Mathematics High School

## Answers

**Answer 1**

The **solution **used to make 40% of salt solution is** 12 grams** and 70% of **salt **solution is **8 grams.**

Let us consider 'a' represents the 40% of salt in water.

And 'b' represents the 70% of salt in water.

Total salt required to make 52% salt **solution** = 20 grams

Required equations is :

a + b = 20

⇒ a = 20 - b ___( 1 )

40% of a + 70% of b = 52% of 20 grams

⇒ 0.40a + 0.70b = 10.4 ___( 2 )

Substitute the** value** of 'a' in equation ( 2 ) from (1) we get,

0.40( 20 - b ) + 0.70b = 10.4

⇒8 - 0.40b + 0.70b = 10.4

⇒ 0.30b = 10.4 - 8

⇒ b = 2.4 / 0.30

⇒ b = 8

⇒ a = 12

Therefore, the **solution **used by Serena for 40% is 12 grams and 70% solution is 8 grams.

The above question is incomplete , the complete question is:

Serena is making an experiment. For that, she needs 20 grams of a 52% solution of salt. She has two large bottles of salt water: one with 40% and the other with 70% of salt in them. How much of each must she use to make the solution she needs?

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## Related Questions

9,37,39,13 Find the median and mean of the data set

### Answers

Rearrange first

9,13,37,39

median=13+37÷2

=25

median is 25

mean=9+13+37+39÷4

=98÷4=24.5

Mean=24.5

the meese's company claims that you should find an average of 240 240 orange candies in the jumbo bag of 600 600 candies. the orange candies are normally distributed and have a standard deviation of 6 6 candies. if you sampled a number of these bags and found between 225 225 and 250 250 orange pieces, how would you write this interval as a probability?

### Answers

The** probability **of finding between 225 and 250 orange pieces in a sample of jumbo bags is** 0.7966.**

The **probability **of finding between 225 and 250 orange pieces in a sample of jumbo bags can be written using the standard normal distribution. This is done by calculating the z-score of the interval between 225 and 250 and then calculating the probability of getting a value between the **two given points**.

The formula for calculating the z-score is (x-μ)/σ, where x is the value of the interval, μ is the mean (240) and σ is the standard deviation (6). The z-score of the given interval is equal to (-2.5 - (-5))/6 = 0.83.

The probability of getting a **value between** 225 and 250 is equal to the area under the normal curve between the two given points. This area is equal to the** cumulative** probability of the z-score of 0.83, which is equal to 0.7966.

Therefore, the probability of finding between 225 and 250 orange pieces in a sample of jumbo bags is 0.7966.

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Given the functions f(x) = 3(x-4) and g(x) = 2(x - 3), for what values of x is f(x) > g(x)? Use the

properties of inequality and other properties to justify your solution.

### Answers

The values of '**x**' for which **f(x) > g(x) **is when x > 6.

What are inequalities and their types?

Inequality is a relation that **compares **two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When **a > b** is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Are two functions f(x) = 3(x - 4) and g(x) = 2(x - 3).

The values of 'x' for which f(x) > g(x) is **3(x - 4) > 2(x - 3)**.

3x - 12 > 2x - 6.

3x - 2x > 12 - 6.

x > 6.

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Find a possible formula for the trigonometric function whose values are in the following table.

### Answers

**Answer:**

-3

**Step-by-step explanation:**

I WILL MARK BRAINLIST AND SET THIS 100 POINTS BUT PLS ANSWER CORRECTLY.THIS IS GRADED OUT OF 100% I need 80% to pass for an A- PLS YALL!

### Answers

**Answer:**

The third angle is 60

**Step-by-step explanation:**

The interior angle of a triangle is equal to the 180 minus the exterior angle.

[tex]180-80= 100[/tex]

So one of the interior angles is equal to 100

All of the interior angles of a triangle add up to 180

[tex]180=100+20+x[/tex]

[tex]x=60[/tex]

pleaseeee help quicklyyy

### Answers

**Answer:**

**Step-by-step explanation:**

area of field=1/2(a+b)h

a=12

b=20

h=?

h=pythagoras theorem

a²+b²=c²

a²+8²=17²

a²+64=289

a²=289-64

a²=221

a=√221

a=14.9

area of field=1/2(12+20)14.9

area=238.4m²

£19.75×3=£59.25

A student bought a pair of sunglasses in the USA. He paid $35.50 in the USA. In England, an identical pair of sunglasses costs £26.99 The exchange rate is £1 = $1.42. How much more did he pay for them in England compared to the USA?

### Answers

**Answer:all you do is multiply 26.99*1.42**

**this equals 38.33 dollars**

**35.50 is less than 38.33**

**thus, USA is cheaper than England.**

**Step-by-step explanation:**

The coordinates of midpoint M and endpoint C of a segment are M(25.4, 60.1) and C(18.3, 72.5). Find the coordinates of the other endpoint.

(11.2, 84.9)

(21.85, 66.3)

(32.5, 47.7)

(37.8, 53)

### Answers

The **coordinates **of the other **endpoint** include the following: C. (32.5, 47.7).

How to determine the coordinates of BC?

In order to determine the **midpoint** of a **line segment** with two (2) endpoints, we would add each point together and then divide by two (2):

Midpoint BC = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Next, we would determine the coordinate of B with **midpoint** AB at (25.4, 60.1) as follows;

25.4 = (18.3 + x₂)/2

50.8 = 18.3 + x₂

x₂ = 50.8 - 18.3

x₂ = 32.5.

For the other co-ordinate of B on **line segment** BC, we have:

60.1 = (72.5 + y₂)/2

120.2 = 72.5 + y₂

y₂ = 120.2 - 72.5

y₂ = 47.7.

Therefore, the coordinate of B is (32.5, 47.7).

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question: 2.35 a contractor wishes to build 9 houses, each dif- ferent in design. in how many ways can he place these houses on a street if 6 lots are on

### Answers

There is only 1 **way** to place the houses on the street.

If the contractor wishes to build 9 **houses**, each different in design, and there are 6 lots available on the street, there are 6 choose 9 (written as 6C9) ways to place these houses.

However, this number is not possible since 6C9 = 0,

which means there are no **combinations** of 6 elements taken 9 at a time.

A more appropriate calculation would be 6 choose 6 (written as 6C6), which represents the **number of ways **to place the 9 houses on the 6 available lots if each house must occupy a lot.

In this case, 6C6 = 1,

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Joey lives in Ohio and his cousin Grayson lives in Oregon. On Wednesday Joey and Grayson meet online to play their favorite video game together. Joey gets home from school at 4:20 p.m est, and Grayson gets home at 4:00 p.m pst. Grayson logs on when he gets home from school what time est do the boys meet to play the game?

Morgan is traveling from Dallas, Texas to San Francisco California. She has the choice of two airlines . She will check two bags, want wi-fi access and does not want a meal on the plane. She does not mind a layover if it will get her a better deal. Which of the following is the ever desk and how much would she save ?

### Answers

Based on the information, she can infer that the **children** meet at 7:00 pm **EST** to play video games. Additionally, the best flight ticket for Morgan is **Sunset** **airline** since it is $12 cheaper than Autumn airline.

How to know the EST time at which the children connect?

According to the information, Joey is in Ohio and Grayson is in Oregon. These two states have different time zones, in the case of Ohio it is (-5) and in the case of Oregon it is (-8). Therefore, they connect to play at 7:00 pm **EST **because when Grayson arrives at his house at 4:00 pm, in Ohio it is 7:00 pm. However, Joey is already connected since 4:20 pm that he arrived at his house.

What is the best ticket for Morgan?

To identify which is the best ticket for Morgan, we must add all the services that she wants to include in her plane trip and then find the difference between the value of the two tickets.

**Sunset airline:**

$219 + $80 + $30 = $329

Autumn airlines:

$261 + $40 + $40 = $341

$341 - $329 = $12

According to the above, **Sunset airlines** ticket is cheaper.

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# 7.

5 years ago Riley bought a dryer. Every year

for the past 5 years the dryer has lost 15 percent

of its value. The current value of the dryer is

$100. How much did Riley pay for the dryer 5

years ago?

### Answers

The amount that Riley paid for the **hair dryer **is $225.37.

How much was paid for the hair dryer?

Given the information in the question, the **dryer **is **depreciating **in value. **Depreciation **is when the value of an asset declines with the passage of time.

The formula that can be used to determine the amount paid for the **hair dryer **is:

p = FV / (1 - r)^n

Where:

p = current price of the **dryer **r = rate of depreciation n = number of years

p = $100 / (1 - 0.15)^5

p = $100 / 0.85^5

p = $225.37

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The population of Japan,

, is

The population of Brazil,

, is

You are given that

It can be shown that

The population of Pakistan is

.

You are given that

Work out the population of Pakistan.

Give your answer in standard form.

### Answers

The **population** of Pakistan is calculated as; 1.82 × 10⁸

How to solve proportion problems?

The parameters for the **population** are;

**Japan **Population; J = 1.30 × 10⁸

**Brazil** Population; B = 1.95 × 10⁸

Now, the **ratio** of J:B = x : x + 5

Thus;

(1.30 × 10⁸)/(1.95) × 10⁸ = x/(x + 5)

Solving this gives x = 10

Now, we are told that;

J:P = x : x + 4

Where P is **pakistan population**

Thus;

(1.30 × 10⁸)/P = 10/(10 + 4)

(1.30 × 10⁸)/P = 10/14

P = 14(1.30 × 10⁸)/10

P = 1.82 × 10⁸

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in a random sample of eighteen people, the mean time at lunch was 28.4 minutes with a standard deviation of 8.2 minutes. assuming the data are normally distributed, what would be the 85% confidence interval?

### Answers

The 85% **confidence interval** for the mean time at lunch is (25.01, 31.79) minutes.

In a **random sample** of eighteen people, the **mean** time at lunch was 28.4 minutes.

**Standard deviation** of 8.2 minutes.

A common method to calculate the confidence interval for the mean of a normal distribution is to use the Z-score. For a 85% confidence interval, the Z-score is 1.44. Therefore, the confidence interval can be calculated as:

The confidence interval formula in statistics is used to describe the amount of uncertainty associated with a sample estimate of a population **parameter**.

If [tex]$$n \geq 30$ & Confidence Interval $=\bar{x} \pm z_{\alpha / 2}(\sigma / \sqrt{ n})$ \\[/tex][tex]$$n\le 30$ & Confidence Interval $=\bar{x} \pm z_{\alpha / 2}(\sigma / \sqrt{ n})$ \\[/tex]

Where,

n= Number of terms

[tex]$\overline{\mathrm{x}}[/tex]= Sample Mean

[tex]$\sigma[/tex]=Standard Deviation

[tex]$z_{\alpha / 2}[/tex]= Value corresponding to a2 in z table

[tex]$t_{\alpha / 2}[/tex]= Value corresponding to a2 in t table

[tex]$\alpha[/tex]=(1 - Confidence Level /100)

So for the given data, the confidence interval would be:

=28.4 ± 1.44 * 8.2 / √18

=28.4 ± 1.44 * 8.2 / 4.24

=28.4 ± 3.39

=(25.01, 31.79)

Therefore, the 85% confidence interval for the mean time at lunch is (25.01, 31.79) minutes.

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Please help me with this

### Answers

Working out and answer:

One way to compute a 15% tip for a bill is to multiply it by 0.15.

A restaurant bill was $42.40.

what do i do ??????

im in middle school

### Answers

The **amount **of **tip **will be $6.36. And the **total amount **of the restaurant bill with the tip will be $48.76.

What is the percentage?

The **amount **of any product is given as though it was a proportion of a hundred. The **ratio **can be expressed as a quarter of 100. The phrase % translates for one **hundred percent**. It is symbolized by the character '%'.

The **percentage **is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

One way to **compute **a 15% tip for a bill is to **multiply **it by 0.15. A restaurant bill was $42.40.

Then the **amount **of tip is given as,

Tip amount = $42.40 x 0.15

Tip amount = $6.36

The** total amount **is given as,

Total amount = $42.40 + $6.36

Total amount = $48.76

The **amount **of **tip **will be $6.36. And the **total amount **of the restaurant bill with the tip will be $48.76.

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Montana decided to start his ball from the second diamond from the left along the bottom rail. He is planning to aim at the third diamond from the top right. If he hits the ball sufficiently hard, will the ball eventually reach a pocket? If so, show the path of the ball. Explain the steps used to solve the problem and write a concluding statement

### Answers

**Answer:**

To determine whether the ball will eventually reach a pocket, we need to determine if the ball will collide with any other balls or obstacles on the way to its target. If there are no obstacles, and the ball has enough force and the correct trajectory, it will reach the target pocket.

To show the path of the ball, we can draw a straight line connecting the starting position and the target pocket. This line represents the trajectory of the ball if it is not obstructed by any other balls or obstacles.

In conclusion, without any obstacles in the way, if Montana hits the ball with enough force and the correct trajectory, the ball will reach the target pocket. It is important to consider any potential obstacles or interference when planning a shot in billiards.

16) show all ur equation steps

### Answers

The system of equations has unique **solution** (4, -17).

What is a linear system of equations?

A system of linear **equations** consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The **solution** to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of **equations** are y=-6x+7--------(I) and 4x+3y=-35 --------(II).

Substitute equation (I) in equation (II0, we get

4x+3(-6x+7)=-35

4x-18x+21=-35

-14x=-56

x=4

Substitute x=4 in equation (I), we get

y=-6(4)+7

y=-24+7

y=-17

So, solution is (4, -17)

Here, a₁=6, b₁=1, c₁=-7

a₂=4, b₂=3 and c₂=35

Now, 6/4 = 1/3

3/2≠1/3

Equations has unique solution (Intersecting lines)

Therefore, the system of equations has unique **solution** (4, -17).

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please solve for x..

### Answers

The **value **for **question 5** is **15 **and for the** question 6** is **10**.

Do you know the Chord Theorem?

This theorem says that if **two chords **intersect, the **product **of its segments will be **equal**.

The question gives two circles each one with two chords. For solving the exercise, you should apply the Chord Theorem.

**Exercise 5**

Segments of chord 1 = 23 and x

Segments of chord 2 = 23 and 15

Applying the Chord Theorem, you have:

23*x=23*15

23x=345

x=345/23

x=15

**Exercise 6**

Segments of chord 2= x+5 and 28

Segments of chord 2 = 2x and 21

Applying the Chord Theorem, you have:

(x+5)*28=2x*21

28x+140=42x

-42x-28x=-140

-14x=-140

x=-140/-14

x=10

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Shopping at savers mart, Lisa buys her children four shirts and three pairs of pants for $85.50. She returns the next day and buys three shirts and five pairs of pants for $115.00. What is the price of each shirt and each pair of pants?

### Answers

The **price** of each **shirt** is $7.5.

The price of each **pant** is $18.5.

What is an equation?

An **equation** isa mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

**Cost of shirts** = x

**Cost of pants** = y

Lisa buys her children four shirts and three pairs of pants for $85.50.

She returns the next day and buys three shirts and five pairs of pants for $115.00.

This means,

We can make two **equations**.

4x + 3y = 85.50

3x + 5y = 115

Now,

4x + 3y = 85.50

4x = 85.50 - 3y

x = (85.50 - 3y)/4

**Substituting** in 3x + 5y = 115.

3 (85.50 - 3y)/4 + 5y = 115

256.5 - 9y + 20y = 460

11y = 460 - 256.6

11y = 203.4

y = 18.5

And,

x = (85.50 - 3y)/4

x = (85.50 - 55.5)/4

x = 30/4

x = 7.5

Thus,

The **cost** of the **shirt** is $7.5.

The cost of the **pant** is $18.5.

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I NEED HELP ASAPPPP!!!

Fill in the blanks.

First bulb: When 3 is the input, the output is _____. When 10 is the input, the output is _______.

Second bulb: When 3 is the input, the output is _____. When 10 is the input, the output is _______.

### Answers

When 3 is the **input**, the output is 30 and When 10 is the input, the output is 150.

What is Ratio?

A ratio is an ordered **pair** of numbers a and b, written a / b where b does not equal 0.

We need to find the **output** When 3 is the input and 10 is the input.

When 3 is the input, the output is 30. When 10 is the **input**, the output is 150 Based on the plots, both bulbs have y increasing as x increases.

Therefore, first bulb and second bulb are both **increasing**.

Hence, When 3 is the input, the **output** is 30 and When 10 is the input, the output is 150.

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a city received more than 16 in of snow the inequality is

### Answers

The **inequality **of the** statement **is x > 16

How to determine the inequality

From the question, we have the following parameters that can be used in our computation:

a city received **more than **16 in of snow

In **inequality**, more than mean >

So, we have the following representation

Snow > 16

Represent the **snow **with x

So, we have the following representation

x > 16

Hence, the **inequality **is x > 16

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The bar graph shows the number of floral arrangement sales each day for one week. What percent of the sales were on Friday or Saturday? Round to the nearest hundredth of a percent.

### Answers

The **percent **of sales happened on **Friday **and **Saturday **are respectively, 26.3% & 31.6%

What is the percentage?

The percentage is a mathematical term, which means a number or a **ratio **which is represented in **fractions **of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

The bar graph,

In which, **Horizontal **digits are representing number of shirts,

And **vertical **component is representing week days

The number of shirts sold on Friday = 50

The number of shirts **sold **on Saturday = 60

Percentage of sales on Friday = ?

**Percentage **of sales on Saturday = ?

Total sales = Monday + Tuesday + Wednesday + Thursday + Friday + Saturday

= 15+ 10 + 20 + 35 + 50 + 60

= 190

Percentage of sales on Friday = (50/190)x100

= 26.300 %

Percentage of sales on Saturday = (60/190)x100

= 31.600 %

Therefore, the percentage on Friday and Saturday are respectively, 26.3% & 31.6%

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Please help! so stuck on this! (Find the standard form of the equation and explain)

### Answers

**Answer:**

The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side.

**Step-by-step explanation:**

Jaya is the middle of three siblings whose ages are consecutive even integers. If the sum of their ages is 84, find Jaya’s age

### Answers

**Answer:**

26

**Step-by-step explanation:**

Let jaya's age be a, so consecutive EVEN #s can be written as

a, a+2, a+4

sum = 84 = 3a +6

so 3a = 78

a=26

Find all the missing sides and angles of this triangle. Round to the nearest tenth if necessary.

Right triangle ABC. Hypotenuse = 7 units. Angle B = 70 degrees.

### Answers

**Triangle **ABC with a **hypotenuse **of 7 units and angle B equal to 70 degrees,

side AC is 5.3 units side BC is 4.7 units. Angle C is 20 degrees.

How to find the sides of the triangle

Since triangle ABC is a **right triangle **and angle B is 70 degrees, it can be deduced that angle C must be 90 - 70 = 20 degrees.

assuming

length of side AC = a

length of side BC = b.

Using the **Pythagorean theorem**, we can find the values of a and b.

a^2 + b^2 = 7^2

a^2 = 7^2 - b^2

a = √(7^2 - b^2)

Using the **tangent function **

tan C = b/a

tan 20 = b/√(7^2 - b^2)

Solving for b, we get:

b = tan(20) * √(7^2 - b^2)

We can use numerical methods to find the approximate value of b. Using a calculator, we can find that b is approximately 4.7. Rounding to the nearest tenth, b is 4.7 units.

Finally, using the Pythagorean theorem again, we can find the value of a:

a^2 + b^2 = 7^2

a^2 = 7^2 - b^2 = 7^2 - 4.7^2

a = √(7^2 - 4.7^2)

a = √(7^2 - 22.09)

Using a calculator, we can find that a is approximately 5.3. Rounding to the nearest tenth, a is 5.3 units.

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Which graph below does not represent a function of x? A B 5432 1 0 1 2 3 4 5 S43N 5 y 2 -5 -4 -3 -2 -1 0 -1 -2 24EN -4 -5 1 2 3 4 5 C D 5 3 2 0 1 2 3 4 5 5 737 7 4 2 1 -5-4-3 -2 -10 -1 N345 -2 -4 -5 DU 1 2 3 4 5

### Answers

The **graph **that represents the compound **inequality **–3 < n < 1 is option C.

What is inequality?

The two sides of a **mathematical **equation having an **inequality **must be equal. We compare two values via inequality rather than equations. The equal sign is replaced by the signs less than (or less than or equal to), greater than (or greater than or equal to), or not equal to.

The straight line from -3 to 1 with a hollow circle at the -3 point and the 1 point serves as the graph for the compound inequality -3 n 1. This is because n can only have values larger than -3, excluding -3, and less than -1, excluding -1, according to the symbol.

Therefore, the graph that represents the compound inequality –3 < n < 1 is option C.

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Shawn walks 5 miles in a southeast direction from his house. He stops for lunch then walks 6 miles in a northeast direction from his lunch spot. What is the shortest distance Shawn can walk to return home.

### Answers

Shortest **distance** to reach home = 7.81 miles

What is Pythagoras theorem?

**Pythagoras** theorem states that "In a **right**-angled triangle, the **square** of the **hypotenuse** side is equal to the **sum** of squares of the other two **sides**".

Given, Shawn walks 5miles in southeast from his house.

After having lunch he walks 6 miles north east.

Angle between both **directions** is 90°.

By the figure

AB = 5miles

BC = 6 miles

Shortest distance to return home is AC

By **Pythagoras** theorem

AC² = AB² + BC²

= 5² + 6²

AC² = 25 + 36

AC² = 61

AC = √61

AC = 7.81 miles.

Hence, 7.81 miles is the shortest **distance** to reach home.

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Finding the Error

A 2-column table with 4 rows. Column 1 is labeled Tons with entries 2, 4, 10, 12. Column 2 is labeled Pounds with entries 4,000, 8,000, 20,000, 40,000. 40,000 is crossed out. An arrow goes from 2 to 12 and a second arrow goes from 4,000 to 40,000.

What error did the student most likely make?

The student multiplied by 6 instead of 10.

The student multiplied by 10 instead of 6.

The student used the ratio of 1:4,000 instead of 2:4,000.

The student used the ratio of 2:2,000 instead of 1:2,000.

### Answers

The student most likely made the error of using the ratio of 2:2,000 instead of 1:2,000

A school has 120 students. On Friday, 72 students went on a field trip. What percent of the students did NOT go on the field trip?

### Answers

The **percentage **of the students who did not go on the **trip **will be 40%.

What is the percentage?

The **percentage **is defined as representing any **number **with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a school has 120 students. On Friday, 72 students went on a field trip.

The number of the students who did not go to the trip are:-

N = 120 - 72 = 48

The percentage will be calculated as:-

Percentage = 48 / 120

Percentage = 0.4 x 100

Percentage = 40%

Therefore, the total of 40% of the students will not have attended the trip.

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suppose that i decide to connect both 9v battery terminals ( and -) to the same row on the same side of the central ravine. there is a problem with this idea. what is the problem?

### Answers

Literally nothing occurs. On the off chance that the** two terminals** are at an equivalent voltage, no ongoing streams, any more than if you contacted two impartial bits of metal together.

Cases 1 and 3 are basically something very similar. There's a **voltage** difference, so current normally streams. In any case, you don't have a circuit, so when **electrons** stream from the lower positive voltage (which is zero assuming it's released) to the higher positive terminal, the electrons develop and make a static charge that balances the voltages. This occurs in a small part of a second, so the current is negligible, and voltage promptly stops.

The **standard metric unit** on electric potential difference is the volt, truncated V and named to pay tribute to Alessandro Volta. One Volt is identical to one Joule per Coulomb. In the event that the electric potential difference between two areas is 1 volt, one Coulomb of charge will acquire 1 joule of potential energy when moved between those two areas. In the event that the electric potential difference between two areas is 3 volts, one coulomb of charge will acquire 3 joules of potential energy when moved between those two areas.

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