If possible factor. Find LCD. Multiply both sides by LCD. Solve show all work.

Answer:

The [tex]66[/tex]th term is [tex]363[/tex].

Step-by-step explanation:

To find the [tex]n[/tex]th term, the formula is [tex]7n - 99[/tex]. Since we want to find the [tex]66[/tex]th term, we can plug [tex]n[/tex] for [tex]66[/tex]. So our expression is now [tex]7 \cdot 66 - 99 =[/tex] [tex]66[/tex]th term. Solving this we have

[tex]462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\[/tex]. Therefore, the [tex]66[/tex]th term is [tex]\boxed{363}[/tex].

Answer:

a₆₆ = 363

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then

a₆₆ = - 92 + (65 × 7)

      = - 92 + 455

     = 363

The chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and if it is not $40 the gain is:

1) 50%, $0

2) 25%, $20

3) 75%, $30

4) 50%, $20

So, the option (4) 50%, $20 is the correct option.

The given question is asking what the chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and what the gain will be if it is not $40.

Mathematically, this can be broken down as follows:

There is a 50% chance that the temperature will be lower than average, in which case the stock price for ABC will increase by $20. Thus, the expected gain from investing in ABC is 50% x $20 = $10.

There is a 25% chance that the temperature will be higher than average, in which case the stock price for XYZ will increase by $20. Since you are not investing in XYZ, your expected gain from this is 0.

Therefore, the expected gain from investing in ABC and not investing in XYZ is 50% x $10 + 25% x $0 = $10 + $0 = $10.

Since you are investing in two shares of ABC stock, your expected gain is 2 x $10 = $20. Thus, there is a 50% chance that your gain will be $40, and otherwise your gain will be $20.

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Answer: your mom

Step-by-step explanation:

answer

C(9, 5) - C(6, 5) + C(3, 1) = 126 - 6 + 3 = 123

explanation

The first term, C(9, 5), represents the number of ways to select 5 restaurants out of 9, regardless of type. The second term, C(6, 5), represents the number of ways to select 5 non-seafood restaurants out of 6. To find the number of ways that at least one of the selected restaurants will serve seafood, we subtract the number of ways to select 5 non-seafood restaurants and add the number of ways to select exactly 1 seafood restaurant, represented by C(3, 1).

The result, 123, represents the number of ways that at least one of the selected restaurants will serve seafood.

The graph of the quadratic function is on the image at the end.

Here we want to graph the quadratic function:

f(x) = -x² - 2

To do so, we can complete the table of values by evaluating the function.

if x = ±2 then:

f(±2) = -(±2)² - 2 = -4 - 2 = -6

if x =  ±1

f(±1) = -(±1)² - 2 = -1 - 2 = -3

if x = 0

f(0) = -(0)² - 2 =  - 2 = -2

Then we have the points:

(-2, -6), (-1, -3), (0, -2), (1, -3), (2, -6)

Now just graph these points and connect them with a curve. The graph of the parabola is below.

Answer:

he weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.

Step-by-step explanation:

To find the weight of 15 bags in kilograms, we can first convert the weight of one bag from pounds to kilograms and then multiply by the number of bags:

1 pound = 0.453592 kilograms

So the weight of one bag in kilograms is:

42 pounds * 0.453592 kilograms/pound = 19.05 kilograms

The weight of 15 bags in kilograms is:

15 bags * 19.05 kilograms/bag = 285.75 kilograms

To find the volume of 15 bags in cubic yards, we can first convert the volume of one bag from cubic feet to cubic yards and then multiply by the number of bags:

1 cubic yard = 27 cubic feet

So the volume of one bag in cubic yards is:

2 cubic feet / 27 cubic feet/cubic yard = 2 / 27 = 0.07407 cubic yards

The volume of 15 bags in cubic yards is:

15 bags * 0.07407 cubic yards/bag = 1.111 cubic yards

Therefore, the weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.

The interpret the numbers in this model is -17,732 is a constant amount credited from the savings account, 367 is the amount saved per year of age, 1300 is the amount saved per year of education.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0. In mathematics, a linear equation is an equation that may be put in the form [tex]{\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0, } where x_{1}, \ldots, x_{n} are the variables, and {\displaystyle b, a_{1}, \ldots, a_{n}}[/tex] are the coefficients, which are often real numbers.

Given that;

The equation of savings account balance as balance= −17,732 + 367×age + 1,300×years education + 0.116×household wealth.

Now,

-17,732 is a constant amount credited from the savings acount

367 is the amount saved per year of age

1300 is the amount saved per year of education

0.116 is the amount save per household wealth

Therefore, the following are the interpretations of the equation.

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The volume of the cylinder is approximately 9,558.4 cubic inches.

The volume V of a right circular cylinder is given by the formula:

V = πr^2h

where r is the radius of the circular base and h is the height of the cylinder.

In this case, the radius is 8 inches and the height is 15 inches. Substituting these values into the formula, we get:

V = π(8^2)(15)

= π(64)(15)

= 3,040π cubic inches

Therefore, the volume of the cylinder is 3,040π cubic inches. If you want an approximate value, you can use the approximation π ≈ 3.14 and calculate:

V ≈ 3,040(3.14)

≈ 9,558.4 cubic inches

So, the volume of the cylinder is approximately 9,558.4 cubic inches.

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Answer:

Step-by-step explanation:

18-5=13

18-9=9

Answer:

(C) 29

Step-by-step explanation:

Using the unitary method, we found that the unit rate of slime is 0.2 cups per container.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.

Given,

 Number of cups of slime = 7.2

  Number of containers = 36

 Unit rate = Amount of slime in each container

Using the unitary method we can find the unit rate.

7.2 cups = 36 containers

1 container = 7.2/36 = 0.2 cups.

Therefore using the unitary method, we found that the unit rate of slime is 0.2 cups per container.

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Step-by-step explanation:

Hope it helps :) #CarryOnLearning

The value of the expression 4(2x - 1) when x = 6 is 44. Option A

Algebraic expressions are defined as expressions that are made up of coefficients, terms, variables, factors and constants.

They are also identified with arithmetic operations, such as;

From the information given, we have that;

4(2x - 1)

expand the bracket, we get;

8x - 4

Substitute the value of x as , we have;

8(6) - 4

Multiply

48 -4

Subtract the values

44

Hence, the value is 44

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The required solution of the given expression δ = 0.0002. as of the given conditions

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given |x - 3| < δ, we want to find a value of delta such that |5x - 15| < 0.001.

Starting with the inequality |x - 3| < δ, we can substitute x = 3 + delta or x = 3 - δ. Let's consider the case x = 3 + δ,

|5x - 15| = |5(3 + δ) - 15|
            = |15 + 5δ- 15|
                = |5δ|

Now, we want |5δ| to be less than 0.001. So, we can divide both sides of the inequality by 5,

|5δ|/5 < 0.001/5

|δ| < 0.001/5

Therefore, if the delta is less than 0.001/5, we have |5x - 15| < 0.001.

Similarly, if x = 3 - delta, we have:

|5x - 15| = |5(3 - δ) - 15| = |15 - 5δ - 15| = |-5δ|

|-5δ|/5 < 0.001/5

|δ| < 0.001/5

So, if δis less than 0.001/5, then |5x - 15| < 0.001 for both x = 3 + delta and x = 3 - δ.

Therefore, if |x - 3| < 0.001/5, then |5x - 15| < 0.001.

So, δ= 0.001/5 = 0.0002.

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[tex] \large \blue{ \large\tt{C ) \$500}}[/tex]

_____________

[tex] \: [/tex]

Given:-

[tex] \: [/tex]

By using formula:-

[tex] \boxed{ \rm{ \pink{Simple \: interest= \frac{Principal × Time × Rate}{100}}}}[/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:)

Answer: the answer is c.$500 hope that helps !

Step-by-step explanation: I took the test

The quotient rule is proved below.

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

Given is the expression -

Q(x) = F(x)/G(x)

Quotient rule in calculus is a method used to find the derivative of any function given in the form of a quotient obtained from the result of the division of two differentiable functions. Mathematically, for a function f(x), we can write -

f'(x) = [u(x)/v(x)]' = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²

Now, let f(x) = u(x) and g(x) = v(x).

Q(x) = u(x)/v(x)

Q(x) = u(x) v⁻¹(x)

Using the product rule -

Q'(x) = u'(x) v⁻¹(x) + u(x) {d/dx v⁻¹(x)}

Q'(x) = u'(x) v⁻¹(x) + u(x) (-1)(v(x)⁻²) v'(x)

Q'(x) = u'(x)/v(x) - u(x)v'(x)/v²(x)

Q'(x) = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²

Therefore, the quotient rule is proved above.

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Answer:

x = 9.75

Step-by-step explanation:

1 / 4 * ( 8x + 2) = 20

( 8x + 2) = 20 / (1/4)

8x + 2 = 20 * 4

8x + 2 = 80

8x = 78

x = 9.75

Answer:

x=39/4  (39 over 4 as a fraction)

Answer:

Step-by-step explanation:

To find the value of x such that f(x) = g(x), we need to set the two functions equal to each other and solve for x.

First, let's define the variables:

f(x) = 2x² - x - 6 is a quadratic function with x as the variable.

g(x) = x² - 4 is also a quadratic function with x as the variable.

Now, to find the value of x such that f(x) = g(x), we set the two functions equal to each other:

2x² - x - 6 = x² - 4

Next, we simplify this equation by subtracting x² from both sides:

x² + x - 10 = 0

This is a quadratic equation, which we can solve for x using either the quadratic formula or by factoring.

Let's try factoring:

x² + x - 10 = (x + 5)(x - 2) = 0

So either x + 5 = 0 or x - 2 = 0. Solving for x, we find that:

x = -5 or x = 2

These are the two values of x such that f(x) = g(x).

After 40 years, the account has a total balance of $49.450.80.

Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.

here, we have,

Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.

The total contributions would be $100 x 480 = $48,000.

The interest earned on the account balance can be calculated as follows:

Interest = Account balance * Interest rate

At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:

Year 1: $48,000 * 1.5% = $720

Balance = $48,000 + $720 = $48,720

Year 2: $48,720 * 1.5% = $730.80

Balance = $48,720 + $730.80 = $49,450.80

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Answer:

p = x(y)(z)

Step-by-step explanation:

product is multiplication.

multiplication has no specific order.

The number of pounds in  [tex]1\frac{1}{2}[/tex] pounds and and 8 ounces is 2 pounds.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We know that 1 pound = 16 ounces.

As there are [tex]1\frac{1}{2}[/tex] pounds=1.5×16= 24 ounces.

The total number of ounces in   [tex]1\frac{1}{2}[/tex] pounds and 8 ounces is

24+8

32 ounces.

Now let us convert Ounces to pounds.

we divide the number of ounces by 16.

Therefore, 32 ounces is equal to 32/16 = 2 pounds.

Hence, 2 pounds will be there in  [tex]1\frac{1}{2}[/tex]  pounds and 8 ounces

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The condition which satisfy the congruency of the given triangle is

BC≈QR.

Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'

To show that triangle ABC≈triangle PQR by SSS,

In this type of congruency, all the sides of the triangle ABC is equivalent to the all the sides of the triangle PQR.

Given, AC≅PR, AB≅PQ.

The another one condition is BC≅QR.

Hence, the condition which satisfy the congruency of the given triangle is BC≈QR.

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The probability of choosing a preschooler who is a girl and prefers the color blue is 0.3 or 30%.

The total number of preschoolers who were asked about their color preference is 70. Out of these, 35 girls chose pink, 15 girls chose blue, 5 boys chose pink, and 15 boys chose blue.

To find the probability of choosing a girl who prefers blue, we need to use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Here, the favorable outcome is choosing a girl who prefers blue. We can see that 15 girls chose blue as their preferred color. Out of these, we need to choose a girl, so the total number of favorable outcomes is 15.

The total number of outcomes is the total number of preschoolers, which is 70. Out of these, the number of girls is 35+15=50. Therefore, the total number of outcomes where a girl can be chosen is 50.

Putting these values in the formula, we get:

Probability = 15/50 = 0.3

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Complete Question;

70 preschoolers were asked whether they preferred blue or pink.

35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color.

Assuming one of the preschoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.

Answer:

0.075 is a hundred times smaller than 7.5

Step-by-step explanation:

Answer:

The product of (4 + 3i)(5 - 2i) can be calculated using the distributive property:

(4 + 3i)(5 - 2i) = 4 × 5 + 4 × -2i + 3i × 5 + 3i × -2i

= 20 - 8i + 15i - 6i^2

= 20 + 7i - 6(-1)

= 26 + 7i

So the answer is (4) 26 + 7i.

I believe the answer is (d) 26 + 7i.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-3}-\underset{x_1}{(-1)}}} \implies \cfrac{1 +1}{-3 +1} \implies \cfrac{ 2 }{ -2 } \implies - 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-1)}) \implies y +1 = - 1 ( x +1) \\\\\\ y+1=-x-1\implies {\Large \begin{array}{llll} y=-x-2 \end{array}}[/tex]

Answer:

When it comes to right trangles, to find the value of x, what ever 9 plus x is, it is equal to 24.

You want to subtract 9 and 24 to get the x value:

24 - 9 = 15

x = 15

Step-by-step explanation:

Hope it helps! =D

Hi there, here's your answer:

Given a right angled triangle

With the hypotenuse as 24 units and one of the legs as 9 units
To find:

The 3rd side denoted as 'x'

Solution:

We use Pythagoras Theorem:

[tex]a^2 + b^2 = c^2[/tex]

Where a and b are the legs and c is the hypotenuse.

We know the value of c and b

And a = x
Thus,

[tex]x^2 = c^2 - b^2[/tex]

[tex]x^2 = 576 - 81\\[/tex]

[tex]== > x^2 = 495\\[/tex]

Or
[tex]x = \sqrt{495} = 3\sqrt{55} = 22.248[/tex] units

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