What is length of DF?

Answer:

7.4 cm

Step-by-step explanation:

Volume of sphere

v = (4/3)πr³

Volume of hemisphere will be half that

v = (2/3)πr³

(2/3)πr³ = 839

multiply both sides by 3/2

πr³ = 1,258.5

Divide both sides by π

r³ = 400.5929917623

Take the cube root of both sides

r = 7.3717022001

Rounded

r = 7.4 cm

Answer:

0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.

Step-by-step explanation:

We use the normal approximation to the binomial distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

A company's sales force makes 400 sales calls, with 0.25 probability that a sale will be made on a call.

This means that [tex]n = 400, p = 0.25[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 400*0.25 = 100[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.25*0.75} = \sqrt{75}[/tex]

What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made?

Using continuity correction, this is [tex]P(55+0.5 \leq X \leq 75-0.5) = P(55.5 \leq X \leq 74.5)[/tex], which is the p-value of Z when X = 74.5 subtracted by the p-value of Z when X = 55.5.

X = 74.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{74.5 - 100}{\sqrt{25}}[/tex]

[tex]Z = -2.94[/tex]

[tex]Z = -2.94[/tex] has a p-value of 0.0016

X = 55.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55.5 - 100}{\sqrt{25}}[/tex]

[tex]Z = -5.14[/tex]

[tex]Z = -5.14[/tex] has a p-value of 0

0.0016 - 0 = 0.0016

0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.

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Answer:

  ∛(64/125) = 4/5

Step-by-step explanation:

Maybe you want to express ...

  [tex]\displaystyle\left(\frac{125}{64}\right)^{-\frac{1}{3}}=\left(\frac{64}{125}\right)^{\frac{1}{3}}=\boxed{\sqrt[3]{\frac{64}{125}}}[/tex]

__

The denominator of the fractional exponent is the index of the radical. The other applicable rule of exponents here is a^-b = 1/a^b.

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Answer:

  (x, y) = (2, 1)

Step-by-step explanation:

The graph of these equations is attached. The solution is ...

  (x, y) = (2, 1)

Answer:

18

Step-by-step explanation:

Hope this help!!!

Have a nice day!!!

Answer:

[tex]\sec \theta = \frac{\sqrt{22}}{4}[/tex]

Step-by-step explanation:

Given

[tex]\tan^2 \theta = \frac{3}{8}[/tex]

Required

[tex]\sec\ \theta[/tex]

We have:

[tex]\sec^2\theta = 1 + \tan^2 \theta[/tex]

This gives:

[tex]\sec^2\theta = 1 + \frac{3}{8}[/tex]

Take lcm and solve

[tex]\sec^2\theta = \frac{9+3}{8}[/tex]

[tex]\sec^2\theta = \frac{11}{8}[/tex]

Take square roots

[tex]\sec \theta = \frac{\sqrt{11}}{\sqrt 8}[/tex]

[tex]\sec \theta = \frac{\sqrt{11}}{2\sqrt 2}[/tex]

Rationalize

[tex]\sec \theta = \frac{\sqrt{11}}{2\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}[/tex]

[tex]\sec \theta = \frac{\sqrt{22}}{4}[/tex]

Answer:

answer is B

Step-by-step explanation:

i got it right on edg

Respuesta:

10.0 minutos

Explicación paso a paso:

Distancia total recorrida caminando de C a A pasando por T:

500 yardas + 700 yardas = 1200 yardas

Tiempo necesario para recorrer 200 yardas = 14 minutos

Caminando directamente de C a A:

La distancia se puede obtener usando una relación trigonométrica:

Hipotenusa = √ (opuesto² + adyacente²)

Hipotenusa = √500² + 700²

Hipoteno = 860.23252 yardas

Por eso ; Si

1200 yardas = 14 minutos

860.23252 yardas = x

Multiplicar en cruz:

1200x = 12043,255

x = 12043,255 / 1200

x = 10.036 minutos

El tiempo necesario para caminar directamente será: 10.0 minutos

Answer:

f(-3) = -1/3

Step-by-step explanation:

-3 is less than -2 so we use the first function  1/x

f(-3) = 1/-3

Answer:

-1/3

Step-by-step explanation:

-3 is less than -2, so use the first one, 1/x and substitute -3 in

1/(-3)=-1/3

Answer:

B on edge

Step-by-step explanation:

Answer:

The length of segment ZY is of [tex]\sqrt{73}[/tex] units.

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

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

In this question:

Point Z has coordinates (-5,1)

Pount Y has coordinates (3,4).

The length of segment ZY is the distance between points Z and Y. Thus

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

[tex]D = \sqrt{(-5-3)^2+(1-4)^2}[/tex]

[tex]D = \sqrt{8^2+3^2}[/tex]

[tex]D = \sqrt{73}[/tex]

The length of segment ZY is of [tex]\sqrt{73}[/tex] units.

Answer:

1628.89

2593.74

2653.30

Because the interest forms an exponential function. This means that the amount of interest earned in each period is increasing and should therefore be more than double.

Step-by-step explanation:

A: 1000*(1.05)¹⁰= 1628.89

B: 1000(1.1)¹⁰= 2593.74

C: 1000(1.05)²⁰= 2653.30

D: Because the interest forms an exponential function. This means that the amount of interest earned in each period is increasing and should therefore be more than double.

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Answer:

  (x, y) = (-1, -16) or (3, 0)

Step-by-step explanation:

Perhaps you want to solve the system of equations ...

Substituting the first expression for y into the second equation gives ...

  x^2 +2x -15 -4x = -12

  x^2 -2x -3 = 0 . . . . . . . . add 12

  (x -3)(x +1) = 0 . . . . . . .  factor

Solutions are the values of x that make the factors zero: x = 3, x = -1.

The corresponding values of y are ...

  y = -12 +4x

  y = -12 +4{-1, 3} = -12 +{-4, 12} = {-16, 0}

The solutions to the system are ...

  (x, y) = (-1, -16) or (3, 0)

Answer:

5

Step-by-step explanation:

Given :

Y α 1/x

Y = k/x

Where, k = constant of proportionality ;

y = 3 ; x = 10

3 = k / 10

k = 10 * 3

k = 30

Equation becomes :

Y = 30/x

Y =? ; when x = 6

Y = 30 / 6

Y = 5

Answer:

C

Step-by-step explanation:

You can determine this by the third and fourth quartiles.

Answer:

C

Step-by-step explanation:

1,4,4,9,10,10,14

We know the smallest number is 1 and the largest number is 14, so they are left and right whiskers

1,4,4, 9, 10,10,14

The middle number is the 4th number, which is 9 so it is the middle number of the box

Taking the numbers on the left

1,4,4

The middle number is 4  so it is the left hand side of the box

Taking the numbers on the right

10,10,14

10 is the middle number so it is the right hand side of the box

Answer:

70 feet

Step-by-step explanation:

as perimeter of triangle =

23+15+32= 70 feet

Answer:

Solution given:

side 1=23ft.

side 2=15ft

side 3=32ft

we have

perimeter=sum of all sides

=23+15+32=70ft

70ft tape will be needed.

Answer:

i think it is 46

Step-by-step explanation:

Answer:

2.9lbs

Step-by-step explanation:

there are 14oz in a pound so 14/16 is 0.875. Rounded up to .9lbs.

Answer:

Divido es numero

Step-by-step explanation:

1. 1045.90

2. 579.60

3. 634.15

4. 1084.71

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Answer:

  A.  18

Step-by-step explanation:

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

Here, the parallel bases have lengths 3 and 9. The height is 3, so the area is ...

  A = 1/2(3 +9)(3) = 18

The area of the trapezoid is 18 square units.

Answer:

C) 6

by-step explanation:

QUESTION:- Find the value of x.

A. 30

B. 60

C. 90

D. 120

ANSWER:-

ALL ANGLE SUMS HAVE SAME LOGIC OF STRAIGHT LINE ANGLES = 180°

[tex]y + x + y - x = 180[/tex]

[tex]2y = 180 \\ y = 90[/tex]

[tex]2x + y + x = 180[/tex]

[tex]3x + 90 = 180 \\ 3x = 90 \\ x = 30 \degree[/tex]

Answer:

30 degrees

Step-by-step explanation:

2x + y + x = 180

y + x + y - x = 180

3x + y = 180

2y = 180

y = 90

3x + 90 = 180

3x = 90

x = 30

Answer:

(examples) n = 2

n = 3

n = 4

Step-by-step explanation:

to demonstrate, all you do is select a number to represent 'n' and plug it in.

so for example, n = 2:

2(2) + 3(2) = 5(2)

4 + 6 = 10, which is true.

Answer:

16 slices

Step-by-step explanation:

Given :

Number of pizzas ordered = 4

Number of slices per pizza = 4

If 4 pizzas are each sliced into 4 parts ; the we have :

Pizza 1 = 4 slices

Pizza 2 = 4 slices

Pizza 3 = 4 slices

Pizza 4 = 4 slices

Total slices = (4 +4 +4 +4) = 16 slices

the second equation is correct

Step-by-step explanation:

I got it right on the test

Answer:

33.5 kg

Step-by-step explanation:

Each 59 cans are about 1 kg.

He collected 1978 cans.

How many times 59 cans did he collect?

1978/59 = 33.5

He collected 1978 cans which is 33.52 times 59 cans, so he collected 33.5 kg

Answer:

The company needs to sell either 30 or 40 items.

Step-by-step explanation:

We are given that the cost for selling x items given by the function:

[tex]C(x)=40x+180[/tex]

And the revenue for selling x items is given by:

[tex]R(x)=68x-0.4x^2[/tex]

The profit function is the cost function subtracted from the revenue function:

[tex]P(x)=R(x)-C(x)[/tex]

Substitute and simplify:

[tex]\displaystyle \begin{aligned} P(x)&=(68x-0.4x^2)-(40x+180)\\&=68x-0.4x^2-40x-180\\&=-0.4x^2+28x-180\end{aligned}[/tex]

To find how many items must be sold in order to obtain a weekly profit of $300, we can let P equal 300 and solve for x. So:

[tex]300=-0.4x^2+28x-180[/tex]

Solve for x. Subtract 300 from both sides:

[tex]-0.4x^2+28x-480=0[/tex]

We can divide both sides by -0.4:

[tex]x^2-70x+1200=0[/tex]

Factor:

[tex](x-40)(x-30)=0[/tex]

Zero Product Property:

[tex]x-40=0\text{ or } x-30=0[/tex]

Solve for each case:

[tex]x=40\text{ or } x=30[/tex]

So, in order to obtain a weekly profit of $300, the company need to sell either 30 or 40 items.

Answer:

-4374

Step-by-step explanation:

Given :

a1 = 2 ; r = - 3

The nth term of a geometric series :

A(n) = ar^(n-1)

The 8th term :

A(8) = 2(-3)^(8-1)

A(8) = 2(-3^7)

A(8) = 2(−2187)

A(8) = - 4374

Answer:

Step-by-step explanation:

New Total equals Previous Total plus the Check value

New Total minus Previous Total   equals   the Check value

Her new total is  -  Tasta's bank account was = Check value