The sum of the numerator and denominator of the decimal is found as 111.
Define the term common fraction?A fraction with an integer for both the numerator and denominator is referred to as a common fraction or vulgar fraction.A fraction with an integer for both the numerator and denominator is described to as a common fraction or vulgar fraction.A ratio can be named with a common fraction.Boys outnumber females in a class 4:3, or 4/3. 4/3 is a popular proportion.As for the given question;
The decimal number is given as;
0.12 bar
Decimal to fraction conversion
100(0.12 bar) = 12(0.12 bar)
99.(0.12bar) = 100(0.12bar) - (0.12 bar)
99.(0.12bar) = 12 × 0.12bar - 0.12bar
99.(0.12bar) = 12
0.12 bar = 12/99 (lowest fraction)
Thus, in the result the numerator is found as 12 and the denominator is found as 99.
Add = 12 + 99
Add = 111
Thus, the sum of the numerator and denominator of the decimal is found as 111.
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T
4) a) On the grid, draw
the line y = 3
b) On the grid, draw
the line x = -2
6
5
4
-3-
2
1-
-3 -2 -1 0
-1-
-2
1
2
3
4
5
Fe
Be
1.
2.
3
4
Answer:
Step-by-step explanation:
will mark brainliest
Find the x-intercept and the y-intercept of the graph of the equation.
4x + 5y = 20
The x-intercept is
The y-intercept is
(Type an integer.)
(Type an integer.)
The x-intercept and y-intercept of the graph is (5,0) and (0,4)
How to find the intercept ?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.
1. To find the x-intercept we put y=0
The equation becomes
4x + 5(0) = 20
4x = 20
x = [tex]\frac{20}{4}[/tex]
x = 5
∴ The x-intercept is (5,0)
2. To find the y-intercept we put x=0
The equation becomes
4(0) + 5y = 20
5y = 20
y = [tex]\frac{20}{5}[/tex]
y = 4
∴ The y-intercept is (0,4)
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how many ways are there to put $4$ balls into $3$ boxes, given that the balls are not distinguished and neither are the boxes?
Answer:
Step-by-step explanation:
think that there are 15 ways ... call the boxes A, B, and C.
You could put all four b***s into either box A, or box B, or box C ---> 3 ways.
You could put three ball into one box and the other ball into another box:
-- 3 into A, 1 into B, 0 into C; or 3 into A, 0 into B, 1 into C; or 1 into A, 3 into B, 0 into C; or 1 into A, 0 into B, 3 into C; or 0 into A, 3 into B, 1 into C; or 0 into A, 1 into B, 3 into C ---> 6 ways
You could put two balls into one box and the other two balls into another box:
-- 2 into A, 2 into B, 0 into C; or 2 into A, 0 into B, 2 into C; or 0 into A, 2 into B, 2 into C ---> 3 ways.
You could put two b***s into one box and one ball into each of the other two boxes:
-- There are three boxes that could get the two b***s ---> 3 ways
Total: 3 + 6 + 3 + 3 = 15 ways.
A line is subdivided according to the golden ratio, with a smaller piece having a length of 5 meters. What is the length of the entire line?
The length of the entire line which is subdivided according to golden ratio is 13.09 meters.
What is Golden Ratio?
The golden ratio is a special number approximately equal to 1.618
We find the golden ratio when we divide a line into two parts so that, the whole length divided by the long part is also equal to the long part divided by the short part
Let smaller part of a line be b and long part be a
Golden ratio = a + b/a = a/b = 1.618
According to the given question:
Length of smaller part of line = 5 meters
Let the longer length of the line be x
∴ Total length of line = 5 + x
Using Golden ratio to find the entire length of line
x/5 = 1.618
x = 8.09
Calculating length of entire line = 5 + x = 5 + 8.09 = 13.09
∴ Length of entire line is 13.09 meters
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Compare the slope-intercept and point-slope forms of a linear equation.
It is possible to determine a line's direction and steepness by looking at its slope.
What is slope?Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
A line's basic formula in gradient intercept form is y=mx + b. It is rewritable in point-slope form.
When y-b is equal to m(x-0), the location is the y-intercept (0,b).
The basic equation for a line with m=slope and (k,h) a position on the line is y-h=m(x-k).
By determining y and adding constant variables, the equation can be recast in slope-intercept form.
Y = mx-mk + h, where h-mk = b is the y-intercept in this form.
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Dan uses the equation g left parenthesis x right parenthesis equals 5 x plus 50 to model the balance of his savings account after saving for x weeks. What is the value and meaning of g left parenthesis 60 right parenthesisblank in the context of the problem?
The value is 350.
From the question, we have
Dan uses the equation g(x)=5x+50 to model the balance of his savings account after saving for x weeks.
g(x)=5x+50
substituting the value x = 60, we get
g(60)=5*60+50
=300+50
=350
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Translate the following equation into a verbal sentence x/4 - y = -2(x/y)
The given equation x/4 - y = -2(x/y) can be expressed in a verbal sentence as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.
How to express the mathematical equation in the form of a verbal sentence?
To express the mathematical equation in the form of a verbal sentence, we have to express the operations by using sentences.
Let's take an example,
x + y = 4.
Then the verbal form will be the sum of two numbers is 4.
Hence, the given expression can be expressed as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Dimensions of the area enclosed is l = 800 ,b = 800 and the maximum area = 6,40,000 square yards.
Given:
Liana has 3200 yards of fencing to enclose a rectangular area.
Let l and b be the length and breadth.
we know that:
perimeter of rectangle = 2(l+b)
2l + 2b = 3200
l+b = 1600
b = 1600 - l
Area of rectangle A = lb
= l*1600-l
= 1600 l - l^2
Apply derivative:
dA/dl = 1600 - 2l
1600 - 2l = 0
1600 = 2l
l = 1600/2
l = 800
l+b = 1600
b = 1600 - 800
= 800
Area = 800*800
= 6,40,000
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13. What is the length of the missing side, x?
40 in.
51°
35 in.
49 in.
74°
55°
X
For the given triangles the length of the missing side x is 56in.
As given in the question,
Two triangles are given ,
Let the triangle with measurement 40in. and 35in. be A and another is B.
In triangle A,
Let missing angle be α
Sum of all the angles in the interior of a triangle is equal to 180°
51°+ 74° + α = 180°
⇒α = 55°
In triangle B.
Let missing angle be β,
74° + 55° + β = 180°
⇒β= 51°
By AAA both the triangles are similar.
Length of corresponding sides are in proportion.
40: x = 35 : 49
⇒x = ( 40×49)/35
⇒x= 56in.
Therefore, for the given triangles the length of the missing side x=56in.
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easy analyzing (due in 20 minutes)
Answer: f = 12m
Step-by-step explanation:
Starting at mile 5 we notice it's 60. But now at mile 7, we notice its 84. This means that we increase by 12 for each mile. Ergo, the answer should be f = 12m.
The difference between five-halves of a number
and 17 is 48.
The required expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
What are algebraic expressions ?An algebraic expression (or) a variable expression is a aggregate of phrases through the operations together with addition, subtraction, multiplication, division, etc. For instance, allow us to have a study the expression 5x + 7. Thus, we will say that 5x + 7 is an instance of an algebraic expression.
CalculationWords can be expressed algebraically.
The algebraic expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
Let the number be x.
Five-halves of x is: 5/2x
So the difference between and 17 is:
5/2x - 17 = 48 or 17 - 5/2x = 48
Combine both expressions
[tex]| 17 - \frac{5}{2}x|[/tex] = 48
Hence, the required expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
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\frac{2x^3t^3}{xt^2}\:\cdot \frac{\left(3xt\right)^3}{9x^2t}
Answer:
[tex]6x^{3}t^{3}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{\left(3xt\right)^3}{9x^2t}[/tex]
[tex]\textsf{Apply exponent rule} \quad (ab)^c=a^c \cdot b^c:[/tex]
[tex]\implies \dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{3^3x^3t^3}{9x^2t}[/tex]
[tex]\implies \dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{27x^3t^3}{9x^2t}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{bd}:[/tex]
[tex]\implies \dfrac{2x^3t^327x^3t^3}{xt^29x^2t}[/tex]
Collect like terms:
[tex]\implies \dfrac{2 \cdot 27x^3x^3t^3t^3}{9x^2xt^2t}[/tex]
Multiply the numbers 2 and 27:
[tex]\implies \dfrac{54x^3x^3t^3t^3}{9x^2xt^2t}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies \dfrac{54x^{3+3}t^{3+3}}{9x^{2+1}t^{2+1}}[/tex]
[tex]\implies \dfrac{54x^6t^6}{9x^3t^3}[/tex]
Separate like terms:
[tex]\implies \dfrac{54}{9} \cdot \dfrac{x^6}{x^3}\cdot \dfrac{t^6}{t^3}[/tex]
Divide the numbers 54 and 9:
[tex]\implies 6 \cdot \dfrac{x^6}{x^3}\cdot \dfrac{t^6}{t^3}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 6 \cdot x^{6-3}\cdot t^{6-3}[/tex]
[tex]\implies 6 \cdot x^{3}\cdot t^{3}[/tex]
[tex]\implies 6x^{3}t^{3}[/tex]
Evaluate 3 (2x - 1).
Answer:
6x - 3
Step-by-step explanation:
3 ( 2x - 1 )
= 3 ( 2x ) - 3 ( 1 )
= 6x - 3
Answer:
x=1/2 or 0.5 or just 6x-3
Step-by-step explanation:
3(2x-1)
distribute.
6x-3
get 6x alone
6x=3
divide
x=3/6
x=1/2 or 0.5
WORD PROBLEMS INVOLVING SIMULTANEOUS EQUATIONS:
The cost of a bottle of water is Rsx.
The cost of a bottle ofjuice is Rsy.
The total cost of 9 bottles of water and 3 bottles of juice is Rs 153.
The total cost of 6 bottles of water and 5 bottles of juice is Rs 147.
Find the cost of a bottle of water and the cost of a bottle of juice.
Step-by-step explanation:
9x + 3y = 153
6x + 5y = 147
the first equation can be divided by 3 and then multiplied by 2. and from that we can subtract equation 2 :
9x + 3y = 153 | /3
3x + y = 51 | ×2
6x + 2y = 102
- 6x + 5y = 147
-----------------------
0 -3y = -45
3y = 45
y = 15
3x + y = 51
3x + 15 = 51
3x = 36
x = 12
1 bottle of water costs Rs 12.
1 bottle of juice costs Rs 15.
What is x−16=−88? I don't know what it is
Answer:
x = -72
Step-by-step explanation:
So first you need to get x on its own, so you you need to get rid of -16 by adding +16 which you get 0.
so now x=-88
whatever you do on one side you do on the other, so add 16 to the other side (-88) so you get -72.
x = -72
so the answer is -72
Thank you <3
A spinner with 9 equal sections is numbered 1 through 9. The probability of spinning a 3 is 1/9. What is the probability of not spinning a 3 is what
The probability of not spinning a 3 is 8/9
How to determine the probability that the number 3 is not spun?From the question, the given parameters are:
Number of sections = 9
Sections = Number 1 to 9
The probability of spinning a 3 = 1/9
The above probability can be represented as
P(3) = 1/3
The probability that the number 3 is not spun is the complement of the probability of spinning a 3
This is calculated as
P(3) + P(Not 3) = 1
Substitute the known values in the above equation So, we have the following equation
1/9 + P(Not 3) = 1
Evaluate the like terms
P(not 3) = 8/9
Hence, the probability is 8/9
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Expand and Simplify (x+5)(x-2)
Answer:
[tex]x^2+3x-10[/tex]
Step-by-step explanation:
To expand you must do this:
[tex]x*x+(-2x)+(5x)-10\\x^2-2x+5x-10\\x^2+3x-10[/tex]
Please help with the unfilled spots! :)
The value of [tex](x_{1},y_{1})= (-9,-6)[/tex] and the value of [tex](x_{2},y_{2})= (-1,-12)[/tex],according to the question.
What do you mean by XY coordinates?
The x and y coordinates are a component of the x-axis and y-axis in a 2D space in the Cartesian coordinate system. The x and y coordinates for a point in space are expressed as an ordered pair (x, y). The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.
According to the data in the given question,
We have:
The coordinates of points A are (-9,-6).
The coordinates of points W are (-1,-12).
In this question,
[tex](x_{1},y_{1})= (-9,-6)[/tex]
[tex](x_{2},y_{2})= (-1,-12)[/tex]
Therefore, the value of [tex](x_{1},y_{1})= (-9,-6)[/tex] and the value of [tex](x_{2},y_{2})= (-1,-12)[/tex].
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The area of a square foot ball field is
16900cm². calculate the length of the field.
AREA OF A SQUARE= LENGTH* LENGTH
16900= L²
TAKE THE SQUARE ROOTS OF BOTH SIDES
√16900 =√L²
L= 130
THEREFORE THE LENGTH OF THE FIELD IS 130cm.
Mason is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Mason will earn $30 every time one of his songs is played in a commercial and he will earn $80 every time one of his songs is played in a movie. Mason earned a total of $470 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Mason's songs were played. Define the variables that you use to write the system.
Answer:
Get the roundend answer to 10
Step-by-step explanation:
a yield sign measures 24 inches on each of its three sides. what is the area of the sign? (round your answer to one decimal place.)
A yield sign measures 24 inches on each of its three sides ( equilateral )then the area of the sign is 249.4
Given,
24 inches on each of its three side. (See in attached picture)
Consider ADB,
As it is an equilateral triangle, BD = BC/2 = 12 inches
By Pythagoras theorem,
AB^2 = BD^2 + AD^2
24^2 = 12^2 + AD^2
24^2 – 12^2 = AD^2
576-144 = AD^2
432= AD^2
20.78= AD
Area = ½ (base * height)
= ½ (24*20.78)
= 249.4
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What amount of pure acid must be added to 400 mL of a 40% acid solution to produce a 60% acid solution?
Answer:
600ml
Step-by-step explanation:
Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
A. Write an equation that can be used to solve for the number of days until the plant has a height of 30 cm. Use d to represent the number of days. Label each part of your equation with what it represents.
B. How much does the plant still have to grow?
C. Solve for the value of d. What does this value represen in this problem?
PLEASE SOLVE ALL
A) The equation is 22 + (d * 1/2) = 30
B) The plant that still have to grow 8 cm more
C) d = 16 days, d represents the number of days
Step-by-step explanation:
Given:
Initial height (basil plant at buying) = 22cm
Plant grows on everyday = 1/2cm
A) Given:
Total height (to be grown) = 30 cm.
The equation is,
Initial height+ ( number of days * plant grows on everyday) = Total height
22 + (d * 1/2) = 30 → equation 1
B) The plant that still have to grow = Total height - Initial height
= 30 - 22
= 8 cm
C) Solving the value d using equation 1:
22 = 30 - (d * 1/2)
44 = 60 - d
d = 16 days
Hence, A) The equation is 22 + (d * 1/2) = 30.
B) The plant that still have to grow 8 cm more.
C) d = 16 days, d represents the number of days.
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Can anyone write the equation of the graph?
The absolute equation in the graph is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we can see that the lines on the graph has a sharp v-shape
Graphs that have this form are absolute value graphs
The general form of an absolute value equation is expressed as
y = |x - h| + k
From the above form, we have
Vertex = (h, k)
By definition, the vertex of a function is either the maximum point or the minimum point
On the given graph, the minimum point is (3, 5)
So, we have the following representation
(h, k) = (3, 5)
Substitute (h, k) = (3, 5) in the above equation
So, we have:
y = |x - 3| + 5
Hence, the function represented by the graph has an equation of f(x) = |x - 3| + 5
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Solve for x.
2/x^2−4 − 1/x+2 = 3/x−2
In regards to the question above, the solution for the equation is x=-2(1+2x)/x^2-4.
What is the equation known as?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. Equations come in two varieties: identities and conditional equations.
How to solve this:
2/x^2-4 -1/x+2=3/x-2
collecting like terms
2/x^2-4 -1/x+2 -3/x-2=0
Divides through by:
x^2-42 -1(x-2) -3(x+2)/x^2-4=0
Remove bracket: 2-x+2-3x-6/x^2-4
Lastly, collecting like terms:
2+2-6-x-3x/x^2-4-2-4x/x^2-4
=-2(1+2x)/x^2-4
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the price of a car was increased by 4% to £22 what was the price before
13.80
Step-by-step explanation:
22 - 4% is your answer
When the p-value is used for hypothesis testing, the null hypothesis is rejected if?.
If the p-value is less than or equal to the selected significance level, the null hypothesis is rejected; otherwise, it is not. In other words, if p, reject[tex]H_{0}[/tex]; if p>, do not reject [tex]H_{0}[/tex].
In null hypothesis testing, this criterion, also known as (alpha), is frequently set to 05. If there is less than a 5% chance that the null hypothesis would be accepted and a result as spectacular as the effects that result would occur, the null hypothesis is rejected. When this happens, the result is said to be statistically significant.
The null hypothesis would be rejected if a statistical test was conducted with a threshold of relevance = 0.1, 0.05, & 0.01.
If the P value is smaller than alpha, the preset level of statistical significance, the alternative hypothesis is considered instead of the null hypothesis.
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Show all your work!
First find the k= COP x
K=18-12=1.5
X=1.5(10)
Y=1.5 =
y
४/५
es, Show all your work!
y
of
y
First find the k= COP x
Answer:
Step-by-step explanation:
COP = Constant of Proportionality. • y varies directly to x. > If 10 miles varies directly to 5 minutes,. – then 10 = y and 5 = x. • Unit Rate (1, r). > (x, y).
What is the m
9.4
m
15.1
K
Step-by-step explanation:
imagine a circle with J being the center, and JK being the radius.
then
sin(J) = 15.1/JK
cos(J) = 9.4/JK
we have one trigonometric function, where we don't need to calculate JK first : tangent.
tan(J) = sin(J)/cos(J) = 15.1/JK / 9.4/JK = 15.1/9.4 =
= 1.606382978...
J = 58.09705252...° ≈ 58.1°
the probability distribution of all possible values of the sample mean is called the . select one: a. central probability distribution b. standard error c. sampling distribution of the sample mean d. random variation
The probability distribution of all possible values of the sample mean is called the sampling distribution of the mean.
What is meant by the sampling distribution of the mean?
An accurate probability distribution of a statistic is known as a sampling distribution, and it is created by repeatedly sampling a certain population. It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.Why is sampling essential and what does it mean?
Sampling is the process of choosing a portion of the general population or a subset of social phenomena to be investigated. The primary goal of sampling is to make assumptions about the larger group based on data collected from the smaller group. The selection of a representative sample is the primary means of achieving this.Learn more about Probability
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