17) Charles is saving $7 each week. He earns an
extra $15 by mowing his neighbor's lawn. How
many weeks will he need to save in order to have
saved $127?

We know that the mean (μ) is 800 hours and the standard deviation (σ) is 85 hours. We are trying to find the number of light bulbs that will last more than 1010 hours.

First, we need to standardize the value of 1010 hours using the formula:
z = (x - μ) / σ
where x is the value we are trying to find the probability for.

Plugging in our values, we get:
z = (1010 - 800) / 85 = 2.47
Now, we can use a standard normal distribution table or calculator to find the probability that a randomly selected light bulb will last more than 1010 hours. The area under the curve to the right of 2.47 is 0.0068.

Therefore, the expected number of light bulbs that will last more than 1010 hours out of 610 is:
3 x 0.0068 x 610 = 12.42

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Dividing in math is the process of finding the quotient of two numbers.

The formula for dividing two numbers is a/b = c, where a and b are the two numbers being divided and c is the quotient.

Division is a mathematical operation that is used to split a whole number into parts. It is the opposite of multiplication, which combines numbers together. The formula for division is A / B = C, where A is the dividend (the number being divided), B is the divisor (the number dividing the dividend), and C is the quotient (the result of the division). To calculate, you divide the dividend by the divisor and the quotient is the resultTo calculate the quotient, you must divide a by b. For example, if we wanted to divide 8 by 4, we would divide 8 by 4 to get 2. The calculation would look like this: 8/4 = 2. As a result, 8 divided by 4 is equal to 2.

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The y-intercept of the function f(x) = 2(0.5)^x is 2. This means that the graph of the function intersects the y-axis at the point (0, 2).

To find the y-intercept of the function f(x) = 2(0.5)^x, we need to determine the value of f(x) when x is equal to 0.

Let's substitute x = 0 into the equation:

f(0) = 2(0.5)^0

Since any number raised to the power of 0 is equal to 1, we have:

f(0) = 2(1)

Simplifying further, we get:

f(0) = 2

Therefore, the y-intercept of the function f(x) = 2(0.5)^x is 2. This means that the graph of the function intersects the y-axis at the point (0, 2).

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Answer:

Step-by-step explanation:

look at the drawing as two HALF circles and substract the larger half circle from the smaller half circle or the difference between two circles divided by two

A = π r² for a WHOLE circle     A / 2 is the area for a HALF circle

Area of the rainbow is     Large Circle Area / 2  - Small Circle Area / 2

=  (π r²/2 large - π r²/2 small)

=  (π r² large - π r² small) / 2

=  π( r² large -  r² small) / 2

= π ((18cm)² - (12cm)²) / 2

= π(324 -144)cm² / 2

= 282.74   <----------------  FINAL ANSWER

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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The expression as a number in scientific notation is 4.2 * 10^5

The expression is given as:

quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared

Rewrite properly as:

[7 * 10^3 * 5.4 * 10^4]/[9 * 10^2]

Evaluate the product of 7 and 5.4

So, we have:

[37.8* 10^3 * 10^4]/[9 * 10^2]

Evaluate the product of 10^3 and 10^4

So, we have:

[37.8* 10^7]/[9 * 10^2]

Evaluate the quotient of 37.8 and 9

So, we have:

[4.2 * 10^7]/[10^2]

Evaluate the quotient of 10^7 and 10^2

So, we have:

4.2 * 10^5

Hence, the expression as a number in scientific notation is 4.2 * 10^5

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The distance from the point to the given plane is 16/7 units.

To find the distance from a point to a given plane, we can use the formula:

distance = |ax + by + cz - d| / √(a^2 + b^2 + c^2)

where (x, y, z) are the coordinates of the point, and a, b, c, and d are the coefficients of the plane equation.

In this case, the point is (1, -3, 4) and the plane equation is 3x + 2y + 6z = 5.

Let's plug in the values:

distance = |(3*1) + (2*(-3)) + (6*4) - 5| / √(3^2 + 2^2 + 6^2)

Simplifying:

distance = |3 - 6 + 24 - 5| / √(9 + 4 + 36)
distance = |16| / √49
distance = 16 / 7

Therefore, the distance from the point (1, -3, 4) to the plane 3x + 2y + 6z = 5 is 16/7 units.

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Answer:

5a

Step-by-step explanation:

\(5\cdot \:a\\\\\)

5 multiply a

5a

Answer:

5, 30, and 70

Step-by-step explanation:

Multiply by  number of quarters by 5 to get the number of nickels.

The estimated market value of Citrus County's assets, with an average duration of 8 and a market value of $1 million, would be approximately $1,055,284 if the interest rate changes to 4%.

In this case, the assets have an average duration of 8. When the interest rate changes from 5% to 4%, the change in interest rates is 1%. By applying the duration formula, the estimated percentage change in the market value of the assets would be approximately -8% (negative duration multiplied by the change in interest rates).

To calculate the estimated market value, we need to multiply the estimated percentage change (-8%) by the current market value ($1 million) and add it to the current market value. Thus, the estimated market value would be approximately $1,055,284 (1,000,000 + (1,000,000 * -8%)).

Duration is a measure of the sensitivity of an asset's price to changes in interest rates. It provides an estimate of the percentage change in the market value of an asset for a given change in interest rates. The duration formula states that the percentage change in the market value of an asset is approximately equal to the negative duration multiplied by the change in interest rates.

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Answer:

5

Step-by-step explanation:

16 - 11 = 5

Answer:

Length of RK=27

Step-by-step explanation:

Basically, you add both parts OR and OK, in order to get RK.

The mathematical model of an abstract syntax tree (AST) for a programming language's block (BL) statement typically involves representing the syntax of the statement using a tree structure.

This tree structure consists of nodes that correspond to different components of the statement, such as keywords, variables, operators, and expressions. The AST provides a way to parse and interpret the syntax of the statement, allowing for efficient compilation and execution of the code.

The model can be represented using various algorithms and data structures, such as recursive descent parsing or top-down parsing. Ultimately, the AST serves as a tool for developers to analyze, optimize, and debug their code, and is an essential component of many modern programming languages.

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Answer:

e) none of these​

Explanation:

Answer:

e) None of these.

Step-by-step explanation:

Let the unknown number be x, then:

0.65*320 + x = 686

208 + x = 686

x = 686 - 208

= 478

Answer:

96mm²

Step-by-step explanation:

a√ a²+ 4h²

4 √4² + 4(12)²

4 √4² + 4 (144)

4√4² + 576

97. 2 mm²

got it!

the answer is 67

hope that helped

The random variable x as the number of defective cameras in the sample are:

a. P(X =0) = qCn/NCn

                = 2/10

P(X=1) = 2 × (pC1 × qC1)/ NCn

          = 6/10

P(X=2) = pCn/ NCn

           = 2/0

b. The distribution function of:

\(X=[(0,\frac{2}{10} ),(1,\frac{6}{10} ),(2,\frac{2}{10} )]\)

c. The expected number of defective cameras is:

=> 2/3

Probability suggests "possibility" or "chance." When an event is certain to occur, its probability of happening is 1, and when it is definite that it cannot occur, its possibility of occurring is 0.

The given information:

Total number of cameras N = 6

Total number of defective cameras p = 3

Total number of non - defective cameras q = 3

Total number of sample taken n = 2

X can be 0, 1, or 2 . Because, if we pull out 2 cameras, we can have 0, 1, or 2 defective ones.

1) X = number of defective cameras.

We must draw 2 of the 3 non defective cameras and there is a total of ways of drawing 2 cameras out of 6.

P(X =0) = qCn/NCn

            = 3C2/ 6C2

            = 2/10

We must draw 1 out of the 3 non defective cameras and 1 out of the 3 defective cameras.

P(X=1) = 2 × (pC1 × qC1)/ NCn

          = 2 × (3C1 × 3C1) / 6C2

          = 2 × 3/10

          = 6/10

We must draw 2 of the 3 defective cameras

P(X=2) = pCn/ NCn

           = 3C2/6C2

           = 2/10

2) The probability distribution of X is computed as :

The set of order pair

\([x_i,p(x_i);i = 1, 2, 3,...,n,...]\)

specifies the probability distribution function of random variable X. Therefore,

The distribution function of:

\(X=[(0,\frac{2}{10} ),(1,\frac{6}{10} ),(2,\frac{2}{10} )]\)

3) The expected value of X is computed as:

Let \(X_j\) be the indicator random variable that takes value 1 if jth cameras in the sample (of size 2) is defective, and 0 otherwise i.e.,

\(I_j={^1_0\)   if jth camera in the sample is defective otherwise

The no. of defective cameras = \(X_1+X_2\)

Expected no. of defective cameras

\(=E(X_1+X_2)\\=E(X_1)+E(X_2)\\=2E(X_1)\)

Now, \(E(X_1)\) is equal to the probability that the first cameras is defective i.e.,

\(E(X_1)=\frac{2_C_1}{6_C_1}\)

          = 2/6

          = 1/3

Therefore, expected number of defective cameras is:

2 ×  \(E(X_1)\) = 2 × 1/3

                 = 2/3

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The given question is incomplete, So i take similar question:

Suppose that a box contains 6 cameras and that 3 of them are defective. A sample of 2 cameras is selected at random, with replacement.

a. Define the random variable X as the number of defective cameras in the sample.

b. Write the probability distribution for X.

c. What is the expected value of X?

The volume and surface area of the ice cream cone are given by adding

the volume and surface area of the component parts.

Responses (approximate values)

i) 1,696.46 cm³

ii) 229.68 cm²

iii) 169.45 cm³

iv) 565.49 cm²

v) 10 cones

Given:

The diameter of the cylinder = 12 cm

Height of the cylinder, h = 15 cm

Height of the cone, h = 12 cm

Diameter of the cone, D = 6 cm

Shape of the cap of the cone = Hemispherical

i) The capacity of the container = The volume of the cylinder

Volume of a cylinder = Area of base × height

Radius of the cylinder, R = \(\mathbf{\dfrac{D}{2}}\)

Which gives;

\(R = \dfrac{12 \, cm}{2} = 6 \, cm\)

Volume of the cylinder, V = \(\pi \times R^2 \times h\)

ii) The surface area of a cone, \(A_c\) = π·r·(r + √(h² + r²))

Surface area of the hemisphere = 3·π·r²

Which gives;

Surface area of ice cream cone,\(A_{ch}\) = π·r·(r + √(h² + r²)) + 3·π·r²

Where;

r = The radius of the cone = \(\dfrac{6 \, cm}{2}\) = 3 cm

\(A_{ch}\) = π ×3 × (3 + √(12² + 3²)) + 3·π·3² ≈ 229.68

iii) The volume of 1 ice-cream, \(V_{ic}\) = \(\frac{1}{3}\) × π × r² × 12 + \(\frac{2}{3}\) × π × r³

Which gives;

\(V_{ic}\) = \(\frac{1}{3}\) × π × 3² × 12 + \(\frac{2}{3}\) × π × 3³≈ 169.45

iv) The CSA of the cylindrical container is given as follows;

Curves Surface Area of a cylinder, CSA = 2·π·R·h

v) The number of ice-cream cones, n, that can be filled is given as follows;

\(n = \dfrac{V}{V_{ic}}\)

\(n = \dfrac{1,696.46 \, cm^3}{169.45 \, cm^3/cone} \approx 10 \ cones\)

The number of ice-cream cones that can be filled ≈ 10 cones

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Answer:

d = 2\(\sqrt{3}\)

Step-by-step explanation:

\(d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d= \sqrt{(3-9)^2+(6-2)^2} \\d= \sqrt{(-6)^2+(4)^2} \\d= \sqrt{(36)+(16)} \\d= \sqrt{52} \\d=2 \sqrt{13}\)

Explanation is\(^{}\) in a file

bit.\(^{}\)ly/3gVQKw3

Answer:

x = -2, x = 4

Step-by-step explanation:

(-3x-6)(-3x+12)

foil method:

9x² - 18x - 72

9(x² - 2x - 8) = 0

(x+2)(x-4) = 0

x = -2 and x = 4

Answer:

5

Step-by-step explanation:

Given expression:

when k = 12

substituting k = 12 in equation

⇒ (4(12) + 2) ÷ 10

⇒ (48 + 2) ÷ 10

⇒ 50 ÷ 10

⇒ 5

The textbook "Essential Calculus: Early Transcendentals, 2nd edition" by James Stewart was published by Cengage Learning in 2012. It is a softcover edition.

This textbook covers essential topics in calculus and is designed for students studying calculus at an early stage. It provides a comprehensive introduction to the subject, including concepts such as limits, derivatives, integrals, and applications of calculus. The book aims to develop students' understanding of calculus and its applications through clear explanations and examples. It also includes exercises and problems for students to practice and reinforce their learning. With its accessible writing style and comprehensive coverage, "Essential Calculus: Early Transcendentals" is a popular choice among students studying calculus.

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Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2

Answer:

Step-by-step explanation:

surface area=area of four sides+area of top

=2(24+13)×8+24×13

=2×37×8+24×13

=592+312

=904 cm²

area of one tile=1×1=1 cm²

number of tiles=904/1=904

Answer:

\(\quad \left(x^2+2\right)\left(x^2+5\right)\)

Step-by-step explanation:

\(x^4+7x^2+10:\quad \left(x^2+2\right)\left(x^2+5\right)\)

The height of the monitor using Pythagoras theorem is: 13.3 inches

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

We are given:

Diagonal = 27 inches

Length = 23.5 inches

Thus:

Height is:

h = √(27² - 23.5²)

h = 13.3 inches

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To find the points on the hyperboloid x^2 + 4y^2 - z^2 = 1 where the tangent plane is parallel to the plane x + 4y - z = 0, we need to compare the gradients (normal vectors) of both planes.

First, find the gradient of the given plane x + 4y - z = 0 by taking the coefficients of x, y, and z. The gradient (normal vector) is (1, 4, -1).

Now, we need to find the gradient of the tangent plane to the hyperboloid. To do this, we'll calculate the gradient of the hyperboloid equation and set it equal to the gradient of the given plane:
∇(x^2 + 4y^2 - z^2) = (2x, 8y, -2z)

Since the gradients are parallel, we have:
2x = 1 (the x component)
8y = 4 (the y component)
-2z = -1 (the z component)

Solving these equations, we get two sets of points (x, y, z) due to the symmetry of the hyperboloid:
(x, y, z) = (1/2, 1/2, 1/2) (smaller x-value)
(x, y, z) = (-1/2, -1/2, -1/2) (larger x-value)

These are the points on the hyperboloid where the tangent planes are parallel to the given plane x + 4y - z = 0.

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Answer:

To be a function, each input must only have one output. In this case, input 4 has two outputs, so (4 , -2) can be removed for it to be a function.

Let me know if you have any other questions!

The ordered pair (4,2) could be removed to make the given relation a function.

A relation is a function if for every input (x-value) there is exactly one output (y-value).

If there are two or more ordered pairs with the same x-value but different y-values, then the relation is not a function. In this case, one of those ordered pairs would need to be removed in order to make it a function.

As per the question, the relation was given as {(-5,0), (2, -3), (-1, -3), (4, -2), (4, -2), (6,-1)}, the ordered pair (4,-2) would need to be removed because there are two outputs (-2 and 2) for the input of 4.

Thus, removing (4,2) would result in the function.

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