Solve: You have a machine with a screen and three buttons: red, green, and blue. If you press the red button, the number on the screen is doubled. If you press the green button, the number on the screen is tripled. If you press the blue button, the number on the screen is multiplied by itself. The number 1 is displayed on the screen. What is the least number of times you need to press a button to get the number 2592 on the screen.

Answer: 12

Step-by-step explanation: Just multiplied them

DE is approximately 30.3 inches to the nearest tenth of an inch.

The Law of Sines is a trigonometric formula used to find unknown sides and angles in any triangle, whether it is acute, obtuse, or right-angled. It relates the lengths of the sides of a triangle to the sine of the opposite angle.

The formula for the Law of Sines is:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the opposite angles.

We can use the Law of Sines to solve for DE.

The Law of Sines states that for any triangle ABC,

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the side lengths opposite the angles A, B, and C, respectively.

In this case, we know that:

m∠D = 42°

m∠E = 63°

EF = 24 in.

Let x be the length of DE.

Then, applying the Law of Sines to ∆DEF, we have:

x/sin(63°) = 24/sin(42°)

Solving for x, we get:

x = (24*sin(63°))/sin(42°) ≈ 30.3

Therefore, DE is approximately 30.3 inches to the nearest tenth of an inch.

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Assuming he drives at a speed of 60 miles per hour, it will take him 5.5 hours to drive the 330 miles.

If Harold drives 330 more miles at the same rate of 60 miles per hour, we can use the formula:

distance = rate x time

Let t be the time in hours it takes to drive the additional 330 miles. Then we have:

330 = 60t

Solving for t, we get:

t = 330/60

t ≈ 5.5 hours

Therefore, it takes approximately 5.5 hours to drive the additional 330 miles at a rate of 60 miles per hour.

Full question "Harold will drive 330 more miles at the same rate. Assume he drives at a speed of 60 miles per hour, how long does it take to drive the 330 miles?'

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The following factors work to reduce conflict and promote positive interaction between grieving couples who have lost a child by death is open and honest communication, expressing emotions in each other's company, and the ability of partners to reframe each other's behavior in a positive way. The correct option is B. 1, 2, and 4

When grieving couples lose a child due to death, it can lead to tension in their relationship, leading to conflicts between the couple. However, some factors work to reduce conflicts and promote positive interaction between grieving couples who have lost a child by death.

These factors include the following:

:Open and honest communication: Open communication is essential when it comes to expressing emotions, needs, and expectations from one another. It helps to build understanding, trust, and positive interaction between the couples. Honest communication provides room for clarification and better comprehension of each other's feelings and needs

Reframing each other's behavior in a positive way helps to build a healthy relationship and reduce conflicts.Crying separately to minimize the open grief and pain: Crying separately does not help reduce conflicts between the couple as it promotes distance and an unhealthy way of dealing with grief. It is important to grieve together and find support from each other to heal and move forward.

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Answer:

18. x = 80°

19. y = 85°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

18.

x + x + 20 = 180

2x = 160

x = 80

Answer: x = 80°

y + y + 10 = 180

2y = 170

y = 85

Answer: y = 85°

Answer: x = 80°  and  y = 85°

Step-by-step explanation: In a cyclic quadrilateral, opposite angles add up to 180°.

x + (x + 20) = 180  and

y + (y + 10) = 180.

Solving for x

x + (x + 20) = 180

x + x + 20 = 180

2x = 180 - 20

2x = 160

2x/2 = 160/2

x = 80°

Solving for y

y + (y + 10) = 180

y + y + 10 = 180

2y = 180 - 10

2y = 170

2y/2 = 170/2

y = 85°

Answer:

length = 42 in , width = 14 in

Step-by-step explanation:

given the width is [tex]\frac{1}{3}[/tex] of the length , then

y - 4 = [tex]\frac{1}{3}[/tex] (2y + 6) ← multiply both sides by 3 to clear the fraction

3y - 12 = 2y + 6 ( subtract 2y from both sides )

y - 12 = 6 ( add 12 to both sides )

y = 18

then

length = 2y + 6 = 2(18) + 6 = 36 + 6 = 42 in

width = y - 4 = 18 - 4 = 14 in

According to the question, the exact value of side x in the Trina are  34.641016151377546in.

Value is an intangible concept that refers to the worth of something, whether it is tangible or intangible. It is based on the perceived benefits and costs associated with the thing in question. Value can be subjective, as different people may place different worth on the same item. Value can also be objective, as there may be a set market price for a certain item.

The exact value of side x in the triangle can be determined by using the law of sines. The law of sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all sides of a triangle.

Therefore, we can set up the following equation:

(20in/sin30°) = (x/sin60°)

Solving for x, we get:

x = 20in×(sin60°/sin30°)

x = 20in×(√(3)/1)

x = 20in×√(3)

x = 34.641016151377546in

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The exact value of side x in the Trina, according to the question, is 34.641016151377546in.

Where you cannot predict the value, you must be specific. An exact number is a value that can be determined with absolute precision. Counted quantities of objects or sure unit conversions are examples of exact numbers.

The term "approximate number" refers to a number that is close to the precise number, and there is always a difference among exact and approximate numbers. For instance, are exact integers because no approximation is required.

As a result, we can construct the following equation:

(20in/sin30°) = (x/sin60°)

Solving for x, we get:

x = 20in×(sin60°/sin30°)

Simplify the above equation,

x = 20in×(√(3)/1)

x = 20in×√(3)

The value of x is,

x = 34.641016151377546in

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The complete question is,

What is the exact value of side x in the Trina for below? 20in 30 degree and X? Determine the exact value of side x.

The number of feet of fabric will the individual need to make 11 blankets is 79.2 feet

To find out how many feet of fabric the individual will need to make 11 blankets, we can use the unitary method.

We know that the individual used 7.2 feet of fabric to make one blanket. So, to find out how much fabric is needed to make 11 blankets, we can set up a proportion

7.2 feet of fabric is needed for 1 blanket

x feet of fabric is needed for 11 blankets

We can solve for x by cross-multiplying and then dividing

7.2 × 11 = x

x = 79.2 feet

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Answer:

  a) 22e^-0.01t kilograms

  b) about 19.906 kilograms

Step-by-step explanation:

You want an equation for the amount of salt in a 15 kL brine tank initially containing 22 kg of salt if 150 L/min of the contents is replaced by pure water.

The quantity of salt s(t) in kilograms can be described by the differential equation ...

  s(0) = 22; s'(t) = -150/15000·s(t)

The solution can be found by separation of variables.

  [tex]\displaystyle\dfrac{ds}{dt}=-0.01s\\\\\int{\dfrac{1}{s}}\,ds=-0.01\int{}\,dt\\\\\ln{s}=-0.01t+c_1\\\\s=c_2\cdot e^{-0.01t}\qquad\text{where $c_2$ is $s(0)=22$}\\\\\boxed{s(t)=22e^{-0.01t}}[/tex]

The amount of salt remaining after 10 minutes is ...

  s(10) = 22·e^(-0.01·10) = 22·e^-0.1

  s(10) ≈ 19.906 . . . . kilograms

There is about 19.906 kg of salt in the tank after 10 minutes.

__

Additional comment

The initial rate of change of the amount of salt is -22/100 kg/min, so after 10 minutes, we expect an approximate reduction by 2.2 kg to 19.8 kg. Since the rate slows as salt is removed, the value 19.9 kg after 10 minutes is reasonable.

There are a couple of places where the integration constant can be put in the equation for the salt quantity. As a multiplier of the exponential function, its value is found in a straightforward way.

Answer: 1/3

Step-by-step explanation:

4 + 8 = 12 so there's 12 marble in the bag and only 4 purple ones. so the probability is 4/12 which we can simplify to 1/3

The value of the sides and angle are;

a = 35. 58

c = 35. 93

x = 8 degrees

It is important to note the different trigonometric identities and their ratios.

They are represented as;

tan θ = opposite/adjacent

cos θ = adjacent/hypotenuse

sin θ = opposite/hypotenuse

From the diagram given, we have;

tan 82 = a/5

cross multiply the values

a = 7.1153(5)

a = 35. 58

Using the Pythagorean theorem;

c² = 35. 8² + 5 ²

Find the values

c² = 1265. 93 + 25

c = 35. 93

The sum of angles in a triangle is 180

90 + 82 + x = 180

x = 180 - 172

x = 8 degrees

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a. (x + 6)(x + 6) expands and simplifies to x² + 12x + 36.

b. (x + 8)(x - 5) expands and simplifies to x² + 3x - 40.

c. (x - 5)(x - 2) expands and simplifies to x² - 7x + 10.

Expansion and simplification are two related processes in algebra that involve manipulating mathematical expressions. Expansion involves multiplying out the terms in an expression to get a longer form, while simplification involves reducing an expression to a shorter, more manageable form.

In the given question,

a.To expand and simplify (x + 6)(x + 6), we can use the distributive property as follows:

(x + 6)(x + 6) = x(x + 6) + 6(x + 6)= x² + 6x + 6x + 36= x² + 12x + 36.

b.To expand and simplify (x + 8)(x - 5), we can use the distributive property as follows:

(x + 8)(x - 5) = x(x - 5) + 8(x - 5)= x² - 5x + 8x - 40= x²+ 3x - 40

Therefore, (x + 8)(x - 5) expands and simplifies to x²+ 3x - 40.

c.To expand and simplify (x - 5)(x - 2), we can use the distributive property as follows:

(x - 5)(x - 2) = x(x - 2) - 5(x - 2)= x² - 2x - 5x + 10= x²- 7x + 10

Therefore, (x - 5)(x - 2) expands and simplifies to x² - 7x + 10.

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Answer:

X= 567890

Step-by-step explanation:

Answer:

See below, please.

Step-by-step explanation:

Using the zero product property, we can set each factor equal to zero and solve for x:

(x² - 9)(x + 4) = 0

(x² - 9) = 0 or (x + 4) = 0

For the first factor, we can factor it further as the difference of squares:

(x + 3)(x - 3) = 0

So, either (x + 3) = 0 or (x - 3) = 0, giving us:

x = -3, x = 3, or x = -4

Therefore, the values of x for which (x² - 9)(x + 4) = 0 are -3, 3, and -4.

Answer: I believe the answer is 7

Step-by-step explanation:

To solve this I just divided 56 by 8, the answer then is 7. Hope this helps!!!

The slope of the line of best fit in the scatterplot below can be determined using the formula for the slope of a line:
Slope = (y2-y1)/(x2-x1)

In this case, x1 = 3, y1 = 12, x2 = 6, y2 = 19. So, the slope of the line of best fit is (19 - 12) / (6 - 3), which equals 7/3 or 2.33.
The line of best fit is the line that best represents the data on a scatterplot. It is the line that is closest to all the data points in the graph. The slope of the line of best fit helps to indicate whether the data points are moving in a positive or negative direction. If the slope is positive, the data points are increasing, and if the slope is negative, the data points are decreasing.
A positive slope, like the one in this example, means that as x increases, y also increases. This means that in this case, as the x-values (3 and 6) increase, the y-values (12 and 19) also increase.

The slope of the line of best fit can also be used to make predictions about values of y, given values of x. For example, if x = 8, then y = 26, because the slope of the line of best fit is 2.33, and 8*2.33 = 19.8, which is approximately equal to 26.
Overall, the slope of the line of best fit on this scatterplot is 2.33, which is a positive number. This indicates that as the x-values increase, the y-values also increase, and it can also be used to make predictions about y-values, given x-values.

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it might be 12

this is because there are6 pairs and 2 pairs

2×6=12

Answer:24

Step-by-step explanation: 6 times 2 = 12 times 2= 24

Karla's three brothers can buy a maximum of 4 pieces of candy if they divide the money evenly.

What is division?

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. Division is denoted by the symbol "÷" or "/", and it is usually expressed as a fraction or a quotient.

To solve this problem, we need to determine the amount of money represented by the shaded region. Here are the steps:

Assuming that each small square represents $0.01 and there are 143 shaded cells, the total amount of money represented by the shaded region is:

143 cells x $0.01/cell = $1.43

Now, we need to divide $1.43 evenly among Karla's three brothers to find the maximum number of pieces of candy each brother can buy.

$1.43 ÷ 3 = $0.476666...

Since we cannot buy fractional pieces of candy, we need to round down to the nearest whole number. Therefore, each of Karla's three brothers can buy a maximum of:

$0.47 ÷ $0.10/piece = 4 pieces of candy

So each of Karla's three brothers can buy a maximum of 4 pieces of candy if they divide the money evenly.

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we need to buy at least 694 tickets to have a probability of winning at least 50%.

We can use the binomial distribution formula to solve this problem. Let X be the number of tickets we need to buy to have a probability of winning at least 50%. Then:

P(X ≥ 1) ≥ 0.5

This means that the probability of winning with at least one ticket is at least 50%. We can find this probability using the complement rule:

P(X ≥ 1) = 1 - P(X = 0)

The probability of not winning with any ticket is:

P(X = 0) = (999/1000)^n

where n is the number of tickets we buy. Therefore:

1 - (999/1000)^n ≥ 0.5

Simplifying this inequality, we get:

(999/1000)^n ≤ 0.5

Taking the logarithm of both sides, we get:

n log(999/1000) ≤ log(0.5)

n ≥ log(0.5) / log(999/1000)

n ≥ 693.15

Therefore, we need to buy at least 694 tickets to have a probability of winning at least 50%.

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Therefore, the area that the carpet needs to cover is: LW - 18 square feet.

Area is a mathematical term that refers to the amount of space occupied by a two-dimensional object or shape. It is typically measured in square units such as square feet, square meters, or square inches.

Here,

If the tiled floor is excluded from the area that needs to be covered by the carpet, then we need to find the area of the living room without the tiled floor and add the tiled floor's area to it.

Let's assume that the living room is a rectangular shape with length L and width W.

The area of the living room without the tiled floor is:

Area = L x W - (6 x 3) (since the tiled floor has an area of 6 ft x 3 ft)

Area = LW - 18 square feet

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The statement "we have data that is a continuous variable. it is a measurement of time between events. this is a situation where we should evaluate a histogram for a likely exponential distribution" is true because when dealing with continuous data representing time between events, it is common to evaluate a histogram to determine if it follows an exponential distribution.

If the data represents the time between events and it is a continuous variable, it is common to evaluate the histogram to see if it follows an exponential distribution. The exponential distribution is often used to model the waiting time between independent events that occur at a constant average rate, and it has a continuous range of values that can be plotted as a histogram.

To evaluate whether the data follows an exponential distribution, you can plot a histogram and visually check if it has a single peak and a decreasing tail, which are characteristic of the exponential distribution. You can also use statistical tests such as the Kolmogorov-Smirnov test or the Anderson-Darling test to assess the goodness-of-fit between the data and the exponential distribution.

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To create an 80% alcohol solution, the pharmacist must therefore mix 2.17 cm3 of pure alcohol with 10 cm3 of the 8% alcohol solution.

A value or combination of values that satisfy an equation or system of equations are referred to as solutions in mathematics. For instance, if we substitute x = 2 into the equation, we get 2(2) + 3 = 7, which is a true statement, hence the answer to the equation 2x + 3 = 7 is x = 2. Similar to this, an equation system may have one or more solutions that simultaneously fulfil every equation in the system. Finding answers to equations or systems of equations is a key component of many branches of mathematics and has significant applications.

given

Find out how much pure alcohol is now contained in the 8% solution to start.

An 8% alcohol solution in 10 cm3 contains:

There are 0.8 cm3 of pure alcohol in 0.08 x 10 cm3.

Let's now calculate the amount of pure alcohol that has to be added to achieve an 80% solution using the alligation method.

We must add pure alcohol to the solution to raise the concentration from 8% to 100%. In order to connect 100% to 8% in the left column, we place 100% in the right column. There is a 92% discrepancy between these two percentages.

We put 80% in the middle column because we aim to arrive at an 80% solution. Between 80% and 100%, there is a 20% difference.

Now, we may construct the subsequent equation:

20/92 = x/10

After finding x, we obtain:

[tex]x = 2.17 cm^3[/tex]

To create an 80% alcohol solution, the pharmacist must therefore mix 2.17 cm3 of pure alcohol with 10 cm3 of the 8% alcohol solution.

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Answer:

Step-by-step explanation:

E

Answer:

To create a line plot for this data, we can first convert all the fractions to a common denominator, such as eighths:

Monday: 6/8 of an hour

Wednesday: 4/8 of an hour

Friday: 2/8 of an hour

Sunday: 4/8 of an hour

Then, we can draw a number line with tick marks representing each day of the week and plot a dot for each amount of time spent working out:

0         1         2         3         4

|---------|---------|---------|---------|   <- Number line

         .     .

       .             .

   .                     .

.                             .

To find out how much time June should work out each day to spend an even amount of time working out, we can first find the total amount of time she spent working out:

6/8 + 4/8 + 2/8 + 4/8 = 16/8 = 2 hours

Since there are four days she worked out, to find out how much time she should work out each day, we can divide the total time by four:

2 hours ÷ 4 = 0.5 hours

Therefore, June should work out for 0.5 hours, or 30 minutes, each day to spend an even amount of time working out.

The other diagonal of the rhombus is 4 cm.

The other diagonal of the rhombus can be found using the formula for the area of a rhombus, which is A = (d₁ × d₂)/2, where d₁ and d₂ are the lengths of the diagonals.

We're given that the area of the rhombus is 20 cm² and that one diagonal (d1) is 10 cm. Plugging these values into the formula, we get:

20 = (10 × d₂)/2

Simplifying, we get:

20 = 5 d₂

Dividing both sides by 5, we get:

d₂ = 4

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This can be calculated by multiplying the number of tickets sold by their respective prices: 200 x $35 = $7,000 and 50 x $40 = $2,375.

The local theater fundraiser sold 200 pre-event tickets at $35 each and 50 at-the-door tickets at $40 each to generate a total revenue of $9,375. This can be calculated by multiplying the number of tickets sold by their respective prices: 200 x $35 = $7,000 and 50 x $40 = $2,375.

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There was this one person that said, 'hey how old are you?' of course I lied. then another asking me to change my profile to something inappropriate.

The smallest font size that Doug should use in the text on his slides is 24 points.

The reason for this is that smaller font sizes can make the text difficult to read, especially from a distance.

According to industry standards, the recommended minimum font size for slide presentations is 24 points.

This is because smaller font sizes can be challenging to read, especially if the audience is sitting at the back of the room or if the slides are being viewed on a small screen.

While 20 points may seem like a reasonable font size, it's still small enough to make it difficult for some people to read the text.

Therefore, to ensure that all members of the audience can read the text on the slides, it's best to use a font size of at least 24 points.

In addition to using a larger font size, it's also essential to use a clear and legible font.

Sans-serif fonts such as Arial, Helvetica, or Calibri are recommended for presentations as they are easy to read, even from a distance.

It's also important to keep the contrast between the text and the background high to make it easier to read the text.

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Answer:

-407/42

Step-by-step explanation:

-8 6/7 - 5/6

-8 6/7 = -62/7

-62/7 - 5/6

= -372/42 - 35/42

= -407/42

Answer:

The Factor Theorem and Synthetic Division are not the same. The Factor Theorem states that if a polynomial f(x) has a root c, then x - c is a factor of f(x). Synthetic Division is a way of dividing a polynomial by a binomial.

Step-by-step explanation:

To use Synthetic Division, you first need to find the coefficients of the polynomial. Then, you set up the synthetic division table with the binomial on top and the coefficients of the polynomial on the bottom. Starting with the first coefficient, you multiply it by the first term of the binomial and write the product below the coefficient. Then, you add the two numbers below the product and write the sum below that. Continue until you reach the end of the binomial. The remainder at the bottom of the table is the remainder when f(x) is divided by x - c.

If the remainder is 0, then x - c is a factor of f(x).

The probability that no student will withdraw from the course is approximately 0.008 or 0.8%, assuming a binomial distribution with n=90 and p=0.05.

Since each student's decision to withdraw or not is independent of others, we can model the number of students who withdraw as a binomial random variable with n=90 and p=0.05.

To find the probability that no student will withdraw from the course, we want to find P(X=0), where X is the number of students who withdraw. This is given by the binomial probability mass function:

P(X=0) = (n choose 0) * p^0 * (1-p)^(n-0) = (90 choose 0) * 0.05^0 * 0.95^90

Using a calculator or software, we find:

P(X=0) ≈ 0.008

Therefore, the probability that no student will withdraw from the course is approximately 0.008 or 0.8%.

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