a number is tripled and then increased by four. the result is seventy-nine. what is the original number?

Answer: 2.5

Step-by-step explanation:

The altitude of an equilateral (or isosceles) triangle bisects the side to which it is drawn.

The grades and gender is 29/59

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

              A              B             C              Total

Male       20            13            7                 40

Female    9               2            8                 19

Total        29            15            15               59

Total candidates who have A grade = 20+9 = 29

So, the probability that the student got an A

= 29/59

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Answer:

  5/6 mile

Step-by-step explanation:

The formula for the area of a rectangle can be used with the given values to write an equation for the length of the farmland.

__

Here is the equation for the area of a rectangle.

  A = LW . . . . . area is the product of length and width

When we fill in the area and width, we have ...

  5/9 mi² = L(2/3 mi) . . . . . equation for the length of the farmland

Solving this equation gives ...

  L = (5/9)/(2/3) mi . . . . . . . . divide by the coefficient of L

  L = (5/9)/(6/9) mi = 5/6 mi . . . . . perform the division

The length of Sandra's farmland is 5/6 mile.

Answer:

I have done the 1st 2 sums in proper systematic manner. The remaining sums I'll be writing only the main formula and substitution. I hope you will write the missing sentences .

Step-by-step explanation:

.Also I would appreciate it if you could marke my answer as BRAINLIEST and THANK ME.｡◕‿◕｡

Answer:

Step-by-step explanation:

1. hypotenuse = 89

2. hypotenuse = 85

3. hypotenuse = 97

4. hypotenuse = 153

5. hypotenuse = 34

6. hypotenuse = 113

7. hypotenuse = 916

8. hypotenuse = 170

9. hypotenuse = 394

10. hypotenuse = 61

Given:

The given equation is 5y=3x-5

Find: Draw the graph

Explanation:

It is given that 5y=3x-5. Substitute x=0 into the given equation we have

[tex]5y = 3x - 5[/tex]

[tex]5y = 3(0) - 5[/tex]

[tex]5y = - 5[/tex]

[tex]y=-1[/tex]

Now, substitute x=5 into the given

equation we have

[tex]5y = 3(5)-5[/tex]

[tex]5y = 15-5[/tex]

[tex]5y = 10[/tex]

[tex]y = 2[/tex]

The points are (0,-1) and (5,2).

Therefore, the required graph is

Hence, the required graph is obtained.

The median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a box and whisker plot shown in the picture.

From the box plot, the line between the box ends represents the median of the data.

The median = 40

The least number of smartphones distributed = 33

Q3 = 48

Thus, the median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.

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Answer:

P=2l+2W

if l=12 and W=8

then,

P=2L+2W

=2.18+2.8

=36+16

=52

Answer:

amount of coloured fabric in mm = 48

amount of white fabric in mm = 12

ratio = white fabric : coloured fabric = 12 : 48 = 1:4

The values of x and y such that AB is perpendicular to CD will be 19 and 14.5.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

AB and CD intersect at point E.

If measure angle AED equals 6x – 24 and measure angle CEB equals 4y + 32.

Then the values of x and y such that AB is perpendicular to CD will be

6x – 24 = 90

        6x = 114

          x = 19

Then we have

4y + 32 = 90

       4y = 58

         y = 14.5

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Answer:

V = (s^3)/6  (Answer B )

Step-by-step explanation:

If the length of a side of the base is s, then the height of the pyramid is half that, or s/2.

The volume of a pyramid with a square base and base side length S and height H is V = (1/3)(S^2)(H).

In this case, the formula is V = (1/3)(s^2)(s/2), or V = (s^3)/6  (Answer B)

Answer:

A. is the answer

Answer:

x = -2

Step-by-step explanation:

1. Square both sides
x^2 +3x + 6 = x^2
2. Subtract x^2 from both sides
3x + 6 = 0
3. Subtract 6 from both sides and divide by 3
x = -2

The answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The question is incomplete.

The complete question is:

Which expression is modeled by this arrangement of tiles? 40 positive tiles are broken up into 10 groups of 4 positive tiles.

Please refer to the attached picture.

We have a rectangular shape as shown in the picture.

Total number of square units = 40

Each row has 10 units cube.

Each cube = 40/10

Thus, the answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.

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The weight of the chocolate frosting if it is 55% cocoa powder will be 272.25 grams.

The quantity of anything is stated as though it were a fraction of a hundred.

Mama bear wants to bake a cake with chocolate frosting for her twin's birthday party.

She uses a package containing 495 grams of cocoa powder for the frosting.

Then the weight of the chocolate frosting if it is 55% cocoa powder will be

⇒ 0.55 × 495

⇒ 272.25 grams

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Answer: 3/4

Step-by-step explanation:

Answer:

Option C.  [tex]g(x)=(\frac{1}{3}x)^2[/tex]

Step-by-step explanation:

Given a function to start with, extra operations that are done outside of the given function, cause vertical transformations, whereas operations that are done inside of the function cause horizontal transformations.

Transformations on the outside

Ex. [tex]g(x)=(x^2)-3[/tex]  is subtracting 3 outside, so its transformation is vertical.

Transformations on the inside

Ex. [tex]g(x)=(x-7)^2[/tex] is subtracting 7 inside, so its transformation is horizontal.

For any function, stretches or compressions occur by multiplying by positive numbers larger or smaller than 1.

Multiplying by numbers larger than one, quantities get larger, and multiplying by a positive number less than one, quantities get smaller.

For example, [tex]\$10*2 = \$20[/tex], but [tex]\$10*\frac{1}{2} = \$5[/tex]

For transformations, this intuition needs a small modification:

Multiplying on the outside

When multiplying outside of the function, things outside happen normally, and since it is happening outside, it is in a vertical direction.

Ex. Multiplying outside by 3, things get larger (stretch) vertically to 3 times as much as (300% of) normal (away from a height of zero).

Multiplying outside by [tex]\frac{1}{2}[/tex] , things get smaller (compress) vertically down to [tex]\frac{1}{2}[/tex] as much as (50% of) normal (toward a height of zero).

"g" is lower than "f", so it may have been compressed vertically (see alternative solution at end).

Looking at the only options with multiplication outside (A & B), option B multiplies by 3 (greater than 1), so it would stretch "f" even taller.

Option A, does compress "f" vertically (by 1/3), but doesn't compress it enough to arrive at the point (3,1) defined on function "g". Note ordered pair (3,1) on "g", meaning when you input "3", you get out "1".  

Putting 3 into the "f" function, f(3)=9.  Since one-third (the transformation in Option A) of 9 is 3, not 1, Option A doesn't compress "f" enough.

Multiplying on the inside

When multiplying inside, transformations happen horizontally, and inside things happen "backwards".

So, if multiplying inside by 4, (...normally things get bigger...) things actually get smaller (compressed) horizontally, reduced to 1/4 (the reciprocal of 4) the size (toward a horizontal distance of zero).

If multiplying by a number less than one (but positive), like [tex]\frac{1}{3}[/tex] , (...things normally get smaller...) things will actually get larger (stretch) in the horizontal direction out to triple (the reciprocal of [tex]\frac{1}{3}[/tex]) as much as normal.

Looking options C & D (where multiplication happens inside), both have multiplication by a positive number less than one (... normally would make things smaller...), which will stretch "f" out horizontally.

Looking at the red point (3,1), the blue function does have a height-matched point at (1,1).

Measuring horizontal distances, (3,1) is 3-units from the y-axis, whereas (1,1) is only 1-unit away.  Thus, the "g" is 3 times as far as "f", meaning a horizontal stretch outward by 3.

Answer C multiplies inside by [tex]\frac{1}{3}[/tex], so it actually makes things 3 times bigger horizontally.

The correct answer is option C.

To verify, from (3,1), put 3 into the option C g(x) --  it gives "1" as an output.

[tex]g(x)=(\frac{1}{3}x)^2\\g(3)=(\frac{1}{3}(3))^2\\g(3)=(1)^2\\g(3)=1\\[/tex]

This function could have been compressed vertically to obtain the red graph.

Note that f(3)=9.

The point (3,1), on the red function, is only at a height of 1 ... 1/9th the height of the blue function.  We could compress the "f" vertically by 1/9th to transform the blue function into the red function.

Vertical transformations come from operations outside, and outside things behave "normally", so to vertically compress by 1/9th, just multiply on the outside by 1/9th.

Thus, an alternative answer to transform f(x) to g(x) is [tex]g(x)=\frac{1}{9}(x^2)[/tex]

Two last things:

Simplifying this function we just obtained we get [tex]g(x)=\frac{1}{9}x^2[/tex]

Returning to the function that we chose for our answer in option C, [tex]g(x)=(\frac{1}{3}x)^2[/tex]

[tex]g(x)=(\frac{1}{3}x)(\frac{1}{3}x)[/tex]

[tex]g(x)=\frac{1}{9}x^2[/tex]

Note that the transformation answer for this problem (Option C) and our alternative solution both simplify and match perfectly, so they both represent the same end result.

Answer:

The total number of registered doctors in this year are 307345.

Step-by-step explanation:

Let the total number of doctors who registered in this year are x

Given that the total number of female doctors in total registered doctors are 54400

According to the question 17.7 percent of the total registered doctors are the female doctors

Hence the total number of  registered doctors who are females are 17.7% of x

which is written as 17.7*x÷100

According to the question 17.7x÷100= 54400

as we are given that the total number of female doctors are 54400

now

17.7x = 54400×100

x= 54400×100÷17.7

x= 307344.633 ≈ 307345

Therefore there are 307345 doctors who registered that year.

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For the function F(x)=[tex]a(x+k)^{1/n}+C[/tex] the value of a is less than zero and the correct option is option d.

Given the value of function  F(x)=[tex]a(x+k)^{1/n}+C[/tex].

We have to put the function equal to 0 for finding the nature of a and C is a fixed number in the function :

a[tex](x+k)^{1/n}[/tex]+C=0

a[tex](x+k)^{1/n}[/tex]=-C

a=-C/[tex](x+k)^{1/n}[/tex]

Since negative sign is coming before a and the value of rest of the expression cannot be negative so the value of a should b negative which means less than 0. The rest of the expression cannot be negative because it has a power of 1/n which only gives positive values like modulas.

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The English phrase of the obtained equation is 12 times z subtracted by 3. The obtained equation after solving is 12z -23

Simplifying means making something easier to do or comprehend, as well as making something less difficult.

Given data;

z be the unknown number

Given conditions;

1. The difference between a number and −23.

2.−23 is equal to the product of the number and 13.

The mathematical form of the given phrase is;

⇒ z - (-23) = z × 13

⇒z+23 = 13z

⇒12z -23

The English phrase of the obtained equation is 12 times z subtracted by 3.

Hence the simplification of the given expressions is 12z -23.

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Answer: The player expects to lose 184.21 dollars.

=========================================================

Explanation:

X = net winnings in dollars

Ignore the "28" because it's really not that relevant here. All we care about is the probability 1/38 which is the probability of winning money. The probability of losing money is 1 - (1/38) = 37/38. Put another way: there's 1 way to win, and 37 ways to lose.

If the player wins, then they walk away with 7+245 = 252 dollars

If the player loses, then their "winnings" is -7

So either X = 252 or X = -7 are the only two options.

Let's form a table showing those options with their corresponding probabilities.

[tex]\begin{array}{|c|c|} \cline{1-2}X & P(X)\\\cline{1-2}252 & 1/38\\\cline{1-2}-7 & 37/38\\\cline{1-2}\end{array}[/tex]

Now multiply each X value and P(X) value across the rows.

252*(1/38) = 6.631579

-7*(37/38) = -6.815789

These values are approximate.

[tex]\begin{array}{|c|c|c|} \cline{1-3}X & P(X) & X*P(X)\\\cline{1-3}252 & 1/38 & 6.631579\\\cline{1-3}-7 & 37/38 & -6.815789\\\cline{1-3}\end{array}[/tex]

Add up the results of the third column

6.631579 + (-6.815789) = -0.18421

This represents the net winnings for any average spin of the wheel. The player unfortunately expects to lose, on average, about $0.18421 or 18.421 cents per spin.

Do this 1000 times and the player should expect to lose about

1000*(0.18421) = 184.21 dollars

Keep in mind that due to the random nature of roulette wheel, the player may get lucky or their luck may be worse than what is described. The idea is that over the long run, the average should be somewhat close to losing 184.21 dollars.

Another way to think of it could be to have 1000 players doing the same game (rather than have 1 person play the same game 1000 times). Some players may get lucky, while others may not get so lucky. But their collective average should be losing that $184.21

The degree of dispersion in your data collection is indicated by variance.
It is given by the formula:
[tex]\overline{d}= \sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}[/tex]

To determine the values of a certain set of scattered data, the standard deviation formula is utilized. The dispersion of the quantities or data from the mean is how the standard deviation is simply defined. The conclusion drawn from a lower standard deviation is that the results are fairly near to the average. Higher values, on the other hand, indicate a significant dispersion from the mean. The standard deviation number can never be negative, it should be positive.

It is given by the formula:

[tex]s_d = \sqrt{\sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}} =\sqrt{\overline{d}}[/tex]

We have that the mean of the values is:  

at 8 AM [tex]\overline{x}=\frac{97.9+99.3+97.9+97.6+97.4}{5}=98.02[/tex]

at 12 AM [tex]\overline{x}=\frac{98.5+99.7+98+97.4+97.6}{5}=98.24[/tex]

Using the above definitions we have that

at 8 AM [tex]\overline{d}=\frac{(98.02-97.9)^2+(98.02-99.3)^2+(98.02-97.9)^2+(98.02-97.6)^2+(98.02-97.4)^2}{5}=0.4456[/tex]

[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.4456}=0.6675[/tex]

at 12 AM

[tex]\overline{d}=\frac{(98.24-98.5)^2+(98.24-99.7)^2+(98.24-98)^2+(98.24-97.4)^2+(98.24-97.6)^2}{5}=0.6744[/tex]

[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.6744}=0.8212[/tex]

In general, [tex]\mu_d[/tex] represents the mean of the differences from the population of matched data.

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Answer:

They could make at most 5 teams and its not possible to make everyone on team.

Step-by-step explanation:

If there are 4 players on a team, then we use 23 ÷ 4 = 5.75, 0.75 is not enough for 1, so there are 3 players remaining after making 5 teams.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x = 25°[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 4x - 13 = 2x + 37[/tex]

[ Alternate Exterior Angle ]

[tex]\qquad \tt \rightarrow \: 4x - 2x = 37 + 13[/tex]

[tex]\qquad \tt \rightarrow \: 2x = 50[/tex]

[tex]\qquad \tt \rightarrow \: x = \cfrac{50}{2} [/tex]

[tex]\qquad \tt \rightarrow \: x = 25 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

a)  initial height = 0 m

b)  8 s

c)  vertex = (4, 32)

    maximum height = 32 m

Step-by-step explanation:

Given equation:

[tex]h=-2t^2+16t[/tex]

where:

The initial height of the arrow will be at the beginning of its journey, so when t = 0

Substitute t = 0 into the equation and solve for h:

[tex]\implies h=-2(0)^2+16(0)[/tex]

[tex]\implies h=0[/tex]

Therefore, the initial height of the arrow is 0 m.

The arrow will hit the ground when the height is 0 m.

Substitute h = 0 into the given equation:

[tex]\implies -2t^2+16t=0[/tex]

Factor out -2t:

[tex]\implies -2t(t-8)=0[/tex]

Therefore:

[tex]\implies -2t=0 \implies t=0[/tex]

And:

[tex]\implies t-8=0 \implies t=8[/tex]

Therefore, the arrow will hit the ground at 8 seconds.

The vertex is the turning point of a parabola - it's minimum or maximum point.

As the leading coefficient for the given equation is negative, the parabola opens downwards and so its vertex is its maximum point.

There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.

We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds.  Therefore, t = 0 and t = 8 are the x-intercepts.  The midpoint is halfway between zero and 8, so the midpoint is t = 4

To find the y-coordinate, substitute t = 4 into the equation and solve for h:

[tex]\implies h=-2(4)^2+16(4)[/tex]

[tex]\implies h=-32+64[/tex]

[tex]\implies h=32[/tex]

Therefore, the coordinates of the vertex are (4, 32)

The maximum height is the y-coordinate of the vertex.

Therefore, the maximum height is 32 m

Answer:

D: (–∞, ∞); R: [–11, ∞)

Step-by-step explanation:

The domain of a quadratic function is all real numbers, so eliminate the third and fourth options.

Also, since the coefficient of [tex]x^2[/tex] is positive, we know the graph opens up and thus has a minimum.

This means that the first option must be wrong since the range has a maximum, not a minimum.

Therefore, the correct answer is Option 2.

Answer:

D: (–∞, ∞); R: [–11, ∞)

Step-by-step explanation:

I honestly don't know the answer but the other person said this so I'm putting it as my answer ill update this answer when i find out if its right or not.

update I GOT A 100% woop woop

The question is incomplete. Below you will find the missing graph.

The lowest value of the range of the function shown on graph is (B) -2.

A graph is the pictorial representation of the function or mathematical relation (Equation or Inequality etc).

The lowest value of the graph is the value of y when y=f(x) gives the least value.

From the given graph we can clearly see that at x=3 the graph of the given function approaches the least value which is -2.

So the lowest value of the range of the function shown on the graph is -2.

Hence the correct option is (B).

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The percentage decrease would be 70 percent.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

The price of an item has dropped to 27$ today. Yesterday it was 90.

90 - 27 = 63

The percentage decrease;

63 / 90 x 100= 70%

Hence, The percentage decrease would be 70 percent.

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The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.

An absolute value function is defined as a function that contains an algebraic expression within absolute value symbols.

The absolute value function is f(x) = |x| is defined as,

f(x )

x = x < x = 0 < x = -x

Observe that the graph is V-shaped.

The vertex of the graph is (0,0).

The domain is the set of all real numbers.

The x-intercept and the y-intercept are both 0.

Hence, The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.

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