Tom and Rob are brothers who like to make bets about the outcomes of different contests between them. Before the last bet, the ratio of the amount of toms money to the amount of robs money was 4:7. Rob lost the latest competition, and now the ratio of the amount of robs money is 8:3. If rob had $280 before the last competition, how much rob have now that he lost the bet?

Answer:

Step-by-step explanation:

The associative property of multiplication states that the product is the same regardless of their grouping. In this case, after simplifying the expression given, we can see that indeed the products are the same hence that fact that they have different grouping

Number 3. is wrong the correct answer is D.

The equation of the exponential graph is y = 100(0.5)^x

On the graph, we have the following points

(x,y) = (0,100) and (1,50)

An exponential equation is represented as:

y = ab^x

Where a = y, when x = 0.

This means that

a = 100

So, we have:

y = 100b^x

At the point (1,50), we have:

50 = 100b^1

Evaluate

50 = 100b

Divide both sides by 100

b = 0.5

Substitute b = 0.5 in y = 100b^x

y = 100(0.5)^x

Hence, the equation of the exponential graph is y = 100(0.5)^x

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In mathematics, it is common to combine two inequalities into a single compound inequality to indicate a range for a variable. Inequalities are also used in describing alternative hypotheses in statistics and conversions between measurement systems.

It is indeed sometimes possible to represent two separate inequalities as a single compound inequality in mathematics. This technique is often used to indicate that a value lies within a certain range. For instance, to show that a number x is greater than 1 but less than 3, we can write two inequalities: x > 1 and x < 3. These can be combined into a single compound inequality 1 < x < 3.

Inequalities are often used in various mathematical contexts, such as solving equations, graphing regions on a coordinate plane, or expressing ranges. Furthermore, in statistics, the alternative hypothesis is typically denoted using inequality symbols (≠, >, or <), showing a predicted difference or relationship.

To express equivalences between different measurement systems, a common approach is to use 1 as an exact value on one side of the equation, with the other side being inexact. Mathematically, you can rearrange equations for convenience into formats showing direct or indirect proportionalities, simplifying complex relationships into more manageable forms.

The speed of the truck in feet per second will be 105.6 ft per second.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.

Another example could be kilo gram to gram.

1 mile = 5280 feet

And

1 hour = 60 minutes

1 hour = 60 × 60 seconds = 3600 seconds

Now

Given the speed of the truck is

⇒ 72 miles/hour

⇒ 72 × 1 mile/1 hour

⇒ 72 ×  5280 feet/3600 seconds

⇒  105.6 feets/second

Hence "The speed of the truck in feet per second will be 105.6 ft per second".

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Final answer:

The growth of Spanish colonies was hindered by the vast distance between the colonies and Spain, restrictive economic policies, environmental depletion, exploitation of resources, and conflict. The decline in indigenous populations and internal governmental strife also played significant roles.

Explanation:

Factors Hindering the Growth of Spanish Colonies

The growth of the Spanish colonies was hindered by several factors after the initial period of discovery and conquest. First, the distance and the expanse of the Atlantic Ocean created significant challenges for effective communication and administration between the colonies and Spain. Second, the rigid economic policies imposed by the Spanish Crown, which restricted colonial trade to raw materials to Spain and finished goods from Spain, limited economic diversification and local development.

Additionally, environmental depletion and exploitation of resources, alongside harsh treatment and violence against Indigenous populations, led to a decrease in the native labor force. As a substitute, the Spanish were compelled to import African slaves, which transitioned the labor system but did not solve the inherent problems of the colonial economy.

The desire for precious metals, such as silver and gold, and the competition for conversion to Catholicism often came at a substantial human cost, leading to significant loss of indigenous life due to disease and conflicts. Revolts and uprisings, such as the Pueblo Revolt, as well as internal government conflicts and higher tax burdens on the Criollos were also among the contributing factors that hindered the growth and stability of Spanish colonies.

Final answer:

To find the length of MN, we can set up an equation using the fact that LN + LM = MN and substitute the given values. Solving for x, the length of MN is found to be 4.9 units.

Explanation:

To find the length of MN, we can use the fact that LN = 5.7 and LM = 1.3. We are also given that MN = x + 2.1. Since LN and LM are known, we can set up an equation using the fact that LN + LM = MN.

LN + LM = MN

5.7 + 1.3 = MN

Then, we can substitute the given value of MN = x + 2.1 into the equation and solve for x.

5.7 + 1.3 = x + 2.1

7 = x + 2.1

x = 7 - 2.1

x = 4.9

Therefore, the length of MN is 4.9 units.

Answer:

B

Step-by-step explanation:

3x+5x= 8x

5x^3 - 2x^3= 3x^3

-2x^2= -2x^2

13+11=24

Answer:

The factored form of the expression [tex]\( -4d^3 + 28d^2 - 4d \)[/tex] is [tex]\( -4d(d - 1)(d - 1)(6d - 1) \).[/tex]

Explanation:

To factor the expression [tex]\( -4d^3 + 28d^2 - 4d \)[/tex], we can first look for the greatest common factor (GCF) among the terms. In this case, the GCF is [tex]\( -4d \).[/tex]

So, we can factor out [tex]\( -4d \)[/tex] from each term:

[tex]\[ -4d(d^2 - 7d + 1) \][/tex]

Now, let's focus on factoring the quadratic expression inside the parentheses, [tex]\( d^2 - 7d + 1 \)[/tex]. To factor this quadratic expression, we need to find two numbers that multiply to give the constant term (1) and add to give the coefficient of the linear term (-7d). Since the constant term is 1, the only possible combination is 1 and 1.

So, we can rewrite the expression as:

[tex]\[ -4d(d^2 - 7d + 1) = -4d(d^2 - d - 6d + 1) \][/tex]

Now, we can group the terms and factor by grouping:

[tex]\[ -4d((d^2 - d) + (-6d + 1)) \][/tex]

[tex]\[ -4d(d(d - 1) - 1(6d - 1)) \][/tex]

Now, we can factor further:

[tex]\[ -4d(d - 1)(d - 1)(6d - 1) \][/tex]

Answer:

Step-by-step explanation:

Notice to facts:

The expression has a common factor 6n. Then,

6n⁴-24n³+18n = 6n(n³-4n²+3).

In order to factor the term n³-4n²+3 we use Ruffini-Horner rule, which gives us that

n³-4n²+3 = (n-1)(n²-3n-3).

Then,

6n⁴-24n³+18n = 6n(n³-4n²+3) = 6n(n-1)(n²-3n-3).

If you don't know the formula for the general solution of second degree equation, you are done. Otherwise, it is only to use it in the quadratic factor.

Answer with Step-by-step explanation:

We spent $37.50 for two sweaters.

Each sweater costs the same amount.

Cost of each sweater=$37.50/2

                                  =$18.75

The amount of money you spend varies directly with the number of sweaters you buy.

We have to find the constant of variation.

Here, cost of each sweater is the constant of variation.

Hence, constant of variation is:

$18.75

The solution of expression is,

⇒ d = 5/16

We have to given that,

An expression is,

⇒ 3.2 - 4d = 2.3d + 3

Now, We can simplify the expression for solution as,

⇒ 3.2 - 4d = 2.3d + 3

Add 4d both side,

⇒ 3.2 - 4d + 4d = 2.3d + 3 + 4d

⇒ 3.2 = 6.3d + 3

Subtract 3 both side,

⇒ 3.2 - 3 = 6.3d

⇒ 0.2 = 6.3d

⇒ 6.3d = 0.2

Divide 6.3 both side,

⇒ d = 0.2/6.4

⇒ d = 20/64

⇒ d = 5/16

Thus, The solution of the expression is, d = 5/16

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The area of the triangle is 270 square centimeters.

To find the area of a triangle, we can use the formula A = (1/2)bh, where A represents the area, b represents the base length, and h represents the height. In this case, we are given the area of one triangle (150 square centimeters) when its height is 20 centimeters and its base length is 15 centimeters. Plugging these values into the formula, we get:

A = (1/2)(15)(20) = 150

Now, we can use this equation to find the area of another triangle with a height of 30 centimeters and a base length of 18 centimeters:

A = (1/2)(18)(30) = 270 square centimeters

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Answer: [tex]51.4^{\circ}[/tex]

Step-by-step explanation:

We know that the sum of all the exterior angles of a regular polygon with n sides is [tex]360^{\circ}[/tex].

The measure of an exterior angle of a regular n-sided polygon is given by :-

[tex]\dfrac{360^{\circ}}{n}[/tex]

Now, the measure of an exterior angle of a regular 7-sided polygon is given  by :-

[tex]\dfrac{360^{\circ}}{7}=51.4285714286^{\circ}\approx51.4^{\circ}[/tex]

Hence, the  measure of an exterior angle of a regular 7-sided polygon =[tex]51.4^{\circ}[/tex]

0.10d +0.25q = 7.00

 multiply everything by 100 to get rid of decimals

q = d+7 ( 7 more quarters than dimes)

10d +25(d+7) = 700

10d + 25d +175 = 700

35d +175 = 700

 subtract 175 from each side

35d =525

d = 525 / 35 = 15

15 dimes

 quarters = 15 +7 = 22