What is the equation of the line parallel bto the given line with an x-intercept of 4?

Volume= 4/3πr^3

r = 18m

Volume = 4/3*3.14*18^3

Volume = 4/3*3.14*5832

Volume= 24416.639999 m^3

For the given vectors u = -i + 2j + k and v = -2i - 5j - 8k, the solution is:

u = (-1, 2, 1)

v = (-2, -5, -8)

u · v, = -16

Write the vectors in component form:
u = (-1, 2, 1)
v = (-2, -5, -8)

Compute the dot product (u · v) using the formula:
u · v = (u1 * v1) + (u2 * v2) + (u3 * v3)

Substitute the components of u and v into the formula:
u · v = (-1 * -2) + (2 * -5) + (1 * -8)
u · v = 2 - 10 - 8
u · v = -16

So, the given vectors are:
u = -i + 2j + k or (-1, 2, 1)
v = -2i - 5j - 8k or (-2, -5, -8)
and their dot product, u · v, is -16.

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Answer: x=43

Step-by-step explanation:

Looks like the 2 angles are a linear pair, 2 angles that make up a line.  So if added they equal 180

Equation:

x + 7 + 3x + 1 = 180                   >Combine like terms

4x +8 = 180                               >Subtract 8 from both sides

4x = 172                                    >Divide both sides by 4

x = 43

The square of a number is increased by 5 times the number \(6x^{2} +5x-4=0\)

What is quadratic equation?
A quadratic equation is a second order equation written as a\(x^{2}\) + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

Product of 6 and the square of a number is increased by 5 times the number, he result is 4.

Consider x as the number,

The question can be written as:

\(6(x^{2} )+5(x)=4\)

\(6(x^{2} )+5(x)-4=0\)

Hence, the answer for the given question is \(6x^{2} +5x-4=0\).

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

The probability that if you choose 2 people randomly, exactly one will need an x-ray is 0.4.

The probability that if you choose 2 people randomly from the 16 in the hospital, exactly one will need an x-ray is as follows:
Firstly, calculate the probability of choosing one person who needs an X-ray and one person who doesn't.

There are 4 people who need an x-ray and 12 who don't, so the probability for this is (4/16) * (12/15).

Now, calculate the probability of choosing one person who doesn't need an X-ray and one person who does. This is (12/16) * (4/15).

Now, add the probabilities to find the total probability.

The probability that exactly one person will need an x-ray is

(4/16) * (12/15) + (12/16) * (4/15) = 2/5

=0.4.

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The probability that if you choose 2 people randomly, exactly one will need an x-ray is 0.4 or 40%.

If there are 16 people in a hospital and 4 need an xray, the probability that if you choose 2 people randomly, exactly one will need an xray is 0.56.

Total number of people in a hospital = 16

Number of people who need an x-ray = 4

Thus, the probability that if you choose 2 people randomly, exactly one will need an x-ray is given by;

P(one needs an x-ray) = (Number of people who need an x-ray × Number of people who do not need an x-ray) / Total number of people × Total number of people - 1

P(one needs an x-ray) = (4 × 12) / 16 × 15

P(one needs an x-ray) = 0.08

P(one doesn't need an x-ray) = (Number of people who need an x-ray × Number of people who do not need an x-ray) / Total number of people × Total number of people - 1

P(one doesn't need an x-ray) = (12 × 4) / 16 × 15

P(one doesn't need an x-ray) = 0.32

Now, we have to add both the probabilities of exactly one person needing an x-ray and exactly one person not needing an x-ray;

P(exactly one person needs an x-ray) = P(one needs an x-ray) + P(one doesn't need an x-ray)

P(exactly one person needs an x-ray) = 0.08 + 0.32P(exactly one person needs an x-ray) = 0.4

The probability that if you choose 2 people randomly, exactly one will need an x-ray is 0.4 or 40%.

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The volume of the cylindrical bucket with a height of 35 cm and a base diameter of 21 cm is approximately 10971.9 cubic centimeters when rounded to the nearest tenth.

To calculate the volume of a cylindrical bucket, we can use the formula:

Volume = π * r^2 * h

where π is a constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cylinder.

Given that the base diameter is 21 cm, we can find the radius (r) by dividing the diameter by 2:

r = 21 cm / 2 = 10.5 cm

The height (h) of the bucket is given as 35 cm.

Now we can substitute these values into the volume formula:

Volume = π * (10.5 cm)^2 * 35 cm

≈ 3.14159 * 110.25 cm^2 * 35 cm

≈ 10971.94 cm^3

Rounding the answer to the nearest tenth of a cubic centimeter, the volume of the cylindrical bucket is approximately 10971.9 cm^3.

Therefore, the volume of the cylindrical bucket is approximately 10971.9 cubic centimeters.

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Answer:

∠B = 78°

Step-by-step explanation:

∠C = 1/2 arc AB = 1/2(120°) = 60°   because it is an inscribed angle

∠B = 180° - 42° - 60° = 78°

The measure of  ∠ B is  78°.

An inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

According to the question

m ∠ A= 42º.

mAB = 120°

By  inscribed angle theorem :

mAB = 2 m∠C

120° = 2 m∠C

m∠C = 60°

now,

according to the sum of angle of triangle

m ∠ B + m∠C + m ∠ A = 180°    

m ∠ B +60° + 42º= 180°  

m ∠ B = 78°

Hence, the measure of  ∠ B is  78°.

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Answer:

7,650 lb

Step-by-step explanation:

each ton is 2,000 pounds, and there is 4.

so 8,000 -350=7,650

The solution of the subtraction operation is equal to 7,650 lb

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS - Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We need to Subtract 350 lb. from 4 tons.

We know that each ton is 2,000 pounds, and there is 4.

so, the subtraction is;

8,000 -350=7,650

The answer is 7,550 lb. so the correct option is D.

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Answer:

the square root of 75 is either \(\sqrt75\) or 8.66

Step-by-step explanation:

A grade of 85.75 or higher is required to be in the top 40% of the class.

Standard deviation is a statistical measure that represents the amount of variability or dispersion in a set of data values. It measures the degree of spread of the data values from the mean (average) of the data set.

To calculate the standard deviation of a data set, you first need to calculate the mean of the data set. Then, for each data point in the set, you calculate the difference between the data point and the mean. These differences are squared and then summed together. Finally, the sum is divided by the total number of data points minus one, and the square root of this value is taken to obtain the standard deviation.

To find the grade required to be in the top 40%, we need to find the z-score corresponding to the 60th percentile (100% - 40% = 60%).

We can use the standard normal distribution, where the mean (μ) is 0 and the standard deviation (σ) is 1, to find the z-score.

The formula for the z-score is:

z = (x - μ) / σ

where x is the value we want to find the z-score for.

To find x, we can rearrange the formula as:

x = μ + z * σ

where μ = 83 and σ = 11 (given in the problem statement).

To find the z-score for the 60th percentile, we can use a standard normal distribution table or a calculator that has a normal distribution function. Using a standard normal distribution table, we find that the z-score corresponding to the 60th percentile is approximately 0.25.

Plugging in the values, we get:

x = 83 + 0.25 * 11

x = 85.75

Therefore, a grade of 85.75 or higher is required to be in the top 40% of the class.

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When Deshawn installs a shelf bracket, the width of the shelf that will fit without overhang will be 3 inches.

From the complete information, the other two sides have been given as 4 inches and 5 inches.

The Pythagoras theorem will be used in this case and it goes thus:

4² + Width² = 5²

Width² = 5² - 4²

Width² = 25 - 16

Width² = 9

Width = ✓9

Width = 3

In conclusion, the width is 3 inches.

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Answer: y=-2x³

Step-by-step explanation: To determine the equation of the transformed function, we need to consider the direction and degree of the transformation. Since the graph is reflected about the x-axis and compressed vertically by a factor of 2, the equation is y = -2x^3. Therefore, the correct answer is O y=-2x³.

Answer: y=2/5x+b

Step-by-step explanation:

a) The Corresponding minimum UGPA = 3.70

b) The range of middle 50% values will be: (3.28, 3.52).

A measure of how many standard deviations below or above the population mean a raw score is called z score. It will be positive if the value lies above the mean and negative if it lies below the mean. It is also known as standard score. It indicates how many standard deviations an entity is, from the mean. In order to use a z-score, the mean μ and also the population standard deviation σ should be known. A z score helps to calculate the probability of a score occurring within a standard normal distribution. It also enables us to compare two scores that are from different samples.

a) z score corresponding to top 5% area = 1.645

Hence, Corresponding minimum UGPA = 3.40 + 1.645*0.18 = 3.70

b) z score corresponding to middle 50% area = -0.67, 0.67

Hence, The range of middle 50% values will be:

(3.40 - 0.67*0.18, 3.40 + 0.67*0.18)

(3.28, 3.52)

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Answer:

Step-by-step explanation:

A century has 100 years in it. months only has a max of 31 dates. The following years are perfect squares, 01,04,09,16,25,36,49 64,81,100

It will be 10 square root dates.

The matrix of the relation r={(1,2),(2,3),(3,4),(4,5)} on the set x={1, 2, 3, 4, 5}; ordering of x:1,2,3,4,5 is as follows.

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

A relation is a set of ordered pairs.

The matrix of a relation is constructed by using its ordered pairs with their respective values as its entries, and its rows and columns by its domain and range, respectively.

So, the relation r is given as{(1,2),(2,3),(3,4),(4,5)}

The elements in the rows of the matrix correspond to the elements of x, while the elements in the columns of the matrix correspond to the elements of x as well, in that order.

So, the matrix of r on x can be written as:

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

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The null hypothesis is that at most 70% of people who eat fast food more than 2x a week are overweight, and the alternative hypothesis is that more than 70% of people who eat fast food more than 2x a week are overweight.

Null hypothesis is a statistical hypothesis that claims there is no significant difference between a specified population parameter and the observed sample statistics. While alternative hypothesis is a statistical hypothesis that suggests that there is a significant difference between a specified population parameter and the observed sample statistics.In the given scenario, the null hypothesis and the alternative hypothesis will be:

Null hypothesis (H0): At most 70% of people who eat fast food more than 2x a week are overweight. (This means less than 70% are overweight)Alternative hypothesis (Ha): More than 70% of people who eat fast food more than 2x a week are overweight.

:We can evaluate the null hypothesis by testing the probability of a sample occurring, assuming the null hypothesis is true. If the probability of a sample is very low, it implies that it is unlikely that the sample was obtained assuming that the null hypothesis was true, and we can reject the null hypothesis and accept the alternative hypothesis

.In conclusion, the null hypothesis is that at most 70% of people who eat fast food more than 2x a week are overweight, and the alternative hypothesis is that more than 70% of people who eat fast food more than 2x a week are overweight.

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Answer: The larger number is 11

Step-by-step explanation: You would want to start with the given which is 7 more than another and 63 being the ending number. So first you would want to subtract 7 from 63 (63-7=56), now you would have to figure out how to evaluate 56 out into 3 parts of a number and 4 parts of a larger number. That number would be 4, 4x3=12 subtract 12 from 56 (56-12=44), then you are left to divide 44 by 4, which gets you 11. Once you are finished with your math you would check that this is correct by seeing if the number split in 4 is larger than the number split in 3. As you can see 11 is a lot larger number than 4 is.

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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ok

Measures base = 3cm

height = 4cm

tall = x

volume = 144 cm^3

Volume = Area of the base * tall

Area of the base = (3 * 4) / 2 = 12/2 = 6 cm^2

144 = 6*x

x = 144/6

x = 24 cm

Result: The chocolate is 24 cm tall.

There are 120 boats in the marina using algebraic equation.

We shall represent the number of boats in the marina with the letter x so that we derive an algebraic equation to solve for x as follows:

number of white boats = 5x/6

number of blue boats = 2/5 of (x - 5x/6)

number of blue boats = 2/5 × x/6

number of blue boats = x/15

number of red boats = 12

so that;

5x/6 + x/15 + 12 = x

LCM of the denominators is 30

(25x + 2x + 360)/30 = x

27x + 360 = 30x {cross multiplication}

30x - 27x = 360 {collect like terms}

3x = 360

x = 360/3 {divide through by 3}

x = 120

Therefore, there are 120 boats in the marina using algebraic equation.

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The size of a crowd at a political rally which occupies a rectangular space with dimensions of 500 feet by 600 feet is 66667 persons.

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

\(A=a\times b\)

Here, (a)is the length of the rectangle and (b) is the width of the rectangle

The size of a crowd at a political rally that occupies a rectangular space with dimensions of 500 feet by 600 feet has to estimated.

First find out the area of this rectangular space using the above formula.

\(A=500\times600\\A=300000\rm\; ft^2\)

As each person occupies 4.5 square feet. Thus, the number of person feet in, 300000 square ft are,

\(n=\dfrac{300000}{4.5}\\n\approx66667\)

Thus, the size of a crowd at a political rally which occupies a rectangular space with dimensions of 500 feet by 600 feet is 66667 persons.

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       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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percentage = 32%

From the question, we have

percentage  = ((2*f(.9))-1)/2

=((2*.816)-1)/2

=0.632/2

= 31.6%

= 32% (approx )

Percentage:

Use the percentage formula to express a number or percentage in terms of 100. % simply indicates one out of one hundred. An expression for a number between 0 and 1 can be made using the percentage formula. It is a number that is represented as a fraction of 100. The sign % is used to denote it and it is mostly used to compare and calculate ratios. The formula for percentage increases is the ratio of the increased value to the original value multiplied by 100. It is described in percentage form. If anything is valued more highly, both its value and proportion will rise.

Complete question:

The percentage of area under the normal curve between the mean and -0.9 standard deviations from the mean is ____%. Round to the nearest integer as needed.

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the answer is 16 because the arc divides the angle into two equal half

Answer:

6

Step-by-step explanation: