Which of the following pairs of numbers has 16 as their greatest common factor?


32, 48

32, 48

32, 62

32, 62

48, 36

48, 36

42, 16

42, 16

The sin(-184) can be expressed as cos 86° as a function of a positive acute angle.

To express a trigonometry identity as a function of a positive acute angle, we need to find the quadrant in which that given identity is located.

Here, we have a negative trigonometry identity: Sin (-184)

Recall that:

So, to turn that to a positive sign, we add 360

=sin(-184 + 360)

= sin(176)

To find the positive acute angle, we have:

x = cos(176 - 90)

x = cos 86°

Therefore, we can conclude that the sin(-184) can be expressed as cos 86° as a function of a positive acute angle.

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Answer: 32

Step-by-step explanation:

f(6) = 6^2-4 = 36-4 = 32

Answer:

The are consecutive interior angles.

Answer:

[tex]\frac{8}{21}[/tex]

Step-by-step explanation:

let S be the sample space for this experiment.

card(S) = 10C4 = 210

Let E be the event “having 3 female and only one  male”

card(E) = 6C3 × 4C1 = 80

therefore

p(having 3 female and only one male escaped) is 80/210

[tex]\frac{80}{210} =\frac{8}{21}[/tex]

Answer:

12a

Step-by-step explanation:

If I'm understanding your question correctly, 3(4a), or 3 × (4a), is simply 12a.

Answer: 12a

Step-by-step explanation:

Multiply:

3(4a)

⇒3 × 4a

⇒12a Answer

hope that helps...

Sure, post the questions.

Answer:

4

Step-by-step explanation:

Mean (Average) 5

Median 4

Range 9

Mode 2, appeared 2 times

Geometric Mean 3.8971508839086

Largest 10

Smallest 1

Sum 45

Count 9

Sorted Data Set: 1, 2, 2, 3, 4, 6, 8, 9, 10

The depth of the water at the deepest point in the waterslide and to the nearest hundredth of a meter is approximately 0.19 meters. (Correct choice: A)

In this question we should apply the concepts of right triangles and trigonometric functions to determine the height of the water within the waterslide. A geometric diagram of the cross section of the waterslide is presented below, which indicates the existence of circular symmetry.

Now we proceed to determine the height of the water:

cos α = (0.5 m/0.75 m)

α ≈ 48.190°

y = (0.75 m) · sin 48.190°

y = 0.559 m

x = 0.75 m - 0.559 m

x = 0.191 m

The depth of the water at the deepest point in the waterslide and to the nearest hundredth of a meter is approximately 0.19 meters. (Correct choice: A)

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Answer:

5 : 1

Step-by-step explanation:

Unit conversion (between cm and mm) : 1 cm = 10 mm

⇒ 4 cm : 8 mm

⇒ 4 x 10 mm : 8 mm

⇒ 40 mm : 8 mm

⇒ 5 : 1

Answer:

17965.1

Step-by-step explanation:

Formula: V = 4/3 pi r^3

r = d/2

r = 32.5/2

r = 16.25

V = 4/3 * 3.14 * (16.25)^3

V = 17965.05   to the nearest tenth is

V = 17965.1  

Answer: its free

Step-by-step explanation:

Answer:

1. Binary number system only uses 2 digits: 0 and 1.

2. Octal number system uses 8 digits: 0,1,2,3,4,5,6,7 with the base of 8.

3. Decimal number system uses 10 digits: 0,1,2,3,4,5,6,7,8,9 with a base of 10.

4. Hexadecimal number system uses 16 digits and alphabets: 0,1,2,3,4,5,6,7,8,9 and A,B,C,D,E,F with the base of 16.

5. Quinary number system uses 0,1,2,3,4 with 5 as the base.

Absolute value is a number's distance from 0 on the number line.

A prime factor is a number with no factors other than one and itself.

The smallest quantity divisible by every number of the set is known as the least common multiple.

The denominator of a fraction can never be zero since a number divided by zero is not defined.

If the numerator is greater than or equal to the denominator, the fraction is called an improper fraction.

A mixed fraction is the sum of a whole number and a fraction.

To simplify a fraction is to convert it into a form which the numerator and denominator have no common factor other than one.

Step-by-step explanation:

Hope this helps :)

Answer:

1) 1.1 seconds

2) 13.5 feet

[tex]\rightarrow \sf -16t^2 + 5t + 15 = 0[/tex]

Apply quadratic formula:

[tex]\rightarrow \sf t= \dfrac{-5\pm \sqrt{5^2-4\left(-16\right)\cdot \:15}}{2\left(-16\right)}[/tex]

Simplify following

[tex]\rightarrow \sf t=-\dfrac{-5+\sqrt{985}}{32},\:t=\dfrac{5+\sqrt{985}}{32}[/tex]

In decimal form:

[tex]\rightarrow \sf t=-0.825 ,\:t=1.137[/tex]

Conclusion:

As time is be only positive: t = 1.1 seconds

[tex]\rightarrow \sf h=-16t^2 + 5t + 15[/tex]

insert t = 0.5

[tex]\rightarrow \sf h=-16(0.5)^2 + 5(0.5) + 15[/tex]

simplify

[tex]\rightarrow \sf h=13.5[/tex]

Answer:

i got 17.4km/H pretty sure im right

Answer:

y = -2x + 5

Step-by-step explanation:

Slope-intercept form: y = mx + b

The slope of the line, m, is -2 because the line shows a negative trend and moves right 1 unit every time a point moves down 2 units.

The y-intercept, b, is 5 because the line crosses that number once on the y-axis.

Answer:

c

Step-by-step explanation:

(5y - 1) = 4y + (9y - 4) = 5y

2y > .75

Answer:

C. The solution set is {y|y > 0.75}.

Step-by-step explanation:

Given :

Add 4 to each side.

Subtract 5y from each side.

Solution set

C. The solution set is {y|y > 0.75}.

Answer:

6.28 meters

Step-by-step explanation:

Circumference is the distance around the circle, given by:

C = pi•d

C = 3.14 • 2

C = 6.28 meters

Answer:

6.28 Meters

Step-by-step explanation:

2pi * r

= 2*3.14

= 6.28 Meters

We need a maximum enlargement of n = 18 terms in order to guarantee this level of accuracy for Simpon's Rule.

The estimation of Simpson's rule follows an approach where the value of the definite integral [tex]\int\limits^a_b f{x} \, dx[/tex] is approximated by using a parabolic method of approximation for each subinterval of the interval [a, b].

The formula for calculating Simpon's rule can be expressed as:

[tex]\mathbf{\int ^b_a f(x) d \simeq \dfrac{\Delta x}{3}[y_o+4y_1+2y_2+4y_3+2y_4+...+4{y_{n-1} +y_n}}[/tex]

Given that:

[tex]\mathbf{\int ^1_0 7ex^2 dx }[/tex],

We need to determine the fourth derivative; i.e.

[tex]\mathbf{f'(x) = 14xe^{x^2}}[/tex]

[tex]\mathbf{f''(x) = 14ex^2 +28x^2e^{x^2} = (14+28x^2)e^{x^2}}[/tex]

[tex]\mathbf{f'''(x) = 56xe^{x^2} +2(14+28x^2)e^{x^2} = (84x+48x^3)e^{x^2}}[/tex]

[tex]\mathbf{f^{iv}(x) = (84+144x^2)e^{x^2} +2x(84x+48x^3)e^{x^2} = (84x+312x^2+96x^4)e^{x^2}}[/tex]

The maximum value of the 4th derivative on the interval [0,1] is:

[tex]\mathbf{f^{iv}(1) = 624e}[/tex] and the error is bounded by:

[tex]\mathbf{\Bigg| \dfrac{f^{iv}(1) (1-0)^5}{180n^4} \Bigg| = \dfrac{624e}{180n^4}=\dfrac{52e}{15n^4}}[/tex]

Now for the error to be less than 0.0001; we have:

[tex]\mathbf{\dfrac{52e}{15n^4} < 0.0001}[/tex]

[tex]\mathbf{52e < 0.0015n^4}[/tex]

[tex]\mathbf{n^4 > \dfrac{52e}{0.0015}}[/tex]

[tex]\mathbf{n > \sqrt[4]{ \dfrac{52e}{0.0015}}}[/tex]

n ≅ 17.52.

Therefore, we can conclude that we need a maximum of n = 18 terms in order to guarantee this level of accuracy for Simpon's Rule.

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Answer

(12y-35)

(4yx3y-5x7)

Answer:

12y² - 43y + 35

Step-by-step explanation:

Multiply each term of the first binomial by each term of the second binomial. Then combine like terms.

(4y - 5)(3y - 7) =

= 4y × 3y + 4y × (-7) + (-5) × 3y + (-5) × (-7)

= 12y² - 28y - 15y + 35

= 12y² - 43y + 35

The range tells us the possible y-values that occur in the function.

When describing the range, we can write an inequality using y.

When describing the range of a quadratic function, we typically use the ≥ or ≤ symbols when writing the inequality.

To write the range of a quadratic function,

We're given:

Because we're directly given the vertex, we just have to determine now whether the parabola opens up or down.

The other points that fall on the graph that we're given all have a lower y-coordinate value than 4, that means this parabola opens down.

Therefore, all other y-values for the function will be less than 4.

Therefore, y ≤ 4.

y ≤ 4

Answer:

3(4x+6)=24

Step-by-step explanation:

The distribute property is when you distribute the what is inside of the parentheses.

Answer:

an example would be -5(x+9)=-5

now distribute -5 to x and -5 to9

= -5x-45= -5

Answer:So I think the answer might be 88

Answer: 85 sqm

Step-by-step explanation: So 5 litres of Retail paint will cover 65sqm- one coat, and 5 litres of Trade paint will cover 85 sqm- one coat.

The probabilities are: 20/52, 31/52, 651/2704, 14/31

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in to predict how likely events are to happen.

given: Event A is “game played when warmed up” and Event B is “more shots made than missed.”

Now, P(A)= 20/52

P(B)= 31/52

P(A and B)= P(A)*P(B)

                 = 20/52*31/52

                  = 651/2704

P(A|B)= 14/52÷31/52

        =14/31

Hence, the probability is: 20/52,31/52,651/2704 and 14/13

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Answer:

x=-2   x=-1

Step-by-step explanation:

2x^2 + 6x = -4​

Add 4 to each side

2x^2 + 6x +4= -4+4

2x^2 + 6x +4=0

Factor out 2

2( x^2 +3x+2) = 0

Divide by 2

x^2 +3x +2 =0

( x+2)(x+1) =0 ​​

Using the zero product property

x+2 =0  x+1 =0

x=-2   x=-1

Answer:

x = -1, -2

Step-by-step explanation:

Bring the constant term to the left hand side :

Divide throughout by 2 :

Splitting the middle term :

Factors obtained :

Finding the zeros :

Answer:

D' : (2, 1)

E' : (2, 3)

A' : (5, 3)

Step-by-step explanation:

Answer:

D' = (2, -3)

E' = (2, -1)

A' = (5, -3)

Step-by-step explanation:

Coordinates are :

The transformation rule is :

Point D'

Point E'

Point A'

The equation that represents the horizontal parabola given on the graph is:

y² = -8x

The equation of a quadratic function, of vertex (h,k), is given by:

x = a(y - k)² + h

In which a = 1/p is the leading coefficient.

In this problem, the vertex is (0,0), hence h = k = 0, and:

ay² = x.

The directrix is at x = 2, and the parabola opens left, hence:

p = -4(2 - 0) = -8.

Hence the equation is:

y² = px = -8x.

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Answer:

Multiplication

The solution of given equation x = -20

Step-by-step explanation:

step (i) :-

given equation = -(x/4) = 5

multiply '1' on both sides we get

[tex] = - (( - \frac{x}{4} )) = - 5[/tex]

[tex] = \frac{x}{4} = - 5[/tex]

step (ii) :-

multiply '4' on both sides we get

[tex] = \: \: \: \: \: \frac{x}{4} \: \: \times \: 4 \: \: = - 5 \times 4[/tex]

Cancellation '4' on left side we get

x = -20

conclusion:-

The solution of given equation x = -20

Using an exponential function, it is found that the loan balance b after n years is given by:

[tex]b(n) = 1000(1.12)^n[/tex]

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, we have that:

Hence the balance b after n years is given by:

[tex]b(n) = 1000(1.12)^n[/tex]

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The expression written as a product is:

[tex](-4.5)^6*(-4.5)^{-2}[/tex]

And written as a power:

[tex](-4.5)^4[/tex]

Here we need to remember the two rules:

[tex]a^n = \frac{1}{a^{-n}}[/tex]

[tex]a^n*a^m = a^{n + m}[/tex]

Using the first one, we can write the quotient as a product:

[tex]\frac{(-4.5)^6}{(-4.5)^2} = (-4.5)^6*(-4.5)^{-2}[/tex]

Now we can use the second property to write the expression as a single power, we will get:

[tex]\frac{(-4.5)^6}{(-4.5)^2} = (-4.5)^6*(-4.5)^{-2} = (-4.5)^{6 - 2} = (-4.5)^4[/tex]

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Answer:

[tex]V =288 \pi \ mm^3[/tex]

Step-by-step explanation:

[tex]V =\frac{4}{3} \pi r^{3}[/tex]

   [tex]=\frac{4}{3} \pi \left( 6\right)^{3}[/tex]

   [tex]=\left( \frac{4}{3} \right) \times \pi \times 216[/tex]

   [tex]=\left( \frac{4}{3} \right) \times 216\times \pi[/tex]

   [tex]=288\times \pi[/tex]

Answer:

IT IS B

Step-by-step explanation:

SOURCE: TRUST ME BRO