Given the two original statements, can a true conclusion be met? If so, what would it be? If not, why not?

1) If it is June, then it is summer.
2) It is summer.

Conclusion:

Answer: A is the right answer. The probability of the alarm code beginning with a number greater than 7 =[tex]\frac{^2P_1\times\ ^9P_3}{^{10}P_4}[/tex].

Step-by-step explanation:

Given:A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.  

there is only 2 numbers which are greater than 7 i.e. 8 and 9. ∴ there is 2 possibility for first place.

For the remaining 3 digits there is 9 possibilities (including 1 which would left after choosing 1 from first place )

No of ways for the alarm code beginning with a number greater than 7=[tex]^2P_1\times\ ^9P_3[/tex]

Total ways of code with 4 digits=[tex]^{10}P_4[/tex]

Therefore the probability of the alarm code beginning with a number greater than 7 =[tex]\frac{^2P_1\times\ ^9P_3}{^{10}P_4}[/tex].

The probability that a randomly selected marble is either large or green is approximately 0.6333 or you can express it as a fraction: 19/30.

Consider the total number of marbles that satisfy either of these conditions.

Total large marbles: 19

Total green marbles: 5

However, the large marbles include the green marbles, so we need to subtract the overlap:

Number of large green marbles: 5

Total marbles that are either large or green = Total large marbles + Total green marbles - Number of large green marbles

Total marbles that are either large or green = 19 + 5 - 5

= 19

Now, we'll find the probability by dividing the total marbles that are either large or green by the total number of marbles:

Probability = (Total marbles that are either large or green) / (Total number of marbles)

Probability = 19 / (19 + 11)

Probability ≈ 0.6333 (rounded to four decimal places)

Therefore, the probability that a randomly selected marble is either large or green is approximately 0.6333 or you can express it as a fraction: 19/30.

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The probability that randomly selected marble from the box is large or green is 0.7667.

The probability of selecting a large or green marble from a box can be found by analysing the given information. We have 19 large marbles, out of which 5 are green. We also have 11 small marbles, out of which 6 are small and green since small marbles cannot be large. This means there are a total of 30 marbles (19 large and 11 small), and 9 of them are green. To calculate the probability that a marble is large or green, we need to include all large marbles (since they meet one condition) and add the small green marbles (since they meet the other condition, but aren't already counted with the large marbles).

The number of favorable outcomes is therefore 19 (large marbles) plus 4 (small green marbles), since 5 large marbles have already been counted as green, we don't count them again. That makes a total of 23 favorable outcomes. The probability is the number of favorable outcomes divided by the total number of marbles:

Probability = 23 / 30. As a decimal rounded to four places, this is approximately 0.7667.

1000 chips minimize the production cost in the given equation, and the minimum cost for producing these chips is $20.

To find the number of chips that minimizes the cost in the given quadratic equation, y = 0.000015x^2 - 0.03x + 35, we can use the vertex formula for a parabola, which is derived from the general quadratic equation.

The general form of a quadratic equation is y = ax^2 + bx + c, and the x-coordinate of the vertex, which gives us the number of chips that minimizes the cost, can be found using x = -b/(2a). For our equation, a = 0.000015 and b = -0.03.

Substituting the values of a and b into the vertex formula:

Now, we plug this value back into the original equation to find the minimum cost:

This gives us the minimum cost and the number of chips that lead to this cost. Therefore, 1000 chips minimize the cost, and the minimum cost for producing these chips is $20.

Answer:

AA' + BB' + CC' + DD' +EE' = 27.5 inches

Step-by-step explanation:

A translation moves all points of a figure the same distance in the same direction. If line segment YZ is 5.5 inches long, then the distance between original point A and translated point A' would be 5.5 inches. That is also valid to the other points. So, length of AA' = BB' = CC' = DD' = EE' = 5.5 inches. In consequence, AA' + BB' + CC' + DD' +EE' = 5*5.5 inches = 27.5 inches

Answer:

[tex]P=12n+8[/tex]

Step-by-step explanation:

A square is a geometric figure that is made up of four equal and parallel sides.

The perimeter is the contour of a surface or figure.  In other words, in a figure, the perimeter is the sum of all its sides.

In this sense, since in a square all its sides are equal, the perimeter of a square is given by:

[tex]Perimeter=P=l+l+l+l=4l\\\\Where:\\\\l=Length \hspace{3}of \hspace{3}one\hspace{3} of\hspace{3} its\hspace{3} sides[/tex]

So, in this case:

[tex]l=3n+2[/tex]

Therefore the perimeter is:

[tex]P=3n+2+3n+2+3n+2+3n+2[/tex]

Adding like terms:

[tex]P=(3n+3n+3n+3n)+(2+2+2+2)=12n+8[/tex]

Answer:

The expresion for the phrase is:

[tex]\frac{2x}{8}[/tex]

Step-by-step explanation:

In order to get the expression for the phrase, we have to understand the described operations in it.

The phrase starts with "the quotient of...", therefore the expression must be a fraction:

[tex]\frac{A}{B}[/tex]

To get what is the numerator (A) and the denominator (B), we have to analyze carefully the rest of the phrase: "...2 times a number and 8"

In this case, the word "and" separates the numerator from the denominator:

Numerator: "2 times a number"

This unknown number is called x

Therefore, numerator of the fraction (A) is:

[tex]A = 2x[/tex]

And the Denominator: "8"

Therefore: [tex]B=8[/tex]

Finally, replacing values:

[tex]\frac{A}{B} = \frac{2x}{8}[/tex]

The two function types where f(x) tends to 0 as x approaches negative infinity are the reciprocal function (y=1/x) and the root function (y=√^n x) where n is even and greater than zero.

The question asks which function types have the end behavior f(x) → 0 as x → -∞ (negative infinity). To answer this, we consider the given functions:

Of these functions, the ones that exhibit the end behavior of f(x) heading towards zero as x heads towards negative infinity are:

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Answer:

[tex]7.4\times 10^{-3}\ mm[/tex]

Step-by-step explanation:

Actual measurement of diameter of a blood cell is 6 to 8 μm

Let diameter be d

[tex]1\mu m=10^{-6}\ m[/tex]

[tex]6\times 10^{-6}\ m\leq d\leq 8\times 10^{-6}\ m[/tex]

Now we check the given measurement between the range.

Change into meter. As we know 1000 mm = 1 m or 1 mm = 10⁻³ m

[tex]7.4\times 10^{-3}\times 10^{-3}\ m[/tex]

[tex]7.4\times 10^{-6}\ m[/tex]

[tex]7.4\times 10^{3}\times 10^{-3}\ m[/tex]

[tex]7.4\ m[/tex]

So, [tex]7.4\times 10^{-6}\ m[/tex] lie between [tex]6\times 10^{-6}\ m\leq d\leq 8\times 10^{-6}\ m[/tex]

Hence, [tex]7.4\times 10^{-6}\ m[/tex] more reasonable measurement of diameter of blood cell because it lies between range of diameter of blood cell.

Answer:

-24

Step-by-step explanation:

We are given that

[tex]b(n)=-8-2(n-1)[/tex]

We have to find the 9th term in the sequence.

Substitute n=1

Then, we get

[tex]b(1)=-8[/tex]

Substitute n=2

Then,we get

b(2)=-8-2(2-1)=-8-2=-10

n=3

b(3)=-8-2(3-1)=-8-4=-12

[tex]d_1=b(2)-b(1)=-10-(-8)=-2[/tex]

[tex]d_2=b(3)-b(2)=-12-(-10)=-2[/tex]

[tex]d_1=d_2=d=-2[/tex]

When the difference  between two consecutive terms is constant then, the sequence is called arithmetic sequence.

Therefore, the given sequence is in A.P

The nth term of A.P is given by

[tex]a_n=a+(n-1)d[/tex]

We have, [tex]a=b(1)=-8[/tex]

[tex]d=-2[/tex]

n=9

Substitute the values in the formula

[tex]a_9=-8+(9-1)(-2)=-8-16=-24[/tex]

[tex]a_9=b(9)=-24[/tex]

The number of bags of sand that Jack need to fill the box completely are:

                                        2

The length(l) of the sand box is 3 feet, width(w) is 6 inches, and height(h) is 2.4 inches.

Also,

1 foot=12 inches

This means that:

1 inch=1/12 foot

i.e.

6 inches=0.5 feet

i.e.

w=0.5 feet

and

h=2.4 inches

i.e.  h=0.2 feet

Now, we find the volume of the rectangular box.

The volume of the rectangular box is given by:

Volume=lwh

Hence,

Volume=3×0.5×0.2

i.e.

Volume=0.3 cubic feet.

Also, the volume of one bag of sand= 0.15 cubic feet

This means that the number of bags of sand that will fill the box completely is:

(Volume of rectangular box) / (Volume of one bag of sand)

=   0.3/0.15

=2

Hence, number of bags =2

Answer:

D. Multiply equation A by −3.

Step-by-step explanation:

We have been given a system of equations.

Equation A: [tex]x + z = 6[/tex]

Equation B: [tex]2x + 3z = 1[/tex]

We are asked to determine the possible step used in eliminating the z-term.

We can see that coefficient of z term is  equation B is 3, so eliminate z term from the both equations the coefficient of z term is equation A should be [tex]-3[/tex].

We can make coefficient of z term to [tex]-3[/tex] in equation A by multiplying equation A by [tex]-3[/tex] that will give us:

[tex]-3\cdot x + -3\cdot z =-3\cdot 6[/tex]

[tex]-3x-3z =-18[/tex]

Now, adding equation A and equation B the z term will get eliminated.

Therefore, option D is the correct choice.

Final answer:

To find the total number of cars sold in Chicago, we can use percentages and proportions. We can set up a proportion and solve for the unknown variable. The total number of cars sold in Chicago is 1700.

Explanation:

To solve this problem, we can use the concept of percentages and proportions. We are given that 85% of all cars sold in Chicago are some color other than black, and we also know that 300 black cars were sold. We need to find the total number of cars sold in Chicago.

First, let's find the ratio of black cars to colored cars. Since the percentage of colored cars is 85%, the percentage of black cars would be 100% - 85% = 15%. We can express this as a ratio by writing it as 15/100.

Now, let's set up a proportion:

x/300 = 85/15

Next, we can cross-multiply and solve for x:

15x = 300 * 85

x = (300 * 85) / 15

x = 1700

Therefore, the total number of cars sold in Chicago is 1700.

x = hours

car 1 left an hour before car 2 so you have 55(x+1)

car 2 = 75x

 add them together to equal miles driven:

55(x+1) + 75x = 380

55x+55 + 75x = 380

 combine like terms:

130x+55 = 380

 subtract 55 from each side:

130x = 325

divide both sides by 130

x = 325 /130 = 2.5

x = 2.5 hours

 so 2.5 hours