The probability that no one in the United States will be struck and killed by lightning tomorrow is approximately 0.835, or 83.5%.
To find the probability that no one in the United States will be struck and killed by lightning tomorrow, we can use the Poisson distribution, which models the number of rare events occurring in a fixed period of time, given the average rate of occurrence.
The Poisson distribution has the following probability mass function:
P(X = k) = (e^(-λ) * λ^k) / k!
where:
X is the random variable representing the number of events (in this case, the number of people struck and killed by lightning)
λ is the average rate of events per unit of time (in this case, the average number of people struck and killed by lightning per day)
We can use the data given in the problem to estimate the value of λ:
λ = (2457 deaths) / (36 years * 365 days/year) ≈ 0.18 deaths/day
Now we can use the Poisson distribution to find the probability that no one in the United States will be struck and killed by lightning tomorrow:
P(X = 0) = (e^(-0.18) * 0.18^0) / 0! ≈ 0.835
This means that there is a high likelihood that no one will be killed by lightning tomorrow, given the historical average rate of lightning deaths.
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Meredith's new Pomeranian puppy is 7 inches tall and 9 inches long. She wants to make a drawing of her new Pomeranian to put in her locker. If the sheet of paper she is using is 3 inches long by 5 inches, find an appropriate scale factor for Meredith to use in her drawing. (please answer I need help)
Answer:
2.3333 inches
Step-by-step explanation:
To find the appropriate scale factor, we need to determine how many times smaller the piece of paper is compared to the dog. We can start by finding the ratio of the length of the paper to the length of the dog:
3 inches / 9 inches = 1/3
Similarly, the ratio of the width of the paper to the height of the dog is:
5 inches / 7 inches = 5/7
So, the smaller of these two ratios, 1/3, is the appropriate scale factor for Meredith to use in her drawing. This means that the length of the dog in the drawing will be 9 inches * 1/3 = 3 inches, and the height will be 7 inches * 1/3 = 2.3333 inches.
0.5 + 0.163 (3 has a line over it) and i need to find it in a fraction
Answer:
[tex]\mbox{\large $0.5 + 0.16 \bar {3}$ = \boxed{\dfrac{199}{300}}}[/tex]
Step-by-step explanation:
[tex]0.16\bar{3} = 0.16333333333\\[/tex]
the 3 repeats until infinity
Let's multiply this by 100 to move the non-repeating part to the left of the decimal point
0.1633333333...... x 100 = 16.333333333333333...
.333333 = 1/3
Therefore the recurring number multiplied by 100 is
[tex]16 + \dfrac{1}{3} = \dfrac{16 \times 3 + 1}{3}=\dfrac{49}{3}[/tex]
Since this fraction was arrived at by multiplying by 100, divide this fraction by 100 to get back the fraction in its original decimal value of 0.163333
[tex]\dfrac{49}{3} \div 100[/tex]
To divide by a number, multiply by the reciprocal of that number
Reciprocal of 100 is 1/100:
[tex]\dfrac{49}{3} \div 100 = \dfrac{49}{3} \times \dfrac{1}{100} = \dfrac{49}{300}[/tex]
(You can verify this by dividing 49 by 300 in a calculator and seeing that the result is 0.163333333333333333333 i.e. 0.16333 recurring
We want to add 0.5 to this.
0.5 = [tex]\dfrac{1}{2}[/tex]
so
0.5 + 0.16333333 = 0.6633333
[tex]= \dfrac{1}{2} + \dfrac{49}{300}[/tex]
We can write [tex]\dfrac{1}{2}[/tex] as [tex]\dfrac{150}{300}[/tex] by multiplying numerator and denominator by 150
So we get
[tex]0.5 + 0.1633333 = \dfrac{150}{300} + \dfrac{49}{300} = \dfrac{150+49}{300} = \dfrac{199}{300}[/tex]
If you perform this division on a calculator you will get the answer as 0.663333 = [tex]0.66\bar{3}[/tex] which is what you get when you add 0.5 and [tex]0.16\bar{3}[/tex]
A figure is dilated by a scale factor of 3 and is rotated 90° clockwise.
Complete the description of the transformations that will transform the image back into the original figure. Drag and drop each choice into the correct boxes to complete the sentences below.
Answer:
Answer is Below ------v
1. clockwise
2. 3
1. (y, -x)
2. (3x,3y)
Write an inequality for the graph below.
Answer:
Y < (1/3) x - 5
6.RP.3d-2016 (#39) Fei Yen's dog eats 8 ounces of dog food each day. Fei Yen bought a 28-pound bag of dog
food. How many 8-ounce servings are in a 28-pound bag of dog food?
A 14
B 56
C 224
D 448
There are 56 servings in a 28 pound bag of dog food.
What is Unitary Method ?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Each day Fei yen's dog eat dog food = 8 ounces
Fei yen bought a 28 pound bag of dog food.
And we know that 1 pound = 16 ounces
Then ,the food in ounces
= 28 x 16
= 448 ounces
Now, the number of 8 ounces servings are in a 28 pound bag of dog food
= 448 / 8
= 56
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a poker hand consists of ive cards drawn from a standard 52-card deck. find the expected number of aces in a poker hand given that the irst card drawn is an ace.
The expected number of aces in a poker hand given that the first card drawn is an ace is 0.235.
If the first card drawn is an ace, then there are only 3 aces left in the deck of 51 cards from which to draw the remaining 4 cards. Therefore, we can model the number of aces in the poker hand as a binomial random variable with parameters n = 4 (the number of cards after the first ace) and p = 3/51 (the probability of drawing an ace from the remaining deck).
The expected number of aces in a poker hand given that the first card drawn is an ace can be calculated as follows:
E(X) = np = 4 * 3/51 = 12/51 = 0.235
Therefore, the expected number of aces in a poker hand given that the first card drawn is an ace is approximately 0.235.
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____ The given question is incorrect, the correct question is given below:
A poker hand consists of five cards drawn from a standard 52-card deck. find the expected number of aces in a poker hand given that the first card drawn is an ace.
You and your friend just finished playing a game. Your final score was 24 and her final score was -13. By how many points did you win
Answer: 37 points
Step-by-step explanation:
Find (1/3x−3)+(−3/4x−5)
Answer:
-5x-96/12
Step-by-step explanation:
Firstly we want ot combine the multiplied terms into one fraction:
(1x/3-3)+(-3/4 x-5)
Then we multiply by 1:
(x/3-3)+(-3/4 x-5)
Find common denominator:
(x/3+3(-3)/3)+(-3/4 x-5)
Combine fractions with common denominator:
(x+3(-3)/3)+(-3/4 x-5)
Multiply the numbers:
(x-9/3)+(-3/4 x-5)
Combine multiplied terms into a single fraction:
x-9/3+(-3x/4 -5)
Find common denominator:
x-9/3+(-3x/4 + 4(-5)/4)
Combine fractions with common denominator:
x-9/3+(-3x + 4(-5)/4)
Multiply the numbers:
x-9/3 + (-3x-20/4)
Find common denominator:
4(x-9)/12 + 3(-3x-20)/20
Combine fractions with common denominator:
4(x-9)+3(-3x-20)/12
Distribute:
4x-36+3(-3x-20)/12
Distribute:
4x-36-9x-60/12
Subtract the numbers:
4x - 96 - 9x/12
Combine like terms:
-5x - 96/12
Answer: -5x-96/12
The start of a quadratic sequence is shown
below.
What is the nth term rule for the sequence?
-5, -2, 3, 10, 19,
Answer:
nth term = n²-6
Step-by-step explanation:
we know our nth-term formula is going to be of the form an² + bn + c. We just have to find a, b, and c.
In this series,
-5, -2, 3, 10, 19....
a=1, b=0, c=-6
nth term = n²-6
if n=1 then,
nth term=1²-6
⇒nth term=-5
Which best describes the graph of y≥-x² +8x-2?
The vertex is at (4, -14) The parabola is a solid line that opens down. Shading is above the line.
The vertex is at (4, 14). The parabola is a solid line that opens down. Shading is above the parabola.
The vertex is at (-4,-14). The parabola is a dotted line that opens down. Shading is below the parabola.
O The vertex is at (-4, 14). The parabola is a solid line that opens down. Shading is below the parabola.
A statement which best describes the graph of y ≥ -x² + 8x - 2 include the following: B. The vertex is at (4, 14). The parabola is a solid line that opens down. Shading is above the parabola.
How to determine the true statements about this quadratic function?Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).
By critically observing the graph of the given quadratic function, we can logically deduce that the solutions (roots) and vertex are as follows;
x = 0.258, y = 0.
x = 7.742, y = 0.
Vertex = (4, 14).
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Select the correct answer. A line t runs upward to the right through two parallel horizontal lines r and s, forming 8 angles numbered from 1 to 8. Given: Transversal t passes through parallel lines r and s. Prove: ∠3 ≅ ∠6 ∠4 ≅ ∠5 Statement Reason 1. r || s given 2. ∠3 ≅ ∠7 ∠4 ≅ ∠8 For parallel lines cut by a transversal, corresponding angles are congruent. 3. What is the next step in the proof? Choose the most logical approach. A. Statement: ∠1 ≅ ∠8 and ∠2 ≅ ∠7 Reason: Congruent Supplements Theorem B. Statement: m∠3 + m∠4 = 180° and m∠7 + m∠8 = 180° Reason: Linear Pair Theorem C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
Answer:
The correct answer is C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles.
This statement uses the definition of supplementary angles, which states that two angles are supplementary if their measures add up to 180 degrees. Since ∠3 and ∠6 are corresponding angles, and ∠4 and ∠5 are also corresponding angles, their measures must add up to 180 degrees in order for the parallel lines to be cut by the transversal.
Answer:
Option, D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
Step-by-step explanation:
In this question that you have put:
7 ≅ ∠6 and ∠8 ≅ ∠5 Reason =
Vertical Angles Theorem ( Or in similar terms VAT )
Make sure that you remember the following:
vertical angles are the angles that are opposite each other when the two line " meet together "
Thus, your answer to your questions is.
D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
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a radioactive substance decays exponentially. a scientist begins with 100 milligrams of a radioactive substance. after 29 hours, 50 mg of the substance remains. how many milligrams will remain after 38 hours?
After 38 hours, there will be 43.1 mg of the radioactive substance remaining.This means that the amount of a radioactive substance decreases exponentially over time
Radioactive decay follows an exponential decay curve. This means that the amount of a radioactive substance decreases exponentially over time. The equation for this is: [tex]A(t) = A0*e^(-λ*t\\[/tex])Where A(t) is the amount of substance at time t, A0 is the initial amount of substance, and λ is the decay constant. In this problem, A0 = 100 mg, t = 29 hours, and A(t) = 50 mg. We can use this to solve for λ:50 mg = 100 mg * [tex]e^(-λ*29)λ =[/tex] -0.027Now that we have the decay constant, we can calculate the amount of substance remaining after 38 hours:A(38) = 100 mg * [tex]e^(-0.027*38[/tex]).A(38) = 43.1 mg.Therefore, after 38 hours, there will be 43.1 mg of the radioactive substance remaining.
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pls help me i need now and if the answer is correct i give free BRAINLIEST HERE!!!!
THANK YOU
The measures of the angles formed by the cords and secant in the circle are found using circle theorems and presented as follows;
m∠1 = 47.5°[tex]m\widehat{BD}[/tex] = 110°m∠COD = 55°[tex]m\widehat{CD}[/tex] = 20°m∠AOC = 100°m∠APB = 25°m∠ADB = 25°[tex]m\widehat{CD}[/tex] = 90°[tex]m\widehat{AB}[/tex] = 70°[tex]m\widehat{CD}[/tex] = 100°What is a secant of a circle?A secant is a line that has two points of intersection on a circle.
The specified parameters are;
1. The measure of arc [tex]m\widehat{AB}[/tex] = 80°, and the measure of [tex]m\widehat{CD}[/tex] = 15°
Angle at the center of the circle = 2 × Angle at the circumference
Angle at the center of the circle = The arc angle of the circle
Therefore;
m∠DAC = 15°/2 = 7.5°
m∠ACO = 80°/2 = 40°
The external angle of a triangle theorem, indicates that we get;
m∠1 = 40° + 7.5° = 47.5°
m∠1 = 47.5°
2. m∠BOD = 100°, [tex]m\widehat{AC}[/tex] = 90°
The intersecting chords theorem indicates that we get;
m∠BOD = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])
Therefore; 100° = (1/2)×(90° + [tex]m\widehat{BD}[/tex])
[tex]m\widehat{BD}[/tex] = 2 × 100° - 90° = 110°
[tex]m\widehat{BD}[/tex] = 110°
3. [tex]m\widehat{AB}[/tex] = 90°, [tex]m\widehat{CD}[/tex] = 20°
Therefore; m∠ACO = 90°/2 = 45°
m∠DAC = 20°/2 = 10°
The external angle theorem indicates that we get;
m∠COD = 45° + 10° = 55°
m∠COD = 55°
4. m∠1 = 35°, [tex]m\widehat{AB}[/tex] = 50°, therefore;
m∠ACO = 50°/2 = 25°
m∠CAO = 35° - 25° = 10°
[tex]m\widehat{CD}[/tex] = 2 × m∠CAO
Therefore; [tex]m\widehat{CD}[/tex] = 2 × 10° = 20°
[tex]m\widehat{CD}[/tex] = 20°
5. m∠AOC = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])
Therefore; m∠AOC = (1/2)×(90° + 110°) = 100°
m∠AOC = 100°
6. [tex]m\widehat{CD}[/tex] = 20° and [tex]m\widehat{AB}[/tex] = 70°
The external secant, tangent theorem, indicates that we get;
m∠APB = (1/2) × ([tex]m\widehat{AB}[/tex] - [tex]m\widehat{CD}[/tex])
m∠APB = (1/2) × (70° - 20°) = 25°
m∠APB = 25°
7. [tex]m\widehat{AB}[/tex] = 50°,
The angle at the center of a circle is twice the angle subtended at the circumference, therefore;
m∠ADB = 50°/2 = 25°
m∠ADB = 25°
8. m∠CAD = 45°
The angle formed by an arc at the center of a circle theorem, indicates that we get;
[tex]m\widehat{CD}[/tex] = 2 × m∠CAD
[tex]m\widehat{CD}[/tex] = 2 × 45° = 90°
[tex]m\widehat{CD}[/tex] = 90°
9. m∠ACB = 70°
m∠ACB is the angle subtended by the arc [tex]m\widehat{AB}[/tex] on the circumference
Therefore;
[tex]m\widehat{AB}[/tex] = 2 × m∠ACB
[tex]m\widehat{AB}[/tex] = 2 × 70° = 140°
[tex]m\widehat{AB}[/tex] = 70°
10. m∠AOB = 80°, [tex]m\widehat{AB}[/tex] = 60°
m∠(AOB) = (1/2) × ([tex]m\widehat{AB}[/tex] + [tex]m\widehat{CD}[/tex])
Therefore; m∠(AOB) = 80° = (1/2) × (60 + [tex]m\widehat{CD}[/tex])
80° = (1/2) × (60 + [tex]m\widehat{CD}[/tex])
[tex]m\widehat{CD}[/tex] = 2 × 80° - 60° = 100°
[tex]m\widehat{CD}[/tex] = 100°
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Please help need help asap :))
The side of the triangle from shortest to longest can be arranged as,
ACABBCWhat is a triangle?A triangle is a polygon with three sides such that the sum of all the interior angles is always 180°.
In a triangle, the side opposite to the biggest angle is always the lengthiest, while the side opposite to the smallest angle is the shortest.
Given that the measure of ∠A is 100°, therefore, the length of the side BC will be the lengthiest.
Also, the measure of ∠B is 20°, therefore, the length of the side AC will be the shortest.
Hence, BC > AB > AC.
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Need help with this for school
Answer: 135
Step-by-step explanation:
Counting by 5 The last point at the end of the box and whisker plot is 135
The width of a rectangle is the length minus 8 units. The area of the rectangle is 9 square units. What is the length, in units, of the rectangle?
Answer: The length is 9 units and the width is 1 unit
Step-by-step explanation:
We can use the formula for the area of a rectangle to solve this problem. The formula is A = l * w, where A is the area, l is the length, and w is the width.
We have A = 9, and we know that w = l - 8. Substituting this into the formula, we get:
9 = l * (l - 8)
We can rearrange this to solve for l:
9 = l^2 - 8l
Adding 8l to both sides of the equation, we get:
9 + 8l = l^2
Subtracting 9 from both sides, we get:
8l = l^2 - 9
We can factor this to get:
l(l - 9) = 0
Since the product of two numbers is zero only when one of them is zero, we can set each factor equal to zero and solve:
l = 0 or l - 9 = 0
Adding 9 to both sides of the second equation, we get:
l = 9
Therefore, the length of the rectangle is 9 units.
Y-1= -1/3(x-6) in standard form
Answer:
x + 3y = 9
Step-by-step explanation:
Can you please help me with 11, 12,13 and 14 please it will mean a lot
first one is a
Step-by-step explanation:
Select the correct answer.
Consider this function.
f(x) = 6log₂x - 3
Over which interval is function f increasing at the greatest rate?
OA. [2, 6]
OB. [1/8, 1/2]
OC. [1, 2]
OD. [1/2,1]
The function f(x) = 6log₂x - 3 increasing at the greatest rate in the interval [1/8, 1/2].
What are maxima and minima?The maxima and minima of a function are the extreme values within the range; in other words, they are the maximum and minimum values of a function, respectively, at a given position.
Let the function be f(x) = 6log₂x - 3
For the interval x ∈ [2, 6]
f(x) ∈ [-0.678, 3]
For the interval x ∈ [1/8, 1/2]
f(x) ∈ [ -9.96, -5.32]
For the interval x ∈ [1, 2]
f(x) ∈ [-3, -0.67]
For the interval x∈ [1/2, 1]
f(x) ∈ [-5.32, -3]
The function increased most rapidly in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
Therefore, the range [1/8, 1/2] is where the function f(x) = 6log₂x - 3 increases at the fastest pace.
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A baker uses the equation y=12x to predict the revenue generated from selling x cakes she uses equation y=450+4.5x to model the cost to produce x cakes.
The complete question:
A baker uses the equation y = 12x to predict the revenue generated from selling a cakes. She uses equation y= 450 +4.5x to
model the cost to produce a cakes:
What does (60, 720), the solution of the system -450 +4.5x &
y=12x represent?
Solution:-
The solution of the system (-450 + 4.5x, y = 12x) at (60, 720) represents :
a. The point where the revenue generated from selling 60 cakes is 720 dollars
b. The cost to produce those 60 cakes is 720 dollars.
What is a system of equations?In geometry, A system of equations is a collection of two or more equations with the same set of unknown variables. In solving a system of equations, we try to calculate values for each of the unknowns that will satisfy each and every equation in the system.
The given system of equations is:
y = 12x (equation 1)
y = 450 + 4.5x (equation 2)
where x represents the number of cakes produced and sold, y represents the revenue generated from selling x cakes, and 450 + 4.5x represents the cost to produce x cakes.
To find the solution of the system, we can substitute equation 1 into equation 2, and solve for x as follows:
12x = 450 + 4.5x
7.5x = 450
x = 60
Substituting this value of x into equation 1 gives us:
y = 12(60)
y = 720
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for which type of function does linear approximation always give the exact value of f ( x ) for x near the starting point? linear quadratic exponential logarithmic linear approximation never gives the exact value.
By applying the slope of the function at that point, linear approximation provides an estimate of the value of a function close to a beginning point.
When estimating the value of a function at a nearby location, linear approximation uses the slope of the function at a particular position. In order to arrive at the starting position, it first calculates the difference between the two points, multiplies it by the slope, and adds it. This provides a rough estimate of the function's value at the new location. A technique for calculating a function's value close to a beginning point is called linear approximation. It is predicated on the notion that a linear function can be used to roughly approximate the function close to the point of interest. This indicates that the value of the function at surrounding places can be inferred from the slope of the function at the point in question.
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which expression is equivalent to 5^6
a.125 x 125 b. 6 x 5 c. 35 x 6 x 6 x 6 d. 25 x 5 x 5 x 5
The expression that is equivalent to 5^6 is A.125 x 125
What are index forms?Index forms are defined as mathematical forms of writing numbers that are too large or small in more convenient forms.
Other terms for index forms are called standard forms or scientific notations.
They are also described as numbers or variables that are raised to an exponent.
From the information given, we have that;
5⁶
This is replicating 5 in 6 places, we have the representation as;
5 × 5 × 5 × 5 × 5 × 5
Hence, the expression is 125 x 125
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Please help (will mark as brainlest)
Answer:
1)10abc^2+6a^2bc
2)6.6x^2yz-2.8xy^2z+0.5xyz^2
Step-by-step explanation:
two numbers are in the ratio 5:4 if the smaller is 32 find the greater one.
Answer:
The greater number is 40.Step-by-step explanation:
Greetings!!!
The given two numbers ratio.
[tex] \frac{5}{4} [/tex]
The smaller number is 32
[tex] \frac{5}{4} \times 32[/tex]
convert elements into fraction
[tex] \frac{5}{4} \times \frac{32}{1} [/tex]
Apply fraction rule
[tex] \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} [/tex]
Multiply the numbers
[tex] \frac{5 \times 32}{4 \times 1} [/tex]
Divide the numbers
[tex] \frac{32}{8} = 8 \\ 8 \times 5 = 40[/tex]
Hope it helps!!!
If f(x) = 2x - 9 and g(x) = x² + 3, what is (f + g)(4)?
2. The diagram shows a wall where the two shaded parts are painted in yellow. 20 m 12 m 16 m 15 m 0.1 litre of paint is required to paint an area of 1 m². What is the volume, in litres, of yellow paint required to paint the two shaded parts?
Answer: The two shaded parts of the wall have a combined area of 20m * 12m + 16m * 15m = 240 + 240 = 480 square meters.
Therefore, the volume of yellow paint required is 480 * 0.1 = 48 litres.
Step-by-step explanation:
Point D is the centroid of ABC, BD = 4x + 2 and DF = 3r. Find the value of x
Given point D is the centroid of triangle ABC, BD = 4x + 2 and DF = 3x and the value of x is -1
Centroid is a term used in triangles and it is equals to the reciprocal of three-second of the distance from each midpoint of the given triangle to each vertices.
Given point D is the centroid of triangle ABC, BD = 4x + 2 and DF = 3x and Centroid is a term used in triangles and it is equals to the reciprocal of three-second of the distance from each midpoint of the given triangle to each vertices.
we know that,
BD = 4x+2
DF = 3x
So by the given formulae, we used to solve the x value as,
BD = (1/(3/2)) [DF]
BD = (2/3)[DF]
4x+2 = (2/3)(3x)
4x+2 = 2(x)
4x+2 = 2x
4x-2x = -2
2x = -2
x = -1
Therefore, the value of x is x = -1
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How do you do this problem? can you show me how to do it? I am struggling on this
The values and graph of the equation 3x - 2y = 6 is attached below while the slope is 3/2
What is equation of lineThe equation of a straight line can be represented in various forms. One of the most commonly used forms is the point-slope form, which is represented as:
y - y1 = m (x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line, which is the rate of change of y with respect to x.
Another common form of the equation of a line is the slope-intercept form, which is represented as:
y = mx + b
where m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.
In this problem, we need to write the table of values and the find the slope of the line.
3x - 2y = 6
rewriting this equation;
2y = 3x - 6
y = 3x/2 - 3
when y = 0
0 = 3x/2 - 3
3x/2 = 3
3x = 2 * 3
3x = 6
x = 2
when x = 0
y = 3(0)/2 - 3
y = 0 - 3
y = -3
The slope of the line can be calculated using the two points from above.
slope (m) = y₂ - y₁ / x₂ - x₁
m = -3 - 0 / 0 - 2
m = 3/2
The slope is 3/2
The graph of the equation is attached below
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0/1
12. Ashton picked 6 pounds of pecans. He used of the pecans in a soup recipe. Ashton then
splits the pecans that are left in pound bags. How many bags of pecans does he have?
Ashton has 4.5 bags of pecans. since you can't have half a bag, he might need to round up to 5 bags
What is Fraction?A fraction represents a part of a whole.
If Ashton used 1/4 of the pecans in a soup recipe, he has 3/4 of the pecans left.
To find out how many pounds of pecans he has left.
we can multiply the original amount of pecans by 3/4:
3/4 x 6 pounds = 4.5 pounds
So Ashton has 4.5 pounds of pecans left to split into bags.
If he splits the remaining pecans into 1-pound bags, then he has:
4.5 pounds ÷ 1 pound/bag = 4.5 bags
Therefore, Ashton has 4.5 bags of pecans. However, since you can't have half a bag, he might need to round up to 5 bags
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The complete question
Ashton picked 6 pounds of pecans. He used 1/3 of the pecans in a soup recipe. Ashton puts the pecans that are left in 1/4 pound bags. How many bags of pecans does he have
question 8
help me asap
The sector area of the sector defined by the minor arc CB is given as follows:
7.5 cm².
What is the area of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr².
We have that the radius is half the diameter, hence it's measure is given as follows:
r = 3 cm.
The angle measure of arc CB is given as follows, considering that BD is half the circle = 180º.
CB + 84º = 180º.
CB = 96º.
An entire circle has an angle of 360º, hence the area of the sector is given as follows:
A = 96/360 x π x 3²
A = 7.5 cm².
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