Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Answer:

T=10

Step-by-step explanation:

Answer:

t=10

Step-by-step explanation:

you multiply each side by 2.5 so 4*2.5= 10

Answer:

Step-by-step explanation:

If a scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour and the function y = 35 ∙ 3x models the number of bacteria after x hours, in order to estimate when there will be about 550 bacteria in the culture we will substitute y = 550 into the modeled equation and calculate the value of x as shown;

If y = 35*3x

when y = 550

550 = 35*3x

Dividing both sides by 35;

550/35 = 35*3x/35

3x = 550/35

x = 550/3*35

x = 550/105

x = 5.24

This means that there will be 550 bacteria in the culture after approximately 5 hours

Answer:

30 books

Step-by-step explanation:

1. Find what 2/3 of Brett's books is.

2/3 of 72 or 0.667 x 72 = 48

2. Find what 2/3 of Charlie's books is.

2/3 of 27 or 0.667 x 27 = 18

3. Find the difference between 2/3 of Brett's books (48) and 2/3 of Charlie's books (18).

48 - 18 = 30

Adam has 30 books.

Answer:

[tex] s = 14.1 [/tex]

Step-by-step explanation:

Find s using the Law of Cosines:

m < S = 31°

SR = q = 21

SQ = r = 9

QR = s = ?

Thus,

[tex] s^2 = r^2 + q^2 - 2(r)(q)*cos(S) [/tex]

[tex] s^2 = 9^2 + 21^2 - 2(9)(21)cos(31) [/tex]

[tex] s^2 = 81 + 441 - 378*0.8572 [/tex]

[tex] s^2 = 522 - 324.0216 [/tex]

[tex] s^2 = 197.9784 [/tex]

[tex] s = \sqrt{197.9784} [/tex]

[tex] s = 14.07 [/tex]

[tex] s = 14.1 [/tex] (to the nearest tenth)

Answer:

The answer is option 2.

Step-by-step explanation:

First, you have to find the length of CD using Tangent Rule, tanθ = opposite/adjacent:

[tex] \tan(θ) = \frac{oppo.}{adj.} [/tex]

[tex]let \: θ = 48[/tex]

[tex]let \: oppo. = cd[/tex]

[tex]let \: adj. = ad = 110[/tex]

[tex] \tan(48) = \frac{cd}{110} [/tex]

[tex]cd = 110 \tan(48)[/tex]

[tex]cd = 122.17 \: feet[/tex]

Next, you have to find the length of BC using Sine Rule:

[tex] \sin(θ) = \frac{oppo.}{hypo.} [/tex]

[tex]let \: θ = 65[/tex]

[tex]let \: oppo. = cd = 122.17[/tex]

[tex]let \: hypo. = bc[/tex]

[tex] \sin(65) = \frac{122.17}{bc} [/tex]

[tex]bc = \frac{122.17}{ \sin(65) } [/tex]

[tex]bc = 134.8 \: feet \: (near.tenth)[/tex]

Answer:

[tex]\boxed{134.8 \: \mathrm{ft}}[/tex]

Step-by-step explanation:

Let’s take triangle ACD.

Find length CD.

tan θ = [tex]\frac{opposite}{adjacent}[/tex]

tan (48) = [tex]\frac{CD}{110}[/tex]

110 tan (48) = CD

CD ≈ 122.167

Let’s take triangle BCD.

Find length BC.

sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

sin (65) = [tex]\frac{122.167}{BC}[/tex]

BC = [tex]\frac{122.167}{sin(65)}[/tex]

BC ≈ 134.796

Answer:

38.5°

Step-by-step explanation:

Given that the height of the building is 8 yard and the distance between Jonathan and the building is 10 yards.

The sun is at the top of the building, let the distance between Jonathan laying on the ground and the top of the building be x. Using Pythagoras:

x² = 10² + 8²

x² = 100 + 64

x² = 164

x = √164 = 12.86 yards

For a triangle with sides a, b, c and their respective opposite angles A, B, and C. The sine rule is given as:

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Let the angle that the sunlight hit the ground be y°. The andle between the building and the ground is 90°. Therefore using sine rule:

[tex]\frac{8}{sin(y)}=\frac{12.86}{sin(90)}\\\\sin(y)=\frac{8*sin(90)}{12.86}\\\\sin(y)=0.622\\\\y=sin^{-1}0.622\\\\y = 38.5^0[/tex]

Answer:

6 ft and 8 ft

Step-by-step explanation:

let x be the length of one leg then (x + 2) is the other leg.

Using Pythagoras' identity in the right triangle, that is

x² + (x + 2)² = 10² ← expand left side and simplify

x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide all terms by 2 )

x² + 2x - 48 = 0 ← in standard form

(x + 8)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

But x > 0 ⇒ x = 6

Thus the 2 sides are 6 ft and x + 2 = 6 + 2 = 8 ft

Answer:

[tex]\boxed{D = 15.8\ units}[/tex]

Step-by-step explanation:

The coordinates are (0,9) and (-8,-4)

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

D = [tex]\sqrt{(-8-0)^2+(-4-9)^2}[/tex]

D = [tex]\sqrt{(-8)^2+(-13)^2}[/tex]

D = [tex]\sqrt{81+169}[/tex]

D = [tex]\sqrt{250}[/tex]

D = 15.8 units

Answer:

15.3

Step-by-step explanation:

The coordinates are (0,9) and (-8,-4)

Distance of two points formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Plug in the values.

[tex]D=\sqrt{(-8-0)^2+(-4-9)^2}[/tex]

[tex]D=\sqrt{(-8)^2+(-13)^2}[/tex]

[tex]D=\sqrt{64+169}[/tex]

[tex]D=\sqrt{250}[/tex]

[tex]D= 15.264338...[/tex]

[tex]D \approx 15.3[/tex]

Answer:

The correct option is;

Q and v

Step-by-step explanation:

The line of best fit can be found by the dividing area method through the  following steps;

1) The dots in the plot are divided into equal number of dots on both sides of a dotted line through S

2) By eye judgement, mark the center of the data dots on each side of the dotted line for example points Q and V

3) Draw a line through the graph passing through point Q and V to get the best fir line.

Answer:

Q V

Step-by-step explanation:

If wrong please tell me so I can fix my answer for you guys.

:)))

Answer:

108

Step-by-step explanation:

To find x, you need the geometric mean. First, find the second part of 225 by doing 225 - 144 = 81. Now, to find geometric mean, do 81 x 144 = 11,664; [tex]\sqrt{11,664} = 108[/tex].

The missing length in the right triangle as given in the task content is; 108.

It follows from the complete question that the triangle given is a right triangle and the missing length can be calculated as;

First, find the second part of 225 by

225 - 144 = 81.

Now, to find geometric mean,

81 × 144 = x²

11,664 = x²

x = 108

Thus, The missing length in the right triangle as given in the task content is; 108.

Read more on missing length;

https://brainly.com/question/28040679

#SPJ2

[tex] {3x}^{2} - 4x - 12 = 0[/tex]

[tex]a = 3[/tex]

[tex]b = - 4[/tex]

[tex]c = - 12[/tex]

Formula:

[tex] \boxed{x = \dfrac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }[/tex]

Replacing:

[tex]x = \dfrac{ -( - 4) \pm \sqrt{ { (- 4)}^{2} - 4(3)( - 12)} }{2(3)} [/tex]

Option: C).

Answer:

see explanation

Step-by-step explanation:

1) 6c + 15(1) = 75

6c = 60

c = 10 packs of cupcakes

2) 6c + 15(7) = 75

6c + 105 = 75

6c = -30

c = -5, since he bought more brownies than needed, he does not need to buy any cupcakes.

Answer:

6c+15b=75

1)If the treasurer buys 1 package of brownie bites

6(1)+15b=75

15b=75-6

b=69/15=4.6 ( means the treasure needs to buy 5 packages).

2): If the treasurer buys 7 packages of brownie bites,

6c+15(7)=75

6c+105=75

c=-30/6=-5( you can not buy negative amount)

the treasure does not need to buy, because brownies are enough and more.

Answer:

The answer is option B.

Explanation:

A rule that uniquely associates elements of one set A with the elements of another set B and each element in set A maps to only one element in set B.

Each element from X is related to only one element in Y. But it is okay for two different elements in X to be related to the same element in Y. So its  still a function. Let suppose

{ (1,a) , (2, b) , (2, c) , (3, d) }

This relation is not a function from X to Y because the element 2 in X is related to two different elements, b and c.

Answer:

$24

Step-by-step explanation:

Inversely proportional means that the two variables (price and weight in this case) will always have the same product. Therefore, we can write the following equation:

25 * x = 20 * 30 (where x is the price of a 25 oz. racquet)

25x = 600

x = $24

Answer:

x = -7

Step-by-step explanation:

5x+8=3x-6

Subtract 3x from each side

5x-3x+8=3x-3x-6

2x+8 = -6

Subtract 8 from each side

2x+8-8 = -6-8

2x = -14

Divide by 2

2x/2 = -14/2

x = -7

Answer: x= -7

Step-by-step explanation:

[tex]5x+8=3x-6[/tex]

[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]

[tex]5x+8-8=3x-6-8[/tex]

[tex]5x=3x-14[/tex]

[tex]\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}[/tex]

[tex]5x-3x=3x-14-3x[/tex]

[tex]2x=-14[/tex]

[tex]\mathrm{Divide\:2\:\:on\:\:both\:sides\:}[/tex]

[tex]-14/2=-7[/tex]

[tex]x=-7[/tex]

Answer:

For this case we know that [tex]\frac{2\pi}{3}= 120 degrees[/tex]. For this case we want to find:

[tex] arctan(tan(\frac{2\pi}{3}))[/tex]

Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:

[tex]  arctan(tan(\frac{2\pi}{3})) = I(\frac{2\pi}{3}) = \frac{2\pi}{3}[/tex]

Step-by-step explanation:

For this case we know that [tex]\frac{2\pi}{3}= 120 degrees[/tex]. For this case we want to find:

[tex] arctan(tan(\frac{2\pi}{3}))[/tex]

Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:

[tex]  arctan(tan(\frac{2\pi}{3})) = I(\frac{2\pi}{3}) = \frac{2\pi}{3}[/tex]

Answer:

B.

Step-by-step explanation:

Well we know that

[tex]224=2^{5} *7[/tex]

so we can get the 2 outside of the radical

[tex]x^{11} =(x^{5} )^{2} *x[/tex]

and we can get the x^2 outside too.

[tex]y^8=y^5*y^3[/tex]

and we also can get y outside.

so we have:

[tex]2x^{2}y\sqrt[5]{7xy^3}[/tex]

Answer: 26 games in total.

Step-by-step explanation:

If in each game we have one winner and one loser, then after each game we have one less player.

first, out of 37 players, we can write it as 36 players  + 1 player that does not play in the first round

the 36 players play games. Because in each game we need 2 players, we have a total of 36/2 = 18 games

in those 18 games, we eliminate 18 players, so now we have 37 - 18 = 19 players.

Now, we can write 19 = 18 players + 1 player that does not play this round.

From the 18 players, we have 18/2 = 9 games.

And from those 9 games, we lose 9 players, so now we have:

19 - 9 = 10 players.

Now from those 10 players, we have 10/2 = 5 games, so after those 5 games we have 10 - 5 = 5 players.

Now we can write 5 = 4 players + 1 player that does not play this round.

from the 4 players we have 4/2 = 2 games, after those 2 games we end with 5 - 2 = 3 players.

And from those last 3 players, we have two games, where in each game one player is eliminated until we have only one winner.

Then the total number of games is:

18 + 9 + 5 + 2 + 2 = 26 games

Answer:

The shortest altitude = 8 cm

Step-by-step explanation:

Where we have the sides given by

15 cm, 17 cm, 8 cm

From cosine rule, we have;

a² = b² + c² - 2×b×c×cos(A)

We have

For the side 15 cm,

15² = 17² + 8² - 2×17×8 cos A

-388 = -612×cos×A

A = 61.93°

17² = 15² + 8² - 2×15×8 ×cos B

0 = -240·cos B

B = 90°

Therefore, 17 is the hypotenuse side and 15 and 8 are the legs, either of which can be the height which gives the shortest altitude as 8 cm

Answer:

work is shown and pictured

Answer:

C

Step-by-step explanation:

Brainliest?

Answer: y = 2x+1

Step-by-step explanation:

It is the only line with (1,3) as a solution.  A slower algebraic way to solve this would be to plug in 1 for x and 3 for y, then, out of the equations in which it works, plug in -2 for x and -3 for y.  The equation that remains true for both points is the answer.

Hope it helps <3

Answer:

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

Step-by-step explanation:

The line passes through (1, 3).

The solution of the line is the points it crosses.

x = 1

y = 3

Plug x as 1 and y as 3 in the equation.

y = -2x + 1

3 = -2(1) + 1

3 = -2 + 1

3 = -1 False

Plug x as 1 and y as 3 in the equation.

y = 2x + 1

3 = 2(1) + 1

3 = 2 + 1

3 = 3 True

Plug x as 1 and y as 3 in the equation.

y = x - 1

3 = 1 - 1

3 = 0 False

Plug x as 1 and y as 3 in the equation.

y = -x + 1

3 = -(1) + 1

3 = -1 + 1

3 = 0 False

Answer:

B. 1296 in.^2

Step-by-step explanation:

The rectangles are similar, and sides ST and YZ are corresponding sides.

The linear scale factor is k = YZ/ST = 24/8 = 3

The area scale factor is k^2 = 3^2 = 9

A = 144 sq in. * k^2 = 144 sq in. * 9 = 1296 sq in.

Answer: B. 1296 in.^2

Answer:

4)1,296in^2

5)510.4ft

Step-by-step explanation:

4)

24/8=3 This is the dilation

144/8=18 This is the side length for QRST

18*3=54 The side length for WXYZ

24*54=1296 The area of WXYZ

5)

319*8/5 Your fence with a scale factor of 8/5

319*1.6 Changing 8/5 into fraction form

319*1.6=510.4 The length of the friend's fence.

Hope this helps. I could not see the end of the last question so I am sorry if it is not written properly.

Have a good day!

Answer: (4,90)

Step-by-step explanation:

In a coordinate pair, the first number represents the x-axis and the second represents the y-axis.

Hope it helps <3

Answer:

C (4,90)

Step-by-step explanation:

In the graph, the point P is on 4 along the x-axis,

and 90 on the y-axis,

therefore making it's coordinates (4, 90).

Hope this helped! :)

Answer: 40/41

Step-by-step explanation:

The cosine can be represented as adjacent/hypotenuse.  Thus, the cosine of C is 40/41

Answer:

Solution,

BC = 40

AC = 41

Now,

[tex]cos \: theta \: = \frac{adjacent}{hypotenuse} [/tex]

[tex]cos \: c \: = \frac{bc}{ac} [/tex]

Plugging the values

[tex]cos \: c \: = \frac{40}{41} [/tex]

Hope this helps..

Good luck on your assignment..

Answer:

m<R=48.2 to the nearest tenth

Step-by-step explanation:

1. sin(m<T)=2/3

m<T=arcsin(2/3)=41.81 degrees

m<R=180-90-m<T=180-90-41.81=48.19 degrees

Answer:

4%

Step-by-step explanation:

We can write the following equation:

20 * (x / 100) + 60 * 0.12 = 80 * 0.10 (Note that since we're writing the percentages as decimals, x% becomes x / 100 as a decimal.)

x / 5 + 7.2 = 8

x / 5 = 0.8

x = 4%

Answer:

Its B. on edge

Step-by-step explanation:

got it right on my test

Answer:

its 147

Step-by-step explanation:

yes

Answer:

39 students

Step-by-step explanation:

let x represent the number of students taking both current event and foreign language

there are : 70 eight grader taking current event and 54 taking foreign

70+54-x=93

-x=93-124

x= 31 students taking both

number of eighth graders take only a current events class and not a foreign language class: 70-31=39 students

Answer:

14

Step-by-step explanation:

7x2=14

Answer:

14,7

Step-by-step explanation: if it is being divided by 2 it is 14 and 7