Given that Cos60=sin30=1/2 and cos30=sin60=root3/2.Evaluate tan60-1/1-tan30​

Answer:

millions

Step-by-step explanation:

the possibilities are endless

Answer:

3.3333333333333333333333 just 3.3

Step-by-step explanation:

Answer:  120 ways

Step-by-step explanation:

given data:

no of chocolate = 10pcs

to be shared among three individuals who are John, Harry and Donald.

there is no restriction to how it can be shared amongst them.

this Problem can be solved using combination as the order with which it would be shared doesn’t matter.

solution:

n = 10

r = 3

= 10C3

= n! / ( n - r )! r !

= 10! / ( 10 - 3 ! ) 3!

= 10! / ( 7! ) 3!

= 120

the chocolate can be shared amongst them in 120ways.

Answer:

19

Step-by-step explanation:

The shortest path is a straight line.  The slope of that line is:

m = (25 − 1) / (1 − (-3))

m = 6

The point where the ant intersects the y-axis has an x-coordinate of 0.  The slope between that point, and any other point on the line, is 6.

6 = (y − 1) / (0 − (-3))

y = 19

Answer: C

Step-by-step explanation:

For this problem, let's find the inverse for all f(x) and see which pairs with the g(x). To find the inverse, you replace the x with y and y with x. Then you solve for y.

A. Incorrect

[tex]y=\frac{x-8}{4} +9[/tex]                                 [replace x with y and y with x]

[tex]x=\frac{y-8}{4} +9[/tex]                                  [subtract both sides by 9]

[tex]x-9=\frac{y-8}{4}[/tex]                                  [multiply both sides by 4]

[tex]4(x-9)=y-8[/tex]                            [add both sides by 8]

[tex]4(x-9)+8=y[/tex]

This does not match g(x), therefore, they are not inverses of each other.

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

B. Incorrect

[tex]y=4(x-12)+2[/tex]                         [replace x with y and y with x]

[tex]x=4(y-12)+2[/tex]                         [subtract both sides by 2]

[tex]x-2=4(y-12)[/tex]                        [divide both sides by 4]

[tex]\frac{x-2}{4} =y-12[/tex]                                [add both sides by 12]

[tex]\frac{x-2}{4} +12=y[/tex]

This does not match g(x), therefore, they are not inverses of each other.

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

C. Correct

[tex]y=3(\frac{x}{2})-4[/tex]                                [replace x with y and y with x]

[tex]x=3(\frac{y}{2} )-4[/tex]                                [add both sides by 4]

[tex]x+4=3(\frac{y}{2} )[/tex]                                [divide both sides by 3]

[tex]\frac{x+4}{3} =\frac{y}{2}[/tex]                                       [multiply both sides by 2]

[tex]\frac{2(x+4)}{3} =y[/tex]

This matches g(x), therefore, they are inverses of each other.

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

D. Incorrect

[tex]y=3(\frac{2}{x} )-10[/tex]                             [replace x with y and y with x]

[tex]x=3(\frac{2}{y} )-10[/tex]                             [add both sides by 10]

[tex]x+10=3(\frac{2}{y} )[/tex]                              [divide both sides by 3]

[tex]\frac{x+10}{3} =\frac{2}{y}[/tex]                                     [multiply both sides by y]

[tex](y)(\frac{x+10}{3} )=2[/tex]                              [multiply both sides by [tex]\frac{3}{x+10}[/tex] or divide by [tex]\frac{x+10}{3}[/tex]]

[tex]y=\frac{6}{x+10}[/tex]

This does not match g(x), therefore, they are not inverses of each other.

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

After going through each problem, we found that the correct answer is C.

Answer:

9 units

Step-by-step explanation:

First of all, let us understand the meaning of dilation.

Dilation means to change the size of any image or line or a figure.

Dilation can be used to enlarge (dilation by a factor greater than 1) the original figure.

OR

Dilation can be used to make the image smaller (dilation by a factor lesser than 1) the original figure.

Here, we are given that an image with 4 points ABCD is dilated by a scale factor of [tex]\frac{1}{3}[/tex].

Its sides will be AB, BC, CD and DA.

Perimeter is equal to the sum of all the sides of a closed figure.

So, perimeter of ABCD = AB + BC + CD + DA = 27 units ...... (1)

Now, it is dilated by a scale factor of [tex]\frac{1}{3}[/tex].

So, all the sides will become smaller i.e.

A'B' = [tex]\frac{1}{3}[/tex] AB

B'C' = [tex]\frac{1}{3}[/tex] BC

C'D' = [tex]\frac{1}{3}[/tex] CD

D'A' = [tex]\frac{1}{3}[/tex] DA

Perimeter of A'B'C'D' = A'B' + B'C' + C'D' + D'A' = [tex]\frac{1}{3}[/tex]AB + [tex]\frac{1}{3}[/tex]BC + [tex]\frac{1}{3}[/tex]CD + [tex]\frac{1}{3}[/tex]DA

[tex]\frac{1}{3}[/tex] (AB + BC + CD + DA ) = [tex]\frac{1}{3} \times 27[/tex](By equation (1))

Perimeter of A'B'C'D' = 9 units

Answer:

$35.88

Step-by-step explanation:

Multiply 29.9 by 1.20 to get the original price

hope this helps:)

Answer:

90

Step-by-step explanation:

90.05

2 . Check the number to the right of it:

90.05

If the number is greater than or equal to 5, we round up. If it's less than or equal to four, we round down.

Zero is less than four. This means we round down.

90.05 ≈ 90

Hope this helps.

Answer:

y = (x − 4) / 3

Step-by-step explanation:

y = 3x + 4

To find the inverse, switch x and y, then solve for y.

x = 3y + 4

x − 4 = 3y

y = (x − 4) / 3

Answer:

the opposite of 10 is -10

Step-by-step explanation:

Graph it on -10

Answer:

Just draw a solid dot in the position positive 10 on the number line

Step-by-step explanation:

Notice that the opposite of 10 is "negative 10" (-10), and the opposite of this (-10) is "positive 10" (10). So the opposite of the opposite takes you back to the original number (positive 10)

Answer:

So the unit price of the trail - mix is $4.80 per pound

Step-by-step explanation:

Sam paid $3.60 for 3/4 pound of his favorite trail-mix.

What it means is that said paid for 3/4 = 0.75 of a pound for $3.60

So let's determine how much he could have paid for a complete pound

$3.60= 0.75 pound

X= 1 pound

$X*0.75 pound= $3.60*1 pound

$x= ($3.60*1 pound)/0.75 pound

$x=$3.60/0.75

$x= $4.80

So the unit price of the trail - mix is $4.80 per pound

Answer:

b. 8.91,8.9,8.19,8.1,8.098

c. 20.005,20,19.06,2.05,1.905

Answer:

b.  8.91,  8.9, 8.19,  8.1, 8.098.

c. 20.005, 20, 19.06, 2.05, 1.905.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

The value of x in the triangle is given by trigonometric relations and the value is x = 8.86 units

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ABC

Now , the height of the triangle is BC = 5.5 units

Let the angle be θ = 50°

Now ,

From the trigonometric relations ,

cos θ = adjacent / hypotenuse

Substituting the values in the equation , we get

cos θ = 5.5 / x

Multiply by x on both sides of the equation , we get

x ( cos θ ) = 5.5

Divide by cos θ on both sides of the equation , we get

x = 5.5 / cos θ

when θ = 50°

x = 5.5 / cos 50°

x = 5.5 / 0.642787

x = 8.556 units

Therefore , the value of x = 8.56 units

Hence , the value of x of triangle is x = 8.56 units

To learn more about trigonometric relations click :

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The complete question is missing, so i have attached it

Answer:

A) Reject the null hypothesis

B) Reject the null hypothesis

C) Fail to reject the null hypothesis

D) Reject the null hypothesis

Step-by-step explanation:

A) We are given;

Ha: μ > μ_o (This is thus, a one-tail problem)

n = 11

T = 1.91

Using online p-value from t-score calculator as attached with a DF = n - 1 = 11 - 1 = 10, and t-value = 1.91, and significance level of 0.05, and 1 tail, we have;

The p-value is 0.042602

P-value is less than significance level, thus, we will reject the null hypothesis

B) We are given;

Ha: μ < μ_o (This is thus, a one-tail problem)

n = 17

T = -3.45

Using online p-value from t-score calculator as attached with a DF = n - 1 = 17 - 1 = 16, and t-value = 1.91, and significance level of 0.05, and 1 tail, we have;

The p-value is  0.001647

P-value is less than significance level, thus, we will reject the null hypothesis

C)We are given;

Ha: μ ≠ μ_o (This is thus, a two-tail problem)

n = 7

T = 0.83

Using online p-value from t-score calculator as attached with a DF = n - 1 = 7 - 1 = 6, and t-value = 0.83, and significance level of 0.05, and 2 tail, we have;

The p-value is 0.438308.

P-value is higher than the significance level, thus, we will fail to reject the null hypothesis.

D) We are given;

Ha: μ > μ_o (This is thus, a one-tail problem)

n = 28

T = 2.13

Using online p-value from t-score calculator as attached with a DF = n - 1 = 28 - 1 = 27, and t-value = 2.13, and significance level of 0.05, and 1 tail, we have;

The p-value is 0.021218

P-value is lower than the significance level, thus, we will reject the null hypothesis

P-value is lower than the significance level, thus, we will reject the null hypothesis.

Answer:

(r. q) (7) = [tex] \pm 220[/tex]

(q.r) (7) = [tex] \pm 220[/tex]

Step-by-step explanation:

[tex]q(x) = {x}^{2} + 6 \\ q(7) = {7}^{2} + 6 = 49 + 6 = 55\\ r(x) = \sqrt{x + 9} \\ r(7) = \sqrt{7 + 9} = \sqrt{16} = \pm 4 \\ \\ (r.q)(7) = r(7).q(7) = \pm 4 \times 55 = \pm220 \\ \\ (q.r)(7) = q(7).r(7) = 55 \times \pm 4 = \pm220 [/tex]

Answer:

hello your question has a missing table attached below is the missing table

Answer : 0.55%

Step-by-step explanation:

The complete table related to the answer given above is attached below

using a 0.10 level of significance the percentage of the variance in the Y-values that shows a linear relationship with the X-values = 0.55%

The values for X^2 , y^2  and x*y is determined an entered into a table ( attached below as well )

Hey there! I'm happy to help!

Let's look at all of the perfect squares (numbers with integer square roots) so that we can see where the square root of 12 lies.

√1=1

√4=2

√9=3

√16=4

√25=5

√36=6

√49=7

√64=8

√81=9

√100=100

We see that √12 would be in between √9 and √16 (3 and 4), so the square root of 12 is in between 3 and 4.

I hope that this helps! Have a wonderful day! :D

The square root of 12 lies between the whole numbers 3 and 4.

The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way.

Let's look at all of the perfect squares (numbers with integer square roots) so that we can see where the square root of 12 lies.

√1=1

√4=2

√9=3

√16=4

√25=5

√36=6

√49=7

√64=8

√81=9

√100=100

We see that √12 would be in between √9 and √16 (3 and 4), so the square root of 12 is in between 3 and 4.

Therefore, the square root of 12 lies between the whole numbers 3 and 4.

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Answer:

The answer to your question is 6.4 feet

Hello, first of all we can notice that

[tex]5^2-3*5-10=25-15-10=0[/tex]

and

[tex]2*5-10=0[/tex]

and 0 divided by 0 is undetermined.

So, we need to factorise and simplify first.

[tex]x^2-3x-10=(x-5)(x+2)\\\\\text{Because we already known that 5 is a zero...}\\\\\text{... and the sum of the zeroes is 3 = 5 - 2 and the product is -10 = 5 * (-2).}[/tex]

For x different from 5, we can write

[tex]\dfrac{x^2-3x-10}{2x-10}=\dfrac{(x-5)(x+2)}{2(x-5)}=\dfrac{x+2}{2}[/tex]

So, the limit when x tends to 5 is

[tex]\dfrac{5+2}{2}=\boxed{\dfrac{7}{2}}[/tex]

Thank you

Answer:

(6,5)

Step-by-step explanation:

In (1,2), 1 is is x so any number added to it goes to the right or left.  2 is y so any number added to it goes up or down.  It says translate right 5 units so that will be for x, a.k.a 1.  

1+5= 6 (new x)

Same with y, a.k.a 2.  It says up 3 units, so it must mean add on to y.

2+3= 5 (new y)

We now take our new values and put them back in the parentheses:

(6,5)

Answer:

i) [tex]\frac{17}{12}[/tex], ii) Approximately 1.42, iii) The answer to this is given by the reduced fraction, as decimal form has an infninite periodic component.

Step-by-step explanation:

(i) A ratio written as a reduced fraction:

Given ratio is now simplified to its reduce form:

1) [tex]\frac{153}{108}[/tex] Given

2) [tex]\frac{51}{36}[/tex] Modulative property/Existence of multiplicative inverse/Definition of division/[tex]\frac{\frac{x}{y}}{\frac{w}{z}} = \frac{x\cdot z}{y\cdot w}[/tex]

3) [tex]\frac{17}{12}[/tex] Modulative property/Existence of multiplicative inverse/Definition of division/[tex]\frac{\frac{x}{y}}{\frac{w}{z}} = \frac{x\cdot z}{y\cdot w}[/tex]/Result

(ii) A ratio written as a decimal rounded to hundredths:

[tex]\frac{17}{12} \approx 1.42[/tex]

(iii) What is the answer to this?

The answer to this is given by the reduced fraction, as decimal form has an infninite periodic component.

Answer:

AB = PQ

Step-by-step explanation:

ABC = PQR

The angles are equal and the segments are equal

for the angles

A = P

B = Q

C = R

For the segments

AB = PQ

BC = QR

AC = PR

Answer:

Line AB is approximately equal to Line PQ

goes by 2 then turns to a negative every 3 numbers

Step-by-step explanation:

Answer:

40 students

Step-by-step explanation:

and all the frequencies

there should one student per tally mark because the tally is measuring grades

Hope that helped!!! k

Answer:

[tex]\Huge \boxed{40}[/tex]

Step-by-step explanation:

Adding all the frequencies in the frequency distribution gives the total number of students.

[tex]6+10+8+9+7=40[/tex]

The number of students in class VIII whose marks obtained in an examination are 40.

Answer:

5 x 10 - 8 = ?

Step-by-step explanation:

Brainliest please!

Answer:

5×17-8

Step-by-step explanation:

First you multiply 5 by 17 and then you subtract 8

Answer:

x=34

Step-by-step explanation:

x + (x + 11) =79

Combine like terms

2x+11 = 79

Subtract 11 from each side

2x+11-11 = 79-11

2x = 68

Divide by 2

2x/2 = 68/2

x = 34

Answer:

[tex]\Huge \boxed{x=34}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex]x+x+11=79[/tex]

Combining like terms.

[tex]2x+11=79[/tex]

Subtracting 11 from both sides.

[tex]2x=68[/tex]

Dividing both sides by 2.

[tex]x=34[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

$7.00

Step-by-step explanation:

Since each of them are 35 cents per ounce

20 x 0.35 = 7

Answer:

[tex][3,4][/tex] : [tex]r = 1[/tex], [tex][4,5][/tex] : [tex]r = 0.59[/tex], [tex][5,6][/tex] : [tex]r = 0.42[/tex]

Step-by-step explanation:

Given a function [tex]f(x)[/tex] that is continuous on [tex][a,b][/tex], the average rate of change is:

[tex]r = \frac{f(b)-f(a)}{b-a}[/tex]

[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds, dimensionless.

[tex]f(a)[/tex], [tex]f(b)[/tex] - Images of the function evaluated at lower and upper bounds, dimensionless.

Let be [tex]f(x) = \log_{2}(3\cdot x - 6)[/tex], then:

[tex][3,4][/tex]

[tex]a = 3[/tex] and [tex]b = 4[/tex]

[tex]f(3) = \log_{2}[3\cdot (3) - 6][/tex]

[tex]f(3) \approx 1.585[/tex]

[tex]f(4) = \log_{2}[3\cdot (4) - 6][/tex]

[tex]f(4) \approx 2.585[/tex]

[tex]r = \frac{2.585-1.585}{4-3}[/tex]

[tex]r = 1[/tex]

[tex][4,5][/tex]

[tex]a = 4[/tex] and [tex]b = 5[/tex]

[tex]f(4) = \log_{2}[3\cdot (4) - 6][/tex]

[tex]f(4) \approx 2.585[/tex]

[tex]f(5) = \log_{2}[3\cdot (5) - 6][/tex]

[tex]f(5) \approx 3.170[/tex]

[tex]r = \frac{3.170-2.585}{5-4}[/tex]

[tex]r = 0.59[/tex]

[tex][5,6][/tex]

[tex]a = 5[/tex] and [tex]b = 6[/tex]

[tex]f(5) = \log_{2}[3\cdot (5) - 6][/tex]

[tex]f(5) \approx 3.170[/tex]

[tex]f(6) = \log_{2}[3\cdot (6) - 6][/tex]

[tex]f(6) \approx 3.585[/tex]

[tex]r = \frac{3.585-3.170}{6-5}[/tex]

[tex]r = 0.42[/tex]

Answer:

Please mark me as brainliest :)

Step-by-step explanation: