Find 2 consecutive even numbers such that the sum of the
greater number and twice the smaller number is 44.

Answer:

  116

Step-by-step explanation:

Given the ratio 1.2 : 29, you want x in the equivalent ratio 4.8 : x.

Equivalent ratios can be written as a proportion:

  1.2/29 = 4.8/x

Multiplying by 29x, we have ...

  1.2x = 29(4.8)

Dividing by 1.2 gives ...

  x = 29(4.8/1.2) = 29(4) = 116

The ratio is the same as 4.8 to 116.

__

Additional comment

A proportion like this can be written 4 ways. The solution takes only one step if the unknown is in the numerator.

  \(\dfrac{1.2}{29}=\dfrac{4.8}{x},\quad\dfrac{29}{1.2}=\dfrac{x}{4.8},\quad\dfrac{1.2}{4.8}=\dfrac{29}{x},\quad\dfrac{4.8}{1.2}=\dfrac{x}{29}\)

Answer:

7cm²

Step-by-step explanation:

volume of a triangular prism=1/2×b×h×l

1/2×b×h=cross sectional area

84cm³=C.A×12

C.A=84/12

base area=7cm²

The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.

Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.

Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.

The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.

The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.

Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.

The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.

The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.

However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.

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There are 1140 different possible ways to select 3 restaurants out of 20 for the promotional program.

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.The combination formula, which is: can be used to resolve this issue.

n C r = r! * (n-r)!

where r is the number of restaurants to be chosen, and n is the total number of restaurants (20 in this case). (3 in this case).

By replacing these values, we obtain:

20 C 3 = 20! / (3! * (20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140

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Arcs get their angle measure from the central angle they're in, in this case the central angle of 86°, central to arcED, has a counterpart of a twin vertical angle across the center, since both vertical angles are identical twins that means the central angle for arcAB is 86° also, and that's the arcAB's measure too.

Perimeter of the parallelogram = 210 in.

Area of parallelogram = 2,484 in.²

Perimeter of parallelogram = 2(a + b), where a and b are its sides.

Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.

Given:

a = 51 in.

b = 54 in.

h = 46 in.

Perimeter of the parallelogram = 2(54 + 51) = 210 in.

Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²

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Answer:

probability of getting exactly 500 heads= 1

Step-by-step explanation:

If a coin is tossed, the probability of obtaining a head = 0.5

If a coin is tossed, the probability of obtaining a tail= 1- probability of obtaining a head

If a coin is tossed, the probability of obtaining a tail=1-0.5

If a coin is tossed, the probability of obtaining a tail=0.5

So if 1000 coin are tossed, the probability of getting exay 500 heads which is already the half of 1000 is 1

The values of the constants m and c include the following:

m = -1.3

c = 7.1

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c    ...equation 1.

-11 = 3m + c    ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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Tan(angle) = opposite/ adjacent

tan(42) = 67/x

x =67/tan(42)

X = 74.411

rounded to nearest tenth : x = 74.4

Answer:

The appropriate answer is "0.9803".

Step-by-step explanation:

According to the question,

The probability of sample proportion differs from population proportion by les than 4% will be:

= \(P(-\frac{0.04}{\sqrt{\frac{0.23\times 0.77}{602} } }<z<\frac{0.04}{\sqrt{\frac{0.23\times 0.77}{602} } } )\)

= \(P(-\frac{0.04}{\sqrt{\frac{0.1771}{602} } }<z<\frac{0.04}{\sqrt{\frac{0.1771}{602} } } )\)

= \(P(-2.33<z<2.33)\)

= \(0.9803\)

Answer:

The perimeter of the floor plan shown as an algebraic expression in x is:

P = 4x - 8

To find the perimeter, you add up the lengths of all four sides.

Two sides have length x, and the other two sides have length x - 4.

So, the perimeter is:

P = x + x + (x - 4) + (x - 4)

P = 4x - 8

Therefore, the answer is P = 4x - 8.

Answer:

x represents nickels = 2

3x represents number of quarters = 6

Step-by-step explanation:

x represents nickels

3x represents number of quarters

We'll multiply each of those times the value of the coin they represent, and make that equal to the total amount of money Mark has to get the value of x

x(0.05) + 3x(0.25) = 1.60

0.05x + 0.75x = 1.60

0.80x = 1.60

x = 2 = number of nickels

So 3x = 6 = number of quarters

Checking the math:

2(0.05) + 6(0.25)= 0.10 + 1.50 = 1.60

Answer:

x=3

Step-by-step explanation:

y=-x+3

0=-x+3

x=3

Answer: 3 (c)

Step-by-step explanation:

2 * 3 = 6 therefore 15 * 3 = 45$

3 * 2 = 6 therefore 21 * 2 = 42$

Answer: serbia

Step-by-step explanation:

The solution to the given problem of equation comes out to be quotient : x² +x+6+2/(x+2)  and remainder is 2.

We have to find the remainder and quotient

Given : synthetic division for

x³ + 3x² + 8x + 14

------------------------

x + 2

Write the problem in synthetic division format

-2  | 1 3 8 14

        -2 -2  

------------------------

    1   1  6

Carry down the leading coefficient, unchanged, to below the division symbol

-2  |    1 3 8 14

          -2 -2

---------------------------

        1  1   6

Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:

1(-2)=-2

-2 |  1 3 8 14

       -2 - 2

------------------

    1    1   6

=> We get:

As x² +x+6+ 2/(x+2)

and remainder is 2

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Answer:

Solution,

\( {x}^{2} - x - 2 \\ = {x}^{2} - (2 - 1)x - 2 \\ = {x}^{2} - 2x + x - 2 \\ = x(x - 2) + 1(x - 2) \\ = (x - 2)(x + 1)\)

Hope this helps...

Good luck on your assignment..

Answer:

2·2·2·2 = 16

Step-by-step explanation:

everytime a number is raised by another, that means you are going to multiply the base number  times itself as many times as the exponents tells you. this is a little but tricky to explain, so let me give you some examples:

2² → in this case the base number is 2 and the exponent is 2 as well, so you will multiply 2 times itself, 2 times:

2² = 2 · 2 = 4

2³ → in this case the base number is 2 and the exponent is 3, so you will multiply 2 times itself, 3 times:

2³ = 2 · 2 · 2 = 8

In the question asked, 2 is being raised by 4, so you will multiply 2 times itself, 4 times:

2^4 = 2·2·2·2 = 16

the same format will be used regardless of the base number and the exponent

i hope this helps! :)

Answer:

Let x=numerator,

y=denominator.

y=x+7 - - - - - (i)

(x+3)/(y+3) = 2/3

(Cross multiply)

3(x+3)=2(y+3)

3x+9=2y+6

(subtract 9 from both sides)

3x+9–9=2y+6–9

3x=2y+6–9

3x=2y-3 - - - - - - - (ii)

(substitute the value of equation (i) into (ii))

3x=2(x+7)-3

3x=2x+14–3

3x=2x+11

(subtract 2x from both sides)

3x-2x=2x+11–2x

x=11.

(substitute the value of x into equation (i))

y=7+11

y=18.

so numerator =11,

numerator =11,denominator = 18.

So original fraction is 11/18.

3/11th of original fraction is

= 11/18 x 3/11

= (11x3)/(18x11)

= 3/18

=1/6.

Answer = 1/6.

Answer:

Step-by-step explanation:

let numerator be x and denominerator be y

according to the question equation is

1+x /7+x+6=1/2( do cross multiplication)

7+x+6=2(1+x)

13+x=2+2x

13-2=2x-x

11=x

numerator =x+1=11+1=12

therefore numerator is 12

for denominerator

substitute the value of x in (7+x+6)

=7+11+6

24

The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b² + c² - a²)/2bc

cos B= (a² + c²- b²)/2ac

cos C = (a²+ b²- c²)/2ab  

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s² + s² - s²)/(2s×s)

cos A = (s² )/(2s²)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s² + s² - s²)/(2s×s)

cos B = (s²)/(2s²)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s² + s² - s²)/(2s×s)

cos C = (s² )/(2s²)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

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Answer:

no lo se xd sorry

no la se jjgtubxdtjk

Answer:

f(-4) = -8

Step-by-step explanation:

Okay fo if f(n) is f(-4), then n = -4.

f(-4) = 3/4n - 5

f(-4) = 3/4 (-4) -5

f(-4) = -3 - 5

f(-4) = -8

Hope this helps and I hope u have an Amazing day!!

(a) Based on the total attendance data provided, a bar chart can be constructed to visualize the attendance trends over time. The horizontal axis represents the years (2011, 2012, 2013, 2014), and the vertical axis represents the total attendance. The bars will correspond to the attendance numbers for each year.

(b) A side-by-side bar chart can be created to compare the attendance by visitor category with the year as the variable on the horizontal axis. The visitor categories (school, general, member) will be represented by different colors or patterns, and the bars will show the attendance for each category in each year.

(c) By analyzing the charts from parts (a) and (b), we can observe the trends in zoo attendance.

(a) The bar chart of total attendance over time shows the following trend: In 2011, the attendance was 350,621. It decreased slightly in 2012 to 341,875, remained relatively stable in 2013 at 342,340, and then decreased again in 2014 to 330,113.

(b) The side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis provides a visual comparison of attendance for each category over the years.

The chart reveals that the general category consistently had the highest attendance throughout the years, followed by the school category. The member category consistently had the lowest attendance.

(c) Based on the charts from parts (a) and (b), it can be observed that there has been a general decline in zoo attendance over the years, with a notable decrease from 2011 to 2014.

The drop in attendance could indicate a potential issue that the zoo needs to address in order to attract more visitors.

Additionally, the consistently lower attendance in the member category suggests that the zoo may need to reconsider its membership benefits and strategies to retain and attract more members.

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Answer:

20 because the breathe is 18 to get it length

Answer:

70% of people did not order popcorn at the movie theater on Saturday.

Step-by-step explanation:

first, add to get the total amount of people

150 + 350 = 500

now that we have the total, divide the people that did not buy popcorn by the total amount of people

350/500 = 0.7

then, multiply that by 100

0.7 x 100 = 70

your final answer would be 70%

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3500\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases}\)

\(A=3500\left(1+\frac{0.02}{1}\right)^{1\cdot 5}\implies A\approx 3864.28~\hfill \underset{earned~interest}{\stackrel{3864.28~~ - ~~3500}{\approx 364.28}}\)