The table shown gives values of the function y=g(x) for selected values of x.​

Answer:

6

Step-by-step explanation:

The product of three consecutive numbers is divisible by ​6

Let us say the numbers are x, x+1 , x+2

if x = 1,

Product of the three consecutive numbers,

(1)(2)(3)

=> 6, which is divisible by 6

if x = 2,

Product of the three consecutive numbers,

(2)(3)(4)

=> 24, which is divisible by 6

Similarly if we take any 3 consecutive numbers their product will be divisible by 6.

domain is  (- infinity, infinity)

range is (- infinity, infinity)

The values of variables, such as the height of the table can be found by writing equations of their relationships

The height of the table is 105 cm

The reason the above height value is correct is as follows;

Known parameters:

The diagram shows a table, a cat and a mice

Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice

From the given diagram, we have;

Height of the table + Height of the cat - Height of the mice  = 120 cm

∴ x + y - z = 120...(1)

Height of the table + Height of the mice - Height of the cat   = 90 cm

∴ x + z - y = 90...(2)

Adding equation (1) to equation (2) gives;

x + y - z + (x + z - y) = 120 + 90 = 210

x + y - z + (x + z - y) = 210

However;

x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x

∴ x + y - z + (x + z - y) = 2·x = 210

x = 210/2 = 105

Therefore;

The height of the table, x = 105 cm

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Answer:

h=A-πr²÷2πr

Step-by-step explanation:

Making h subject

A=2πrh+πr²

A-πr²=2πrh

A-πr²÷2πr=h

h=A-πr²÷2πr

Answer:

The answer is [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].

Step-by-step explanation:

To solve for (h), start by subtracting ([tex]\pi r^{2}[/tex]) from both sides, and the equation will look like [tex]A-\pi r^{2}= 2\pi rh+\pi r^2-\pi r^2[/tex]. The next step is to simplify the equation, which will look like [tex]A-\pi r^{2} =2\pi rh[/tex].

Next, divide both sides of the equation by [tex]2\pi r[/tex], and it will look like [tex]\frac{A-\pi r^{2} }{2\pi r} =\frac{2\pi rh}{2\pi r}[/tex]. Finally, simplify the equation, and the answer will be [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].

Answer:

The answer for thid equation is x = -5/3

Given:

A figure of a construction.

To find:

The correct option that represent the given construction.

Solution:

We know that, if a transversal line intersect two parallel lines, then the corresponding angles are equal.

In the given figure, two corresponding angles are constructed by using the compass.

Since the corresponding angles are equal, therefore the construction represents the parallel lines through a point.

Therefore, the correct option is B.

Exact Surface Area = 378pi

Approximate Surface Area = 1186.92

The approximate surface area uses pi = 3.14

The units are cm^2 or "square cm".

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

Work Shown:

SA = surface area of cylinder

SA = 2*pi*r^2 + 2*pi*r*h

SA = 2*pi*7^2 + 2*pi*7*20

SA = 2*pi*49 + 2*pi*140

SA = 2*49*pi + 2*140*pi

SA = 98pi + 280pi

SA = 378pi ..... exact surface area

SA = 378*3.14

SA = 1186.92 ..... approximate surface area

----------

Side note: The diameter 14 cuts in half to get the radius r = 7

Answer:

1187.52

Step-by-step explanation:

Use the formula [tex]2\pi rh+2\pi r^{2}[/tex].

r= 7 (half of your diameter, which is 14)

h = 20

Fill in your radius and height.

[tex]2\pi (7)(20)+2\pi (7^{2})[/tex]

Enter your equation into a calculator and you'll get 1187.52202.

When rounded to the nearest hundredths, you get 1187.52

Answer:

So, to fill the tray completely , he needs 3 bags of sand.

Step-by-step explanation:

Tray dimensions,

length = 0.8 m

Width = 0.6 m

height = 0.1 m

Volume of one sand bag = 17000 cm^3

Let the volume of the tray is V.

V = length x idth x height

V = 0.8 x 0.6 x 0.1 = 0.048 m^3

Number of sand bags

[tex]n=\frac{0.048}{17000\times 10^{-6}}\\\\n = 2.82[/tex]

So, to fill the tray completely , he needs 3 bags of sand.

9514 1404 393

Answer:

  (x^(1/2))(x^(1/2)) = x^(1/2 +1/2) = x^1 = x

Step-by-step explanation:

The rule of exponents is ...

  (x^a)(x^b) = x^(a+b)

From which ...

  (x^a)(x^a) = x^(a+a) = x^(2a)

So, if we want two identical factors that have a product of x = x^1, then the exponents of those factors will be such that ...

  x^(2a) = x^1

  2a = 1

  a = 1/2

The square root is defined as one of two identical factors that have a product equal to the specified value. That is ...

  (√x)(√x) = x

Above, we have shown that ...

  (x^(1/2))(x^(1/2)) = x

so, we can conclude ...

  √x = x^(1/2)

_____

Additional comment

In like fashion, we can show that the n-th root of a number is the same as that number to the 1/n power. It's really a matter of definition. Since the square of x^(1/2) is x, we call x^(1/2) the square root. It is used commonly enough that it has its own symbol: √x.

Answer:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:

Answer:

split the other three in half

Step-by-step explanation:

Answer:

Y= -x^2+12x-36

Step-by-step explanation:

Answer:

x = [tex]\frac{1}{3}[/tex]   y = -1

Step-by-step explanation:

x = 0 to solve for y

[tex]y=3x-1[/tex]

[tex]y=3(0)-1[/tex]

[tex]y=-1[/tex]

y = 0 to solve for x

[tex]y=3x-1[/tex]

[tex]0=3x-1[/tex]

Add 1 to both sides

[tex]1=3x[/tex]

Divide by 3 to isolate x

[tex]\frac{1}{3} =x[/tex]

Answer:

120 times

Step-by-step explanation:

On a dice, there are 6 sides.

Since one of these sides is a 5, the chance of rolling a five is 1/6.

Find how many times Malachy can expect to roll a five by multiplying 720 by 1/6:

720(1/6)

= 120

So, Malachy can expect to roll a five 120 times

Answer:

Uuuzu7ggijjrudidjdiwisiwiwieie

The statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

a quadrilateral is a four-sided polygon, having four edges and four corners.

DEFG is a parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides.

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

DF=FG is a true statement.

The diagonal passing through a parallelogram are equal in length.

EF=DG is a true statement

The opposite sides of a parallelogram are equal.

∠DEG ≅ ∠FGE are congruent angles.

Because the opposite angles of a triangle are equal in meausure.

Hence, the statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

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#SPJ2

Answer:

Yes, because they are identical to eachother

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -2 - -2)/(2 - -6)

   = (-2+2)/(2 +6)

    = 0/8

   = 0

Answer:

Slope is 0

Step-by-step explanation:

Slope formula is (y2-y1)/(x2-x1)

-2 - (-2)/2 - (-6)

0/8

0

Answer:

10

Step-by-step explanation:

Total pizza topped with pepperoni, sausage or pepperoni and sausage = 33

Number of pizzas with pepperoni = 29

Number of pizzas with pepperoni and sausage = 15

Pizza with pepperoni only = 29 - 15 = 14

Pizza with sausage only = 33 - 29 = 4

Pepperoni only than sausage only :

14 - 4 = 10

Answer:

.60 + .40 + 3.00 = 4.00

Step-by-step explanation:

Answer:

$ 4

Step-by-step explanation:

six dimes (.10 each) = .60

8 nickels (.05 each)= .40

3 dollars (1.00 each) = 3.

Add together

Answer:

B) $85,167

Step-by-step explanation:

u got discount 45% so u just have to pay 55% of it

cost = 55% x $154,85 = $85,1675

Answer:

C. -2x +3y-6=0

this is the answer

Answer:

a) 0.0171 fluid ounces.

b) 0% probability that the average fill volume of 22 bags is below 5.95 ounces

c) The mean should be of 6.153 fluid ounces.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation of 0.08 fluid ounces.

This means that [tex]\sigma = 0.08[/tex]

(a)What is the standard deviation of the average fill volume of 22 bags?

This is s when n = 22. So

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]s = \frac{0.08}{\sqrt{22}}[/tex]

[tex]s = 0.0171[/tex]

(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?

We have that [tex]\mu = 6.16[/tex]. The probability is the p-value of Z when X = 5.95. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{5.95 - 6.16}{0.0171}[/tex]

[tex]Z = -12.3[/tex]

[tex]Z = -12.3[/tex] has a p-value of 0.

0% probability that the average fill volume of 22 bags is below 5.95 ounces.

(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?

[tex]X = 6.1[/tex] should mean that Z has a p-value of 0.001, so Z = -3.09. Thus

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-3.09 = \frac{6.1 - \mu}{0.0171}[/tex]

[tex]6.1 - \mu = -3.09*0.0171[/tex]

[tex]\mu = 6.153[/tex]

The mean should be of 6.153 fluid ounces.

Answer:

10.9 %

Step-by-step explanation:

46 - 41 = 5

5/46 * 100% = 10.8695652174%

Rounded

10.9 %

Answer:

y = -4x+14

Step-by-step explanation:

First find the slope

m = (y2-y1)/(x2-x1)

m = (2-10)/(3-1)

   =-8/2

   = -4

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = -4x+b

Substitute a point into the equation

10 = -4(1)+b

Add 4 to each side

14 = b

y = -4x+14

Answer:

[tex]c < 4[/tex]

Step-by-step explanation:

Move the constant to the right-hand side and change its signs:

[tex]c < 16 - 12[/tex]

Subtract the numbers:

[tex]c < 16 - 12 = c < 4[/tex]

Answer:

4√2 and 5+4√2

Step-by-step explanation:

Let the two numbers be x ad y

Smaller = y

Bigger = x

If a positive real number is 5 more than another, then;

x = 5 + y ... 1

When - 10 times the smaller is added to the square of the larger, the result is 57, then;

-10y + x² = 57 ...2

Substitute 1 into 2;

-10y + (5+y)² = 57

-10y + 25+10y+y² = 57  

y²+25 = 57

y² = 57 - 25

y² = 32

y = √32

y = 4√2

Since x = 5 + y

x = 5 + 4√2

Hence rhe numbers are 4√2 and 5+4√2

Answer:

[tex]Probability = \frac{4}{15}[/tex]

Step-by-step explanation:

B1 = first bag

B2= second bag

B3 = third bag

Let A = ball drawn is red

Since, there are three bags.

Probability of choosing one bag=  P(B1) = P(B2) = P(B3) = 1/3.

From B1: Total balls = 10

3 red + 7 black balls.

Probability of drawing 1 red ball from it , P(A) = 3/10.

From B2: Total balls = 10

8 red + 2 black

Probability of drawing 1 red ball is, P(A) = 8/10

From B3 : Total Balls = 10

4 red + 6 black

Probability of drawing 1 red ball, P(A) = 4/10 .

To find Probability given that the ball drawn is red, that the ball is drawn from the third bag by Bayes' rule.

That is , P(B3|A)

                     [tex]=\frac{\frac{1}{3} \times \frac{4}{10}} { \frac{1}{3} \times \frac{3}{10} + \frac{1}{3} \times\frac{8}{10} + \frac{1}{3} \times \frac{4}{10}}[/tex]

                    [tex]=\frac{4}{30} \times \frac{30}{15}\\\\=\frac{4}{15}[/tex]

Therefore, the probability that it is drawn from the third bag is 4/15.

Answer:

4/15

Step-by-step explanation:

Solution of conditional probability problem:

Given:

Bags (3R,7B), (8R,2B), (4R,6B)

Let

P(R,i) = probability of drawing a red AND from bag i

P(R, 1) = 3/10 * (1/3) = 3/30

P(R, 2) = 8/10 * (1/3) = 8/30

P(R, 3) = 4/10 * (1/3) = 4/30

Let

Let P(R) = probability of drawing a red from any bag

P(R) = sum P(R,i)  for i = 1 to 3   using the addition rule

= 3/30 + 8/30 + 4/30

= 15/30

= 1 / 2

Conditional Probability of drawing from the third bag GIVEN that it is a red

= P(3 | R)

= P(R, 3) / P(R)

= 4/30 / (1/2)

= 8/30

= 4 / 15

(Since all bags contain 10 balls, by intuition, 4 red from third / 15 total red = 4/15)

Answer:

Step-by-step explanation: