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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:

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.

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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Answer:

10.9 %

Step-by-step explanation:

46 - 41 = 5

5/46 * 100% = 10.8695652174%

Rounded

10.9 %

Answer:

48

Step-by-step explanation:

n = 25(1.18)^4

n = 48.469444

Rounded to 48

Answer:

48 views.

Step-by-step explanation:

18% = 0.18 as a decimal fraction.

The increase in number of books per week is  found by multiplying by 1.18.

The equation is  an exponential one and is:

V = 25(1.18)^t  where V = views and t = number of weeks.

So after 4 weeks :

V = 25 (1.18)^4

= 48.47

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:

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:

4c^2+7c-5=0

4c^2+7c=5

4c^2+7c=5

4c^2+7c-5=0\quad :\quad c=\frac{-7+\sqrt{129}}{8},\:c=\frac{-7-\sqrt{129}}{8}\quad \left(\mathrm{Decimal}:\quad c=0.54472\dots ,\:c=-2.29472\dots \right)

Hope This Helps!!!

Answer:

C) c = -7 ± √129 / 8

Step-by-step explanation:

x = (-b ± √ (b² – 4ac) ) / 2a

[quadratic formula]

where ax² + bx + c = 0.

[quadratic / square trinomial]

given 4c² + 7c – 5 = 0,

↓ ↓ ↓

a b c

where c = x,

c = (-b ± √ (b² – 4ac) ) / 2a.

c = (-(7) ± √ ((7)² – (4)(4)(-5)) ) / 2(4)

c = (-7 ± √ (49 – (-80)) ) / 8

c = (-7 ± √ (129) ) / 8

c = -7 ± √129 / 8

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:

C

Step-by-step explanation:

Mean is calculated as

mean = [tex]\frac{sum}{count}[/tex] , then

[tex]\frac{sum}{40}[/tex] = 70 ( multiply both sides by 40 )

sum = 40 × 70 = 2800 → C

Answer: c<2

Step-by-step explanation:

-6c<-12

c<-12/-6

c<2

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:

split the other three in half

Step-by-step explanation:

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:

C 0.90

Step-by-step explanation:

Add 0.10 and 0.80=0.90

Answer:

D

Step-by-step explanation:

P(A and B)=P(A)×P(B)=0.80×0.10=0.08

Answer:

A dilation by a factor of three about Point T followed by a translation of two units downwards.

Step-by-step explanation:

When transforming functions, we will reflect/dilate the figure first and then translate it. This is directly from the order of operations.

Since we are trying to determine the transformation that was performed, we can try to map ΔS'T'U' onto ΔSTU. We can start by translating the figure and then determining any reflections/dilations.

First, we can translate ΔS'T'U' up two units to map T' onto T. This is represented by the black triangle in the image below. Let the black triangle be ΔS''T''U''. (T'' and T are the same point.)

Next, notice that from Point T'' to U'', we move nine units right and six units up.

From Point T to Point U, we move three units right and two units up.

Likewise, from Point T'' to S'', we move six units left and nine units up.

From Point T to Point S, we move two units left and three units up.

Therefore, to map ΔS''T''U'' onto ΔSTU, we dilate ΔS''T''U'' about Point T by a factor of 1/3.

Hence, by reversing the transformations, to acquire ΔS'T'U', we can see that we will dilate ΔSTU by a factor of three about Point T and then a perform a translation of two units downwards.

Answer:

Yes, because they are identical to eachother

Step-by-step explanation:

Answer:

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

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:

Y= -x^2+12x-36

Step-by-step explanation:

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.

Answer:

DE = 24

Step-by-step explanation:

The midsegment DE is half the length of the third side AC , that is

DE = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × 48 = 24

domain is  (- infinity, infinity)

range is (- infinity, infinity)

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:

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

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:

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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