Solve the inequality
- 7x<35
What are the solutions? Select the correct choice below and fill in the answer box to complete your
choice.
A. X > greater or equal to
B. X <
C. X < less than or equal to
D. X >

The equation of the line tangent to the function y = x^3 + 3x^2 + 2 at its point of inflection is: y = -3x - 6.

To find the equation of the line tangent to the function y = x^3 + 3x^2 + 2 at its point of inflection, we need to determine the derivative of the function and evaluate it at the point of inflection. First, let's find the derivative of y with respect to x: dy/dx = 3x^2 + 6x. The point of inflection occurs where the second derivative of the function changes sign. Taking the derivative of dy/dx, we have: d^2y/dx^2 = 6x + 6. Setting d^2y/dx^2 equal to zero and solving for x, we find: 6x + 6 = 0; x = -1.  At x = -1, the point of inflection is (-1, y) on the original function. To find the slope of the tangent line at this point, we substitute x = -1 into the derivative: dy/dx = 3(-1)^2 + 6(-1) = -3. So, the equation of the line tangent to the function at its point of inflection is: y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values, we have: y = -3x + b

To find b, we substitute the coordinates of the point of inflection (-1, y):y = -3(-1) + b; y = 3 + b. Since the point of inflection lies on the line, we can substitute the y-value and solve for b: 3 + b = x^3 + 3x^2 + 2; b = -6. Therefore, the equation of the line tangent to the function y = x^3 + 3x^2 + 2 at its point of inflection is: y = -3x - 6.

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Given that the second student chosen is a girl, the probability that both students are female is 0.175.

The occurrence of likely events is referred to as probability. It is the branch of mathematics concerned with numerical estimates of the likelihood of an event occurring or a statement being true.

Probability is nothing but likelihood of something is to occur. When we are unsure about the outcome of an event, we can discuss the probabilities of certain outcomes—how likely they are.

The probability of selecting a girl from the class is

\(= \frac{Number\ of\ girls}{ Total\ number\ of\ students}= \frac{14}{26}\\\\= \frac{7}{13}\)

It is known that the one of the chosen student from 2 students is girl, the probability of having both girls will be:

\(= \frac{7}{16} * \frac{6}{15}\\\\= 0.175\)

Hence, the probability is 0.175.

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Your question is incomplete, here is the complete question.

Your statistics class has 26 students in it - 14 girls and 12 boys.Your teacher uses a calculator to select two students at random to solve a problem on the board. Given that the second student chosen is a girl, what is the probability that the first student was also a girl?

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Cost of large candle (a) = 25 each

Cost of small candles (y) = 10 each

Amount needed = $600

Number of each that must be sold to raise needed amount:

25a + 10y = 600.

Here a = number of large candles that must be sold at the price

y = number of small candles that must be sold at the price

Summing the revenue both should result in the required amount.

Answer:

\(x=\pm\sqrt{26}\)

Step-by-step explanation:

\(ln(x^2-25)=0\)

\(e^{ln(x^2-25)}=e^0\)

\(x^2-25=1\)

\(x^2=26\)

\(x=\pm\sqrt{26}\)

The potential solutions of expression is,

⇒ x = ± √26

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ ln (x² - 25) = 0

Now, We can simplify the expression as;

⇒ ln (x² - 25) = 0

⇒ (x² - 25) = e⁰

⇒ (x² - 25) = 1

⇒ x² = 26

⇒ x = ± √26

Thus, The potential solutions of expression is,

⇒ x = ± √26

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The current cost of the hardcover dictionary is $304.62

Given,

The cost of a hardcover dictionary in 1983 = $145.75

The current CPI = 209

We have to find the current cost of hardcover dictionary;

CPI;- Consumer Price Index

The tool used to gauge inflation is the consumer price index (CPI). It is used to calculate the typical difference in pricing of household goods between two specified periods.

Here,

Current cost of hardcover dictionary = Cost in past x CPI/100

Current cost of hardcover dictionary = 145.75 x 209/100

Current cost of hardcover dictionary = 145.75 x 2.09

Current cost of hardcover dictionary = 304.6175

That is,

The current cost of the hardcover dictionary is $304.62

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Answer :pls delete my answer.

Answer: 3x(x-5) (x+5)

Step-by-step explanation Step 1: Factor out comon coeffecient factor. 3x3 (exponent) - 75x.- 3(x3 (exponent)-25x)

Step 2: Find One factor. 3x(x2(exponent)-25)

Step 3 an final step: Find One factor again. Factor by grouping, Factor by grouping again, Factor by grouping a third time. Edit: I hope this was helpful and I wish the best of luck to the person that asked this question and people that want to know this question.

Answer:

2 (w+i)

Step-by-step explanation:

Because 2xw and 2xi

I am pretty sure that is correct

Answer:  2 (w+i)

Step-by-step explanation:

The soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day for the soft drink vendor, we need to use the formula P(x) = 0.001x^2 + 3x + 1800, where x is the number of cans of soda pop sold in one day.

To find the maximum profit, we need to find the vertex of the parabola represented by the profit function. The x-coordinate of the vertex is given by -b/2a, where a = 0.001 and b = 3. Plugging in these values, we get x = -3/(2*0.001) = -1500.

Since the soft drink vendor cannot sell a negative number of cans, we know that the maximum profit occurs at the closest whole number to x = -1500, which is x = 1500.

To find the maximum profit per day, we can plug in x = 1500 into the profit function:

P(1500) = 0.001(1500)^2 + 3(1500) + 1800 = $5250

Therefore, the soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day and the number of cans needed to reach that profit, we'll first need to find the critical point of the given quadratic profit function, P(x) = -0.001x^2 + 3x - 1800.

Step 1: Find the derivative of P(x) with respect to x. This will give us the rate of change of profit as the number of cans sold changes.

P'(x) = -0.002x + 3

Step 2: Set the derivative equal to zero and solve for x. This will give us the critical point where the maximum profit occurs.

-0.002x + 3 = 0

x = 1500 cans

Step 3: Substitute the critical point (x = 1500) back into the profit function P(x) to find the maximum profit.

P(1500) = -0.001(1500)^2 + 3(1500) - 1800

P(1500) = $600

So, the maximum profit per day is $600, and the soft drink vendor must sell 1500 cans to reach the maximum profit.

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The maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

The profit function for the soft drink vendor is given by:

P(x) = \(0.001x^2 + 3x + 1800\)

To find the maximum profit, we need to find the vertex of the parabola represented by this function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

where a = 0.001 and b = 3. Substituting these values, we get:

x = -3 / (2 * 0.001) = -1500

Since the value of x cannot be negative in this context, we know that the maximum profit occurs at x = 1500. To find the maximum profit, we substitute this value of x into the profit function:

P(1500) =\(0.001(1500)^2 + 3(1500) + 1800 = $4800\)

Therefore, the maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

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Binomial Distribution:

Label "Binomial" is typed in cell C16 and "Distribution" in cell D16.

The values of n, p, and x are taken from cells F16, H16, and the desired cell, respectively.

The following probabilities are calculated:

o P(x = 21) = 0.0402

o P(x ≤ 16) = 0.0138

o P(x > 10) = 0.9983

o P(15 ≤ x ≤ 23) = 0.7063

o P(15 < x < 23) = 0.6359

Normal Distribution:

Label "Normal" is typed in cell C24 and "Distribution" in cell D24.

The values of mean and standard deviation are taken from cells F24 and H24, respectively.

The following probabilities are calculated:

o P(x < 80) = 0.8413

o P(x > 65) = 0.9332

o P(55 < x < 85) = 0.8664

o The values of x1 and x2 are calculated using the norm.inv function, with a probability of 0.05 in cell H29. The value of x1 is found to be 58.9293 and x2 is found to be 89.0707.

In part 2, the binomial distribution is used to find the probabilities of a local college basketball team winning certain number of games in a 30-game season. The probability of winning a single game is given, and the number of games won is treated as a discrete variable. The binom.dist function is used to calculate the probabilities.

In part 3, the normal distribution is used to find probabilities of scores on a national statistics exam. The mean and standard deviation of the exam scores are given, and the scores are treated as a continuous variable. The normal dist function is used to calculate probabilities of a score being below or above a certain value, or within a certain range. The norm.inv function is used to find the corresponding value of the score given a certain probability.

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Answer:

220%

Step-by-step explanation:

\(Percentage\ Increase/Decrease=\frac{Final\ Quantity\ - Initial\ Quantity}{Initial\ Quantity} *100\\Percentage\ Increase/Decrease=\frac{16-5}{5}*100\\=11*20\\=220\ \%\)

As Final quantity is larger than the Initial Quantity, the net percent is an increase.

The graphs that can be used here are Box plot, Histogram, Scatter plot and Bar chart.

What exactly is a box plot?

A box plot, also known as a box and whisker plot, is a graphical summary of a set of data through five statistics: the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value.

The box in the plot represents the interquartile range (IQR), which is the range between the first and third quartiles (Q1 and Q3). The median is shown by a line inside the box. The whiskers extend from the box to the smallest and largest data points that are within 1.5 times the IQR from the nearest quartile. Any data points that fall outside of the whiskers are shown as individual points or outliers.

Now,

To compare the range and shape of Jace's electric-vehicle data to gas-powered vehicle data, we can use the following data displays:

Box plots: We can create box plots for both sets of data to compare their ranges and shapes. The box plots can be arranged side-by-side for easy comparison.

Histograms: We can create histograms for both sets of data to compare their shapes. The histograms can be overlaid on top of each other for easy comparison.

Scatter plots: We can create a scatter plot with range on the x-axis and fuel efficiency on the y-axis for both sets of data. This will allow us to compare the ranges and shapes of both sets of data on a single graph.

Bar charts: We can create bar charts to compare the average range and fuel efficiency for both sets of data. The bar charts can be arranged side-by-side for easy comparison.

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To divide 3p2 + бр + 2 by Зp2, we can use long division.

First, we divide 3p2 by Зp2, which gives us 3p. We write 3p above the division sign and multiply 3p by Зp2, which gives us 3p3. We write 3p3 under the first term of the dividend (3p2) and subtract, which gives us:
       3p2 + бр + 2
   Зp2 | 3p2 + бр + 2
        - 3p3
Next, we bring down the next term of the dividend (бр), which gives us:
       3p2 + бр + 2
   Зp2 | 3p2 + бр + 2
        - 3p3
         -----
           бр + 2
We now repeat the process with бр + 2. We divide бр by Зp2, which gives us б/Зp, and write б/Зp above the division sign. We multiply б/Зp by Зp2, which gives us бp2, and write it under бр. We then subtract, which gives us:
       3p2 + бр + 2
   Зp2 | 3p2 + бр + 2
        - 3p3
         -----
           бр + 2
           б/Зp
         -----
            2p + 2
We bring down the last term of the dividend (2), which gives us:
       3p2 + бр + 2
   Зp2 | 3p2 + бр + 2
        - 3p3
         -----
           бр + 2
           б/Зp
         -----
            2p + 2
              2
         -----
              0
Since there is no remainder, the quotient is 3p + б/Зp + 2. We can write it as:
       3p2 + бр + 2
   Зp2 | 3p2 + бр + 2
        - 3p3
         -----
           бр + 2
           б/Зp
         -----
            2p + 2
              2
         -----
              0

So, 3p2 + бр + 2 divided by Зp2 is equal to 3p + б/Зp + 2.
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Answer:

first you do 11-3 to get 8. then you multiply 8 and 6 to get 48

Answer:

D.

Step-by-step explanation:

It's not linear but it is decreasing.

Answer: Firstly, we take a look at the Y numbers to figure out if we're increasing or decreasing. Obviously, the numbers are going into the negatives so we know it's decreasing. After plotting the graph you'll see it's constant and in a straight line making it linear. So, your answer would be decreasing; linear.

Answer:

738.1

Step-by-step explanation:

What is 55% of 1342?

738.1

Hope it helped brainiest plz and thank you!!!!!!!

Answer:

738.1

Step-by-step explanation:

The best way to assign values for a simulation using a random digits table for this scenario would be:School A: 9th grade is represented with 0 and 1. 10th grade is represented with 2 and 3. 11th grade is represented with 4 and 5. 12th grade is represented with 6 and 7.School B: 9th grade is represented with 0, 1, 2, and 3. 10th grade is represented with 4, 5, and 6. 11th grade is represented with 7 and 8. 12th grade is represented with 9.This method assigns two digits to each grade level in School A, allowing for an equal chance of selecting each grade level. In School B, four digits are assigned to 9th grade, three digits are assigned to 10th grade, two digits are assigned to 11th grade, and one digit is assigned to 12th grade, reflecting the percentage breakdown of the population.

Answer:

Thankkkkkkkkkkkkksssssssa

Answer:

Yes, Felix does have enough flour for 8 people. The initial recipe is able to feed only 4 people, needing 140 g of flour. If he needs to feed 8 people, he will need 280 g of flour. Felix has more than enough flour for 8 people.

Step-by-step explanation:

Answer:

So for the geometric mean, you would multiply the two numbers and put them under a radical

Step-by-step explanation:

3 times 10= 30

=\(\sqrt{30}\)

The solution is : the geometric mean between 3 and 10 is √30.

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.

here, we have,

Given:  two numbers 3 and 10

we have,

To Find: Geometric number of numbers in 3 and 10

Solution:

Let first number be a

Let second number be b

Geometric mean of two numbers a and b is √ab

Now,

First number is 3

Second number is 10

Geometric mean of both numbers is :

√3×10

=√30

Geometric mean is √30.

Hence, The solution is : the geometric mean between 3 and 10 is √30.

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\(\text{L.H.S}\\\\=\dfrac{\cos^2 t +4\cos t +4}{\cos t +2 }\\\\\\=\dfrac{(\cos t)^2 + 2\cdot 2\cos t+2^2}{\cos t +2}\\\\\\=\dfrac{(\cos t +2)^2 }{\cos t +2}\\\\\\=\cos t +2\\\\\\=\dfrac 1{\sec t} +2\\\\\\=\dfrac{2\sec t +1}{\sec t}\\\\\\=\text{R.H.S}\\\\\text{Proved.}\)

Answer:

8 possible outcomes

Step-by-step explanation:

When flipping a quarter three times, each flip can result in two possible outcomes: either landing heads (H) or tails (T).

Since each flip is independent, the total number of possible outcomes for flipping a quarter three times can be found by multiplying the number of outcomes for each flip together.

For three flips, the total number of possible outcomes is:

2 x 2 x 2 = 8

So, there are 8 possible outcomes when Alexandre flips a quarter three times.

The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

The median is the middle value when an odd number of data values are arranged in order.

The median is an important concept in statistics that helps to describe the central tendency of a dataset. When dealing with an odd number of data values, finding the median is straightforward. First, you need to arrange the values in either ascending or descending order. Once the data is ordered, the middle value is the median. For example, if you have the following dataset: 1, 3, 5, 7, 9. The median is the middle value, which in this case is 5. It is important to note that the median is not affected by extreme values or outliers. It is a reliable measure that represents the central value in a dataset.

In summary, when an odd number of data values are arranged in order, the middle value is known as the median. It is a measure of central tendency that helps to describe the middle value in a dataset.

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Answer:

.85

Step-by-step explanation:

Compound interest formula

\(PV(1+\frac{i}{n})^{nt}\)

Melanie:

\(3800(1+\frac{.02}{4})^{(6*4)\\}\\=3800(1+.005)^{24}\\3800*1.1272=4283.21\)

Sebastian:

\(3800(1+\frac{.02}{12})^{12*6}\\3800(1.0017)^{72}\\3800*1.1274=4284.06\)

4824.06-4283.21= .85

If x varies directly with the square of y​ and inversely with the cube root of z​, the value of x when y = 1 and z = 27 is x = 1.

Given that,

x varies directly with the square of y​ and inversely with the cube root of z.

For some constant k,

x = k y²/ ∛z

Also, we have, x=24​ when y=4​ and z=8.

24 = k (4)²/ ∛(8)

24 = 16 k / 2

24 = 8k

k = 3

So the equation is,

x = 3y²/ ∛z

When y = 1 and z = 27,

x = 3 (1)²/ ∛(27)

x = 3 / 3

x = 1

Hence the value of x = 1.

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the probability that a student scored greater than 65 is 0.2389.

The probability that a student scored greater than 65 can be calculated using the standard normal distribution and the z-score. The z-score represents the number of standard deviations a value is from the mean, and can be calculated as follows:

z = (x - mean) / standard deviation

Where x is the score of interest (65)

Mean is the average score of the students (70)

Standard deviation is the standard deviation of the scores (7).

Plugging in the values, we get

z = (65 - 70) / 7 = -0.714.

Using a standard normal distribution table, we can find the probability that a student scored greater than 65 by finding the area to the right of the z-score. The probability of a student scoring greater than 65 is approximately 0.2389, or 23.89%.

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Answer:

each time the numbers are being multiplied by 10

Step-by-step explanation:

1 × 10 = 10

10 × 10 = 100

100 × 10 = 1,000

hope this helps :)

When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

Given,

The cost of Carpet per square foot = $4

Total cost of the carpet = $616

We know

Area of the rectangle = Length × Width

Length = 14 feet

Consider the width of the rectangular room as x

Then the area of the room = 14x

Total cost of carpet = Area of the rectangular room× Cost of carpet per foot

Substitute the values

14x×4=616

14x=154

x=11 feet

Hence, When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

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Answer:102

Step-by-step explanation:

The interior angles of a triangle have to measure 180 degrees, which is an isosceles triangle, and 39+39=78.

180-78=102.Therefore the  answer is 102