2. State two (2) values of θ (theta) to the nearest degree forsin θ = − 0. 966

The given figure is;

It is given that :

The measurements of angles 1 and 3 are the same.

The measurement of angle 2 equals 110°.

PART A:

Since, angle 1 , 2 and 3 are lie at the same point on the same line

Thus, from the property of angle on a line

Sum of all angles on a strainght line at a point is equal to 180 degree

thus;

Angle1 + Angle2 + Angle 3 = 180

Angle 1 + Angle 2 + Angle1 = 180 {Angle1 = Angle 3, given}

2(Angle 1) + Angle 2 = 180

2 (angle 1) + 110 = 180 {Angle 2 = 110, given}

2(Angle 1) = 180 -110

2(Angle 1) = 70

Angle 1 = 70/2

Angle 1 = 35

Since, angle 2 = 110

The sum of angle 1 and 2 is 110 + 35

Sum of angle 1 and 2 = 145

PART B:

From the properties of the rectangle;

All the angles of a rectangle are 90°

In the given rectangle;

Thus, in the triangle form by the angle3, 4 and the right angle

Sum of all angles in a triangle is equal to 180

Angle 3 + Angle 4 + 90 = 180

35 + Angle 4 + 90 = 180

Angle 4 + 125 = 180

Angle 4 = 180 - 125

Angle 4 = 55

.....

We are given the equality

and told to solve for a. That is, we should apply mathematical operations on both sides of the equality so we "isolate" variable a on one side of the equality. We start by multiplying both sides by a, so we get

Now, we subtract 2a from both sides. We get

We can factor on the left side a as a common factor, so we get

Finally, we divide by (g-2) on both sides, so we get

Her take home salary is $2400 and she wants to spend no more than 15% on her car payment. Therefore, she can afford no more than 0.15*2400 = $360 on her car payment.

The given equation is

First, we need to elevate each side to the third power.

Second, subtract x and 1 on both sides.

Third, we elevate the equation to the square power to eliminate the root

Now, we use the formula to solve the squared binomial.

Now, we solve this quadratic equation

We need to find two number which product is 48 and which difference is 16. Those numbers are 12 and 4, we write them down as factors.

So, the possible solutions are

However, we need to verify each solution to ensure that each of them satisfies the given equation. We just need to evaluate it with those two solutions.

As you can observe, the solution 12 doesn't satisfy the given equation.

SOLUTION

From the question, the Perimeter of the rectangle is 19.4 cm and we want to find the width. The perimeter of a rectangle is given by

Applying this, we have

Hence the width is 3.7 cm, option C

The given expression is

To factorize this, we find the square root of each term.

Then, we use the difference of perfect square which states

So, we have

-2

Replace u by -2, and check if the equality remains

1-9u = 19

1-9(-2) = 19

1-(-18)=19

1+18 = 19

19=19

-2 YES

7

1- 9(7) = 19

1-63 = 19

-62=19

NO

0

1-9(0) = 19

1= 19

NO

6

1-9(6) = 19

1-54=19

-53=19

NO

(A) The customer that owns a 3-kW system exports 120 kWh monthly to the grid will have the following bills for both companies:

For ZG&E that collects $3 per kWh on a monthly basis, the monthly bill will be

For Ready Edison that collects $0.06 per kWh exported energy monthly, the computation of bill will be

(B) The customer that owns a 5-kW system exports 300 kWh monthly to the grid will have the following bills for both companies:

For ZG&E that collects $3 per kWh on a monthly basis, the monthly bill will be

For Ready Edison that collects $0.06 per kWh exported energy monthly, the computation of bill will be

If the line is parallel to y = -3/4 x + 1/4 then the slope is -3/4

the form of an equation is y = mx +b

In this case m = -3/4

Using the point given (4, -2) we will find the value of b:

y = mx + b

y = -3/4 x + b

Using the values of the point (4, -2).... x = 4 and y = -2

-2 = (-3/4)(4) + b

Solving for b:

-2 = -3 + b

-2 + 3 = b

1 = b

b = 1

Therefore the equation would be:

y = (-3/4)x + 1

Answer:

y = (-3/4)x + 1

We were told that Mai made $192 for 12 hours of work. This means that the amount that she made per hour is

192/12 = $16

Given that her constant rate is $16 per hour,

let x = the number of hours would she have to work to make $128. Then, we have the following equations

1 = 16

x = 128

By crossmultiplying, we have

16x = 128

x = 128/16

x = 8

She has to work for 8 hours

Answer:

100 times

Step-by-step explanation:

[tex]\frac{10^{9} }{10^{7} }[/tex]  = [tex]10^{2}[/tex] = 100

When you are dividing exponents with the same bases, you subtract the exponents.

Answer:

3 x 10^9 is larger than 3 x 10^7 by 2,970,000,000

Step-by-step explanation:

Explanation

We are given the following:

We are required to determine the perimeter of the rectangular sheet.

This is achieved thus:

We know that the perimeter of a rectangle is given as:

Therefore, we have:

Hence, the answer is:

Answer: divide each term from the original expression (3x3+27x2+9x ) by the GCF (3x), then write it in the parenthesis

Step-by-step explanation:

Answer:

You take it out and place it as a multiple.

Step-by-step explanation:

5x+15

GCF = 5

5(x+3)

Hope that helps

The decibel value for this cats purr round to the nearest decibel is; 25

Decibel (dB) is a unit for expressing the ratio between two physical quantities, such as measuring the relative loudness of sounds. One decibel (0.1 bel) is equal to 10 times the common logarithm of the power ratio.

Decibels are a unit of measure used to describe how loud a sound is. Now, I₀ is the intensity of threshold sound, which is sound that can barely be perceived by the human ear.

The loudness of a sound, in decibels, with intensity I is given by;

dB = 10 log₁₀(I/I₀)

We are given the intensity of a cat’s purr as I = 320I₀

Thus;

dB = 10 log₁₀(320I₀/I₀)

dB = 10 log₁₀(320)

dB = 25.05 ≈ 25

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1. Test statistic:

To find the test statistic, we use the formula:

Solving for Z, we have:

Thus, the test statistic is 1.421

2. P-value:

To find the p-value, we check the Z-distribution table.

The value for the p-value is

(We multiply by 2 because it is a two-tailed test.

3. Comparison:

The alpha level is 0.001.

Thus, the p-value is greater than the alpha level

The cost of 200 rectangular pieces of canvas given its dimensions is $36.

The first step is to determine the area of one of the rectangular pieces. A rectangle is a two-dimensional quadrilateral with four right angles.

Area of a rectangle = length x width

6 X 4 = 24 in²

The next step is to determine the area of the 200 rectangular pieces.

Area of the 200 rectangular pieces = 200 x 24in² = 4,800 in²

The last step is to determine the cost of the 200 rectangular pieces.

Total cost = total area x cost per squared inches

3 / 4 x 4800 = 3600 cents = $36

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This is the graph of the function

The answer is (8,0)

Given:

Alisa walks 3.5 miles in 30 minutes.

To find:

The number of miles if she walks 45 mins.

Explanation:

The unit rate for speed is,

The distance covered when she walks 45mins,

Final answer:

The number of miles she walks in 45mins is 5.25miles.

1/100

To get the fraction of the square shaded we would use the rows and columns

For the row:

The total on the 1st row = 1

The first row is divided into 10. This means each box in the first row: 1/10

One of the box is shaded. This implies the fraction shaded in the first row is 1/10

For the column:

The total on the 1st column = 1

The column is also divided into 10 box which means each box represent 1/10

Since one of the box in the column is shaded, it represent 1/10

Fraction of the whole square shaded = fraction shaded in the row × fraction shaded in the column

Fraction of the whole square shaded = 1/10 × 1/10

Fraction of the whole square shaded = 1/100

The right angled triangle is given with reference angle theta.

The opposite side (facing the reference angle) is 3, while the hypotenuse (facing the right angle) is 5. The adjacent shall be calculated using the Pythagoras' theorem as follows;

Therefore, the trigonometric functions of angle theta are shown as follows;

The converted money in Canadian dollars is $111.6.

Given that, Irlene has just returned from a business trip in Britain with £200 of uncashed traveler's cheques.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the converted Canadian dollars be x.

x = 200 × 0.5544 + 0.65% of 200 × 0.5544

= 110.88 + 0.0065 × 110.88

= 111.60072

≈ 111.6

Therefore, the converted money in Canadian dollars is $111.6.

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Find slope m, in equation y= mx + b

m = Y/X =( y - y')/ (x - x')

m= (5 - -5 )/ (-3 -3) = 10/-6 = -5/3

Now find b

b = y - mx

= 5 - (-5/3)•-3

. = 5 - 5 = 0

b = 0

Then answer is, equation is

y = (-5/3)x

From the first diagram shown, we can see that 1 cupcake costs $1.5

To get the price of 5 cupcakes

Since 1cupcake = $1.5

5 cupcakes = $x

cross multiply

1 * x = 5 * 1.5

x = $7.5

Hence 5 cupcakes will cost $7.5

Since 1cupcake = $1.5

18 cupcakes = $x

cross multiply

1 * x = 18 * 1.5

x = $27

Hence 5 cupcakes will cost $27

To get the number of cupcakes priced $18

Since 1cupcake = $1.5

x cupcake = $18

1.5x = 18

divide both sides by 1.5

1.5x/1.5 = 18/1.5

x =

Find the next two numbers in the pattern -243, 81, -27, 9​

Notice that all the values in the series are value of 3 raise to the power of a number.

-243 =

Solution:

In the figure;

Thus;

Thus;

In order to determine the ratio of the perimeters for the given rectangles, first calcualte their perimeters. Use the following formula:

P = 2w + 2l

w: width

l: length

For the smaller rectangle you have:

w = 2cm

l = 4 cm

P = 2(2cm) + 2(4cm) = 4cm + 8cm = 12cm

For the bigger triangle you have:

w' = 4cm

l' = 8cm

P' = 2(4cm) + 2(8cm) = 8cm + 16cm = 24cm

Then, you have:

P/P' = 12cm/24cm = 1/2

Hence, the ratio is 1:2

The number of bacteria that weighs 1 gram are,

Determine the number of bacteria in a sample that weighs 21 grams.

So answer is,

To creat a 4 - digit code, we need to consider that for each digit we have 10 options:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9 -----> 10 options for each digit.

Next, we multiply the number of options we have for each digit. In this case, since we need the code to have 4 digits:

We multiply 4 times 10.

And the result is:

He has 10,000 ways to create a 4-digit code.

the rational number :

-1 ³/₄ is located as point 1

14/8 is located as point 5

1.125  is located as point 6

-0.875 is located as point 4

What is number line ?

Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.

Here,

the rational number -1 ³/₄ is located as point 1, as -1 ³/₄ is greater then -1 and less then -2 on number line and is 3/4 of the gap between -1 and -2.

the rational number 14/8 is located as point 5, as 14/8 is greater then 0 and less then 1 on number line and is 3/4 of the gap between 0 and 1.

the rational number 1.125  is located as point 6, as 1.125 is greater then 1 and less then 2 on number line and is 1/8th  of the gap between 1 and 2.

the rational number -0.875 is located as point 4, as -0.875 is greater then 0 and less then -1 on number line and is 1/8 th of the gap between -1 and 0.

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From the statement of the problem we know that:

• the principal amount of money invested is P = $85000,

• the rate per year is 7.5%, in decimals r = 0.075,

• the time is t = 5 years.

The interest earnt I is equal to the difference between the total accrued amount A and the principal amount P:

Replacing by the data of the problem we find that the simple interest is:

Answer

The simple interest is $31875.