Write the verbal sentence as an equation. let y represent the number

a box holds nine smaller boxes. each of the smaller boxes holds nine plastic containers. each plastic contai.er holds nine bags.

svp [43]

So, basically ..you just multiply
9*9*9*9
6561

4 0

2 years ago

A log splitter uses a pump with hydraulic oil to push a piston, attached to which is a chisel. The pump can generate a pressure

faust18 [17]

we are given

The pump can generate a pressure of 2.3x107 pa

so,

$p=2.3*10^7$

a radius of 0.041 m

so,

$r=0.041m$

a stroke lasting 29 s, the piston moves 0.57 m

so,

$h=0.57m$

$t=29s$

Firstly, we will find area

$A=\pi r^2$

$A=\pi (0.041)^2$

$A=0.00528$

now, we can use power formula

$P=\frac{W}{t}$

F=pA

W=Fh

so, W=pAh

we can plug it

$P=\frac{p*A*h}{t}$

now, we can plug values

$P=\frac{2.3*10^7*0.00528*0.57}{29}$

now, we can simplify it

Power=2386.92414 watt.........Answer

6 0

2 years ago

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3

butalik [34]

Answer:

The answer is below

Step-by-step explanation:

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3 miles.

a) Start by drawing a diagram of this situation. Your diagram might include a coordinate plane, the cell tower, and a circle representing the cell tower's coverage boundary.

a) A house is located 5 miles north of the center of the town and is to the east of the cell tower. If the house lies on the boundary of the cell tower's coverage, how far east of the center of the town is the house?

Answer:

Let the center of the town represent the origin (0,0). Also 1 unit = 1 mile. Since the cell tower is located 3 miles east and 4 miles north of the center of a small town, it is represented by A(3, 4)

The cell tower has a coverage of radius 3 miles. This can be represented by a circle with equation:

(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius. Hence:

(x - 3)² + (y - 4)² = 3²

(x - 3)² + (y - 4)² = 9

The diagram is drawn using geogebra.

b) The house is 5 miles north. It can be represented by y = 5 line.

To find the distance east of the house we have to substitute y = 5 and solve for x, hence:

(x - 3)² + (y - 4)² = 9

(x - 3)² + (5 - 4)² = 9

(x - 3)² + 1 = 9

(x - 3)² = 8

(x - 3) = √8

x - 3 = ±2.83

x = 3 ± 2.83

x = 5.83 or 1.83

Since it is to the east to the cell tower, hence x = 5.83.

Therefore the house is located 5.83 miles to the east of the cell tower

8 0

2 years ago

Below is a scale drawing of the town swimming pool in the drawing the longest side of the pool has length of 10 inches Paco crea

quester [9]

Answer:

2:1 that is 2 inches in real life is equal to 1 inch in the drawing.

Step-by-step explanation:

We are given the following in the question:

Longest side of the pool = 10 inches

Longest side of the pool in drawing = 5 inches

Scale:

We find the ratio of the real length of pool and the measurement of the length of the pool in the drawing.

$\text{Scale} = \dfrac{10\text{ inches}}{5\text{ inches}} = 2:1$

Thus, we can say Paco's new drawing follows a scale of 2:1 that is 2 inches in real life is equal to 1 inch in the drawing.

6 0

2 years ago

Read 2 more answers

From Statistics and Data Analysis from Elementary to Intermediate by Tamhane and Dunlop, pg 265. A thermostat used in an electri

Leviafan [203]

Answer:

$t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =2*P(t_{(9)}>2.32)=0.0455$

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Step-by-step explanation:

Information given

data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0

We can calculate the sample mean and deviation with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=201.77$ represent the sample mean

$s=2.41$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =200$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value for the test

Hypothesis to test

We want to determine if the true mean is equal to 200, the system of hypothesis are :

Null hypothesis: $\mu = 200$

Alternative hypothesis: $\mu = 200$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

The statistic is given by:

$t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =2*P(t_{(9)}>2.32)=0.0455$

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

4 0

2 years ago