which two statements would produce a tautology?

Step-by-step explanation:

Given that Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. We are to calculate the probability that Rita will need to pick atleast 5 beads before she picks a grey bead from her collection.

Prob for drawing atleast 5 beads before she picks a grey bead from her collection

= 1-Prob for drawing atleast one grey beed in the first 5 draws.

(Because these two are complementary events)

no of grey beeds drawn in first 5 trials is

Bi=(5,1/6)

Prob for drawing atleast one grey beed in the first 5 draws.

=1-Prob of no grey

Hence required prob=P(X=0 in first 5 draws)

= 0.4018

6th beeds onwards can be grey also.

Nearest answer is c)0.45

Answer:

o.45

Step-by-step explanation:

i just did the test

Answer:

Step-by-step explanation:

We will use following steps to measure exactly 4 gallons of water with the help of 5 gallons and 3 gallons empty jugs.

1). Fill 3 gallons jug completely.

2). Pour this 3 gallons of water into 5 gallons jug. Now we have 3 gallons of water in 5 gallons jug and 3 gallons jug empty.

We can add 2 gallons of water in the empty space of 5 gallons jug more.

3). Fill the 3 gallons jug with the water again.

4). Pour this water into 5 gallons jug which can hold 2 gallons of water more.

Now we have 5 gallons of jug filled fully and 1 gallon water remaining in the 3 gallons jug.

5). Empty the 5 gallons jug completely.

6). Pour the remaining 1 gallon of remaining water in 3 gallons jug into 5 gallons jug.

7). Fill the 3 gallons jug completely and pour it into 5 gallon jug.

8). Finally we have 4 gallons of water in the 5 gallons jug.

Answer:

13 Compute using the 2 right angles, we know that m<FIG=90* and

Answer:

When conducting an analysis of variance analysis on a set of samples and the null hypothesis is rejected, we can test for the difference between treatment can be tested with the aid of a t-test. This is employed when 2 related groups are involved. Independent sample, paired sample or one-sample t-test can be conducted.

Step-by-step explanation:

A t-test is a test statistic used to make inferences that determine the differences that exist statistically between 2 related groups. It tells us if the 2 groups tested are from the same population. There are 3 types of t-test namely independent sample t-test, paired-sample t-test and one-sample t-test

Answer:

The answer is A because 45x2= 90 miles and 80×1 = 80 miles and 90-80= 10 so Vehicle A travels 10 miled farther than Vehicle B. Hope that helps!

Vehicle which travels the farthest is vehicle A and the distance it travels farther is 10 miles.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Speed of vehicle A = 45 miles per hour

Speed of vehicle B = 80 miles per hour

Vehicle A travels for 2 hours.

Total distance travelled = Speed × Time = 45 × 2 = 90 miles

Vehicle B travels for 1 hour.

Distance travelled = 80 miles

Vehicle A travels farthest since the distance is greater for A.

Difference in the distance = 90 - 80 = 10 miles

Hence the vehicle A travels 10 miles farther.

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Answer:

c = 5.5

Step-by-step explanation:

We can find the slope of the line using the given points (5,5) and (-3,1) using rise over run:

-4/-8 = 1/2

Now, we can plug in the slope and a point into the equation y = mx + b to find b:

5 = 1/2(5) + b

5 = 2.5 + b

2.5 = b

Then, we can plug in 6 in the point (6,c) to find c:

y = (1/2)(6) + 2.5

y = 3 + 2.5

y = 5.5

c = 5.5

Answer:

c = 5.5

Step-by-step explanation:

Find the slope with two points

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

m = (1-5)/(-3-5)

   = -4/-8

   = 1/2

If all the points are on the same line, then they have the same slope

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

Using the first and third points

1/2 = (c-5)/(6-5)

1/2 =  (c-5)/1

1/2 = c-5

Add 5 to each side

5+1/2 = c

5.5 =c

Hey there! :)

Answer:

(x - 9)(x - 3)

Step-by-step explanation:

We are given the polynomial:

x² - 12x + 27

Factor the equation by finding two numbers that sum up to -12 and multiply into 27. The numbers -9 and -3 satisfy these conditions:

Therefore, the equation in factored form would be:

(x - 9)(x - 3)

(x - 9)(x-3)

multiply the first and last numbers of the equation to get 27

find two numbers that multiply to 27 and add to  - 12 [the middle number]

- 9 and -3 multiply to 27 and add to  - 12

because there is no coefficient on the x2, thats your answer. (x - 9)(x-3)

hope that makes some sense :)

...with 6 dice

15,625 / 46,656

33.49 %

31,031 / 46,656

66.51 %

Answer:

21794.495 units/month

Step-by-step explanation:

Some data are missing which i can assume as per requirement of the Question.

Let us consider that profit generated by a product is given by

p(x) =4√x

Also, consider that the profit keeps changing at a rate of $1000 per month.

Now, Using the chain rule we can write

dp/dx=(dp/dt)÷(dx/dt).

So, we  can calculate

dp/dx=2x^(-1/2)=2/√x.

As per  question we have to find out  dx/dt

Since, dx/dt= (dp/dt)/(dp/dx),

so plugging  x=1900  we get 1000√1900/2=21794.495 units/month increase in sales.

Answer:

x-intercept: 2 y-intercept= -4

Step-by-step explanation:

First, change the given equation 4x-2y>8 to slope-intercept form, which is y=mx+b. We do this by solving for y.

4x-2y>8. Subtract 4x from each side

-2y> -4x+8. Divide by -2. Don't forget to switch the sign!

y< 2x-4  is our equation in slope-intercept form.

Now, we can graph it. We know the slope (m)= 2 and the y-intercept= -4. Start at -4 and move up two, over one, making points until you can form a line. We can see from the graph that when x=0, (0, -4) y= -4. When y=0, (2, 0), x=2. These are our intercepts of the graph!

Hope this helps!

The graph of inequality 2x - y > 4 is shown in image.

We have to given that,

The inequality is,

⇒ 4x - 2y > 8

Since, A relation by which we can compare two or more mathematical expression is called an inequality.

Now, We can simplify it as,

⇒ 4x - 2y > 8

Take 2 as common,

⇒ 2 (2x - y) > 8

⇒ 2x - y > 4

So, The graph of inequality 2x - y > 4 is shown in image.

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Answer:

SSS

Step-by-step explanation:

ST is congruent to SQ

QP is congruent to TP

SP is congruent to SP (reflexive property)

3 sides are congruent, SSS

Answer:

SSS Postulate

Step-by-step explanation:

According to side-side-side postulate, the triangles are congruent

Since,

=> TP = PQ

=> ST = SQ

=> SP = SP (Common)

Answer:

The answer is option B.

Step-by-step explanation:

f(x) = √x

g(x) = x - 7

To find f o g(x) replace every x in f (x) by

g(x)

That's

[tex]f \: o \: g \: (x) = \sqrt{x - 7} [/tex]

Hope this helps you

Answer:

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

Step-by-step explanation:

Given;

Confidence interval CI = (a,b) = (0.036, 0.086)

Lower bound a = 0.036

Upper bound b = 0.086

To express in the form;

p-e< p < p+e

Where;

p = mean Proportion

and

e = margin of error

The mean p =( lower bound + higher bound)/2

p = (a+b)/2

Substituting the values;

p = (0.036+0.086)/2

Mean Proportion p = 0.061

The margin of error e = (b-a)/2

Substituting the given values;

e = (0.086-0.036)/2

e = 0.025

Re-writing in the stated form, with p = 0.061 and e = 0.025

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

Answer:

There are six possible forms of 4-digit numbers consisting of two odd digits and two even digits:

OOEE

OEOE

OEEO

EEOO

EOEO

EOOE

Each of the three forms starting with (O)dd digits can form 5^4 = 625 numbers, since there are 5 odd and 5 even digits.

Each of the three forms starting with (E)ven digits can form 4*5^3 = 500 numbers, since the first digit cannot be zero.

Therefore, the total numbers possible is 3*(625+500)

= 3,375

Step-by-step explanation:

Answer:

Therefore the x - coordinate of the minimum is x = -8

Step-by-step explanation:

[tex]y = 2x^2 + 32x + 56 = 2(x^2 + 16x ) + 56 = 2(x^2 + 16x +64 - 64) + 56 \\= 2(x^2 + 16x +64) - 128 + 56 = 2(x+8)^2 - 72[/tex]

Therefore the x - coordinate of the minimum is x = -8

Answer:

  5/9

Step-by-step explanation:

  total present = males + females = 60 + 48 = 108

The desired ratio is ...

  males/total present = 60/108 = 5/9

The ratio of the males to the total number of people present is 5/9

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

Giiven,

No. of males present at rally = 60

No. of females present at rally = 48

Total no. of people present = males + females = 60 + 48 = 108

The ratio of the males to the total number of people present = No. of males /Total present

∴ No. of males/Total present = 60/108 = 5/9

Thus, the ratio of the males to the total number of people present is 5/9

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Answer:

A) 8

Step-by-step explanation:

The average of two numbers is 7.

6 and x have an average of 7.

sum of terms / number of terms = average

(6 + x)/2 = 7

6+x = 14

x = 8

The number is 8.

Answer: a 8

i forgot how I got that answer

[tex]-9x+3y = 0\\\\-9x = -3y\\\\3x = y\\\\\\12x+4y =24\\\\3x+y = 6\\\\y+y=6\\\\2y =6\\\\y =3 \\\\3x=y\\\\x = 1\\\\(x,y) = (1,3)[/tex]

Answer:

A discrete data set because there are a finite number of possible values.

Step-by-step explanation:

We are given the following data set below;

When a car is randomly selected, it is found to have 8 windows.

Firstly, as we know that the discrete data is that data that have countable or finite values, and also we can observe at a point value.

On the other hand, the continuous data is that data in which there is a range of values and we can't count or observe each and every value.

So, in our question; as we can observe that we can count all the windows and it is also a finite number which means that the given data set is a discrete data set because there are a finite number of possible values.

Answer:

452.4

Step-by-step equation:

surface area of a sphere formula= 4πr²

plug 6 in for r

4π(6)² =452.389 rounded  to 452.4

Answer:

93 ft

Step-by-step explanation:

the area of a triangle is :

A = (b*h)/2 where b is the base and h the height(here t)

4092 = (88*t)/2

2*4092 = 88*t

t= (4092*2)/88 = 93 ft

Answer:

  see attached

Step-by-step explanation:

The limit as x gets large is the ratio of the highest-degree terms. In most cases, the limit can be found by evaluating that ratio. Where an absolute value is involved, the absolute value of the highest-degree term is used.

If the ratio gives x to a positive power, the limit does not exist. If the ratio gives x to a negative power, the limit is zero.

The arrangement of functions according to the given condition

[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]

[tex]h(x)=\frac{x^{3} -x^{2} +4}{1-3x^{2} }[/tex]

[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]

[tex]i(x)=\frac{x-1}{|1-4x| }[/tex]

[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]

[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]

[tex]f(x)=\frac{x^{2} -1000}{x-5}[/tex]

[tex]j(x)=\frac{x^{2}-1 }{|7x-1|}[/tex]

A limit is the value that  a function approaches as the input approaches some value.

According to the given question

[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]

⇒[tex]\lim_{nx\to \infty} \frac{5x^{2} -1}{x^{2} +1}[/tex]

⇒[tex]\lim_{x \to \infty} \frac{x^{2} }{x^{2} } \frac{5-\frac{1}{x^{2} } }{1+\frac{1}{x^{2} } }[/tex]

= 5           ([tex]\frac{1}{x^{2} } = 0[/tex] ,as x tends to infinity  [tex]\frac{1}{x^{2} }[/tex] tends to 0)

[tex]i(x)=\frac{x-1}{|1-4x|}[/tex]

⇒[tex]\lim_{x \to \infty} \frac{x-1}{|1-4x|}[/tex] =  [tex]\lim_{x \to \infty} \frac{x}{x} \frac{1-\frac{1}{x} }{|\frac{-1}{4}+\frac{1}{x} | }[/tex]  =[tex]\frac{1}{\frac{1}{4} }[/tex] =[tex]\frac{1}{4}[/tex]

As x tends to infinity 1/x tends to 0, and |[tex]\frac{-1}{4}[/tex]| gives 1/4

[tex]f(x)= \frac{x^{2} -1000}{x--5}[/tex]

⇒[tex]\lim_{x \to \infty} \frac{x^{2} -1000}{x-5}[/tex]= [tex]\lim_{x \to \infty} \frac{x^{2} }{x} \frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex]= [tex]\lim_{x \to \infty} x\frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex] ⇒ limit doesn't exist.

[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]

⇒[tex]\lim_{x\to \infty} \frac{4x^{2} -6}{1-4x^{2} }[/tex]=[tex]\lim_{x\to \infty} \frac{x^{2} }{x^{2} } \frac{4-\frac{6}{x^{2} } }{\frac{1}{x^{2} } -4}[/tex]  [tex]= \lim_{n \to \infty} \frac{4}{-4}[/tex] = -1

As x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0.

[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]

⇒[tex]\lim_{x\to \infty} \frac{|4x-1|}{x-4}[/tex] = [tex]\lim_{x \to \infty} \frac{|x|}{x} \frac{4-\frac{1}{x} }{1 -\frac{4}{x} } }[/tex] = 4

as x tends to infinity 1/x tends to 0

and |x|=x ⇒[tex]\frac{|x|}{x}=1[/tex]

[tex]h(x)=\frac{x^{3}-x^{2} +4 }{1-3x^{3} }[/tex][tex]\lim_{x \to \infty} \frac{x^{3} -x^{2} +4}{1-3x^{3} }[/tex][tex]= \lim_{x \to \infty} \frac{x^{3} }{x^{3} } \frac{1-\frac{1}{x}+\frac{4}{x^{3} } }{\frac{1}{x^{3} -3} }[/tex]  = [tex]\frac{1}{-3}[/tex] =[tex]-\frac{1}{3}[/tex]

[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]

[tex]\lim_{x \to \infty} \frac{5x+1000}{x^{2} }[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{5+\frac{1000}{x} }{x}[/tex] =0

As x tends to infinity 1/x tends to 0

[tex]j(x)= \frac{x^{2}-1 }{|7x-1|}[/tex]

[tex]\lim_{x \to \infty} \frac{x^{2}-1 }{|7x-1|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{|x|}\frac{x-\frac{1}{x} }{|7-\frac{1}{x}| }[/tex]  = [tex]\lim_{x \to \infty} 7x[/tex] = limit doesn't exist.

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Answer: Categorical

Step-by-step explanation:

A quantitative variable is represented by a number.  An example of a quantitative variable would be how many pounds of food the manatees ate.

Hope it helps <3

Answer:

$1.20

Step-by-step explanation:

First we need to find the probability of winning the game.

If there are 8 winning ducks among 50 ducks, and we can pick only one, the probability of winning is 8/50 = 0.16, therefore the probability of losing the game is 1 - 0.16 = 0.84.

The player pays $2 to play, so if the player loses, the owner of the game wins $2, and if the player wins, the owner loses $3 (he receives $2 but pays the prize of $5).

Now, to find the expected value of the game, we just need to multiply the price of winning by the corresponding probability and summing with the same product but related to losing the game:

[tex]Expected\ value = p(winning)*v(winning) + p(losing)*v(losing)[/tex]

[tex]Expected\ value = 0.16 * (-3) + 0.84 * (2)[/tex]

[tex]Expected\ value = \$1.20[/tex]

Answer:

Step-by-step explanation:

Given Forty-two divided by seven plus the quantity three divided by six, the equivalent numerical expression will be;

[tex]\frac{42}{7} + \frac{3}{6}[/tex]

To evaluate the numerical expression, we will find the LCM of the denominator

[tex]\frac{42}{7} + \frac{3}{6} = \frac{6(42)+7(3)}{42}\\ = \frac{252+21}{42}\\= \frac{273}{42}\\= 6.5[/tex]

The value of the expression 6.5

Answer:

Write and simplify this numerical expression.

  Forty-two divided by seven plus the quantity three divided by six

1.  Write the numerical expression.  

✔ 42 ÷ 7 + (3 ÷ 6)

2.  Evaluate within parentheses.  

✔ 42 ÷ 7 + 0.5

3.  There are no exponents to evaluate.

4.  Multiply and divide from left to right.  

✔ 6 + 0.5

5.  Add and subtract from left to right.  

✔ 6.5

Step-by-step explanation:

hope this helps! :)

Answer:

-41

Step-by-step explanation:

(7 + 1) - (11 + 39) =

= 8 - 50

= -41

Answer:

Step-by-step explanation:

Do the work inside parentheses first.  We get:

(8) - (50)(4), or

8 - 200 = -192

Answer:

b. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.

Step-by-step explanation:

A square matrix is said to be invertible if the product of the matrix and its inverse result into an identity matrix.

3  0 -4

2  0  6

-3 0  8

Since the second column elements are all zero, the determinant of the matrix is zero ad this implies that the inverse of the matrix does not exist(i.e it is not invertible )

A square matrix is said to be invertible if it has an inverse.

The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.

The matrix is given as:

[tex]\left[\begin{array}{ccc}3&0&-4\\2&0&6\\-3&0&8\end{array}\right][/tex]

Calculate the determinant

The determinant of the matrix calculate as:

[tex]|A| = 3 \times(0 \times 8- 6 \times 0) - 0(2 \times 8 - 6 \times -3) -4(2 \times 0 - 0 \times -3)[/tex]

[tex]|A| = 3 \times(0) - 0(34) -4(0)[/tex]

[tex]|A| = 0 - 0 -0[/tex]

[tex]|A| = 0[/tex]

When a matrix has its determinant to be 0, then

Hence, the correct option is (b)

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Step-by-step explanation:

Place one point at 3,-6 and the other at 5,-7

It doesn't matter where you place the second point, as long as the slope is -1/2. This means that the line goes one half down for every unit it goes to the right, so it goes down one unit when it goes two units to the right.

Answer:

123.75 g  

Step-by-step explanation:

You have three unknowns: protein (p), carbohydrate (c), and fat (f)

You need three equations for the three unknowns.  They are

(1)    p +   c +   f =    725

(2) 4p + 4c + 9f = 3500

(3) 4p         + 9f = 0.45(3500) = 1575

Subtract (3) from (2)

   4c = 1925

(4)  c =   481.25

Substitute (4) into (1)

    p + 481.25 + f = 725

(5) p +                f = 243.75

Multiply (5) by 4

(6) 4p + 4f = 975

Subtract (6) from (3)

  5f = 600

(7) f =   120

Substitute (7) into (3)

4p + 1080 = 1575

4p             =   495

 p             =    123.75

The diet will include 123.75 g of protein.

Check:

[tex]\begin{array}{rcl}\\123.75 + 481.25 + 120 &=&725\\ 725 & = & 725\\&&\\4(123.75) + 4(481.25) + 9(120) &=& 3500\\495 + 1925 + 1080& =& 3500\\3500 &=& 3500\\&&\\4(123.75) + 9(120) &=& 1575\\495 + 1080&=& 1575\\1575&=& 1575\\\end{array}[/tex]

It checks.

Answer:

b is the answer

Step-by-step explanation: