Challenge 5 Rani, Layla and Tash take part in a basketball competition. Rani scores 4 times as many baskets as Layla. Tash scores 8 baskets less than Rani. They score 100 baskets in total.

Answer:

\(m=-1\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in your 2 points into the formula to find slope m:

\(m=\frac{4-(-2)}{-6-0}\)

\(m=\frac{4+2}{-6}\)

\(m=\frac{6}{-6}\)

\(m=-1\)

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

to know more about unitary method

https://brainly.com/question/28276953

Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer: 68y+106=36-y

Answer:

I think 5.4

Step-by-step explanation:

Take it and divide by the number of sides

The Perimeter of rectangle is 27.4 m

The area of rectangle is product of its length to tis width.

So, Area of rectangle = length  x width

Given:

Area of the flower bed = 20.4 square meters.

length = 12 m

As a rectangle, its area be

A = l x w

20.4 = 12 w

w= 20.4/ 12

w= 1.7

Now, Perimeter of rectangle

= 2( l + w)

= 2( 12+ 1.7)

= 27.4 m

Hence, the Perimeter of rectangle is 27.4 m

Learn more about area of rectangle here:

https://brainly.com/question/13021557

#SPJ2

Answer: x=-6

Step-by-step explanation:

Answer:

x=-6

Step-by-step explanation:

Put it in an equation,

7-2x=19

Solve for x

Subtract 9 on both sides

-2x=12

Divide -2 on both sides

x=-6

Answer:

\(y=-\dfrac{1}{2}x-3\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}\)

Given equation:

\(y=-\dfrac{1}{2}x+1\)

Parallel lines have the same slope.

Therefore, the slope of the line parallel to the given equation is:

\(m=-\dfrac{1}{2}\)

Substitute the found slope and given point (-4, -1) into the point-slope formula:

\(\implies y-(-1)=-\dfrac{1}{2}(x-(-4))\)

\(\implies y+1=-\dfrac{1}{2}(x+4)\)

\(\implies y+1=-\dfrac{1}{2}x-2\)

\(\implies y=-\dfrac{1}{2}x-3\)

Therefore, the equation of the line passing through (-4, -1) and parallel to the given equation is:

\(\boxed{y=-\dfrac{1}{2}x-3}\)

The area is 76- I believe

Answer:

Step-by-step explanation:

4/mx

Answer:

1500kg

Step-by-step explanation:

50*30=1500

Answer:

  61.03°

Step-by-step explanation:

You want the angle opposite the side of length 7 in the triangle with other sides of lengths 4 and 8.

The law of cosines relates the angles of a triangle to the side lengths. For triangle ABC with opposite sides a, b, c, the relation is ...

  c² = a² +b² -2ab·cos(C)

Solving for angle C, we have ...

  cos(C) = (a² +b² -c²)/(2ab)

  C = arccos((a² +b² -c²)/(2ab))

In this triangle, that means ...

  C = arccos((4² +8² -7²)/(2·4·8)) = arccos(31/64)

  C ≈ 61.03°

The angle of interest is about 61.03°.

__

Additional comment

We get the same result from a triangle solver. See the second attachment. (The angle we want is angle B in that attachment.)

<95141404393>

The surface area of cylinder M is approximately 131.95 square feet and the surface area of cylinder N is approximately 319.77 square feet.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that consists of two congruent parallel bases in the shape of circles or ellipses, and a curved surface that connects the bases. The height of a cylinder is the perpendicular distance between the bases. A cylinder is a type of prism, and it can be classified as either a right cylinder or an oblique cylinder depending on whether or not its axis is perpendicular to its bases. Right cylinders have circular bases and their axis is perpendicular to the bases, while oblique cylinders have elliptical bases and their axis is not perpendicular to the bases.

Now,

Let the radius of cylinder M be r and its height be h. Then, the radius and height of cylinder N are both 2r, since the radius is equal to the height.

Since the cylinders are similar, their dimensions are proportional, which means:

(height of N) / (height of M) = 5/3

(radius of N) / (radius of M) = (2r) / r = 2

Using the formula for the surface area of a cylinder, we can write:

Surface area of cylinder M: 2πr² + 2πrh

Surface area of cylinder N: 2π(2r)² + 2π(2r)(5/3)h

We are told that the surface area of cylinder N is 256 square feet greater than the surface area of cylinder M. So we can set up the equation:

2π(2r)² + 2π(2r)(5/3)h = 2πr² + 2πrh + 256

Simplifying and solving for h, we get:

4r² + 20rh/3 = r² + rh + 128

3r² - rh - 128 = 0

(3r + 32)(r - 4) = 0

Since the height of the cylinder cannot be negative, we take the positive solution r = 4. Then, the height of cylinder M is (3/5)(4) = 12/5, and the height of cylinder N is 2(4) = 8.

Using the formulas for surface area, we can find the surface areas of both cylinders:

Surface area of cylinder M: 2π(4)² + 2π(4)(12/5) = 131.95 square feet

Surface area of cylinder N: 2π(2(4))² + 2π(2(4))(8) = 319.77 square feet

Therefore, the surface area of cylinder M is approximately 131.95 square feet and the surface area of cylinder N is approximately 319.77 square feet.

To know more about cylinder visit the link

brainly.com/question/16134180

#SPJ1

5x = 12 + 3

5x = 15

\(x = \frac{15}{5} \\ \)

x = 3

Answer:

3

Step-by-step explanation:

5x-3=12

5x=12+3

5x=15

x=15/5

x=3

Answer:

\(m = 1.5\%\)

Step-by-step explanation:

Given

The attached table

Required

Determine his percentage commission

To do this, we need to calculate the slope (m) of the table as follows:

\(m = \frac{P_2 - P_1}{x_2 - x_1}\)

Where

\((x_1,P_1) = (7000,165)\)

\((x_2,P_2) = (7500,172.5)\)

\(m = \frac{P_2 - P_1}{x_2 - x_1}\) becomes

\(m = \frac{172.5 - 165}{7500- 7000}\)

\(m = \frac{7.5}{500}\)

\(m = 0.015\)

Convert to percentage

\(m = 0.015 * 100\%\)

\(m = 1.5\%\)

Hence, his percentage commission is 1.5%

9514 1404 393

Answer:

  1.56×10^10 cL

Step-by-step explanation:

There are 1000 liters in a cubic meter, so 10^5 centiliters in a cubic meter. The 1.56×10^5 cubic meters will then have ...

  (1.56×10^5 m^3)×(10^5 cL/m^3) = 1.56×10^10 cL

_____

That's 15,600,000,000 cL.

"Centi-" is a prefix meaning 1/100.

Suppose \(f(x) =8^{3x\) and \(g(x) =8^{4x\), function operations that are correct include the following:

A. (f + g)(x) = \(8^{3x} + 8^{4x}\)

B. (f × g)(x) = \(8^{7x}\)

C. (f - g)(x) = \(8^{3x} - 8^{4x}\)

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = \(8^{3x+ 4x}=8^{7x}\)

(f ÷ g)(x) = \(8^{3x- 4x}=8^{-x}\)

Read more on exponent here: brainly.com/question/27858496

#SPJ1

Answer: 4/3 or 2/1.5

Step-by-step explanation:

       The constant of proportionality is also known as the slope. This can be found with change in y over change x.

       Since we have a graph with distinct points, we can use rise over run. For this graph, we will count 3 units up from (0, 0) and 4 units right to (4, 3). This becomes 4/3 or 2/1.5. This is the constant of proportionality.

Set up the synthetic division using the coefficients of the numerator and the root in the denominator. Divide using the rules for synthetic division.−8a2+64a−497+4000a+8

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

To learn more about factorise here,

https://brainly.com/question/10718512

https://brainly.com/question/24734894

The central angle of Bathing = 108 degrees.

In the given pie chart,

Since we know,

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

The whole circle is 360 degrees

which represents 100%.

It is given that,

Bathing = 30%

So have need to find 30% of 360 degrees.

Therefore,

Bathing = (30/100)x360

            =  (30/10) x 36

            = 3x36

            = 108

Hence,

The central angle = 108 degrees.

To learn more about angles visit:

https://brainly.com/question/98924

#SPJ1

The complete question is:

To the nearest degree, what is the measure of the central angle for bathing?

Answer:

43°

Step-by-step explanation:

supplementary angles sum to 180° , then

second angle + 137° = 180° ( subtract 137° from both sides )

second angle = 43°

The probability that the next person will purchase exactly one costume is 319/381.

The overall count of individuals who visited includes all categories of visitors, which comprises of 28 individuals who didn't buy any costume, 319 individuals who acquired one costume, and 34 individuals who bought more than one costume, hence making a total of 381 visitors.

To determine the likelihood of an occurrence, one must divide the number of possible ways that the event could happen by the overall number of potential outcomes.

. Here, the event is a visitor purchasing exactly one costume.

So, the probability that the next visitor will purchase exactly one costume is the number of visitors who purchased exactly one costume (319) divided by the total number of visitors (381).

Therefore, the probability can be written as a fraction 319/381. This fraction cannot be simplified further.

Hence, the probability that the next person will purchase exactly one costume is 319/381.

Read more about probability here:

https://brainly.com/question/13604758

#SPJ1

Answer:

B

Step-by-step explanation:

Answer:

\((-p)-472\)

Step-by-step explanation:

\(-57-2=-59\\-p+8\left(-59\right)\\8\left(-59\right)=-472\\=(-p)-472\)

Simplify  the steps by steps

Subtract the numbers

-p+8(-57-2)

-p+8(-59)

Multiply the numbers

-p +8(-59)

-p-472

Solution

-p-472  Simplify

   100% right                                          hope this helps

Answer:

∠ G = 55°

Step-by-step explanation:

given FG and FH are congruent then Δ FGH is isosceles with base angles G and H being congruent, that is

∠ G = ∠ H

the vertex ∠ F = 70° , then

∠ G = (180 - 70)° ÷ 2 = 110° ÷ 2 = 55°

Both students were incorrect  in their value of ∠ G

The data set which contains an outlier from the given answer choices is; Choice D; {16, 42, 45, 45, 46, 48}.

An outlier in a set of data values is a data value which differs significantly from other data points and hence, tends to affect the mean of such set of data values significantly.

On this note, choice D is the set of data values which contains an outlier.

Read more on outliers;

https://brainly.com/question/2749543

#SPJ1

A. The following are sets A and B:

A = {2, 3, 5, 7, 11}

B = {1, 2, 3, 4, 6, 12}

C. Elements not in A or A' = ∅

B. The Venn diagram is attached

A universal set is a set which consists of all elements related to the given sets. It is denoted by U.

A. Set A:

A = {2, 3, 5, 7, 11}

Set B:

B = {1, 2, 3, 4, 6, 12}

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A' = {1, 4, 6, 8, 9, 10, 12}

C. Elements not in A or A' = ∅

Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.

Hence, the Venn diagram of sets A, B and U has been attached.

Read more on set theory:

https://brainly.com/question/13458417

#SPJ1

Answer:

Step-by-step explanation:

The simplified form of the function is \(f(x) = \frac{x+3}{x}\)

Given the following function as shown:

\(f(x)=\frac{x^2-9}{x^2-3x}\)

This can be factorized as:

\(f(x)=\frac{x^2-3^2}{x(x-3)}\\f(x)= \frac{(x+3)(x-3)}{x(x-3)} \\\)

Cancel out the common terms:

\(f(x) = \frac{x+3}{x}\)

Hence the simplified form of the function is \(f(x) = \frac{x+3}{x}\)\

Learn more on functions here: https://brainly.com/question/10439235

Hi Phoenix! :)

I'm much late lol.

Answer:

\(\boxed{ \cfrac{x + 3}{x}} \)

Step-by-step explanation:

Given:

\( \cfrac{x {}^{2} - 9}{x {}^{2} - 3x } \)

Solution:

[Here the best option is to factorise the expression.]

Rewrite the numerator of the expression as

\( \cfrac{x {}^{2} - 3 {}^{2} }{x {}^{2} - 3x} \)

It can be seen that the numerator is like an algebraic identity:

> a² - b² = (a+b)(a-b)

ATP, numerator : a = x² and b = 3²

Now in the denominator take x common:

(x-3) in the denominator and (x-3) in the numerator gets canceled.

Welp,Done, that's it! :D