Add 7*10^-6 and 2.1*10^-5

Answer:

x = 9.75 and y = 0

Step-by-step explanation:

Since the path of the windsurfer crosses both angles, we can use the fact that the sum of the angles around a point is 180 degrees to set up an equation:

m∠1 + m∠2 + m∠3 = 180°

We know that m∠1 = (8x + 5y)° and m∠2 = (8x + y)°. We can also see from the diagram that m∠3 = 180° - 78° = 102°. Substituting these values into the equation, we get:

(8x + 5y)° + (8x + y)° + 102° = 180°

Simplifying and solving for x and y, we get:

16x + 6y = 78°

8x = 78° - 6y

x = (78° - 6y)/8

We can substitute this expression for x into one of the earlier equations to solve for y:

8[(78° - 6y)/8] + y = 78°

78° - 6y + y = 78°

-5y = 0

y = 0

Now that we know y = 0, we can substitute this value into the equation we found for x:

x = (78° - 6(0))/8 = 9.75

Step-by-step explanation:

If x and y vary inversely, we can write the equation:

xy = k

where k is a constant of proportionality. To solve for k, we can use the values x = -3 and y = 4:

(-3)(4) = k

-12 = k

So the equation relating x and y is:

xy = -12

To find y when x = 6, we can plug in these values and solve for y:

(6)y = -12

y = -2

So when x = 6, y = -2.

The volume of the pyramid will be equal to 96 in^3.

We are given that square pyramid has a base length of 6 inches and a height of 8 inches.

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex] is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, thus its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

Therefore, the volume of the pyramid;

V = 1/3 a^2 h

V = 1/3(6^2)(8)

V = 1/3(36)(8)

V = 96 in^3

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The  graph of g(x) = f(x - 1) - 5 is: C: The graph of g(x) is shifted 1 unit right and 5 units down.

Some of the terminologies in shifting of functions are:

1. Shift graph functions y = f(x) to the left: This means that we will be adding inside the function.

y= f(x + b)  , where b is constant

2. Shift graph function y = f(x) to the right means that we will be subtracting inside the function

y =  f(x - b)

3. To shift graph function y = f(x) up by b units means that we would be adding outside the function:

y = f(x) + b

4. To shift graph down by b units means that we would be subtracting outside the function:

y = f(x) - b

Therefore, by the definition we can say that the graph of g(x) = f(x-1)-5 is the graph of f(x) 1 units to the right and 5 units down.

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If Lerato spends ²/₅ of her money, loses ¹/₃ of what is left, and still has R6 left, the amount of money she had to begin with was R15.

The beginning amount that Lerato had can be determined using fractional addition and subtraction.

Fractional addition and subtraction involve the addition and subtraction of fractional or proportional values.

The amount of money Lerato spend = ²/₅

The amount left = ³/₅ (1 - ²/₅)

The amount lost = ¹/₃ x ³/₅

= ¹/₅

The total amount spent and lost = ³/₅ (²/₅ + ¹/₅)

The amount of money left after spending and losing ³/₅ = R6

R6 = ²/₅

Proportionately, ²/₅ = R6, ⁵/₅ = R15 (R6 x ⁵/₂).

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The amount of money that should be in the account at the end of 4 years of investment would be = $114.

To calculate the total amount of money that will be in an account at the end of a given time can be calculated using the given formula below;

Simple interest = principal× time×rate/100

where;

principal = $100

rate = 3.5%

time = 4 years

simple interest = 100×3.5×4/100

= 14

Therefore the total amount of money that will be in the account at the end of 4 years = 100+14 = $114.

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The value of 6 [4(-5)^n-1] when n is 1 is 24

This simply means replacing a known value for an unknown value in an expression.

For example, 5x²+2 , the value of the expression when x is -2 is solved by substituting -2 for x in the expression.

5x²+2 = 5(-2)² +2

= 5×4 +2

= 20+2

= 22

Similarly, the value of 6 [4(-5)^n-1] when n= 1 can be calculated by substituting 1 for n in the expression.

6 [4(-5)^n-1] = 6(4(-5)^1-1)

= 6(4(5)^0)

= 6 × 4 × 1

= 24

Therefore the value of 6 [4(-5)^n-1] when n= 1 is 24

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The z-score corresponding an x-value of 64 is 3

From the question, we have the following parameters that can be used in our computation:

x = 64

Mean = 55

Standard deviation = 3

using the above as a guide, we have the following:

z = (x - mean)/Standard deviation

Substitute the known values in the above equation, so, we have the following representation

z = (64 - 55)/3

Evaluate

z = 3

This score may or may not be considered to be statistically significant or statistically insignificant

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Answer:

Step-by-step explanation:

you rigt

After considering all the given options we conclude that the probability of selecting a point inside the rectangle randomly falls outside the triangle, which is Option B.

The probability regarding a point selected randomly within the rectangle is in the square is given by the ratio of the area of the square to the area of the rectangle.
The evaluated area  regarding the given square is
4² = 16 sq units.
The area of the rectangle is 12 x 8 = 96 sq units. Then , after evaluation the probability regarding  a specified point taken randomly inside the rectangle is in the square is
16/96
= 1/6
= 0.1667 or 16.7%
The probability concerning a point taken randomly within the rectangle is outside the triangle is given by subtracting the area of the triangle from the area of the rectangle and then dividing by the area of the rectangle.
The area of the triangle is
(1/2) x base x height
= (1/2) x 4 x 5
= 10 sq units.
Then, the probability that a point chosen randomly inside the rectangle is outside the triangle is
(12 x 8 - 10)/(12 x 8)
= 94/96
= 0.9792 or 97.9%
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The length of side l of the triangle using sine rule is: 46 inches

Sine rule is used to show the relationship between the sides and angles of a triangle. It is given as:

a/sinA = b/sinB = c/sinC

Where A, B, C are the angles and a, b and c are the opposite sides to the angles.

Thus:

63/sin 114 = l/sin 42

(63 * sin 42)/sin 114 = 46 inches

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Answer:

Step-by-step explanation:

The formula for a function is in vertex form is

y=a(x-h)²+k    

(h,k) is vertex

a is stretch

if it were facing down there would be a - in front

You question:

(-4,1) is vertex

it's facing up and there is no stretch

y=(x+4)+1                   you can expand

y=x²+8x+17

Therefore, after the water cooler is fully filled, there will be about 211.38 gallons of water inside.

Eight pints or 4.564 liters make up a gallon, a unit of liquid or dry capacity.

The cylinder's diameter is specified as 3 feet, so its radius must be half that, or 1.5 feet. The cylinder is described as having a height of 4 feet.

When we enter these values into the formula, we obtain:

V is equal to (1.5)2(4) = 28.26 cubic feet.

We are aware that one cubic foot contains about 7.48 gallons of water. Therefore, we need to multiply the volume of the cylinder by 7.48 to get how many gallons of water are in the water cooler when it is fully filled.

The result of multiplying 28.26 by 7.48 is:

211.38 liters

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The value of x corresponding to a z-score of -2.25 is 5.75.

What is z-score ?

A z-score is a standardized score that expresses the distance of a data point from the mean in terms of the number of standard deviations. It indicates how many standard deviations a data point is above or below the mean of the distribution.

Given that x follows a normal distribution with mean μ = 8 and standard deviation σ = 1, we can find the z-score corresponding to a given value of x using the formula:

z = (x - μ) / σ

To find the value of x corresponding to a z-score of -2.25, we can rearrange the above formula as follows:

x = μ + z * σ

= 8 + (-2.25) * 1

= 8 - 2.25

= 5.75

Therefore, the value of x corresponding to a z-score of -2.25 is 5.75.

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Answer:

0.2 because Density = Mass / Volume

Density = 25 / 50

Density= 0.2 g/cubic cm

Answer:

The smallest angle in this quadrilateral is 36°.

Step-by-step explanation:

[tex]x + 2x + 3x + 4x = 360[/tex]

[tex]10x = 360[/tex]

[tex]x = 36[/tex]

So x, the smallest angle in this quadrilateral, is 36°.

Answer:

Within one year, she'll have:

500 + 100 × 12 which is $1,700.

Quite unsure as the question seems incomplete. But based on the given details, here's your answer..

Answer:

The area is 92 square yards.

Step-by-step explanation:

We can decompose this figure into a rectangle and a triangle.

First, we can find the area of the rectangle.

A(rect) = length × width

A(rect) = 10 × 8

A(rect) = 80 yd²

Next, we can find the area of the triangle.

A(triangle) = (1/2) × base × height

[tex]A(\text{triangle}) = \dfrac{1}{2} \, (13 - 10) \times 8[/tex]

[tex]A(\text{triangle}) = \dfrac{3}{2} \times 8[/tex]

[tex]A(\text{triangle}) = 12 \text{ yd}^2[/tex]

Finally, we can add the two shapes' areas to get the area of the entire figure.

A = A(rect) + A(triangle)

A = 80 yd² + 12 yd²

A = 92 yd²

Answer: 92 yd²

Step-by-step explanation:

Decomposition means to break the shape into parts, but it's not necessary to break apart.

This is a trapezoid turned sideways A=1/2(b1+b1)h

b1=10

b2=13

h=8

A=1/2(10+13)8 =92 yd²

if you decompose, you can make the top a triangle and bottom a rectangle.

A(triangle) = 1/2(b)(h)     b=3   h=8

                 1/2(b)(h)

                 = 12

A(rectangle)=bh     b=10     h=8

                  =10*8

                   =80

Add the 2 and you get 92 again

Answer: Its 5/2 or 2/5 but I think the right one is 5/2.

The answer is 5/2.

Step-by-step explanation: Please give Brainlist.

Hope this helps!!!!

I will answer more of your questions.

(Expert Answered)

If she uses  a previous estimate of 0.58, n = 733

If she does not use any prior estimates, n = 752

Here, E is given as 0.03

For 90% confidence level, Z* = 1.645

Using formula for margin of error we have

0.03 = 1.645 x (√0.58(1 - 0.58) / n)

n = 733

without prior estimates the value of p = 0.5

Then we have

0.03 = 1.645 x (√0.5(1 - 0.5) / n)

n = 752

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Answer: [tex]\tt{a.\fra{2}{3}}[/tex]

Step-by-step explanation:

If cos A = sqrt(5)/3 and tan A < 0, we can use the fact that:

sin^2 A + cos^2 A = 1

to find the value of sin A. First, we can square both sides of the equation cos A = sqrt(5)/3 to get:

cos^2 A = 5/9

Then, we can use the identity sin^2 A = 1 - cos^2 A to get:

sin^2 A = 1 - cos^2 A

sin^2 A = 1 - 5/9

sin^2 A = 4/9

Taking the square root of both sides gives us:

sin A = +/- 2/3

However, we know that tan A < 0, which means that the sine and cosine functions have opposite signs in the quadrant where angle A lies. Since cosine is positive (given by cos A = sqrt(5)/3), angle A must lie in either the first or fourth quadrant, where sine is positive or negative, respectively. Therefore, we can eliminate the negative solution and conclude that:

sin A = 2/3

The coordinate of the other endpoint (x₂, y₂) of the line segment will be (8, -3).

Given that:

Midpoint, (x, y) = (3, 1)

First endpoint, (x₁, y₁) = (-2, 5)

The coordinate of the other endpoint of the line segment is calculated as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

(3, 1) = [(-2 + x₂) / 2, (5 + y₂) / 2]

(6, 2) = [(-2 + x₂), (5 + y₂)]

(x₂, y₂) = (6 + 2, - 5 + 2)

(x₂, y₂) = (8, -3)

The coordinate of the other endpoint (x₂, y₂) of the line segment will be (8, -3).

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Angle B, in the triangle ABC is solved to be 116 degrees

Angle B is solved using the concept of triangles and exterior angle relationship. This helps to know that addition of exterior angle to ∠B to angle B results to 180 degrees. Hence we have that:

exterior angle to ∠B + ∠B = 180

given data:

∠B = (15x − 19)°

exterior angle to ∠B is (9x − 17)°

plugging in gives

9x − 17 + 15x − 19 = 180

9x + 15x = 180 + 19 + 17

24x = 216

x = 9

For m∠B = (15x − 19)°

= 15 * 9 - 19

= 116 degrees

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Answer:

32 yards = 96 feet (1 yard = 3 feet, so 32 yards x 3 feet/yard = 96 feet)

1 foot = 12 inches, so 4 feet = 48 inches

3 miles = 5,280 yards (1 mile = 1,760 yards, so 3 miles x 1,760 yards/mile = 5,280 yards)

Therefore, the conversions are:

The monthly cost would be $138 if choose not to pay in full.

If you get a discount of 10% for being a good driver, then the cost of the policy before the full payment discount is:

1,025 × 0.9 = 922.50

If you pay the policy in full, you get an additional discount of 10%, so the cost of the policy after both discounts is:

922.50 × 0.9 = 830.25

If you choose not to pay in full, then you will not get the additional discount.

The policy cost is spread over 6 months, so the monthly cost would be:

= 830.25 / 6

= 138.38

Rounding this to the nearest dollar,

= 138

Thus, the monthly cost would be $138.

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Taxable income = $81,120,Total tax owed = $4,732.50 + $414.40 = $5,146.90 per year,Annual net pay = $81,120 - $5,146.90 = $75,973.10,Fortnightly net pay = $75,973.10 / 26 = $2,922.81

An amount of money that a government asks people to pay based on their income, property value, etc., and  is used to pay for things that the government does.

The accountant's gross income for two weeks is $3,120, so his gross income for the year is:

3120 x 26 = $81,120

Since they are not allowed to deduct tax, their taxable income equals their gross income:

Taxable income = $81,120

ii. Using the presented tax table, we can determine the accountant's tax liability:

Taxable income = $81,120

Income tax over $80,000 = (81,120 - $80,000) x 0.37 = $414.40

Income tax over $37,000 = ($37,000 - $18,200) x 0.325 = $4,732.50

Total tax liability = $4,732.50 + 414.40 = $5,146.90 per year

iii. An accountant's annual net salary is his gross income minus  tax liability:

Annual net salary = $81,120 - $5,146.90 = $75,973.10

iv. The accountant's semi-monthly net salary is the annual net salary divided by 26:

Net salary for two weeks = $75,973.10 / 26 = $2,922.81

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In the realm of computer networking, a traversable network is a structure in which any message or packet can be efficiently transmitted from one node to another without impediment.

Essentially, this implies that all nodes within the network are interconnected, devoid of any isolated segments that could impede data transmissions.

It should be noted that to ensure a network's traversability, several paths may be established between two given nodes or it might connect each node to a key switch or hub for communication purposes. Designing a topology with reliability and expedience at the core is essential for facilitating successful functioning, as traversable networks allow for information and resources to be sent swiftly - and without potential delay or loss. An overview was given based on the information.

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