An oral surgeon is tracking how many patients were referred to him by various local dentists. In the past year, 5 dentists made the following number of referrals:

9 patients
6 patients
6 patients
5 patients
8 patients

What was the mode of the numbers of referrals?

Answer:

Step-by-step explanation:

f = v + at....solving for t

f = v + at....subtract v from both sides

f - v = at....divide both sides by a

(f - v) / a = t or could also be : t = f/a - v/a <==

The equivalent equation for the given expression f = v + at  is (f - v) / a = t. The correct option is C.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

The given expression is f = v + at, where, the final velocity of an object, f, with an initial velocity, V, and an acceleration rate, a, over time, t.

The given expression for ' t ' is calculated as:-

f = v + at....solving for t

f = v + at....subtract v from both sides

f - v = at....divide both sides by a

(f - v) / a = t

The above expression can also be written as given below:-

t = f/a - v/a <==

Hence, the expression  f = v + at for t will be equal to (f - v) / a = t. Then the correct option is C.

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Answer:

(0,5)

Step-by-step explanation:

we have

[tex]2x+3y > 12[/tex] ----> inequality A

[tex]x-y\leq 1[/tex] ----> inequality B

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities of the system (makes true both inequalities)

Verify each ordered pair

Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B and then compare the results

case 1) (0,5)

For x=0,y=5

Inequality A

[tex]2(0)+3(5) > 12[/tex]

[tex]15 > 12[/tex] ----> is true

so

The ordered pair satisfy inequality A

Inequality B

[tex]0-5\leq 1[/tex]

[tex]-5\leq 1[/tex] ---> is true

so

The ordered pair satisfy inequality B

therefore

The ordered pair would be a solution of the system

case 2) (5,2)

For x=5,y=2

Inequality A

[tex]2(5)+3(2) > 12[/tex]

[tex]16 > 12[/tex] ----> is true

so

The ordered pair satisfy inequality A

Inequality B

[tex]5-2\leq 1[/tex]

[tex]3\leq 1[/tex] ---> is not true

so

The ordered pair not satisfy inequality B

therefore

The ordered pair is not a solution of the system

case 3) (0,4)

For x=0,y=4

Inequality A

[tex]2(0)+3(4) > 12[/tex]

[tex]12 > 12[/tex] ----> is not true

so

The ordered pair not satisfy inequality A

therefore

The ordered pair is not a solution of the system

case 4) (6,0)

For x=6,y=0

Inequality A

[tex]2(6)+3(0) > 12[/tex]

[tex]12 > 12[/tex] ----> is not true

so

The ordered pair not satisfy inequality A

therefore

The ordered pair is not a solution of the system

Answer:

x = 6

y = 0

Explanation:

−2x+y=−12;3y−2x=−12

Rewrite equations:

−2x+y=−12;−2x+3y=−12

Solve −2x+y=−12 for y

−2x+y=−12

−2x+y+2x=−12+2x(Add 2x to both sides)

y=2x−12

Substitute 2x−12 for y in −2x+3y=−12

−2x+3y=−12

−2x+3(2x−12)=−12

4x−36=−12 (Simplify both sides of the equation)

4x−36+36=−12+36 (Add 36 to both sides)

4x=24

Divide both sides by 4

4x / 4 = 24 / 4

x = 6

Substitute 6 for x in y=2x−12

y=2x−12

y=(2)(6)−12

y=0 (Simplify both sides of the equation)

Answer:

first C then B

Step-by-step explanation:

The distance Raphael needs to travel goes down by time. Therefore the y-value (the amount of distance) will go down as the x-value (the amount of time) will go up. So C.

The speed of the rollercoaster is increasing as time goes by. Therefor the y-value (the speed) will go up and the x-value (the amount of time) will also go up. So B.

Time is almost always moving forward so you can almost always assume x will go up.

Answer:

Step-by-step explanation:

Because 4 to the power of -3 divided by 4 to the power of -1 switched (Like when there is a negative exponent you move the number or variable to the other side of the fraction) and scince both have a negative number you switch both. and 1-3 is -2 so you switch it to the bottem and put a 1 at the top.

                                         ^^Hope this helps!

The expressions equivalent to 4^-3 / 4^-1 are 1/4^2 and (4^-1)^-3.

In the subject of mathematics, the given expression is 4^-3 / 4^-1. To simplify this expression, you need to understand two rules of exponents:

Applying these two rules, 4^-3 / 4^-1 = 4^-3 * 4^1 = 4^(1 - 3) = 1/4^2.

Another way to simplify the expression is to use the rules of exponents to rewrite each part independently. 4^-3 = 1/4^3 and 4^-1 = 1/4. Therefore, 4^-3 / 4^-1 = (1/4^3) / (1/4) = 4, which is equivalent to (4^-1)^-3.

Therefore, the equivalent expressions are (B) 1/4^2 and (D) (4^-1)^-3.

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Answer:

4u+16

Step-by-step explanation:

first multiply the outside bumber(in this case its 4) by each of the numbers and variables inside. (making u turn into 4u) and ( making 4 turn into 16 bcs 4x4=16

Answer:

- 12

Step-by-step explanation:

The rate of change is measured by the slope m of the data

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, - 2) and (x₂, y₁ ) = (5, - 26) ← 2 ordered pairs from the table

m = [tex]\frac{-26+2}{5-3}[/tex] = [tex]\frac{-24}{2}[/tex] = - 12

Rate of change = - 12

Answer;

Given that;

n/8=9

Here n is the numerator and 8 is the denominator we know that 8 is divided here so when we take it to the left side we get;

n=9 * 8. (9 multiplied with 8)

n=72

Hence answer only;

n/8=9

n=9 *8

n=72

Hence answer only;

n=72

After solving  n/8=9 you will get n = 72.

To solve the equation n/8 = 9 for n, we need to isolate the variable by performing inverse operations.

Step 1: Multiply both sides of the equation by 8 to eliminate the fraction:

8 * (n/8) = 8 * 9

This simplifies to n = 72.

Therefore, the solution to the equation n/8 = 9 is n = 72. When n is divided by 8, the result is 9. This means that 72 is the value that satisfies the equation and makes it true.

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Answer:

Step-by-step explanation:

8+?=19

19-8=11

Y=11

Final answer:

To solve the equation 19 = 8 + y for y, you subtract 8 from both sides which gives you y = 11.

Explanation:

The equation provided, 19 = 8 + y, is a simple linear equation where you are solving for the variable y. To find the value of y, you need to isolate y on one side of the equation.

Here is the step-by-step process:

Start with the original equation: 19 = 8 + y.

To isolate y, you need to get rid of the 8 on the right side of the equation. You can do this by subtracting 8 from both sides of the equation.

Subtracting 8 from both sides gives us: 19 - 8 = y.

Simplify the left side: 11 = y.

Therefore, y equals 11.

Answer:

x= 40°

Step-by-step explanation:

Please see attached picture for full solution.

Key concepts:

- Corresponding angles are equal to each other

- The sum of the angles in a triangle add up to 180°

Answer:

The smallest amount is [tex]\£6,911[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1[/tex]  

substitute in the formula above

[tex]8,000=P(1+\frac{0.05}{1})^{1*3}[/tex]  

solve for P

[tex]8,000=P(1.05)^{3}[/tex]  

[tex]P=8,000/(1.05)^{3}[/tex]  

[tex]P=\£6,910.70[/tex]  

Round to the nearest pound she can invest

The smallest amount is [tex]\£6,911[/tex]

Answer:

I believe the answer to this question is: X=5.

Measure of one of the vertical angle is 156°

Solution:

The measure of angles given are (x + 104)° and 3x°.

The given angles are vertical in order.

If two lines meet at a point, then the angle formed in vertical positions are equal.

That is vertically opposite angles are equal.

⇒ 3x° = (x + 104)°

⇒ 3x° = x° + 104°

Subtract x° on both sides of the equation to equal the expression,

⇒ 3x° – x° = x° + 104° – x°

⇒ 2x° – x° = 104°

⇒ 2x° = 104°

Divide both sides of the expression by 2, we get

⇒ x° = 52°

Substitute x° = 52° in one of the vertical angle.

3x° = 3 × 52° = 156° (or)

x° + 104° = 52°+ 104° = 156°

Hence the measure of one of the vertical angle is 156°.

Answer:

20

Step-by-step explanation:

add all of them together and divide by 7

Answer: 20

Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set.

So to find the mean of the data set shown here, let's begin by adding the numbers.

15 + 28 + 25 + 22 + 11 + 12 + 27

This will be divided by how many numbers are in the set which is 7.

So we have [tex]\frac{15 + 28 + 25 + 22 + 11 + 12 + 27}{7}[/tex]

Adding the numbers, we get 140.

140 is divided by the number of numbers in the set or 7.

140 divided by 7 is 20.

So the mean of the set of data shown here is 20.

Each new term is found by multiplying the last term by 2

1*2 = 2

2*2 = 4

2*4 = 8

2*8 = 16

and so on

Therefore the common ratio is r = 2.

The starting term is a = 1

The general nth term is [tex]a*(r)^{n-1} = 1*(2)^{n-1} = 2^{n-1}[/tex] where n is an integer (aka whole number) and n starts at n = 1.

Answer:

[tex]\$973.80[/tex]  

Step-by-step explanation:

The complete question is

How much money will Alondra make if she invests $900 in an account that pays 8.2% interest compounded annually for one year?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=1\ year\\ P=\$900\\ r=8.2\%=8.2/100=0.082\\n=1[/tex]

substitute in the formula above

[tex]A=900(1+\frac{0.082}{1})^{1*1}[/tex]  

[tex]A=900(1.082)^{1}[/tex]  

[tex]A=\$973.80[/tex]  

Answer:

Step-by-step explanation:

y ∞ 1/x

y = k/x

Where k is the constant of proportionality

When x = 3 and y = 5

5 = k/3

Cross multiply

k = 5×3

k = 15

The equation is y = 15/x

The given relationship Y varies inversely with X and when X is equal to 3, Y equals to 5 which leads us to the equation Y = 15/X which illustrates this inverse variation.

The given question states that Y varies inversely with X and provides us with a pair of values - X = 3, Y = 5. In mathematics, when one quantity Y varies inversely as another X, it can be represented by the equation Y = k/X where k is the constant of variation. To find k, we will substitute the given X and Y values into the equation leading to 5 = k/3. Simplifying, we find k = 5*3, that is, k equals 15. Therefore, the equation that represents this inverse variation is Y = 15/X.

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Answer:

[tex]\large\boxed{x=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

[tex]15-0.5(4x-2)+4x=17\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\15+(-0.5)(4x)+(-0.5)(-2)+4x=17\\\\15-2x+1+4x=17\qquad\text{combine like terms}\\\\(-2x+4x)+(15+1)=17\\\\2x+16=17\qquad\text{subtract 16 from both sides}\\\\2x+16-16=17-16\\\\2x=1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{1}{2}\\\\x=\dfrac{1}{2}[/tex]

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-4)}}}\implies \cfrac{-1+2}{3+4}\implies \cfrac{1}{7}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{\cfrac{1}{7}}[x-\stackrel{x_1}{(-4)}]\implies y+2=\cfrac{1}{7}(x+4) \\\\\\ y+2=\cfrac{1}{7}x+\cfrac{4}{7}\implies y=\cfrac{1}{7}x+\cfrac{4}{7}-2\implies y=\cfrac{1}{7}x-\cfrac{10}{7}[/tex]

The number 28 is divided by the number 3 in fraction form is  9 1/3.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The number 28 is divided by the number 3.

This can be written in fraction form as 28/3.

Now, 3×9 = 27.

Therefore, 28/3.

= 9 1/3.

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Answer: X = 8.67

Step-by-step explanation:

Answer:

1 1/2 hours

Step-by-step explanation:

divide 3/2 and whatever you got is your answer

Answer:

Step-by-step explanation:

It takes 9 minutes to fill a depth of [tex]\frac{3}{5}[/tex] meters.

Filling  [tex]\frac{3}{5}[/tex] meters take 9 minutes time.

Filling 3 meters of the aquarium takes [tex]5\times9[/tex] = 45 minutes time (Multiplying by 5 both the numbers).

In order to fill 1 meter of the aquarium it will take [tex]\frac{9\times5}{3} = 15[/tex] minutes (Dividing by 3 both the numerical values).

Answer:

The rate is 15 minutes per meter.

Step-by-step explanation: please give brainliest

Answer:

y = -21

Step-by-step explanation:

15 ft by 6 ft is the aswerk

15 ft by 6 ft. is the answer

Answer:

(e) =1/2x^3y^4      (f)=y/3x^2

Answer:

$ 16.84

Step-by-step explanation:

First take 40 percent of 26 by doing 26 times .4 which gives you 10.4 and then do 26- 10.4 (because it was marked down) which gives you 15.6 and then you multiply 15.6 by .08 giving you 1.248 and then you add 1.248 + 15.6 to give you 16.84

Answer:

Slope= -3/4

Step-by-step explanation: