Use the form |x – b | ≤ c or |x – b | ≥ c to write an absolute value
inequality that has the solution set x ≤ –9 or x ≥ –5.

Answer:

5 + 1/x = 11/5

Podemos simplificar esta ecuación multiplicando ambos lados por 5x, lo que da:

25x + 5 = 11x

Ahora, podemos resolver x aislando la variable en un lado de la ecuación:

25x - 11x = -5

14x = -5

x = -5/14

Por lo tanto, la solución a la ecuación es x = -5/14

1) Using the Law of Syllogism, we can combine statement 1 and statement 3 to conclude that Sally weighs more than Jill's car:

If something weighs more than 2000 pounds, then it weighs more than Jill’s car.

Sally weighs more than 2000 pounds.

Therefore, Sally weighs more than Jill's car.

2) Using the Law of Detachment, we can apply statement 2 to our conclusion from the Law of Syllogism to conclude that Sally is too heavy for the bridge:

If something weighs more than Jill’s car, then it is too heavy for the bridge.

Sally weighs more than Jill's car.

Therefore, Sally is too heavy for the bridge.

The Law of Syllogism opines that if two conditional statements have the same terms, then we can combine them to form a conclusion.

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion is also true.

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Answer:20

Step-by-step explanation:

40/2=20

20 days of giving away 2 tickets

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Answer:

1km:100decameter(dam)

Step-by-step explanation:

so 35dam:0.35km

and 35dam:0.00035m

The equation of the axis of symmetry of the parabola is x = 7.

We have,

The axis of symmetry of a parabola is a vertical line that passes through the vertex.

Now,

The equation of the axis of symmetry is the vertical line passing through the x-coordinate of the vertex.

And,

The x-coordinate of the vertex is 7.

Now,

So the equation of the axis of symmetry is x = 7.

Thus,

The equation of the axis of symmetry of the parabola is x = 7.

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Answer:

Step-by-step explanation:

3/4 : 1/8 =

3/4 x 8 =

24/4 =

6

The event lasted for 11,700 seconds.

Time is an essential concept that we use to measure the duration of events. In this context, let's consider an event that lasts for 3 hours and 15 minutes.

To convert time from hours and minutes to seconds, we need to know the number of seconds in an hour and a minute.

There are 60 minutes in an hour, and each minute has 60 seconds.

=> (3 x 60 x 60) = 10,800

=> 15 x 60 = 900

To find the total time of the event, we need to add the time in seconds for the hours and minutes, which is

=> 10,800 seconds + 900 seconds = 11,700 seconds.

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Answer:

8 people bought economy and 2 bought first class

Step-by-step explanation:

there are 10 person and total is 1580 so 250+ 9(135)=1460 which is wrong so we gonna try adding 2(250) and 8(135) which got us 1580

The correct definitions are matched.

A) Perpendicular line = a line that intersects another line at a right angle.

B) Circle = the set of all points in a plane that are equidistant from a given point.

C) Line segment = a part of a line that begins at one point and ends at another point.

D) Angle = the amount of turn between two straight lines that share a common point.

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The surface area of the larger can is approximately 674.375 square centimeters.

We have,

The ratio of the corresponding linear measures of two similar cans is 4 to 7.

The ratio of their surface areas will be the square of this ratio, which is (4/7)² = 16/49.

Let A be the surface area of the larger can.

(220 cm²) / A = 16/49

220 cm² x 49 = A x 16

10780 cm² = A x 16

A = 10780 cm² / 16

A = 674.375 cm²

Therefore,

The surface area of the larger can is approximately 674.375 square centimeters.

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The percent of saline solution in brand B  is 10.83%

Let's assume that brand B has x gallons of the 100% saline solution.

The amount of salt in brand A is 18% of 6 gallons = 0.18 * 6 = 1.08 gallons.

When the two brands are mixed, the total volume of the mixture is 6 + x gallons, and the total amount of salt is 1.08 + x gallons.

Since the resulting mixture is 18 gallons of 8% saline solution, we can set up the equation:

(1.08 + x) / (6 + x) = 0.08

Solving for x, we get:

1.08 + x = 0.48 + 0.08x

0.92x = 0.6

x = 0.65

So, brand B has 0.65 gallons of the 100% saline solution.

Therefore, the percent of saline solution in brand B is:

0.65 / 6) * 100% = 10.83%, which rounded to the nearest whole number is 11%.

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The coordinates of the vertices for the image is A′(−3, 6), B′(0, 10), C′(−3, 3).

The vertices of the preimage triangle ABC are given as A(-3,3), B(0,7), and C(-3,0). To translate the preimage 3 units up, we need to add 3 to the y-coordinate of each vertex. Therefore, the vertices of the image triangle A'B'C' will be A'(-3,6), B'(0,10), and C'(-3,3). Thus, option B, A′(−3, 6), B′(0, 10), C′(−3, 3), is the correct answer.

To check the answer, we can plot the points on a coordinate plane and observe that the image triangle is obtained by moving the preimage triangle 3 units up. Translation is a type of transformation in which the position of a figure is changed without changing its shape or orientation.

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The probability that the customer is served by Charter with market share of 30% is equal to 34.9%.

Let A be the event that the customer is served by Charter,

and B be the event that the customer is experiencing an internet speed of 12Mbps.

Probability of A given B, which can be written as P(A|B).

Use Bayes' theorem to find P(A|B),

P(A|B) = P(B|A) × P(A) / P(B)

P(A) = 0.3 (the market share of Charter)

and P(B) = P(B/A) × P(A) + P(B / A') × P(A'),

where P(A') = 1 - P(A) = 0.7 (the market share of Xfinity).

P(B|A), the probability of experiencing an internet speed of 12Mbps given that the customer is served by Charter,

All speeds between 7Mbps and 15Mbps are equally likely.

This implies, the probability of experiencing a speed of 12Mbps given Charter is,

P(12Mbps/A) = 1 / (15Mbps - 7Mbps)

                     = 1 / 8

P(B|A'), the probability of experiencing an internet speed of 12Mbps given that the customer is served by Xfinity,

All speeds between 10Mbps and 20Mbps are equally likely.

This implies, the probability of experiencing a speed of 12Mbps given Xfinity is,

P(12Mbps|A') = 1 / (20Mbps - 10Mbps)

                     = 1 / 10

Now substitute all the values into Bayes' theorem,

P(A|B) = P(B|A) × P(A) / [P(B|A) × P(A) + P(B |A') × P(A')]

= (1/8) × 0.3 / [(1/8) × 0.3 + (1/10) × 0.7]

= 0.349

Therefore, the probability that the customer is served by Charter given that they are experiencing an internet speed of 12Mbps is 0.255, or about 34.9%.

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The formula for the volume of a circle is V = (4/3)πr³, where r is the radius obtained by dividing the diameter by 2.

First, it's important to understand what the diameter of a circle represents. The diameter is the distance across the circle, passing through the center. In contrast, the radius is the distance from the center of the circle to any point on the edge.

Now, let's consider the statements given:

Substitute the diameter value for r in the formula and calculate as usual.

This statement is incorrect because the formula for the volume of a circle involves the radius, not the diameter. If we substitute the diameter for the radius, we would end up with the wrong answer.

Divide the diameter by 2 to find the radius, and then use the volume formula as usual.

This statement is correct. Since the radius is half the diameter, dividing the diameter by 2 will give us the radius. We can then use the formula for the volume of a circle, which is V = (4/3)πr³, where r is the radius.

Multiply the diameter by 2 to find the radius, and then use the volume formula as usual.

This statement is incorrect. If we multiply the diameter by 2, we would end up with the diameter, not the radius. Again, we need to use the radius in the formula for the volume of a circle.

To summarize, when given the diameter of a circle and asked to find its volume, we should divide the diameter by 2 to find the radius and then use the volume formula as usual.

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Answer:

[tex]\Large \boxed{\boxed{\textsf{$x=\frac{47}{7}, y=15$}}}[/tex]

Step-by-step explanation:

The shape inside the circle is a quadrilateral. The following property of circle geometry can be used to solve the problem:

[tex]\large \boxed{\text{"The opposite angles of a cyclic quadrilateral are supplementary"}}[/tex]

Consider any quadrilateral, where the vertices touch on the circumference of a circle: ABCD, with origin O, as s

Required to prove: ∠ABC + ∠ADC = 180°

Let ∠AOC = 2x as shown in attached image.

∴ 2∠ABC = ∠AOC (using another property that "the perpendicular bisector of a chord passes through the circle's centre")

⇒ ∠ABC = x.

Now let ∠AOC = 2y.

Similarly, ∠ADC = y

⇒ ∠ABC + ∠ADC = x + y.

∵ It is clear that 2x + 2y = 360°,

⇒ x + y = 180°

∴∠ABC + ∠ADC = 180°, and hence statement is true.

Now, solving for x:

7x + 1 + 105° = 180

7x + 106 = 180

7x = 74

∴x = 74/7

Solving for y:

4y + 14 + 7y + 1 = 180

11y + 15 = 180

11y = 165

∴y = 15

Answer:

Step-by-step explanation:

50%

Jocelyn would need to save $1333.33 each year with 7% interest.

To calculate how much Jocelyn needs to save for the down payment over the next three years, we first need to determine the total down payment required. If the down payment is stated as $4000, then that is the total amount needed.

Assuming that Jocelyn wants to make the down payment in three years, we can calculate how much she needs to save each year by dividing the total down payment by three:

$4000 / 3 years = $1333.33 per year

So Jocelyn would need to save approximately $1333.33 each year for the next three years in order to have enough for the $4000 down payment.

Correct Question :

JUST $4000 DOWN PAYMENT!

LOW 7% INTEREST RATE!

5 YEARS TO REPAY YOUR LOAN!

In order to afford the down payment, how much will Jocelyn need to save for each of the next three years

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The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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Answer:

Step-by-step explanation:

On a given day, a greengrocer sold 81 oranges and 43 melons. Write the ratio of oranges to melons in the form 1: n. Give any decimals in your answer to 2 d.p.

orange = 81

melons = 43

ratio 81 : 43

divide both side by 81

1 : 0.53

Answer: herefore, the average cost of the items Roy bought is $14.07.

Step-by-step explanation:

To find the average cost of the items Roy bought, we need to add up the total cost of all his purchases and divide by the total number of purchases.

Strategy:

1. Add up the cost of all Roy's purchases.

2. Count the number of purchases.

3. Divide the total cost by the number of purchases to find the average cost.

Explanation:

We will use this strategy because it is a straightforward way to find the average cost of multiple items. We will add up all the costs and divide by the number of purchases to get the average cost.

Calculations:

Total cost = (4 x $3.55) + $10.76 + $15.35 + $55.27 + $16.98

Total cost = $14.20 + $10.76 + $15.35 + $55.27 + $16.98

Total cost = $112.56

Number of purchases = 4 (coffee) + 2 (lunch) + 1 (groceries) + 1 (hardware store)

Number of purchases = 8

Average cost = Total cost / Number of purchases

Average cost = $112.56 / 8

Average cost = $14.07

Therefore, the average cost of the items Roy bought is $14.07.

The value of a third-degree polynomial function with real coefficients and the given zeros are,

⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i

We have to given that;

Zeroes of the polynomial are,

⇒ 7, i

Now, The value of a third-degree polynomial function with real coefficients and the given zeros are,

⇒ P (x) = (x - 7)² (x - i)

⇒ P (x) = (x² + 49 - 14x) (x - i)

⇒ P (x) = (x³ - ix² + 49x - 49i - 14x² + 14ix)

⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i

Thus, The value of a third-degree polynomial function with real coefficients and the given zeros are,

⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i

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Answer:

When rolling two number cubes, the possible outcomes of the sum of the numbers on the top faces are from 2 (1+1) to 12 (6+6). Since we want to know how many times we can expect the sum to be 7, we need to count the number of ways to get a sum of 7.

The pairs of numbers that add up to 7 are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, there are 6 ways to get a sum of 7.

Each time we roll the two number cubes, the probability of getting a sum of 7 is 6/36 or 1/6, since there are 6 possible outcomes that result in a sum of 7 out of a total of 36 possible outcomes.

Therefore, if we repeat this process 300 times, we can expect to get a sum of 7 approximately (1/6) x 300 = 50 times.

So we can expect the two cubes to add to exactly 7 about 50 times when rolled 300 times.

Step-by-step explanation:

The probability of getting exactly 9 heads out of 15 tries when flipping a fair coin is approximately 0.19638 or about 19.64%.

We have,

The probability of getting a head or a tail when flipping a fair coin.

= 1/2 or 0.5

Assuming the coin is unbiased and each flip is independent of the previous flips.

To find the probability of getting 9 heads out of 15 tries, we need to use the binomial probability formula:

= P(9 heads out of 15 tries)

= [tex]^{15}C_9[/tex] x (0.5)^9 x (0.5)^6

Now,

P(9 heads out of 15 tries)

= 5005 x (0.5)^9 x (0.5)^6

= 0.19638 (rounded to five decimal places)

Thus,

The probability of getting exactly 9 heads out of 15 tries when flipping a fair coin is approximately 0.19638 or about 19.64%.

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Step-by-step explanation:

If slope r and slope m are perpendicular , their product must give negative one.

That is r ×m = -1

r = -1 /m

m = -1 /r

The resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.

Let R be the resistance of the wire,

L be the length of the wire,

d be the diameter of the wire, and

k be a constant of variation.

Then we have the equation:

R = k * L / d^2

Solving for k to find the resistance of a wire of varying length and diameter.

We can create an equation using the information provided:

15611 = k * 700 / 0.2^2

Solving for k, we get:

k = 15611 * 0.2^2 / 700

k ≈ 0.1799

Using k to calculate the resistance of a wire with a length of 1800 feet and a diameter of 0.45 inches:

15037.45 ohms = 0.1799 * 1800 / 0.452 R

As a result, the resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.

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a) the   proportion of even numbers in the population is 2/3 or approximately 0.667.

b. Sample Proportions and Probability Distribution Table is attched.

c) c. The mean of the sampling distribution of the sample proportion of even numbers is approximately 0.3333.

d. The sample poportion is a biased estimator of the population proportion because   the  sample proportions do not target the proportion of even numbers in   the population.

a. The population consists of 2, 6, and 7. The proportion of even numbers in the population is 1/3 since only 6 is even.

b. We can find the proportion of even numbers in each sample as follows:

2,2:   2/2 = 1

2,6: 1/2 = 0.5

2,7: 1/2  = 0.5

6,2: 1/2 =   0.5

6,6:   2/2 = 1

6,7: 1/ 2 = 0.5

7, 2: 1/2 = 0.5

7,6: 1/2 = 0.5

 7,7: 0/2   =0

This means that

   0 ⇒     1/9

  0.5⇒    5/9

   1  ⇒    3/9 (or 1/3)

So the above is summarized onto the table attached.

C)  The mean of the sampling distribution    of the sample proportion of even numbers is the weighted average of the possible values of the sample proportion,

where the weights are the probabilities of each value. Hence,

(0 x 1/9) +   (0.5 x 6/9 ) + (1 x 2/  9)

= 1/3

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The domain of this relation is [0, 5].

The range of this relation is [-4, 3].

No, this relation is not a function.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graphs shown in the image attached above, we can reasonably and logically deduce the following domain and range for graph 4:

Domain = [0, 5].

Range = [-4, 3].

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The solution to the system of inequalities 2x − y < 4 and x + y < −1 is the intersection of the shaded regions below the lines 2x - y = 4 and x + y = -1, labeled AB on the graph. Regions A and B represent the solutions to each individual inequality.

To solve the system of inequalities 2x − y < 4 and x + y < −1, we can use the following steps

Solve each inequality for y in terms of x

2x - 4 < y

-x - 1 < y

Plot the boundary lines for each inequality as dotted lines. To do this, we can use the equality signs instead of the inequality signs.

2x - 4 = y

-x - 1 = y

Shade the region that satisfies each inequality. To do this, we can test a point that is not on the boundary line in each inequality. For example, we can test (0,0) in the first inequality

2(0) - 0 < 4

0 < 4

Since (0,0) satisfies the first inequality, we shade the region below the line 2x - y = 4. Similarly, we can test (0,-2) in the second inequality

(0) + (-2) < -1

-2 < -1

Since (0,-2) satisfies the second inequality, we shade the region below the line x + y = -1.

The solution to the system of inequalities is the intersection of the shaded regions, which is labeled AB in the graph. The shaded region labeled AB is the region that satisfies both inequalities, which is the region below both lines.

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