Solve for the missing variable. Round to the nearest hundredth.
X
8
20

Applying the trigonometric ratios, the equations that can be used are:

sin 45 = BC/9

cos 45 = BC/9

In the given image below, to find the unknown lengths of the triangle, we would apply the following trigonometric ratios:

To find AC, use the cosine ratio, CAH.

To find BC, use the sine ratio, SOH.

sin 45 = opp/hyp = BC/9

sin 45 = BC/9

cos 45 = adj/hyp = BC/9

cos 45 = BC/9

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Answer: A, E

Step-by-step explanation: Sin(45)=BC/9 ; cos(45)=Bc/9

Answer:

if I am sick, then I will not come to school.

Step-by-step explanation:

The sample size needed to obtain a margin of error of 0.05 for the estimation of a population proportion is 384.

Given margin of error of 0.05 and confidence interval of 95%.

We have to find the sample size needed to obtain a margin of error of 0.5 with confidence level of 95%.

Margin of error is the difference between real values and calculated values.

The formula of margin of error is as under:

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where

z is the critical value of z for given confidence level

n is sample size

σ is population standard deviation

We have not given population standard deviation so we will use the following formula:

Margin of error=z*[tex]\sqrt{p(1-p)}[/tex]/[tex]\sqrt{n}[/tex]

We have to find z value for 95% confidence level.

z value=1.96

We know that [tex]\sqrt{p(1-p)}[/tex]<=1/2

put [tex]\sqrt{p(1-p)}[/tex]=1/2

Margin of error=1.96*1/2/[tex]\sqrt{n}[/tex]

0.05=1.96*0.5/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=0.98/0.05

[tex]\sqrt{n}[/tex]=19.6

squaring both sides

n=384.16

After rounding off we will get

n=384.

Hence the sample size needed to obtain a margin of error of 0.05 is 384.

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The point F as described in the task content is at point; 0.6 on the number line.

Since it follows from.tge task content that; point D is at -3, and point E Is at 6, it follows that the length of segment, DE is; |-3-6| = 9.

Consequently, since the ratio of Df to FE ls 2:3

It follows that point F is at -3 + (2/5) × 9.

Point F is therefore at 0.6 on the number line.

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Using proportions, it is found that each farmer bought 68,008 kg.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each t has 1000 kg, hence the amount of maize seeds in kg is given as follows:

6460 x 1000 + 760 = 6,460,760 kg

The amount per farmer is:

6,460,760/95 = 68,008 kg.

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Answer:

2/x

Step-by-step explanation:

Given that the distance and angle of elevation of the tree from P are 50 m. and 32°, and Q is 100 m. from P, we have;

a. The height of the tree is approximately 31.2 m.

b. i. The distance of Q from the base of the tree is 50•√5 m.

ii. The angle of elevation of the top of the tree from Q is approximately 15.6°

iii. The bearing of the tree from Q is 296.565°

a. tan(32°) = Height/50

Height = 50 × tan(32°) = 31.243 m.

b. i. The distance, d, of Q from the base of the tree is given by Pythagorean theorem as follows;

d = √(100² + 50²) = 50•√5

ii. The angle of elevation is given by trigonometric ratios as follows;

[tex]tan (\theta) = \frac{31.243}{50 \cdot \sqrt{5} } [/tex]

Which gives;

[tex]\theta= arctan \left( \frac{31.243}{50 \cdot \sqrt{5} } \right) \approx 15.6 ^{ \circ} [/tex]

iii. The angle formed at Q by the lines from Q to the point P and Q to the tree is found as follows;

Angle = arctan(50/100) ≈ 26.565°

The angle between the direction north of Q and a line from Q to the tree is therefore;

90° - 26.565° = 63.435°

The bearing, which is the angle described clockwise from the direction north of Q and the direction from Q to the tree, is therefore;

Bearing = 360° - 63.435° = 296.565°

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Answer:

[tex]\huge\boxed{\sf x = 65 \textdegree}[/tex]

Step-by-step explanation:

Using trigonometric ratio cos.

Here,

[tex]\displaystyle cos \theta =\frac{adjacent}{hypotenuse} \\\\cos \ x =\frac{12}{28} \\\\cos \ x = 0.43\\\\x = cos^{-1} 0.43\\\\x = 65 \textdegree\\\\\rule[225]{225}{2}[/tex]

The figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet is a square with side lengths of 7 and one third feet.

From the information given, the actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet.

The new length will be:

= 2 × 3 2/3

= 7 1/3

Therefore, the new length is 7 1/3 feet.

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Q14)

a) The smallest prime number is 2. The smallest composite number is 4.

b) Rs 720 - 20 [as loss]

=> Rs 790 = SP

c) Rs 500 - 30 [as profit]

=> Rs 470 = CP

d) a° + b° = 180°

Hope it helps you!

Answer:

  10.  20.9°

  11.  73.2°

Step-by-step explanation:

The inverse sine function is used to find the angle from its sine value.

In each case, the equation is of the form ...

  a/sin(x) = b/c

Multiplying both sides by c/b·sin(x), we find the solution is ...

  sin(x) = ac/b . . . . . find sin(x)

  x = arcsin(ac/b) . . . . . find the corresponding angle

For the given values a=7.2, b=13, c=sin(40°), we have ...

  x = arcsin(7.2sin(40°)/13) ≈ 20.9°

For the given values a=6.53, b=√40, c=sin(68°), we have ...

  x = arcsin(6.53sin(68°)/√40) ≈ 73.2°

Step 1

Using the points (2,0) and (-2, -3), we get the slope is

[tex]\frac{-3-0}{-2-2}=\frac{3}{4}[/tex]

Step 2

Using the point (2,0), the equation is

[tex]y=\frac{3}{4}(x-2)[/tex]

Step 3

Using the distributive property, we get [tex]y=\frac{3}{4}x-\frac{3}{2}[/tex].

table 1, and table 2 are the answers.

we know that any function is increasing when for an increase in x-values, y-value should also increase

we will verify each table

table-1:

we can see that

x increase as -3, -2, -1 , 0, 1,2

y is also increasing -6,-3,-1,1,3,6

so, this is increasing

table-2:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but it is asking between -2 to 1

y-values are -4,-1,1,4.....which is increasing

so, this is  increasing

table-3:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but y changes from -3 to -5 .....which is decreasing

so, this is not increasing

table-4:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but y changes from 7 to 1 .....which is decreasing

so, this is not increasing

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Answer: -x

Apply Multiplicative Distribution Law:- 1/5 * 5x - 1/5 * 20 - 1/2 * 4x - 1/2 *(-8)

Determine the sign for multiplication or division: 1/5 * 5x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8

Cross out the common factor: x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8

Cross out the common factor: x - 4 - 1/2 * 4x + 1/2 * 8 - 4 - 2x + 1/2 * 8

Cross out the common factor: x - 4 - 2x + 1/2 * 8

Cross out the common factor:  x - 4 - 2x + 4

Reorder and gather like terms: (x - 2x) + (- 4 + 4)

Collect coefficients for the like terms: (1 - 2) * x + (- 4 + 4)

Calculate the sum or difference :  - x + (- 4 + 4)

The sum of two opposites equals 0: -x

Answer: -x

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Answer:

D) Substitute 5 into each expression and evaluate them.

Step-by-step explanation:

The double number line that shows the other values of packages and pencils is A. A double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48.

It should be noted that a number line simply means a line which numbers are marked a intervals to illustrated numerical operations.

In this case, the double number line with 5 equally spaced tick marks. The line labeled Packages, reads from left to right: 0, 1, 2, 3, 4. The line labeled Pencils, reads from left to right: 0, 12, 24, 36, 48 illustrate this information

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The value of y from the given figure is 6√3

From the given figure, according to the theorem;

H² = 6² - 3²

H² = 36 - 9

H²  = 27

H = 3√3

Determine the value of y using the same theorem;

y² = 9² + ( 3√3)²

y² = 81. + 27

y = √108

y = 6√3

Hence the value of y from the given figure is 6√3

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The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

VAT = 13% = 0.13 * 8000 = 1040

Selling price - VAT = 11300 - 1040 = 10260

Profit = [(10260 - 8000)/8000] * 100% = 28.25%

The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%

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The equation in slope intercept form is y = -4x/3 + 10

The representations are given as:

So, we have:

2 * x + 1.5 * y = 15

Evaluate the product

2x + 1.5y = 15

Subtract 2x from both sides

1.5y = -2x + 15

Divide through by 1.5

y = -4x/3 + 10

Hence, the equation in slope intercept form is y = -4x/3 + 10

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Answer:

1/12

Step-by-step explanation:

the chances of rolling a 3 is 1/6

there are 3 numbers more than 3 on a number die, 4,5, and 6

which is 3/6 or 1/2 if you decide to simplify

to find the probability you want you have to multiply the fractions by each other

1/6x1/2=1/12

The total number of bars of kitkat Mr hassell had in total is 3 1/2 bars

Total bars of KitKat = 6 × 3/4

= (6×3)/4

= 18/4

= 9/2

= 4 1/2 bars

Number of bar remaining after eating 1 bar = 4 1/2 - 1

= 3 1/2 bars

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For the function g(x) we have:

The function g(x) is given by applying transformations to f(x), the transformations are:

The function is:

[tex]g(x) = -(x + 2)^2 + 5[/tex]

The graph is the one you can see below:

There you can see that the vertex is at (-2, 5), then the line of symmetry is:

x = -2.

And we have a maximum at the vertex, which is y = 5.

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Answer:

Associative Property

For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4.

Answer:
3rd Option!

Step-by-step explanation:

EDGE 2022; good luck

[tex]ac {}^{2} = cb {}^{2} + ba {}^{2} - 2(cb)( ba)(cos \alpha ) \\ ac {}^{2} = 21 {}^{2} + 26 {}^{2} - 2(21)(26)(cos112) \\ ac {}^{2} = 441 + 676 - 1092(cos112) \\ ac {}^{2} = 1526.07 \\ ac = 39.065[/tex]

Answer:

Step-by-step explanation:

The length of the wall = 125m

The area of the Playground = 10000[tex]m^{2}[/tex]

What is geometry?

A branch of mathematics that broadly deals with the measurement, properties, and connections of points, lines, angles, surfaces, and solids: the investigation of qualities of given elements that hold true even after being subjected to predetermined transformations.

Given data:

Perimeter of the playground=410m

length of the wall = 80m

The playground's width can be calculated as follows if its length is 80 meters:

(Formula of Perimeter of a rectangle)

P=2(L+B)              

410=2(80 +B)

410= 160 + 2B

2B= 410-160

2B= 250

B= 125 m

This results in a 125 m length for the playground.

The area of playground.

Area = Length x Width

Area = 80 x 125

area = 10000[tex]m^{2}[/tex]

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Based on the angle of the seesaw and the height off the ground, the maximum length of the seesaw is 2 meters.

This can be found as:

Sin 30° = 1 / Maximum length

Solving gives:

Sin 30° = 1 / Maximum length

Ml = 1 / Sin 30°

= 1 / 0.5

= 2 meters

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The population after 20 minutes is 14.

We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-        

            After 1 hour, the population is 3*10

            After 2 hours, -> 3*3*10

            After 3 hours, -> 3*3*3*10

Make a function from above observation in the increasing

              number of the  insects per hour

              This can be generalized as a function of t, the time in hours:

              f(t) = (3^t) * 10

putting the values in the function and get the desired answer,

                             P = (3^t) * 10

             Since 20 minutes is equal to (1/3) hours, t can be substituted for

             (1/3) in order to calculate the population size after 20 minutes:

                  P = (3^(1/3)) * 10 = 14.422 ≈ 14

The population after 20 minutes is 14.

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Answer:The population after 20 minutes is 14.

We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-        

           After 1 hour, the population is 3*10

           After 2 hours, -> 3*3*10

           After 3 hours, -> 3*3*3*10

Make a function from above observation in the increasing

             number of the  insects per hour

             This can be generalized as a function of t, the time in hours:

             f(t) = (3^t) * 10

putting the values in the function and get the desired answer,

                            P = (3^t) * 10

            Since 20 minutes is equal to (1/3) hours, t can be substituted for

            (1/3) in order to calculate the population size after 20 minutes:

                 P = (3^(1/3)) * 10 = 14.422 ≈ 14

The population after 20 minutes is 14.

Step-by-step explanation:

If the function is

[tex]y = 4 e^x \cos(3x)[/tex]

then we have derivatives

[tex]Dy = 4 e^x \cos(3x) - 12 e^x \sin(3x)[/tex]

[tex]D^2y = -32 e^x \cos(3x) - 24 e^x \sin(3x)[/tex]

Now consider the linear ODE

[tex]aD^2y + bDy + cy = 0[/tex]

Substituting [tex]y[/tex] and its derivatives reduces the equation to

[tex](-32a + 4b + 4c) \cos(3x) + (-24a - 12b) \sin(3x) = 0[/tex]

Now,

[tex]-24a - 12b = 0 \implies b = -2a[/tex]

[tex]-32a + 4b + 4c = 0 \implies c = 10a[/tex]

Then the minimal ODE with the given solution is

[tex]aD^2y -2a Dy + 10ay = 0[/tex]

or

[tex]\boxed{D^2y  -2 Dy + 10y = 0}[/tex]

Answer:

$ 51.36

Step-by-step explanation:

To find the sales tax multiply the tax rate by the cost of the product and then add to the cost.

Sales tax = tax rate * cost price

              = 7% * 48

              = 0.07 * 48

              = $ 3.36

Cost price = cost of product + sales tax

                 = 48 + 3.36

                 = $ 51.36

The statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial

Polynomial expression are equation that has a leading degree of 2 and above. For instance the following expressions are polynomials.

ax^2+bx+c and;

mx^2+nx+p

Take the sum of the polynomials

P(x) =. ax^2+bx+c

f(x) = mx^2+nx+p

Since both expressions are quadratic in nature, hence the sum will result in a polynomial that is quadratic in nature.

Based on the explanation above, we can conclude that the statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial

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