Can you find the sum of three consecutive even integers that add up to 153 ?

After pouring some water from container A into container B, the new height of the water in both containers will be equal.

When container A is filled with water to the brim, it reaches its maximum capacity. Let's assume the initial height of the water in container A is h.

When some water is poured from container A into container B, the water level in both containers will gradually equalize until they reach the same height. Let's denote this new height as H.

The reason the water levels equalize is due to the principle of fluid equilibrium. When the containers are connected and the water is allowed to flow, the water seeks a common level. This occurs because the pressure at the same height in a fluid is equal.

Therefore, after pouring water from container A to container B, the final height of the water in both containers will be H, which indicates that the water has reached an equilibrium point where the pressure is equal in both containers.

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Yes the triangle with dimension 3 cm , 4cm , 5 cm is  a right angled triangle.

Given,

Dimensions : 3 cm , 4cm , 5 cm .

Here,

In any right angled triangle the Pythogoras theorem holds trure .

Pythogoras theorem ,

P² + B² = H²

P = perpendicular

B = base

H = hypotenuse .

So,

In triangle ,

3cm , 4cm , 5cm

Apply pythogoras theorem .

Let ,

P =3cm

B = 4cm

H = 5cm

3² + 4² = 5²

25 = 25 .

Thus the triangle is right angled triangle .

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Answer:

h = -1.356

Step-by-step explanation:

Remark

This is one of those questions where you could solve for h in the formula and then just put values in for all the other variables. Since you have posted this on Brainly, I'll just use the formula given and my last step will be one of division

Formula

S = 2 * pi * r^2  + 2 * pi * r * h   Put the givens into the formula

Givens

S = 175 in^2

pi = 3.14

r = 6

h = ?

Solution

175 = 2 * 3.14 * 6^2 + 2 * 3.14 * 6 * h         Combine

175 = 226.08 + 37.68*h                             Subtract  226.08 from both sides

175-226.08 = 37.68*h                                Combine

-51.08 = 37,68*h                                         Divide by 37.68

h = - 51.08/37.68

h = -1.356

Comment

This is impossible. No value of measurement can be negative. But it is what you get when using the numbers given

For the first loan, the final payment is $1,576.25. For the second loan, the final payment is $0. The calculations consider the given interest rates and compounding periods.



To determine the final payment for the first loan, we need to calculate the accumulated value of the loan after six years. For the first year, interest is compounded quarterly at a rate of 10% per annum. The accumulated value after one year is $10,000 * (1 + 0.10/4)^(4*1) = $10,000 * (1 + 0.025)^4 = $10,000 * 1.1038125.For the next three years, interest is compounded semi-annually at a rate of 8% per annum. The accumulated value after four years is $10,000 * (1 + 0.08/2)^(2*4) = $10,000 * (1 + 0.04)^8 = $10,000 * 1.3604877.

Finally, for the remaining two years, interest is compounded annually at a rate of 7.5% per annum. The accumulated value after six years is $10,000 * (1 + 0.075)^2 = $10,000 * 1.157625.To find the final payment, we subtract the payments made so far ($5,000 and $6,000) from the accumulated value after six years: $10,000 * 1.157625 - $5,000 - $6,000 = $1,576.25.For the second loan, we calculate the accumulated value after six years using the given interest rates and compounding periods for each period. The accumulated value after two years is $5,000 * (1 + 0.09/4)^(4*2) = $5,000 * (1 + 0.0225)^8 = $5,000 * 1.208646.

The accumulated value after four years is $5,000 * (1 + 0.10/12)^(12*2) = $5,000 * (1 + 0.0083333)^24 = $5,000 * 1.221494.Finally, the accumulated value after six years is $5,000 * (1 + 0.10)^2 = $5,000 * 1.21.To find the final payment, we subtract the payments made so far ($2,500 and $2,500) from the accumulated value after six years: $5,000 * 1.21 - $2,500 - $2,500 = $0.

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The area of ABCD is 62.4ft²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

The area of triangle is expressed as;

A = 1/2bh

The area of ABCD = area ABD + area BDC

cos55 = AD/10

0.57 = AD/10

AD = 0.57 × 10

AD = 5.7

AB = √ 10² - 5.7²

AB = √100 - 32.49

AB = √ 67.51

AB = 8.2

Area = 1/2 × 5.7 × 8.2

= 23.1 ft²

Angle C = 180-( 38+44)

angle C = 180 - 82

C = 98°

Finding DC

sin38/DC = sin98/10

DC = 10sin38/sin98

DC = 6.2/ 0.99

= 6.3

Area = 1/2absinC

= 1/2 × 6.3 × 10× sin98

= 62.4ft²

Therefore area of ABCD

= 62.4 + 23.1

= 85.5 ft²

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The probability of rolling exactly a 1 when a dice is picked randomly from two 4-sided dice and three 6-sided dice is 0.4 or 40%.

To calculate the probability of rolling exactly a 1 when a dice is picked randomly from two 4-sided dice and three 6-sided dice, we need to determine the total number of dice and the number of dice that have a 1 as a possible outcome.

There are two 4-sided dice and three 6-sided dice, so the total number of dice is 2 + 3 = 5.

Out of these five dice, we need to determine how many have a 1 as a possible outcome.

Among the two 4-sided dice, there is only one die (out of two) that has a 1 as a possible outcome.

Among the three 6-sided dice, there is also one die (out of three) that has a 1 as a possible outcome.

Therefore, there are a total of two dice that have a 1 as a possible outcome.

The probability of rolling exactly a 1 when a dice is picked randomly is calculated by dividing the number of favorable outcomes (two dice) by the total number of possible outcomes (five dice):

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 2 / 5

Probability = 0.4

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The total distance of the race = 8.91  miles

Solution :

Miles :

There are 5,280 feet in one mile. Simply divide 5,280 feet by your average stride length to learn how many steps it will take to walk a mile. If your average stride length is 2 feet, for example, it will take 2,640 steps to walk a mile.

One part of the race is 3.21 miles

another part of the race is 5.7 miles

Total :

add of both trails

= 3.21+5.7

= 8.91

The total distance of the race = 8.91  miles

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The boxes of candy sold by Roger are 29/30.

According to the question,

We have the following information:

Roger sold 1/3 as much candy as Sally sold.

Sally sold \(2\frac{9}{10}\) boxes of candy.

Now, first we will convert the boxes of candy sold by Sally from the mixed fraction.

(More to know: there are three kinds of fraction: mixed fraction, proper fraction and improper fraction. We need to change mixed fraction in most of the cases to solve the questions further.)

We have:

29/10

Now, we know that the boxes of candy sold by Roger is 1/3 of 29/10.

So, we have the following expression:

\(\frac{1}{3}* \frac{29}{10}\)

29/30

Hence, the boxes of candy sold by Roger is 29/30.

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Answer:

(-3,0)

Step-by-step explanation:

The vertex is the maximum  of a downward facing parabola

The maximum is (-3,0)

Answer:

280

Step-by-step explanation:

\(\frac{5}{8} *x = 175\\\\ \frac{x}{8}=35\\ x=35*8=280\)

The number is 280.

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

Let the number be x.

According to the given question.

\(\frac{5}{8}\) of number is 175.

The linear equation in one variable of the above statement is given by

\(\frac{5}{8}(x) = 175\)

Solve the above linear equation in one variable for x.

\(\frac{5}{8} x = 175\)

⇒ \(5x = 175(8)\)             ( multiplying both the sides by 8)

⇒ \(5x = 1400\)

⇒ \(x = \frac{1400}{5}\)               ( dividing both the sides by 5)

⇒ \(x =280\)

Hence, the number is 280.

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The probability for the third woman to have a girl is 50%, not influenced by the outcome of the previous two pregnancies.

The probability for a woman to have a girl is 50%. So, the probability for two women to have girls is (0.5 x 0.5 = 0.25 or 25%).

However, this does not mean that the third woman will also have a girl. Each pregnancy is independent and the outcome of one pregnancy does not affect the outcome of another.

So, the probability for the third woman to have a girl is still 50%, regardless of the outcome of the other two pregnancies. The probability of having three girls in a row is 0.25 x 0.5 = 0.125 or 12.5%.

Therefore, the probability for the third woman to have a girl is 50%, not influenced by the outcome of the previous two pregnancies.

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There are 52 sets of cards with the same rank, 1824 sets of cards with different ranks, and 11232 sets of cards where two of the cards have the same rank and the third has a different rank.

(a) To find the number of sets of cards where the cards have the same rank, we need to choose one rank out of the 13 available ranks. Once we have chosen the rank, we need to choose 3 cards from the 4 available suits for that rank. The total number of sets can be calculated as:

Number of sets = 13 * (4 choose 3) = 13 * 4 = 52 sets

(b) To find the number of sets of cards where the cards have different ranks, we need to choose 3 ranks out of the 13 available ranks. Once we have chosen the ranks, we need to choose one suit from the 4 available suits for each rank. The total number of sets can be calculated as:

Number of sets = (13 choose 3) * (4 choose 1) * (4 choose 1) * (4 choose 1) = 286 * 4 * 4 * 4 = 1824 sets

(c) To find the number of sets of cards where two of the cards have the same rank and the third card has a different rank, we need to choose 2 ranks out of the 13 available ranks. Once we have chosen the ranks, we need to choose 2 cards from the 4 available suits for the first rank and 1 card from the 4 available suits for the second rank. The total number of sets can be calculated as:

Number of sets = (13 choose 2) * (4 choose 2) * (4 choose 2) * (4 choose 1) = 78 * 6 * 6 * 4 = 11232 sets

Therefore, there are 52 sets of cards with the same rank, 1824 sets of cards with different ranks, and 11232 sets of cards where two of the cards have the same rank and the third has a different rank.

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Answer:

implicit array sizing

Step-by-step explanation:

The statement "int grades[] = { 100, 90, 99, 80 };" initializes an integer array called "grades" with the values 100, 90, 99, and 80. The given statement is an example of initializing an integer array in C++.

The array is named "grades" and has an unspecified size denoted by the empty square brackets []. The values inside the curly braces { } represent the initial values of the array elements.

In this case, the array "grades" is initialized with four elements: 100, 90, 99, and 80. The first element of the array, grades[0], is assigned the value 100, the second element, grades[1], is assigned 90, the third element, grades[2], is assigned 99, and the fourth element, grades[3], is assigned 80.

The array can be accessed and manipulated using its index values. This type of initialization allows you to assign initial values to an exhibition during its declaration conveniently.

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Answer:

x+35/5=2

x+35=10

x=-25

Answer:

\(\frac{1}{5} x\)+7=2, x=-25

\(\frac{m}{7} -7=3\), m= 105

\(\frac{3}{5} x+7=-20, x= -45\)

\(-\frac{2}{7} t+5=17, t=-42\)

4.9x+4.2=9.1, x=1

Explanation for last two:

\(-\frac{2}{7}t+5=17\)  

Step 1: Subtract 5 from both sides.

\(\frac{-2}{7} t+5-5=17-5\)

\(\frac{-2}{7} t=12\)

Step 2: Multiply both sides by 7/(-2).

\((\frac{7}{-2} )*( \frac{-2}{7}t )= (\frac{7}{-2} )*(12)\)

t=−42

4.9x+4.2=9.1

Step 1: Subtract 4.2 from both sides.

4.9x+4.2−4.2=9.1−4.2

4.9x=4.9

Step 2: Divide both sides by 4.9.

\(\frac{4.9x}{4.9} \frac{4.9}{4.9}\)

x=1

Domain: [-5, 1)

Range: [-4, 7)

The range and domain of the graphed function are:

Domain: [-5, 1)

Range: [-4, 7)

If a function is graphed on a coordinate plane, all values on the x-axis are the domain while those on the y-axis make up the range of the function.

In the given graphed function, the domain starts from -5 up to 1, while the range starts from -4 up to 7.

Therefore, the domain and range are:

Domain: [-5, 1)

Range: [-4, 7)

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AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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The shape of the probability distribution for the random walk problem depends on the values of p and q. When p = q, the distribution is symmetric, while if p and q have different values, the distribution becomes asymmetric.

The shape of the probability distribution for the problem of the random walk can be determined by considering the values of p and q, where p represents the probability of moving in one direction and q represents the probability of moving in the opposite direction.
(a) In this case, we are given that p = q = 1/2, which means that there is an equal probability of moving in either direction.
When p = q = 1/2, the probability distribution for the random walk problem will have a symmetric shape. This means that the probabilities of moving to the left and the right are the same. For example, if we start at position 0 and take 20 steps, the probability of ending up at position +10 will be the same as the probability of ending up at position -10.
It is important to note that the specific values of p and q do not affect the shape of the distribution. As long as p = q, the distribution will be symmetric.

(b) Now, let's consider a different scenario where p = 0.6 and q = 0.4. In this case, the probability of moving in one direction is greater than the probability of moving in the opposite direction. This will result in an asymmetric probability distribution.
For example, if we start at position 0 and take 20 steps, the probability of ending up in a positive position will be higher than the probability of ending up in a negative position. The distribution will be skewed towards the positive position.

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The slope of the secant line PQ can be found by calculating the difference in y-coordinates divided by the difference in x-coordinates between the points P and Q. In this case, when x = 16.1, the slope of PQ can be determined.

To find the slope of the secant line PQ, we need to calculate the difference in y-coordinates and the difference in x-coordinates between the points P(16, 9) and Q(x, √(x) + 5). The slope of a line is given by the formula: slope = (change in y) / (change in x).

Given that P(16, 9) lies on the curve y = √(x) + 5, we can substitute x = 16 into the equation to find the y-coordinate of point P. We get y = √(16) + 5 = 9.

Now, for Q(x, √(x) + 5), we have x = 16.1. Substituting this value into the equation, we find y = √(16.1) + 5.

To find the slope of PQ, we calculate the difference in y-coordinates: (√(16.1) + 5) - 9, and the difference in x-coordinates: 16.1 - 16. Then, we divide the difference in y-coordinates by the difference in x-coordinates to obtain the slope of PQ when x = 16.1.

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According to the given statement , Emily can make 227,468,710 possible display arrangements with 11 plants in each spot.

To find the number of possible display arrangements, we need to calculate the number of ways to choose 11 plants from a total of 66 plants. This can be calculated using the combination formula.

The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen at a time. Plugging in the values, we get 66C11 = 66! / (11!(66-11)!) = 227,468,710. Thus, Emily can make 227,468,710 possible display arrangements with 11 plants in each spot.

1. We are given that there are 33 spots in the window display, and each spot can hold 11 plants.
2. Emily has a total of 66 plants to choose from, all of different types.
3. To find the number of possible display arrangements, we need to calculate the number of ways to choose 11 plants from the total of 66 plants.
4. Using the combination formula, nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen at a time.
5. Plugging in the values, we get 66C11 = 66! / (11!(66-11)!) = 227,468,710.
6. Therefore, Emily can make 227,468,710 possible display arrangements with 11 plants in each spot.

Emily can make 227,468,710 possible display arrangements with 11 plants in each spot.

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Answer:

20 + 16 = 36

Step-by-step explanation:

The conjecture: "The sum of two positive even integers is always an odd integer" can be easily be proven false with a counterexample.

Pick A=20 and B=16, both are positive even integers.

The sum of both A + B = 36 is an even integer. This is a counterexample because being even is the contrary of being odd.

Counterexample: 20 + 16 = 36

In fact, the conjecture is always false, since there cannot be found any pair of positive integers whose sum is odd.

Other possible counterexamples are:

10 + 8, 700 + 40, 12 + 14, etc.

Answer:

B= 18x

Step-by-step explanation:

use identity :  (a+b)² = a²+2ab+b²   you have a =3x  and b =3 so: B =2ab

the second term of this trinomial is : 2ab  means : 2(3x)(3) = 18x

(3x +3)2=9x2+2(3x)(3)+3²

Answer:

18 tables: $143

t tables: $35 + $6t

Step-by-step explanation:

35 + 6t

35 + 6(18) = 35 + 108 = 143

Answer: A

Step-by-step explanation:

r = j + 3

We subtitube r to find j,

r = 9          j = 9 + 3 = 12

r = 15         j = 15 + 3 =18

r = 21         j = 21 + 3 = 24    

And we found A as answes.

Answer:

Step-by-step explanation:

Table C is the correct one

You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The relationship between the two variables in a bivariate data set is graphically represented by a scatter plot. Consider them to be the graphic depiction of two data sets that have been combined by allocating each axis in the plot to a distinct variable.

Due to the presence of two variables, this type of data is known as bivariate data. Only 1 variable may be displayed on a line plot. You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The standard deviation of each variable and the covariance between them must first be determined in order to calculate the Pearson correlation. Covariance is subtracted from the product of the standard deviations of the two variables to get the correlation coefficient.

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The domain of the function is all real numbers and  range is  y ≥ -1.

Since the vertex is at (1,-1), the axis of symmetry is x = 1.

This means that the domain of the function is all real numbers.

To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.

However, since the parabola opens upwards, there is no upper bound on the y-values.

Therefore, the range is given by y ≥ -1.

Hence, the domain of the function is all real numbers and  range is  y ≥ -1.

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The height of the tree is approximately 30.60 meters.

To find the height of the tree, we can use the trigonometric relationship between the height of an object, the length of its shadow, and the angle of elevation of the sun.

Let's denote the height of the tree as h and the length of its shadow as s. The angle of elevation of the sun is given as 38 degrees.

Using the trigonometric function tangent, we have the equation:

tan(38°) = h / s

Substituting the given values, we have:

tan(38°) = h / 84.75ft

To convert the length from feet to meters, we use the conversion factor 1ft = 0.3048m. Therefore:

tan(38°) = h / (84.75ft * 0.3048m/ft)

Simplifying the equation:

tan(38°) = h / 25.8306m

Rearranging to solve for h:

h = tan(38°) * 25.8306m

Using a calculator, we can calculate the value of tan(38°) and perform the multiplication:

h ≈ 0.7813 * 25.8306m

h ≈ 20.1777m

Rounding to two decimal places, the height of the tree is approximately 30.60 meters.

The height of the tree is approximately 30.60 meters, based on the given length of the shadow (84.75ft) and the angle of elevation of the sun (38 degrees).

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