Algebra problem below!


The sum of two consecutive even integers is -50

What are the numbers?

Final answer:

Tossing a dime and then tossing a quarter are independent events because one toss does not affect the other. Picking a card from a deck, keeping it, and picking another is a dependent event because the first pick changes the composition of the deck for the second pick.

Explanation:

To determine whether the two events mentioned are dependent or independent, we can use the definition of statistical independence. If the outcome of the first event does not affect the outcome of the second event, then the events are independent. If the outcome of the first event influences the outcome of the second event, then the events are dependent.

For the first scenario, tossing a dime and then tossing a quarter are independent events. This is because the result of tossing the dime has no effect on the result of tossing the quarter, much like having a nickel and a dime in your pocket and pulling one out, replacing it, and pulling one out again with probabilities being independent.

For the second scenario, when you pick a card from a deck of cards, keep the card, and then pick another one, the events are dependent. This is because the first card you draw and keep affects the composition of the deck from which the second card is drawn. It's like not replacing the first coin before pulling out the second one; your chances change based on the first outcome.

Using the concept of compound events and the law of the probability of compound events, we can see that independent events allow us to calculate the probability of any outcome when combining two independent events. Conversely, with dependent events, the probability of the subsequent event is influenced by the outcome of the preceding one.

Answer:

£56 did  Hannah receive Last week

Step-by-step explanation:

Let the number be x.

As per the statement:

Zoe and Hannah share tips in the ratio 3:7.

Then;

Total Zoe share = 3x

Total Hannah share = 7x

It is also given that Last week , Zoe received £24.

⇒3x = 24

Divide both sides by 3 we have;

x = 8

Hannah receive Last week = 7x = 7(8) =  £56

Therefore, £56 did  Hannah receive Last week

43 +x = 2(15+x)=

43 + x = 30 +2x

43 = 30 +x

13 =x

13 years

43+13 = 56

15 +13 = 28 ( 28*2 = 56)

Final answer:

To create a system of linear equations with the solution (-3, 9), we need to construct two equations that intersect at this point, for example, y = -3x + 18 and y = 2x + 15.

Explanation:

To write a system of linear equations with the solution (-3, 9), we can create two separate equations that intersect at this point. Using the equation provided, y = 9 + 3x, we can see that the point (-3, 9) satisfies this equation since plugging in x = -3 gives us y = 9 + 3(-3) = 9 - 9 = 0, which is incorrect. We must correct the mistake and ensure that the solution (-3, 9) satisfies both equations in our system.

A correct form of the first equation would be y = -3x + 9 (not y = 9 + 3x as provided), since plugging x = -3 yields y = -3(-3) + 9 = 9 + 9 = 18, which is also incorrect. Therefore, we need to be careful in constructing our equations.

Let's construct two new equations correctly:
First, we start with the equation y = -3x + 18, which does satisfy the condition when x = -3 and y = 9. Next, we can create a different equation with the same solution. For instance, if we want another equation, we might use the slope-intercept form, y = mx + b. We can choose a different slope (m), for example, m = 2, and find b such that when x = -3, y = 9:

y = mx + b
9 = 2(-3) + b
9 = -6 + b
b = 15

So, the second equation is y = 2x + 15. The system of linear equations with the solution (-3, 9) is:

1. y = -3x + 18
2. y = 2x + 15

Answer:

The solution for t is  [tex]\frac{w}{(r_1+r_2)}[/tex]

Step-by-step explanation:

The given expression is [tex]w = t(r_1+r_2)[/tex]

We need to solve for the 't' ,

To solve for t, divide [tex]w = t(r_1+r_2)[/tex] by [tex](r_1+r_2)[/tex]

[tex]\frac{w}{(r_1+r_2)} = t[/tex]

Hence, The solution for t is  [tex]\frac{w}{(r_1+r_2)}[/tex]

Answer: 3.1 %

Step-by-step explanation:

Given : The probability that Shania is on time for school is [tex]\dfrac{1}{2}[/tex]

Since the each day is independent of other.

Then , the probability that Shania arrives on time for school for the next 5 days will be :_

[tex]=(\dfrac{1}{2})^5=\dfrac{1}{32}=0.03125\approx3.125\%\approx3.1\%[/tex]

Hence, the  probability that Shania arrives on time for school for the next 5 days.  = 3.1 %

Answer:

The intensity was [tex]5.02377\times 10^{18}[/tex]

Step-by-step explanation:

We are given

An earthquake registered 7.4 on the Richter scale

so, RC=7.4

the reference intensity of this quake was 2.0 × 10^11

so,

[tex]I_r=2.0\times 10^{11}[/tex]

now, we can use formula

[tex]RS=log(\frac{I}{I_r} )[/tex]

now, we can plug values

[tex]7.4=log(\frac{I}{2.0\times 10^{11}} )[/tex]

now, we can solve for I

[tex]10^{7.4}=\frac{I}{2.0\times 10^{11}}[/tex]

[tex]I=10^{7.4}\times 2.0\times 10^{11}[/tex]

[tex]I=5.02377\times 10^{18}[/tex]

To find the intensity of an earthquake registered on the Richter scale, use the formula based on the magnitude difference and energy ratio.

The intensity of the earthquake can be calculated using the Richter scale formula, which relates the magnitude difference to the energy ratio.

Answer:

90000

Step-by-step explanation:

A significant figure is a number different from zero that assigns the value of the quantity.

In this case, you have four significant figures, not counting the zeros. To round this, you need the first upper number with only one significant figure.

For that, we use 9 because is the next number from 8, and then complete the value with zeros.

87600.2 will be 90000.0

It would take 90 minutes to unload a truck containing 2700 packages at a rate of 30 packages per minute.

This problem involves performing a simple division operation. Given that 30 packages are unloaded from a truck each minute and there are a total of 2700 packages on the truck, we find the time it would take to unload the truck by dividing the total number of packages by the number of packages that can be unloaded each minute.

We solve the problem as follows:

Therefore, it would take 90 minutes to unload the entire truck.

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The answer is x=7, because if you use PEMDAS you will come up with x=7.

An Internet service company earned $770 in set-up fees for new homes in a neighborhood. For each new set-up they charged $35. Then they performed 22 new set ups. So option B is correct.

Two expressions with an equal sign is called equation.

An Internet service company earned $770 in set-up fees for new homes in a neighborhood. They charged $35 for each new set-up, then number of new setups we have to find,

Internet service company earned =$770

For each new set-up they charged $35

Number of set ups they perform = x

35x=770

x=770/35

x=22

Therefore 22 new setups are performed.

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Answer with Step-by-step explanation:

We have to determine the value of x on solving the system of linear equations:

2x-y = 11

x+3y = -5

2x-y=11

Adding y on both sides and subtracting by 11 on both sides, we get

y=2x-11

Putting value of y in x+3y = -5

x+3(2x-11) = -5

x+6x-33 = -5

7x -33 = -5

adding 33 on both sides, we get

7x= 28

Dividing by 7 on both sides, we get

x=4

Hence, Correct option is:

d. 4

The length of the line segment YX in rectangle YVWX is [tex]\rm 8\sqrt{3} \; units[/tex] and it can be determine by using the trignometric properties and properties of rectangle.

Given :

The length of the line segment YX in rectangle YVWX can be determine by using the trignometric properties.

[tex]\rm tan \theta = \dfrac{Perpendicular}{Base}[/tex]

[tex]\rm tan 60 = \dfrac{24}{VW}[/tex]

[tex]\rm \sqrt{3} = \dfrac{24}{VW}[/tex]

[tex]\rm VW =8\sqrt{3}\;units[/tex]

In rectangle opposite sides are equal. Therefore, [tex]\rm VW=YX = 8\sqrt{3}\;units[/tex].

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[tex]\rm VW=YX = 8\sqrt(3)\;units.[/tex]

The length of the line segment YX in rectangle YVWX is \rm 8√(3)  \; units and it can be determine by using the trignometric properties and properties of rectangle.

Given :

YV = XW = 24 units
[tex]\rm \angle VXW = 30^\circ\\\rm \angle XWV = 90^\circ\\\rm \angle XVW = 60^\circ[/tex]
The length of the line segment YX in rectangle YVWX can be determine by using the trignometric properties.

[tex]\rm tan \theta = (Perpendicular)/(Base)\rm tan 60 = (24)/(VW)\rm √(3) = (24)/(VW)\rm VW =8√(3)\;units[/tex]

In rectangle opposite sides are equal. Therefore, [tex]\rm VW=YX = 8√(3)\;units[/tex].

To make enough cookies to fill 24 boxes containing 6 cookies each, you need to make 12 dozen cookies.

To find out how many dozen cookies you need to make, you need to divide the total number of cookies by 12.

In this case, there are 24 boxes with 6 cookies each, so the total number of cookies is 24 x 6 = 144.

Dividing 144 by 12 gives us 12 dozen cookies.

The vertex of the quadratic equation y = 6x^2 - 24 + 30 is (2, -6).

The given equation is y = 6x^2 - 24x + 30.

To find the vertex of this quadratic equation, we can use the formula x = -b/2a.

In this equation, a = 6 and b = -24. Plugging these values into the formula, we get x = -(-24)/(2*6) = 24/12 = 2.

Now, substitute this value of x into the equation to find the corresponding y-coordinate of the vertex.

Substituting x = 2, we get y = 6(2)^2 - 24(2) + 30 = 12 - 48 + 30 = -6.

Therefore, the vertex of the given quadratic equation is (2, -6).

If ABC measures 46 degrees, then the central angle ADC measures 23 degrees.

Using the inscribed angle theorem we can connect the central angle ABC and the inscribed angle ADC.

The reason why is because they both cut off the minor arc AC

Angle ABC is given to be 46 degrees,

The formula we use is shown below

The central angle = 2*(inscribed angle)

The angle ABC = 2*(angle ADC)

46 = 2*(angle ADC)

46/2 = 2*(angle ADC)/2 ... divide both sides by 2

23 = angle ADC

angle ADC = 23 degrees.

Therefore, If ABC measures 46 degrees, then the central angle ADC measures 23 degrees.

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In this case, we are simply asked to find for the value of:

xbya or abxy

Since we know that given values of ab and xy, therefore abxy is:

abxy = 37 * (1 / 37)

abxy = 37 / 37

abxy = 1

Answer: 134°F

Step-by-step explanation:

Given : A scientist is measuring the temperature change and a chemical compound the temperature dropped 11° Fahrenheit per hour from the original temperature .

Let x be the original temperature.

Then , the compound temperature after t hours is given by :_

[tex]y=x-11t[/tex]

At t= 4 hours and x= 90°F, we have

[tex]90=x-11(4)\\\\\Rightarrow\ x-44=90\\\\\Rightarrow\ x=90+44=134[/tex]

Hence , the  compounds original temperature = 134°F