Numbers 1 - 10 are written on cards and placed in a bag. Find the probability of choosing a number greater than 5 or choosing an odd number. ...?

Final answer:

Using the Law of Cosines, the length of the third side of the obtuse triangle is x = sqrt(52) or x = 2sqrt(13).

Explanation:

To find the length of the third side of an obtuse triangle with sides of lengths 4 and 10 and an area of 12, you can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the equation c^2 = a^2 + b^2 - 2ab * cos(C) can be used to find the length of side c.

In this case, let's assume that the third side of the triangle has length x. We can set up the equation as x^2 = 4^2 + 10^2 - 2*4*10 * cos(C), where C is the angle opposite side x.

Simplifying the equation, we get x^2 = 116 - 80*cos(C).

Since we know that the area of the triangle is 12, we can use the formula Area = 0.5 * a * b * sin(C) to find the value of sin(C). Plugging in the given values, we get 12 = 0.5 * 4 * 10 * sin(C). Solving for sin(C), we find sin(C) = 0.6.

Using this value of sin(C), we can then find the value of cos(C) by using the trigonometric identity sin^2(C) + cos^2(C) = 1. Substituting sin(C) = 0.6, we get 0.6^2 + cos^2(C) = 1. Solving for cos(C), we find cos(C) = 0.8.

Now, we can substitute the value of cos(C) into the equation x^2 = 116 - 80*cos(C), giving us x^2 = 116 - 80*0.8. Simplifying further, we get x^2 = 52, which means that the length of the third side is either x = sqrt(52) or x = -sqrt(52).

However, since we are dealing with the length of a side, it cannot be negative. Therefore, the length of the third side is x = sqrt(52), which simplifies to x = 2sqrt(13).

The value of the x is 5/4 when y=25 if y=15 when x=3/4 the answer would be 5/4

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

x and y are in a proportional relationship if y=15 when x=3/4,

y ∝ x

y = kx

15 = k(3/4)

k = 20

y = 20x

Plug y = 25

25 = 20x

x = 25/20

x = 5/4

Thus, the value of the x is 5/4 when y=25 if y=15 when x=3/4 the answer would be 5/4

The complete question is:

x and y are in a proportional relationship if y=15 when x=3/4, find x when y=25.

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Answer:

The answer is C, 6.4 inches

Step-by-step explanation:

Answer:

[tex]y=(x+8)^{2}[/tex]

Step-by-step explanation:

we have that

The ordered pairs [tex](1, 81), (2, 100), (3, 121), (4, 144)[/tex], and [tex](5, 169)[/tex] represent a function

The rule that that represent this function is equal to

[tex]y=(x+8)^{2}[/tex]

Verify

For [tex]x=1[/tex] -----> Find the value of y in the equation

[tex]y=(1+8)^{2}=81[/tex] -----> is correct

For [tex]x=2[/tex] -----> Find the value of y in the equation

[tex]y=(2+8)^{2}=100[/tex] -----> is correct

For [tex]x=3[/tex] -----> Find the value of y in the equation

[tex]y=(3+8)^{2}=121[/tex] -----> is correct

For [tex]x=4[/tex] -----> Find the value of y in the equation

[tex]y=(4+8)^{2}=144[/tex] -----> is correct

For [tex]x=5[/tex] -----> Find the value of y in the equation

[tex]y=(5+8)^{2}=169[/tex] -----> is correct

''90 feet in 2.5 hours'' have fastest speed.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

There are some distances and time.

Now,

For Option A;

⇒  18 feet in 20 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 18/20

               = 0.9 feet per minutes

For Option B;

⇒  90 feet in 2.5 hours

⇒ 90 feet in 150 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 90/150

               = 0.6 feet per minutes

For Option C;

⇒  20 yards in 1.5 hours

Since, 1 yards = 3 feet

⇒ 60 feet in 90 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 60/90

               = 0.67 feet per minutes

For Option D;

⇒  3 2/3 yards in 15 minutes

Since, 1 yards = 3 feet

⇒ 11 feet in 15 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 11/15

               = 0.73 feet per minutes

Hence, Clearly ''90 feet in 2.5 hours'' have fastest speed.

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Final answer:

After converting each option to the same unit of speed, it's clear that Option A with a speed of 0.9 feet per minute is the fastest.

Explanation:

To determine which speed is the fastest, we need to convert each option into the same unit of speed, typically feet per minute or meters per second for consistency. Here, we'll choose feet per minute for simplicity.

Option A: 18 feet in 20 minutes = 0.9 feet/minute

Option B: 90 feet in 2.5 hours (150 minutes) = 0.6 feet/minute

Option C: 20 yards (60 feet) in 1.5 hours (90 minutes) = 0.67 feet/minute

Option D: 3 2/3 yards (11 feet) in 15 minutes = 0.73 feet/minute

Comparing these speeds, Option A is the fastest with 0.9 feet per minute.

Answer:

C:63.76

Hope this helps

Final answer:

Ria will need 63.76 Indian rupees to buy one US dollar according to the given exchange rate.

Explanation:

The student is asking how many Indian rupees are needed to buy one US dollar based on the given exchange rates. According to the given information, the exchange rate from dollars to rupees is 63.76. This means that one US dollar is equivalent to 63.76 Indian rupees. The other exchange rate provided, which is the value of a rupee in terms of dollars (0.015), is not directly relevant to the question being asked. Therefore, Ria will need 63.76 Indian rupees to buy one US dollar.

After performing the calculations based on the provided formula and values, Katie will have approximately $9127 in her college savings account when she turns 18. The closest option given in the question would be C) $9287.

To solve this problem, you would input the given values into the formula V = P(1 + r)t where P is the principal amount (in this case $5000), r is the annual interest rate (3.5% or 0.035 when expressed as a decimal), and t is the number of years (18).

When you substitute these values in, the equation becomes V = 5000(1 + 0.035)18.

Using a calculator, you'll find that V equates to approximately $9127. Therefore, Katie will have approximately $9127 in her account when she turns 18. The correct answer among the given options is thus closest to option C) $9287.

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Answer:

The answer is A

Step-by-step explanation:

You need to use the midpoint formula of (x1+x2)/2,(y1+y2)/2

put in the actual points will look like this. (3x+5+x-1)/2,(3y-y)/2

now solve to get (4x+4)/2,(2y)/2

finish (2x+2,y)

Final answer:

The coordinates of the midpoint of the line segment with endpoints A(3x + 5, 3y) and B(x - 1, -y) are (2x + 2, y), using the midpoint formula.

Explanation:

To find the coordinates of the midpoint of a line segment with endpoints A and B, you can use the midpoint formula, which is ((x₁ + x₂)/2, (y₁ + y₂)/2). For the given endpoints A(3x + 5, 3y) and B(x - 1, -y), substituting the coordinates into the formula gives us the midpoint coordinates as follows:

Hence, the coordinates of the midpoint of AB are (2x + 2, y).

Answer:

Option D.

Step-by-step explanation:

The given vertices of quadrilateral ABCD are A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4).

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, we get

[tex]AB=\sqrt{\left(-4-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{0^2+(2)^2}=\sqrt{4}=2[/tex]

Similarly,

[tex]BC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-2\right)\right)^2}=3[/tex]

[tex]CD=\sqrt{\left(-1-\left(-1\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=2[/tex]

[tex]AD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-4\right)\right)^2}=3[/tex]

[tex]AB = CD[/tex]

[tex]BC = AD[/tex]

Measure of diagonals:

[tex]AC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{13}[/tex]

[tex]BD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=\sqrt{13}[/tex]

[tex]AC = BD[/tex]

Since measure of opposite sides are equal and measure of diagonals are equal, therefore the given quadrilateral ABCD is a rectangle.

Hence, the correct option is D.

A 'space cushion' increases safety by providing more time to react and decreasing the force of impact in a collision, akin to how airbags and crumple zones function in a vehicle.

The concept of a "space cushion" around your vehicle pertains to having a safe distance between your vehicle and others on the road. This increases the time you have to react to unexpected events and minimizes the force of impact during a collision, related to the physics principle of impulse. A larger space cushion effectively reduces the net force on your vehicle and its occupants by allowing more time for the vehicle to come to a stop or slow down. Features like airbags and crumple zones in cars serve a similar purpose by increasing the time over which a collision occurs, thereby reducing the impact force. This is crucial because the severity of injuries incurred during a vehicle accident is often directly related to the force exerted on the occupants.

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Answer: B. negative

Step-by-step explanation:

Given: In a linear equation, the independent variable increases at a constant rate while the dependent variable decreases at a constant rate.

We know that the slope of a line is given by :-

[tex]k=\dfrac{\text{change in y}}{\text{change in x}}[/tex]

According to the given information, if independent variable increases at a constant rate while the dependent variable decreases at a constant rate, then the slope of line will be :-

[tex]k=\dfrac{\text{Negative}}{\text{Positive}}=\text{Negative}[/tex]

Hence, the slope of line = Negative.

Solution:

As, you can see that shape 1 and shape 2 are not congruent nor the shape 1 is dilated by any factor to get the shape 2.

Both the shapes are concave polygon.

The base length of two shapes are equal .

→2 ×  AB  =  P Q  →(approx)

→BC=QR

→2 × CD= RS→→→(approx)

If translation has taken place, all the vertices has been translated by same amount.

So, option (4) is true,which is Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2."

Answer:

Option B. y = 8x - 7

Step-by-step explanation:

Parallel lines don't have the common points or the points of intersection.

In a system of equations has no solutions out of which one equation is y = 8x + 7

So a line parallel to this line will have no solutions.

For parallel lines slope will be same as 8, so the equation will be

y = 8x - 7

Option B. y = 8x - 7 will be the answer.

Answer:

15

7

Just to simplify the answer above.

Step-by-step explanation:

The given statement:

The condition ∑ Fi = 0 is sufficient to assure that a rigid body is in equilibrium is a

TRUE statement.

According to the condition for the equilibrium of a rigid body, the vector sum of all the forces acting on the body must be zero.

The first condition of equilibrium for a rigid body is as follows:

                             ∑ Fi = 0

where the expression  ∑ Fi are the sum of all the forces acting on the body.

Hence, the given statement is a TRUE statement.