There were females and males present at the high school pep rally. Find the ratio of males to the total number of people present. Express as a simplified ratio.

Answer:

161/184 or 0.875

Step-by-step explanation:

Total number of cans = 24 cans

Total number of diet soda = 3 cans

Total number of regular soda = 21 cans

We are asked to find the probability that:that at least one contain regular soda if two cans are selected randomly

We have two ways for this happening

a) two of the cans are regular soda

b) one of the cans is regular , while one is diet

Hence,

Probability (that at least one contain regular soda) = Probability(that two of the cans are regular soda) + Probability ( one of the cans is regular , while one is diet)

Probability(that two of the cans are regular soda) = 21/24 × 20/23

= 35/46

Probability ( one of the cans is regular , while one is diet) = 21/24 × 3/23

= 21/184

Probability (that at least one contain regular soda) = 35/46 + 21/184

We find the Lowest common multiple of the denominators = 184

= 35/46 + 21/184

= (35 × 4) + (21 × 1)/184

= 140 + 21/184

= 161/184

= 0.875

Therefore, the probability that at least one can contains regular soda = 161/184 or 0.875

Answer:  ($143.69, $156.31)

Step-by-step explanation:

Confidence interval to estimate  population mean :

[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]

, where [tex]\sigma[/tex] = population standard deviation

n= sample size

[tex]\overline{x}=[/tex] Sample mean

z= critical value.

As per given,

n= 40

[tex]\sigma[/tex] = $15.50

[tex]\overline{x}=[/tex] $150

Critical value for 99% confidence level = 2.576

Then, 99% confidence interval for the population mean:

[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]

Hence, the required confidence interval : ($143.69, $156.31)

Answer:

1

Step-by-step explanation:

We can find the slope using

m= ( y2-y1)/(x2-x1)

   = ( -8 - -4)/( 4 - 8)

   =  ( -8 +4)/( 4 - 8)

   = -4 / -4

   = 1

Answer:

slope equals 1

Step-by-step explanation:

To do this you would need to do an equation that is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex] so in this case -8 would be y2 and -4 would be y1 and 4 would be x2 and 8 would b e x1 so if you plug it into the equation we would get [tex]\frac{-8-(-4)}{4-8}[/tex] and if we simplify we get [tex]\frac{-4}{-4}[/tex] which simplifies to 1 so the slope would equal 1

Answer: x = 6.32 or -0.32

Step-by-step explanation:

2x² - 6x + 10  = 0

No we divide the expression by 2 to make the coefficient of x² equals 1

We now have

x² - 3x + 5     = 0

Now we remove 5 to the other side of the equation

x² - 3x          = -5

we add to both side square of  half the coefficient of x which is 3

x² - 3x + ( ⁻³/₂)²  = -5 + (⁻³/₂)²

(x  -  ³/₂)²           = -5 + ⁹/₄

Resolve into fraction

(x  - ³/₂)²             = ⁻¹¹/4

Take the roots of the equation

 x - ³/₂               = √¹¹/₄

 x - ³/₂               = √11/₂

x                       = ³/₂ ± 3.32/₂

                         = 3+ 3.32 or 3 - 3.32

                         =  6.32 or - 0.32

Answer:

37

Step-by-step explanation:

To find the fifth term , we have to take the value of n as 5

So, F(5)= 6.5 (5) +4.5

= 32.5 + 4.5

= 37

Answer:

(f+g)(x)= 9x² + 9x

(f+g)(3) = 108

Step-by-step explanation:

f(x)=8x² +7x

g(x)= x² +2x

(f+g)(x) = f(x) + g(x) = 8x² +7x +x² +2x = 9x² + 9x

(f+g)(x)= 9x² + 9x

(f+g)(3)= 9*3² + 9*3 = 108

Answer:

[tex]\boxed{9}[/tex]

Step-by-step explanation:

The two angles are complementary to each other.

That means they add up to 90 degrees.

[tex]5x+15+30=90[/tex]

[tex]5x+45=90[/tex]

[tex]5x=45[/tex]

[tex]x=9[/tex]

Answer:

x = 9

Step-by-step explanation:

So you know that the total is 90 degrees.

What you need to do is create an equation.

5x + 15 + 30 = 90

Then, solve the equation like this.

5x + 15 + 30 = 90

5x + 45 = 90

5x = 90 - 45

5x = 45

x = 45 ÷ 5

x = 9

Hope this helps! :)

Answer:

a)The calculated value t = 4.111 > 1.9925 at 5 % level of significance

Null hypothesis is rejected

The claim that the average time on death row is not 15 years

b) The p-value is 0.000101<0.05

we reject Null hypothesis

The claim that the average time on death row is not 15 years

Step-by-step explanation:

Step(i):-

Sample size 'n' =75

Mean of the sample x⁻ = 17.8

standard deviation of the sample (S) = 5.9

Mean of the Population = 15

Null hypothesis:H₀:μ = 15 years

Alternative Hypothesis :H₁:μ≠15 years

Step(ii):-

Test statistic

                         [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

                        [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }=\frac{17.8-15}{\frac{5.9}{\sqrt{75} } }[/tex]

                    t = 4.111

Degrees of freedom

ν = n-1 = 75-1=74

t₀.₀₂₅ = 1.9925

The calculated value t = 4.111 > 1.9925 at 5 % level of significance

Null hypothesis is rejected

The claim that the average time on death row is not 15 years

P-value:-

The p-value is 0.000101<0.05

we reject Null hypothesis

The claim that the average time on death row is not 15 years

Answer:

Step-by-step explanation:

[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]

Convert the mixed number to an improper fraction

[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]

To divide by a fraction, multiply the reciprocal of that fraction

[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]

Reduce the number with the G.C.F 7

[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]

Reduce the numbers with the G.C.F 17

[tex] \frac{5}{6} \times \frac{3}{2} [/tex]

Reduce the numbers with the G.C.F 3

[tex] \frac{5}{2} \times \frac{1}{2} [/tex]

Multiply the fraction

[tex] \frac{5}{4} [/tex]

In mixed fraction:

[tex]1 \frac{1}{4} [/tex]

Hope this helps..

Good luck on your assignment...

Answer:

(0,5)

Step-by-step explanation:

The solution to the system is where the two graphs intersect

From the graph, the graphs intersect at x = 0 and y =5

Step-by-step explanation:

I have trouble with these types of questions as well, but hopefully this might help.

The answer is 47 pounds

Explanation:

1. First, let's calculate the amount of money that was spent on chicken

$5 per pound of chicken x 25 pounds = $125

2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.

$454 (total) - $125 (chicken)  =  $329

3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.

$329 / $7 = 47 pounds

Answer:

[tex]\large \boxed{\text{Eight days}}[/tex]

Step-by-step explanation:

1. Calculate the hours

[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]

2. Calculate the days

[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]

Answer:

x=-11

Step-by-step explanation:

x+8=-3

x=-3-8 :- collect like term

since we are adding two negative numbers, we will let the number be negative but add them.

x=-11

Hope it helps :)

Answer:

x=-11

Step-by-step explanation:

x+8=-3

collect like terms;

x=-3-8

x=-11

Answer:

angle JKL =  120 degrees

Step-by-step explanation:

Since arc JL is 60 degrees, the central angle is also 60 degrees.

Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.

Consider quadrilateral JKLM whose sum of internal angles = 360.

Therefore

angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees

angle JKL + 90 + 60 + 90 = 360

angle JKL = 360 - 90 - 60 -90 = 120 degrees

Answer:

120 degrees

Step-by-step explanation:

Since arc JL is 60 degrees, the central angle is also 60 degrees.

Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.

look at quadrilateral JKLM whose sum of internal angles = 360.

Therefore

angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees

angle JKL + 90 + 60 + 90 = 360

Hi there! :)

Answer:

Given the information, we can write an equation in slope-intercept form

(y = mx + b) to graph the line:

Plug in the slope for 'm', the y-coordinate of the point given for 'y', and the

x-coordinate given for 'x':

-4 = -2/3(-7) + b

-4 = 14/3 + b

Solve for b:

-12/3 = 14/3 + b

-12/3 - 14/3 = b

-26/3 = b

Therefore, the equation of the line is y = -2/3x - 26/3 (Graphed below)

Some points on the line include:

(-7, -4)

(-4, -6)

(0, -26/3)

(2, -10)

(5, -12)

Answer:

x = 65°

Step-by-step explanation:

Naming the sides of the parallelogram formed ABCD as shown in the attached image to this solution.

Angle A = 2x (vertically opposite angles are equal)

Angle A = Angle C (opposite angles of a parallelogram are equal)

Angle A = Angle C = 2x

(Angle C) + 50° = 180° (Sum of angles on a straight line is 180°)

2x + 50° = 180°

2x = 180° - 50° = 130°

x = (130°/2) = 65°

Hope this Helps!!!

Answer:

65 degrees

Step-by-step explanation:

Answer: Parents and children ( till the age of 5) of Norway

Step-by-step explanation:

Here, A large study of over 2000 parents and children in Norway found that toddlers who regularly slept less than 10 hours per night or woke frequently (three or more times) at night tended to experience more emotional and behavioral problems when they reached age five.

Since the study involved a large random sample of mothers and children and was conducted over several years.

So, the population of interest in this survey is "Parents and children ( till the age of 5) of Norway".

Answer:

  $0.50

Step-by-step explanation:

Let's remove common factors from the equations.

Subtracting the first equation from the second, we find the cost of an apple:

  (2x +y) -(x +y) = 1.75 -1.25

  x = 0.50

The cost of one apple is $0.50.

Answer:

c. $50.37

Step-by-step explanation:

Close price was $56.11 and net change was $5.74. so subtract the net change from the close to get yesterday's price.

Answer:

c.50.37

Step-by-step explanation:

Answer:

Option One:

type : linear growth

a : 120

b : 130

Option 2:

type: linear growth

d : 121

e : 133

Step-by-step explanation:

its right on EDG 2020

Option One:

type: linear growth

a: 120

b: 130

Option 2:

type: linear growth

d: 121

e: 133

Linear growth occurs with the aid of including an equal amount in each unit of time. An exponential increase happens while a preliminary population will increase by the same percent or issue over the same time increments or generations.

Linear and exponential relationships vary within the way the y-values change whilst the x-values increase with the aid of a steady quantity: In linear dating, the y-values have identical variations. In an exponential relationship, the y-values have identical ratios.

Learn more about Linear growth here: brainly.com/question/4025726

#SPJ2

Answer:

z(max) = 650 $

x₁ = 10 units

x₂ = 15 units

Step-by-step explanation:

That is a linear programming problem, we will use a simplex method to solve it

Formulation:

Let´s call  x₁  number of chairs   and x₂ number of tables then :

Item              (in hours)     cutting       assembly      finishing        Profit ($)

Chairs (x₁)                              1                   2                     1                      20

Tables (x₂)                              2                   1                      1                      30

Availability                           40                 42                   25

Objective Function

z  =  20*x₁   +  30x₂   ( to maximize) subject to:

x₁  +  2x₂   ≤  40

2x₁  + x₂    ≤  42

x₁ + x₂     ≤    25

x₁  ,   x₂  >= 0

Using excel or any other software we find:

z(max) = 650

x₁ = 10

x₂ = 15

The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674

Let x represent chairs, and y represent tables

So, the given parameters are:

Cutting:

So, the constraint is:

[tex]\mathbf{x + 2y \le 40}[/tex]

Assembly:

So, the constraint is:

[tex]\mathbf{2x + y \le 42}[/tex]

Finishing:

So, the constraint is:

[tex]\mathbf{x + y \le 25}[/tex]

The unit profit on the items are:

So, the objective function to maximize is:

[tex]\mathbf{Max\ z = 20x + 30y}[/tex]

And the constraints are:

[tex]\mathbf{x + 2y \le 40}[/tex]

[tex]\mathbf{2x + y \le 42}[/tex]

[tex]\mathbf{x + y \le 25}[/tex]

[tex]\mathbf{x,y \ge 0}[/tex]

Using graphical method (see attachment for graph), we have the following feasible points:

[tex]\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}[/tex]

Calculate the objective function using the feasible points.

[tex]\mathbf{z = 20 \times 10 + 30 \times 15}[/tex]

[tex]\mathbf{z = 650}[/tex]

[tex]\mathbf{z = 20 \times 17 + 30 \times 8}[/tex]

[tex]\mathbf{z = 580}[/tex]

[tex]\mathbf{z = 20 \times 14.67+ 30 \times 12.67}[/tex]

[tex]\mathbf{z = 673.5}[/tex]

Approximate

[tex]\mathbf{z = 674}[/tex]

Hence, the maximum revenue is 674

Read more about linear programming at:

https://brainly.com/question/14225202

Answer:

The doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.

Step-by-step explanation:

68 % of the knee replacement surgery patients implies that the ages lies within x = x₀ ± σ where x₀ = mean age = 58 years and σ = standard deviation = 8.25 years

So, the ages lies between x₀ + σ and x₀ - σ

So, the ages lie between 58 - 8.25 = 49.75 years

and 58 + 8.25 = 66.25 years

So the doctors can expect the middle 68 % of their knee replacement surgery patients to be between 49.75 years and 66.25 years.

Answer:

  C.  10

Step-by-step explanation:

The given information tells you that triangles YZX and YZA are congruent, so ZA = ZX = 10.

Answer:

48

Step-by-step explanation:

If x varies inversely as y, we have:

[tex]x \propto \frac{1}{y} \\\implies x = \frac{k}{y}[/tex]

When x=2, y=96

[tex]2 = \frac{k}{96}\\k=192[/tex]

When x=8, y=24

[tex]8 = \frac{k}{24}\\k=192[/tex]

Therefore, the constant of proportionality, k=192.

The equation connecting x and y is:

[tex]x = \frac{192}{y}[/tex]

When x=4

[tex]4 = \frac{192}{y}\\4y=192\\y=48[/tex]

The missing value in the inverse variation given in the table is 48.

Answer:

Below

Step-by-step explanation:

Using the proprtionality relation:

● 8/10 =5/x

● (4*2)/(5*2) = 5/x

Simplify using 2

● 4/5 = 5/x

Multiply both sides by 5

● (4/5)*5 = (5/x)*5

● 4 = 25/x

Switch x and 4

● x= 25/4

■■■■■■■■■■■■■■■■■■■■■■■■■

Again use the proportionality relation but this time with y.

● 8/10 =7/y

8/10 = 4/5

● 4/5 = 7/y

Multiply both sides by 5

● (4/5)*5 =(7/y)*5

● 4 = 35/y

Switch 4 and y

● y = 35/4

Step-by-step explanation:

here, the given point is (-7,-3)

now, by the formula,

p(x,y)= p-1 (-y+a+b,x-a+b) ( p-1 is p das)

p(-5,3)= p-1 (-13,-1) is answer.

hope it helps..

Answer:

Optimal production = 600 gold pens

Revenue  = 600*7 = $4200 gold pens

Step-by-step explanation:

The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.

A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.

B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.

Because of maintenance procedures,

C. the grinder can be operated no more than 30 hours per week and

D. the bonder no more than 50 hours per week.

The company makes

E. $5 on each silver pen and

F. $7 on each gold pen.

How many of each type of pen should be produced and sold each week to maximize profits?

Solution:

We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.

1. From A and C, the maximum number of silver pens

x <= 30*60 / 1 = 1800 and

x <= 50*60 /3 = 1000  ....................(1)   bonder governs

2. from A & D, the maximum number of gold pens

y <= 30*60 / 3 = 600 .....................(2) grinder governs

y <= 50*60 / 4 = 750

3. From D,

x + 3y <= 30*60 = 1800  ...................(limit of grinder) ..... (3)

3x + 4y <= 50*60 = 3000 .................(limit of bonder)  .......(4)

Need to maximize profit,

Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.

The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4).  Using slope intercept form,

(y-480) = -(5/7)(x-360)

or y=-(5/7)x + (737+1/7)    [the purple line] which violates the red line, so not a solution.

Next try the point (0,600)

(y-600) = -(5/7)(x-0), or

y = 600 - (5/7)x   [the black line]

As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of

Revenue  = 600*7 = 4200 gold pens

We can correctly rewrite the equation: 4(5+3) = 2(22-6) by distributing each side.

4(5+3) = 2(22-6)

4(8) = 2(16)

32 = 32

Once you finish distributing each side, you can check to see if it is equal on both sides.

In our case it is since they both equal 32 after distributing the terms.

Answer:

C.

Step-by-step explanation:

So, here's what you need to remember:

If we have a function f(x) and a factor k:

k(f(x)) will be a vertical stretch if k is greater than 1, and a vertical compression if k is greater than zero but less than 1.

f(kx) will be a horizontal compression if k is greater than 1, and a horizontal stretch if k is greater than zero but less than 1.

We are multiplying 0.5 to the function. In other words: 0.5f(x).

This is outside the function, so it's vertical.

0.5 is less than 1, so this would be a vertical compression