a) The ratio 20 minutes to 1 hour can be written in the form 1:n.
Find the value of n.
n =

Answer:

1 / 2

Step-by-step explanation:

Total times spun = 4

Probability of getting gray 2 times = 2 / 4 = 1 / 2

Answer:

1. Skyler's processes are incorrect. She put (3^6)^x = 9, but when working with exponential problems, both sides have to have the same base. 3 does not equal nine, so you can automatically rule out her approach.

2. Robert's processes are correct. He set both bases equal to each other and then solved for the exponents.

3. Kaitlyn is also correct, she set the bases equal to 3 and solved for the exponents.

Step-by-step explanation:

When working with exponents, the goal is to get the bases equal to each other. In this case, you could have set it equal to 9 (which Robert did) or you could have set it equal to 3 (like Kaitlyn did). But you never want the bases to be conflicting, which is what Skyler did. Just by looking at the problem and using deductive reasoning, it is likely that Robert and Kaitlyn are both correct, since they have the same answers, although they used different methods, but it is still important to look at the steps.

Skyler's one mistake was setting 3 = 9, because that is impossible. If you plug in her answer of 3/2 into x, you get a ridiculous number of 19,683 = 9, which is not possibly true. For the others, when you plug in 1/3, you get 729^(1/3) = 9, so 9=9.

Hopefully this makes sense, if not, I can try to explain it better. Thanks much & have a wonderful day.

The explanation of whether Skyler, Robert or Kaitlyn were correct/wrong and the reason from their processes is that;

1) Skyler is wrong because she didn't make the bases of both sides to be equal before equating the exponents.

2) Robert is correct because he made the bases of both sides to be the same before equating the exponents.

3) Kaitlyn is correct because she made the bases of both sides to be the same before equating the exponents.

The problem skyler wants to solve is;

729^(x) = 9

The first step is to reduce 729 to the lowest base to get; [3^(6)]^(x) = 9

Next she did was to equate 6x to 9.

When working with equality of exponents both sides ought to have the same base and so she could have converted 9 to have same base of 3 as the left hand side after which she will equate the exponents.

So skyler is wrong.

We saw that skyler didn'take both bases equal to each other but now Robert has done the correct thing by having;

9^(3x) = 9¹

After which he equated the exponents to get;

3x = 1

x = 1/3

Thus; Robert is correct

Kaitlyn is also correct because she followed the same correct pattern of ensuring the bases are the same before equating their exponents.

Read more about laws of exponents at; https://brainly.com/question/11761858

The missing number in the boxes using the concept of perfect square are;

1) 4

2) 7 and 2

3) 4

4) 3 and 9

5) 3

A perfect square is defined as a number that is the square of a whole number. For example, 36 is a perfect square being the square of 6. Other perfect squares that are between 0 and 1000 are 1, 4, 9, 16, 25, 3649, 64, e.t.c

1st box: We see it as;

___ * 2 * 2

Using the concept of perfect squares and the pattern given, we can say that the missing number is 4

2nd box: 14 * __ * ___

Using the concept of perfect squares and the pattern given, we can say that the missing numbers are respectively 7 and 2

3rd box: 2 * 8 * ___

Using the concept of perfect squares and the pattern given, we can say that the missing number is 4

4th box: __ * 3 * _____

Using the concept of perfect squares and the pattern given, we can say that the missing numbers are respectively 3 and 9

5th: 3 * ____

Using the concept of perfect squares and the pattern given, we can say that the missing number is 3

Read more about perfect squares at; https://brainly.com/question/3617398

#SPJ1

\(\large \mathfrak{Solution : }\)

let's solve for y :

value of y = 5

Answer:

\(y=5\)

Step-by-step explanation:

\(4y=38-\frac{1}{2}\left(4y+16\right)\)

→ Multiply fractions:- \(a\times\frac{b}{c} =\frac{a\times b}{c}\)

\(\frac{1\cdot \left(4y+16\right)}{2}\)

\((4y+16)=4y+16\)

\(4y=38-\frac{4y+16}{2}\)

→ Multiply both sides by 2:-

\(y\cdot \:2=38\cdot \:2-\frac{4y+16}{2}\cdot \:2\)

\(8y=76-\left(4y+16\right)\)

\(76-(4y+16)=-4x+60\)

\(8y=-4y+60\)

→ Add 4y to both sides:-

\(8y+4y=-4y+60+4y\)

\(12y=60\)

→ Now, divide both sides by 12:-

\(\frac{12y}{12}=\frac{60}{12}\)

\(y=5\)

OAmalOHopeO

The standard deviation of ages in the room increases, while the median of ages stays approximately the same.

Standard deviation is a measure of the variability of a set of data points. The addition of a 30-year-old mother and an infant to the group of ten five- and six-year-olds increases the spread of the ages, thus increasing the standard deviation.

The median, on the other hand, is the middle value in a set of data points. Since the median only depends on the order of the values, not their magnitude, adding a mother and an infant to the group of children does not significantly affect the median age in the room, which would still be close to 5 or 6 years old.

Learn more about standard deviation

brainly.com/question/20450242

#SPJ4

Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

To Learn More About Programming

https://brainly.com/question/24361247

#SPJ11

Given:

Kaci earned scores of 78, 88, 87, and 91 on her first four science tests.

She has one more test to take and wants to get an average score of 80 or more on her tests.

Let the score of the final test = x

So, the average of the scores will be equal to or greater than 80

So, we have the following inequality

Solve for x:

So, the minimum score will be 56

Let Xk be independent and normally distributed with common mean 22 and standard deviation 11 (so their common variance is 1.1.). The value of p(-[infinity] ≤ ∑k=181 Xk ≤ 172.89) ≈ 0.0265.

The common variance of independent and normally distributed random variables with a common mean can be computed with the formula

σ² = Var[Xk]

= 1.1.

This can be solved by finding the standard deviation, which is equal to the square root of the variance as

σ = sqrt(1.1)

= 1.0488.

The sum of the independent and identically distributed normal random variables can be expressed as a normal random variable with a mean equal to the sum of the individual means and a variance equal to the sum of the individual variances.

Thus, we can express this random variable as ∑k=181 Xk ~ N(22 * 181, 1.1 * 181).

To solve the given problem, we need to compute the probability that the sum of the random variables lies between -infinity and 172.89.

Since the sum of normal random variables follows the normal distribution, we can standardize the sum by subtracting the mean and dividing by the standard deviation.

Let Z be the standardized random variable.

Then Z = (X - μ)/σ

Z = (∑k=181 Xk - μ)/σ, where μ = 22 * 181 and σ = sqrt(1.1 * 181).

We need to compute P(-infinity ≤ Z ≤ (172.89 - μ)/σ) = P(Z ≤ (172.89 - μ)/σ) .

Since the standard normal distribution is symmetric about zero.

This can be solved using standard normal tables or a calculator to obtain P(Z ≤ -1.9309) ≈ 0.0265 (rounded to four decimal places).

Therefore, p(-[infinity] ≤ ∑k=181 Xk ≤ 172.89) ≈ 0.0265 (rounded to four decimal places).

To know more about standard deviation, visit:

https://brainly.com/question/29115611

#SPJ11

The initial amount, a, in the exponential function g(x) = 14 × 2x is 14, and the growth factor, b, is 2.

This can be determined by looking at the equation and noting that the coefficient of x is 2, which indicates that the base of the exponential is 2. We can also calculate the initial amount and growth factor mathematically.

To calculate the initial amount, a, we can take the equation g(x) = 14 × 2x and set x = 0, yielding g(0) = 14 × 20, which simplifies to 14. To calculate the growth factor, b, we can take the natural log of both sides of the equation to yield ln(g(x)) = ln(14 × 2x).

Simplifying this gives

ln(g(x)) = ln(14) + ln(2x).

We can then divide both sides by x to yield

ln(g(x))/x = ln(14) + ln(2)/x.

We can then take the limit as x approaches 0, which yields

ln(g(0))/0 = ln(14) + ln(2)/0.

This simplifies to

ln(g(0)) = ln(14) + ln(2), which can be rearranged to

ln(2) = ln(g(0)) - ln(14).

Taking the exponential of both sides gives us

2 = e^(ln(g(0)) - ln(14)), which simplifies to

2 = g(0)/14, or b = g(0)/14 = 2.

This shows that the initial amount, a, is 14, and the growth factor, b, is 2.

Learn more about exponential function:

https://brainly.com/question/30241796

#SPJ4

Answer:

B. 14,000

I hope that this helps you, have a wonderful day!

The best estimate from the option is 14,000 since 14,000 is the nearest value from the option to 12763.

Given,

18 x 709

We need to find the best estimate.

We need to multiply each number of one number with the other number and add them to get the product.

Example:

21 x 34 =

21 x 3 = 63

21 x 4 = 84

    2 1

x  3 4

    84

+ 63    

  71 4

We have,

18 x 709

We can write it as:

709 x 18

709 x 8 = 5672

709 x 1 = 709

             709

            x  18

           5672

     +   709  

          12762

Thus the best estimate from the option is 14,000 since 14,000 is the nearest value from the option to 12763.

Learn more about how to multiply numbers here:

https://brainly.com/question/12069004

#SPJ2

Answer:

  $9408 more than she started with

Step-by-step explanation:

The amount added to Patterson's account each month is ...

  $2575 -1029 -312 -450 = $784

After 12 months, she has added ...

  12 × $784 = $9408

After 12 months, Patterson has added $9408 to her account.

The value of the additional data point is 36

To find the value of the additional data point, we can use the concept of the sample mean.

Given the data set: 23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19.

The sample mean of this data set is 26.5.

To find the value of the additional data point, we can use the formula for the sample mean:

(sample mean) = (sum of all data points) / (number of data points)

In this case, we have 11 data points in the original data set. Let's denote the value of the additional data point as x.

Therefore, we can set up the equation:

26.5 = (23 + 28 + 20 + 33 + 42 + 12 + 19 + 50 + 36 + 25 + 19 + x) / 12

Multiplying both sides of the equation by 12 to eliminate the fraction, we have:

318 = 282 + x

Subtracting 282 from both sides of the equation, we find:

x = 318 - 282

x = 36

Know more about sample mean here;

https://brainly.com/question/33323852

#SPJ11

.

The simplified form of the polynomial is \(-(a^2 / (6b^3)).\)

Polynomials are algebraic expressions that consist of variables and coefficients. The variables are often referred to as "indeterminates." The word polynomial comes from the terms "poly" and "nomial," which mean "many" and "terms," respectively. When you combine exponents, constants, and variables using mathematical operations such as addition, subtraction, multiplication, and division (excluding division by a variable), you get a polynomial. Depending on the number of terms it has, a polynomial can be categorized as a monomial, binomial, or trinomial.

To simplify this expression, we can use the following rules of exponents:

\(a^m/a^n = a^{(m-n) }\)(when the bases are the same)

\(a^{-m} = 1/a^m\\(1/b^m) = b^{-m}\)

Using these rules, we can simplify the expression as follows:

\(-6a^3b^{-1}/36ab^2 = - (6/36) \times a^{(3-1)} \times b^{(-1-2)}\\\\= - (1/6) \times a^2 \times b^{(-3)}\\\\= - (a^2 / (6b^3))\)

Therefore, the simplified form of the expression is \(-(a^2 / (6b^3)).\)

Learn more about polynomials, by the following link.

https://brainly.com/question/2833285

#SPJ1

Answer:

25minutes

Step-by-step explanation:

Given the following

Time Isabella started getting ready = 5:25pm

Time she finished = 5:50pm

Total number of time she took to get ready = 5:50pm - 5:25pm

Total number of time she took to get ready = 0:25pm

This means that Isabella took 25minutes to get ready

Answer:

6 places to the right....

If we consider the two vectors a and b with known magnitudes of 1 m and 10 m respectively, but unknown directions, we can still perform some calculations with these vectors. However, without knowing their directions, we cannot determine the resultant vector of their addition or subtraction.

The direction of a vector is a crucial component in determining the overall effect of the vector. Therefore, to fully understand the impact of vectors a and b, we need to know their directions as well.
Based on the information given, you have two vectors: vector a with a magnitude of 1 m and vector b with a magnitude of 10 m. However, since the directions of these vectors are unknown, you cannot determine their specific position, direction, or any further information about their relationship to each other. To analyze or perform operations on these vectors, you would need additional information regarding their directions.

Know more about vectors here;

https://brainly.com/question/29740341

#SPJ11

Answer: 1st image: option 2

2nd image: (x, y) ==> (x+4, y-9) ==> option 4

Step-by-step explanation:

1st image: Reflection over the y-axis means that all x-coordinates are negated while the y-coordinates remain the same.

A: (2, -2) ==> A' (-2, -2)

B: (-2, 5) ==> B' (2, 5)

C: (-4, 2) ==> C' (4, 2)

Answer: option 2

A to A', B to B', C to C'

Purple to Blue

2nd image: 1st, the purple triangle moves 4 units to the right (x ==> x+4)

Then, the purple triangle moves 9 units down to become the blue triangle (y ==> y-9)

(x, y) ==> (x+4, y-9) ==> option 4

Answer: its b

Step-by-step explanation:

Beta decay is a type of radioactive decay that occurs in certain atomic nuclei. It involves the transformation of a neutron or proton within the nucleus into the other.

In the case of Lanthanum-144 (La-144), a neutron undergoes beta decay to convert into a proton, resulting in the formation of Cerium-144 (Ce-144).

The equation for the beta decay of La-144 into Ce-144 is as follows:

La-144 → Ce-144 + β¯

In this equation, the La-144 nucleus decays into the Ce-144 nucleus. To conserve charge, a beta particle (β¯) is emitted. The beta particle can be either an electron (β-) or a positron (β+), depending on the specific type of beta decay occurring in the nuclide.

Learn more about Beta decay here : brainly.com/question/21370162

#SPJ11

Answer:

3

Step-by-step explanation:

because two plus two

Given:

Total number of scholars = 60

Fraction of scholars doing Woah = 1/12

Fraction of scholars doing flossing = 2/3

Fraction of scholars dabbing = 4/30

The rest of the scholars are doing the Orange Justice.

To find the number of scholars doing Orange Justice, let's first find the number doing Woah, Sare Flossing and dabbing.

Number doing Orange Justice = Total - Woah - Sare Flossing - Dabbing =

60 - 5 - 40 - 8 = 7

Therefore, 7 scholars are doing the Orange Justice.

ANSWER:

7

The required equation of the plane parallel to the plane 3x − 4y + 6z − 9 = 0 is 3x - 4y + 6z = 13. And the required equation of the normal line to the plane at the point (3,1,2/3)

To find the equation of a plane parallel to the plane 3x − 4y + 6z − 9 = 0, follow these steps:

1. The given equation of the plane is: 3x − 4y + 6z − 9 = 0.

  Rewriting it, we have: 3x - 4y + 6z = 9.

2. The normal vector to the given plane can be calculated as: n = <3, -4, 6>.

  Any plane parallel to the given plane will have the same normal vector.

3. Let P(x, y, z) be any point on the required plane. The vector joining the point P(x, y, z) and a point Q(1, 1, 1) on the given plane will be perpendicular to the normal vector of the required plane.

4. The vector joining P(x, y, z) and Q(1, 1, 1) is PQ = <x - 1, y - 1, z - 1>.

5. The equation of the required plane can be written as: ax + by + cz = d, where a, b, c, and d are constants.

6. Substituting PQ = <x - 1, y - 1, z - 1> in the equation, we get:

  (3, -4, 6) ⋅ (x - 1, y - 1, z - 1) = 0.

7. Simplifying the dot product, we have:

  3(x - 1) - 4(y - 1) + 6(z - 1) = 0.

  This can be further simplified to: 3x - 4y + 6z = 13.

Therefore, the equation of the plane parallel to 3x − 4y + 6z − 9 = 0 is 3x - 4y + 6z = 13.

Additionally, if you need to find the equation of the normal line to the plane at a given point (3, 1, 2/3), follow these steps:

1. The given point on the plane is (3, 1, 2/3).

2. The normal vector of the plane is n = <3, -4, 6>.

3. The equation of a line in point-normal form is given by: (x - x₁)/a = (y - y₁)/b = (z - z₁)/c.

4. Let the equation of the line passing through the given point be: (x - 3)/a = (y - 1)/b = (z - 2/3)/c.

5. Since the line is normal to the plane and parallel to the vector n, the direction ratios of the line are the same as those of the vector n.

  Hence, the direction ratios of the line are (a, b, c) = <3, -4, 6>.

6. Therefore, the equation of the normal line is: (x - 3)/3 = (y - 1)/(-4) = (z - 2/3)/6.

Learn more about parallel

https://brainly.com/question/22746827

#SPJ11

What is the Area of Trapezoid?

The area of a trapezoid is the total space covered by its sides. An interesting point to be noted here is that if we know the length of all sides we can simply split the trapezoid into smaller polygons like triangles and rectangles, find their area, and add them up to get the area of the trapezoid. However, there is a direct formula that is used to find the area of a trapezoid if we know certain dimensions.

Area of Trapezoid Formula :

The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given.

The formula for the area of a trapezoid is expressed as,

A = 1/2 (a +b) h

where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b)

Learn more about Area of Trapezoid at:

https://brainly.com/question/1034014

#SPJ4

Answer:

I think about 27 memory cards.

Step-by-step explanation:

4,000 divided by 150 = 26.6666666667

I'm thinking this is the answer.

Answer:

The nth term of the sequence will be:  n²/n+1

Step-by-step explanation:

Given the sequence

1/2 , 4/3 , 9/4 , 16/5

The values in the numerator are:

2, 3, 4, 5

It is clear that every successive value in the numerator can be determined by adding 1 to the previous value.

i.e.

3 = 2+1

4 = 3+1

5 = 4+1

Thus, the nominator contains the sequence rule: n+1

The values in the denominator are:

1, 4, 9, 16

It is clear that every value in the denominator is the square of the sequence number.

i.e.

1 = 1²

2 = 2²

3 = 3²

4 = 4²

5 = 5²

so

The denominator defines the rule n².

Thus, the nth term of the sequence will be:  n²/n+1

The new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

(a) To find the angle that the pilot should turn to head towards Louisville, we first need to find how far off course the pilot has gone in 15 minutes. At an average speed of 220 miles per hour, the pilot would have flown a distance of:

d = rt = 220 mi/hr × (15 min / 60 min/hr) = 55 miles

Since the pilot was 10 degrees off course, they have effectively traveled 10/360 of the circumference of a circle with radius 55 miles. The length of this arc is:

s = rθ = 55 mi × (10/360) = 1.528 mi

To head towards Louisville, the pilot needs to turn to a heading that is 10 degrees in the opposite direction. The angle θ that the pilot needs to turn is given by:

θ = 2arctan(s/2d) = 2arctan(1.528 mi / 2(330 mi)) ≈ 0.266 radians ≈ 15.26 degrees

So the pilot needs to turn approximately 15.26 degrees to head towards Louisville.

(b) Let's call the distance the pilot needs to travel after correcting course "x". We can use the formula for distance to find "x":

x = 330 mi - 2(55 mi) = 220 mi

To complete the trip in a total time of 90 minutes, the pilot must spend 75 minutes flying at the new speed and 15 minutes turning to the correct heading. Therefore, the time spent flying at the new speed is 75 minutes - 15 minutes = 60 minutes. The new speed can be found using the formula for average speed:

average speed = total distance / total time

We want the new speed to cover a distance of 220 miles in 60 minutes:

average speed = 220 mi / (60 min / 60) = 220 mi/hr

So the new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

Learn more about average speed here

https://brainly.com/question/30726319

#SPJ11

A correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.

A correlation can be defined as the relationship that exists between two variables when one of them is related to the other in some way.

It is also a measure that expresses the extent to which two variables are closely or linearly related which entails that they change together at a constant time.

Hence, correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.

Learn more about correlation here:

https://brainly.com/question/4219149

#SPJ1

In 120 different variations of this model car are possible.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.

Calculating the sum of two numbers multiplied together is the process of multiplication. Simple tests in addition, subtraction, multiplication, and division will be given. 2. a noncount noun The process or occurrence of something of a certain kind multiplying occurs when their quantity or number increases.

Given,

There are five different ways to choose a car's color.

3 different car transmission selection options are available.

There are four different interior automobile selection options.

There are two different ways to pick a car's engine.

The potential number of car variations is thus:

Multiplying:

5 × 3 × 4× 2

120

In 120 different variations of this model car are possible.

To learn more about multiplication, visit:

https://brainly.com/question/5992872

#SPJ4

Answer:

\( \sin0\)

Step-by-step explanation:

\( \tan0 \cos0 = \frac{ \sin0 }{ \cos0} \cos0 \\ \\ \)

Therefore,

\( \tan0 \cos0 \: = \sin0 \)

The probability that at least three of the four dice show the same value, i.e., three of the dice showing the same number and the fourth one having any of the other five numbers can be calculated using binomial probability.

Binomial probability is a statistical function that applies when there are only two possible outcomes of a given event, and both outcomes are independent of one another. It can be utilized to determine the likelihood of achieving a certain number of successful outcomes in a specific number of trials. There are two possibilities for a given roll, either it can match with one of the previously rolled values or it cannot. The chance that the next roll is not a matching number is 5/6. The probability that all four numbers are different is (5/6)4 = 0.4822530864. Therefore, the probability that at least three of the four dice show the same value is 1 - 0.4822530864 = 0.5177469136. This implies that the likelihood of having at least three of the four dice show the same number is approximately 51.77 percent.In the formula, p is the probability of a success on any given trial, q is the probability of a failure on any given trial, n is the number of trials, and x is the number of successes. As a result, the formula is as follows:

P(x ≥ k) = ΣnCk pkq(n - k)

Where, k is the minimum number of successes that must be obtained to meet the condition.

Therefore, the probability that at least three of the four dice show the same value is 0.5177469136.

To learn more about statistical function visit:

brainly.com/question/30070005

#SPJ11

Answer:

x = 5/3

Step-by-step explanation:

4x= x + 5

3x=5

x = 5/3