Mathematics College

A = h/2 * (a + b ); for h

Answers

Answer 1

[tex]A=\dfrac{h}{2}(a+b)\\ 2A=h(a+b)\\ h=\dfrac{2A}{a+b} [/tex]

Answer 2

h/2 * (a + b )=A
h/2=A/(a+b)
h=2A/(a+b)

Related Questions

what is 802 and 6 hundredths in expanded form

Answers

800+ 2+ 0.06

Hope this helps!

what is the answer to simplify 10y-7y

Answers

When you subtract 10y-7y you get 3y.

Since the variable(y) have same power 1, we can subtract them.10y-7y will be 3y.

simplify sin(2x+7y)+sin(2x-7y)

Answers

sin(a+b)=sin a * cos b + sin b cos a
sin(a-b)=sin a * cos b - sin b cos a

Lisa is asked to draw a triangle with the following specifications:

two angles are complementary
the side between the two complementary angles has a length of 10 centimeters

Which of the following statements about this triangle is true?
A.
More than one triangle exists with the given conditions, and all instances must be right triangles.

B.
More than one triangle exists with the given conditions, and all instances must be isosceles triangles.

C.
Exactly one triangle exists with the given conditions, and it must be a right triangle.

D.
Exactly one triangle exists with the given conditions, and it must be an isosceles triangle.

Answers

Let the measures of the 2 complementary angles be α and β.

α+β are complementary means, their sum is 90°. So the measure of the remaining 3rd angle is 180°-90°=90°.

This means the triangle is a right triangle, with the length of the hypotenuse equal to 10 cm.

let the length of the sides be a and b.

So lisa can draw any right triangle, with sides a and b, such that

[tex] a^{2} + b^{2} = 10^{2}=100[/tex]

which means, infinitely many triangles.

Answer:

A.More than one triangle exists with the given conditions, and all instances must be right triangles.

42 out of 96 support a candidate in an office election what percent of the vote is that

Answers

divide

42/96 = 0.4375

0.4375*100 = 43.75 percent

round the answer as needed.

A new surgery is successful 75% of the time. if the results of 10 such surgeries are randomly sampled, what is the probability that fewer than 9 of them are successful

Answers

Final answer:

This is a binomial probability problem where we calculate the probability of fewer than 9 successful surgeries out of 10, given a success rate of 75% for each surgery. The probabilities of 0 to 8 successful surgeries are calculated and summed up.

Explanation:

The question asks for the probability that fewer than 9 out of 10 surgeries are successful, given that each surgery has a 75% chance of being successful. This is a binomial probability problem since each surgery can result in either success (75%) or failure (25%), and we are dealing with a fixed number of independent trials (10 surgeries).

To solve this, we first calculate the probability of exactly 8 successes, exactly 7 successes, and so on down to 0 successes, then sum these probabilities. The binomial probability formula is P(x) = (nCx) * (p^x) * ((1-p)^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and nCx is the combination of n items taken x at a time.

However, calculating each probability individually and summing them can be tedious, and tools or calculators designed for binomial distributions are often used to compute this more efficiently. For a result of fewer than 9 successes, we would add the probabilities of getting 8, 7, ..., down to 0 successful surgeries.

The half life of cobalt -60 (used in radiation therapy) is 5.26 years ( actual data ).how much of a 200 g sample of cobalt-60 will remain after 26.3 years

Answers

Without getting into exponential functions this can be done rather easily.
For every half-life, one half of an isotope decays.
26.3 / 5.26 = 5
26.3 years is exactly 5 half-lives.
After EACH half-life we have one half of what we previously had.

So after one half-life we have 50%
2 half-lives 25%
3 half-lives 12.5%
4 half-lives 6.25%
5 half-lives 3.125%

So, how much is left of the 200 gram sample?
200 * .03125 = 6.25 grams

Final answer:

The amount of cobalt-60 will decrease with each half-life, which is 5.26 years. After 5 half-lives (26.3 years), the 200g sample will reduce to 6.25g.

Explanation:

The subject of the question is the half-life of a radioactive substance, in this case, cobalt-60. Half-life is the time required for half the atoms in a sample to decay. Given that the half-life of cobalt-60 is 5.26 years, and we are interested in a period of 26.3 years, we first classify this period into 'half-life' units, which equals 26.3 / 5.26 = 5 half-lives.

With each half-life, the quantity of cobalt-60 is cut in half. We start with a 200g sample and after 5 half-lives, the amount of cobalt-60 would decrease as follows:

After the 1st half-life = 200/2 = 100g After the 2nd half-life = 100/2 = 50gAfter the 3rd half-life = 50/2 = 25gAfter the 4th half-life = 25/2 = 12.5gAfter the 5th half-life = 12.5/2 = 6.25g

Therefore, after 26.3 years, only 6.25g of the original 200g sample of cobalt-60 will remain.

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If you choose a card at random from a well shuffled deck of 52 cards, what is the probability that the card chosen is not a heart

Answers

Sample space ={13 H + 13 D + 13 S + 13 C} = 52 cards

P(getting one heart) = 13/52 = 1/4
P( getting NO heart) = 1-1/4 = 3/4 = 0.75

The probability that the card chosen is not a heart is 0.75

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

Sample space ={13 H + 13 D + 13 S + 13 C}

= 52 cards

The total number of cards in a deck is 52

Number of cards with hearts = 13

Therefore, P(getting one heart) = 13/52 = 1/4

P( getting NO heart) = 1-1/4 = 3/4 = 0.75

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Two buses leave at the same time traveling in opposite directions. One bus travels at 63mph and the other at 62mph. How soon will they be 187.5
miles apart?

Answers

recall your d = rt, distance = rate * time

the buses are traveling in opposite directions, but both are taking off at the same time
let's say bus A is going at 63mph and bus B is going at 62mph, so, we know their "r" rate for each

ok, after they had travelled for "t" time, they're both 187.5 miles apart, at that instant, bus A has been travelling for "t" hours and bus B has been also travelling for "t" hours as well

now, if bus A covered say "d" miles in those "t" hours, then bus B covered the slack from 187.5 and "d", or 187.5 - d

thus

[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{bus A}&d&63&t\\ \textit{bus B}&187.5-d&62&t \end{array} \\\\\\ \begin{cases} \boxed{d}=63t\\ 187.5-d=62t\\ ----------\\ 187.5-\boxed{63t}=62t \end{cases}[/tex]

solve for "t".

Precalc: Vector word problem:
A channel flows from north to south at a rate of 15 mph.
A sailboat heads at an angle of 30 degrees upstream at 40 mph.
A strong wind blows towards northwest at 30 mph.

a. Write each vector in component form.

Answers

bearing in mind that [tex]\bf \begin{cases} x=rcos(\theta )\\\\ y=rsin(\theta ) \end{cases} [/tex]

I can make this much from that, check the picture below.

The vector representing the flow from North to South is 0, -15.The vector representing the sailboat is [tex]15\sqrt{3} ,\;15[/tex].The vector representing the strong wind blowing towards northwest is [tex]-15\sqrt{2},\;15\sqrt{2}[/tex] .

What is a vector?

A vector can be defined as an element of a vector space, which represents an object that has both magnitude and direction.

Assuming that; [tex]\left \{ {{x=rcos \theta} \atop {y=rsin \theta}} \right.[/tex]

For the channel:

Rate, r = 15 mph.

The vector representing the flow from North to South is given by:

[tex]15 cos (\frac{3\pi}{2} ), \; 15 sin (\frac{3\pi}{2} )\\\\15(0),\; 15(-1)[/tex]

Vector = 0, -15

For the sailboat:

Rate, r = 40 mph.Angle = 30 degrees upstream.

The vector representing the sailboat is given by:

[tex]40 cos (30 ), \; 40 sin (30)\\\\30(\frac{\sqrt{3} }{2} ),\; 30(\frac{1 }{2} )\\\\15\sqrt{3} ,\;15[/tex]

Vector = [tex]15\sqrt{3} ,\;15[/tex]

For the strong wind:

Rate, r = 30 mph.

The vector representing the strong wind blowing towards northwest is given by:

[tex]30 cos (\frac{3\pi}{4} ), \; 30 sin (\frac{3\pi}{4} )\\\\30(\frac{-\sqrt{2} }{2} ),\; 30(\frac{\sqrt{2} }{2} )\\\\-15\sqrt{2},\;15\sqrt{2}[/tex]

Vector = [tex]-15\sqrt{2},\;15\sqrt{2}[/tex]

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Ace Hardware sells boxes of wrenches ($ 100) and hammers ($300). Howard ordered 40 boxes of wrenches and hammers for $ 8,400. How many boxes of each are in the order.

Answers

100w+300h=8400

h+w=40, h=40-w, using this h in the first equation gives you:

100w+300(40-w)=8400 perform the indicated multiplication on left side

100w+12000-300w=8400 combine like terms on the left side

-200w+12000=8400 subtract 12000 from both sides

-200w=-3600 divide both sides by -200

w=18, and since h=40-w

h=40-18=22

So Howard ordered 18 boxes of wrenches and 22 boxes of hammers.

Answer:

18 boxes of wrenches and 22 boxes of hammers.

Step-by-step explanation:

how do you write 10 X 3 ten's in standard form?

Answers

Standard Form - 300 the 10 means its like this 400 500

what are 3 different ways to make tbe number 15638 with only hundreds tens and ones

Answers

Crssfffffffffdawfc1346666432c

Answer:

156 hundreds, 3 tens and 8 ones.155 hundreds, 12 tens and 18 ones155 hundreds, 10 tens and 38 ones

Step-by-step explanation:

The easiest way is to divide the number by 100, 10 and 1 in that order so:

15638/100=156.38 <- From this number you take only the integer (or the number without decimals), and that would be your hundreds, for this case 156 is the integer part, so 156 hundreds.

Next we take take the 38 we had left from the above division, and we divide it by 10.

38/10=3.8 <- we apply exactly the same steps as before but with the tens, working only with the integer, meaning 3, so you end up with 3 tens.

Last but not least, the rest, that is 8, will be your ones. In this case, just 8 ones.

Your first answer would be 156 hundreds, 3 tens and 8 ones.

Now, the combinations are infinite, if you take one from the hundreds it becomes 10 tens or 100 ones, and if you take 1 from the tens you get 10 ones. So you could have

155 hundreds (155-1), 12 tens (3+10-1), and 18 ones. Or any permutation you prefer.

For quick studies, it is easier to round down to the nearest 5 or 0, so another way to see this would be:

155 hundreds, 10 tens, and 38 ones.

A population, with an unknown distribution, has a mean of 80 and a standard deviation of 7. for a sample of 49, the probability that the sample mean will be larger than 82 is

Answers

Since the distribution is unknown, we have to think of the CLT (Central Limit Theorem):
n = 49

μ(x) = μ →→ μ(x) = μ = 80

σ(x) = σ/(√v) →→ 7/√49 = 7/7 = 1

Z(x) = (X-μ)/[σ(x)]

Z(x) = (82-80) /1
Z(x) = - 2
For Z= - 2, the area (probability) = -0.0228 (from the left)
and due to symmetry this area is equal in absolute value to the sample larger than 82 (to the right), hence the P(X>82) = 0.228

what is the axis of symmetry of y=3x^2+6x+5

Answers

Answer: The axis of symmetry is the equation x = -1

----------------------------------------------

Explanation:

The equation y = 3x^2+6x+5 is in the form y = ax^2+bx+c

In this case, a = 3, b = 6, c = 5.

We will plug a = 3 and b = 6 into the formula below

x = -b/(2*a)
x = -6/(2*3)
x = -6/6
x = -1

Therefore, the axis of symmetry is x = -1

This is the vertical line that passes through the vertex. We can reflect the parabola over this line to have one half of the curve line up perfectly with the other half of the curve.

On a cross-country trip, a couple drives 500 mi (miles) in 10h on the first day, and 400 mi in 8h on a second day. the average speed for the whole trip is:

Answers

The average speed = total distance ÷ total time traveled

The average speed = [500+400] ÷ [10+8]
The average speed = 900 ÷ 18 = 50 miles/hour

a rectangle has a length of 7 meters longer than double the width. the perimeter is 134 meters. find the dimensions of the rectangle.

Answers

check the picture below.

what's the length? well, l = w + 7.

6nsquared - 5nsquared + 7nsquared simplify the expression

Answers

6n^2-5n^2= n^2

n^2+7n^2= 8n^2

Final answer: 8n^2
Remember that all of these terms are like terms so you can just add/subtract coefficients.

The equation is 6n^2-5n^2+7n^2. Since the exponents are the same, you can just add and subtract. 6n^2-5n^2=n^2. N^2+7n^2=8n^2. The answer to this is 8n^2. I hope this helps! :)

Given that 3^x = 4^y = 12^z, show that z = (xy)/(x+y).

Answers

[tex]3^{x} = 4^{y} = 12^{z}[/tex]
[tex]3^{x} = 4^{y} = (4 \cdot 3)^{z}[/tex]
[tex]3^{x} = 4^{y} = 4^{z} \cdot 3^{z}[/tex]

[tex]\text{Let a } = 3^{x} = 4^{y} = 4^{z} \cdot 3^{z}[/tex]
[tex]log_3a = x[/tex]
[tex]log_4a = y[/tex]
[tex]log_{(4 \cdot 3)}a = z[/tex]

Using change of base:
[tex]x = \frac{lna}{ln3}[/tex]
[tex]y = \frac{lna}{ln4}[/tex]
[tex]z = \frac{lna}{ln(4 \cdot 3)}[/tex]

[tex]ln3 = \frac{lna}{x}[/tex]
[tex]ln4 = \frac{lna}{y}[/tex]
[tex]ln(4 \cdot 3) = \frac{lna}{z}[/tex]

Now, ln(4 · 3) = ln(4) + ln(3)

[tex]\frac{lna}{z} = \frac{lna}{x} + \frac{lna}{y}[/tex]
[tex]\frac{1}{z} = \frac{1}{x} + \frac{1}{y}[/tex]
[tex]\frac{1}{z} = \frac{x + y}{xy}[/tex]

[tex]\therefore z = \frac{xy}{x + y}[/tex]

Final answer:

To show that z = (xy)/(x+y) given that 3^x = 4^y = 12^z, logarithms and the properties of exponents are used to simplify and solve for z.

Explanation:

The problem given is to show that if 3^x = 4^y = 12^z, then z = (xy)/(x+y). To solve this, we can use logarithms or equate the expressions to a common variable. Since 12 = 3 × 4, it means that 12^z = (3^z)(4^z).

Remember that the original equations given were 3^x = 12^z and 4^y = 12^z.

Substituting z into these equations we have 3^x = 3^z × 4^z and 4^y = 3^z × 4^z.

Taking logarithms, we find

[tex]log(3^x) = log(3^z) + log(4^z) and log(4^y) = log(3^z) + log(4^z).[/tex]

Applying the power rule of logarithms, the equations simplify to

[tex]x log(3) = z log(3) + z log(4)[/tex]and [tex]y log(4) = z log(3) + z log(4).[/tex]

Dividing these equations by log(3) and log(4) respectively gives

[tex]x = z + z(log(4)/log(3))[/tex] and [tex]y = z + z(log(3)/log(4)).[/tex]

Adding these equations, we get

[tex]x + y = 2z + z[(log(4)/log(3)) + (log(3)/log(4))],[/tex]

which simplifies to x + y = 2z because [tex](log(4)/log(3)) + (log(3)/log(4)) = 1.[/tex]Finally, solving for z gives z = (xy)/(x+y) as desired.

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)= 96t-16t^2 . After how long will it reach its maximum height? Do not round your answer.Time: ___ seconds

Answers

The time taken to reach the maximum height = 3 s

Further explanation

Quadratic function is a function that has the term x²

The quadratic function forms a parabolic curve

The general formula is

f (x) = ax² + bx + c

where a, b, and c are real numbers and a ≠ 0.

The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value

So the maximum is if a <0 and the minimum if a> 0.

After t seconds, a ball height h (in feet) is given by the function h (t) = 96t-16t²

The maximum value of the function is obtained if the first derivative of the function h (t) = 0

96-32t = 0

96 = 32t

t = 3 s

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The maximum height

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the fencing

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domain of the function

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Final answer:

The ball reaches its maximum height after 3 seconds. This is determined by finding when the derivative of the height function h(t) = 96t - 16t² equals zero and solving for t.

Explanation:

To determine the time at which the ball reaches its maximum height, we need to analyze the function h(t) = 96t - 16t². Here, h(t) represents the height of the ball after t seconds. The ball achieves its maximum height when the derivative of the height function with respect to time is zero (i.e., when its upward velocity is zero).

To find this, we can take the derivative of h(t) and set it equal to zero to find the critical points:

h'(t) = d/dt (96t - 16t²) = 96 - 32t.

Setting the derivative equal to zero:

96 - 32t = 0

32t = 96

t = 96/32 = 3 seconds.

Therefore, the ball reaches its maximum height after 3 seconds.

1 2 3 4 5 6 7 8 9 10 TIME REMAINING 58:03 The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the standard form of the equation for this line?

Answers

Final answer:

The standard form of the equation for the line passing through (-5, -1) and (10, -7) is y = x - 17.

Explanation:

The standard form of the equation for the line passing through the points (-5, -1) and (10, -7) can be found using the point-slope form given, which is y + 7 = (x - 10).

First, let's convert this equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Subtracting 7 from both sides of the equation, we get y = x - 17.

This is the standard form of the equation for the line passing through (-5, -1) and (10, -7).

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what is 2500g converted to kg

Answers

1000 g = 1 kg
2500 g = 2,5 kg

How many different 7-digit numbers can be formed using the digits in the number 5,474,575?

Answers

5474575^7 or 147384858537001988985939934535924916546630859375

17.16 is 62.4% of what

Answers

divide them

17.16/0.624 = 27.5

27.5 is the answer

double check by multiplying 27.5 by 62.4%

27.5*.624 = 17.16

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. to test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. the value of the test statistic in this problem is approximately equal to

Answers

The value of the test statistic in this problem is approximately equal to [tex]\frac{0.83-0.9}{\sqrt{\frac{(0.9)(0.1)}{100} } }[/tex]

Explanation:

Aspirin also known as acetylsalicylic acid, is a medication used to reduce pain, fever, or inflammation. A test statistic is the random variable that calculated from sample data it used in a hypothesis test. You can use test statistics to determine whether to reject the null hypothesis or not. The test statistic can compare the data with what is expected under the null hypothesis

A survey (a general view, examination, or description of someone or something) claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. to test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. the value of the test statistic in this problem is approximately equal to [tex]\frac{0.83-0.9}{\sqrt{\frac{(0.9)(0.1)}{100} } }[/tex] where

a = People who indicate that they recommend aspirin = 0.83

b = the actual proportion of doctors who recommend aspirin = 0.9

c = the actual proportion of doctors who not recommend aspirin = 1-0.9 = 0.1

d = a random sample = 100

[tex]\frac{a-b}{\sqrt{\frac{(b)(c)}{d} } } =\frac{0.83-0.9}{\sqrt{\frac{(0.9)(0.1)}{100} } }[/tex]

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Solve the quadratic equation by completing the square. x^2-14x+42=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas.
Form: ______
Solution: _______

Answers

x^2 - 14x + 42 = 0
x^2 - 14x = -42
x^2 - 14x + 49 = 49 - 42
(x - 7)^2 = 7
x - 7 = (+-) sqrt 7
x = 7 (+-) sqrt 7

solutions are : x = 7 + sqrt 7 and x = 7 - sqrt 7

x^2-14x+42=0 subtract 42 from both sides

x^2-14x=-42 halve the linear coefficient, square it, add it to both sides, in this case: (14/2)^2=7^2=49, add 49 to both sides

x^2-14x+49=7 now the left side is a perfect square...

(x-7)^2=7 take the square root of both sides

x-7=±√7 add 7 to both sides

x=7±√7

The above is the two solutions, 7+√7 and 7-√7

I am not sure what they mean by the proper form other than perhaps the point when you have a complete square as in the point in the process where you have a perfect square...

(x-7)^2=7

A business has $11,080 to spend on new laptops and tablet computers for its salespeople. The laptops cost $515 each. The tablets cost $285 each. The business wants each salesperson to have either a laptop or a tablet. There are 30 salespeople. How many of each type of computer should the business buy?

Answers

L = number of laptops bought
T = number of tablets bought

ok.. so, we know there are 30 salespeople.... so... the business is getting 30 of devices.. .so, whatever L is and T is, we know L + T = 30

each laptop is 515 bucks, so if they buy L amount, they'd end up paying 515*L or 515L bucks

each tablet is 285, so if they buy T tablets they'd end up paying 285*T or 285T bucks for them.

whatever those may be, we know all they have is 11,080. so 515L + 285T = 11080

[tex]\bf \begin{cases} L+T=30\implies \boxed{T}=30-L\\ 515L+285T=11080\\ ----------\\ 515L + 285\left( \boxed{30-L} \right)=11080 \end{cases}[/tex]

solve for L, to see how many laptops they'd get.

what about the tablets? well, T = 30 - L.

515x + 285y = 11,080

x + y = 30

Liz is using the distributive property to evaluate the expression 27(36) by using friendlier numbers. Her work is shown below.

Liz’s Work

27(36)
Step 1
27(3 + 12)
Step 2
27(3) + 27(12)
Step 3
81 + 324
Step 4
405

What was the first error that Liz made?
Step 1 should have been 27(6 + 30).
Step 2 should have been 27(3) + 12.
Step 3 should have been 27(30)(12).
Step 4 should have been 16,244.

Answers

Liz attempted to factor 36. Since 36 = 3*12 and not 3+12, this is not the way to go. In stead of factoring 36, she should have split it into a friendly sum, like 36=30+6.

Then Step 1 should have been 27(6+30).

Answer:

Step-by-step explanation:

The numbers 1 through 9 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random.

What is the probability that the drawn slips are "1", "2", "3", and "4", in that order?

Answers

Let's think of the problem as follows.

Write all the 4-digit numbers that can be formed using the digits from 1 to 9, without repetition, in pieces of paper, and put them in a bag. What is the probability of picking the 4-digit number 1234, among these numbers.

The connection of the 2 problems is as follows:

The 4-digit number, for example 5489, represents drawing first 5, then 4, then 8, then 9 , in the original question.

we did not allow repetition, because for example the number 8918 would represent drawing 8, then 9, then 1 then 8 (again!!), which is not possible, so we lose the connection between the problems.

So there are in total 9*8*7*6= 3024 4-digit numbers, with non-repeating digits.

One of these numbers is 1234 (representing drawing 1, then 2, then 3, then 4)

among these 3024 numbers, the probability of picking 1234 is
[tex] \frac{1}{3024}= 0.00033[/tex]

We could have solved this problem also as :

P(drawing 1, 2, 3, 4 in order)= [tex] \frac{1}{9} * \frac{1}{8} * \frac{1}{7} * \frac{1}{6} = \frac{1}{3024} [/tex]

Answer:[tex] \frac{1}{3024}= 0.00033[/tex]

Final answer:

The probability of drawing the slips '1', '2', '3', and '4' in that order is 1/126 or approximately 0.0079.

Explanation:

The probability that the drawn slips are '1', '2', '3', and '4', in that order, can be calculated by considering the number of favorable outcomes and the total number of possible outcomes.

There are 9 slips in the box, so the total number of possible outcomes is 9 choose 4, which is denoted as C(9,4) or 9!/(4!(9-4)!), which simplifies to 126.

Since we want the slips to be drawn in a specific order, the number of favorable outcomes is 1, because there is only 1 way to arrange the slips in the order '1', '2', '3', and '4'.

Therefore, the probability is 1/126, which simplifies to approximately 0.0079 or 0.79%.

What is the value of s and the length of side BC if ABCD is a rhombus?

Answers

Step 1

Find the value of s

we know that

In a Rhombus all sides are congruent

[tex]AB=BC=CD=DA[/tex]

[tex]AB=9s+29\\CD=10s-16[/tex]

equate AB and CD

[tex]9s+29=10s-16\\[/tex]

Combine like term

[tex]10s-9s=29+16\\[/tex]

[tex]s=45\ units[/tex]

The answer Part a) is

the value of s is [tex]45\ units[/tex]

Step 2

Find the value of side AB

[tex]AB=9s+29[/tex]

substitute the value of s

[tex]AB=9*45+29=434\ units[/tex]

Remember that the sides are congruent

[tex]AB=BC=CD=DA[/tex]

therefore

the answer Part b) is

The length of the side BC is [tex]434\ units[/tex]

The value of s is 45 and the length of side BC is; 434.

What is a Rhombus?

A rhombus is a plane shape of the form given I'm the attached image with all its sides equal.

Hence,

AB = BC = CD = DA

To determine the value of s;

10s - 16 = 9s + 29

10s-9s = 29+16

s = 45.

The length of side BC = CD = 10(45) - 16 = 450 - 16

The length of side BC = 450 -16 = 434