Given the expression
[tex]\frac{6409}{61}[/tex]Next is to know how many 61 can go in 6409. Using the calculator, you can see that it is 105 with a remainder of 4
We will then have to express the fraction in the form:
[tex]Q\text{ +}\frac{R}{D}[/tex]Q is the quotient = 105
R is the remainder = 4
D is the divisor = 61
Substituting these values into the expression we will have:
[tex]\begin{gathered} \frac{6409}{61}=105+\frac{4}{61} \\ \frac{6409}{61}=105\frac{4}{61} \end{gathered}[/tex]Hence the solution written as a whole number and fraction is 105 4/61
Please help me with this..
Answer:
40/36=20/x
X=18
Step-by-step explanation:
it solve by Proportion and proportion
Answer:
Area of the small rectangle is 9m²
in an election, suppose that 55% of the voters in fact support funding the new crc library building. a news organization wants to predict the outcome of the election by sampling 80 voters. what is the probability that less than 49% of the sampled voters support the new crc library building? this would result in the news organization making a wrong prediciton.
The new organization making a wrong prediction cannot be determined.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen.
According to the problem,
p = 55% ≅ 0.55
n = 80 voters
The probability that less than 49% ≅ 0.49 of the sampled voters support the new library building can be calculated as,
p( p < 0.49 ) = p( z < (0.49 - 0.55) / √(0.55*(1 - 0.55)/80) )
where, z = { p - p/ √(p(1 - p)/n) }
p( p < 0.49 ) = p( z < ( -0.06) / √(0.55*0.45/80))
= p( z < ( -0.06) / √(0.2475/80))
= p( z < ( -0.06) / [tex]\sqrt{0.00309375}[/tex] )
= p( z < ( -0.06) / 0.055621488 )
= p( z < ( -1.078719793) )
p( p < 0.49 ) = p( z < ( -1.079) )
p( p < 0.49 ) ≅ 0.140071 ( From the normal standard table )
The calculated probability is unpredictable. Therefore, We cannot say that the new organization is making a wrong prediction.
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In circle M with m \angle LMN= 42m∠LMN=42 and LM=14LM=14 units, find the length of arc LN. Round to the nearest hundredth.
The length of the arc is 1.63
In circle M with m \angle LMN= 42m∠LMN=42
The diagram shows a sector of a circle, center M
The radius of the circle is 14 units
The angle LMN = 42
We need to find the perimeter of the sector
s = r∅
Where ∅ is the angle subtended by the arc
r is the radius of the circle
s = 14 (42/360)
s = 14 (7/60)
s = 1.63
Therefore, the length of the arc is 1.633
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solve for X using cross multiplication 4x-3/3 = x+8/2 x= []
Answer:
x=6
Explanation:
Given the equation:
[tex]\frac{4x-3}{3}=\frac{x+8}{2}[/tex]First, cross multiply:
[tex]2(4x-3)=3(x+8)[/tex]Next, open the brackets:
[tex]8x-6=3x+24[/tex]Subtract 3x from both sides of the equation:
[tex]\begin{gathered} 8x-3x-6=3x-3x+24 \\ 5x-6=24 \end{gathered}[/tex]Add 6 to both sides of the equation:
[tex]\begin{gathered} 5x-6+6=24+6 \\ 5x=30 \end{gathered}[/tex]Finally, divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{30}{5} \\ x=\frac{6\times5}{5} \\ x=6 \end{gathered}[/tex]The value of x is 6.
Solve right triangle ABC for all missing parts. Express angles in decimal degrees.a = 200.7 km, c= 401.5 kmRound to the nearest hundred
Using the Pythagorean Theorem we get:
[tex]c^2=a^2+b^2\text{.}[/tex]Therefore:
[tex]b^2=c^2-a^2\text{.}[/tex]Substituting a=200.7km and c=401.5km we get:
[tex]b^2=(401.5km)^2-(200.7km)^2.[/tex]Solving the above equation for b we get:
[tex]\begin{gathered} b=\sqrt[]{(401.5km)^2-(200.7km)^2} \\ =\sqrt[]{161202.25km^2-40280.79km^2} \\ =\sqrt[]{120921.76km^2}\approx347.74km\text{.} \end{gathered}[/tex]Now, from the given diagram we get that:
[tex]\begin{gathered} \cos B=\frac{a}{c}, \\ \sin A=\frac{a}{c}\text{.} \end{gathered}[/tex]Substituting a=200.7km and c=401.5km we get:
[tex]\begin{gathered} \cos B=\frac{200.7\operatorname{km}}{401.5\operatorname{km}}=\frac{2007}{4015}\text{.} \\ \sin A=\frac{200.7\operatorname{km}}{401.5\operatorname{km}}=\frac{2007}{4015}\text{.} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} B=\cos ^{-1}(\frac{2007}{4015})\approx60.00^{\circ}, \\ A=\sin ^{-1}(\frac{2007}{4015})\approx30.00^{\circ}, \end{gathered}[/tex]Answer:
[tex]\begin{gathered} b=347.74\operatorname{km}, \\ B=60.00^{\circ}, \\ A=30.00^{\circ} \end{gathered}[/tex]
Janice and Donald worked together for 2 hours to build a picnic table, after which Donald continued working for 1 hour without Janice to finish the job. If each is working alone, Janice typically takes 2 less hours than Donald to build a picnic table. Based on this information, how long would it have taken for Janice to build the picnic table alone? Do not include the units in your answer.
To solve this problem the first thing we have to do is identify our variables
The time taken by Janice will be represented by a j, and the time taken by Donald by a d.
• Donald builds the picnic table in hours: , 1/d, of the picnic table per hour
,• Janice builds the picnic table ,j=d-2, in hours: ,1/(d-2), of the picnic table per hour
Now we will get our equation to solve
Janice and Donald worked together for 2 hours to build a picnic table, after which Donald continued working for 1 hour without Janice to finish the job.
[tex]\begin{gathered} 2(\frac{1}{d}+\frac{1}{d-2})+1(\frac{1}{d})=1Table \\ \frac{2}{d}+\frac{2}{d-2}+\frac{1}{d}=1Table \\ \frac{3}{d}+\frac{2}{d-2}=1\text{Table} \\ \frac{2d+3(d-2)}{d(d-2)}=1\text{table} \\ 2d+3d-6=d^2-2d \\ d^2-2d-5d+6=0 \\ d^2-7d+6 \end{gathered}[/tex]We factor our equation to find Donald's time
[tex]\begin{gathered} (d-6)(d-1)=0 \\ d_1=6 \\ d_2=1 \end{gathered}[/tex]They gave us 2 values but we discarded the value of d=1 because the joint calculations would give negative calculations then
[tex]\begin{gathered} j=d-2 \\ j=6-2 \\ j=4 \end{gathered}[/tex]Donald takes 6 hours to set up a table and Janice takes 4 hours.Each basket contains 3 identical bags of stuffing and 6 pound bag of rice.
The total pounds of rice will be 18 pounds.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, each basket contains 3 identical bags of stuffing and 6 pound bag of rice. The total pounds will be:
= 3 × 6
= 18 pounds
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Complete question
Each basket contains 3 identical bags of stuffing and 6 pound bag of rice. What is the total pounds of rice?
m∠1 =?
m∠2 = ?
m∠3 = ?
Answer:
1= 31 degrees
2= 121 degrees
3= 47 degrees
Step-by-step explanation:
IMPORTANT: SUM OF ALL THREE ANGLES OF A TRIANGLE EQUAL 180
For angle 1 we add 59+90 since those are the 2 known angles
90+59=149
Now subtract by 180
180-149=31
Angle 1 is equal to 31
Now for angle 2 we subtract 59 from 180 since it is on a flat surface the sum of those angles will equal 180 degrees
180-59=121
Angle 2 is 121 degrees
Now for angle 3 we add 121 and 12 since we know those 2 angles
121+12=133
Now subtract from 180
180-133= 47
Angles 3 is 47 degrees
Hopes this helps please mark brainliest
Find the domain and function of the graph
The Domain of the function is given as 2, 6 and 3 ≤ x ≤ 5.
Given that,
A graph of the function is shown, we have to determine the domain of the graph,
The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.
here,
The function is defined on the values of x, as 2, 6 and from 3 to 5,
So the domain of the function is said to be as 2, 6 and 3 ≤ x ≤ 5.
Thus, the Domain of the function is given as 2, 6 and 3 ≤ x ≤ 5.
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An amusement park charges $35.50 for admission. On Saturday 6789 people visited the park. About how much money did the park earn from admission that day?
ESTIMATE PLEASE!!
Which relationship between x and y in the equation shows a proportional relationship? o y=+3 o y y= 12 O y = 2x + 6 o y = 12x
Braelyn is writing an equation to represent the perimeter of a rectangle with the width equal to half the length. she knows that the perimeter is equal to 18 units and needs to find the length and width of the rectangle. which equations represent this relationship? select the four correct answers. x one-half x = 18 2 x x = 18 2 (x) 2 (2 x) = 18 x one-half x x one-half x = 18 2 (x one-half x) = 18 2 x one-half x = 18
The correct options are 2,3,4,5, according to given question.
What do you mean by equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to data in the given question,
We have the given information:
P = 18
w= l/2
Perimeter of a rectangle equals to twice the sum of length and width:
P= 2(l+w)
If we assume width = x, then:
l = 2x
2(x+2x) = 18 or
2x + 4x = 18
If we assume length = x, then:
w = 1/2x
2(x + 1/2x) = 18 or
2x + x = 18
Therefore, the correct options are below:
x + one-half x = 18 === incorrect
2 x + x = 18 === correct
2 (x) + 2 (2 x) = 18 === correct
x + one-half x + x + one-half x = 18 === correct, same as second option
2 (x + one-half x) = 18 === correct, same as second option
2 x + one-half x = 18 === incorrect
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help meeeeeeeeeeeeeee pleaseeeeeee help meeeeeeeeeeeeeee pleaseeeeeee
Answer:
Width = 4.7 m, Length = 6.7 m
Step-by-step explanation:
Let the width be [tex]w[/tex]. Then, the length is [tex]w+2[/tex].
[tex]w(w+2)=32 \\ \\ w^2+2w-32=0 \\ \\ w=\frac{-2 \pm \sqrt{2^2-4(1)(-32)}}{2(1)} \\ \\ w \approx 4.7 (w>0) \\ \\ w+2 \approx 6.7[/tex]
The table shows the temperature (v) at different altitudes (x). This is a linear relationship. Find the y-intercept for this relationship. 0 Altitude (ft), X Temperature (°F). 2,000 61 4,000 53 6,000 45 8,000 10,000 12,000 37 29 21 69 They-Intercept for this relationship is b =
Find the value of 3a + 2b if a = 4 and b = (-9) (*Substitute*)
Question:
Find the value of 3a + 2b if a = 4 and b = (-9) .
Solution:
Let the following expression
[tex]3a\text{ + 2b}[/tex]now, if a = 4 and b = -9, and we substitute them in the previous expression, we obtain:
[tex]3(4)\text{ + 2(-9) = 12 - 18 = -6}[/tex]then, we can conclude that the correct answer is:
[tex]-6[/tex]I need to find the surface area. it's a cut sphere with a diameter of 14.
Given data:
The diameter of the cut sphere, D=14 in.
The radius of the cut sphere is,
[tex]\begin{gathered} r=\frac{D}{2} \\ r=\frac{14}{2} \\ r=7\text{ in} \end{gathered}[/tex]The cut sphere is called a hemisphere.
The surface area of a sphere is
[tex]A_1=4\pi r^2[/tex]So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,
[tex]\begin{gathered} A_2=\frac{4\pi r^2}{2} \\ A_2=2\pi r^2 \end{gathered}[/tex]The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,
[tex]A_3=\pi r^2[/tex]Therefore, the total area of the hemisphere is,
[tex]\begin{gathered} A=A_2+A_3 \\ A=2\text{ }\pi r^2+\pi r^2 \\ A=3\text{ }\pi r^2 \end{gathered}[/tex]The total surface area of a hemisphere is,
[tex]\begin{gathered} A_{}=3\text{ }\pi r^2 \\ A=3\text{ }\pi\times7^2 \\ A=461.8in^2 \end{gathered}[/tex]Therefore, the total surface area of the cut sphere is 461.8 square inches.
Please please please help me and show the steps too I really need to understand this!
Yes I will mark brainliest!
The value of x for the ΔPRT is 7.
As its given in the question that ΔKMN ≅ ΔPRT (congruent)
MN = 20
KN = 25
KM = 15
RT = 3x - 1
Therefore,
MN = RT
KM = PR
KN = PT
So, RT = MN
3x - 1 = 20
3x = 20 + 1
3x = 21
x = 21/7
x = 7
Hence, x = 7.
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Convert form the giving stand and Form of a linear equation to the slope-intercept form of a linear equation x + 5y = 5
The slope-intercept form of a linear equation is given by the expression:
y=mx+b, so in this case you just have to solve the equation for y by inverse operations to solve equations:
x+5y=5
5y=5-x
y=5/5-x/5
y=-1/5x+1
so I am doing Eureka math and 7th grade kinda need help....rewrite the expression by using distributive property and collecting like terms. 2 4/5v - 2/3(4v+1 1/6)
Answer:
2/15v + 7/9
Step-by-step explanation:
We take our base equation, then we will make every mixed number into an improper fraction. This will give us 14/5v - 2/3(4v+ 7/6). Then we will open the parentheses. This gives us: 14/5v - 8/3v+ 14/18. We will bring both the v's to a common denominator, giving us 42/15v - 40/15v+ 14/18. Then we can subtract and simplify. 2/15v + 7/9.
match the correct base shape to each prism. some cards may be used more than once.
Looking at figure A, we have a prism with a triangular base that looks like a right triangle.
Since the prism has a right triangular base, the base shape is a right triangle (shape 5).
Looking at figure B, we have a prism with a pentagonal base.
Since the prism has a pentagonal base, the base shape is a pentagon (shape 1).
Looking at figure C, we have a prism with a triangular base that looks like an equilateral triangle.
Since the prism has an equilateral triangle base, the base shape is an equilateral triangle.(shape 4).
Looking at figure D, we have a prism with a triangular base that looks like an equilateral triangle.
Since the prism has an equilateral triangle base, the base shape is an equilateral triangle.(shape 4).
△I'J'K' is a translation of △IJK. Write the translation rule.
The △IJK is shifted 9 units toward left and then shifted 10 units toward down to get △I'J'K' by applying translation rule.
What is the translation rule?
An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. Slides are a common term used to describe translations. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."
The coordinate of the vertices of △IJK are K(3, 7), I(1,2), J(6, 5).
The coordinate of the vertices of △I'J'K' are K(-6, -3), I(-8, -8), J(-3, -5).
The difference between x-coordinate of △IJK and △I'J'K' corresponding vertices are 3 - (-6) = 1 - (-8) = 6 - (-3) = 9
The difference between y-coordinate of △IJK and △I'J'K' corresponding vertices are 7 - (-3) = 2 - (-8) = 5 - (-5) = 10.
Thus △IJK is shifted 9 units toward left and then shifted 10 units toward down to get △I'J'K'.
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Write a quadratic equation in standard form whose graph passes through the given points (1,2) (2,-1) (3,-6)
we have
Write a quadratic equation in standard form whose graph passes through the given points (1,2) (2,-1) (3,-6)
A quadratic equation in standard form is equal to
y=Ax^2+Bx+C
substitute the given values
(1,2)
2=A(1^2)+B(1)+C
2=A+B+C ------> equation 1
(2,-1)
-1=A(2^2)+B(2)+C
-1=4A+2B+C -------> equation 2
(3,-6)
-6=A(3^2)+B(3)+C
-6=9A+3B+C -------> equation 3
step 1
In the equation 1 isolate the variable A
A=2-B-C -------> equation 4
step 2
substitute equation 4 in equation 2 and 3
-1=4(2-B-C)+2B+C
-1=8-4B-4C+2B+C
-1=8-2B-3C
2B+3C=
What is the vertical change from Point A to Point B?
What is the horizontal change from Point A to Point B?
What is the rate of change shown on the graph? Give
the answer as a decimal rounded to the nearest tenth, if
necessary
The vertical change from point A to point B is 1. The horizontal change from point A to point B is 2. The rate of change in the graph is 0.5.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
As per the given,
Point A translate to point B on a straight line.
The Coordinate of point A is (2,1).
The Coordinate of point B is (4,2).
Vertical change = 2 - 1 = 1
Horizontal change = 4 - 2 = 2
Slope = vertical change / horizontal change
Slope = 1/2 = 0.5
Hence "The vertical change from point A to point B is 1. The horizontal change from point A to point B is 2. The rate of change in the graph is 0.5".
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A fruit juice owner has three types of juices. 320 liters of the first kind, 350 liters of the second kind, 400 liters of the third kind. How many bags with the amount of each juice will he be able to do?
Three types of juice means 3!
that is ., 3*2*1 =6
He will be able to fill 6 bags with the specified amount of each juice.
In mathematics, the term "factorial" refers to the sum of all positive integers that are less than or equal to a certain positive integer, which is followed by an exclamation point.
What is a factorial problem?In a factorial, you multiply the supplied integer by all of the positive whole numbers that are less than it. To put it another way, = n (n 1) ... 2 1.The mathematical operation known as a factorial, denoted by the symbol (! ), multiplies a number (n) by each number that comes before it. The factorial function instructs you to multiply all the whole numbers starting at the selected number and going all the way down to one. In further mathematical terms, a number's factorial (n!) equals n (n-1).When a group of variables are independent happenings, a factorial distribution occurs. In other words, there is no interaction between the variables; for two events, x and y, the probability of x remains constant when y is taken into account. Therefore,To learn more about factorial refer to:
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer: 2 =
27⁰
111°
answer x=
The measure of angle of a triangle x is 42°.
According to the question,
We have the following information:
In a triangle, the measurements of two of its angles are 27° and 111°.
We know that the sum of three angles of a triangle is 180°.
So, we have the following expression to find the value of x:
27+111+x = 180
Adding the numbers on the left hand side:
(Note that the variable can not be added to any integer. It can only be added to the same variable.)
138+x = 180
Subtracting 138 from both the sides:
x = 180-138
x = 42°
Hence, the value of x for the given triangle is 42°.
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graph the circle which is centered at (-5,1) and which has a point (-2,-3) on it
We can start by placing the center at (-5,1).
The radius of the circle will be the distance between the center and the point (-2,-3).
If we graph this two points, we can use an angle protractor to draw the circle passing through point P(-2,-3) and centered at (C(-5,1):
Solve four-sixths minus three-twelfths equals blank. Solve five-sixths minus three-fourths equals blank. Solve five-ninths minus two-sixths equals blank. Solve nine-twelfths minus eleven-eighteenths equals blank. Solve four-ninths minus four-tenths equals blank. Solve six-sevenths minus five-fourteenths equals blank.
Solve two-fifths minus one-seventh equals blank. Solve four-sixths minus three-fifths equals blank. Solve four-sixths minus three-eighths equals blank. Solve seven-eighths minus nine-sixteenths equals blank. Please solve all 10 questions no explanation needed but you can add one if you want
Answer:
Step-by-step explanation:
first you need to make sure that the fractions you are adding and subtracting have like denominators. To do this you need to find the least common multiple between the two
1. 4/6 - 3/12= 8/12 - 3/12 Answer: 5/12
2. 5/6 - 3/4 = 10/12 - 9/12 Answer: 1/12
3. 5/9 - 2/6= 10/18 - 6/18 Answer 4/ 18 (reduces to 2/9 for simplest terms)
4. 9/12 - 11/18 = 27/36 - 22/36 Answer: 5/36
5. 4/9 - 4/10 = 40/90 - 36/90= 4/90 ( reduces to 2/45)
6. 6/7 - 5/14= 12/14-5/14 Answer 7/14 (reduces to 1/2
7. 2/5- 1/7= 14/35 - 5/35 Answer 8/35
8. 4/6 - 3/5 = 20/30 - 18/30 Answer 2/30 (1/15 simplified
Two planes, which are 2660 miles apart, fly toward each other. Their speeds differ by 65mph. If they pass each other in 4 hours, what is the speed of each?
EXPLANATION
Since the two planes are 3400 miles apart, and their speed differs by 80 mph, we can apply the following relationship:
2660 / 4 = 665 mph
Assuming that x is the speed of the slower plane and y is the speed of the faster, we have:
(1) x + 65 = y
(2) x + y = 665 [Combined speed of both planes]
Plugging in (1) in (2):
x + (x + 65) = 665
Removing the parentheses:
x + x + 65 = 665
Adding like terms:
2x + 65 = 665
Subtracting -50 to both sides:
2x = 665 - 65
Subtracting numbers:
2x = 600
Dividing both sides by 2:
x = 300
Plugging in x=315 into (1):
300 + 65 = 365
In conclusion, the speed of both planes is:
Slower plane = 300 mph
Fastest plane = 365 mph
The scale along each als is 1.State the interval where f (2)
We have the following:
replacing:
[tex]\begin{gathered} f(2)The answer is the interval (-6, 9)Raymond invested $4, 000 in a new company. The value of his investment has been growing at a rate of 6% per year for the last 5 vears. Write a function to represent the growth of his investment of $4,000, where A is the total value of his investment and t is the time invested in years. What is the total value of his investment after 5 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000\left(1+\frac{0.06}{1}\right)^{1\cdot 5} \implies A=4000(1.06)^5\implies A \approx 5352.90[/tex]
now, we're assuming is a 6% growth of the current amount per year, namely compounded, as opposed to simple interest.