Answer:327
Step-by-step explanation:
Because you already have the equation, all you need to do is plug in the value for X. If X is equal to 4, our equation would look like this:
y = 78 * 4 + 15
Because of order or operations (PEMDAS), we do multiplication first.
y = 312 + 15
y = 327
Hope this helped!
inside a square with side length $10$, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. what is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles?
Using the concepts of equilateral triangle, we got that 2.113 is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles.
Firstly we find the side length of equilateral triangle , G is the midpoint of side FE.
Let GE=x, since G is the midpoint due to that DE=GB.
So, using basic trigonometry=DG^GB=x√3.
Thus DB=2x√3.
Since DB is the diagonal of ABCD, it has length 10√2 Then we can set up the equation 2x√3=10√2. So the side length of the triangle is
2x=(10√2)/√3.
Now look at the diagonal AC it is made up of twice the diagonal of the small square plus the side length of the triangle. Let the side length of the small square be y:
Let the side length of the small square be y:
AC=y√2 + [(10√2)/√3]+y√2=10√2.
Solving for y:
=>y√2+y√2 + (10√2√3)/3=10√2
=>y√2+y√2 + (10√6)/3=10√2
=> [3y√2+3y√2 + (10√6)] /3=10√2
=>6y√2+10√6=30√2
=>6y√2 = 30√2-10√6
=>y√2 = (30√2-10√6)/6
=>y = (30√2-10√6)/6√2
=>y = (60-20√3)/12
=>y= 5(3−√3)3 or 2.113
Hence, inside a square with side length 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles is to be 2.113.
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Finding Angle Measures When Parallel Lines Are Cut By a Transversal
Answer:
Since angle 8 is 95 degrees, we will have to either subtract or use the rules to solve this!
Lets find angle 1 first!
Since opposite angles are the same, angle 1 will be 95 degrees!
Angle 2 will wave subtracting used to find it!
180 - 95 = 85
Angle 2: 85 degrees
Angle 3 is the same as angle 2 so 85 degrees!
Angle 4 is the same as angle 8 and 1 so 95 degrees!
Angle 5 is the same as 8, 4, and 1 so 95 degrees!
Angle 6 is the same as angle 3 and 2 degrees!
Angle 7 will be 85 by subtraction!
Angle 8 is given and it is 95!
Have an amazing day!!
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X Use FOIL to solve (x+2)(x+1): Write x squared as x2
x2+3x+2
x+2x+2
Ox-2x-2
0/2
X
After using FOIL, the final answer will be
x2 + 3x + 2
What is the FOIL method?
The typical way of multiplying two binomials is known as the FOIL method since FOIL is a shorthand for it. The acronym FOIL stands for the following four terms that describe the item: (Each binomial "initial" term is multiplied together.) The FOIL method is a memory aid for the procedures involved in multiplying two binomials. The result of multiplying the first term, outer term, inner term, and last term is the product of two binomials: (a+b)(c+d)=ac+ad+bc+bd.
Solution explained:
A/Q we have
(x+2)(x-1)
= x * x + x + 2x + 2 (After expanding and applying distributive property)
= x2 + x + 2x + 2
= x2 + 3x + 2
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Q5.
Heres a formula
r = √(w² − h² )
Work out the value of r when w=9√2 and h=5root6.
Give your answer in the form
a√b
where a and b are integers greater than 1.
Answer:
r = 2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
using the rules of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
([tex]\sqrt{x}[/tex] )² = x
substitute the given values of w and h into the equation
r = [tex]\sqrt{w^2-h^2}[/tex]
= [tex]\sqrt{(9\sqrt{2})^2-(5\sqrt{6})^2 }[/tex]
= [tex]\sqrt{162-150}[/tex]
= [tex]\sqrt{12}[/tex]
= [tex]\sqrt{4(3)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]
= 2[tex]\sqrt{3}[/tex]
Special right triangles
In the special right triangle, x has a value of √3/2
Special Right TriangleA special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle.
To find the value of x, we should take into consideration that two of the sides of the triangle are equal to each other.
Using Pythagoras theorem;
[tex](\sqrt{3}) ^2 = x^2 + x^2\\3 = 2x^2\\x^2 = \frac{3}{2} \\x = \sqrt{\frac{3}{2} }[/tex]
The value of x in the triangle is √3/2
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marley's bank charges a $3 service fee each time money is whithdrawn from another bank's atm. Marley is traveling and must withdraw money from another bank's atm 4 times. Which expressions model the charge in the balance of her account due to service fees?
The expressions represent the service fee charge on her account balance is 4x+3.
Given that,
Every time money is withdrawn from an ATM run by a different bank, Marley's Bank levies a $3 service fee. Marley needs to make four ATM withdrawals from a different bank while she is abroad.
We have to find which expressions represent the service fee charge on her account balance.
The expression we can write as,
4x+3
Because 4 times he has taken from ATM money and adding the service fee $3.
Therefore, The expressions represent the service fee charge on her account balance is 4x+3.
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Find the value of x.
The value of x on the given sides of the rectangles is 4.
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
Given, The area of the shaded region is 39.
As the smaller rectangle is inside the whole larger rectangle,
∴The area of the smaller rectangle subtracted from the area of the whole larger rectangle is the area of the shaded region.
So, (2x - 1)(x + 3) - (x - 2)(x + 1) = 39.
2x² + 6x - x - 3 - x² - x + 2x + 2 = 39.
x² + 6x - 1 = 39.
x² + 6x - 40 = 0.
x² + 10x - 4x - 40 = 0.
x(x + 10) - 4(x + `10) = 0.
(x + 10)(x - 4) = 0.
(x + 10) = 0 Or (x - 4) = 0.
x = - 10 Or x = 4.
Now if we put x = - 10 the lengths will be negative which is inappropriate.
So, the value of x that satisfies is 4.
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I need help please please
In the given triangle LMN, measure of side LM = 18in. and measure of angle MLN is 28° then the measure of side LN = 18in. , m ∠M = 76° and
m ∠N = 76°.
As given in the question,
In the given triangle LMN,
Measure of side LM = 18in.
Measure of angle MLN is equal to 28°
It is given that side LM ≅ LN
LM = 18 in.
LN = 18in.
In a triangle LMN ,
In a triangle opposite sides are congruent to each other then angle opposite to them also congruent to each other.
LM ≅LN
⇒m ∠N = m ∠M
In a ΔLMN,
Let x° be the measure of angle M and N each.
m ∠M + m ∠N + m ∠L = 180°
⇒ x° + x° + 28° = 180°
⇒ 2x° = 180° -28°
⇒2x° = 152°
⇒ x = 76°
Therefore, in the given triangle LMN, measure of side LM = 18in. and measure of angle MLN is 28° then the measure of side LN = 18in. , m ∠M = 76° and m ∠N = 76°.
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The surface area of this cylinder is 6,732.16 square feet. What is the height? Use 3.14 and round your answer to the nearest hundredth 16 ft=radius h feet
The height of the cylinder whose surface area and radius are as given in the task content is; 67 ft.
What is the surface area of the cylinder?It follows from the task content that the height of the cylinder as described by the surface area and radius above be determined.
On this note, recall that the surface area of a cylinder is given by the formula;
Surface area = 2πrh
Therefore;
6732.16 = 2 × 3.14 × 16 × h
h = 6732.16/100.48
h = 67.
Consequently, the height of the cylinder which is as described is; 67 ft.
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a fair 6-sided die is repeatedly rolled until an odd number appears. what is the probability that every even number appears at least once before the first occurrence of an odd number?
The probability that every even number appears at least once before the first occurrence of an odd number is [tex]\frac{1}{20}[/tex]
Take [tex]A_{k}[/tex] - the event that odd number appeared on the k-th throw, B - every even number appeared at least once.
Let’s find P(B|[tex]A_{k}[/tex]) . Note that this probability is 0 for k∈{1,2,3} as you need k≥4 to place all distinct even numbers before the odd one.
Now for k≥4 we need to use the formula of inclusions and exclusions: P(B¯|[tex]A_{k}[/tex])=P(C2+C4+C6|[tex]A_{k}[/tex])=
=P(C2|[tex]A_{k}[/tex])+P(C4|[tex]A_{k}[/tex])+P(C6|[tex]A_{k}[/tex])−P(C2C4|[tex]A_{k}[/tex])−P(C2C6|[tex]A_{k}[/tex])−P(C4C6|[tex]A_{k}[/tex]) where Ci is the event that the dice i is missing.
These probabilities are:
P(Ci/[tex]A_{k}[/tex])=[tex](\frac{2}{3} )^{k-1}[/tex]
P(CiCj|[tex]A_{k}[/tex])=[tex](\frac{1}{3} )^{k-1}[/tex]
So
P(B|[tex]A_{k}[/tex])=1–P(B¯|[tex]A_{k}[/tex])=1−3⋅[tex](\frac{2}{3} )^{k-1}[/tex]+3[tex](\frac{2}{3} )^{k-1}[/tex].= 1 − [tex]\frac{9}{2}[/tex].[tex](\frac{2}{3} )^{k}[/tex]+9[tex](\frac{1}{3} )^{k}[/tex]
Now as P([tex]A_{k}[/tex])= [tex]\frac{1}{2^{k} }[/tex]we conclude that
P(B) = ∞∑k=4P(B/[tex]A_{k}[/tex])P([tex]A_{k}[/tex])= ∞∑k=4([tex](\frac{1}{2} )^{k}[/tex]−[tex]\frac{9}{2}[/tex][tex](\frac{1}{3} )^{k}[/tex]+9.[tex](\frac{1}{6} )^{k}[/tex])=
=[tex]\frac{\frac{1}{16} }{\frac{1}{2} }[/tex]−[tex]\frac{\frac{1}{18} }{\frac{2}{3} }[/tex]+[tex]\frac{\frac{1}{144} }{\frac{5}{6} }[/tex] = [tex]\frac{1}{8}[/tex] -[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{120}[/tex] =[tex]\frac{6}{120}[/tex] = [tex]\frac{1}{20}[/tex]
the probability that every even number appears at least once before the first occurrence of an odd number is [tex]\frac{1}{20}[/tex]
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Shivani won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives
Shivani a bucket of fish to divide evenly among 3 dolphins. Each dolphin gets 6 fish.
Which equation can you use to find the number of fish f in the bucket before Shivani feeds
the dolphins?
Pls help ASAP
Answer:
Step-by-step explanation:
f/4 = 3
Choose the expression that is equivalent to 1/5 x 3
Answer:
0.2
Step-by-step explanation:
1/5 is equvalent with 10/5=0.2
7x 3,012=7(____+____)
Answer:
7x 3,012=7(__3000__+__12_) = 21084
Darnelle has a $10,000, three-year loan with an APR of 5%. She uses the table below to compute information on the loan.
a. What is her monthly payment?
b. What is the total of all her monthly payments?
c. What is the total finance charge?
A group of friends wants to go to the amusement park. They have $89.50 to spend on parking and admission. Parking is $7.75, and tickets cost $27.25 per person, including tax. Write and solve an equation which can be used to determine p, the number of people who can go to the amusement park.
I had trusted a VERIFIED answer and got it wrong, so for everyone in the future, here is the correct answer.
Answers:
Equation: 27.25p + 7.75 = 89.5
Answer: p = 3
The equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3
The total amount that they have to spend on parking and admission = $89.50
The parking cost = $7.75
The ticket cost including tax = $27.25
Consider the number of people who can go to amusement park as p
Then the equation will be
7.75 + 27.25p = 89.50
Subtract both side of the equation by 7.75
27.25p + 7.75 - 7.75 = 89.50 - 7.75
27.25p = 81.75
Divide both side of the equation by 27.25
27.25p / 27.25 = 81.75 / 27.25
p = 3
Hence, the equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3
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the group gives 50% of the money they raised to youth programs. this year the team gave $3,100 to youth programs
Using the percentage of money the group gave out to the youth program, the amount of money the group raised is 6200 dollars.
How to find the amount the group raised?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.
The group gives 50% of the money they raised to youth programs. This year the team gave $3,100 to youth programs.
Therefore, the amount of money the group raised can be calculated as follows:
let
x = amount of money raised by the group
Hence,
50% of x = 3100
50 / 100 × x = 3100
50x / 100 = 3100
cross multiply
50x = 3100 × 100
50x = 310000
divide both sides by 50
50x / 50 = 310000 / 50
x = 6200
Therefore, the group raised 6200 dollars this year.
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3/8 x 4/3 please help me I’ve been stuck at this
Answer:
1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
3/8*4/3
The 3 can be cancel out
you can also cancel out 8 and 4
leaving you with 1/2
If x is 60% of y and y is 30% of z, x is what percent of z?
Answer:
18%
Step-by-step explanation:
x is 60% of y[tex]x = y*\frac{60}{100} =y*0.6=0.6y\\x=0.6y[/tex]
y is 30% of z[tex]y = z*\frac{30}{100} =z*0.3=0.3z\\y=0.3z[/tex]
x is what percent of z?
Since x = 0.6y and y = 0.3z:
[tex]\%=\frac{x}{z} *100\\\\\%=\frac{0.6y}{z}*100\\ \\\%=\frac{0.6(0.3z)}{z} *100\\\\\%=\frac{0.18z}{z} *100\\\\\%=0.18*100\\\\\%=18[/tex]
Lucy owes three of her friends 5.60 each how much money does Lucy owe in total
Answer:
16.80
Step-by-step explanation:
The ratio is 1:5.60. Where 1 is the amount of friends and 5.60 is the amount owed. Since there are 3 friends, multiply 5.60 by 3.
Answer: 16.8
Step-by-step explanation: basically multiply 5.60 by 3 (5.60 x 3 = 16.8) or add 5.60 3 times (5.60 + 5.60 + 5.60 = 16.8)
find the common difference d to make 5 comma space x comma space y comma space 32 as a part of an arithmetic sequence.
The common difference 9 will make 5, x, y, 32 an arithmetic sequence of 5, 14, 23, 32.
It is given that the arithmetic sequence is
5, x, y, 32
We know that for any arithmetic sequence the term aₙ is
aₙ = a + (n - 1)d
where,
a = first term
n = order of the value in the sequence
Since x is the second term
x = 5 + (2 - 1)d
or, x = 5 + d
Similarly,
y = 5 + 2d
32 = 5 + 3d
or, 3d = 27
or, d = 9
Hence, x = 14
y = 5 + 18
= 23
Hence, the common difference is 9
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Lourdes is reading a biography for her history class. She reads 30 pages each day. After 9 days, Lourdes has read (3)/(5) of the biography. Write a linear equation to represent the number of pages Lourdes still has to read after x days.
The linear equation is z = 450 - 30 x, where z is the number of pages Lourdes has left to read after x days
We need to write a linear equation to represent the number of pages
Lourdes has left the number of pages to read after x days
Lourdes reads 30 pages each day
Lourdes will read for x days
The number of pages Lourdes will read in x day = 30 x
The left pages will be the difference between the total pages of the
book and the pages Lourdes read.
After 9 days Lourdes completes 3/5 of the total number of pages.
So the number of pages Lourdes reads after 9 days = 30×9 = 270 pages.
Let The total number of pages in the book = y
Therefore 3/5 × y = 270.
So y = 270 × (5/3) = 450 pages.
The total number of pages in the book = 450 pages.
Lourdes will read 30 x in x days
The number of pages left = 450 - 30 x
Assume that z represents the number of pages Lourdes has left to read after x days
z = 450 - 30 x
The linear equation is z = 450 - 30 x, where z is the number of pages Lourdes has left to read after x days
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Suppose conditional p→ q is true and conditional q→ r is false. Must the conditional p →r also be false? Explain.
Answer:
no
Step-by-step explanation:
the conditional p-> r is the basically both of the beginning 2 conditionals combined
what is
S+2c=47
5s+8c=201
s=?
c=?
step by step answer
The values of the variables s and c are 13 and 17, respectively.
We are given a system of two equations. The equations are linear in nature. Each equation represents a straight line. We need to find the solution to the system of linear equations. The coordinates of the intersection point of the straight lines are the solution. The equations are given below.
s + 2c = 47
5s + 8c = 201
We will substitute the value of s from the first equation into the second equation.
s = 47 - 2c
5s + 8c = 201
5(47 - 2c) + 8c = 201
235 - 10c + 8c = 201
235 - 2c = 201
2c = 235 - 201
2c = 34
c = 17
We will substitute the value of c into the first equation to find the value of s.
s = 47 -2c
s = 47 - 2(17)
s = 47 - 34
s = 13
Hence, the values of s and c are 13 and 17, respectively.
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what happens to the probability of rejecting the null hypothesis as the obtained statistic decreases
if n decreases then the value of level of significance of each samples [tex]\alpha[/tex] decreases
1. Critical Value: The value of the statistic for which the test just rejects the null hypothesis at the given significance level.
2. Power of the Test: The probability that the test correctly rejects the null hypothesis when the alternative is true.
3. Significance Level: The prescribed rejection probability of a statistical hypothesis test when the null hypothesis is true.
4. Size of the test: The probability that the test incorrectly rejects the null hypothesis when it is true.
if n decreases then the value of level of significance of each samples [tex]\alpha[/tex] decreases and hence 1- [tex]\alpha[/tex] increases which are called the rejection of test sample increases
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If f(x) = 4x5 - x - 3, then what is the remainder when f(x) is divided by x - 3?
The remainder of the division of the given polynomial by (x - 3) is 966.
From the question, we have
f(x) = 4x^5 - x - 3
The remainder of the division is the f(x) at x= 3
f(3) = 4*3^5 - 3 - 3
=972-6
=966
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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The mean of a normal distribution is 400 kilos. The standard deviation is 10 kilos. What is the probability of a weight between 420 kilos and the mean of 400
kilos?
****
0.1932
O 0.4772
0.4332
O0.5000
Second option is correct 0.04772.
The probability of a weight between 420 kilos and the mean of 400
kilos = 0.4772
Mean of a normal probability distribution is μ = 400 kilos
And standard deviation σ = 10 kilos
Let x be the variable in kilos.
X is between 400 kilos and 420 kilos
P( 400 < X < 420 ) = P ( 400 - μ < X - μ < 420 - μ)
= P ( (400-μ)/σ < (X-μ)/σ < (420-μ)/σ )
= P ( (400 - 400) /10 < Z < (420 - 400)/10 )
= P ( 0 < Z < 2 )
= 0.4777 from the table appendix B1.
The link for the appendix table B1 :
www.webassign.net%2Faswsbe13%2Fappendix-b.pdf&usg=AOvVaw3QlkaDTdGZ1Z01YZPYCL6h
The probability of a weight between 420 kilos and the mean of 400
kilos = 0.4772
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Find a polynomial function with real coefficients that has the given zeros
-1, 8,3 - 21,
A polynomial function with real coefficients that has the given zeros -1, 8, 3, -21 is x^4−11x^3−197x^2−297x+504.
In the given question we have to find a polynomial function with real coefficient that has the given zeros -1, 8,3, -21.
The given zeros are -1, 8,3 - 21.
Let the variable is x.
So the factor from the given zeros are
(x-1), (x+8), (x+3), (x-21)
To find the polynomial we multiply the factors to each other.
=(x-1)(x+8)(x+3)(x-21)
We firstly multiply the factor with the pair of two using the distributive property.
={x(x-1)+8(x-1)}{x(x+3)-21(x+3)}
=(x^2-x+8x-8)(x^2+3x-21x+63)
Simplifying
=(x^2+7x-8)(x^2-18x+63)
=x^2(x^2+7x-8)-18x(x^2+7x-8)+63(x^2+7x-8)
=(x^4+7x^3-8x^2)-(18x^3+126x^2-144x)+(63x^2+441x-504)
=x^4+7x^3-8x^2-18x^3-126x^2+144x+63x^2+441x-504
=x^4−11x^3−197x^2−297x+504
Hence, a polynomial function with real coefficients that has the given zeros -1, 8, 3, -21 is x^4−11x^3−197x^2−297x+504.
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A & B = (A + B) x A + (A - B) divided by B. find the value of 4 & - 2.
Answer:
-7
Step-by-step explanation:
A= 4
B= -2
((4-2) × 4 + (4+2))/-2
14/-2
-7
5.03 exam Solve three and two fifths plus three and four sixths
Answer:
seven and two thirtieths
Step-by-step explanation:
3 2/5 + 3 4/6 find an equal value between 5 and 6
3 12/30 + 3 20/30
12+20=32
32/30=1 2/30
3+3+1=7
7 2/30
There are two more quarters than dimes and as many nickles as quarters and dimes together. The total amount of money is 3.75. How many quarters, dimes and nickles are there?
Answer: 9 quarters, 7 dimes, & 16 nickels
Step-by-step explanation:
We set number of dimes as d:
Number of quarters: d + 2Number of nickels: d + 2 + d = 2d + 2So, set up the equation to solve:
[tex]0.10d+0.25(d+2)+0.05(2d+2)=3.75\\\\0.10d+0.25d+0.5+0.1d+0.1=3.75\\\\0.45d=3.75-0.5-0.1=3.15\\\\d=7[/tex]
So now that we know there're seven dimes, we can plug them in our initial equations to find the number of quarters and nickels:
Number of quarters: d + 2 = 7 + 2 = 9Number of nickels: d + 2 + d = 2d + 2 = 2(7) + 2 = 16