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Answer:

Option C.

Step-by-step explanation:

We know that for two vectors:

A = 〈a₁, a₂, a₃ 〉and  B =〈b₁, b₂, b₃〉.

The dot product between A and B is:

A.B = IAI*IBI*cos(θ)

Where θ is the angle between the vectors.

And the dot product can be also written as:

A.B = a₁*b₁ + a₂*b₂ + a₃*b₃

With that, we can find the angle between our vectors.

In this case, the vectors are:

A = 〈6, –3, 1〉 and B = 〈8, 9, –11〉

The modules are:

IAI = √( 6^2 + (-3)^2 + 1^2) = 6.78

IBI = √( 8^2 + 9^2 + (-11)^2) = 16.31

And the dot product between A and B is:

A.B = 6*8 + (-3)*9 + 1*(-11) = 10

Then we have that:

10 = IAI*IBI*cos(θ) = ( 6.78)*(16.31)*cos(θ)

10/(6.78*16.31) = cos(θ)

Now remember the inverse cosine function, Acos(x), this function has the property:

Acos(cos(x)) = x

If we apply this to both sides, we get:

Acos(10/(6.78*16.31)) = Acos(cos(θ)) = θ = 84.8°

The correct option is C.

Answer:

they would continue to make a profit because the decrease in price is 5%

Step-by-step explanation:

Answer:

[tex]Area = 12004[/tex] square inches

Step-by-step explanation:

Given

[tex]q = 110[/tex]

[tex]o = 970[/tex]

[tex]\angle P =167[/tex]

Required

The area of the triangle

To do this, we use:

[tex]Area = \frac{1}{2} * o * q * sin(P)[/tex]

So, we have:

[tex]Area = \frac{1}{2} * 970 * 110 * sin(167^\circ)[/tex]

[tex]Area = \frac{1}{2} * 970 * 110 * 0.2250[/tex]

[tex]Area = 12003.75[/tex]

Approximate

[tex]Area = 12004[/tex]

Answer:

12001

Step-by-step explanation:

Answer:

[tex]\frac{2x^5+6x^3+12x}{2x} = x^3+3x^2+6[/tex]

Step-by-step explanation:

Answer:

∠ QST = 68°

Step-by-step explanation:

∠ QST + ∠ RSQ = ∠ RST , that is

∠ QST + 64° = 132° ( subtract 64° from both sides )

∠ QST = 68°

Answer:

[tex]X=24.1decibels[/tex]

Step-by-step explanation:

From the question we are told that:

Loudness function [tex]L= 10 log_{10} R[/tex]

Sound of a person [tex]S_p=80\ decibels\ or 10^8[/tex]

Number of persons talking [tex]n=20 people[/tex]

Generally the Relative intensity for 20 people is mathematically given by

Relative intensity for[tex]R_{20}=[/tex][tex]20*10^8[/tex]

Relative intensity for[tex]R_{20}=[/tex][tex]20^8[/tex]

Generally the loudness for 20 people is mathematically given by

[tex]L_{20}= 10 log_{10} R[/tex]

[tex]L_{20}= 10 log_{10} 20^8[/tex]

[tex]L_{20}= 10 (8 log_{10} 20)[/tex]

[tex]L_{20}= 104.1 decibels[/tex]

Therefore increase in loudness X is given as

[tex]X=104.1-80=-52.90[/tex]

[tex]X=24.1decibels[/tex]

Answer:

y=mx-c

Step-by-step explanation:

follow to explain

Answer:

6 poinnts per question

Step-by-step explanation:

Answer:

x = the number of points for each question

6 = number of questions

36 = total number of points

number of questions times the number of points will equal total points

6x = 36

divide both sides by 6

6x/6 = 36/6

x= 6

Step-by-step explanation:

Answer:

The rocket will hit the floor at 9.57 seconds

Step-by-step explanation:

Given

[tex]G(x) = -16x^2 + 150x + 30[/tex]

Take off height = 30ft

Initial velocity= 150ft/s

Required [Missing from the question]

Time to hit the ground

The rocket will hit the ground at:

[tex]G(x) = 0[/tex]

So, we have:

[tex]0 = -16x^2 + 150x + 30[/tex]

Rewrite as:

[tex]16x^2 - 150x - 30=0[/tex]

Solve using quadratic formula, we have:

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

Where:

[tex]a= 16\\ b = -150\\ c = -30[/tex]

So, we have:

[tex]x = \frac{-(-150) \± \sqrt{(-150)^2 - 4*16*(-30)}}{2*16}[/tex]

[tex]x = \frac{150 \± \sqrt{22500 +1920}}{32}[/tex]

[tex]x = \frac{150 \± \sqrt{24420}}{32}[/tex]

[tex]x = \frac{150 \± 156.27}{32}[/tex]

Split:

[tex]x = \frac{150 + 156.27}{32}\ or\ \frac{150 - 156.27}{32}[/tex]

[tex]x = \frac{306.27}{32}\ or\ \frac{-6.27}{32}[/tex]

Time cannot be negative;

So:

[tex]x = \frac{306.27}{32}[/tex]

[tex]x = 9.57[/tex]

Hence, the rocket will hit the floor at 9.57 seconds

Answer:

Step-by-step explanation:

Suppose a sample of 879 new car buyers is drawn. Of those sampled, 210 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Answer:

[tex]x^{3}[/tex]

Step-by-step explanation:

Answer:

[tex]\boxed {\boxed {\sf m= \frac {-1}{2}}}[/tex]

Step-by-step explanation:

Slope is equal to the change in y over the change in x.

[tex]m= \frac {y_2-y_1}{x_2-x_1}[/tex]

where (x₁, y₁) and (x₂, y₂) are the points the line passes through. We are given the points (-6, 1) and (4, -4). Therefore, if we match the values in the points to the corresponding variables:

Substitute the values into the formula.

[tex]m= \frac {-4-1}{4--6}[/tex]

Solve the numerator.

[tex]m= \frac {-5}{4--6}[/tex]

Solve the denominator.

[tex]m= \frac{-5}{10}[/tex]

Simplify the fraction. Both the numerator and denominator are divisible by 5.

[tex]m= \frac {-5/5}{10/5}[/tex]

[tex]m= \frac{-1}{2}[/tex]

The slope of the line is -1/2

Answer:

5 & 6

Step-by-step explanation:

The nearest two perfect squares are √25 and √36 which are 5 and 6

759.3 when rounded

8 is the hundredth, since it's more than 5, you'll have to make 2 a 3

Answer:

are you looking for the substiution

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

this is because it does not follow the pythogras theorem which states that a^2+b^2=c^2

Answer:

360 × 3 ÷ 8 = 135

360 - 135 = 225

Answer:

32n

Step-by-step explanation:

Product means to multiple

So “product of a number” is something times a variable, in this case I used “n” to represent “number” but you don’t have to use “n” if you don’t want to, you could other letters to represent the “number”. The “number” is unknown so that way it is a variable.

The “and 32” is what the “number” is multiple to, so the answer would be: 32n

Answer: y = 4/5 - 6.2

y = mx + b

first get the 2 points and plug it in to the equation

y - y1 = m (x -x1)

y - 3 = 4/5 (x - 4)

y - 3 = 4/5x - 3.2

add 3 on both sides

y = 4/5 - 6.2

Step-by-step explanation:

Answer:

C. 60 blue marbles

Step-by-step explanation:

10 marbles are taken out of the bag.                                    

6 marbles taken out are red.

So the other 4 marbles taken out are blue.

200 ÷ 4 = 50

and 50 is close to 60.

Let me know if this helps!

Answer:

Mode = 8, Range = 7

Step-by-step explanation:

The majority of the plots fall in 8 misses.

Maximum minus minimum equals the range. So 9 - 2 = 7

Answer: [tex]810m^{2}[/tex]

Step-by-step explanation:

First, we divide the composite figure into two distinct geometric shapes. This would be a triangle and a square. To find the triangle we use the formula:

A = 1/2bh

To find the base of the triangle we can add:

9 + 9 + 18 = 36

Now we plug in and solve:

A = 1/2bh

A = 1/2(36)(27)

= 1/2(972)

= 486

To find the square, we can use length x width:

18×18 = 324

Now, we add the sums together:

486 + 324 = 810

Answer:

8/17

Step-by-step explanation:

Answer:

a) $6,875

Step-by-step explanation:

S.I. = P×R×T/100

= 55,000 × 2.5 × 5/100

= 687500/100

= $6,875

Answer:

There are 35 students in the class

Step-by-step explanation:

We would divide 21 by 60%

21/0.6 = 35 students.

Answer:

35 students are in the class

Step-by-step explanation:

21/x 60/100

cross multiply so you will get

2100 = 60x

divide each side by 60x

2100/60 = 35

21 students out of 35