1. Which fractions are equivalent to 25/45. Please give two examples.

2. Which describes independent events?

Spinning two fours on a spinner divided into four numbered sections.

Selecting two kings from a standard deck of cards by choosing a card at random, placing it in your pocket, then choosing the second card.

Selecting two green marbles by choosing one from a bag at random, giving the first to a friend, then choosing another.

Selecting the names of two siblings by choosing slips of paper from a hat at random, pinning the selected slip on a bulletin board, and then selecting another.

4.32*10^5

To write scientific number must be greater than one but less than 10

A percentage is a way to describe a part of a whole. The best option for the customer to buy is option A.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

Let the cost price of a cereal box be represented by x.

Given that the box usually contains 450 grams of cereal. Therefore, the unit rate for each option can be written as,

Option A

Weight of cereal = 20% more cereal

= 450 grams + 20% of 450 grams

= 450 grams + 90 grams

= 540 grams

Unit rate for option A = $x / 540 grams

Option B

Cost price of cereal = 15% off the price

= x - 15% of x

= x + 0.15x

= 0.85x

Unit rate for option A = $0.85x / 450 grams

Assume that option A is good. Now, if we subtract unit rate of option B from unit rate of option A then two of the cases are possible, if the value of the result is positive then the unit rate of option A is bigger while if the value is negative unit rate of option B is bigger.

Difference = (x/540) - (0.85x/450)

= (450x - 459x)/243000

= -9x/243,000

= -x/27,000

Further, since the difference is negative, therefore, the unit rate of option B is bigger. But since the value of option B is bigger it is costly and not the correct option to buy.

Hence, the best option for the customer to buy is option A.

Learn more about Percentages here:

https://brainly.com/question/6972121

#SPJ2

Answer:

The decimal of the fraction rounded to the nearest hundredth is

[tex]\frac{43}{14}=3.07[/tex]  

Step-by-step explanation:

Given : Expression [tex]\frac{43}{14}[/tex]  

To find : What is the decimal of the fraction rounded to the nearest hundredth?

Solution :

Step 1 - Write the fraction

[tex]\frac{43}{14}[/tex]  

Step 2 - Divide the numerator by denominator,

[tex]\frac{43}{14}=3.071[/tex]  

Step 3 - Convert to the nearest hundredth,

[tex]3.071\approx 3.07[/tex]

Therefore, The decimal of the fraction rounded to the nearest hundredth is

[tex]\frac{43}{14}=3.07[/tex]  

The diameter is increasing at a rate of approximately 100 / 300π cm/s when the radius is 5 cm.

To find the rate at which the diameter is increasing, we need to differentiate the formula for the volume of a sphere with respect to time:

V = (4/3)πr^3

Where V is the volume and r is the radius.

Let's differentiate V with respect to t:

dV/dt = (4/3)π(3r^2)(dr/dt)

We know dV/dt = 100 cm^3/s and r = 5 cm, so plug in these values:

100 = (4/3)π(3(5^2))(dr/dt)

Simplifying the equation gives us:

dr/dt = 100 / (4π(3(5^2)))

dr/dt ≈ 100 / 300π

So, the diameter is increasing at a rate of approximately 100 / 300π cm/s when the radius is 5 cm.

The baby meerkat weighs 29 grams.

First, we need to ensure our units are the same, so we'll convert 776 grams to kilograms.

There are 1,000 grams in a kilogram, so 776 grams is equivalent to 0.776 kilograms.

Given that the adult meerkat is 0.747 kilograms heavier than the baby meerkat, we can calculate the baby meerkat's weight by subtracting.

Baby meerkat weight = Adult meerkat weight - Additional weight

Baby meerkat weight = 0.776 kg - 0.747 kg

Baby meerkat weight = 0.029 kg

To express this in grams, we multiply by 1,000:

Baby meerkat weight in grams = 0.029 kg × 1000

= 29 grams

Answer:

D)  $ 300

Step-by-step explanation:

Here, the cost ( in dollars ) of x products is defined by the function,

[tex]C=0.25x^2-80x+300[/tex]

Since, if the no units are produced,

x = 0,

Hence, the cost would be,

[tex]C=0.25(0)^2-80\times 0+300[/tex]

[tex]=0-0+300[/tex]

[tex]=\$ 300[/tex]

Option D is correct.

The cost is $300 if no units are produced.

To find the cost when no units are produced, which are shown by x and we need to evaluate the cost function C at x = 0. The cost function is given by [tex]C = 0.25x^2 - 80x + 300.[/tex]

Let's substitute x = 0 into the function:

[tex]C(0) = 0.25(0)^2 - 80(0) + 300[/tex]

[tex]C(0) = 0 - 0 + 300[/tex]

[tex]C(0) = 300[/tex]

Therefore, the cost when no units are produced is $300.

This corresponds to the constant term in the cost function, which represents the fixed costs that are incurred regardless of the number of units produced.

The value of x from the given circle is 4.6 units.

From the given figure, the radius is 9.7 units.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Here,

9.7 =5.1+x

⇒ x=9.7-5.1

⇒ x=4.6 units

Therefore, the value of x from the given circle is 4.6 units.

To learn more about the circle visit:

https://brainly.com/question/11833983.

#SPJ2

The correct answer is D. on edg

Answer:

Its a triangle

Shane and his family spent a total of $103 at the movie theatre, which includes the cost of 6 tickets at $12 each and $31 on popcorn and drinks.

Shane and his family bought 6 tickets for $12 each, thus the total cost of the tickets is 6 * $12 which equals $72. Afterwards, they spent an additional $31 on popcorn and drinks. To find out how much they spent altogether at the movie theatre, we have to add the cost of the tickets and the cost of the popcorn and drinks. Therefore, $72 (for the tickets) + $31 (for the snacks) = $103. So, Shane and his family spent a total of $103 at the movie theatre.

https://brainly.com/question/31575023

#SPJ12

Answer:

WrItE wHaT yOu FeElLlLlL

Step-by-step explanation:

The expression for the width of a rectangle when the width is given by the algebraic expression 2x3 - 8x2 + 2x + 12.is already stated in its complete form.

The student is asking about finding an expression for the width of a rectangle with given algebraic expressions for length and width. Since the student has provided the expressions for both length and width, we do not need to perform any calculations or manipulations to answer the question directly. The length of the rectangle is given as x-2, and the width of the rectangle is given by the expression 2x3 - 8x2 + 2x + 12. There are no further instructions to simplify or modify, so the expression for the width as provided is complete.

The solution to the equation 12^x - 2 = 20, when solved for x and rounded to the nearest ten-thousandth, is x = 1.4624.

To solve the equation 12^x - 2 = 20, we first need to isolate the exponential term. This can be done by adding 2 to both sides of the equation resulting in 12^x = 22. Next, we take the logarithm of both sides to solve for x. We can use any logarithmic base, but common practice is to use base 10 or the natural logarithm (base e). The next steps are:

Calculating the value on a calculator gives us x ≈ 1.4624. Therefore, the solution to the equation, rounded to the nearest ten-thousandth, is x = 1.4624.

The correct answer is option (b) "x ≈ 1.2056."

To solve the equation [tex]\(12^{(x-2)} = 20\)[/tex], we can take the logarithm of both sides.

Let's use the natural logarithm (ln) for this:

[tex]\[ \ln(12^{(x-2)}) = \ln(20) \][/tex]

Using the logarithm property [tex]\( \log_a(b^c) = c \cdot \log_a(b) \)[/tex], we can rewrite the left side:

[tex]\[ (x-2) \cdot \ln(12) = \ln(20) \][/tex]

Now, solve for (x):

[tex]\begin{aligned}& x-2=\frac{\ln (20)}{\ln (12)} \\& x=\frac{\ln (20)}{\ln (12)}+2\end{aligned}[/tex]

Now, calculate the value:

[tex]\begin{aligned}& x \approx \frac{\ln (20)}{\ln (12)}+2 \\& x \approx \frac{2.9957}{2.4849}+2 \\& x \approx 1.2056\end{aligned}[/tex]

So, the solution to the equation is approximately [tex]\( x \approx 1.2056 \)[/tex]

Complete Question:

Solve [tex]\(12^{(x-2)} = 20\)[/tex]. Round to the nearest ten-thousandth.

a. x ≈ 1.0792

b. x ≈ 1.2056

c. x ≈ 3.2056

d. x ≈ 1.3010

Answer:

Option B. $155

Step-by-step explanation:

Jay Ward has already been taxed on his earning on $107,600.

So on this paycheck only  ($110,100 - $107,600) = $2,500 of his earnings are taxable for social security tax.

Social security tax rate = 6.2%

Hence, social security tax amount = 6.2% × 2500

                                                         = 0.062 × 2500

                                                         = $155

Option B. $155 is the answer.

Answer:

K′(−6, −4); L′(−3, −3)

Step-by-step explanation:

Got it right on the test

To answer the questions, we need to use the concepts of probability.

To answer the questions, we need to use the concepts of probability.

a. The number of airplanes arrive and depart the airport per hour can be calculated by multiplying the probabilities of a flight departing and arriving on time. Although the exact numbers are not given, the probability of a flight departing and arriving on time is 0.81, which can be used as an estimate.

b. To find the probability that there are exactly 100 arrivals and departures in one hour, we need to use the concept of the binomial distribution. However, we don't have enough information to calculate the probability.

c. To find the probability that there are at most 100 arrivals and departures in one hour, we can use the concept of the cumulative distribution function of the binomial distribution. Again, we don't have enough information to calculate the probability.

The question is about calculating probabilities and involves understanding conditional probability, probability distributions, and statistical methods. It requires more data to answer parts a, b, and c. The remaining parts of the question can be approached with standard statistical methods and concepts.

The question pertains to the field of probability within mathematics and involves calculations based on given probabilities for airplane flights departing and arriving on time. The data presented involve conditional probabilities and the characteristics of certain probability distributions. It is essential to understand these concepts to solve the exercises provided. Unfortunately, the given information does not contain sufficient details to answer parts a, b, and c as they require additional specific data about the actual number of flights or arrivals and departures per hour. However, the remaining parts of the question can be approached with standard statistical methods such as using z-scores for normal distributions, applying properties of uniform distributions for waiting times, understanding the concept of rate-determining steps in a process, and conducting hypothesis tests about a population mean given a sample.

Answer:

6(x+20)

Step-by-step explanation:

6x:  2*3

120:  2*2*3*5

The GCF of 6x*120 is 2*3

so the factored expression is 6(x+20)

Final answer:

Using equivalent ratios is like adding fractions with unlike denominators as it involves finding a common value to work with.

Explanation:

Using equivalent ratios is similar to adding fractions with unlike denominators because both involve finding a common value to work with. When adding fractions, we look for a common denominator so that we can add the numerators. With equivalent ratios, we find a common multiplier to scale the ratios, which allows us to compare or combine the quantities represented by the ratios.

Here's a step-by-step process:

Convert the given ratios to fractions by writing them as a fraction with the given quantities as the numerator and denominator.

Find a common denominator for the fractions. This involves identifying the least common multiple (LCM) of the denominators.

Multiply the numerators and denominators of the fractions by the appropriate multiples to get equivalent fractions with the same denominator.

Compare or combine the quantities represented by the equivalent fractions.

134.235 cube inches is the volume of a cylinder with a radius of 1.5 inches and a height of 19 inches.

Volume = base area x height

Radius of cylinder (r) = 1.5 inches

Height of cylinder (h) = 19 inches

Value of π = 3.14

To Find :

The volume of a cylinder.

Explanation :

Let, volume of a cylinder be "R".

We know that,

Volume of a cylinder = πr²h

[ Put the values ]

↪ R = 3.14 × (1.5)² × 19

↪ R = 3.14 × 2.25 × 19

↪ R = 7.065 × 19

↪ R = 134.235 cube inches

Therefore,

The volume of a cylinder is 134.235 cube inches.

To learn more about volume, refer;

brainly.com/question/1578538

#SPJ2

The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 15 are 1, 3, 5, and 15.

To find the factors of 12 and 15, you need to identify the numbers that can evenly divide these two numbers without leaving a remainder. Here's how you can find the factors:

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 15: 1, 3, 5, 15.

The answer is blue i just took the test.

Answer:

the answer is A

Step-by-step explanation: