This data set represents the widths in yards of pieces of fabric used by a sewing group.

What is the mean of this data set?

{113, 14, 23, 12, 114}

Enter your answer as a fraction in simplest form in the box.

help

Answer:

40%

Step-by-step explanation:

6.75 + 1.25 = 8 (Total she just spent)

8 (Total she just spent) + 12 (Total she had left) = 20 (Total she started with)

8/20 = 0.4 = 40%

(Total spent / total she started with = 40%)

[tex]\\ \rm\rightarrowtail \dfrac{sin(180+A)+2cos(180+A).cos(A-180)}{2cos^2(360+A)-cos(-A)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2(cos^2A-sin^2A)}{2cos^2A-cosA}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2cos^2A-2sin^2A}{cosA(2cosA-1)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-sinA+2-2sin^2A-2sin^2A}{cosA(2cosA-1)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-sinA-4sin^2A}{cosA(2cosA-1)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-sinA(4sinA-1)}{cosA(2cosA-1)}[/tex]

[tex]\\ \rm\rightarrowtail -tanA\left(\dfrac{4sinA-1}{2cosA-1}\right)[/tex]

Answer:

Area: 24   Perimeter: 20

Step-by-step explanation:

Area (multiply side 1 by side 2):

4×6=24

Perimeter (add all of the sides together):

4+4=8

6+6=12

8+12=20

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 4.80}}{\left( \cfrac{5}{100} \right)4.80}\implies 0.24~\hfill \underset{\textit{price including tax}}{\stackrel{4.80~~ + ~~0.24}{5.04}}[/tex]

Answer:

the second one is an example of a rational function

A beam of length 10m can support a weight of 62kg.

It is given that

Weight W ∝ 1/ Length L

W ∝ 1/L

W = k/L...........eq1

where k is constant of proportionality

The constant of proportionality is the ratio that relates two given values.

It is given that when L= 2m, W = 310kg

310 = k/2

k = 620

So put the k value in eq1,

eq1 becomes,

W = 620/L

when L = 10

W = 620/10

W =62kg

Therefore, a beam of length 10m can support a weight of 62kg.

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Answer:

70 meters

Step-by-step explanation:

Based on the given conditions, formulate:: 45x5/3

Cross out the common factor: 14x5

Calculate the product or quotient: 70

The width of the parking lot in the drawing is, 70 milliliters.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

She used the scale 5 millimeters: 3 meters.

And, The actual width of the parking lot is 42 meters.

Hence, We can formulate;

The width of the parking lot in the drawing = 42 × 5 / 3

                                                                  = 70 milliliters

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The value of z is equal to 50.28.

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

These numbers are represented by a ratio between two integers numbers ([tex]\frac{a}{b}[/tex]), where b[tex]\neq[/tex]0.  Besides, this ratio can be simplified in decimal form.

For solving this equation, firstly, rewrite the information given:

                                          [tex]y=512x \;(1)\\ \\ z=50.25+x \;(2)\\ \\ y=15.5 \;(3)[/tex]

As the question gives the values for y, you can find x.

                                        [tex]y=512x\\ \\ 15.5=512x\\ \\ x=\frac{15.5}{512} =0.03[/tex]

Applying x=0.03 in the equation (3), you can find z.

                              [tex]z=50.25+x \\ \\ z=50.25+0.03\\ \\ z=50.28[/tex]

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Here for 120, the expression for the start root and end root is given  

[tex]\sqrt{120} =2\sqrt{30}[/tex]

Here we need to find [tex]\sqrt{120}[/tex]

By simplifying the given expression, we get:

[tex]120=2\times2\times2\times3\times5[/tex]

[tex]120=(2^{2} )\times3\times5[/tex]

by taking square roots on both sides we get

[tex]\sqrt{120} =2\sqrt{30}[/tex]

Thus for 120, the expression for the start root and end root is given  [tex]\sqrt{120} =2\sqrt{30}[/tex]

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Answer:

2 square root 30x

Step-by-step explanation:

A on Edge

Answer:

(0.5, -3)

Step-by-step explanation:

(-3, -1) (4, -5)

midpoint formula

(x1 + x2) /2, (y1 + y2) /2

-3 + 4 = 1 / 2 = 0.5

-1 + -5 = -6 / 2 = -3

We're given:

To find the area of the garden alone, we can subtract the area of the garden from the combined area of the garden and walkway:

[tex]4.5(8x + 4)-4(5.5x + 1.5)[/tex]

Open up the parentheses:

[tex]= 36x +18 -22x - 6[/tex]

Combine like terms:

[tex]= 36x +18 -22x - 6\\= 14x +18 - 6\\= 14x +12[/tex]

The area of the walkway around the garden is 14x + 12.

Step-by-step explanation:

11.

x is sin(60) in a circle with radius of 8.

x = sin(60)×8 = 6.92820323... ≈ 6.9

12.

x is sin(30) in a circle with radius "diagonal length".

6 is cos(30) in the same circle.

6 = cos(30)×r

r = 6/cos(30) = 6.92820323...

x = sin(30)×r = 3.464101615... ≈ 3.5

13.

similar to 12.

but we refer to the angle at the bottom right vertex.

remember, the sum of all angles in a triangle is always 180°.

so, the angle over there at the right is

180 - 90 - 68 = 22°

x = sin(22)×r

25 = cos(22)×r

r = 25/cos(22) = 26.96336857...

x = sin(22)×r = 10.10065565... ≈ 10.1

14.

9 is the sine of the complementary angle of 49 in a circle with radius x.

the complementary angle is the angle that adds up with the original angle to 90° and is therefore

90 - 49 = 41°

9 = sin(41)×x

x = 9/sin(41) = 13.71827778... ≈ 13.7

18.

we use the extended Pythagoras :

c² = a² + b² - 2ab×cos(C)

with c being the side opposite of the angle C.

so we have

LK² = 16² + 24² - 2×16×24×cos(29) =

= 256 + 576 - 768×cos(29) =

= 832 - 671.7079351... = 160.2920649...

LK = 12.66065026... ≈ 12.7

19.

law of sine

a/sin(A) = b/sin(B) = c/sin(C)

with the sides being always opposite to the corresponding angles.

to find the angle at H we need to find the angle at G first, because we don't know GF yet.

so,

28/sin(76) = 18/sin(G)

sin(G) = 18×sin(76)/28 = 0.623761538...

G = 38.59134528...°

remember the 180° rule in triangles.

H = 180 - 76 - G = 65.40865472...° ≈ 65.4°

20.

GF is now calculated using the law of sine again.

28/sin(76) = GF/sin(H)

GF = 28×sin(H)/sin(76) = 26.23980579... ≈ 26.2

Answer:

Step-by-step explanation:

Minimum Amount = circumference of the pond.

Formulas

C = pi * d

Givens

pi = 3.14

d = 30 feet

Solution

C = pi*d             Substitute for the givens.

C = 3.14 * 30      Multiply

C =  94.2

Step-by-step explanation:

[tex]m + 148 = 3m + 10[/tex]

[tex]148 - 10 = 3m - m[/tex]

therefore

3m = 138

m = 138/3

m = 46°

pls give brainliest

Answer:

break it down to prime factorization

so the ans will be 2^3 * 3^2 *11

To determine how the graph of the parent function [tex]y = x^2[/tex] is transformed to create the graph of the new function [tex]y = -(x – 1)^2 – 5[/tex], we need to analyze the individual transformations one by one Therefore the correct option is A.

1. Translation: (x – 1) This term inside the function represents a horizontal translation of the graph. When we subtract 1 from x, the entire graph is shifted to the right by 1 unit. Hence, this function is translated right 1 unit. 2. Reflection: (-) The negative sign outside the function reflects the graph across the x-axis. Thus, the graph opens downward.

3. Vertical Transformation: -5 The term -5 outside the function causes a vertical shift of the graph downward by 5 units. In summary, the graph of the new function [tex]y = -(x – 1)^2 – 5[/tex]  undergoes the following transformations: - Translated right 1 unit due to (x – 1) - Reflected (opens downward) due to the negative sign - Translated down 5 units due to -5 Therefore, the correct answer is A. Translated right 1 and down 5 only

Hence the correct option is A

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so the investigator found the skid marks were 75 feet long hmmm what speed will that be?

[tex]s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ d=75 \end{cases}\implies s=\sqrt{30(0.7)(75)}\implies s\approx 39.69~\frac{m}{h}[/tex]

nope, the analysis shows that Charlie was going faster than 35 m/h.

now, assuming Charlie was indeed going at 35 m/h, then his skid marks would have been

[tex]s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ s=35 \end{cases}\implies 35=\sqrt{30(0.7)d} \\\\\\ 35^2=30(0.7)d\implies \cfrac{35^2}{30(0.7)}=d\implies 58~ft\approx d[/tex]

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Here, We have

The given function represents the total distance in miles covered by the traveller.

For initial interval that is x = 1 , Distance covered by the traveller

[tex]\sf{ f(x) = -45x + 270 }[/tex]

[tex]\sf{ f(1) = - 45(1) + 270 }[/tex]

[tex]\sf{ f(1) = - 45 + 270 }[/tex]

[tex]\sf{ f(1) = 225 }[/tex]

For final interval that is x = 3, Distance covered by the traveller

[tex]\sf{ f(x) = - 45x + 270 }[/tex]

[tex]\sf{ f(1) = - 45(3) + 270 }[/tex]

[tex]\sf{ f(1) = - 135 + 270 }[/tex]

We have to find the average rate of change over the given time interval

Average rate of change in the given time interval

[tex]\sf{ = }{\sf{\dfrac{ f(1) + f(3) }{3 - 1}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{ 225 + ( -135) }{ 2}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{ 225 - 135 }{ 2}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{ 90 }{ 2}}}[/tex]

[tex]\sf{ = 45 }[/tex]

Hence, The average rate of change over the given interval is 45 miles per hour.

Answer:

Four coordinate pairs that could serve as the other endpoint of the given line segment are given by:

Step-by-step explanation:

One endpoint of (4,-12), length of 5 units.

Four possible pairs:

it depends on the original question. here are 2 ways to solve depends on the question

7x³ - x²/2x³

7x³ - 1/2x

but if the problem is

(7x³-x²)/(2x³)

[x²(7x-1)]/(2x³)

(7x-1) / (2x)

Answer:

.25

Step-by-step explanation:

.25 or 1/4 is one-fourth of 1

You can divide 1 by 4 to get .25

Answer: 16

Step-by-step explanation:

Answer:

5145cm²

125/343=1875/x

x=1875×343÷125=5145

Answer:

A

Step-by-step explanation:

It could just be it was dilated (I think thats the word) by 3. 6×3=18, 8×3=24

Answer:

y = 8sqr3,

x = 4sqr3

Step-by-step explanation:

Use SOH CAH TOA, to solve this.

Here I know the opposite, so I could use either SOH either TOA or both to find the 2 unknowns.

To find y, I would use SOH, which is Sin(angle) = opposite/hypotenuse.

When I rearrange it, I get opposite/Sin(angle) = hypotenuse.

Now let's fill in with the values to give:

12/sin(60) = 8sqr3

And then to find x, let's use TOA, which is Tan(angle) = opposite/adjacent.

Rearrange it to get opposite/Tan(angle) = adjacent. This gives us a side x with a value of:

12/tan(60) = 4sqr3

Answer: 43

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

-5x + 10 > -15

-5x + 10 - 10 > -15 - 10

-5x > -25

-5x / -5 > -25/(-5)

x < 5