what is a rational number between 9.6 and 9.7

Final answer:

The zeros of the equation -3x^4+27x^2+1200=0 are x = 16 and x = -25.

Explanation:

To find the zeros of the equation -3x^4+27x^2+1200=0, we can use the quadratic formula. Let's set our equation equal to zero:

-3x^4+27x^2+1200=0

Now, we can use the quadratic formula, which states that for an equation in the form ax^2+bx+c=0, the solutions are given by:

x = (-b ± sqrt(b^2-4ac))/(2a)

Applying this formula to our equation, we get:

x = (-27 ± sqrt(27^2-4(-3)(1200)))/(2(-3))

Simplifying further, we have:

x = (-27 ± sqrt(729+14400))/(-6)

x = (-27 ± sqrt(15129))/(-6)

x = (-27 ± 123)/(-6)

So the two solutions are:

x = (-27 + 123)/(-6) = 16

x = (-27 - 123)/(-6) = -25

The best simulation for the probability of selecting two girls is Simulation 2, which uses two standard decks of cards, with hearts and diamonds representing girls. The probability that both selected members are girls is 25%.

To simulate the probability that both class members participating in the academic challenge are girls, Simulation 2 would be more appropriate. Since each class has half boys and half girls, just like a standard deck of cards has half red suits (hearts and diamonds representing girls) and half black suits (spades and clubs representing boys), this simulation effectively mirrors the class demographics.

To calculate the probability of selecting a girl from both classes, consider the probability of drawing a heart or diamond from one deck, which is 1/2 or 0.5. Since the events are independent (what happens in one draw does not affect the other), we can multiply the probabilities for the two events: 0.5 (probability of a girl from Class A) * 0.5 (probability of a girl from Class B) = 0.25. Therefore, the probability of both selected members being girls is 25%.

Answer:

7 octaves

Step-by-step explanation:

Total number of keys in piano = 88 keys

Numbers of keys in each group called octave= 12 unique keys

We have to find the number of complete octaves on piano

Number of octaves consists of 12 keys= [tex]\frac{Total number of keys}{12}[/tex]

Number of octaves consists of 12 keys= [tex]\frac{88}{12}[/tex]

Number of octaves consists of 12 keys= 7 octaves

Hence, the correct answer is 7 octaves

Final answer:

The sum of two consecutive integers being composite is disproved by the example 7 + 8 = 15, which is prime.

Explanation:

Counterexample: The sum of any two consecutive integers being a composite number is disproved by the example: 7 + 8 = 15, which is a prime number and not composite.

Explanation: A composite number is a positive integer that has more than two distinct positive divisors. In the case of 7 + 8 = 15, 15 only has divisors 1 and 15, making it a prime number, not composite.

Understanding Conjectures: Counterexamples are essential in mathematics to disprove conjectures by showing cases where the given rule or statement does not hold true.

Answer:

23.7 yards

Step-by-step explanation:

Given :A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower. The wire makes an angle of 65° with the ground

To Find: Draw a diagram and find the length of the guy wire

Solution :

Refer the attached figure

We are given that A guy wire is stretched from the top of a tower to a point 10 yards from the base of the tower i.e. AC = 10 yards

We are also given that wire makes an angle of 65° with the ground i.e. ∠BAC = 65°

Now to find the length of the guy wire i.e. AB

We will use trigonometric ratio.

[tex]cos\theta = \frac{Base}{Hypotenuse}[/tex]

[tex]cos 65 ^{\circ} = \frac{AC}{AB}[/tex]

[tex]0.4226= \frac{10}{AB}[/tex]

[tex]AB= \frac{10}{0.4226}[/tex]

[tex]AB= 23.66[/tex]

Thus AB = 23.66 yards ≈ 23.7 yards

Hence the length of the guy wire is 23.7 yards

x=6 loves because it just does

Answer:  The total surface area is 2784 sq. inches.

Step-by-step explanation: We are given to find the total surface area of the given figure.

Let us divide the figure into two two cuboids 1 and 2 as shown in the attached figure.

We know that the surface area of a cuboid with length 'l', breadth 'b' and height 'h' is given by

[tex]S.A.=2(l_1b_1+l_1h_1+h_1b_1).[/tex]

The dimensions of the cuboid 1 are

[tex]length,~l_1=14~\textup{inches},\\\\breadth,~b_1=12~\textup{inches},\\\\height,~h_1=24-10=14~\textup{inches}.[/tex]

The dimensions of the cuboid 2 are

[tex]length,~l_2=30~\textup{inches},\\\\breadth,~b_1=14~\textup{inches},\\\\height,~h_1=10~\textup{inches}.[/tex]

Therefore, surface area of cuboid 1 is given by

[tex]S.A_1\\\\=2(l_1b_1+l_1h_1+h_1b_1)\\\\=2(14\times 12+14\times 14+14\times 12)\\\\=2(532)\\\\=1064~\textup{sq. inches.}[/tex]

And surface area of cuboid 2 is given by

[tex]S.A_2\\\\=2(l_2b_2+l_2h_2+h_2b_2)\\\\=2(30\times 14+30\times 10+14\times 10)\\\\=2(420+300+140)\\\\=2(860)\\\\=1720~\textup{sq. inches}.[/tex]

Thus, the total surface area of the figure is

[tex]S.A.=S.A_1+S.A_2=1064+1720=2784~\textup{sq. inches}.[/tex]

The length of cricket is longer than ladybug.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

Sandra used benchmark fractions to describe some insects she collected she said the ladybug is about 1/4 inch long and the cricket is about 2/3 inch long.

Here, The length of ladybug = 1/4 inch

And, The length of cricket = 2/3 inch

Now, By comparing we get;

⇒ 1/4 and 2/3

⇒ 3/12 and 8/12

⇒ 3/12 < 8/12

Hence, The length of cricket is longer than ladybug.

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Let us represent the allowance spent by Noah on Monday by the letter "x".

We know that all the fractions must always add up to 1 in such questions.

Thus, if Noah spent 1/6 of his allowance on Tuesday and 3/6 of it on Friday and he spend x amount on Monday, then these spendings must add up to 1.

In other words,

[tex] x+\frac{1}{6}+\frac{3}{6}=1 [/tex]

[tex] x+\frac{1+3}{6}=1 [/tex]

Thus, [tex] x+\frac{4}{6}=1 [/tex]

[tex] \therefore x=1-\frac{4}{6}=\frac{6-4}{6}=\frac{2}{6}=\frac{1}{3} [/tex]

Thus Noah spent a third or [tex] \frac{1}{3} [/tex] of her allowance on Monday.

Answer:

$300

Step-by-step explanation:

1.automobile​ insurance : ​$700 semiannual premium

Annual premium = $700×2=$1400

2.

Health​ insurance :$145 per month

Annual premium= $145×12=$1740

3. Life insurance: $450 annual

Total annual premium

$1400+$1740+$450=$3590

Hence his monthly expenses on premium =

[tex]\frac{3590}{12}[/tex]

=$299.16

=$300 Approximately

Number of square feet of tile will be needed to cover the kitchen floor is 238 square feet.

Given that, a rectangular kitchen floor measures 18 feet by 15 feet.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Area of a rectangular kitchen floor

= 18×15

= 270 square feet

Area covered by a stove

= 3×4

= 12 square feet

Area covered by a refrigerator

= 4×5

= 20 square feet

Area covered by tiles

= 270-(12+20)

= 270-32

= 238 square feet

Therefore, number of square feet of tile will be needed to cover the kitchen floor is 238 square feet.

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Solution:

we are given that

6 students share 4 bagels equally.

we have been asked to find that

How many pieces does each person get?

Here we will have to use the concept of division. Because we are dividing bagels among the students.

So To get the number of pieces each will get divide 6 by 4.

Number of Pieces for each boys [tex] =\frac{6}{4}=\frac{3}{2}=1\frac{1}{2} \\ [/tex]

If 5/9 of a tank can be filled in 2 minutes, it would take 3.6 minutes to fill the whole tank by setting up a proportion and solving for the time.

If 5/9 of a tank can be filled in 2 minutes, then to find the time it takes to fill the whole tank, we can set up a proportion. Since time is directly proportional to the amount of the tank filled, we have the following relationship:

Fraction of tank filled / Time to fill that fraction = 1 (whole tank) / x minutes

So, 5/9 of the tank is to 2 minutes as 1 whole tank is to x minutes:

(5/9) / 2 = 1 / x

Cross-multiplying gives us:

5x = 18

Dividing both sides by 5:

x = 18/5

x = 3.6 minutes

Therefore, it would take 3.6 minutes to fill the whole tank.

Final answer:

To find out how long it takes to fill the entire tank, set up the proportion of (5/9) of the tank in 2 minutes to (9/9) of the tank in x minutes, which gives x = 3.6 minutes for the whole tank to be filled.

Explanation:

If 5/9 of a tank can be filled in 2 minutes, we can set up a direct proportion to find out how long it would take to fill the entire tank. We are trying to find the time required to fill 9/9 (or the whole tank) if 5/9 takes 2 minutes. To solve this, we calculate:

Set up the proportion where the fraction of the tank filled is directly proportional to the time taken: (5/9) / 2 = (9/9) / x minutes.

Now we solve for x, which represents the total time to fill the tank: x = (2 minutes * 9/9) / (5/9).

Simplify the right side: x = 2 minutes * (9/5).

Calculate the value of x: x = 3.6 minutes.

Therefore, it will take 3.6 minutes to fill the entire tank.

Final answer:

To find the time it takes for two jets to be 9128 miles apart, calculate their combined speed and divide the total distance by this speed, resulting in approximately 14 hours.

Explanation:

To find the time taken for the jets to be 9128 miles apart:

Calculate the combined speed of the two jets by adding their speeds together: 377 mph + 275 mph = 652 mph.

Divide the total distance of 9128 miles by the combined speed of the jets to get the time taken: 9128 miles ÷ 652 mph ≈ 14 hours.