John has two types of boxes. The smaller box can store 8 tins of coffee and the bigger box can store 12 tins of coffee. If the total number of boxes is 20 and he has 184 tins of coffee, by forming a pair of simultaneous equations, find the number of each kind of box.​

Answer:

m∠R = 72°

Step-by-step explanation:

As ΔPQR and ΔUVW are congruent, m∠R = m∠W.

Equate the expressions for the two angles and solve for x:

⇒ m∠R = m∠W

⇒ 10x - 18 = 8x

⇒ 10x - 18 + 18 = 8x + 18

⇒ 10x = 8x + 18

⇒ 10x - 8x = 8x + 18 - 8x

⇒ 2x = 18

⇒ 2x ÷ 2 = 18 ÷ 2

⇒ x = 9

Substitute the found value of x into the expression for m∠R:

⇒ m∠R = 10x - 18

⇒ m∠R = 10(9) - 18

⇒ m∠R = 90 - 18

⇒ m∠R = 72°

Therefore, m∠R = 72°.

Answer: 8

Step-by-step explanation: 3.18 divided by 0.39 is 8 (without the decimals)

By considering the areas of the two rectangles, we have shown that 2x² - 5x - 18 = 0

The value of length AB is 4.5 cm

From the question, we are to show that 2x² - 5x - 18 = 0

From the given information,

The total area of the compound shape ABCDEF is 36 cm²

That is,

Total area = 36 cm² = Area of small rectangle + Area of big rectangle

From the given diagram, we can write that

Area of small rectangle = x(x -4)

Area of small rectangle = x² - 4x

and

Area of big rectangle = (2x + x)(x -2)

Area of big rectangle = 3x(x - 2)

Area of big rectangle = 3x² - 6x

∴ 36 = x² - 4x + 3x² - 6x

36 = 4x² -10x

4x² -10x - 36 = 0

Divide through by 2

2x² - 5x - 18 = 0

Thus, we have shown that 2x² - 5x - 18 = 0

Now, we are to determine the value of length AB

The value of length AB is x cm.

Therefore, we will solve for x

From,

2x² - 5x - 18 = 0

2x² + 4x - 9x - 18 = 0

2x(x + 2) -9(x + 2) = 0

(2x - 9)(x + 2) = 0

2x - 9 = 0 OR x + 2= 0

2x = 9 OR x = -2

x = 9/2 OR x = -2

x = 4.5 OR x = -2

Since x cannot be negative, the value of x is 4.5

Thus,

AB is 4.5 cm

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The temperature when the plane reaches an altitude of 4,000 will be 560°F.

It should be noted that temperature simply means the degree of hotness and coldness of a body.

In this case, there is a 14°F drop in temperature for every thousand feet that an alplane climbs into the sky.

Since the the temperature on the ground is 616, the temperature when the plane reaches an altitude of 4,000 will be:

= 616 - 14(4000/1000)

= 616 - 14(4)

= 616 - 56

= 560°F

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By using Distribution of the sample mean,  “It will have less variation”. So option B is correct.

With Large numbers of successive random samples, the mean of the sampling distribution is equal to the mean population (µ). The variability of each sampling distribution decreases in increase of sample size..

so that they become increasingly more Leptokurtic distribution .

As a sample size increases, sample variance (variation between observations) increases but the variance of the standard error decreases.

The mean of the sample means would be equal to μ (approx.), the mean  from which the samples were drawn. However,  the sample means will depend on the size of the samples, since big  samples are more likely to give estimated means that are equal to the true mean of the population(Approx. )

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Answer:

The mako shark swims first

Step-by-step explanation:

mako shark swim's at 40kilometre per hr

ablue whale swim's at 20km per hr

When Eva advanced to the next round of the contest, the inequality that describes the number of questions will be 3x + 5y > 60

It should be noted that an inequality will simply used to illustrate the expressions that aren't equal. This is illustrated with the use of greater than, less, than, etc.

In this case, the contestants receive 3 points for each correct multiple choice question and 5 points for each correct free response question, and they must score more than 60 points to advance to the next round.

Therefore, the inequality that describes the number of questions will be:

= 3(x) + 5(y) > 60

= 3x + 5y > 60

where x = number of multiple choice questions,

y = number of free response questions,

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Answer:

3x+5?

Step-by-step explanation:

Not 100% sure but yh

Answer:

3 x 3 x 3 or 3 to the 3rd power :)

Step-by-step explanation:

Lets solve! :)

3 x 3 x 3

9 x 3

27

The volume of the tank would be 27s :)

Have an amazing day!!

Please rate and mark brainliest!

The distribution that x follow approximately is a Poisson distribution

Given that the the average number of Salmonellosis cases per month in Illinois is 2.56

We now find the approximate distribution of X :

If outcomes the random variable are occurring on a certain time period or in a certain space, then random variable is called Poisson random variable.

In our case, X is the monthly count of Salmonellosis food poisoning cases , so outcomes are occurring on time period of month and are discrete.

Hence distribution of X : the monthly count of Salmonellosis cases follows a Poisson distribution.

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Answer:

[tex]\textsf{3.} \quad \dfrac{5}{6}x+ 10=y[/tex]

4.  See below.

[tex]\textsf{5.} \quad \dfrac{10}{3}x-2=y[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{1}{3}x-\dfrac{2}{5}y=-4[/tex]

[tex]\textsf{Add \;$\dfrac{2}{5}y$ \; to both sides}:[/tex]

[tex]\implies \dfrac{1}{3}x-\dfrac{2}{5}y+\dfrac{2}{5}y=-4+\dfrac{2}{5}y[/tex]

[tex]\implies \dfrac{1}{3}x=\dfrac{2}{5}y-4[/tex]

Add 4 to both sides:

[tex]\implies \dfrac{1}{3}x+4=\dfrac{2}{5}y-4+4[/tex]

[tex]\implies \dfrac{1}{3}x+4=\dfrac{2}{5}y[/tex]

[tex]\textsf{Multiply both sides by \; $\dfrac{5}{2}$}:[/tex]

[tex]\implies \dfrac{5}{2} \cdot \dfrac{1}{3}x+ \dfrac{5}{2} \cdot4=\dfrac{5}{2} \cdot \dfrac{2}{5}y[/tex]

[tex]\implies \dfrac{5}{6}x+ 10=y[/tex]

[tex]\boxed{\begin{minipage}{3cm}$\dfrac{1}{3}x-\dfrac{2}{5}y=-4\\\\\underline{\phantom{\dfrac{1}{3}x}+\dfrac{2}{5}y\phantom{=-4}\dfrac{2}{5}y}\\\\\dfrac{1}{3}x=\dfrac{2}{5}y-4\\\underline{+4 \phantom{)=3y}+4\phantom{)))))}}\\\\\dfrac{1}{3}x+4=\dfrac{2}{5}y\\\\\underline{\phantom{)}\times\dfrac{5}{2}\phantom{))))}\times \dfrac{5}{2}}\\\\\dfrac{5}{6}x+10=y$ \end{minipage}}[/tex]

See the attachment for the highlighted mistake.

The mistake Mike made is that he did not divide 10x by 3.

Given equation:

[tex]10x-3y=6[/tex]

Add 3y to both sides:

[tex]\implies 10x-3y+3y=6+3y[/tex]

[tex]\implies 10x=6+3y[/tex]

Subtract 6 from both sides:

[tex]\implies 10x-6=6+3y-6[/tex]

[tex]\implies 10x-6=3y[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{10x}{3}-\dfrac{6}{3}=\dfrac{3y}{3}[/tex]

[tex]\implies \dfrac{10}{3}x-2=y[/tex]

[tex]\boxed{\begin{minipage}{3cm}$10x-3y=6\\\underline{\phantom{10x}+3y\phantom{=6}+3y}\\\\10x=3y+6\\\underline{-6 \phantom{)=3y}-6\phantom{)))))}}\\\\\dfrac{10x-6}{3}=\dfrac{3y}{3}\\\\\dfrac{10}{3}x-2=y$ \end{minipage}}[/tex]

Answer:

x + 2y = 5

Step-by-step explanation:

y = mx + b the m is the slope or gradient.  

y=2x+3  The slope is 2.

When lines are perpendicular,  the slopes are opposite inverses of each other.  So, the perpendicular slope to 2 is -1/2.  I would write the answer in the point slope of the line and then change the equation to the stand form

y -2 = -1/2(x -1)  Distribute the -1/2

y - 2 = -1/2x + 1/2  Add 1/2 x to both sides

1/2x + y -2 = 1/2  Add 2 to both sides

1/2x +y = 5/2  Multiply by 2 to clear the decimal

x + 2y = 5

The addition according the place value is 12.39

The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its location in the number, which might result in a number having two comparable digits with distinct values.

Place value refers to how much a digit is worth in relation to where it is in a number, such as the ones, tens, hundreds, and so on. For instance, 5 in 3458 has a place value of 5 tens, or 50. However, 5 thousands, or 5,000, is used to represent the place value of 5 in 5781. Understanding that a digit can have the same value regardless of where it appears in the number is crucial.

Given:

Eli used the place value strategy to add the numbers 4.69 and 7.7.

So, to add using place value strategy we use place value to break the addends into tens and ones.

Now, we add the tens and ones individually to find the whole sum.

So, breaking 4.69

at ones = 4

at tenth = 6

at hundredth = 9

In 7.7

at ones= 7

at tenth = 7

at hundredth = 0

Now, adding according to the place value

=(0 + 9 ) x 1/100 + (7 + 6) x 1/10 + (4 +7) x1

=9/100 + 13/10 + 11

=0.09 + 1.3 + 11

=12.39

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Answer:

A

Step-by-step explanation:

seventy and twenty-three thousandths = 70.023

Answer:

A

Step-by-step explanation:

thank

you

:D

Answer:

-4.9, negative four and eight ninths, four and seven tenths, 490%

Step-by-step explanation:

4 7/10 =approx. 4.7

-4 8/9 = -4.888889

490% = 4.9

-4.9

Red ribbon is 77.34 much longer than brown ribbon.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.

The difference is the name given to the solution to a subtraction issue.

Given Data

Natalie has a piece of red ribbon that is 79.39 inches long

a piece of brown ribbon that is 2.05 inches long

Difference of red ribbon from brown ribbon:

= 79.39 - 2.05

= 77.34

Red ribbon is 77.34 much longer than brown ribbon.

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Answer: this should be more then 5 coins

Step-by-step explanation:

Answer:

√2 is between the integers 1 and 2.

the distance between the point H (- 2, 2) and point I (6, 2) is 8 units.

We are given the coordinates of the point as:

H = (- 2, 2)

I = (6, 2)

We need to find the distance between the two points.

We get that:

x₁ = - 2

y₁ = 2

x₂ = 6

y₂ = 2

Distance formula is given as:

Distance = √(y₂ - y₁)² + (x₂ - x₁)²

Substituting the values in the formula, we get that:

D = √(2 - 2)² + (6 + 2)²

D = √ 0² + 8²

D = √8²

D = 8 units.

Therefore, the distance between the point H (- 2, 2) and point I (6, 2) is 8 units.

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The coordinates of the point that is 2/4 the way from A to B are (1, 7).

The coordinates of the point that divides a segment into a fractional component, n (n+m), or an arbitrary ratio, n:m, are given by:

   x = [n ⁄ (n+m)] (x₂ - x₁) + x₁  and y = [n ⁄ (n+m)] (y₂ - y₁) + y₁

Given:

For this problem, n = 2 and m = 2 since (2 ⁄ (2+2) = 2 ⁄ 4,  ( x,₁ y₁) =(-2, 5) and ( x₂, y₂) = (4, 9)

Where n and m are both positive integers, [n (n+m)] is the required distance ratio from the beginning position, (x₁, y₁)  are the coordinates of one endpoint, and (x₂, y₂) are the coordinates of the other endpoint.

x = [n ⁄ (n+m)] (x2 - x1) + x1

  = (2/4 ) (4 - (-2)) + (-2)

  =  (2/4 ) (4 + 2) + (-2)

  = (2/4 ) × 6 + (-2)

  =  3 - 2 = 1

y = [n ⁄ (n+m)] (y2 - y1) + y1

  =  (2/4 ) (9 - 5) + 5

  =  (2/4 ) (4) + 5

   =  2 + 5 = 7

Therefore, the coordinates of the point are (1, 7).

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Answer:

first find 40 squared

[tex] {40}^{2} \\ = 1600[/tex]

1598,1599, 1600, 1601,1602

You can see that 1600 is between 1599 and 1601

The equivalent rates for each of the given options are;

A) 1 goal in 2 games

10 goals in 20 games

B) 1 km jogged in 6 min

5 km jogged in 12 min

C) 1 pizza eaten in 5 minutes

2 pizzas eaten in 10 minutes

D) 2 penalties in 5 games​

20 penalties in 50 games​.

We want to write two equivalent rates for the given rates.

It should be noted that different rates that have the same value are equivalent rates. You can find an equivalent rate the same way you find equivalent ratios which is to divide or multiply the numerator and the denominator by the same number.

A) 5 goals in 10 games can also be written as;

5/10 = 1/2 = 10/20

These equivalent rates are;

1 goal in 2 games

10 goals in 20 games

B)  10 km jogged in 60 min;

10/60 = 1/6 = 5/12

These equivalent rates are;

1 km jogged in 6 min

5 km jogged in 12 min

C) 6 pizzas eaten in 30 min;

6/30 = 1/5 = 2/10

These equivalent rates are;

1 pizza eaten in 5 minutes

2 pizzas eaten in 10 minutes

D)  10 penalties in 25 games​;

10/25 = 2/5 = 20/50

These equivalent rates are;

2 penalties in 5 games​

20 penalties in 50 games​.

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Answer:

[tex]\angle K[/tex]

Step-by-step explanation:

When looking for corresponding angles, compare their order in the names. Since T and K are the first letters in the names of the triangles, they correspond.

The proportional relationship between the number of centerpieces and the total cost for the centerpieces is graphed at the end of the answer.

A graph represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:

y = kx.

The constant k is called the slope of the unit rate of the situation, measuring by how much y changes when x changes by 1.

In the context of this problem, the cost of each centerpiece is of $5.50, hence the constant is given as follows:

y = 5.5x.

The number of centerpieces cannot be negative, hence the domain of the relation is given as follows:

x ≥ 0.

Considering this domain, the graph of the relation is given at the end of the answer.

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The linear function that contains the point (-4, -3) and is perpendicular to the line 4x + 5y = 15 is given by:

y = 5/4x + 2.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

When two lines are perpendicular, the multiplication of their slopes is of -1, hence, considering the line is perpendicular to 4x + 5y = 15, we have that:

5y = 15 - 4x

y = 3 - 4/5x

Then:

-4/5m = -1

m = 5/4

Hence the rule is:

y = 5/4x + b

When x = -4, y = -3, hence the intercept b is found replacing these points into the equation as follows:

-3 = 5/4(-4) + b

-3 = -5 + b

b = 2.

Hence the equation is:

y = 5/4x + 2.

Both perpendicular equations are graphed at the end of the answer.

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With the annual interest of 1%, the total saving after 5 years is $6060.

Interest:

Interest is the amount for a particular principal amount of money at some rate of interest.

Given,

You earn $100 per month and want to save 10% in a savings account.

Here we have to use the savings calculator to find out how much your total savings would be in 5 years if your account has an annual interest rate of 1%.

Through the given details we have identified that,

Monthly earning = $100

Saving per month = 10%

So, in amount it can be

=> 100 x 10/100 = $10

So, for one year the saving without interest is

=> 10 x 12 = 1200

So, When we add the interest of 1% for the year,

Then the interest amount for one year will be,

=> 1200 x 1/100 = 12

So, the total amount including interest for one year,

=> 1200 + 12 = 1212

So, the savings after 5 years will be,

=> 5 x 1212

=> 6060.

Therefore, the total saving amount after 5 years is $6060.

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