Solve the equation: 3(x−3) + 2x= −49

A.) x= - 8
B.) x = - 2
C.) x = - 40
D.) x= - 50/3

Evaluating  f(3) and f(3.1) is  is approximately -2.1.

To evaluate f(3), we substitute x = 3 into the given function:

f(3) = 3(4 - 3) = 3

To evaluate f(3.1), we substitute x = 3.1 into the function:

f(3.1) = 3.1(4 - 3.1) = 3.1(0.9) = 2.79

To approximate f'(3), we can use the difference quotient formula:

f'(3) ≈ [f(3.1) - f(3)] / [3.1 - 3]

Substituting the values we calculated:

f'(3) ≈ (2.79 - 3) / (3.1 - 3)

     ≈ (-0.21) / (0.1)

     ≈ -2.1

Therefore, f'(3) is approximately -2.1.

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Answer: 7.7 miles

Step-by-step explanation:

2.5x + 5.75 = 25 (x = each mile traveled)

2.5x = 25 - 5.75

2.5x = 19.25

x = 7.7 miles

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:

4

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

To graph y = x² + 4x + 6 with 5+ points using an x/y chart, follow these steps:

Step 1: Create an x/y chart with five rows and two columns. Label the first column x and the second column y.

Step 2: Choose five values for x. You can choose any values you want as long as you plug them into the equation in the next step. In this example, we will use -3, -2, -1, 0, and 1. Write these values in the first column of your chart.

Step 3: Plug each value of x into the equation y = x² + 4x + 6 to find the corresponding value of y. Write these values in the second column of your chart. To make it simpler, here are the calculations for each point:When x = -3: y = (-3)² + 4(-3) + 6 = 3When x = -2: y = (-2)² + 4(-2) + 6 = 2When x = -1: y = (-1)² + 4(-1) + 6 = 1When x = 0: y = (0)² + 4(0) + 6 = 6When x = 1: y = (1)² + 4(1) + 6 = 11

Step 4: Plot each point on the x/y chart. The x value goes on the horizontal axis (x-axis) and the y value goes on the vertical axis (y-axis). Once you have plotted all five points, connect them with a smooth curve to create the graph of y = x² + 4x + 6. The graph is shown in the figure below.

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Answer:

3

Step-by-step explanation:

factors of 12: 1, 2, 3, 4, 6 and 12

factors of 27: 1, 3, 9, and 27

hope it helps :)

Answer:

D

Step-by-step explanation:

By looking at this scatter plot we can see that the points generally go down when looking at the graph from left to right.

This somewhat straight line that is created is going in a negative direction.

That means that it is not only a linear finction, but is also negative.

The boundary line of the inequality y < (1/3)x + 1 is the equation y = (1/3)x + 1 with a dashed line because the inequality does not include the line itself.

To graph this line, we can start by plotting the y-intercept, which is the point (0, 1). From there, we can use the slope of 1/3 to find additional points on the line. For example, if we move 3 units to the right (increasing x by 3), we move up 1 unit (increasing y by 1), so we can plot the point (3, 2). Similarly, if we move 3 units to the left (decreasing x by 3), we move down 1 unit (decreasing y by 1), so we can plot the point (-3, 0).

Using these points, we can draw a dashed line through them to represent the boundary line of the inequality:

      |

   3  |         *

       |      *    

   2  |   *

       |*      

   1  |  

       |

   0  | *    

       |

       ---------------

          -3   0   3   6   x

The correct graph showing the boundary line of y < (1/3)x + 1 is the one with a dashed line passing through the points (0, 1), (3, 2), and (-3, 0), as shown above.

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Answer:

postulates, common notions, and axioms

The equation which will determine the number of pennies after the nth day will be an= 10+(n-1)2, since the situation is an arithmetic progression.

A series of numbers known as an arithmetic progression or arithmetic sequence (AP) has a constant difference between each subsequent term and its predecessor. The common difference of that arithmetic development is the constant difference.

The term "finite arithmetic progression" or "arithmetic progression" refers to a limited segment of an arithmetic progression. An arithmetic series is the total of a finite math progression.

The total of all the words in a sequence can be used to very broadly define a series. All of the words in the sequence must, however, clearly relate to one another.

In this question,

Since Sam received 10 pennies,

a₁= 10

Everyday he receives 2 pennies,

d=2

As the common difference is the same throughout, it is an arithmetic progression. Therefore, the nth term will be,

aₙ= a₁+(n=1)d

Substituting the values, we get

aₙ= 10+(n-1)2

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The 10,000 seconds can be stated as 166.6777 minutes and 2.7778 hour.

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

We have 10,000 sec

As, 1 minute= 60 seconds

So, In minutes

= 10000/60

= 1000/6

= 166.6667 minutes

Now, 1 hour= 60 minutes

So, In hour

= 10000/ 60 x 60

= 10000/3600

= 2.7778 hour

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The given statement is True.

What is developing logarithms?

The emergence of logarithms was predicted by comparing arithmetic and geometric series.

True. John Napier is credited with developing logarithms and Henry Briggs is known for working with Napier to advance the concept and promote its use.

Together, they created the logarithmic tables that became a powerful tool in mathematics and science.

Therefore, The given statement is True.

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Answer:

well it depends on how many collars you have, and if there is an image you should attach it to the question

A decrease in the price of potato chips, a substitute good, will have the following effect on the market for pretzels, assuming it is initially in equilibrium:

1. Increase in Quantity Demanded: The decrease in the price of potato chips will make them relatively cheaper compared to pretzels. As a result, some consumers who previously purchased pretzels may switch to buying potato chips instead. This will lead to an increase in the quantity demanded for potato chips.

2. Decrease in Quantity Supplied: With an increase in the quantity demanded of potato chips, some potato chip producers may shift their resources towards meeting the higher demand. This can result in a decrease in the quantity supplied of pretzels as resources are diverted away from their production.

3. Decrease in Price of Pretzels: Due to the decrease in quantity supplied, the supply of pretzels will be reduced. As a result, the equilibrium price of pretzels may increase as consumers compete for the limited supply.

4. Potential Increase in Demand for Pretzels: While the decrease in the price of potato chips may lead some consumers to switch to potato chips, there may also be consumers who view pretzels as a complementary good to potato chips. These consumers may increase their demand for pretzels due to the lower price of potato chips.

Overall, the effect of a decrease in the price of potato chips on the market for pretzels is likely to result in a decrease in the quantity supplied of pretzels, a potential increase in the demand for pretzels, and a possible increase in the equilibrium price of pretzels.

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Answer: x=4

Step-by-step explanation:

G(4) = 4x4 +3

G(4) = 16 + 3

G(4) = 19

The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 g/dL is approximately 0.455 or 45.5%.

To determine the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11, we would need specific information regarding the distribution of hemoglobin levels for individuals in that age group. Without such data, it is not possible to provide an exact probability.

However, if we assume that the hemoglobin levels follow a normal distribution, we can make some general calculations based on mean and standard deviation assumptions. Let's suppose that the mean hemoglobin level for individuals older than 35 is 10 g/dL, and the standard deviation is 1.5 g/dL. Again, note that these values are hypothetical and used for illustrative purposes.

To find the probability, we can calculate the z-scores for the lower and upper limits of the desired range (9 and 11, respectively) using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

For 9 g/dL:

z1 = (9 - 10) / 1.5 = -0.67

For 11 g/dL:

z2 = (11 - 10) / 1.5 = 0.67

Next, we can use a standard normal distribution table or a calculator to find the area under the curve between these z-scores. This area represents the probability of a person's hemoglobin level being between 9 and 11.

Suppose we find that the area under the curve is approximately 0.455 (45.5%).

Therefore, based on these assumptions, the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 g/dL is approximately 0.455 or 45.5%.

It's important to note that this probability calculation is based on hypothetical assumptions and may not accurately reflect the true distribution and statistics of hemoglobin levels for individuals older than 35. For precise probabilities, specific data and statistical analysis should be considered.

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Step-by-step explanation:

10x+1=12x-5

1+5=12x-10x

6=2x

6/2=2x/2

3=x

Answer:

1)Yes

2)No

Step-by-step explanation:

1) 3x^2 = -27

3 (-3)^2 = -27

Once you substitute your value in for x, you can follow the rule PEMDAS to solve the equation.

3 (-9) = -27

-27 =-27

2) 10 - 5x = y

In an ordered pair, the first number is x and the second number is y.

10 - 5 (-4) = 10

10 - 20 = 10

-10 = 10

-10 ≠ 10

PEMDAS: A rule that states solving an equation by the order of operations:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Answer: x= 0

Step-by-step explanation:

5x + 4 = 2(x + 2)       First distribute on the right side  of the equation

5x + 4 = 2x + 4         Subtract 2x from both sides

-2x          -2x

     3x + 4  =  4        Subtract 4 from both sides

          -4         -4

    3x = 0      Divide both side by 3

     x = 0

(a) Using the given data, we can verify the calculations as follows: ∑x = 245, ∑x^2 = 14,755, ∑y = 224.

(b) To compute the sample mean, variance, and standard deviation for the percentage success of mallard duck nests (x), we use the formulas:

Sample Mean (x) = ∑x / n

Variance (s^2) = (∑x^2 - (n * x^2)) / (n - 1)

Standard Deviation (s) = √(s^2)

(c) Applying the formulas, we can compute the sample mean, variance, and standard deviation for x as follows:

Sample Mean (x) = 245 / 5 = 49

Variance (s^2) = (14,755 - (5 * 49^2)) / (5 - 1) = 4,285

Standard Deviation (s) = √(4,285) ≈ 65.5

Similarly, for the percentage success of Canada goose nests (y), the calculations can be done using the same formulas and the given values from part (a).

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Answer:

i) ABCDEF has an area of 98m

ii) Flower bed has an area of 6m

iii) The area of the grass is 92m

Hope this helps!

Step-by-step explanation:

The area of a triangle is  \(\frac{1}{2}\) × L × H

The area for the triangle flower bed will be \(\frac{1}{2}\) × 6m × 2m or 6m.

In order to find the entire area of ABCDEF, draw a segment FC to create a trapezoid and a rectangle. The rectangle has an area of 77m ( 7 × 11 ). The trapezoid has a formula of \(\frac{1}{2}\) × ( b + b ) × h, this would be \(\frac{1}{2}\) × ( 10 + 11 ) × 2.

The trapezoid has an area of 21, this added to the rectangle's area of 77 equals 98m as the total area of the garden.

Subtract the area of the flower bed ( 6 ) from the area of the garden, and you get an area of 92m. This is the area of grass.

Answer:

6 is the largest -7 is the smallest

Step-by-step explanation:

An equation in slope-intercept form for the line of best fit is y = -0.29x + 80.43.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (5, 79), an equation of this line in slope-intercept form can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 79 = (77 - 79)/(12 - 5)(x - 5)

y - 79 = -2/7(x - 5)

y = -2x/7 + 10/7 + 79

y = -0.29x + 80.43

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Answer:

<1+<2+<4+57=123

<6=123-57

<6=66

<1=66÷6

ans:<1=11

Answer:

Bus 18 is more consistent than Bus 47 based on the IQR, which is smaller for Bus 18 (16) compared to Bus 47 (24), indicating less spread of data between the 25th and 75th percentiles.

Step-by-step explanation:

Answer: The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

How to obtain the measures of spread?

First, we consider the dot plot, which shows the number of times that each observation appears in the data set.

Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data set.

The interquartile range is a better measure of spread compared to the range of a data set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Step-by-step explanation:

Interference is a property of ALL the given wave options, which are light waves, sound waves, and water waves.

Interference is the phenomenon of two or more waves combining to form a resultant wave of greater, lower, or the same amplitude.

When two waves meet at the same point at the same time, they either combine constructively (resulting in the formation of a wave of greater amplitude) or destructively (resulting in the formation of a wave of lower amplitude).

For instance, when two sound waves or light waves meet, they create a resultant wave whose amplitude is equal to the sum of the two original waves.

This is known as constructive interference.

On the other hand, when two waves meet and their amplitudes are in opposite directions, they produce a resultant wave whose amplitude is equal to the difference between the two waves.

This is known as destructive interference.

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The  major disadvantage of crude rates is that option (a) they do not permit comparison of populations that vary in composition

Crude rates are a simple method for calculating the frequency of an event or condition in a population, usually expressed as a rate per a specific population size or time period. However, they have a major limitation in that they do not account for differences in population characteristics or composition, such as age, sex, or socioeconomic status.

This means that crude rates may not accurately reflect the true differences in the occurrence of the event or condition between different populations. To overcome this limitation, age-standardized rates or other adjusted measures can be used to compare populations with different compositions.

Therefore, the correct option is (a) they do not permit comparison of populations that vary in composition

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