In RSM camp, there are four counselors for every fifty seven students and three teachers for every five counselors. Chapter Reference b Ms. Rifkin asked all 16 teachers present at the camp to attend a teachers meeting. Find the number of students attending the camp that summer

Answer:

3737

Step-by-step explanation:

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[tex]\bf \stackrel{dividend}{\cfrac{48}{100}}\div \stackrel{divisor}{\cfrac{8}{10}}\implies \cfrac{48}{100}\cdot \cfrac{10}{8}\implies \cfrac{10}{100}\cdot \cfrac{48}{8}\implies \cfrac{1}{10}\cdot \cfrac{6}{1}\implies \cfrac{6}{10}\implies \cfrac{3}{5}[/tex]

Answer:

4[tex]\frac{7}{12}[/tex] cups of Salsa.

Step-by-step explanation:

Flora is making Salsa for a party.

Every 1 cup of chopped tomatoes makes 2[tex]\frac{3}{4}[/tex] = [tex]\frac{11}{4}[/tex] cups of Salsa

She uses 1[tex]\frac{2}{3}[/tex] = [tex]\frac{5}{3}[/tex] cups of tomatoes

1[tex]\frac{2}{3}[/tex] cups of tomatoes makes:

[tex]\frac{5}{3}[/tex] ×  [tex]\frac{11}{4}[/tex] ÷ 1 = [tex]\frac{55}{12}[/tex] = 4[tex]\frac{7}{12}[/tex] cups of Salsa.

Answer:

The answer to this is 11.666.....

Step-by-step explanation:

To find mean we add up all value and in this case we add all of which resulting into 105 and to find out average we must divide by the amount of terms (this case numbers)

105/9 gives us an answer of 11.666...

Hope this helps and enlightens your day

To find the mean, you add up all of the numbers, then divide the sum by the amount of numbers you have.

You have 9 numbers:

22, 7, 22, 1, 7, 18, 16, 6, 6

Now you need to add them together

22 + 7 + 22 + 1 + 7 + 18 + 16 + 6 + 6 = 105

Now you divide:

[tex]mean=\frac{105}{9}=\frac{35}{3}[/tex] or 11.6666666666.......

Answer:

[tex](2x)^2=28[/tex]

Step-by-step explanation:

The equation for the area of a square is [tex](x)^2=A[/tex]

In this case, the value within the parenthesis are the lengths of each side.

As you are doubling the length of the side and know the area, the equation can be written as follows

[tex](2x)^2=28[/tex]

Answer:

1). This is a right angle triangle = TRUE

2). The hypotenuse of the triangle has a length of 21 = FALSE ("C" is the hypotenuse which makes 21 and 20 the leg of the triangle)

3). One of the legs has a length of 20 = TRUE

4). The length of "c" can be found by 202 + c2 = 212 = FALSE (To calculate the hypotenuse of the triangle you should use the formula a² + b² = c² )

"A" and "C" are the correct answers <3

Answer:

(k + 1)/-21 = 1

k + 1          = 1 . (-21)

k + 1          = - 21

k               = -21 - 1

k               = -22

*this might not be enough so feel free to ask any question

Answer:

6) LA = 90 units² and SA = 202 units²

7) LA = 377 units² and SA = 477.5 units²

8) LA = 208 units² and SA = 232 units²

9) LA = 455 units² and SA = 591 units²

Step-by-step explanation:

* Lets revise the rules of lateral area and surface area

- Lateral area of the solid = perimeter of its base × its height

- Surface area = lateral area + 2 × area of its base

* Now lets solve the problems

6) The solid is a rectangular prism

- Its base is a rectangle with dimensions 8 units and 7 units

- Its height is 3 units

∵ Perimeter of the rectangle = 2(L + W)

∴ Perimeter of the base = 2(8 + 7) = 2(15) = 30 units

∴ LA = 30 × 3 = 90 units²

∵ Area of the rectangle = L × W

∴ Area of the base = 8 × 7 = 56 units²

∴ SA = 90 + 2 × 56 = 90 + 112 = 202 units²

7) The solid is a cylinder

- Its base is a circle with diameter 8 units

∴ Its radius = 8 ÷ 2 = 4 units

- Its height is 15 units

∵ The perimeter of the circle is 2πr

∴ The perimeter of the base = 2π(4) = 8π

∴ LA = 8π(15) = 120π = 376.99 ≅ 377 units²

∵ The area of the circle = πr²

∴ The area of the base = π(4)² = 16π

∴ SA = 120π + 2 × 16π = 120π + 32π = 152π = 477.5 units²

6) The solid is a triangular prism

- Its base is a triangle with sides 5 , 5 , 6 units and height 4 units

- Its height is 13 units

∵ Perimeter of the triangle is the sum of the 3 sides

∴ Perimeter of the base = 5 + 5 + 6 = 16 units

∴ LA = 16 × 13 = 208 units²

∵ Area of the triangle = 1/2 × base × height

∴ Area of the base = 1/2 × 6 × 4 = 12 units²

∴ SA = 208 + 2 × 12 = 208 + 24 = 232 units²

9) The solid is a prism

- Its base is an isosceles trapezium with parallel bases 7 units and 10

 units, 2 non-parallel bases 9 units and height 8 units

- Its height is 13 units

∵ Perimeter of the trapezium is the sum of its sides

∴ Perimeter of the base = 7 + 10 + 9 + 9 = 35 units

∴ LA = 35 × 13 = 455 units²

∵ Area of the trapezium = 1/2(b1 + b2) × h

∴ Area of the base = 1/2(7 + 10) × 8 = 68 units²

∴ SA = 455 + 2 × 68 = 455 + 136 = 591 units²

Answer:

Step-by-step explanation:

[tex]x=4\\\\-25x>100\qquad\text{change the signs}\\25x<-100\qquad\text{divide both sides by 25}\\x<-4\qquad\bold{NOT}\to4<-4\qquad\bold{FALSE}\\\\-25x\geq100\qquad\text{change the signs}\\25x\leq-100\qquad\text{divide both sides by 25}\\x\leq-4\qquad\bold{NOT}\to4\leq-4\qquad\bold{FALSE}\\\\25x<100\qquad\text{divide both sides by 25}\\x<4\qquad\bold{NOT}\to4<4\qquad\bold{FALSE}\\\\25x\leq100\qquad\text{divide both sides by 25}\\x\leq4\qquad\bold{YES}\to4\leq4\qquad\bold{TRUE}[/tex]

Put the value of x = 4 to each inequality:

-25x > 100 → -25(4) > 100 → -100 > 100 FALSE

-25x ≥ 100 → -25(4) ≥ 100 → -100  ≥ 100 FALSE

25x < 100 → 25(4) < 100 → 100 < 100 FALSE

25x ≤ 100 → 25(4) ≤ 100 → 100 ≤ 100 TRUE

Answer:

Andy = 84 and Bart = 105

Step-by-step explanation:

Given that the ratio is 4 : 5 = 4x : 5x

Andy loses 9 thus 4x - 9

ratio 4x - 9 : 5x = 5 : 7, that is

[tex]\frac{4x-9}{5x}[/tex] = [tex]\frac{5}{7}[/tex] ( cross- multiply )

25x = 7(4x - 9) ← distribute

25x = 28x - 63 ( subtract 28x from both sides )

- 3x = - 63 ( divide both sides by 3 )

x = 21

Hence

Andy = 4x = 4 × 21 = 84 marbles

Bart = 5x = 5 × 21 = 105 marbles

Answer:

The correct answer option is B. 21.

Step-by-step explanation:

We are given a figure where the line KL is intersecting another line MN such that angle from K to N is equal to the angle opposing it which is the angle measuring [tex](5x)[/tex].

Measure of angle K - N = 90° + 15° = 105°

Since angle K - N = angle M - L, we can write it as:

105° = 5x

x = 105/5

x = 21

Therefore, the correct answer option is B. 21.

Answer:

The correct answer is option B

21

Step-by-step explanation:

From the figure we can see a number of line segments

To find the value of x

Let the point of intersection of line segments be 'o'

From the figure we get, <KON and <MOL are vertically opposite angles

m<KON = m<MOL

90 + 15  = 5x

5x = 105

x = 105/5 = 21

Therefore the value of x = 21

Answer:

x=7

Step-by-step explanation:

We know that When we total the angles in the same arm od trapezoid wee will obtain 180°.

Hence :

12x+3+13x+2=180

25x+5=180

5x+1=36

5x=35

x=7

Greetings From Poland :)

Answer:

the answer is D:  median

Step-by-step explanation:

Median and mean are measures of center.

Mean is best to use when the data distribution is symmetric or mostly symmetric, whereas median is best to use when the data distribution is not symmetric, or skewed.

Since the data distribution is skewed and not symmetric, the median is the best measure of center for the data.

You would do 180 - 115 and that gives you the < for 7

Answer:

1. 65 deg

2. 115 deg

3. 115 deg

Step-by-step explanation:

1.

Angles 7 and 8 are supplementary. Their measures add to 180 deg.

m<7 + m<8 = 180

m<7 + 115 = 180

m<7 = 180 - 115

m<7 = 65

2.

Since lines p and q are parallel lines cut by a transversal, corresponding angles 6 and 8 are congruent.

m<6 = m<8

m<6 = 115

3.

Angles 1 and 6 are vertical angles, so they are congruent.

m<1 = m<6

m<1 = 115

Answer:

1) The equation of the line in point slope form is equal to [tex]y-11=\frac{4}{3}(x-9)[/tex]

2) The equation of the line in slope intercept form is equal to [tex]y=\frac{4}{3}x-1[/tex]

3) The equation of the line in standard form is equal to [tex]4x-3y=-3[/tex]

Step-by-step explanation:

we have that the line passes through the points

(9,11) and (21,27)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{27-11}{21-9}[/tex]

[tex]m=\frac{16}{12}[/tex]

[tex]m=\frac{4}{3}[/tex]

step 2

Find the equation of the line into point slope form

The equation of the line is

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{4}{3}[/tex]

[tex]point (9,11)[/tex]

substitute

[tex]y-11=\frac{4}{3}(x-9)[/tex] -----> equation of the line into point slope form

step 3

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

[tex]y-11=\frac{4}{3}(x-9)[/tex]

[tex]y=\frac{4}{3}x-12+11[/tex]

[tex]y=\frac{4}{3}x-1[/tex] -----> equation of the line in slope intercept form

step 4

Find the equation of the line in standard form

[tex]Ax+By=C[/tex]

where

A is a positive integer

B and C are integers

[tex]y=\frac{4}{3}x-1[/tex]

Multiply by 3 both sides to remove the fraction

[tex]3y=4x-3[/tex]

[tex]4x-3y=-3[/tex] ----> equation of the line in standard form

420(0.882)^16 ~ 56.3 grams left

Answer: 56.3

Step-by-step explanation:

14.5...?

Hope this helps!

Answer:

50/27

Step-by-step explanation:

Answer:

[tex]\large\boxed{\dfrac{\frac{-2}{3}}{6}\div\dfrac{\frac{-3}{5}}{10}=\dfrac{50}{27}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\frac{-2}{3}}{6}\div\dfrac{\frac{-3}{5}}{10}=\left(\dfrac{-2}{3}\div6\right)\div\left(\dfrac{-3}{5}\div10\right)=\left(\dfrac{-2\!\!\!\!\diagup^1}{3}\cdot\dfrac{1}{6\!\!\!\!\diagup_3}\right)\div\left(\dfrac{-3}{5}\cdot\dfrac{1}{10}\right)\\\\=\left(-\dfrac{1}{9}\right)\div\left(-\dfrac{3}{50}\right)=\dfrac{1}{9}\cdot\dfrac{50}{3}=\dfrac{50}{27}[/tex]

ANSWER

[tex]1 \frac{11}{16} ounces[/tex]

EXPLANATION

It was given that,a bottle of la belle bœuf contains 3/8 ounces of perfume.

We want to find how many ounces of perfume would 4 1/2 bottles contain.

If 1 bottle contains 3/8 ounces;

Then 4½ bottles should contain more ounces.

If more less divides.

4½ bottles contain

[tex] \frac{4 \frac{1}{2} \times \frac{3}{8} }{1} [/tex]

[tex] = \frac{27}{16} [/tex]

=1.6875 ounces.

4 (1/2) bottles of  la belle bœuf contains 1 (11/16) ounces of perfume.

To find out how many ounces of perfume are in 4(1/2) bottles of La Belle Bœuf, we need to multiply the amount of perfume in one bottle by the number of bottles.

First, let's convert 4(1/2) bottles into an improper fraction:

Next, multiply by the amount in one bottle:

Therefore, 4(1/2) bottles of La Belle Bœuf contain 1 (11/16) ounces of perfume.

The least number 4 and 10 go into is 20. (4 goes into 20 five times and 10 goes into 20 two times)

Answer:

The area is [tex]28\ m^{2}[/tex]

Step-by-step explanation:

I assume that the figure is a square

The area of a square is equal to

[tex]A=b^{2}[/tex]

where

b is the length side of the square

In this problem we have

[tex]b=2(\sqrt{7})=2\sqrt{7}\ m[/tex]

substitute in the formula

[tex]A=(2\sqrt{7})^{2}[/tex]

[tex]A=28\ m^{2}[/tex]

Answer:

The answer is C.

The true statement about triangle ABC​ is sin A=cos C. Therefore, option C is the correct answer.

From the given triangle ABC, CA=13 units, BA=12 units and BC=5 units.

Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.

Here,

sin A= Opposite/Hypotenuse

BC/CA=5/13

cos C= Adjacent/Hypotenuse

BC/CA=5/13

So, sin A=cos C

The true statement about triangle ABC​ is sin A=cos C. Therefore, option C is the correct answer.

To learn more about the heights and distance visit:

brainly.com/question/24271007.

#SPJ2

Answer:

1: 8

Step-by-step explanation:

4 : 32

Divide both the left and right side by 4

4/4 =1

32/4 = 8

4:32  becomes  1:8

Answer:

sorry i do not know

Step-by-step explanation:

[tex]x = 0.4828282[/tex]

[tex]1000x = 482.828282[/tex]

[tex]999x = 482.346[/tex]

[tex]x = \frac{482}{999} + \frac{362}{1000} [/tex]

[tex]x = \frac{843638}{999000} [/tex]

Answer:

[tex]\dfrac{239}{495}[/tex]

Step-by-step explanation:

[tex]\text {Let x = } 0.4 \overline {82}[/tex]

[tex]1000x = 482. \overline {82}[/tex]

[tex]10x = 4. \overline {82}[/tex]

[tex]1000x - 10x = 482. \overline {82} - 4. \overline {82}[/tex]

[tex]990x = 478[/tex]

[tex]x = \dfrac{478}{990}[/tex]

[tex]x = \dfrac{239}{495}[/tex]

Answer:

2x+3y-5=0

Step-by-step explanation:

We have been given two points  (4,-1) and (-2,3). Now we need to find about

what is the equation of the line that passes through (4,-1) and (-2,3).

Slope of the line through the points  (4,-1) and (-2,3)  is given by:

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

[tex]m=\frac{3-\left(-1\right)}{-2-4}=\frac{3+1}{-6}=\frac{4}{-6}=-\frac{2}{3}[/tex]

Now plug the slope [tex]m=-\frac{2}{3}[/tex] and point (4,-1) into point slope formula

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

[tex]y--1=-\frac{2}{3}\left(x-4\right)[/tex]

[tex]y=-\frac{2}{3}x+\frac{5}{3}[/tex]

or we can rewrite that as 2x+3y-5=0

Hence final answer is 2x+3y-5=0

The answer is:

The second option

[tex]2x+3y-5=0[/tex]

To know which is the equation of the line, we need to follow the next steps:

Find the slope of the line:

We are given the points:

[tex](-2,3)\\(4,1)[/tex]

Where,

[tex]x_1=4\\y_1=-1\\x_2=-2\\y_2=3[/tex]

Also, we know that we can calculate the slope of a function using the following formula:

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

Now, using the slope formula, and substituting the given points, we have:

[tex]m=\frac{3-(-1)}{-2-4}[/tex]

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

[tex]m=-\frac{2}{3}[/tex]

Find the "b" value:

In order to find "b" we need to substitute any of the given points, we know that line pass through both of the given points, so, substituting the point (4,-1), we have:

Writing the slope form of the function,

[tex]y=mx+b[/tex]

[tex]y=-\frac{2}{3}x+b[/tex]

[tex]-1=-\frac{2}{3}*(4)+b\\\\b=-1+\frac{2}{3}*(4)=-1+\frac{8}{3}=\frac{-3+8}{3}=\frac{5}{3}[/tex]

Now that we know the slope and "b", we can write the equation of the line in slope-intercept form:

Writing the equation of the equation, we have:

[tex]y=-\frac{2}{3}x+\frac{5}{3}[/tex]

Then, by multiplying each side of the equation by 3 in order to simplify the fractions, we have:

[tex]3y=(3)*(-\frac{2}{3}x)+(3)*(\frac{5}{3})[/tex]

[tex]3y=-2x+5[/tex]

Rewriting the equation, we have:

[tex]2x+3y-5=0[/tex]

Hence, we have that the correct option is the second option, the equation of the line that passes through the given points is:

[tex]2x+3y-5=0[/tex]

Have a nice day!

Answer:

x=200

Step-by-step explanation:

x−y=80

3/5 = y/x

Multiply the second equation by x

3/5 x = y/x *x

3/5 x = y

Substitute this into the first equation for y

x-y =80

x - 3/5x = 80

2/5 x = 80

Multiply each side by 5/2 to isolate x

5/2 *2/5x = 80 *5/2

x = 200

Answer:

y = 23

Step-by-step explanation:

Since it's a rhombus, we know that the two diagonals are perpendicular.

That means that angle 1 is necessary a right angle, so it's worth 90 degrees since it's at the meeting point of the two perpendicular diagonals.

So, we have

∠1 = 4y - 2

All we have to do is to replace ∠1 by its value (90) and solve the mini-equation:

90 = 4y - 2

92 = 4y

y = 23

Answer:

4.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Just count all of the groups

Width= 8 cm

Because 192 / 2 = 96 / 12 = 8

SA= (perimeter * height) + 2 (length * width)

SA= (20*12)+2(2*8)

SA= 240+32

SA= 272 cm2

Answer:

Width : [tex]8cm[/tex]

Surface Area : [tex]272cm^2[/tex]

Step-by-step explanation:

Let's consider the formula for the volume of a rectangular prism.

[tex]V=whl[/tex]

Plug the values we know into the equation.

[tex]192=w*2*12 \\ \\ 192=24w \\ \\ w=8[/tex]

So the width is 8cm.

Now let's consider the formula for the surface area of a rectangular prism.

[tex]A=2(wl+hl+hw)[/tex]

Plug in the values we know into the equation.

[tex]A=2(16+24+96) \\ \\ A=2*136 \\ \\ A=272[/tex]

So the surface area is [tex]272cm^2[/tex].

Answer:

24x-20

Step-by-step explanation:

4(6x-5)

Distribute the 4

4*6x -4 *5

24x-20

Answer:

24x-20

Step-by-step explanation:

4*6x=24x

4*5=20

24x-20

Answer:

B

Step-by-step explanation:

The question is on inverse of functions

f(x)=2x-9 -----------to find f ⁻(x)

replace f(x) with y;

f(x)=2x-9----------------y=2x-9

replace y with x and x with y

y=2x-9------------------x=2y-9

solve for y

x=2y-9

x+9=2y

(x+9)/2 =y

replace y with g(x) or f ⁻(x)

g(x)=x+9 /2