Answer:
14 1/3
Step-by-step explanation:
You have to divide 86 by 6, which gives you 14 with a remainder of 2. This would result in 14 2/6, or simplified: 14 1/3
Answer:
14 2/6
Step-by-step explanation:
We want to transform 86/6 into a mixed number. We can achieve this by following these steps:
Step 1: Divide the numerator (86) by the denominator (6):
86 / 6 = 14 remainder 2
Step 2: Build your answer using the quotient (14) as the whole number and the remainder (2) as the numerator, keeping the same denominator (6). Thus,
The improper fraction 86/6
is equivalent to 14 2/6
simplest form is 14 1/3
Solve each equation. Check each solution. 3x - 2 / 12 - 1 / 6 =1 / 6
The solution of the equation (3x -2)/12 -1/6 = 1/6 is at x = 2.
According to the given question.
We have an equation (3x -2)/12 -1/6 = 1/6 .
As we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.
Therefore, the solution of the equation (3x -2)/12 -1/6 = 1/6 is given by
(3x -2)/12 -1/6 = 1/6
⇒ (3x -2)/12 = 1/6 + 1/6 (adding 1/6 both the sides)
⇒ (3x -12)/12 = 2/6
⇒ (3x -2)/12 = 1/3
⇒ (3x -2) = (1/3)12
⇒ 3x -2 = 4
⇒ 3x = 4 + 2
⇒ 3x = 6
⇒ x = 6/3
⇒ x = 2
Hence, the solution of the equation (3x -2)/12 -1/6 = 1/6 is at x = 2.
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3. Find the mode and mean of the following:
Number of TVs
0
1
2
3
4
Frequency
3
15
9
11
1
Mode =
Mean =
A mode can be defined as a statistical term that is used to denote the value that appears most frequently (often) or occurs repeatedly in a given data set. This ultimately implies that, the mode of a data set simply refers to the data point with the highest frequency.
By critically observing the frequencies for the number of TVs shown in the table above, we can logically deduce that the mode is equal to 1.
What is a mean?A mean can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
How to determine the mean for males?Mathematically, the mean for this data can be calculated by using the following formula:
Mean = [F(x)]/n
Frequency, n = 3 + 15 + 9 + 11 + 1
Frequency, n = 39.
Total number of TVs = 0(3) + 1(15) + 2(9) + 3(11) + 4(1)
Total number of TVs = 0 + 15 + 18 + 33 + 4
Total number of TVs = 70
Substituting the parameters into the formula, we have;
Mean = 70/39
Mean = 1.80.
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The possible values of x are given. by x minus 4 is greater than or equal to -1. what is the greatest possible value of -5x
Answer:5
Step-by-step explanation:
What is the sum of the first 7 terms of the geometric series below? 1,2,4,8, ,,
Answer:
idududydysehwghsysysgsbebeywyehe
Answer:
S₇ = 127
Step-by-step explanation:
the sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^n-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{2}{1}[/tex] = 2 , then
S₇ = [tex]\frac{1(2^7-1)}{2-1}[/tex] = [tex]\frac{2^7-1}{1}[/tex] = [tex]2^{7}[/tex] - 1 = 128 - 1 = 127
The figure MNP will be reflect across the y- axis. If point M starts at (1, 2), what is the coordinate of M´?
Answer:
M' (- 1, 2 )
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
M (1, 2 ) → M' (- 1, 2 )
Pls help for brainly 2 Figure JKLMN is reflected across the x-axis to form figure J'K'L'M'N'.
4
-6 <-4 -2 o
J
2
M'
4
M
6
N
8
Decide if each statement about figures JKLMN and J'K'L'M'N' is true or false.
Choose True or False for each statement.
a. The y-coordinate of J' is the
opposite of the y-coordinate of J.
b. L' is located at (-3,-4).
c. N and N' both are at the same
distance from the y-axis.
d. L' is located 3 units above the x-axis.
True False
OOOO
O
OO
O
50
Turn in 0. = AA
Page
The result of true and false is-
a) True: J and J' are opposite of y axis.
b) False: Location of L' is (-3, -4).
c) True: N and N' are at same distance.
d) False: L' is at 3 unit above x axis.
What is defined as the reflection on coordinates?The x-coordinates of a point remain constant when it is reflected across the X-axis. However, the Y-coordinates are changed into their inverse signs. As a result, the X-axis reflection of a point (x, y) is (x, -y).As per the given graph;
Part a: True: J and J' are opposite of y axis.
It is clear from the graph that J and J' lies on the opposite side of Y-axis.
The coordinate of J = (2, -6) and J' = (2, 6).
Part b: False: The location of L' is not (-3, -4)
The correct Location of L' is (3, 4) as seen from the graph.
Part c: True: N and N' are at same distance.
The coordinates of N and N' are (5, -5) and (5, 5).
Thus, they are at the same distance from the both axis.
Part d: False: L' is at 3 unit above x axis.
Point L' lies at the distance of 4 units from the x axis.
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Work out the length x in the triangle below.
If your answer is a decimal, give it to 1 d.p.
area = 26 m²
13 m
x
30°
PLEASE HELP WITH THIS QUESTION!!
Answer:
x = 8
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] absinC
where a and b are 2 sides of the triangle and C the angle between them
here a = 13 , b = x , C = 30° and A = 26 , then
[tex]\frac{1}{2}[/tex] × 13 × x × sin30° = 26 ( multiply both sides by 2 to clear the fraction )
13x × sin30° = 52 ( using the exact value of sin30° = [tex]\frac{1}{2}[/tex] )
13x × [tex]\frac{1}{2}[/tex] = 52 ( multiply both sides by 2 to clear the fraction )
13x = 104 ( divide both sides by 13 )
x = 8
If you get an identity when trying to solve a system of two linear equations, the system's graph
must be
a) two parallel lines
b) two lines that are the same
c) two intersecting lines
d) two perpendicular lines
e) None of the above
Answer:
a) two parallel lines
Step-by-step explanation:
Two parallel lines have the same slope
Let's take a concrete example:
y = 2x + 4 (slope =2, y-intercept = 4)
y = 2x + 10 (slope = 2, y-intercept = 10)
Lines are parallel to each other
If you try to solve this equation you get
2x + 4 = 2x + 10
Subtracting 2x on both sides gives you the identity 4 = 10 (a contradiction)
This means the 2 line equations are inconsistent
Expand each binomial. (x-2)⁴
The expand each binomial. (x - 2)⁵ is:
x⁴ - 8x³ + 24x² - 32x + 16
What is a polynomial?A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.
Depending on the number of terms it can be :
monomialbinomialtrinomialWe solve first by perfect square trinomial, then we apply the distributive property.
(a - b) = a² + 2ab + b²(x - 2)⁴ = (x- 2)²(x - 2)²
(x - 2)⁴ = (x² - 4x + 4)(x² - 4x + 4)
(x - 2)⁴ = (x⁴ - 4x³ + 4x²) + (-4x³ + 16x² - 16x) + (4x² - 16x + 16)
(x - 2)⁴ = x⁴ - 4x³ + 4x² -4x³ + 16x² - 16x + 4x² - 16x + 16
(x - 2)⁴ = x⁴ - 8x³ + 24x² - 32x + 16
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a. What is the sum of the finite arithmetic series 4+9+14+19+24+ . . . . . . . +99 ?
The sum of the arithmetic series 4+9+14+19+24+ . . . . . . . +99 is S(20) = 1030
The given series:
4+9+14+19+24+ . . . . . . . +99
We can conclude:
a(1) = 4
a(n) = 99
d = 9 - 4 = 5
Find n using the formula of nth term.
a(n) = a(1) + (n-1) . d
99 = 4 + (n -1). 5
99 = 5n - 1
5n = 100
n = 20
Find the sum for the n terms using the sum formula of an arithmetic series:
S(n) = n/2 (a(1) + a(n))
Substitute n = 20, a(1) = 4, and a(20) = 99
S(20) = 20/2 . (4 + 99)
= 10 . 103 = 1030
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Rewrite in simplest terms: -8(10r + 10r - 6) - 3r
HELP ME
After simplifying the expression - 8 ( 10 r + 10 r - 6 ) - 3 r, we get the result as 48 - 163 r.
We are provided with an expression:
- 8 ( 10 r + 10 r - 6 ) - 3 r
We need to write the given expression in the simplest terms that is we need to simplify the expression.
So, we will use the property of BODMAS here.
Solving the bracket first , the expression will become:
= - 8 ( 10 r + 10 r - 6 ) - 3 r
= -8 ( 20 r - 6 ) - 3 r
Now, opening the bracket, we get that:
= - 160 r + 48 - 3 r
Now, combining the like terms, we get the result as:
= - 163 r + 48
= 48 - 163 r
Therefore, after simplifying the expression - 8 ( 10 r + 10 r - 6 ) - 3 r, we get the result as 48 - 163 r.
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what is the answear for 12x+7x 2 squared +5x+9x 2 squared
Answer: x=4
Step-by-step explanation:
it is impossible to solve x
Write the first five numbers of two different patterns in which 12 is the third number.
Write the first five numbers of two different patterns in which 12 is the third number.
Pattern 1= 4, 8, 12, 16, 20
Pattern 2= 2,4,12,48,240
How to calculate the patterns?
Pattern 1=multiples of 4
4*1=4
4*2=8
4*3=12
4*4=16
4*5=20
Pattern 2= tn=(tn-1)*n
t1=2
t2=2*2=4
t3=4*3=12
t4=12*4=48
t5=48*5=240
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Write an equation of a parabola with vertex at the origin and the given focus.
focus at (0,7)
The equation that defines the parabola with vertex at the point (0, 0) and focus at (0, 7) is:
y = x²/28
A parabola is a quadratic function that can move on any axis, it is composed of:
vertexfocal axisdirectrixThe equation that defines a parabola can be given by:
(x - h)² = 4p(y - k)(y - k)² = 4p(x - h)This will depend on its aperture
In this case we have the vertex of the parabola at the point (0, 0) and the focus at the point (0, 7) this is displaced on the y-axis upward, so the parabola is of the form y = x²
(x - 0)² = 4p(y - 0)
Focus
f = (0, 0 + p)
0 + p = 7p = 0 + 7p= 7(x- 0)² = 4*7(y - 0)
(x - 0)² = 28(y - 0)
y = x²/28
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please help me with my math!!!!!!!!!!!!!!!!!!!!!!!!
(3/5)^4 and 27/125 which equals 0.216m^3
lengths of corresponding side of 2 similar right ratio is 4:5 and hypotenuse of the smaller triangle is 24 inches long. How many inches long is the hypotenuse of the larger triangle?
The hypotenuse of the larger triangle is 30 inches
How many inches long is the hypotenuse of the larger triangle?The ratio is given as
Ratio = 4 : 5
The smaller triangle has a length of 24 inches
So, we have
24 : Larger triangle = 4 : 5
Multiply 4 : 5 by 6
So, we have:
24 : Larger triangle = 24 : 30
By comparison, we have
Larger triangle = 30
Hence, the hypotenuse of the larger triangle is 30 inches
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f (x) = 8 (1.25) ^ -2.5
Write the function rule for the function shown below reflected in the given axis.
f(x) = 6x; x-axis
Let g(x) be the reflection of f(x) in the x-axis. What is the function rule for g(x)?
g(x)=
The function rule for g(x) is g(x) = -6x
How to determine what is the function rule for g(x)?The equation of the function f(x) is given as
f(x) = 6x
From the question, we understand that:
The function g(x) is the reflection of the function f(x) over the x-axis
This means that
g(x) = -f(x)
So, we have
g(x) = -6x
Hence, the function rule for g(x) is g(x) = -6x
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Im confused on the rug question. If you can when you give me the answer can you explain it also?
I think it's trying to get you to find the side length of the square by using a square root on the area.
Assuming that's the case;
Remember that a square has equal side lengths all around, otherwise it would just be a rectangle. You can actually take the square root of a square to get the side length (hence the name square root). A square root is what number you must multiply by itself to get the root, so for example the square root of 25 is 5 because you can multiply 5 by 5 to get 25. The square root of 100 is 10, because you can multiply 10 by itself to get 100. So you would write this as [tex]\sqrt{100}[/tex], which simplifies down to 10.
Two inequalities are solved. The first one has the solution ‒3 ≤ x < 2, and the other has the solution (‒1, 4]. If both inequalities must be true at the same time and x is an integer, how many possible solutions are there? (A) 5 (B) 4 (C) 3 (D) 2 (E) 1
The total number of possible solutions for both the inequalities to be true at the same time are 3.
What is inequality?Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.
Given in the question is the solution of two inequalities as a function of x.
Since, both the inequalities must be true at the same time, this means that only those solutions will be taken into consideration which are common to both. In order to do so, we have to find the intersection of the sets representing their solutions. Now,
Solution set for inequality 1 → S[1] ∈ [-3, 2)
Solution set for inequality 2 → S[2] ∈ (-1, 4]
The set representing the solution for the existence of both the inequalities at the same time is -
S = S[1] ∩ S[2] = [-3, 2) ∩ (-1, 4] = [0, 1, 2]
n(S) = 3
Therefore, the total number of possible solutions for both the inequalities to be true at the same time are 3.
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Which ratios have a unit rate greater than 1? Choose ALL that apply.
9
8
9/5
5
-
miles: hour
6
miles: 3 hours
4)
1
4 miles: 3 hours
3
7 miles:
34
hour
121-1/4
2 miles : 3 hours
1
3
318
mile: 2 hours
Answer:
A and E (top left and bottom middle)
Step-by-step explanation:
Unit rates are found when a ratio has a denominator of 1. For the sake of simplicity, I will give the options in the image letter designations. A, B, and C are the top three from left to right, and D, E, and F are the bottom 3 from left to right.
A
[tex]\frac{9}{5} miles:\frac{5}{6}hour[/tex]
Because ratios can be written as fractions, this ratio can be written:
[tex]\frac{\frac{9}{5}}{\frac{5}{6}}[/tex]
That's a mess! Another way to divide fractions is to multiply by the reciprocal of the denominator:
[tex]\frac{9}{5}*\frac{6}{5}[/tex]
Since none of the terms can be cross-cancelled, multiply!
[tex]=\frac{54}{25}[/tex]
Since the numerator is greater than the denominator, the unit rate is greater than one!
B
[tex]4miles:3\frac{1}{3}hours[/tex]
Start by turning the mixed number into an improper fraction:
[tex]3\frac{1}{3}=\frac{10}{3}[/tex]
Now compare by multiplying 4 over 1 by the reciprocal of 10 thirds:
[tex]\frac{4}{1}*\frac{3}{10}[/tex]
Cross-cancel and multiply:
[tex]=\frac{2}{5}[/tex]
Since the numerator is less than the denominator, the unit rate is less than one!
C
[tex]2\frac{1}{2} miles:3hours[/tex]
Convert the mixed number into an improper fraction:
[tex]2\frac{1}{2} =\frac{5}{2}[/tex]
Multiply by the reciprocal of 3:
[tex]\frac{5}{2}*\frac{1}{3}[/tex]
Multiply!
[tex]\frac{5}{6}[/tex]
Since the numerator is less than the denominator, the unit rate is less than one!
D
[tex]\frac{9}{5} miles :3hours[/tex]
Multiply by the reciprocal of 3:
[tex]\frac{9}{5}*\frac{1}{3}[/tex]
Cross cancel and multiply!
[tex]=\frac{3}{5}[/tex]
Since the numerator is less than the denominator, the unit rate is less than one!
E
[tex]7 miles :\frac{3}{4}hour[/tex]
Multiply by the reciprocal of 3 fourths:
[tex]\frac{7}{1}*\frac{4}{3}[/tex]
Multiply:
[tex]=\frac{28}{3}[/tex]
Since the numerator is greater than the denominator, the unit rate is greater than one!
F
[tex]\frac{1}{3}mile:2\frac{3}{8}hours[/tex]
Convert the mixed number into an improper fraction:
[tex]2\frac{3}{8}=\frac{19}{8}[/tex]
Multiply one third by the reciprocal of 19 eighths:
[tex]\frac{1}{3}*\frac{8}{19}[/tex]
Multiply!
[tex]=\frac{8}{57}[/tex]
Since the numerator is less than the denominator, the unit rate is less than one!
What are the coordinates of the point on the directed line segment from (-6, -10)
to (6, 8) that partitions the segment into a ratio of 2 a to 1?
The coordinates of line segment are (2,2)
What is section formula?The section formula is the method used to get the coordinates of a point on a line segment that divides it into two segments.Lets’s imagine that the line segment marked with the coordinates A ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and B has a point P(x,y) that splits it ([tex]x_{2}[/tex],[tex]y_{2}[/tex]). To find the coordinates, we use the section formula, which is described mathematically as.
P(x, y) =([tex]\frac{m.x_{2}+n.x_{1} }{m+n}[/tex],[tex]\frac{m.y_{2}.n.y_{1} }{m+n}[/tex])
Given that : the point on the directed line segment from (-6,-10) to (6,8) that partitions the segment into a ratio of 2 to 1
Consider two points P([tex]x_{1} ,y_{1}[/tex]) and Q([tex]x_{2},y_{2}[/tex]).Finding the coordinates of the point R that divides PQ in the ratio m: n is necessary because [tex]\frac{PR}{RQ}[/tex] = [tex]\frac{m}{n}[/tex].
Here , p = (-6, -10)
Q= (6, 8)
m :n = (2,1)
x = [tex]\frac{m.x{2} +n.x_{1} }{m+n}[/tex]
y = [tex]\frac{m.y_{2}+n.y_{1} }{m+n}[/tex]
by putting value we get,
x= 2 , y= 2
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Write the equation for each line. Use slope-intercept form. m = 4/5 and the y -intercept is (0,7) .
The equation of the line in slope-intercept form with a slope of 4/5 and y-intercept of (0 , 7) is y = (4/5)x + 7.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
Given that the slope of the line is 4/5 and the y-intercept is (0 , 7), write the equation of the line by simply plugging in its values.
y = mx + b
y = (4/5)x + 7
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Find and interpret the z-score for the data value given.
The value 86 in a dataset with mean 101 and standard deviation 19
Round your answer to two decimal places.
The value is i 5.3
standard deviations
below
the mean.
Using z-scores, it is found that:
The value is 0.79 standard deviations below the mean.
What is the z-score formula?The z-score of a measure X of a variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the parameters are given as follows:
[tex]X = 86, \mu = 101, \sigma = 19[/tex]
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (86 - 101)/19
Z = -0.79.
The value is 0.79 standard deviations below the mean.
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a₁ is the first term of a sequence, r is a common ratio, and d is a common difference. Write the first five terms. a₁ =19, d=-4
The first five terms of an arithmetic sequence with first term 19 and common difference -4 are 19, 15, 11, 7, 3
The given parameters:
a₁ = 19, d = -4
d is the common difference, hence, the given sequence is an arithmetic sequence.
In an arithmetic sequence, the formula for the nth term is given by:
a(n) = a(1) + (n - 1) . d
We can also find the terms using recursive formula. The nth term of an arithmetic sequence is equal to the (n-1)th term plus the common difference, d. Mathematically,
a(n) = a(n -1) + d
Let us start from n = 1
a(1) = 19 (given)
a(2) = a(1) + d = 19 + (-4) = 15
a(3) = a(2) + d = 15 + (-4) = 11
a(4) = a(3) + d = 11 + (-4) = 7
a(5) = a(4) + d = 7 + (-4) = 3
Thus, the first five terms are 19, 15, 11, 7, 3
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How are algebraic expressions and numerical expressions alike? How are they different? Include examples to justify your reasoning.
The algebraic expression is the expression that contains numbers and variables and the numerical expression is the expression that contains numbers and operations
Given,
The algebraic expression is the expression that contains numbers and variables
Example : x+3
The numerical expression is the expression that contains numbers and operations
Example : 2+6
Hence, the algebraic expression is the expression that contains numbers and variables and the numerical expression is the expression that contains numbers and operations
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The formula for the volume of a cylinder is V = r²h.
a. Solve the formula for the height of h.
b. Using the above formula, a cylinder has a volume of 628 cubic inches and a radius of 10
inches. What is the height of the cylinder rounded to the nearest inch?
Answer:
628=10^h
Step-by-step explanation:
Solve for h in the equation above and you will get your answer. Hope this helps!
State whether the sentence is true or false. If false, replace the underlined term to make a true sentence.
Tossing a coin and then tossing another coin is an example of dependent events .
False, Tossing a coin and then tossing another coin is an example of dependent events .
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.If false, replace the underlined term to make a true sentence. Tossing a coin and then tossing another coin is an example of dependent events .
The outcome of tossing a coin does not affect the out come of rolling a number cube.
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A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (4, 5) and (3, 2), what is the equation for a parallel street that passes through (2, −3)?
y = 3x + 11
y = 3x − 9
y equals negative 1 third times x plus 1
y equals negative 1 third times x minus 7 thirds
The equation of the line parallel to the first line is y = 3 · x - 9. (Correct choice: B)
How to determine an equation of the line parallel to another line
In this question we must derive the equation of the line for a given street and look for another equation of the line parallel to the previous one. Lines are first order polynomials of the form y = m · x + b, where m and b are the slope and the y-intercept, respectively.
Now we present the procedure in detail. First, find the equation of the first line:
5 = 4 · m₁ + b₁ (1)
2 = 3 · m₁ + b₁ (2)
(m₁, b₁) = (3, - 7)
Second, determine the equation of the line parallel to the line found in the previous step: (Please notice that two lines are parallel to each other when they share the same slope but have different y-intercepts)
- 3 = 3 · 2 + b₂
b₂ = -3 - 6
b₂ = - 9
The equation of the line parallel to the first line is y = 3 · x - 9. (Correct choice: B)
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Answer: The correct answer is B
Dile
A college radio station has an $800 monthly CH.
budget. 60% of this budget is spent on media. The
station receives a 30% media discount. How much
money will the station save annually?
12
Answer:
$144
Step-by-step explanation:
$800 × .60 = $480 spent on media
$480 × .30 = $144 media discount
