What is the range of y = sin(x)?

A)-1≤ y ≤1

B)-2π≤y≤2

C)-0.5≤ y ≤0.5

Answer:

Given function:

[tex]q(x)=9x^2-24x+16[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],  find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]ac=9 \cdot 16=144[/tex]

Two numbers that multiply to 144 and sum to -24 are: -12 and -12

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies q(x)=9x^2-12x-12x+16[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies q(x)=3x(3x-4)-4(3x-4)[/tex]

Factor out the common term [tex](3x-4)[/tex]:

[tex]\implies q(x)=(3x-4)(3x-4)[/tex]

Therefore:

[tex]\implies q(x)=(3x-4)^2[/tex]

The probability for event F or C is 0.80, or the value of the P(F or C) is 0.80 option (D) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The question is incomplete.

The complete question is:

Insurance company executives surveyed 200 young adults about their first motor vehicle. The results of the survey are given in the following two-way table(please refer to the attached picture)

A survey participant is randomly selected. Let F be the event that the participant’s first motor vehicle had four cylinders and let C be the event that the participant’s first motor vehicle was a car. What is the value of P(F or C)?

We have to find the value of P(F or C):

[tex]\rm P( F \ or \ C) = \dfrac{118+6+18+16+2}{118+6+18+16+12+20+2+6+2}[/tex]

[tex]\rm P( F \ or \ C) = \dfrac{160}{200}[/tex]

P(F or C) = 0.80

Thus, the probability for event F or C is 0.80, or the value of the P(F or C) is 0.80 option (D) is correct.

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The unit rate of change of y with respect to x is less in the graph

The attached graph represents the missing information in the question

The graph passes through the following points

(0,0) and (5,1)

The rate of change of the graph is then calculated as:

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

This gives

[tex]m = \frac{1-0}{5-0}[/tex]

Evaluate

m = 0.2

The equation is given as:

y = 6.5x

The slope of the above equation is 6.5

By comparison, 6.5 is greater than 0.2

Hence, the unit rate of change of y with respect to x is less in the graph

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Answer:

The equation

Step-by-step explanation:

i did it on khan academy

The second data set represents the boxplot because in the box plot the measure of statistics is the same as the data set option second is correct.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

We have given a data set and a box plot shown in the picture.

From the boxplot we can see:

Minimum value = 2

Q1 = (2+4)/2 = 3

Median = (4+6)/2 = 5

Q3 = (8+10)/2 = 9

Maximum value = 10

The second data set:

{2, 3, 3, 4, 5, 5, 8, 10, 10}

Minimum value = 2

Q1 = (2+4)/2 = 3

Median = (4+6)/2 = 5

Q3 = (8+10)/2 = 9

Maximum value = 10

Thus, the second data set represents the boxplot because in the box plot the measure of statistics is the same as the data set option second is correct.

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Answer:

  d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))

Step-by-step explanation:

The Law of Sines tells us that sides of a triangle are proportional to the sine of the opposite angle. This can be used along with a trig identity to demonstrate the required relation.

__

The law of sines applied to the top triangle is ...

  BC/sin(A) = AC/sin(θ)

Triangle ABC is isosceles, so the base angles at B and C are congruent. Then the angle at vertex A is ...

  ∠A = 180° -θ -θ = 180° -2θ

A trig identity tells us the sine of an angle is equal to the sine of its supplement. That means the sine of angle A is ...

  sin(A) = sin(180° -2θ) = sin(2θ)

and our above Law of Sines equation tells us ...

  BC = sin(A)/sin(θ)·AC = k·sin(2θ)/sin(θ)

__

The law of sines applied to the bottom triangle is ...

  DC/sin(B) = BC/sin(D)

  d/sin(α) = BC/sin(β)

Multiplying by sin(α) we have ...

  d = BC·sin(α)/sin(β)

__

Using our expression for BC gives the desired relation:

  d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))

Answer:

14.3%

Step-by-step explanation:

5 students got an A out of 35 total students. This means that the probability of students getting an A is 5/35 = 0.1428

Answer:

36 feet

Step-by-step explanation:

1 yard 3 feet

Answer:

By using the formulas of circle and geometry, we find that ∠CED = 65°.

Step-by-step explanation:

We know that the measure of the interior angle is the half sum of the arcs comprising it and its opposite, so

∠CED = 0.5 × (arc AB + arc CD)

See the attached figure with letters to better understand the problem

arc AB = 82° (by central angle)

arc CD = 48° (by central angle)

Substitute the values in the formula above

∠CED = 0.5 × (82° + 48°)

∠CED = 0.5 × 130°

∠CED = 65°

Therefore the answer is ∠CED = 65°

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Answer:

58 cm

Step-by-step explanation:

if both shapes are squares, then the perimeter must be divide by all 4 equal sides

36 / 4 = 9, so each side of the first shape is 9 cm

40 / 4 =10 , so each side of the second shape is 10 cm

by putting the shapes together two of the side seal 1 side of each shape but 10-9 is 1 so add all three sides of the rest of the shape,

so 9+ 9+ 9= 27, then the three side of the second shape,

so 10+ 10+ 10= 30, then that extra 1 cm of difference from the size difference when put together,

so 27+ 30+ 1= 58 cm

Answer:

B. Arm circles

Hope you have a great day :)

The proportion and the median are two of the most popular and useful methods of standardizing for size and comparing distributions.

Proportion is the fraction of favorable cases from the total number of cases. It is defined for both population and sample.

Median is defined as the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half of it.

Therefore, the proportion and the median are two of the most popular and useful methods of standardizing for size and comparing distributions.

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Answer:

36kg

Step-by-step explanation:

The dog eats 16kg per week, which is 32kg in 2 weeks

The cat eats 2kg per week, which is 4kg in 2 weeks

32+4=36

It should be noted that 16/25 can be converted to a terminating decimal number is 0.64.

Do the fractions 6/7 and 16/25 convert to repeating or terminating decimal numbers.

In this case, 6/7 converts to repeating decimal numbers. You could represent it, so you don't have to repeat the decimals infinitely, by putting a bar over the repeating decimals like 0.857142 with a bar going over from the 8 to the 2.

Also, 16/25 can be converted to a terminating decimal number which is 0.64.

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In the given triangle, it should be noted that ADC is the same as BCD due to SAS congruence.

From the information given,

AD = BC

BCD = ADC.

This depicts the concept of SAS. In this case, the two-sided will be equivalent.

Also, it should be noted that DAC and CBD are equal according to the vertical angle theorem.

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Answer:

see picture ....

Step-by-step explanation:

Answer:

24 gallons

Step-by-step explanation:

Since the 2 gallons of gas increased the fill ratio from 1/6 to 1/4, we can find how much of the tank the 2 gallons filled by solving the equation 1/4 - 1/6 = 1/12. This means that each gallon of gas is 1/24th of the tank.

Thus, the tank has a fuel capacity of 24 gallons.

Answer:

24

Step-by-step explanation:

Let x be the total fuel capacity of the tank, in gallons.

Then from the given information

x/6 + 2 = x/4,

Multiplying both sides by 12 to remove the fractions, we get

2x + 24 = 3x so x = 24. 

Therefore, the total fuel capacity of the tank is 24 gallons.

Answer:

The value of x should be greater than 3.

Step-by-step explanation:

Given that,

The AB is 12 units.

The AC is 15 units.

We need to find the value of BC.

Based on the above information, the calculation is as follows:

As we know that

The sum of two sides length is always more than the 3rd one.

Based on this,

12 + 15 > x

x < 27

15 + x >12

x >-3

12 + x > 15

x >3

Answer:

5,6,8,8,9,18

Step-by-step explanation:

...................

Answer:

-23

Step-by-step explanation:

f(2)= 2*2-6 = -2

g(-3)= -3-2*9 = -21

---> f(2)+G(-3)= -2-21 = -23

Answer: -23

Step-by-step explanation:

     f(2) + g(-3) means that we will substitute 2 as x into the function f, and add that to -3 substituted as x into function g.

     First, we will find the substituted and simplified values of these functions.

f(x) = 2x - 6

f(2) = 2(2) - 6

f(2) = -2

[tex]-----[/tex]

g(x) = x - 2x²

g(-3) = (-3) - 2(-3)²

g(-3) = -21

     Lastly, we can add them.

f(2) + g(-3)

-2 + -21

-23

Answer:

156 cm²

Explanation:

This figure is a trapezium.

Formula of Area of Trapezium = 1/2 × (a + b)  × height

Here given:

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

Area of trapezium: 1/2  × (9 + 30)  × 8 = 156 cm²

Answer:

area of the trapezium is 156

Step-by-step explanation:

Answer: 19

Step-by-step explanation:

g(4) = 4² + 3

g(4) = 16 + 3

g(4) = 19

The degree of freedom is 6.

The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.

Given:

rows= 3

column= 4

So, degree of freedom

= (row-1)(column-1)

=(3-1)(4-1)

=2*3

=6

Hence, the degree of freedom is 6.

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Answer:

The degree of freedom is 6.

Step-by-step explanation:

Got it right on the test.

Answer:

2 1/4

Step-by-step explanation:

[tex]\text{First I'd recommend replacing the number with just n.}\\\text{Now, multiply this number by 2:: 2n}\\\text{Multiply 10 by it:: 2n*10}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{6 is subtracted from (2n*10):: (2n*10)-6}[/tex]

[tex]\text{This gives a total of 20}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{(2n*10)-6=20}[/tex]

Answer:

x = 9

Step-by-step explanation:

x/3 = 6/2

~Simplify

x/3 = 3

~Rewrite

1/3x = 3

~Multiply 3 to both sides

x = 9

Best of Luck!

Answer: x=9 ✅

Step-by-step explanation:

Hii student, I'd love to help you out! (:

In this problem, we need to solve a proportion. This is fun, right?

3,2,1 - start!

Solving proportions is easy as winking, if you are familiar with a skill that is known as "cross multiplying".

We have these two proportions:

(oh and by the way, proportions are just equivalent (equal) fractions. That's all proportions are. Nothing more)

Our proportions are:

[tex]\large\boldsymbol{\cfrac{x}{3}=\cfrac{6}{2}}[/tex]

We multiply x times 2 and 3 times 6; upon  doing that we obtain.

[tex]\multimap\quad \tt 2x=18[/tex]

Did you see that? 2 fractions turned into a little equation that we can solve within 5 seconds (or faster)!

To do that we simply divide both sides by 2, since x is multiplied by 2 and we need to get it all by itself on one side of the equal sign)

[tex]\multimap\quad \tt x=9[/tex]

Woohoo! We found the answer! ✨

Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

[tex]\underbrace[/tex]

Answer:

  C) straight line through (1, 3) ... (-3, -7)

Step-by-step explanation:

The linear equation will describe a straight line. The slope and general location of the line on a graph can be estimated from its x- and y-intercepts.

__

The x-intercept is the value of x that satisfies the equation when y=0.

  -5x +2·0 = 1

  x = -1/5 . . . . . . divide by the coefficient of x

The y-intercept is the value of y that satisfies the equation when x=0.

  -5·0 +2y = 1

  y = 1/2 . . . . . . divide by the coefficient of y

The intercept values mean the line crosses the positive y-axis and the negative x-axis. It will have a positive slope. Points on the line that have integer x- and y-coordinates will have coordinates that have the same sign.

Of the offered answer choices, A and B are eliminated because the graph is not a curve. D is eliminated because the suggested points have coordinates with opposite signs. The correct choice is C:

  It is a straight line joining the points (1, 3), (3, 8), and (-3, -7)

The value ∠y is 40⁰. So the correct option is option B

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

Here,  given that;   ΔUVW ≅ ΔXYZ

∠u = ∠x = 70⁰

∠v = ∠y = a⁰

∠w = ∠z = 70⁰

We know that,

Sum of angles of a triangle is 180⁰.

∠x + ∠y + ∠z = 180⁰

70⁰ + a⁰ + 70⁰ = 180⁰

a⁰ + 140⁰ = 180⁰

a⁰ = 180⁰ - 140⁰

a⁰ = 40⁰

Thus, the value ∠y is 40⁰.

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The characteristics of a nonisomorphic spanning tree are:

This refers to the quality of a group of things not having the same form and is popularly used in mathematics to show and make identifications of maths objects that are structurally well-defined.

Hence, we can see that your question is incomplete so I gave you a general overview of the topic for better understanding.

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Answer:

The smallest number all three numbers can be divided by is 4.

Step-by-step explanation:

12/4=3

16/4=4

24/4=6

Hope this helps!

If not, I am sorry.