In your own words, define the unit rate in an equation of proportional relationship y= kx.

Answer:

25%

Step-by-step explanation:

Each flip has a 50% probability of landing heads.  Two in a row would be (50%)*(50%) = 25%

[Note:  25% of $40 is $10].  Don't waste your time.

The probability that the last marble removed is non-red is 2/3.

According to the given question.

Total number of marbles in a bucket = 3

And, a person arbitary pulls out each marble one at a time.

So, there are 6 possible sequences of removing 3 marbles.

Let R be the red marble, B be the blue marble and G be the green marble.

The possible sequences or sample space for removing marbles are: {RBG, RGB, BGR, BRG, GRB and GBR}.

Let A denotes the event of removing the non-red marbles at the last.

The favorable cases for event A are: RBG, RGB, BRG and GRB.

As, we know that probability of any event is calculated as by taking the ratio of total number of favorable outcomes to the total number of outcomes.

Thereofre,

The probability that the last marble removed is non-red

= 4/6

= 2/3

The probability that the last marble removed is non-red is 2/3.

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we conclude that the correct option is A, the slope is:

"the average number of pounds per foot tall"

The linear equation:

y = 48.3*x - 127

Relates the height, x, and the weight, y of an adult.

Then the slope, which is 48.3, should have units of mass over height.

Now, if x is in feet and y is in pounds, then the slope has units of pounds/feet.

Then it represents the mean number of pounds per feet. So we conclude that the correct option is A:

"the average number of pounds per foot tall"

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Answer:

16 square units

Step-by-step explanation:

You find the area by multiplying the base times the height.  The base or horizonal length is 4.  You get this from the ordered point x (4,0).  The x coordinate 4, tells us that the point x is 4 spaces to the right of zero, so the length or base is 4.

The height is also 4.  You get this from the point S (2,4)  The y coordinate of 4 tells you how high up the point is.

4 x 4 = 16

Answer:

-7

Step-by-step explanation:

[tex]f(10) = 5-g(10)\\=5-(2(10)-8)\\=5-(20-8)\\=5-(12)\\=-7[/tex]

By evaluating the function, we conclude that f(10) = -7

Here we know that:

g(x) = 2x - 8

And f(x) = 5 - g(x).

Then we can write:

f(x) = 5 - (2x - 8) = 5 - 2x + 8 = -2x + 13

Now we want ot evaluate it in x = 10, this means replace the variable by the number 10.

f(10) = -2*10 + 13 = -20 + 13 = -7

Then, we conclude that f(10) = 7

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Answer: 42

Step-by-step explanation:

angle t is 42 degrees

Answer:

  ∠T = 42°

  PT = 14.4

  QT = 19.4

Step-by-step explanation:

An angle and its adjacent side are given in the right triangle. The other two sides can be found using trig relations. The third angle can be found using the angle sum theorem.

The mnemonic SOH CAH TOA is intended to remind you of the relations between sides of a right triangle and the trig functions of its angles. The relations relevant to this triangle are ...

  Cos = Adjacent/Hypotenuse   ⇒   Hypotenuse = Adjacent/Cos

  Tan = Opposite/Adjacent   ⇒   Opposite = Adjacent×Tan

Then the missing side lengths are ...

  QT = QP/cos(Q) = 13/cos(48°) ≈ 19.4282 ≈ 19.4

  PT = PQ×tan(Q) = 13×tan(48°) ≈ 14.43796 ≈ 14.4

The angle sum theorem tells you the sum of angles in a triangle is 180°. This means the acute angles in a right triangle are complementary.

  ∠T = 90° -48° = 42°

The solution to the triangle is ...

  ∠T = 42°

  PT = 14.4

  QT = 19.4

__

Additional comment

The attachment shows the solution from one of many available triangle solvers. Some calculators have triangle solver functions built in.

The total price paid by Mr. Thapa as per the new rating will be equal to Rs 180.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total distance traveled by Mr. Thapa = 5 km = 5000 meters.

The initial price paid for the taxi = Rs 14

Then, the meter was flagged down, then the fare went to rs 7.20 per 200 m.

Let the price paid after 5 km is x.

So, the ratio will be,

200 m = Rs 7.20

5000 m = x

Perform cross-multiplication,

200x = 5000 × 7.20

200x = 36000

x = 36000/200

x = Rs 180

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Answer:

  140 cm

Step-by-step explanation:

The distance of the foot of the ladder from the building can be found using the Pythagorean theorem (or your knowledge of Pythagorean triples). Once the two distances are found, their difference can be found.

The 650 cm ladder reaches 520 cm up the side of the building. The ratio of these side lengths is 650/520 = 5/4, suggesting these are the sides of a 3-4-5 right triangle. The distance from the building is ...

  (3/5)×650 cm = 390 cm.

Alternatively, the distance (a) from the building can be found using the Pythagorean relation ...

  a² +b² = c²

  a² +520² = 650²

  a = √(422500 -270400) = √152100 = 390 . . . cm

The 650 cm ladder reaches 520 +80 = 600 cm up the side of the building. The ratio of these side lengths is 650/600 = 13/12, suggesting these are the sides of a 5-12-13 right triangle. The distance from the building is ...

  (5/13)×650 cm = 250 cm

Again, the Pythagorean theorem can be used to obtain the same result:

  a = √(422500 -360000) = √62500 = 250 . . . cm

The difference between the two distances is ...

  390 cm -250 cm = 140 cm

The foot of the ladder will be 140 cm closer to the building.

Recall that for [tex]|x|<1[/tex], we have the convergent geometric series

[tex]\displaystyle \sum_{n=0}^\infty x^n = \frac1{1-x}[/tex]

Now, for [tex]\left|\frac x5\right| < 1[/tex], we have

[tex]\dfrac1{5 - x} = \dfrac15 \cdot \dfrac1{1 - \frac x5} = \dfrac15 \displaystyle \sum_{n=0}^\infty \left(\frac x5\right)^n = \sum_{n=0}^\infty \frac{x^n}{5^{n+1}}[/tex]

Integrating both sides gives

[tex]\displaystyle \int \frac{dx}{5-x} = C + \int \sum_{n=0}^\infty \frac{x^n}{5^{n+1}} \, dx[/tex]

[tex]\displaystyle -\ln(5-x) = C + \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}[/tex]

If we let [tex]x=0[/tex], the sum on the right side drops out and we're left with [tex]C=-\ln(5)[/tex].

It follows that

[tex]\displaystyle \ln(5-x) = \ln(5) - \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}[/tex]

or

[tex]\displaystyle \ln(5-x) = \boxed{\ln(5) - \sum_{n=1}^\infty \frac{x^n}{5^n n}}[/tex]

Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 2 ) and (x₂, y₂ ) = (- 18, 2 )

m = [tex]\frac{2-2}{-18-6}[/tex] = [tex]\frac{0}{-24}[/tex] = 0

The slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

m = ( y₂ - y₁) / (x₂ - x₁)

It is given that the two points are (6, 2) and (-18, 2).

The two-point can be represented as,

(x₁, y₁  ) = (6, 2)

(x₂, y₂ ) =(-18, 2)

The slope of the line can be obtained as,

m = ( y₂ - y₁) / (x₂ - x₁)

m = (2-2) / (-18-6)

m =0 / -24

m =0

Thus, the slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.

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[tex]4r {}^{3} s - rs + 7r {}^{3} s + 8rs - 3 + 8rs + 6 \\ add \: \: terms \: \: of \: \: same \: \: variables \\ 11r {}^{3} s + 15rs + 3[/tex]

The surface area of the pyramid is 34.8 in²

Since the figure is a square pyramid, its surface area, A = 4 × area of triangular face + area of square base.

Area of triangular face A' = 1/2bh where

So, A' = 1/2 × 4.3 in × 3 in

A' = 1/2 × 12.9 in²

A' = 6.45 in²

Area of square base A" = L² where L = length of base = 3 in

So, A" = (3 in)²

= 9 in²

Surface area of pyramid, A = 4A' + A"

= 4 × 6.45 in² + 9 in²

= 25.8 in² + 9 in²  

= 34.8 in²

So, the surface area of the pyramid is 34.8 in²

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she should use 2 by 6

Step-by-step explanation:

2 divided by 6 will give 0.3 in 1d.p

Answer:

y = [tex]\frac{1}{2}[/tex] x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 1) ← 2 points on the line

m = [tex]\frac{1-0}{0-(-2)}[/tex] = [tex]\frac{1}{0+2}[/tex] = [tex]\frac{1}{2}[/tex]

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = [tex]\frac{1}{2}[/tex] x + 1 ← equation of line

The straight line equation is :

[tex]\boxed {y = mx + c}[/tex]

Here, c = 1 as it intersects (0, 1) on the y-axis.

The slope is :

Hence, the equation will be :

y = 0.5x + 1

I hope it helped you solve the problem.

Good luck in your studies!

Answer:

-15 would be the answer because if it's below sea level it would have a negative sign in front of 15

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

h(x) = -1/3x+2 where we need to find -4h(9)

h(9): x = 9

h(x) = -1/3(9) + 2

h(x) = -3 + 2

h(x) = -1

-4h(9) is -4h(x):

-4(-1) = 4

The equation of the vertical asymptote of the function [tex]g(x)=4log_{2} (x-2)+5[/tex] is x=2.

Vertical asymptotes are vertical lines that represent the zeros of a rational function's denominator. Asymptotes can also occur in other situations, such as logarithms. It occurs at the x-value that is outside the domain of the function, therefore the graph can never cross it.

There may be a vertical asymptote along the vertical line if a portion of the graph is about to turn vertical. At the point of x along which you discovered the vertical asymptote, the function's value changes to either ∞ or -∞. A vertical asymptote, however, must never touch the graph.

Graph the function [tex]g(x)=4log_{2} (x-2)+5[/tex]

(x,y)= (3,5), (4,9), (6,13)

From graph we can see that the graph is turning to be vertical from x=2. So, the equation of vertical asymptote of the function is x=2.

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The complete question is:

“What is the equation of the vertical asymptote of [tex]g(x)=4log_{2} (x-2)+5[/tex]? enter your answer in the box.”

Answer:

Your answer is 7^2.

Step-by-step explanation:

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

Have a great day,

Nish

The equivalent expression is [tex]7^{2}[/tex].

We have the following expression -

[tex]\frac{7^{-3} }{7^{-5} }[/tex]

We have to find its equivalent value.

[tex]f(x, y) =\frac{A^{x} }{A^{y} }[/tex]

In order to divide two exponents with same base, we use the 'Quotient property of exponents.

The equivalent expression can be written as -

f(x, y) = [tex]A^{x} A^{-y} = A^{x-y}[/tex]

In the question given we have -

[tex]\frac{7^{-3} }{7^{-5} }[/tex]

Using the property discussed above -

[tex]7^{-3}\;7^{5}[/tex] = [tex]7^{-3+5}[/tex] = [tex]7^{2}[/tex]

Hence, the equivalent expression is [tex]7^{2}[/tex].

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Answer:

The third one as they have no links really

The radius of the table can be either 13 inches or 73 inches.

Let the radius of the table be r inches and the corner be the origin.

The coordinates of the center of the table exist (r, r).

The equation for the circumference of the table exists (x−r)²+(y−r)²=r².

The mark at the edge of the table exists 18 inches from one wall and 25 inches from the other wall. Therefore, the coordinates of this point exist (18, 25). It could also be (25, 18) but it does not make any difference to our estimations.

As the mark exists on the edge, it meets the requirements of the equation of the circumference of the table.

(18−r)² + (25−r)² = r²

324−36r+r²+625−50r+r² = r²

r²−86r+949 = 0

(r − 13)(r − 73) = 0

r = 13 inches and r = 73 inches

Therefore, the radius of the table can be either 13 inches or 73 inches.

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Answer:

$525

Step-by-step explanation:

We can find the original price by using the formula x - 0.36x = 336, where x is the original price, 0.36 is the discount percentage (converted to decimal form), and 336 is the total amount paid after the discount is applied:

[tex]x-0.36x=336\\0.64x=336\\x=525[/tex]

To check and further understand why the formula works, we can simply apply the discount to the original price and subtract the number from the original price:

525 * 0.36 = 189

525 - 189 = 336

Modeling the first formula gives us:

525 - (0.36 * 525) = 336

525 - 189 = 336

Answer:$6

Step-by-step explanation:

If only 3 got the children's price, that means there were 4 adult tickets.
4*11=44

62-44=18

18/3=6

$6 per child ticket

Part A

Using the Pythagorean on the right triangle PQR, with PQ and QR as the legs and PR as the hypotenuse,

[tex]14^2 +6^2 =(PR)^2\\\\(PR)=\sqrt{14^2 +6^2}\\\\PR \approx \boxed{15.23 \text{ ft}}[/tex]

Part B

[tex](QR)^2 +6^2 =16^2\\\\(QR)^2 =16^2 -6^2\\\\QR=\sqrt{16^2 -6^2}\\\\QR \approx \boxed{14.83 \text{ ft}}[/tex]

Answer:

2/5 or 0.4

Step-by-step explanation:

First we have to make equation into the gradient slope form :

y=mx+c    m is gradient and c is y-intercept

15y-6x=8

First we add 6x to both sides :

15y = 6x+8

Now we divide both sides by 15 :

y = 6x+8 / 15

Split the fraction on the right :

y = 6x/15 + 8/15

6x/15 = 6/15x

Our gradient will be 6/15 = 2/5 or 0.4

Hope this helped and have a good day

According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7

Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.

Given,

n = 66

We know that,

According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:

[tex]k=1+log_{2} n[/tex]

Here, n is equal to 66 and by substituting the value to the equation we get:

[tex]k=1+log_{2} (66)[/tex]

k = 7.0444

k ≈ 7

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Answer:

10

Step-by-step explanation:

By the alternate interior angles theorem,

[tex]4x=2x+20 \\ \\ 2x=20 \\ \\ x=10[/tex]

Using the Pythagorean Theorem, it is found that the unknown side length of the triangle is of 7.9 cm.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Researching this problem on the internet, we have that:

Hence:

x² + 9² = 12²

x = sqrt(12² - 9²)

x = 7.9 cm.

The unknown side length of the triangle is of 7.9 cm.

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Step-by-step explanation:

I just answered this. how often did you post that question ?

she added 54-48 = 6g.

how many % of 48g are these 6g ?

100% = 48

1% = 100%/100 = 48/100 = 0.48g

how many % are 6g ?

as many as how often 1% (0.48g) fits into 6g :

6 / 0.48 = 12.5%