The graph below shows the graphs of the linear function Y = 7x and the exponential function y=7%.

Which statement is true?

1. The growth rate of the exponential function exceeds the growth rate of the linear function for -1sx53.

2. The growth rate of the exponential function exceeds the growth rate of the linear function for 0≤x≤3.

3. The growth rate of the exponential function exceeds the growth rate of the linear function for-15xs1.

4. The growth rate of the exponential function exceeds the growth rate of the linear function for 1sxs 3.

Answer:  roughly 151.81788 square meters of metal

=====================================================

Explanation:

The base is a square with side lengths x, so its area is x*x = x^2

Let h be the height of the tank. We have four identical wall panels that have area of xh square meters. The four walls lead to a lateral surface area of 4xh. Overall, the entire tank requires x^2+4xh square meters of metal. We're ignoring the top since the tank is open.

-----------

Let's set up a volume equation and then isolate h.

volume = length*width*height

108 = x*x*h

108 = x^2*h

x^2*h = 108

h = 108/(x^2)

-----------

Plug that into the expression we found at the end of the first section.

x^2+4xh

x^2+4x(180/(x^2))

x^2+(720/x)

------------

Depending on what class you're in, the next step here will vary. If you are in calculus, then use the derivative to determine that the local min happens at approximately (7.11379, 151.81788)

If you're not in calculus, then use your graphing calculator's "min" feature to locate the lowest point on the f(x) = x^2+(720/x) curve.

This lowest point tells us what x must be to make x^2+(720/x) to be as small as possible, where x > 0.

In this context, it means that if the square base has sides approximately 7.11379 meters, then you'll need roughly 151.81788 square meters of metal to form the open tank. This is the least amount of metal required to build such a tank, and that will have a volume of 108 cubic meters.

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:

18

Step-by-step explanation:

Hope this help!!!

Have a nice day!!!

Answer:

(x)^2+ (y+2)^2 = 49

Step-by-step explanation:

The standard form of a circle is

(x-h)^2+ (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-0)^2+ (y--2)^2 = 7^2

(x)^2+ (y+2)^2 = 49

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:

Fail to reject the null hypothesis

[tex]CI = (-4.278, 0.478)[/tex]

Step-by-step explanation:

Given

[tex]n_1=n_2 = 18[/tex]

[tex]\bar x_1 = 12.7[/tex]    [tex]\bar x_2 = 14.6[/tex]

[tex]\sigma_1 = 3.2[/tex]    [tex]\sigma_2 = 3.8[/tex]

[tex]\alpha = 0.05[/tex]

Solving (a): Test the hypothesis

We have:

[tex]H_o : \mu_1 - \mu_2 = 0[/tex]

[tex]H_a : u1 - u2 \ne 0[/tex]

Calculate the pooled standard deviation

[tex]s_p = \sqrt\frac{(n_1-1)\sigma_1^2 + (n_2-1)\sigma_2^2}{n_1+n_2-2}}[/tex]

[tex]s_p = \sqrt\frac{(18-1)*3.2^2 + (18-1)*3.8^2}{18+18-2}}[/tex]

[tex]s_p = \sqrt\frac{419.56}{34}}[/tex]

[tex]s_p = \sqrt{12.34}[/tex]

[tex]s_p = 3.51[/tex]

Calculate test statistic

[tex]t = \frac{x_1 - x_2}{s_p*\sqrt{1/n_1 + 1/n_2}}[/tex]

[tex]t = \frac{12.7 - 14.6}{3.51 *\sqrt{1/18 + 1/18}}[/tex]

[tex]t = \frac{-1.9}{3.51 *\sqrt{1/9}}[/tex]

[tex]t = \frac{-1.9}{3.51 *1/3}[/tex]

[tex]t = \frac{-1.9}{1.17}[/tex]

[tex]t = -1.62[/tex]

From the t table, the p value is:

[tex]p = 0.114472[/tex]

[tex]p > \alpha[/tex]

i.e.

[tex]0.114472 > 0.05[/tex]

So, the conclusion is that: we fail to reject the null hypothesis.

Solving (b): Construct 95% degree freedom

[tex]\alpha = 0.05[/tex]

Calculate the degree of freedom

[tex]df = n_1 + n_2 - 2[/tex]

[tex]df = 18+18 - 2[/tex]

[tex]df = 34[/tex]

From the student t table, the t value is:

[tex]t = 2.032244[/tex]

The confidence interval is calculated as:

[tex]CI = (x_1 - x_2) \± s_p * t * \sqrt{1/n_1 + 1/n_2}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/18 + 1/18}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/9}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * 1/3[/tex]

[tex]CI = -1.90 \± 2.378[/tex]

Split

[tex]CI = (-1.90 - 2.378, -1.90 + 2.378)[/tex]

[tex]CI = (-4.278, 0.478)[/tex]

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

[tex] \huge \underline \mathcal{Answer}[/tex]

The given angles forms linear pair, and we know the angles forming linear pair are supplementary,

Therefore,

Angle MHJ + Angle MHL = 180°

Let's solve :

Value of variable m = 10°

[tex] \mathrm{✌TeeNForeveR✌}[/tex]

Answer:

1.  1/3

2. 0

Step-by-step explanation:

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

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:

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.

Answer:

H0 : μd = 0

H1 : μd > 0

Step-by-step explanation:

The scenario described above can be compared statistically using a paired test mean as the mean if the two groups are dependent, the two restaurants, Albuquerque and Santa Fe are both restaurant locations of a single restaurant company. Hence, to test the mean difference, we use the paired test statistic. Defined thus `

Null hypothesis ; H0 : μd = 0 and the Alternative hypothesis ; H1 : μd > 0

Answer:

Two Sample T test with Ha = Albernuque>Santa Fe

Step-by-step explanation:

Khan

Answer:

Step-by-step explanation:

(B). 2√2

Answer:

[tex]Total = 4.8 * 10^{10}[/tex]

Step-by-step explanation:

Given

[tex]h = 1.2 * 10^8[/tex] --- households

[tex]g = 400[/tex] --- gallons

Required

The number of households

To do this, we simply multiply the average households by the gallons.

[tex]Total = g* h[/tex]

[tex]Total = 400 * 1.2 * 10^8[/tex]

[tex]Total = 480 * 10^8[/tex]

Rewrite as:

[tex]Total = 4.8 * 10^2 * 10^8[/tex]

[tex]Total = 4.8 * 10^{10}[/tex]

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:

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:

A ≈ 26.6° (nearest tenth)

Step-by-step explanation:

The diagram shows a right triangle. To solve for A, we would apply trigonometric ratio formula.

Reference angle = <A

Opposite = 6 m

Adjacent = 12 m

Apply TOA

Tan A = Opp/Adj

Substitute

Tan A = 6/12

Tan A = 0.5

A = [tex] Tan^{-1}(0.5) [/tex]

A ≈ 26.6° (nearest tenth)

Answer:

ans : option 2nd

Step-by-step explanation:

total angle substand perimeter of circle so,

so solve by using unitary methods

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:

(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:

40%

Step-by-step explanation:

Because you want to know the total percent the price increased so you add the amounts. 30% plus 10% makes 40%

Answer:

6144π ft³ ; 19292.2 ft³

Step-by-step explanation:

The volume of the cylinder Given above :

Volume of cylinder, V = πr²h

r =Radius = 16 ; h = 24 ft

V = π * 16² * 24

V = 256 * 24 * π

V = 6144π

Using π = 3.14

V = 6144 * 3.14 = 19292.16

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:

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

Answer:

0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Rate of 18 customers per hour.

This is [tex]\mu = 18n[/tex], in which n is the number of hours.

10 minute interval:

An hour has 60 minutes, so this means that [tex]n = \frac{10}{60} = \frac{1}{6}[/tex], and thus [tex]\mu = 18\frac{1}{6} = 3[/tex]

What is the probability that more than 4 customers arrive in a 10 minute interval?

This is:

[tex]P(X > 4) = 1 - P(X \leq 4)[/tex]

In which:

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

Then

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]

[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]

[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex] = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 = 0.8152[/tex]

And

[tex]P(X > 4) = 1 - P(X \leq 4) = 1 - 0.8152 = 0.1848[/tex]

0.1848 = 18.48% probability that more than 4 customers arrive in a 10 minute interval.

Answer: 1.5 < x < 4

Step-by-step explanation:

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.