Leon graph y=12- 0.05 x to represent the number of gallons of gas left in his car after driving x miles.

Answer:

no solution

Step-by-step explanation:

Given

- 3 | 6n - 2 | + 5 = 8 ( subtract 5 from both sides )

- 3 | 6n - 2 | = 3 ( divide both sides by - 3 )

| 6n - 2 | = - 1

The absolute value always returns a positive value and so

| 6n - 2 | ≠ - 1

Hence there is no solution to the equation

What is the length of the actual car in feet and inches? 4/5 ft 48/72in

Answer:

P(n) = 0.5

Step-by-step explanation:

For two events which are independent, we use the multiplication rule which states P (A and B) = P(A) * P(B). Substitute P(m) = 0.4 and P(m and n) = 0.2 into this formula.

P (m and n) = P(m) * P(n)

0.2 = 0.4*P(n)

Divide by 0.4 on both sides.

0.2 / 0.4 = P(n)

0.5 = P(n)

Answer:

The mean is 5

the median is also 5

and the mode is 1

Step-by-step explanation:

Answer:60,61,73,75,79,81,81,81,92,96,98

Step-by-step explanation: Mean:80

                                             Median:81

                                            Mode:81

Answer:

no simplify. answer is:

b. log(1/7)

ANSWER

d.

[tex] \frac{1}{7} [/tex]

EXPLANATION

We want to simplify

[tex] {10}^{ log( \frac{1}{7} ) } [/tex]

Recall that the common logarithm has a base of 10.

This implies that,

[tex] {10}^{ log( \frac{1}{7} ) } = {10}^{ log_{10}( \frac{1}{7} ) } [/tex]

Recall again that:

[tex] {p}^{ log_{p}(q) } = q[/tex]

Therefore,

[tex] {10}^{ log( \frac{1}{7} ) } = {10}^{ log_{10}( \frac{1}{7} ) } = \frac{1}{7} [/tex]

right isosceles

rs:34&rs=rt+st

rt:17

st:17

ab=[(x(a)-x(b))+(y(a)+y(b))]

Answer:

Isosceles.

Step-by-step explanation:

We are going to check it with the distance formula

d(R,T) = [tex]\sqrt[2]{(3-4)^{2}+(-3-1)^{2}}[/tex]

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

= [tex]\sqrt[2]{1+16}[/tex]

=  [tex]\sqrt[2]{17}[/tex].

d(T,S) = [tex]\sqrt[2]{(4-8)^{2}+(1-0)^{2}}[/tex]

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

= [tex]\sqrt[2]{16+1}[/tex]

=  [tex]\sqrt[2]{17}[/tex].

d(S,R) = [tex]\sqrt[2]{(8-3)^{2}+(0-(-3))^{2}}[/tex]

= [tex]\sqrt[2]{(5)^{2}+(3)^{2}}[/tex]

= [tex]\sqrt[2]{25+9}[/tex]

=  [tex]\sqrt[2]{34}[/tex].

Then, as the triangle has two sides with the same length, the triangle is isosceles.

I am thinking the answer is 225. Sorry if I'm wrong!

The first month has the equation raised to 11 which is the number of months left in the period.

So each month the equation would be the same except it would be raised to 1 less than the previous month.

Month 2 = 50(1.003)^10

Month 3 = 50(1.003)^9

Month 4 = 50(1.003)^8

Month 5 = 50(1.003)^7

Month 6 = 50(1.003)^6

Month 7 = 50(1.003)^5

Month 8 = 50(1.003)^4

Month 9 = 50(1.003)^3

Month 10 = 50(1.003)^2

Month 11 = 50(1.003)^1

Month 12 = 50(1.003) ( the last month would not be raised to anything)

Answer:

600

Step-by-step explanation:

its 50 X 12

thats how you would solve that

Answer:

x = ±√2

Step-by-step explanation:

         x - 1 =     1/(x + 1)

(x -1)(x + 1) =     1     Multiplied each side by x + 1

       x² - 1 =     1     Difference of two squares

           x² =     2     Add 1 to each side

           x  = ±√2

x-1 is the reciprocal of x+1 when x = -√2 or x = √2.

Check:

(a) x = -√2

  -√2 - 1 = 1/(-√2 + 1)

-(√2 + 1) = (√2 +1)/[(-√2 +1)(√2 + 1)]

-(√2 + 1) = (√2 +1)/(-2 +1)

-(√2 + 1) = (√2 +1)/(-1)

-(√2 + 1) = -(√2 +1)

(b) x = √2

√2 - 1 = 1/(√2 + 1

√2 - 1 = (√2 - 1)/[(√2 + 1)(√2 - 1) ]

√2 - 1 = (√2 - 1)/(2 - 1)

√2 - 1 = (√2 - 1)/1

√2 - 1 = √2 - 1

OK.

Answer:x = ±√2

Step-by-step explanation: this is because reciprocal means the numerator and denominator switches

So the equation is x-1=1/(x+1)

And you solve for it thats how u get the answer

Answer:

I dont really know the answer.. but ill try; if its wrong I am so sorry;

Step-by-step explanation:

First you must get the area of a circle, which is; A= pi r squared

and all you have to do is fill it in like this;

A= 3.14 x 2.0

           ^

    A= 6.28

Answer:

280 degrees.

Step-by-step explanation:

To convert radians to degrees we multiply by 180/pi:

angle O = 14pi/ 9 * 180 / pi

=  14*180 / 9

=  280 degrees.

The angle 0=14pi/9 radians can be converted to degrees by using the conversion factor 1 radian = 57.3°. Multiplying the given angle in radians by the conversion factor results in an equivalent angle of 280° in degrees.

To convert the angle from radians to degrees, we use the conversion factor 1 rad = 57.3°. The problem provides the angle 0 = 14pi/9 radians. By using the conversion factor, the process of conversion would be as follows:

Therefore, the angle 0=14pi/9 radians is equal to 280° in degrees.

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Answer:

16.033 min

Step-by-step explanation:

We can write Newton's Law of Cooling as

T = Tₐ + (T₀ - Tₐ)e^(-kt), where

Tₐ = ambient temperature of the surroundings

T₀ = initial temperature of the object

k = the cooling constant

t = the time

(1) Calculate the cooling constant

Data:

T =   110 °F

T₀ = 180 °F

Tₐ =  70 °F

 t =   20 min

Calculation:

110 = 70 + (180 - 70)e^(-k×20)

40 = 110e^(-20k)

0.363 64 = e^(-20k)

-1.0116 = -20k

k = 0.050 580 min⁻¹

(2)After adding cream

(a) Calculate T₀  

2 oz × 40 °F + 12 oz × 180 °F = 14 oz × T₀

80 °F + 2160°F = 14T₀

2240 °F = 14T₀

T₀ = 160 °F

(b) Calculate the time to cool to drinking temperature

110 = 70 + (160 - 70)e^(-0.050 580t)

40 = 90e^(-0.050 580t)

0.444 44 = e^(-0.050 580t)

-0.810 93 = -0.050580t

t = 16.033 min

It will take 16.033 min for the mixture to reach drinking temperature

To determine the time it takes for the mixture to reach drinking temperature, we first calculate the initial temperature of the mixture after adding 2 ounces of 40°F cream to the 180°F coffee, which turns out to be 165°F. Then, according to Newton's Law of Cooling, the time it takes for the mixture to decrease from 165°F to the drinking temperature of 110°F would be the same as the time it took for the original coffee to cool from 235°F to 180°F, given the cooling constant doesn't change when we add the cream. Therefore, the mixture will take approximately 20 minutes to reach drinking temperature.

To determine the time it takes for the mixture to reach drinking temperature, we first need to calculate the initial temperature of the mixture. When you add 2 ounces of 40°F cream to the 180°F coffee, the temperature of the mixture instantly becomes the weighted average of the temperature of the coffee and of the cream. Thus, we have:

(12 * 180 + 2 * 40) / (12 + 2) = 165°F.

Now we need to calculate the time it takes for the mixture to decrease from 165°F to the drinking temperature of 110°F. According to Newton's Law of Cooling, the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. If we assume that the proportionality constant (or the cooling constant) doesn't change when we add the cream, then the time it takes for the mixture to cool from 165°F to 110°F will be the same as the time it took for the original coffee to cool from 235°F (165 + 70) to 180°F (110 + 70), which is 20 minutes. We can conclude that the mixture will take approximately 20 minutes to reach drinking temperature.

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Answer:

56 in.

Step-by-step explanation:

By proportion  8/5 = L/35  where L is the length of the picture.

5L = 8*35

L = 8*35/5

L = 56 in.

The length of a similar picture frame is Option (a) 56 in.

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A ratio indicates how many times one number contains another. It is expressed as a:b where a and b are parameters for any given set of relation.

Given length to width ratio is 8:5.

We have to find the length of similar picture frame which has a width of 35 inches.

Let length of the picture frame be L inches.

Using ratio equation for solving, we have

   8:5 = L:35

⇒ 8/5 = L/35

∴  L = (8/5) * 35 = 56 inches.

Therefore the length of a similar picture frame is Option (a) 56 in.

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1.5 • 3.142= 4.713 should be the answer

Answer:   4.5π  ≈  14.14 cm²

Step-by-step explanation:

[tex]Area_{\ circle}=\pi \cdot r^2\\\\Area_{\ semicircle}=Area_{\ circle}\div 2\\\\\\A=\dfrac{\pi \cdot 3^2}{2}\\\\\\.\quad =\dfrac{9}{2}\pi\\\\\\.\quad =4.5\pi\\\\\\.\quad =14.14[/tex]

Destructimous had 6 ultra power blasts.

The total number of blasts Destructimous has is:

Total blasts = Sonic blasts + Heat rays

Total blasts = 7 + 13

Total blasts = 20

Now, we know that Destructimous has a 2/7 chance of using its ultra power blast. To find out how many ultra power blasts it fires, we calculate 2/7 of the total blasts:

Ultra power blasts = (2/7) * Total blasts

Ultra power blasts = (2/7) * 20

Ultra power blasts = 40/7

Now, since we can't have a fraction of a blast, we need to round this number to the nearest whole number. In this case, 40/7 is approximately 5.71, so when rounded, it's 6.

So, Destructimous had 6 ultra power blasts.

-------------------------------------

Answer:

230.4

feet

Explanation:

arc length  

=

circumference  

×

fraction of circle

×

×

×

×

=

2

π

r

×

165

360

×

×

×

×

=

2

×

π

×

80

×

165

360

×

×

×

×

=

230.4

feet to nearest tenth

Step-by-step explanation:

The length of the intercepted arc between those two cars on the Ferris wheel is 73.3 ft

Since the distance between the two cars is the length of an arc, we need to know what the length of an arc is.

The length of an arc is given by L = Ф/360 × 2πr where

Given that for the ferris wheel

Substituting the values of the variables into the equation, we have

L = Ф/360 × 2πr

L = 140°/360 × 2π × 30 ft

L = 14/36 × 60π ft

L = 14/3 × 5π ft

L = 70π/3 ft

L = 219.91 ft/3

L = 73.3 ft

So, length of the intercepted arc between those two cars on the Ferris wheel is 73.3 ft

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Answer:

D.

Step-by-step explanation:

50-20=30 (because of the initial cost)

Then multiply 30*0.5=60

so she can buy less than or equal to 60

Answer:

D. S ≤ 60

Step-by-step explanation:

Ella has $50.00 and the registration fee is $20. This means that she would have $30.00 to buy songs and each song costs $0.50, so:

$30.00/$0.50= 60

The number of songs that she would be able to buy is 60.

According to this, the inequality that gives the maximum number of songs that she can buy is S ≤ 60 as it indicates that the maximum number of songs (s) that she can buy is less than or equal to 60.

Answer:

15  cookies

Step-by-step explanation:

We have 20 cookies and we know that three quarters of them were burned. To find the number of cookies burned, divide the 20 cookies into 4 equal parts.

This will give you 4 parts of 5 cookies.

[5] + [5] + [5] + [5]

Then they tell us that 3 quarters were burned. This means that of these 4 parts [5] + [5] + [5] + [5], 3 were burned. Then take 3 of these parts and add them.

[5] + [5] + [5] = 15 cookies.

This is the same as multiplying:

[tex]20 * \frac{3}{4} = 15[/tex]

It’s a if the quotation is bigger than the dividend the answer is just a mixed number

To assess the evidence of Hypothesis testing, the students need to determine the likelihood of the proportion of Millennial students at their campus that live at home with their parents being 36% or higher.

The question here is regarding the testing of a population proportion using statistical hypothesis testing, specifically a one-sample z-test. The null hypothesis (H0) is that the population proportion is equal to a specified value, in this case, 36%). The alternative hypothesis (Ha) is that the population proportion is greater than the specified value (more than 36%).

The question we need to answer is 'If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be more than 36%?'

The scenario suggests an indication towards a right-tailed z-test as we're looking to see if the data indicates a proportion >36%. However, as with all statistical tests, one should be cautious about drawing definitive conclusions without additional context and understanding the potential for sampling variability and error.

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Answer:

There are 16 terms in the sequence.

Step-by-step explanation:

The given sequence is

14348907, ..., 9, 3, 1

The first term of the sequence is

[tex]a_1=14348907[/tex]

The last term of the sequence is [tex]l=1[/tex]

The common ratio is [tex]r=\frac{1}{3}[/tex]

The nth term of this sequence is;

[tex]a_n=a_1(r)^{n-1}[/tex]

We plug in the common ratio and the first term to get;

[tex]a_n=14348907(\frac{1}{3})^{n-1}[/tex]

The find the number of terms in the sequence , we plug in the last term of the sequence.

This implies that;

[tex]1=14348907(\frac{1}{3})^{n-1}[/tex]

[tex]\frac{1}{14348907}=(\frac{1}{3})^{n-1}[/tex]

[tex]\Rightarrow 3^{-15}=3^{-(n-1)}[/tex]

Since the bases are the same, we equate the exponents;

[tex]-15=-(n-1)[/tex]

[tex]15=n-1[/tex]

[tex]15+1=n[/tex]

[tex]n=16[/tex]

Answer:

Step-by-step explanation:

First att all, let's take angle B... It's bigger than 180° and smaller than 360. Then: 180 < 6x < 360. So 6x = 288°. The only alternative what's correct is the first one.

I hope I helped you

5y+2x=10y=−25x+2246810−2−4−6−8−10246810−2−4−6−8−10Let's solve for x.5y+2x=10Step 1: Add -5y to both sides.2x+5y+−5y=10+−5y2x=−5y+10Step 2: Divide both sides by 2.2x2=−5y+102x=−52y+5Answer:x=−52y+5

Do make the intercepts twice as big, you simple divide the function by 2, but leave it =10.

The function 5y+2x=10 has intercepts (0,2) and (5,0)

Therefore by dividing by 2 we get 2.5y+x=10 which is your answer. It has intercepts (0,4) and (10,0)

Answer:

There are 21 luxury vehicles in 3 shipments sent to a dealership . Which of the following expresses the ratio of shipments to luxury vehicles?

A. 21/3

B. 21 to 3

C. 21:3

D. 3:21

Step-by-step explanation:

Answer:

The answer is D. 3:21 Hope this helps!

Answer:

264 cubic meters

Step-by-step explanation:

The sea turtle habitat at the zoo has a total volume of 264 cubic meters.

To find the total volume of the sea turtle habitat, which consists of two connected aquariums, you can calculate the volume of each aquarium separately and then add them together.

For the first aquarium:

- Length = 6 meters

- Width = 4 meters

- Height = 2 meters

The volume of the first aquarium is calculated as:

Volume_1 = Length * Width * Height

Volume_1 = 6 m * 4 m * 2 m

Volume_1 = 48 cubic meters

For the second aquarium:

- Length = 8 meters

- Width = 9 meters

- Height = 3 meters

The volume of the second aquarium is calculated as:

Volume_2 = Length * Width * Height

Volume_2 = 8 m * 9 m * 3 m

Volume_2 = 216 cubic meters

Now, to find the total volume of the sea turtle habitat, you add the volumes of the two aquariums together:

Total Volume = Volume_1 + Volume_2

Total Volume = 48 cubic meters + 216 cubic meters

Total Volume = 264 cubic meters

So, the total volume of the sea turtle habitat at the zoo is indeed 264 cubic meters, as provided.

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Answer:

Step-by-step explanation:

Yesterday, her rate was 8mph, her time was x hours.

Today, her rate was 13mph, her time was 13 - x hours.

So the total distance she biked on the two days is

d = 8x + 13(13 - x), or 169 - 5x

Answer:

[tex]8x+13(9-x)[/tex] or [tex]-5x+117[/tex] miles.

Step-by-step explanation:

Let x represent number of hours Carmen biked yesterday.

[tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]

We have been given that yesterday Carmen's average speed was 8

miles per hour. So distance covered in x hours would be [tex]8x[/tex].

We are also told that Carmen biked for a combined total time of 9

hours. So the number of hours biked second day would be [tex]9-x[/tex]. The distance covered in [tex]9-x[/tex] at a speed of 13  miles per hour would be [tex]13(9-x)[/tex].

Total distance covered by Carmen would be: [tex]8x+13(9-x)[/tex]

[tex]8x+117-13x[/tex]

[tex]8x-13x+117[/tex]

[tex]-5x+117[/tex]

Therefore, the total distance covered by Carmen in the two days would be [tex]-5x+117[/tex] miles.

Answer:

  72

Step-by-step explanation:

1 out of 10 do not recommend naps, so 9 times as many do recommend naps.

  9 × (8 doctors) = 72 doctors . . . . . recommend naps

Answer:

For a unique solution, there must be as many consistent, independent equations as there are variables.

Step-by-step explanation:

Each equation lets you write an expression for one variable in terms of the others in that equation. That expression can be substituted throughout the system, reducing the number of equations and variables by one each.

After n-1 such substitutions in a system of n equations, there will be one equation left. If that is an equation in one variable, then the solution to the system can be easily found. If more than one variable remains (> n variables in n equations), then the system cannot be solved for definitive values of each of the variables.

___

If the equations are inconsistent, there is no solution. If the equations are dependent, then there is no unique solution.

To solve a system of linear equations, one generally requires the same number of equations as there are variables for a unique solution, otherwise the system may have either an infinite number of solutions or none.

To solve a system of linear equations, you generally need as many equations as there are variables. If you have two variables, you should have two linear equations to find a unique solution. For example, the equations 3x - 2y = 24 and 3x + 9y = 30 form a system that can be solved because there are two equations with two variables (x and y).

If there are more variables than equations, then you may either have infinitely many solutions or no solution, depending on the equations' consistency. If you have fewer equations than variables, as in the case of three variables with only two equations, you typically have an undetermined system where you can choose one variable as a parameter and express the others in terms of it, leading to an infinite number of solutions.

For homogeneous equations where the vector b is zero (Ax = 0), the solutions form a subspace of the vector space, and nontrivial solutions exist if the system is not of full rank.

Answer:

[tex]\large\boxed{x=\dfrac{27}{2}\to x=13\dfrac{1}{2}\to x=13.5}[/tex]

Step-by-step explanation:

[tex]\dfrac{2}{3}x-2=7\qquad\text{add 2 to both sides}\\\\\dfrac{2}{3}x-2+2=7+2\\\\\dfrac{2}{3}x=9\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{2}{3\!\!\!\!\diagup_1}x=3\cdot9\\\\2x=27\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{27}{2}\\\\x=\dfrac{27}{2}\to x=13\dfrac{1}{2}\to x=13.5[/tex]