Solve
-3
x + 3
solution: x =
-
243-1/
+
Choose...
extraneous solution: x =
5
and identify any extraneous solutions.
Choose...

The volume of the canister is 339.1 cubic inches.

The volume of a cylinder is calculated by using the formula V=πr²h, where r is the radius of the cylinder and h is the height of the cylinder.

The radius of the cylinder is half of the diameter, so the radius of the canister is 3 inches.

Using the formula, we can calculate the volume of the canister as follows:

V = π×3²×12

V = 108×3.14

V = 339.1 cubic inches

Therefore, the volume of the canister is 339.1 cubic inches.

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The alternative hypothesis (H1) would be that the mean of the bottles of cream is not equal to 8 ounces, indicating that the containers are being filled incorrectly. It can be written as: H1: μ ≠ 8 ounces where μ represents the population mean of the bottle cream fillings.

In the given scenario, the null hypothesis would be that the bottles of cream are being filled correctly with a mean of 8 ounces. The alternative hypothesis would be that the bottles of cream are not being filled correctly, meaning the true mean of the population is different from 8 ounces. However, the specific form of the alternative hypothesis would depend on the direction of the problem. If we are interested in knowing whether the mean filling amount is greater than or less than 8 ounces, we would use a one-tailed alternative hypothesis. If we are interested in determining whether the mean filling amount is simply different from 8 ounces, we would use a two-tailed alternative hypothesis.

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An expression represents the product of 3 and ((5/4)n+1.8) is 3.75n + 5.4

The correct answer is an option (D)

Consider the expression  ((5/4)n + 1.8)

First we write the fraction 5/4 in the decimal form.

5/4 = 1.25

So, the expression ((5/4)n + 1.8) becomes,

((5/4)n + 1.8)

=   (1.25 n + 1.8)                         ..........(1)

Now consider the product of 3 and ((5/4)n + 1.8)

3 ×  ((5/4)n + 1.8)

= 3 × ((1.25)n + 1.8)                          ............(from statement (1))

= (3 × (1.25 n)) + (3 × 1.8)

= (3 × 1.25)n + 5.4

= 3.75n + 5.4

Thus, 3 ×  ((5/4)n + 1.8) = 3.75n + 5.4

The correct answer is an option (D)

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Which expression represents the product of 3 and (5/4n + 1.8)? (SHOW WORK PLEASE)

A) 5.55n

B) 9.15n

C) 3.75n + 1.8

D) 3.75n + 5.4

If Ross family purchased washer and dryer set worth $1135 for 9 payments of $132.51 each, then the "interest-rate" of loan is 6.76%.

We first find the total amount of interest paid over the course of the loan.

The total amount of payments made will be:

⇒ 9 payments × $132.51 per payment = $1192.59,

We know that, total amount of interest paid is difference between total amount paid and the amount of original loan:

⇒ Interest = $1192.59 - $1135 = $57.59,

Now, we use formula for "simple-interest" to find percentage rate of loan:

⇒ Simple interest = (principal × rate × time)/100,

The principle is = $1135,

Time of loan in years is = 9/12 = 0.75 year, interest is = $57.59.

So, Rate = (100 × interest)/(principal x time),

Substituting the values,

We get,

⇒ Rate = (100 × $57.59)/($1135 × 0.75),

⇒ Rate = 6.76%

Therefore, the percentage rate of loan is 6.76%.

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The given question is incomplete, the complete question is

Ross family buys a washer and dryer set for $1135 and agrees to make 9 payments of $132.51 each, Find her percentage rate of the loan.

If coffee and cream are complements, an increase in the price of coffee will cause the demand for cream to fall.

If coffee and cream are complementary goods, it means that they are typically consumed together. For example, many people enjoy drinking coffee with cream as an additive. If the price of coffee increases, then the demand for coffee is likely to fall because consumers are less willing to purchase it at the higher price.

When the demand for coffee falls, the demand for cream is also likely to fall because people will be purchasing less coffee to which they would add cream. In other words, as the demand for coffee decreases, so does the demand for cream. This is because the two goods are consumed together, and a decrease in demand for one good affects the demand for the other good.

Therefore, the correct answer is that an increase in the price of coffee will cause the demand for cream to fall. It is important to note that this refers to a change in demand, not just a change in quantity demanded. If the price of coffee increases, the demand for cream will shift to the left, reflecting a decrease in overall demand for cream at all prices.

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The percent error from 50 to 45 rounded to the nearest percent is 10%.

We have -

the correct value : 50

the calculated value : 45

We can write the %error as -

%error = |(calculated value - correct value)|/(calculated value) x 100

%error = |45 - 50|/50 x 100

%error = 5/50 x 100

%error = 10

So, the percent error from 50 to 45 rounded to the nearest percent is 10%.

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Answer:

The top right graph. I have circled this one in the attached figure to avoid confusion

Step-by-step explanation:

The solution to the system of equations will be the value of x and y where both lines in the graph intersect

The two equations are
y = (1/3) x   (1)

and

x + 3y = 6  (2)

Substitute y = (1/3) x   in the second equation:
x + 3y = 6

=> x + 3 · (1/3)x = 6

=> x + x = 6

=> 2x = 6

=> x = 6/2 = 3

At x = 3, y = (1/3) ·3 = 1

So the solution is (3, 1)

The second graph(top right) has lines intersecting at x = 3, y = 1 i.e. point(3, 1)

So this graph represents the solution to the system of equations

Answer:

If the area of the square office is 148 ft², then the length of one side can be found by taking the square root of the area: √148 ≈ 12.17

So the length of one side of Joseph's office is closest to B.) 12 feet

Answer:

12 ft

Step-by-step explanation:

Area of square = S²

We Know

He used a 148 ft² carpet.

Which length of one side of Joesph's office is in feet?

We take

√148 ≈ 12 ft

So, the answer is 12 ft

To find the probability of rolling an odd number, we need to add up the probabilities of rolling 1, 3, or 5.  Therefore, the probability of rolling an odd number on this loaded die is 4/7.

1. There are 6 numbers on a die (1, 2, 3, 4, 5, and 6).
2. 3 appears twice as often as the other numbers, while the other 5 numbers are equally likely.

Let's assume the probability of getting each of the other numbers (1, 2, 4, 5, 6) is x. Since 3 appears twice as often, its probability would be 2x. The total probability is 1, as one of these numbers will definitely show up when the die is rolled:

1x + 1x + 2x + 1x + 1x + 1x = 1
7x = 1
x = 1/7

Now, let's find the probability of rolling an odd number (1, 3, or 5):
First, we need to find the probability of rolling each number on the loaded die. Since 3 appears twice as often as the other numbers, its probability is 2/8 or 1/4. The probability of rolling each of the other five numbers is 1/8.

P(1) = x = 1/7
P(3) = 2x = 2(1/7) = 2/7
P(5) = x = 1/7

The probability of rolling an odd number is the sum of the probabilities of rolling a 1, 3, or 5:

P(odd) = P(1) + P(3) + P(5) = (1/7) + (2/7) + (1/7) = 4/7

So the probability of rolling an odd number on this loaded die is 4/7.

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Answer:

Using the Pythagorean theorem:

c^2 = a^2 + b^2

where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Plugging in the given values:

c^2 = 48^2 + 14^2

c^2 = 2304 + 196

c^2 = 2500

Taking the square root of both sides:

c = √2500

c ≈ 50

Therefore, the length of the hypotenuse is about 50 cm (rounded to the nearest tenth).

Answer:

i dont see an X

Step-by-step explanation:

were is the X

The values are

1. (2√2 + 1)² =  9 + 4√2

2. (√2 -√3)² =  5- 2√6

1. (2√2 + 1)²

Using the Algebraic Identity

(a+ b)² = a² + 2ab + b²

So, (2√2 + 1)²
= (2√2)² + 1²  + 2 (2√2)

= 8 + 1 + 4√2

= 9 + 4√2

2. (√2 -√3)²

Using the Algebraic Identity

(a- b)² = a² - 2ab + b²

So, (√2 -√3)²
= (√2)² + (√3)²  - 2 (√2)(√3)

= 2 + 3 - 2√6

= 5- 2√6

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The rate at which the tip of the shadow moves away from the person when the person is 10 ft from the pole is 0.08 ft/s.

To solve this problem, we need to use the concept of similar triangles. Let's call the height of the pole "h" and the length of the person's shadow "s." We can set up a proportion:

(person's height) / s = h / (s + x)

where x is the distance between the person and the pole, and we are looking for the rate at which s is changing with respect to time. Differentiating both sides with respect to time, we get:

-(person's height) / s² (ds/dt) = h / (s + x)² (ds/dt + dx/dt)

Solving for ds/dt, we get:

ds/dt = -(h/s²) / (1 + x/s)² (dx/dt)

We know that h = 18 ft, x = 10 ft, and we are given dx/dt = 4 ft/s. We also know that s = 30 ft when the person is 10 ft from the pole. Substituting these values into the equation above, we get:

ds/dt = -(18/900) / (1 + 10/30)² (4) = -0.08 ft/s.

Note that the negative sign indicates that the tip of the shadow is moving away or opposite to the person.

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The number of tickets are 42 Adult,  18 Children and  24 Senior tickets

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

Adult: Child = 7 : 3

Adult : Senior = 7 : 4

When combined, we have

Adult: Child : Senior = 7 : 3 : 4

The number of tickets is 84

i.e. Tickets = 84

So, we have

Adult = 7/14 * 84 = 42

Child = 3/14 * 84 = 18

Senior = 4/14 * 84 = 24

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The probability that the next four trials will result in at least one subscription is =[tex]1 - (1-p)^{4}[/tex]under the condition that streamers' decisions are independent.

Then the  probability of at least one success in four trials is evaluated by performing the formula

[tex]P(at least one success) = 1 - P(failure in one trial)^{n }[/tex]

here n =  number of trials.

Assuming that streamers' decisions are independent,

we could use this formula to evaluate the probability of at least one subscription in four trials.

Then, if we consider that the probability of a subscription is p,

then the probability of no subscription is (1-p)

Hence, the probability of at least one subscription in four trials is

P(at least one subscription) = 1 - P(no subscription in four trials)

=[tex]1 - (1-p)^{4}[/tex]

The probability that the next four trials will result in at least one subscription is =[tex]1 - (1-p)^{4}[/tex]under the condition that streamers' decisions are independent.

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The area of the regular hexagon is approximately 428.5 cm².

The segment a that is drawn from the center of the polygon perpendicular to one of its sides is called the apothem.

To find the area of the polygon, we can use the formula:

Area = (1/2) × apothem × perimeter

We know that the apothem (a) is 7√3 cm and the side length (s) is 14 cm. To find the perimeter, we need to know how many sides the polygon has. Let's assume that it is a regular hexagon (a polygon with six sides), since that is a common shape.

The perimeter of a regular hexagon with side length s is given by:

Perimeter = 6s

Substituting s = 14 cm, we get:

Perimeter = 6(14) = 84 cm

Now we can plug in the values for apothem and perimeter into the formula for area:

Area = (1/2) × a  Perimeter

= (1/2) × 7√3 cm × 84 cm

≈ 428.5 cm²

Rounding to the nearest tenth and including the correct units, the area of the regular hexagon is approximately 428.5 cm².

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The slope of the lines is -1, and the equation of the parallel line is y = - x - 6.

Since, The parallel line passes through the points (-4,-2) and (-3,-3).

Therefore, the slope of the line is,

Slope = (-2 + 3) / (-4 + 3)

         = 1/-1

         = -1

Hence, The equation of the parallel line that is passing through point P is,

y = mx + c

y = -x + c

-3 = -(-3) + c

-3 -3 = c

c = -6

Hence, the slope of the lines is -1, and the equation of the parallel line is,

⇒ y = - x - 6.

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The equation of the line in point-slope form is y - 2 = 5x - 5.

As per the diagram, we can clearly see that the equation of the line passes through the points (1, 2) and ((2, 10).

Apply the formula as described below:

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

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

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

So, the equation of the line that passes through the points (1, 2) and ((2, 10) is,

y - 2 = (10 - 2)/(2 - 1) (x - 1)

y - 2 = 5x - 5

y  = 5x - 3

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So after solving  the value of x is approximately 18.7 inches .Here we can use basic propotionality theorem

Corresponding sides in similar triangles are those sides that share the same orientation in each triangle with respect to the angles. We can observe from the presented problem that:

Side AB of triangle ABC corresponds to side AE of triangle AEF.

Side BC of triangle ABC corresponds to side EF of triangle AEF.

Side AC of triangle ABC corresponds to side FA of triangle AEF.

These corresponding sides are in the same relative position in each triangle and are proportional to each other, which is the key property of similar triangles.

As a result of the similarities between triangles ABC and AEF, their respective sides are proportionate. With this information, we can construct a proportion and find x:

AB / AE = BC / EF

3 / 14 = 4 / x

3x = 56

x ≈ 18.7

So the value of x is approximately 18.7 inches.

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The measure of the central angle for the slice of the pie chart representing sleep is 30 degrees.

To find the measure of the central angle of the slice representing sleep, we need to know what percentage of the 24 hours was spent sleeping.

If Burt slept for 2 hours, then the remaining time he was awake for 24 - 2 = 22 hours.

Therefore, the percentage of time spent sleeping is

2 / 24 * 100% = 8.33%

To convert this percentage to an angle in degrees, we use the formula

Angle = Percentage * 360

So, the central angle of the slice representing sleep is

8.33% * 360 = 30 degrees (rounded to the nearest degree).

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It will take approximately 12 days for the virus to grow from 70 to 310.

To calculate this, we can use the formula for exponential growth:

Nt = N0 x [tex]2^{(t/T)[/tex]

where Nt is the final population size, N0 is the initial population size, t is the time period, T is the doubling time, and 2 is the base of the exponential function.

Using the data given, we can solve for T:

So the doubling time of the virus is approximately 2.87 days.

To find how long it takes to grow from 70 to 310, we can use the same formula:

Therefore, it will take approximately 12 days for the virus to grow from 70 to 310.

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Answer:

The volumes of the cones area s follows:

3. 5.2 inches cube

4. 188.4 inches cube

The volume of the cone can be found as follows:

volume of a cone = 1 / 3 πr²h

where

Therefore,

3.

volume of the cone = 1 / 3 πr²h

r = 1 inches

h = 5 inches

Hence,

volume of the cone = 1 / 3 × π × 1² × 5

volume of the cone = 5π / 3

volume of the cone = 5.2 inches³

4.

volume of the cone = 1 / 3 πr²h

r = 6 metres

h = 5 metres

Hence,

volume of the cone = 1 / 3 × π × 6² × 5

volume of the cone = 180π / 3

volume of the cone = 188.4 inches³

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To solve this word problem, you need to get the LCM (Least Common Multiple) of 5 and 3, as it will give you the number of days until Sally practices piano and plays volleyball on the same day again.

One way to solve the problem is to list out the days on which Sally plays volleyball and practices piano, and then look for the next day on which she does both. We can start by marking today as day 0, and then adding 5 and 3 to find the days on which Sally plays volleyball and practices piano, respectively:Day 0: Sally plays volleyball and practices piano

Day 3: Sally practices piano

Day 5: Sally plays volleyball

Day 6: Sally practices piano

Day 9: Sally practices piano

Day 10: Sally plays volleyball

Day 12: Sally practices piano

Day 15: Sally plays volleyball

Day 15 is the next day on which Sally plays volleyball and practices piano.

Alternatively, we can use the LCM of 3 and 5 to find the next time Sally plays volleyball and practices piano. The LCM of 3 and 5 is 15, which means that Sally plays volleyball every 15 days and practices piano every 15 days. Since Sally did both today, the next time she will do both is in 15 days.

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The solution is: The remainder is 0.

A) 0

Here, we have,

When x is divided by 11, we have a quotient of y and a remainder of 3

x/11 = y + 3

x = 11y + 3 ........(1)

When x is divided by 19, we have a remainder of 3 also

x/19 = p + 3 (p = quotient)

x = 19p + 3 ..........(2)

Equate (1) and (2)

x = 11y + 3 = 19p + 3

11y + 3 = 19p + 3

11y = 19p + 3 -3

11y = 19p

Divide both sides by 11

11y/11 = 19p/11

y = 19p/11

y and p are integers. 19 is a prime number. P/11 is also an integer

y = 19(integer)

This implies that y is a multiple of 19.

When divided by 19, there is no remainder.

The remainder is 0.

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complete question:

When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?A. 0B. 1C. 2D. 3E. 4

Answer:

First one is: 216

Second one is: 249

Step-by-step explanation:

Explanation for the first one:

•Its even

•The tens digit is 1

•If you multiple each one one will get 12

•h is less than u

Explanation for the second one:

•Its odd

•u is more than t

•h is prime

•t=2h --> 4=2x2

•4 is a square number (2x2) and 9 is also a square number (3x3)

Answer:

216

249

Step-by-step explanation:

First Q:

h = u - 4

t = 1

(u-4)(1)(u) = 12

u² - 4u = 12

u² - 4u - 12 = 0

(u-6)(u+2) = 0

u = 6, -2      disregard the negative root

h = 6-4 = 2

Therefore, the number is 216

Second Q:

Just start guessing;  start with the lowest prime number, 2, and see if it works.

h = 2

t = 2h = 2(2) = 4

u is odd, so the lowest digit that is a square and less than 4 is 9

Therefore, the number is 249

The area of the segment of the circle is 13.9cm²

To calculate the area of segment of the circle, we can use the formula which is given as;

A = (1/2) * r² * [(π/180)θ - sinθ]

In the problem, our data given are;

Substituting the values into the formula;

A = (1/2) * 6² * [(π/180)45 - sin45]

A = 0.5 * 36 * [(3.14/180)45 - sin45]

A = 0.5 * 36 * 0.773

A = 13.9cm²

The segment area is 13.9 squared meters

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The interval of convergence for the power series is the set of all values of x for which the series converges. The table mentioned in your question likely shows the values of x for which the series converges or diverges.

The interval of convergence for a power series is determined by finding the values of x for which the series converges absolutely. The convergence or divergence of a power series can be determined using various tests, such as the ratio test or the root test.
Once the interval of convergence is found, it can be summarized as a range of values for x. For example, if the interval of convergence is (-3, 5], then the series converges for all values of x between -3 and 5, inclusive.

Hence, the interval of convergence for a power series is the set of all values of x for which the series converges, and it can be determined by finding the values of x for which the series converges absolutely.

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There are 10 possible selections of groups of 2 students.

We have,

Number of students in chess club= 5

and, 2 students selected at random.

So, the possible number of selection

= C(5, 2)

= 5! / 2! (5-2)!

= 5!/ 2! 3!

= 5 x 4 /2

= 10

Thus, there are 10 possible selection.

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