To be a right triangle it must comply with the following:
[tex]a^2+b^2=c^2[/tex]Where:
a = 6
b = 8
c = 10
So:
[tex]\begin{gathered} 6^2+8^2=10^2 \\ 36+64=100 \\ 100=100 \end{gathered}[/tex]This means that it is a right triangle.
Answer: Yes, It is a right triangle
Consider the following data:x-2-1 0 1P(X=x) 0.10.10.20.2Step 4 of 5: Find the value of P(X < 2). Round your answer to one decimal place.20.4
STEP - BY - STEP EXPLANATION
What to find?
P(X < 2)
Given:
[tex]P(X<2)=P(X=-2)+P(X=-1)+P(X=0)+P(X=1)[/tex]From the given table;
P(X=-2) = 0.1
P(X=-1)=0.1
P(X=0)=0.2
P(X=1)=0.2
Substitute the values into the formula above and simplify.
[tex]P(X<2)=0.1+0.1+0.2+0.2[/tex][tex]=0.6[/tex]Hence, P(X < 2)=0.6
ANSWER
0.6
A square window has an area of x² + 12x + 36 square feet. Find the length of oneside of the square
Solution
Given that a square window has an area of x² + 12x + 36
[tex]\begin{gathered} Area\text{ of square = l}^2 \\ Where\text{ l = length of the square} \\ Thus,\text{ length of the square= }\sqrt{Area}\text{ of the square} \end{gathered}[/tex][tex]\begin{gathered} l=\sqrt{x²+12x+36} \\ l=\sqrt{(x^2+6x+6x+36}) \\ l=\sqrt{x(x+6)+6(x+6)} \\ l=\sqrt{(x+6)(x+6)} \\ l=\sqrt{(x+6)^2} \\ l=x+6 \end{gathered}[/tex]The length of one side of the square = x+6
In Mr. Senter's classroom, 2/3 of the students play sudoku. Of the students who play sudoku, 3/8 also play chess. If there are 24 students in his class, how many play sudoku and chess?how did she get 9
The number of students given are 24.
The students who play sudoku is,
[tex]\frac{2}{3}\times24=16.[/tex]Out of the students who play sudoku , the students who play chess are
[tex]16\times\frac{3}{8}=6.[/tex]Therefore the students who play sudoku are 16 and play chess are 6.
The number of students who play both chess and sudoku is,
[tex]\text{ n}(C\cup S)=n(C)+n(S)-n(C\cap S)[/tex]Substitute the values,
[tex]24=16+6-n(C\cap S)[/tex][tex]n(C\cap S)=24-22[/tex][tex]n(C\cap S)=2.[/tex]Thus , the number of students who play both chess and sudoku is, 2.
Can you help me understand how to do this please?
The given equation is
- 26 = 2(u - 7) - 8u
The first step is to expand the parentheses on the right side of the equation by multiplying the terms inside by the term outside. We have
- 26 = 2u - 14 - 8u
The next step is to collect like terms. The terms containing u will be on one side of the equation while the constant terms would be on the other side.
By adding 14 to both sides of the equation, we have
- 26 + 14 = 2u - 14 + 14 - 8u
- 12 = 2u - 8u
- 12 = - 6u
- 6u = - 12
Dividing both sides of the equation by - 6, we have
- 6u/- 6 = - 12/- 6
u = 2
What is the solution set of y=-1/6x+4
2 step equations solve each equation. Show yourselves steps -18=6a-6x/-3 + 11 =233+2v=1116=k/3 - 11 -6g -12 = -602a+5-5a+1 combine like terms m-4+3m-2 combine like terms
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
-18=6a-6
a = ?
Step 02:
-18 = 6a - 6
-18 + 6 = 6a
- 12 = 6a
-12 / 6 = a
- 2 = a
The answer is:
a = - 2
What is the ratio of all the apples in the bag to red and green ?
There are 11 apples on the basket, if 5 of them are green and the rest are red, to determine the number of red apples, you have to calculate the difference between the total and the number of green apples:
[tex]11-5=6[/tex]a) There are 6 red apples on the basket, the ratio of all apples to red apples can be expressed as follows:
First, write the total number of apple and then write the number of red apples, separate both values by a colon
[tex]11\colon6[/tex]b) To write the ratio of red apples to green apples you have to write the number of red apples on the basket and the number of green apples, both values separated by a colon:
[tex]6\colon5[/tex]evaluate the expression 4-2i/3i
and write the result in the form a+bi
The given expression in the form of (a + ib) can be written as -
-2/3 + i(4/3).
What is a expression? What is a mathematical equation? What is Equation Modelling? What are complex numbers?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. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted [i], called the imaginary unit and satisfying the equation -
[tex]{\displaystyle i^{2}=-1}[/tex]
Every complex number can be expressed in the form a + bi, where [a] and [b] are real numbers
We have the following expression -
(4 - 2i)/3i
We have -
(4 - 2i)/3i
4/3i - 2i/3i
- 2/3 + i(4/3)
Therefore, the given expression in the form of (a + ib) can be written as -
-2/3 + i(4/3).
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3) Select all ratios that are equivalent to 4:5 A. 2: 2.5 B. 2:3 C. 3: 3.75 D. 7:8 E. 8:10 F. 14: 27.5
For two ratios to be equivalent, its means and extremes if multiplied must be equal to each other.
[tex]\begin{gathered} \frac{a}{b}=\frac{c}{d} \\ ad=bc \end{gathered}[/tex]Let's start with Option A.
[tex]\begin{gathered} \frac{4}{5}=\frac{2}{2.5} \\ 4\times2.5=2\times5 \\ 10=10 \end{gathered}[/tex]Since they are equal, then Option A is equivalent to 4/5.
Let's check Option B.
[tex]\begin{gathered} \frac{4}{5}=\frac{2}{3} \\ 4\times3=2\times5 \\ 12\ne10 \end{gathered}[/tex]Let's check Option C.
[tex]\begin{gathered} \frac{4}{5}=\frac{3}{3.75} \\ 4\times3.75=5\times3 \\ 15=15 \end{gathered}[/tex]Let's check Option D.
[tex]\begin{gathered} \frac{4}{5}=\frac{7}{8} \\ 4\times8=5\times7 \\ 32\ne35 \end{gathered}[/tex]Let's check Option E.
[tex]\begin{gathered} \frac{4}{5}=\frac{8}{10} \\ 4\times10=5\times8 \\ 40=40 \end{gathered}[/tex]FInally, let's check Option F.
[tex]\begin{gathered} \frac{4}{5}=\frac{14}{27.5} \\ 4\times27.5=5\times14 \\ 110\ne70 \end{gathered}[/tex]Hence, only Option A, Option C, and Option E are equivalent to ratio 4/5.
Write a quadratic equation in factored form if it has x-intercepts 2 and -1 and y-intercept 6.
We have to write a quadratic equation, in factored form, that has an x-intercept at x=2 and x=-1, and a y-intercept 6.
As the x-intercepts are the roots of the function, we can write the equation as:
[tex]y=a(x-2)(x+1)[/tex]The parameter a will be defined in order to have a y-intercept at y=6. That means that, when x is 0, the value of the function is y=6.
Then, we can replace x with 0 and y with 6 and find the value of a:
[tex]\begin{gathered} y=a(x-2)(x+1) \\ 6=a(0-2)(0+1) \\ 6=a(-2)(1) \\ 6=-2a \\ a=\frac{6}{-2} \\ a=-3 \end{gathered}[/tex]With the value of a=-3, we can write the factorized form of the equation as:
[tex]y=-3(x-2)(x+1)[/tex]Graph:
Answer: y=-3(x-2)(x+1)
Francis went on a business trip to Minneapolis, Minnesota, and stayed at a hotel for one night at a rate of $150, plus tax. The state of Minnesota has a general sales tax rate of 6.875%, and the city of Minneapolis has a general sales tax rate of 0.5%. In addition, Hennepin County, where Minneapolis is located, has a 0.25% sales tax for transit improvement and a 0.15% sales tax to finance a baseball stadium. Not only that, but there is an additional lodging tax in Minneapolis of 3%. Help Francis determine his total bill at the hotel. Round all your answers to the nearest cent. How much money was Francis charged by the state of Minnesota at its general sales tax rate?How much money was Francis charged by the city of Minneapolis at its general sales tax rate? How much money was Francis charged by Hennepin County for transit improvement? How much money was Francis charged by Hennepin County to help finance a baseball stadium?
Francis went on a business trip to Minneapolis, Minnesota, and stayed at a hotel for one night at a rate of $150, plus tax. The state of Minnesota has a general sales tax rate of 6.875%, and the city of Minneapolis has a general sales tax rate of 0.5%. In addition, Hennepin County, where Minneapolis is located, has a 0.25% sales tax for transit improvement and a 0.15% sales tax to finance a baseball stadium. Not only that, but there is an additional lodging tax in Minneapolis of 3%. Help Francis determine his total bill at the hotel. Round all your answers to the nearest cent.
How much money was Francis charged by the state of Minnesota at its general sales tax rate?
How much money was Francis charged by the city of Minneapolis at its general sales tax rate?
How much money was Francis charged by Hennepin County for transit improvement?
How much money was Francis charged by Hennepin County to help finance a baseball stadium?
part 1How much money was Francis charged by the state of Minnesota at its general sales tax rate?
we have that
the sales tax rate is 6.875%
6.875%=6.875/100=0.06875
Multiply by $150
150(0.06875)=$10.31
part 2How much money was Francis charged by the city of Minneapolis at its general sales tax rate?
the sales tax rate is 0.5%
0.5=0.5/100=0.005
Multiply by $150
150(0.005)=$0.75
part 3How much money was Francis charged by Hennepin County for transit improvement?
sales tax is 0.25%
0.25/100=0.0025
150(0.0025)=$0.38
part 4How much money was Francis charged by Hennepin County to help finance a baseball stadium?
the sales tax is 0.15%
0.15/100=0.0015
150(0.0015)=$0.23
part 5additional lodging tax in Minneapolis of 3%
3/100=0.03
150(0.03)=$4.5
part 6
the total bill is equal to
150+10.31+0.75+0.38+0.23+4.5=$166.17
the total bill is $166.17Four students tried to create factor rainbows for the number 81. Complete the statements below about the number 81.
3⁴ is factor rainbows for the number 81.
What does a math factor mean?
A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them.81 is a perfect square number.
Hence, we can express it as 9 × 9 = 81.
9 can further be factored as 3 × 3 = 9.
Factor of 81 = 1,3,9,27,81
negative factor of 81 = -1,-3,-9,-27,-81
prime factors of 81 = 3 * 3 * 3 * 3 = 3⁴
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Find the opposite of the given number 18/19
The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0, then we have to invert the sign of the original number, if we have a positive one and we are told to find its opposite we just put it a negative sign, if the original number is negative then we rewrite it as a positive number.
In this case, we have 18/19, then the opposite number of it is -18/19
What is the first step to solve 1/4x- 5=8
Given the equation :
[tex]\frac{1}{4}x-5=8[/tex]The first step is to add 5 to both sides
so,
[tex]\frac{1}{4}x-5+5=8+5[/tex]Solve 5x + 6 = 7 for x.
x = 1/5
Explanations:The given equation is:
5x + 6 = 7
Step 1: Collect like terms
Note that 6 becomes -6 when it crosses to the right side of the equality sign
5x = 7 - 6
5x = 1
Step 2: Divide both sides by 5
5x / 5 = 1 / 5
x = 1 / 5
I need help with this problem pleaseAfter number it says number of visits
The inequality: 2.5v + 20 ≥ 40
v ≥ 8
Explanation:Rewards for signing up = 20
let the number of visits = v
rate = 2.5 points per visit
Amount needed for a free movie ticket is atleast 40 points
Atleast 40 is reperesented as ≥ 40
Rewards for signing up + rate (number of visits) ≥ 40
20 + 2.5(v) ≥ 40
The inequality:
2.5v + 20 ≥ 40
Solving the inequality:
2.5v + 20 - 20 ≥ 40 - 20
2.5v ≥ 20
v ≥ 20/2.5
v ≥ 8
Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x))f(x) = 2x2 + 16g(x) = /5x^3
Given the functions
[tex]\begin{gathered} f(x)=2x^2+16 \\ g(x)=\sqrt[]{5x^3} \end{gathered}[/tex]First, we get the composite function
[tex]f(g(x))=f(\sqrt[]{5x^3})[/tex]To get f(√5x³), we will substitute x in f(x) with √5x³ as shown:
[tex]f(g(x))=2(\sqrt[]{5x^3})^2+16[/tex]The square root and power 2 cancel each other
[tex]\begin{gathered} f(g(x))=2(5x^3)+16 \\ \text{Simplify} \\ f(g(x))=10x^3+16 \end{gathered}[/tex]Answer:
[tex]f(g(x))=10x^3+16[/tex]Hello could you please help me with this problem. Write and equation in standard form of the line that passes through (2,-3) and (-3,7).
Given:
point (2,-3) and (-3,7)
First, solve for the slope of the line
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{substitute} \\ (x_1,y_1)=(2,-3) \\ (x_2,y_2)=(-3,7) \\ \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7-(-3)}{-3-2} \\ m=\frac{7+3}{-5} \\ m=\frac{10}{-5} \\ m=-2 \end{gathered}[/tex]Now that we have solved for the slope, substitute it to the slope-intercept form y = mx + b to find the y-intercept. Use the point (2,-3) but using (-3,7) works just as well.
[tex]\begin{gathered} y=mx+b \\ -3=(-2)(2)+b \\ -3=-4+b \\ -3+4=b \\ b=1 \end{gathered}[/tex]The slope intercept form of the line is
[tex]y=-2x+1[/tex]Rearrange it to follow the standard form Ax + By = C, and we have
[tex]\begin{gathered} y=-2x+1 \\ y+2x=-2x+2x+1 \\ 2x+y=\cancel{-2x+2x}+1 \\ \\ \text{The equation of the line that passes through (2,-3) and (-3,7) in standard form is} \\ 2x+y=1 \end{gathered}[/tex]Solve the following system of equations by using elimination: x + 2y = 8 -x - 3y = 2
Solve the following system of equations by using elimination:
[tex]\begin{cases}x+2y=8\ldots\ldots\text{.}(1) \\ -x-3y=2\ldots\ldots(11)\end{cases}[/tex]Using Elimination method:
[tex]\begin{gathered} \begin{cases}x+2y=8 \\ \frac{-x-3y=2}{-y=10}\end{cases}\text{+} \\ \text{divide both side by -1} \\ -\frac{y}{-1}=\frac{10}{-1} \\ y=-10 \end{gathered}[/tex]Substitute the value of y in equation (1):
[tex]\begin{gathered} x_{}+2y=8 \\ x+2(-10)=8 \\ x-20=8 \\ x=8+20 \\ x=28 \end{gathered}[/tex]Therefore the value of x = 28 and y = -10
Hence the correct answer is (x,y) = (28,-10)
Fernando picks a marble at random. without putting the first marble back he picks second marble at random are thertwo events dependent or independent
Given the word problem, we can deduce the following information:
1. Fernando picks a marble at random.
2. Without putting the first marble back, he picks a second marble at random.
To determine if the events are dependent or independent, we first note that dependent events influence the probability of other events, while independent events do not affect one another.
Since Fernando picks a marble without putting the first marble back, the probability of the second pick is affected.
Therefore, the answer is dependent.
Use the following statement to answer parts a) and b). Two hundred raffle tickets are sold for $3 each. One prize of $1000 is to be awarded. Winners do not have their ticket costs of $3 refunded to them. Raul purchases one ticket.a) Determine his expected value.b) Determine the fair price of a ticket.
Fom the question, the following can be derived:
Ticket price = $3
Winning price = $1000
Probability of winning (Pwin) = (1/200)
Probability of not winning (Ploss) = [1 - (1/200)] = 199/200
The net income if Raul wins (Nwin) = $1000 - $3 = $997 (when there is no refund)
The net loss if Raul does not win (Nloss) = -$3
(a) We are to determine his expected value:
To determine his expected value, we using this:
(Pwin * Nwin) + (Ploss * Nloss)
((1/200) * 997) + ((199/200) * -3)
4.985 - 2.985 = 2
The expected value is 2.
(b) We are also to determine the fair price of a ticket
To get the fair price of a ticket, we will add the cost of ticket and the expected value:
Cost of ticket + Expected value
3 + 2 = 5
Therefore, the fair price of a ticket is 5.
The equation 4.05p + 14.40 = 4.50(p +3) represents the number p of pounds of peanuts you need to make trail mix. How many pounds of peanuts do you need for the trail mix?
The equation given is a one variable equation, "p".
The question asks to find the value of "p", which is the pounds of peanuts.
So, we need to solve the euqation for "p".
[tex]4.05p+14.40=4.50(p+3)[/tex]First, we need to put all the terms that have "p" in one side. For this, we will have to use the distributive property in the parenthesys first:
[tex]\begin{gathered} 4.05p+14.40=4.50p+4.50\cdot3 \\ 4.05p+14.40=4.50p+13.50 \end{gathered}[/tex]Now, we can substract 4.05p in both sides to get the "p" term of the left to the right:
[tex]\begin{gathered} -4.05p+4.05p+14.40=-4.05p+4.50p+13.50 \\ 14.40=(4.50-4.05)p+13.50 \\ 14.40=0.45p+13.50 \end{gathered}[/tex]Now, we do the same for the 13.50, substract it in both sides:
[tex]\begin{gathered} 14.40-13.50=0.45p+13.50-13.50 \\ 0.9=0.45p \\ 0.45p=0.9 \end{gathered}[/tex]Now, we can divide both sides by 0.45:
[tex]\begin{gathered} \frac{0.45p}{0.45}=\frac{0.9}{0.45} \\ p=2 \end{gathered}[/tex]So, the answer is p = 2, thus, you need 2 pounds of peanuts for the trail mix.
what is the degree of the polynomial5z^3-2z^4-9z^2+z
The degree of a polynomial is the highest power in the inividual terms
Hence the degree of this polynomial is 4
Suppose that among the 5000 students at a high school, 1200 are taking an online class and1700 prefer watching basketball to watching football. Taking an online class and preferringbasketball are independent. How many students are taking an online course and preferbasketball to football?
Solution:
Given:
[tex]\begin{gathered} total=5000 \\ n_{online\text{ class}}=1200 \\ n_{basketball}=1700 \end{gathered}[/tex]Since both events are independent, then;
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Hence,
[tex]\begin{gathered} P(online)=\frac{1200}{5000} \\ P(basketball)=\frac{1700}{5000} \\ Hence,\text{ } \\ P(online\cap basketball)=\frac{1200}{5000}\times\frac{1700}{5000} \\ P(online\cap basketball)=\frac{51}{625} \\ P(online\cap basketball)=0.0816 \end{gathered}[/tex]The number of students taking an online course and prefer basketball to football is;
[tex]\begin{gathered} n(online\cap basketball)=0.0816\times5000 \\ n(online\cap basketball)=408 \end{gathered}[/tex]Therefore, the number of students taking an online course and prefer basketball to football is 408
Find the area of the shape shown below. 7TH As 6 Asy TATUS 2 Col units? Stuck? Watch a video or use a hint. Pro Raport a problem
Answer:
Step-by-step explanation:
Find a.Round to the nearest tenth:2 cmс1501050a=a = [ ? ]cmLaw of Sines: sin A=sin Bb=sin Cсa
In the given triangle ABC ,
Sum of the angles of of a triangle is 180 degrees.
Therefore,
[tex]\begin{gathered} \angle A\text{ + }\angle B\text{ + }\angle C\text{ = 180} \\ \angle A\text{ + 105 + 15 = 180} \\ \angle A=\text{ 180 - 120} \\ \angle A\text{ = 60} \end{gathered}[/tex]By using sine rule,
[tex]\frac{a}{\sin A}\text{ = }\frac{b}{\sin B}[/tex]Substituting the given values in the given equation,
[tex]\begin{gathered} \frac{a}{\sin60}\text{ = }\frac{2}{\sin 105} \\ a\text{ = }\frac{2\sin 60}{\sin 105} \\ a\text{ = 1.7931 } \\ a\text{ }\approx\text{ 1.8 }cm \end{gathered}[/tex]John needs to wrap the edge of his rectangular desk with duct tape He knows the width is 10/8 of a meter and the length of a meter How much duct tape does he need to wrap the desks perimeter
13/4 m or 3.25 meters
1) Given the width is 10/8 meter
The length is 3/8 meter
2) To wrap the rectangular desk let's use this formula, for the Perimeter (2p):
2p= 2(w+l) Plug into w and l the measures
2p = 2(3/8 +10/8) Proceed with the sum within the parentheses
2p = 2(13/8) Distribute the factor
2p =13/4
3) Hence, the perimeter is 13/4 or 3.25 meters
You have a bank account in which your balance increases annually at a rate of 4%. If your initial investment was $100. Write an equation that represents your balance.
Initial investment = $100
The balance increases annually at a rate = 4%
The increased amount = 4% of $100
This gives
[tex]\frac{4}{100}\times\text{\$}100=\text{\$}4[/tex]Hence the investment increase annually by $4 yearly
In the second year the investment will increase by 2 x $4 = $8
In the third year the investment will increase by 3 x $4 = $$12
This implies that
In n years
The investment will increase by n × $4 = $4n
The balance at n years is given as
Balance = Investment + year increment
This is as shown below
[tex]\text{Balnace }=\text{ \$100 }+\text{ \$4n}[/tex]Describe the net of a rectangular prism with a length of 12 centimeters a width of 9 centimeters and height of 5.
There would be a line of 4 rectangles, and 2 rectangles on the top and bottom of the second one. The first and third rectangles would have a width of 12, and the first and fourth would have a width of 9.
The rectangles on the top and bottom would also have a width of 9. The 4 rectangles would have a height of 5, and the 2 rectangles on the top and bottom would have a height of 12.
the product in simplest form.
5/6 2/5
Answer:
1/3
Step-by-step explanation:
[tex]\frac{5}{6}*\frac{2}{5} = \frac{5*2}{6*5} =\frac{10}{30} = \frac{1}{3}[/tex]
5 and 5 cancel out, 2 becomes 1, and 6 simplifies to 3.