For what value of x is sin ( x ) = cos 62, where 0 < x < 90?

476 x 0.001 = 0.476

0.476 x 10¹ = 4.76

4.76 x 10³ = 4,760

47.6 x 0.1 = 4.76

We have to find the following products of the equations.

The basic rule for multiplication between numbers with decimal points can be described through some examples first.

Decimal point is shifted leftwards up to the power of 10 which is divided with it. Also decimal point is shifted rightwards when multiplied with powers of 10.

Now we will find the product for each equation:

For 476 × 0.001, 0.001 = 1/1000

Therefore, 476 × 0.001 = 476 × 1/1000 = 0.476 [decimal point shifted left]

For 0.476 × 10¹ = 0.476 × 10 = 4.76 [decimal point shifted right]

For 4.76 × 10³ = 4.76 x 1000 = 4760 [decimal point shifted right]

For 47.6 x 0.1 = 47.6 x 1/10 = 4.76 [decimal point shifted left]

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There are 40 different combinations of colors and dashboard options available to this buyer.

Combination is a counting technique where the order of the selected items from a collection does not matter. The formula in finding the number of combinations when ‘r’ items are chosen out of a total of ‘n’ objects.

nCr = n! / [r! (n - r)!]

If there are 2 of 5 options for seat colors, then using the formula, the number of combinations for the seat color is:

5C2 = 5! / [2! (5 - 2)!]

5C2 = 120 / 12

5C2 = 10

If there are 3 of 4 options for dashboard accessories, then using the formula, the number of combinations for the dashboard accessories is:

4C3 = 4! / [3! (4 - 3)!]

4C3 = 24 / 6

4C3 = 4

Multiplying the two results will give the total number of different combinations of colors and dashboard options available.

combination =  10 x 4

combination = 40

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Main Answer:

Height decreased in 1 second is 80 cm

Explanation:

The total amount of height decreased is 120.

Total amount of time taken is 1.5 s.

Height decreased in 1 second = [tex]\frac{120}{1.5}[/tex]

⇒ [tex]\frac{1200}{15}[/tex]

⇒ 80 cm

Therefore, height decreased in 1 second is 80 cm.

The expression [tex]\sqrt{n}[/tex]  which is the third option represents the side length, in feet, of the bulletin board.

It is given in the question that the area of the bulletin board is n square feet.

We have to find the expression that represents the side length, in feet, of the bulletin board.

Let the side, in feet of the bulletin board be x.

We know that,

Area of a square =[tex]side^2[/tex]

We have, side = x

Hence we can write,

Area of a square = [tex]x^2[/tex] square feet

Hence,

[tex]x^2=n[/tex]

Square rooting on both sides, we get

[tex]\sqrt{x^2}=\sqrt{n}\\\\x=\sqrt{n}[/tex]

Hence the expression [tex]\sqrt{n}[/tex] which is the third option represents the side of the square bulletin.

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The most appropriate choice for Conjecture and Counter examples will be given by

There is atleast one zoo, may be in Africa or any other countries,  where the number of elephants is more than the number of giraffes. This is the required counterexample of this conjecture.

What is Conjecture and Counter examples?

Suppose an information is provided where the information is incomplete or insufficient, then any conclusion formed based on that information is called Conjecture.

Suppose, a statement  have been given a statement. If one can provide an example where the conditions of the statement are satisfied but the conclusion is false, then that example is called counter example.

Here,

Counterexample of "There are always more elephants in a zoo than giraffes."

There is atleast one zoo, may be in Africa,  where the number of elephants is more than the number of giraffes.

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The surface area of the regular pyramid is 151.9 m².

The surface area of the regular pyramid can be found as follows:

surface area of the pyramid = A + 1 / 2 ps

where,

Therefore,

A = 61.9 m²

p = 6 × 5 = 30 m

s = 6m

Hence,

surface area of the pyramid = 61.9 + 1 / 2 × 30 × 6

surface area of the pyramid = 61.9 + 180 / 2

surface area of the pyramid = 61.9 + 90

surface area of the pyramid = 151.9 m²

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The maximum value of the function is at (8, 7).

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Answer:

10

Step-by-step explanation:

I'm going to estimate [tex]\sqrt{30}[/tex]. Because root 25 is 5 and root 26 is 6, root 30 is around 5.5. 5.5 + 6.2 is around 10.

Don't say you are going to mark as brainliest if you don't have brainliest.

The slope of this straight line is equal to: A. 2

A slope is also referred to as gradient and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

By critically observing the given graph, we can logically deduce the following points:

Note: Each interval on this graph represents 1 unit.

Substituting the given points into the formula, we have;

Slope = Δy/Δx

Slope = (-3 - 1)/(-1 - 1)

Slope = -4/-2

Slope = 2

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Answer:

4t + 1.

Step-by-step explanation:

Use the General form of the differential:

If y = ax^n,  

dy/dx = anx^(n-1)

So:-

y = 2t^2 + t + 1

dy.dt = 2*2t^(2-1) + t^(1-1) + 0

         = 4t + 1.

the distance between two points is 3.5 cm

The length of the line segment bridging two locations in a plane is known as the distance between them. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to determine the separation between any two locations on an x-y plane or coordinate plane.

(1,-2) (1,1.5)

distance between two points is

= [tex]\sqrt{(1-1)^{2} + (1.5+2)^{2}[/tex]

= 3.5 cm

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Using simple interest, it is found that the amounts invested are given as follows:

Simple interest is used when there is a single compounding per time period, usually measured in years.

The amount of money after t years in is modeled by:

A(t) = P(1 + rt)

In which:

The interest accrued over t years is:

I(t) = Prt.

For this problem, we have that:

From the interest earned, we have that:

[tex]I_1 + I_2 = 677[/tex]

In which:

Replacing both these relations in the sum of interests, we have that:

0.072P + 0.07(9000 - P) = 677

0.002P = 677 - 0.07(9000)

P = (677 - 0.07(9000))/0.02

P = 2350.

Hence she invested $2,350 at a rate of 7.2% and $6,650 at a rate of 7%, as 9000 - 2350 = 6650.

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Answer:

x=6

Step-by-step explanation:

we know that

slope formula is,

m=(y2-y1) / (x2-x1)

where m=-3

x1=x,y1=-4 and x2=2,y2=8,

-3=(8-(-4))/(2-x)

Now solving the expression

we get,

-6+3x=12

3x=18

x=6

Answer:

c=9

Step-by-step explanation:

[tex]11=c+2 \\ \\ c=9[/tex]

Based on the number of cookies in the bag of cookies, if María Fernanda is to reach in and select 2 chocolate chip cookies, the probability of that happening is 6.46%

The events that María Fernanda picks one chocolate chip cookie and then another, are both independent events.

To find the probability of independent events, the formula is:

= Independent event probability 1 x Independent probability 2

Find the total number of cookies:

= 7 chocolate chip cookies + 5 peanut butter cookies + 6 sugar cookies + 8 oatmeal cookies

= 26 cookies

The probability of two chocolate cookies being picked by María Fernanda is:

= Number of chocolate cookies / Number of total chips x Number of chocolate cookies left / Number of cookies left

= 7 / 26 x 6 / 25

= 42 / 650

= 21 / 325

= 6.46%

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The main number of apples in each bag is eight therefore 12 bags contain 96 apples.

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every discipline of mathematics, including trigonometry, calculus, and coordinate geometry.

Given that :There are 12 bags of apples on a market store. The main number of apples in each bag is eight

Eight apples on average fit into each bag.

We need to figure out how many apples are in the 12 bag.

The total number of apples is 8×12 = 96.

Therefore, 12 bags contain 96 apples.

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Answer: 2.7156

Step-by-step explanation:

Using Bidmas: we do the brackets first so 8.131 + 3.7024 = 11.8334

Then 14.549 - 11.8334 = 2.7156

Hope this helps :)

Answer:

Step-by-step explanation:

Answer:

Surface area: 432 Area: 576

Step-by-step explanation:

Surface area fomula: 2lh+2wl+2wh

Area formula:lh

The dimensions of the bookmark is 14cm.

The perimeter of a shape is the space surrounding it. Space inside a shape is measured by area. Learn how to compute the area and perimeter of various forms. The perimeter of a square is equal to four times the length of its side, and its area is equal to the square of that length. As a result, the square's perimeter will be as follows: perimeter = 4 x side = 4 area units. As a result, given a square's size, we can determine its perimeter.

Given data

Area = 160cm

Perimeter = 56

Area = side²

Perimeter = 4(a)

Putting values in perimeter

Perimeter = 4a

56 = 4a

a = [tex]\frac{56}{4}[/tex]

a = 14

The dimensions of the bookmark is 14cm.

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Answer:

18/20

Step-by-step explanation:There are 20 total cards and 2 are brown so answer would be 18/20.

Step-by-step explanation:

if I understand correctly, one side of the square is 2m⁴n.

so, the area of the square is

side² = (2m⁴n)² = 4m⁸n²

because

(2m⁴n)² = 2m⁴n × 2m⁴n

and that is 4m⁸n²

The value of the expression : [(x – 2) ^2(x + 2)] ^2 will be (x³ - 4x² + 10x + 8)².

It should be noted that the information simony wants us to multiply the expressions that are given. In this case, they can be computed individually. This will be:

(x - 2)² = (x - 2)(x - 2)

= x² - 2x - 2x + 4.

= x² - 4x + 4

This will be:

(x² - 4x + 4)(x - 2)

= x³ - 2x - 4x² + 8x + 4x - 8

= x³ - 4x² + 10x + 8

We will then square the above value. This will be (x³ - 4x² + 10x + 8)².

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To translate figure ABCD into A'B'C'D' rotate 90° about D and then reflect across AB.

When a figure is relocated from one place to another without changing its size, shape, or orientation, a transition known as translation takes place.

If we know which way the figure is moving and how much, we can draw the translation in the coordinate plane.

Every point of the object must be translated by the same amount and in the same direction.

To translate figure ABCD into A'B'C'D' rotate 90° about D and then reflect across AB.

option (d)

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In functions, value of x = 45 and y = 45

What is function in math?

6)  x = 15

 y = 49

3x = 3 * 15 = 45

y - 4 = 49 - 4 = 45

7)  3x + 23 = 4x

    4x - 3x = 23

     x = 23

    y =  4 * 23 =   92°

8) y + 12 = 5x °

  3x + 50  =

According to the question

     y + 12 = 3x  + 50

      5x   = 3x + 50

      2x = 50

        x = 25

y + 12 = 5x °

y = 5 * 25 - 12

y = 125 - 12 =   113

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The actual cost of the food and entertainment be $2,400.

For the given question;

The amount spent by Juan's company = $2,350.

The amount spent of the food = $1,500.

The amount spent on entertainment = $900.

Thus, the actual amount will be;

Actual amount = food + entertainment

Actual amount = $1,500 +  $900

Actual amount = $2,400.

Thus, the actual cost of the food and entertainment be $2,400.

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Answer:

x=[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

5x(2-4)=2(5x-4)

1. First we expand the brackets

     10x-20x=10x-8

2. we can simplify the equation to

       -10x=10x-8

3. we want to find the value of x so we get all of the x on one side so we would -10x on both side

  -20x=-8

4. to find the value of x we divide each side by -20 this gives us

x=[tex]\frac{8}{20}[/tex]

(it's not a negative as the negative cancel each other out as negative divided by negative gives us positive)

5. However we can simplify the fraction by dividing the top and bottom by     4 (this is because the highest common factor for both number is 4) this gives

 x=[tex]\frac{2}{5}[/tex]

6. Therefore -4 is not a solution for the equation

your answer is B

your welcome