Factor 80+60. Write your answer in the form a(b+c) where a is the GCF of 80 and 60.

The price of gasoline and oil will be equal in price after 4 years when the price of gasoline is $2.27 per gallon and decreases at the rate of $0.03 every two months.

To find out when the price of gasoline and oil will be equal, we have to set the two prices equal to each other and solve for time. The price of gasoline decreases at the rate of $0.03 every two months and the price of oil increases at a rate of $0.05 every six months.

We can start with the initial prices and solve for the time when they are equal:

$2.27 - 0.03t = 0.45 + 0.05t

where t represents the time in years.

Solving for t, we get:

$2.27 - 0.03t = 0.45 + 0.05t

$1.82 = 0.08t

t = 22.5

Since t is in months, we have to divide by 12 to convert it to years:

t = 22.5 / 12 = 1.875

So the price of gasoline and oil will be equal in price after approximately 4 years.

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The number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

To calculate the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels, we can use the concept of stars and bars.

First, we need to ensure that we have at least one of each type of bagel. So, we take one bagel of each type, which leaves us with 14 bagels to buy.

Now, we can use stars and bars to distribute the remaining 14 bagels among the 6 types of bagels. We represent the 14 bagels as stars and the 5 possible locations between the types of bagels as bars.

Using this method, we need to distribute 14 stars among 5 bars, which can be done in

(14+5-1) choose (5-1) = 18 choose 4 = 3060 ways.

Therefore, the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.

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The number of choices for all the possible passwords are 43,056,000

Given, we have to make a password which includes 4 characters and 4 even digits. And none of the characters or digits can be used more than once. So, For the first character we have 26 choices as we can use any character from the alphabet. For the 2nd character we get 25 choices as we cant choose the first character already twice. Similarly, for 3rd character we get 24 choices and for 4th character we get 23 choices.

Now for the digits, we can only use even digits 0,2,4,6,8 with no repetition allowed. Therefore, for first digit we can choose any digit so we get 5 choices. For the 2nd digit we get 4 choices. For the 3rd digit we get 3 choices. For the 4th digit we get 2 choices.

Noe, to find all the possible combinations , we just need to multiply all the choices :

⇒ 26 x 25 x 24 x 23 x 5 x 4 x 3 x 2

⇒ 43,056,000

Therefore, the total number of all the possible combination of passwords according to the given condition is 43,056,000.

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Answer: 1/3

Step-by-step explanation: The ratio of multiplication problems to total problems is 12:36, which can be simplified to 1:3.

Answer:

A

Step-by-step explanation:

Hi there.
We know this math exam has 12 multiplication and 24 division problems, making the overall exam questions 36 problems. (12+24=36)

The ratio is the fraction equivalent comparison between two variables. In this case, it's multiplication problems over total problems.

We know multiplication problems as 12, and we calculated the total, which is 36.

The answer would be 12/36; but it's divisible by 12 and can be further simplified to 1/3.

The perimeter of the rectangle is 2ab² ( 5ab² + 3)

The area of the rectangle is 15a³b^6

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let l=5a²b^4  ,   w= 3ab²

Perimeter = 2(l+w)

                 = 2(5a²b^4 + 3ab² )

                 =2 [ ab² ( 5ab² + 3)]

                 = 2ab² ( 5ab² + 3)

Area = l*w

        =  5a²b^4 *3ab²

        = 15a³b^6

The perimeter of the rectangle is 2ab² ( 5ab² + 3)

The area of the rectangle is 15a³b^6

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The value of x and y is -2 and 5

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Using elimination method

y =−4x−3 equation 1

y=−2x + 1 equation 2

subtract equation 1 from 2

0 = 2x +4

collect like terms

2x = -4

x= -4/2

x = -2

substitute -2 for x in equation 1

y = -4(-2)-3

y = 8 -3

y = 5

therefore the value of x and y are -2 and 5 respectively.

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Answer:

2

Step-by-step explanation:

the prime factorization of the number 90 is

2, 3, 3, 5

Hugh poured 100 kilograms of water into 10 kg of salt. He made 110 kilograms of 9.09 % salt solution.

To find the mass of the solution add the mass of salt and the mass of the solution. To find the concentration of the solution divide the salt mass by the total mass of the solution and multiply by 100.

Here we have  

Hugh poured 100 kilograms of water into 10 kg of salt.

After adding 100 kilograms of water to 10 kg of salt.  

The total mass of the solution = 100 + 10 = 110 kg

The concentration of salt

= [ Mass of salt/ Mass of solution] × 100

= [ 10/110] × 100 = 9.09%      

Therefore,

Hugh poured 100 kilograms of water into 10 kg of salt. He made 110 kilograms of 9.09 % salt solution.  

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The angle to the nearest tenth of a degree, we round the result to 50.7 degrees.

In trigonometry, cosine is a function that takes an angle as an input and produces a numeric value between -1 and 1 as an output. The cosine of an angle A is represented by cos A. In this problem, cos A is given to be 0.8945. To find the angle, we can use the inverse cosine function (or arccosine) which returns the angle in radians. To obtain the angle in degrees, we can multiply by 180/π (which is equal to 57.2958). The angle A is then equal to 50.6 degrees.  To find the angle to the nearest tenth of a degree, we round the result to 50.7 degrees.

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Answer: (2) $17,200

Step-by-step explanation:

We know the commission = 4,300. So we need to find a number (Let's x) times 25% (equal to 0.25) equal to 4,300

Put all that into an equation: x times 0.25 = 0.25x

0.25x=4,300

Now, all we need to do is solve for x.

Divide both sides by 0.25 to get 17200

The probability that when a theft occurs, at least one of the 5 systems will detect it is approximately 0.9997.

How likely something is to occur is known as its probability. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

We can solve this problem using the complement rule. The probability that none of the 5 systems detect the theft is given by:

(1 - 0.82)^5 = 0.00033124

So the probability that at least one system detects the theft is:

1 - 0.00033124 = 0.99966876

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The restocking fee for an item with an original price of $180 and a restocking fee of 6% is $10.80.

A restocking fee is a fee that is charged when a customer returns an item, usually to cover the costs associated with processing the return and getting the item back in a sellable condition. The fee is typically calculated as a percentage of the original price of the item.

In this problem, we are given that the restocking fee is 6% and the original price of the item is $180. To find the restocking fee, we can use the formula:

Restocking fee = (Percentage fee / 100) x Original price

In this case, the percentage fee is 6% or 0.06 (since 6% is equivalent to 6/100). The original price is $180. Substituting these values into the formula gives:

Restocking fee = (0.06) x $180

Restocking fee = $10.80

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To solve this system of linear equations, we need to find the values of x and y that make both equations true at the same time. One method to solve this is to use elimination or substitution.

First, let's rearrange the first equation:

y = 2x

Next, we can substitute y = 2x into the second equation:

-7x + 3y = 2

-7x + 3(2x) = 2

-7x + 6x = 2

-x = -2

So, x = 2.

Finally, we can use the first equation to find y:

y = 2x

y = 2 * 2

y = 4

So, the solution to the system of equations is (x, y) = (2, 4).

The value of x in the polygon is 30

from the question, we have the following parameters that can be used in our computation:

Exterior angles = x, 2x, 4x, 5x, 8x, and 10x.

The sum of exterior angles of a polygon is 360

Using the above as a guide, we have the following:

x + 2x + 4x + 5x + 8x + 10x = 360

Evaluate the like terms

30x = 360

So, we have

x = 12

Hence, the value of x is 12

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Answer:

roughly 88 but 87.9645943005...

Step-by-step explanation:

First, the formula for the circumference of a circle is 2pi(r), so plugging in 14 yards, you get 28pi roughly 88 but for an actual answer 87.9645943005

The probability that Omar randomly selects a sugar cookie from the bag eats it, then randomly selects an oatmeal cookie is 0.06.

Omar buys a bag of cookies that contains,

5 chocolate chip cookies,9 peanut butter cookies, 6 sugar cookies, and 7 oatmeal cookies,

We have to find the probability that Omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie

Total number of cookies in bag = 27

the probability that Omar randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie

[tex]=\frac{6}{27}.\frac{7}{26}\\\\=0.0598 =0.06[/tex]

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Using, the mathematical inequalities, we can conclude that the total number of occupied rooms on Friday is 10.

Number of rooms in the inn = 10

It is given that One-half of the rooms are reserved for Friday which means 5 rooms were initially reserved on Friday.

Now, 12 more rooms are reserved for Friday.

So, the Initial reservation for Friday = 5

Final reservations for Friday = 5 + 12 = 17

Now, Final reservations for Friday(17) > Total number of rooms in the inn(10).

As the reservation exceeds the capacity of the hotel, 7 reservations will be cancelled and all 10 rooms will be occupied on Friday.

Hence, the total number of occupied rooms on Friday is 10.

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Answer: $3,500

Step-by-step explanation: 15000-5000=10000

0.7*10,000=700.

700*5=$3,500

The critical value if the hypothesis is to be tested at the 0.05 level of significance is 1.96 . So, option C is the correct answer.

To test the hypothesis that Woof Chow has a market share of 25%, we need to conduct a hypothesis test with the null hypothesis that the true proportion of dog owners who use Woof Chow is 0.25, and the alternative hypothesis that the true proportion is not 0.25.

Since the sample size n is large (n = 100), we can use the normal distribution to perform this test. The critical value for a two-tailed test at the 0.05 level of significance is given by:

z_critical = ±1.96

This value corresponds to the 2.5th and 97.5th percentiles of the standard normal distribution. The critical value is ±1.96 because we want to be 95% confident that the true proportion of dog owners who use Woof Chow is within a certain range, and the 95% confidence interval corresponds to two standard deviations from the mean.

To determine whether or not to reject the null hypothesis, we would calculate a test statistic (z-score) based on the sample proportion, and compare it to the critical value. If the test statistic falls outside the critical value, we would reject the null hypothesis and conclude that Woof Chow does not have a market share of 25%.

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Answer:

Step-by-step explanation:

You want the lateral area, base area, and total area of a square pyramid with a base 3 ft on a side and a slant height of 4 ft.

The area of one triangle is ...

  A = 1/2bh

  A = 1/2(3 ft)(4 ft) = 6 ft²

Then the area of the four triangular faces is ...

  area of triangles = 4×6 ft² = 24 ft²

The area of the square base is ...

  A = s²

  A = (3 ft)² = 9 ft²

The area of the square base is 9 ft².

The total surface area is the sum of the lateral area and the base area:

  total surface area = area of triangles + area of square = 24 ft² +9 ft²

  total surface area = 33 ft²

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a) The probability that at most one is a six is 5/6.

b) The probability that at most one is a six is 2/3.

In the question two dice are rolled in a random experiment and we have to find what is the probability that at most one is a six and if the two faces are different, what is the probability that at most one is a six.

a) The probability that at most one is a six is 5/6. There are only 6 possible outcomes when rolling two dice, and 5 of those outcomes involve at most one six: (1,2), (1,3), (1,4), (1,5), (2,5).

b) The probability that at most one is a six is 2/3. If the two faces are different, there are only 3 possible outcomes: (1,2), (2,3), (3,4). 2 of those outcomes involve at most one six: (1,2), (2,3). Thus, the probability is 2/3.

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Answer:

Step-by-step explanation:

You are currently converting speed units from foot per minute to miles per hour 1 ft/min = 0.011363636 mph foot per minute ft

so 0.011363636 times 2000 equals 27.727272

so your answer is [B]

Students raised $225 in the first week and $90 in the second week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a student club has a goal to raise $750 to buy new books for a library.

In the first week, the club raised 30% of its goal.

Now, 30% of 750

= 30/100 ×750

= 3×75

= $225

In the second week, the club raised 12% of its goal.

Now, 12% of 750

= 12/100 ×750

= 0.12×750

= $90

Hence, students raised $225 in the first week and $90 in the second week.

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The force is 80,000 Dynes.

We know that when we talk about the joint variation then we have a lot of variables that are being altered at the same time and this is what we are going to work on in the questions that we have here.

We are told that;

C α mr/t^2

Then;

C = kmr/t^2

k = Ct^2/mr

k = 6000 * 2^2/6 * 10

k = 400

Then, to find C;

C = 400 * 18 * 100/3^2

C = 80,000 Dynes

\

Hence, we can see from the calculation that the centrifugal force that is required is 80,000 Dynes.

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No, this sample of celebrities taken by Zach is not random.

A random sample is the one in which there is no predictability and it is totally instantaneous.

Hair in the human condition is as has served the first 45 celebrities to arrive at the movie premiere. Firstly it is a movie premiere show only a few selected celebrities who have been invited and above that people who are main cast in the movie must arrived early.

Because our condition is being implemented here we cannot say that this is random sample of celebrities.

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According to the model, around 521 people will be infected in three days.

A unitary method is a mathematical technique where we use ratios and proportions to find the value of an unknown quantity.

Let's start by breaking down the problem. We know that there are currently 392 people infected and the virus is spreading at a rate of 11% each day. This means that for every 100 people, 11 people are getting infected. To calculate how many people will be infected in three days, we need to use a unitary method.

To do this, we need to calculate the total increase in the number of infected people over three days. Since the virus is spreading at a rate of 11% each day, the total increase over three days will be 33% (11% x 3). We can then use this percentage increase to calculate the total number of people infected in three days.

To find the total number of people infected in three days, we can use the following formula:

Total infected = current infected + (current infected x percentage increase)

Plugging in the values from the problem, we get:

Total infected = 392 + (392 x 0.33)

Total infected = 392 + 129.36

Total infected ≈ 521

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Answer:

3

Step-by-step explanation:

The measure of each angle is [tex]3(75)-100=125^{\circ}[/tex].

The statement "The margin of error is a key component of a confidence interval, as it reflects the uncertainty in the estimate due to sampling error." is true

A confidence interval is a range of values that likely contains the true value of a population parameter, such as the mean or proportion. It is created by taking a sample from the population and calculating a point estimate, such as the sample mean or proportion.

To account for this uncertainty, we use the concept of a margin of error, which represents the maximum amount by which the point estimate could be off from the true parameter.

The sample size refers to the number of observations in the sample. The larger the sample size, the more precise the estimate is likely to be, since there is less variability and sampling error.

The level of confidence refers to the degree of certainty that the true parameter lies within the confidence interval. A higher level of confidence means a wider interval, since we need to be more certain that the true parameter is included.

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1) Note that the volume of water that was already in the pool when the hose was turned on today is 2000 gallons of water.

2) The equation that represents the relationship between the volume of water in the pool in gallons "V) and the elapsed time in hours, t, since the hose was turned on today is V = 800t + 2000.

Note that to get the right expression above we have to solve for the slope of the graph.

1) To arrive at the answer in 1 above, we only have to examine the y-intercept. since at time (t) =0 the volume of water (gallons) indicated on the graph is 2000 gallons, thus, it is correct to state that:

"the volume of water that was already in the pool when the hose was turned on today is 2000 gallons of water."

2) From the graph, we can see the equation must be linear.
That is:

y = mx + b

Where y = V = Volume of Water in the Pool in Gallons

m = Slope

x = t = elapsed time in hours
b = y- intercept = already given as 2000

Thus:

To get m (slope) we need to use the above equation:
m = rise/run = y2-y1/x2-x1

Take
y1 = 6000

y2 = 10,000

x1 = 5

x2 = 10

Substituting the given values, we get:

m = (10,000 - 6,000) / (10 - 5)

m = 4,000 / 5

m = 800

Therefore, the slope of the line passing through the points (5, 6000) and (10, 10,000) is 800.
Having derived m, the full expression is thus given as:

V = 800t + 2000.

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