Question 6

One gallon of water weighs 8.34 lb. How much weight is added to a fire truck when its tank is filled

with 750 gal of water?

Question 7

1

a)  The initial height is 5 feet.

b) The maximum height is 17 feet.

c) The horizontal displacement is 26.3 feet

The height of the ball is modeled by the given quadratic equation:

y = (-1/12)x² + 2x + 5

The ball leaves the child's hands at the beginning, so to get the height at that point we just need to evaluate this in x = 0, we will get:

y = (-1/12)*0² + 2*0 + 5

y = 5

The height is 5 feet.

b) To get the maximum height we need to find the vertex, in this case the vertex is at:

x = -(2/2)*-12 = 12

Then the maximum height is:

y =  (-1/12)*12² + 2*12 + 5 = 17 feet.

Lastly, the ball will hith the ground when y = 0, then we need to solve:

(-1/12)*x² + 2x + 5 = 0

x²  -12*2x - 12*5 = 0

x²  -24x - 60 = 0

The quadratic formula gives:

[tex]x = \frac{24 \pm \sqrt{(-24)^2 -4*1*-60} }{2}[/tex]

The positive solution gives:

x = 26.3

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Based on the information in the image, the values of the symbols in order would be: 5, 9.86, 9.93, 7.91. 10.56.

To find the equivalent value of each symbol we must apply the Pythagorean theorem and find the value of the hopotenuse of all triangles as shown below:

Triangle 1:

Triangle 2:

Triangle 3:

Triangle 4:

Triangle 5:

According to the above, the values of the symbols in order would be:

5, 9.86, 9.93, 7.91. 10.56.

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The first term of the GP is 4 and the common ratio is 3. We can now substitute these values into the formula for the sum of the first 10 terms to get 118096.

What is Geometric Progression?

A progression of numbers with a constant ratio between each number and the one before

Let the first term of the geometric progression be denoted by "a" and the common ratio be denoted by "r".

We know that the 4th term is 108, so we can use the formula for the nth term of a GP to write:

a*r³ = 108 .....(1)

We also know that the 8th term is 8748, so we can write:

a*r⁷ = 8748 .....(2)

To find the sum of the first 10 terms, we can use the formula for the sum of a finite geometric series:

S = a(1 - rⁿ)/(1 - r)

where S is the sum of the first n terms of the GP. We want to find the sum of the first 10 terms, so we plug in n = 10:

S = a(1 - r¹⁰)/(1 - r)

We now have two equations (1) and (2) with two unknowns (a and r). We can solve for a and r by dividing equation (2) by equation (1) to eliminate a:

(ar⁷)/(ar³) = 8748/108

r⁴ = 81

r = 3

Substituting r = 3 into equation (1) to solve for a, we have:

a*3³ = 108

a = 4

Therefore, the first term of the GP is 4 and the common ratio is 3. We can now substitute these values into the formula for the sum of the first 10 terms to get:

S = 4(1 - 3¹⁰)/(1 - 3)

S = 4(1 - 59049)/(-2)

S = 4(59048)/2

S = 118096

Therefore, the sum of the first 10 terms of the GP is 118096.

118096.

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Answer:

x = 30

Step-by-step explanation:

We know

The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.

2x + 3x + 10 = 160

5x + 10 = 160

5x = 150

x = 30

There are 92 elements in A but not in B.

In mathematics, a set is a well-defined collection of objects or elements. Sets are denoted by uppercase symbols, and the number of elements in a finite set is denoted as the cardinality of the set enclosed in curly braces {…}.

Empty or zero quantity:

Items not included. example:

A = {} is a null set.

Finite sets:

The number is limited. example:

A = {1,2,3,4}

Infinite set:

There are myriad elements. example:

A = {x:

x is the set of all integers}

Same sentence:

Two sets with the same members. example:

A = {1,2,5} and B = {2,5,1}:

Set A = Set B

Subset:

A set 'A' is said to be a subset of B if every element of A is also an element of B. example:

If A={1,2} and B={1,2,3,4} then A ⊆ B

Universal set:

A set that consists of all the elements of other sets that exist in the Venn diagram. example:

A={1,2}, B={2,3}, where the universal set is U = {1,2,3} 

n(A ∪ B) = n(A – B) + n(A ∩ B) + n(B – A)

Hence, There are 92 elements in A but not in B.

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If f is analytic and never zero on a domain D, then the graph (x,y,|f(x+iy)|) has no "pits". This follows from the fact that Re(f(z)) has no local minima in D.

Exercise 15 establishes the following result: if f is analytic and never zero on a domain D, then the the real part of f(z) has no local minima in D.

To use this result to establish the statement that |f(z)| has no local minima in D, we can use the fact that[tex]|f(z)|=\sqrt{real part of f(z))^2 + \ img part of f(z) )^2[/tex] . Since the sum of two non-negative functions is non-negative, it follows that if  the real part of f(z)  has no local minima in D, then |f(z)| has no local minima in D either.

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The minimum number of hikers who could have walked between 6 miles and 17 miles is 9 as it lies in the common interval of 10 ≤ x ≤ 15.

The minimum value of a set of numbers or a function is the smallest value within that set or range, while the maximum value is the largest value within the same set or range.

a) The minimum number of hikers who could have walked between 6 miles and 17 miles is 9 as it lies in the common interval of 10 ≤ x ≤ 15.

b) The maximum number of hikers who could have walked between 6 miles and 17 miles is 19.

a) The least value inside the target range is attained. when:

The two hikers in the 5 x 10 interval cover fewer than 6 miles.

The 8 hikers in the range 15-20-20 cover a distance of more than 17 miles.

As a result, the minimum is 9, or somewhere between 10 and 15 persons.

b) The maximum number in the desired range will be obtained when:

The two hikers in the 5 x 10 interval cover fewer than 6 miles.

Less than 17 miles are covered by the 8 hikers in the period of 15 to 20.

The maximum number is then determined as follows:

2 + 9 + 8 = 19 hikers.

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[tex] \huge \: \tt \green{Answer} [/tex]

Olivia and kieran share ratio 2 : 5

[tex] \texttt{olivia's share \: of \: money = £42 }= \frac{2}{7} \\ [/tex]

Total Amount of Money = Olivia's share of money × Reciprocal of olivia's share

[tex] \tt \: = > 42 \times \frac{7}{2} \\ \\ = > 147[/tex]

Kieran's share of Money =

[tex] = > 147 \times \frac{5}{7} \\ \\ = > \sf{ \pink{£105}}[/tex]

The matrix A of the linear transformation T(M) with respect to the standard basis for U2×2 is given by:

T([1000]) = [8 0]

[0 0]

T([0010]) = [0 0]

[0 9]

T([0001]) = [0 1]

[0 0]

To find the matrix A of the linear transformation T(M), we need to apply T to each basis vector of U2×2 and express the result as a linear combination of the basis vectors for U2×2. We can then arrange the coefficients of each linear combination as the columns of the matrix A.

Let's begin by finding T([1000]). We have:

T([1000]) = [8097][1000][8097]^-1

= [8 0]

[0 0]

To express this result as a linear combination of the basis vectors for U2×2, we need to solve for the coefficients c1, c2, and c3 such that:

[8 0] = c1[1000] + c2[0010] + c3[0001]

Equating the entries on both sides, we get:

c1 = 8

c2 = 0

c3 = 0

Therefore, the first column of the matrix A is [8 0 0]^T.

Next, we find T([0010]). We have:

T([0010]) = [8097][0010][8097]^-1

= [0 0]

[0 9]

Expressing this as a linear combination of the basis vectors for U2×2, we get:

[0 0] = c1[1000] + c2[0010] + c3[0001]

Equating the entries on both sides, we get:

c1 = 0

c2 = 0

c3 = 0

Therefore, the second column of the matrix A is [0 0 0]^T.

Finally, we find T([0001]). We have:

T([0001]) = [8097][0001][8097]^-1

= [0 1]

[0 0]

Expressing this as a linear combination of the basis vectors for U2×2, we get:

[0 1] = c1[1000] + c2[0010] + c3[0001]

Equating the entries on both sides, we get:

c1 = 0

c2 = 1

c3 = 0

Therefore, the third column of the matrix A is [0 1 0]^T.

Putting all of this together, we have:

A = [8 0 0]

[0 0 1]

[0 0 0]

Therefore, the matrix A of the linear transformation T(M) is:

T([1000]) = [8 0]

[0 0]

T([0010]) = [0 0]

[0 9]

T([0001]) = [0 1]

[0 0]

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Answer:

The first discount of 50% means Jason paid 50/100 x £88 = £44 for the jacket.

Then, the second discount of 25% means he paid 75/100 x £44 = £33 for the jacket.

Therefore, the final sale price that Jason paid for the jacket was £33.

Answer:

Find the area A of the sector shown in the picture

76 degrees

6

Step-by-step explanation:

To find the area of a sector, we need to know the measure of the central angle and the radius of the circle.

If the central angle of the sector is 76 degrees, and the radius of the circle is 6, we can use the formula for the area of a sector:

A = (θ/360) * π * r^2

where θ is the central angle in degrees, r is the radius of the circle, and π is a constant approximately equal to 3.14.

Plugging in the given values, we get:

A = (76/360) * π * 6^2

Simplifying:

A = (0.2111) * π * 36

A = 7.57 square units (rounded to two decimal places)

Therefore, the area of the sector is approximately 7.57 square units.

There are infinitely many irrational numbers between 1 and 6. This is because between any two distinct rational numbers, there is an infinite number of irrational numbers.

In the case of the interval between 1 and 6, there are infinitely many rational numbers between them, and therefore there must be infinitely many irrational numbers between them as well. This is due to the fact that the set of real numbers is uncountable, meaning that there is no finite or countably infinite list that contains all of its elements.

Thus, the answer is rather a statement about the infinite nature of the set of irrational numbers between 1 and 6.

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Answer:

Hence, factors are 3x,(x−4y).

Step-by-step explanation:

We need to factorise 3x 2 −12xy

Here we can take 3x common.

Thus we have 3x 2−12xy=3x(x−4y)

Hence, factors are 3x,(x−4y).

Answer: 3x ( x - 4y )

Step-by-step explanation:

Factorizing 3x²-12xy

3x ( x - 4y )

Therefore, when h = 6 and j = 5, the value of hj - h² is -6.

Arithmetic operations are basic mathematical operations that involve manipulating numbers to perform calculations. There are four main arithmetic operations:

Addition: Adding two or more numbers together. The symbol used to represent addition is "+", and the result is called the sum.

Subtraction: Subtracting one number from another. The symbol used to represent subtraction is "-", and the result is called the difference.

Multiplication: Multiplying two or more numbers together. The symbol used to represent multiplication is "×" or "*", and the result is called the product.

Division: Dividing one number by another. The symbol used to represent division is "÷" or "/", and the result is called the quotient.

These operations can be combined to perform more complex calculations. Additionally, there are other arithmetic operations, such as exponentiation (raising a number to a power) and finding roots, which involve using arithmetic principles.

by the question.

To evaluate the expression hj - h² for h = 6 and j = 5, we simply substitute these values into the expression and perform the arithmetic operations:

hj - h² = (6)(5) - 6²

= 30 - 36

= -6

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Mr. Woodstock will need to purchase 144 meters of wire to fully encircle his land. He will need to measure the length of the four sides of the land and add them together. The four sides measure 36 meters + 36 meters + 16 meters + 16 meters, which equals a total of 104 meters. He should buy enough wire to cover an additional 40 meters to account for any extra material he may need. Therefore, he needs to purchase 144 meters of wire for his fencing.

The result of the division in ordinary decimal notation is 300.

Scientific notation, also known as standard form or exponential notation, is a method of expressing very large or very small numbers in a compact and standardized way.

To perform the indicated operation, we need to divide 0.00036 by 0.0000012.

First, let's express both numbers in scientific notation

0.00036 = 3.6 x 10^(-4)

0.0000012 = 1.2 x 10^(-6)

Now we can divide the two numbers and simplify

3.6 x 10^(-4) / 1.2 x 10^(-6) = (3.6 / 1.2) x 10^(-4-(-6)) = 3 x 10^(2)

Finally, we can convert this result back to ordinary decimal notation

3 x 10^(2) = 300

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The given question is incomplete, the complete question is:

Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation. 0.00036/0.0000012

Answer:

The answer to your problem is, B, 0.5

Step-by-step explanation:

We are given the following table below;

              X             Y               Z             Total

A             32           10             28              70

B              6             5              25              36

C             18            15              7                40

Total       56           30            60              146

As we know that the conditional probability formula of P(A/B) is given by:

P(A/B) =  [tex]\frac{P(AnB)}{P(b)}[/tex]

P(C/Y) = [tex]\frac{P(CnY)}{P(Y)}[/tex]

P ( Y ) = [tex]\frac{30}{146}[/tex] and P(CnY) = [tex]\frac{15}{146}[/tex] [ because of the third column shown ]

Thus, the answer is, B. 0.5

Feel free to ask any questions down below \/ !

The correct interpretation of the confidence interval is We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27 that is option A.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific degree of confidence, this is the range of values you anticipate your estimate to fall inside if you repeat the test. In statistics, confidence is another word for probability.

Given,

Confidence interval, CI = 62.63 +/- 17.64

CI = ( 44.99 , 80.27 )

The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.

Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.

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Complete question:

To investigate hospital costs for pets in a certain state, researchers selected a random sample of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner was recorded and used to create the 95 percent confidence interval $62.63±$17.64.

Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?

Answer:

P = x(4x+7)/(x+2)(x+1)

Step-by-step explanation:

P = 2l + 2w. If x/x+2 = l and x/x+1 = w:

P = (2x/x+2) + (2x/x+1)

P = (2x(x+1)/(x+2)(x+1)) + (2x(x+2)/(x+1)(x+2))

P = (2x(x+1) + 2x(x+2))/(x+2)(x+1)

P = (4x squared + 7x)/(x+2)(x+1)

P = x(4x+7)/(x+2)(x+1)

Answer:

Step-by-step explanation:

16350$

Answer:

16 407.1

Step-by-step explanation:

Answer:

B. A student was most likely to have summer as their favorite season, whether or not they have allergies

Step-by-step explanation:

If you look at the chart. There is a majority under the summer column. Both those who have and don't have allergies favor summer.

The formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.

Degrees Kelvin and Degrees Fahrenheit are two temperature measuring measures that are widely used across the globe. While Kelvin is an international standard unit of measurement, Fahrenheit is mostly used in the United States.

The fact that they measure temperature on distinct scales explains the difference between degrees Fahrenheit (F) and degrees Kelvin (K). Whereas Kelvin is based on a scale of 100 degrees between the freezing and boiling temperatures of water at normal atmospheric pressure, Fahrenheit is based on a scale of 180 degrees between these extremes.

Given that, K = 5/9 (F - 459.67).

To obtain F in term of K we isolate the value of F as follows:

K = 5/9 (F - 459.67)

Multiplying both sides by 9/5, we get:

(9/5) K = F - 459.67

Adding 459.67 to both sides, we get:

F = (9/5) K + 459.67

Hence, the formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.

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Answer:

(2, -3)

Step-by-step explanation:

You must choose from the 3 ways to solve the system of equations:

1. Substitution

2. Elimination

3. Graphing (least recommended)

My example is going to be substitution, as folllows:

2x - y = 7

(Add y to both sides)

2x = y + 7

(Subtract 7 from both sides)

y = 2x - 7

Now, we are able to use substitution in the next equation with the other equation!

3x + 4y = -6

(Replace y with what y equals -- other equation)

3x + 4(2x -7) = -6

(Simplify the parantheses)

3x + 8x - 28 = -6

(Add 28 to both sides)

3x + 8x = -6 +28

3x + 8x = 22

(CLT - Combine like terms)

11x = 22

(Divide 11 from both sides)

x = 2

Now, we will find what y is by plugging x into the other equation.

y = 2x - 7

x = 2

y = 2(2) - 7

y = 4 - 7

y = -3

y = -3

x = 2

Since we found both of the variables' values, we found our coordinate pairs to solve this equation!

Answer: (2, -3)

Answer:

This is false.

Step-by-step explanation:

Since absolute value bars change negatives into positives and positive into themselves (positives) we can put the example:

[tex]-|8|\\[/tex]

When we remove the absolute value bars, 8 will still equal 8. But, we have a negative, therefore the 8 has a negative after being simplified with absolute value.

x = -8, not positive 8.

Answer:

Ther are no values of x that would make this statement true. There is no solution.

Step-by-step explanation:

In response to the stated question, we may respond that As a result, the fraction length of the hexagon's side is roughly 16.97 cm, which is closest to option C. (16 cm).

A fraction is a number that represents a portion of a whole or a ratio between two quantities in mathematics. It is represented as a top number (numerator) over a bottom number (denominator) divided by a horizontal line, also known as a vinculum. The fraction 3/4, for example, represents three-quarters of a whole that has been divided into four equal parts. Proper fractions, improper fractions , and mixed numbers are all ways to express a fraction. A suitable fraction is one in which the numerator is less than the denominator, for example, 2/5.

We can calculate the length of the other leg of the right triangle, which is also half the side of the hexagon, using the Pythagorean theorem:

[tex]$(fracs2 )2 + (fracs2 )2 = 122$\\$fracs244 + fracs244 = 144$\\$\frac{s^2}{2} = 144$\\$s^2 = 288$\\$s = sqrt288 = about 16.97$[/tex]

As a result, the length of the hexagon's side is roughly 16.97 cm, which is closest to option C. (16 cm).

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By answering the question the answer is So the area of ​​the rectangle is area 1/2 square inch. 

The size of an area on a surface can be expressed as area. The open surface or boundary area of ​​a three-dimensional object is called the surface area, and the area of ​​the planar area or planar area refers to the area of ​​the shape or planar layer. The total amount of space occupied by a planar (2-D) surface or shape of an object is known as its area. Draw a square on paper with a pencil. two-dimensional character. The area of ​​a shape on paper is the space it occupies. Imagine a square made up of more compact unit squares.  

It's not entirely clear what shape is being referred to here, but assuming it's a 2 inch by 1/4 inch rectangle, you can calculate the area by multiplying the length and width of the rectangle.

Area = Length x Width

Area = 2" x 1/4"

Area = (2/1) inch x (1/4) inch

Area = 1/2 square inch

So the area of ​​the rectangle is 1/2 square inch. 

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By answering the question the answer is So the area of ​​the rectangle is area 1/2 square inch.

The size of an area on a surface can be expressed as area. The open surface or boundary area of ​​a three-dimensional object is called the surface area, and the area of ​​the planar area or planar area refers to the area of ​​the shape or planar layer. The total amount of space occupied by a planar (2-D) surface or shape of an object is known as its area. Draw a square on paper with a pencil. two-dimensional character. The area of ​​a shape on paper is the space it occupies. Imagine a square made up of more compact unit squares.  

It's not entirely clear what shape is being referred to here, but assuming it's a 2 inch by 1/4 inch rectangle, you can calculate the area by multiplying the length and width of the rectangle.

Area = Length x Width

Area = 2" x 1/4"

Area = (2/1) inch x (1/4) inch

Area = 1/2 square inch

So the area of ​​the rectangle is 1/2 square inch.

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Find the area of 2 inches long times 1/4

There are no points at which the function has its direction of fastest change along the vector i + j. This is because the equations lead to a contradiction.

The exercise asks to find all the points at which the function f(x, y) = x^2 + y^2 - 8x - 16y has its direction of fastest change along the vector i + j.

To find the points, we need to solve the equation:

(2x - 8)i + (2y - 16)j = k(i + j)

where k is a constant. Since the direction of fastest change is along the vector i + j, we know that the left-hand side of the equation represents the gradient vector of f(x, y).

Equating the x and y components of the gradient vector to the corresponding components of the vector i + j, we get:

2x - 8 = k

2y - 16 = k

Equating these two expressions for k, we get:

2x - 8 = 2y - 16

Solving for y in terms of x, we get:

y = x - 4

Substituting this expression for y into the equation of the gradient vector, we get:

2x - 8 = k

2(x - 4) - 16 = k

Simplifying, we get:

2x - 8 = k

2x - 24 = k

Substituting the first equation into the second, we get:

2x - 24 = 2x -

Simplifying, we get:

16 = 0

This is a contradiction, which means there are no points at which the function has its direction of fastest change along the vector i + j.

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Answer:

Let's call the speed of the jet in still air "j" and the speed of the wind "w".

When flying with the tailwind, the effective speed of the jet is j + w. We know that it can travel 2040 miles in 4 hours, so:

2040 = 4(j + w)

Simplifying this equation, we get:

j + w = 510

When flying into the headwind, the effective speed of the jet is j - w. We know that it can only travel 1560 miles in 4 hours, so:

1560 = 4(j - w)

Simplifying this equation, we get:

j - w = 390

Now we have two equations with two variables:

j + w = 510

j - w = 390

We can solve this system of equations using elimination. Adding the two equations, we get:

2j = 900

Dividing both sides by 2, we get:

j = 450

So the speed of the jet in still air is 450 mph.

Now we can use either equation to solve for the speed of the wind. Let's use the first equation:

j + w = 510

Substituting j = 450, we get:

450 + w = 510

Subtracting 450 from both sides, we get:

w = 60

So the speed of the wind is 60 mph.

Step-by-step explanation:

The value of h(x) using exponents are as follows:

For -1, the value of h(x)=1/10

For 0, the value of h(x) = 1

For 1, the value of h(x) = 10

For 2, the value of h(x) = 100

For 3, the value of h(x) = 1000

The exponent of a number tells us how many times the original value has been multiplied by itself. For instance, 2×2×2×2 can be expressed as [tex]2^{4}[/tex] the result of 4 times multiplying 2 by itself. Thus, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."

Generally speaking, [tex]x^{n}[/tex] denotes that x has been multiplied by itself n times. Here x is the base and n is the power.

Now here, as we put the value of x in the equation, h(x) we can get the value of h(x) for each value of x.

So,

For -1, the value of h(x)=1/10

For 0, the value of h(x) = 1

For 1, the value of h(x) = 10

For 2, the value of h(x) = 100

For 3, the value of h(x) = 1000

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