
x + 4 = -2 + 4 = 2
They're -2, 0, and 2.
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Identify x-intercepts, the vertex, and axis of symmetry of the graph f(x)= 1/4x (x-1)(x+7)
x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.
What is, axis of symmetry, vertex and x - intercept?
A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.
A line's x-intercept is the location at which the x-axis is crossed.
Consider, the given equation,
[tex]f(x) = \frac{1}{4}(x - 1)(x + 7)[/tex]
Let,
[tex]y = \frac{1}{4}(x - 1)(x + 7)[/tex] ..(1)
To find x - intercept, plug y = 0 in above equation,
[tex]\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7[/tex]
Therefore, x = 1 and x = -7 are the x - intercepts.
Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.
So,
[tex]x = \frac{-7+1}{2} = \frac{-6}{2} = -3[/tex]
Plug x = -3 in equation (1)
[tex]y = \frac{1}{4}(-4)(4) = -4[/tex]
Therefore, the vertex is, (-3, -4).
The x - coordinate of the vertex is the axis of symmetry.
Therefore, axis of symmetry is x = -3.
Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.
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Divide and answer in simplest form: 45 ÷ 2
Answer:22.5
Step-by-step explanation:
find the product and represent in the simplest form of 12/17 × 3/8
Answer:
9/34
Step-by-step explanation:
I find when multiplying fractions, its easier to separate them into the numerator and denominator.
So we have 12 x 3, and 17 x 8
12 x 3 = 36
17 x 8 = 136
So we have 36/136
Simplified, that is 9/34
If Eof= 26 and FOG= 38, then what is the measure of BOG? The diagram is not to scale.
If EOF = 26 and FOG= 38, then the measure of BOG would be 64 degrees.
What is a measure of angle?
An angle is measured in degrees, thus the term "degree measure." Because one complete revolution equals 360 degrees, it is divided into 360 parts. Each stage of the revolution represents a degree.
The given data:
A measure of EOF = 26 and a measure of FOG = 38.
Then we can say that OF is an angle bisector of angle EOG.
Then the measure of BOG = EOF + FOG
= 26 + 38
= 64 degrees.
Hence, If EOF = 26 and FOG= 38, then the measure of BOG would be 64 degrees.
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q1 suppose you take a sample of 16 people and ask them how fast they drive on interstate 94. after collecting your sample, you calculate that the mean is 75mph with a variance of 9mph. calculate a 90% confidence interval for the average speed of all drivers on i94.
A 90% confidence interval for the average speed of all drivers on interstate 94 is (73.69, 76.31)
Given that,
Imagine asking a sample of 16 people how quickly they travel on Interstate 94. You determine the average speed to be 75 mph and the variance to be 9 mph after gathering your sample.
Solution is as given below :
90% Confidence Interval for μ is
μ = X ± tₐ/2 (n-1) 5/[tex]\sqrt{n}[/tex]
μ = 75 ± (1.75) * 3/[tex]\sqrt{16}[/tex]
μ = (73.69, 76.31)
Consequently, a 90% confidence interval for the interstate 94 average speed of all drivers is μ = (73.69, 76.31)
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For a science project each student needs 5 paper plates. If there are
15 students working on the project, how many paper plates are needed?
Answer:75
Step-by-step explanation:
since there are 15 students and they each need 5 plates you just do 15x5 and get 75
in how many ways can a community. of five be selected from eight students if two particular students are to be included.
To select the community, there are 20 ways available.
What is Combination?
A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant.
Solution:
Since 2 particular students are to be included,
we have to arrange 3 students from 6 students.
nCr = n! / (n-r)!*r!
6C2 = 6!/ (6-3)! 3!
6C2 = 6*5*4*3!/ 3! * 3*2
6C2 = 5*4 = 20
Thereofre, there exists 20 ways of doing the above mentioned.
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3. The mean of five positive numbers is 4. When another number is added, the mean becomes 8. Find the number added.
the answer
Answer:
28
Step-by-step explanation:
mean is when you add all the numbers divide it by the amount of terms
So to find the sum of the terms we just multiply 5 by 4
20 is the sum and since the mean is 8 with 6 terms we multiply those also
8x6
48 and to find the number we subtract 48 by 20
48-20
28
Hopes this helps please mark brainliest
the cat and rabbit's weight is 10 kg and so the dog and rabbit is 20 kg and the dog and cats weight isn24 kg so the question is what their weight togetheer> cat,dog,rabbit??
Answer:
27
Step-by-step explanation:
The cat weighs 7 kg.
The rabbit weighs 3 kg.
The dog weighs 17 kg.
You can check these answers by adding them together.
A cat plus the rabbit is 10 kg.
The rabbit and the dog is 20 kg.
The dog and cat is 24 kg.
Write the first four terms of the sequence defined by the explicit rule. f(n) = 3n + 6
The first four terms of the sequence would be -
9, 12, 15, 18
What is a Sequence?Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -
3, 6, 9, 12, 15
x, x + 2, x + 4, x + 6
We have the following sequence -
f(n) = 3n + 6
We can write the first four terms as -
f(1) = 3 x 1 + 6 = 9
f(2) = 3 x 2 + 6 = 12
f(3) = 3 x 3 + 6 = 15
f(4) = 3 x 4 + 6 = 18
Therefore, the first four terms of the sequence would be -
9, 12, 15, 18
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Need help ASAP find the value of x in the triangle below
Answer:
x = 12
Step-by-step explanation:
Creating an equationAngles in a triangle add up to 180 degrees.
This means that 6x - 19 + 3x + 7 + 84 = 180
Solving for x6x - 19 + 3x + 7 + 84 = 180
==> combine like terms
9x + 72 = 180
==> subtract 72 from both sides
9x = 108
==> divide both sides by 9
x = 12
I am stuck on the last part can u please help me?
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
66.6% = 0.6666... = [tex]\frac{2}{3}[/tex]
Answer:
Fraction = 2/3
Step-by-step explanation:
Given information,
→ Percentage = 66.6%
→ Decimal = 0.6
→ Fraction = ??
Then the required fraction is,
→ Percentage ÷ 100
→ 66.6/100
→ 2/3
Hence, the fraction is 2/3.
lins bike travels 100 meters when her wheels rotate 55 times . whats the circumferences of her wheels
Answer:
Using formula to calculate the circumference of wheel: c=d/n
where
D is the distance bike travel
n is the number of times rotation
C is the circumference of the wheel
As per the statement:
Lin’s bike travels 100 meters when her wheels rotate 55 times.
here, n = 55 rotation and D = 100 meter.
then by definition:
meter c=100/55=20/11
Therefore, the circumference of her wheel is 1 9/11
let s be the total amount heidi spent for scarves. each of the 4 scarves that she bought cost the same. write an expression for the cost of each scarf
The expression for the cost of each scarf is s/4.
According to the question,
We have the following information:
Let s be the total amount Heidi spent for scarves. each of the 4 scarves that she bought cost the same.
Now, the cost of 1 scarf can be easily found by dividing the total cost of the scarves by the number of scarves.
(If we would have to find the cost of 15 scarves then first we would have used division and then multiplication.)
So, we have the following expression:
4 scarves = s
Cost of one scarf = s/4
Hence, the expression for the cost of each scarf is s/4.
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What is the image point of (-8, 1) after the transformation 7x-axis R180°?
The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).
What is a rotation?A rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).
For a dilation with a scale factor of 2, we have:
Point A (-8, 1) → (-8 × 2, 1 × 2) = Point A' = (-16, 2)
By applying a rotation of 180° to the given point, the coordinates of its image is given by:
(x, y) → (-x, -y)
Points A' = (-16, 2) → Points A' = (-(-16), -(1)) = (16, -1).
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Complete Question:
What is the image point of (-8, 1) after the transformation D₂ о R180°?
twelve fair dice are rolled. what is the probability that the product of the numbers on the top faces is prime?
Probability that the product of the numbers on the top faces is prime is 1/2(1/6)⁴.
Define probability.In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution. Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.
Given,
12 fair dice rolled,
Probability that the product of the numbers on the top faces is prime:
⁶C₅ × (1/6)⁵ × ³C₁/⁶C₁
6 × (1/6)⁵ × 3/6
1/2(1/6)⁴
Probability that the product of the numbers on the top faces is prime is 1/2(1/6)⁴.
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find the missing side lengths, leave your answer in simplest form.
The missing side lengths are (m = 4[tex]\sqrt{6}[/tex] , n = 6[tex]\sqrt{2}[/tex]).
According to given triangle, Using triangular formula;
tan 30 = [tex]\frac{2\sqrt{6} }{n}[/tex]
⇒[tex]\frac{1}{\sqrt{3} }[/tex] = [tex]\frac{2\sqrt{6} }{n}[/tex]
⇒ n = [tex]6\sqrt{2}[/tex]
n = [tex]6\sqrt{2}[/tex]
Similarly,
sin 30 = [tex]\frac{2\sqrt{6} }{m}[/tex]
⇒ [tex]\frac{1}{2}[/tex] = [tex]\frac{2\sqrt{6} }{m}[/tex]
⇒ m = [tex]4\sqrt{6}[/tex]
m = [tex]4\sqrt{6}[/tex]
so,
m = [tex]4\sqrt{6}[/tex] and n = [tex]6\sqrt{2}[/tex]
So, the correct option is D.
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