Simplify (1+√3) (2-√3).

Answer:

30

Step-by-step explanation:

It is an equalateral triangle

Answer:

1607.68 square miles

Step-by-step explanation:

use pi r squared

Answer:

Step-by-step explanation:

diameter = 64  miles

r =64/2 = 32 miles

Area of semicircle = πr²/2

                              = 3.14*32*32/2

                             = 1607.68 sq.miles

Answer:

(a) 0.25

(b) 0.944

(c) 0.444

(d) 0.167

Step-by-step explanation:

There are six possible outcomes for each die, which means that the number of possible outcomes is:

[tex]n=6*6 = 36[/tex]

(a) In order for each die to show four or more spots they will both have to land on a four, five or six. The probability of this happening is:

[tex]P(A) = \frac{3*3}{36}=0.25[/tex]

(b) There are only two possible outcomes for which the sum is three (1 and 2, or 2 and 1). The probability of the sum NOT being three is:

[tex]P(B) = 1-\frac{2}{36}=0.944[/tex]

(c) If neither a one or a six must appear, then there are 4 possible outcomes for each die, the probability is:

[tex]P(C) = \frac{4*4}{36}=0.444[/tex]

(d) For each one of the six possible numbers on the first die, there is only one on the second die for which the sum of the spots is 7, totaling six possible ways to sum 7:

[tex]P(D) = \frac{6}{36}=0.167[/tex]

The required probability output from a throw of two six sided dice are as follows :

The sample space for two throw of a six-sided die :

Recall :

A.) Obtaining 4 or more spots :

Required spot = (5, 6, 7) on each die = 3 × 3 = 9 outcomes

P(4 or more spot) = 9/36 = 0.25

B.) Sum of spot is not 3 :

Sum of spot = 3 ; (1, 2) and (2, 1) = 2 possible outcomes

P(sum not 3) = 1 - (2/36) = 1 - 1/8 = 17/18 = 0.944

C.) neither a one nor 6 appears :

Required = (2, 3, 4, 5) = 4 × 4 = 16

P(neither 6 nor 1) = 16/36 = 4/9 = 0.44

D.) Sum of spot equals 7

Required = (1, 6),(6,1),(5,2),(2,5),(3,4),(4,3) = 6 outcomes

P(sum equals 7) = 6/36 = 1/6 = 0.167

Learn more :https://brainly.com/question/18405415

Answer:

9/25

Step-by-step explanation:

Don't worry, I just took this test and got it correct. Best of luck to you all!

Answer:

C. F(x) = 4x² + 1

Step-by-step explanation:

→The function F(x) shifted 1 unit upwards, meaning there needs to be a 1 being added to the function.

→In addition, the function F(x) has grown narrower, compared to the function G(x). This is from the absolute value of a number being greater than 1, which is being multiplied.

This means the correct answer should be "C. F(x) = 4x² + 1."

Answer:

Step-by-step explanation:

For the null hypothesis,

H0 : p = 0.63

For the alternative hypothesis,

Ha : p < 0.63

This is a left tailed test

Considering the population proportion, probability of success, p = 0.63

q = probability of failure = 1 - p

q = 1 - 0.63 = 0.37

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 478

n = number of samples = 800

P = 478/800 = 0.6

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76

From the normal distribution table, the area below the test z score in the left tail 0.039

Thus

p = 0.039

Answer:

-3.66

Step-by-step explanation:

Answer:

€113.67

Step-by-step explanation:

£3 = €4

£85.40 is €x

Cross multiply.

[tex]4 \times 85.4=3x[/tex]

[tex]3x=341.6[/tex]

[tex]\frac{3x}{3}=\frac{341.6}{3}[/tex]

[tex]x=113.86666...[/tex]

Answer:

Step-by-step explanation:

Answer:

S = ⅙ π (65^³/₂ − 5^³/₂)

Step-by-step explanation:

z = x² + y², 1 < z < 4

Surface area is:

S = ∫∫√(1 + (fₓ)² + (fᵧ)²) dA

where fₓ and fᵧ are the partial derivatives of f(x,y) with respect to x and y, respectively.

fₓ = 2x, fᵧ = 2y

S = ∫∫√(1 + (2x)² + (2y)²) dA

S = ∫∫√(1 + 4x² + 4y²) dA

For ease, convert to polar coordinates.

S = ∫∫√(1 + 4r²) dA

S = ∫∫√(1 + 4r²) r dr dθ

At z = 1, r = 1.  At z = 4, r = 4.

So 1 < r < 4, and 0 < θ < 2π.  These are the limits of the integral.

S = ∫₀²ᵖⁱ∫₁⁴√(1 + 4r²) r dr dθ

To integrate, use u-substitution.

u = 1 + 4r²

du = 8r dr

⅛ du = r dr

When r = 1, u = 5.  When r = 4, u = 65.

S = ∫₀²ᵖⁱ∫₅⁶⁵√u (⅛ du) dθ

S = ∫₀²ᵖⁱ (⅛ ∫₅⁶⁵√u du) dθ

S = ∫₀²ᵖⁱ (¹/₁₂ u^³/₂ |₅⁶⁵) dθ

S = ∫₀²ᵖⁱ (¹/₁₂ (65^³/₂ − 5^³/₂)) dθ

S = (¹/₁₂ (65^³/₂ − 5^³/₂)) θ |₀²ᵖⁱ

S = (¹/₁₂ (65^³/₂ − 5^³/₂)) (2π)

S = ⅙ π (65^³/₂ − 5^³/₂)

Answer:

The height of the ball is at it's maximum 1.5 units of time after launch.

Step-by-step explanation:

Suppose we have a quadratic function in the following format:

[tex]h(t) = at^{2} + bt + c[/tex]

If t is negative, the maximu value of h(t) will happen at the point

[tex]t_{MAX} = -\frac{b}{2a}[/tex]

In this question:

[tex]h(t) = -25t^{2} + 75t + 24[/tex]

So

[tex]a = -25, b = 75, c = 24[/tex]

Then

[tex]t_{MAX} = -\frac{b}{2a} = -\frac{75}{2*(-25)} = 1.5[/tex]

The height of the ball is at it's maximum 1.5 units of time after launch.

Answer:

The value of x^3 + 1/x^3 is 47/x + 1/x^3 - 1/x^5

Step-by-step explanation:

x^4 + 1/x^4 = 47

x^4 = 47 - 1/x^4

x^3 + 1/x^3 = 1/x(x^4 + 1/x^2)

x^4 = 47 - 1/x^4

x^3 + 1/x^3 = 1/x(47 - 1/x^4 + 1/x^2) = 47/x - 1/x^5 + 1/x^3 = 47/x + 1/x^3 - 1/x^5

Answer:

Part a

For this case n = 4. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506[/tex]

Part b

For this case n = 365. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776[/tex]

Step-by-step explanation:

We can use the future vaue formula for compound interest given by:

[tex] A= P(1+ \frac{r}{n})^{nt}[/tex]

Where P represent the present value, r=0.0675 , n is the number of times that the interest is compounded in a year and t the number of years.

Part a

For this case n = 4. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506[/tex]

Part b

For this case n = 365. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776[/tex]

Answer:

A.

Step-by-step explanation:

In the attached file

Answer:

473 feet.

Step-by-step explanation:

Let's look at the image below. We have that the angle of elevation from Justin parking spot is 11º and the height of the building is 92 feet and we need to know how far from the building is Justin parked, in other words, we need to find x in the image.

We can see that to find x we can use a trigonometric function (in this case is tan since we have the Opposite side (92 feet) and we need the Adjacent side (x)

Thus we have:

[tex]Tan11= \frac{92}{x} \\0.1943=\frac{92}{x}\\ x=\frac{92}{0.1943}\\ x=473.49\\x=473[/tex]

Thus, Justin is parked 473 feet away from the center court.

Answer:

Step-by-step explanation:

2 3x6

the 3 is an exponet so supost to be smaller

the answer-  2^3 x^6

i think its right

Answer:

14.2% students

Step-by-step explanation:

279 / 1960 = 0.142

0.142 x 100% = 14.2 %

Answer:

1.46666 miles / minutes

88 miles per hour

Step-by-step explanation:

The speed is distance over time

44 miles / 30 minutes

1.46666 miles / minutes

or if we want in miles per hour

44 miles / .5 hours

88 miles per hour

Answer:

1.467 mile/minute

Step-by-step explanation:

you should divide the distance on the time i.e. 44/30

Answer: 600 of the 500ml energy drinks be sold be sold at $45

Step-by-step explanation:

The linear relationship between the price (p) of 500ml soft drink and the number sold (x) is expressed as

x = ap + b

At N$20 she sells 1500 of the 500ml soft drinks. This means that the first equation would be

1500 = 20a + b - - - - - - - - -1

the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. This means that the new quantity sold is 1500 - 200 = 1300

The price at which they were sold is

20 + (50/100 × 20) = $30

The second equation would be

1300 = 30a + b - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

200 = - 10a

a = 200/- 10 = - 20

Substituting a = - 20 into equation 2, it becomes

1300 = 10 × - 20 + b

1300 = - 200 + b

b = 1300 + 200 = 1500

The linear relationship becomes

x = - 20p + 1500

If x = 600, then

600 = - 20p + 1500

- 20p = 600 - 1500 = - 900

p = - 900/ - 20

p = $45

Answer:

2

Step-by-step explanation:

-13+3b=-5-b

4b=8

b=2

Answer:

11 y 23

Step-by-step explanation:

Nombrando los números como [tex]x[/tex] y [tex]y[/tex],

Planteamos las siguientes ecuaciones:

[tex]xy=253[/tex] (el producto de los numeros es 253)

[tex]x=2y+1[/tex] (uno de los enteros debe ser uno más que el doble del otro).

Sustituimos la segunda ecuación en la primera:

[tex](2y+1)(y)=253[/tex]

resolvemos para encontrar y:

[tex]2y^2+y=253\\2y^2+y-253=0[/tex]

usando la formula general para resolver la ecuación cuadrática:

[tex]y=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

donde

[tex]a=2,b=1,c=-253[/tex]

Sustituyendo los valores:

[tex]y=\frac{-1+-\sqrt{1-4(2)(-253)} }{2(2)} \\\\y=\frac{-1+-\sqrt{2025} }{4}\\ \\y=\frac{-1+-45}{4} \\[/tex]

usando el signo mas obtenemos que y es:

[tex]y=\frac{-1+45}{4} \\y=\frac{44}{4}\\ y=11[/tex]

(no usamos el signo menos, debido a que obtendriamos fracciones y buscamos numeros enteros)

con este valor de y, podemos encontrar x usando:

[tex]x=2y+1[/tex]

sustituimos [tex]y=11[/tex]

[tex]x=2(11)+1\\x=22+1\\x=23[/tex]

y comprobamos que el producto sea 253:

[tex]xy=253[/tex]

[tex](23)(11)=253[/tex]

Answer:

5

Step-by-step explanation:

We have x-2 = 5

x-2 = 5 we separate parenthesis.

x(-2) = 5(+2)

x = 7

We can check this as what the x-2 is saying is  7-2 = 5

Answer:

Since it is an equilateral triangle,

Perimeter = 3s = 3 x side

=> 15 = 3 X (x - 2)

=> 15 = 3(x - 2)

=> 15 = 3x - 6

=> 3x = 15 + 6

=> 3x = 21

=> x = 21/3

=> x = 7

When x = 7,

=> Side = 7 - 2 = 5 inches

Since, it is an equilateral triangle all sides are of 5 inches each.

Answer:

Car: 60%

Motorcycle: 30%

Truck: 10%

Step-by-step explanation:

Car: [tex]\frac{12}{12+6+2} =\frac{12}{20} =\frac{60}{100}[/tex] or 60%

Motorcycle: [tex]\frac{6}{12+6+2} =\frac{6}{20} =\frac{30}{100}[/tex] or 30%

Truck: [tex]\frac{2}{12+6+2} =\frac{2}{20} =\frac{10}{100}[/tex] or 10%

Answer:

Top prism = 262 in.² Bottom prism = 478 in.²

Step-by-step explanation:

top prism:

front + back: 5 x 3 = 15

sides: 19 x 4 x 2 = 152

bottom: 19 x 5 = 95

15 + 152 + 95 = 262

bottom prism:

front + back: 5 x 6 x 2 = 60

sides: 19 x 6 x 2 = 228

top + bottom: 19 x 5 x 2 = 190

60 + 228 + 190 = 478

Answer:

B. F(x) = 3(x - 2)² - 2

Step-by-step explanation:

→The function F(x) narrowed, meaning the absolute value being multiplied to the function is greater than 1.

→The function F(x) flipped over the x-axis, this means that the number being multiplied has to be a negative.

→The function F(x) shifted to the left 2 units, this means there needs to be a 2 being added.

→The function F(x) shifted downwards 2 units, meaning there needs to be a 2 being subtracted from the whole function.

This gives us the correct answer of "B. F(x) = 3(x - 2)² - 2."

Answer:

3¹²

Step-by-step explanation:

Move 3⁻² to the numerator using the negative exponent rule

1/b-n = bⁿ

(3⁵)² ⋅ 3²

Multiply the exponents

3¹⁰ · 3²

Multiply by adding the exponents

3¹⁰⋅ 3²

3¹²

Answer:

£2.70 fig rolls and £5.72 crisps

Step-by-step explanation:

£1.08+0.54+£1.08= £2.70 fig rolls

£1.43+£1.43+£1.43-£1.43= £2.86 x 2= £5.72 for 6 packets of crisps

£2.70+ £5.72= £8.42

Answer:

Board Games: 30%

Karaoke: 50%

Bowling: 20%

Step-by-step explanation:

Board Games: [tex]\frac{3}{3+5+2} =\frac{3}{10} =\frac{30}{100}[/tex] or 30%

Karaoke: [tex]\frac{5}{3+5+2} =\frac{5}{10} =\frac{50}{100}[/tex] or 50%

Bowling: [tex]\frac{2}{3+5+2} =\frac{2}{10} =\frac{20}{100}[/tex] or 20%

Answer:

Board Games: 30%

Karaoke: 50%

Bowling: 20%

Step-by-step explanation:

3 + 5 + 2 = 10 so there are 10 family members.

3 out of 10 equals 30%

5 out of 10 equals 50%

2 out of 10 equals 20%

Please mark Brainliest if correct

Hope this helps!

Answer:

d: please note I am not sure about this but look at my reasoning and maybe you can find your own answer that you are sure about.

D: i am sure about this.

Step-by-step explanation:

From what I looked up, i believe what you are talking about is deductive reasoning, which is based off of facts. It can't be a or b because that wasn't defined in the statement. Squares and rectangles are not the same thing since you can have a square that is a rectangle, but a rectangle that is not a square, so D is correct.

corresponding angles i believe since they are matching

I know that the 2 lines are parallel because 5 and 6 are alternate interior angles since they are on opposite sides.

4 and 6 are not vertical or right angles, so it must be d, also they follow what a corresponding angle is, which is them being matching.

Answer:

13. B

14. D

Step-by-step explanation:

13. Law of Detachment says that if two statements are true then we can derive a third true statement. So, for example, say the first statement is that you are a human. Say the second statement is that you breathe. You can write this as: if you are a human, you breathe. In this case, if you have a square, then you have a rectangle. You have a quadrilateral.

14. 4 and 6 are corresponding angles, since you can tell that there are two parallel lines from angle 5 = angle 6. You can also use angle addition theorem.