Answers
Answer:
y=4x+1
Step-by-step explanation:
Our slope is 4/1 or 4, so we know 4x is our slope. Then our y intercept is at (0,1), so we know our b=1. So we know our equation is y=4x+1.
-Hope this helped.
Related Questions
Find m/1 and m/2
1
95°
2
m<1 =
m<2=
Answers
Answer: 85
Step-by-step explanation:
What is the probability of drawing an event number then drawing a diamond out of a deck?
Answers
Probability is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability of drawing an even number from a deck of cards is 5/13.
The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The number of even numbers in a deck of cards.
= 5 x 4
= 20
The number of diamonds in a deck of cards.
= 4
Now,
The probability of drawing an even number from a deck of cards.
= 20 / 52
= 10/26
= 5/13
Now,
The remaining cards.
= 52 - 20
= 32
The probability of drawing diamonds after drawing the even numbers.
= Number of diamonds / remaining cards
= 4 / 32
= 1/8
Thus,
The probability of drawing an even number from a deck of cards is 5/13.
The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.
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which statement explains why ABC is congruent to A’B’C’?
Answers
The distance of all the side of ΔABC and ΔA'B'C' are equal which makes them congruent triangles.
What is congruent triangles?
When all 3 corresponding sides and every one 3 corresponding angles area unit equal in size, 2 triangles area unit aforementioned to be congruent.
Main Body:
First let us find the co-ordinates of both the triangles.
A= (3,5)
B = (-2, 3)
C= (-4,-1)
A' =(10,-5)
B'= (5, -3)
C' =(3,1)
Distance between two points = d=√((x₂ – x₁)² + (y₂ – y₁)²).
In ΔABC
Distance of side AB = √((3 –(-2) )² + (5 –3 )²)
= √5² +2²
= √29
Distance of side BC = √((-2-(-4) )²+ (3 -(-1 )²)
= √20
Distance of side CA = √((3-(-4) )² + (5-(-1) )²)
= √7² + 6²
= √85
Distance of side A'B' = √((10 -5)² + (-5-(-3))²
= √(5² +2²)
= √29
Distance of side B'C' = √ ((5-3)² + (-3 -1)² )
= √ (2)² +4²
= √20
Distance of side C'A' = √((10-3)² + ( -5-1)²)\
= √(7)² + 6²
= √85
This shows each side of ΔABC is equal to side of ΔA'B'C'.
hence the triangles are congruent.
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4.
The sum of two odd consecutive integers is 88. Find the integers.
Answers
Answer:
43 and 45
Step-by-step explanation:
→ State an expression for 2 odd consecutive numbers
2x + 1 and 2x + 3
→ Find the sum
4x + 4
→ Equate to 88
4x + 4 = 88
→ Minus 4 from both sides
4x = 84
→ Divide both sides by 4
x = 21
→ Substitute into original expressions
43 and 45
Solve The Problem
All the students in grades 3, 4 and 5 are going on a field trip to Coney Island
Each grade has 125 students. The cafeteria needs to pack lunches. About how
many students are going on the trip? Represent the exact amount of student
in all three grades using an array, How many students are there altogether?
Answers
The number of Students going on the trip is 375.
In the question,
It is given that:
There are 125 students in Grade 3.
There are 125 students in Grade 4.
There are 125 students in Grade 5.
So, Total number of students going on trip = Number of students in Grade 3 + Number of students in Grade 4 + Number of students in Grade 5
= 125 + 125 + 125 = 375.
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The area of the play area is 286.56 square feet. A border is planned around the perimeter of the play area. How many feet of material are needed for the border?
Answers
Answer:
Step-by-step explanation:
The length of material needed for the border is the perimeter of the backyard play area
How to calculate the length of material needed
The area of the play area is given as:
The area of a trapezoid is calculated using:
Where L1 and L2, are the parallel sides of the trapezoid and H represents the height.
The given parameter is not enough to solve the length of material needed.
So, we make use of the following assumed values.
Assume that the parallel sides are: 25 feet and 31 feet long, respectively.
While the other sides are 10.2 feet and 8.2 feet
The length of material needed would be the sum of the above lengths.
So, we have:
Using the assumed values, the length of material needed for the border is 74.4 feet
1. Two spherical solids have masses of 15g and 405kg respectively. If the radius of the smaller sphere is 10cm. Find the radius of the bigger sphere.
2. Triangle PQR is such that the angle P=90° and PQ=37cm. Find RP when angle Q=16° degrees (Use tan 46°=1.04).
Answers
The radius of the bigger sphere is 30cm.
Two spherical solids have masses of 15g and 405kg respectively
Mass is directly proportional to volume for same metal (Density)
Let Mass of Solid 1 be M₁ and Volume be V₁
Mass of Solid 2 be M₂ and Volume be V₂
Now M₁/M₂ = V₁/V₂
Volume of sphere is directly proportional to R³
So, M₁/M₂ = V₁/V₂ = R₁³/R₂³
15/405000 = 10³/x³
∛15/∛405000 = 10/x
2.466/73.986 = 10/x
2.466x = 73.986 x 10
x = 739.86/2.466
x = 30
Therefore, the radius of the bigger sphere is 30cm.
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In the acute triangle ABC with angle ACB = 60°, M is the midpoint of side AB. Points D and E are the height points on sides BC and AC, respectively. Show: The triangle MDE is equilateral
Answers
An equilateral triangle in geometry is a triangle with three equal-length sides. An equilateral triangle has congruent sides, which means that each side is the same length. The triangle MDE is equilateral only because it is midpoint of ACB
Explain about the Acute triangle?If the square of the longest side is smaller than the sum of the squares of the two smaller sides, the triangle is said to have an acute angle according to Pythagoras's theorem. Given a triangle with sides "a," "b," and "c," with side "a" being the longest, the triangle is steeply angled if "a2" exceeds "b2" plus "c2."
By adding the squares of the triangle's two smaller sides and comparing the result to the square of the largest side, you may determine whether the triangle is acute, right, or obtuse. The triangle is sharp because this total is higher.
Isosceles, equilateral, or scalene acute triangles are all possible. An acute triangle's longest side is located across from its biggest angle.
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Find the number of decibels for the power of the sound given. Round to the nearest decibel.
A rocket engine,
2.51 ⨯ 10−5
watts/cm2
Answers
The 2.51 × 10⁻⁵ Watts/cm² sound intensity of the sound from the rocket engine has a decibel level of 114 dB
What is a decibel?A decibel is a unit to measure the relative loudness of sound or to express the ratio electrical or acoustic power.
The intensity of the sound of the rocket engine = 2.51 × 10⁻⁵ Watts/cm²
Converting the unit of the sound intensity to Watts/m² gives;
1 cm² = 0.0001 m²
10,000 cm² = 1 m²
2.51 × 10⁻⁵ Watts/cm² = 10000 × 2.51 × 10⁻⁵ Watts/m² = 0.251 Watts/m²
The equation for the decibel from the power of sound is presented as follows;
[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{I}{I_0} \right)[/tex]
Where;
I₀ = 10⁻¹² W/m²
Which gives;
[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{0.251 }{10^{-12}} \right) = 113.9967373215 \approx 114[/tex]
The number of decibels for the power of the sound given to the nearest decibel by the rocket engine is 114 decibels
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Jaden has a part-time job working for a landscaping company. He earns $25 for each lawn-mowing job, l, and $20 for each pulling-weeds job, w. This can be modeled by 25l+20w. Evaluate for l=4 and w=6 to find how much money Jaden will earn for 4 lawn-mowing jobs and 6 pulling-weeds jobs. Please helpppp
Answers
Answer:
220.
Step-by-step explanation:
If you plug in 4 for L and 6 for W, you are left with 25(4) + 20(6), which is equivalent to 100+120 = $220
Answer:
220
Step-by-step explanation:
The Helping Hands Student Club set a goal to raise $4,000 by the end of the school year for a project. After 3 months, it reaches 42% of its goal. How much was raised during the first 3 months?
Answers
During the first 3 months students club has raised fund of $1680.
Given that, The Helping Hands Student Club set a goal to raise $4,000 by the end of the school year for a project.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
After 3 months, it reaches 42% of its goal.
The fund raised during the first 3 months is
42% of 4000
= 42/100 × 4000
= 42×40
= $1680
Therefore, during the first 3 months students club has raised fund of $1680.
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Answer:
$1,680
Step-by-step explanation:
HELP FOR BRIANLEST
Answers
The function will be;
⇒ y = 3x - 1
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The domain and the range is shown in table.
Two points on the line are (2, 5) and (7, 20).
Now,
Since, The equation of line passes through the points (2, 5) and (7, 20).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (20 - 5) / (7 - 2)
m = 15 / 5
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - 5 = 3 (x - 2)
⇒ y - 5 = 3x - 6
⇒ y = 3x - 6 + 5
⇒ y = 3x - 1
Therefore, The function will be;
⇒ y = 3x - 1
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Find the average rate of change.
Answers
The average rate of change = 1.59 ≈ 2
The average rate of change can be calculated by
1) The first one = [tex]\frac{3 + 0}{2}[/tex] = 1.5
2 ) the second can also be solved by ; 8 + 2/ 2 = 5
3 ) the third one will be 20 + 6 / 2 = 13
4) 8.5
5) 12.5
To calculate the average rate of change
we will first add all the distance
Adding all the distance we will get the sum = 3 + 8 + 20 + 10 + 10 = 51
The total time = 2 + 6 + 9 +15 = 32
Thus the average rate of change = 51 / 32 = 1.59
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F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2)
I need to factor and find the zeros.
Answers
Answer:
[tex]\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)[/tex]
[tex]\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=3x^3-2x^2-11x+10[/tex]
If (x + 2) is a factor then:
[tex]\implies f(x)=(x+2)(ax^2+bx+c)[/tex]
Expand:
[tex]\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c[/tex]
[tex]\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c[/tex]
[tex]\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c[/tex]
To find a, compare the coefficients of x³:
[tex]\implies a=3[/tex]
To find b, substitute the found value of a into the coefficient for x² and compare:
[tex]\implies 2a+b=-2[/tex]
[tex]\implies 2(3)+b=-2[/tex]
[tex]\implies b=-8[/tex]
To find c, compare the constants:
[tex]\implies 2c=10[/tex]
[tex]\implies c=5[/tex]
Therefore:
[tex]\implies f(x)=(x+2)(3x^2-8x+5)[/tex]
Now factor (3x²-8x+5):
[tex]\implies 3x^2-3x-5x+5[/tex]
[tex]\implies 3x(x-1)-5(x-1)[/tex]
[tex]\implies (3x-5)(x-1)[/tex]
Therefore the factored function is:
[tex]\implies f(x)=(x+2)(3x-5)(x-1)[/tex]
Zero Product Property
[tex]\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}[/tex]
To find the zeros, set each factor equal to zero and solve for x:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies 3x-5=0 \implies x=\dfrac{5}{3}[/tex]
[tex]\implies x-1=0 \implies x=1[/tex]
Therefore, the zeros of the function are:
[tex]x=-2, \quad x=\dfrac{5}{3},\quad x=1[/tex]
The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given
by the function D(h) = 111.7√/h. Find the height that would allow a person to see 40 kilometers.
h=km
(Round to two decimal places as needed.)
...
Answers
Answer:
0.13 km
Step-by-step explanation:
Rearrange the formula to solve for [tex]h[/tex]:
[tex]D(h)=111.7\sqrt{h}[/tex]
[tex]\frac{D(h)}{111.7}=\sqrt{h}[/tex]
[tex](\frac{D(h)}{111.7})^2=(\sqrt{h})^2[/tex]
[tex](\frac{D(h)}{111.7})^2=h[/tex]
Then, substitute the distance of 40 km:
[tex](\frac{40}{111.7})^2=h[/tex]
[tex]0.13\approx{h}[/tex]
The scale on a map states that 1 centimeter corresponds to 15 kilometers Find how far apart two cities are if their corresponding points on the map are 13 centimeters apart
Answers
In this case, they are both centimetres, so they remain constant. The true size, 15km, is then multiplied by 13/ 1. Then, 20 × 13 = 195. As a result, the answer is 195 kilometres.
What is scale?The term scale refers to the relationship that exists between a measurement on a model and the corresponding measurement on the actual object. A scale of 1:5 means that the size of one unit in the drawing represents five units in reality. A scale of 1:5 is used, for example, if a giraffe with a real-world height of 150 inches is represented as 30 inches on the drawing. A ratio, such as 1:100, is used to represent a scale.A drawing at a scale of 1:100 indicates that the object is 100 times smaller than it would be in real life. You could also say that one unit in the drawing equals one hundred units in real life.Therefore,
The map has a scale = 1 cm
Corresponds to = 15 kilometers
Map centimeters apart = 13 cm
Then you simply multiply the true size
= 15km, by 13/ 1.
Then, 20 x 13 = 195.
Hence, the answer is 195 kilometers.
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Expand the brackets in each expression and then
combine like terms where possible.
a -7(7a + 4b) + 10a - 10b
4x-10 y
b 6(2x+6y) -
Answers
The expanded form of 7(7a + 4b) + 10a - 10b and 6(2x+6y) will be 59x+18b and 12x+12y.
What is expanded form?
The expanding form can be used to indicate the value of each digit in a number in arithmetic. Numbers that are expressed as the sum of each digit multiplied by its place value are known as expanded numbers.
It is given that,
a) 7(7a + 4b) + 10a - 10b
b) 6(2x+6y) -
a)
[tex]=7(7a + 4b) + 10a - 10b \\\\ =49a+28b+10a-10b \\\\ =49a+10a+28b-10b \\\\ =59a+28b-10b \\\\ =59a+18b[/tex]
b)
= 6(2x+6y) -
=12x+12y
Thus, the expanded form of 7(7a + 4b) + 10a - 10b and 6(2x+6y) will be 59x+18b and 12x+12y.
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A wasp is 1.39-10 meters long.
A pygmy rabbit is 24-10¹ meters long.
How much langer is the pygmy rabbit than the
wase?
Answers
Pygmy rabbit is 22.61-10 meters longer than the wasp.
Given:
A wasp is 1.39-10 meters long.
A pygmy rabbit is 24-10¹ meters long.
Pygmy rabbit longer than the wasp = size of pygmy rabbit - size of wasp.
= (24 - 1.39)-10meters
= 22.61-10 meters.
Therefore pygmy rabbit is 22.61-10 meters longer than the wasp.
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2÷7756
Find the quotient.
77.56 divided by .2 = ?
Answers
By division, the following results are obtained
[tex]2 \div 7756\\[/tex] = 0.0025
[tex]77.56 \div 0.2 = 387.8[/tex]
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
The quotients of the two divisions are shown below-
[tex]2 \div 7756\\[/tex] = 0.0025
[tex]77.56 \div 0.2\\7756 \div 20 \\387.8[/tex]
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Elizabeth and Herman are collecting aluminum cana for a frundraiser at their school. Elizabeth was able to collect 50 cans each day from Monday to Friday, Herman was able to collect double that amount each day except Friday, when he collected none. Each can is worth 2 cents. What are the quantities in this situation?
Answers
The total cans collected by both Elizabeth and Herman is 650 and the total amount of money realized is 1300 cents.
What is rate?A rate is a ratio in which the two terms being compared have different unit's.For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.
The aluminum cans collected by Elizabeth from Monday to Fridays is 50× 5days = 250 cans
Herman collected double from Monday to Thursday and collected non on Friday, therefore the total cans collected by Herman = 50×2× 4 days= 400cans
the total cans collected = 250+ 400 cans = 650cans
therefore the total money realized since 1 can is with 2 cent is 650× 2= 1300cents
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Hank rents 9 cases of plates.He has 250 guests attending the banquet. There are 30 plates in each case. Did Hank rent enough plates? Explain
Answers
Answer:
yup
Step-by-step explanation:
so to find the amount of plates he has we :
30*9 = 270
How many guests :
250
Hank has 20 extra plates,
hope this helps :)
Complete the model to find-9 + 3 Show your work
Answers
Answer:
Answer is 0. If you have to owe someone 9 dollars and they give you nine back it is 0. You can also rearrange the problem to 9-9 (same thing) which is 0
What is an equation of the line that passes through the point ( − 6 , − 8 ) (−6,−8) and is parallel to the line x − 2 y = 6 x−2y=6?
Answers
An equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6 is y=x/2-5.
Given that, an equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
We know that, the slope of a line parallel to given line is m1=m2.
Here, x−2y=6
⇒ 2y=x-6
⇒ y=x/2-3
So, slope = 1/2
The slope of a line parallel to the given line = 1/2
Now, put m=1/2 and (x, y)=(-6, -8) in y=mx+c and solve for c
-8=1/2(-6)+c
⇒ c=-8+3
⇒ c=-5
Thus, y=x/2-5
Therefore, an equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6 is y=x/2-5.
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A single ticket to the magic show costs ttt dollars, but there is a discount of 5\%5%5, percent per ticket if a group buys 101010 tickets.
The expression 10t-10\cdot 0.05t10t−10⋅0.05t10, t, minus, 10, dot, 0, point, 05, t describes the total cost of buying 101010 tickets for a group.
Match each amount in the situation with the expression that represents it.
Situation
Expression
(Kahn academy)
Answers
The total cost for the group of ten people after discount is 10 t - 0.5 t.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Discount = 5%
Total tickets= 10
We have t represents the cost of one ticket.
So, For 10 person the cost of the ticket = 10t
Now, after discount the price of tickets
= 5% of 10t
= 0.5 t
Hence, the total cost for the group of ten people after discount is 10 t - 0.5 t.
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Deduce the following in standard form: 3 −
Answers
The standard form of the given fractions are;
(i) −45/30
(ii) 16/−36
(iii) −3/−15
(iv) 68/−119
How to write fractions in standard form?
A fraction is said to be in standard form when both the numerator and denominator are co-prime numbers. Thus;
1) −45/30; Divide both numerator and denominator by 15 to get;
(−45 ÷ 15)/30
= -3/2.
(2) 16/−36; Divide both numerator and denominator by 4 to get;
(16 ÷ 4)/(−36 ÷ 4)
= -4/9
(iii) −3/−15; Divide both numerator and denominator by -3 to get;
(-3 ÷ 4)/(−15 ÷ 4)
1/5
(iv) 68/−119; Divide both numerator and denominator by 19 to get; -4/7
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Complete question is;
Reduce each of the following rational numbers in standard form:
(i) −45/30
(ii) 16/−36
(iii) −3/−15
(iv) 68/−119
Which equation represents this statement?
3 times the sum of 4 and a number is 18.
O 3 +4n = 18
O 3n+ 4 = 18
O 3.4+ n = 18
O 3 (n+4)= 18
Answers
The equation represents the statement "3 times the sum of 4 and a number is 18 " is option (D) 3(n+4) = 18
The statement is
3 times the sum of 4 and a number is 18
The equation is the the mathematical statement the represents the relationship between two expression or variables with an equal sign.
Consider the unknown number = n
Sum of 4 and the number = n + 4
3 times the sum of 4 and the number = 3(n + 4)
3 times the sum of 4 and a number is 18
3(n + 4) = 18
Hence, the equation represents the statement "3 times the sum of 4 and a number is 18 " is option (D) 3(n+4) = 18
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If India works overtime, she receives an
hourly rate of 1-times her regular hourly 1/2
rate. What is her hourly overtime rate?
Answers
After solving, 50% is her hourly overtime rate.
In the given question,
India works overtime, she receives an hourly rate of 1-times her regular hourly 1/2 rate.
We have to find her hourly overtime rate.
India is working overtime so her regular hourly rate is 1/2.
Evaluating the expression
We find her hourly overtime rate in percentage.
She receive overtime rate for 1 time is 1/2 rate.
We can write 1/2 as 0.5.
To express it as percentage we multiply and divide by 100.
= 0.5 × 100/100
= 50%
Hence, 50% is her hourly overtime rate.
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If the area to the left of x in a normal distribution is 0.193, what is the area to the right of x?
Answers
The area to the right of x in the normal distribution is 0.807
What is the normal distribution?The normal distribution is the probability distribution that helps to find the probability for continuous variables.
For a probability x, for a normal distribution, we have that
P(X ≤ x) + P(X ≥ x) = 1
How to find the area to the right of x?Since the area to the left of x in a normal distribution is 0.193, we require the area to the right of x.
Since P(X ≤ x) + P(X ≥ x) = 1 where
P(X ≤ x) = area to the left of x P(X ≥ x) = area to the right of xMaking P(X ≥ x) subject of the formula, we have that
P(X ≥ x) = 1 - P(X ≤ x)
Given that P(X ≤ x) = 0.193
Substituting this into the equation, we have
P(X ≥ x) = 1 - P(X ≤ x)
P(X ≥ x) = 1 - 0.193
P(X ≥ x) = 0.807
So, the area to the right of x is 0.807
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Use the literal symbols listed at the end of the problem to translate the given statement into an algebraic formula.
In a given weight, the number of grams equals 454 times the number of pounds. (g. p)
Choose the correct formula below.
A. g=454 +p
C. p=454g
E. g=454-p
G. g= 454
——
p
B. p=454 +g
D. p=454-g
F. g=454p
H. g= p
—
454
Answers
Pounds = p
Number(g) = 454 x p
Which means;
g = 454p
The temperature dropped 2 f every hour for 6 hours.what total number of degrees the temperature changed in the 6 hours?
Answers
The total number of degrees the temperature changed in the 6 hours is 12°F
Here,
The temperature dropped 2°F every hour for 6 hours.
We have to find,
The total number of degrees the temperature changed in the 6 hours.
Fahrenheit is a scale for measuring temperature, in which water freezes at 32 degrees and boils at 212 degrees. It is represented by the symbol ° F.
Now,
The temperature dropped 2°F every hour for 6 hours.
1 hour = 2°F
6 hour = 6 x 2 = 12°F
Hence, The total number of degrees the temperature changed in the 6 hours is 12°F.
Learn more about Degree in Fahrenheit here:
brainly.com/question/26141817
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