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The equation of the line y = 3x + 10 in standard form is 3x - y = -10.

Given the equation of line in the question:

y = 3x + 10

To write the equation of the line in standard form, we need to rearrange the equation so that the x and y terms are on the left side and the constant term is on the right side of the equation.

It is expressed as;

Ax + Bx = C

y = 3x + 10

Subtracting 3x from both sides, we get:

y - 3x = 3x - 3x + 10

y - 3x = 10

Reorder

-3x + y = 10

Multiply each term by -1

-3x(-1) + y(-1) = 10(-1)

3x - y = -10

Therefore, the equation in standard form is 3x - y = -10.

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there are 6 red counters, 24 blue counters, and 5 green counters in the bag, based on the given information.  The given information provides us with the ratio of red to blue counters in a bag, which is 2:5. This means that for every 2 red counters in the bag, there are 5 blue counters.

Let the number of red counters in the bag be 2x, where x is a constant. Then, the number of blue counters in the bag is 5x. We are also given that there are 9 more blue counters than before, so the new number of blue counters is 5x + 9.

We know that there are 35 counters in total, so we can write an equation based on this information:

2x + 5x + 5x + 9 = 35

Simplifying this equation, we get:

12x + 9 = 35

Subtracting 9 from both sides, we get:

12x = 26

Dividing both sides by 12, we get:

x = 2.1667

Since we cannot have a fraction of a counter, we can round x up to 3.

Therefore, the number of red counters in the bag is 2x = 2(3) = 6, and the number of blue counters in the bag is 5x + 9 = 5(3) + 9 = 24.

Finally, we can find the number of green counters in the bag by subtracting the number of red and blue counters from the total number of counters:

35 - 6 - 24 = 5

So there are 5 green counters in the bag.

In summary, there are 6 red counters, 24 blue counters, and 5 green counters in the bag, based on the given information.

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Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle and π is a mathematical constant approximately equal to 3.14159.

In this case, the diameter of the circle is 58, so we can substitute this value into the formula:

C = πd

C = π(58)

C ≈ 182.09

Therefore, the circumference of the circle with diameter 58 is approximately 182.09 units. Note that the units of measurement were not specified in the question, so the units of the answer will depend on the units used for the diameter.

We can ensure trigonometric functions compute values appropriately by validating the results against known values. In order to ensure that the argument is in a short interval surrounding a place where an approximation is highly accurate, one performs a range reduction prior to computing things like a cos or sin.

By comparing the results to established values, we can make sure trigonometric functions compute values correctly. As an example, if we wanted to validate the cosine of 45 degrees, we could compare the result to the known value of 0.707. If the computed value is within a small margin of error of the known value, then we can assume the trigonometric function is computing values appropriately.

In order to calculate functions like cos or sin, one must first perform a range reduction to make sure the input is inside a narrow range surrounding a point where an approximation is highly accurate. It is typically close to zero.

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A human organism developing in the uterus from the ninth week until birth is called a(n) fetus.

A fetus is the term used to describe a human organism that is developing in the uterus from the ninth week of gestation until birth. During this time, the fetus undergoes significant growth and development, as all of the major organs and body systems are formed and begin to function.

The ninth week of gestation is considered a significant milestone in fetal development, as most of the critical stages of organogenesis have been completed by this time. From this point onward, the fetus primarily grows and matures in preparation for life outside of the womb.

During the remaining weeks of gestation, the fetus undergoes a number of important developmental processes, including continued brain development, growth of the nervous system, and development of the lungs and other vital organs. At the same time, the fetus also gains weight and size, and begins to develop a layer of fat that will help to regulate body temperature after birth.

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Answer:

eqn of line : x-3y=15

slope1=m= -coefficient of x/coefficient of y=1/3

As lines are parallel slope must be equal.

slope3=m'=1/3

passing points of second line =(0,7)

eqn of line = (y-y')=m(x-x')

=(y-7)=1/3(x-0)

=y-7=1/3x

=1/3x-y+7=0

=x-3y+21=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the benchmarks between which 3/8 falls, we need to identify the nearest fractions with denominators that are multiples of 8.

The fraction 3/8 is halfway between 1/4 and 1/2, which can be written as 2/8 and 4/8 respectively. So, we know that 3/8 is greater than 2/8 and less than 4/8.

Therefore, the benchmarks between which 3/8 falls are 2/8 and 4/8. Alternatively, we can express these fractions as decimals and say that 3/8 falls between 0.25 and 0.5.

Answer:

1+2=90° .so complementary angle

Answer:

≈283,39 mm^2

Step-by-step explanation:

The diameter is 19 mm, so the radius is half diameter (9,5 mm)

[tex]a = \pi \times {r}^{2} = 3.14 \times {9.5}^{2} = 3.14 \times 90.25 ≈ 283.39[/tex]

d. Reflect across the x-axis and translate up 4 and right 3, this transforms the pre-image to the composite image.

What is composite image?

A composite image is the result of applying multiple transformations to a given pre-image. It is formed by first applying one transformation to the pre-image and then applying another transformation to the resulting image, and so on.  The final result is the composite image.

Let's analyze the given options:

a. Reflect across the y-axis and translate 4 down and three left.

This transformation would reflect the pre-image across the y-axis, which would change the signs of the x-coordinates, and then translate it 4 units down and 3 units left. However, this transformation would not result in the composite image provided.

b. Rotate 180° and reflect across the x-axis.

This transformation would rotate the pre-image 180 degrees counterclockwise around the origin, which would change the signs of both the x and y-coordinates, and then reflect it across the x-axis. This transformation would not result in the composite image provided.

c. Rotate 90° and translate 4 up and 3 right.

This transformation would rotate the pre-image 90 degrees counterclockwise around the origin, which would swap the x and y-coordinates and negate the new x-coordinate, and then translate it 4 units up and 3 units right. This transformation would not result in the composite image provided.

d. Reflect across the x-axis and translate up 4 and right 3.

This transformation would reflect the pre-image across the x-axis, which would change the signs of the y-coordinates, and then translate it 4 units up and 3 units right. This transformation would result in the composite image provided.

Therefore, the correct answer is d. Reflect across the x-axis and translate up 4 and right 3.

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Answer:

Step-by-step explanation:

Credits : sqdancefan (Brainly.com)

I changed some of it myself  :)

Answer:

A) intercept: 0 profit : Maximum(max) : max profit. increasing x <4 ; decreasing x > 4

B) average slope: ≈50, about $50 increasing profit for each $1 increasing in price.

Step-by-step explanation:

A) The vertical axis of the graph represents profit, so the x-intercepts represent prices in the produce 0 profit. The maximum value of the graph is the maximum profit that can be obtained for anyprice

The higher or largest number of the chart is the maximum reach

B) We read the value of f(1) from the graph to be about 120, so the average rate of change is about ...

(f(4) -f(1))/(4 -1) = (270 -120)/(3) = 50

The average rate of the change from x = 1 to x = 4 is about 50.* This means profit will increase on average $50 for each $1 increase in price in what interval.

______

* if we take the peak profit to be $270 we can write f(x) as ...

f(x) 16.875x(x-8)

Then f(1) = 118.15 ad average rate if changed is 50.625. For the purpose here, we judge the extra precision to be pointless

The triangle shown in the image above that has sides 8, 24, and 25 is a right triangle because it satisfies the Pythagorean theorem.

A triangle with sides 8, 24, 25 is a right triangle.

This is because the sides satisfy the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse).

In this case, we have:

8² + 24² = 64 + 576 = 640

25² = 625

Since 8² + 24² = 25², the triangle satisfies the Pythagorean theorem, and is therefore a right triangle.

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the expectation of buying one ticket is $2

Expectation if a person buys one ticket A person is interested in buying a ticket for a lottery that offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold at $3 each. The expected return is calculated using the following formula:

Expectation = (Probability of winning Prize 1 × Value of Prize 1) + (Probability of winning Prize 2 × Value of Prize 2) + (Probability of winning Prize 3 × Value of Prize 3)To determine the expectation, we must first determine the probability of winning each of the three prizes.

Since one thousand tickets are sold and only one person can win the first prize, the probability of winning the $1000 prize is 1/1000 or 0.001. Similarly, the probability of winning the $500 prize is 1/1000 or 0.001. Since five $100 prizes are available and only one person can win each prize, the probability of winning any one of the five $100 prizes is 5/1000 or 0.005.

Therefore, the expectation is calculated as follows: Expectation = (0.001 × $1000) + (0.001 × $500) + (0.005 × $100)Expectation = $1 + $0.50 + $0.50Expectation = $2Thus, the expectation of buying one ticket is $2. This means that the average value of a ticket is $2, and a person can expect to win $2 on average by purchasing a ticket. Since the cost of a ticket is $3, the expected return is less than the cost of the ticket, and therefore, it is not a good investment from a financial standpoint.

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The information indicates that the correct answer is 9.76% annually.

The area of mathematics that deals with the characteristics of surrounding space, spatial interactions between distinct objects, and the shape of particular items.

It would take 19 years between 1996 and 2015 in all.

We are aware that the equation: gives a geometric mean of a collection of n positive numbers.

GM =  [tex]((x1)(x2)(x3).............)^{1/n}[/tex]

This would provide us with the product of these values' nth roots.

Thus, the following would be the formula indicating rate of rise over time: -

GM =  [tex](value at the end of the period / value at the start of the period)^{1/n} -1[/tex]

[value at the end of the period / value at the start of the period

Value at the conclusion of the time is equal to 241,364,256, hence the statement stands.

The initial value was 40,257,000.

n = 19

Using values, we obtain:

=[tex](241,364,256/40,257,000)^{1/19} -1[/tex]

= (5.995)1/19 - 1

= 0.0976

= 9.76% per year

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The value of x using similar triangles theorem is = 13/3.

Triangles that resemble one another but may not be exactly the same size are said to be comparable triangles.

When two objects have the same shape but different sizes, they can be said to be comparable.

This indicates that comparable shapes superimpose one another when amplified or de-magnified.

The term "Similarity" refers to this characteristic of like shapes.

Now in the given figure,

the proportion of the triangles' side is same.

So, 12/4 = 13/x

x = 13/3

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According to the question this equation represents a single point in the xy-plane, and does not have a constant rate of change. It doesn't have a linear function as a result.

When the roots and solutions of two equations match, they are said to be equivalent. The same number, symbols, or expression must be added to or subtracted from both the equation's two sides to produce an equivalent equation. By multiplying or dividing both sides of an equation by a nonzero number, we can also obtain an analogous equation.

Equation representing a linear function:

Y is equivalent to x plus 5 times the negative one-fourth.

Linear functions have a constant rate of change, which means that as x increases or decreases by a certain amount, y also changes by a constant amount. The equation y equals negative one fourth times x plus 5 has a constant slope of negative one fourth, which means that for every increase of one in x, y will decrease by one fourth. This is a characteristic of a linear function.

The equation y equals two thirds times x squared represents a quadratic function, which has a curved graph.

The equation x = 5 is a linear equation, but it only represents a vertical line passing through x = 5. It does not have a slope or a y-intercept, which are necessary for a linear function.

The equation 2x + 7 = 12 can be simplified to a linear equation of the form y = mx + b by solving for y:

2x + 7 = 12

2x = 5

x = 5/2

Substituting x = 5/2 back into the equation gives:

y = 2(5/2) + 7 = 12

This equation represents a single point in the xy-plane, and does not have a constant rate of change. Therefore, it is not a linear function.

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Answer:

area=188

Step-by-step explanation:

12×14=168 for the area of the rectangle

2×10=20

20÷2=10 for the area of triangle

168+10+10=188

area=188

Answer:

Apparently it's 4800 according to desmos.

Step-by-step explanation:

Step-by-step explanation:

x y

-3 150

-2 300

-1 600

0 4800

As you can see, for negative values of x, the area burned becomes smaller and smaller as x becomes more negative. This is because the equation y = 4800(2)^x has a base of 2, which means that as x becomes more negative, 2^x becomes smaller and smaller, causing y to become smaller and smaller as well.

The probability that a librarian chooses a fiction book, then a nonfiction book, then a fiction book is approximately 0.305.

The solution to this problem is a probability calculation.

To calculate the probability of selecting a fiction book, then a nonfiction book, then a fiction book from a selection of 10 nonfiction books and eight fiction books, we need to use the multiplication rule of probability.

The multiplication rule states that the probability of two or more independent events happening together is equal to the product of their individual probabilities.

To apply this rule, we'll break down the question into three events:

Probability of choosing a fiction book = 8/18 = 4/9

Probability of choosing a nonfiction book (after selecting a fiction book) = 10/17

Probability of choosing a fiction book (after selecting a nonfiction book) = 8/16 = 1/2

Now we can use the multiplication rule:4/9 * 10/17 * 1/2 = 0.305 (rounded to three decimal places)

Therefore, the approximate probability that the librarian will choose a fiction book, then a nonfiction book, then a fiction book is 0.305.

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The given series diverges to negative infinity as the terms cancel out, leaving only two terms at the beginning and end of the series.

To determine the convergence of the given series, we can use the telescoping series method.

Let's write out a few terms of the series to see if we can spot a pattern:

n=1: 1/2 - 3/4 = -1/4

n=2: 2/3 - 4/5 = -2/15

n=3: 3/4 - 5/6 = -1/8

n=4: 4/5 - 6/7 = -2/35

...

We can see that the terms of the series cancel out, leaving only two terms at the beginning and end of the series. Therefore, we can write the series as:

∑ (n/n+1 - n+2/n+3) = 1/2 - (n+2)/(n+3)

As n approaches infinity, the second term approaches 1, so the series diverges to negative infinity.

Therefore, the given series diverges.

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_____The given question is incomplete, the complete question is given below:

Which of the series in exercises 17–56 converge, and which diverge? use any method, and give reasons for your answers

(∑ ∞ to n = 1) = (n/n+1 - n+2/n+3)

Clark completed a self-administered questionnaire, which is also known as an online survey.

This type of survey is administered online and is completed by the participant (in this case, Clark) without the assistance of a researcher or interviewer. It can be delivered through an online form or through an email or online survey link.

The questionnaire typically includes multiple-choice questions, short-answer questions, and rating scales that the participant can answer with a click or tap. After the participant completes the survey, their answers are collected and analyzed by the researcher. This type of survey is a cost-effective and convenient way to collect data from a large number of people in a short amount of time.

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The height of the trapezoid is 7 ft.

The formula for the area of a trapezoid is:

A = 1/2 * (a + b)h

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

Given A = 24.5 ft², a = 3 ft and b = 4 ft. We can solve for h. That is:

A = 1/2 * (a + b)h

24.5 = 1/2 * (3 + 4)h

24.5 = 1/2 * (7)h

24.5 = 3.5h

h = 24.5/3.5

h = 7 ft

Therefore, the height of the trapezoid is 7 ft.

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If Kelly is flying a kite to which the angle of elevation is 70 degrees. The string on the kite is 65 meters long. The kite is about 61 meters above the ground.

We can use trigonometry to solve the problem. Let's call the height of the kite above the ground "h".

Using trigonometry, we can write:

sin (70) = h / 65

Solving for h, we get:

h = 65 * sin(70)

h= 65 * 0.9397

h ≈ 61 meters

Therefore, the kite is about 61 meters above the ground.

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The expression that best represents the total cost of the charter bus for the field trip is 12n + 50

The total cost of the charter bus for the field trip consists of a $50 reservation fee and an additional $12 per student.

If n represents the number of students going on the field trip, then the expression for the total cost can be written as:

Total cost = 12n + 50

This expression represents the variable cost of the charter bus, which depends on the number of students going on the field trip.

The fixed cost of $50 is added to the variable cost to give the total cost.

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Cards are dealt from a standard shuffled deck of cards until the first ace is drawn. So the chance that the next card is a king is 0.05 percent.

            When drawing a card from a standard deck of 52 cards, the chance of drawing an ace is 4/52 or 1/13. After an ace has been drawn, there are 51 cards left in the deck, and 4 of them are kings.

           So, the probability of drawing an ace and then a king is

                     (1/13) × (4/51) = 4/663.

There are 4 different aces that could be drawn, each with the same probability of

                      (1/13) × (4/51) = 4/663,

So we multiply by 4 to account for all the possible aces that could be drawn.

Therefore, the total probability of drawing an ace and then a king is

                     (4/663) × 4 = 16/663.

         Once an ace has been drawn, there are 51 cards remaining in the deck, and only one of them is a king. Therefore, the probability of drawing a king after an ace has been drawn is 1/51.

         The probability that the next card is a king after the first ace is drawn is thus:

                    (16/663) × (1/51) = 16/33663

                                              = 1/2104.

      This simplifies to 0.0475 percent or approximately 0.05 percent.

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The range of scores is 0 to 10. Since everyone in the class scored 6 out of 10, the lowest possible score is 0 and the highest possible score is 10.

The range is the difference between the highest and the lowest of the  given scores. In this case, it's 4 (10-6).

Therefore, the range of scores is 0 to 10. It is important to note that the range is a measure of the spread of scores in a dataset, and in this case, the spread is from the lowest possible score of 0 to the highest possible score of 10.

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Step-by-step explanation:

(explanation is given in your another question please check)