I toss an unfair coin 12 times. This coin is 65% likely to show up heads. Calculate the probability of the following.
a. 11 heads:
b. 2 or more heads:
c. 7 heads:
d. 9 tails:
e. 8 or less heads:

Answer:

x < 5

Step-by-step explanation:

The total amount is 595$ and the amount Helena want to leave for equipement is 420$

The amount helena can use is 175$

each ticket costs 35$

so Helena can oly buy 5 tickets or less

x < 5     with x the number of tickets

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:

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:

[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:

[tex]1x=\frac{1\sqrt{129} }{8}[/tex]

Step-by-step explanation:

In between the 1 and the [tex]\sqrt{129}[/tex] goes this symbol: ±

hope this helps!

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:

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:

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:

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:

The variable n represents the number of times in a year in which we compound the interest rate

Step-by-step explanation:

The periodic compound interest formula is given as;

A = P( 1 + r/n)^nt

The variable n represents the number of times in a year in which the interest rate is compounded

Answer:

C

Step-by-step explanation:

According to SohCahToa, cosine is adjacent over the hypotenuse.

The adjacent when looking from angle b, is 21.

The hypotenuse of this triangle is 29.

So Cos B=21/29

Answer:

The correct option is (B).

Step-by-step explanation:

The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.

In this case, we need to test the claim that the majority of voters oppose a proposed school tax.

The hypothesis can be defined as follows:

H₀: The proportion of voters opposing a proposed school tax is not a majority, i.e. p ≤ 0.50.

Hₐ: The proportion of voters opposing a proposed school tax is a majority, i.e. p > 0.50.

It is provided that the test statistic value and p-value are:

z = 1.23

p-value = 0.1093

The probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic is 0.1093.

The significance level of the test is:

α = 0.05

The p-value of the test is larger than the significance level of the test.

p-value = 0.1093 > α = 0.05

The null hypothesis will not be rejected.

Concluding that there is not enough evidence to support the claim.

Thus, the correct option is:

"If the null hypothesis is true, then the probability of getting a test statistic that is as or more extreme than the calculated test statistic of 1.23 is 0.1093. This result is not surprising (or considered unusual) and could easily happen by chance"

Answer:

the dimensions of the poster with the smallest area is 36cm by 54cm

Step-by-step explanation:

✓Let us represent the WIDTH of the printed material on the poster as "x"

✓Let us represent the HEIGHT of the printed material on the poster as "y"

✓ The given AREA is given as 864 cm2

Then we have

864 cm2= xy ...................eqn(1)

We can make "y" subject of the formula.

y= 864/x .......................eqn(2)

✓The total height the big poster which includes the 9cm margin that is at the bottom as well as the top is

(y+18)

✓The total width of the poster which includes the 6cm margin that is at the bottom as well as the top is

(x+12)

✓Then AREA OF THE TOTAL poster

A= (y+18)(x+12) ...................eqn(3)

Substitute eqn (2) into eqn(3)

A= ( 18+ 864/x)(x+12)

We can now simplify by opening the bracket, as

A=18x +1080 +10368/x

A= 18x +10368/x +1080

Let us find the first derivative of A which is A'

A'= 18-(10368/x²)

If we set A' =0

Then

0= 18- (10368/x²)

18= (10368/x²)

x²= 10368/18

x²= 576

x=√576

x=24

The second derivatives will be A"= 2(10368)/x³ and this will be positive for x> 0, and here A is concave up and x=24 is can be regarded as a minimum

The value of "y" when x=24 can now be be calculated using eqn(2)

y= 864/x

y= 864/24

y=36cm

✓The total width of the poster= (x+12)

= 24+12=36cm

✓The total height big the poster= (y+18)=36+18=54cm

the dimensions of the poster with the smallest area is 36cm by 54cm

Answer:

The total width of the paper [tex]=36 cm.[/tex]

The total height of the paper [tex]=54cm[/tex]

Step-by-step explanation:

Given information:

Top margin of the paper = 9 [tex]cm\\[/tex]

Bottom margin of the paper = 6 [tex]cm\\[/tex]

Area of the printed material = [tex]864[/tex] [tex]cm^2[/tex]

Let, the width of the printed material = [tex]x[/tex]

And the height of the printed material = [tex]y[/tex]

So, Area [tex]x \times y=864[/tex] [tex]cm^2[/tex]

After including margins;

Width of the paper [tex]= (x+12)[/tex]

Height of the paper [tex]= (y+18)[/tex]

Area [tex](A) = (y+18) (x+12)[/tex]

[tex]A=18x+(10368/x)+1080\\[/tex]

Take first derivative:

[tex]A'= 18- (10368/x^2)[/tex]

When [tex]A'=0[/tex]

Then,

[tex]18-(10368/x^2)=0\\x^2=576\\x=24[/tex]

Now ,when we take second derivative and check if it is positive or not ,

We find that it is grater than zero so the obtained value can be consider as minimum and can be proceed for further solution.

Hence ,

[tex]x \times y=864\\y=864/24\\y=36\\[/tex]

Now ,

The total width of the paper

[tex]= 24+12\\=36 cm.[/tex]

And , total height of the paper

[tex]=36+18\\=54 cm.[/tex]

For more information visit:

https://brainly.com/question/14261130

Answer:

Speed of the jet is 563.02 miles/hr

Speed of the jet stream is 122.83 miles/hr

Step-by-step explanation:

The average time for going from Seattle to New York is 4.3 hours

The distance between these places is 2421 miles

The average time for going back (impaired by jet stream) is 5.5 hours

If we designate the speed of the jet = v

and the speed of the jet stream = u

then on the return trip, the relative speed of the jet = v - u

Also, recall that distance = speed x time

For the going trip, the distance covered by the jet = 4.3 x v = 2421 miles

For the return trip, the distance covered by the jet = 5.5 x (v - u)  = 2421 miles

= 5.5(v - u)

these translate into the following equation written below

4.3v = 2421              ....equation 1

5.5(v - u) = 2421      ....equation 2

solving, equation 1, we'll have

4.3v = 2421

v = 2421/4.3 = 563.02 miles/hr  this is the speed of the jet

substituting the value of v into equation 2, we'll have

5.5(v - u) = 2421

5.5(563.02 - u) = 2421

3096.61 - 5.5u = 2421

3096.61 - 2421 = 5.5u

675.61 = 5.5u

u = 675.61/5.5

u = 122.83 miles/hr   this is the speed of the jet stream

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:

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

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

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:

A

Step-by-step explanation:

A divisor refers to a number by which another number is to be divided.

So what this question is practically asking us is that which of the values in the options to 2 decimal places is the result dividing the population by the number of seats

Thus we have;

140,000/9 = 15,555.55555 which to 2 decimal places is 15,555.56

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

Answer:

∠1 is 150°

∠2 is 30°

∠3 is 150°

∠4 is 30°

Step-by-step explanation:

∠1 is vertically opposite to ∠3 so they are equal

360° - (150° + 150°) = 360° - 300° = 60°

∠2 and ∠4 must sum to 60°

Step-by-step explanation:

From the question

∠1 is opposite to ∠ 3 and vertically opposite angles are equal

So

∠1 = ∠ 3

That's

∠ 3 and ∠ 4 are on a straight line and angles on a straight line add up to 180°

So to find ∠4, subtract ∠3 from 180°

That's

∠ 4 = 180 - ∠ 3

∠ 4 = 180 - 150

Since ∠ 4 and ∠ 2 are opposite they are also equal

That's

∠ 4 = ∠ 2

Therefore

Hope this helps you

[tex] v = \sqrt{4900} + \sqrt{8100} = 70 + 90 = 160[/tex]

Answer: D. 160

It is possible to draw a single straight line to pass through more than one point on the red curve. Therefore, the graph fails the vertical line test. We have cases where one input leads to more than one output.

Answer:

AC = 25.5 or 1.5

Step-by-step explanation:

If they are on a line and they are in the order ABC

AB + BC = AC

12+13.5 = AC

25.5 = AC

If they are on a line and they are in the order CAB

CA + AB = BC

AC + 12 =13.5

AC = 13.5 -12

AC = 1.5

If they are on a line and they are in the order ACB

That would mean that AB is greater than BC and that is not the case

Answer:

(a) (1,5)

(b) Every subset of a cartesian product is a relation, therefore this is a relation.

(c) The relation IS NOT a function.

Step-by-step explanation:

(a)

(1,5)

Notice that  3(1) +1 = 4  < 5 therefore (1,5) is an order pair that satisfies the equation.

(b)

Every subset of a cartesian product is a relation, therefore this is a relation.

(b)

A relation is a function of  the following condition holds

if    (a,b) and (c,b) belong to the relation then (a=c)

In this case, (1,5), (0,5) belong to the relation but  0 is different than 5, therefore the relation IS NOT a function.

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.

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:

3

Step-by-step explanation:

336 / n = k + 2/n, where k is an integer

336 = kn + 2

334 = kn

2007 / n

(2004 + 3) / n

(334×6 + 3) / n

334×6/n + 3/n

6k + 3/n

The remainder is 3.

Answer:

the answer would be calculations

Step-by-step explanation:

because they have do determine if the check out times differ between the two systems so they need to calculate the difference between the two