The graph below shows a system of equations:

The x-coordinate of the solution to the system of equations is _____

Answer: 3,500 feet

Step-by-step explanation:

To determine the original altitude for the third day, identify the y-intercept of the graph.

Therefore, the original altitude was 3,500 feet.

Answer: my question was a little different but i posted an image of the correct answer.

Step-by-step explanation:

To determine the original altitude for the third day, identify the y-intercept of the graph.

Therefore, the original altitude was 4,000 feet.

Answer:

46 housewives read all three magazines.

Step-by-step explanation:

Given:

        n(A) = 150

        n(B) = 200

        n(C) = 156

        n(A∩B) = 48

        n(B∩C) = 60

        n(A∩C) = 52

         n(A∪B∪C) = 300

so we know the relation as:

  n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)

∴ n(A∩B∩C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C)  - n(A∪B∪C)

                    = 150 + 200+ 156 - 48 - 60 - 52 - 300

                   = 46

Hence the number of housewives that had read all three magazine is 46.

Answer:

46 housewives read all three magazines.

Step-by-step explanation:

Answer:

0.0548

Step-by-step explanation:

The distribution of life span for a certain type of battery is approximately normal with mean 2.5 hours and standard deviation 0.25 hour.

To find the the probability that a selected battery will have a life span of at most 2.1 hours, we need to first determine the z-score for x=2.1 hours using

[tex]z = \frac{x - \mu}{ \sigma} [/tex]

We substitute the values to get:

[tex]z = \frac{2.1 - 2.5}{0.25} = - 1.6[/tex]

We read read -1.6 from the standard normal distribution table to get:

P(X≤2.1)=0.0548

The probability that the selected battery will have a life span of at most 2.1 hours is 0.0548.

Given information:

The life span of a battery is the amount of time the battery will last.

The distribution of life span for a certain type of battery is approximately normal with a mean of 2.5 hours and a standard deviation of 0.25 hours.

The z-value for the probability that the selected battery will have a life span of at most 2.1 hours will be calculated as,

[tex]z=\dfrac{x-\mu}{\sigma}\\z=\dfrac{2.1-2.5}{0.25}\\z=-1.6[/tex]

Now, use the standard normal distribution table or curve to get the value of required probability as,

[tex]P(x=2.1)=0.0548[/tex]

Therefore, the probability that the selected battery will have a life span of at most 2.1 hours is 0.0548.

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Solution:

The given pyramid has 3 lateral triangular side

The figure is attached below

Base of triangle = 12 unit

Find the perpendicular

By Pythagoras theorem

[tex]hypotenuse^2 = opposite^2 + adjacent^2[/tex]

Therefore,

[tex]opposite^2 = 10^2 - 6^2\\\\opposite^2 = 100 - 36\\\\opposite^2 = 64\\\\opposite = 8[/tex]

Find the lateral surface area of 1 triangle

[tex]\text{ Area of 1 lateral triangle } = \frac{1}{2} \times opposite \times base[/tex]

[tex]\text{ Area of 1 lateral triangle } = \frac{1}{2} \times 8 \times 12\\\\\text{ Area of 1 lateral triangle } = 48[/tex]

Thus, lateral surface area of 3 triangle is:

3 x 48 = 144

Thus lateral area for the pyramid with the equilateral base is 144 square units

The total number of digits used to write all the integers from 1 to 12 are 15.

Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.

Given that, Rena wrote all the integers from 1 to 12.

So, the integers from 1 to 12 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Here, 1 to 9 are single digits

10, 11 and 12 has two digits

Thus total number of digits = 9×1+3×2

= 9+6

= 15

Therefore, the total number of digits are 15.

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The total number of digits Rena wrote is:

[tex]\[\boxed{15}\][/tex]

To find the total number of digits Rena wrote when she wrote all the integers from 1 to 12, we need to consider each range of numbers separately based on their digit counts.

1. Single-digit numbers (1 to 9):

  - There are 9 single-digit numbers.

  - Each single-digit number contributes 1 digit.

  - Total digits from 1 to 9:

[tex]\[ 9 \times 1 = 9 \][/tex]

2. Two-digit numbers (10 to 12):

  - There are 3 two-digit numbers: 10, 11, and 12.

  - Each two-digit number contributes 2 digits.

  - Total digits from 10 to 12:

[tex]\[ 3 \times 2 = 6 \][/tex]

Adding the digits from both ranges gives us the total number of digits:

[tex]\[9 + 6 = 15\][/tex]

Thus, the total number of digits Rena wrote is:

[tex]\[\boxed{15}\][/tex]

Answer:

202.8

Step-by-step explanation:

The geometric mean of 2 numbers a and b is

[tex]\sqrt{ab}[/tex]

Here a = 30 and mean = 78, thus

[tex]\sqrt{30b}[/tex] = 78

To clear the radical square both sides

([tex]\sqrt{30b}[/tex] )² = 78², that is

30b = 6084 ( divide both sides by 30 )

b = [tex]\frac{6084}{30}[/tex] = 202.8

The probability of not getting a odd number is 1/2

Answer:

1/2

Step-by-step explanation:

Ur chances are 1 out of 2 bc there are even and there are odd numbers.

Hope this helps!

Answer:

x = 2

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

12-4x-x=2

Combine like terms

12 -5x =2

Subtract 12 from each side

12-5x-12 =2-12

-5x = -10

Divide each side by -5

-5x/-5 = -10/-5

x =2

For this case we have that the perimeter of the figure is given by the sum of the lengths of the sides, that is:

[tex]14 + 18 + 3 + 4 + 3 + 4 + 3 + 4 + (14-9) + (18-12) = 64[/tex]

Thus, the perimeter of the figure is 64 centimeters.

Now, we find the area of the figure:

We have that by definition, the area of a rectangle is given by:

[tex]A = a * b[/tex]

Where:

a and b are the sides of the rectangle

We have 4 vertical rectangles from left to right:

[tex]A_ {1} = 14 * (18-12) = 14 * 6 = 84 \ cm ^ 2\\A_ {2} = (3 + 3 + 3) * 4 = 9 * 4 = 36 \ cm ^ 2\\A_ {3} = (3 + 3) * 4 = 6 * 4 = 24 \ cm ^ 2\\A_ {4} = 3 * 4 = 12 \ cm ^ 2[/tex]

Thus, the total area is[tex]A_ {t} = 156 \ cm ^ 2[/tex]

Answer:

The perimeter of the figure is 64 centimeters.

[tex]A_ {t} = 156 \ cm ^ 2[/tex]

Answer:

$14.8

Step-by-step explanation:

There is a mistype in the question. It should say: ... si cada uno de ellos hicieron una contribución de dieciseis pesos...

So if everybody contributes $14, they make a total of 14*x, where x denotes the number of students. In this scenario, $4 are left, calling y to the cost of the trip, then:

14*x = y - 4 (eq. 1)

In the other scenario, everybody contributes $16 and $6 are in excess, so

16*x = y + 6 (eq. 2)

subtracting eq. 1 to eq. 2:

16*x - 14*x = y + 6 - (y - 4)

2*x =  y + 6 - y + 4

2*x = 10

x = 10/2 = 5

Replacing this value in eq. 1:

14*5 = y - 4

70 + 4 = y

y = $74

If every student pays: 74/5 =  $14.8, then they would get altogether the exact cost of the trip

Answer:

around $6000 the real answer is $5253.5

Step-by-step explanation:

Using distance formula we find that length is 13.

Hope this helps.

Answer: C. 2

Step-by-step explanation:

1. combine like terms

-6x + 4 = -8

2. Make x be by itself by subtracting -4 by both sides of the equal sign

-6x = -12

3. Divide both sides by -6, then negatives will cancel out

x= 2

(hope this helped)

Answer:

c. 2

Step-by-step explanation:

simplify:

3x-9x+7-3 = -8

-6x+4 = -8

Subtract 4 from both sides:

-6x = -8 - 4

-6x = -12

Divide both sides by -6:

x = -12/ -6

Answer

x= 2

Answer:

967

Step-by-step explanation:

0.1 x 9670 = 967

The number of full time employees is 17 and the number of part time employee is 9

Step-by-step explanation:

Step 1 :

Let f represent the number of full time employee and p represent the number of part time employee

Total number of employees = 26

Hence we have f + p = 26

Step 2 :

Wages of full time employee  = $275

Wages of part time employee = $140

Total wages paid by Jeds = $ 5935

Hence we have 275 f + 140 p = 5935

Step 3:

Solving the equations obtained in step 1 and step 2 we have

f + p = 26, Multiplying by 275 = > 275 f + 275 p = 7150

275 f + 140 p = 5935

Subtracting equation 2 from 1 we have

135 p = 1215 => p = 9

Substituting this in f + p = 26 gives, f + 9 = 26

So f = 17

Step 4 :

Answer :

The number of full time employees is 17 and the number of part time employee is 9

Answer:

31

Step-by-step explanation:

Answer:

The number is 31

Step-by-step explanation:

Step 1:  Distribute

1/8 (x + 9) = 5

1/8x + 9/8 = 5

Step 2:  Subtract 9/8 from both sides

1/8x + 9/8 - 9/8 = 5 - 9/8

1/8x = 31/8

Step 3:  Multiply both sides by 8

1/8x * 8 = 31/8 * 8

x = 31

Answer:  The number is 31

Answer:

-1/6

​

Step-by-step explanation:

(−9,8) and (−21,10)

−21−(−9)

10−8  

Plug in.  

−21+9

10−8

​  

The negative of a negative is a positive.  

−12

2

​  

Add/Subtract.  

−  

6

1

​

A positive divided by a negative is a negative.Cancel the common factor of 2.

Final answer:

The slope of the line that passes through the points (-9, 8) and (-21, 10) is calculated using the slope formula and is -1/6.

Explanation:

The slope of a line that passes through two points (x1, y1) and (x2, y2) is calculated using the formula:

slope (m) = (y2 - y1) / (x2 - x1).

For the points (−9, 8) and (−21, 10), the slope can be calculated as follows:

m = (10 - 8) / (−21 - (−9))

m = 2 / (−12)

m = −1/6 (which is the slope in simplest form).

Therefore, the slope of the line that passes through the points (−9, 8) and (−21, 10) is −1/6.

Answer:−

-20 √ 7

Step-by-step explanation:

Answer:

531.441

Step-by-step explanation:

8.1*8.1*8.1 = Volume of a cube

Solution:

Given that,

The costs for going to a dog beach are $7 for 1 dog, and $2 for each  additional dog

Let "x" be the number of dogs

where x is greater  than or equal 1

Cost y is $7 for the first dog and $2 for each of the other dogs

Therefore,

y = 7 + 2(x - 1)

x - 1 means the additional dogs

Therefore,

y = 7 + 2x - 2

y = 2x + 5

Thus the equation is found

Answer:

237.09m

Step-by-step explanation:

Let's use the tan rule to find the length of the adjacent side.

Tan rule is given as

[tex]Tan \theta=\frac{Opposite \ side}{Adjacent \ side}\\[/tex]

[tex]\theta[/tex]=67° , and Adjacent length is given as 100m.

We therefore need to find the length of the adjacent side.

[tex]Tan\theta=\frac{X}{100}\\Tan 67\textdegree=\frac{X}{100}\\X=Tan \ 67\textdegree \times 100\\X=235.58m[/tex]

To find height of the rock, we add X value to transit height=[tex]235.58+1.5=237.09m[/tex]

*See pic for graphic illustration

The height of the rock formation is approximately [tex]230\ meters[/tex].

Given:

[tex]\text{Distance from the base of the rock formation to the transit, d = 100\ m}[/tex]

[tex]\text{Angle of elevation, \( \theta = 67^\circ \)}[/tex]

[tex]\text{Height of the transit above the ground, \( h = 1.5 \) m}[/tex]

Let [tex]\( H \)[/tex] denote the height of the rock formation.

First, we need to find the vertical distance from the transit to the top of the rock formation using the tangent function:

[tex]\[ \tan(\theta) = \frac{H - h}{d} \][/tex]

Substitute the given values:

[tex]\[ \tan(67^\circ) = \frac{H - 1.5}{100} \][/tex]

Calculate [tex]\( \tan(67^\circ) \)[/tex]

[tex]\[ \tan(67^\circ) = 2.281 \][/tex]

Now, solve for [tex]\( H -1.5 \)[/tex]

[tex]\[ 2.281 = \frac{H - 1.5}{100} \][/tex]

Multiply both sides by [tex]100[/tex] to solve for [tex]\( H -1.5 \)[/tex]

[tex]\[ 2.281 \times 100 = H - 1.5 \][/tex]

[tex]\[ 228.1 = H - 1.5 \][/tex]

Add 1.5 to both sides to solve for [tex]\( H \)[/tex]

[tex]\[ H = 228.1 + 1.5 \][/tex]

[tex]\[ H = 229.6 \][/tex]

[tex]\[ H = 230\ m \][/tex] (Round to the nearest meter)

Answer:

D. $500

Step-by-step explanation:

Answer:

Step-by-step explanation:

$500

Answer:

It will take 27.19 years

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

[tex]A=Pe^{rt}[/tex] , where

∵ Steve deposits $1250 in an account

∴ P = 1250

∵ The account paying 3.4% annual interest compounded continuously

∴ r = 3.4%

- Change it to decimal by dividing it by 100

∴ r = 3.4 ÷ 100 = 0.034

∵ The account balance will reach to $3150.5

∴ A = 3150.5

- Substitute The values of A, P and r in the formula above to find t

∵ ​[tex]3150.5=1250e^{0.034t}[/tex]

- Divide both sides by 1250

∴  ​[tex]2.5204=e^{0.034t}[/tex]

- Insert ㏑ to both sides

∴ ​[tex]ln(2.5204)=ln[e^{0.034t}][/tex]

- Remember that [tex]ln(e^{n})=n[/tex]

∵  [tex]ln(e^{0.034t})=0.034t[/tex]

∴ ​ln(2.5204) = 0.034t

- Divide both sides by 0.034

∴ 27.18875 = t

∴ t ≅ 27.19

It will take 27.19 years

Question:

Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?

There are 15 cups in a gallon

Answer:

The expression to find the number of cups of water she drinks in a week is:

[tex]\frac{15\ cups}{1\ gallon} \times \frac{0.5\ gallons}{1\ day} \times \frac{7\ days}{1\ week}[/tex]

Solution:

Given that,

1 gallon = 15 cups

[tex]\frac{15\ cups}{1\ gallon}[/tex]

Katrina drinks 0.5 gallons of water per day

1 day = 0.5 gallons

[tex]\frac{0.5\ gallons}{1\ day}[/tex]

Find the number of cups of water she drinks in a week

1 week = 7 days

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

Thus the expression to find the number of cups of water she drinks in a week is:

[tex]\frac{15\ cups}{1\ gallon} \times \frac{0.5\ gallons}{1\ day} \times \frac{7\ days}{1\ week}[/tex]

Answer:

y= 2/3x + 28/3

Step-by-step explanation:

First, write your equation as y=2/3x+b. Plug in your coordinate into the equation, it should look like this: 6=2/3(-5)+b. Multiply 2/3 by -5 to get -10/3. It should look like this: 6= -10/3+b. Add 10/3 to both sides to get your y-intercept of 28/3. Go back to your original equation and plug 28/3 into b. This is your final equation: y= 2/3x + 28/3. Hope this helped!

Answer:

the correct answer for 28 is 5*b

5b

The rectangle with a length of 7 units and a width of 4 units, and with one vertex at the origin (0,0), has been successfully created using the segment tool.

Open the drawing tool or any software that allows you to draw shapes and use the segment tool to begin the construction.

First, mark the origin (0,0) on the canvas as one of the vertices of the rectangle.

Now, move the cursor 7 units to the right from the origin along the x-axis and place a point. This point represents the opposite vertex of the rectangle on the right side.

Next, move the cursor 4 units up from the origin along the y-axis and place another point. This point represents the opposite vertex of the rectangle on the top side.

To complete the rectangle, draw straight lines connecting the following points: (0,0) with (7,0), (7,0) with (7,4), (7,4) with (0,4), and finally, (0,4) back to (0,0).

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Answer:

$14

Step-by-step explanation:

$20 minus the $6 she came back with equals $14, which is what she spent.

(20-6=14)

Answer:

$14

Step-by-step explanation:

Take 6 away from 20