A toy was sent in a box 8 inches long, 5 inches wide, and 15 inches high? What is the volume of the box?

Answer:

Step-by-step explanation:

Step-by-step explanation:

180 ° - 146°=34°

Where by isosceles triangle is 180

The specific name of the quadrilateral is kite

The measures of the missing angles are 75 degrees each

To determine the measure of the angle, we need to know the different properties of a kite.

The properties of a kite includes;

Since the adjacent angles are equal, we have that;

105+ x = 180

collect the like terms, we have;

x = 180 - 105

x = 75 degrees

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The quadrilateral is a kite and the missing angles are 105° and 45°

A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

A kite has a pair of equal angle and the diagonals of a kite meets at 90°.

In a kite , there are two pairs of congruent or equal sides.

This means that the missing angles are

The opposite angle to 105 is also 105°

The fourth angle is calculated as;

105+105+105+x = 360

= 315 +x = 360

x = 360- 315

x = 45°

Therefore the quadrilateral is a kite and the missing angles are 105° and 45°

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The interesting or surprising thing we can learn about converting between improper fractions and mixed numbers is that to know how large or small a fraction formed from mixed number.

A mixed number, or fraction is a number having two parts one is integer (whole number) and other is a proper fraction (having numerator is less than its denominator). An example of a mixed number is \(2\frac{1}{\\ 2} \\ \). An improper fraction is defined when the top number (numerator) is larger than the bottom number (denominator). For example, \( \frac{8}{5} \).

To change an improper fraction to a mixed number follow these steps.

The conversion between improper fractions and mixed numbers or mixed to improper is a best way to be able to understand fractions and recognize how large or small a fraction is.

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Answer:

1/4

Step-by-step explanation:

25% is 1/4

Answer:

Angle Bisector I believe

Step-by-step explanation:

Apologies if I am wrong

Answer:

  4 seconds

Step-by-step explanation:

Given the equation y = -16t² +28t +144 describes a ball's height as a function of time in seconds, you want to know when the ball will hit the ground.

The ball will hit the ground when the value of y is zero.

  0 = -16t² +28t +144

  t² -7/4t -9 = 0 . . . . . divide by 16

  t² -7/4t +(7/8)² = 9 +(7/8)² . . . . . complete the square

  t = 7/8 +√(9 49/64) = 7/8 +3 1/8 = 4 . . . . take the square root, add 7/8

The ball will hit the ground after 4 seconds.

Using the given natural abundances of titanium-46, titanium-47, and titanium-48, we find that the average atomic mass of titanium on this planet is approximately 46.4 amu.

To calculate the average atomic mass of titanium on another planet, we need to consider the natural abundances of its isotopes. The average atomic mass is calculated by multiplying the mass of each isotope by its relative abundance and summing up these values.

Let's assume that the three isotopes of titanium on this planet are denoted as titanium-46, titanium-47, and titanium-48. The natural abundances of these isotopes are given as follows:

Isotope Natural Abundance

Titanium-46 70%

Titanium-47 20%

Titanium-48 10%

To calculate the average atomic mass, we multiply the mass of each isotope by its relative abundance and sum up these values. The atomic masses of titanium-46, titanium-47, and titanium-48 are approximately 46.0 amu, 47.0 amu, and 48.0 amu, respectively.

Average Atomic Mass of Titanium:

(46.0amu×70%)+(47.0amu×20%)+(48.0amu×10%)

=(32.2amu)+(9.4amu)+(4.8amu)

=46.4amu

Therefore, the average atomic mass of titanium on this planet is approximately 46.4 atomic mass units (amu).

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Answer:

30

Step-by-step explanation:

five is half of ten

15 is half of 30

Converting the integral, the integral in cylindrical coordinates is `∭ (16 - r²) dz dy dx` where `0 ≤ r ≤ 4` and the integral in spherical coordinates is `∭ (16r² - r⁴) sin θ dr dθ dϕ` where `0 ≤ r ≤ 4`, `0 ≤ θ ≤ π` and `0 ≤ ϕ ≤ 2π`.

Now we convert the given integral in cylindrical coordinates: Given, `V x² + y² ≤ 16`Here, `x = r cos θ` and `y = r sin θ`So, `x² + y² = r²`

Therefore, `V r² ≤ 16` or `0 ≤ r ≤ 4`So, the integral becomes:`∭ V (16 - r²) dz dy dx` where `0 ≤ r ≤ 4`

So, the integral becomes, `∭ (16 - r²) dz dy dx` where `0 ≤ r ≤ 4`

Now, we convert the given integral in spherical coordinates: Given, `V x² + y² + z² ≤ 16`Here, `x = r sin θ cos ϕ`, `y = r sin θ sin ϕ` and `z = r cos θ`So, `x² + y² + z² = r²`

Therefore, `V r² ≤ 16` or `0 ≤ r ≤ 4`

So, the integral becomes:`∭ V (16 - r²) r² sin θ dr dθ dϕ` where `0 ≤ r ≤ 4`, `0 ≤ θ ≤ π` and `0 ≤ ϕ ≤ 2π`

So, the integral becomes, `∭ (16r² - r⁴) sin θ dr dθ dϕ` where `0 ≤ r ≤ 4`, `0 ≤ θ ≤ π` and `0 ≤ ϕ ≤ 2π`

Now, let's evaluate the integral:`∭ (16 - r²) dz dy dx``∭ (16 - r²) dz dy dx``∭ (16 - r²) dz dy dx``∫ dx ∫ dy ∫ (16 - r²) dz``∫ dx ∫ dy (16z - r²z) |_0^16``∫ dx (16y - r²y)|_0^√(16 - x²)``(16x - r²x)|_0^√(16 - y²)``(16 - r²)r/3|_0^4``(16r/3 - 64/3) dr``(8r² - 64r)/3 |_0^4``256/3 - 512/3``= - 256/3`

Therefore, the integral in cylindrical coordinates is `∭ (16 - r²) dz dy dx` where `0 ≤ r ≤ 4` and the integral in spherical coordinates is `∭ (16r² - r⁴) sin θ dr dθ dϕ` where `0 ≤ r ≤ 4`, `0 ≤ θ ≤ π` and `0 ≤ ϕ ≤ 2π`.

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The mean of a single roll is given as μ = 3.5, and the variance is given as \(σ^2\) = 2.92.

The sample size for the first five rolls is n1 = 5, and the sample size for the remaining ten rolls is n2 = 10.

The mean of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:

μ(x¯1−x¯2) = μ(x¯1) - μ(x¯2) = μ - μ = 0

The variance of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:

σ^2(x¯1−x¯2) = (σ^2(x¯1)/n1) + (σ^2(x¯2)/n2)

where σ^2(x¯1) is the variance of the sample mean for the first five rolls and σ^2(x¯2) is the variance of the sample mean for the remaining ten rolls.

Since each roll of the die is independent, the variance of the sample mean for each sample is given as:

σ^2(x¯1) = σ^2/ n1 = 2.92/5 = 0.584

σ^2(x¯2) = σ^2/ n2 = 2.92/10 = 0.292

Substituting these values in the above equation, we get:

σ^2(x¯1−x¯2) = (0.584/5) + (0.292/10) = 0.1468

Therefore, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is:

σ(x¯1−x¯2) = sqrt(σ^2(x¯1−x¯2)) = sqrt(0.1468) = 0.3835 (rounded to four decimal places)

Hence, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is 0.3835.

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Answer:

3

Step-by-step explanation:

hope it helped

Answer:

Yes, because, even though all angles match, one is larger than the other. So just having the same angles is no guarantee they are congruent.

Step-by-step explanation:

Answer:

Same Angles

because, even though all angles match, one is larger than the other. So just having the same angles is no guarantee they are congruent.

Step-by-step explanation:

Hope this Helps!

Answer: Side Angle Side

Answer:

B.

She can rotate triangle DEF 180and then compare the angles and sides. She will see that the triangles are congruent by the Side Angle Side theorem.

Step-by-step explanation:

Answer:

$48.24

Step-by-step explanation:

33% of 72 = 23.76

72 - 23.76 = 48.24

student can answer the questions on the test in 16,384 different ways if they answer every question.

To determine the number of ways a student can answer the questions on a multiple-choice test containing 7 questions with four possible answers for each question, we will use the multiplication principle. The multiplication principle states that if there are a number of independent choices, then the total number of possible outcomes is the product of the number of choices.
Identify the number of questions and possible answers. In this case, there are 7 questions and 4 possible answers for each question.
Calculate the number of ways to answer each question. Since there are 4 possible answers for each question, there are 4 ways to answer each of the 7 questions.
Apply the multiplication principle. To find the total number of ways to answer all 7 questions, multiply the number of ways to answer each question:
Total number of ways = (4 ways for question 1) x (4 ways for question 2) x ... x (4 ways for question 7)
Perform the calculation. Since there are 7 questions and 4 ways to answer each question, the total number of ways is:
Total number of ways = 4^7 = 16,384

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The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

To solve the quadratic equation 3x^2 - 9x - 12 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = -9, and c = -12. Substituting these values into the quadratic formula, we have:

x = (-(-9) ± √((-9)^2 - 4 * 3 * (-12))) / (2 * 3)

= (9 ± √(81 + 144)) / 6

= (9 ± √(225)) / 6

= (9 ± 15) / 6.

We have two possible solutions:

For the positive root:

x = (9 + 15) / 6

= 24 / 6

= 4.

For the negative root:

x = (9 - 15) / 6

= -6 / 6

= -1.

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

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The values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C

Complementary angles are defined as angles that sum up to 90 degrees.

Example:

If x and y are complementary angles, then;

x + y = 90°

From the information given, we have the angles;

since they are complementary, then;

2x - 7 + 3x + 2 = 90

collect like terms

2x + 3x = 90 + 5

Add like terms

5x = 95

Make 'x' the subject of formula

x = 95/5

x = 19

But;

m∠WYX = (2x − 7) = ( 2(19) - 7) = 38 - 7 = 31°

m∠WYZ = (3x + 2)° = (3(19) + 2) = 57 + 2 = 59°

Thus, the values of m∠WYX and m∠WYZ are 31° and 59° respectively. Option C

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The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Answer:

The answer is 16.

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

just simply add all of the terms together.

The fraction of senators who are either Democrats or Republicans is 59/100.

In the 115th Congress, there are a total of 100 senators. Among them, Democrats make up 46/100 (or 46%) of the senators, while Republicans make up 13/25 (or 52%) of the senators.

To find the fraction of senators who are either Democrats or Republicans, we add the fractions representing each party's representation:

46/100 + 13/25

To add these fractions, we need a common denominator. The least common multiple of 100 and 25 is 100, so we can rewrite the fractions with a common denominator

46/100 + 52/100

Now, we can add the numerators and keep the denominator unchanged:

(46 + 52)/100

Simplifying the numerator, we have:

98/100

This fraction can be further simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

49/50

Therefore, the fraction of senators who are either Democrats or Republicans is 49/50, or approximately 0.98.

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Answer: yes

Step-by-step explanation:

Answer:

B. The second confidence interval would be 3 times as wide as the original confidence interval.

Step-by-step explanation:

i actually dont know but thnks for the points BTW

Answer: HK is about 14.2 yards.

Step-by-step explanation: To find HK, we need to use the triangle angle sum theorem, which states that the sum of all the interior angles of a triangle is 180 degrees. We can use this theorem to find the missing angle in triangle HJK.

We know that m<H = 40° and m<K = 50°. So, m<J = 180° - (40° + 50°) = 90°. This means that triangle HJK is a right triangle, and we can use the Pythagorean theorem to find HK.

The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, HK is the hypotenuse, and JK and HJ are the other two sides. So, we have:

\(HK^2 = JK^2 + HJ^2 HK^2 = (13 yards)^2 + (HJ)^2\)

To find HJ, we need to use trigonometry. We can use the tangent ratio, which relates an acute angle in a right triangle to the opposite side and the adjacent side. In this case, we can use angle H:

tan(H) = opposite/adjacent tan(40°) = HJ/JK HJ = tan(40°) * JK HJ = tan(40°) * 13 yards HJ ≈ 11 yards

Now, we can plug this value into the Pythagorean theorem and solve for HK:

HK^2 = (13 yards)^2 + (11 yards)^2 HK^2 = 169 yards^2 + 121 yards^2 HK^2 = 290 yards^2 HK = √290 yards HK ≈ 14.2 yards

Therefore, HK is about 14.2 yards long. Hope this helps! =)

Answer:

-4+3x/2

Step-by-step explanation:

The curve of the given vector equation is shown below: It can be seen that the arrow points towards the positive x-axis, which is in the direction of increasing t.

To sketch curve of the given vector equation, r(t) = < t , 2 - t , 2t >, and indicate with an arrow the direction in which t increases, we need to follow some steps.

Step 1: Create a table for the vector. We need to create a table and fill in the values for t, x, y, and z. Let's do it below:

\(tt (time)xx (position)x(t)x(t)(2−t)(2−t)2t2t\)

Step 2: Plotting the points. We can plot the points by simply taking the x, y and z values from the table created above. The curve will pass through these points. The curve will be three-dimensional.

Step 3: Indicate the direction of t. To indicate the direction of t, we use an arrow on the curve. The arrow is drawn such that it starts from the initial point and points in the direction in which the parameter (in this case, t) increases. In this problem, since t increases in a positive direction, we take the arrow pointing towards the positive x-axis.

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Given the n™ term of a number sequence, the first three terms of the sequence are 0, 2 and 6

The sequence is given as:

n^2 - n​

To write down the first three terms of the sequence, we set n =1, 2 and 3

So, we have:

When n = 1

n^2 - n​ = 1^2 - 1

Evaluate

n^2 - n​ = 0

When n = 2

n^2 - n​ = 2^2 - 2

Evaluate

n^2 - n​ = 2

When n = 3

n^2 - n​ = 3^2 - 3

Evaluate

n^2 - n​ = 6

Hence, the first three terms of the sequence are 0, 2 and 6

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