(6 1/7 divided by x + 3 5/9) / 4 1/6 = 1 1/3 what is x
Answers
let's firstly convert the mixed fractions to improper fractions and them proceed.
\(\stackrel{mixed}{6\frac{1}{7}}\implies \cfrac{6\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{43}{7}} ~\hfill \stackrel{mixed}{3\frac{5}{9}}\implies \cfrac{3\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{32}{9}} \\\\\\ \stackrel{mixed}{4\frac{1}{6}}\implies \cfrac{4\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{25}{6}} ~\hfill \stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\)
\(\cfrac{ ~~ \frac{6\frac{1}{7}}{x}+3\frac{5}{9} ~~ }{4\frac{1}{6}}~~ = ~~1\frac{1}{3}\implies \cfrac{ ~~ \frac{ ~~ \frac{43}{7} ~~ }{x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}\implies \cfrac{ ~~ \frac{43}{7x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}\)
\(\cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{25}{6}\cdot \cfrac{4}{3}\implies \cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{50}{9}\implies \cfrac{43}{7x}~~ = ~~\cfrac{50}{9}-\cfrac{32}{9} \\\\\\ \cfrac{43}{7x}~~ = ~~\cfrac{18}{9}\implies \cfrac{43}{7x}=2\implies 43=14x\implies \cfrac{43}{14}=x\implies 3\frac{1}{14}=x\)
Related Questions
7.1 The data in the table below represent the distance (in km) that the learners from Exhibition High School walked to school the morning before a Mathematical Literacy test and the marks (out of 50) that they obtained for the test. Use the data below to answer the questions that follow. TABLE 2: Distance (in km) travelled by learners 0,2 0,75 2,4 3 3,2 0,5 1,3 1,5 1,4 0,8 TABLE 3: Marks obtained for the test 49 34 20 15 18 38 29 28 25 30 0,3 3 0,2 0,75 0,3 37 19 43 38 39 7.1.1 Identify the SECOND shortest distance walked by a learner. 7.1.2 Determine the highest mark scored by a learner. 7.1.4 Determine the median of the test marks. 1,2 1,2 0,8 0,5 1 7.1.3 Name ONE data collection instrument used to collect this data. 7.1.5 Determine the mode of the test marks. 30 27 33 40 28 7.1.6 Calculate the mean mark for this test. 0,25 1,8 2,6 1,2 1,8 39 25 41 30 28 (2) (3) (2) 7.1.7 Is the data in the table regarding the distance travelled by learners an example of continuous or descrete data? (2) [16]
Answers
The median of the test marks is 28.5.
What is median of data?The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. For a small data set, you first count the number of data points (n) and arrange the data points in increasing order.
Marks obtained for the test 49 34 20 15 18 38 29 28 25 30.
15, 18, 20, 25, 28, 29, 30, 34, 38, 49
The highest mark scored by a learner is 49
The median of the test marks is (28+29)/2
= 28.5
Therefore, the median of the test marks is 28.5.
Learn more about the median here:
https://brainly.com/question/28060453.
#SPJ1
A .Write an equation for the trend line in slope -intercept form .
Answers
Given:
The graph of a trend line.
To find:
The equation of the trend line is slope intercept form.
Solution:
From the given graph it is clear that the equation of the trend line is passes through the points (0,25) and (5,50).
Slope of the line is:
\(m=\dfrac{y_2-y_1}{x_2-x_1}\)
\(m=\dfrac{50-25}{5-0}\)
\(m=\dfrac{25}{5}\)
\(m=5\)
The line passes through the point (0,25). So, the y-intercept of the line is 25.
Slope intercept form of a line is:
\(y=mx+b\)
Where, m is slope and b is y-intercept.
The slope intercept from of the line is:
\(y=(5)x+(25)\)
\(y=5x+25\)
Therefore, the equation for the trend line in slope -intercept form is \(y=5x+25\).
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
352, 345, 338, ...
Find the 37th term.
Answers
Answer:
09
Step-by-step explanation:
Six customers are buying gasoline at Miguel's Gasoline Station. The number of gallons bought and the total cost of their purchases are plotted on the graph below.
What is the price per gallon at Miguel's Gasoline Station?
Responses
$2.50
Answers
Based on the line on the graph, the price per gallon at Miguel's Gasoline Station is equal to: B. $2.50
How to calculate the price per gallon?In order to calculate the price per gallon at Miguel's Gasoline Station, we would have to determine the slope of the line representing the number of gallons bought and the total cost of their purchases are plotted on the graph below (see attachment).
Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
By critically observing the graph (see attachment), we can logically deduce that the line passes through the following points:
Points (x, y) = (4, 10)Points (x, y) = (8, 20)Substituting the given parameters into the formula, we have;
Slope, m = (20 - 10)/(8 - 4)
Slope, m = 10/4
Slope, m = 2.5
Read more on slope here: brainly.com/question/3493733
#SPJ1
Dean Wormer wants to compare the grade point average of athletes at Faber College with the overall grade point average at Faber College. She randomly selects three students from each team and determines that their combined grade point average, 2. 3, is the same as that of all students at Faber. In this example, what is the population
Answers
yes it is the same as that of all students at Faber GPAs as 2.32 and lower will mean that a track team athlete will be recommended for extra tutoring and population is 2.3* student number
What is the definition of a population?
In ordinary usage, a population is a distinct group of individuals with shared citizenship, identity, or characteristics. In statistics, a population is a representative sample of a larger group of people (or even things) with one or more characteristics in common.
When the distribution is normal, we use the z-score formula.
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
learn more about of population here
https://brainly.com/question/17045760
#SPJ4
consider a little league team that has 13 players on its roster. a. how many ways are there to select 9 players for the starting lineup? b. how many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters? c. suppose 6 of the 13 players are left-handed. how many ways are there to select 3 left-handed outfielders and have all other 6 positions occupied by right-handed players?
Answers
There are 715 ways to select 9 players for the starting lineup.
Permutation is used whenever there is arrangement or where order is important . denoted by \(P(n,r)=\frac{n!}{(n-r)!}\)
n= no of item , r = no of items to be arranged.
Combination is used when there is selection . denoted by\(C(n,r)=\frac{n!}{r!(n-r)!}\)
n=no of item , r= no of item to be selected.
Part (a)
In the given question
we have to select 9 players out of 13 player , combination will be used
\(C(13,9)=\frac{13!}{9!*(13-9)!}=\frac{13*12*11*10*9!}{9!*4!} =\frac{13*12*11*10}{4*3*2}\)=715 ways.
Part(b)
In this part we have to find how many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters.
Since the batting order is important , permutation will be used.
\(P(13,9)=\frac{13!}{4!} =\frac{13*12*11*10*9*8*7*6*5*4!}{4!} =13*12*11*10*9*8*7*6*5\)
=259459200 ways.
Part(c)
In this part we have to do selection of 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.
Since order is not important Combination will be used.
To select 3 left handers from total 6 left handers = C(6,3)
& to select 6 positions of left handers from remaining 7 right handers=C(7,6)
No of ways of selection = C(6,3)*C(7,6)
\(=\frac{6!}{3!*(6-3)!} *\frac{7!}{6!*(7-6)!} \\ \\= \frac{6!}{3!*3!} *\frac{7!}{6!*1!} \\ \\\)
On solving further we get
\(= \frac{7!}{3!*3!} =\frac{7*6*5*4*3!}{3!*3*2*1} =7*5*4=140ways\)
Therefore ,(a)There are 715 ways to select 9 players for the starting lineup.
(b) there are 259459200 ways to to select 9 players for the starting lineup and a batting order for the 9 starters and 140 ways .
(c)there are 140 ways to select 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.
Learn more about Permutation& Combination here https://brainly.com/question/13480867
#SPJ4
what is the coordinate system that is an extension of the terrestrial coordinate system on the celestial sphere
Answers
The coordinate system that is an extension of the terrestrial coordinate system on the celestial sphere is called the celestial coordinate system.
The coordinate system that is an extension of the terrestrial coordinate system onto the celestial sphere is known as the celestial coordinate system.
The celestial coordinate system is used to locate and describe objects in the sky, such as stars, planets, and other celestial bodies.
Similar to the terrestrial coordinate system, the celestial coordinate system utilizes a set of coordinates to specify the position of an object. However, due to the spherical nature of the celestial sphere, the celestial coordinate system has some differences.
In the celestial coordinate system, the celestial sphere is divided into two main components: the celestial equator and the celestial poles.
The celestial equator is an imaginary circle that represents the projection of the Earth's equator onto the celestial sphere. It divides the celestial sphere into the northern and southern celestial hemispheres.
To specify the position of an object in the celestial coordinate system, two primary coordinates are used:
declination (DEC) and right ascension (RA).
Declination is similar to latitude and measures the angular distance of an object north or south of the celestial equator, while right ascension is similar to longitude and measures the angular distance of an object eastward from a reference point known as the vernal equinox.
With the celestial coordinate system, astronomers and stargazers can precisely locate and track celestial objects across the sky, enabling them to study and explore the vastness of the universe.
For similar question on coordinate system.
https://brainly.com/question/25072940
#SPJ11
A company made 700000 profit last year. It says this was 12percent more than the year before. What was the profit made the year before
Answers
Answer:
784000
Step-by-step explanation:
Given data
Profit = 700000
Let us begin by finding what 12% of 700000 is
=12/100* 700000
=0.12* 700000
=84000
Hence the profit made last years was
=84000+700000
=784000
A sign made of aluminum is in the shape of a pyramid. The base is a triangle with a base of 3 feet and a height of 5 feet. The height of the sign is 6 feet. The aluminum costs $8 per cubic foot. What is the cost of the sign?
A) $722
B) $240
C) $120
D) $168
Answers
The cost of the pyramid shape sign is $240.
What is a pyramid?A pyramid is a 3D figure that has a base made of a polygon and faces that are all triangular and connected. The conventional shape of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this section, let's study more about pyramids.
We know the volume of a pyramid is (1/3)×length of the bese×width of the base×height.
∴ The volume of the pyramid with base length of 6feet, base width of 3feet and height 5 feet is,
= (1/3)×6×3×5 cubic feet.
= 30 cubic feet.
Given, The aluminum costs $8 per cubic foot.
∴ The total cost of the pyramid is = (30×8) = $240.
learn more about pyramids here :
https://brainly.com/question/17615619
#SPJ1
two sides of a triangle measure 18 and 13 meters which measure could represent the perimeter of the triangle
Answers
Therefore, when the triangle's perimeter is 38 meters and its two sides are 18 meters and 13 meters, respectively, the opposite side of the perimeter is 7 meters.
what is perimeter ?An isolated path that surrounding, delimits, or embraces a two-dimensional shape or a single-dimension length sometimes referred to as the boundary. The perimeter of either an ellipse or circle refers itself to outermost area. The perimeter measurement has many legitimate applications. This perimeter of a form is its edge's circumference. Discover how to determine the perimeter by adding the lengths of such sides of various forms. Your can always find the perimeter of a polygon by multiplying its multiplicative inverse. The perimeter of an object is the space it around. At your house, a contained garden is one illustration. The perimeter of anything is the area encircling it. For a 50 feet x 50 feet yard, a 200 foot fence is required.
given
The distance surrounding a closed-plane figure is its perimeter, or P.
P is equal to a plus b plus c, where a, b, and c are the lengths of the three sides, and let c be the third side's undetermined length.
P = 38 m, a = 13 m, and b = 18 m are the values provided. Now, to determine the third side's length c,
P = a + b + c
38m = 13m, 18m, and c
38 m = 31 m + c
38 m minus 31 m Equals 31 m minus 31 m plus c
7 m = 0 + c
7 m = c
Therefore, when the triangle's perimeter is 38 meters and its two sides are 18 meters and 13 meters, respectively, the opposite side of the perimeter is 7 meters.
To know more about perimeter visit:
https://brainly.com/question/6465134
#SPJ1
According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year? (Round your answer to 4 decimal places.)
Answers
Answer:
0.471
Step-by-step explanation:
Calculation for the probability that they spend less than $2,000 per year on insurance per year
First step is to find the base
Base =$2,000-$400
=$1,600
Second step is to find the probability using this formula
P=1/b+a×base
Where,
b represents $3,800
a represents $400
base represents $1,600
Let plug in the formula
P=1/$3,800-$400×$1,600
Hence,
P=1×$1,600/$3,800-$400
P=$1,600/$3,400
P=0.471
Therefore the probability that they spend less than $2,000 per year on insurance per year will be 0.471
You deposit $200 in an account that earns simple interest at an annual rate of
6.5%. How much money is in the account after 3 years?
show work pleaseeee
Answers
Interest = Principal x Rate x Time
where:
Principal is the amount of money deposited
Rate is the annual interest rate (as a decimal)
Time is the length of time (in years) the money is invested
In this case, the principal is $200, the rate is 6.5% per year (or 0.065 as a decimal), and the time is 3 years. Plugging these values into the formula, we get:
Interest = $200 x 0.065 x 3 = $39
So the interest earned over 3 years is $39. To find the total amount of money in the account after 3 years, we add the interest to the principal:
Total amount = Principal + Interest = $200 + $39 = $239
Therefore, there will be $239 in the account after 3 years.
tom goes on hoilday south africa
Answers
Answer:
Yes, good for him. lol
Step-by-step explanation:
Answer:
what he do there?
suppose a research report states that the result of a between subjects one-way anova is f (3, 32) = 3.47 should the researcher reject the null hypothesis if using alpha = .05
Answers
Based on the given information, the researcher should not reject the null hypothesis if using an alpha level of 0.05.
In hypothesis testing, the null hypothesis is typically assumed to be true until there is sufficient evidence to reject it. To determine whether to reject the null hypothesis, researchers often compare the calculated F-value from an ANOVA test with the critical F-value. The critical F-value is based on the significance level (alpha) chosen for the test. In this case, the given F-value is 3.47 with degrees of freedom (3, 32), indicating that there are three groups and a total of 32 observations. To make a decision, the researcher needs to compare the calculated F-value to the critical F-value. If the calculated F-value is greater than the critical F-value, the null hypothesis is rejected. However, if the calculated F-value is less than or equal to the critical F-value, the null hypothesis is not rejected. Since the critical F-value corresponding to alpha = 0.05 is not provided in the question, we cannot determine whether the null hypothesis should be rejected.
Learn more about ANOVA test here: https://brainly.com/question/30457832
#SPJ11
A recipe for 24 cookies calls for 4 tablespoons of sugar. If you make 40 cookies and use 5 tablespoons, will the cookies taste the same? Explain
Answers
Answer:
Step-by-step explanation:
No, because they wouldn't contain the same amount of sugar per cookie
for the first recipe - 24 cookies with 6 tablespoons
thats 6/24 so 0.25 tablespoons of sugar per cookie
for the second recipe - 36 cookies with 10 tablespoons
thats 10/36 so 0.276 tablespoons per cookie
the cookies in the second recipe would be slightly sweeter than the cookies in the first
The 24cookies per 4 sugar tbsps calls for 1 tbsp for every 6 cookies. This makes the ratio 6:1.
If u divide 40/5, you will get a ratio of 8:1. This means 1 tbsp of sugar in every 8 cookies. Making the cookies less sugary
i can’t fail please help
Answers
Hey there!
The answer is 6:54
The time on the clock shows 6:20, because the hour hand is after the 6, and the minute hand is on the 4 (which we multiply by 5 to get the minutes).
If it takes her 8 minutes to walk to the bus, 10 to pack lunch, and 16 to get dressed, that's a total of 8 + 10 + 16 minutes, or 34 minutes.
So, we add that to the minutes, so 20 + 34 = 54, therefore the time is 6:54 when she arrives.
Have a terrificly amazing day! :)
Answer:
Yanice should get up at 5:43 to be on time for the bus.
The football players get ready to go to class at 8:17 A.M.
Gymnastics is 50 minutes longer than the piano lessons.
Hope this helps ;)
A scientist needs 0.25 kilograms of a substance to conduct some experiments. The substance can only be purchased in milligrams. Which of the following amounts of the substance should the scientist order? 250,000 milligram 0.00025 milligrams 0.00000025 milligrams 250 milligrams
Answers
There are thing we must already know:
\(\begin{gathered} 1\text{kilogram}=1,000\text{gram} \\ 1\text{gram}=1,000milligram \end{gathered}\)From this, we must know that:
\(1\text{kilogram}=1,000,000\text{milligram}\)The scientis needs 0.25kilograms. From this we calculate:
\(0.25\text{kilograms}=0.25\times1000000milligrams=250,000milligrams\)find the function inverse g(x) = 4 − 32x
Answers
Answer:
The inverse operation is multiplication
Step-by-step explanation:
a circle of a certain radius has the property that if an angle has its vertex at the center of the circle, the area it subtends is numerically the same as the arc length. find the radius of the circle.
Answers
An angle has its vertex at the center of the circle the area it subtended is numerically the same as the arc length. Therefore, the radius of the circle is 1 radian, or 57.29 degrees.
Let's consider a circle having radius as r units.
The circumference subtends an angle of 360° or 2π radians at the center.
Now, take the ratio.
Here, x is the unknown angle subtends by the arc of length equal to radius.
2πr ÷ r
= 2π÷x
⇒ x =1 radian.
Or in degrees
2πr ÷ r
=360°÷x
x= 360°÷2π
= 360° ÷ 6.28
= 57.29 degrees.
Therefore, the radius is 57.29 degrees or 1 radian.
Learn more about Angle:
https://brainly.ph/question/25593501
#SPJ4
Using the midpoint method, the absolute value of the (price) elasticity of demand calculated for a change in price between $10 and $2 is
Group of answer choices
A < 1
B 1
C > 1
Answers
The price elasticity of demand measured using midpoint method, for a price change between $10 and $2 can be determined as follows:Price elasticity of demand (mid-point method) = [ΔQ / {(Q1 + Q2)/2}] ÷ [ΔP / {(P1 + P2)/2}]Given that P1 = $10, P2 = $2, Q1 = Q2, and the price has decreased from $10 to $2.
Therefore, the midpoint price (P) = (P1 + P2) / 2 = ($10 + $2) / 2 = $6The midpoint quantity (Q) = (Q1 + Q2) / 2 = Q1 / 2 + Q2 / 2 = Q / 2 + Q / 2 = Q.ΔP = $2 − $10 = −$8ΔQ = Q − Q = 0Hence, the absolute value of the price elasticity of demand using the midpoint method for a change in price from $10 to $2 is :Price elasticity of demand (mid-point method) = [ΔQ / {(Q1 + Q2)/2}] ÷ [ΔP / {(P1 + P2)/2}]E = [0 / {Q / 2}] ÷ [−8 / $6]E = 0 ÷ −1.3333E = 0
So, the correct answer is option B: 1.
To know more about elasticity visit:
https://brainly.com/question/30999432
#SPJ11
(5a-ab) (2ay-by)
\( {2}^2( {2}^{4 - ?}5 {} ){?} \)
Answers
Answer:
a = 0
b = 5
y = 0
Step-by-step explanation:
it's all on the picture please answer
Answers
Answer:
60 units squared
Step-by-step explanation:
use for mula A= bh/2
15*8=120
120/2= 60
A=60
Answer:
60
Step-by-step explanation:
area of triangle = (base x height) : 2
base = 15
Height = 8
= ( 15 x 8 ) : 2
= 120 : 2
= 60
([1 + 7)^2]^2 x (12^2)^0
Answers
Answer:
64
Step-by-step explanation:
5 estrells
Evaluate the expression for s= -1 and t = 9.
-st
Answers
Answer:
9
Step-by-step explanation:
s= -1 t= 9
-(-1) * 9 = 1 * 9= 9
two negatives multiplied is a positive
2 times the radius equals the....
Answers
Answer:
diameter
Step-by-step explanation:
double the radius is the diameter
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.
Answers
Answer:
(6x+1)^2
Step-by-step explanation:
Factor using the perfect square rule.
Properties of equilateral triangles…………………….
Answers
Answer:
20.
Step-by-step explanation:
All sides and angles are the same length on equilateral triangles.
All sides will be 20u long and all angles will be 60° each.
8
To rent a car, Jorge spent $415 in rental
fees plus $86 for insurance. He also paid
$2 per day for tolls, plus $5 per day for
roadside assistance. Jorge rented the car
for a total of 12 days.
Based on the expression below, what is
the total amount of money that Jorge
spent? (6.7A | Lesson 5)
1
415 +86 + 12(2 + 5)
Answers
Find the quotient.
(12x2 - 10x-12) = (3x + 2)
Answers
PLEASE ANSWER I MARK AS BRAINLIST ❗️❕❗️PLEASE
Answers
Answer:
D and E
Hope this help for you
Red