Mateo bought 4.54 pounds of Fuji apples and 3.7 pounds of Golden Delicious apples.

The diagonals of a rectangle enclose an angle of measure 78 degree

katrin2010 [14]

The area of the rectangle with a perimeter of 36 cm is determined as: 80.1 cm².

<h3>What is the Area of a Rectangle?</h3>

Area of a rectangle = (length)(width).

<h3>Given the following:</h3>

Angle of measure 78 degree enclosed by the diagonals of the rectangle

Perimeter = 36 cm

To find the area, we need to find the length and width of the rectangle using the trigonometric ratios.

A side of the rectangle = x cm

The other side = (36 - 2x)/2 = (18 - x) cm

Angle of the diagonal base = (180 - 78)/2 = 51°

Apply the tangent ratio to find x:

Tangent ratio is tan ∅ = opposite/adjacent side of a right triangle. We have the following,

∅ = 51°

Opposite side = x cm

Adjacent side = (18 - x) cm

Tan 51° = x/(18 - x)

1.235 = x/(18 - x)

1.235(18 - x) = x

22.23 - 1.235x = x

22.23 = x + 1.235x

22.23 = 2.235x

22.23/2.235 = 2.235x/2.235

x = 9.946 cm (one side length)

The other side length = 18 - x = 18 - 9.946 = 8.054 cm

Area of the rectangle = (9.946)(8.054)

Area of the rectangle = 80.1 cm²

Learn more about the area of rectangle on:

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3 0

2 years ago

Find all of the polar coordinates of point P if p=(1,-pi/6)

Mama L [17]

Answer:

The all polar coordinates of point P are (1 , -pi/6 + 2nn) and (-1, -pi/6+(2n+1)n).

Step-by-step explanation:

The polar coordinates can be written as (r,Ф)= (r,Ф+2nn) or (r,Ф) =(-r,Ф+(2n+1)n) and n is any integer value.

We are given p=(1,-pi/6)

P(r,Ф), then r = 1 and Ф = -pi/6

The polar coordinates will be

P(r,Ф)= (r,Ф+2nn) = (1 , -pi/6 + 2nn) and n is any positive integer and the value of r is positive.

P(r,Ф) =(-r,Ф+(2n+1)n) = (-1, -pi/6+(2n+1)n) and n is any positive integer and the value of r is negative.

The all polar coordinates of point P are (1 , -pi/6 + 2nn) and (-1, -pi/6+(2n+1)n)

6 0

3 years ago

Read 2 more answers

In tests of a computer component, it is found that the mean time between failures is 937 hours. A modification is made which is

VladimirAG [237]

Answer:

Null hypothesis is $\mathbf {H_o: \mu > 937}$

Alternative hypothesis is $\mathbf {H_a: \mu < 937}$

Test Statistics z = 2.65

CONCLUSION:

Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

P- value = 0.004025

Step-by-step explanation:

Given that:

Mean $\overline x$ = 960 hours

Sample size n = 36

Mean population $\mu =$ 937

Standard deviation $\sigma$ = 52

Given that the mean time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours

Null hypothesis is $\mathbf {H_o: \mu > 937}$

Alternative hypothesis is $\mathbf {H_a: \mu < 937}$

Degree of freedom = n-1

Degree of freedom = 36-1

Degree of freedom = 35

The level of significance ∝ = 0.01

SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;

from t-table t(0.99,35), the critical value = 2.438

The test statistics is :

$Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}$

$Z = \dfrac{960-937 }{\dfrac{52}{\sqrt{36}}}$

$Z = \dfrac{23}{8.66}$

Z = 2.65

The decision rule is to reject null hypothesis if test statistics is greater than critical value.

CONCLUSION:

Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

The P-value can be calculated as follows:

find P(z < - 2.65) from normal distribution tables

= 1 - P (z ≤ 2.65)

= 1 - 0.995975 (using the Excel Function: =NORMDIST(z))

= 0.004025

6 0

3 years ago

2(x-3)=5(x-3)+10<br><br><br> Need urgent help

ArbitrLikvidat [17]

Step-by-step explanation:

2(x-3)=5(x-3)+10

=> 2x - 6 = 5x - 15 + 10

=> -6 + 15 -10 = 5x - 2x

=> 5x -2x = 15 - 6 - 10

=> 3x = 15 - 16

=> 3x = -1

$= > x = \frac{ - 1}{3} (ans)$

4 0

3 years ago

What is are the numbers to P.I.E

Finger [1]

Answer:

Step-by-step explanation:

4 0

3 years ago