Answer with explanation:
For a Lopsided coin ,probability of getting Head is equal to [tex]\frac{1}{3}[/tex] For a Lopsided coin ,probability of getting Tail is equal to [tex]\frac{1}{3}[/tex].
→Probability of getting Tail > Probability of getting Head
→Coin is heavier from tail side and lighter from Head side.
→→We have to Calculate number of flips of coin that is needed to have both heads and tails appear at least once.
[tex]\rightarrow P(\text{Head})=\frac{1}{3}\\\\ \frac{1}{3} \times x=1\\\\x=3\\\\\rightarrow P(\text{Tail})=\frac{2}{3}\\\\ \frac{2}{3} \times y=1\\\\y=\frac{3}{2}[/tex]
→We need to find common multiple of 3 and [tex]\frac{3}{2}[/tex].
Least common multiple of 3 and [tex]\frac{3}{2}[/tex] is 6.
→So,on Average number of flips of this coin are needed to have both heads and tails appear at least once=6 tosses
Matilda sits on her back porch for one hour every morning for a week and record the types and numbers of birds that viste her bird feeder what kind of study is this ?
Observational study.
------APEX
Answer:
d.Step-by-step explanation:
The choices for this question are
a. Double-blind study
b. Experiment
c. Sample survey
d. Observational study
The right answer would be d. Observational study, because this type of study is defined as an empirical and non-experimental research where all information is obtained by observation. When we apply this study, we try to find a cause-effect relation by observing the phenomenon as it naturally happens, that is, without interfering with the course of events like experimental investigations do.
So, in this case, Matilda is just observing, without altering anything that could influence the birds. She just sits observe and recover information, that's an observational study.
Therefore, the right answer is d.
The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 60t − 1.5t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop?
Answer:
20 seconds
Step-by-step explanation:
Given:
Position of car = s(t) = 60t-1.5t^2
The speed is the change in position.
So,
[tex]Speed\ of\ car=\frac{ds}{dt} = \frac{d}{dt} (60t) -\frac{d}{dt} (1.5t^2)\\=60-2t(1.5)\\=60-3t[/tex]
When the car will stop, the speed will be zero.
[tex]60-3t=0\\3t=60\\t = \frac{60}{3}\\ t=20[/tex]
Therefore, the car will stop after 20 seconds of applying the break ..
Vineet solved a system of equations by substitution. In his work, he substituted an expression for one of the variables and solved for the value of the other. This resulted in the equation 7 = 9. What can Vineet conclude?
He can conclude that the system of equations has no solution since one equation in it always results with false equivalency.
Hope this helps.
r3t40
He can conclude that the system of equations is inconsistent, i.e. it has no solution.
Step-by-step explanation:We know that we get a no solution when we get a expression which is always false.
Here,
Vineet solved a system of equations by substitution.
In his work, he substituted an expression for one of the variables and solved for the value of the other.
This resulted in the equation 7 = 9.
which is a false identity.
since 7 can never be equal to 9.
Hence, the system of equations is inconsistent , it has no solution.
Determine the next term in the sequence: 3, 6, 12, …
A: 15
B: 18
C: 24
D: 36
Answer:
C) 24
Step-by-step explanation:
The patter here is that you multiply the previous term by 2 to get the next term. So 3*2 is 6, 6*2 is 12, and 12*2 is 24.
The next term in the sequence: 3, 6, 12, … is 24. This can be obtained by finding the nth term and finding the 4th term.
What is a sequence ?A collection of items in a particular order and repetitions are allowed.
Arithmetic Sequence:a, a+d, a+2d, ..., a+(n-1)d, where a is the first term, d is the common difference and a+(n-1)d is the nth term.
Geometric Sequence:a, ar, ar¹, ..., arⁿ⁻¹, where a is the first term, r is the common ratio and arⁿ⁻¹ is the nth term.
What is the next term ?Given that, 3, 6, 12, …⇒this is a Geometric Sequence with nth term,
aₙ=3rⁿ⁻¹, n=1,2,3,...
From the given sequence, a₁=3, r=2
when n=1, a₁=3(r¹⁻¹)=3(r⁰)=3(2⁰)=3×1=3when n=2, a₂=3(r²⁻¹)=3(r¹)=3(2¹)=3×2=6when n=3, a₃=3(r³⁻¹)=3(r²)=3(2²)=3×4=12when n=4, a₄=3(r⁴⁻¹)=3(r³)=3(2³)=3×8=24Hence the next term in the sequence: 3, 6, 12, … is 24. Thus option C is the correct answer.
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If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, what is the height of the cup? Use 3.14 to for pi. Round your answer to the nearest hundredth. 6.76 inches 18.56 inches 21.97 inches 23.00 inches
Answer:
21.97 in
Step-by-step explanation:
Use the formula for the volume of a cone, fill in the given information, and solve for the height.
V = (1/3)πr²h
23 in³ = (1/3)(3.14)(1 in)²h . . . . . . . . with given numbers
3·23 in³/(3.14 in²) = h ≈ 21.97 in . . . . . divide by the coefficient of h
Answer:
21.97 inches
Step-by-step explanation:
If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, the height of the cup is 21.97 inches.
Round your answer to the nearest hundredth.
The terminal side of θ passes through the point (−5,−6). What is the exact value of cosθ in simplified form?
5√61/61
−5√61/61
−6√61/61
6√61/61
Answer:
proof my answer is correct
Step-by-step explanation:
The exact value of cosθ in simplified form is -5√61 / 61.
What is Trigonometry?One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.
We have,
The terminal side of θ passes through the point (−5,−6).
Now, Hypotenuse
= √(-5)² + (-6)²
= √25+36
=√61
Using Trigonometry
cos θ = Adjacent side/ Hypotenuse
cos θ = -5/ √61
Now, rationalizing
cos θ = -5/√61 x √61/√61
cos θ = -5√61 / 61
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x^4 - 1 =
A. (x+1)(x-1)(x^2+1)
B. ( X+1)^2(x-1)^2
C. (X+1)^3(X-1)^1
D. (x-1)^4
Answer:
A
Step-by-step explanation:
Given
[tex]x^{4}[/tex] - 1 ← a difference of squares which factors in general as
a² - b² = (a - b)(a + b)
here [tex]x^{4}[/tex] = (x²)² ⇒ a = x² and b = 1
[tex]x^{4}[/tex] - 1 = (x² - 1)(x² + 1)
x² - 1 ← is a difference of squares and factors as
x² - 1 = (x - 1)(x + 1), so
(x² - 1)(x² + 1) = (x - 1)(x + 1)(x² + 1), hence
[tex]x^{4}[/tex] - 1 = (x - 1)(x + 1)(x² + 1) → A
Answer:
A. (x + 1)(x - 1)(x^2 + 1).
Step-by-step explanation:
Using the difference of 2 squares (a^2 - b^2 = (a + b)(a - b) :
x^4 - 1 = (x^2 - 1)(x^2 + 1).
Now repeating the difference of 2 squares on x^2 - 1:
(x^2 - 1)(x^2 + 1 = (x + 1)(x - 1)(x^2 + 1).
What would be the steps for finding the equation for the function f(x) based on the graph (the blue line) and what would the equation be? Please include steps that are universal to finding the equation of any possible graphed function, as I really don't even know where to begin and would like to be able to solve problems like this on my own one day. Thanks! :)
Answer:
f(x) = -2|x-2| +4
Step-by-step explanation:
Step 1: recognize this as an inverted, scaled, and translated absolute value function.
Step 2: identify the scale factor as 2, because each section has a "rise" of 2 for each "run" of 1. The scale factor is -2 because the function is inverted (reflected across the x-axis).
Step 3: identify the vertex* as (2, 4).
Step 4: Use the scale factor and translation information to make the transformation ... (let abs(x) represent the absolute value function)
f(x) = (scale factor)×abs(x -horizontal shift) + (vertical shift)
f(x) = -2|x -2| +4
_____
* The vertex is an identifiable point on the graph of this function. Knowing how the vertex is translated tells you how the whole function is translated. In general, you want to use an identifiable point (a turning point, point of symmetry, extreme point, whatever) when you're trying to determine the translation. For some functions, like a line, there is no specific identifiable point, so determining any specific translation is difficult or impossible.
_____
Comment on writing functions from graphs
One of the reasons for studying different functions is so you can learn to recognize their shape, and associate a formula and certain properties with that shape.
_____
The attached graph shows the parent absolute value function in blue and the transformed function f(x) in red.
NEED HELP QUICK!!!!Charmaine is riding her bike. The distance she travels varies directly with the number of revolutions (turns) her wheels make. See the graph below.
(a) How many revolutions does Charmaine make per foot of distance traveled?
(b) What is the slope of the graph?
Answer:
Step-by-step explanation:
Circumference of the wheel = (pi)d = 45*3.14 = 141.3 inches
----
Distance traveled in inches: 5*141.3 = 706.5 inches
---
Distance traveled in feet: 706.5/12 = 58.875 feet
How to find the surface area of a regular pyramid?
Step-by-step explanation:
[tex]l \times w + l \sqrt{( \frac{w}{2}) ^{2} + {h}^{2} } + w \times \sqrt{( \frac{l}{2} )^{2} + {h}^{2} } [/tex]
L = length base
w = width base
h = height
Answer:
[tex]S=\dfrac{ns^2}{4}\left(\cot{\left(\dfrac{180^{\circ}}{n}\right)}+\sqrt{3}\right)[/tex]
Step-by-step explanation:
A "regular pyramid" is a pyramid whose base is a regular polygon and whose edges are all the same length. Thus each face is an equilateral triangle.
A hexagonal regular pyramid will look like a hexagonal pancake, as the vertical height of it will be zero. A regular pyramid with 7 or more faces cannot exist, because the apexes of the triangular faces cannot meet at a point.
__
For an edge length of "s", the area of each triangular face is (√3)/4×s². There are n of those faces, so the lateral area (LA) will be ...
LA = ns²(√3)/4
The area of the regular polygon base will be the product of half its perimeter and the length of its apothem (a). The apothem is ...
a = (s/2)cot(180°/n)
So, the area of the base (BA) is ...
BA = (1/2)(ns)(s/2)cot(180°/n) = ns²cot(180°/n)/4
The total surface area of the regular pyramid is then ...
S = BA + LA
S = (ns²/4)(cot(180°/n) +√3) . . . . for edge length s and n faces (3≤n≤5)
Mercury is 0.39 AU from the sun. What is its distance from the sun in kilometers?
Answer:
The distance between the sun and Mercury is 58 343 220 km.
Step-by-step explanation:
1 AU/149,598,000 kilometers = 0.39 AU/x
1x = (149,598,000)(0.39)
x = 58 343 220
For this case we have by definition that an Astronomical Unit (AU) equals 149,598,000 kilometers.
We propose a rule of three to find the distance of Mercury to the sun in kilometers.
1 AU -------------> 149,598,000 km
0.39 AU ---------> x
Where "x" represents the distance in kilometers:
[tex]x = \frac {0.39 * 149,598,000} {1}\\x = 58,343,220[/tex]
Answer:
58,343,220 km
A kite is 85 feet high with 100 feet of string let out. What is the angle of elevation of the string with the ground? Please show all work.
Answer:
58°
Step-by-step explanation:
A right triangle can be drawn to model the geometry of the problem. The hypotenuse of the triangle is the length of the string, 100 ft. The side opposite the angle is the height of the kite above the ground, 85 ft.
The mnemonic SOH CAH TOA reminds you of the relationship between sides and angles.
Sin = Opposite/Hypotenuse
sin(α) = (85 ft)/(100 ft) = 0.85
The angle whose sine is 0.85 is found using the arcsine (inverse sine) function:
α = arcsin(0.85) ≈ 58.2°
The angle of elevation is about 58°.
_____
When using your calculator to find the values of inverse trig functions, make sure it is in degrees mode. Otherwise, you're likely to get the answer in radians (≈ 1.01599 radians).
4. Find the value of sin 34°. Round to the nearest ten-thousandth.
O A 0.6745
B 0.8290
C 0.5291
D 0.5592
Answer:
Option D is correct.
Step-by-step explanation:
We need to find the value of sin 34°.
We can find the value by putting it in the calculator
sin 34° = 0.5592
So, Option D is correct.
Answer:option d is correct
Step-by-step explanation:
Anthony is saving for a Xbox one he currently has the $165 saved and earned $40 per week doing chores around the house if an Xbox cost 500+10% sales tax how long will it take for him to save that amount
Answer:
10 weeks
Step-by-step explanation:
Let w represent the number of weeks Anthony will be saving. Then he wants ...
165 + 40w = 500 +0.10×500
40w = 385 . . . . . subtract 165 and simplify
w = 9.625 . . . . . . divide by 40
It will take Anthony 9.625 ≈ 10 weeks to save that amount.
Match the vocabulary word to its correct definition.
Answer:
1 -> f
2 -> e
3 -> d
4 -> a
5 -> c
6 -> g
7 -> b
Step-by-step explanation:
Let consider the options as a,b,c,d,e,f,g
1. Bell curve -> f
2. Data set -> e
3. Histogram -> d
4. Mean -> a
5. Normal distribution -> c
6. Standard deviation -> g
7. Variance -> b
The task is to match vocabulary words to their definitions, a common task in an English class. It involves comparing words with definitions and identifying matches. This helps students understand new words.
Explanation:Given that the task at hand is to match vocabulary words to their correct definitions, this is a task typically found in an English class. This activity involves comparing a list of words with a list of definitions, then identifying which definition corresponds to each word. For example, the word 'gratify' can be matched with the definition 'give (someone) pleasure or satisfaction'. This process helps students better understand and remember the meanings of new words.
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the following is a 3-step proof. Starting with the given, complete the proof. Given: m 5 = m 6 Prove:m 3 = m 4
The question is vague and lacks crucial contextual information required to provide a reliable mathematical proof.
Explanation:Unfortunately, the question is ambiguous and it lacks the sufficient details to be able to provide a reliable proof. Based on the information provided it appears to be algebraic or geometric. If it's an algebraic equation, such as m+5 = m+6, the proof m+3 = m+4 would not hold since this would imply that 3 = 4 which is not true.
If it's related to geometric figures like angles or sides of a triangle where m represents the measure of an angle or length of a side, we need concrete contextual information to proceed. With more specific details, the required steps to solving your problem could be accurately outlined.
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To prove m3 = m4, we use the given information that m5 = m6 and apply the transitive property of equality.
Given: m5 = m6
We need to prove: m3 = m4
Using the given information, we can see that m5 = m6. This means that the measures of angles 5 and 6 are equal.
By the transitive property of equality, if m5 = m6 and m6 = m3, then m5 = m3.
Similarly, if m5 = m6 and m6 = m4, then m5 = m4.
Therefore, we have proven that m3 = m4.
Suppose you just received a shipment of six televisions. Three of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not work?
Answer:
.6094
Step-by-step explanation:
Please help on these questions about Slopes on Graphs !!!!
Answer:
a) {C, D}, {B, E}, A . . . . four possible equivalent answers (explanation below)
b) Line C shows a "directly proportional" relationship
Step-by-step explanation:
Slope is the ratio of "rise" (vertical change) to "run" (horizontal change). Positive changes are "up" and "right".
Line A -- has no vertical change, so its slope is 0.
Line B -- changes 1 unit vertically for each 4 units horizontally, so its slope is 1/4.
Line C -- changes 1 unit vertically for each 2 units horizontally, so its slope is 1/2.
Line D -- changes 1 unit vertically for each 2 units horizontally, so its slope is 1/2. This is the same slope as line C, so neither is greater than the other.
Line E -- changes 1 unit vertically for each 4 units horizontally, so its slope is 1/4. This is the same slope as line B, so neither is greater than the other.
If we use alphabetical order to rank equal slopes, then the slopes (greatest to least) are ...
C (1/2), D (1/2), B (1/4), E (1/4), A (0)
_____
A "directly proportional" relationship graphs as a straight line through the origin. The only line passing through the point where the x- and y-axes meet is line C.
Line C represents a proportional function.
Danny is installing a fence around his rectangular yard. His yard is 20 feet long by 45 feet wide. If the fencing he picked out costs 25$ per foot, how much money will Danny spend on the fence?
Find the perimeter of the yard ( the distance around the yard).
A rectangle has two sides of each dimension.
The perimeter is 20 + 20 + 45 + 45 = 130 feet.
Now multiply the total feet by the cost per foot:
130 feet x 25 per foot = $3,250 total.
Danny needs to spend on his yard $3250 to fencing.
What is a rectangle?The rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Length of fence = Perimeter of his yard(rectangle)
Perimeter of rectangle = 2( length + width).
Perimeter of fence =2 ( 20 + 45 )
The perimeter of fence =130 foot.
Now
Cost = $25 per foot
So,
Cost of 130 feet at the rate of $25 per foot
⇒ 130 × 25 = $3250
Hence, Danny needs to spend on his yard $3250 to fencing.
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[30 points] Help with volume! A circular swimming pool has a radius of 7 m and a depth of 1.4 meters. It is filled to the top with water. It develops a leak and loses 5 cubic meters of water every 2 hours. After how long would the water in the swimming pool be at a depth of 0.9 m?
use 3.14 for pi.
Volume of a cylinder pi × r squared × depth.
Round your answer to the nearest hours.
PLEASE give an explanation with your answer! A detailed answer will get Brainliest. :)
Answer:
Around 31 hours
Step-by-step explanation:
So since the formula for cylinder is pi × r squared × depth, you will get 215.51 cubic meters. When it's 0.9 m, it will be 138.54.
The pool has a leak and loses 5 cubic meters every 2 hours.
Subtract 5 from 215.51 until you get 140.51 when you can no longer subtract 5.
It will be 15 times. Which is 30 hours. Subtract 2.5 from 140.51 and you get around 138.01. Now that was an hour. 30+1= 31 hours
Given: 3x+52=13
Prove: x = 7
write a two column proof
The answer x = 7 is false here is why.
[tex]3x+52=13\Longrightarrow3x=-39[/tex]
This further simplifies to solution,
[tex]x=-\dfrac{39}{3}\Longrightarrow\boxed{x=-13}[/tex]
Hope this helps.
r3t40
Final answer:
The two-column proof format shows that the solution to the given equation 3x + 52 = 13 is x = -13, which contradicts the statement x = 7 to be proven. Either the given equation or the proof is incorrect as x = 7 cannot be derived from the equation provided.
Explanation:
Two Column Proof
When given the equation 3x + 52 = 13, we are asked to prove that x = 7. To do this, we can use a methodical approach in a two-column proof format where we list each step of the solution process alongside the reason for each step, as follows:
3x + 52 = 13: Given equation.
3x = 13 - 52: Subtract 52 from both sides.
3x = -39: Simplify.
x = -39 / 3: Divide both sides by 3.
x = -13: Simplify.
This results in x = -13, which contradicts the initial statement that we need to prove (x = 7). Therefore, either there is a mistake in the given equation or the proof is incorrect. Based on the provided information, x = 7 cannot be directly proven from the equation 3x + 52 = 13.
Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get? A. 4^2 ? 3^3 B. 3^3 + 4^2 C. 4 ? 3^3 D. 3^3 ? 4^2 E. 3^2 ? 4^3
"Alia gets 4^2 fewer than Kelly, who gets 3^3."
So it's about a subtraction.
[tex]\boxed{3^3-4^2}[/tex]
Hope this helps.
r3t40
Answer:
D. 3^3 - 4^2
Step-by-step explanation:
4^2 fewer than 3^3 is ...
3^3 - 4^2 . . . . . matches choice D
Can someone please help me with this math question. please fill all blanks URGENT PLEASE ANSWER
Answer:
Δ ABC was dilated by a scale factor of 1/2, reflected across the x-axis
and moved through the translation (4 , 1)
Step-by-step explanation:
* Lets explain how to solve the problem
- The similar triangles have equal ratios between their
corresponding side
- So lets find from the graph the corresponding sides and calculate the
ratio, which is the scale factor of the dilation
- In Δ ABC :
∵ The length of the vertical line is y2 - y1
- Let C is (x1 , y1) and B is (x2 , y2)
∵ B = (-2 , 0) and C = (-2 , -4)
∴ CB = 0 - -4 = 4
- The corresponding side to BC is FE
∵ The length of the vertical line is y2 - y1
- Let F is (x1 , y1) , E is (x2 , y2)
∵ E = (3 , 3) and F = (3 , 1)
∵ FE = 3 - 1 = 2
∵ Δ ABC similar to Δ DEF
∵ FE/BC = 2/4 = 1/2
∴ The scale factor of dilation is 1/2
* Δ ABC was dilated by a scale factor of 1/2
- From the graph Δ ABC in the third quadrant in which y-coordinates
of any point are negative and Δ DFE in the first quadrant in which
y-coordinates of any point are positive
∵ The reflection of point (x , y) across the x-axis give image (x , -y)
* Δ ABC is reflected after dilation across the x-axis
- Lets find the images of the vertices of Δ ABC after dilation and
reflection and compare it with the vertices of Δ DFE to find the
translation
∵ A = (-4 , -2) , B = (-2 , 0) , C (-2 , -4)
∵ Their images after dilation are A' = (-2 , -1) , B' = (-1 , 0) , C' = (-1 , -2)
∴ Their image after reflection are A" = (-2 , 1) , B" = (-1 , 0) , C" = (-1 , 2)
∵ The vertices of Δ DFE are D = (2 , 2) , F = (3 , 1) , E = (3 , 3)
- Lets find the difference between the x-coordinates and the
y- coordinates of the corresponding vertices
∵ 2 - -2 = 4 and 2 - 1 = 1
∴ The x-coordinates add by 4 and the y-coordinates add by 1
∴ Their moved 4 units to the right and 1 unit up
* The Δ ABC after dilation and reflection moved through the
translation (4 , 1)
Answer:ABC was dilated by a scale factor of 1/2, reflected across the x-axisand moved through the translation (4 , 1)
Step-by-step explanation:
A curve passes through the point ????0, 5???? and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?
Answer:[tex]y=2x^2[/tex]
Step-by-step explanation:
Given Curve passes through [tex]\left ( 0,5\right )[/tex]
Also the slope of the curve at every point p is twice the Y-coordinate of p
Let the coordinate of p be[tex] \left ( x,y\right )[/tex]
Therefore
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=2y[/tex]
[tex]\frac{dy}{y}=2dx[/tex]
Integrating both sides
[tex]\int \frac{dy}{y}=\int 2dx[/tex]
[tex]\ln y=2x+c[/tex]
Substituting values
[tex]\ln 5=c[/tex]
[tex]\ln \frac{y}{5}=2x[/tex]
[tex]y=2x^2[/tex]
Help please!!!! Quickly and will mark as brainliest!!!!!!!!!
Answer:
a) 4 calories per minute
b) 0.25
Step-by-step explanation:
a) If you look at the line it intercepts the x and y axis at the origin (0,0). therefore if you take any point on the line you will see that the calories per minute are constant:
Look at point (40,10)
Calories per minute = x/y = 40/10 = 4
Look at point (80,20)
Calories per minute = x/y = 80/20 = 4
b) you can use any two points on the line. Lets use point 1 as (20,5) and point 2 as (60,15).
The slope of a straight line is defined as:
slope = (y2-y1)/(x2-x1) = (15-5)/(60-20) = 0.25
Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slopeequals6, passing through (negative 2,5)
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})~\hspace{10em} slope = m\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=6[x-(-2)]\implies y-5=6(x+2) \\\\\\ y-5=6x+12\implies y=6x+17\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
It's going to be Lindsay's birthday soon, and her friends Martin, Sylvia, Tad, and Yvonne have contributed equal amounts of money to buy her a present. They have $25.00 to spend between them. Determine how much each contributed.
Aaron reads 9 books from the library each month for p months in a row. Write an expression to show how many books Aaron read in all. Then, find the number of books Aaron read if he read for 6 months.
Answer: 1) Each friend had contributed $6.25.
2)The expression to show how many books Aaron read in p months :
[tex]y=9p[/tex]
He reads 54 books in 6 months.
Step-by-step explanation:
1) Given : The total number of friends who contributed equal amounts of money to buy a present. : 4
The total amount they have = $25
Since all the friends contributed the same amount.
Thus , the amount each had contributed :
[tex]=\dfrac{\text{Amount collected}}{\text{Number of friends}}\\\\=\dfrac{25}{4}=6.25[/tex]
Hence, each friend had contributed $6.25.
2) Given : The number of books Aron reads each month = 9 books
Let the number of months be 'p'.
Then the expression to show how many books Aaron read in p months .
[tex]y=9p[/tex]
Then , the number of books Aaron read if he read for 6 months.
[tex]y=9(6)=54[/tex]
Hence, he reads 54 books in 6 months.
Its in the picture below
a: 1% decay
b: 10% decay
c: 9% growth
d: 90% growth
Answer:
b: 10% decay
Step-by-step explanation:
Expressed as a percentage change, the growth is usually the value of the base of the exponential function after 1 has been subtracted. That result is expressed as a percent:
0.9 - 1 = -0.10 = -10% . . . . . 10% decay
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The "t/12" exponent means this is the decay that is experienced over 12 units of time. This might be the annual decay, where t is expressed in months, for example.
Convert the angle \theta=100^\circθ=100 ∘ theta, equals, 100, degree to radians. Express your answer exactly.
Answer:
5pi/9 radians
Step-by-step explanation:
2 pi radians = 360 deg
pi radians = 180 deg
100 deg * pi rad/(180 deg) = 10/18 pi rad = 5/9 pi rad = 5pi/9 radians
Choose the correct simplification of the expression (2x - 6)(3x2 - 3x - 6). (4 points) Select one: a. 6x3 - 24x2 + 6x + 36 b. 6x3 - 24x2 + 6x - 36 c. 6x3 + 24x2 - 6x + 36 d. 6x3 - 24x2 + 6x + 12
Answer:
a. 6x^3 - 24x^2 + 6x + 36
Step-by-step explanation:
These are expanded using the distributive property, which is also used for collecting terms.
(2x - 6)(3x2 - 3x - 6) = 2x(3x^2 - 3x - 6) - 6(3x^2 - 3x - 6)
= 6x^3 -6x^2 -12x -18x^2 +18x +36
= 6x^3 +(-6-18)x^2 +(-12 +18)x +36
= 6x^3 -24x^2 +6x +36 . . . . . . matches selection A
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Comment on strategy
For multiple-choice questions, it often works well to find a way to identify a viable answer with the minimum amount of work. Comparing these answer choices, you can see that determining the correct values of the x-term and the constant term will let you pick the right choice.
The constant term is easy, because it is simply the product of the constants (-6)(-6) = 36. This narrows the choices to A and C.
The x-term will be the sum of products of x-terms and constants:
2x(-6) +(-6)(-3x) = -6(2x-3x) = -6(-x) = 6x
This narrows the choices to A alone.