What number line represents the solution to the inequality below

-6< -2x

Answer:

x = 1,6 in   ( the side of the corner squares )

V(max) = 67,58 in³

Step-by-step explanation:

The cardboard is:

L = 12 in          w  =  8 in

Let´s call "x" the side of the square from the corner:

Then the sides of the base of the open box are:

( L - 2*x )    and    ( w - 2*x )     and   x is the height

( 12  -  2*x )  and  ( w  - 2*x )

V(ob) = (L - 2*x ) * (  - 2*x ) * x

Wich is a function of x

V(x) = [( 12 - 2*x ) * ( 8 - 2*x ) ]*x

V(x) = ( 96 - 24*x - 16*x + 4*x²) * x

V(x) = 96*x - 40*x² + 4*x³

Tacking derivatives on both sides of the equation

V´(x) = 12*x² - 80*x + 96

V´(x) = 0     12*x² - 80*x + 96 = 0

Solving for x

x₁,₂ = 80 ± √ 6400 - 4608 / 24

x₁,₂ = 80 ± 42,33 / 24

x₁ = 5,10       We dismiss this solution since 2*x  becomes 2*5,10 = 10,20

ant this value is bigger than 8 inches

x₂ = 1,60 in

Therefore dimensions of the box

a = 12 - 2*x     ;  a =  12 - 3,20  ;  a = 8,8 in

b = 8 - 2*x   ; b = 8 - 3,20  ; b =  4,80  in

And the volume of the open box is:

V(max) = 8,8*4,8*1,6

V(max)  =  67,58 in³

How do we Know that is the maximun value for V?

We find  V´´(x)  = 24*x - 80     for  x = 1,6 is negative ( V´´(x) = - 41,6 therefore V (x) has  a local maximun for a value of x = 1,6

Answer:

14

Step-by-step explanation:

angle 90° is opposite the side x. angle 45° is opposite side 7√2.

x/sin 90 = (7√2)/sin 45

multiply both sides by sin 90 (sin 90 is = 1).

x = (7√2)/sin 45

 = 14

Answer:

Right Isosceles triangle

Step-by-step explanation:

The Square on the triangle represents a right angle

An Isosceles triangle is a triangle that has 2 sides equal and 1 a different length

Answemath is 270

Step-by-step explanation:

According to the information, we can infer that the correct expression is (10 * 7) + (2 * 7) (option D).

To find the correct expression we must look at the graph and interpret the information it has. In this case, some tiles are white and others are gray, so they would represent different elements. In this case, the white area is 10 * 7 tiles, so this would be the first part of the expression.

On the other hand, the second part of the expression would be 7 * 2, which represents the length, length and width of the gray area. According to the above, the correct expression would be (10 * 7) + (2 * 7), the first part in parentheses represents the white area and the second part in parentheses represents the gray area.

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Answer:

n = 5

Step-by-step explanation:

Since this is a right triangle, we can use trig

tan theta = opp /adj

tan 30 = n / 5 sqrt(3)

5 sqrt(3) tan 30 = n

5 sqrt(3) * 1/ sqrt(3) = n

5 = n

Now we have to,

find the required value of n.

Now we can,

Use the trigonometric functions.

→ tan(θ) = opp/adj

Let's find the required value of n,

→ tan (θ) = opp/adj

→ tan (30) = n/5√3

→ n = 5√3 × tan (30)

→ n = 5√3 × √3/3

→ n = 5√3 × 1/√3

→ [n = 5]

Hence, the value of n is 5.

Answer:

Below!

Solution of Question A:

Given:

20 - (20 x 15/100) = New price

=> 20 - (1 x 15/5) = New price

=> 20 - (3) = New price

=> $17 = New price

Solution of Question B:

Given:

50 - (50 x 25/100) = New price

=> 50 - (25/2) = New price

=> 50 - 12.5 = New price

=> $37.5 = New price

\(BrainiacUser1357\)

Answer:

6:2 or 1:3

Step-by-step explanation:

Not really sure how to explain this, but I hoped this helped!

Answer:

1/6

Step-by-step explanation:

There are 6 CD

P( song from 6th ) = number of CD's that are 6th/ total

                                = 1/6

Answer:

x=4

Step-by-step explanation:

1. isolate the variable by subtracting 7 on both sides: 4x=23-7

2. simplify: 4x=16

3. divide both sides by 4: x=16/4

4. simplify: x=4

Answer:

x=4

Step-by-step explanation:

4x+7=23

Collect like terms

4x=23-7

4x=16

Divide both sides by the co-efficient of x

4x/4=16/4

x=4

Answer:

4=No

-3=No

2=Yes

0=No

Step-by-step explanation:

enter enter all the factors into the equation and see which one equals -28 on both sides at the end.

i) the original distance when the lighthouse is due West of the ship is 7 km

ii) The time in minutes when the lighthouse is due West of the ship is 21 minutes

iii) The distance in km of the ship from the lighthouse when the lighthouse is due West of the ship is 29.97 km

To solve this problem, we'll use the concepts of relative velocity and trigonometry. Let's break down the problem into three parts:

i) Finding the original distance when the lighthouse is due West of the ship:

The ship's velocity is given as 21 km/h at a bearing of 052°. Since the ship observed the lighthouse due North, we know that the angle between the ship's initial heading and the lighthouse is 90°.

To find the distance, we'll consider the ship's velocity in the North direction only. Using trigonometry, we can determine the distance as follows:

Distance = Velocity * Time = 21 km/h * (20 min / 60 min/h) = 7 km (to three significant figures).

ii) Finding the time in minutes when the lighthouse is due West of the ship:

To find the time, we need to consider the change in angle from 052° to 312°. The difference is 260° (312° - 052°), but we need to convert it to radians for calculations. 260° is equal to 260 * π / 180 radians. The ship's velocity in the West direction can be calculated as:

Velocity in West direction = Velocity * cos(angle) = 21 km/h * cos(260 * π / 180) ≈ -19.98 km/h (negative because it's in the opposite direction).

To find the time, we can use the formula:

Time = Distance / Velocity = 7 km / (19.98 km/h) = 0.35 h = 0.35 * 60 min = 21 minutes (to three significant figures).

iii) Finding the distance in km of the ship from the lighthouse when the lighthouse is due West of the ship:

We can use the formula for relative velocity to find the distance:

Relative Velocity = sqrt((Velocity in North direction)² + (Velocity in West direction)²)

Using the values we calculated earlier, we have:

Relative Velocity = sqrt((21 km/h)² + (-19.98 km/h)²) ≈ 29.97 km/h (to three significant figures).

Therefore, the ship is approximately 29.97 km away from the lighthouse when the lighthouse is due West of the ship.

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The value of m that satisfies the equation -3 + m = 9 is m = 12.

To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.

-3 + m = 9

To move -3 to the other side, we can add 3 to both sides of the equation:

-3 + 3 + m = 9 + 3

Simplifying, we have:

m = 12

Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.

None of the provided answer options (A, B, C, D) match the correct solution.

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2(3x - z)

substitute x =-6 and z = 3 in the above

2[3(-6) - 3]

2[ -18 - 3]

2[-21]

= - 42

Answer:

x=10.25

Step-by-step explanation:

Angle 1 = (5x+24)°

Angle 2 = (9x-17)°

The two angles are equal. It means,

(5x+24)°=(9x-17)°

Taking like terms together,

5x-9x=-17-24

-4x=-41°

Dividing each side by -4

x=10.25°

So, the value of x is 10.25.

Answer:

C)  I, III, IV, II

Step-by-step explanation:

Convert each number into a decimal:

\(\textsf{I.} \quad \dfrac{58}{67}=0.86567...\)

\(\textsf{II.} \quad 0.58\%=\dfrac{0.58}{100}=0.0058\)

\(\textsf{III.} \quad 58\%=\dfrac{58}{100}=0.58\)

\(\textsf{IV.} \quad 5.8\%=\dfrac{5.8}{100}=0.058\)

Comparing the tenths of all the numbers, 8 is the biggest tenth, so 58/67 is the largest number.

The next biggest tenth is 5, so 58% is the next largest number.

The two remaining numbers have zero tenths, so compare their hundredths. 5 is the largest hundredth, so 5.8% is the next largest number.  Therefore, 0.58% is the smallest number.

Therefore, the given set of numbers in order from greatest to least is:

Answer:

c) I, III, IV, II

Step-by-step explanation:

Values of l, ll, lll & lV respectively,

→ 58/67, 0.58%, 58%, 5.8%

→ 0.87, 0.0058, 0.58, 0.058

Arranging them in descending order,

→ 0.87 > 0.58 > 0.058 > 0.0058

→ 0.87, 0.58, 0.058, 0.0058

→ l, lll, lV, ll

Hence, the option (c) is correct.

Answer:

get some more help I don't understand

Answer:

a) there are 7,854,000 number of ways the random selections can be arranged

b) the required probability is 0.0445

Step-by-step explanation:

Given that;

you have 12 pair of long pants, 6 pair of short pant and 17 t-shirt which in total;

Total = 12 + 6 + 17 = 35

a) number of ways a random selection of 9 pair of long pants, 4 pair of short pants and 13 t-shirts can be arranged;

⇒ [ 12   ×    [ 6     ×    [ 17

     9 ]          4 ]           13 ]

= (12! / (9! 3!)) (6! / (4! 2!)) (17! / (13! 4!))

= (220) (15) (2380)

= 7,854,000

Therefore there are 7,854,000 number of ways the random selections can be arranged

b)

Number of ways of selecting 25 item from 35 items;

⇒ [ 35        

    25 ]

=

(35! / (25! 10!) = 183.579,396

now number of ways to select 10 pair of long pants, 3 pairs of short pantts and 12 t-shirt;

⇒ [ 12   ×    [ 6     ×    [ 17

     10 ]         3 ]           12 ]

= (12! / (10! 2!)) (6! / (3! 3!)) (17! / (12! 5!))

= (66) (20) (6188)

= 8,168,160

So, Required probability = 8,168,160 / 183,579,396

= 0.0445

So the required probability is 0.0445

Answer:

Step-by-step explanation:

The answer is A. to set aside land for animals as more people moved west

Answer:

So,

let the amount of each transaction be x.

3x= 115.25+77.73

x= 192.98÷

x= 64.327

each transaction was of 64.327

Step-by-step explanation:

since the amount left is -77.73 then three equal transaction will also include 115.25+77.73= 1 92.98

192.98 was the total amount used

Answer:

I'm pretty sure 70 liters

Step-by-step explanation:

because 60÷10=6

so 70÷10=7

Option (B) is correct. Thus, percentage of students with scores between 70 and 130 is 95% .

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. The average degree of variability in your data set is represented by the standard deviation.

It reveals the average deviation of each score from the mean. Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that √(5.2/5) = 1.01 will be the standard deviation.

Here:

μ = 100, σ = 15

Thus we have

30 μ - kσ = 70

= 100 – k(15) = 70

= k= 30/15 = 2

Also we have, μ + Ασ: = 130

100+ k(15) = 130

k = 30/15 = 2

Now, the percentage of students with scores between 70 and 130 is same as the percentage of students between μ - 2σ, μ+ 2σ  and by empirical rule the area between μ (+-) 2σ  is 95%. Thus, percentage of students with scores between 70 and 130 is 95%

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Answer:

2 quarters,2dimes,6nickels

Answer:

1) 9

2) 27

3) Read explanation below!

Step-by-step explanation:

1) Use the Pythagorean theorem to find AD. Show your working

To find '?' we first have to expand the indices...

Now work out '?'

2) Find AC. Show your working

We have found out that AD is 9 and to find AC we have to add 18!

3) Is ΔABC a right triangle? Explain

We can that ΔABC is not a right angle as none of the angles in the triangle are 90°!  If it was a right angled triangle we would see the ∟sign on one of the angles. Even though there are two of those in the middle it does not count as the question is asking about ΔABC!!

Have a lovely day :)

Answer:

40 miles

Step-by-step explanation:

She wants to run x miles.

She already ran 24 miles, and that is 60% of x.

60% of x = 24

0.6x = 24

x = 24/0.6

x = 40

Answer: 40 miles

The formula "total += number" provides an illustration of how to calculate the sum of numbers given that the number is saved in the variable number and the total is saved in the variable total (i.e., an accumulator).

When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.

Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labeled "+" is defined can all be added together, in addition to numbers.

Series are summations of infinite sequences.

These are related to the idea of limits but are not covered in this article.

Given that the number is stored in the variable number and the total is saved in the variable total, the formula total += number gives an example of how to calculate the sum of numbers (i.e., an accumulator).

Therefore, the formula "total += number" provides an illustration of how to calculate the sum of numbers given that the number is saved in the variable number and the total is saved in the variable total (i.e., an accumulator).

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Correct question:

What represents an example to calculate the sum of numbers (that is, an accumulator), given that the number is stored in the variable number and the total is stored in the variable total?

Answer:

48 cans must be sampled.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.99}{2} = 0.005\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.005 = 0.995\), so Z = 2.575.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

The machine is calibrated so that the population standard deviation is 0.04 ounces.

This means that \(\sigma = 0.04\)

How many filled cans must be sampled so that we estimate the mean fill volume within 0.015 ounces with 99% confidence?

n cans must be sampled, and n is found when M = 0.015. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.015 = 2.575\frac{0.04}{\sqrt{n}}\)

\(0.015\sqrt{n} = 2.575*0.04\)

\(\sqrt{n} = \frac{2.575*0.04}{0.015}\)

\((\sqrt{n})^2 = (\frac{2.575*0.04}{0.015})^2\)

\(n = 47.2\)

Rounding up, 48 cans must be sampled.

Answer:

candidate b because it's mostly likely to have more people i think

Answer:7 x 2 − 14 x + 5

Step-by-step explanation:

1 In general, given a{x}^{2}+bx+cax  

2

+bx+c, the factored form is:

a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})

a(x−  

2a

−b+  

b  

2

−4ac

​

​

)(x−  

2a

−b−  

b  

2

−4ac

​

​

)

2 In this case, a=7a=7, b=-14b=−14 and c=5c=5.

7(x-\frac{14+\sqrt{{(-14)}^{2}-4\times 7\times 5}}{2\times 7})(x-\frac{14-\sqrt{{(-14)}^{2}-4\times 7\times 5}}{2\times 7})

7(x−  

2×7

14+  

(−14)  

2

−4×7×5

​

​

)(x−  

2×7

14−  

(−14)  

2

−4×7×5

​

​

)

3 Simplify.

7(x-\frac{14+2\sqrt{14}}{14})(x-\frac{14-2\sqrt{14}}{14})

7(x−  

14

14+2  

14

​

​

)(x−  

14

14−2  

14

​

​

)

4 Factor out the common term 22.

7(x-\frac{2(7+\sqrt{14})}{14})(x-\frac{14-2\sqrt{14}}{14})

7(x−  

14

2(7+  

14

​

)

​

)(x−  

14

14−2  

14

​

​

)

5 Simplify  \frac{2(7+\sqrt{14})}{14}  

14

2(7+  

14

​

)

​

  to  \frac{7+\sqrt{14}}{7}  

7

7+  

14

​

​

.

7(x-\frac{7+\sqrt{14}}{7})(x-\frac{14-2\sqrt{14}}{14})

7(x−  

7

7+  

14

​

​

)(x−  

14

14−2  

14

​

​

)

6 Simplify  \frac{7+\sqrt{14}}{7}  

7

7+  

14

​

​

  to  1+\frac{\sqrt{14}}{7}1+  

7

14

​

​

.

7(x-(1+\frac{\sqrt{14}}{7}))(x-\frac{14-2\sqrt{14}}{14})

7(x−(1+  

7

14

​

​

))(x−  

14

14−2  

14

​

​

)

7 Remove parentheses.

7(x-1-\frac{\sqrt{14}}{7})(x-\frac{14-2\sqrt{14}}{14})

7(x−1−  

7

14

​

​

)(x−  

14

14−2  

14

​

​

)

8 Factor out the common term 22.

7(x-1-\frac{\sqrt{14}}{7})(x-\frac{2(7-\sqrt{14})}{14})

7(x−1−  

7

14

​

​

)(x−  

14

2(7−  

14

​

)

​

)

9 Simplify  \frac{2(7-\sqrt{14})}{14}  

14

2(7−  

14

​

)

​

  to  \frac{7-\sqrt{14}}{7}  

7

7−  

14

​

​

.

7(x-1-\frac{\sqrt{14}}{7})(x-\frac{7-\sqrt{14}}{7})

7(x−1−  

7

14

​

​

)(x−  

7

7−  

14

​

​

)

10 Simplify  \frac{7-\sqrt{14}}{7}  

7 7−  14  to  1-\frac{\sqrt{14}}{7}1−  7 14

7(x-1-\frac{\sqrt{14}}{7})(x-(1-\frac{\sqrt{14}}{7}))

7(x−1−  7 /14 )(x−(1−  7 14 )) 11 Remove parentheses.

7(x-1-\frac{\sqrt{14}}{7})(x-1+\frac{\sqrt{14}}{7})

7(x−1−  7/ 14 .7(x−1+ 7 14 )