WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:

Answer:

see below

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos ? = adj / hyp

cos ? = 30/48

Taking the inverse cos of each side

cos ^ -1 cos ? = cos ^ -1 ( 30/48)

? = 51.31781255

To the nearest degree

? = 51

Since this is a right triangle, we can use trig functions

cos ? = adj / hyp

cos ? = 40/53

Taking the inverse cos of each side

cos ^ -1 cos ? = cos ^ -1 ( 40/53)

? = 40.99935365

To the nearest degree

? = 41

Since this is a right triangle, we can use trig functions

tan ? = opp/adj

tan ? = 1/2

Taking the inverse tan of each side

tan ^ -1 tan ? = tan ^ -1 ( 1/2)

? = 26.56505118

To the nearest degree

? = 27

Since this is a right triangle, we can use trig functions

sin ? = opp / hyp

sin ? = 29/35

Taking the inverse sin of each side

sin ^ -1 sin ? = sin ^ -1 ( 29/35)

? = 55.95226763

To the nearest degree

? = 56

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

All the triangles are right triangles, we can use trigonometric functions.

5) cos θ  = adj / hyp

cos x = 30/48

cos⁻¹ cos x = cos⁻¹ (30/48)

x = 51.31781...

x ≈ 51

6) cos θ = adj / hyp

cos x = 40/53

cos⁻¹ cos x = cos⁻¹ (40/53)

x = 40.99935...

x ≈ 41

7) tan θ = opp/adj

tan x = 1/2

tan⁻¹ tan x = tan⁻¹ (1/2)

x = 26.56505...

x ≈ 27

8) sin θ = opp / hyp

sin x = 29/35

sin⁻¹ sin x = sin⁻¹ (29/35)

x = 55.95227...

x ≈ 56

Answer:

About 11 (10.9955742876...)

Step-by-step explanation:

Circumference=(pi) (diameter) or C=πd

Hope this helps!

The circumference of the circle is about 11 inches.

We are given that the diameter of a circle is 3.5 inches.

Noted that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

Therefore circumference of the circle = 2πr

Circumference=(2πr)

The diameter or C = πd

diameter = 3.5 inches

Circumference=(3.5 x 3.14)

Circumference = (10.99) inches

Learn more about circumference here;

brainly.com/question/12512221

#SPJ2

Answer:

a = 7

b = 7

c = 14             [Correct option is B. 14]

Step-by-step explanation:

Since the shape is a parallelogram, to solve this problem, use some of the properties of a parallelogram:

(i) Opposite sides are parallel and congruent. Being congruent means the sides are identical. In other words, they have the same length.

From the diagram, this means that sides PQ and SR are identical. i.e

=> PQ = SR

=> 6a + 10 = 8a - 4          [collect like terms and solve]

=> 14 = 2a

=> a = 7

(ii) Opposite angles are congruent. Angles PQR and PSR are identical. i.e

<PQR = <PSR = (9b + 2)°

Also,

<SPQ = <SRQ = (18b - 11)°

(iii) Consecutive angles are supplementary. The sum of any two angles that are not opposite to each other is 180°. i.e.

<SPQ + <PQR = 180°

<PQR + <QRS = 180°

<QRS + <RSP = 180°

.

.

.

Also,

<PSR + <SPQ = 180°      

(9b + 2)° + (18b - 11)° = 180°        [expand bracket and solve for b]

9b  + 2 + 18b - 11 = 180

27b - 9 = 180

27b = 189

b = 7

Now, since a = 7 and b = 7;

c = a + b = 7 + 7 = 14

Therefore;

a = 7

b = 7

c = 14

Answer:

Hey there!

Circumference: [tex]2\pi r+95+95[/tex]

Area: [tex]\pi r^2+70(95)[/tex]

r=35

Circumference: 410

Area: 10498.

Hope this helps :)

Answer:

Area=  10498.5 cm²

Step-by-step explanation:

Area of rectangle= l x w

= 95 x 70 = 6650

Area of circle = πr²

= π x 35²

= 1225π

=3838.5 cm²

Area of shape: 6650 + 3848.5 = 10498.5 cm²

Answer:

36°

Step-by-step explanation:

<U + < V + <W = 180° (sum of angles in a triangle)

<W = 54°

The tangent is always perpendicular to the radius drawn to the point of tangency...

therefore,

<U = 90°

90° + <V + 54° = 180°

144° + <V = 180°

<V = 180° - 144°

<V = 36°

Answer:

V=36

Step-by-step explanation:

tangent makes rigt angle with radius angle U=90

W+V+U=180

V=180-90-54

V=36

Answer:

It has two solutions.

Step-by-step explanation:

Let as consider the given options are  

It has no solution.

It has one solution.

It has two solutions.

It has infinitely many solutions.

The given equation is

[tex]\dfrac{3}{4z}=\dfrac{1}{4z-3}+5[/tex]

Multiply both sides by 4z(4z-3).

[tex]3(4z-3)=4z+5(4z(4z-3))[/tex]

[tex]12x-9=4z+80z^2-60z[/tex]

[tex]0=-12x+9+80z^2-56z[/tex]

[tex]0=80z^2-68z+9[/tex]

It is a quadratic equation.

Therefore, it has two solutions.

Answer:

It has 1 solution

Step-by-step explanation:

I did the test I put the guys above me in and got it wrong

Answer:

The fence must have:

220 meters

Step-by-step explanation:

The perimeter of the field is equal to the long of the fence round the field.

then:

perimeter = 2(long + wide)

perimeter = 2(85 + 25)

perimeter = 2*110

perimeter = 220m

Answer:

Step-by-step explanation:

In an isosceles trapezoid, two pairs of adjacent angles are supplementary. It means that the sum of the adjacent angles is 180°

Looking at the diagram, angle X and angle W are adjacent angles. It means that

X + W = 180

Since X = 105, then

105 + W = 180

W = 180 - 105 = 75°

Since W = b + 25°, then

b + 25° = 75

b = 75 - 25 = 50°

Answer: In an isosceles trapezoid, two pairs of adjacent angles are supplementary. It means that the sum of the adjacent angles is 180°Looking at the diagram, angle X and angle W are adjacent angles. It means that X + W = 180Since X = 105, then105 + W = 180W = 180 - 105 = 75°Since W = b + 25°, thenb + 25° = 75b = 75 - 25 = 50°

Step-by-step explanation:

Answer:

I think that it should be

[tex] {(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]

Step-by-step explanation:

Here,

we take , a - b = A,b-c = B , c - a= C

A+B+C = 0

we know that,

[tex] {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)[/tex]

Here , A+B+C = 0

so,

A^3 +B^3 + C^3 = 3 ABC

now we put the values

[tex]{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]

I am done .

I think that it should be

{(a - b)}^{3}  +  {(b - c)}^{3}  +  {(c - a)}^{3}  = 3(a - b)(b - c)(c - a)

Step-by-step explanation:

Here,

we take , a - b = A,b-c = B , c - a= C

A+B+C = 0

we know that,

{a}^{3}  +  {b}^{3}  +  {c}^{3}   - 3abc = (a + b + c)(  {a}^{2}  +  {b}^{2}  +  {c}^{2}  - ab - bc - ca)

Here , A+B+C = 0

so,

A^3 +B^3 + C^3 = 3 ABC

now we put the values

{(a - b)}^{3}  +  {(b - c)}^{3}  +  {(c - a)}^{3}  = 3(a - b)(b - c)(c - a)

I am done .

Answer:

5 cm

Step-by-step explanation:

As we can see in the attached figure that G is the point at which the three medians of the triangle meet  i.e we called the centroid

And, according to the property of the centroid, it divides the medians in ratio i.e 2:1

DG: CG = 2 : 1

Since the DG is 10 cm

So, the CG would be half of DG i.e 5 cm

Hence, the CG is 5 cm

Therefore the first option is correct

Answer:

the answer is 5 cm

Step-by-step explanation:

Answer:

26.25 cm²

Step-by-step explanation:

The area of the shaded part is the area of the shaded triangle subtract the area of the white triangle.

Since the triangles are similar then the ratios of corresponding sides are equal.

let the height of the white triangle be h, then

[tex]\frac{12}{9}[/tex] = [tex]\frac{10}{h}[/tex] ( cross- multiply )

12h = 90 ( divide both sides by 12 )

h = 7.5

shaded area = [tex]\frac{1}{2}[/tex] × 12 × 10 - [tex]\frac{1}{2}[/tex] × 9 × 7.5 = 60 - 33.75 = 26.25 cm²

Answer: A. 51%

Step-by-step explanation:

Area of circle = [tex]\pi r^2[/tex] , where r = radius of the circle.

In the figure below, we have the complete question.

According to that,

Radius of outer circle = 7ft

Radius of inner circle = 5ft

The probability that the thumbtack will be placed on the inner circle

[tex]=\dfrac{\text{Area of inner circle}}{\text{Area of outer circle}}\\\\=\dfrac{\pi (5)^2}{\pi (7)^2}\\\\=\dfrac{25}{49}[/tex][π is canceled from numerator and denominator

in percent, [tex]\dfrac{25}{49}\times100=51.0204081633\%\approx51\%[/tex]

So, the probability that the thumbtack will be placed on the inner circle = 51%

Hence, the correct option is A. 51%.

Answer:

Blank 1: 3

Blank 2: 31

Step-by-step explanation:

f(x) = 2x + 7

Plug x as -2

2(-2) + 7

-4 + 7

= 3

Plug x as 12

2(12) + 7

24 + 7

= 31

Answer:

No answer can be found

Step-by-step explanation:

There isn't any value to find and express in simplest form lol.

Answer:

12

Step-by-step explanation:

Answer:

A. 4x¹¹ + x⁷ + 3x³ - 5x + 9

Step-by-step explanation:

order the exponents from largest to smallest. variables always come first; therefore, -5x before 9

Answer:

≈23.66

Step-by-step explanation:

Height ---> x

base ---> 5x

Formula for area of triangle: (base*height)/2

((5x)(x))/2 = 1400

[tex]5x^{2}[/tex]/2 = 1400

[tex]5x^{2}[/tex] = 1400 · 2 = 2800

[tex]x^2[/tex] = 2800/5 = 560

x= √560 ≈ 23.66

Answer:

3√6

Step-by-step explanation:

tan60=opp/adj

opp(d)=tan60*3√2=√3*3√2=3√6

Answer:

Step-by-step explanation:

In triangle DEF, we have:

Given:

<EDF=56

<EFD=84

So, <DEF =180 - 56 - 84 =40 (sum of triangle angles is 180)

____________

DE is a midsegment of triangle ACB

( since CD=DA(given)=>D is midpoint of [CD]

and BE = EA => E midpoint of [BA] )

According to midsegment Theorem,

(DE) // (CB) "//"means parallel

and DE = CB/2 = FB =CF

___________

DEBF is a parm /parallelogram.

Proof: (DE) // (FB) ( (DE) // (CB))

AND DE = FB

Then, <EBF = <EDF = 56

___________

DEFC is parm.

Proof: (DE) // (CF) ((DE) // (CB))

And DE = CF

Therefore, <DCF = <DEF =40

___________

In triangle ACB, we have:

<CAB =180 - <ACB - <ABC =180 - 40 - 56 =84(sum of triangle angles is 180)

[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK! [/tex]

Answer:

22 units.

Step-by-step explanation:

In 45- 45- 90 triangles, there is a 1 to 1 to the square root of 2 formula. Each side length measures 1x, while the hypotenuse measures x times the square root of 2.

In this case, the hypotenuse measures 22 and the square root of 2 units. To find the value of x, simply divide that by the square root of 2 units, and you get x = 22 units. Multiply that by 1, and you get 22 units, which is the length of the leg of the triangle.

Hope this helps!

Answer:

f(x) = x⁵ + 3x³ - 2 I think, if its incorrect I apologize

Step-by-step explanation:

Answer:

Option C

x²+ 2x -24=0

x²+6x-4x-24= 0

x(x+6) -4(x+6) = 0

(x+6)(x-4) = 0

x= -6 and 4

Therefore, for x = 4 and -6 , the above given equation is true.

Answer:

Step-by-step explanation:

Hello!

To compare different prices of several brands of a product the best is to express the price for the same quantities of product.

Since the three options are original in 300g, 450g and 600g, I'll express all prices on a base of 100g of product. You can use simple rule of three for this:

Option 1

300g cost $3.89

100g cost [tex]\frac{100*3.89}{300} = $1.296[/tex]

Option 2

450g cost $ 4.77

100g cost [tex]\frac{100*4.77}{450}= $1.06[/tex]

Option 3

600g cost $ 6.59

100g cost [tex]\frac{100*6.59}{600}= 1.098[/tex]

So:

Option 1: $1.296/ 100g

Option 2: $1.06/100g

Option 3: $1.098/100g

The cheapest option is number 2

I hope this helps!

the answer would end up rounding to 31. :)

Answer:

6.93 cm

Step-by-step explanation:

You have a right triangle (90°), so you do as follow:

If I understand correctly, you are looking for the hypotenuse so

[tex]cos(30) = \frac{PQ}{QR} = \frac{8 cm}{QR}[/tex]

That is equal to [tex]QR = cos(30)*8 cm = 6.928 cm[/tex]

Answer: 5.0693 ounces

Step-by-step explanation:

For a 6 ounce cup to overflow, then the cup content is beyond 6 ounce, at 2%

P(x > 6) = 2% = 0.02; similarly

P(x<6) = 1 - P(x > 6)'.

P(x<6) = 1 - 0.02 = 0.98

The z-score for 0.98 = 2.326

The z - formular for a normally distributed goes thus :

Zscore =(observed score - mean) / standard deviation

Substituting the vamus :

2.326 = (6 - mean) / 0.4

2.326 × 0 4 = 6 - mean

0.9304 = 6 - mean

Mean = 6 - 0.9304

Mean = 5.0693

Answer:

36 : 6 and -6

12 = [tex]2\sqrt{3} , -2\sqrt{3}[/tex]

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Step-by-step explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

_________________________________________________

36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 = [tex]2^2*\sqrt{3} *\sqrt{3}[/tex]

[tex]\sqrt{12} = 2\sqrt{3}[/tex]

also

12 = [tex]-2\sqrt{3} *-2\sqrt{3}[/tex]

[tex]\sqrt{12} = -2\sqrt{3}[/tex]

___________________________________

1.96 = 196/100 = (14/10)^2

1.96 = 196/100 = (-14/10)^2

hence

[tex]\sqrt{1.96} = 14/10 \ or -14/10[/tex]

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of  0.64 = 0.8 and -0.8

_________________________________

400 = 20^2

400 = (-20)^2

[tex]\sqrt{400} = 20\\\sqrt{400} = -20\\[/tex]

__________________________________

25/36 = (5/6)^2

25/36 = (-5/6)^2

[tex]\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6[/tex]

Answer:

11.25

Step-by-step explanation:

12*12/12-3/4

PEMDAS says multiply and divide first

from left to right

144/12 - 3/4

12 -3/4

12 - .75

Then add and subtract

11.25

Answer:

[tex]\frac{45}{4}[/tex]

Step-by-step explanation:

Apply PEDMAS

P - parenthesis

E - exponents

D - division

M - multiplication

A - addition and S - subtraction  

Division is first.

12 × [tex]\frac{12}{12}[/tex] - [tex]\frac{3}{4}[/tex]

12 × 1 - [tex]\frac{3}{4}[/tex]

Followed by multiplication.

12 - [tex]\frac{3}{4}[/tex]

Subtract the numbers next.

[tex]\frac{12}{1} -\frac{3}{4}[/tex]

Make the denominators same by LCM.

[tex]\frac{48}{4} -\frac{3}{4}[/tex]

[tex]\frac{45}{4}[/tex]

Answer:

a.

Explanation:

In the chart, the average temperature of each month at the beginning of the year gradually rises until August, where it begins to decrease. This trend is displayed in graph a. Additionally, each month on the x-axis is shown correctly because the months should only span numbers 1-12.

Answer: the answer is A

Step-by-step explanation: hope this helps :D can u plz give a brainliest

Correct question :

There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 7 9 . There are 28 red marbles in the bag and each is equally likely to be chosen. Work out how many marbles in total there must be.

Answer:

Total number of marbles = 36

Step-by-step explanation:

Marbles in bag: Red and Blue only

Probability of randomly choosing a red marble = 7/9

Number of red marbles = 28

Total number of marbles in the bag =?

Probability = required outcome / Total possible outcomes

P(red marble) = required outcome (number of red marbles) / Total possible outcomes(total number of marbles

7/9 = 28 / total number of marbles

Total number of marbles * 7/9 = 28

Total number of marbles = 28 ÷ 7/9

Total number of marbles = 28 * (9/7)

= 252 / 7

Total number of marbles = 36