The value of x in the equation (x - 2)/3 + 1/6 = 5/6 is: x = 4
How to Solve an Equation?To solve a given equation, find the value of the variable in the equation by isolating the variable to one side using the necessary properties of equality.
Given the equation, (x - 2)/3 + 1/6 = 5/6:
(x - 2)/3 + 1/6 = 5/6
Subtract both sides by 1/6:
(x - 2)/3 + 1/6 - 1/6 = 5/6 - 1/6 (subtraction property of equality)
(x - 2)/3 = 4/6
Multiply both sides by 3:
(x - 2)/3 × 3 = 4/6 × 3 (multiplication property of equality)
x - 2 = 2
Add both sides by 2:
x - 2 + 2 = 2 + 2 (addition property of equality)
x = 4
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8- 2 (2p-6) = 52-2 ( 1 + 7n ) -5n = -78
usLet u s fully expand the first equation
8 - 4p + 12 =52
simpliying gives
20-4p=52
subtracting 20 from both sides gives
-4p = 32
and finally, dividing both sides by -4 gives
p = 8
For the second equation, expanding LHS gives
-2 - 14
I am trying to make a study guide and I need an explanation on this answer please
Given:
A movies rent for $3.00 except on tuesday, the rent is $0.49.
The cost saved by renting a movie on a Tuesday is,
[tex]\frac{3-0.49}{3}=\frac{2.51}{3}=0.8367[/tex]The percentage is,
[tex]\begin{gathered} 0.8367\times100=83.67\text{ \%}\approx84\text{ \%} \\ \end{gathered}[/tex]Answer: option B)
36. The histogram shows the ages of the first 45 U.S. presidents on their firstInauguration Day.13TFrequency12111098765432104075Age (years)The ages of 20 of the 45 presidents are shown below.42, 43, 45, 46, 49, 52, 53, 54, 54, 57, 57, 58, 59, 61, 62, 62, 66, 66, 69, 72A certain president's age is in the interval labeled T.What could be the acceptable range for the interval?42 to 4443 to 4945 to 4947 to 54
Note that the graph shows us that the minimum and maximum value of the ages are 40 and 75, respectively.
We can count the number of bars on the histogram. We see that the are 7 bars in total.
Each bar consider the same age span, so that means that each bar represent an age span of the same amount of years.
To calculate this range, we first find the difference between the maximum and the minimum, that is
[tex]75-40=35[/tex]Now, we divide this number by the total number of bars. That is
[tex]\frac{35}{7}=5[/tex]So, each bar represents a range of 5 years .
Since the minimu is 40, this means that the first bar should represent ages from 40-44. Note that despite the difference between 44 and 40 is only 4, since we are including age 40 in the first bar, we have numbers 40,41,42,43,44 (5 numbers ) associated to the first bar.
This means that for the next one, which is the range T we are looking for, the correspondent age range should be 45-49
I need help please it’s hard (please explain it well)
Solution:
Given a right right rectangular prism with made of of unit cubes
Note that A unit cube has 6 square faces with each side 1 unit long
Volume of a unit cube = 1 x 1 x 1 = 1 cubic unit
Total unit cubes present = 60 unit cubes.
To find the volume of the prism by whole unit cube:
The volume of the prism with the whole unit cube = volume of 1 unit cube x 60 = 1 x 60 = 60 cubic units
To find the volume with 1/2 unit cube:
If the divide each of the 60 units cubes into half, we will have a total of 120 half unit cubes
Volume of a half unit cube = (Volume of a unit cube) / 2
= 1/2 = 1/2 cubic unit
Thus, The volume of the prism with the half unit cubes = 120 x volume of a half unit cube
= 120 x 1/2 = 60 cubic units
In conclusion, the difference between finding the volume of the prism by whole unit cubes and 1/2 unit cubes is that the that the volume of each 1/2 unit cube will be multiplied by 120 while that of each whole unit cube will be multiplied by 60
One integer is 8 less than another integer. The product of the lesser integer and -5 is 28 more than the greater integer. What are the integers?
Let the lesser integer be "x".
So, the greater integer will be "x + 8".
Given,
Product of lesser and "-5" is 28 MORE THAN greater.
We can write the equation as:
[tex]x\times-5=(x+8)+28[/tex]We can simplify this equation and solve for x. The steps are shown below:
[tex]\begin{gathered} x\times-5=(x+8)+28 \\ -5x=x+36 \\ -5x-x=36 \\ -6x=36 \\ x=\frac{36}{-6} \\ x=-6 \end{gathered}[/tex]Less integer (x) is -6, and
Greater integer (x+8) is -6 + 8 = 2
Answer
-6 and 2
Write and solve an equation to answer the question. A truck rental is $20 plus $.30/mi. Find out how many miles Ken traveled if his bill was $41.30. Ken traveled_____ miles.
As given by the question
There are given that the truck rent is $20 plus $0.30 per mile.
Now,
The equation of the given statement is shown below:
[tex]20+0.30x=41.30[/tex]Then,
From the given equation, solve for the value of x
So,
[tex]undefined[/tex]The following this gives the number a pet for each of 12 students find the moods of this data set if there is more than one mode right them separated by commas if there is no mold click on low mode
Explanation
In the question, we are given the number of pets for 12 students below.
[tex]0,3,1,0,4,3,1,3,2,1,4,0[/tex]The mode of a set of values is the number that occurs the most in the data set. Based on this definition, we can go through the data set and pick the number that represents the above concept.
From the above, we can see that three numbers embodies the definition of a mode. Therefore the mode of the data set is
Answer
[tex]\text{Mode = 0,1,3}[/tex]what causes an eathquake
Earthquakes are caused by human activity, like tunnel construction, filling reservoirs that leads to a sudden release of stress along faults in the earth's crust.
What causes an Earthquake?
An earthquake is caused as a result of a sudden slip on a fault in the earths outermost layer.
The genesis of this discussion is that the tectonic plates are usually moving slowly. However, these tectonic plates may get stuck at their edges as a result of undergoing friction. Now, after the stress on the edge overcomes the friction, there would be an earthquake that would release energy in form of waves travelling through the earth's crust that leads to the shaking of the earths surface that humans experience in an earthquake.
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the American Cancer Society do the fundraiser at Allegany State Park that involved a rowing race on Red House Lake . there were 25 boats entered fee in the fundraiser took in 7500 in entry fees.how much was the entry fee for each row
Given the number of boats = 25
There are 12 rowers in each boat
So, the total number of rowers = 25 x 12 = 300
The total fundraiser = $7500
So, to find the entry fee for each rower, divide 7500 by 300
so, the entry fee =
[tex]\frac{7500}{300}=\frac{75}{3}=25[/tex]so, the answer will be $25
What is the value of the expression 8w-5x when w= 4 and x = 2
The value is 22
Explanation:Given:
[tex]8w\text{ - 5x}[/tex]To find:
the value of the expression when w = 4 and x = 2
To determine the value, we will substitute the values for x respectively and w :
[tex]\begin{gathered} =8(4)\text{ - 5\lparen2\rparen} \\ \\ =\text{ 32 - 10} \\ \\ =\text{ 22} \end{gathered}[/tex]I will show you the pic
Problem:
Solution:
Remember that the slope-intercept form of the line is given by the formula
y = mx+b
where m is the slope of the line, and b is the y-intercept of the line (when x = 0). Now, let the following equation:
-4x+2y= 8
to rewrite it in the form slope-intercept form (y = mx+b), then we should solve the given equation for y, that is:
2y = 4x +8
If we divide by two we obtain the equivalent:
y = 2x + 4
then 2 is the slope of the line and (0,4) is the y-intercept. Then, we can conclude that the graph of this line is:
The question is on the paper, please help
The distribution is normal with u=0.261 and u= 0.034, hence N(0.261, 0.034).
a) Draw a normal density curve for the batting average distribution. The typical derivation of the mean uses label points 1, 2, and 3.
b) Average above 0.329 are
100% - 95% = 5%
B/C its symmetric, 5%/2= 2.5%
c) The batting averages between 0.227 and 0.295 are 68%
Alternative method,
The normal distribution is used to determine that X% of players are in danger.
What is the Normal Distribution of Probabilities?The z-score formula can be used to resolve issues related to normal distributions.
The Z-score quantifies the deviation of the statistic from the mean in standard deviations. The p-value for this Z-score is then located by consulting the z-score table after the Z-score has been determined. The risk that the measure's value is below X, or the percentile of X, is given by this p-value. The likelihood that the value of the measure is higher than X is obtained by deducting 1 from the p-value.
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3 x ³-8x -x + 4 = x-1 using long division
Answer:
use followimg steps to your answer
What/punch/is the strongest? All ratios listed below are juice concentrate to water. Show
vour work.
A. 2:3?
B. 6:7?
C. 5:7?
D. 10:15?
Answer: Your answer will be D.
The greatest common factor of 60 and 100
1. Mark earned $8.75 an hour plus an additional
$200 in tips working at a restaurant. He earned
more than $506.25 this week. How many hours
could he have worked this week?
What is the slop intercept for (-1,0) and (4,-5)
The slope intercept form of the line for (-1,0) and (4,-5) is y = -x -1.
We know that,
Slope intercept form of a line is given by:-
y = mx + c
Where,
m is the slope of the line,
c is the y -intercept of the line and,
(x,y) is the ordered pair of each point on the line
We know that,
m = (-5-(-1))/(4 - 0) = (-5 +1)/4 = -4/4 = -1
Putting (-1,0) in the line, we get
0 = (-1)*(-1) + c
0 = 1 + c
c = -1
Hence, the equation of the line is given by:-
y = -1x -1 = -x - 1
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67 km 230 m + 11 km 879 m
Answer:
79.10900 kilometers
Step-by-step explanation:
Answer:
79 kilometers 109 meters
f(x) = a(x - h)² + k.
f(x) = 3x² + 6x + 2.
Answer:
f(x) = 3(x + 1)² - 1a = 3, h = - 1, k = - 1
Step-by-step explanation:
It is assumed you need to convert the given function into vertex form.
Converting in below steps:
f(x) = 3x² + 6x + 2 = 3(x² + 2x) + 2 = 3(x² + 2x + 1) - 3 + 2 = 3(x + 1)² - 1We got:
a = 3, h = - 1, k = - 1Solution:17.Graph each system and determine the number of solutions that it has. If it has one solution,name it.A. X +2y=4y= -1/2x+2B. 2x-y=1y=-3
Systems of Equations
Given the system:
[tex]\begin{gathered} x+2y=4 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]It's required to graph and find the solutions of the system.
Solving the first equation for y:
[tex]\begin{gathered} 2y=-x+4 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]We can see both equations are exactly the same, so there is only one equation and one line.
Let's give x some values and graph the line.
x = 0:
[tex]\begin{gathered} y=-\frac{1}{2}\cdot0+2 \\ y=2 \end{gathered}[/tex]x = 2
[tex]\begin{gathered} y=-\frac{1}{2}\cdot2+2 \\ y=1 \end{gathered}[/tex]With the points (0, 2) and (2, 1) we graph the line as follows.
Since the number of equations is greater than the number of unknowns, the system has infinitely many solutions. For example, (0, 2) and (2, 1) are solutions for the system.
2A tennis team bought 8 yards of red fabric to make head bands. If each head band takes į of a yard of fabric, howmany head bands can the team make?You would useto solve this problemThe tennis team can make head bands.
headbandThe illustration of the question is shown below
Since a length of 8 yards of the fabric is bought
Using j to represent the number of the head band
To determine the number of headbands that can be made from the fabric, we will simply divide 8 by j
=>
[tex]undefined[/tex]brian spent 14$ on fruit at the grocery store. He spent a total of 35$ at the store. What percent of the total did he spend on fruit?
I dont know how to do this so whatever helps:)
The function which represents the phone rate is a straight line, which can be gotten by the following formula:
[tex]y=mt+b[/tex]Where m is the slope, and b the point where the y-axis is crossed by the line.
Let's get the slope first:
[tex]m=\frac{27-25}{20-0}=\frac{2}{20}=\frac{1}{10}[/tex]And b = 25 because (0, 25) is where the line has crossed the cost axis.
Therefore:
[tex]y=C(t)=\frac{1}{10}t+25[/tex]For his phone service Bob pays the monthly fee of $30 and he pays an additional five cents per minute of use. At least he has been charged in a month is $94.70. What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes and solve you’re in equality for m.
We can write an expression for the cost of Bob's phone service as follows:
First, remember that five cents are 0.05 dollars.
[tex]C=30+0.05m[/tex]Where C is the cost and m are the minutes.
We know that at least he has been charged in a month is $94.70.
We can express this as an inequality:
[tex]30+0.05m\ge94.70[/tex]To find the possible number of minutes, we have to solve the previous equation for m. This is:
[tex]\begin{gathered} 0.05m\ge94.70-30 \\ 0.05m\ge64.70 \\ m\ge\frac{64.70}{0.05} \\ m\ge1294 \end{gathered}[/tex]Therefore, the possible numbers of minutes he has used in his phone in a month are:
[tex]m\ge1294[/tex]find the real solutions of 9-l2xl=2
Answer
x = -7/2, 7/2
Step-by-step explanation
Given the equation:
[tex]9-|2x|=2[/tex]Subtracting 9 at both sides of the equation:
[tex]\begin{gathered} 9-9-\lvert2x\rvert=2-9 \\ -\lvert2x\rvert=-7 \end{gathered}[/tex]Dividing by -1 at both sides of the equation:
[tex]\begin{gathered} \frac{-\lvert2x\rvert}{-1}=\frac{-7}{-1} \\ |2x|=7 \end{gathered}[/tex]Now we have two options:
[tex]\begin{gathered} 2x=7 \\ \text{ Or} \\ 2x=-7 \end{gathered}[/tex]Solving the first option:
[tex]\begin{gathered} 2x_1=7 \\ \frac{2x_1}{2}=\frac{7}{2} \\ x_1=\frac{7}{2} \end{gathered}[/tex]Solving the second option:
[tex]\begin{gathered} 2x_2=-7 \\ \frac{2x_2}{2}=\frac{-7}{2} \\ x_2=-\frac{7}{2} \end{gathered}[/tex]A conical circus tent has a 20 ft central pole that supports it. The slant height of the tent is 26 ft long. Explain how to find the angle the tent pole makes with
the sides of the tent.
26 ft
20 ft
The central pole forms a right triangle with the floor of the tent. The
the length of the side of the tent, which is
Applying
is
V
of the missing angle is the ratio of the length of the central pole to
we find that the angle the tent pole makes with the sides of the tent
The angle the pole makes with the tent is 39.7°.
What is an angle?
An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle.
Angles formed by two rays are located in the plane containing the rays.
Trigonometric ratio: the trigonometric ratio is used to demonstrate the relationship between the sides and angles of a right-angled triangle.
Let θ represent the angle the pole makes with the tent.
Using trigonometric ratios:
cos(θ) = 20/26
θ = 39.7°
Therefore, the angle the pole makes with the tent is 39.7°.
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Stephanie weighed a gallon of water that measured 8.75 pounds. A gallon of water should weigh 8.33 pounds. What is Stephanie’s percent of error?
Considering the definition of percent of error, the Stephanie’s percent of error in this case is 5.042%.
Definition of percent of errorPercent of error is a measure of how inaccurate a measurement is, standardized based on the size of the measurement.
In other words, the percent of error allows knowing the differences between the estimated value and the real value. The error may be due to the measurement method (tool or human error) or due to approximations used in the calculation (for example, rounding errors).
To calculate the percent of error you must:
Subtract the real value from the estimated value.Divide the result by the real number.Determines the absolute value of the result. The absolute value of a number is its distance from zero on a number line. Thus, the absolute value of a positive number is the number itself, and the absolute value of a negative number is its opposite.Multiply the result by 100 to get the value in percentage.Therefore, the expression for calculating the percent of error is
percent of error= [|real value - estimated value|÷ real value]×100
Stephanie’s percent of errorIn this case, you know:
Real value= 8.33 poundsEstimated value= 8.75 poundsReplacing in the definition of percent of error:
percent of error= [|8.33 pounds - 8.75 pounds|÷ 8.33 pounds]×100
Solving;
percent of error= [|-0.42 pounds|÷ 8.33 pounds]×100
percent of error= [0.42 pounds÷ 8.33 pounds]×100
percent of error= 0.05042×100
percent of error= 5.042%
Finally, the percent of error in this case is 5.042%.
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What is 2x1/5
PLEASE HELP ASAP
Answer:
2/5
Step-by-step explanation:
2 can also be written in fraction form as 2/1
So, you have 2/1 times 1/5. So, you multiply numerators and you multiply denominators.
Numerators: 2 times 1 =2
Denominators: 1 times 5 =5
So, you have 2/5
3x – 5 + 6x + 7Step by step please I need help ASAP!!!
Given the expression
[tex]3x-5+6x+7[/tex]To simplify this expression you have to perform the mathematical operations to all "alike" terms, this is, those who have the unknown value "x" go together and those that do not have the unknown go to another group:
[tex]\begin{gathered} 3x+6x-5+7 \\ 9x+2 \end{gathered}[/tex]in NPQ, U is the centroid. If PU=24 find UT
The length of UT is 12
Generally, the property of the centroid is that it is at a point that splits the length of the median into a ratio of 1 to 2
What this mean in this case is that if we look at the centroid U, it splits PT into PU and UT which are in the ratio of 2 to 1
Hence, from the above, we can deduce that UT is exactly half of PU
Thus;
[tex]\begin{gathered} UT\text{ = }\frac{1}{2}\times PU \\ \\ UT\text{ = }\frac{1}{2}\times24 \\ \\ UT\text{ = 12} \end{gathered}[/tex]