The battery standby duration (in hours) of a new model of cell phone is known to be normally distributed. Ten pieces of such new model of cell phone supplied from the manufacturer are randomly chosen and the actual standby durations are recorded as below:

48.2 47.8 45.6 47.2 49.3

51.2 44.2 45.4 49.2 43.6

(a) Calculate the unbiased estimates of population mean and standard deviation of battery standby duration (in hours) of the new cell phone.

Answer:

a₁₁ = 37

Step-by-step explanation:

There is a common difference between consecutive terms, that is

1 - (- 3) = 5 - 1 = 9 - 5 = 13 - 9 = 4

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3 and d = 4 , then

a₁₁ = - 3 + (10 × 4) = - 3 + 40 = 37

Answer:

x=2

Step-by-step explanation:

A line that intersects a circle in two points is called a secant line, and this is the case for both line DE and AE.

For two secant lines that intersect outside of the circle, such as the ones here, we can say that

CE * DE = BE * AE

Therefore, we need to then define these lines.

CE is x+4, BE is x+1, AE = (BE + AB) = 11+x+1 = 12+x, and DE = (CE + DC) = 1+x+4 = 5+x

We then have

(x+4) * (5+x) = (x+1) * (12+x)

expand

5x + x² + 20 + 4x = 12x+x²+12+x

x²+9x + 20 = x²+13x+12

Next, we want to congregate all values to one side so we can solve for x. This can be done by subtracting both sides by (x²+13x+12) to get

-4x + 8 = 0

subtract 8 from both sides to isolate the x and its coefficient

-4x = -8

divide both sides by -4 to isolate the x

x = 2

Answer:

c) The golf ball will travel 260.8 yards.

d) Hence the residual is 4.2 yards.

Step-by-step explanation:

c) y' = 2.8333x - 22.4967

Now the golf ball will travel [tex]= 2.8333\times100 - 22.4967[/tex]= 260.8 yards

here y'= 260.8 yards.

d) The residual is : y - y' = 265 - 260.8 = 4.2 yards.

Answer:

a)  [tex]y=260.8333~yd[/tex]

b) [tex]\Delta d=4.1667~yd[/tex]

c) [tex]y=260~yd[/tex]

d) [tex]\Delta y'=0.8333~yd[/tex]

Step-by-step explanation:

Given:

equation of line, [tex]y=2.8333x-22.4967[/tex]

x = club-head speed​ (in miles per​ hour)

y = the distance a golf ball travels​ (in yards)

a)

x = 100 mph

Then the distance travelled by the ball:

(put the given value of x in the above eq.)

[tex]y=2.8333\times 100-22.4967[/tex]

[tex]y=260.8333~yd[/tex]

b)

If the observed distance in the above case comes out to be 265 yards then the residual value will be:

[tex]\Delta d=265-260.8333[/tex]

[tex]\Delta d=4.1667~yd[/tex]

c)

From the calculated value when rounding it to the nearest tenth:

[tex]y=260~yd[/tex]

d)

The residual on rounding the calculated value to the nearest tenth:

[tex]\Delta y'=260.8333-260[/tex]

[tex]\Delta y'=0.8333~yd[/tex]

Answer:

how?

Step-by-step explanation:

I didnt get question

Answer:

b

Step-by-step explanation:

The experimental probability that the number cube shows 4 is 2/7.

Experimental probability is a probability that is determined on the basis of a series of experiments.

Given that, a number cube is rolled 14 times, we need to determine the experimental probability that the number cube shows 4,

The formula to calculate the experimental probability is:

P(E) = Number of times an event occurs/Total number of times the experiment is conducted

P(E) = 4/14 = 2/7

Hence, the experimental probability that the number cube shows 4 is 2/7.

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Answer:

[tex]{ \tt{distance = speed \times time}} \\ { \tt{ = 56 \times 3 \frac{1}{2} }} \\ = { \tt{196 \: miles}}[/tex]

Answer:

Brooke = 1 hr 50 min

Lamont = 100 min = 1 hr 40 min

Because 60 min = 1 hr

Lamont was faster

Hope this helped

Answer: D

Step-by-step explanation:

Answer:

The answer to the equation is C

Answer:

-2/5 is the answer

I hope this will help you

Answer:

-2/5

Step-by-step explanation:

Just add the top numerator together -4 + 2 = -2

Answer:

x = 15

Step-by-step explanation:

2x+10+4x+80=180

or, 2x+4x=180-80-10

or, 6x=90

or, x=15

Answered by GAUTHMATH

Answer:

5x less than 300  - 165

Step-by-step explanation:

It will take 27 days to take in animals without exceeding its occupy limit.

An expression which is made up of variables and constants , along with algebraic operation (addition , subtraction etc ) is called Algebraic expression.

According to the question :

165 + (x) 5 = 300

5x = 135

x = 27

Hence , it will take 27 days to occupy the limit

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Answer:

2sinx.Cosx=cosx

2sin90°.cos90°=cos90°

2×1.0=0

0=0

Answer:

13.2 cm

Step-by-step explanation:

using the Pythagorean theorem, we can find the length of the other leg, since this is a right triangle. The equation is a^2 + b^2 = c^2, A and B being the legs and C being the hypotenuse. Since we are finding the other leg, we can switch the equation around to find A/B instead. (A/B being the legs). so we get: B^2 = C^2 - A^2 ; then we simplify [tex]b=\sqrt{c^2-a^2}[/tex]

We plug in the numbers given:

[tex]b = \sqrt{16^2-9^2}\\b=\sqrt{256-81}\\b=\sqrt{175} \\b= 13.229[/tex]

rounded to nearest tenth: 13.2

The measure of the other leg in the right triangle is 13.22 cm.

A triangle with one angle measuring 90° is called a right triangle.

Given that, a right triangle has a leg measuring 9 cm and its hypotenuse is 16 cm longs, we need to find the other side,

So, using the Pythagoras theorem,

16² = 9² + x²

x = √256-81

x = √175

x = 13.22

Hence, the measure of the other leg in the right triangle is 13.22 cm.

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Answer:

[tex]\frac{y^{2}}{25}-\frac{x^{2}}{3}=1[/tex]

Step-by-step explanation:

Para resolver este problema debemos tomar en cuenta los datos que nos dan y la ecuación de una hipérbola. Comencemos con los datos:

centro: (0,0)

focos: [tex](0,-\sqrt{28}),(0,\sqrt{28})[/tex]

eje conjugado = [tex]2\sqrt{3}[/tex]

por los focos podemos ver que la hipérbola se dirige hacia el eje y, por lo que debemos tomar la siguiente forma de la ecuación de la parábola:

[tex]\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1[/tex]

de los focos podemos obtener que:

[tex]c=\sqrt{28}[/tex]

y del eje conjugado podemos saber que al dividir la longitud del eje conjugado dentro de 2 obtenemos b, así que:

[tex]b=\sqrt{3}[/tex]

podemos utilizar la siguiente fórmula para obtener a:

[tex]c^{2}-a^{2}=b^{2}[/tex]

si despejamos a en la ecuación obtenemos lo siguiente:

[tex]a=\sqrt{c^{2}-b^{2}}[/tex]

ahora podemos sustituir los valores:

[tex]a=\sqrt{(\sqrt{28})^{2}-(\sqrt{3})^{2}}[/tex]

[tex]a=\sqrt{28-3}[/tex]

[tex]a=\sqrt{25}[/tex]

a=5

así que media vez conozcamos a, podemos sustituir los datos en la ecuación de la hipérbola así que obtenemos lo siguiente:

[tex]\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1[/tex]

[tex]\frac{y^{2}}{(5)^{2}}+\frac{x^{2}}{(\sqrt{3})^{2}}=1[/tex]

[tex]\frac{y^{2}}{25}+\frac{x^{2}}{3}=1[/tex]

si graficamos la hipérbola, queda como en el documento adjunto.

Answer: A

Screenshot of calculator

Answer:

38.46%

Step-by-step explanation:

We are given;

Total population; n(S) = 26000

Number that read English news paper; n(E) = 5000

Number of people that read nepali; n(N) = 12000

Number that read both English and nepali; n(E n N) = 1000

Thus from probability laws, number that read either English or nepali is;

n(E u N) = n(N) + n(E) - n(N n E)

n(E u N) = 12000 + 5000 - 1000 = 16000

Thus;

number that read neither English nor nepali is;

n(E' u N') = n(S) - n(E u N)

n(E' u N') = 26000 - 16000 = 10000

Thus, the percentage is;

10000/26000 × 100% = 38.46%

Answer:

eju 48, 23w6yuw43wdgn

Step-by-step explanation:

Answer:

The population in 8 years will be of 7313.

Step-by-step explanation:

Population of a town:

The population of a town, after t years, with a doubling time of n years, is given by:

[tex]P(t) = P(0)(2)^{\frac{t}{n}}[/tex]

The initial population of a town is 4200​, and it grows with a doubling time of 10 years.

This means that [tex]P(0) = 4200, n = 10[/tex]

So

[tex]P(t) = 4200(2)^{\frac{t}{10}}[/tex]

What will the population be in 8 ​years?

This is P(8). So

[tex]P(8) = 4200(2)^{\frac{8}{10}} = 4200(2)^{0.8} = 7313[/tex]

The population in 8 years will be of 7313.

Answer:

a. Produce more, as long as the resources are also available

Step-by-step explanation:

from brainly itself

scouteo

Ace

The correct answer is A) produce more, as long as the resources are also available.

As displayed on a production possibilities curve, an increase in technology will allow a society to produce more, as long as the resources are also available.

A production possibilities graph is a valid representation of the available ways an economy is able to use the resources. In this case, an increase in technology will allow a society to produce more, as long as the resources are also available means that as long there are enough resources in the market, technology in a country helps with the production of more things to be consumed or traded.  

Answer:

Range = highest value - lowest value

Explanation:

This is the required formula to find range from a distribution table.

Answer:

(x+9)(x+5)

Step-by-step explanation:

find 2 numbers that add to 14 and multiply to 45

Answer:

523.6

Step-by-step explanation:

Not sure how to explain •-•

Hope it helps c:

Answer: use formula pi r^3

3.14 × 5 x 5 x 5 x 4 ÷ 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The answer is Tonya's phone had the greater initial trade-in value.

Leo's phone decreases at an average rate slower than the trade in value of Tonya's phone.

Step-by-step explanation:

Given

Tonya

[tex]f(x) = 490 * 0.88^x[/tex]

Leo

[tex]x \to g(x)[/tex]

[tex]0 \to 480[/tex]

[tex]2 \to 360[/tex]

[tex]4 \to 470[/tex]

Solving (a): The phone with greater initial value

The initial value is when x = 0. So, we have:

[tex]f(x) = 490 * 0.88^x[/tex]

[tex]f(0) = 490 * 0.88^0[/tex]

[tex]f(0) = 490 * 1[/tex]

[tex]f(0) = 490[/tex]

From Leo's table

[tex]g(0) = 480[/tex]

By comparison;

[tex]f(0) > g(0)[/tex]

i.e.

[tex]490 > 480[/tex]

So: Tonya's had the greater initial trade-in value

Solving (b): The phone with lesser rate

An exponential function is:

[tex]y = ab^x[/tex]

Where:

[tex]b \to rate[/tex]

For Tonya

[tex]b = 0.88[/tex]

For Leo, we have:

[tex](x_1,y_1) = (0,480)[/tex]

[tex](x_2,y_2) = (2,360)[/tex]

So, the equation becomes:

[tex]y = ab^x[/tex]

[tex]480 = ab^0[/tex] and [tex]360 = ab^2[/tex]

Solving [tex]480 = ab^0[/tex], we have:

[tex]480 = a * 1[/tex]

[tex]480 = a[/tex]

[tex]a= 480[/tex]

[tex]360 = ab^2[/tex] becomes

[tex]360 = 480 * b^2[/tex]

Divide both sides by 480

[tex]0.75 = b^2[/tex]

Take square roots

[tex]0.87 = b[/tex]

[tex]b=0.87[/tex] -- Leo's rate

By comparison; Leo's rate is slower i.e. 0.87 < 0.88

Answer:

Area of triangle1/2b*h Now you can do

The area of the triangle is 9000 square centimeters

Let the sides in order of length be represented as:

x, y and z.

So, we have:

z = 80 + y

z = 130 + x

P = 540

The perimeter is calculated as:

P = x + y + z

So, we have:

x + y + z =540

Substitute z = 130 + x

x + y + 130 + x =540

Evaluate the like terms

2x + y = 410

Substitute z = 130 + x in z = 80 + y

130 + x  = 80 + y

Evaluate the like terms

x - y = -50

So, we have:

2x + y = 410

x - y = -50

Add both equations

3x = 360

Divide by 3

x = 120

Substitute x = 120 in z = 130 + x

z = 130 + 120

z = 250

Substitute z = 250 in z = 80 + y

250 = 80 + y

y = 170

So, we have:

x = 120

y = 170

z = 250

The area is then calculated as:

[tex]Area = \sqrt{s * (s -x) *(s - y) * (s -z)[/tex]

Where

s = P/2 = 540/2

s = 270

So, we have:

[tex]Area = \sqrt{270 * (270 -120) *(270 - 170) * (270 -250)[/tex]

Evaluate

Area = 9000

Hence, the area of the triangle is 9000 square centimeters

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Answer:

nt ooooo

o

Step-by-step explanation:

options b is not correct

Answer:

B is right option

Step-by-step explanation

A reflex angle is an angle that measures greater than 180 degrees and less than 360 degrees.