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The amount of money they have altogether is $105.

i - b = $15 equation 1

1/2i = 2/3b

3i = 4b

i = 4b/3 equation 2

Where:

i = amount of money Isiah has

b = amount of money Bob has

Substitute for the value of i in equation 1

4b/3 - b = $15

1/3b = $15

Multiply both sides of the equation by 3

b = $45

Substitute for $45 in equation 1

i - $45 = $15

Add $45 to both sides of the equation

i = $45 + $15

i = $60

$60 + $45 = $105

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An equation to show the additional number of cases of water Mr. Brown needs is y = 24x - 3, where y = 333 bottles and x = 14.

An equation is a mathematical statement that claims that two mathematical expressions are equal.

An equation contains the equation symbol (=).

The number of bottles in his office = 17 bottles

The total number of bottles required = 350 bottles

The total number of additional bottles of water required, y = 333

1 case of water bottles = 24 bottles

The equation to show the additional cases required is y = 24x - 3, where y = 333 bottles and x = 14.

Check:

y = 24x - 3

333 = 24(14) - 3

333 = 336 - 3

333 = 333

Thus, an equation to show the additional number of cases of water Mr. Brown needs is y = 24x - 3, where y = 333 bottles and x = 14.

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Answer:

18/45 and 14/35

Step-by-step explanation:

15/25 are not equivalent fractions

12/35 are also not equivalent

14/21 are not equivalent either

18/45 and 14/35 are the only equivalent fractions.

The meaning of \(\( \mathbb{N}=\bigcap \left \{X:X inductive \right \}\) is that the set of natural numbers is the intersection of all inductive sets.

The set of natural numbers is inductive because it satisfies both of these conditions. The set is non-empty because it contains the number 1. And if x is a natural number, then x+1 is also a natural number.

In other words, a set is inductive if it satisfies the following two conditions:

The concept of an inductive set is important in mathematics because it allows us to define the set of natural numbers.

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Answer:

14.55

Step-by-step explanation:

\((2x + 1)(x + 1)\)

•Distribute

\((2x + 1)(x + )\)

\(2x(x + 1) + 1( x + 1)\)

•Distribute

\(2x(x + 1) + 1(x + 1)\)

\(2x² + 2x1(x + 1)\)

•Multiply

\(2x² + 2x + 1(x + 1)\)

\(2x² + 2x + x + 1\)

•Combine like terms

\(2x² + x + x + 1\)

\(2x²+ 3x + 1\)

Solution:

\(2x² + 3x + 1\)

Explanation:

see the graph

Answer:

60

Step-by-step explanation:

180-(100+20)=x

x=60

9514 1404 393

Answer:

  a) 0.8

  b) 0.05

  c) 0.01875

Step-by-step explanation:

The denominator will need to have equal powers of 2 and 5 to be a power of 10.

a) 4/5 = (4/5)(2/2) = 8/10 = 0.8

__

b) 1/20 = 1/(2²·5) = (1/20)(5/5) = 5/100 = 0.05

__

c) 3/160 = 3/(2⁵·5) = (3/160)(625/625) = 1875/10000 = 0.01875

Following the pattern, the most likely next step in the series is given by the pentagon in option B.

We have to look at the number of points in each figure, hence:

Hence, the number of points increases by one for each figure, meaning that in the next step, the figure should have 5 points, representing a pentagon.

Among the options given for the answer, only one, option B, has 5 points, with the pentagon, as:

Hence, the most likely next step in the series is given by the pentagon in option B.

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Answer:

С.

Step-by-step explanation:

From the options provided the only one that represents a proportional relationship was The cost of purchasing a box of socks for $1.75 per sock plus $2.15 for the box. This is because the total cost of the boxes depends on the number of socks that are bought since every pair of socks that are bought comes with a box which causes the total costs of the boxes to increase. Therefore, the number of sock pairs and the number of boxes has a proportional relationship.

The total cash due at signing is $3,700 at the local dealership..

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

The total cash due is calculated as:

Down payment: $1,800

Security deposit: $400

Acquisition fee: $300

Total: $1,800 + $400 + $300

Apply the addition operation, and we get

= $3,700

Thus, the total cash due at signing is $3,700.

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Answer: 5x + (1)y = -25

Step-by-step explanation:

Simple addition and subtraction

- 2 + 7 = 5

- 4 + 5 = 1

- 8 - 17 = - 25

5x + (1)y = -25

The desired polynomial function of degree 6 with -3 as a zero of multiplicity 3, 0 as a zero of multiplicity 2, and 1 as a zero of multiplicity

\($x^6 + 6x^5 + 11x^4 - 6x^3 - 27x^2 - 18x\).

To find a polynomial function of degree 6 with the given zeros and multiplicities, we can start by writing out the factors of the polynomial in factored form, and then multiplying them together. The factors will have the form \($(x-a)^n$\), where a is a zero of the polynomial and n is the multiplicity of the zero.

Since -3 has a multiplicity of 3, we have three factors of (x+3):

\($$(x+3)^3$$\)

Similarly, since 0 has a multiplicity of 2, we have two factors of x:

\($$x^2$$\)

Finally, since 1 has a multiplicity of 1, we have one factor of (x-1):

(x-1)

To get the polynomial, we can multiply all these factors together:

\($$(x+3)^3 \cdot x^2 \cdot (x-1)$$\)

Expanding this out, we get:

\($x^6 + 6x^5 + 11x^4 - 6x^3 - 27x^2 - 18x\)

This is the desired polynomial function of degree 6 with -3 as a zero of multiplicity 3, 0 as a zero of multiplicity 2, and 1 as a zero of multiplicity

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Answer:

The answer would be C. $36.00

Step-by-step explanation:

Off the bat we can cancel out A because it isn't possible.

One way to find the answer would be to find 60% of each answer.

To find the percent of something, we take the % (in this case it is 60) and move the decimal over 2 to the left, leaving us with 0.60

For B: 34.56 x 0.60 = 20.74 so close but not quite

For D: 81.20 x 0.60 = 46.72 so not right

For C: 36.00 x 0.60 = 21.60 so C is the answer

Answer:

Step-by-step explanation:

In this problem we are required to provide the expression for the two scenarios highlighted

The first scenario is

"Each pound of trout costs $30, and the company charges a $2 fee for

shipping the order"

The expression for the above scenario is given as

30x + 2, 0 < x < 10

The second scenario is

"if Karen orders 10 or more pounds, the trout costs only $24 per pound, but the shipping fee is $6."

The expression for the second scenario is

24x + 6, x > 10

Answer:

The algebraic expression is \(g(m) = 100 + 75m\)

Step-by-step explanation:

In this problem, we should find an expression for g(m), which is the number of gallons of water in the tank after m minutes. So

The number of gallons of water in a tank, that already has 100 gallons in It, after being filled at 75 gallons per minute for m minutes.

Initially 100 gallons.

For each minute m, 75 gallons are added. So the model should be given by:

\(g(m) = 100 + 75m\)

Answer:

C. 24

Step-by-step explanation:

The denominators are 6 and 8.

The least common multiple of 6 and 8 is 24.

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

It is bc 3x5=15 and 2x 5=10 so 10/15 + 5x3=15 and 1x3=3 so 10/15 + 3/15= 13/15

Answer:

48

Step-by-step explanation:

Answer:  48

Step-by-step explanation:

Answer:

8x+7x+44.4=180

15x=180-44.4

15x =135.6

X=9.04

8x=9.04×8=72.32

Uri paid a total of $85.47 for the landscaping service including tax and tip.

Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.

Given that company charged $74 for the service plus 5% tax.

The tax is 5%, that is:

Tax = 5% of $74 = 0.05 x $74 = $3.70

Cost after tax = $74 + $3.70 = $77.70

Now, tip is 10%:

Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77

Total cost = $77.70 + $7.77 = $85.47

Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.

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Answer:

18 minutes

Step-by-step explanation:

6 towels in 3 minutes

36 towels = ?

36/6 x 3

= 18

Answer:

0

Step-by-step explanation:

7 + (-8) + 2 + (-1)

is the same as:

7 - 8 + 2 - 1

Simplify these:

-1 + 1

Solve:

0

Answer:

Point (-11, 3) would be located in quadrant II/quadrant 2 on a coordinate plane.

Answer:

5x+8y≤80

Step-by-step explanation:

trust me ;)

Answer:

5x+8y< 80

Step-by-step explanation:

The total amount should be less than 80 or equal to

Dummy variables:

Ice Clean Flavor, Gender, Shoe Color, Number on an Athlete's Jersey, Ice Cream Flavor

Quantitative Variables:

Time to run a marathon, Flat-Screen TV, Height, Hours Spent Researching Core, Calories in Desserts

A dummy variable, often known as an indicator variable or simply a dummy, is a variable in regression analysis that accepts the values 0 or 1 to signify the lack or presence of a category effect that would be anticipated to change the outcome. 

Any variable where the data indicate amounts is referred to be a quantitative variable (e.g. height, weight, or age). Any variable where the data represent groupings is referred to as a categorical variable. This comprises categories (like where people placed in a race), rankings (like cereal brands), and binary results (e.g. coin flips).

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The complete question is:

For use in a linear regression model, categorize which of the following variables should be represented as dummy variables and which can be represented as quantitative variables.

ITEMS

CATEGORY

Answer:

A

Step-by-step explanation:

We want to solve the equation:

\(5\sin(2x)=3\cos(x)\)

To do so, we can rewrite the equation.

Recall the double-angle identity for sine:

\(\sin(2x)=2\sin(x)\cos(x)\)

By substitution:

\(5\left(2\sin(x)\cos(x)\right)=3\cos(x)\)

Distribute:

\(10\sin(x)\cos(x)=3\cos(x)\)

We can subtract 3cos(x) from both sides:

\(10\sin(x)\cos(x)-3\cos(x)=0\)

And factor:

\(\cos(x)\left(10\sin(x)-3\right)=0\)

Hence, our answer is A.

*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0 and we cannot divide by 0. Hence, we should subtract and then factor.

Answer:

A. cosx(10sinx-3)=0

Step-by-step explanation:

5(2sinxcosx)=3cosx

10sinxcosx-3cosx=0

cosx(10sinx-3)=0