2
Find the slope and y-intercept from the following graph of a linear equation.
4
-5
-4
-3
- 2
N
2
3
4
5
-1
X
-2
-3
-
-5
Answer:
is 5
Step-by-step explanation:m
..
Directions: Find the unit rate (per 1) for eac
your work for each.
Find each unit rate. Round your answer to the
1. type 800 words in 12 minutes how many words per minute
The unit rate for typing words is 66.67 words per minute.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
You type 800 words in 12 minutes.
To find the unit rate:
The unit rate means, terms per 1 minute.
We have used minute for this particular expression.
Use division operation,
Unit rate = 800 / 12 words per minute.
Unit rate = 66.67 words per minute.
Therefore, 66.67 words per minute is the unit rate.
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please help me solve
The equation for the line of best fit is: C. y = 0.894x + 0.535.
How to determine the equation for the line of best fit?In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;
x y x² y² xy__
5 4 25 16 20
6 6 36 36 36
9 9 81 81 81
10 11 100 121 110
14 12 196 144 168
Sum 438 398 415
Next, we would calculate the mean of the x and y variables as follows;
Mean = [∑(x)]/n
Mean = 44/5
Mean, \(\bar{x}\) = 8.8
Mean = [∑(y)]/n
Mean = 42/5
Mean, \(\bar{y}\) = 8.4
∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)
∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4
∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²
∑(x - \(\bar{x}\))² = 50.8
Now, we can determine the slope coefficient for the line of best fit:
Slope (b) = 45.4/50.8
Slope (b) = 0.894.
Lastly, we would determine the intercept (a) as follows;
\(a = \bar{y} - b\bar{x}\)
a = 8.4 - (0.894)8.8
a = 0.535
Therefore, the required equation is y = 0.894x + 0.535.
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Find the area of each parallelogram below. Show all of your work.
Answer:
i
Step-by-step explanation:
Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.
hope this helps
<3
srry if this is wrong
Olivia measures the heights of two trees and the lengths of their shadows. She notices that the height of each tree and the length of its shadow are directly proportional. One of the trees has a height of 15 m and a 10 m long shadow. The other tree has a 14.4 m long shadow. Calculate its height, in metres (m). Give any decimal answers to 1 d.p. 15 m 10 m ? m 14.4 m
Step-by-step explanation:
directly proportional means
y = kx
with k being a constant factor for all values of x.
we get k by using the given data point (10, 15).
15 = k×10
k = 15/10 = 1.5
so, now for the other tree we know k and x and calculate y
y = 1.5×14.4 = 21.6 m
it is 21.6 m tall (its height is 21.6 m).
ANSWER ASAP PLEASE PLEASE Which equation represents the relationship between the number of shades of the shape, s, and the number of hexagons, n?
Answer:
s=4n+2
Step-by-step explanation:
1 hexagon has 6 sides 4(1)+2=6
2 hexagons have 10 sides (the shared side disappears_ 4(2)+2=10
3 hexagons have 14 sides 4(3)+2=14
Angle α lies in quadrant II, and tanα=−12/5. Angle β lies in quadrant IV, and cosβ=35.
What is the exact value of cos(α+β)?
Enter your answer in the box.
Answer:
Step-by-step explanation:
[-5/13] 3/5 +12+13 [-4/5 = - 63/65
Find the distance between point P and line L
The distance between point P and line L is 16/9√(13).
To find the distance between point P and line L, we can use the formula for the distance between a point and a line in two-dimensional space. The formula is as follows:
Let P = (x1, y1) be the point and L be the line ax + by + c = 0. Then the distance between P and L is:
|ax1 + by1 + c|/√(a² + b²)
To find a, b, and c for the given line, we need to put it in slope-intercept form y = mx + b by solving for y.
2x - 3y = 12=> 2x - 12 = 3y=> (2/3)x - 4 = y
The slope of the line, m, is the coefficient of x, which is 2/3. Therefore, the line is:
y = (2/3)x - 4The values of a, b, and c are: a = 2/3b = -1c = -4
Now we can substitute the coordinates of P and the values of a, b, and c into the formula for the distance between a point and a line.
Let P = (3, 5).|a(3) + b(5) + c|/√(a² + b²)= |(2/3)(3) - 1(5) - 4|/√[(2/3)² + (-1)²]= |-4/3 - 4|/√(4/9 + 1)= 16/9√(13).
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Calculate the probability for the following situation, then select the correct answer:
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a head AND an odd number on the die AND a card greater than 6 (assume the ace is equal to 1) from the deck?
The probability is P = 0.135
How to find the probability?
First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.
P(head) = 1/2P(odd number) = 3/6 (there are 3 odd numbers on the dice)P(card greater than 6) = 28/52 (28 cards with numbers larger than 6).The joint probability is given by the product between the individual probabilities, so we get:
P = (1/2)*(3/6)*(28/52) = 0.135
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What is the range of the conic section?
(yl-3≤y≤3)
Answer:
1the answer for this is easy it is 4.4
a recipe uses x cups of flour and y cups of sugar. a baker makes n batches of the recipe. to help determine what ingredients he needs, the baker writes the expression nx + ny. what does ny represent?
y = number of cups of sugar for one batch
ny = number of cups of sugar for n batches
n is some positive whole number and so is y. So let's say that n = 5. This would mean ny = 5y represents the number of cups of sugar needed for five batches.
what is the value of x that makes l1||l2
Answer: 10
Step-by-step explanation:
By the alternate interior angles theorem,
\(4x=2x+20\\2x=20\\x=10\)
Please help me please
MATH: GRAPHS AND FUNCTIONS 3. HELP! 12 PTS (HARD)
Answer:
Step-by-step explanation:
An investor wants to save money to purchase real estate. She buys an annuity with yearly payments that earn 5.3% interest compounded annually payments will be made at the end of each year find the total value of the annuity in 16 years if each yearly payment is 693.
The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity,
P is the yearly payment,
r is the interest rate per compounding period, and
n is the number of compounding periods.
In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.
Let's substitute these values into the formula and calculate the total value of the annuity:
FV = 693 * ((1 + 0.053)^16 - 1) / 0.053
FV = 693 * (1.053^16 - 1) / 0.053
Using a calculator, we can evaluate the expression inside the parentheses:
1.053^16 ≈ 1.9738
Substituting this value back into the formula:
FV = 693 * (1.9738 - 1) / 0.053
FV = 693 * 0.9738 / 0.053
FV ≈ 12739.62
Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
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Mikhail wants to invest $3,800.00 in a savings account. Determine the simple interest rate required for Mikhail's investment to grow to $11,500.00 in 20 years.
The simple interest rate for Mikhail's investment to grow to $11,500.00 in 20 years is solved to be 10.13%
How to find the simple interest rateThe rate for the simple interest tis calculated using the formula for simple interest.
The formula is stated as
Simple interest = Principal * time * rate / 100
In the problem the give data include
principal = $3,800.00
rate = ?
time = 20 years
simple interest = $11,500.00 - $3,800.00 = $7700
plugging in the values
Simple interest = Principal * time * rate / 100
7700 = 3800 * 20 * r / 100
7700 * 100 = 3800 * 20 * r
770 000 / (3800 * 20 ) = r
r = 10.13%
The interest rate is 10.13%
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Trina has a credit card that uses the adjusted balance method. For the first 10
days of one of her 30-day billing cycles, her balance was $780. She then
made a purchase for $170, so her balance jumped to $950, and it remained
that amount for the next 10 days. Trina then made a payment of $210, so her
balance for the last 10 days of the billing cycle was $740. If her credit card's
APR is 17%, which of these expressions could be used to calculate the
amount Trina was charged in interest for the billing cycle?
OA. (30)($780)
365
B.
O C.
D.
0.17
365
0.17
365
0.17
365
30
30
(10 $780+10 $950 +10 $210)
30
10
$780+10$950+10 $740
30
•30) ($570)
The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is (APR / 365) x 30 days x adjusted balance.
What is the adjusted balance method?The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.
The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.
Credit card interest method = adjusted balance method
Beginning balance = $780
Purchase = $170
Payment = $210
Adjusted balance, AB = $740 ($780 + $170 - $210)
APR = 17% = 0.17 (17/100)
The interest charged = (APR / 365) x 30 days x adjusted balance
= $10.34 [(0.17/365) x 30 x $740]
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solve each equation by finding square roots. If the equation has no real number solution, write no solution. 5z^2-45=0
Answer:
Z = +3
Step-by-step explanation:
3 squared is 9 and 9 times 5 is 45 so 45 minus 45 is zero
Answer:
Z = +or- 3, or Option A, would be the best answer choice out of the ones provided above.
..vertex: (4, -1)
f(3) = -6
Answer:
\(\huge\boxed{f(x)=-5(x-4)^2-1=-5x^2+40x-81}\)
Step-by-step explanation:
The vertex form of an equation of a parabola:
\(f(x)=a(x-h)^2+k\)
\((h;\ k)\) - vertex
We have
vertex \((4;\ -1)\to h=4;\ k=-1\)
\(f(3)=-6\)
Therefore we have:
\(f(x)=a(x-4)^2+(-1)=a(x-4)^2-1\)
Substitute \(x=3\) and \(f(3)=-6\)
\(a(3-4)^2-1=-6\qquad|\text{add 1 to both sides}\\\\a(-1)^2=-6+1\\\\a(1)=-5\\\\a=-5\)
Finally:
\(f(x)=-5(x-4)^2-1=-5(x^2-2(x)(4)+4^2)-1\\\\=-5(x^2-8x+16)-1=-5x^2+(-5)(-8x)+(-5)(16)-1\\\\=-5x^2+40x-80-1=-5x^2+40x-81\)
4.2 The Court lines are 50 mm wide. Court paint covers 7 m² per litre of paint. 4.2.1 Calculate the total length of the centre circle and the two goal semi circles to be repainted. You may use the formula: Total length Circumference of a centre circle + 2 x Circumference of a semicircle =
The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.
How to calculate the Calculate the total length of the centre circle and the two goal semi circles to be repaintedGiven:
Court lines are 50 mm wide.
Court paint covers 7 m² per litre of paint.
The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr
Radius of the entire circle = 9 m / 2 = 4.5 m
Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m
Circumference of the centre circle = 2π(4.45 m) = 27.94 m
Next, let's calculate the circumference of the semicircles:
The semicircles are half circles, so the circumference is given by the formula: Circumference = πr
The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.
Circumference of a semicircle = π(4.5 m) = 14.14 m
Total length = Circumference of the centre circle + 2 x Circumference of a semicircle
Total length = 27.94 m + 2(14.14 m)
Total length = 56.22 m
Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.
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has anyone took the Transformations and Congruence Unit Test for math in 8th grade connexus
Answer:
yea I did a few years ago but I’m in 11th grade now
Step-by-step explanation:
I will mark you brainiest!
Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a leg = 5?
A) 5, 5, 5
B) 5, 1, 5
C) 1, 5, 5
D) 1, 1, 5
The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.
Explain about property of the right triangles?The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.
A triangle's (of all varieties) cumulative sum of angles is 180°.The length of a triangle's two longest sides added together is longer than for third side.Similar to this, the length of a third side of a triangle's third side is shorter than the difference between its two sides.For the given question:
Triangle with degree angles - 45-45-90
It means two legs are of same length 5 units.
Then, hypotenuse H will be:
H² = 5² + 5²
H² = 25 + 25
H² = 50
H = 5√2
Thus, the correct third side of the triangle will be 5√2.
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I don’t know how to do this problem help me!!
\(x-9z^5+4z+11+2z^5+14=-5z^5-3z+25\\x=2z^5-7z\)
Therefore, it's \(2z^5-7z\).
10-10=69.420!!!!!!!!!!
XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
The calculated value of k on the line is 9
How to determine the value of kFrom the question, we have the following parameters that can be used in our computation:
XZ is the perpendicular bisector of segment WY
This means that
WX = XY
substitute the known values in the above equation, so, we have the following representation
3k - 4 = 2k + 5
So, we have
3k - 2k = 4 + 5
Evaluate
k = 9
Hence, the value of k is 9
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Find the probability that a randomly selected point within the square falls in the red-shaded triangle. 3 3 4 P = [?] 4
The required probability is 3 √7 / 32.
Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.
Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7
The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is: P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.
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The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger
has a waiting time greater than 2.25 minutes.
Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
(Simplify your answer. Round to three decimal places as needed.)
The probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is given as follows:
0.75.
What is the uniform probability distribution?It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.
The probability of finding a value above x is:
\(P(X > x) = \frac{b - x}{b - a}\)
Uniformly distributed between 0 and 9 minutes, hence the parameter are given as follows:
a = 0, b = 9.
Hence the probability is given as follows:
P(X > 2.25) = (9 - 2.25)/(9 - 0)
P(X > 2.25) = 0.75.
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NO LINKS!!! URGENT HELP PLEASE!!
1. If P dollars is deposited in a savings account that pays interest at a rate of r% per year compounded continuously, find the balance after t years. Round your answer to the nearest cent
P = 120
r = 2 1/2
t = 8
2. An investment of P dollars increased to A dollars in t years. If the interest was compounded continuously, find the interest rate. Round your answer to the nearest whole number
A = 4055
P = 1000
t = 20
______%
Answer:
1: the balance after 8 years is approximately $151.78.
2: is approximately 7%.
Step-by-step explanation:
1: The balance after t years with continuous compounding can be calculated using the formula:
B = Pe^(rt)
Where:
P = 120 dollars (initial deposit)
r = 2.5% = 0.025 (interest rate in decimal form)
t = 8 years
Substituting these values into the formula, we get:
B = 120e^(0.025*8) ≈ 151.78
Therefore, the balance after 8 years is approximately $151.78.
2: The interest rate can be found using the formula:
A = Pe^(rt)
Taking the natural logarithm of both sides and solving for r, we get:
r = ln(A/P) / t
Where:
A = 4055 dollars (final amount)
P = 1000 dollars (initial investment)
t = 20 years
Substituting these values into the formula, we get:
r = ln(4055/1000) / 20 ≈ 0.0774
Converting to a percentage and rounding to the nearest whole number, we get:
r ≈ 7%
Therefore, the interest rate, if compounded continuously, is approximately 7%.
Answer:
1. $146.57
2. 7%.
Step-by-step explanation:
1.
The formula for continuous compounding is:
A = Pe^(rt)
Where:
A = the balance after t years
P = the principal amount
r = the annual interest rate (expressed as a decimal)
t = the time in years
To use this formula, we first need to convert the annual interest rate to a decimal:
r = 2 1/2 = 2.5%
r = 2.5/100 = 0.025
Now we can plug in the values:
A = 120e^(0.025*8)
A ≈ $146.57
Therefore, the balance after 8 years is approximately $146.57
2.
The formula for continuous compounding is: A = Pe^(rt)
Where:
A = the balance after t years
P = the principal amount
r = the annual interest rate (expressed as a decimal)
t = the time in years
We can rearrange this formula to solve for the interest rate:
r = ln(A/P)/t
Where ln represents the natural logarithm.
Now we can plug in the given values:
r = ln(4055/1000)/20
r ≈ 0.069or 7.1%
Therefore, the interest rate, rounded to the nearest whole number, is 7%.
Thereeeeeeeeeeeeeeeeeeeeeeee
Answer:
1. 0.5%
2. 3%
3. 20%
4. 250%
5. 500%
hope this helps have a blessed day :)
What numbers round to 200,000 when rounded to the nearest hundred thousand? Select all that apply.
165,400 and 220,574
=================================================
Explanation:
The value in the hundred thousands digit of 165,400 is "1". Just to right of it is "6", which is five or more, meaning we bump that "1" up to "2". Everything else gets replaced with a zero.
The number 165,400 rounds to 200,000 when rounding to the nearest hundred thousand. The number 165,400 is closer to 200,000 than it is to 100,000.
-------------------------
In 220,574 we have the first "2" in the hundred thousands digit with another "2" just to the right of it. Since that second "2" is not five or more, we replace everything with zeros to get 200,000. We won't bump that first "2" up by one.
220,574 is closer to 200,000 than it is to 300,000.
These two sections help show why choices C and D are the answers.
--------------------------
Something like 142,026 rounds to 100,000 for similar reasoning as the previous section. So we can rule out choice B.
Choice A rounds to 100,000 as well, so we can rule it out also.
Choice D rounds to 1,000,000 which means we cross it off the list.