In a recent survey,5 out of every 11 dentists recommend fluoride. If there are 690 dentists surveyed, how many are recommend fluoride?

Formulas used :

[tex]loga^ x = x \ log a[/tex]

[tex]logab = log a + logb[/tex]

Steps :

[tex](x+y)^2 = 125xy\\\\log(x+y)^2 = log(125xy)\\\\2log(x+y) = log 125 + log x + log y\\\\2log(x+y) = log 5^3+ log x + log y\\\\2log(x+y) = 3 log 5 + log x + log y\\\\[/tex]

Answer:

1. The preimage and image are congruent

2. Any line segment connecting the corresponding points between the preimage and image is bisected by the line of reflection

3. Corresponding angles on the preimage and image are congruent

4. Corresponding points of the preimage and image are equidistant from the line of reflection.

Answer:

The tower is approximately 57.34 meters long

Step-by-step explanation:

The given parameters are;

The type of triangle formed by ΔABC = Non-right triangle

The measure of ∠ACB = 55°

The horizontal displacement of the tower, BX = 5 m

The length of BC = 45 m

Therefore, we have;

Triangle ΔABC type = Right triangle

By the tangent to an acute angle, θ, in a right triangle, we have;

[tex]Tan(\theta) = \dfrac{Opposite \, side \ length}{Adjacent\, side \ length}[/tex]

Where θ is the 55°, we have angle, we have;

[tex]Tan(55^{\circ}) = \dfrac{XA}{XC}[/tex]

BC = BX + XC

∴ XC = BC - BX

XC = 45 m - 5 m = 40 m

[tex]\therefore Tan(55^{\circ}) = \dfrac{XA}{40}[/tex]

XA = 40 × tan(55°) ≈ 57.126

The type of triangle formed by ΔABX = Right triangle

According to Pythagoras theorem, AB² = XA² + BX²

∴ AB = √((40 × tan(55°))² + 5²) ≈ 57.34

The length of the tower, AB ≈ 57.34 m

Answer:

C. It is shifted 4 units down.

Step-by-step explanation:

Shifted four units down. When a number is at the end of the equation, it means that that number shifts up or down depending on its sign.  

Answer:

It is shifted 4 units down

Step-by-step explanation:

When we have a function the constant number that is not multiplied by a variable, in this case, 4 in the first function, indicates where the function will intercept the y-axis, or when x is equal to 0.

In this case, we have two functions:

y = 5x^2 - 4, in which -4 is the constant that will determine where the function intercepts the y-axis. So if we say that we have x=0, then y=-4

In the second function we have:

y= 5x^2, this function is very similar but we don´t have another number after 5x^2, so we will have a similar graph but when x = 0 then y = 0.

So the first graph is shifted 4 units down. We can see this in the attachment.

It shifted 4 u it’s to the left

It is shifted 4 units to the left.

Answer:

24000ml or 24L

Step-by-step explanation:

wxhxl = volume

20cm x 30cm x 40cm = volume

volume = 24000cm3

1cm3 = 1ml

24000cm3 = 24000ml

1000ml = 1L

24000ml = 24L

Answer:

1/4

Step-by-step explanation:

Let a₁, a₂, a₃ and a₄ be the four numbers. Since the geometric mean of the first 3 positive numbers is 4, we have that

∛(a₁a₂a₃) = 4. (1)

Also the geometric mean of the four numbers is 2, we have that ⁴√(a₁a₂a₃a₄) = 2   (2).

So, taking the cube of (1), we have

[∛(a₁a₂a₃)]³ = 4³

a₁a₂a₃ = 64  (3)

Also, taking the fourth power of equation (2), we have

[⁴√(a₁a₂a₃a₄)]⁴ = 2⁴  

a₁a₂a₃a₄ = 16  (4)

Dividing (4) by (3), we have

a₁a₂a₃a₄/a₁a₂a₃ = 16/64

a₄ = 1/4

The fourth value is 1/4

Answer:

x=8

Step-by-step explanation:

-4 = 12 - 2x

when plus 12 goes to the left hand side it changes its sign so,

-4 -12 = -2x

- * - is plus so add 4 and 12 but keep the sign - because 12 is the greatest number and its sign is -

-16=-2x

when -2 comes to the left hand side it changes its from multiplication to division.So,

-16/-2=x

8=x

we will get positive 8 because minus and minus also gets cancel.

Answer:

x=8

Step-by-step explanation:−4=12−2x

−4=12−2xSwap sides so that all variable terms are on the left hand side.

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.−2x=−4−12

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.−2x=−4−12Subtract 12 from −4 to get −16.

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.−2x=−4−12Subtract 12 from −4 to get −16.−2x=−16

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.−2x=−4−12Subtract 12 from −4 to get −16.−2x=−16Divide both sides by −2.

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.−2x=−4−12Subtract 12 from −4 to get −16.−2x=−16Divide both sides by −2.x=−16÷-2

Divide −16 by −2 to get 8.

Divide −16 by −2 to get 8.x=8

Added you

____________

Answer:

All shapes except the cone with 5in radius and 8in height

Step-by-step explanation:

Volume of the cylinder with radius 5in and height 8in is expressed as;

V = πr²h

V = 3.14*5²*8

V = 3.14*25*8

V = 628 square inches

The volume of the cylinder is greater than 500in³

Volume of the cone with radius 5in and height 24in is expressed as;

V = 1/3πr²h

V = 1/3*3.14*5²*24

V = 3.14*25*8

V = 628 square inches

The volume of the cone is greater than 500in³

Volume of the spheree with radius 5in is expressed as;

V = 4/3πr³

V = 4/3π(5)³

V = 4/3 * 3.14 * 125

V = 523.33 square inches

The volume of the sphere is greater than 500in³

Answer:

x ≈ 52.6°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{17}{28}[/tex] , then

x = [tex]cos^{-1}[/tex] ([tex]\frac{17}{28}[/tex] ) ≈ 52.6° ( to the nearest tenth )

Answer:  Choice C.  [tex]3\sqrt{17}[/tex]

================================================

Work Shown:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(12-15)^2 + (-21-(-9))^2}\\\\d = \sqrt{(12-15)^2 + (-21+9)^2}\\\\d = \sqrt{(-3)^2 + (-12)^2}\\\\d = \sqrt{9 + 144}\\\\d = \sqrt{153}\\\\d = \sqrt{9*17}\\\\d = \sqrt{9}*\sqrt{17}\\\\d = 3\sqrt{17}\\\\d \approx 12.3693169\\\\[/tex]

I used the distance formula for those steps above.

The two points were (x1,y1) = (12,-21)  and (x2,y2) = (15,-9) but you could swap the order.

As an alternative route, you can plot the two points on the same xy grid. Then form a right triangle such that the hypotenuse is between the two points mentioned. The pythagorean theorem should lead you to the same answer as above. In fact, the distance formula is basically a modified version of the pythagorean theorem.

Answer:

x = 24, x = -16

Step-by-step explanation:

Given the function f(x) = 0.5|x – 4| – 3, we are to find the values of x for f(x) = 7

Substitute f(x) = 7 into the expression;

7 = 0.5|x – 4| – 3

For the positive function

7 = 0.5(x – 4) – 3

7 = 0.5x - 2 - 3

7 = 0.5x - 5

7+5 = 0.5x

12 = 0.5x

12 = x/2

Swap

x/2 = 12

x = 12 * 2

x = 24

For the negative function

7 = 0.5-(x – 4) – 3

7 = 0.5(-x +4) - 3

7 = -0.5x +2 - 3

7 = -0.5x - 1

7+1 = -0.5x

8 = -x/2

Swap

-x/2 = 8

-x = 8 * 2

-x = 16

x = -16

Hence the required values of x are -16 and 24

Answer:

33

Step-by-step explanation:

Trust me it'll work.

Answer:

24.

Step-by-step explanation:

By definition,  factorial 4

= 4!

= 4*3*2*1

= 24.

a³ + b³ + c³ + 3abc = ( a + b + c)(a² + b² + c² + ab + bc + ca)

if a + b + c = 0. then a³ + b³ + c³ = 3abc

here a + b + c = 15 + (-9) + (-6)

a + b + c = 15 - 15

a + b + c = 0

so a³ + b³ + c³ = 3abc

15³ + (-9)³ + (-6)³ = 3(15)(-9)(-6)

= 2430

so the answer is 2430

Answer:

vertex point at (-2|11)

f(x)=-2*((x+2)^2+1*-11/2) (simplified)

Step-by-step explanation:

f(x)=-2*x^2+-8*x+3  

f(x)=-2*(x^2+4*x+-3/2) ( Factor out )

f(x)=-2*(x^2+4*x+(2)^2+-1*(2)^2+-3/2) ( Complete the square )

f(x)=-2*((x+2)^2+-1*(2)^2+-3/2) ( Use the binomial formula )

hope this helped, I didn't get much to work with so if i'm wrong i'm sorry

Answer:

[tex]50 \pi \: sq \: ft.[/tex]

Explanation:

as we can see that the sector bounded by the 180° arc is a semi- circle

area of a circle =

[tex]\pi {r}^{2} [/tex]

area of semi circle =

[tex] \\ \frac{\pi {r}^{2} }{2} [/tex]

[tex] = \frac{\pi {10}^{2} }{2} \\ = 50\pi[/tex]

For which situations is it appropriate to use a sample? Select three options.

What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck?

What is the average number of rainbows each year in Honolulu?

How many pedestrians would use a walkway built over a busy road?

How many police cars are equipped with computers?

What is the most popular car color in the teachers’ parking lot?Answer:

Step-by-step explanation:For which situations is it appropriate to use a sample? Select three options.

What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck?

What is the average number of rainbows each year in Honolulu?

How many pedestrians would use a walkway built over a busy road?

How many police cars are equipped with computers?

What is the most popular car color in the teachers’ parking lot?

Answer:

The answer is "The decimal could be five-tenths".

Step-by-step explanation:

Given value:

[tex]\to 67.5 \times 4. \_= \_ .50[/tex]

Let the decimal value is: (2)

[tex]\to 67.5 \times 4. 2= 283 .50[/tex]

28000 is the answer.

you count two numbers from front and approximate

Answer:

Starting from

2(-x) = 3x - 5

Distribute

-2x = 3x - 5

add 2x to both sides

0 = 5x - 5

Add 5 to both side

5 = 5x

Flip

5x = 5

Answer:

[tex](180-73)=z+114/2[/tex]

[tex]107*2=z+114[/tex]

[tex]z=214-114[/tex]

[tex]z=100[/tex]

❄ B. 100

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

hope it helps...

have a great day!!

In the given circle in which angles are 73°,96°,114° then the value of z is equal to 100 which is option b.

Circle is a shape consisting fall points in a plane thata are at a given distance from a given distance from a given point which is the centre of the circle.

In the circle we can see the following:

(180-73)=(z+114)/2

107*2=z+114

214=z+114

z=214-114

=100

Hence in the given circle in which angles are 73°,96°,114° then the value of z is equal to 100 which is option b.

Learn more about angles at https://brainly.com/question/25716982

#SPJ2

Answer:

What are the statements?

Step-by-step explanation:

You have to list the statements.

Answer:

C

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

3 hrs and 20 minutes

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

Amount of money discounted

= $40 - $24

= $16

Percentage of discounted money

= 16/40 x 100%

= 40%

Answer:

Step-by-step explanation:

it has a 50/50 chance if it lands on tailes it is 50/50

The question is incomplete. The complete question is :

To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by the equation g = 748u, where g is the total number of gallons of water used and u is the number of units. Determine which statements about the relationship are true. Check all that apply.

g is the dependent variable.

u is the dependent variable.

g is the independent variable.

u is the independent variable.

The variables cannot be labeled without a table of values.

The variables cannot be labeled since any value can be selected for either

Solution :

Given equation :

g = 748 u

Here, g = total number of gallons of water used

         u = number of units

Customers uses the number of units of water.

The unit of water is independent of the total number of gallons of water used.

So the number of units u is an independent variable.

But the value of gallons of water depends on the number of units that is used.

Therefore, number of gallons of water g is a dependent variable.

Thus, we can say that :