A dentist kept a record of the number of new cavities his patients had per year for the last 10 years. The scatterplot below shows the average number of new cavities per year for patients in the 4-to 32-year age range. Which of the following best describes the trend line of the data shown in the scatterplot? O a horizontal line a line with a negative slope, a line with a positive slope,no trend line

Answer:

C

Step-by-step explanation:

The average change in the amount of flour is the sum of the changes after each recipe divided by the number of recipes.

Sum of changes:

Average:

3 recipes.

Total is -10.

-10/3 = 3 with rest 1. So as a mixed number, the correct answer is option C.

From the given equation y=16, it implies that the line has no slope.

Hence, the slope is zero (0).

From the given point:

The equation of the line is given by the equation:

Hence, the equation of the line is y=43

Answer:

x = 5√3

Step-by-step explanation:

We will use the Pythagorean theorem with a and b as the lengths of the legs, and c as the length of the hypotenuse.

a² + b² = c²

We need two of the three lengths of a, b, and c, so we can find the third length.

The height divides the equilateral triangle into two right triangles.

Look at one of the right triangles.

One leg is half the side of the triangle.

a = 10/2 = 5

One leg is the height.

b = x

The hypotenuse is the side of the equilateral triangle.

c = 10

a² + b² = c²

5² + x² = 10²

25 + x² = 100

x² = 75

x = √75

x = 5√3

Answer: b

Step-by-step explanation:

The units of weight of watermelon on the digital scale could be kilogram, gram and pounds.

According to the question,

We have the following information:

A watermelon is placed on a digital scale. The scale reads 10.5.

We know that there are several units of measurements for every physical quantity. For example, the units for measuring length are kilometers, meters, centimeters, feet, inches and many more.

In the same way, there are many units for measurements of weight. However, in most of the cases for the weight on a digital scale, it can be kilogram, gram or pound.

So, it could 10.5 kg or 10.5 g or 10.5 pounds.

Hence, the units of the weight of watermelon on the digital scale could be kilogram, gram and pounds.

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The distance, in miles, between Mora's house and her cousin's house will be 3000 miles as "2 centimeters on the map represent 300 miles. On the map, the distance between her house and her cousin's house is 20 centimeters."

The unitary method involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel. The unitary method is a way of finding any required quantity's value by first finding the value of the unit (one) quantity.

here,

2 cm=300 miles

1 cm=150 miles

so,

20 cm=

150*20=3000 miles

Mora's residence and her cousin's residence are separated by 3000 miles in miles "On the map, a centimeter equals 300 miles. Her house is 20 centimeters from her cousin's house, according to the map."

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Answer:

Step-by-step explanation:

11000*0.91=10010

10010*0.91=9109.1(approximately 9109)

keep going until you find the year you want

Answer: 9.7 seconds

Step-by-step explanation:

[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]

To plot the graph of the function:

According to your graphing software, we need to find the smallest value of the function, and any point at the positive slope side of the function. Let's start with the minimum point. Let's use the general formula for an absolute value function:

The coefficients 'b' and 'c' determinates how much the function was translated from the origin. The 'b' determinates in the x-axis, and the 'c' determinates in the y-axis.

If the 'b' is positive, the function translated to the left, if it is negative the function translated to the right.

If the 'c' is positive the function went up, and if it is negative it went down.

Now let's analyze our h(x) function. Our coefficients are:

Which means our minimum point is

Now, we just need to calculate any point to the right of x = -1.

Let's calculate for x = 0.

The second point is (0,7)

The root of the given equation is x = -114/33.

We are given an equation. The equation has one variable. It is linear in nature. The equation is given below.

(x-6)/4 - 4 = (3x/2) + (2x+1)/5​

We need to find the root of the equation. First of all, we will move all the terms containing the variable "x" to one side of the equation.

(x-6)/4 - (3x)/2 - (2x+1)/5​ = 4

Now we will multiply the terms with the LCM of all the denominators.

20*[(x-6)/4 - (3x)/2 - (2x+1)/5] = 20*4

5(x-6) - 10(3x) - 4(2x+1) = 80

5x - 30 - 30x - 8x - 4 = 80

-33x - 34 = 80

-33x = 114

x = -114/33

Hence, the root of the given equation is x = -114/33.

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The required number of tasks should each employee do are 10.

The Remainder of the worth left after the division. In the event that a number (profit) isn't totally distinguishable by another number (divisor) we are left with a worth once the division is finished. This worth is known as the rest of. For instance, 10 isn't precisely separated by 3. Since the nearest esteem, we can get 3 x 3 = 9.

As there are 43 clean-up tasks that need to be completed,

And four employees

Number of task for one employee = 43/4 = 10, and 3 is remainder.

So, each employee does the 10 number of tasks, and 3 is obtain as a remainder.

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Answer:

True

Explanation:

The equation in the point-slope form of the line is -7 = -5/4x -8.

One of the three forms we can use to express a straight line is the point-slope form, also referred to as the point-gradient form.

This form is helpful since it allows us to find the equation of the line by only knowing the slope and one point along the line.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, the point-slope form is:

The equation of the point-slope form: y = MX + b

Where y is the y coordinate and b is the x coordinate and m is the slope.

Now, get the point-slope form as follows:

y = MX + b

-7 = -5/4x -8

Therefore, the equation in the point-slope form of the line is -7 = -5/4x -8.

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Answer big number

Step-by-step explanation: you start with 500 then 700 for 2nd then 900 for 3rd 1100 for 4th 1300 for 5th 1500 for 6th

Answer: 6,000

Step-by-step explanation:

If it starts with 500 on the first birthday, and each year he deposits the same amount as the previous plus 200 then we get 700 for the 2nd year.
3rd year: deposits 900

4th year: deposits 1100

5th year: deposits 1300

6th year: deposits 1500

500+700+900+1100+1300+1500=6000

Answer: $6000

Here, we seek the angle adjacent to one of the given sides' length.

When given the hypothenuse and the adjacent lengths, we employ the SOH CAH TOA formulae.

This gives us:

Where

adjacent = 15

Hypothenuse = 34

Employing back into the formulae, we have:

The missing angle is approximately 64 degrees

The value of side CA of the right angle triangle is 8.85.

Trigonometry is the branch of mathematics that set up a relationship between the sides and angles of right-angle triangles. The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths.

Given that △ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘.

The value of side CA is calculated, from the right angle triangle applying the angle property,

tan41 = (7.7)/(CA)

CA = (7.7)/(tan41)

CA = 8.85

Therefore, the value of side CA of the right angle triangle is 8.85.

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Answer:

C.

Step-by-step explanation:

you have to divide the numbers

Answer:

C and about 400 hats

Step-by-step explanation:

So you'd have to round up to 1600 for the first equation and for the second one it's about 400 because 1600/4=400

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The measure is 5.

From the question, we have

E is the circumcenter. The distance from circumcenter to all of their vertices from that triangle are the same, so

NE =EP

⇒13x -28 = 6x +7

⇒13x -6x = 28 +7

⇒7x = 35

⇒x= 5

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

Complete question: Find value of x, measure of NE,MD?

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Using cosine rule, the length of side t is 31.5 unit

Cosine rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The formula is given as

t² = s² + u² -3su cos(T)

let's define our variables

substituting the values into the formula

t² = 34² + 40.5² -2(34)(40.5)cos49

t² = 1156 + 1640.25 - 1806.79

t² = 989.46

t = √989.46

t = 31.5

The length of t is 31.5 unit

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Step-by-step explanation:

x + y = 180° (linear pair)

Also, x = 3y (corresponding angles are equal)

So, 4y = 180

y = 45°

x = 135°

The probability of winning $600 or less if you play the game 10 times, assuming that each game is independent IS 0.5630.

A popular probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It totals the number of trials when each trial has an equal chance of producing a particular result. The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.

Given,

Cash prize = $100

Probability of winning the game = 0.7

Using binomial distribution,

P(4 ≤X≤ 6) = P( X = 4) + P( X = 5) + P( X = 6)

P( 4 ≤ X ≤ 6)

= 1/4(0.6)⁴(0.4)⁴ + 10/5 (0.6)⁵(0.4)⁵ + 10/6 (0.6)⁶(0.4)⁶

= 0.1115 + 0.2007 + 0.2508

= 0.5630

The probability of winning $600 or less if you play the game 10 times, assuming that each game is independent IS 0.5630.

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Answer:

Step-by-step explanation:

1+2+4=7

70/7=10

10 x 1=10     10 x 2=20    10 x 4=40

10:20:40

In order to determine the number of required square feet to paint the nose cone, use the following formula for the surface area of a cone without the base:

where

r: radius of the base of the cone = 3 ft

l: slant height of the cone = 6 ft

replace the previous values of the parameters into the formula for S and simplify:

Hence, 56,5ft^2 are required

Answer: since the distance between f and g is 20 units and is then reduced to 4 units long, it's scale factor would be 0.2

Step-by-step explanation:

Sorry if you get this wrong, i tried really hard on this and watched a video

Let:

x = original sides.

x + 4 = new width

x - 2 = new feet

So:

(x + 4)(x - 2) = 91

x² - 2x + 4x - 8 - 91 = 0

x² + 2x - 99 = 0

Factoring:

(x + 11)(x - 9) = 0

x = -11 (the lenght can't be negative so this answer is not valid)

x = 9 ft

Based on the given function,

a) The price that yields the maximum profit is $20.

b) The maximum profit is $6,050

Function

Function defines the relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Given,

A rock club's profit from booking local bands depends on the ticket price. Using past receipts, the owners find that the profit p can be modeled by the function p = -15t² + 600t + 50, where t represents the ticket price in dollars.

Here we need to find the price that yields maximum profit and the amount of maximum profit.

In order to find the price that yield the maximum profit, we have to find the value of t, that can be obtained by using the formula,

t = -b/2a

According to the given function the values of a = -15 and the value of b = 600

Apply these values on the given function then we get,

t = -600/ 2(-15)

t = -600/-30

t = 20

Therefore, the price that yields the maximum profit is $20.

Now, we need to find the maximum profit, by apply the value of t as 20 in the given function then we get,

p = -15(20)² + 600(20) + 50

P = -15(400) + 12000 + 50

p = -6000 +  12000 + 50

p = 6000 + 50

Therefore, the maximum profit is $6,050.

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First, locate any two point from the line.

(15, 150) and (25, 130)

x₁ = 15 y₁= 150

x₂ = 25 y₂ = 130

Next, is to find the intercept.

Substitute x=15 y=150 and m=-2 into y=mx + b and solve for b

That is;

150 = 15(-2) + b

150 = -30 + b

Add 30 to both-side of he equation

150 + 30 = b

180 = b

Form the equation by substituting m=-2 and b=180 into y=mx + b

y = -2x + 180

Hence, the line function is y = -2x + 180

By applying the distributive property of multiplication, an expansion of this mathematical expression can be written as 3(x - 2) = 3x - 6.

In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Mathematically, the distributive property of multiplication can be represented by this mathematical expression:

a(b + c) = ab + ac.

a(b - c) = ab - ac

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

3(x - 2) = 3(x) - [3(2)]

3(x - 2) = 3x - 6

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