19 3/5 × 20 2/5 secial product patterns to find the product

Step-by-step explanation:

Volume of ice =   10 X 10 X 20 = 2000 cm^3

tank volume increase will be the same

   100 x 40 x HEIGHT = 2000

            Height = 2000/ ( 100 X 40) =  .5 cm height increase

The melting of the ice block would raise the water level in the tank by approximately 0.5 centimeters. This can be answered by the concept of Volume

To calculate the amount of water that would be displaced by the ice block, we need to first find its volume, which is 10 x 10 x 20 = 2000 cubic centimeters. Since 1 cubic centimeter of water has a mass of 1 gram, the mass of the ice block would be 2000 grams or 2 kilograms.

When the ice block melts, it will turn into water and occupy the same volume, which would displace an equal amount of water in the tank. The volume of the tank is 100 x 40 x h, where h is the increase in water level. Setting the volume of the ice block equal to the increase in the water level, we get:

2000 = 100 x 40 x h

h = 0.5 centimeters

Therefore, the melting of the ice block would raise the water level in the tank by approximately 0.5 centimeters.

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the equation that relates the time it took James to sort the supplies for b bags is: t = 1.5b

option D.

Sherry sorted enough supplies for 10 bags in 30 minutes (from 10:10 a.m. to 10:40 a.m.). Let's call the rate at which Sherry sorted the supplies "r."

Then, we can write:

r = 10 bags / 30 minutes

r = 1/3 bags per minute

Since James sorted twice as fast as Sherry, his rate is 2r:

2r = 2/3 bags per minute

To find the time it took James to sort b bags, we can use the formula:

time = (amount of work) / (rate of work)

In this case, the "amount of work" is b bags, and the "rate of work" is 2/3 bags per minute. So, we get:

time = b / (2/3)

time = (3/2) b

Therefore, the equation that relates the time it took James to sort the supplies for b bags is:

t = (3/2) b

So, the correct answer is (D) t = 1.5b.

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Solving the statement, we get the equation x=2.5-y

Exponents are a mathematical notation used to represent repeated multiplication of a number by itself. Exponents are written as a superscript to the right of the base number, which is the number being multiplied.

given equation:

3²ˣ × [tex]9^{y}[/tex] = 243

Simplifying the expression on the right-hand side, we get:

3²ˣ × [tex]9^{y}[/tex]  = 3⁵

Using the property of exponents that states that when multiplying powers with the same base, we can add their exponents, we get:

[tex]3^{2x+2y}[/tex] = 3⁵

For the equation to hold, the exponents on both sides must be equal. Therefore:

2x + 2y = 5

Dividing both sides by 2, we get:

x + y = 2.5

x=2.5-y

Hence, solving the statement, we get the equation x=2.5-y

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The two triangles therefore meet the Angle-Angle (AA) similarity criterion, which specifies that two angles of one triangle must be congruent with two angles .

Angles are typically modeled with a symbol that resembles a tiny arc between the angle's two sides, with a dot at the vertex. For illustration, angle BAC might be used to represent the angle created by the vectors AB and AC, with point A serving as the vertex. Calculus, geometry, trigonometry, and other branches of mathematics all depend on angles. They are used to calculate different quantities linked to angles and their trigonometry, to measure distances and areas, and to describe the shapes and sizes of objects.

given

Triangles ABD and ECD in the given figure are comparable triangles since they share the same shape and have equal corresponding angles. Angles ADB and CDE are equal because they are formed when parallel lines AB and CD are intersected by transversal BD, and angle BAD and angle EDC are also equal because they are formed when parallel lines AD and EC are intersected by transversal BD. In particular, angle ABD and angle ECD are both right angles (90 degrees).

The two triangles therefore meet the Angle-Angle (AA) similarity criterion, which specifies that two angles of one triangle must be congruent with two angles of another triangle in order for the triangles to be comparable.

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The values of x and w in the two triangles are w = 50and x = 24

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

two triangles

The sum of angles in a triangle is 180 degrees

This means that

w = 180 - 2 * 65

And we have

x = 180 - 2 * 78

When evaluated, we have

w = 50

x = 24

Hence, the values are w = 50and x = 24

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Answer:

51%

Step-by-step explanation:

31,408-20,800=10,608÷20,800=0.51×100=51.

You subtract the retail price from the original and you divide the number you get by the original price and then times the number by a hundred.

The notation of the probability of two events being not independent is option (c) P(B|A) = P(B)

The notation for the probability of two events being not independent is P(B|A) ≠ P(B).

None of the options presented directly corresponds to this notation. However, we can use the concept of independent events to determine the probability of two events being not independent.

If two events A and B are independent, then P(B|A) = P(B). Therefore, if P(B|A) ≠ P(B), then A and B are not independent.

P(B|A) = P(B), which represents the probability of B given A assuming that A and B are independent events.

Therefore, the correct option is (c) P(B|A) = P(B)

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The given question is incomplete, the complete question is:

A and B are two events. The notation for conditional probability is P(B|A).

Which notation is the probability of two events being not independent?

a. P(B|A) = P(A and B) / P(A)

b. P(B|A) = P(A) / P(B)

c. P(B|A) = P(B)

d. P(B|A) = P(B) / P(A)

Let x be the cost of a hot dog and y be the cost of a cheeseburger. Then we can set up the following system of equations:

3x + 2y = 31.25

5x + 2y = 41.75

We can solve for one of the variables by subtracting the first equation from the second:

5x + 2y - (3x + 2y) = 41.75 - 31.25

2x = 10

x = 5

Substituting x = 5 into either of the equations above gives:

3(5) + 2y = 31.25

15 + 2y = 31.25

2y = 16.25

y = 8.125

Therefore, a hot dog costs $5 and a cheeseburger costs $8.125.

Answer:

Answer: 40j - 16 = 40j + (-16) (Additive inverse property) = 40j + (-1)(16) (Distributive property) = 40j + (-1)(4)2 (FOIL - first, outer, inner, last) = (40j + (-1)4) + (-1)2 (Order of operations - parentheses first) = (40j - 4) + (-1)2 (Distributive property) = 36j - 2

Answer:

8(5j−2)

Step-by-step explanation:

1 / 4

Let's find the greatest common factor of 40

8 is greatest common factor

40j/8 - 16/8

=

8(5j-2)

Answer:

x^3 + 16x^2 + 64x First, we need to check if there is a greatest common factor (GCF) that we can factor out. In this case, we can factor out "x" since it is a common factor in all the terms: x(x^2 + 16x + 64) Now, we need to factor the quadratic trinomial inside the parentheses. We can do this by finding two numbers that multiply to 64 and add up to 16. These numbers are 8 and 8: x(x + 8)(x + 8) Therefore, the factored form of the trinomial expression is: x(x + 8)^2 I hope this helps!

0 / 350

Given:

[tex]3x+2x=34-5-4[/tex]

[tex]5x=29-4[/tex]

[tex]5x=25[/tex]

[tex]x=25\div5[/tex]

Answer:

x = 5

Given: 3x+4+2x+5=34

first combine similar values,

3x + 2x and 4 + 5

5x + 9 = 34

time for substitution

5x + 9 - 9 = 34 - 9

5x = 25

divide by the value of x in this instance it is 5

5x = 25 / 5

x= 5

now to check we will plug in 5 for x

3(5) +4+2 (5) +5=34

15 + 4 + 10 + 5 = 34

19 + 15 = 34

34 = 34✓

Hope this helps, happy learning =D

Answer:

61st term = 547

Step-by-step explanation:

The formula for the nth term of an arithmetic sequence is

[tex]a_{n}=a_{1}+(n-1)d[/tex], where a1 is the first term, n is the term position (e.g., 1st or 61st) and d is the common difference.

We already know that a1 = 7 and the n = 61.  We can find the common difference by finding the difference of any two consecutive terms with the smaller term being subtracting from the larger:

Thus, if we use 7 and 16, our common difference (d) is:

d = 16 - 7 = 9

Now, we can simply plug in everything to the formula to find the 61st term:

[tex]a_{61}=7+(61-1)*9\\ a_{61}=7+60*9\\ a_{61}=7+540\\ a_{61}=547[/tex]

a. Mason's error is that he flipped the inequality sign. The correct solution is x > 6.

b. This indicates that any value of x greater than 6 (but not equal to 6) will satisfy the inequality x > 6.

An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to). Inequalities can be used to describe a range of values that a variable can take, rather than just a single value.

a. Mason's error is that he flipped the inequality sign. The correct solution is x > 6.

b. To show the correct solution on the number line, we start by marking 6 on the number line with an open circle (since x is not equal to 6). Then, we shade the area to the right of 6, because x is greater than 6. The graph should look like this:

0 1 2 3 4 5 6o 7 8 9

--------

shaded

This indicates that any value of x greater than 6 (but not equal to 6) will satisfy the inequality x > 6.

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To determine when the ball strikes the ground, we need to find the value of t when the height h(t) is 0.

The equation for the ball's height h at time t seconds after launch is:

h(t) = -4.9t^2 + 9.31t + 239.12

Setting h(t) to 0, we get:

0 = -4.9t^2 + 9.31t + 239.12

We can solve this quadratic equation using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -4.9, b = 9.31, and c = 239.12.

Answer: 6.12 seconds

Step-by-step explanation:

To find when the object strikes the ground, we need to find the time t when the height h(t) is equal to 0 (since the ground is at height 0). We have the equation:

h(t) = -4.9t² + 9.31t + 239.12

To find the time when the object strikes the ground, we need to find the value of t when h(t) = 0:

0 = -4.9t² + 9.31t + 239.12

This is a quadratic equation of the form at² + bt + c = 0, where a = -4.9, b = 9.31, and c = 239.12. We can solve this equation for t using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

Plugging the values of a, b, and c into the formula, we get:

t = (-(9.31) ± √((9.31)² - 4(-4.9)(239.12))) / (2(-4.9))

t = (-9.31 ± √(86.6161 + 4694.336)) / (-9.8)

t = (-9.31 ± √(4780.9521)) / (-9.8)

t ≈ (-9.31 ± 69.14) / (-9.8)

We will have two possible values for t:

t₁ ≈ (-9.31 + 69.14) / (-9.8) ≈ 6.12 (rounded to two decimal places)

t₂ ≈ (-9.31 - 69.14) / (-9.8) ≈ 8.00 (rounded to two decimal places)

Since the height function describes the motion of the ball from a platform, we can discard the negative solution as it represents an invalid time before the ball is launched. Thus, the object strikes the ground at approximately t ≈ 6.12 seconds.

Answer:

Step-by-step explanation:

Area = length x height
A = 2.4 x 5.6
A = 13.44 in^2

Step-by-step explanation:

Decrease is   49500 - 44055 = 5445 dollars

What percent of 49500   is   5445 ?

5445 / 49500   x 100% = 11% decrease

a) If the true rate of rejection is 10%, then the probability that the production will be suspended based on a sample of 15 bearings is 10%.

b)  The assumptions made in part a are that the sample of 15 bearings is representative of the population of bearings produced, and that each bearing is independent of the others.

To ensure that the production process is producing quality products, samples of 15 bearings are taken periodically and carefully inspected. If more than 2 bearings in a sample of 15 fail to meet the required specifications, production is suspended for necessary adjustments.

a) If the true rate of rejection is 10%, what is the probability that the production will be suspended based on a sample of 15 bearings? To answer this question, we need to use the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent trials. In this case, the number of trials is 15, and the probability of success (i.e., a bearing not meeting the required specifications) is 10%.

b) The assumptions allow us to use the binomial distribution to calculate the probability of having a certain number of bearings fail to meet the required specifications in a sample of 15. Additionally, we assume that the true rate of rejection is 10%, which may not always be the case.

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The test statistic for this hypothesis test is -0.3886.

In statistical hypothesis testing, a test statistic is a numerical value that is calculated from a sample of data and used to determine whether to accept or reject the null hypothesis.

To calculate the test statistic for this hypothesis test, we need to use the formula for the proportion test

z = (p - P) / sqrt(P(1-P) / n)

Where

p is the proportion of Canadian content in the sample (33/100 = 0.33)

P is the hypothesized proportion (35% = 0.35)

n is the sample size (100)

Substituting the values, we get

z = (0.33 - 0.35) / sqrt(0.35(1-0.35) / 100)

z = -0.02 / 0.0516

z = -0.3886

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Holt linear exponential smoothing or  Holt-Winters exponential smoothing technique is best for data with a trend but no seasonality.

For trend but nonseasonal data, Holt linear exponential smoothing (aka double exponential smoothing) or Holt-Winters exponential smoothing (aka triple exponential smoothing) can be used to compare single exponential smoothing or Exponential smoothing is better than post-winter smoothing.

Holt's linear exponential smoothing method uses his two smoothing factors:

One for the level of the series and one for the trend. Suitable when data show a linear trend.

Holt-Winter exponential smoothing adds his third seasonal smoothing factor to Holt's linear exponential smoothing method. Appropriate when the data show trends over time and exhibit seasonal patterns. Therefore, Holt's linear exponential smoothing method is best when the data show a linear trend. Holt-Winters exponential smoothing is more appropriate when trends are more complex and there is evidence of seasonality.

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4/3 Gallons of wood sealant are needed to cover the floor of Jose's vacation home.

To determine how many gallons of wood sealant are needed to cover the floor, first, we need to find the relationship

between the surface area of the hemispherical ceiling and the floor.

Calculate the surface area of the hemispherical ceiling.

The surface area of a hemisphere is given by the formula [tex]3πr^2[/tex], where r is the radius.

Calculate the surface area of the floor.

The floor is a circle, so its surface area is given by the formula[tex]πr^2[/tex].

Determine the ratio between the surface areas.

Divide the surface area of the floor by the surface area of the hemispherical ceiling: [tex](πr^2) / (3πr^2).[/tex] The [tex]πr^2[/tex]terms

cancel out, leaving 1/3.

Apply the ratio to the amount of wood sealant used for the ceiling.

Since Jose used 4 gallons of wood sealant for the ceiling, we can multiply this by the ratio to find the amount needed

for the floor: 4 gallons × (1/3) = 4/3 gallons.

Therefore, 4/3 gallons of wood sealant are needed to cover the floor of Jose's vacation home.

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Answer:

A system of linear system equation usually has a single solution but some time it can have no solution or infinte solution(Same line)

By the AA similarity theorem, we can conclude that triangles FGH and FPQ are similar.

To prove that triangles FGH and FPQ are similar, we need to show that their corresponding angles are congruent and their corresponding sides are proportional.

Angle F in triangle FGH corresponds to angle F in triangle FPQ

Angle H in triangle FGH corresponds to angle Q in triangle FPQ

Angle G in triangle FGH corresponds to angle P in triangle FPQ

From the problem, we know that angle F = 63 degrees and angle H = 30 degrees. We also know that angle GPQ = 93 degrees, which means angle G + angle P = 93 degrees. Therefore, angle G = 93 degrees - angle P

Using the fact that the sum of angles in a triangle is 180 degrees, we can find angle Q:

Angle FGH: angle F + angle G + angle H = 63 degrees + (93 - angle P) + 30 degrees = 186 - angle P degrees

Triangle FPQ: angle F + angle P + angle Q = 180 degrees

Therefore, angle Q = 180 - angle F - angle P = 117 - angle P degrees

Now, we can compare the corresponding sides:

Side FG in triangle FGH corresponds to side FQ in triangle FPQ

Side GH in triangle FGH corresponds to side PQ in triangle FPQ

Side FH in triangle FGH corresponds to side PQ in triangle FPQ

To show that these sides are proportional, we can use the Angle-Angle (AA) similarity theorem and We already know that angle F in triangle FGH corresponds to angle F in triangle FPQ, and angle G in triangle FGH corresponds to angle P in triangle FPQ. We just showed that angle Q in triangle FPQ corresponds to angle H in triangle FGH. Therefore, we have two pairs of corresponding angles that are congruent.

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it will take Shannon about 80 months for her money to double if she deposits it into a savings account that earns 10.99% interest compounded quarterly.

Shannon's funds will double in value during the following period of time, according to the quarterly compound interest formula:

[tex]A = P(1+r/n)^{nt}[/tex]

where n is the number of times interest is compounded each year, r is the yearly interest rate, P is the principal amount, A is the amount after t years, and t is the amount of time in years.

Shannon currently has P/2 dollars, which is half of what she needs. Finding t when A = 2P will help us determine how long it will take for her money to double.

We are aware that n = 4 and r = 10.99%. (since interest is compounded quarterly). Solving for t using these values as input results in:

[tex]2P = P/2(1 + 0.1099/4)^{(4t) }\\4 = (1 + 0.1099/4)^{(4t)} log(4) \\= 4t log(1 + 0.1099/4)^ t = log(4)/(4 log(1 + 0.1099/4))[/tex]

t ≈ 6.7 years

Rounding this to the nearest month gives:

t ≈ 80 months

Therefore, it will take Shannon about 80 months for her money to double if she deposits it into a savings account that earns 10.99% interest compounded quarterly.

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We need to find the GCF of 72 and 90 to solve this problem. We can calculate it in the following manner.

To solve this problem, we need to find the greatest number of party bags April can make with no candies left over. This means we need to find the greatest common factor (GCF) of 72 and 90.

The GCF of two numbers is the largest number that divides evenly into both of them. In this case, we need to find the largest number that can divide both 72 and 90 without any remainder.

Once we have found the GCF, we can divide both 72 and 90 by it to find the maximum number of party bags April can make with no candy left over.

Therefore, we need to find the GCF of 72 and 90 to solve this problem.

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Answer:

First find slope. m = (y2 - y1)/(x2 - x1) = (6 -1)/(-6 --3) = 5/-3. then. use. y - y1 =. m (x - x1). which gives. y - 1 = -5/3(x - 3)

Step-by-step explanation:

The distance between the points (15, -17) and (-20, -5) is 37.

The distance formula is a mathematical formula used to find the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and can be used to find the distance between any two points, whether they are on the same line or on different lines.

We can use the distance formula to find the distance between two points:

[tex]\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

Let [tex]\rm (x_1,y_1)[/tex] = (15,-17) and [tex]\rm (x_2, y_2)[/tex] = (-20,-5)

Then, plugging into the formula, we get:

[tex]\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

[tex]\rm = \sqrt{(-20-15)^2 + (-5-(-17))^2}[/tex]

[tex]= \sqrt{(-35)^2 + (12)^2}[/tex]

[tex]= \sqrt{1225+144}[/tex]

[tex]= \sqrt{1369}[/tex]

= 37

Therefore, the distance between the points (15, -17) and (-20, -5) is 37.

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Complete question:

Find the distance between point (15,-17) and (-20,-5).

Answer:

186 inches

Step-by-step explanation:

8×6=48

5.5×16=88

10×5=50

48+88+50=186