Please see image attached. I am not able to solve, even after using the formula

Please See Image Attached. I Am Not Able To Solve, Even After Using The Formula

Answers

Answer 1

Given:

Total number of cub scouts is 20 and the number of scout is 10 more than 2 times the number of adult leaders.

Required:

We need to find the number of adult leaders.

Explanation:

Lets consider cub scouts as c and adult leaders as a so the

[tex]c=20[/tex]

and the formula for adult is

[tex]\begin{gathered} c=2a+10 \\ 20=2a+10 \end{gathered}[/tex]

simplify as:

[tex]\begin{gathered} 10=2a \\ a=5 \end{gathered}[/tex]

Final answer:

Number of adult leaders is 5


Related Questions

(I don't know if there are tutors here right now at this time but it's worth a try.) Please help me I really really don't understand this, it's going to take me a while to understand this. X(

Answers

[tex]\begin{gathered} 3(b+5)=4(2b-5) \\ 3b+15=8b-20 \\ 15+20=8b-3b \\ 5b=35 \\ b=\frac{35}{5} \\ b=7 \end{gathered}[/tex][tex]3(b+5)=4(2b-5)[/tex]

by the distributive law x(y+z)=zy+xz, we have

[tex]\begin{gathered} 3b+3(5)=4(2b)-4(5) \\ 3b+15=8b-20 \end{gathered}[/tex]

Then we use the properties of inequalities, we can switch both sides, and if we add or multiply something on both sides the equality remains

[tex]\begin{gathered} 3b+15=8b-20 \\ \end{gathered}[/tex]

we want the variables and the numbers without variables to be in different side, so, first we add 20 to both sides, note that the -20 will be cancelled

[tex]\begin{gathered} 3b+15+20\text{ = 8b-20+20} \\ 3b+15+20=8b \end{gathered}[/tex]

we want to left all the numbers with variable on the right side so we substract 3b (add -3b) to both sides. Same as before, the 3b will be cancellated (we can change the order in the sum)

[tex]\begin{gathered} -3b+3b+15+20=-3b+8b \\ 15+20=8b-3b \end{gathered}[/tex]

of course, you're welcome

I was asking if you have understood my explanation so far

tell me

it doesn't matter the order, in fact, when you get used to the method you can work with both at the same time

any other question?

yes, you could substrac 3b first

For example

[tex]\begin{gathered} 2+3x=6-x \\ 2+3x+x=6-x+x \\ 2+3x+x=6 \\ -2+2+3x+x=-2+6 \\ 3x+x=6-2 \\ 4x=4 \\ \end{gathered}[/tex]

sadly I will need to leave since my shift is over, but if you ask another question one of my partners will help you

Have a nice evening!!!!

then we add like terms and switch both sides

[tex]5b=35[/tex]

And then we multiply by 1/5 both sides

[tex]\begin{gathered} 5\frac{1}{5}b=\frac{35}{5} \\ b=\frac{35}{5} \\ b=7 \end{gathered}[/tex]

Find an angle with θ with 0∘ < θ < 360∘ that has the same :

Sine as 220∘ : θ = _______ degrees

Cosine as 220∘ : θ = _______ degrees

Answers

The complete trigonometry ratios are sin(220) = -sin(40) and cos(220) = cos(140) and the angles are 40 and 220 degrees

How to determine the measure of the angles?

Angle 1

The trigonometry ratio of the angle is given as

sin(220)

Expand the above expression

sin(220) = sin(180 + 40)

Apply the sine rule

sin(220) = sin(180)cos(40) + cos(180)sin(40)

Evaluate the ratios

sin(220) = 0 x cos(40) - sin(40)

So, we have

sin(220) = - sin(40)

So, the measure of the angle is 40 degrees

Angle 2

The trigonometry ratio of the angle is given as

cos(220)

Expand the above expression

cos(220) = cos(360 - 140)

Apply the cosine rule

cos(220) = cos(360)cos(140) + sin(140)sin(360)

Evaluate the ratios

cos(220) = 1 x cos(140) + sin(140) x 0

So, we have

cos(220) = cos(140)

So, the measure of the angle is 140 degrees

Read more about trigonometry ratios at

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Classify each Polynomial by degree and number of terms.1. X^3 + 5x 2. X^2 - 2x - 1 3. 5x^4 4. 6x^5 - 3x^2 + 7x + 9 5. -11x - 5 6. 4x^2 + 10 7. 128. 9x^3 - x^2 + 6x - 1]9. -3x^5 + 6x^4 v- 8THESE ARE THE OPTIONS Degree Name using degree 0 Constant 1 Linear 2 quadratic 3 Cubic 4 quartic 5 quintic 6 6th degreeTHESE ARE ALSO THE OTHER OPTIONSTerms NAME USING # OF TERMS1, monomial 2 , binomial3 trinomial4 or more polynomial

Answers

[tex]\begin{gathered} x^3+5x\text{ has a highest degree of 3 (from }x^3\text{) and is therefore cubic.} \\ \text{It has only two terms which makes it a binomial} \end{gathered}[/tex][tex]\begin{gathered} x^2-2x-1\text{ has a highest degree of 2 (from }x^2\text{) and is therefore quadratic} \\ \text{It has three terms which makes it trinomial} \end{gathered}[/tex][tex]\begin{gathered} 5x^4\text{ has a highest degree of 4, and is therefore quartic.} \\ \text{Since it has only one term, then this is a monomial} \end{gathered}[/tex][tex]\begin{gathered} 6x^5-3x^2+7x+9\text{ has a highest degree of 5 (from }6x^5\text{) therefore it is quintic} \\ \text{It has four terms, and is a polynomial} \end{gathered}[/tex][tex]\begin{gathered} -11x-5\text{ has a highest degree of 1 (from }-11x\text{) and is therefore linear.} \\ \text{It has two terms which makes it binomial.} \end{gathered}[/tex][tex]\begin{gathered} 4x^2+10\text{ has a highest degree of 2 (from }4x^2\text{) and is therefore quadratic.} \\ \text{It has two terms which makes it binomial.} \end{gathered}[/tex][tex]\begin{gathered} 12\text{ has no variable which makes it a constant.} \\ \text{Since it is the only term, then this is a monomial} \end{gathered}[/tex][tex]\begin{gathered} 9x^3-x^2+6x-1\text{ has a highest degree of 3 (from }9x^3\text{) which makes it cubic} \\ \text{It has 4 terms and is thus a polynomial} \end{gathered}[/tex][tex]\begin{gathered} -3x^5+6x^4v-8\text{ has a highest degree of 5 (both from }-3x^5\text{ and }6x^4v\text{)} \\ \text{This makes it a quintic} \\ \text{Since it has three terms then this is a trinomial} \end{gathered}[/tex]

need help with this problem, find the length of the darkened arc. C is the center of the circle

Answers

Notice that the central angle measures 138 degrees, We have a property of the circle that says that the measure of a central angle is equal to the arc between its sides.

Therefore, the arc measures 138 degrees

What is the answer to 6x + =5

Answers

Answer:

x = 5/6 or x = 0.83

Step-by-step explanation:

6x + =5

6x + 0 = 5

6x = 5

6x/6 = 5/6

x = 5/6 or x = 0.83

6. Diagram this statement. Then answer the questions (22) that follow. One third of the 60 questions on the test were true false. (a) How many of the questions on the test were true- false? (b) How many of the questions on the test were not true- false? (C) What percent of the questions were true-false?

Answers

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x+y=22x+7y=9can u help me solve this equation

Answers

Keeping Od, this is the solution:

x + y = 2

2x + 7y = 9

___________

Step 1: Let's isolate x in equation 1, as follows:

x + y = 2

x = 2 - y

__________________

Step 2: Let's substitute x and solve for y in equation 2, this way:

2x + 7y = 9

2 (2 - y) + 7y = 9

4 - 2y + 7y = 9

4 + 5y = 9

Subtracting 4 at both sides:

4 + 5y - 4 = 9 - 4

5y = 5

Dividing by 5 at both sides:

5y/5 = 5/5

y = 1

_______________________

Step 3: Let's substitute y and solve for x in the first equation, as follows:

x + y = 2

x + 1 = 2

Subtracting 1 at both sides:

x + 1 - 1 = 2 - 1

x = 1

_____________________

Step 4: Let's write the solution as an ordered pair, this way:

(1, 1)

what is the driving distance between the police station and Art Museum

Answers

First, locate the coordinate points (x,y) of each place, by looking at the graph:

Police station = (0,-4)

Art museum = (6,1)

Apply the distance formula:

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

Replacing:

[tex]D=\sqrt[]{(6-0)^2+(1-(-4))^2}=\sqrt[]{6^2+5^2}=\sqrt[]{36+25}=\sqrt[]{61}=7.81[/tex]

Jackie planted a tomato plant that was 4 inches tall. The plant grew by 150% of its height after 3 weeks. How tall was the plant after the 3 weeks?

Answers

[tex]10\:inches[/tex]

1) Problems like these, we can solve by writing an equation.

2)Since that tomato plant grew 150% after three weeks we can write the following

[tex]\begin{gathered} 4\cdot(1+1.5)= \\ 4(2.5)=10 \\ \end{gathered}[/tex]

Note that in the parentheses we have the factor of growth. Since it's 150% we can add to 1 and write 1 +1.5=2.5

3) Thus, the answer is:

[tex]10\:inches[/tex]

a rectangular Garden has a length of 10 m and a width of 8 meters fill in the Box to show the perimeter and the area of the garden

Answers

[tex]\text{Area}_{\text{garden}}=80m^2[/tex][tex]\text{Perimeter}_{\text{garden}}=36\text{ m}[/tex]

Explanation

Step 1

Area,To find the area of a rectangle, multiply its height by its width

then

[tex]\text{Area}_{rec\tan gle}=length\cdot width[/tex]

Let

length=10 m

width=8 m

replace,

[tex]\begin{gathered} \text{Area}_{rec\tan gle}=length\cdot width \\ \text{Area}_{rec\tan gle}=10\text{ m }\cdot\text{ 8 m} \\ \text{Area}_{rec\tan gle}=80m^2 \end{gathered}[/tex]

Step 2

find the perimeter:

Perimeter is the distance around the outside of a shape,so for the garden the perimeter is

[tex]\text{Perimeter}_{rec\tan gle}=2(length+width)[/tex]

replace,

[tex]\begin{gathered} \text{Perimeter}_{\text{garden}}=2(10m+8m) \\ \text{Perimeter}_{\text{garden}}=2(18\text{ m)} \\ \text{Perimeter}_{\text{garden}}=36\text{ m} \end{gathered}[/tex]

I hope this helps you

True or false if a set of points all lie on the same plane they are called collinear

Answers

Coplanar and collinear set of pointsMeanings

We have that a group of points can be:

Coplanar: if they lie in the same plane

Collinear: if they lie in the same line

Answer- False: they are called coplanar

evaluate B-( - 1/8) + c where b =2 and c=- 7/4

Answers

Answer: 3/8

Step-by-step explanation:

Given:

[tex]B-(-\frac{1}{8} )+c[/tex]

replace variables with their given values: b = 2 and C = 7/4

[tex]2-(-\frac{1}{8})+\frac{-7}{4}[/tex]

to make subtracting and addition easier, make each number has the same common denominator.

[tex]\frac{16}{8} -(-\frac{1}{8})+(\frac{-14}{8})[/tex]

Finally, solve equation.

***remember that subtracting a negative is the same as just adding and adding by a negative is the same as simply subtracting.

[tex]\frac{16}{8} -(-\frac{1}{8})+(\frac{-14}{8})=\frac{16}{8} +\frac{1}{8}-\frac{14}{8}[/tex]

= 3/8

Answer:

3/8

Step-by-step explanation:

2 - (-1/8) + (-7/4)

= 17/8 - 7/4

= 17/8 + -7/4

= 3/8

DEF is a right triangle. If FE= 12 and DE= 5, find DF.

Answers

Answer:

DF = 13

Explanation:

The Pythagoras theorem says that

[tex]FE^2+ED^2=DF^2[/tex]

Now in our case,

FE = 12

ED =

Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible Through (15,5) and (5,15)

Answers

Given that the required linepasses through the points (15, 5)and (5, 15).

Find the slope of the line using teo-point formula.

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{15-5}{5-15} \\ =\frac{10}{-10} \\ =-1 \end{gathered}[/tex]

Substitute the value of m into theslope-intercept form y = mx+c.

[tex]y=-x+c[/tex]

Plug in the point (5, 15)to find c, the y-intercept.

[tex]\begin{gathered} 15=-5+c \\ c=20 \end{gathered}[/tex]

Thus, y = -x + 20, which is the required equation of line.

Brian is looking to add tile to one wall in his kitchen, each tile is a rectangle that measures
14 inches by 2 inches. The wall that Brian wants to tile is a rectangle that measures
44.25inches by 51 inches. How many bie's will Brian need to cover the wall?

Answers

Using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.

What is a rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can also be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.

So, tiles needed to cover the wall:

The formula for the area of a rectangle: l × b

Calculate the area of a tile as follows:

l × b14 × 228 in²

Now, calculate the area of the wall as follows:

l × b44.25 × 512,256.75 in²

Then, tiles needed to cover the wall:

2,256.75/2880.59

Which means: 80½

Therefore, using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.

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3. Express the given integral as the limit of a Riemann sum but do not evaluate:

Answers

Expression of the integral [tex]\int\limits^3_0 {(x^{3}-6x) } \, dx[/tex] as the limit of a Riemann sum without any evaluation will be

Lim(n → ∞) ∑(n = 1 → ∞) [{(27i³/n³) - (18i/n)} * (3i/n)]

As per the question statement, we are provided with an integral [tex]\int\limits^3_0 {(x^{3}-6x) } \, dx[/tex] ,

And we are required to determine the expression of the above mentioned integral as the limit of a Riemann sum without any evaluation.

To start with, we need to know the formula [Δx = {(b - a)/n}]

And here, from our given integral [tex]\int\limits^3_0 {(x^{3}-6x) } \, dx[/tex], we get that, (a = 0) and

(b = 3). Therefore substituting the values of "a" and "b" in the formula to calculate Δx, we get,

[Δx = {(3 - 0)/n} = (3/n)]

Also, [(x[tex]_{i}[/tex]) = {a + (Δx)i} = {0 + (3/n)i) = (3i/n)],

Given, [ρ(x) = (x³ - 6x)], and thus, [ρ(x[tex]_{i}[/tex]) = ρ(3i/n)]

Or, [ρ(x[tex]_{i}[/tex]) = {(3i/n)³ - 6(3i/n)}]

Or, [ρ(x[tex]_{i}[/tex]) = {(27i³/n³) - (18i/n)}]

Then, Lim(n → ∞) ∑(n = 1 → ∞) ρ(x[tex]_{i}[/tex])Δx

= Lim(n → ∞) ∑(n = 1 → ∞) [{(27i³/n³) - (18i/n)} * (3i/n)]

Reimann Sum: In Mathematics, a Riemann sum is a certain kind of approximation method for an integral by a finite sum. Named after renowned German mathematician Bernhard Riemann, one very common application of the Reimann Sum is in approximating the area of functions or lines on a graph, and also the length of curve.

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100 POINTS AND BRAINLY FOR THE CORRECT ONLY ANSWER IF U UNDERSTAND THE QUESTION!
A line includes the points (10,6) and (2,7). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

PLEASE AND THANK U

Answers

Answer:

[tex]y-6=-\dfrac{1}{8}(x-10)[/tex]

Step-by-step explanation:

To find the equation of a line that passes through two points, first find its slope by substituting the given points into the slope formula.

Define the points:

(x₁, y₁) = (10, 6)(x₂, y₂) = (2, 7)

Substitute the points into the slope formula:

[tex]\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-6}{2-10}=\dfrac{1}{-8}=-\dfrac{1}{8}[/tex]

Therefore, the slope of the line is -¹/₈.

[tex]\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}}[/tex]

To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:

[tex]\implies y-6=-\dfrac{1}{8}(x-10)[/tex]

Create three different proportions that can be used to find BC in the figure above. At least one proportion must include AC as one of the measures.

Answers

We are given two similar triangles which are;

[tex]\begin{gathered} \Delta AEB\text{ and }\Delta ADC \\ \end{gathered}[/tex]

Note that the sides are not equal, but similar in the sense that the ratio of two sides in one triangle is equal to that of the two corresponding sides in the other triangle.

To calculate the length of side BC, we can use any of the following ratios (proportions);

[tex]\frac{AE}{ED}=\frac{AB}{BC}[/tex][tex]\frac{AB}{AC}=\frac{AE}{AD}[/tex][tex]\frac{AE}{AB}=\frac{AD}{AC}[/tex]

Using the first ratio as stated above, we shall have;

[tex]\begin{gathered} \frac{AE}{ED}=\frac{AB}{BC} \\ \frac{8}{5}=\frac{6.5}{BC} \end{gathered}[/tex]

Next we cross multiply and we have;

[tex]\begin{gathered} BC=\frac{6.5\times5}{8} \\ BC=4.0625 \end{gathered}[/tex]

ANSWER:

[tex]BC=4.0625[/tex]

Find the average rate of change of the function in the graph shown below between x=−1 and x=1.

Answers

Answer:

Step-by-step explanation:

The last description actually clarifies the given equation. The equation should be written as: f(x) = 2ˣ +1. The x should be in the exponent's place.

The average rate of change, in other words, is the slope of the curve at certain points. In equation, the slope is equal to Δy/Δx. It means that the slope is the change in the y coordinates over the change in the x coordinate. So, we know the denominator to be: 2-0 = 2. To determine the numerator, we substitute x=0 and x=2 to the original equation to obtain their respective y-coordinate pairs.

f(0)= 2⁰+1 = 2

f(2) = 2² + 1 = 5

Segment EF is rotated 90° clockwise around the origin and then translated by (-6, y + 7).
The resulting segment E" F" has coordinates E" (-4, 5), F"(-1,-2).
What are the coordinates of the segment EF?

does anyone know this??

Answers

Answer:

E = 2,2     F = 5,-9

Step-by-step explanation:

First, you have to add (6, -7) to both coordinates (that being (-4,5)(-1,-2)

This results in E = 2,-2    and F = -5,-9

Next, you need to rotate both coordinates 90 counterclockwise, resulting in: E being (2,-2) and F being (5,-9)

Hope this helped!

all i need is for question 14 to be answered please help

Answers

Given

The path of particle 1 is,

[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]

And, the path of second particle is,

[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]

To model the path of the two particles in cartesian form and to find whether, the two particles collide.

Explanation:

It is given that,

The path of the first particle is,

[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]

That implies,

[tex]x=2t-6,\text{ }y=t^2-2t[/tex]

Consider,

[tex]\begin{gathered} x=2t-6 \\ 2t=x+6 \\ t=\frac{x+6}{2} \end{gathered}[/tex]

Therefore,

[tex]\begin{gathered} y=(\frac{x+6}{2})^2-2(\frac{x+6}{2}) \\ y=\frac{x^2+12x+36}{4}-\frac{2x+12}{2} \\ y=\frac{x^2+12x+36-2(2x+12)}{4} \\ y=\frac{x^2+12x+36-4x-24}{4} \\ y=\frac{x^2+8x+12}{4}\text{ \_\_\_\_\_\_\_\_\_\_\lparen1\rparen} \end{gathered}[/tex]

Also, the path of second particle is,

[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]

That implies,

[tex]x=\sqrt{t+6},\text{ }y=-3+2t[/tex]

Consider,

[tex]\begin{gathered} y=-3+2t \\ 2t=y+3 \\ t=\frac{y+3}{2} \end{gathered}[/tex]

Therefore,

[tex]\begin{gathered} x=\sqrt{t+6} \\ \Rightarrow x^2=(t+6) \\ \Rightarrow x^2=(\frac{y+3}{2})+6 \\ \Rightarrow x^2=\frac{y+3+12}{2} \\ \Rightarrow2x^2=y+15 \\ \Rightarrow y=2x^2-15\text{ \_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]

Hence, y=(x^2+8x+12)/4, y=2x^2-15 are the paths of the two particles respectively.

The graph of the path of the two particles are,

From, this it is clear that the particle collide at the points (-2.686, -0.568) and (3.829, 14.324).

The solution to the equation4(x + 2) =3(5-x) is:

Answers

ANSWER:

The value of x is 1, that is, the solution of the equation is 1

STEP-BY-STEP EXPLANATION:

We have the following equation:

[tex]4\cdot(x+2)=3\cdot(5-x)[/tex]

Solving for x:

[tex]\begin{gathered} 4x+8=15-3x \\ 4x+3x=15-8 \\ 7x=7 \\ x=\frac{7}{7} \\ x=1 \end{gathered}[/tex]

Select the correct answer from each drop-down menu.Glven: W(-1, 1), X(3, 4), Y(6, 0), and Z(2, -3) are the vertices of quadrilateral WXYZ.Prove: WXYZis a square.

Answers

ANSWER

all four sides have a length of 5

EXPLANATION

The distance between two points (x₁, y₁) and (x₂, y₂) is,

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

Let's find the distance between each pair of points, WX, XY, YX, and WZ,

[tex]WX=\sqrt{(3-(-1))^2+(4-1)^2}=\sqrt{(3+1)^2+(4-1)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]XY=\sqrt{(6-3)^2+(0-4)^2}=\sqrt{(3)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex][tex]YZ=\sqrt{(2-6)^2+(-3-0)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]WZ=\sqrt{(2-(-1))^2+(-3-1)^2}=\sqrt{(2+1)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

Hence, using the distance formula we found that all four sides have a length of 5.

An online bookstore is having a sale. All paperback books are $6.00 with a flat shipping fee of $1.25. you purchase "b" booms and your total is "c". What is the independent variable?$6.00"c" cost"b" books$1.25

Answers

Let:

c = total

a = cost of each book

w = flat shipping fee

Therefore, the total is given by:

[tex]c=ab+w[/tex]

where:

b = number of books

[tex]c=6x+1.25[/tex]

The independent variable is:

"b" books

Can I Plss get some help I got stuck I don’t know how to find x

Answers

Using Sine of angles to evaluate for x

The formula is,

[tex]sin\theta=\frac{Opposite}{Hypotenuse}[/tex]

Given:

[tex]\begin{gathered} Opposite=x \\ Hypotenuse=19 \\ \theta=21^0 \end{gathered}[/tex]

Therefore,

[tex]\begin{gathered} sin21^0=\frac{x}{19} \\ \therefore x=19\times sin21^0 \end{gathered}[/tex]

Simplify

[tex]x=6.80899\approx6.81\text{ \lparen2 decimal places\rparen}[/tex]

Hence,

[tex]x=6.81[/tex]

The long-distance calls made by South Africans are normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes for 1500 south Africans what is the expected number of callers whose calls last less than 15 minutes?

Answers

The question provides the following parameters:

[tex]\begin{gathered} \mu=16.3 \\ \sigma=4.2 \end{gathered}[/tex]

For 15 minutes, the z-score is calculated using the formula:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

At x = 15:

[tex]z=\frac{15-16.3}{4.2}=-0.3[/tex]

The probability is calculated using the formula:

[tex]P(X<15)=Pr(z<-0.3)=Pr(z<0)-Pr(0From tables, we have:[tex]\begin{gathered} Pr(z<0)=0.5 \\ Pr(0Therefore, the probability is given to be:[tex]\begin{gathered} P(X<15)=0.5-0.1179 \\ P(X<15)=0.38 \end{gathered}[/tex]

The expected number of callers will be calculated using the formula:

[tex]\begin{gathered} E=xP(x) \\ At\text{ }x=1500 \\ E=1500\times0.38 \\ E=570 \end{gathered}[/tex]

Therefore, the expected number of callers whose calls last less than 15 minutes is 570 callers.

{x|x ≤ - 6}
Write written interval motion and graph the interval

Answers

The inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).

What exactly is interval notation?

The number line's left to right location in the solution is indicated using interval notation (i.e., which part of the number line is shaded). Endpoints that are part of the solution are denoted by parentheses, while those that are not are denoted by brackets.For instance, the expressions -3x2, [-3,2], and xR|-3x2 denote that x is between -3 and 2 and might be either endpoint.

Interval Notation x<-6. x<−6 x < - 6.

 Convert the inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).

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A study shows that 28% of the population has high blood pressure. The study also shows that 86% of those who do not have high blood pressure exercise at least 90 minutes per week, while 32% of those with high blood pressure exercise at least 90 minutes per week. Which of the following relative frequency tables could the study provide?

Answers

The study can provide relative frequency table 2 (starting from the top)

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. The word per cent means per 100. It is denoted by the symbol “%”.

The total percentage of two or more ratios in a thesame entity is 100. For example, In a population, 28% has HBP (high blood pressure)

This means that number of those that do not have HBP will be 100 - 28 = 72%

86% of those who did not have HBP exercise at least 90 minute per week i.e

86% of no HBP ,exercise >or = 90 = (86/100) × 72 = 62%( nearest whole number)

Those that do exercise <90 minute per week = 72-62= 10%

32% of those with HBP exercise at least 90 minute( >or = 90 minutes) =( 32\100) × 28= 9%( nearest whole number)

Those with HBP and exercise <90= 28- 9= 19%

Therefore Table 2 starting from the top clearly shows this data.

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41 increased by 4 is what number ?

Answers

The statement

41 increased by 4

The word increase mean adding to the given number 41

Hence,

The statement can be expressed as

[tex]41+4[/tex]

Simplifying the result gives

[tex]41+4=45[/tex]

Therefore, the answer is

[tex]45[/tex]

45
41 + 4 = (41-1+4=44+1=45)
41 + 4 = 45 (40+5=45)
(41-1=40 4 + 1 = 5 + 40 = 45)
Therefore, 41 increased by 4 (41+4) would be 45. Please correct me if I’m wrong.

A triangle has vertices P (4.1), Q (4, 5) and R (7,5) What is the area of ∆PQR? (Area= 1/12 basexheight)

Answers

First, plot the points on a graph and form the triangle:

By looking at the triangle we can see that:

Base: 2

Height: 4

Area : 1/2 x 2 x 4 = 4 units2

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