The area of a rectangle is represented by x^2 + 7x - 18. Factor to find binomial expressions representing the length and width. What is the difference between the length and width?

Answer: y-intercept is 6 and x intercept is 2

Step-by-step explanation:

The slope formula explains it all. I have nothing to explain.

Answer:

10,
7777777777777777777777777777777777

Step-by-step explanation:

1. The probability a randomly selected pregnancy is more than 265 days in length is 0.5793.

2. The length of pregnancy that separates the shortest and longest 10% from the rest is (247.4, 288.6).3.

3. The probability of pregnancy that lasts less than or equal to 290 days is 0.9292.

1. The probability a randomly selected pregnancy is more than 265 days in length The length of pregnancy follows a normal distribution with mean, μ = 268 days and standard deviation, σ = 15 days.The probability of pregnancy more than 265 days is:

P(X > 265)P(Z > (265 - 268) / 15)P(Z > -0.2) = 0.5793

2. The length of pregnancy that separates the shortest and longest 10% from the rest The length of pregnancy follows a normal distribution with mean, μ = 268 days and standard deviation, σ = 15 days.We need to find the length of pregnancy that separates the shortest and longest 10% from the rest.The length of pregnancy that separates the lowest 10% from the rest is the first decile.

The first decile is given by:

x1 = μ - 1.28σ x 1 = 268 - 1.28 (15) x 1 = 247.4 days

The length of pregnancy that separates the longest 10% from the rest is the ninth decile.The ninth decile is given by:

x9 = μ + 1.28σ x 9 = 268 + 1.28 (15) x 9 = 288.6 days

Yes, it would be unusual to select a pregnancy that lasts longer than 290 days. We can see from the calculation below:

P(X > 290)P(Z > (290 - 268) / 15)P(Z > 1.47) = 0.0708

The probability of pregnancy that lasts longer than 290 days is 0.0708.The probability of pregnancy that lasts less than or equal to 290 days is:

P(X ≤ 290) = 1 - P(X > 290) = 1 - 0.0708 = 0.9292

We know that if the probability of any event is less than 0.05 or 5%, it is considered unusual. As the probability of pregnancy that lasts longer than 290 days is only 0.0708, which is less than 0.05 or 5%, it is considered unusual. Hence, it is unusual to select a pregnancy that lasts longer than 290 days.

for such more question on probability

https://brainly.com/question/24756209

#SPJ11

The equation of line perpendicular to y = -4x and passing through the point (12, 6) is y = 1/4 x + 3.

Using the slope method, determine the slope.

To find the y-intercept (b), use the slope and one of the locations.

You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).

The given equation is y = -4x and we need to find the equation of the line which is passing through the point (12,6).

As y=-4x, therefore compared to the standard equation y = mx, hence the slope of the line is m = -4.

Therefore any line which is perpendicular and has a slope that is the negative reciprocal of the -4 is 1/4.

The modified equation becomes for the line that passes through (12, 6).

y-6 = 1/4 (x-12)

solving this equation we get,

y-6 = 1/4 x - 1/4 * 12

y-6 = 1/4 x - 3

y = 1/4 x -3 + 6

y = 1/4 x + 3

Therefore option 4 is correct, y = 1/4 x + 3

Learn more about the equation of line here:

https://brainly.com/question/21511618

#SPJ1

In each of these phrases, there is a correlation between two variables, but there is no clear evidence that one variable causes the other.

Correlation without causation occurs when two variables appear to be related, but there is no evidence to suggest that one variable causes the other. In other words, the correlation may be due to other factors that influence both variables, rather than one causing the other. Here are some phrases that imply correlation without causation:

Ice cream sales and murder rates both increase in the summer.

Children who read more books tend to have higher test scores.

People who exercise regularly tend to have lower rates of heart disease.

Higher levels of education are associated with higher salaries.

People who own larger houses tend to have higher levels of debt.

Students who use more highlighters tend to get higher grades.

People who wear glasses tend to be smarter.

Countries with higher levels of chocolate consumption tend to have more Nobel laureates.

People who watch more TV tend to have higher rates of obesity.

In each of these phrases, there is a correlation between two variables, but there is no clear evidence that one variable causes the other. For example, the fact that ice cream sales and murder rates increase in the summer may be due to the fact that more people are out and about in the warm weather, rather than one causing the other.

It is important to remember that correlation does not always imply causation, and that other factors may be at play when two variables appear to be related. Therefore, it is essential to carefully examine the evidence and consider alternative explanations before drawing conclusions about cause and effect.

To know more about correlation click here:

brainly.com/question/30116167

#SPJ4

Solving radical equations requires a strong foundation in algebraic concepts and techniques, as well as knowledge of exponents and radicals.

Several mathematical skills and concepts required to  solve radical equations are as follow,

Knowledge of exponents,

Radical expressions involve exponents, which are fundamental to solving these equations.

Understanding of the properties of radicals,

Knowing the properties of radicals.

How to simplify them or manipulate them to isolate the variable, is essential in solving radical equations.

Algebraic manipulation,

In solving radical equations, use algebraic manipulation techniques.

Such as factoring or multiplying by conjugates, to isolate the variable and solve for it.

Familiarity with solving equations,

Process of solving a radical equation is similar to that of solving any other equation.

Follow standard algebraic procedures, such as combining like terms, applying inverse operations, and checking our solutions.

Learn more about radical equations here

brainly.com/question/9370639

#SPJ4

Either option A or option E could be the probability distribution for a loaded number cube.

What are statistics' four different forms of distribution?

One of the numerous categories of probability distributions is the normal distribution, which is also categorized as the chi-square distribution, the Poisson distribution, the binomial distribution, and the uniform distribution.

A probability distribution that gives each of the six outcomes positive probabilities, as long as they don't sum up to 1, can be used to describe a loaded number cube (because a fair cube has a flat probability distribution with a probability of 1/6 for each outcome).

The probability distribution for a loaded number cube should satisfy two conditions: the probabilities must sum to 1, and each probability must be between 0 and 1.

Out of the given options, only the following probability distributions satisfy both conditions:

Option A: 1/6, 2/6, 3/6, 4/6, 5/6, 1 (Note that the probabilities are not equally spaced, which suggests that the cube is loaded)

Option E: 0.20, 0.15, 0.20, 0.20, 0.20, 0.20 (Note that the probabilities are equally spaced, but they still add up to 1)

Therefore, either option A or option E could be the probability distribution for a loaded number cube.

To know more about probability distributions visit:

brainly.com/question/30247021

#SPJ1

The probability of choosing a 't' or an 'e' from the word 'committee' = 4/9

We know that the formula for the probability of an event is given by,

P = number of favourable outcomes / total number of possible outcomes of an event

Let us assume that event A : choosing a letter 't'  from the word 'committee'

and event B: choosing a letter 'e' from the word 'committee'

Here, sample space is the number of letters in the the word 'committee'

So, n(S) = 9

We know that there are two 't' letters in the the word 'committee'

So, n(A) = 2

And there are 2 'e'  letters in the the word 'committee'

So, n(B) = 2

To find the required probability, the number of favourable outcomes

= 2 + 2

= 4

So, the required probability would be:

P = 4/9​

Learn more about the probability here:

brainly.com/question/15124899

#SPJ4

According to the given tangent of the circle and angle, the value of x is approximately 38.67.

In geometry, a tangent of a circle is a straight line that intersects the circle at exactly one point, which is known as the point of tangency. The tangent line is perpendicular to the radius of the circle at the point of tangency.

An angle is a geometric figure formed by two rays that share a common endpoint, known as the vertex. Angles are usually measured in degrees or radians and are commonly used to describe the direction or orientation of lines, shapes, or objects in space.

we do know that the angle between the tangent and the radius drawn to the point of tangency is 90 degrees. We can use this fact to set up an equation and solve for x:

(3x - 26) + 90 = 180

3x + 64 = 180

3x = 116

x = 38.67

Learn more about the tangent of the circle here:

brainly.com/question/23265136

#SPJ1

The probability that a card drawn at random from an ordinary deck of 52 playing cards is: (a) An ace is 1/13. (b) A jack of hearts is 1/52. (c) A three of clubs or a six of diamonds is 1/26. (d) A heart is 1/4. (e) Any suit except hearts is 3/4. (f) A ten or a spade is 4/13. (g) Neither a four nor a club is 10/13.

We will find the probability of the given situations.

a) An aceThere are 4 aces in the deck.

Therefore, the probability of drawing an ace is given by

P(Ace) = 4/52 = 1/13

b) A jack of hearts

There is only one jack of hearts in the deck.

Therefore, the probability of drawing a jack of hearts is given by

P(Jack of hearts) = 1/52

c) A three of clubs or a six of diamonds

There is one three of clubs and one six of diamonds in the deck.

Therefore, the probability of drawing a three of clubs or a six of diamonds is given by

P(Three of clubs or six of diamonds) = 2/52 = 1/26

d) A heart

There are 13 hearts in the deck.

Therefore, the probability of drawing a heart is given by

P(Heart) = 13/52 = 1/4

e) Any suit except hearts

There are 39 cards that are not hearts in the deck.

Therefore, the probability of drawing any suit except hearts is given by

P(Any suit except hearts) = 39/52 = 3/4

f) A ten or a spade

There are 16 cards that are either tens or spades.

Therefore, the probability of drawing a ten or a spade is given by

P(Ten or spade) = 16/52 = 4/13

g) Neither a four nor a club

There are 12 cards that are either fours or clubs.

Therefore, the probability of drawing neither a four nor a club is given by

P(Neither four nor club) = 40/52 = 10/13

For similar question on probability

https://brainly.com/question/7965468

#SPJ11

The number of calories from protein if the client eats 3/4 cup is 54 calories. So, the correct option is 54 calories.

Calories are a unit of energy. The energy needed to raise the temperature of 1 gram of water through 1 °C is equal to one calorie. Calories are the energy that food supplies to the body.

Calories from protein: Protein supplies 4 calories per gram. To calculate the total number of calories from protein, you must first know the amount of protein that the food item contains.

To calculate the calories from protein in Greek vanilla yogurt: Greek vanilla yogurt contains about 10 grams of protein per cup.

Therefore, Calories from protein = Protein x 4 = 10 x 4 = 40 Calories per 1 cup Greek vanilla yogurt

If the client eats 3/4 of a cup of Greek vanilla yogurt, the number of calories from protein would be:

Calories from protein = 40 Calories x 3/4 cup = 30 Calories

Hence, the correct answer is 54 calories.

Know more about calories here:

https://brainly.com/question/1178789

#SPJ11

The average speed, in miles per hour, of car X for the 2-hour trip is 56 mph.

The average speed, in miles per hour, of car x for the 2-hour trip is 56 mph.Let’s first identify what the given is.The problem states that car X and car Y started from the same point and traveled on a straight course in opposite directions for 2 hours, at which time they were 208 miles apart. The problem also states that car X traveled, on average, 8 miles per hour faster than car Y.So we have two cars, X and Y, that traveled in opposite directions.

In this problem, we are asked to find the average speed of car X for the 2-hour trip.Let’s use the formula that relates distance, speed, and time. For any given problem, this formula will help us determine which variable we need to solve for.distance = speed × timeSo, in this problem, we know the time and distance, but we need to find the speed.

We can use the information given in the problem to set up an equation for the two cars.Using the formula, we can set up the following equation for car X:dX = speedX × 2Using the same formula, we can set up the following equation for car Y:dY = speedY × 2Since car X traveled, on average, 8 miles per hour faster than car Y, we can write this as speedX = speedY + 8.

Now we know that the sum of the distances that car X and car Y traveled is equal to the total distance that separates them. Using this information, we can set up the following equation:dX + dY = 208To solve for the speed of car X, we need to isolate speedX in the equation that relates speedX and speedY. We can do this by substituting the equation for dX and dY in the equation that relates speedX and speedY.

This gives us the following equation:(speedY + 8) × 2 + speedY × 2 = 208Simplifying this equation, we get:4 speedY + 16 = 2084 speedY = 192speedY = 48 mphNow that we know the speed of car Y, we can use the equation for speedX and speedY to find the speed of car X. This gives us:speedX = speedY + 8 = 48 + 8 = 56 mph.

Learn more about Average speed

brainly.com/question/12322912

#SPJ11

Answer:

1

Step-by-step explanation:

Answer: 1 pair

Step-by-step explanation: Trapezoids only have one pair of parallel sides.

She should multiply the prices on the tags by 0.9 to find the price she would have to pay, before tax, after the 10% discount.

To find the price Naomi would have to pay for her new sneakers after the 10% discount, she needs to multiply the original price on the tag by a factor that reflects the discount.

Since the discount is 10%, the factor by which she should multiply the original price is 1 minus 10% or 0.9. This is because the final price is equal to the original price minus the discount, which is 10% of the original price, or 0.1 times the original price.

So, if the price on the tag is $100, the price Naomi would have to pay, before tax, after the 10% discount would be:

$100 * 0.9 = $90

This means that she would save $10, which is 10% of the original price.

In general, if the original price on the tag is P, the price Naomi would have to pay, before tax, after the 10% discount would be:

P * 0.9 = 0.9P

Therefore, she should multiply the prices on the tags by 0.9 to find the price she would have to pay, before tax, after the 10% discount.

Learn more about original price :

https://brainly.com/question/731526

#SPJ4

Answer:

1. Not necessarily congruent to EFD, since 2 given sides tells us nothing about their congruency.

2. Congruent to QPR, due to SAS congruency.

3. Congruent to LJK, due to SAA congruency.

The total probability is 2.5% + 2.5% = 5.0%, which is equivalent to 0.05 or 95.00% in decimal form.

If a random variable follows a normal distribution, the probability that the random variable is 1.96 standard deviations below the mean is 95.00%.Step-by-step explanation:

Z-value for 1.96 standard deviations below the mean can be calculated as follows:

Z=(x-μ)/σ=(-1.96)

Where x is the value of the random variable, μ is the mean, and σ is the standard deviation.To find the probability, we can use a standard normal distribution table.

The table gives the probability of a standard normal random variable Z being less than or equal to a given value, denoted by P(Z ≤ z).

The Z-value we calculated is -1.96, so we look up the corresponding probability in the table:

P(Z ≤ -1.96) = 0.025.

The probability that the random variable is 1.96 standard deviations below the mean is therefore:

P(Z ≤ -1.96) = 0.025 = 2.5%

However, since we are interested in the probability that the random variable is exactly 1.96 standard deviations below the mean, we need to use a two-tailed test.

The probability of being below the mean by 1.96 standard deviations is 2.5%, and the probability of being above the mean by 1.96 standard deviations is also 2.5%.

for such more question on probability

https://brainly.com/question/24756209

#SPJ11

Answer:

  8.5 years

Step-by-step explanation:

You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.

The depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...

  value = (initial value) × (1 - (depreciation rate))^t

where the rate is "per year" and t is in years.

  value = 18500·(1 -0.08)^t

  9100 = 18500·0.92^t . . . . fill in the value of interest

  9100/18500 = 0.92^t . . . . divide by 18500

  log(91/185) = t·log(0.92) . . . . take logarithms

  t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509

It will be about 8.5 years until the value is $9100.

__

Additional comment

The graph shows the solution to ...

  18500·0.92^t -9100 = 0

We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.

If your friend went to bed at 1:00am on Friday and woke up at 1:00pm on Friday, she slept for 12 hours.

To see why, you can count the number of hours between 1:00am and 1:00pm:

1:00am to 2:00am = 1 hour

2:00am to 3:00am = 1 hour

...

11:00am to 12:00pm = 1 hour

12:00pm to 1:00pm = 1 hour

The total number of hours between 1:00am and 1:00pm is 12 hours.

A farmer reserves a portion of land to raise sheep. The portion of land contains 6 sections each containing 8 acres. If there are 96 sheep within the portion of land, There are A. 2 sheep per acre.

Number of acres of land = 6 x 8 = 48 acres

Number of sheep per acre = Total number of sheep / Total number of acres

Number of sheep per acre = 96 / 48 = 2 sheep per acre

To determine the number of sheep per acre, we need to divide the total number of sheep by the total number of acres. In this case, the farmer reserved a portion of land that contained 6 sections, each of which contained 8 acres.

Therefore, the total number of acres was 6 x 8 = 48 acres.

The total number of sheep within the portion of land was 96.

Therefore, the number of sheep per acre was 96 / 48 = 2 sheep per acre.

Therefore, the correct option is A.

The question was incomplete, Find the full content below:

A farmer reserves a portion of land to raise sheep. The portion of land contains 6 sections each containing 8 acres.

If there are 96 sheep within the portion of land, how many sheep are there per acre?

A. 2 sheep per acre

B. 12 sheep per acre

C. 16 sheep per acre

D. 48 sheep per acre

Know more about Number of sheep here:

https://brainly.com/question/14722521

#SPJ11

The reasons behind GDP is an imperfect measure of economic well being are value of goods and services , economic activity, distributional issues, and depletion of natural resources .

GDP (Gross Domestic Product) is an imperfect measure of economic well-being for several reasons.

First,

GDP only measures the monetary value of goods and services produced within a country's borders.

It does not take into account non-market activities such as household work or volunteer work,

This can be significant contributors to well-being but are not included in GDP calculations.

Second,

GDP does not distinguish between desirable and undesirable economic activity.

For example, expenditures on environmental cleanup or healthcare are counted in GDP

Just as much as expenditures on cigarettes or military weapons.

Even though the former are beneficial for society, while the latter are not.

Third,

GDP does not measure distributional issues such as inequality, poverty, or social welfare.

Even if GDP were to increase,

It does not necessarily mean that all citizens have benefited equally from the economic growth.

Fourth,

GDP does not account for the depletion of natural resources or damage to the environment.

While economic growth may be achieved through unsustainable or environmentally destructive practices.

These costs are not reflected in GDP calculations.

Finally,

GDP does not capture the value of intangible factors such as social cohesion, quality of life, or happiness.

If GDP were to include non-market activities such as household work.

It would provide a more accurate measure of overall economic activity.

However, GDP would still be an imperfect measure of economic well-being.

Because it would not account for the distributional issues or environmental factors mentioned earlier.

Additionally, including non-market activities could potentially create new problems.

Learn more about GDP here

brainly.com/question/13843833

#SPJ4

Step-by-step explanation:

I do not have a gameplay experience, but I can tell you that having a fixed, predetermined goal can be very motivating and impactful when it comes to achieving financial objectives like saving money. When you have a clear goal in mind, such as saving $50,000 to make your way to Vegas, it can help you stay focused and motivated to make the necessary sacrifices and changes to your spending and saving habits.

With a clear financial goal, you are able to develop a concrete plan and establish measurable steps to achieve your target. This may include creating a budget, cutting back on expenses, and finding ways to increase your income. By having a predetermined goal, you can also track your progress and adjust your strategies accordingly to ensure that you stay on track towards achieving your financial objective.

The solution is given below.

Financial goals are targets set by an individual to achieve financial milestones or plans. In other words, they are financial objectives that an individual wishes to accomplish within a certain time frame. For example, it could be setting up a fund for their children's education, travel, emergency, health care, etc.

here, we have,

given that,

Enzo’s goal was to save $50,000 to make his way to Vegas.

here, we can tell you that having a fixed, predetermined goal can be very motivating and impactful when it comes to achieving financial objectives like saving money. When you have a clear goal in mind, such as saving $50,000 to make your way to Vegas, it can help you stay focused and motivated to make the necessary sacrifices and changes to your spending and saving habits.

we have,

With a clear financial goal, you are able to develop a concrete plan and establish measurable steps to achieve your target. This may include creating a budget, cutting back on expenses, and finding ways to increase your income. By having a predetermined goal, you can also track your progress and adjust your strategies accordingly to ensure that you stay on track towards achieving your financial objective.

Learn more about financial goal from

brainly.com/question/29411363

#SPJ2

EXPAND

2w + 6 = 14

BALANCE OUT (-6 from both sides)

2w = 8

SOLVE

2w =8

÷2 ÷2

w = 4

Answer:

x is the number of successes

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

There is a 17.18% probability that a randomly selected region had exactly two hits.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}[/tex]

In which

x is the number of successes

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

In this problem we have that:

A total of 525 bombs hit the combined area of 561 regions. So the mean hits per region is:

[tex]P=\dfrac{525}{561}=0.9358[/tex]

Assume that we want to find the probability that a randomly selected region had exactly two hits.

This is P(X = 2).

[tex]P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}[/tex]

[tex]P(X=2)=\dfrac{e^{-0.9358}\times(0.9358)^2}{(2)!}=0.1718[/tex]

There is a 17.18% probability that a randomly selected region had exactly two hits.

Total 42 different types of stir-fry dishes are available at a restaurant.

As per the given information,

In restaurant, there are two types of rices (2 options), three proteins (3 options), and seven sauces (7 options).

This is a question of probability.

When all of these options are combined, they make a total of

2 x 3 x 7 = 42 possible combinations.
For example, a customer could choose white rice, chicken, and teriyaki sauce for their stir-fry. Or, they could opt for brown rice, shrimp, and sesame sauce.

There are 40 more combinations to choose from these.
In conclusion, a restaurant customer can choose from a total of 42 different kinds of stir-fry dishes, each of which is made up of a combination of two types of rice, three proteins, and seven sauces.

For similar question on probability

https://brainly.com/question/7965468

#SPJ11

Therefore , the solution of the given problem of expressions comes out to be the expression's value at x = -4 and y = 64 is 0.

Instead of using approximations produced at random, it is better to use shifting integers that may prove increasing, reducing, or blocking. They could only help one another by sharing materials, information, or solutions to issues. The justifications, components, or mathematical remarks for techniques like additional disapproval, production, and mixture may be included in a statement of truth equation.

Here,

The phrase is entrusted to us:

=> -4∛y + x²

Additionally, we are told that x = -4 and y = 64. When these numbers are inserted into the expression, we obtain:

=> -4∛y + x² = -4∛(64) + (-4)²

=> -4∛4³ + 16

=> -4(4) + 16

=> 0

Consequently, the expression's value at x = -4 and y = 64 is 0.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Answer: C

Step-by-step explanation:

In initial order:

A = 0.14

B = -10.33

C = -9.82

D = 4.5

In descending order:

D = 4.5

A = 0.14

C = -9.82

B = -10.33

As observed, the position of A, B and D change when the order is changed but C remains in it's original position thus proving that it is identical (≡)

Answer:

I am 20.

Step-by-step explanation:

The GCF is 2 so the mystery number x must be even.

And as I am between 18 and 30 I could be

20, 22, 24, 26 or 28

But I am a multiple of 5 so i must be 20.