Carla drove her truck 414 miles on 18 gallons of gasoline. How many miles did she drive per gallon?

Answer: x= -1, z=2, y= -4

Step-by-step explanation:

System of equations:

-5x - 4y - 3z= 15  +

-10x + 4y + 6z= 6

-15x         + 3z = 21  ------>  3 (-5x + z) = 7.3

-5x + z = 7

now,

-10x + 4y + 6z= 6

2(-5x + z) + 4y + 4z = 6

14 + 4y + 4z = 6

7 + 2y + 2z = 3

2y + 2z= -4

y+z=-2

Now we were using the equation: 20x + 4y + 4z = -28

20x + 4(y+z) = 20x -8= - 28

20 x = -20

x= -1

With this we can find y and z

X=-1

-5x + z = 7

z= 2

y+z=-2

y=-4

Finally we have: x= -1, z=2, y= -4

I hope this can help you.

Thank you

The probability that the average price is between $153 and $155 is 0.04.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The average price of a math textbook =$158

The standard deviation =$26

The mean= 158

n =number of textbooks randomly chosen which is 40

n=10

Then

σ = 26

σₓ = σₓ/√n

= 26/√40

Therefore. σₓ² = 16.90

For the group of 48, find the probability that the average price is between $153 and $155.

The probability that the average price is between $153 and $155

= 0.04

Learn more about probability here;

https://brainly.com/question/11234923

#SPJ1

Answer:

y = 1/3x - 7/3

Step-by-step explanation:

y2 - y1 / x2 - x1

-1 - (-3) / 4 - (-2)

2/6

= 1/3

y = 1/3x + b

-1 = 1/3(4) + b

-1 = 4/3 + b

-7/3 = b

Answer:

Any value that has x less than or equal to 19 is a solution

Step-by-step explanation:

x – 5 ≤ 14

Add 5 to each side

x – 5+5 ≤ 14+5

x  ≤ 19

Any value that has x less than or equal to 19 is a solution

Answer:

[tex]\boxed{x\leq 19}[/tex]

Step-by-step explanation:

[tex]x-5\leq 14[/tex]

[tex]\sf Add \ 5 \ on \ both \ sides.[/tex]

[tex]x-5+5 \leq 14+5[/tex]

[tex]x\leq 19[/tex]

5X + 8 = 53

5X = 53 - 8

X = 45 / 5

X = 9

Answer:

X=9

Step-by-step explanation:

5X+8=53

To solve this we need to make X the subject of the equation that means X should be alone on one side of the equation. Taking the following steps

5X=53-8

5X=45

X=45/5

X=9

Answer: 0.9844

Step-by-step explanation:

given data:

sample size n = 6

It’s assumed that half the population are male and the remaining half are females

F = 1/2

M = 1/2

the probability that the investigator would draw altleats one male

P ( x ≥ 1 ) =

= 1 - ( 0.5 ) ^ 6

= ( 0.5 )^6

= 0.9844

Answer:

vertical angles

Step-by-step explanation:

Angle 1 and 3 are vertical angles.  The angles are made from the same lines and share a vertex.  They are opposite it each other

Answer:

400

Step-by-step explanation:

First, the firm produces 100 sets its first year. This means that our equation starts at 100. Next, the total number of calculator sets in 5 years is 4500. With y₁ representing the amount of calculator sets produced during year 1, y₂ representing the amount of sets during year 2, and so on, we can say that

y₁+y₂+y₃+y₄+y₅ = 4500

100 + y₂+y₃+y₄+y₅ = 4500

Next, we are given that the production increases uniformly by an amount each year. Representing that amount as a, we can say that

y₁+a = y₂

y₂+a = y₃

y₁+a+a = y₃

y₁+ 2 * a = y₃

and so on, so we have

100 + y₂+y₃+y₄+y₅ = 4500

100 + (100+a) + (100+2a) + (100+3a) + (100+4a) = 4500

500 + 10a = 4500

subtract 500 from both sides to isolate the a and its coefficient

4000 = 10a

divide both sides by 15 to isolate a

a = 400

Answer:

Hello,

answer D 48°

Step-by-step explanation:

In the right triangle down, a+42°=90° ==> a=90°-42°=48°

Answer:

Step-by-step explanation:

Equation of a circle is given by

( x - h)² + ( y - k)² = r²

where r is the radius and

( h , k) is the center of the circle

From the question the radius R = 1/3

the center ( h ,k ) = (4/3 , -8/3)

Substituting the values into the above equation

We have

[tex](x - \frac{4}{3} )^{2} + {(y - - \frac{8}{3}) }^{2} = ({ \frac{1}{3} })^{2} [/tex]

We have the final answer as

[tex](x - \frac{4}{3} )^{2} + {(y + \frac{8}{3}) }^{2} = \frac{1}{9} [/tex]

Hope this helps you

Answer:

The temperature of the 5th day was 3°C

Step-by-step explanation:

Mean temperature of the first 4 days = 8°C

Note that:

Mean = Sum of temperatures ÷ number of days

∴ 8 = sum of temperature ÷ 4

[tex]= 8 = \frac{sum\ of\ temperatures}{4}[/tex]

[tex]= sum\ of\ temperatures\ = 8\ \times\ 4 = 32[/tex]

Therefore the sum of the first 4 days = 32

Let the temperature of the next day (the fifth day) be m

Hence,

sum of the temperatures of first 5 days = 32 + m - - - - (1)

Next, the sum of the first 5 days can be calculated from the given average of the first 5 days as follows:

Mean temperature of the first 5 days = 7

[tex]Mean = \frac{sum\ of\ temperatures}{number \ of\ days}\\\\7 = \frac{sum\ of\ temperatures}{5} \\sum\ of\ temperatures\ = \ 7\ \times\ 5\ = 35\\sum\ of\ temperature\ of\ the\ first\ 5\ days\ =\ 35 - - - - - (2)[/tex]

Now, you will notice that equation (1) = equation (2)

∴ 32 + m = 35

m = 35 - 32 = 3

therefore, the temperature of the 5th day was 3°C

Answer:

0.5 km/min and 1km

Step-by-step explanation:

30 km in an hour

30 km in 60 mins, 30/60 km in one minute so she cycle 0.5km/min. They will cover 1 km in 2 minutes

Answer:

Cohen's d : 1.00

Step-by-step explanation:

We know that M₁ = 18, and M₂ = 14. Given that the pooled variance for the these two samples are 16, S²Pooled = 16, and therefore S - pooled = 4.

The formula to solve for the value of Cohen's d is as follows,

d = M₁ - M₂ / S - pooled,

d = 18 - 14 / 4 = 4 / 4 = 1

Therefore the value of Cohen's d = 1

Answer:

x = 2 is the solution to x + 1.5 = 3.5

Step-by-step explanation:

x + 1.5 = 3.5

   -1.5      -1.5

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

x = 2

Answer:

Step-by-step explanation:

Given:

Total amount = $20,000

Assume

Government bonds = x

Municipal bonds = y

Computation:

1. Invest total money

x + y ≤ 20,000

2. invest no more than $5,000 into municipal bonds

y ≤ 5,000

3. at least twice as much into government bonds.

x ≥ 2y

Step-by-step explanation:

1965 round to the nearest tenth is 1970

Answer:

1965.0

Step-by-step explanation:

Answer:

C° = 71.6056

Step-by-step explanation:

Law of Cosines: c² = a² + b² - 2abcosC°

Step 1: Plug in known variables

29² = 30² + 15² - 2(30)(15)cosC°

Step 2: Evaluate

841 = 900 + 225 - 900cosC°

-59 = 225 - 900cosC°

-284 = -900cosC°

71/225 = cosC°

cos⁻¹(71/225) = C°

C° = 71.6056

And we have our answer!

Answer:

  79.0°

Step-by-step explanation:

The Law of Cosines is used for this purpose. It tells you ...

  a² = b² +c² -2bc·cos(A)

Solving for A gives ...

  cos(A) = (b² +c² -a²)/(2bc) = (15² +29²-30²)/(2(15)(29)) = 166/870

Using the inverse cosine function, we find the angle to be ...

  A = arccos(166/870) ≈ 79.00026°

  A ≈ 79.0°

Answer:

Option D, 12

Step-by-step explanation:

4x-8=80/2

or, 4x-8=40

or, 4x=48

or, x=12

Answer:

Given:-  

m∠DEF= (4x-8) °

m DE= 80°

Using a property :- m ∠DEF= 1/2 (m DE)

[tex](4x-8)[/tex] ° [tex]= 1/2 (80)[/tex]

[tex](4x-8)[/tex]° [tex]=(40)[/tex] °

[tex]4x-8=40[/tex]

Add 8 to both sides:-

[tex]4x=48[/tex]

Divide both sides by 4:-

[tex]\frac{4x}{4}=\frac{48}{4}[/tex]

[tex]x=12[/tex]

OAmalOHopeO

Answer:

t=1, u=-2, w=-2

Step-by-step explanation:

Step-by-step explanation:

8x² + 7y² - z² + 2yz + 3xz - 5xy

x 2x - 3y

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

-24x²y - 21y³ + 3yz² - 6y²z - 9xyz + 15xy²

+ 16x³ + 14xy² - 2xz² + 4xyz + 6x²z - 10x²y

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

16x³-21y³-34x²y+6x²z+29y²x-6y²z-2xz²+3yz²-5xyz

Answer:

A  has the points plotted correctly

Step-by-step explanation:

We need to plot the data

A  has the points plotted correctly

B  has the point ( 10,5) plotted on (9,5)

C is missing (-6,-5)

D is missing (-6,-5) and has (-2,1) instead of (-2,-1)

Answer:

A.

Step-by-step explanation:

It would be very helpful to write the points individually from the data. Take the x value and place it with its corresponding y value:

(1,4) ; (2,2) ; (-2,-1) ; (-2,-6) ; (5,-4) ; (-6,-5) ; (10,5)

Now find the graph that has each of these points. You can write these down and cross them out if you find them on the graph, and once you find the graph where all of these points are crossed out, that's the correct graph.

The correct graph is A.

:Done

Answer:

(3,1) is the midpoint

Step-by-step explanation:

To find the x coordinate of the midpoint, average the x coordinates of the endpoints

(7+-1)/2 = 6/2 =3

To find the y coordinate of the midpoint, average the y coordinates of the endpoints

(10+-8)/2 = 2/2 = 1

(3,1) is the midpoint

Answer:

(3, 1)

Step-by-step explanation:

We can use the formula [ (x1+x2)/2, (y1+y2/2) ] to solve for the midpoint.

7+(-1)/2, 10+(-8)/2

6/2, 2/2

3, 1

Best of Luck!

Answer:

D) Prospective observational study

Step-by-step explanation:

A study which gathers data moving forward is called a prospective study.  Since the data is gathered on students without controlling the setting moving forward, it is a prospective observational design.

Answer:

A. 14z - 28

Step-by-step explanation:

simplify z² - 3z

a. z(z - 3)

the denominator on the right has z(z - 3). but it is also multiplied by (z - 2)

this means the numerator must also be multiplied by (z - 2)

14 x (z - 2) = 14z - 28

hope this helps :)

Answer:

2x[tex]\leq[/tex]14

Step-by-step explanation:

Answer:

2x ≤ 14

Step-by-step explanation:

twice a number   is no more than     14

               2x                     ≤                 14

Answer:

  (a) -2.3°/min

  (b) -2.9°/min

Step-by-step explanation:

The average rate of change is the ratio of the difference in R values to the difference in the corresponding t values.

(a) m = (157.6 -226.6)/(30 -0) = -69/30 = -2.3 . . . degrees per minute

__

(b) m = (61.6 -119.6)/(70 -50) = -58/20 = -2.9 . . . degrees per minute

please mark this answer as brainlist

Answer:

multiplication prop of equality, (multiplying both sides by 6)

simplifying, (not distrib prop as there is no parentheses)

Addition prop of equality, (adding 18 to each side)

simplifying

Answer:

(d-4)(c-9)

Step-by-step explanation:

cd-9d-4c+36

d(c-9)-4(c-9)

pull out the (c-9),

(d-4)(c-9)