Please help with 3 4 and 5

The plane's true bearing is $27.9°N of W, and its estimated ground speed is 473.3 mph.

Math is made more fascinating and enjoyable using Speed Maths (Vedic Maths). by assisting the child in quickly performing some improbable computations. By combining the correct amount of enjoyment, memory, skills, memory recall, and formula application, your child will become a superstar performer.

Let's start with the airplane's speed.

A bearing of N25°W corresponds to a anticlockwise angle of 65° when measured from the westward direction (W).

As a result, the airplane's velocity vector can be divided into its north-south and east-west components as shown below:

V_A,north = 480 cos(65°) ≈ 200.5 mph (northward)

V_A,west = 480 sin(65°) ≈ 447.3 mph (westward)

V_W,north = 45 sin(75°) ≈ 43.5 mph (northward)

V_W,west = 45 cos(75°) ≈ 11.3 mph (westward)

To find the net velocity of the airplane, we can add the north-south and east-west components of the airplane velocity and wind velocity separately:

V_net,north = V_A,north + V_W,north ≈ 200.5 + 43.5 ≈ 244.0 mph (northward)

V_net,west = V_A,west + V_W,west ≈ 447.3 + 11.3 ≈ 458.6 mph (westward)

Now we can use the Pythagorean theorem to find the magnitude of the net velocity:

|V_net| = sqrt(V_net,north² + V_net,west²) ≈ 473.3 mph

To find the actual bearing of the airplane, we can use the inverse tangent function:

tan⁻¹(V_net,north / V_net,west) ≈ 27.9°

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Answer: Check down below!!!

Step-by-step explanation:

   8x² = 6x² + 5x²

   This problem can be solved by combining like terms. To do this, we add up the coefficients of the x² terms:

8x² = 6x² + 5x²

8x² = 11x²

Now, we can isolate x² by subtracting 11x² from both sides of the equation:

8x² - 11x² = 11x² - 11x²

-3x² = 0

Finally, we can divide both sides of the equation by -3 to get:

(-3x²)/(-3) = 0/(-3)

x² = 0

So the solution is x = 0.

   -7x² + 6 = x² - 7x²

   This problem can be solved by combining like terms. To do this, we add up the coefficients of the x² terms:

-7x² + 6 = x² - 7x²

-7x² + x² = -7x² + 6

-6x² = 6

Now, we can isolate x² by dividing both sides of the equation by -6:

(-6x²)/(-6) = 6/(-6)

x² = -1

So the solution is x = ±√(-1), which is an imaginary number.

   7x² + 9x² = -6x² - 7x

   This problem can be solved by combining like terms. To do this, we add up the coefficients of the x² terms:

7x² + 9x² = -6x² - 7x

16x² = -6x² - 7x

Now, we can isolate x² by adding 6x² to both sides of the equation:

16x² + 6x² = -6x² + 6x² - 7x

22x² = -7x

Finally, we can divide both sides of the equation by 22 to get:

22x²/22 = -7x/22

x² = -7x/22

So the solution is x = ±√(-7/22), which is a complex number.

The dot product of two vectors [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex]  in terms of the positive scalar quantities a, b, c, and d is:

[tex]\vec{A}.\vec{B}=-ab[/tex]

The scalar product of two vectors [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex] is given by the formula:

[tex]\vec{A}.\vec{B}=(a_1*b_1) + (a_2*b_2) + (a_3*b_3)[/tex]

Where a₁, a₂, and a₃ are the components of vector [tex]\vec{A}[/tex] and b₁, b₂, and b₃ are the components of vector [tex]\vec{B}[/tex].

In this case, vector A = (ai - bk) and vector B = (- cj + dk), so the components of vector A are a₁ = a, a₂ = 0, and a₃ = -b, and the components of vector B are b₁ = 0, b₂ = -c, and b₃ = d.

Plugging these values into the formula for the dot product, we get:

[tex]\vec{A}.\vec{B}=(a*0) + (0*-c) + (-d*b)\\\\\vec{A}.\vec{B}= 0 + 0 + (-bd) \\\\\vec{A}.\vec{B}=-bd[/tex]

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Answer:

Number is -10

Step-by-step explanation:

Let Number be x

so, 5x= 30+8x

Take 30 other side and 5x other side

so, 8x-5x=-30

3x=-30

x=-10

HOPE THIS HELPS... THANK YOU

If a 0.10 significance level is used in place of a 0.05 significance level, the power of the test will generally increase. As we are increasing the probability of rejecting the null hypothesis.

The significance level (alpha) of a hypothesis test determines the probability of making a Type I error, which is the probability of rejecting the null hypothesis when it is actually true. The power of a test, on the other hand, is the probability of correctly rejecting the null hypothesis when it is actually false (i.e., the probability of detecting a true effect).

By using a higher significance level (0.10 instead of 0.05), we are increasing the probability of rejecting the null hypothesis, which means we are more likely to detect a true effect. This results in an increase in the power of the test. However, it's worth noting that using a higher significance level also increases the risk of making a Type I error, which means we have to be careful when interpreting the results of the test.

In summary, increasing the significance level generally increases the power of the test, but it also increases the risk of making a Type I error

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Answer:

lol

Step-by-step explanation:

that sucks

The obtuse angle θ which has the same value of sin(-275) is 95°, which is in the second quadrant.

What are the different quadrants of trigonometric identities?

The first quadrant has angles between 0 and 90 degrees. The second quadrant has angles between 90 and 180 degrees. The third quadrant contains angles between 180 and 270 degrees. The fourth quadrant contains angles between 270 and 360 degrees. All six trigonometric functions have positive values in the first quadrant.  The only positive values in the second quadrant are sine and cosecant. The only positive values are tangents and cotangents in the third quadrant. The only positive values in the fourth quadrant are cosine and secant.

We are asked to find an obtuse angle θ such that 0 ≤ θ ≤ 2π and has the same sine as -275°.

The value of sin(-275°) = 0.996

Since the value of sin(-275°) is positive, the angle θ should be in the first or second quadrant, because the sine of angles in the first and second quadrants is positive.

But the θ should be an obtuse angle.

So θ should be in the second quadrant.

sin(-275) = sin(360-275) = sin 85° = 0.996

sin(180 - 85) = sin(95)  = 0.996

Therefore the obtuse angle θ which has the same value of sin(-275) is 95°, which is in the second quadrant.

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The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in (4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in (6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Answer: We know that the volume of a cuboid is given by the product of its length, width and height, or V = l * w * h. In this case, the length is 250 cm and the height and width are both x cm. So, the volume can be written as:

V = 250 * x * x

Substituting the given value of V = 4840 cm³, we get:

4840 = 250 * x * x

Dividing both sides by 250, we get:

19.36 = x * x

Taking the square root of both sides, we get:

x = ±√19.36

Since the side length of a square must be positive, we use the positive square root:

x = ±4.4 cm

Therefore, the side length of the square cross-section is 4.4 cm.

Step-by-step explanation:

The area of the triangle is 72 units².

The area of a triangle can be found using sine as follows:

area of a triangle = 1 / 2 ab sin C

Hence,

Therefore,

area of a triangle = 1 / 2 × 12 × 24 × sin 30

area of a triangle = 1 / 2 × 288 × sin 30

area of a triangle = 1 / 2 × 288 × 0.5

area of a triangle = 1 / 2 × 144

area of a triangle = 72 units²

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As per the ratio, the number of men on the sight-seeing tour is 4.

In the given sight-seeing tour, we are told that there were 14 people in total. We are also given the ratio of women to children, which is 5 to 2. This means that for every 5 women on the tour, there were 2 children.

To find the number of men on the tour, we need to first find the number of women and children. We can do this by dividing the total number of people by the ratio of women to children.

Let's use a variable to represent the number of sets of 5 women and 2 children. We'll call this variable "x".

So, the number of women on the tour is 5x and the number of children is 2x.

Now, we can set up an equation to find the value of x:

5x + 2x = 14

This equation represents the total number of women and children on the tour, which is equal to 14.

Simplifying the equation, we get:

7x = 14

Dividing both sides by 7, we get:

x = 2

This means that there were 2 sets of 5 women and 2 children on the tour. So, the number of women is:

5x = 5(2) = 10

The number of children is:

2x = 2(2) = 4

Now, we can find the number of men by subtracting the number of women and children from the total number of people:

14 - 10 = 4

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Step-by-step explanation:

here, 4 days = 20 miles

so, 1 day = 5 miles

hence, x miles = 5x miles

Answer:

Step-by-step explanation:

4x + 9 = x + 30

3x + 9 = 30

3x = 21

x = 7

Answer:

Step-by-step explanation:

The gardener used 5/8 of the soil, which is equal to 10 * 5/8 = 10 * 0.625 = 6.25 pounds.

So, he used 6.25 pounds of soil in the garden.

The gardener had 10 - 6.25 = 3.75 pounds of soil left.

Answer:

{y l y > 9}

Step-by-step explanation:

Given function:

[tex]f(x)=3^x+9[/tex]

The given function is an exponential function.

The parent function is the basic equation before the function has undergone any transformation(s).  Therefore, the parent function of the given function is:

The range of the parent function is restricted to positive real numbers as it never takes a negative value.  Furthermore, it never reaches zero (although it approaches y = 0 as x → -∞).  Therefore, the range of the parent function is {y | y > 0}.

As the given function has been translated up 9 units (by the addition of "+ 9"), the range of the given function is translated 9 units up.  So as x approaches negative infinity, y approaches (but never reaches) 9. Therefore, the range of the given function is:

Factor the polynomial by factoring out the greatest common factor, 7x2 + 5 - x = 6x2 + 10

x = -5

Soultion:

→ 7 × 2 + 5 - x = 6 × 2 + 10

Multiply.

→ 14 + 5 - x = 12 + 10.

Combine like terms.

→ 19 - x = 24

Isolate x (I'm going to add x and subtract 24 from both sides to avoid changing signs)

Answer

→ = x = -5

The rounded number to the nearest thousands place is 9,910,000

To change a number into an approximation having fewer significant digits is called rounding a number.

Given that, a number 9,909,937 we are asked to round it,

9,909,937 in words =

nine million nine hundred nine thousand nine hundred thirty-seven

Therefore, to round to the nearest thousand;

You rounded to the nearest thousands place. The 9 in the thousands place rounds up to 10 because the digit to the right in the hundreds place is 9.

Because the thousands place was rounded up from 9 to 10, the thousands place becomes 0 and the ten thousands place is increased by 1. When a 9 is rounded up to 10, that place value becomes 0, and we add 1 to the previous place value.

9,910,000

When the digit to the right is 5 or greater we round away from 0. 9909937 was rounded up and away from zero to 9,910,000

Hence, the rounded number to the nearest thousands place is 9,910,000

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Answer:

18.84

Step-by-step explanation:

Answer:

The possible values of the constant b are:

[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]

Step-by-step explanation:

The coefficient of x² in the expansion of (2 - x)(3 + bx)³ can be found by expanding the brackets.  

Expand the cubed part by using the (a + b)³ formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Therefore:

[tex]\begin{aligned}(3 + bx)^3 &= (3)^3 + 3(3)^2(bx) + 3(3)(bx)^2 + (bx)^3\\&= 27 + 27bx + 9b^2x^2 + b^3x^3\end{aligned}[/tex]

So:

[tex](2-x)(3 + bx)^3 = (2-x)(27 + 27bx + 9b^2x^2 + b^3x^3)[/tex]

To find the coefficient of the term in x², multiply the constant in the first parentheses by the coefficient of the term in x² in the second parentheses and add this to the product of the coefficient of the term in x in the first parentheses and the coefficient of the term in x in the second parentheses:

[tex](\bold{2}-x)(27 + 27bx + \bold{9b^2}x^2 + b^3x^3)\\\phantom{.}\underbrace{\uparrow \qquad \qquad\qquad\qquad\;\uparrow}\\ \phantom{wlwww}\text{multiply}[/tex]

[tex](2-x)(27 + \bold{27b}x + 9b^2x^2 + b^3x^3)\\\phantom{bbb..}\underbrace{\uparrow \qquad \quad\;\uparrow}\\ \phantom{ww.w}\text{multiply}[/tex]

Therefore, the expression for the coefficient of x² is:

[tex]2 \cdot 9b^2 + (-1) \cdot 27b[/tex]

Since the coefficient of x² in the expansion is 45, set the expression to 45 and solve for b:

[tex]\begin{aligned}2 \cdot 9b^2+(-1) \cdot 27b&=45\\18b^2-27b&=45\\18b^2-27b-45&=0\\9(2b^2-3b-5)&=0\\2b^2-3b-5&=0\\2b^2-5b+2b-5&=0\\b(2b-5)+1(2b-5)&=0\\(b+1)(2b-5)&=0\\\\ \implies b+1&=0 \implies b=-1\\ \implies 2b-5&=0 \implies b=\dfrac{5}{2}\end{aligned}[/tex]

Therefore the possible values of the constant b are:

[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]

Answer:

10.00 & 0.05

Step-by-step explanation:

[tex]10.00 - 0.05 = 9.95[/tex]

The amount of money as change is $ 0.05 and the amount of money given is $ 10.00

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the cost of the item = $ 9.95

The amount of money given = $ 10.00

So , the amount of money received as change = amount of money given - cost of the item

On simplifying the equation , we get

The amount of money received as change = 10.00 - 9.95

The amount of money received as change = $ 0.05

Hence , the amount of change is $ 0.05

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Answer:

Step-by-step explanation:

To determine whether a value is greater than or less than a specific result from an equation, you would need to substitute the value into the equation and solve for the result. For example, if you want to determine if the value "a" is greater than or less than the result of the equation -2x^2 + 16x - 36, you would substitute "a" for the variable x and solve for the result:

-2x^2 + 16x - 36 = -2a^2 + 16a - 36

Then you can compare the value of the result to "a" to determine whether it is greater than or less than.

If the result is greater than "a", you would write:

-2a^2 + 16a - 36 > a

If the result is less than "a", you would write:

-2a^2 + 16a - 36 < a

And if the result is equal to "a", you would write:

-2a^2 + 16a - 36 = a

It's important to note that the comparison only holds for a specific value of "a". The equation -2x^2 + 16x - 36 could have many solutions where the result is greater than, less than, or equal to "a".

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Explanation:

2/3 of 150 = (2/3)*150 = 100 employees are male and 150-100 = 50 employees are female. This is before the resignations.

After the resignations happen, we would have:

The chances of picking a female employee at random would be 40/120 = 1/3 which is the final answer.

Notice how the chances haven't changed from earlier (male = 2/3 chance, so 1-2/3 = 1/3 are the chances of picking a woman). Why is this? Well notice the ratio of 20 men to 10 women resigning. This ratio is 2:1, meaning twice as many men resigned. Furthermore, notice how 2/3 is twice that of 1/3.

This keeps the same proportion of men to women. Therefore, the odds haven't changed.

Gold costs less than platinum per ounce because the slope of the graph for gold is less than that of the chart for platinum. The slope of the graph tells you the unit rate in dollars per ounce.

In Mathematics, a slope is sometimes referred to as rate of change and it is 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 (rate of change) can be calculated by using this mathematical expression;

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the graph of the weight of gold and platinum, we can reasonably infer and logically deduce that the slope (unit rate) of the graph for gold is less than the slope (unit rate) of the graph for platinum.

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Complete Question:

Use the drop-down menus to complete the statements to match the information shown by the graph.

A graph has weight (ounces) on the x-axis, and cost (dollars) on the y-axis. A line labeled gold starts at (0, 0) and has a positive slope. A line marked platinum starts at (0, 0) and has a greater positive slope than gold.

Gold costs ---------------- platinum per ounce because the ----------- of the graph for gold is -------------that of the chart for platinum. The --------of the graph tells you the unit rate in _____.

Step-by-step explanation:

The constant in an expression is the number without any letters attached to it.

Looks like B and E are the only ones with constant. The other 3 only have numbers attached to numbers

Answer:

x = -2, y = -4

Step-by-step explanation:

Take the first equation-   -2y = 2 - 3x
Arrange it first-
-3x + 2y = -2

Multiply is by 5 on both sides
5(-3x + 2y) = 5(-2)
-15x + 10y = -10

Take the second equation-    -5y = 10 - 5x
Arrange it-
-5x + 5y = -10

Multiply is by 2 on both sides
2(-5x + 5y) = 2(-10)
-10x + 10y = -20

Subtract second equation from the first one-

  -15x + 10y = -10
-  -10x + 10y = -20
= -5x = 10

-5x = 10
x = 10/(-5)
x = -2

Substitute the value of x in Equation 1
-2y = 2 - 3(-2)
-2y = 2 + 6
-2y = 8
y = 8/(-2)
y = -4

Hope it helps ;)

Answer:

Mai spent 60% of her total spending on fruit

Step-by-step explanation:

To find the percentage of the total spent on fruit, we can divide the amount spent on fruit by the total amount paid and multiply by 100 to express the answer as a percentage.

First, let's find the amount spent on things other than fruit: $15 total spent - $9 spent on fruit = $6 spent on other things.

Next, we divide the amount spent on fruit by the total amount spent: $9 on fruit / $15 total spent = 0.6.

Finally, we multiply by 100 to express the answer as a percentage: 0.6 * 100 = 60%.

So Mai spent 60% of her total spending on fruit.

The best describes EB is diameter of circle because it is a chord of circle which passes through the center.

A circle is a two-dimensional object made up of points that are spaced out from a given point (centre) on the plane by a fixed or constant distance (radius). The fixed point is referred to as the circle's origin or centre, and the fixed distance between each point and the origin is referred to as the radius.

The following components make up a circle:

Circumference: Also known as a circle's perimeter, circumference is the distance a circle travels around its circumference.

Radius: The radius is the distance a circle's center is from any point on its edge.

A diameter is a straight line that links two places on the circle's edge and passes through the center.

So that EB is describes as diameter of circle because it is a chord of circle which passes through the center.

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A large tank hold 1. 9 time 10 to the 7th power gallons of oil. The amount of oil that can be stored in 9 tanks is 1.71 x 10^8 gallons in scientific notation.

To find the amount of oil that can be stored in 9 tanks that each hold 1.9 x 10^7 gallons of oil, we can use the following steps:

Write down the number of gallons that one tank can hold: 1.9 x 10^7 gallons. Multiply this value by the number of tanks: 1.9 x 10^7 gallons/tank x 9 tanks.

To multiply the two numbers, we can simply multiply the coefficients (1.9 and 9) and add the exponents (7 in this case): (1.9 x 9) x 10^(7+0) gallons.

Simplifying the coefficient gives us 17.1, so the amount of oil that can be stored in 9 tanks is 17.1 x 10^7 gallons.

Finally, we can express this result in scientific notation by writing it as 1.71 x 10^8 gallons, since 17.1 is equivalent to 1.71 x 10.

Therefore, the amount of oil that can be stored in 9 tanks is 1.71 x 10^8 gallons in scientific notation.

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The answer is 1.25 ft-lb. This can be calculated by multiplying 15 ft-lb by (9 in. / 12 in. per ft), which equals 1.25 ft-lb. The amount of work needed to stretch a spring 9 inches beyond its natural length is 1.25 ft-lb.

1. Convert 9 in. to feet by dividing 9 in. by 12 in. per ft.

2. Multiply the result (0.75 ft) by 15 ft-lb, which equals 1.25 ft-lb.

The amount of work needed to stretch a spring 9 inches beyond its natural length is 1.25 ft-lb. This can be found by taking the given work required to stretch the spring 1 foot (15 ft-lb) and multiplying it by the ratio of the desired distance (9 in.) to 1 foot (12 in. per ft). First, the desired distance of 9 inches must be converted to feet by dividing it by the conversion factor of 12 inches per foot. This results in 0.75 feet. This number is then multiplied by the given work of 15 ft-lb to yield 1.25 ft-lb of work. This is the amount of work needed to stretch the spring 9 inches beyond its natural length.

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If you multiply the left side of an equation by 4, what must you multiply the right side of the equation by 4

Here you you multiply the left side of an equation by 4.

According to the solving for unknow rule you must perform same function to both side of the equation. If you multiply the left side of an equation by any integer then you must multiply the same integer on right hand side of the equation

To maintain equality, you must multiply the right side of the equation by 4 as well.

This is because the left side of the equation represents the same quantity as the right side, so any operation that is performed on one side must also be performed on the other side to preserve the equality.

Therefore, you must multiply the right side of the equation by 4

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