What fraction goes into the blank to make the fraction comparison true?

2/3 < ?

Answer:

TR is the smallest side.

RS is in the middle.

ST is the largest side.

Step-by-step explanation:

Angle R is the biggest angle, so it is opposite from the biggest side (not R) side ST.

Angle S is the smallest angle so it is opposite from the smallest side (not S) side TR.

The third angle is in between, so the opposite side is in between.

Answer:

An equivalent algebraic expression of -(b-5) using distributive property is

-b+5

Step-by-step explanation:

We need to use distributive property to solve the expression -(b-5)

The distributive property states that \(a(b+c)=ab+ac\)

Using distributive property to solve the expression -(b-5)

\(-(b-5)=-(b)-1(-5)\\=-b+5\)

So, an equivalent algebraic expression of -(b-5) using distributive property is

-b+5

Answer: 1. x=−7+5y+4z,   y=7/5+x/5−4z/5,  z=7/4+x/4−5y/4

2. x=−1−10y−4z         y=−1/10−x/10−2z/5       z=−1/4−x/4−5y/2

3. x=−5−8y−4z          y=−5/8−x/8−z/2            z=−5/4−x/4−2y

Step-by-step explanation:

Answer:

3 1/5+4.5+5 3/10=

16/5+4.5+53/10=

3.2+4.5+5.3=

13

Step-by-step explanation:

The HCF of 10, 20, and 50 is 10. The HCF (Highest Common Factor) of 10, 20, and 50 can be found by finding the common factors of the given numbers and then selecting the highest one.The common factors of 10, 20, and 50 are: 1 and 2.

Therefore, the highest common factor is 2.For instance, The highest common factor of two or more numbers is the largest number that can divide the given numbers exactly. The factors of 10 are 1, 2, 5, and 10. Factors of 20 are 1, 2, 4, 5, 10, and 20. The factors of 50 are 1, 2, 5, 10, 25, and 50.

As a result, the HCF of 10, 20, and 50 is 2. Here's a quick technique to find HCF:List all of the prime numbers that divide each of the numbers being considered separately.

Multiplying the common prime factors will give the highest common factor.Let's use the above-mentioned method to find the HCF of 10, 20, and 50:10 = 2 × 5.20 = 2 × 2 × 5.50 = 2 × 5 × 5.

The highest common factor of the numbers is the product of the smallest number of prime factors present in both the numbers, which is 2 × 5 = 10.Therefore, the HCF of 10, 20, and 50 is 10.

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Answer:

First, you need to understand the vocabulary.
Saying x less than y means that you are subtracting from y. Your x here is 0.04, and your y is 1.38

y-x = 1.38-0.04 = 1.34

49 would be the answer I hope it helps

Answer:

Result = 49.495

Step-by-step explanation:

17.3% of 286.1=49.4953

rounded~49.495

Hope this helps as well

Answer:

1) 10

2) 16

Step-by-step explanation:

1) 2x+15=37-2

2x+15=35

2x=35-15

2x=20

2 2

x=10

2)10x-8=9x+8

10x-9x=8+8

x=16

Hope this helps ❤

Answer:

x+8=3x

Step-by-step explanation:

4x=20

4x/4=20/4

x=5

The solution to the first equation is x=5.

x/2=8

2(x/2)=2(8)

x=16

The solution to the second equation is x=16.

x+8=3x

x+8-x=3x-x

8=2x

8/2=2x/2

x=4

The solution to the third equation is x=4.

x=x+5/2

x-x=x+5/2-x

-x=5/2

x=-5/2

The solution to the fourth equation is x=-5/2.

The equation x+8=3x has the solution to x=4.

Step-by-step explanation:

4x = 20

x = 20/4 = 5

x/2 = 8

x = 8 x 2 = 16

x + 8 = 3x

8 = 3x - x

8 = 2x

8/2 = x

4 = x

x = x + 5/2

2x = 5/2

x = 5/2 x 2

x = 5

The company should charge $3653.33 for its premium in order to have an expectation of $0 for the policy (i.e., make no profit and make no loss).

Let X be the random variable representing the death of a 70-year-old female. Then X follows a Bernoulli distribution with the probability of success p = 0.048711. If the 70-year-old female dies within one year, the insurance company has to pay the beneficiary of the policy $75,000. Otherwise, the company does not have to pay anything.

Since the company wants to make no profit and no loss, the expected value of the policy should be $0.

Therefore, the company should charge a premium such that the expected value of the policy equals the cost of the policy. The expected value of the policy is given by: E(X) × 75,000 where E(X) is the expected value of X.

Since X follows a Bernoulli distribution, the expected value of X is: p = 0.048711

Therefore, the premium charged by the company should be:0.048711 × 75,000 = 3653.33.

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The insurance company should charge $3653.33 for the premium amount to have an expectation of $0 for the policy.

The solution to the given problem is as follows:

Given: The probability that a 70-year-old female in the U.S. will die within one year is about 0.048711.

The insurance company is preparing to sell a 70-year-old female a one-year, $75,000 life insurance policy.

We need to find out how much should it charge for its premium in order to have an expectation of $0 for the policy.

Let X be the random variable that represents the death of the 70-year-old woman within one year and it follows a Bernoulli distribution with parameter P(X = 1) = 0.048711.

The insurance company is selling the life insurance policy of $75,000 which would be paid out only if the woman dies within a year.

Therefore, the company's liability is $75,000 if she dies within a year and it charges 'x' for the premium amount to have an expectation of $0 for the policy.

The expectation of the policy for the company can be calculated as follows:E(X) = 0 * P(X = 0) + 75000 * P(X = 1) = 75000 * 0.048711 = $3653.33

The insurance company should charge $3653.33 for the premium amount to have an expectation of $0 for the policy.

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The distance between the two towers is 30 meters, and the height of the second tower (Tower B) is 90 meters.

We have two towers. Let's call the first tower Tower A, and the second tower Tower B. The height of Tower A is given as 30 meters. The angle of elevation of the top of Tower A from the foot of Tower B is 60 degrees. The angle of elevation of the top of Tower B from the foot of Tower A is 30 degrees. Our goal is to find the distance between the two towers and the height of Tower B.

In triangle ABC, where A is the foot of Tower A, B is the top of Tower B, and C is the top of Tower A:

tan(30 degrees) = AB / BC

Since tan(30 degrees) = 1 / √3, we can rewrite the equation as:

1 / √3 = AB / BC

Cross-multiplying, we get:

BC = AB * √3

In triangle ABC:

tan(60 degrees) = AC / BC

Since tan(60 degrees) = √3, we can rewrite the equation as:

√3 = AC / BC

Substituting the value of BC from Step 3:

√3 = AC / (AB * √3)

Cross-multiplying, we get:

AC = AB * 3

We have two equations:

BC = AB * √3

AC = AB * 3

Dividing equation 2 by equation 1:

AC / BC = 3 / √3

Simplifying, we get:

√3 = 3 / √3

Cross-multiplying, we get:

3 = 3

Since 3 = 3 is a true statement, we can conclude that the two towers are at the same distance as their heights. Therefore, the distance between the two towers is 30 meters.

Using the value of the distance between the towers (30 meters), we can substitute this value into one of the previous equations to find the height of Tower B. Let's use equation 2:

AC = AB * 3

Substituting AB with the distance (30 meters):

AC = 30 * 3

Simplifying, we find:

AC = 90 meters

Therefore, the height of Tower B is 90 meters.

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Answer:

the answer is 5

Step-by-step explanation:

A system of equation is 1680mi3hr = p−w×600×2hr -p + w  for a jet airliner travels 1680 miles in 3hours with a tail wind.

Let p be  the speed of the jet airliner

and w  be the speed of the tail wind

It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get

1680mi3hr = p−w×600×2hr = p + w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation, we use

200mph = p - w

Add w to both sides:

p = 200mph + w

Using the value of x, we can found the value of w using system of equations.

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

On dividing by 2:

50mph = w

So the speed of the tail wind is 50mph.

Therefore, 200mph = p - 50mph

Add 50mph on both sides:

250mph = p

Hence, speed of jet airliner is 250mph.

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Answer:

7.2 pints

Step-by-step explanation:

a) 1 bowl --- 0.3 pints of soup

Since he has 24 bowls,

total amount of soup in the bowls

= 24(0.3)

= 7.2 pints

Thus, Martin put 7.2 pints of soup into the bowls.

There is a 2 in 12 chance of drawing a penny

Step-by-step explanation:

Answer: 2/12

Step-by-step explanation:

There are 12 coins all together, and 2 pennies which means there is a 2/12 chance to draw a penny. Then they replace the penny and draw another time, so by replacing the penny the probability doesn't change and there is still a 2/12 chance of drawing a penny.

Answer:

x>9

Step-by-step explanation:

2x−6>12

Step 1: Add 6 to both sides.

2x−6+6>12+6

2x>18

Step 2: Divide both sides by 2.

2x

2

>

18

2

Answer:

x belong (9;+infinity)

Step-by-step explanation:

2x-6>12

2x>18

x>18/2

x>9

x belong (9;+infinity)

When a distribution is shown as a symmetrical bell-shaped curve then the mean, median, and mode are equal i.e., option (a) is correct.

A symmetrical bell-shaped curve, also known as a normal distribution or Gaussian distribution, is characterized by its symmetry around the mean.

In this type of distribution, the mean, median, and mode all coincide at the center of the curve.

This means that the central tendency measures, such as the mean (average), median (middle value), and mode (most frequent value), are all equal.

Option (a) states that the mean, median, and mode are equal, which aligns with the properties of a symmetrical bell-shaped curve. This equality occurs because the data is evenly distributed on both sides of the mean, resulting in a balanced distribution.

Options (b) and (d) suggest that the mean is either less than or greater than the median and mode, which does not hold true for a symmetrical distribution.

In a symmetrical distribution, the mean is located at the center of the data, and the median and mode share the same value as the mean.

Option (c) mentions moderate uniformity, but a symmetrical bell-shaped curve does not specifically indicate uniformity. Uniformity refers to a distribution where all data points have equal probability, resulting in a flat line.

In contrast, a symmetrical bell-shaped curve indicates a normal distribution with the majority of data concentrated around the mean, gradually decreasing towards the tails.

Therefore, based on the given options, option (a) is the correct conclusion when the distribution is shown as a symmetrical bell-shaped curve.

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Answer:

40

Step-by-step explanation:

If angle x is a right angle, meaning 90 degrees, and the right angle is dissected into two angles with one of them being 50 degrees that leaves 40 degrees left to complete the 90 degree right angle

Answer:

each person would get 6.66 dollars and 2 dollars would remain left iver

The value of x is 1.

Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.

Given

Dimension of parallelogram P 10 and x + 3.

Dimension of parallelogram P' 20 and 8.

The value of x.

Lenght of P' = Dilation x Lenght of P

              20 = Dilation x 10

      Dilation = 2

Then

width of P' = Dilation x width of P

8 = 2 (x + 3)

4 = x + 3

x = 1

So the value of x is 1.

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Answer:

the value of x is 1

Step-by-step explanation:

The correct expression for the estimated model is: In (odds ratio) = -7.8562 +0.0304 Income + 1.2804 Lawnsize. This model was created using binary logistic regression analysis to study the characteristics that differentiate home owners who have a lawn service (code 1) and those who do not (code 0).

The additional information available for these 30 home owners includes family income (Income, in thousands of dollars) and lawn size (Lawn Size, in thousands of square feet). The estimated model shows that for every one unit increase in income,

the odds of having a lawn service increase by 0.0304, and for every one unit increase in lawn size, the odds of having a lawn service increase by 1.2804. This information can be useful for the marketing manager to target potential customers based on their family income and lawn size.
The correct expression for the estimated model in this case is:

ln(odds ratio) = -7.8562 + 0.0304 Income + 1.2804 Lawn Size

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Using equations, we can find that he purchased 6 footballs.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example.

Here in the question,

Let the number of footballs purchased be f.

Let the number of basketballs purchased be b.

Cost of each football = $60.

Cost of each basketball = $30.

Total amount spent = $450

Now,

60f + 30b = 450

Given,

2b = f

⇒ b = f/2

Putting the value of b in the equation,

60f + 30(/2f) = 450

⇒ 60f + 15f = 450

⇒ 75f = 450

⇒ f = 6

Therefore, he purchased 6 footballs.

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The volume of the solid is approximately 807.08 cubic units.

To determine the volume of the solid, we can use the method of cylindrical shells.

Imagine taking a slice of the solid parallel to the base, with the cross-sectional area being a square of side length x (where x is a function of the height). The volume of this slice is the product of the square area and the height. The height of the slice is equal to the difference in the radii of two consecutive circular cross sections.

The radius of the larger circular cross-section can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the radius) is equal to the sum of the squares of the other two sides (the height and half the side length of the square). Thus, we have:

r² = x² + (15-x)²

Solving for x, we get:

x = 15 * √(1 - (r/15)²)

The volume of the slice is then given by:

V = x² * (15 - x)

To find the total volume of the solid, we integrate this expression with respect to r from 0 to 15. The result is approximately 807.08 cubic units.

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Answer:

i cannot understand

Step-by-step explanation:

The standard size for legal paper in North America and Canada is 8.5 inches by 14 inches.

The standard size for legal paper in North America and Canada is 8.5 inches by 14 inches. On the other hand, A4 paper, which measures 8.5 inches by 11 inches, is the standard legal paper size in Europe and the majority of other nations. Moreover, the legal-size bond paper is 8.5 inches x 14 inches.

Here are the legal size paper dimensions in different units; let's have a look.

Legal paper size in inches: 8.5 inches x 14 inches

Legal size paper in cm: 21.6cm x 35.6 cm

Legal paper size in mm: 216mm x 356mm

A4 Paper which is considered a legal paper size in Europe, etc., has the following dimensions in different units:

A4 paper dimensions in inches: 8.5 inches x 11 inches

A4 paper dimensions in cm: 216 x 279mm

A4 paper dimensions in mm: 21.6 x 27.9 cm

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Answer:

\(\frac{48}{13}\approx 3.7\)

Step-by-step explanation:

Two triangles are similar by AAA ( Angles B and B' are right angles, the two angles in C are congruent because opposite by the vertex, and the third by difference). Corresponding sides are in proportion. In particular \(x:6=8:13 \leftrightarrow 13x=6\cdot8 \rightarrow x = \frac{48}{13} \approx 3.7\)

The only possible ratio is 4 : 11.

Therefore, option A is correct.

Given that a farmer has 75 hens, in which some hens are white, and the rest are red, we need to determine the possible ratio of white hens to red hens on the farm,

To determine the possible ratio of white hens to red hens on the farm, we need to examine the options provided and check if any of them are possible given the information provided.

Let's consider each option:

(A) 4:11

If the ratio of white hens to red hens is 4:11, it means that for every 4 white hens, there are 11 red hens.

This ratio add up to a total of 15 hens, which is a multiple of 75.

so, option (A) is a possible ratio.

(B) 5:15

Similarly, if the ratio of white hens to red hens is 5:15, it means that for every 5 white hens, there are 15 red hens.

This ratio add up to a total of 20 hens, which is not a multiple of 75.

so, option (B) is not possible.

(C) 3:1

If the ratio of white hens to red hens is 3:1, it means that for every 3 white hens, there is 1 red hen.

If we have 3 white hens and 1 red hen, the total number of hens would be 4.

Since 4 is not a multiple of 75. so, this ratio is not possible.

(D) 3:5

If the ratio of white hens to red hens is 3:5, it means that for every 3 white hens, there are 5 red hens.

If we have 3 white hens and 5 red hens, the total number of hens would be 8.

Since 8 is not a multiple of 75. so, this ratio is not possible.

(E) 3:4

If the ratio of white hens to red hens is 3:4, it means that for every 3 white hens, there are 4 red hens.

If we have 3 white hens and 4 red hens, the total number of hens would be 7.

Since 7 is not a multiple of 75. so, this ratio is not possible.

Hence the only possible ratio is 4 : 11.

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