Which of the following answer choices would satisfy the inequality below? -2.74 < x < -2.35​

The zeros for the expression is x <= 1

From the question, we have the following parameters that can be used in our computation:

-3x + 43/ x + 7 >= 5

Multiply both sides of the inequality by x + 7

So, we have the following representation

-3x + 43 >= 5x + 35

Evaluate the like terms

This gives

8 >= 8x

So, we have

1 >= x

This gives

x <= 1

Hence, the zeros is x <= 1

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We have the height of the rectangle equal to h = 37.5 inches.

A rectangle is actually about a right triangle. We can use the Pythagorean theorem to generate an expression to find the height of the rectangle.

We know that:

\(c^2=a^2+b^2\) so replacing it with the width and length of the rectangle, we get :

\(c^2=h^2+w^2\)

We were not given values for the width and length, just their relationship to each other, and we can use that to find an equation in the variable h:

So, \(c^2=h^2+w^2\)

\((56)^2=h^2+(h+4)^2\)

\(3136=h^2+h^2+8h+16\)

\(0=2h^2+8h+16-3136\)

\(0=2h^2+8h-3,120\)

Since we cannot factor this, we can use the quadratic formula to solve for the height h, where, a = 2 , b = 8, c = -3,120

h = (-b ±\(\sqrt{b^2-4ac}\)) /2a

Now, Plug all the values:

h = (-8 ± \(\sqrt{8^2-4(2)(-3120)})/4\))

h = -8 ± \(\sqrt{64+24,960}/4\)

h =( -8 ± \(\sqrt{25,024})/4\)

h = (-8 ± 158.180)/4

There are two possible solutions, so we have:

\(h_1=\frac{-8+158.180}{4}\)                      \(h_2=\frac{-8-158.180}{4}\)

\(h_1 = 37.545\)                           \(h_2=-41.545\)  

\(h_1\) ≈ 37.5 in.                          \(h_2\) ≈ -41.5 in.

We cannot use \(h_2\) because a negative height is absurd and undefined. Thus, we have the height of the rectangle equal to h = 37.5 inches.

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Answer:

\(x=\boxed{6.6}\)

\(\overline{\sf DE}=\boxed{13.2}\:\:\sf units\)

Step-by-step explanation:

Geometric Mean Theorem - Altitude Rule

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments.  The ratio of one segment to the altitude is equal to the ratio of the altitude to the other segment:

\(\sf \dfrac{segment\:1}{altitude}=\dfrac{altitude}{segment\:2}\)

From inspection of the given diagram:

\(\begin{aligned}\sf \dfrac{segment\:1}{altitude} & = \sf \dfrac{altitude}{segment\:2}\\\\\implies \dfrac{5}{9} & = \dfrac{9}{2x+3}\\\\5(2x+3) & = 81\\\\10x+15 & = 81\\\\10x & = 66\\\\ \implies x & = 6.6\end{aligned}\)

Substitute the found value of x into the expression for DE:

\(\begin{aligned}\sf \overline{DE} & = 2x+3\\\implies \sf \overline{DE} & = 2(6.6)+3\\& = 13.2+3\\& =16.2\:\: \sf units\end{aligned}\)

60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

According to the question,

We have the following information:

3 digits integers are to be made from 1,2,3,4 and 5

So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.

Now, we have:

Total number of digits = 5

Number of digits to be made = 3

So, we have:

\(^{5} P_{3}\)

Solving this expression:

5*4*3

60

Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

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Answer:

The answer is the 2nd one

Step-by-step explanation:

Answer:

J (22hrs)

Step-by-step explanation:

812 divided by 14= 58

1,276 divided by 58= 22 hrs

The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

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Answer:

26

Step-by-step explanation:

5x-17+3x-11=180

8x - 28 = 180

8x = 208

x =26

Answer:

x=11

Step-by-step explanation:

The sum of the angles of a triangle is 180

We know the angle with a box is 90

90 + 5x-2  + 3x+4 = 180

Combine like terms

8x +92 = 180

Subtract 92 from each side

8x+92-92 = 180-29

8x = 88

Divide each side by 8

8x/8 = 88/8

x = 11

Answer:

The domain of y = f(x) is [0,8]

Step-by-step explanation:

Since the straight line with negative slope begins on the y-axis at (0. 9) and exits the plane at (8, 1), we get is domain from the minimum and maximum values of x for which the function is valid.

So, the minimum value of x at which the function is valid is x = 0 and the function is y = f(0) = 9.The maximum value of x at which the function is valid is x = 8 and the function is y = f(8) = 1.

So, the domain of the function y = f(x) is [0,8]

Answer:

y = f(x) is [0,8]

Step-by-step explanation:

Answer:

k = - 18

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - 2

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, - 12) and (x₂, y₂ ) = (6, k)

m = \(\frac{k+12}{6-3}\) = \(\frac{k+12}{3}\) = - 2 ( multiply both sides by 3 )

k + 12 = - 6 ( subtract 12 from both sides )

k = - 18

By evaluating P(x) for each of the possible rational roots, we find that the rational roots of P(x) = 0 are: x = -2, 1/7, and 2/7. To find the rational roots of the polynomial P(x) = 7x³ - x² - 5x + 14, we can apply the rational root theorem.

According to the theorem, any rational root of the polynomial must be of the form p/q, where p is a factor of the constant term (14 in this case) and q is a factor of the leading coefficient (7 in this case).

The factors of 14 are ±1, ±2, ±7, and ±14. The factors of 7 are ±1 and ±7.

Therefore, the possible rational roots of P(x) are:

±1/1, ±2/1, ±7/1, ±14/1, ±1/7, ±2/7, ±14/7.

By applying these values to P(x) = 0 and checking which ones satisfy the equation, we can find the actual rational roots.

By evaluating P(x) for each of the possible rational roots, we find that the rational roots of P(x) = 0 are:

x = -2, 1/7, and 2/7.

These are the rational solutions to the polynomial equation P(x) = 0.

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Answer: $3.55

Step-by-step explanation:

5 oranges * $2.84/4 oranges =

5 oranges * $0.71/1 orange=

5 oranges/1 orange * $0.71=

5/1 * 0.71=

5*0.71=$3.55

Answer:

2,120 or 2,121.8

Step-by-step explanation:

It depends on the answers

3% of 2,000 is 60 dollars you add the 60 dollars to the bank account 2000 + 60 = 2060 3% of 2060 is 61.8

The number of players the team can bring to the tournament = 19 .

Given : amount raised by team = $1775.50

            rent of bus = $901.50

            budget for meal per player = $46

To find : the number of players the team can bring to the tournament

Equation :

taking bus charge as y - intercept ( since it does not depend on the no . of members riding on it )

taking meal amount as slope ( since it depends on the no . of members a team can bring to the tournament )

Let x be the no . of players a team can bring to the tournament .

Therefore , the equation is :

1775.50 = 46 x + 901.50

874 = 46 x

x = 19

Hence , the number of players the team can bring to the tournament = 19 .

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The type of scale used to evaluate the food at a new restaurant on 7-point scales with bipolar adjectives such as good-bad and inexpensive-expensive is known as a Likert scale.

This type of scale is commonly used in surveys to measure attitudes and opinions towards a particular topic, in this case, the food at a new restaurant. A Likert scale consists of a series of statements or adjectives that respondents are asked to rate on a scale that ranges from strongly disagree to strongly agree or, in this case, from bad to good and from inexpensive to expensive.

The bipolar adjectives used in the scale allow for a clear distinction between the positive and negative aspects of the food, which helps to ensure that the responses are more accurate and meaningful. The 7-point scale provides a wider range of options than a binary scale, which allows for more nuanced and detailed responses.

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B. sigma^infinity_k = 0 x^k + 3, and the interval of convergence is (-1, 1).

To find the power series representation for g(x), we need to rewrite g(x) in terms of the given geometric series.

Notice that g(x) can be written as:
g(x) = x^3/1 - x = x^3 * (1/1-x)

We can now substitute the formula for the geometric series to get:

g(x) = x^3 * sigma^infinity_k = 0 x^k
= sigma^infinity_k = 0 (x^3 * x^k)
= sigma^infinity_k = 0 x^(k+3)

Therefore, the power series representation for g(x) is:
sigma^infinity_k = 0 x^(k+3)

The interval of convergence of this series is the same as that of the geometric series, which is |x| < 1.

In interval notation, this can be written as (-1, 1).

Therefore, the correct answer is B. sigma^infinity_k = 0 x^k + 3, and the interval of convergence is (-1, 1).

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Answer:

B

Step-by-step explanation:

Option B is the set of range

Answer:

srry just wanted the points but goodluck

Step-by-step explanation:

i am a bum

A theoretical hypothesis is a hypothesis that attempts to provide an explanation for a scientific question or phenomenon by proposing a theoretical framework or model. (option b).

Theoretical hypotheses are often used in scientific research to guide investigations and to help researchers make predictions about what they expect to observe. They are essential to the scientific method because they provide a basis for developing testable predictions and designing experiments to confirm or reject them.

A theoretical hypothesis is a hypothesis that attempts to provide an explanation for a scientific question or phenomenon.

This statement is accurate. As discussed earlier, a theoretical hypothesis is a type of hypothesis that proposes a theoretical framework or model to explain a scientific question or phenomenon.

Therefore, statement b is the most accurate description of a theoretical hypothesis.

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Answer:

15 cm

Step-by-step explanation:

Since the square's side length is 8 cm, and one of its sides is the short leg of the triangle, the short leg of the triangle is 8 cm

Using the pythagorean theorem, solve for b (the missing side length x)

a² + b² = c²

8² + b² = 17²

64 + b² = 289

b² = 225

b = 15

So, the missing side length is 15 cm

From the given information, cholesterol level X follows the N(222, 37) distribution.

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be calculated by using the z-score formula as follows:

z = (x - μ) / σ

For lower limit x1 = 200, z1 = (200 - 222) / 37 = -0.595

For upper limit x2 = 240, z2 = (240 - 222) / 37 = 0.486

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be computed as

P(200 ≤ X ≤ 240) = P(z1 ≤ Z ≤ z2) = P(Z ≤ 0.486) - P(Z ≤ -0.595) = 0.683 - 0.277 = 0.406

In this population, 90% of men have a cholesterol level that is at most X90.The z-score corresponding to a cholesterol level of X90 can be calculated as follows:

z = (x - μ) / σ

Since the z-score separates the area under the normal distribution curve into two parts, that is, from the left of the z-value to the mean, and from the right of the z-value to the mean.

So, for a left-tailed test, we find the z-score such that the area from the left of the z-score to the mean is 0.90.

By using the standard normal distribution table,

we get the z-score as 1.28.z = (x - μ) / σ1.28 = (X90 - 222) / 37X90 = 222 + 1.28 × 37 = 274.36 ≈ 274

The cholesterol level of 90% of men in this population is at most 274 mg/dl.

The distributions that we can consider to be approximately normal are the sampling distribution of mean BMI for random samples of 60 adults and the sampling distribution of mean BMI for random samples of 9 adults.

The reason for considering these distributions to be approximately normal is that according to the Central Limit Theorem, if a sample consists of a large number of observations, that is, at least 30, then its sample mean distribution is approximately normal.

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Answer: $972.7972 or $973

To find the amount of money Mary should deposit each quarter, we will use the following equation:

Where:

P = deposit made n times

i = is the interest rate r compounded m times per year

Since Mary wants to invest every three months, that would be 4 times per year and have the interest rate of 2% = 0.02,

The amount she wants to save is A = $12000, and she will invest 12 times, n = 12.

Substituting these to the formula and we will have:

This means that Mary has to pay approximately $972.7972 or $973 each quarter.

Answer:

looks like 3 hours

Step-by-step explanation:

at 4 hours its equal

a) The mean for the given data is 11.44

b) The median for the given data is 11

c) The mode for the given data is 11

d) The maximum score received by a student is 18

e) The minimum score received by a student is 3

f) The range for the given data is 15

g) The interquartile range for the given data set {12, 6, 9, 5, 11} is 6

h) The third quartile for the given data set  {0, 8, 14, 17, 7} is 15.5

i) The third quartile for the given data set {14, 11, 9, 3, 12} is 13

j) The interquartile range for the given data set {3, 8, 9, 11, 5}  is 6

The interquartile range is a measure of statistical dispersion in descriptive statistics, which is the spread of the data. The IQR is also known as the middle 50% spread, the fourth spread, or the H-spread.

a) Mean=(12+8+11+10+6+7+10+13+14+15+9+18+17+15+3+11+11)/18

=11.44

Therefore, mean=11.44

b) Median= n is even

Then,

((n/2 )th +((n/2)+1)th)/2

=(11+11)/2

=11

Therefore, median=11

c) Mode= The number that is repeated highest number of times

Mode=11

Therefore, mode=11

d) The maximum score received by a student is 18

e) The minimum score received by a student is 3

f) Range=maximum-minimum

=18-3

=15

Therefore, Range=15

g) Median=9

Q₁=(5+6)/2=5.5

Q₃=(11+12)/2=11.5

Interquartile range=|Q₃-Q₁|

=|11.5-5.5|

=6

The interquartile range for the given data set {12, 6, 9, 5, 11} is 6

h) Median=10

Q₃=(14+17)/2=15.5

The third quartile for the given data set  {0, 8, 14, 17, 7} is 15.5

i) Median=11

Q₃=(12+14)/2=13

The third quartile for the given data set {14, 11, 9, 3, 12} is 13

j) Median=8

Q₁=(3+5)/2=4

Q₃=(9+11)/2

Interquartile range=|Q₃-Q₁|

=|10-4|

=6

The interquartile range for the given data set {3, 8, 9, 11, 5}  is 6

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ANSWER

EXPLANATION

The surface area of a cone is given as:

where r = radius; l = slant height

From the question:

Therefore, the surface area of the cone, in terms of pi, is:

Answer:

x < -3 or x > 3

second answer choice

Step-by-step explanation:

 The symbol "∨" between p and q represents a disjunction and can be replaced with the word "or" to turn p ∨ q into p or q.

Plug in x < -3 in for p and x > 3 for q, and now you have:

x < -3 or x > 3

which is the same as the second answer choice.

So, the answer is x < -3 or x > 3, or the second answer choice.

I hope you find my answer helpful.

Thus, there are 208 positive integers less than 1000 that are divisible by exactly one of 7 and 11. The rules used to find the number of positive integers less than 1000 that are divisible by exactly one of 7 and 11 are:

a. The principle of inclusion-exclusion for sets: This rule is used to count the number of integers that are divisible by both 7 and 11, and subtract them from the total number of integers that are divisible by either 7 or 11. This gives us the number of integers that are divisible by exactly one of 7 and 11.

b. The division rule: This rule is used to find the number of integers that are divisible by a certain number within a given range. For example, we can use the division rule to find the number of integers less than 1000 that are divisible by 7.

c. The product rule: This rule is used to find the number of ways two or more events can occur together. In this case, we can use the product rule to find the number of integers that are divisible by both 7 and 11.

d. The sum rule: This rule is used to find the total number of ways two or more events can occur separately. In this case, we can use the sum rule to find the total number of integers that are divisible by either 7 or 11.

By using these rules, we can find the number of positive integers less than 1000 that are divisible by exactly one of 7 and 11.

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The correct number line representation is the third one from top

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Consider:

- 6x + 2 ≤ 14

=> -6x  ≤ 14 - 2

=>   -6x  ≤ 12

On dividing both sides by  -6, we get

x≥ -2

Consider:

-2x - 4> -6

=> -2x > -6+4

=> -2x > -2

On dividing both sides by  -2, we get

x < 1

Combine the answers:

x≥ -2  or x < 1

So the correct number line representation is the third one from top

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The box and whisker plot can be created by :

Minimum value - 6

Maximum Value - 15

Median - 10

Quartiles - Q1 - 7.5, Q2 - 10, Q3 - 13.5

To create a box and whisker plot for the given data set {6,7,7,8,9,10,10,10,10,13,13,14,14,15,15}, we need to first find the minimum value, maximum value, median, and quartiles.

Minimum value: 6

Maximum value: 15

Median: To find the median, we need to first arrange the data set in ascending order:

6,7,7,8,9,10,10,10,10,13,13,14,14,15,15

The median is the middle value in the data set, which is 10.

Quartiles: To find the quartiles, we need to divide the data set into four equal parts.

First quartile (Q1): The first quartile is the median of the lower half of the data set. In our case, the lower half of the data set is:

6,7,7,8,9,10

The median of this set is (7+8)/2 = 7.5.

Second quartile (Q2): The second quartile is the median of the entire data set, which we already found to be 10.

Third quartile (Q3): The third quartile is the median of the upper half of the data set. In our case, the upper half of the data set is:

10,10,10,10,13,13,14,14,15,15

The median of this set is (13+14)/2 = 13.5.

Now, we can use the above information to create the box and whisker plot.

The horizontal line inside the box represents the median (10). The bottom of the box represents the first quartile (7.5), and the top of the box represents the third quartile (13.5). The whiskers extend from the box to the minimum value (6) and maximum value (15).

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