How could you prove that 2.5 is a rational number?

Answer:

Graph A bc it's the only graph that shows that every 3 years his investment doubles.

The fοur integers are all equal tο 9, and the range is 12.

The cοllectiοn, analysis, interpretatiοn, presentatiοn, and οrganisatiοn οf data are all tοpics that fall under the umbrella οf statistics, a subfield οf mathematics.

Let's call the fοur integers a, b, c, and d.

Since the median is 9, we knοw that either b οr c must be 9. Let's assume b = 9.

Since the mοde is 9, we knοw that either a, c, οr d must be 9. Let's assume a = 9.

Nοw we have twο cases:

Case 1: c = 9

In this case, we have a, b, c, and d all equal tο 9, which gives us a mean οf 9.

Case 2: d = 21

In this case, we have a = 9, b = 9, c = 12, and d = 21, which gives us a mean οf 12.

Hοwever, we were tοld that the mean is 9, sο we can cοnclude that the first case is the cοrrect οne.

Hence, the fοur integers are all equal tο 9, and the range is 12.

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Complete Question:

Four integers have a mean of 9, a median of 9, a mode of 9 and a range of 12.

Find the four integers

Answer:  Refer to the drawing below

Explanation:

Complementary angles always add to 90 degrees.

Draw a right angle, aka 90 degree angle. Plot points A, B and D on it as shown below. Then add point C somewhere inside the rectangular region formed by this right angle. Lastly, connect a segment from B to C. This helps form angles ABC and CBD. Note how these smaller angles combine to a 90 degree angle.

(angleABC) + (angleCBD) = angle ABD = 90 degrees

The angles are adjacent because they share a common wall, which in this case is segment BC.

Answer:

The surface area of a rectangular prism is given by the formula:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively. We are given that the surface area of the prism is 1,060 cm², and that the base has measurements 8 cm and 10 cm.

Substituting these values into the formula, we get:

1060 = 2(8)(10) + 2(8)h + 2(10)h

Simplifying and solving for h, we get:

1060 = 160 + 16h + 20h

1060 = 160 + 36h

900 = 36h

h = 25

Therefore, the height of the prism is 25 cm.

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Answer:

Answer is AAAAAAAAAAAA

Step-by-step explanation:

AAAAAAAA the first one

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

so

x = 128°

The mean absolute deviation(MAD) of the given data set is 2.6(rounding to nearest tenth).

What is mean absolute deviation?

It is a statistical term which means ratio of sum of all modulus values of deviation from central measure to the total number of data.

Formula is

Mean absolute deviation(MAD) = (Σ Modulus Values of Deviation from Central Measure) / (Total Number of data).

Given data set is { 7, 3, 4, 1, 9}

At first arranging the data in ascending order we get { 1, 3, 4, 7, 9}

For MAD we need mean at first.

Mean=(1+3+4+7+9)/5

Mean= 24/5

Mean = 4.8

Formula for MAD is attached in the file.

Now | (1-4.8), (3-4.8), (4-4.8), (7-4.8), (9-4.8) |

     =|(-3.8), (-1.8), (-0.8), 2.2,4.2|

sum of all values (3.8+1.8+0.8+2.2+4.2)= 12.8

12.8/5=  2.56

Hence, the value is 2.6(rounding to nearest tenth)

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Answer:

x = -8

Step-by-step explanation:

-9 (x+2) = 54

-9x - 18 = 54

-9x = 72

x = -8

Hope this helps :)

Let me know if there are any mistakes!!

Answer:

-5.5

Step-by-step explanation:

Answer:

3/16

Step-by-step explanation:

P(6,7,8 and 'T') = 3/8 x 1/2 = 3/16

Answer:

12/64

Step-by-step explanation:

We have numbers 1-8 = /8

We have the numbers 6, 7, 8 on the spinner = 3/8

We have the event it doesn't get over 8 too = 8/8-3/8 = 5/8

To use if the question has two events for spinner.

We toss a coin = H or T = 1/2

We convert a 3/8 and 1/2 to same HCF = 4/8 = ( 2x 4 = 8)

3/8 x 4/8 = 12/64

If the bill of all the orders is more than $1.25, then taking 20% discount is more cost effective.

Let us assume the bill on all orders be x. So, equating the value of 20% discount with $1.

Forming the equation -

x - 20%×x = 1

Converting percentage to fraction

x - 20x/100 = 1

Taking LCM, we get

100x - 20x = 100

Performing subtraction on Left Hand Side of the equation

80x = 100

Shifting 80 to Right Hand Side of the equation and performing division

x = 100 ÷ 80

x = 5/4

x = 1.25

So, if the bill of all the orders is more than $1.25, then taking 20% discount is more cost effective.

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The number of outcomes, using the Fundamental Counting Theorem, is given as follows:

A. Red exactly 3 times and Purple exactly 2: 10.

B. Red at least ounce in 4 spins: 175.

C. Red at least ounce in 5 spins: 781.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

Item a is used with the combination formula, as it is an arrangement of five elements with 3 and 2 repetitions, hence the number of outcomes is:

\(C_{5,3} = \frac{5!}{3!2!} = 10\)

The Fundamental Counting Principle states that if there are n independent trials, each with \(n_1, n_2, \cdots, n_n\) possible results, the number of outcomes is calculated by the multiplication of the factorials as presented as follows:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

For item b, in four spins, each with four outcomes, the parameters are given as follows:

\(n_1 = n_2 = n_3 = n_4 = 4\)

Hence the number of outcomes is:

N = 4^4 = 256.

For no red results, the parameters are as follows:

\(n_1 = n_2 = n_3 = n_4 = 3\)

Hence:

N = 3^4 = 81.

Hence the number of outcomes with at least one red is:

256 - 81 = 175.

For item 3, the lone difference is that there are five trials, hence:

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The range of the function on the graph is y > -6

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is an exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

In this case, it is -6 i.e. the point where it intersects with the y-axis

So, the range is y > -6

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Answer:

( \(\frac{20}{7}\), - \(\frac{12}{7}\) )

Step-by-step explanation:

4x - 5y = 20 → (1)

2x + y = 4 → (2)

subtract 2x fro both sides in (2)

y = 4 - 2x → (3)

substitute y = 4 - 2x into (1)

4x - 5(4 - 2x) = 20 ( distribute parenthesis and simplify left side )

4x - 20 + 10x = 20

14x - 20 = 20 ( add 20 to both sides )

14x = 40 ( divide both sides by 14 )

x = \(\frac{40}{14}\) = \(\frac{20}{7}\)

substitute this value into (3)

y = 4 - 2(\(\frac{20}{7}\) ) = \(\frac{28}{7}\) - \(\frac{40}{7}\) = - \(\frac{12}{7}\)

solution is ( \(\frac{20}{7}\) , - \(\frac{12}{7}\) )

The equation of the line that is parallel and perpendicular to y = -8x + 6 and passes through the point (7, 5) are y = -8x + 61 and  \(y = \frac{1}{8}x + \frac{33}{8}\) respectively.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

y = -8x + 6

Using the slope intercept:

Slope m = -8

Since the desired line is parallel, it will have the same slope.

Therefore, the slope of the parallel line is also -8.

Plug in the slope m = -8 and the poin (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

( y - 5) = -8( x - 7 )

Simplify

y - 5 = -8x + 56

y = -8x + 56 + 5

y = -8x + 61

The equation of the parallel line is y = -8x + 61.

For the perpendicular line:

The slope of the perpendicular line will be the negative reciprocal of -8, which is 1/8.

Hence, plug slope m = 1/8 and point (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

\(y - 5 = \frac{1}{8} ( x + 7 )\\\\y - 5 = \frac{1}{8}x + \frac{7}{8} \\\\y = \frac{1}{8}x + \frac{7}{8} + 5\\\\y = \frac{1}{8}x + \frac{33}{8}\)

Therefore, the perpendicular line is \(y = \frac{1}{8}x + \frac{33}{8}\).

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

Answer D

Step-by-step explanation:

120 + 81+ 39=240 silver bikes

80+54+26= 160 black bikes

Total 200 + 135 + 65= 400

240+ 160=400

Answer:

Answer is C

Step-by-step explanation:

ap3xxx

Option D is the correct answer, which is atom x is in a column to the right of atom y on the periodic table.

We know that mass is increased as the atomic number increases and it depends on the primary number of protons and neutrons in the atoms.

So mass should be increased across periodic table rows from left to right and down periodic table columns.

There is a formula to calculate the maas no:

mass no=num of Protons+No of neutrons.

for x:

No of protons=19-10=9<----- It is a fluorine

for y:

No of protons=16-8=8<-----it is oxygen.

So the answer can be "Atom X is a row below Atom Y on the periodic table," Thus the atomic mass is higher than that of Atom Y's, making it lower on the periodic table.

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Answer:

See below!

Step-by-step explanation:

8, 3, 8, 6, 3, 3, 3, 6, 7

Here, Range is:

= Highest value - Lowest value

= 8 - 3

= 5

Here, the mode is:

= 3 (occurring 4 times)

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

The least positive number with this property is given as follows:

N = 280.

A number N gives remainder 0 when divided by 8, it gives remainder 0, when divided by 7 and it is an even multiple of 5, hence the number is multiple of these 3 numbers.

Before obtaining the number, we must obtain the least common multiple of 8, 7 and 5, factoring them by prime factors as follows:

8 - 7 - 5|2

4 - 7 - 5|2

2 - 7 - 5|2

1 - 7 - 5|5

1 - 7 - 1|7

1 - 1 - 1.

Hence:

lcm(8,7,5) = 2³ x 5 x 7 = 280.

280 is an even multiple of 5, as it is an even number, hence it is the least positive number N with the property in this problem.

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let h= 3, k=-2

radius (r) = 11 ,then

(x-h)^2 + ( y-k)^2 = r^2

(x-3)^2 + ( y+2)^2 = 11^2

x^2 -6x +9 + y^2 +4y +4 = 121

x^2 + y^2 - 6x +4y -108 = 0 is the required eq

Answer: Yes

Step-by-step explanation:

Most fractions can be simplified into smaller fractions, while some are in it's simplest form. When putting a bit in its simplest form it is much easier to compare to other fractions  

What I did first tried to simplify all the factions, starting with 1 1/2.

After looking at 1 1/2, I can see that it is in its simplest form.

Then looking at 1 2/4 I can see that it can be simplified into 1 1/2.

Lastly looking at 1 3/6 I can see that it can be simplified into 1 1/2.

The value of x for the equation to have infinite solution is 12

For an equation to have infinite solution, the expression on both sides must be equal

Given the expression below

3x–18=3(x–10)+ x

expand

3x - 18 = 3x - 30 + x

Equate

-18 = -30 + x

x = -18 + 30

x = 12

Hence the value of x for the equation to have infinite solution is 12

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Answer:

There is enough evidence to support the claim of the manufacturers that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.

Then, the null and alternative hypothesis are:

\(H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0\)

The significance level is 0.05.

The sample 1 (hybrid), of size n1=21 has a mean of 32 and a standard deviation of 6.

The sample 2 (non-hybrid), of size n2=31 has a mean of 21 and a standard deviation of 3.

The difference between sample means is Md=11.

\(M_d=M_1-M_2=32-21=11\)

The estimated standard error of the difference between means is computed using the formula:

\(s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{6^2}{21}+\dfrac{3^2}{31}}\\\\\\s_{M_d}=\sqrt{1.714+0.29}=\sqrt{2.005}=1.4158\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{11-0}{1.4158}=\dfrac{11}{1.4158}=7.77\)

The degrees of freedom for this test are:

\(df=n_1+n_2-2=21+31-2=50\)

This test is a right-tailed test, with 50 degrees of freedom and t=7.77, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=P(t>7.77)=0.0000000002\)

As the P-value is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.