Mast 1 broadcast radio signals that can be heard within a radius of 15km.
Mast 2 broadcast radio signals that can be hear within a radius of 20km.

Using the slope-intercept form, the slope, y-intercept and equation of the graph are -1/7, 5 and y = -1/7x + 5 respectively

The general equation of straight line is given in slope-intercept form as

y = mx + c.

In the graph given, the function is a straight line with slope and y-intercept.

Taking two points from the graph.

The slope of the equation can be calculated using the points

slope (m) = y₂ - y₁ / x₂ - x₁

m = 1 - 0 / -2 - 5

m = 1 / -7

The slope is -1/7

From the graph, we can see the point in which the line passes through the y - axis and it is known as the y - intercept.

The y - intercept on this graph is 5

The slope- intercept form can be written as

y = -1/7x + 5

a) When x = -1, y = ?

y = -1/7x + 5

y = -1/7(-1) + 5

y = 1/7 + 5

y = 36/7

b) When y = 7, x = ?

y = -1/7x + 5

7 = -1/7x + 5

x = -14

c) The y - intercept of the graph is 5

d) The x-intercept of the graph is at -2.2

e) The slope of the line is -1/7

f) The equation of the line is given as y = -1/7x + 5

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Number of servings that are in a full box of cereal is 8.33 servings

Total quantity of cereal contains in the box = [tex]12\frac{1}{2}[/tex] cups

Convert the mixed fraction to simple fraction

[tex]12\frac{1}{2}[/tex] cups = 25/2 cups

Total quantity of cereal eats in each serving = [tex]1\frac{1}{2}[/tex] cups

Convert the mixed fraction to simple fraction

[tex]1\frac{1}{2}[/tex] cups = 3/2 cups

Number of servings in a full box of cereal = Total quantity of cereal contains in the box ÷ Total quantity of cereal eats in each serving

Here we have to use the division

Substitute the values in the equation

Number of servings in a full box of cereal = 25/2 ÷ 3/2

= 25/2 × 2/3

= 25/3

= 8.33

Therefore, a full box contains 8.33 servings

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The simplest form of the ratio r:h:u is 5 : 8 : 14.

What is the ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

We have,

r : h  = 5 : 8   .........(i)

h : u =  4:7    ........(ii)

Multiplying the (i) and (ii) by numbers that will make 'h' have the same value in the ratios

Multiplying (i) by 1

(r : h)*1  = (5 : 8)*1

= r : h  = 5 : 8  

Multiplying (ii) by 2

(h : u)*2 =  (4:7) *2

= 8 : 14

the ratio r : h : u in the simplest form = 5 : 8 : 14.

Hence, the simplest form of the ratio r:h:u is 5 : 8 : 14.

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Peggy's method will make more money.

Compound interest is the sum of interest on principal and interest on interest of previous period.

Given, that principal is same in both cases,

Also, Peggy will get total interest = 2×6 = 12%.

Whereas, Larry will get 1 % per quarter compounded quarterly.

Therefore, Larry will get (101/100)⁸%.

Hence, 12 > (101/100)^8 and Simple interest method will make more money.

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Appraisal , If the insured and this insurer are unable to reach an understanding regarding the actual cash value or the extent of the loss, then, upon the written demand of either party, each shall choose a qualified and impartial appraiser and notify the other of the appraiser selected within 20 days of the demand.

What does the word "appraisal" mean?

A valuation by an authorized person of a piece of property, such as real estate, a company, a collectible, or an antique, is known as an appraisal.          

                                            An accreditation from a regulatory body overseeing the appraiser's area of practice is required for an authorized appraiser.

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There are 45 different ways in which two of them can be selected as the best students in the class.

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations).

A k-combination of a set S is officially defined as a subset of S's k unique elements.

Total number of students = 10

Number of students to be selected = 2

No. of ways = 10C2

                   = (10*9)/2

                   = 5*9

                   = 45

Hence, there are 45 different ways in which two of them can be selected as the best students in the class.

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The inverse of y = √x - 10 + 4 is y = x^2 + 26 + 8x

What in mathematics is inverse?

A function that "undoes" another function is known as an inverse in mathematics. To put it another way, if f(x) produces y, then y will produce x when y is fed into f's inverse function. Invertible refers to a function that has an inverse, which is represented by the symbol f1.

Given that:

J(x) = √x - 10 + 4

y = √x - 10 + 4

now replace x with y

x = √y - 10 + 4

now solve for y , x = √y - 10 + 4

x + 4= √y - 10

Squaring both the side

x^2 + 16 + 8x = y - 10

y = x^2 + 26 + 8x

Hence the inverse of y = √x - 10 + 4 is y = x^2 + 26 + 8x

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Answer:

B

Step-by-step explanation:

Answer choice B would equal -3/4

Answer: A) y = 5x – 13

Step-by-step explanation:

The equation is y=mx + b

We know the slope is 5 and the y-intercept is at ( 0, -13)

So our equation is y = 5x - 13

So, the answer is A

Converting 7π/21 to degrees will be 60°.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees. Although it is not a SI unit—the radian is the SI unit of angular measure—it is mentioned as an accepted unit in the SI brochure.

Angles are measured in terms of radians. Angles are measured using the degree and radian units. In calculus and the majority of other branches of mathematics, angles are typically or generally measured in radians.

It should be noted that in order to convert radians yo degrees, you've to multiply by 180/π since a full circle is 360°.

This will be illustrated as:

= 7π / 21 × 180 / π

= 7/21 × 180

= 60°

The value is 60°.

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Answer:

3) 4.47 miles

Step-by-step explanation:

AC is the the hypotenuse

so, 6*6 = 36, and 4*4 = 16

36-16=20

square root of 20 is 4.472135...

so, 4.47

Answer:

124

Step-by-step explanation:

1,240/10 is 124. You divide by 10.

The number of packages of 10 for the 1240 pot holders is 124.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of pot holders = 1240

Number of pot holders in one pack = 10

The number of packages.

= 1240 ÷ 10

= 1240/10

= 124

Thus,

The number of packages of 10 is 124.

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The list that shows the low tides from lowest to highest is -1.6 < -0.8 < 1.58 < 2.6 and this can be determined by using the given data.

The correct option is A).

Given,

In the question:

The table shows the dates, times, and high and low tide heights.

Now, According to the question:

The following steps can be used in order to determine the list that shows the low tides from lowest to highest:

Step 1 - According to the given table, the low tide on Thursday, Feb 7 at 1;26 am is 2.6 ft.

Step 2 - According to the given table, the low tide on Thursday, Feb 7 at 2:29 pm is -0.8 ft.

Step 3 - According to the given table, the low tide on Friday, Feb 8 at 2:24 am is 1.5 ft.

Step 4 - According to the given table, the low tide on Friday, Feb 8 at 3:16 pm is -1.6 ft.

Step 5 - Arrange the data of low tides given in the above steps in increasing order:

-1.6 < -0.8 < 1.58 < 2.6

The correct option is A).

Hence, The list that shows the low tides from lowest to highest is -1.6 < -0.8 < 1.58 < 2.6 and this can be determined by using the given data.

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Answer:

0

Step-by-step explanation:

10x + 12 = 2(5x+6)

or, 10x + 12 = 10x + 12

or, 10x - 10x = 12 - 12

or, 0 = 0

.

. . so, 0 is the answer.

Step-by-step explanation:

10x + 12 = 2(5x + 6)

10x + 12 = 10x + 12

10x + 12 = 10x + 12

10x + 12 - 12 = 10x + 12 - 12

10x = 10x

10x - 10x = 10x - 10x

____________________________________________

Answer:

f(x)=7

Step-by-step explanation:

f(x)= 1/2x+5 ; x=4

f(4)= 1/2(4)+5

f(4)= 2+5

f(x)=7

Hope this helps, because I just did this lesson and I was confused at first, but with practice you will get it!

The solution to the given inequality that is x+4y<4 is (-8,-2) as it only gives the correct result for the equation.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Here,

x+4y<4

(-8,-2)

-8+4*-2=-16<4

The provided inequality, x+4y4, has a solution of (-8,-2) because it alone provides the solution to the equation.

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Answer: No, it is not proportional.

Explanation:

We can see that Diego opened an account with $20, meaning that there is going to be a y-intercept of 20 in a graph. Therefore, with a y-intercept of 20 and not zero, we can say that there is not a proportional relationship between and time and amount saved for Diego.

The system is consistent and independent.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have the system of equations:

y = 4x - 4

y = -4x + 4.

Let's take the quotient between both the equations as;

(y/y) = (4x - 4)/(-4x + 4)

1 = (4x - 4)/(-4x + 4)

Solve for x;

1*(-4x + 4) = 4x - 4

-4*x + 4 = 4x - 4

-4x - 4x = -4 - 4

-8*x = -8

x = -8/-8 = 1.

To find the value of y, we can input this value of x in one of the equations:

y = 4 x1 - 4 = 0.

Then we have only one solution, (1, 0).

Therefore, the system is consistent and independent.

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Yes, these values indicate a difference in popularity. Using a 0.01 significance level, the p-value for this test is 0.0018, which is less than the significance level.

This means that there is statistical evidence to support the claim that there is a difference in the candidate's popularity between men and women.

1. The candidate has a population of voters that he wishes to test to see if there is a difference in his popularity between men and women.

2. He conducts a survey of 250 men and 250 women, 44% of the men favoring his candidacy and 52% of the women favoring his candidacy.

3. To determine if there is a significant difference between the two samples, we first calculate the difference in proportions between the two groups:

52% - 44% = 8%.

4. We then use a 0.01 significance level to conduct a two-tailed z-test for proportions to determine if there is a statistically significant difference between the two groups.

5. The p-value for this test is 0.0018, which is less than the significance level of 0.01.

6. This means that there is statistical evidence to support the claim that there is a difference in the candidate's popularity between men and women.

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Answer:  Just add them up. 5 1/20

Step-by-step explanation:

1+1+2=4. For the fractions, find the LCM. The LCM is 20 so you make all the fractions denominator 20. 2/20, 4/20, 15/20. Now you get 5 1/20 in the end

Answer: 39 crackers

Step-by-step explanation:

There are seven days a week

Only Friday, he eats half, so 6 left

6 times 6 = 36

36+ 3= 39

An inequality that combines two simple inequalities is known as a compound inequality.

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Answer:

$3624.48

Step-by-step explanation:

This is a bank interest formula that is -> P(1 +/- r/n)^rt

3500(1 + 0.035/12)^12*1

The answer is 3624.48

The cyclist takes 0.36 hours to travel 4.5 miles.

Here given that,

The distance travelled by the cyclist 3.75 miles.

Time = 0.3 hour

Distance / Time = Speed

By substituting,

3.75 / 0.3

= 12.5 miles per hour is the speed.

2) Distance = 4.5 miles, speed = 12.5 miles per hour.

Distance / Speed = Time

Time = 4.5 / 12.5

=0.36 hours

Therefore it takes 0.36 hours to travel 4.5 miles.

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Answer:

Length = 50 ft

Width = 15 ft

Area = 750 ft²

Step-by-step explanation:

Define the variables:

Create two equations with the given information.

Given:

⇒ 3L = 10W

Given:

⇒ 2W + 2L = 130

Rearrange the second equation to make W the subject:

⇒ 2(W + L) = 130

⇒ W + L = 65

⇒ W = 65 - L

Substitute this into the first equation and solve for L:

⇒ 3L = 10(65 - L)

⇒ 3L = 650 - 10L

⇒ 13L = 650

⇒ L = 50

Substitute the found value of L into the second equation and solve for W:

⇒ 2W + 2(50) = 130

⇒ 2W + 100 = 130

⇒ 2W = 30

⇒ W = 15

Therefore:

Substitute the found values of W and L into the formula for area of a rectangle to find the area of the pool:

⇒ Area = W × L

⇒ Area = 15 × 50

⇒ Area = 750 ft²

Answer:i don’t know

Step-by-step explanation:

As per the requirement of body fat measurement, we measure the body fat in continuous data type.

Measureable data is referred to as continuous data. The values in this data are not constant and can take on an endless number of different forms. You can also divide these measures up into smaller, independent components.

Since it may employ decimal points and have infinite values, it is more precise and comprehensive than discrete data.

The type of data that would be used to describe percent of body fat is continuous data. An example of the continuous data type is Height of a person.

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If a car is traveling at 50 mph due south at a point 1 mile north of an intersection. the radar gun register at -62.6 mph.

Distance can be defined as how far an object is from another object.

Distance of the first car north of the intersection point =y

Distance of the police car west of the intersection  =x

Distance between the cars =s

s² =x² +y²

x=1.4 miles or 0.25 miles

y =1/2 miles or 0.50 miles

Pythagoreans theorem

Distance between cars

s =√x²+y²

s=√(0.25 miles)² +(0.50 miles)²

s =0.559 miles

Hence,

ds/dt = [0.25 miles/ 0.559 miles (-40 mph)] + [0.50 miles/0.559 miles (-50 mph)

ds/dt = -17.89 + -44.7

ds/dt = - 62.59mph

ds/dt =- 62.6 mph (Approximately)

Therefore the distance is 62.6 mph.

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