Match the following expression 12(x-3)+18=6(x-3) with the number of solutions below.
A.One solution?
B.No solution ?
Or
C.All solution?

Answer:

T ≥ 80 T-shirts

Answer:

x \(\geq\)80

Step-by-step explanation:

I got it on Khan Academy:

The definition of the gradient vector for point a to b is defined below.

Vector:

In math vector value consists of magnitude and direction.

Given,

Here we need to find the gradient vector of point a or point b.

According to the definition of vector, a multidimensional input have partial derivatives, you might wonder what the full derivative of such a function is. Here in the case of scalar-valued multivariable functions, meaning those with a multidimensional input but a one-dimensional output, the answer is the gradient.

Where as the gradient of a function f, denoted as ∇f,

Where f, is the collection of all its partial derivatives into a vector.

Here the point a and b is more horizontal because of the partial derivative nature of vector.

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Answer/Step-by-step explanation:

The sum of the interior angles of triangle equals 180 degrees, so the measurement of Angle A can be found by calculating the sum of the two angles shown, then subtracting the sum from 180 degrees. The measure of Angle A is 36 degrees.

A random variable is a variable that can take on different values based on the outcomes of a random event or experiment. It associates a numerical value with each outcome of the event.

Different Types of Random Variables:

1. Discrete Random Variable: A random variable that can take on a countable number of distinct values. For example, the number of heads obtained when flipping a coin multiple times.

2. Continuous Random Variable: A random variable that can take on any value within a certain range. For example, the height of individuals in a population.

Probability Density Function (PDF):

In the context of continuous random variables, the probability density function (PDF) represents the relative likelihood of different values occurring. It gives the probability of a random variable falling within a particular range of values. The PDF is denoted by f(x) and satisfies the following conditions:

1. f(x) is non-negative for all x.

2. The area under the PDF curve over the entire range of x is equal to 1.

Given the PDF: f(x) = c(2x - 1), 0 ≤ x ≤ 2, we need to determine the value of c and compute the mean and standard deviation of X.

To find the value of c, we integrate the PDF over its range and set it equal to 1:

∫[0 to 2] c(2x - 1) dx = 1

Solving this integral equation will give us the value of c.

Once we have the value of c, we can compute the mean (expected value) and standard deviation of X using the formulas:

Mean (μ) = ∫[0 to 2] x * f(x) dx

Standard Deviation (σ) = √(∫[0 to 2] (x - μ)^2 * f(x) dx)

To find the probabilities (a), (b), (c), and (d), we integrate the PDF over the given intervals:

(a) P[0 ≤ x ≤ 0.5] = ∫[0 to 0.5] f(x) dx

(b) P[1.0 ≤ x ≤ 2.0] = ∫[1.0 to 2.0] f(x) dx

(c) P[x = 0.8] = 0 (since it's a continuous random variable, the probability at a single point is always 0)

(d) P[x ≥ 1.5] = ∫[1.5 to 2.0] f(x) dx

By evaluating these integrals, we can find the respective probabilities.

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Answer:

Step-by-step explanation:

We can solve this in either of two approaches:  Mathematically or Graphically.

Mathematically

y=-(3/4)(x-4)^2+12  where y is the height of the ball, and x is the time, in seconds.

We want to know how many seconds for the height to be 0, so y=0.

0 = -(3/4)(x-4)^2+12

-12 = -(3/4)(x-4)^2

12*(4/3) = (x-4)^2

16 = (x-4)^2

x = 8 and 0 (the initial point).]

It will reach the ground in 8 seconds

Graphically

Plot the function and find the time, x, when the graph passes through the x axis (after t = 0).  Attached.

Yes, there are certain holidays that tend to experience lower numbers of flights. One such holiday is Thanksgiving Day in the United States.

Many people stay at home to celebrate with their families, resulting in decreased air travel. Additionally, Christmas Day and New Year's Day also tend to have fewer flights as people typically spend these holidays with their loved ones. Other holidays like Easter and Memorial Day may also see lighter travel, but the extent of reduced flights may vary depending on various factors such as cultural and regional differences.

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Answer:

Step-by-step explanation:          

\(49x^2-42x+(\frac{42}{2})^2=49x^2-42x+(\frac{42}{2} )^2\)    (completing the square)  

  \(49x^2-42x+441=49x^2-42x+21^2\)

                              \(=(7x-21)^2\)

So    \(49x^2-42x+441=(7x-21)^2\)

Solution: The required constant is 441.

Remember:    Completing the square IN \(ax^2+bx+c\) involves adding  \((\frac{b}{2} )^2\)     to both sides of the equation. THIS KEEPS IT BALANCED AND ALLOWS US TO MAKE A PERFECT SQUARE.    

Answer: The answer is 3

Step-by-step explanation:

Answer:

B. \( y = kx \) , where k is the constant of proportionality.

Step-by-step explanation:

Given that quantity x and y is directly proportional to each other, which means as one variable increases, the other increases as well. Thus, the constant of proportionality, which is often denotes with the alphabet k, can be represented by the following equation:

\( y = kx \) , where, k is the constant of proportionality.

Constant of proportionality, k, is gotten when you divide the value of y by the value of x.

Answer:

20

Step-by-step explanation:

2 get well cards

4 anniversary cards

6 greeting cards

8 birthday cards

Answer:

x is corresponding with the angle that equals 130 so it equals 130 too

Step-by-step explanation:

The answer you are looking for is 2√5, which is the same thing as √20.

Solution/Explanation:

Writing out the problem first

√45-√5

Testing different values to try to get the square root to be 5

Testing 2:

Take 2

Square it

2²=4

Divide 45 by 4

Nope, this will not work. It will not have a √5, and the base will not be a whole number. Now, let's try 3.

Take 3

Square it

3²=9

Divide 45 by 9, which is 5. For extra checking, you can multiply 9 by 5, which is 45, just to make sure that you calculated everything correctly.

Three works. So, now, we can have 3 as the base and 5 as the square root.

So, now, we can formulate a more simplified problem:

3√5-√5

To make it more easy to simplify more, we can write it out like this:

3√5-1√5

Subtract the bases 3 and 1. You will get 2. The √5 will remain the same.

2√5

So, therefore, the final answer to this problem is 2√5.

Hope this helped answer your question for you. Good day to you.

Answer:

3rd one

Step-by-step explanation:

The probability can be calculated using the binomial distribution formula, considering a preliminary polling result of approximately 52% of people voting in favor.

Identify the parameters:

- Probability of voting in favor: p = 0.52

- Sample size: n = 250

Determine the event of interest:

We want to calculate the probability of having more than half of the sample vote in favor of the congressman.

Calculate the probability using the binomial distribution formula:

The probability of having x successes in a binomial distribution with parameters n and p is given by the formula:

P(X = x) = (n choose x) * p^x * (1 - p)^(n - x)

In this case, we want to find the probability of having more than 125 successes (voters in favor), so we calculate:

P(X > 125) = P(X = 126) + P(X = 127) + ... + P(X = 250)

Calculate the cumulative probability:

To calculate the cumulative probability, we sum up the individual probabilities from Step 3:

P(X > 125) = P(X = 126) + P(X = 127) + ... + P(X = 250)

Calculate the final probability:

Using this cumulative probability, we can subtract it from 1 to find the probability of having more than half of the sample vote in favor:

P(X > 125) = 1 - [P(X = 0) + P(X = 1) + ... + P(X = 125)]

Calculate the probability using a statistical calculator or software:

To obtain the precise probability, you can use a binomial probability calculator or statistical software that allows you to input the parameters (n and p) and calculate the desired probability.

By following the above steps and using the appropriate calculations, you can obtain the accurate probability value for the given scenario.

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-0.457 .

To calculate the standard deviation needed for 96% of the boxes to contain 24 ounces or more, you can use the z-score formula. This formula is used to calculate the number of standard deviations away from the mean a data point is.

In this case, the mean is 24.8 ounces and the desired data point is 24 ounces. To get the standard deviation, the following equation can be used:
z = (x - μ)/σ

Where x is 24, μ is the mean (24.8), and σ is the standard deviation.

Rearranging the equation to solve for σ, the standard deviation can be calculated as:
σ = (x - μ)/z

Since we want to calculate the standard deviation for 96% of the boxes containing 24 ounces or more, we can use the z-score of 1.75. Substituting this into the equation:
σ = (24 - 24.8)/1.75 = -0.457

Therefore, the standard deviation needs to be -0.457 in order for 96% of the boxes to contain 24 ounces or more.

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In comparison to the current selling price of $463.20, the cost to members with the additional 40% markdown is $185.25.

Given, a computer shop spends $463.2 to purchase a computer system.

Additionally, the selling price was initially set at $772, but the retailer later announced a 40% reduction online.

Find the current selling price here:

existing selling price;

employ a formula for percentages,

= $772- (40% × $772)

= $772 - (0.4× $772)

= $772 - $308.80

= $463.20

To determine the pricing for club members at a 40% extra discount:

employ a formula for percentages,

= $463.20 - (40% × $463.20)

= $463.20 - (0.4 × $463.20)

= $463.20 - $46.32

= $185.25

As a result, the members will pay $185.25 in addition to the current selling price of $463.20.

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Answer:

Bet $100 and remove all non-face cards.

Step-by-step explanation:

Each option may be answered on the basis of the ratio of face cards to non-face cards, which we'll say is R.

a. removing all of the black cards  No.  The vale of R does not change.  R is the same for both black and red cards, so removing one color does not change R.

b. removing all non-face cards  Yes.  The only cards left are face cards.  The odds of drawing 2 face cards in a row from this modified deck is 100%

c. removing all kings  No.  Face cards are being removed and will thus lower the probability of picking one.

d. removing all of the red cards  No.  Same reasoning as in (a.).

Answer:

5/6 x 48 = 5 x 8=40

Step-by-step explanation:

Pls mark as brainliest

Answer:

40

Step-by-step explanation:

\( \frac{5}{6} \times 48 \\ \frac{5 \times 48}{6} \\ \frac{240}{6} = 40\)

Answer:

there is one line of symmetry if you look closely at the shape

(a) We have shown that there exists an element b ∈ B that is an upper bound for A.

(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.

(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.

Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).

Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.

(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.

Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.

This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.

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Answer:

Left box:  1/2n

Right box = 2n - 22

Step-by-step explanation:

Since we want one-half the number and n represents the unknown number, we have 1/2n on the left-hand side of the equation.

Thus, you want to put 1/2n in box on the left.

Twice the number and 22 less than this is given by:  y: 2n - 22 less than this means we subtract.  Thus, we have 2n - 22 as the numerator on the right hand side of the equation.

Thus, you want to put 2n - 22 in the box on the right.

The system in the requested form, using prime notation for derivatives and ï notation for variables, is ï' = e^2tï - 8tï' + 7sin(t) and ï'' = 2tan(t)ï' + 7ï - 2cos(t).

The system can be written in the form:

x' = e^2tx - 8ty + 7sin(t)

y' = 2tan(t)y + 7x - 2cos(t)

Using prime notation for derivatives, the system becomes:

x' = e^2tx - 8ty + 7sin(t)

y' = 2tan(t)y + 7x - 2cos(t)

Furthermore, we can write x and y using ï' notation as:

x = ï

y = ï'

Substituting these expressions into the system, we have:

ï' = e^2tï - 8tï' + 7sin(t)

ï'' = 2tan(t)ï' + 7ï - 2cos(t)

In summary, the system in the requested form is:

ï' = e^2tï - 8tï' + 7sin(t)

ï'' = 2tan(t)ï' + 7ï - 2cos(t)

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Answer:

8(h)=x

Step-by-step explanation:

Matt earns 8 dollars for every hour he works. So you multiply the total numbers worked (h) by 8. That will give you the amount of money he's made(x) so the equation would be 8(h)=x

There is a limit in Microsoft Excel on the number of rows and columns an Excel file can contain. An Excel file may have upto 256 columns and 65536 rows.

Now, According to the question:

There is a limit in Microsoft Excel on the number of rows and columns an Excel file can contain. An Excel file may have upto 256 columns and 65536 rows.

Excel sheet:-

In Microsoft Excel, a sheet is often called a worksheet. A sheet is a single page that contains its own collection of cells to help you organize your data. There can be many sheets in your Excel document and you can see the sheets listed as tabs along the bottom of your document.

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The ornaments consist of two identical cones.

The formula for the surface area of a cone is:

SA = πr² + πrl

Since the cones are identical, the radius (r) and slant height (l) are the same for both cones in each ornament. Let's call them r1 and l1.

The total surface area of each ornament is:

SA_ornament = 2(πr1² + πr1l1)

We know that one bottle of paint covers 213 cm², so we can set up the following equation:

SA_ornament * bottles = 60 * 213

Substituting the given value of pi:

2(3.14r1² + 3.14r1l1) * bottles = 60 * 213

Simplifying:

6.28r1² + 6.28r1l1 = 6390

Since we have two variables and only one equation, we need another equation to solve for r1 and l1.

We know that the two cones are identical, so their dimensions are related by a scale factor of 1:2. Let's call the radius and slant height of the larger cone r2 and l2, respectively. Then:

r2 = 2r1

l2 = 2l1

The volume of each ornament is:

V_ornament = (1/3)πr1²l1 + (1/3)πr1²l1 = (2/3)πr1²l1

The scale factor for volumes is (1/4)³ = 1/64, since the radius and height are scaled by 1/4. Therefore:

V_ornament_B = (1/64)V_ornament_A = (1/64)(112π) = 7/4π

The volume of each ornament B is 7/4π.

The volume of 60 ornaments B is:

60 * 7/4π = 105π

We can now solve for r1 and l1 by substituting r2 = 2r1 and l2 = 2l1 into the surface area equation:

6.28r1² + 6.28(2r1)(2l1) = 6390

Simplifying:

6.28r1² + 25.12r1l1 = 6390

We don't need to solve for r1 and l1 explicitly. We just need to use the fact that the volume of each ornament B is (2/3)πr1²l1 and substitute the value of the volume and the relation between r1 and l1 into the equation above to get:

r1 ≈ 7.27 cm

l1 ≈ 14.54 cm

Finally, we can calculate the total surface area of each ornament B:

SA_ornament_B = 2(3.14 * 7.27² + 3.14 * 7.27 * 14.54) ≈ 1158.6 cm²

And the number of bottles of paint needed:

bottles = (60 * 1158.6) / 213 ≈ 326.4

Therefore, Tim needs about 327 bottles of paint to paint 60 ornaments.

Answer:

Yes; 256

Step-by-step explanation:

Take the square root of 65536

\(\sqrt{65536} = 256\)

256 to the power of 2 = 65536

Answer:

Step-by-step explanation: