Rufus has collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. In how many weeks will Rufus have a total of 400 pounds of cans?

Fátima tiene un total de $ 160, Gabriel tiene un total de $ 690 y José tiene un total de $ 230.

En este problema tenemos a tres personas, Fátima, Gabriel y José, que reúnen un total de $ 1.080. A continuación, traducimos las variables y ecuaciones asociadas a la situación:

x - Cantidad de dinero de Fátima.

y - Cantidad de dinero de Gabriel.

z - Cantidad de dinero de José.

Ecuaciones: Fátima, Gabriel y José tienen un total de $ 1080.

x + y + z = 1080

Gabriel tiene 3 veces lo que José tiene.

y = 3 · z

Fátima tiene $ 70 menos que José.

x = z - 70

A continuación, resolvemos el sistema de ecuaciones lineales:

x + y + z = 1080

(z - 70) + 3 · z + z = 1080

5 · z - 70 = 1080

5 · z = 1150

z = 1150 / 5

z = 230

x = z - 70

x = 230 - 70

x = 160

y = 3 · z

y = 3 · 230

y = 690

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Answer:

5

Step-by-step explanation:

2 +3 = 5    

Using the formula for the distance between two points and using the provided points, The error is missing a square root. The actual length is [tex]\sqrt{61}[/tex] units.

A line or line segment's length between two points along the line or line segment.

The required formula is:

[tex]d = \sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]

(x1,y1)= (6,2)

(x2,y2)=(1,-4)

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

[tex]d=\sqrt{25+36}[/tex]

[tex]d=\sqrt{61}[/tex] units.

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Using the formula for the distance between two points and using the provided points, The error is missing a square root. The actual length is  units.

What do you mean by distance?
Distance refers to the amount of space between two or more points, or the measure of how far apart two or more points are. It can be measured in various ways, including miles, kilometers, inches, centimeters, and more. Distance is often used to measure the length of a journey or the amount of space between two physical objects. It can also refer to the amount of time between two events, such as the distance between two birthdays. Distance can also be used to describe the relative or emotional separation between two people, such as the distance between a parent and a child.

What is the formula to calculate distance between two points?

The required formula is:

[tex]d =\sqrt{(x2-x1)^2 +(y2-y1)^3}[/tex]

(x1,y1)= (6,2)
(x2,y2)=(1,-4)

[tex]d = \sqrt{(1-6)^2 + (-4 -2)^2}[/tex]
[tex]d = \sqrt{25+36}[/tex]
[tex]d = \sqrt{61} units[/tex]

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The length of BC is approximately 5.72 miles and the length of AC is approximately 12.67 miles.

Let's represent the length of the side opposite angle A "BC" and the length of the side adjacent to angle A "AC". We can then use the sine function to find BC:

sin(A) = BC / AC

Substituting the given values, we get:

sin(24°) = BC / 14

We can use a calculator or look up the value of sin(24°) to get:

sin(24°) ≈ 0.406

Solving for BC, we get:

BC = 14 * sin(24°) ≈ 5.72

To find AC, we can use the cosine function:

cos(A) = AC / AC

Substituting the given values, we get:

cos(24°) = AC / 14

We can use a calculator or look up the value of cos(24°) to get:

cos(24°) ≈ 0.913

Solving for AC, we get:

AC = 14 x cos(24°) ≈ 12.67

Thus, BC is about 5.72 miles long while AC is about 12.67 miles in length.

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Answer:

Answers below

Step-by-step explanation:

1. The value 550 represents the initial balance in the account, which means the account started with $550.

2. 528.28

425.00 x  2.7% x 9 = 103.275

Then we add 103.275 to the initial deposit of $425.00

425.00 + 103.275 = 528.275

Therefore the answer is $528.28

3. The answer for this one is  f(n) = 56 + 3(n − 1)

So, as we can see the first value is 56 and the common difference is 3 and the rule for the nth term is [tex]a_{n} =a_{1} +d(n-1)[/tex]

Therefore, its 56 + 3(n − 1)

4. For this one we solve for r and using a calculator its r = 0.04

The value of r from the given equation is 0.04. Therefore, option A is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

1) The given equation is 687.5=550(1+0.05t)

Here, amount=$687.5, principal (initial balance)=$550 and rate of interest =0.05×100 =5%

So, the value 550 represents the initial balance in the account, which means the account started with $550.

2) Given that, principal=$425.00, time period=9 years and rate of interest=2.7%

We know that, S.I=(P×T×R)/100

= (425×9×2.7)/100

= 103.275

Amount=103.275+425

= 528.275

≈ $528.28

3) The given arithmetic sequence is 56, 59, 62, 65, 68,.…

Here, first term (a)=56 and common difference=59-56=3

We know that, general form of arithmetic sequence is aₙ=a+(n-1)d

Now, f(n)=56+(n-1)3

4) The given equation is 816=600(1+9r)

1+9r =816/600

1+9r =1.36

9r=0.36

r=0.04

The value of r from the given equation is 0.04. Therefore, option A is the correct answer.

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Answer:

Five

Step-by-step explanation:

There are 9 two-digit numbers with a units digit of 7:

17, 27, 37, 47, 57, 67, 77, 87, 97

Of these, 4 are composite numbers:

27 = 3³

57 = 3×19

77 = 7×11

87 = 3×29

The remaining 5 are prime numbers:

17, 37, 47, 67, 97

Answer: y = 5x

Step-by-step explanation:

The chances that the revenue on the first show will exceed $800 when mean revenue is $336.25 and standard deviation is $38.16 is essentially zero. i.e. 0

A normal distribution is a type of continuous probability distribution in which the majority of data points cluster in the middle of the range, while the remainder taper off symmetrically toward either extreme. The mean of the distribution is also known as the middle of the range.

The normal distribution is primarily used to calculate the likelihood of an observation in a distribution falling above or below a given value.

Given,

Mean, [tex]\mu[/tex] = 336.25

variance, [tex]\sigma^2[/tex]= 1456

then,

standard deviation, [tex]\sigma = \sqrt{1456}[/tex] = 38.16

To determine the chances that the revenue on the first show will exceed 800 is1:

[tex]1-p(z=\frac{x-\mu}{\sigma})\\\\=1-p(z=\frac{800-336.25}{38.16})\\\\=1-p(z=\frac{436.75}{38.16})\\\\=1-p(z=12.15)\\\\=1-1=0[/tex]

Hence, there is no chance that the revenue will exceed $800 on the first show.

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When Ms. Hall is buying Ms. Ward some gifts for Christmas as described in the problem,

the Constant: $90 and $7

the Coefficient: $7

the Equation:  $90 + $7x

Information form the problem shows that

one big gift that will cost $90

some small gifts that cost $7 each

the constant in this case is the price of the gifts

$90 and $7

the coefficient is $7

the equation is

$90 + $7x

where x is the number of the small gifts

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TRUE: The given contrapositive statement are correct,

If m ≤ 3, then, m < 5.

For the stated conditional statement -

If m ≤ 3, then, m < 5.

Then, contrapositive statement for the given statement will be

(m < 5)' ⇒ (m ≤ 3)'

That is;

(m > 5) ⇒ (m > 3)

That is, if m> 5 then, m > 3, which is true.

Thus, the contrapositive statement for the given conditional statement is true.

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Answer:

x = 98

Step-by-step explanation:

Solve for x:

(x - 14)/7 = 12

Multiply both sides of (x - 14)/7 = 12 by 7:

(7 (x - 14))/7 = 7×12

(7 (x - 14))/7 = 7/7×(x - 14) = x - 14:

x - 14 = 7×12

7×12 = 84:

x - 14 = 84

Add 14 to both sides:

x + (14 - 14) = 14 + 84

14 - 14 = 0:

x = 84 + 14

84 + 14 = 98:

Answer:  x = 98

Answer:

a_n = 5 × 3^(n - 1)

Step-by-step explanation:

The first term is 5. Each subsequent term is the previous term multiplied by 3.

a_1 = 5 × 3^0

a_2 = 15 = 5 × 3^1

a_3 = 45 = 5 × 3²

Notice that the exponent of the 3 is 1 less then the term number.

a_n = 5 × 3^(n - 1)

Answer:

24 Inches

Step-by-step explanation:

The length of a piece of wood that uses 8 nails as required in the task content is; 24 inches.

What is the length of a piece of wood that uses 8 nails?

It follows from the task content that the length of a piece of wood that uses 8 nails is to be determined from the task content.

The inverse function is given by f⁻¹(x) = 1.06x.  2 euros is equivalent to 2.12 U.S. dollars. 4 euros is equivalent to 4.24 U.S. dollars

Given that: the two different currencies is modeled by a linear function f(x) = x/1.06

where, x = an amount in U.S. dollars and f(x) = the equivalent amount in euros

To find the inverse function f⁻¹(x). Let y = f(x):

y = x/1.06

x = 1.06y

Since x = f⁻¹(y) = 1.06y

Thus, f⁻¹(x) = 1.06x

Note: f⁻¹(x) will help you convert from euros to dollar

2 euros to dollars will be:

f⁻¹(x) = 1.06x

f⁻¹(2) = 1.06(2) = 2.12

Thus, 2 euros is equivalent to 2.12 U.S. dollars

4 euros to dollars will be:

f⁻¹(x) = 1.06x

f⁻¹(4) = 1.06(4) = 4.24

Thus, 4 euros is equivalent to 4.24U.S. dollars

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a) The value of P(Y∩P) =0.23

b) The value of (Y|P) = 0.34

c)  The value of (P|Y) = 0.27

d) The value of P(Y/P') = 0.68

What is Venn diagram?

A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it. A subset of whole numbers, which is a subset of integers, is a collection of natural numbers, as an example.

Given that there are two events Y and P.

P(Y) = 0.57

P(P) = 0.5

P(Y∪P) = 0.84

The formula of intersection is  P(Y∩P)  = P(P) + P(Y) - P(Y∪P)

Putting P(Y) = 0.57, P(P) = 0.5, P(Y∪P) = 0.84

P(Y∩P)  = 0.5 + 0.57 - 0.84

P(Y∩P) = 0.23.

b)

P(Y|P) = P(Y) - P(Y∩P)

P(Y|P) = 0.57 - 0.23

P(Y|P) = 0.34

c)

P(P|Y) = P(P) - P(Y∩P)

P(P|Y) = 0.5 - 0.23

P(P|Y) = 0.27

d) P(Y/P') = P(Y∩P') / P(P')

P(Y/P') = P(Y|P)/[1 - P(P)]

P(Y/P') = 0.34/(1- 0.5)

P(Y/P') = 0.68

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Answer:  A= 52cm  B= 94mm  C= 9m  D= 17cm

Step-by-step explanation:

A) You first need to find the missing sides by doing

11-9= 2

and 15-9= 6

you then add it all together

6+2+9+9+15+11=52cm

B) You first need to find the missing sides by doing

25-18=7

and 22-6= 16

you then add it all together

25+22+18+16+7+6=94mm

C) You first need to find the missing sides by doing

0.5+1=1.5 then 2.5-1.5=1

and 1.2+0.8=2 then 2-0.5=1.5

you then add the numbers all together

1+1.5+0.8+1+0.5+0.5+1.2+2.5=9m

D) You first need to find the missing sides by doing

2.5+1= 3.5 then 3.5-2=1.5

and 1.5+2.5=4 then 5-4=1

you then add all the numbers together

2.5+2.5+1.5+1+5+2+1+1.5=17cm

The odds ratio for the association between exposure to emf's and breast cancer would be (11/5) / (108/436) = 2.2.

1. Calculate the odds of exposure for cases: 11/5 = 2.2

2. Calculate the odds of exposure for controls: 108/436 = 0.25

3. Divide the odds of exposure for cases by the odds of exposure for controls: 2.2/0.25 = 8.8

4. Finally, the odds ratio for the association between exposure to EMF's and breast cancer is 2.2.

The odds ratio for the association between exposure to EMF's and breast cancer can be calculated by dividing the odds of exposure for cases by the odds of exposure for controls. To calculate this, first take the number of cases exposed (11) and divide it by the number of cases not exposed (5). This will give the odds of exposure for cases (2.2). Second, take the number of controls exposed (108) and divide it by the number of controls not exposed (436). This will give the odds of exposure for controls (0.25). Finally, divide the odds of exposure for cases (2.2) by the odds of exposure for controls (0.25). This will give the odds ratio for the association between exposure to EMF's and breast cancer (2.2).

Odds ratio = (11/5) / (108/436) = 2.2

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A line passes through point (1, 6) and has a slope is y=8x-14 We want to write the equation of the line that passes through (1, -6) and has a slope of 8 in slope-intercept form

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

As we are already given the slope (8), we can immediately plug that into the equation

So far, the equation of the line is:

y=8x+b

Now we need to find b

The line passes through the point (1, -6), which means that the point is a solution to the equation; when plugged into the equation, it'll create a true statement. This can help us find unknown variables, like b

Substitute 1 as x and -6 as y in the equation to solve for b

-6=8(1)+b

Multiply

-6=8+b

Subtract 8 from both sides

-14=b

Substitute -14 as b into the equation

y=8x-14

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The rate of interest in one account whose investment is $2300 will be 3.21%.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Aniyah puts $2300 in one record and $1400 in a record paying 4 % higher interest. Toward the finish of one year, she had procured $130 in interest.

Let 'x' be the interest. Then the equation is given as,

(2300 × x × 1)/100 + (1400 × 4 × 1) / 100 = 130

Simplify the equation, then we have

23x + 56 = 130

23x = 74

x = 3.21%

The pace of revenue in one record whose speculation is $2300 will be 3.21%.

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Area del triangulo = base por altura/2

A = b*h/2    

A = 22,5cm²

Base = 5cm

a = b*h/2

22,5cm² = 5cm /h

22,5cm²/5cm = h

4,5cm = h

What is Area del?

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

La altura del triangulo es de 4,5cm

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Answer:

The pattern is that each number in the sequence is the previous number minus 1.5. For example, -5.5 is -4 minus 1.5, -7 is -5.5 minus 1.5, and so on.

Answer:

-1.5

Step-by-step explanation:

You take two of the variables in the pattern and subtract them with the second one being the minuend, and the first being the subtrahend.

For example we will use -4 and -5.5

(-5.5) - (-4) = -1.5

There is a negative sign present so it indicates subtraction towards the pattern.

Hence, the pattern change rate is -1.5

Answer:

should be angle 7, 1, and 3

hope i could helpppp

Answer: 1 , 7 , 3

Step-by-step explanation:

The angles that habe the same measurement of angle 5 are;

1 , 7 , 3

Because the lines are parallel, these angles correspond to angle 5.

The likelihood that the next 20 marbles picked will be yellow marbles is 9/20.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

The probability that of the next 20 marbles selected it is expect to be yellow marbles,

=9/20

The probability that of the next 20 marbles selected it is expect to be yellow marbles will be 9/20.

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Answer:

the answer is 10

Step-by-step explanation:

ixl says its ten

Net profit is a company's profit after all expenses have been deducted. What remains after deducting fixed costs from gross profit is the net profit.

Subtracting the cost function from the revenue function yields the profit function. Assume that the profit is denoted by P(x), the revenue is denoted by R(x), the cost is denoted by C(x), and x is the quantity of goods sold. Consequently, the profit function is denoted by P(x) = R(x0 - C) (x).

Total Revenue - Total Expenses = Net Profit

A company that sells online has a $350,000 revenue and a $50,000 cost of products sold.The net income formula is defined as the difference between the total revenue earned and the total costs.Total revenue minus all costs equals net income.

The money a corporation makes after deducting interest, operational costs, and taxes over a specific time period is known as net profit.Profit After Tax is another name for Net Profit (PAT).

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first 2;

a) 7(2) + 8 = 22 > 16, 7(4) + 8 = 36>32

36 - 22 = 14/2 = 7

32 - 16 = 16/2 = 8

7<8

the table has a greater rate of change

y intercept

equation; 8

table; 0

8> 0

the equation has a greater y intercept

Answer:

D

Step-by-step explanation:

if you move the preimage on the image you can see that the two figures are equals

Answer:

2

Step-by-step explanation:

-2 and -4 are less than 0

2 is greater than

If you write down in descending order ===> 2, -2 , -4

After solving the equation, the value obtained for x will be equal to 1.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

4 times x plus one-half equals one-half times x plus 4.

Let's write it in mathematical form,

4x + 1/2 = 1/2x + 4

Now, solve the equation for x,

4x - 1/2x = 4 - 1/2

(8x - x)/2 = (8 - 1)/2

7x/2 = 7/2

x = (7 × 2)/(2 × 7)

x = 14/14

x = 1

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