(a) There are 21 different ways to choose two different restaurants.
(b)There are 42 different ways to choose two different restaurants.
(c) There are 49 different ways to choose two different restaurants.
In the given question, suppose Ches Tahoe restaurant is one of the 7 largest restaurants in x city.
a. We would like to choose two different restaurants from them. So we have to find how many different ways are there.
There are total 7 largest restaurants in x city.
We have to choose two different restaurants.
So different ways:
n = [tex]^{7}C_{2}[/tex]
Using, [tex]^{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]
n = [tex]\frac{7!}{2!(7-2)!}[/tex]
After solving
n = 21
There are 21 different ways to choose two different restaurants.
b. We would like to choose two different restaurants. one is for our lunch and the other one is for our dinner. We have to find how many different ways are there.
There are total 7 largest restaurants in x city.
We have to choose two different restaurants one for our lunch and the other one for our dinner.
So different ways:
n = [tex]^{7}P_{2}[/tex]
Using, [tex]^{n}P_{r} = \frac{n!}{(n-r)!}[/tex]
n = [tex]\frac{7!}{(7-2)!}[/tex]
After solving
n = 42
There are 42 different ways to choose two different restaurants.
c. We would like to choose two restaurants. one is for your lunch and the other one is for your dinner. We are OK for going to the same restaurants. We have to find how many different ways are there.
There are total 7 largest restaurants in x city.
We have to choose two different restaurants one is for your lunch and the other one is for your dinner OK to the same
So different ways:
n = (7)^2
n = 49
There are 49 different ways to choose two different restaurants.
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Austin's final exam in math had two parts. He had a total of 50 minutes to complete the entire exam. He spent 25 minutes on Part one of the exam.write and solve an equation to show how much time he had left to solve part two
The time Austin had left to solve part two will be 25 minutes.
How to illustrate the equation?It is important to note that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Austin's final exam in math had two parts. He had a total of 50 minutes to complete the entire exam.
Since he spent 25 minutes on Part one of the exam, the time he had left to solve part two will be:
t = 50 - 25
t = 25
The time is 25 minutes.
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7. Laura is conducting an experiment in which she draws a straw. Some of the straws are short,
and some are long. For each trial, she draws a straw, records the result, and replaces the
straw. The table shows the results of 50 trials of the experiment.
Laura will conduct 10 more trials of the experiment. Based on the results in the table, how many of these additional trials will have a result of a a short straw being drawn. :)
Answer:
7
Step-by-step explanation:
Experimental probability is based on the actual results of an experiment (gathered by experimenting repeatedly).
It is calculated by dividing the recorded number of times an event happens by the total number of trials in the actual experiment:
[tex]\boxed{\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}}[/tex]
As the number of trials increases, we would expect for the experimental probability to get closer to the theoretical probability.
Given:
Total number of trials = 50Recorded number of short straws = 35The experimental probability of drawing a short straw is:
[tex]\implies \sf P(short\;straw)=\dfrac{35}{50}=\dfrac{7}{10}[/tex]
If Laura conducts 10 further trials of the experiment, based on the results in the table, the number of additional trials that will have a result of a short straw being drawn is:
[tex]\begin{aligned}\implies \textsf{Additional trials (short straw)} &=\sf experimental\;probability \times number\;of\;trials\\&= \sf \dfrac{7}{10} \times 10\\&= \sf 7\end{aligned}[/tex]
if sin(x y)=3x−2y, then dydx=
The derivative of the given function sin(xy)=3x−2y is obtained as;
dy/dx = 3sec(xy)/x - y/x
Explain the term differentiation?Differentiation is the process of separating something or someone from others. When you distinguish between two toothpaste brands, you draw attention to their differences. The word different is evident in differentiation.The given equation is-
sin(xy) = 3x − 2y
Be sure to account for both sides of this argument.
d/dx(sin(xy)) = d/dx(3x − 2y)
Differentiate the equation's left side.
Set the left side equal to a right side to reform the equation.
x.cos(xy).y' + y.cos(xy) = 3
Solve for y'.
y' = 3sec(xy)/x - y/x
Thus, replace y' with dy/dx
dy/dx = 3sec(xy)/x - y/x
Thus, the derivative of the given function sin(x y)=3x−2y is obtained as;
dy/dx = 3sec(xy)/x - y/x
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How do you write 0.112 as a fraction?
Answer:
112/1000
Step-by-step explanation:
Just put 1 under decimal point and just add as many zeros as digits after that
Which of the following is not a criteria for the construction of triangle ASA SSS AAA SAS?
Answer:
AAA
Step-by-step explanation:
There's no angle angle angle (AAA) because all triangle's angles add up to 180
Sydney invests $100 every month into an account that pays 0.8% annual interest, compounded monthly. Benny invests $80 every month into an account that pays 2.2% interest, compounded monthly. Determine the amount In Sydney's account after l0 years.
[tex]~~~~~~~~~~~~\stackrel{\textit{\LARGE Sydney}}{\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}}}[/tex]
[tex]A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right) \\\\ \qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 100\\ r=rate\to 0.8\%\to \frac{0.8}{100}\dotfill &0.008\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]A=100\left[ \cfrac{\left( 1+\frac{0.008}{12} \right)^{12 \cdot 10}-1}{\frac{0.008}{12}} \right]\left(1+\frac{0.008}{12}\right) \\\\\\ A=100\left[ \cfrac{\left( \frac{1501}{1500} \right)^{120}-1}{\frac{1}{500}} \right]\left(\frac{1501}{1500}\right) \implies {\Large \begin{array}{llll} A \approx 12497.05 \end{array}}[/tex]
Can anyone solve this question ignore the 10. Find:
Part (a)
[tex]\angle CDA=\angle CBA[/tex][tex]AB=AD[/tex][tex]AC=AC[/tex]Part (b)
Yes, the triangles are congruent by RHS.
Which ordered pair below is not a solution to f(x) = x² - 3x + 4?
(1) (0,4)
(2) (1.5,1.75)
(3) (5,14)
(4) (-1,6)
Answer:
(4) (-1,6)
Step-by-step explanation:
f(x) = x² - 3x + 4
1) (0,4) ==>x=0 and f(x)=4
4 = 0² - 3(0) + 4
4 = 0 + 4
4 = 4 ==> true X
2) (1.5,1.75)==> x=1.5 and f(x)=1.75
1.75 = (1.5)² - 3(1.5) + 4
1.75 = 2.25 - 4.5 + 4
1.75 = 2.25 - 0.5
1.75 = 1.75 ==> true X
3) (5,14)
14 = (5)² - 3(5) + 4
14 = 25 - 15 + 4
14 = 10 + 4
14 = 14 ==> true X
4) (-1,6)
6 = (-1)² - 3(-1) + 4
6 = (|-1|)² - (-3) + 4 ==> the square of a negative number is equal to the square
of the absolute value of that number since the square of
a real number is always positive
6 = (1)²+ 3 + 4 ==> subtracting a negative number is equivalent to adding
the positive number
6 = 1 + 3 + 4
6 = 4 + 4
6 = 8 ==> false √√
Hence, the answer is (4) (-1,6).
Every month Ms Smith's pays her car loan through automatic payments from her savings account she's pays the same amount on her car loan each month at the end of the year her savings account balance changed by negative 3,213 from payments made on her car loan What is the change in Ms Smith's saving account balance each month due to her car payments.
The change in Ms Smith's saving account balance each month due to her car payments is of:
-$267.75.
What is a proportion?A proportion is a fraction of a total amount, and this fraction is used along with the basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.
In this problem, the monthly balance change is obtained as follows:
Monthly balance change = Yearly balance change / 12.
(as an year is composed by 12 months).
As stated in the text, the yearly balance change of Ms. Smith's account is given as follows:
-$3,213.
The payments are equal each month, hence the monthly change is of:
Monthly balance change = -3213/12 = -$267.75.
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What is the square root of "0.9"?
The value of [tex]\sqrt{0.9}[/tex] is 0.94868329805. You can't get an accurate answer since the square root is an irrational quantity. But I suppose you could just make it simpler.
The value that a number produces when it is multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For instance, 16 Equals 4. The root symbol or surds is another name for the radical symbol.
The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of three is nine. and the square root of 9, √9 = 3.
Since, 3*3*0.1
= 9*0.1
= 0.9
[tex]\sqrt{3*3*0.1} \\[/tex]
= 3([tex]\sqrt{0.1}[/tex])
[tex]\sqrt{0.9}[/tex] ≈ 0.94868329805
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Correct Question:
What is the value of [tex]\sqrt{0.9}[/tex]
Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.
Which table contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces?
The table that contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces is the second table on the image given at the end of the answer.
How to obtain the viable solutions?The variables for this problem are given as follows:
The input variable b represents the number of books ordered.The output variable w represents the total weights of the books, in ounces.To obtain the viable solutions, we must consider the input variable. The number of books is a countable amount, meaning that it can only assume non-negative integer values.
Thus the first table is incorrect, as it contains a negative amount of books, and the second table is the one that contains only viable solutions in the context of this problem.
Missing InformationThe table is given by the image shown at the end of the answer.
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the random variable x has mean 8 and standard deviation 2. the random variable w is defined as w=7 4x . what are the mean and standard deviation of w ?
The random variable x's mean and standard deviation are 8 and 2, respectively. W=7+ 4x is the formula for the random variable w. The mean of w is E(W) =39
Explain about the Mean?A dataset's mean is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.
Divide the entire number of values by the total number of numbers to find the average. A mean is the term used to describe the mathematical average of a set of two or more data values. Average is also referred to as mean or arithmetic mean.
The mean is the average value of the data. It's easy to calculate: just add up all the numbers, then divide by the total number of numbers. Or, to put it another way, it is equal to the sum divided by the quantity.
The mean is then determined as follows:
E(W) = E (7 + 4X)
This results
E(W) = 7 + 4 E (X)
We thus have:
E(W) = 7 + 4 x 8
E(W) =39
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Standard deviation = 8 and mean = 39.
What is standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.
Given, the formula for mean is E(W) = 7 + 4(X)
∴ E(W) = 7 + 4E(X)
Mean, E(X) equals to 8, hence substituting in the above equation, we get,
E(W) = 7 + 4×8
⇒E(W) = 39
Since, E(W) = 7 + 4(X)
Var(W) = Var(7) + Var(4X)
Since, Var(constant)=0,
Var(W) = Var(4X)
Var(W) = 4²×Var(X), where Var(X)=σₓ²
⇒ Var(W) = 16×σₓ², where σₓ²=2²
⇒ Var(W) = 16×4
⇒ Var(W) = 64
Standard Deviation (SD) = √64 = 8
Thus, standard deviation = 8 and mean = 39.
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solve for x multiple choice question
Answer:
12
Step-by-step explanation:
Using the side splitter theorem, [tex]\frac{x}{32}=\frac{9}{24} \implies x=12[/tex].
The value of x is 12, option (B) is correct.
What is triangle proportionality theorem?A line parallel to one side of a triangle splits the other two sides of the triangle proportionally if the line also crosses the other two sides.
Given that,
Two lines are parallel to each other,
And length of sides are,
32 , x , 24 and 9.
By angle proportionality theorem,
32 / x = 24 / 9
x = (32 × 9) / 24
x = (4 × 9) / 3
x = 4 × 3
x = 12
The required length of x is 12.
Hence, option (B) is correct.
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What is the correct order of steps for bisecting segment AB?
A. Draw a line from point C to point D.
B. Keeping the compass the same width, place the compass on point B, and swing an arc above and below the segment.
C. Place points C and D on the intersection of the arcs created above and below segment AB.
D. Place the compass on point A, and open it wider than half the distance of the segment.
E. Swing an arc above and below the segment.
Answer: E
Step-by-step explanation:
Question 8 options:
Given the coordinates below, determine if ΔFGH and ΔJKL are congruent. If they are, give the reason, if they aren't choose "not congruent".
F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)
FG =
GH =
FH =
JK =
KL =
JL =
Are the triangles congruent?
In the box enter one of the following:
SSS
SAS
Not Congruent
Hence, the three side length of two triangles are same so they are congurent.
What is the congurency?
Two shapes are congruent if they are the same (shape and size)- in other words, if the lengths of the sides and the angles are the same.
It is often useful to know when two triangles are congruent.
Here given coordinates of the triangle [tex]FGH[/tex] and triangle [tex]JKL[/tex] are
[tex]F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)[/tex].
So, the distance formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between [tex]FG[/tex] is
[tex]d=\sqrt{(-2-(-5))^2+(2-10)^2}\\\\d=\sqrt{(-2+5)^2+(2-10)^2}\\\\d=\sqrt{(3)^2+(-8)^2}\\\\d=\sqrt{9+64}\\\\d=\sqrt{73}[/tex]
Distance between [tex]GH[/tex] is
[tex]d=\sqrt{(-9-(-2))^2+(10-(-7))^2}\\\\d=\sqrt{(-9+2)^2+(10+7)^2}\\\\d=\sqrt{(-7)^2+(-9)^2}\\\\d=\sqrt{49+81}\\\\d=\sqrt{130}[/tex]
Distance between [tex]HF[/tex] is
[tex]d=\sqrt{(-5-(-9))^2+(10-(-7))^2}\\\\d=\sqrt{(-5+9)^2+(10+7)^2}\\\\d=\sqrt{(4)^2+(17)^2}\\\\d=\sqrt{16+289}\\\\d=\sqrt{305}[/tex]
Distance between [tex]JK[/tex] is
[tex]d=\sqrt{(9-0)^2+(2-(-5))^2}\\\\d=\sqrt{(9)^2+(2+5)^2}\\\\d=\sqrt{(9)^2+(7)^2}\\\\d=\sqrt{81+49}\\\\d=\sqrt{130}[/tex]
Distance between [tex]KL[/tex] is
[tex]d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-17)^2+(-4)^2}\\\\d=\sqrt{289+16}\\\\d=\sqrt{305}[/tex]
Distance between [tex]LJ[/tex] is
[tex]d=\sqrt{(0-(-8))^2+(-5-(-2))^2}\\\\d=\sqrt{(8)^2+(-5+2)^2}\\\\d=\sqrt{(8)^2+(-3)^2}\\\\d=\sqrt{64+9}\\\\d=\sqrt{73}[/tex]
Since, [tex]FG[/tex]≅[tex]LJ-GH[/tex]≅[tex]JK-HF[/tex]≅[tex]KL[/tex]
Hence, the three side length of two triangles are same so they are congurent.
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Lixin can type 2400 words in 3 hours. Find how many words can he write in 40 minutes.
Answer:
533
Step-by-step explanation:
3 hours = 180 minutes
2400 : 180 = x : 40
x = 2400 * 40 / 180
x = 2400 * 4 / 18
x = 2400 * 2 /9
x = 800 * 2 / 3
x = 1600/3
x = 533.333333
x = 533
Determine if the following values represent a function, and if they do, find f(-7)
(-7,9) (-4,10) (2,6) (-6,3)
The given coordinates represent a function and at f(-7) equals to 9.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have the following coordinates -
(-7, 9) (-4, 10) (2, 6) (-6, 3)
Yes, these coordinates represent a function as a unique value of [x] has only one value of [y]. At x = -7, we can write -
f(-7) = 9
Therefore, the given coordinates represent a function and at f(-7) equals to 9.
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Rewrite in simplest terms: 6(0.7y+0.8z)−4z−6(−0.1z−0.6y)
Please help?
The simplified form can be written as -
7.8y + 1.4z
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
We have the following expression -
6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)
We have -
6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)
(6 x 0.7y + 6 x 0.8z) - 4z + 6 x 0.1z + 6 x 0.6y
4.2y + 4.8z - 4z + 0.6z + 3.6y
7.8y + 4.8z - 3.4z
7.8y + 1.4z
Therefor, the simplified form can be written as -
7.8y + 1.4z
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Maya rakes up the leaves and wants to put them into bags that hold 2\3 of a cubic yard if she rakes 2 1\2 cubic yards of leaves in total how many bags of leaves will she fill.
6)write an expression to show how you can determine the answer to the question
7) draw a picture to model what is happening in the problem using a
8)method of your choice determinate how many bags of leaves that Maya will fill
The expression to determine the number of bags is 2/3 x = 2 1/2 and the number of bags requited is 3 3/4 bags
How to write the expression of the problemInformation from the problem
Maya rakes up the leaves and wants to put them into bags that hold 2\3 of a cubic yard
she rakes 2 1\2 cubic yards of leaves
one bag = 2/3 cubic yard
total leaves raked = 2 1/2 cubic yard
the number of bags required is how many 2/3 cubic yards are there in 2 1/2 cubic yard. this is solved by division
let the number of bags be x
2/3 cubic yard * x = 2 1/2 cubic yard
2/3 x = 2 1/2
x = (2 1/2) / (2/3)
x = 15/4
x = 3 3/4 bags
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The equation T^2 =A^3 shows the relationship between a planets orbital period, T , and the planets mean distance for the sun, A, is astronomical unit, AU. If planet Y is k times the mean distance from the sun as a planet X, by what factor is the orbital period increased
The increase in the orbital period is by a factor of k^3/2. Option D
What is the Kepler laws?From the Kepler's laws, we know that the square of the period of the planet is directly proportional to the cube of the distance of the planet from the sun. We can see that this has been typified by the expression; T^2 =A^3 where T is the period of the planet and A is the distance between the planet and the sun.
Now, we can see that from the relationship, If planet Y is k times the mean distance from the sun as a planet X then the orbital period would be increased by a factor of about k^3/2.
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the greatest amount of sap collected
The greatest amount of sap collected from any one tree is two times.
The maximum amount of sap that can be gathered from a single tree is two times greater than the minimum amount. SAP enables businesses to innovate on anything from cancer therapies to flood mitigation. We support life-saving research and are deeply committed to social responsibility and sustainability. At SAP, we collaborate to create innovations.
Work in a stimulating and rewarding environment by joining us. Minerals and nutrients can be found in tree sap. In the spring, when new buds are growing, a sticky substance that travels through the tree and out onto the branches helps the tree produce energy. Sugars are created as a result of photosynthesis and sent back into the tree, where they serve as sustenance for the tree's growth.
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Correct Question:
The greatest amount of sap collected from any one tree is _____________
question content area top part 1 shannon says that the lines y, y , y, and y could represent the sides of a rectangle. explain shannon's error.
The four equations' coefficients of x can only take two values, thus if one of those values is m, the other solution will be -1/m.
What is the equation?A relation between different terms on either side of the equal sign is described by a straightforward equation.
Simple equations also follow one or a mixture of the four arithmetic computations of addition, simple arithmetic, multiplication, and division.
There are three primary versions of the set of equations: point-slope form, standard form, or slope-intercept form.
So, Shannon's error would be:
In a rectangle, the adjoining sides are perpendicular to one other, whereas parallel runs between the opposing sides.
The slope of parallel lines is equal, and the slope, of a line perpendicular to some other line with a slope, m, is -1/m , thus the slopes of the central axis should be equal, which also gives:
Two sets of systems of equations with equal slopes should make up the equation: B. Y = -x + 6 and Y = -x - 5 are a pair.
Therefore, the slopes of the other two lines are -1/-1 = 1 and the equations of the other two lines are y = x - 4 and y = x - 5 correspondingly.
Therefore, the four equations' coefficients of x can only take two values, thus if one of those values is m, the other solution will be -1/m.
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Correct question;
Shannon says that the lines y=-3x-4,y=-(1)/(3)x+6,y=-4x-5, and y=(1)/(4)x-5 could represent the sides of a rectangle. Explain Shannon's error.
in triangle ABC , seg XY || sideAC , If 2AX = 3BX and XY = 9 , then find the value of AC
The value of AC is 22.5
The property of three parallel lines and their transversals is used to solve this sum. The property explains that if the ratio of the corresponding intercepts made on any other transversal by the same parallel lines is the same as the ratio of the intercepts made on a transversal formed by three parallel lines.
XY ║seg AC
2AX = 3BX
XY = 9
Since, 2AX =3BX
∴ AX÷ BX = 3÷2
AX + BX÷ BX = 3+2÷2
AB ÷ BX = 5÷2
Δ BCA ~ ΔBYX (SAS test of similarity)
( The SAS similarity test determines whether two triangles are similar if the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal.)
∴ BA ÷ BX = AC ÷ XY ( Corresponding sides)
∴ 5÷ 2 = AC ÷ 9
∴ AC = 22.5
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How do you solve 2cos2^x = 1 ?
Answer:
Step-by-step explanation:
Solve for x:
2 cos* (2) =
Divide both sides by 2:
cost (2) =
Take the logarithm base cos(2) of both sides:
Answer:
2inn
X=
iT+ log(-cos(2))
log(2)
i7+ log(-cos(2))
for NE Z
Solve the system by substitution.
y = 8x +6
10x - 5y = 30
x = -2 and y = -10 is the solution of the equations y = 8x +6 and 10x - 5y = 30.
What is Substitution method to solve equations?
The method of substitution involves three steps: Solve one equation for one of the variables. Substitute (plug-in) this expression into the other equation and solve. Resubstitute the value into the original equation to find the corresponding variable. he substitution method is the algebraic method to solve simultaneous linear equations.
Given Equations :
y = 8x +6
10x - 5y = 30
A) Solve equation [1] for the variable y
[1] y = 8x + 6
B) Plug this in for variable y in equation [2]
[2] -5•(8x+6) + 10x = 30
[2] - 30x = 60
C) Solve equation [2] for the variable x
[2] 30x = - 60
[2] x = - 2
D) By now we know this much :
y = 8x+6
x = -2
E) Use the x value to solve for y y = 8(-2)+6 = -10
Solution : {y,x} = {-10,-2}
Hence , x = -2 and y = -10 is the solution of the equations y = 8x +6 and 10x - 5y = 30.
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Linear Inequality Word Problems Harder Kyle has $50 to spend on sandwiches and chips for a picnic. He already bought chips for $2 and will buy sandwiches for $4 each. How many sandwiches can he buy?
Carson owes Nigel $110. If Carson repays this debt at a rate of $15 per week, which graph best represents when, in weeks, Carson’s debt will be less than $50?
Responses
After doing the equitation the at rate of $15 per week.
How to do graph representation?
Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.
Carson owes = $110
At rate of $15 per week.
The graph representation will follows:
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sine rule find the length of ac
The length AC of the triangle ABC is approximately 12.083 centimeters.
How to use the law of sine
The law of sine is a relationship between the sides and the angles of the triangle, which is defined below:
AB / sin C = AC / sin B = BC / sin A
Where:
AB, AC, BC - SidesA, B, C - AnglesFirst, determine the measure of angle C:
AB / sin C = BC / sin A
sin C = (AB / BC) · sin A
sin C = (8.2 / 13.5) · sin 81°
C ≈ 36.865°
Second, determine the measure of angle B:
B = 180° - A - C
B = 180° - 81° - 36.865°
B = 62.135°
Third, determine the length of side AC:
AC / sin B = BC / sin A
AC = BC · (sin B / sin A)
AC = 13.5 · (sin 62.135° / sin 81°)
AC ≈ 12.083 cm
The length AC is approximately equal to 12.083 centimeters.
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Ruby biked a trail that is 3/5 mile each way. After biking 1/4 of the trail, she stopped to rets. What fraction of a mile did Ruby bike before she stopped to rest?
Answer:
7/20 miles
Step-by-step explanation:
get a common denominator
subtract the numerators
then you have the fraction she biked
2(x+ 5) = 3x +1 solve
Answer:
x= 9
Step-by-step explanation:
2(x + 5 ) = 3x + 1
expand the bracket first
2x + 10 = 3x + 1
then collect like terms
2x-3x = 1 - 10
-1x = - 9
and the last step is divide both side by -1
then x = 9
