How many intergers are between √15 and √68

Nathan and Olivia are saving money for school supplies. Nathan saves $2 per week and already has $30 in his bank. Olivia saves $

melomori [17]

Answer:

Nathan: 2x+30

Olivia: 4x+15

Step-by-step explanation:

x is the number of weeks

Nathans account is as follows

2x+30

(2 dollars a week plus the 30 dollars already there)

Olivia's account is as follows

4x+15

(4 dollars per week plus the 15 already in there)

4 0

2 years ago

A security expert claims that exactly 13% of all homeowners have a home security alarm. State H0 and Ha in words and in symbols

soldi70 [24.7K]

Answer:

Two tailed

Step-by-step explanation:

Given that a security expert claims that exactly 13% of all homeowners have a home security alarm.

Here we have to check whether the contention of security expert is correct or not

The test is to be done for the proportion of homeowners who have a home security alarm to total homeowners.

Let p be the proportion.

For this we set up hypotheses as:

$H_0 = p = 13%=0.13\\H_a: p \neq 0.13$

This is a two tailed test

Because alternate is for not equal to. If alternate is for > or < we say one tailed and if not equal to we say two tailed.

3 0

3 years ago

An analysis of sales records for the last 120 weeks gives the following results. Assuming that these past data are a reliable gu

Mila [183]

Answer:

(a) 0.5333

(b) 0.6583

(c) 0.5583

(d) 0.7083

(e) 0.6167

Step-by-step explanation:

Denote the events as follows:

A = a competitor will advertise

NA = a competitor will not advertise

L = Low sales will be achieved

M = Medium sales will be achieved

H = High sales will be achieved

The data provided is of the form:

Low (L) Medium (M) High (H) Total

A 32 14 18 64

NA 21 12 23 56

Total 53 26 41 120

The probability of an event E is:

$P(E)=\frac{n(E)}{N}$

n (E) = favorable outcomes of event E

N = Total number of outcomes

(a)

Compute the probability that next week the competitor will advertise as follows:

$P(A)=\frac{n(A)}{N}=\frac{64}{120}=0.5333$

Thus, the probability that next week the competitor will advertise is 0.5333.

(b)

Compute the probability that next week sales will not be high as follows:

$P(H^{c})=1-P(H)=1-\frac{n(H)}{N}=1-\frac{41}{120}=\frac{120-41}{120}=0.6583$

Thus, the probability that next week sales will not be high is 0.6583.

(c)

The events of achieving a medium or high sales are mutually exclusive.

Since the sales achieved will either be medium or high. They cannot be both.

So, P (M ∩ H) = 0.

Compute the probability that next week there will be medium or high sales will be achieved as follows:

$P(M\cup H)=P(M)+P(H)=\frac{26}{120}+\frac{41}{120}=\frac{26+41}{120}=0.5583$

Thus, the probability that next week there will be medium or high sales will be achieved is 0.5583.

(d)

Compute the probability that next week either the competitor will advertise, or only low sales will be achieved as follows:

$P(A\cup L)=P(A)+P(L)-P(A\cap L)=\frac{64}{120}+\frac{53}{120}-\frac{32}{120}=\frac{85}{120}=0.7083$

Thus, the the probability that next week either the competitor will advertise, or only low sales will be achieved is 0.7083.

(e)

Compute the probability that next week either the competitor will not advertise, or high sales will be achieved as follows:

$P(NA\cup H)=P(NA)+P(H)-P(NA\cap H)=\frac{56}{120}+\frac{41}{120}-\frac{23}{120}=\frac{74}{120}=0.6167$

Thus, the the probability that next week either the competitor will not advertise, or high sales will be achieved is 0.6167.

8 0

3 years ago

Y

zheka24 [161]

Please visit this link: https://youtu.be/_0Ft9HdNg5c

5 0

3 years ago

A 10 foot ladder is leaning against a wall. Call x the distance from the top of the ladder to the ground, and call y the distanc

liq [111]

$-5.3\:\text{ft/s}$

Step-by-step explanation:

We start by applying the Pythagorean theorem to the ladder, with its length L as the hypotenuse:

$L^2 = 100\:\text{ft}^2 = x^2 + y^2$

where x is the vertical distance from the top of the ladder to the ground and y is the horizontal distance from the bottom of the ladder to the wall. Taking the derivative of the above expression with respect to time, we get

$0 = 2x\dfrac{dx}{dt} + 2y\dfrac{dy}{dt}$

Solving for dx/dt, we get

$\dfrac{dx}{dt} = -\left(\dfrac{y}{x}\right)\dfrac{dy}{dt} = -\left(\dfrac{\sqrt{L^2 - x^2}}{x}\right)\dfrac{dy}{dt}$

We know that

$\dfrac{dy}{dt} = 4\:\text{ft/s}$

when x = 6 ft. So the rate at which the top of the ladder is going down is

$\dfrac{dx}{dt} = -\left(\dfrac{\sqrt{100\:\text{ft}^2 - (6\:\text{ft})^2}}{6\:\text{ft}}\right)(4\:\text{ft/s})$

$\:\:\:\:\:\:\:= -5.3\:\text{ft/s}$

The negative sign means that the distance x is decreasing as y is increasing.

5 0

3 years ago

How many intergers are between √15 and √68​

How many intergers are between √15 and √68