The answer is [tex]\frac{32x+105}{120}[/tex].
The area of mathematics known as algebra is used to represent situations or problems using mathematical expressions. In algebra, we combine integers with variables like x, y, and z.
A fraction is a number that is a component of a whole. In algebra, fractions can be added, subtracted, multiplied, and divided just like in basic arithmetic.
The given equation is an algebraic fraction having variables in the numerator. This equation is written as,
[tex]\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)[/tex]
First combine, x with the nearby fraction,
[tex]\begin{aligned}\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)&=\left(\frac{3x}{5}+\frac{3}{4}\right)-\left(\frac{x}{3}-\frac{1}{8}\right)\\&=\frac{3x}{5}+\frac{3}{4}-\frac{x}{3}+\frac{1}{8}\end{aligned}[/tex]
Now, group the fraction with a common denominator,
[tex]\begin{aligned}\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)&=\left(\frac{3x}{5}-\frac{x}{3}\right)+\left(\frac{3}{4}+\frac{1}{8}\right)\\&=\left(\frac{3x\cdot3}{15}-\frac{x\cdot5}{15}\right)+\left(\frac{3\cdot2}{8}+\frac{1}{8}\right)\\&=\left(\frac{9x-5x}{15}\right)+\left(\frac{6+1}{8}\right)\\&=\frac{4x}{15}+\frac{7}{8}\\&=\frac{32x+105}{120}\end{aligned}[/tex]
Therefore, the final answer is [tex]\frac{32x+105}{120}[/tex].
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G is the midpoint for FH what is the length of FG
Since G is the midpoint of FH,
[tex]\begin{gathered} FG=GH \\ \Rightarrow11x-7=3x+9 \\ \Rightarrow11x-3x=9+7=16 \\ \Rightarrow8x=16 \\ \Rightarrow x=2 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} FG=11x-7=11\cdot2-7=22-7=15 \\ \Rightarrow FG=15 \end{gathered}[/tex]The answer is 15, option a.
Select the values that make the inequality u≥8u≥8 true.(Numbers written in order from least to greatest going across.)
To make u >= 8 true, we need to select all of the values that are either equal to OR greater than 8. This means that we must check the following:
8
8.001
8.01
8.1
9
11
13
16
this is a practice problem with more than one answer. it won't allow to me to send the whole picture so the question got cut off and another potential answer. I'll put it here. In the diagram, which of these objects is a radius? Select all that apply. the other option for an answer was EG
We are asked to determine which of the objects are a radius. To do that, let's remember that a radius is a line segment that has one end at the center of a circle and the other end at any circumference point of the circle. Therefore, the segments that are radii are:
[tex]\begin{gathered} \bar{CD} \\ \bar{CB} \\ \bar{CH} \\ \bar{GE} \\ \bar{GF} \end{gathered}[/tex]In a class of 10 students, the ratings are given based on their performance on a test. The following data was taken from ratings given by the class teacher:5, 1, 2, 4, 2, 3, 5, 3, 3, 4Do the ratings earned by the students follow a normal distribution? aNo, because the mean and mode are same bYes, because the data is symmetrical about the mean 3 cNo, because the data is not symmetrical dYes, because the mean is greater than the mode of the data set
Given:
In a class of 10 students, the ratings are given based on their performance on a test. The following data was taken from ratings given by the class teacher:
5, 1, 2, 4, 2, 3, 5, 3, 3, 4
Required:
To choose the correct option
When the members of a family discussed where their annual reunion should take place, they found that out of all the family members, 10 would not go to a park, 9 would not go to a beach, 11 would not go to the family cottage, 3 would go to neither a park nor a beach, 4 would go to neither a beach nor the family cottage, 6 would go to neither a park nor the family cottage, 1 would not go to apark or a beach or to the family cottage,and 2 would go to all three places. What is the total number of family members?
Answer:
20
Explanation:
Let:
• NP = The non-park goers.
,• NB = The non-beach goers.
,• NC = The non-cottage goers.
The Venn diagram below is used to represent the given information:
Given:
• There are 10 non-park goers: a+b+c+g=10
,• There are 9 non-beach goers: b+d+e+g=9
,• There are 11 non-cottages goers: c+e+f+g=11
,• There are 3 non-park and non-beach goers: b+g=3
,• There are 4 non-beach and non-cottage goers: e+g = 4
,• There are 6 non-park and non-cottage goers: c+g=6
,• There is 1 non-park, non-beach, and non-cottage goer: g=1
,• There are 2 who are neither a non-park, non-beach, or non-cottage goer: h=2
So, the total number of family members will be:
[tex]Total=a+b+c+d+e+f+g+h[/tex]Since g=1:
[tex]\begin{gathered} b+g=3\implies b+1=3\implies b=2 \\ c+g=6\operatorname{\implies}c+1=6\operatorname{\implies}c=5 \\ e+g=4\operatorname{\implies}e+1=4\operatorname{\implies}e=3 \end{gathered}[/tex]Next:
[tex]\begin{gathered} c+e+f+g=11 \\ 5+3+f+1=11 \\ f+9=11 \\ f=11-9 \\ f=2 \end{gathered}[/tex]Next:
[tex]\begin{gathered} b+d+e+g=9 \\ 2+d+3+1=9 \\ d+6=9 \\ d=9-6 \\ d=3 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} Total=(a+b+c+g)+d+e+f+h \\ =10+3+3+2+2 \\ =20 \end{gathered}[/tex]The total number of family members is 20.
The area of a field can be expressed as A [tex] = \frac{2x + 6}{x + 1} [/tex]square yards. if the length is[tex]l = \frac{ {x}^{2} - 9 }{2x + 10} [/tex]what is the width? show all work.
Solution
Note: Formula To Use
[tex]Area=lw[/tex][tex]\begin{gathered} A=\frac{2x+6}{x+1} \\ \\ A=\frac{2(x+3)}{x+1} \\ \\ l=\frac{x^2-9}{2x+10} \\ \\ l=\frac{(x-3)(x+3)}{2(x+5)} \\ \\ w=? \end{gathered}[/tex]Substituting the parameter
[tex]\begin{gathered} Area=lw \\ \\ \frac{2(x+3)}{x+1}=\frac{(x-3)(x+3)}{2(x+5)}\times w \\ \\ divide\text{ both side by }(x+3) \\ \\ \frac{2}{x+1}=\frac{x-3}{2(x+5)}\times w \\ \\ w=\frac{2}{x+1}\times\frac{2(x+5)}{(x-3)} \\ \\ w=\frac{4(x+5)}{(x+1)(x-3)} \end{gathered}[/tex]Therefore, the width is
[tex]\frac{4(x+5)}{(x+1)(x-3)}[/tex]The average person blinks about 15000 times a day. The average blink lasts one tenth of a second.How many seconds of one day does the average person spend blinking? (Sleeping does not count!)a. 150,000b. 25c. 15,000d. 1,500
So, the average person blinks 15,000 times a day. Each blink lasts one tenth, that is, 0.1 seconds.
So:
15,000*0.1 = 1,500 seconds.
Letter D
what will the inflation-adjusted cost of a $154,600 house be in 5 years? round to two decimal places.
The inflation-adjusted cost of the house is $166,548.11
Explanation:[tex]\begin{gathered} The\text{ funcion the inflation adjusted cost:} \\ C(t)\text{ = C}_0(1\text{ + r\rparen}^t \\ r\text{ = rate} \\ \text{t = time} \\ C_0\text{ = cost of product} \end{gathered}[/tex][tex]\begin{gathered} From\text{ the information in the question:} \\ C_0\text{ = cost of house =\$154600} \\ r\text{ = 1.5\% = 0.015} \\ t\text{ = 5 years} \\ C(t)\text{ = ?} \\ We\text{ need to find the inflation adjusted cost using the function we were given in the question} \end{gathered}[/tex]substitute the values into the formula:
[tex]\begin{gathered} C(t)\text{ = 154600\lparen1 + 0.015\rparen}^5 \\ C(t)\text{ = 154600\lparen1.015\rparen}^5 \\ C(t)\text{ = 166548.107} \\ \\ To\text{ 2 decimal place, C\lparen t\rparen = 166548.11} \end{gathered}[/tex]The inflation-adjusted cost of the house is $166,548.11
Use the Pythagorean Theorem to find the length of the unknown side in the righttriangle shown below. (Round your answer to the nearest tenth.)817
pythagorean theorm is a^2 + b^2 = c^2
side lengths 8 and 17
8 is a base and 17 is the hypotenuse, the other side is 15
8 15 17 is one of the first 10 Pythagorean triples
8^2 + 15^2 = 17^2
64 + 225 = 289
289 = 289
Examine the sequence of integers below.26, 17, 8, -1, -10, -19Which algebraic expression represents the nth integer in this sequences
Explanation:
Each number in this sequence is the previous number minus 9. This is an arithmetic sequence.
In arithmetic sequences the rule is:
[tex]x_n=a+d(n-1)[/tex]Where a is the first term and d is the distance between terms. In this case the distance is -9 and the first term is 26
Answer:
The algebraic expression that represents the nth integer in the sequence is:
[tex]x_n=26-9(n-1)[/tex]2. Write the equation of the graph below. y 57 4 3 2 1 -5 -4 -3,2 -1 0 1 2 .
A company wants to estimate the mean net weight of all 32-ounce packages of its Yummy Taste cookies at a 95% confidence level. The margin of error is to be within 0.026 ounces of the population mean. The population standard deviation is 0.108 ounces. The sample size that will yield a margin of error within 0.026 ounces of the population mean is:
Explanation
Given that the company wants to estimate the mean net weight of all 32-ounce packages of its Yummy Taste cookies at a 95% confidence level. The margin of error is to be within 0.026 ounces of the population mean. The population standard deviation is 0.108 ounces. The sample size that will yield a margin of error within 0.026 ounces of the population mean is:
Steps
Saul reads every week. In his first week of reading, he read 50 pages. Each week after that, he read 65 pages. Which expression represents the total number of pages Saul has read, where w represents the number of weeks since he first started reading.
Given
In first week , he read 50 pages.
After first week , he read 65 pages.
Find
Expression represents the total number of pages Saul has read
Explanation
Let w represents the number of weeks since he first started reading.
Assume y represent number of pages.
when w = 1 then y = 50 ; w = 2 then y = 65+50=115
we know the equation of line
y = mw + c
so ,
50 = m + c .........(1)
and
115 = 2m + c ............(2)
on solving equation (1) and (2) , we get m = 65 and c = -15
so ,
y = 65w - 15
Final Answer
Therefore , the correct option is 3rd
Determine if the table is linear or exponential. Tables 2 , 3 and 4 are the same
Exponential and linear relations differ in the way the y-values change when the x-values increase by a constant amount, that is, in a linear relationship, the y-values have equal differences and in an exponential relationship, the y-values have equal ratios.
In our first table, when the x-values increase one unit, the y-values decreses 2 units. Similarly, when the x-values increase 2 units, the y-values decrease 4 units and so on:
. Therefore, the first table shows a linear behavior.
On the other hand, table 2,3 and 4 are the same. In those cases, when the x-values increase one unit the, the y-values have a ratio of 2. Similarly, when the x-values increase 2 units the corresponding ratio for the y-values in 4 and so on.
This means that tables 2, 3 and 4 denote an exponential relationship.
when students enter the library they are able to walk anywhere in the library where a bookcase is not present all for bookcases are the same size a diagram below shows the dimensions of the library bookcases what is the area in square feet the available carpet for students to walk
4 rectangles each of dimensions 6ft by 2.5ft: Area of bookcases = 4(L x B) = 4(6x2.5) = 4x15 = 60 square feet
Area of the library = L x B = 40 x 17 = 680 square feet
Area of available carpet to walk on = Area of the library - Area of bookcases = 680 - 60 = 620 square feet
You randomly choose one of the chips without replacing the first chip you choose a second chip. Which question is different find both answers.
The probability of event A and event B is the product of the probability of A snd the probability of B given that A has happened. It is written as
P(A and B) = P(A) x P(BIA)
Considering the first option,
We know that
probability = number of favourable outcomes/total number of outcomes
The total number of outcomes is 6
The probability of choosing a 1, P(A) = 1/6
There are 2 blue chips and since the 1 that was chosen was not replaced, the total number of outcomes would be 5. Thus, the probability of choosing a blue chip given that a 1 has been chosen, P(BIA) is 2/5
Thus, the probability of of choosing a 1 and then a blue chip is
1/6 x 2/5 = 1/15
Considering the second option,
The probability of choosing a 1, P(A) = 1/6
there are 3 even numbers. The probability of choosing an even number given that a green chip has been chosen, P(BIA) = 3/5
Thus, the probability of choosing a 1 and then an even number is
1/6 x 3/5 = 1/10
Considering the third option,
The probability of choosing a green chip, P(A) = 1/6
there are 3 chips that are not red after the green chip has been chosen. The probability of choosing a chip that is not red given that a green chip has been chosen, P(BIA) = 3/5
Thus, the probability of choosing green chip and then an even number is
1/6 x 3/5 = 1/10
Considering the fourth option,
The probability of choosing a number less than 2 is , P(A) = 1/6
there are 3 chips that are even numbers. The probability of choosing a chip that is an even number given that a number less than 2 has has been chosen, P(BIA) = 3/5
Thus, the probability of choosing a number less than 2 and then an even number is
1/6 x 3/5 = 1/10
Thus, the only different option is the first one
I'm not understanding what they're wanting me to do here?? Can someone pls help?
From the given figure,
[tex]\begin{gathered} In\text{ }\Delta ABD,\text{ BD }\perp\text{ AC} \\ \end{gathered}[/tex]By using right angled triangle theorem,
According to right angled triangle theorem, perpendicular drawn on the hypotenuse is equal to the square root of the product of parts in which hypotenuse is divided.
[tex]\begin{gathered} x\text{ = }\sqrt[]{10\text{ }\times\text{ 4}} \\ x\text{ = }\sqrt[]{40} \\ x\text{ = 2}\sqrt[]{10} \end{gathered}[/tex]By using Pythagoras theorem,
[tex]\begin{gathered} AB^2=AD^2+DB^2 \\ z^2=10^2+x^2\text{ } \\ z^2=10^2\text{ + (2}\sqrt[]{10})^2 \\ \end{gathered}[/tex]Further,
[tex]\begin{gathered} z^2=\text{ 100 + 40} \\ z^2\text{ = 140} \\ z\text{ = 2}\sqrt[]{35\text{ }}\text{ } \end{gathered}[/tex]Also,
[tex]In\text{ }\Delta ABC,[/tex]By using Pythagoras theorem,
According to Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the remaining sides.
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ 14^2=z^2+y^2_{_{_{}\text{ }_{}}} \\ z^2=14^2-y^2_{_{_{}}}\text{ } \end{gathered}[/tex]Further,
[tex]\begin{gathered} y^2=14^2-z^2 \\ y^2\text{ = 196 - (2}\sqrt[]{35})^2 \\ y^2\text{ = 196 - 140} \\ \end{gathered}[/tex]Therefore ,
[tex]\begin{gathered} y^2\text{ = 56} \\ y\text{ = 2}\sqrt[]{14} \end{gathered}[/tex]Thus the required values of x , y and z are
[tex]\begin{gathered} x\text{ = 2}\sqrt[]{10}\text{ units} \\ y\text{ = 2}\sqrt[]{14}\text{ units} \\ z\text{ = 2}\sqrt[]{35\text{ }}\text{ units} \end{gathered}[/tex]Convert to radians. (Round to 3 decimal places.)36.45° =___radians
Given:
[tex]36.45\degree[/tex]Required:
To convert the given degree into radian.
Explanation:
To convert the value of the angle in degree, to its equivalent radians, we need to multiply the given value with π/180.
Therefore,
[tex]\begin{gathered} =36.45\times\frac{\pi}{180} \\ \\ =0.6362radians \end{gathered}[/tex]Final Answer:
[tex]36.45\degree=0.6362radians.[/tex]what's the total cost with tax? price $17.95 tax 6%
Answer:
$19.03
Explanation:
Given the price to be $17.95 and a 6% tax, to determine the tax amount we have to find 6% of $17.95;
[tex]\frac{6}{100}\ast17.95=0.06\ast17.95=1.077[/tex]So the tax is $1.08. Let's go ahead and find the total cost by adding the tax to the price;
[tex]1.08+17.95=19.03[/tex]Therefore, the total cost is $19.03.
solve for the value of s
110°
(8s-2)°
The value of s for equation 110=8s-2 will be 14 by solving the linear equation.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. a formula that expresses the connection between two expressions on each side of a sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Here,
110=8s-2
8s=112
s=14
By resolving the linear equation, we obtain the value of s for equation 110=8s-2 as 14.
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Find the slope and y-intercept of the line in the graph. ly 6 5 (0, 3) 3 2 1 1 ( 25) -8 The slope is m and the y-intercept is b =
Slope m is -4; y-intercept b is 3
Here, we want to find the slope and y-intercept of the given plot
The y-intercept is the y-value of the point at which the graph crosses the y-axis
Thus, as we can see, the value is 3
To find the slope, we use the slope equation and supply the points
The equation is as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (0,3)} \\ (x_2,y_2)\text{ = (2,-5)} \\ \\ m\text{ = }\frac{-5-3}{2-0}=\text{ }\frac{-8}{2}=\text{ -4} \end{gathered}[/tex]A plan for a park has a rectangular plot of wild flowers that needs to be enclosed by 54 feet of fencing. Only three sides need to be enclosed because one side is bordered by the parking lot. use Desmos to get your answers. 1. What is the largest area possible for the garden? DO NOT ROUND YOUR ANSWER. ____ squared feet2. What width will produce the maximum area? ____ feet3. What is the length of the garden that will produce the maximum area?
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
a) What is the largest area possible for the garden?
Now, let the length of the rectangular plot be 54 -2x,
and the width of the rectangular plot be x,
so that:
[tex]\begin{gathered} \text{Area = (54 -2x) x = 54 x -2x}^2 \\ \frac{dA}{dx}=\text{ 54 - 4x = 0} \\ We\text{ have that:} \\ 54\text{ = 4x } \\ \text{Divide both sides by 4, we have that:} \\ \text{x = }\frac{54}{4} \\ \text{x = 13. 5} \end{gathered}[/tex]Then, the largest area possible for the garden will be:
[tex]\text{Area = 54x -2x}^2=54(13.5)-2(13.5)^2=729-364.5=364.5ft^2[/tex]b) What width will produce the maximum area?
[tex]Width,\text{ x = 13. 5 fe}et[/tex]c) The length of the garden that will produce the maximum area:
[tex]\text{Length = 54 - 2x = 54 - 2( 13. 5) = 54 -27 = 27 fe}et[/tex]Solve the proportion 10/23=4/x x=
we have
10/23=4/x
multiply in cross
10*x=23*4
10x=92
x=92/10
x=9.2a total of 200 video game players take a survey on their favorite game unknown Kingdom gets 55% of the votes the video game designer wants to know how many players voted for unknown Kingdom write 55% as a rate per hundred
to find out how many players are on the 55% of 200, we can multiply the total players by 55% in decimal form:
[tex]undefined[/tex]Solve the equation for the indicated variable. (Leave ± in the answer as needed)
The given expression is:
[tex]h=td^2[/tex]Therefore,
[tex]td^2=h[/tex]Dividing both sides of the equation by t:
[tex]\frac{td^2}{t}=\frac{h}{t}[/tex]Hence,
[tex]d^2=\frac{h}{t}[/tex]Thus,
[tex]d=\sqrt{\frac{h}{t}}=\frac{\sqrt{h}}{\sqrt{t}}[/tex]To rationalize the equation by √t:
[tex]\begin{gathered} d=\frac{\sqrt{h}}{\sqrt{t}}\times\frac{\sqrt{t}}{\sqrt{t}}=\frac{\sqrt{ht}}{t} \\ d=\frac{\sqrt{ht}}{t} \end{gathered}[/tex]d =
which fraction correctly shows the probability of 7 favorable outcomes and 28 possible outcomes?
Probability is calculated as follows:
[tex]P=\frac{\text{ number of favorable outcomes}}{\text{ number of total possible outcomes}}[/tex]In this case:
[tex]P=\frac{7}{28}=\frac{1}{4}[/tex]The slope of the line below is -1/7. - Write a point-slope equation of the line using the coordinates of the labeled point. 10+ (3,3) - 10 110 - 10+ A. y+3 =-;(x +3) y-3--}(x-3) O C. y+3+7(x+3) O D. y-3 - (x-3)
Point slope formula:
y-y1 = m (x-x1)
Where:
m= slope
(x1,y1) = point of the line
Replacing with the point given (3.3) and slope =-1/7
y+3 = -1/7 (x+3)
If Tia also leaves an 18% tip on the $22 cost of the meal, then how much does she spend on the meal altogether, including both tax and tip?
We have the next information
Cost of the meal
$22
Tip
18%
First, we need to calculate the tip that is 18% of 22
22(.18)= 3.96
the total cost will be
$22+$3.96=$25.96
make k the subject of the formula m= √k+1/4
Answer:
∴ [tex]k = m^{2} - \frac{1}{4}[/tex]
Step-by-step explanation:
[tex]m=\sqrt{k} + \sqrt {(\frac{1}{4})}[/tex]
[tex]m^{2} = k+\frac{1}{4}[/tex]
[tex]k+\frac{1}{4} =m^{2}[/tex]
∴ [tex]k = m^{2} - \frac{1}{4}[/tex]
Michelle earned some money doing odd jobs last summer and put it in a savings account that earns 10% interest compounded quarterly after 6 years there is $100.00 in the account. how much did Michelle earn doing odd jobs
The amount she earned doing the odd job is her principal. The principal can be calculated below
[tex]\begin{gathered} p=\frac{A}{(1+\frac{r}{n})^{nt}} \\ A=\text{accrued amount=100} \\ r=\text{rate}=10\text{ \%=}\frac{10}{100}=0.1 \\ t=6\text{ years} \\ n=4 \\ p=\frac{100}{(1+\frac{0.1}{4})^{24}} \\ p=\frac{100}{(1.025)^{24}} \\ p=\frac{100}{1.80872594958} \\ p=55.2875354186 \\ p=\text{ \$55.29} \end{gathered}[/tex]