Which compound inequality is represented by the graph?
-3≤x<1
-3 < x≤1
x≤-3 or x> 1
x<-3 or x ≥ 1

Answers

Answer 1

The inequality will be the negative 3 ≤ x < 1. Then the correct option is A.

The missing graph is attached below.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Then the inequality will be

-3 ≤ x < 1

Then the correct option is A.

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Which Compound Inequality Is Represented By The Graph?-3x&lt;1-3 &lt; X1x-3 Or X&gt; 1x&lt;-3 Or X 1
Answer 2

Answer:

the answer is A

Step-by-step explanation:


Related Questions

The points (0, -8) and (10, 2) represent the endpoints of a diameter of a circle. Which of the following represents the equation of this circle?

Answers

Answer:

(x-5)²+(y+2)²=200.

Step-by-step explanation:

1) using the given coordinates it is possible to calculate

- the centre of the given circle:

[tex]x_0=\frac{10+0}{2}=5; \ y_0=\frac{2-8}{2}=-2;[/tex]

- the radius of the given circle:

[tex]r=\sqrt{(10-0)^2+(2+8)^2} =\sqrt{200} ;[/tex]

2) finally, the required equation (common form is (x-x₀)²+(y-y₀)²=r²):

(x-5)²+(y+2)²=200.

Suppose a bag contains a set of 10 tiled letters: M, T, O, A, T, P, J, A, K, A You draw a tile from the bag, and record the letter and leave it on the table. You shake up the bag, and draw another tile out of the bag. Calculate the probability you will select the letter M on the first draw and the Letter T on the second draw?

Answers

Answer:

1/90

Step-by-step explanation:

Comment

To begin with, there are 10 tiles.. You draw one and don't replace it. Then you draw another tile from the 9 that remain.  The job is to figure out the probability of that happening.

You have a 1/10 chance of drawing the M.

But now there are only 9 tiles left and you have a 1 in 9 chance of drawing a T

Solution

P(M,T) = 1/10 * 1/9 = 1 / 90

You have a 1 in 90 chance of getting the two tiles in the order you have specified.

What is the value of this expression when c = -4 and d = 10?


A.
2
B.
9
C.
21
D.
41

Answers

The complete question is

"What is the value of this expression when c= -4 and d= 10?

1/4 (c^3+d²)

A.2

B.9

C.21

D.41"

The value of this expression when c = -4 and d = 10 will be option B 9.

What is a simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given expression is

[tex]1/4 (c^3+d^2)\\\\1/4 ((-4)^3+(10)^2)\\\\1/4 ( -64 + 100)\\\\1/4 (36)\\\\9[/tex]

Hence, the value of this expression when c = -4 and d = 10 will be option B 9.

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has a bag containing twenty balls. There are twice as many yellow balls than blue balls, but the yellow balls are only a third of the red balls. The green balls are the same number as the blue balls. How many are each of the colour ball?

Answers

Answer:

Yellow: 4

blue: 2

red: 12

green: 2

urgent help algebra 2

Answers

Slope-intercept you have right:
y=3/4x-7

Point slope form is:
y − y1 = m(x − x1)

so

y +7 = 3/4(x -0)

or

y + 7 = 3/4x

Two angles are complentary if the sum of their measures is 90 °. Find two complentary angles such that one of the angles is 165° less than 4 times the other angle

Answers

Answer:

51° and 39°

Step-by-step explanation:

x + 4x - 165 = 90

5x = 90 + 165

5x = 255

x = 255 / 5

x = 51

4 x 51 = 204

204 - 165 = 39

2 angles are 51 and 39

(3x + 5y = 7
{ 4x - y = 5

Answers

Answer:

Step-by-step explanation:

Solution by substitution method

3x+5y=7

and 4x-y=5

Suppose,

3x+5y=7→(1)

and 4x-y=5→(2)

Taking equation (2), we have

4x-y=5

⇒y=4x-5→(3)

Putting y=4x-5 in equation (1), we get

3x+5y=7

⇒3x+5(4x-5)=7

⇒3x+20x-25=7

⇒23x-25=7

⇒23x=7+25

⇒23x=32

⇒x=32/23

→(4)

Now, Putting x=32/23

in equation (3), we get

y=4x-5

⇒y=4(32/23)-5

⇒y=(128-115)/23

⇒y=13/23

∴y=13/23   and x=32/23

John is 5 years younger than David. Four years later David will be twice as old as John. Find their present age.​

Answers

David will be 10 and John will be 9

I cannot crack this one, somebody please assist me

Answers

These [tex]N[/tex] outcomes make up the entire sample space, so

[tex]\displaystyle \sum_{k=1}^N P(e_k) = P(e_1) + P(e_2) + P(e_3) + \cdots + P(e_N) = 1[/tex]

We're given that [tex]P(e_{j+1}) = 2 P(e_j)[/tex] for all [tex]j\in\{1,2,\ldots,N-1\}[/tex], so

[tex]P(e_1) + 2 P(e_1) + 2^2 P(e_1) + \cdots + 2^{N-1} P(e_1) = 1 \\\\ \implies P(e_1) = \dfrac1{1 + 2 + 2^2 + \cdots + 2^{N-1}} = \dfrac1{2^N - 1}[/tex]

Then we can solve the recurrence relation to get the probability of the [tex]j[/tex]-th outcome,

[tex]P(e_{j+1}) = 2 P(e_j) = 2^2 P(e_{j-1}) = 2^3 P(e_{j-2}) = \cdots \\\\ \implies P(e_{j+1}) = 2^j P(e_1) \\\\ \implies P(e_j) = 2^{j-1} P(e_1) = \dfrac{2^{j-1}}{2^N - 1}[/tex]

The probability of getting this sequence of [tex]k[/tex] outcomes is then

[tex]\displaystyle P(E_k) = P(e_1) + P(e_2) + \cdots + P(e_k) = \sum_{j=1}^k \frac{2^{j-1}}{2^N-1} = \frac{2^k-1}{2^N-1}[/tex]

as required.

Some preliminary results: If [tex]S[/tex] is the sum of the first [tex]n[/tex] terms of a geometric series with first term [tex]a[/tex] and common ratio [tex]r[/tex], then

[tex]S = a + ar + ar^2 + \cdots + ar^{n-1}[/tex]

[tex]\implies rS = ar + ar^2 + ar^3 + \cdots + ar^n[/tex]

[tex]\implies S - rS = a(1 - r^n)[/tex]

[tex]\implies S = \dfrac{a(1 - r^n)}{1 - r}[/tex]

which gives us, for instance,

[tex]1 + 2 + 2^2 + \cdots + 2^{N-1} = \dfrac{1 - 2^N}{1 - 2} = 2^N-1[/tex]

6 Solve each equation. Round to the nearest ten-thousandth. Check your answers.
2.
4x = 19

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\text{4x = 19}\\\\\large\textbf{DIVIDE 4 to BOTH SIDES}\\\\\rm{\dfrac{4x}{4} = \dfrac{19}{4}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\rm{x = \dfrac{19}{4}}\\\\\rm{x = 19 \div 4}\\\\\text{x = 4.75}\\\\\rm{x \approx 4.7500}\\\\\\\huge\text{Therefore, the answer should be: \boxed{\mathsf{4.7500}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Which pairs of angles are congruent?

Answers

Answer:

b) angles 1 and 4 are congruent.

Hope it helps!

my dad began paying me an allowance when i was in eighth grade. what is the indirect object?

Answers

Answer:

Step-by-step explanation:

The answer would be "me" as the indirect object

Each year the Royal London company gives
its employees a gift box containing 6 bags of
coffee, 4 boxes of tea, and 2 boxes of biscuits.
If in the first three years, the number of
employees grew from 2 to 12 to 18, what was
the total quantity of coffee, tea, & biscuits
distributed by the company in those years?

Answers

The total number of tea received in three years is 192.

The total number of coffee received in three years is 128.

The total number of biscuits received in three years is 64.

What is the total quantity of tea, coffee and biscuits distributed in the three years?

The total quantity of tea, coffee and biscuits received in the first year = (6 x 2) , (4 x 2) ,  (2 x 2) = 12, 8, 4 respectively

The total quantity of tea, coffee and biscuits distributed in the second year = (6 x 12) , (4 x 12) ,  (2 x 12) = 72, 48, 24 respectively

The total quantity of tea, coffee and biscuits distributed in the third year = (6 x 18) , (4 x 18) ,  (2 x 18) = 108, 72, 36 respectively

Total number of tea received in three years = 108 + 72 + 12 = 192

Total number of coffee received in three years = 8 + 48 + 72 = 128

Total number of biscuits received in three years = 4 + 24 + 36 = 64

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If x is a positive integer, what is the value of x for the equation (x!-(x-3)!)\23=1?

I think the first step is knowing (x!-(x-3)!) equals to 23, but after that i'm stuck, can someone help me?

Answers

[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]

23 is a prime number, therefore there are two possibilities:

[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]

or

[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]

[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]

Now, we check if any of these solutions is also a solution to the second equation:

[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]

Therefore, 3 is not a solution.

[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]

Therefore, 4 is a solution.

[tex]\text{II.}[/tex]

[tex](x-3)!=23[/tex]

We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.

So, the only solution is [tex]x=4[/tex].

x^2 - 20x= -2x - 80 what is the intermediate step

Answers

x^2 - 18x = -80 (add 2x to both sides)

What is the scale factor from AABC to ADEF?
B
48
AA
6
A4 CE
48
6
O A.
C
B. 8
32
D

Answers

Answer: 8

Step-by-step explanation:

We are going from a smaller triangle to a larger triangle, so the scale factor is greater than 1.

Eliminate A and D.

We know scale factor = (image)/(preimage), so the scale factor is 32/4 = 8

The scale factor of dilation of the triangle is k = 8

What is Dilation?

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔDEF

where the measures of sides of ΔABC are

AB = 6 , BC = 6 and AC = 4

The measure of sides of triangle ΔDEF are

DE = 48 , EF = 48 and DF = 32

The scale factor of dilation k = measure of side DE / measure of side AB

k = 48 / 6

k = 8

Hence , the dilation factor is k =8

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Giving out brainliest to whoever answers!

Answers

Answer: Choice N

Explanation: Since volume consists of *L x W x H, you need to multiply all three components together, 25, 3, and 16. When you multiply all these together, you get your volume, which is 1200 cubic meters. *Length x Width x Height

Please answer this question!! <3 <4 <5 <6 <9

Answers

The correct answer is option C which is the angle LMO is 50°

What is trigonometry?

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

Given that:-

∠O = 70°

∠L = 60°

∠LMO =?

As we know that the sum of the three angles are 180 degree applying this relation:-

∠LOM + ∠OLM  + ∠LMO = 180

70 + 60 +  ∠LMO = 180

∠LMO = 180 - 70 - 60 = 50

Therefore the correct answer is option C which is the angle LMO is 50°

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What is the solution to this system of equations?

Negative 3 x + 5 y = negative 2. 3 x + 7 y = 26.
(4, 2)
(2, 3 and one-third)
no solution
infinitely many solution

Answers

The solution to the system of equation is (-4 , 2) , Option A is the right answer.

What are System Of equation ?

A set of equation whose factors are common are called system of equations.

It is given in the question

3x +5y = -2

3x +7y = 2

On solving this we get

-2y = -4

y = 2

On substitution in any equation

x = -4

Therefore solution to the system of equation is (-4 , 2) , Option A is the right answer.

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Answer:

A.

Step-by-step explanation:

took tha quiz

Graph A: A horizontal line goes from (1, 0.5) to (2, 0.5). Another horizontal line goes form (2, 0.2) to (7, (0, 2). Graph B: A curve starts at (0, 0), curves up to (1, 1), and then curves down to (2, 0).




Which graph represents a density curve, and why?


graph A only, because the curve is above the horizontal axis, and the area under the curve from 2 to 7 is 1


graph B only, because the curve is above the horizontal axis, and the area under the curve is equal to 1.57


both graph A and graph B, because both curves are above the horizontal axis, and both areas are positive


neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1


Pictures posted below

Answers

Answer: neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1

Step-by-step explanation:

Areas under the graphs:

Graph A

[tex](1)(0.5)+(7-2)(0.2)=1.5\\\\[/tex]

Graph B

[tex]\frac{\pi}{2}(1^{2})=\frac{\pi}{2}[/tex]

As neither of these graphs have an area of 1, neither of them are density curves.

The statement - "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.

A few fundamental principles apply to density curves:

A density curve's area beneath it represents probability.A density curve's area under it equals one.Base x height in a uniform density curve equals one.The likelihood that x = a will never occur.The likelihood that x < a is the same as that of x ≤ a.

Neither curve of Graph A nor of Graph B has the area under the curve summed up as 1, though the curve is above the horizontal axis.

Hence, because neither graph has an area of 1, even if both curves are above the horizontal axis, the statement "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.

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A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/h speed and 10 minutes earlier if he walks at a speed of 4 km/h_The distance he has to walk is​

Answers

Answer:

0.5km or 500m

Step-by-step explanation:

Given Distance = Speed x Time

In this case, we should use the difference in speed and time of the 2 scenarios.

Difference in Time = 20 mins(late) + 10 mins(early)

= 30 mins or 0.5 hour

Difference in Speed = 4km/h - 3km/h = 1km/h

Distance = 1km/h x 0.5 hr = 0.5km or 500m.

Find the slope of every line that is parallel to
the line on the graph

Answers

Answer:

[tex] - \frac{1}{6} [/tex]

Step-by-step explanation:

Using the slope formula:

[tex] \frac{ - 1 - 0}{0 - ( - 6)} = - \frac{1}{6} [/tex]

The school play sold $550 in tickets one night. The number of $8 adult tickets was 10 less than twice the number of $5 child tickets. How many tickets were sold for the adults vs the child tickets?

Answers

Answer:

This is my answer↓:

Step-by-step explanation:

He school play sold $550 in tickets one night.

The number of $8 adult tickets was 10 less than twice the number of

$5 child tickets.

How many of each ticket were sold

Let say child ticket sold = x

Adult tickets was 10 less than twice the number of    child tickets.

=> Adult ticket sold = 2x - 10

Child ticket sold = x

$5 child tickets price

=> Revenue = 5x  $

Adult ticket sold = 2x - 10

$8 Adult tickets price

=> Revenue = 8(2x - 10) =16x - 80 $

5x + 16x - 80 = 550

=> 21x = 630

=> x = 30

Child ticket sold = 30

Adult ticket sold = 50

Total ticket sold = 80

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1. Which of the following numbers is
rational?
A. 0.78
B. 0.303003000
C. √6
D. 0.3841697

Answers

Answer:

A. 0.78

Step-by-step explanation:

A rational number is a number that you can express as [tex]\frac{x}{y}[/tex] where [tex]y\neq 0[/tex].

Consider the algebraic expression √ 7 x 18 + 12.1 x 15 + π 4 x 6 + 1 9 . What is the degree of this polynomial? Identify the leading coefficient. Identify the leading term.

Answers

The degree of the provided polynomial is 18, and the leading term is √7.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

We have given an expression:

[tex]= \rm \sqrt{7}x ^{18} + 12.1x^{ 15} + \pi 4 x^ 6 + 1 9[/tex]

As we can see in the expression the greatest degree is 18.

So the degree of the polynomial is 18

And the coefficient of the variable which has a height degree is the leading term.

The leading term = √7

Thus, the degree of the provided polynomial is 18, and the leading term is √7.

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A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as
P = 0.006A2 − 0.02A + 120. Find the age to the nearest year of a man whose normal blood pressure measures 125 mmHg.

Answers

Solving a quadratic equation, the age of the man with a blood pressure of 125 mmHg is of 27 years old.

What is a quadratic function?

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

The pressure is given by:

P = 0.006A² - 0.02A + 120.

When the pressure is of 125 mmHg, we have that:

0.006A² - 0.02A + 120 = 125.

0.006A² - 0.02A - 5 = 0.

Hence the coefficients are a = 0.006, b = -0.02, c = -5, and the solutions, applying the formula are:

A = -30 and A = 27.

Age has to be positive, hence the man is 27 years old.

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Determine the number of zeros of the polynomial function. f(x) = x^4 − 6x

Answers

The factor of the function will be x and (x³ – 6). Then the zeroes of the function will be 0 and √6.

What is a factorization?

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial function is given below.

f(x) = x⁴ − 6x

Then the factor of the function will be

f(x) = x(x³ – 6)

Then the zeroes of the function will be

x = 0, √6

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Each conditional statement below is true. Write its converse. If the converse is also true, combine the statements as a biconditional.If x = —10, then x2 = 100.

Answers

The converse of the statement will be : if x^2 = 100 then x = -10, which is not true.

How to find the true statement?

In order to write a converse of a conditional statement "p then q",  will be "q then p" the hypothesis and conclusion interchanges.

Then the converse of the statement will be :

if x^2 = 100 then x = -10,

which is not true.

Since , x = +10, then x^2 = 100

Therefore, if x^2 = 100 then x = -10, which is not true.

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Help me with this please!!!!

Answers

Answer:

3

Step-by-step explanation:

Cardinalities are the number of elements in a set.

(A∩B∩C) is the very middle part of the circle, and there are 3 elements there.

Here is the histogram of a data distribution. All class widths are 1.
SO
4
3
2-
2 3
Which of the following numbers is closest to the mean of this distribution?
A. 2
OB. 3
O C. 10
OD. 5
5 6 7 8 9 10
E. 4

Answers

The correct answer is option B which is 3

What is mean?

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

Given data:-

4,3,2

The mean will be calculated as:-

Mean = (4 + 3 + 2) / 3

Mean =  9 / 3

Mean = 3

Therefore the correct answer is option B which is 3

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Carlton received 45 votes in the school council election, and Will received 60 votes. What percent of the votes did Carlton receive? PLEASE ANSWER ASAP!!!!!!!What is the exact value of cos(tan1(1))/sin(cos1(32))?Enter your answer, as a simplified fraction, in the box.cos(tan1(1))/sin(cos1(32))= What is the slope of the line that contains the points (-2, 7) and (2, 3)? The function f(x)= StartRoot negative x EndRoot is shown on the graph. Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. As random sample of 20 Clarinex-D users is obtained, and the number of patients who experienced insomnia is recorded. Find and interpret probability that 3 or fewer experienced insomnia as a side effect. i need help with this question (answer choices 15, 5, and 12) You own land worth $44,000 and your building has a replacement cost of $160,000. What would be the value of the property if the appraiser used depreciation of 30 percent PROJECT: EXPLORING IDENTITY1. What is your first name, and why did your family choose to give you this name? What meaning does your name have?2. What is your last name? What is the country of origin of your last name? Does your last name mean anything specific?3. What is your ethnic heritage? If you are multi-ethnic, do you follow the customs of one ethnicity more than the others?4. Who is your closest friend and why did you become friends with him or her? In other words, what qualities do you value the most about your closest friend?5. On a scale from 1 to 10, how much stress do you experience in your life?6. What motivates you in school?7. What is something you used to believe but now know to be incorrect?8. What do you do when you need to remember something?9. Who do you think worries more about body image: guys or girls? Why?10. Describe a time when you thought everyone was watching you only to realize that you weren't being singled out.11. If you were to describe yourself in one sentence, what would you say?12. What do you think you will be like as an adult?13. What advice would you give to someone who told you he/she wanted to become a middle or high school teacher? The maximum number of turning points of a 9th degree polynomial is? Can someone help with this q u e s t i o n p l e a s e The parent function f(x)=x is transformed to g(x) = f(-x) - 2. Which graph represents g(x)? the government should impose household trash limits persuasive essay Somebody help me please..Ill appreciate it alot thank you The canals built across New York made it easier to transport which good? A. fish from New EnglandB. coal from Appalacha C. wheat from the midwestD. cotton from the south Read the paragraph.(1) Dr. Martin Luther King Jr. uses repetition to give his speech rhythm and momentum. (2) "Let freedom ring is a phrase which is used many times in his speech. (3) "Let freedom ring is a phrase that leads to an exciting conclusion.Which revision combines sentence 2 and sentence 3 most effectively?Many times the phrase Let freedom ring is used in his speech because it is an exciting conclusion.Many times the phrase Let freedom ring is used to lead to an exciting conclusion.Let freedom ring is a phrase, and it is used to lead to an exciting conclusion many times.Let freedom ring is a phrase that is used many times to lead to an exciting conclusion.. Directions: Write T if the statement is true or F if False. _____ 1. The Filipinos cannot be compared to anything. _____ 2. The Filipinos bend and sway just like the bamboo when there are problems but remain standing after. _____ 3. The Filipinos are submissive but know when to act or fight. _____ 4. They never learned to fight for their freedom. _____ 5. They are dependent on other races. _____ 6. The Filipinos were once ruled by foreign conquerors. _____ 7. They are easily influenced by other people. _____ 8. They are friendly and good communicators. _____ 9. They can easily adjust to their community and environment. _____ 10. The essay gave us the idea that the Filipino identity is the product of the influences of other races. Use the algebra tiles to model the equation 2x + 4 = 3x + (1). Then complete the sentences. To model 2x + 4, you need: The volume of a can of Pepsi is 0.33liter. There are 12 cans in 1 cartonWhat is the volume of 5 cartons of Pepsi? What is the governments main job, as stated in the Declaration of Independence?A. to provide services such as trash pick-upB. to provide jobs for all peopleC. to protect the basic rights of all peopleD. to declare war on other countries when needed A sample of size 400 was drawn and sample mean was found tbe 99. Test whether this sample could have come from a normalpopulation with mean 100 and variance 64 at 5%significance.