An isosceles triangle has a base that is 3 times the length of its legs. The perimeter of the triangle is 45 cm. What is the length of the base?

Take the square root of each side.

[tex]\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5[/tex]

Answer:

Area = 3w^2 - 6w

Step-by-step explanation:

Area = width * length

width = w

length = 3w - 6

Area = w (3w - 6)

Area = 3w^2 - 6w

Answer:

Area of rectangle = 3w² - 6w

Step-by-step explanation:

      Width = 'w' ft

      three times of width = 3*w = 3w

             six less than 3w = 3w - 6

   length = 3w - 6

     [tex]\sf \boxed{\bf Area \ of \ rectangle = length*width}[/tex]

                                      = (3w - 6)*w

                                      = 3w*w - 6*w

                                      = 3w² - 6w

Answer:

17%

Step-by-step explanation:

Let us say there are 200 people on the JV swim team. That would mean that 110 people do not wear glasses.

Of these 110 people, 30% are in 10th grade. Therefore, 33 people are in 10th grade and do not wear glasses.

This is 33 people ÷ 200 total = 16.5% ≈ 17%

Therefore, there is a 17% probability that a randomly chosen member of the jv swim team does not wear glasses and is in the 10th grade

[NOTE] You could also just do 55% × 30% = .55 × .30 = .165 ≈ .17 ⇒ 17%

Answer:

Step-by-step explanation:

21:

3,7

The probability is that this is least 2 collisions within the next 3 insertions using linear probing is 0.7.

Required probability

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Answer:0.4 as a decimal,2/5 as a fraction

Step-by-step explanation:

Answer:

The cost of one foot of grass sod is $9 and the cost of one shrub is $18.

Step-by-step explanation:

Since Pranv and Paul both bought their supplies from the same store, we can assume that they paid the same price per foot of grass sod and per shrub. From the information given, we know that Pranv spent $90 on 10 feet of grass sod and 5 shrubs, which means that he paid 90/10 = $9 per foot of grass sod and 90/5 = $18 per shrub. We also know that Paul spent $50 on 5 feet of grass sod and 3 shrubs, which means that he paid 50/5 = $10 per foot of grass sod and 50/3 = $16.67 per shrub. Since both Pranv and Paul paid the same price per foot of grass sod and per shrub, the cost of one foot of grass sod is $9 and the cost of one shrub is $18.

In an ideal circumstance, two people using 56k modems could exchange approximately 448,000 bits of digital information in one minute time. This is equal to 56,000 bytes of data per second (56kbps).

In an ideal circumstance, two people using 56k modems could exchange digital information at a rate of 56 kilobits per second (56kbps). To calculate the amount of data transferred in one minute, we need to multiply 56kbps by 60 seconds. This gives us a total of 3,360 kilobits, or 3.36 megabits. Since one byte is equal to 8 bits, we can divide 3.36 megabits by 8 to get the total number of bytes exchanged. This calculation results in 420,000 bytes, or 448,000 bits, of digital information exchanged in one minute of time.

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Answer:

Step-by-step explanation:

Dividing 168 by the smallest prime number          168 ÷ 2 = 84

84 is again divisible by 2                                           84 ÷ 2 = 42

42 is an even number and divisible by 2                   42 ÷ 2 = 21

Now, 21 is divisible by the next prime number, i.e.3   21 ÷ 3 = 7

7 is a prime number itself                                            7 ÷ 7 = 1

Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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The probability that every color will be represented in the sample of 5 is 35/7776.

For the stated question, box contains-

probability = favourable outcome/ total outcome

5 marbles are selected with out replacement.

Thus,

Probability of getting all color will occur is-

P(all color) =  (4C2)*(5C1)*(6C1)*(7C1) + (4C1)*(5C2)*(6C1)*(7C1) + (4C1)*(5C1)*(6C2)*(7C1) + (4C1)*(5C1)*(6C1)*(7C2) / (10C5)⁴

P(all color) = 6*5*6*7 + 4*10*6*7 + 4*5*15*7 + 4*5*6*21 / 36⁴

P(all color) = 1260 + 1680 + 2100 + 2520 / 1679616

P(all color) = 7560 / 1679616

P(all color) = 35/7776

Thus, the probability that every color will be represented in the sample of 5 is 35/7776.

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The curvature at the point (2, 8, −1). x = 2t, y = 8t^3/2, z = −t^2 is 0.039

In this question we need to find the curvature of r(t) = <2t, 8t^3/2, -t^2> at the point (2, 8, -1).

The derivative of r(t) with respect to t is:

r'(t) = <2, 12t^1/2, -2t>

The point (2, 8, -1) corresponds to t = 1,

and r′(1) = <2, 12(1)^1/2, -2(1)>

r'(1) = <2, 12, -2>

|r'(1)| = √(2^2 + 12^2 + (-2)^2)

|r'(1)| = √(4 + 144 + 4)

|r'(1)| = √(152)

|r'(1)| = 12.32

Now, r''(t) = <2, 6t^-1/2, -2>

and r′'(1) = <0, 6, -2>

r′(1) × r′′(1) = <0, 72, 4>

|r′(1) × r′′(1) |

= √(0^2 + 72^2 + 4^2)

=72.11

So, the curvature of r(t) would be,

κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3

k(1) = 72.11 / 12.32³

k(1) =0.039

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Answer: twelve and nine-tenths feet

Step-by-step explanation:

I turned the fractions into decimals cus I find that easier.

5/8 = .625 + 2 = 2.625

2.625(4) = 10.5 (multiply by 4 because it is 4 pieces)

1/5 = 0.2 + 1 = 1.2

1.2(2) = 2.4 (multiply by 2 because it is 2 pieces)

2.4 + 10.5 = 12.9

.9 can also be 9/10ths

Answer:

12 9/10

Step-by-step explanation:

The four pieces of wood: 4 x 2 5/8 = 10.5 or 10 1/2

The two peices of wood: 2 x 1 1/5 = 2.4 or 2 2/5

The total of both: 10 1/2 + 2 2/5= 12.9 or 12 9/10

Option a) ab + bc > ac is correct.

The first method by which we can solve this question is,

We have to know about the property of the triangle,

According to the property of the triangle, if we consider a triangle with lines ab, bc, ac and  -

Therefore, we can conclude that ⇒ ab + bc > ac and ab - bc < ac

In the second method, let us consider the given triangle as right-angled,

So, according to the property of the right-angled triangle or Pythagoras' Theorem,

The square of the hypotenuse is equal to the square of the other two sides, let us consider the sides of the triangle = ab, bc, ac.

ABC is a right-angled triangle -

[tex]ab^{2} + bc^{2} = ac^{2}[/tex]

[tex]ab + bc > ac[/tex]

Therefore, we can conclude that, options a) ab + bc > ac is correct.

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The number of ways cans a president, vice president, and secretary be chosen from a committee of 9 people, assuming one person cannot hold more than one position, is 84.

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

A president, vice president, and secretary be chosen from a committee of 9 people,

Calculate the number of ways by using the combination as shown below,

[tex]N = 9C_3[/tex]

Here, N is the number of ways,

N = 9! / [3!(9-3)!]

N = 9! / [3!6!]

N = 84

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The value of the given logarithm log(750)=2.875.

Commonly employed in science and engineering, the base-10 logarithm is also known as the decimal or common logarithm. Since its derivative is so straight forward, the natural logarithm, whose base is the number e 2.718, is widely used in both mathematics and physics. Computer science typically use the binary logarithm, which has a base of 2.

John Napier developed logarithms as a way to make calculations simpler in 1614. To make high-accuracy calculations simpler, they were quickly embraced by surveyors, scientists, engineers, navigators, and other professionals. Inefficient multi-digit multiplication steps can be swapped out for quicker addition and table lookups when using logarithm tables.

Given,

We have to find the logarithm value of log(750)

By using the logarithm calculator we get

log(750)=2.875

Therefore, the value of the given logarithm log(750)=2.875

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If we want the margin of error for the 90% confidence level to be about 1.5%, then a sample of 3002 is recommended.

In this problem, we want to find n for which  the margin of error for the 90% confidence level to be about 1.5%

From part (a), the 90% confidence interval is (0.435, 0.525)

the margin of error M = 0.015

0.015 = 1.645√(0.48 * 0.52)/n

(√n) ² = (0.015)²

n = 3001.9

n ≈ 3002

Therefore, a sample of 3002 is recommended.

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The complete question is:

Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot a ord it. (a) Calculate a 90% con dence interval for the proportion of Americans who decide to not go to college because they cannot a ord it, and interpret the interval in context. (b) Suppose we wanted the margin of error for the 90% con dence level to be about 1.5%. How large of a survey would you recommend?

the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587

The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.

To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.

We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.

We the look up the probability for a value of 1 in the z-table, which is 0.1587.

This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.

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Answer:

The mass of 100 cubic cm = 1,000 grams.

The mass of 500 cubic cm = 5,000 grams.

Step-by-step explanation:

90/10=9

140/10=14

250/10=25

100x10=1000

500x10=5000

Answer:

To find the difference between the cash price and the hire purchase price, we need to calculate the total hire purchase price.

First, we need to find the outstanding balance after the deposit is paid. We can do this by subtracting the deposit from the cash price:

outstanding balance = cash price - deposit

= Rs 65,000 - Rs 20,000

= Rs 45,000

Next, we need to calculate the total interest to be paid over the 2 1/2 year period. We can do this using the following formula:

total interest = outstanding balance * interest rate * time period

= Rs 45,000 * 18% * 2 1/2 years

= Rs 20,250

Finally, we can add the outstanding balance and the total interest to find the total hire purchase price:

total hire purchase price = outstanding balance + total interest

= Rs 45,000 + Rs 20,250

= Rs 65,250

The difference between the cash price and the hire purchase price is the difference between the total hire purchase price and the cash price. So we can calculate this as follows:

difference = total hire purchase price - cash price

= Rs 65,250 - Rs 65,000

= Rs 250

Therefore, the difference between the cash price and the hire purchase price is Rs 250.

I hope this helps!

= 20 000 + 1.18(65 000 - 20 000)

= 20 000 + 1.18(45 000)

= 20 000 + 53 100

= 73 100

73 100 - 65 000

= 8 100

Therefore, you will spend RS 8 100 more if you buy Hire Purchase Price than the Cash Price of Television.

Answer:  

1/ There are 4 clownfish in the tank now

2/ 4/10

Step-by-step explanation:

1/ We know the original number of clownfish is 2/8, which means there are 2 clownfish in a tank with a total number of 8 fish.

So now she wants to double the clownfish. So there will be 4 clownfish in the tank now.

2/ We know that there was eight fish in the tank, and now there are 2 more, so the total will be 10! And we know that now there are 4 clownfish, so our fraction is 4/10

The equation of the red graph is g(x) = -x².

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

g(x) = -x²

For x = 0, 1, 2, 3, 4, 5, ......

g(1) = 0

g(1) = -1

g(2) = -4

g(3) = -9

g(4) = -16

Thus,

The graph of red graph is g(x) = -x².

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The formula that represents the height h of the tomato plant as a function of the time t in weeks since it was planted is h=8(1.14)^t inches.

The height of a plant is considered to be "h".

The increase percentage per week =14

Compound interest is the interest you earn on interest. This may be illustrated via way of means of the usage of primary math: in case you have $one hundred and it earns 5% interest every year, you may have $one hundred and five on the cease of the primary year. At the cease of the second one year, you may have $110.25.

Now,

h=8(1+r/100)^t

h=8(1+14/100)^t

h=8(114/100)^t

h=8(1.14)^t inches

Therefore, the formula that represents the height h of the tomato plant as a function of the time t in weeks since it was planted is h=8(1.14)^t inches.

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Answer:

Step-by-step explanation:

Let x be the number of 1-point shots and y be the number of 2-point shots. We know that the total number of shots is 59 and the total number of points is 99. We can write these two equations as follows:

x + y = 59

1x + 2y = 99

To solve this system of equations, we can use substitution. We can solve the first equation for y and substitute the result into the second equation:

y = 59 - x

1x + 2(59 - x) = 99

1x + 118 - 2x = 99

-x = -19

x = 19

Now that we know the value of x, we can substitute it into the first equation to find the value of y:

y = 59 - 19 = 40
Therefore, the team made 19 1-point shots and 40 2-point shots.

Answer: $0.99

Step-by-step explanation: 8.5x0.06=0.51. 8.5+0.51=9.01. 10-9.01=0.99. Henry would get $0.99 in change.

From Boston to Kansas City, it takes 20 minutes to get there. When calculating the plane's arrival time, multiply the 360 mph speed from Boston by the 864 mi distance to Chicago.

Regardless of an object's beginning or ending position, we can define distance as the amount of ground it has traveled.

given

When calculating the plane's arrival time, multiply the 360 mph speed from Boston by the 864 mi distance to Chicago.

Distance = rate*time

864 = 360t,

t = 2.4

In other words, the flight arrived after 2.4 hours. Given that this is longer than two hours, divide the number by sixty to determine the time in minutes:

60 * 2.4 = 144 minutes. Assess the flight's travel time from Kansas City now.

It took 2 hours, 4 minutes, or 124 minutes from the time it departed at 8:30 AM to the time it arrived at 10:34 AM.

According to this, the jet from Kansas City arrived 144 – 124 = 20 minutes earlier than the plane from.

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