Find the surface area of the cube.

Finding the p-value of the test using the z-distribution, as we are working with a proportion, it is found that this was a significant difference for levels of significance of 0.02 and lower.

At the null hypothesis, we test if the proportion is of 50.3%, hence:

[tex]H_0: p = 0.503[/tex]

We have a two-tailed test, hence at the alternative hypothesis we test if the proportion is different, that is:

[tex]H_1: p \neq 0.503[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In this problem, the parameters are:

[tex]n = 300, \overline{p} = \frac{171}{300} = 0.57, p = 0.503[/tex]

Hence:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.57 - 0.503}{\sqrt{\frac{0.503(0.497)}{300}}}[/tex]

[tex]z = 2.32[/tex]

Considering a two-tailed test, using a z-distribution calculator, the p-value is of 0.0203. Hence this was a significant difference for levels of significance of 0.02 and lower.

More can be learned about the z-distribution at https://brainly.com/question/26454209

Answer:

Step-by-step explanation:

focus (1 , -7)  ⇒ a = 1  & b = -7

y = 1 ⇒ c = 1

Equation of parabola :

(x - a)² + (y - b)² = (y - c)²

(X - 1)² + (y + 7)² = (y - 1)²

Now, expand.

x² - 2x + 1 + y² + 2*7*y + 7² = y² - 2*y*1 + 1

x² - 2x + 1 + y² - 14y + 49 = y² - 2y +1

x² - 2x + 1 + y² - 14y +  49  - y² + 2y - 1 = 0

x² - 2x  + y² - y²   - 14y + 2y   + 1 + 49 - 1 = 0

x² - 2x  - 12y + 49 = 0

Answer:

1/2

Step-by-step explanation:

The scale factor is 1/2 because each side length of [tex]\triangle{A'B'C'}[/tex] is 1/2 of the length of the side lengths of [tex]\triangle{ABC}[/tex].

Hope this helps :)

Answer:

1/2

Step-by-step explanation:

took the test

Answer:

height of tree is 80 feet.

Step-by-step explanation:

Given:-

To find :-

Solution:-

In the given figure we can see that AB is perpendicular , BC is base and AC is hypotenuse.

We know ,

tan 58° = AB/BC

1.6 = AB/50 feet

(Cross Multiplication)

80 feet :- AB

Note:- Figure is in attachment and is a rough work.

I'll do the first three questions to get you started.

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

Question 1

x = horizontal component of the triangle

cos(angle) = adjacent/hypotenuse

cos(theta) = horizontal/hypotenuse

cos(40) = x/30

x = 30*cos(40)

x = 22.98133329 approximately

This is the horizontal force applies to the suitcase.

Work = force*displacement

Work =  22.98133329*120

Work = 2,757.7599948

Work = 2,758

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Question 2

Add the drone's relative air velocity and the wind velocity vectors.

v+w = (13i + 3j) + (-7i - 2j)

v+w = (13i-7i) + (3j-2j)

v+w = 6i + j

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

Question 3

Check out the diagram below. Focus on the smaller triangle. Notice the placement of angle theta.

sin(theta) = opposite/hypotenuse

sin(40) = x/200

x = 200*sin(40)

x = 128.557521937308

x = 128.558

[tex]a)\\\\(x+2)(x+5)\\\\=x(x+5) + 2(x+5)\\\\=x^2+5x+2x+10\\\\=x^2+7x+10\\\\\\b)\\\\(x+2)(x-3)\\\\=x(x-3)+2(x-3)\\\\=x^2-3x+2x-6\\\\=x^2-x-6[/tex]

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

1a) (x + 2)(x + 5)

⇒ (x × x) + (5 × x) + (2 × x) + (2 × 5)

⇒ (x²) + (5x) + (2x) + (10)

⇒ (x²) + (5 + 2)x + (10)

⇒ (x²) + (7)x + (10)

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

1b) (x + 2)(x - 3)

⇒ (x × x) + (-3 × x) + (2 × x) + (2 × -3)

⇒ (x²) + (-3x) + (2x) + (-6)

⇒ (x²) + (-3 + 2)x + (-6)

⇒ x² + (-1)x - 6 = x² - x - 6

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

Answer:

the quotient of 18 and 3 is 6

Step-by-step explanation:

do the inverse and get 6x3=18

Volume of the cone = 1/3 x base area x height

so

V = 1/3 x pi x r² x h = 1/3 x pi x 2² x 6 = 8 x pi

Answer:

2.25 tablespoons of oregano

Step-by-step explanation:

as Diego use 3x more than Tracy, and you know that Tracy use 0.75 tablespoon, so 0.75 x 3 and you will get 2.25

[tex]18 = 2\times 3 \times 3\\\\30 = 2 \times 3 \times 5\\\\\text{HCF}~ = 2\times 3 = 6[/tex]

Answer:

4-1.5 or 21/5 or 4.2

Step-by-step explanation:

Multiple: 7 * 3/5 = 7 · 3/1 · 5 = 21/5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(21, 5) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seven multiplied by three fifths = twenty-one fifths.

Answer:

  6x² -36x +48

Step-by-step explanation:

The terms in one factor are each multiplied by the terms in the other factor. The resulting partial products are then combined. (This works the same as for numerical "long" multiplication.)

  (2x -8)(3x -6) = 2x(3x -6) -8(3x -6)

  = 6x² -12x -24x +48 . . . . . . . form partial products

  = 6x² -36x +48 . . . . . . . collect terms

Answer:

6x² - 36x + 48

Step-by-step explanation:

(2x-8)*(3x-6) = 2x*3x + 2x* -6 + -8*3x + -8*-6

6x² - 12x - 24x + 48

6x² - 36x + 48 [Answer]

PLEASE RATE!! I hope this helps!!

if you have any questions comment below!!

(I have verified my answer using an online calculator)

Using the permutation formula, it is found that it's number as a ratio of factorials is given by:

[tex]N = \frac{9!}{4!}[/tex]

The order in which the letters are chosen is important, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, five letters will be chosen from a set of nine, hence:

[tex]N = P_{(9,5)} = \frac{9!}{(9-5)!} = \frac{9!}{4!}[/tex]

More can be learned about the permutation formula at https://brainly.com/question/25925367

The cost of the mortgage is $81250

Interests are percentages of a principal

Given the following parameters

Principal = $65000

Rate = 7% = 0.07
Time = 5 years

I = PRT/100
I = 65000*0.07*25
I = 16,250

Cost of mortgage = Principal + Interest

Cost of mortgage = 65000 + 16250
Cost of mortgage = 81,250

Hence the cost of the mortgage is $81250

Learn more on mortgage here: https://brainly.com/question/22846480

Answer:

$72,823

Step-by-step explanation:

just took test

Total left

Answer:

[tex]4\:\dfrac{2}{4}[/tex]

Step-by-step explanation:

Add the amounts of each pie left :

[tex]2 \frac{1}{4}+\dfrac{2}{4}+1 \frac{3}{4}[/tex]

Separate the whole numbers and the fractions:

[tex]\implies 2+ \dfrac{1}{4}+\dfrac{2}{4}+1+\dfrac{3}{4}[/tex]

Add the whole numbers and fractions separately:

[tex]\implies 2+1+\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}[/tex]

[tex]\implies 3+\dfrac{6}{4}[/tex]

Convert 6/4 into a mixed number:

[tex]\implies 3+1\frac{2}{4}[/tex]

Add the whole numbers:

[tex]\implies 4\frac{2}{4}[/tex]

For a monthly sales figures at 5600 and expected to fall for the following 9 months at a rate of 2% each month, the  total sales for the next two years  is mathematically given as

A=11968.04

Generally,  the  total sales  is mathematically given as

A=5600(1-2/100)^9(1+4/100)^24

A=5600(.98)^9(1.04)^24

A=11968.04

In conclusion, total sales for the next two years

A=11968.04

Read more about Arithmetic

https://brainly.com/question/22568180

Check by using sum of angles of triangle = 180°

Answer:

Step-by-step explanation:

Let a = tan⁻¹(x), so tan(a) = x,

[tex]\sin(a)=\frac{x}{\sqrt{1+x^2}}, \cos(a)=\frac{1}{\sqrt{1+x^2}},[/tex]

Let b = tan⁻¹(y), so tan(b) = y,

[tex]\sin(b)=\frac{y}{\sqrt{1+y^2}}, \cos(b)=\frac{1}{\sqrt{1+y^2}},[/tex]

sin( tan⁻¹(x) +  tan⁻¹(y)) = sin(a + b)

= sin(a) cos(b) + cos(a)sin(b)

= [tex]\frac{x}{\sqrt{1+x^2}}\times\frac{1}{\sqrt{1+y^2}}+ \frac{y}{\sqrt{1+y^2}}\times\frac{1}{\sqrt{1+x^2}}[/tex]

[tex]=\frac{x+y}{\sqrt{(1+x^2)(1+y^2)}}[/tex]

Answer:

x =10

Step-by-step explanation:

30:12 is a 2.5 ratio so the smaller one is 2.5x smaller so 25/x = 2.5 or 25/2.5 = x = 10

Answer:

If two numbers have the same exponent for 10, then compare the decimal numbers to determine the greater number. Sometimes you may have to compare two numbers, but only one of them is in scientific notation. In that case, convert the number that is not in scientific notation into scientific notation first. Then, compare the two numbers. Example 1 : Compare 5.62 x 10 6 and 7.39 x 10 5.

Step-by-step explanation:

The general form in scientific notation is

where z is integer

So while comaparing

We usually compare z.z rounded to similar significant numbers .

In rest case

Example

First one is bigger

Answer:

4 ÷ 1,000 = 0.004

Rounding up to 0 as the nearest whole number

Answer: 3 11/12

Step-by-step explanation:

1 1/3 * 2 = 2 2/3

5/8 * 2 = 1 1/4

2 2/3 + 1 1/4 = 3 11/12

Answer:

yw

Step-by-step explanation:

makin a chart :)

Answer:

Hope the picture will help you

[tex]f(x,y)=x^2+y^3\implies \left.\cfrac{}{} 2x+3y^2 \right]_{\stackrel{\textit{\small x=2}}{\textit{\small y=1}}}\implies 2(2)+3(1)^2\implies 7[/tex]

Answer:

I believe your answer is A

Step-by-step explanation:

Rise is over run, the run (x) is increasing by five but, the rise (y) is decreasing by 8 so the answer would be -8/5

Hope this helps! :)

Answer:

8.439

Step-by-step explanation:

Since the marathon is divided on 5 EQUAL sections, and it is 42.195 km long, you only need to divide the length of the marathon by 5.

Answer:

288 ft³

Step-by-step explanation:

The formula to find the volume of a rectangular prism is :

Volume = length × width × height

Let us find it now.

Volume = 4 ft × 12 ft × 6 ft

Volume = 48 ft² × 6 ft

Volume = 288 ft³

Answer:

√89

Step-by-step explanation:

Plug into Distance formula --> √(0-8)^2 + (-3-2)^2

---> √89