The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6. Terrence owns 36 models cars. How many model cars does Jim own? How will the ratio change if Jim and Terrence each sell ten of their model cars?

When the surface area of the cell phone is converted to Cm² it would be. = 59cm²

The surface area of the cell phone screen = 5900mm²

But 10 mm = 1 cm

When squared after calculating the area,

100 mm² = 1 cm²

5900 mm² = X cm²

Make X cm² the subject of formula;

X cm² = 5900/100 = 59cm²

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Answer:

Step-by-step explanation:

A) In a geometric sequence, t_(1)=625 and the common ratio is r=(1)/(5). For what value of n is t_(n)=(1)/(25)?

Step 1: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 2: Substitute the given values into the formula

t_n = 625 * (1/5)^(n-1)

Step 3: Solve for n when t_n = (1/25)

(1/25) = 625 * (1/5)^(n-1)

(1/25) / 625 = (1/5)^(n-1)

(1/5)^(n-1) = (1/25) / 625

(n-1) = log base (1/5) of ((1/25) / 625)

Step 4: Solve for n

n = 1 + log base (1/5) of ((1/25) / 625)

The value of n is the number of terms that have passed when t_n = (1/25).

B) (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

Step 1: Determine the type of sequence

A sequence is an arithmetic sequence if the difference between any two consecutive terms is constant. Since this sequence does not have a constant difference, it is not an arithmetic sequence.

A sequence is a geometric sequence if the ratio between any two consecutive terms is constant. We can see that the ratio between any two consecutive terms is constant, so this sequence is a geometric sequence.

Step 2: Find the common ratio

To find the common ratio, we can divide any two consecutive terms. For example, the common ratio is (3/6) / (2/5) = (3/2) / (6/5) = 5/6.

Step 3: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 4: Substitute the given values into the formula

To use this formula, we need to know the value of t_1. We are given t_1 = (2/5), so:

t_n = (2/5) * (5/6)^(n-1)

This is the formula for the nth term of the sequence (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

The given graph is represented by the function ( x + 2 )(x - 1 )³(x - 3 ). The correct option is A.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

Graphing functions involve drawing a curve on the coordinate plane that represents the function. Every point on a curve (graph) that represents a function satisfies the function equation.

The graph is represented by the function,

( x + 2 )(x - 1 )³(x - 3 )

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The required angle of the elevation at point C to A is given as ∠C = 31°.

The angle of elevation is the angle between a horizontal line of sight and a line of sight that is directed upwards to an object or point. In other words, it is the angle between the horizontal and an observer's line of sight to an object above the observer

Here,
A figure has been shown, Consider triangle ABC, where ∠A = 59, ∠B = 90°,
Since the sum of the angle in the triangle should be 180°.
∠A + ∠B + ∠C = 180
∠C + 90 + 59 = 180
∠C = 90 - 59
∠C = 31°

Thus, the required angle of the elevation at point C to A is given as ∠C = 31°.

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Answer:

30 mm

Step-by-step explanation:

just add the length of each side together

Answer:

There are 12 desktop computers and 20 laptop computers.

Step-by-step explanation:

32:2=16

8:2=4

16-4=12

16+4=20

Answer:

Step-by-step explanation:

Straight line= 180 degrees

|_= 90 degrees

180-90=90

3s-2=52

2s+2=38

52+38=90

s=18

Answer:

200 lb

Step-by-step explanation:

Let her original weight be [tex]x[/tex].

[tex]0.12x=24 \implies x=200[/tex]

The statement regarding the census in this problem is classified as a True statement.

Population: Collection or set of individuals or objects or events whose properties will be studied.

Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.

A Census is when a group of the population is chosen, that is, a sample is chosen, hence the statement for this problem is true.

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Answer:

3.4 x 10⁻²  kg · m²/s²

Step-by-step explanation:

[tex]3.4\times \:10^5=340000[/tex]

The numerator is in g.cm² and the denominator is the same s²

So we only need to convert the numerator from g.cm² to kg.m²

1 kg = 1000 grams = 10³ grams
1 gm = 1/10³ kg
1 gm = 10⁻³ kg

1 m = 100 cm = 10² cm

1 m² = 100² cm² = (10²)² = 10⁴ cm²

Or 1 cm² = 1/10⁴ cm² = 10⁻⁴ cm²

Therefore to convert g · cm² to kg · m² we multiply by

(10⁻³)  · (10⁻⁴) = 10⁻⁷

Therefore 3.4 x 10⁵ g · cm² =  3.4 x 10⁵ x 10⁻⁷ kg · m²

= 3.4 x 10⁻² kg · m²/s²

The slope of the line containing (-1, 5) and (2, -4) will be negative 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are (-1, 5) and (2, -4). Then the slope of the line is given as,

m = (5 + 4) / (- 1 - 2)

m = 9 / (-3)

m = - 3

The slope of the line containing (-1, 5) and (2, -4) will be negative 3.

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The solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).

What is inequality?

An inequality is a mathematical statement that describes a relationship between two values or expressions, where one is greater than, less than, or not equal to the other.

To solve the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex], we can use the concept of interval notation and test each interval to see if it satisfies the inequality. Here are the steps:

Find the critical points of the expression, which are the values that make the expression equal to zero. In this case, the critical points are -5, -4, and -3.

Use these critical points to divide the number line into four intervals: (-∞, -5), (-5, -4), (-4, -3), and (-3, ∞).

Test a value in each interval to see if the inequality is true or false. We can use the sign of the expression to determine this:

For x < -5, all three factors are negative, so the product is negative. Therefore, this interval does not satisfy the inequality.

For -5 < x < -4, the first factor is positive and the other two factors are negative. The product is therefore negative. This interval does not satisfy the inequality.

For -4 < x < -3, the first and third factors are positive and the second factor is negative. The product is therefore positive. This interval satisfies the inequality.

For x > -3, all three factors are positive, so the product is positive. Therefore, this interval satisfies the inequality.

Write the solution set using interval notation. We have found that the solution set is (-4, -3) union ( -3, ∞).

Therefore, the solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).

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Answer:

Step-by-step explanation:

Range: the difference between the highest and lowest values

Heights:

130

142

142

143

144

145

147

147

149

150

151

153

154

154

158

161

162

Formula to find the range

R= H-L

R = range

H = highest value

L = lowest value

    R = 160 - 130.

The range is 30.

The expression which is equivalent to the expression 14x+3−13x+(−2) is:

x +1

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

14x+3−13x+(−2)

Now it can be simplify in the following way:

⇒ 14x - 13x + 3 - 2

the variable and constant terms can be clubbed together,

⇒ x + 1

Hence, the equivalent expression is x + 1

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Answer:

1.02n or 51/50n

Step-by-step explanation:

n + 2% raise = 1.02n and 50/51n

According to the diagram, angle JKL is

Adjacent angles are angles that share a common vertex and a common side, but do not overlap. In a trapezoid, adjacent angles can be any pair of angles that share a common vertex and a common side.

angle JKL and angle MKL are adjacent angels having same vertex at k

angle JKM = angle JKL  angle MKL

94 = angle JKL + 47

angle JKL = 94 - 47

angle JKL = 47

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Mortgage B requires $27,336.60 more interest than mortgage A. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

There are four fundamental mathematical operations that can be used to express any real number; these are referred to as "arithmetic operations." The four operations are multiplication, division, addition, and subtraction.

We are given the principal amount as $80,000.

So, interest on Mortgage A = Total amount payable - principal amount

Interest = $110,158.20 - $80,000

Interest = $30,158.20

Similarly, interest on Mortgage B = Total amount payable - principal amount

So,

Interest = $137,494.80 - $80,000

Interest = $57,494.80

So, difference in interest = $57,494.80 - $30,158.20 = $27,336.60

Hence, mortgage B requires $27,336.60 more interest than mortgage A.

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Suppose that the functions q and r are defined as q(x) = 2x+2 and r(x) = x² +1, the function  (r * q)(4) =(q * r)(4) and they are equal to 170.

Which is the commutative law?

commutative law, in mathematics, is either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba. From these laws, it follows that any finite sum or product is unaltered by reordering its terms or factors.

Given the following functions:

q(x) = 2x+2

r(x) = x² +1

Taking the product

q(x)*r(x) = (2x + 2)(x² +1)

Note that according to the communatative law, (r * q)(x) = (q * r)(x)

(r * q)(4) =(q * r)(4)  = (2(4)+2)((4)² +1)

(r * q)(4) =(q * r)(4)  = (10)(16+1)

(r * q)(4) =(q * r)(4)= 10(17)

(r * q)(4) =(q * r)(4) = 170

Hence, the function  (r * q)(4) =(q * r)(4) and they are equal to 170.

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Answer:

35y^(10)z^(4)

Step-by-step explanation:

Solution Given:

(-5y^(4)z)(-7y^(6)z³)

Here while opening bracket

If their is like terms they can be multiplied ,divided,subtracted as well as added.

So

Here

opening bracket and keeping in serially

-5*-7*y^(4)*y^(6)*z*z^(3)

here if their is like terms their power is added.

And solving remaining one.

35y^(4+6)z^(1+3)

Here -5*-7=35

Again

Solving it.

35y^(10)z^(4)

Answer:

[tex]35y^{10}z^4[/tex]

Step-by-step explanation:

Given expression:

[tex](-5y^4z)(-7y^6z^3)[/tex]

Apply the rule:  (-a) · (-b) = ab

[tex]\implies 5y^4z \cdot 7y^6z^3[/tex]

Multiply the numbers:  5 · 7 = 35

[tex]\implies 35y^4zy^6z^3[/tex]

Collect like terms:

[tex]\implies 35y^4y^6z^3z[/tex]

[tex]\textsf{Apply exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 35y^{(4+6)}z^{(3+1)}[/tex]

Simplify the exponents:

[tex]\implies 35y^{10}z^4[/tex]

Answer: x=56

Step-by-step explanation: Question 2 shows a right angle that is equal to 90 degrees. Since you are already given 34, you just need to subtract 90-34.

Question 4 shows an 180 degree angle and so you need to do the same thing; 180-124

The surface area of a horse with the mass  is 4.5 x 10^6 square centimeters,

From the question, we have the following parameters that can be used in our computation:

S = 10mi

Using the above as a guide, we have the following:

m =  4.5 x 10^5 grams

substitute the known values in the above equation, so, we have the following representation

S =10 * 4.5 x 10^5

So, we have

S =4.5 x 10^6

Hence, the surfave area is 4.5 x 10^6

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Using the equation of the arithmetic sequence given, the first four terms are 59, 52, 45 and 38 respectively

In the sequence given, the progression is an arithmetic progression since it increases by a common difference.

The first term of the sequence is 59 while the common difference is -7.

A = 59 - 7(n - 1)

n = 1

a = 59 - 7(1 - 1)

a = 59

n = 2

a = 59 - 7(2 - 1)

a = 52

n = 3

a = 59 - 7(3 - 1)

a = 45

n = 4

a = 59 - 7(4 - 1)

a = 38

The terms are 59, 52, 45 and 38

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Translation:  Find the first four terms of the sequence given the following

The vertical intercept of the graph is 100,000

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e, is called an exponential function.

Given that, the population p of migrating butterflies satisfies the exponential function p = 100,000 (4/5)ⁿ, where n is the number of weeks,

So, we need to find the vertical intercept of the graph,

We know that, vertical intercept = intercept

To find the y-intercept of a line, we will put x = 0,

here x is n,

So, the y-intercept of the graph is = 100,000 (4/5)⁰ = 100,000×1 = 100,000

Therefore, the vertical intercept of the graph is 100,000

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The numeric value of the marginal revenue at 33 units will be $336.

The sum of the units sold times the price per unit is the revenue. Multiply the output level by the pricing function to get the revenue function.

Revenue function is R(q) = - 8q ^ 2 + 600q

Differentiate with respect to q

R^ prime (q) = - 8(2q) + 600(1)

R' (q)=-16q+600 ...(1)

substitute q = 33 in equation

MR(113) = - 8(33) + 600

=-264 + 600

MR (113)= $336 per unit

The marginal revenue is $336.

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======================================================

Explanation:

If we plugged x = 4 into the expression, then we'll have 0 in the denominator. This causes a division by zero error.

Luckily the numerator factors to (x-4)(x-2)^2. This is found by using the Rational Root Theorem, along with either synthetic division or polynomial long division. I'll skip these steps unless you need me to write them out.

Once we know the numerator factors this way, we can then write the following steps:

[tex]L = \displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}\frac{(\text{x}-4)(\text{x}-2)^2}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}(\text{x}-2)^2\\\\\\L = (4-2)^2\\\\\\L = 4\\\\\\[/tex]

Therefore,

[tex]\displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}=4\\\\\\[/tex]

You can use graphing software like Desmos or GeoGebra to confirm the answer is correct. WolframAlpha is another good choice.

By subtraction we get that, Isabel has to pour 35.25 grams of salt into the container.

The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as 'taking away one number from another'.

According to the information in question:

Total salt = 90.45 grams

Amount of salt poured = 55.2 grams

Thus, the total amount of salt left with her which has to be poured will be calculated by subtraction:

Amount of salt left = 90.45 - 55.2

                               = 35.25 grams

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Answer:

Step-by-step explanation:

y = 2x - 6