What is square root of 68 in simplest radical form?

Answer:

[tex]x >4[/tex]

Step-by-step explanation:

[tex]x+3>19-3x[/tex]

Add 3x and -3 on both parts.

[tex]x+3+3x-3>19-3x+3x-3[/tex]

Combine like terms.

[tex]x+3x>16[/tex]

[tex]4x >16[/tex]

Divide 4 on both parts.

[tex]\frac{4x}{4} > \frac{16}{4}[/tex]

[tex]x >4[/tex]

Answer: The systems are solved by solving for one variable in one of the equations, then substituting that equation into the second equation. Solve for a in the second equation, then substitute the second equation into the first. The Elimination Method: Both equations are in standard form:            Ax + By = C.

Answer:

The solution of the system of equations is (x,y) = (2,0)

Step-by-step explanation:

The equation of a line through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is equal to:

[tex]y-y_1=m(x-x_1)[/tex]

Where [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So, the equation of the line through the points (3, 1) and (–5, –7) is:

[tex]m=\frac{-7-1}{-5-3}=1[/tex]

[tex]y-1=1(x-3)\\y=x-3+1\\y=x-2[/tex]

Then, we have two equations, y=x-2 and y=0.5x -1 , so solving for x, we get:

x - 2 = 0.5 x - 1

x - 0.5x = 2 - 1

x = 2

Replacing x=2 in the equation y=x-2, we get:

y =2 - 2 = 0

Finally, the solution of the system of equations is (x,y) = (2,0)

Answer:The solution of the system of equations is (x,y) = (2,0)

Step-by-step explanation:

Answer:

7.3%

Step-by-step explanation:

Let M = Maths

E = English

P(M ∪ E) = P(M) + P(E) - P( M ∩ E)

From the question:

P(M ∪ E) = 35.7%

P(M) = 18%

P(E) = 24%

P( M ∩ E) = unknown

35.7% = 18% + 24% - P( M ∩ E)

35.7% = 42% - P( M ∩ E)

P( M ∩ E) = 42% - 35.7%

P( M ∩ E) = 7.3%

Therefore, the probability that a student who receives an A in Math course will also receive an A in English course is 7.3%.

Answer:

Step-by-step explanation:

Area of shaded region it is area of hexagon minus area of circle.

A regular hexagon is comprised of six equilateral triangles (of the same sides).

So its area:  [tex]A_1=6\cdot\dfrac{S^2\sqrt3}{4}=\dfrac{3S^2\sqrt3}2[/tex]     {S = side of the triangle}

Height (H) of such a triangle is equal to radius (R) of a circle inscribed in the hexagon:

[tex]R = H = \dfrac{S\sqrt3}{2}[/tex]

Area of shaded region:

[tex]A=A_1-A_\circ=\dfrac{3S^2\sqrt3}2-\pi R^2=\dfrac{6S^2\sqrt3}4-\pi\left(\dfrac{S\sqrt3}2\right)^2=\dfrac{S^2(6\sqrt3-3\pi)}4[/tex]

S = 6 cm

so:

[tex]A=\dfrac{6^2(6\sqrt3-3\pi)}4=\dfrac{36(6\sqrt3-3\pi)}4=9(6\sqrt3-3\pi)=27(2\sqrt3-\pi)\ cm^2\\\\A=27(2\sqrt3-\pi)\ cm^2\approx8.71\ cm^2[/tex]

Answer:

[tex] y = A_o (b)^t[/tex]

With [tex] A_o = 82.6[/tex] the initial amount and t the time on hours and t the time in hours. since the half life is 12 hours we can find the parameter of decay like this:

[tex] 41.3= 82.6(b)^{12}[/tex]

And solving for b we got:

[tex] \frac{1}{2}= b^{12}[/tex]

And then we have:

[tex] b= (\frac{1}{2})^{\frac{1}{12}}[/tex]

And the model would be given by:

[tex] y(t) = 82.6 (\frac{1}{2})^{\frac{1}{12}}[/tex]

Step-by-step explanation:

Assuming this complete question: "A specific radioactive substance follows a continuous exponential decay model. It has a half-life of 12 hours. At the start of the experiment, 82.6g is present. "

For this case we can create a model like this one:

[tex] y = A_o (b)^t[/tex]

With [tex] A_o = 82.6[/tex] the initial amount and t the time on hours and t the time in hours. since the half life is 12 hours we can find the parameter of decay like this:

[tex] 41.3= 82.6(b)^{12}[/tex]

And solving for b we got:

[tex] \frac{1}{2}= b^{12}[/tex]

And then we have:

[tex] b= (\frac{1}{2})^{\frac{1}{12}}[/tex]

And the model would be given by:

[tex] y(t) = 82.6 (\frac{1}{2})^{\frac{1}{12}}[/tex]

Answer:

A i think its a A try. it it that looks correct

Answer:

Its B, 1.2EE6/1.1EE4

Step-by-step explanation:

The density is 109.9, and this is the only equation that gives you this answer

i also took the test!

Answer:

b

Step-by-step explanation:

you need to round 2.51 to 3 because it was the correct answer

Complete Question

Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 0.35 m³ of fluffy

material. The base is 0.5m² and the height is 1m.

What is the length of the pillow?

Give an exact answer (do not round).

Answer:

1.4m

Step-by-step explanation:

A wedge comes in the shape of a Triangular prism. Hence,

Volume of a wedge(Triangular prism) = 1/2 × B × H × L

b = 0.5m

h = 1 m

l = ??

Volume of a wedge = 0.35m³

0.35 = 1/2 × 0.5 × 1 × L

0.35 = 0.25 × L

L = 0.35/0.25

L = 1.4m

Answer:

c. (3x^2-1)(x-7)

Step-by-step explanation:

=(3x^3-21x^2)+(-x+7)

=-(x-7)+3x^2(x-7)

=(3x^2-1)(x-7)

Answer:

hey! it's A and X on edge :)

Answer:

(i) The area of the rabbit cage when the width is 5.2 m is 81.5 m²

(ii) The area of the rabbit cage if Wilson has 40 meters of wire mesh is 75 m²

Step-by-step explanation:

(i) The given relation of the area, A to the width P of the rabbit cage is A = 3·p²

The graph of the function between the values of 0 and 6 inclusive is found as follows;

A,              3·p²

0,               0

1,                1

2,               12

3,               27

4,               48

5,               75

6,               108

Please find attached the graph of A to 3·p²

From the graph, we have when the the width, p, of the rabbit cage = 5.2, the area, A ≈ 81.5 m²

The area of the rabbit cage when the width is 5.2 m = 81.5 m²

(ii) Also from the graph given that the total wire mess with Wilson = 40 meters, we have;

The formula for the perimeter of the cage = The formula for the perimeter of a rectangle = 2×length + 2×width

The formula for the perimeter of the cage = 2×3×p + 2× p = 8·p

Where the total length of the wire mesh available = 40 meters for the cage

The 40 meters of wire mesh will be used round the perimeter of the cage

∴ 40 m. = 8·p

p = 40/8 = 5 m.

At p = 5 m. the area is given as A = 75 m².

Therefore, the area of the rabbit cage if Wilson has 40 meters of wire mesh = 75 m².

Answer:

hello your question lacks some information below is the complete question

Suppose you are designing a cardboard box that must have a volume of  27 cubic feet. The cost of the cardboard is ​$0.15 per square foot. What is the most economical design for the box​ (one that minimizes the​ cost), and how much will the material in each box​ cost?

Answer : Box design , $8.1 ( cost of material in each box)

Step-by-step explanation:

Volume of cardboard box = 27 cubic feet

cost of cardboard = $0.15 square feet

i) The most economical design for the box would be Designing a square box because the dimensions of the box would be [tex]\sqrt[3]{27}[/tex] = 3 ft

ii) The cost of the material for each box can be calculated as

= surfaces * surface area * cost per square foot

= 6 * 3^2 * $0.15

= $8.1

Answer:

A.

Step-by-step explanation:

We need to find the equation where, if x is equal to 3, g(x) is equal to 1, because g(x) passes through the point (3,1)

Then, replacing x by 3 on every option we get:

[tex]g(x)=(\frac{1}{3}x)^2= (\frac{1}{3}3)^2=1\\g(x)=(\frac{1}{9}x)^2= (\frac{1}{9}3)^2=\frac{1}{9}\\g(x)= \frac{1}{3}x^2= \frac{1}{3}3^2=3\\g(x)=3x^2=3*3^2=27[/tex]

So, the answer is A. because g(x) is equal to 1

Answer:

1 Pound of Rock = .01 cubic feet

OR 100 pounds per cubic foot

A) Company needs 500,000 pounds of rock

Volume of Rock to be transported: = 500,000 * .01 =

5,000 cubic feet

B) Volume of each truck 12 * 9 * 8 = 864 cubic feet

C) Trucks needed for entire shipment:

= 5,000 / 864 = 5.78

So, we'll need 6 trucks.

Step-by-step explanation:

Answer:

this. question is not clear please send clear question

We can conclude that -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have the following two functions -

y = -x

AND

y = x

Refer to the graphs attached for both the functions -

y = - x     and     y = x

The graphs as seen pass through the origin. One graph (y = x) has a slope of +1 while the other one (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.

We can conclude that -

To solve more questions on straight line, visit the link below-

https://brainly.com/question/29030795

#SPJ2

Answer:

12 bags of cookies.

Step-by-step explanation:

Since you already start out with $24, you will have a y-intercept of 24. Your slope will be 3, since each bag sells for $3.

Your equation will be y = 3c + 24.

Your sister does not start out with money, so she will have a y-intercept of 0. Her slope will be 5, as each bag sells for $5.

Her equation will be y = 5c.

Since y = y, you can set the two equations equal to each other.

3c + 24 = 5c

5c = 3c + 24

Subtract 3c from both sides

2c = 24

Divide both sides by 2

c = 12

So, they must sell 12 bags of cookies to raise the same amount of money, $60. Yum!

Hope this helps!

Answer:

There is no price difference between the two stores.

Step-by-step explanation:

The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

In this case a paired t-test is used to determine if there is a price difference between the two stores.

The hypothesis for the test can be defined as follows:

H₀: There is no price difference between the two stores, i.e. d = 0.

Hₐ: There is a price difference between the two stores, i.e. d ≠ 0.

From the information provided the sample mean and standard deviation are:

 [tex]\bar d=-0.464\\\\S_{d}=1.019[/tex]

Compute the test statistic value as follows:

 [tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}=\frac{-0.464}{1.019/\sqrt{10}}=-1.4399\approx -1.44[/tex]

The test statistic value is -1.44.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

The degrees of freedom is:

n - 1 = 10 - 1 = 9

Compute the p-value of the test as follows:

[tex]p-value=2\cdot P(t_{\alpha/2, (n-1)}>-1.44)[/tex]

               [tex]=2\cdot P(t_{0.10/2, 9}>-1.44)\\=2\times 0.092\\=0.184[/tex]  

*Use a t-table.

The p-value of the test is 0.184.

p-value= 0.184 > α = 0.10

The null hypothesis was failed to be rejected.

Thus, it can be concluded that there is no price difference between the two stores.

Answer: -6y= -3x-9

Since the slope is -6

y will be -6y

and the rest is -9, -3x

Answer: 17.75

Step-by-step explanation:

The interquartile range(IQR) is the 3rd quartile - the 1st quartile.

How to get quartiles:

First get the median:

3.5, 10.4, 16, 21.7, 27.7

10.4, 16, 21.7

16

Then find the median of the first half of data(3.5, 10.4)

(3.5+10.4)/2 = 6.95

Then find the median of the last half of data(21.7, 27.7)

(21.7+27.7)/2 = 24.7

Then to get the IQR subtract 6.95 from 24.7 to get 17.75

Hope it helps <3

Answer11.3

Step-by-step explanation:

Since there is an odd amount of values

find you lower median by taking the 3 lower numbers and using the middle number 10.4 (Q1)

then find your higher median with the 3 higher numbers and using the middle number 21.7 (Q3)

Then subtract Q3 - Q1

21.7-10.4 giving you the answer 11.3

Answer:

The difference between the two throws is 6/7 yards

Step-by-step explanation:

Beatrice throw=1 7/14 yards

Tilly throw=9/14 yards

Difference between the two throws=Beatrice throw - Tilly throw

=1 7/14 - 9/14

=21/14 - 9/14

= 21-9/14

=12/14

=6/7 yards

The difference between the two throws is 6/7 yards

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

Work Shown:

T = tens digit

U = units digit (aka ones digit)

A number like 27 is really 20+7 = 2*10 + 7*1 = 10*2 + 1*7. We have 2 in the tens digit and 7 in the units digit. So 27 can be written in the form 10T + U where T = 2 and U = 7. Reversing the digits gives 72, so T = 7 and U = 2 now. Clearly the difference between the digits 7 and 2 is not 1, so 27 or 72 is not the answer (as it's just an example).

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

Let T be larger than U. This doesn't work if T = U.

Because T is larger, saying "The difference between the digits is 1" means T - U = 1. We can isolate T to get T = U+1. We'll use this later.

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

If T > U, then the original number 10T+U reverses to the new number 10U+T and it becomes smaller. We are told that it becomes 5/6 of what it used to be.

So,

new number = (5/6)*(old number)

10U + T = (5/6)(10T + U)

6(10U + T) = 5(10T + U)

60U + 6T = 50T + 5U

60U + 6(U+1) = 50(U+1) + 5U ... plug in T = U+1

60U + 6U + 6 = 50U + 50 + 5U

66U + 6 = 55U + 50

66U - 55U = 50-6

11U = 44

U = 44/11

U = 4 is the units digit of the original number

T = U+1

T = 4+1

T = 5 is the tens digit of the original number

The original number is therefore 10T + U = 10*5+4 = 54.

We see the difference in their digits is T-U = 5-4 = 1

The reverse of 54 is 45. The number 45 is 5/6 of 54

45 = (5/6)*54

Answer: $310.31

Step-by-step explanation:

Invested amount (P) = $302

Interest rate (r) = 3.3% per year

Period = 10 months

Recall, simple interest formula :

A = P(1 + rt) where ; A = final amount

Interest = 3.3% = 3.3/ 100 = 0.033

A = $302 ( 1 + 0.033(10/12))

A = $302 (1 + 0.033(0.8333333))

A = $302 ( 1 + 0.0275)

A = $302 ( 1. 0275)

A = $310.305

A = $310.31

Answer:

Type I error

Step-by-step explanation:

Here, we are interested in knowing the type of error that stems from the hypotheses set up

in the question.

From the suggestion of the sample, we know that the food is actually safe but was wrongly labeled as being unsafe.

So in this case, the type of error committed is the type 1 error since the food is actually safe but there was a wrong suggestion of being generally unsafe by the sample

Answer:

[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]

Step-by-step explanation:

The interior angle of a regular heptagon = = 900/7° = 128.57°

Therefore, angle DAB = 128.57°

The interior angle of the square = 90°

Therefore, angle DAC = 90°

Therefore, we have

angle DAB+ angle DAC + angle BAC = 360° (sum of angles at a point (A))

Angle BAC = 360° - angle DAB - angle DAC =  360° - 900/7° - 90° = 990/7°

Angle BAC = 141.43°

Expressing 141.43° as a common fraction gives;

[tex]141.43 ^{\circ}= \dfrac{990}{7} ^{\circ}=141\frac{3}{7} ^{\circ}[/tex]

[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]

 The degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex]

Given, A square and a regular heptagon are coplanar as shown in below figure attached.

We have find the exterior angle of BAC.

We know that, The formula that gives the interior angle measure for a regular polygon with any number of sides is,

[tex]\frac{180(n-2)}{n}[/tex]  where n is the number of sides.  

Since the heptagon has 7 no. of sides.

So regular heptagon's interior angle measures,

[tex]\frac{180(7-2)}{7}=128\frac{4}{7}[/tex]

Hence [tex]\angle A[/tex] will be[tex]128\frac{4}{7}[/tex] degrees.

We know that a square's interior angle is 90 degrees and a heptagon's interior angle is  128.57 degrees. We will subtract those from 360 degrees to find angle BAC.

[tex]\angle BAC = 360 - (\angle A + 90)\\[/tex]

[tex]\angle BAC = 360 - (128\frac{4}{7} + 90)\\\angle BAC=141\frac{3}{7} ^\circ[/tex]

Hence the degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex].

For more details on Exterior angle follow the link:

https://brainly.com/question/2125016            

Answer:

A. (-1,1)

Step-by-step explanation:

6x+2y = 8    

-2y =-2          

6x=6              

6x=6                  

X=1

Answer:

N= 9/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \frac{n - 6}{ - 4} = 6[/tex]

Cross multiply

We have

n - 6 = - 4 × 6

n - 6 = - 24

n = - 24 + 6

Hope this helps you

Answer:

5 < 10x – 3

Step-by-step explanation:

The inequality is 5 - 2x < 8x - 3.

5 < 6x – 3 is incorrect because 8x + 2x = 10x, not 6x.

3x < 8x – 3 is incorrect because 5 - 2x is not 3x, you can't subtract those terms as they are not like terms.

5 < 10x – 3 is correct because 8x + 2x = 10x.

2 – 2x < 8x is incorrect because 5 + 3 = 8, not 2.

Answer:

C on edg

Step-by-step explanation:

Answer:

for exapmle:  (2, 5)          {5=2•2.5}

                       (8, 20)        {20=8•2.5}  

                       (-5,  -12.5}    {-12.5=-5•2.5}

Step-by-step explanation:

    -3y+3x    -3y+3x

            ÷2     ÷2

Answer:

neither

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the translation rule (x, y ) → (x - 2, y + 4 )

Subtract 2 from the original x- coordinate and add 4 to the original y- coordinate, thus

A(0, 3 ) → A'(0 - 2, 3 + 4 ) → A'(- 2, 7 )

B(- 2, - 4 ) → B'(- 2 - 2, - 4 + 4 ) → B'(- 4, 0 )

C(1, 5 ) → C'(1 - 2, 5 + 4 ) → C'(- 1, 9 )