Laura launched a model rocket ​

Answer:

0.62

Step-by-step explanation:

given :
\(\frac{2}{5} * 1\frac{4}{7}\)
\(=\frac{2}{5} *\frac{11}{7}\)
\(= \frac{22}{35}\)
\(=0.62\) as a decimal

Hope it helps

Question:

Alfie tossed a paper cup in the air 150 times and recorded the side it landed on.

     Right side up = 60         Upside down = 53             Side = 37

If Alfie tosses the paper cup 100 more times what is the expected number of times the cup will land on its side?

Answer:

The expected number of times the cup will land on its side is 25 times

Step-by-step explanation:

Given

\(Right = 60\)

\(Upside\ down = 53\)

\(Side = 37\)

Required

First, we calculate the probability of landing on side

\(P(Side) = \frac{n(Side)}{Total}\)

\(P(Side) = \frac{37}{150}\)

\(P(Side) = 0.247\)

Next, we calculate the expected value; E(x) using:

\(E(x) = n * P(x)\)

When tossed 100  more times:

n = 100 and P(x) = P(Side) = 0.247

So:

\(E(x) = 100 * 0.247\)

\(E(x) = 24.7\)

\(E(x) = 25\) --- approximated

Hence, it is expected that it will land on its side 25 times

Answer:

what numbers.

Step-by-step explanation:

Answer:

what are the numbers

Step-by-step explanation:

The value that would complete the table to make the relationship between the two quantity proportional is 4.

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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The lower bound of the 95% confidence interval is given as follows:

7.981 mm.

The level of confidence of the statement is of 95%.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 100 - 1 = 99 df, is t = 1.9842.

The parameters for this problem are given as follows:

\(\overline{x} = 8.1, s = 0.6, n = 100\)

Hence the lower bound of the interval is given as follows:

8.1 - 1.9842 x 0.6/10 = 7.981 mm.

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Answer:

đẹp trai quá đi

Step-by-step explanation:

Answer:

The total paint cost is £380. The total tiles cost is £1800. The total cost is £2180.

Step-by-step explanation:

To know the cost, you need to calculate the area of the community hall.

So together, their area is 1200m2.

Together the two walls have an area of 90m2

Together the two big walls have an area of 240m2

Painting:

They are going to paint the walls and the ceiling and each 10L tin covers 25m2 so:

Area of the walls and ceiling = 600m2 + 90m2 + 240m2 = 930m2

930m2 ÷ 25m2 = 37.5 tins. Since you can't have half a tin, they will need 38 10L tins.

38 x £10 = £380

Floor:

1m2 floor tiles costs £3 so 600m2 x £3 = £1800

Total:

£1800 + £380 = £2180

Answer: A levelling map viewed in Optoprint shows a 0.7mm deviation 'high' in the rear right corner vs the front left 'home' position of the bed.

Step-by-step explanation:

Answer:

I’m pretty sure it’s 23

Step-by-step explanation:

Answer:

I THINK it's 15

Step-by-step explanation:

Answer:

The slope is 3 or 3/1.

Step-by-step explanation:

I figure this out by finding out the two beginning points with this: (x1, y1) , (x2, y2). The two beginning points (-3, -5) , ( -2,-2). Then from there you are counting by 3 to get to the next point. I hope this helps.

Answer:

1

Anything to the 0th power is 1.

Answer:

1

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

\(~~4^2 \times 4^{-5}\\\\=4^{2-5}\\\\=4^{-3}\\\\=\dfrac 1{4^3}\)

The correct simplified form of the expression is x + 5.

a) The mistake that Hannah has made is incorrectly combining the terms 3x and -2x. Instead of subtracting the coefficients of x, she subtracted the entire expression 2x from 3x.

b) To simplify the expression correctly, we need to combine like terms. In this case, the like terms are the ones with the variable x.

The expression 3x + 5 - 2x can be rewritten as (-2x + 3x) + 5.

Now, let's combine the like terms:

(-2x + 3x) + 5 = x + 5

Therefore, the correct simplified form of the expression is x + 5.

To further clarify, Hannah mistakenly thought that subtracting 2x from 3x would result in 1x (or just x). However, when subtracting or adding terms with the same variable, we need to consider the coefficients. In this case, 3x - 2x simplifies to x, not 1x.

It's important to pay attention to the signs and operations when combining terms. In this scenario, Hannah overlooked the need to subtract the coefficients of x and ended up with an incorrect result.

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Answer: no solution

Step-by-step explanation:

\(8x^{2} +32=0\)

Factor out 8

\(8(x^{2} +4)=0\)

no solution

Why?

Think about the graph, \(x^{2}\) shifted up 4 has no zeros, even with a vertical stretch of 8.

Answer:

5

Step-by-step explanation:

slope = rise/run or y-value/x-value

point=(10,50)

50/10=5

slope=5

The top of ladder is moving down the wall at the rate of 1.375 ft/sec .

In the given question we have to find how fast is the top of the ladder moving down the wall.

Let the distance between floor and top point of ladder = x

the distance between wall and bottom point of ladder = y

Using Pythagorean law,

x^2+y^2 = (12)^2

x^2+y^2 = 144.....................(1)

Differentiating with respect to t:

d/dt (x^2+y^2) = d/dt (144)

2xdx/dt+2ydy/dt = 0

Given that

dy/dt = 3

So 2xdx/dt+2y*3 = 0

2xdx/dt+6y= 0

dx/dt = - 3y/x

Using (1):

dx/dt = -3y/√144-y^2  

When y = 5:

dx/dt = -3(5)/√144-(5)^2

dx/dt = -15/√144-25

dx/dt = -15/√119

dx/dt = -15/10.91

dx/dt = -1.375

So the top of ladder is moving down the wall at the rate of 1.375 ft/sec .

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The right question is:

A ladder 12 feet long is leaning against a house. The base of the ladder is pulled away from the wall at a rate of 3ft/sec. How fast is the top of the ladder moving down the wall when its base is 5 feet from the wall?

a. 540 cubic meters of the iceberg is below the water .

b. 480 cubic meters is volume of the iceberg are below the waterline.

Proportion is a mathematical concept that relates two or more quantities in a fixed relationship or ratio. In other words, a proportion is a statement that two ratios are equal. For example, the statement "2/5 equals 4/10" is a proportion, because both ratios simplify to 2:5.

Proportions are often used in problem-solving and real-world applications, such as in cooking recipes, financial calculations, and engineering designs. Proportions can be used to find missing values or to scale up or down quantities while maintaining the same ratio. They can also be used to compare two different sets of data by calculating their relative sizes or growth rates.

a) If 60 cubic meters of the iceberg are visible above the water and the ratio of visible iceberg to total iceberg is 1:9, then we can set up the proportion:

visible iceberg/total iceberg = 1/9

We can solve for the total iceberg by cross-multiplying and simplifying:

visible iceberg/1 = total iceberg/9

total iceberg = 9 * visible iceberg

total iceberg = 9 * 60 cubic meters

total iceberg = 540 cubic meters

b) The total volume of the iceberg is 540 cubic meters, and we know that the visible portion of the iceberg is 60 cubic meters. Therefore, the volume of the iceberg below the waterline is:

total volume - visible volume = 540 - 60 = 480 cubic meters

So, 480 cubic meters of the iceberg are volume.

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The profit for the option writer is $3,900.

In this scenario, the option writer sold a put option on the Canadian dollar with an exercise price of USD 0.76/CAD. The premium received for the option was $0.039/CAD. The contract size is CAD 100,000, and the spot price at maturity is $0.76/CAD. However, since the spot price at maturity is equal to the exercise price of $0.76/CAD, the option is not exercised. As the option writer, the profit is determined by the premium received. In this case, the premium received per contract is $0.039/CAD. Multiplying this by the contract size of CAD 100,000, we get $3,900.

It's important to note that if the spot price at maturity had been lower than the exercise price, the option would have been exercised, resulting in a loss for the option writer equal to the difference between the exercise price and the spot price, multiplied by the contract size.

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Answer:

\(f(t) = 7.23( {1.0114}^{t} )\)

t = 0 represents January 1, 2014

(a)

\(f(6) = 7.23( {1.0114}^{6} ) = 7.739\)

The population of the world is expected to be about 7.739 billion people on January 1, 2020.

(b)

\(7.23( {1.0114}^{t} ) = 10\)

\(t = about \: 28.61 \: years\)

The population of the world is expected to be 10 billion people in about 28.61 years after January 1, 2014 (sometime in August 2042).

Answer:

Step-by-step explanation:

They are testing whether you remember the basic 30,60,90 degree triangle side relationship. The ratio of sides for this triangle are 1 opposite the 30 degree angle, square root of three opposite the 60 degree angle and a hypotenuse of 2 opposite the 90 degree angle.

x/2=2/1

x=4/1=4

bottom answer choice

x/4=3^(1/2)/1

x=4(3^(1/2))

third answer choice

The amount of money Jimmy spends on video games is directly proportional to the number of games he owns.

If A is directly proportional to B, it means A and B will change at the same rate and at the same direction. If A is made twice greater then B will be twice greater as well.

If the relation between A and B can be expressed as a linear equation:

A = kB + C

where k is a constant, then A is directly proportional to B.

Let:

x = the money Jimmy spends on video games

y = the number of games Jimmy owns

From the problem, we can conclude:

x = 50 (y - 333)  

since he will only pay after the 333th video game.

Re-arrange the equation:

x = 50y - 16,650

Notice that the above equation is a linear equation, hence x is directly proportional to y.

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I believe the answer you are looking for is 10^4

Answer:

$5.5 per mile

40 miles

Step-by-step explanation:

Given :

Fixed cost = $10

Variable cost = $3

For a journey of 4 miles ;

Cost = fixed cost + Variable Cost

Cost = $10 + $3x

x = number of miles

Cost = $10 + $3(4)

Cost = $10 + $12 = $22

Average cost per mile for a journey of 4 miles

Cost / number of miles

$22 / 4 = $5.5 per mile

Minimum distance if average per mile is to be less Than 3.25

$3.25 = (10 + 3x) / x

3.25x = 10 + 3x

3.25x - 3x = 10

0.25x = 10

x = 10 / 0.25

x = 40 miles

Answer:

The first one is 5.83 or -5 5/6

The second one is -414 1/3

The last one is 290

F=9/5C+32 is the required equation and Greg statement is true

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that Greg is expressing temperature in farenheit and Josh expressing it in the celsius.

C=5/9(F-32)

We need to rewrite the formula so that Josh can quicly convert the temperature that Greg describes F.

F=9/5C+32

The temperature where John leaves has 77 F.

Let us convert to celsius.

C=5/9(77-32)

C=5/9(45)

C=5(5)

C=25 degrees.

25 degress< 30 degrees.

Hence, F=9/5C+32 is the required equation and Greg statement is true.

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Find the partial derivatives f(x, y) = 3x² + 2y - 7xy

⇒ \(f_x\) = 6x - 7y

⇒ \(f_y\) =  2 - 7x

The given function is,

f(x, y) = 3x² + 2y - 7xy,

We can see that,

This is a function of two variable

To find partial derivatives of the function,

Differentiate the function with respect to x  treating y as a constant,

Then

⇒ \(f_x\) = (δ/δx)(3x² + 2y - 7xy),

⇒ \(f_x\) = 6x - 7y

Now Again differentiate the function with respect to y  treating x as a constant,

⇒ \(f_y\) = (δ/δy)(3x² + 2y - 7xy),

⇒ \(f_y\) =  2 - 7x

Hence the partial derivatives of the given function is,

⇒ \(f_x\) = 6x - 7y

⇒ \(f_y\) =  2 - 7x

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The equivalent expression of 2(x² – 1) + 3x(x – 4) is 5x² - 12x - 2

The equivalent expression of the expression can be found as follows;

2(x² – 1) + 3x(x – 4)

open the brackets

2x² - 2 + 3x² - 12x

Therefore, let's combine like terms

2x² + 3x² - 12x - 2

Let's do the arithmetic for like terms

2x² + 3x² - 12x - 2

5x² - 12x - 2

Therefore, the equivalent expression of  2(x² – 1) + 3x(x – 4) is 5x² - 12x - 2

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The justification is given below:

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

-2x-7=-15

Property: subtraction and division of fraction

-2x-7+7=-15+7

Property: Addition of equality

-2x=-8

Property: Additive Inverse Property

-2x/2 = -8/2

Property: division under equality

x=4

Property: division property

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