Write the equation in slope-intercept form.
- 4x + 2y = -8

Answer:

-$7.905 per day

Step-by-step explanation:

In this question, given that a tank is losing its fuel content at a certain rate, we are to calculate the rate at which the value in dollars of the content of the fuel tank

is changing

Please check attachment for complete solution and step by step explanation

An underground gasoline storage tank is leaking. The tank currently contains 600 gallons of gasoline and is losing 3.1 gallons per day. The rate at which the value of the stored gasoline is changing is -$7.905 per day.

Suppose we make an assumption that the tank initial contains h(x) gallons of gasoline which leak in x days. Then, the rate of change of gasoline per gallon is;

[tex]\mathbf{\dfrac{dh}{dx} =- 3.1 \ \ \ \ \ \ \text{since the gas is leaking (-)}}[/tex]

Also, the rate of change of the gasoline in time(t) per unit change in the quantity can be computed as:

[tex]\mathbf{\dfrac{dt}{dh}=2.55 }[/tex]

Therefore, the value of the stored gasoline changing per unit change of days can be deduced by using the chain rule:

[tex]\mathbf{\dfrac{dt}{dx} = \dfrac{dt}{dh} \times \dfrac{dh}{dx}}[/tex]

[tex]\mathbf{\dfrac{dt}{dx} = -3.1 \times2.55}[/tex]

[tex]\mathbf{\dfrac{dt}{dx} =\$-7.905 \ per \ day}[/tex]

Therefore, we can conclude that the rate at which the value of the stored gasoline is changing is -$7.905 per day.

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[tex]9^{2n-1} = 27^{n+2} \\ ( {3}^{2} ) ^{2n - 1} = ( {3}^{3} )^{ n + 2} \\ {3}^{4n - 2} = {3}^{3n + 6} \\ 4n - 2 = 3n + 6 \\ 4n - 3n = 6 + 2 \\ n = 8[/tex]

Answer: n=8

Answer:

a= 0.6

b= 0.4

c= 0.2

d= 0.8

Step-by-step explanation:

Ons

The value of each letter in the conditional relative frequency table is

Division is an arithmetic operation that is used to determine the quotient of two or more numbers. Division entails grouping a number into equal groups using another number.

a = 180 / 300 = 0.6

b = 120 / 300 = 0.4

c = 40 / 200 = 0.2

d = 160 / 200 = 0.80

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Answer:

The equation is y = -5x - 3.

Step-by-step explanation:

The slope form equation is y = mx+b. So you just have to substitute the m and b value into the equation :

y = mx + b

m = -5

b = -3

y = -5x + (-3)

= -5x - 3

Answer:

integers

Step-by-step explanation:

Answer:

Intergers

Step-by-step explanation:

Intergers are a whole number meaning a number that's not a fraction.

Answer:

8

Step-by-step explanation:

f(1)=7(1-1)+8

f(1)=0+8

f(1)=8

The question is asking us to find the value of the function f(x) = 7(x−1) + 8 when x equals 1. To find this, we substitute 1 in place of x in the equation. So, f(1) = 7(1-1) + 8. Calculating this, 7 multiplied by 0 equals 0, so the equation simplifies to 0 + 8. Therefore, f(1) = 8.

To solve the problem, we must first substitute the value of x in the function `f(x)` which is `7(x−1)+8`.
Here, substitute x = 1:
So we have f(1) = 7*(1-1) + 8.
Simplify the expression inside the parenthesis first (as according to BIDMAS or PEMDAS - operations in parenthetical expressions should be done before multiplication and addition):
7 * (1 - 1) + 8 simplifies to 7 * 0 + 8.
The multiplication operation takes precedence over addition (again per the rules of BIDMAS/PEMDAS), so multiply 7 and 0:
We get 0 + 8.
Finally, perform the addition operation:
0 + 8 equals 8.
So, f(1) = 8.

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just put them how u normally wuld 1 is

3 is 6

4 is 5

2 is 8

5 is 13

Answer: area of the rectangle = 256

area of triangle 1 = 24

area of triangle 2 = 16

area of triangle 3 = 96

area of the trapezoid = 120

Answer:

42 tomatoes

Step-by-step explanation:

tomatoes/boxes = tomatoes/boxes

12/4 = x/14

4x/4 = 168/4

x=42

Answer:

42 rotten tomatoes would likely be found in 14 boxes

Step-by-step explanation:

1) Find how many rotten tomatoes are normally found in one box by dividing the amount of rotten tomatoes by the number of boxes they are found in. [tex]12/4=3[/tex]

2) So, now you know that 3 rotten tomatoes are normally found in one box, but the question is asking how many tomatoes would likely be found in 14 boxes which means you need to multiply the amount of rotten tomatoes found in one box by the amount of boxes you want to know about. [tex]3*14=42[/tex]

Answer:

$45

Step-by-step explanation:

In order to find this we need to understand that every time we bet we are selecting white ball. Because of this we have the chance of getting two times right and two times wrong irrespective of the order. For example we can any of the following orders:

White - White - Black - Black

White - Black - White - Black

Black - White - Black - White

Black - Black - White - White

Irrespective of any of the orders above every time our bet is right (we get white urn) the amount of dollars that we have get increased by half of the current amount. For example on the first turn we are betting $40 (half of initial amount = $80) and if we are right we now have $120 with us. This can be written as

1.5*$80 = $120

Similarly if on first turn we get wrong (black ball) then our amount is half of initial which can be written as

0.5*$80 = $40

So now we know that exactly two times we will be right and exactly two times we will be wrong irrespective of the order because the balls are not replaced hence final solution is:

E(X) = 80*1.5*1.5*0.5*0.5

= $45    

The question is incomplete, the correct question is:

Charles needs to fill a large fish tank with water using a hose. he has two hoses from which to choose. Water flows through each hose at a constant rate. The graph below shows the amount of water, in gallons , that flows through holes A based on the number of minutes used. A total of 110 gallo s of water can flow through Hose B in 10 minutes. Which hose has a faster water rate, in gallons per minute, and what is that rate?

Answer:

Hose B has a faster water flow rate in comparison to Hose A

Step-by-step explanation:

For Hose B,

From the information above, it is said that a total of 110 gallons of water can flow through hose b in 10 minutes. Therefore, divide 110 by 10 to get the amount of water that flows through hose b in gallons in one minute.

So,

110/10=11

y=11 x

This implies that 11 gallons of water flows through hose b in 1 minute.

For Hose A,

Select two points to get the rate of change,and then subtraction of y2 from y1 and x2 from x1 is done

Points selected: (2,12) , (4,24)

(x1,y1)=(2,12)

(x2,y2)=(4,24)

So, Subtract 24 from 12 and 2 from 4

M=y2-y1/x2-x1= 24-12 / 2-4= 12/2=6

This implies that in hose a a total of 6 gallons of water flows in one minute.

Therefore, the equation for hose a is y=6 x

In conclusion, hose b has a faster water flow rate since y=6 x < y=11 x.

Answer:

is b the correct

Step-by-step explanation:

Answer:

Taak 1.12

Mediaan is 5 en het gemiddelde is 5,67

Taak 2 13

De mediaan is 6

Het gemiddelde is 6

Standaarddeviatie is 3,32

Variantie is 11

Aantal werknemers is 13

Step-by-step explanation:

Taak.1 12 medewerkers is gevraagd naar het aantal verlofdagen. Hier zijn de antwoorden: 2, 5, 14, 3, 6, 5, 8, 2, 5, 4, 6, 8. Geef de dominante en de mediaan. Taak 2 13 medewerkers is gevraagd naar het aantal vakantiedagen. Hier zijn de antwoorden: 2, 4, 14, 3, 6, 7, 8, 2, 5, 4, 6, 8, 9. Geef de dominante en mediaan. Zad.3 Bereken de dominante en de mediaan a) Verblijfsafstand in km. b) Aantal werknemers a) b) 0-5 5 5-10 25 10-15 30 15-20 55 20-35 30 25-30 20 30-35 15

Taak. 1 12, wordt de mediaan gegeven door

2, 5, 14, 3, 6, 5, 8, 2, 5, 4, 6, 8 herschikken, we krijgen

2, 2, 3, 4, 5, 5, 5, 6, 6, 8, 8, 14

Daarom is de mediaan 5 en het gemiddelde 5,67

Taak 2 13

2, 4, 14, 3, 6, 7, 8, 2, 5, 4, 6, 8, 9 herschikken, we krijgen

2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 14

De mediaan is het zevende nummer in de rij = 6

Het gemiddelde is ook = 6

Standaarddeviatie = 3,32

Variantie = 11

Aantal werknemers = som van frequentie of aantal gegevens = 13.

Answer:

The first one 24/4

Step-by-step explanation:

Into usually means divide when it's used as a math term,

therefore 24 into fourths means 24 divide by 4.

Answer:

the answer is 24 divided by 4

Step-by-step explanation:

Answer:

5 weeks until they have the same

Arie and Olga have the same amount in their accounts in 8 weeks.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Amount in Arie's account = $46

Arie's each week savings = $8.50

Amount in Olga 's account = $14

Olga 's each week savings = $12.50

Let x be the number of weeks when Arie and Olga will have the same amount in their accounts

Total savings of Arie = 8.5x

Total savings of Olga = 12.5x

Amount in Arie's account = 8.5x + 46

Amount in Olga's account = 12.5x + 14

For, Arie and Olga have the same amount in their accounts

8.5x + 46 = 12.5x + 14

Taking alike terms together,

12.5x - 8.5x = 46 - 14

⇒ 4x = 32

Dividing both side by 4 we get,

x =8 weeks

which is the required number of weeks.

Thus, Arie and Olga will have the same amount in their accounts in 8 weeks.

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Answer:

With an assumption of room height = 8 ft we have;

The area of the room is 800 ft²

Area to be painted = 794.667 ft²

Paint required ≈ 7.95 gallons of paint

Cost of paint = $95.36

Step-by-step explanation:

Here we have if the height of the room is taken as 8 ft,

Therefore the total area in the room is 25 × 8 × 4 = 800 ft²

since the room has a window with three sides, therefore a triangular window of dimensions

4 ft by 3 ft by 6 ft

The area of the window is then

[tex]A = \sqrt{6.5(6.5-4)(6.5-3)(6.5-6)}[/tex]

Where the semi perimeter = (4 + 3 + 6)/2 = 6.5

Area of window, A = 5.333 ft²

Therefore, the total area to be painted = 800 ft² - 5.333 ft² = 794.667 ft².

Therefore the number of gallons of paint required ≈ 7.95 gallons

Cost of paint= $12 × 7.95 = $95.36.

Jeremy will have 72 baseball cards in April.

A consecutive pattern refers to a sequence or order of numbers, letters, or other objects in which each follows in direct and uninterrupted succession from the one that precedes it.

We have,

To solve this problem, we need to determine the pattern of how many cards Jeremy adds to his collection each month.

To do this, we can find the difference between consecutive months:

February minus January: 48 - 36 = 12

March minus February: 60 - 48 = 12

We can see that Jeremy is adding 12 cards to his collection each month.

So to find out how many cards he will have in April, we can add 12 to the number he had in March:

April

= 60 + 12

= 72

Therefore,

Jeremy will have 72 baseball cards in April.

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Answer:

3.14

Step-by-step explanation:

Answer:3.14

Step-by-step explanation:

Options B and C are the correct answer.

The given trigonometric function is y=3cosx+2.

We need to check which of the given options are equivalent to the function y=3 cos x+2.

The given trigonometric function can be solved using complementary angles and even/odd identities.

Complementary angles are sin x=cos(π/2 -x) and cos x=sin(π/2 -x).

Even/odd identities are sin(-x) =-sin x and cos(-x)= cos x.

Now,

From option A:

y=3 sin(x-π/2) +2

using trigonometry identity, we get

y=3 sin(-(x-π/2)) +2

⇒y=-3 sin(π/2 - x)+2

⇒y=-3 cos x+2

From option B:

y= 3sin(x+ π/2) +2

Using Sin(A+B)= sin A cos B+ cos A sin B, we get

y= 3cosx +2

From option C:

y= 3cos(-x) +2 can be written as y=3cosx+2 (cos(-x)=cosx)

From option D:

y= -3cos x-2

Therefore, options B and C are the correct answer.

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Final answer:

The equivalent functions to y=3 cos x+2 are B: y= 3sin(x+ π/2) +2 and C: y= 3cos(-x) +2, as they use the co-function identity and the even property of the cosine function respectively.

Explanation:

The given function is y=3 cos x+2. We need to find functions that are equivalent to this function. The trigonometric identities necessary for this problem are:

Now, considering the given options:

  D. y= -3cos x-2: This is not equivalent because it represents the reflection of the given function over the x-axis and a vertical translation down by 2 units.

Therefore, the equivalent functions are B and C.

6(-4x - 7) - 4(x - 6)       Distribute 6 into (-4x - 7) and -4 into (x - 6)

(6)(-4x) + (6)(-7) + (-4)x + (-4)(-6)  (two negative signs cancel each other out and become positive)

-24x - 42 - 4x + 24    Combine like terms(terms that have the same variable and power/exponent)

-24x - 4x - 42 + 24    (I rearranged the terms to be next to their like term)

-28x - 18      Your answer is D

Answer:

Circular shapes - They are those planner shapes that represent the locus of all the points that has a constant distance from a fixed point on the plane. This constant distance is termed as the radius of the circle and the fixed point is known as the center of the circle.

The center of the circle is enclosed by all the points on its periphery.

The circumference of the circle is the total length of its periphery around the center.

Concentric circles are two circles that have the same center

Step-by-step explanation:

Answer: 2.13

Step-by-step explanation:

1.42/2=0.71

1.42+0.71=2.13

Answer:

The answer to your question is £ 2.13

Step-by-step explanation:

Data

Cost of 1 kg or oranges = £1.42

Cost of the oranges in the scales = ?

Process

1.- Determine the weight of the oranges in the scales.

As we can see the weight of the three oranges is 1.5 kg

2.- Use proportions and cross multiplication to find the cost.

                 1 kg of oranges --------------------- £ 1.42

                 1.5 kg of oranges ------------------   x

                           x = (1.5 x 1.42) / 1

                           x = 2.13 / 1

                           x = £ 2.13

Answer: Inside (depending on your definition).

Step-by-step explanation: Finding the volume of a solid means measuring what space that solid takes up. Volume is a measure of how much matter an object is made up of. Technically, finding the volume of a solid does not mean finding the "inside" or "outside" of a solid. If you are referring to the surface area of a solid as the outside, then the answer to your question would be the inside of the solid.

Answer: Approximately 25187 animals of this species will be left in 2025

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

y = b(1 - r)^x

Where

y represents the population of animals after x years.

x represents the number of years.

b represents the initial population of animals.

r represents rate of decay.

From the information given,

b = 200000

r = 4.5% = 4.5/100 = 0.045

x = 2025 - 1980 = 45 years

Therefore,

y = 200000(1 - 0.045)^45

y = 200000(0.955)^45

y = 25187

Answer:

There'll be approximately 25187.3059 animals of this species in 2025.

Step-by-step explanation:

In this case we have a compounded interest problem, but the interest rate is negative, since the number will be decreasing. To solve it we can use the compound interest formula shown bellow:

M = C*(1 + r)^(t)

Where M is the final amount, C is the initial amount, r is the interest rate and t is the time elapsed.

In this case the time elapsed was from 1980 to 2025, so 45 years. Applying the data to the formula gives us:

M = 200000*(1 + (-0.045))^(45)

M = 200000*(1 - 0.045)^(45)

M = 200000*(0.955)^(45)

M = 25187.3059

There'll be approximately 25187.3059 animals of this species in 2025.

Answer:

a) CD = 6a + 4.5b

b) k = 4

Step-by-step explanation:

CD = CA + AB

CA = -AC

CD = -3b + 6a + 7.5b

CD = 6a + 4.5b

BC is parallel to CD

BC = BA + AC

BC = ka + 3b

BC is a scalar multiple of CD

Scale factor:

3/4.5 = 2/3

k = ⅔(6)

k = 4

Answer:

[tex]z=\frac{125-120}{\frac{12}{\sqrt{40}}}=2.64[/tex]    

P-value

Since is a two sided test the p value would be:  

[tex]p_v =2*P(z>2.64)=0.0082[/tex]  

And the best answer would be

B 0.0082

Step-by-step explanation:

Data given and notation  

[tex]\bar X=125[/tex] represent the mean height for the sample  

[tex]\sigma=12[/tex] represent the population standard deviation

[tex]n=40[/tex] sample size  

[tex]\mu_o =120[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is 120 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 120[/tex]  

Alternative hypothesis:[tex]\mu \neq 120[/tex]  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex]  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]z=\frac{125-120}{\frac{12}{\sqrt{40}}}=2.64[/tex]    

P-value

Since is a two sided test the p value would be:  

[tex]p_v =2*P(z>2.64)=0.0082[/tex]  

And the best answer would be

B 0.0082

Answer:

50.24 mm²

Step-by-step explanation:

Area = pi × r²

3.14 × 4²

50.24 mm²

Answer:

The area equals 50.2654 rounded up 50.27

Step-by-step explanation:

A= pi times radius squared equals pi times 4 squared equals 50.2654 (50.27)

Answer:

The radius is 3 square feet.

(Working is shown in the picture)

The radius of a circle with an area of 28.26 square feet is 3 feet

A radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center.

Given,

Area of the circle = 28.26 square feet

Area of the circle = [tex]\pi r^{2}[/tex]

Then

[tex]28.26 =\pi r^{2}\\ r^{2}=9\\ r=\sqrt{9}\\[/tex]

r = 3 feet

Hence, the radius of a circle with an area of 28.26 square feet is 3 feet

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Answer:

3 cylinder will fill 9 cones with water

Step-by-step explanation:

This problem bothers on mensuration of slides, cone and cylinder

We know that the

Volume of a cylinder = πr²h

Volume of a cone = 1/3(πr²h)

Given that both cylinder and cone has same height and radius

From the given expression we can deduce that the cone is 3 times smaller than the cylinder in volume

So if 1 cylinder will fill 3 cones

Then 3 cylinders will fill x cones

By cross multiplication we have

x= 3*3cones

x= 9 cones

Hence 3 cylinder will fill 9 cones with water

Answer:

9 cones

Step-by-step explanation:

The formula to find a volume of a cylinder is:

V1 = pi*r^2*h

Where r is the base radius and h is the height

The formula to find a volume of a cone is:

V2 = (1/3)*pi*r^2*h

So, if they have the same base radius and same height, we have that:

V1/V2 = 1/(1/3) = 3

The volume of the cylinder is 3 times bigger than the volume of the cone, so each cylinder of water can fill 3 cones.

Is Dennis has 3 cylinders, he is able to fill 3*3 = 9 cones with water.

I think the answer is 6(2n-3)

Answer:

1. x = +/- 2[tex]\sqrt{2}[/tex] - 7

2. x = [tex]3[/tex] +/- [tex]2i\sqrt{3}[/tex]

3. n = [tex]2[/tex] +/- [tex]i\sqrt{2}[/tex]

Step-by-step explanation:

1. Divide both sides by 2: (x + 7)^2 = 8

Square root both sides: x + 7 = +/- 2[tex]\sqrt{2}[/tex]

Subtract 7 from both sides: x = +/- 2[tex]\sqrt{2}[/tex] - 7

2. Square root both sides: x - 3 = [tex]\sqrt{-12}[/tex]

Since there is a negative inside the radical, we need to have an imaginary number: [tex]i=\sqrt{-1}[/tex] . So, [tex]\sqrt{-12} =i\sqrt{12} =2i\sqrt{3}[/tex]

Add 3 to both sides: x = [tex]3[/tex] +/- [tex]2i\sqrt{3}[/tex]

3. Divide by -5 from both sides: (n - 2)^2 = -2

Square root both sides: n - 2 = [tex]\sqrt{-2}[/tex]

Again, we have to use i: [tex]n-2=\sqrt{-2} =i\sqrt{2}[/tex]

Add 2 to both sides: n = [tex]2[/tex] +/- [tex]i\sqrt{2}[/tex]

Hope this helps!

Answer:

1. x = 2sqrt(2) - 7, -2sqrt(2) - 7

2. No real solutions

x = 3 + 2sqrt(3) i, 3 - 2sqrt(3) i

3. No real solutions

n = 3 + sqrt(2) i, 3 - sqrt(2) i

Step-by-step explanation:

1. 2(x + 7)² = 16

(x + 7)² = 8

x + 7 = +/- sqrt(8) = +/- 2sqrt(2(

x = 2sqrt(2) - 7, -2sqrt(2) - 7

2. (x - 3)² = -12

A perfect square can never be negative for real values of x

(x - 3) = +/- i × sqrt(12)

x - 3 = +/- i × 2sqrt(3)

x = 3 +/- i × 2sqrt(3)

3. -5(n - 3)² = 10

(n - 3)² = -2

A perfect square can never be negative for real values of x

n - 3 = +/- i × sqrt(2)

n = 3 +/- i × sqrt(2)

Answer:

see explanation

Step-by-step explanation:

The remainder theorem states that if f(x) is divided by (x - h)

The the remainder is f(h)

(a)

Given f(x) is divided by (x - 1) then remainder is f(1), thus

f(1) = [tex]1^{4}[/tex] + 1³ + 2(1)² + a + b = 7, that is

1 + 1 + 2 + a + b = 7

4 + a + b = 7 ( subtract 4 from both sides )

a + b = 3 ← as required → (1)

(b

Given f(x) is divided by (x + 2) then the remainder is f(- 2), thus

f(- 2) = [tex](-2)^{4}[/tex] + (- 2)³ + 2(- 2)² + 2a + b = - 8, that is

16 - 8 + 8 + 2a + b = - 8

16 + 2a + b = - 8 ( subtract 16 from both sides )

2a + b = - 24 → (2)

Multiply (1) by 2

2a + 2b = 6 → (3)

Add (2) and (3) term by term to eliminate the term in a

3b = - 18 ( divide both sides by 3 )

b = - 6

Substitute b = - 6 into (1)

a - 6 = 3 ( add 6 to both sides )

a = 9

Thus a = 9 and b = - 6

Final answer:

To solve for the constants a and b in the polynomial function f(x), we apply the remainder theorem to the given division scenarios. Setting up and solving a system of linear equations using the remainders allows us to find that a is 9 and b is -6.

Explanation:

The given function is f(x) = x^4 + x^3 + 2x^2 + ax + b, and we need to find the constants a and b given that when f(x) is divided by (x - 1), the remainder is 7, and when divided by (x + 2), the remainder is -8.

To find a + b, we apply the remainder theorem. When a polynomial f(x) is divided by (x - p), the remainder is f(p). Therefore, for (x - 1):

f(1) = 1 + 1 + 2 + a + b = 7
4 + a + b = 7
a + b = 3

Similarly, for (x + 2):

f(-2) = (-2)^4 + (-2)^3 + 2(-2)^2 + a(-2) + b = -8
16 - 8 + 8 - 2a + b = -8
16 - 2a + b = -8

We already know that a + b = 3, so we can set up a system of equations:

a + b = 3

-2a + b = -24

Solving for a and b:

Subtracting the first equation from the second: -3a = -27

Divide by -3: a = 9

Substitute a into the first equation: 9 + b = 3

Solve for b: b = -6