Solve this using the substitution method:

7x+10y=36
y=2x+9

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

2.016

Step-by-step explanation:

In your equasion, I couldn't tell if you need to multipy 0.8^2 by 3.15 or are you asking something else? If you want to multiply, the answer is 2.016.

Answer:

$29.72

Step-by-step explanation:

$120.21-$90.49=$29.72

The length of the third side of the triangle is 8.

The image is that of a right angled triangle. A right angled triangle is a triangle in which one of the angles measure 90 degrees. The sum of angles in the triangle measure up to 180 degrees.

In order to determine the length of the third side, the Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

In the triangle, 15 is the length and 17 is the hypotenuse.

a²  + 15²  = 17²

a²  = 17²  - 15²

a = √(17² - 15² )

a = √(289 -225)

√64 = 8

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Answer:

As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give  call to its mother.

Step-by-step explanation

He said hi Ma.

Given: Diana is driving 182 miles to Orlando for a math convention.

She has already driven x miles of the trip.

So, the remianing distance = (182 - x) miles

Diana drives below 70 miles per hour for the remainder of the trip.

As we know, speed = distance/time

So, the time = distance/speed

The relation between time and speed are inversely

so, when speed decrease, time increase

so, the time of the remaining distance will be:

So, the answer is option D

The volume of the given figure is 1176 cubic cm.

The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).

The volume of the figure is calculated as,

Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )

Volume = 1176 Cubic cm

Hence, the volume of the figure will be equal to 1176 Cubic cm.

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Answer:

Step-by-step explanation:

Let d = daily fee in dollars

Let +m = milage charge in dollars

In words:

( Cost of rental ) = ( number of days rented )x( daily fee ) + ( miles driven )x( milage fee )

For her first trip:

(1) +240.5+=+4d+%2B+450m+

For her 2nd trip:

(2) +146+=+3d+%2B+200m+

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

Multiply both sides of (1) by +3+

Multiply both sides of (2) by +4+,

Then subtract (2) from (1)

Answer:

35 students

Step-by-step explanation:

So if every 3 boys there is 4 girls you can solve that there is 5 times the amount of girls to get to 20. So to solve for the boys you do the same.

3 x 5 = 15

That means there are 15 boys and 20 girls but we want to know the total so what you do is just add 15+20=35

So 35 total students.

Hope that helps and have a great day!

Answer:

I hope it will help you....

Answer:

319.532467532

Step-by-step explanation:

Answer:

shaded area = 538 mi²

Step-by-step explanation:

area of bottom rectangle =  14 * 8 = 112 mi²

area of middle rectangle = 7 * ( 5 + 8 + 30) = 301 mi²

area of the upper rectangle = 5 * 25 = 125 mi²

Total shaded area = 125 mi² + 301 mi² + 112 mi²

                               = 538 mi²

Answer:

  968 square miles

Step-by-step explanation:

Extending the horizontal line segments across the figure divides it into 3 rectangles:

  top: 5 mi × 25 mi

  middle: 17 mi × 43 mi

  bottom: 14 mi × 8 mi

The total area is the sum of products of length and width:

  A = (5×25 +17×43 +14×8) mi² = (125 +731 +112) mi² = 968 mi²

Answer:

7

Step-by-step explanation:

I mean the greatest common factor of a number and itself is just the number right?

Answer:

7

Step-by-step explanation:

We can list out the common factors between 7 and 7.

7: 1, 7

7: 1, 7

As you can see, their greatest common factor is 7.  

By taking a difference between mixed numbers, we can conclude that the distance left is 5/8 of a mile.

We know that the total length of the trail is 2½ miles, and Jorge hikes 1⁷/₈ miles before resting.

So the distance that he has left is equal to the difference between 2½ miles and 1⁷/₈ miles.

Remember that the mixed numbers can be rewritten as:

2½  = 2 + 1/2

1⁷/₈ = 1  + 7/8

So we need to find the difference:

(2 + 1/2) - (1 + 7/8) = ( 2  - 1) + (1/2 - 7/8)

= 1 + (4/8 - 7/8) = 1 - 3/8

Now we can simplify this so we get a single fraction:

1 - 3/8 = 8/8 - 3/8 = 5/8

From this, we can conclude that the distance left is 5/8 of a mile.

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The expression that shows the total oranges amir got in total is x-12 = 4. And amir got 16 oranges in all

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

example of linear expression is 2x+2y = 5. This is a linear expression with two variables x and y.

Let's represent the total no of oranges by x.

Therefore ,

2 bags of oranges with 6 in each bag will amount to 2×6 = 12 oranges.

an addition of 4 loose oranges . Therefore the total number of oranges = 12+4 = x

x = 12+4 or x-12 = 4

= 16

therefore amir got 16 oranges in all

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No, because a scalene triangle has to have all sides that are different lengths. 2 sides being 13 inches would mean that the triangle has 2 sides that are equal, making it an isosceles triangle.

Answer:

  no

Step-by-step explanation:

A triangle is scalene when its sides have three different lengths. Your triangle has two sides with the same measure, so it is isosceles, not scalene.

Answer:

13 24 56 23 56 78 166 Yan Lang po thank

The interest for Part 1 is approximately $385.10.

The interest for Part 2 is approximately $709.31.

The formula is as follows:

Interest is calculated as follows: Principal * Rate * Time

Where

Part 1:

$132,000 is the principal.

(Decimal) Rate = 12% = 0.12

Time = 8 days/365 days.

How much interest is there in Part 1?

Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10

Therefore, the interest for Part 1 is approximately $385.10.

Part 2:

$106,750 as the principal

(Decimal) Rate = 12% = 0.12

Time = 20 days / 365 days.

How much interest will there be in Part 2

Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31

Therefore, the interest for Part 2 is approximately $709.31.

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Step-by-step explanation:

Step 1: Write down the percent divided by 100 like this:  percent/100

Step 2: If the percent is not a whole number, multiply top and bottom by 10 for every number after the decimal point. (For example, if there is one number after the decimal, use 10, if there are two, fuse 100, etc.)

Step 3: Simplify (or reduce) the fraction

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

Given:

The actual height of office building is 13.4 m.

The estimated height of office building is 12 m.

Explanation:

The formula for the absolute error is,

Substitute the values in the formula to determine the absolute error.

The formula for the percent error is,

Substitute the values in the formula to determine the percent error.

So answer is,

Absolute error : 1.4 m

Percent error: 10.4%

Answer:

c) 4x = 20

x = 5

Step-by-step explanation:

Let the number of people in a van = x

Number of people in 4 vans = 4 *x = 4x

4x = 20

Divide both sides by 4

x = 20/4

x = 5

Given statement solution is :-The decision to renegotiate the egg prices should be based on the calculated probability (P) obtained from the z-score calculation.

To determine whether the diner should renegotiate their egg prices with their vendor, we need to assess the likelihood that the sample mean price will be higher than their current price of $4.75 per dozen. We can use the concept of the sampling distribution of the sample mean to make this assessment.

Given that the population standard deviation is known ($0.75) and the sample size is small (n = 5), we can assume the sampling distribution of the sample mean will be approximately normally distributed. The mean of the sampling distribution will be equal to the population mean ($5 per dozen), and the standard deviation of the sampling distribution (also known as the standard error) can be calculated by dividing the population standard deviation by the square root of the sample size.

Standard error (SE) = population standard deviation / √(sample size)

SE = 0.75 / √(5)

SE ≈ 0.3354

Now, we can calculate the probability that the sample mean price will be higher than $4.75 by standardizing the sample mean using the z-score formula:

z = (sample mean - population mean) / standard error

z = ($4.75 - $5) / 0.3354

z ≈ -0.445

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -0.445. Let's assume this probability is P.

If P is sufficiently small (typically less than 0.05), it indicates that the sample mean being higher than $4.75 is unlikely to occur by chance. In such a case, it would suggest that the diner should consider renegotiating their egg prices with their vendor.

However, if P is relatively large (greater than or equal to 0.05), it suggests that the sample mean being higher than $4.75 is reasonably likely to occur by chance. In this scenario, there may not be sufficient evidence to justify renegotiating the egg prices based solely on the sample mean.

Therefore, the decision to renegotiate the egg prices should be based on the calculated probability (P) obtained from the z-score calculation.

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Answer:

A. The model under-predicts the price of this diamond because the residual is positive.

Step-by-step explanation:

The diamond seller has listed its 0.8 weighting diamonds at a price of $10,999. The price of the diamond is set as the market maker. The model is used to predict the price of the diamonds. This model has under predicted the value of diamonds and actual price of diamonds must be higher.

The option that can be used to verify the trigonometric identity, \(tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)\) is option C;

C. \(tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)\)

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

\(tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)\)

The half angle formula for tangent indicates that we get;

\(tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}\)

\(\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}\)

When η = 0, we get;

\(-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}\)

\(cot\left(x \right) = \dfrac{cos(x)}{sin(x)}\)

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)\)

The correct option that can be used to verify the identity is option C

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Work Shown:

Complementary angles add to 90 degrees.

A+B = 90

(3x+18)+(2x+17) = 90

5x+35 = 90

5x = 90-35

5x = 55

x = 55/5

x = 11

Then we can determine each angle:

As a check: A+B = 51+39 = 90 to confirm the answer.

Step-by-step explanation:

48-16 is not an inequality,it's a simple subtraction operation. Please check and come again

Answer: the first thing is your answer :)

thx for the points

Step-by-step explanation:

g

(

x

)

=

x

2

−

3

The parent function is the simplest form of the type of function given.

f

(

x

)

=

x

2

The transformation being described is from

f

(

x

)

=

x

2

to

g

(

x

)

=

x

2

−

3

.

f

(

x

)

=

x

2

→

g

(

x

)

=

x

2

−

3

The horizontal shift depends on the value of

h

. The horizontal shift is described as:

g

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left

h

units.

g

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right

h

units.

In this case,

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of

k

. The vertical shift is described as:

g

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up

k

units.

g

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down

k

units.

Vertical Shift: Down

3

Units

The graph is reflected about the x-axis when

g

(

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: None

The graph is reflected about the y-axis when

g

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of

a

.

When

a

is greater than

1

: Vertically stretched

When

a

is between

0

and

1

: Vertically compressed

Vertical Compression or Stretch: None

Compare and list the transformations.

Parent Function:

f

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: Down

3

Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

image of graph

Answer:

65°

Step-by-step explanation:

The sum of the measures of complementary anfglwes is 90°.

Let a = the measure of the complement.

m<1 + a = 90

25 + a = 90

a = 65