A total of 112 combinations are possible out of all possible combinations when a coin is tossed 10 times and having total of 4 tails and have different start and end faces.
For the given question we have 2 conditions:
condition 1:
when the start turn have head face then the end turn must have tails face as it is given that start and end have different faces.
so in this case 1st and last position is fixed so we have exactly 8 positions.
and given that out of 10 times there must be total of 4 tails and we discussed that last face already have tail face so now out of 8 available positons we have exactly 3 tails in it and rest 5 must be heads.
so we have 8 available positions and we can select any 5 out of them and the number of ways of selection of this is = 8 combination 5 = [tex]8_C__5[/tex] =56 ways
conditon 2:
when the start turn have tail face then the end turn must have head face as it is given that start and end have different faces.
so in this case 1st and last position is fixed so we have exactly 8 positions
and given that out of 10 times there must be total of 4 tails and we discussed that first face already have tail face so now out of 8 available positons we have exactly 3 tails in it and rest 5 must be heads.
so we have 8 available positions and we can select any 5 out of them and the number of ways of selection of this is =8 combination 5 = [tex]8_C__5[/tex] =56 ways
so total number of ways is = no. of ways condition 1+ no. of ways condition 2 = 56 +56 = 112 ways
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PLEASE HELP ASAP WILL MARK YOU BRAINIEST!!
Answer:
A , E
Step-by-step explanation:
side of the square = 10
there are 4 side in the perimeter
10 · 4 = 40
the radius of the semicircle is the value of the side of the square = 10
there are two equals semicircle, so the total perimeter of these shapes is equal to a complete circle
10 · 2 · π = 20π
total perimeter
40 + 20π
that can be expanded in
10 + 10 + 10π + 10 + 10 + 10π
What are the vertex and range of y = |2x 6| 2? (0, 2); 2 < y < [infinity] (0, 2); −[infinity] ≤ y < [infinity] (−3, 2); 2 < y < [infinity] (−3, 2); −[infinity] ≤ y < [infinity]
The vertex of the function is (-3,3) when the function is y=|2x+6|+3 and the range is -∞<y<∞.
Given that,
The function is y=|2x+6|+3
We have to find the vertex and range.
We know that,
What is function?According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. This special sort of relationship is what it is called.
So,
|2x+6|=0
2x=-6
x=-6/2
x=-3
Now,
y=|2(-3)+6|+3
y=|-6+6|+3
y=3
The vertex is (-3,3)
Therefore, The vertex of the function is (-3,3) when the function is y=|2x+6|+3 and the range is -∞<y<∞.
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what is 4+4? 4+4 is 8
Answer: 8
Step-by-step explanation:
4+4 is the same as 4 times 2
They both equal to 8
Question 20
A rectangular courtyard has a cement walkway around its perimeter. The area of the courtyard can be represented by the expression 24(5x - 1).
The area of the cement walkway can be represented by the expression 32(5x-1 + 8)- 24(5x-1). Write an equivalent expression that
represents the area of the cement walkway.square yards
Answer:
Step-by-step explanation:
The area of the courtyard is given by the expression 24(5x - 1), and the area of the cement walkway is given by the expression 32(5x-1 + 8)- 24(5x-1). To find an equivalent expression for the area of the cement walkway, we can first distribute the 32 and the 24 in the second expression to get:
Area of cement walkway = 32 * (5x-1 + 8) - 24 * (5x-1)
= 32 * 5x-32 - 24 * 5x+24 + 32 * 8 - 24
= 160x-1024 - 120x+576 + 256 - 24
= 40x-448 + 256 - 24
= 40x-192
Therefore, an equivalent expression for the area of the cement walkway is 40x - 192. This expression represents the area of the cement walkway in square yards.
You earn 15n dollars for mowing n lawns. How much do you earn for mowing 1 lawn? 7 lawns?
Answer:
Step-by-step explanation:
You plug in the number of lawns mowed for "n"
So 1 lawn would be 15(1) (15 times 1)
15(1)=15
15(2)=30
15(3)=45
15(4)=60
15(5)=75
15(6)=90
15(7)=105
15(8)=120
15(9)=135
15(10)=150
and so on
the average height of women in the united states is 62 inches with a standard deviation of 2 inches. what is the height of a woman who is 1 standard deviations below the mean?
1) To find a standardized score (z-score), take the individual core minus the mean, then divide by the standard deviation: z = (score - mean)/ SD
Shuri's standardized score would be: z = (69.5 - 65)/2.5 = 1.8
2) First, find the z-score for 62 in: z= (62 - 65) / 2.5 = -1.2
Next, look up -1.2 in a z-table. The corresponding number in the table is .1151.
Multiple this number by 100 to get a percentage: .1151 * 100 = 11.51%
Thus 11.51% of people will be less than 62 inches.
3) Outliers are defined differently dependent on who you ask, often values that are 3 standard deviations (or more) above or below the mean are considered an outlier.
Use the same formula for finding a z-score: z= (score - mean)/ SD
For the taller height use 3:
3= (x - 65)/2.5
Do a little algebra and you get: 3(2.5) + 65 = x thus x = 72.5 or taller
For the shorter height, use -3:
-3(2.5) + 65 = x thus x = 57.5 or shorter
If you need to use a different value for an outlier, then use that number in place of +/- 3.
Hence we get the desired answer.
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Your question is incomplete. Please find the missing content below.
A sample of 300 adult women finds that their heights are approximately Normally distributed with an average height of 65 inches and a standard deviation of 2.5 inches.
1) Shuri is 69.5 inches tall. What is her standard score for height?
2) How many women in the sample would you expect to be less than 62 inches tall?
3) How tall or short would a woman have to be to be considered an outlier? Show your work.
a bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 210.0 and a standard deviation of 50.0. if an applicant is randomly selected, find the probability of a rating that is between 176.0 and 214.0.
The probability of a rating that is between 176 and 214 is,
[tex]P(176\leq x\leq 214)=0.21994[/tex]
Since the credit ratings are normally distributed.
Now, apply the formula for normal distribution. Which is shown below,
[tex]z=\frac{x-u}{sd}[/tex]
x=credit ratings for applicants.
u=mean.
sd standard deviation.
From the given information, µ = 210 and σ = 50
For x = 176,
[tex]z=\frac{176-210}{50} =-0.68[/tex]
In the normal distribution table, the probability corresponding to the -0.68 z-score is 0.25175
For x =214,
[tex]z=\frac{214-210}{50} =0.08[/tex]
In a normal distribution table, the probability corresponding to the z score of 0.08 is 0.03788
Thus,
[tex]P(176\leq x\leq 214)=0.25175-0.03181=0.21994[/tex]
Hence, The probability of a rating that is between 176 and 214 is,
[tex]P(176\leq x\leq 214)=0.21994[/tex]
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Make x the subject of m=n+x/p
Answer:
x = mp - np
Step-by-step explanation:
Make x the subject of m = n + x/p
m = n + x/p
subtract n from both sides:
m - n = n + x/p - n
m - n = x/p
multiply both sides by p:
p(m - n) = p(x/p)
x = p(m - n)
distribute p on right side:
x = mp - np
7/15 * (9/-28)...pls answer fast!!,step by step explanation plsssssssssss
The value of the fraction 7/15 * (9/-28) is - 3/20.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
On the other hand, a fraction appears in the numerator or the denominator of a complex fraction. The value will be:
= 7/15 * (9/-28)
= -63 / 420
= -3/20
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is tangent to circle A at point G. If AG = 8 and GI = 15, determine the length of .
1) 17 units
2) 18.3 units
3) 15 units
4) 12.7 units
Answer:
hope u want to know the length of AH.
it is 17 units
Step-by-step explanation:
AGH is 90° (tangent )
AG is 8 units and GH is 15 units (Data)
so using Pythegorus theorem
AG² + GH² = AH²
gives √(8²+15²)
= 17 units
an airplane travels 5032 kilometers against the wind in 8 hours and 6152 kilometers with the wind in the same amount of time. what is the rate of the plane in still air and what is the rate of the wind?
The rate of the plane in still air is 644 kilometers per hour. The rate of the wind is 72 kilometers per hour.
To calculate the rate of the plane in still air and the rate of the wind, we can use the formula Rate = Distance/Time. To calculate the rate of the plane in still air, we can use the distance of 5032 kilometers and the time of 8 hours to get a rate of 644 kilometers per hour. To calculate the rate of the wind, we can subtract the rate of the plane in still air (644 kilometers per hour) from the rate of the plane with the wind (6152 kilometers per hour) to get a rate of 72 kilometers per hour. Therefore, the rate of the plane in still air is 644 kilometers per hour and the rate of the wind is 72 kilometers per hour.
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Select the graph for the solution of the open sentence. Click until the correct graph appears.
3|x| > 6
Answer:
third one:
x<-2 or x>2
Step-by-step explanation:
Answer:
third one
Step-by-step explanation:
]
2x2x2x3x3 = ?⁵
does this work or not?
Why?
what is the size of angle ADC
what is the size of angle ADB
Answer:
∠ADC = 58°∠ADB = 37° BD is a diameterStep-by-step explanation:
You want to know the measures of angles ADB and ADC given that inscribed angle BAC is 21° and exterior angle CBE is 58°.
Exterior angleAngle CBE is exterior to triangle CBA with remote interior angles BAC (21°) and ACB. The exterior angle is equal to the sum of the remote interior angles, so ...
∠CAB +∠ACB = ∠CBE
21° +∠ACB = 58°
∠ACB = 37° . . . . . . . . subtract 21°
a) ∠ADCThe measure of an inscribed angle is half the measure of the arc it intercepts. This means the measures of all inscribed angles that intercept the same arc are the same.
∠ADB = ∠ACB = 37°
∠BDC = ∠CAB = 21°
By the Angle Addition theorem, ...
∠ADC = ∠ADB +∠BDC = 37° +21°
∠ADC = 58°
b) ∠ADBAs we just saw, ...
∠ADB = 37°
c) BDFor angle CAD = 69°, the total of the inscribed angles with vertex A is ...
∠CAD +∠CAB = ∠BAD
69° +21° = 90° = ∠BAD
This means angle BAD intercepts an arc BD of 180°, hence segment BD is a diameter.
__
The attached figure is accurately drawn.
suppose that frida selects a ball by first picking one of two boxes at random and then selecting a ball from this box at random. the first box contains three white balls and two blue balls, and the second box contains four white balls and one blue ball. what is the probability that frida picked a ball from the first box if she has selected a blue ball? (enter the value of the probability in decimal format and round the final answer to one decimal place.)
If Frida chose a blue ball, there is a 3/4 probability that she chose a ball from the first box.
What is probability?The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur.
Probabilistic and odds are two distinct ideas.
Odds are determined by dividing the likelihood of an event by the likelihood that it won't.
So, we have:
Initial box:
3 white balls
2 blue balls.
Next box:
4 white balls.
1 blue ball.
If Frida chose a blue ball, the likelihood that she chose a ball from the first box is:
Probability (P) = (required outcome / Total possible outcomes)
Probability of picking the first box : P(F) = 1/2
Probability of not picking the second box :P(S) 1/2
Probability of picking blue from the first box : P(B | F) = 3/5
Probability of picking blue, but not from the first box : P(Blue not from the second box) P(B|S) = 1/5
If Frida chose a blue ball, there is a chance she chose a ball from the first box:
P(F) * P(B|F) ÷ (P(F) * P(B|F)) + (P(S) * P(B|S))
(1/2 * 3/5) ÷ ((1/2 *3/5) + (1/2 * 1/5)
3/10 ÷ (3/10 + 1/10)
3/10 ÷ 4/10
3/10 * 10/4
= 3/4
Therefore, if Frida chose a blue ball, there is a 3/4 chance that she chose a ball from the first box.
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Read the following statement: If meX = mY and mY = meZ, then m2X = m Z. This statement demonstrates:
the substition property.
the refexive property.
the symmetric property.
the transitive property.
If meX = mY and mY = meZ, then meX = meZ. This statement demonstrates
the transitive property.What is transitive property?According to the transitive property, all the quantities are equal to each other if two quantities are equal to the third quantity.
For the given problem, if meX = mY and mY = meZ, then meX = meZ
The two properties that are equal is meX and mY
since mY is also equal to meZ then transitive property says that meX and meZ are still equal
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The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.(a) What proportion of the students scored at least 26 points on this test, rounded to five decimal places? (b)What is the 31 percentile of the distribution of test scores, rounded to three decimal places?
Using z-scores the answers are found to be, part(a) 0.02280 and part(b) = 22.980 points
What is z-score?Z-score is a value that describes the deviation of a value from the standard deviation. Z-score is the number of standard deviations a given data point lies above or below mean.
What is the formula for z-score?The formula for z-score is,
z = (x - µ) / a
where µ is the mean of data set and a is the standard deviation of the data
For part (a),
z = 26-22/2
z = 2.00
P(x>26) = 0.5 - 0.4772
P(x>26) = 0.02280
For part(b),
To find the value of x we first need to find the value of z-score. z-score at 100 - 31 - 50 = 19% = 0.19
At an area of approximately 0.19, the z-score is 0.49
Using above formula, 0.49 = (x -22)/2
x = 22.980
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Find the radius of the circle which circumference is 22 cm.
Answer:
3.5 cm
Step-by-step explanation:
Circumference: C = 2πr
so radius r = C/2π = 22/2π = 3.5 cm
an online retailer determines that people click on a particular advertisement 2\%2%2, percent of the times it appears. let vvv be the number of times the advertisement appears to get the first person to click on it. assume each click is independent. find the probability that a person first clicks on the advertisement the 8^{\text{th}}8 th 8, start superscript, start text, t, h, end text, end superscript time it appears. you may round your answer to the nearest hundredth.
The probability of the event that a person first clicks on the advertisement the 8th time it appears is approximately 0.0177 (rounded to the nearest hundredth).
To find the probability that a person first clicks on the advertisement the 8th time it appears (vvv = 8), we can use the geometric probability formula:
[tex]P(X = k) = (1 - p)^{(k-1)}* p[/tex]
where:
P(X = k) is the probability of the event occurring on the kth trial,
p is the probability of success (clicking on the advertisement) on a single trial, which is 2% or 0.02 in decimal form,
k is the number of trials (number of times the advertisement appears) until the first success (first click).
In this case, k = 8 (the 8th time the advertisement appears) and p = 0.02.
[tex]P(X = 8) = (1 - 0.02)^{(8-1)} * 0.02\\P(X = 8) = (0.98)^7 * 0.02[/tex]
P(X = 8) ≈ 0.0177
So, the probability of the event that a person first clicks on the advertisement the 8th time it appears is approximately 0.0177 (rounded to the nearest hundredth).
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Please help meeeeee !!????!!!!
Answer: She fills 2 full boxes and has 3 animals left over.
Step-by-step explanation: To find how many full boxes she can fill, we can do 5 x 2, without going over. So, 5 x 2 is 10, so now we subtract 10 from 13 and get 3, so this explains that we that she can fill 2 FULL boxes, yet have 3 animals LEFT OVER. I hoped this helped!
Answer:
2 boxes can be filed completely with 3 stuffed animals left over.
Step-by-step explanation:
Take the number of stuffed animals (13) and dive that by the number that will fit in each box (2). The remainder is how many extra stuffed animals are left.
13 ÷ 2 = 5 remainder 3
passes through the points (-2,-9) and (4, -6)
y=1/2x-8 is the equation of line passing through points (-2,-9) and (4, -6) is
What is Slope of 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.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The points are (-2,-9) and (4, -6)
Slope=-6+9/4+2
=3/6=1/2
Let us find the y intercept by the point (-2, -9)
-9=1/2(-2)+b
-9=-1+b
-9+1=b
-8=b
Hence, the equation of line passing through points (-2,-9) and (4, -6) is y=1/2x-8.
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the number of pieces of cat food in a one-cup scoop is approximately normally distributed with a mean of 344 pieces and a standard deviation of 16 pieces. if a random sample of 28 scoops of cat food is selected, what is the probability that the mean number of pieces will be more than 350 pieces?
Answer:
the probability that the mean number of pieces in a sample of 28 scoops is more than 350 pieces is approximately 0.0228
Step-by-step explanation:
To find the probability that the mean number of pieces in a sample of 28 scoops is more than 350 pieces, we can use the normal distribution.
The standard error of the mean for a sample of size 28 is the standard deviation of the population divided by the square root of the sample size, or 16 / sqrt(28) = 2.8.
This means that the distribution of the sample means is approximately normally distributed with a mean of 344 pieces and a standard error of 2.8 pieces.
To find the probability that the sample mean is more than 350 pieces, we can use the cumulative distribution function of the normal distribution. In this case, we want to find the probability that a normally distributed random variable is greater than 350.
Using a normal distribution calculator or table, we can find that the probability that a normally distributed random variable with a mean of 344 and a standard error of 2.8 is greater than 350 is approximately 0.0228.
Therefore, the probability that the mean number of pieces in a sample of 28 scoops is more than 350 pieces is approximately 0.0228.
I can really use some help anyone?
The linear inequality to represent the number of seashell is w ≥ 14 and the graph is attached below
Linear InequalityLinear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be numerical or algebraic or a combination of both.
In this problem, Ernest needs at least 14 seashells and he plans to glue 30 seashells on the wall.
An inequality to represent this will be
w ≥ 14
The reason why we are using greater than or equal to sign in this problem is that we need "at least" 14 seashells or more than seashells on the wall.
b)
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Solve | x + 5 | - 6 = 7
Answer:
x=8
Step-by-step explanation:
|x+5|−6=7
|x+5|−6+6=7+6
|x+5|=13
|x+5|=13
x+5=13
x+5−5=13−5
x=8
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02.03 Focus Questions
What are linear equations and functions?
What are the different ways of representing a linear function?
How are key features of a linear function identified and interpreted from a graph?
How are key features of a linear function identified and interpreted from a table?
How are key features of a linear function identified and interpreted from an equation?
How are key features of a linear function identified and interpreted from a description?
Linear functions are those whose graph is a straight line and it has the following form. y = f(x) = a + bx.
There are several ways to represent a linear function such ad word form, function notation, tabular form, and graphical form.
The key features of a linear function identified and interpreted from a description as an increasing linear function results in a graph that slants upward from left to right and has a positive slope.
What is a linear function?A linear function can be expressed as a point slope or a line with a slope intercept. The ordered pairs will represent points on the line where a table of values representing the function is provided. According to the values in the table, the gradient of the line is a ratio of rise to run. The gradient and initial value of the function are shown in slope intercept form.
A graph with a positive slope and a left-to-right slope is produced by an increasing linear function. A graph with a negative slope and a left-to-right slant is produced by a decreasing linear function. A graph with a constant linear function looks like a horizontal line.
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2: Angle 1 and Angle 4 are vertical angles. If the measure of angle 1 equals 3x + 14 and the
measure of angle 4 equals 5x − 52, what is the measure of Angle 1?
3: Suppose that ∠ = 3x + 8 and ∠ = 2/3x + 62
If ∠ and ∠ are supplementary
angles, what is the measure of ∠?
4:Angle 2 and Angle 3 are vertical angles. If the measure of angle 2 equals 13x + 27 and the
measure of angle 3 equals 9x + 59, find the value of .
5: Suppose that m∠ABC = 163° and ∠XYZ = 5x + 2. If ∠ABC and ∠XYZ are supplementary
angles, determine the value of x
2. The measurement of angle 1 is 113°
3. The measure of ∠1 = 98° and ∠2 = 82°
4. The value of x is 8.
5. The value of x is 3.
What is the supplementary angle?
Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.
2.
Given that, ∠1 and ∠4 are vertical angle.
According to the vertical angle theorem, if two angles are vertical then they are congruent.
Therefore,
∠1 = ∠4
3x + 14 = 5x − 52
Subtract 5x from both sides:
3x - 5x + 14 = -52
-2x + 14 = -52
Subtract 14 from both sides:
-2x = -66
x = -33
Putting x = -33 in ∠1 = 3x + 14
∠1 = 3× 33 + 14 = 113°
3.
Given that, ∠1 = 3x + 8 and ∠2 = 2/3x + 62 are supplementary angles.
Therefore ∠1 + ∠2 = 180°
3x + 8 + 2/3x + 62 = 180°
11/3 x + 70 = 180°
Subtract 70 from both sides:
11/3 x = 110
x = 110 × (3/11)
x = 30
Putting x = 30 in ∠1 = 3x + 8 and ∠2 = 2/3x + 62
∠1 = 3x + 8 = 3×30 + 8 = 98°
∠2 = 2/3x + 62 = (2/3)×30 + 62 = 82°
4.
Given that, Angle 2 and Angle 3 are vertical angles. If the measure of angle 2 equals 13x + 27 and the measure of angle 3 equals 9x + 59.
Therefore,
∠2 = ∠3
13x + 27 = 9x + 59
Subtract 9x from both sides:
13x - 9x + 27 = 9x -9x +59
4x +27 = 59
Subtract 27 from both sides:
4x = 32
x = 8
5. Given that m∠ABC = 163° and ∠XYZ = 5x + 2 are supplementary angles.
m∠ABC + m∠XYZ =180°
163° + 5x + 2 =180°
165 + 5x = 180
Subtract 165 from both sides:
5x = 15
x = 3
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Answer:
2) m∠1 = 113°
3) 98° and 82°
4) x = 8
Angles = 131°
5) x = 3
Step-by-step explanation:
Question 2If Angle 1 and Angle 4 are vertical angles, then according the Vertical Angles Theorem they are congruent.
Therefore:
⇒ m∠1 = m∠4
⇒ 3x + 14 = 5x - 52
⇒ -2x + 14 = -52
⇒ -2x = -66
⇒ x = 33
To find the measure of Angle 1, substitute the found value of x into the expression for the angle:
⇒ m∠1 = 3x + 14
⇒ m∠1 = 3(33) + 14
⇒ m∠1 = 99 + 14
⇒ m∠1 = 113°
Question 3Given:
∠ = 3x + 8∠ = ²/₃x + 62If the angles are supplementary, they sum to 180°:
⇒ 3x + 8 + ²/₃x + 62 = 180
⇒ ¹¹/₃x + 70 = 180
⇒ ¹¹/₃x = 110
⇒ 11x = 330
⇒ x = 30
Substitute the found value of x into the expressions for the angles:
⇒ ∠ = 3x + 8
⇒ ∠ = 3(30) + 8
⇒ ∠ = 98°
⇒ ∠ = ²/₃x + 62
⇒ ∠ = ²/₃(30) + 62
⇒ ∠ = 82°
Question 4If Angle 2 and Angle 3 are vertical angles, then according the Vertical Angles Theorem they are congruent.
Therefore:
⇒ m∠2 = m∠3
⇒ 13x + 27 = 9x + 59
⇒ 4x + 27 = 59
⇒ 4x = 32
⇒ x = 8
Substitute the found value of x into the expressions for the angles:
⇒ m∠2 = 13x + 27
⇒ m∠2 = 13(8) + 27
⇒ m∠2 = 104 + 27
⇒ m∠2 = 131°
⇒ m∠3 = 9x + 59
⇒ m∠3 = 9(8) + 59
⇒ m∠3 = 72 + 59
⇒ m∠3 = 131°
Question 5Given:
m∠ABC = 163° m∠XYZ = 5x + 2If ∠ABC and ∠XYZ are supplementary, they sum to 180°:
⇒ m∠ABC + m∠XYZ = 180°
⇒ 163 + 5x + 2 = 180
⇒ 5x + 165 = 180
⇒ 5x = 15
⇒ x = 3
a man 6 feet tall walks at a rate of 5 ft / sec away from a light that is 15 feet above the ground. when he is 10 feet from the base of the light, at what rate is the tip of his shadow moving?
On solving the provided question we can say that - rate is the tip of his shadow moving is [tex]d/dt ( s-x) = ds/dt - dx/dt = 25/3 - 5 = 25/3 - 15/3 = 10/3 ft/s = 10/3 ft/s[/tex]
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is what? A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
triangles and the ratios
15 ft s
-------- = --------------
6 ft s-x
Using cross products
[tex]15( s-x) = 6s\\15s -15x = 6s\\15s-6s = 15x\\9s = 15x\\s = 15/9 x\\s = 5/3 x[/tex]
Taking the derivative of each side with respect to time
[tex]ds/dt = 5/3 dx/dt\\We know dx/dt = 5 ft/s\\ds /dt = 5/3 * 5 = 25/3 ft/s\\a) ds/dt = 25/3 ft/s[/tex]
The length of the shadow is ( s-x)
[tex]d/dt ( s-x)\\ds/dt - dx/dt\\25/3 - 5\\25/3 - 15/3\\10/3 ft/s\\b) 10/3 ft/s[/tex]
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Which number line shows the solution to the inequality -2(3x - 1) < 8?
Answer: B
Step-by-step explanation:
1. multiply (-3x+1) by -2 to get -6x+2 -> -6x+2<8
2. then subtract 2 from both sides, -6x+2 -2 < 8 -2 -> -6x<6
3. divide both sides by -6, when dividing an inequality, the inequality symbol switches so you'd have x > -1
so the answer would be B
PLEASE HELP (attached image)
Answer:3
Step-by-step explanation: if you fo it wrong so thats the answer
Jay has an album that holds 500 stamps. Each page of the album holds 5 stamps. If 21% of the album is empt, how many pages are filled with stamps?
Answer: 79 pages
Step-by-step explanation:
100% - 21% = 79%
So we know that Jay has 79% of the stamps
79% = 0.79
Take 500 times 0.79 = 395 stamps
Then we take 395 divided by 5 = 79 pages
So, 79 pages are filled with stamps