If the measure of angle 4 is 43 degrees, then the measure of angle 6 is -------
degrees and the measure of angle 5 is -------- degrees. The measure of angle 8 is -------- degrees and the measure of angle 1 is --------- degrees.

The probability that either doubles are rolled or the sum of the dice is 10 is 2/9.

What is probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of

Total possible outcomes= 36

Probability that either doubles are rolled or the sum of the dice is 10

= 6 (doubles) + 2 (sum is 10, without double (5,5))

=8

P( either doubles are rolled or the sum of the dice is 10)= 8/36

                                                                                           = 2/9

Thus, probability that either doubles are rolled or the sum of the dice is 10 is 2/9.

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Answer:

\(\frac{16}{25}\)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Trust me on this one

The friend's locker (33) is located 13 lockers ahead of your locker (20).

To know location of your friend's locker relative to yours, we will calculate the difference between the locker numbers.

Given data:

The difference between the locker numbers is obtained by subtracting your locker number from your friend's locker number which i:

= 33 - 20

= 13

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The centre height of Sam's tent to the nearest tenth = 7.8 feet.

The length of both sides of the tent (a) = 5ft

The base of the tent is (b)= 6ft

The centre height (c) = ?

Using the Pythagorean theorem

c² = a² + b²

c² = 5² + 6²

c² = 100 + 36

c² = √136

c² = 7.8 feet

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Answer:

infinity  

Step-by-step explanation:

Answer: (5a-x)

Step-by-step explanation:

Divide the numbers infron the the letters by five

So the number infont of the a is 5 and the number infront of x is 1

Answer: - 58

Step-by-step explanation:

First, let us think of this number as x.

The first direction is to add 10 to it which is now x+10

After, we divide this by 6 getting -8.

This would look like (x + 10)/y = -8

Now, we solve

We go backwards so first step Is to multiply -8 by 6. This would get us -48. Then we subtract 10 since we added ten in the first place giving us -58.

The final answer is -58

Answer:

The original number was -58

Step-by-step explanation:

Step 1: Do -8*6 to find out what the numerator was.

Step 2: After finding that the numerator was -48 you would subtract 10 getting -58

Step 3: Check your work : -58+10 = -48

                                            -48/6 = -8

Answer:

Step-by-step explanation:

The side of the square = 3^2/7

Use the law of exponents . If the power is a fraction, that means it is

3^2/7 = 3^2 x 1/7 = 7√9

To find the area you multiply this by itself.

This gives you 1.87...

Hope this helps

Answer:

6 wholes

Step-by-step explanation:

\( \frac{19}{3} = 6 \frac{1}{3} \)

So there are 6 wholes in 19/3.

f(0.5) represents the volume of the smaller box when its' side length is 0.5 cm less than the larger cube

The formula to find the Volume of a cube is:

V = x³

where:

x is the side length of the cube

The cube has a volume of 27 cm³. Thus:

Side length of cube = ∛27 = 3 cm

Since the side length of the smaller cube is x cm less than side length of the larger cube, then we can say that the function to find the volume of the smaller cube is:

V_small: f(x) = (3 - x)³

Thus, f(0.5) is the volume of the smaller box when its' side length is 0.5 cm less than the larger cube

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Answer:

ok

Step-by-step explanation:

Answer:

  400

Step-by-step explanation:

You want to know the number of foxes predicted after 42 years by y = 50·2^x, where x is measured in 14-year periods.

42 years is 42/14 = 3 14-year periods. Using x=3 in the equation, we predict ...

  y = 50·2^3 = 50·8 = 400

foxes.

After 42 years, there will be 400 foxes.

__

Additional comment

It is often convenient to use time measured in 1-year periods. In that case, the equation could be written ...

  y = 50·2^(t/14)

Then t/14 is the number of 14-year periods when t is in years.

It will take A x hours to run the ​-mile state fair​ race at the same constant speed.

To find out how long it takes A to run the ​-mile state fair​ race, we need to use ratio reasoning and the unit rate.

First, let's calculate the unit rate of A's speed:

Speed = Distance / Time

A's speed in the local fair race = miles / hours

Unit rate = (miles / hours) /  = miles/hour

Now we can use the unit rate to find out how long it will take A to run the ​-mile state fair​ race.

Distance = Time x Speed

mile state fair​ race distance =  x miles

Time = Distance / Speed

Time = ( x miles) / ( miles/hour)

Time = x hours

So it will take A x hours to run the ​-mile state fair​ race at the same constant speed.

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Answer:

7

Step-by-step explanation:

Answer:

The number in the hundredths place is 7.

Step-by-step explanation:

Counted the decimal places ^

The future value of the annuity is approximately $17,636.45.

An annuity is a series of equal payments made at regular intervals. In this case, you started an annuity of $200 per month. The interest on the account is 3% compounded monthly.

To calculate the amount of money you will have in 3 years, we can use the formula for the future value of an annuity. The formula is:

FV = P * [(1 + r)^n - 1] / r

Where:
FV is the future value of the annuity
P is the monthly payment ($200)
r is the interest rate per period (3% per month, or 0.03)
n is the number of periods (3 years, or 36 months)

Plugging in the values into the formula, we have:

FV = 200 * [(1 + 0.03)^36 - 1] / 0.03

Calculating this expression, we find that the future value of the annuity is approximately $17,636.45.

Therefore, the correct answer is $17,636.45.

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At time t=2, the velocity vector is ⟨1/2, -1/4, 32⟩, the speed is sqrt(1025)/4, and the acceleration vector is ⟨-1/4, 1/2, 48⟩.

To find the velocity vector, speed, and acceleration vector of the object at time t=2, we need to take the first and second derivatives of the position vector with respect to time.

Position vector: r(t) = ⟨ln t, 1/t, t^4⟩

Velocity vector: v(t) = dr/dt = ⟨1/t, -1/t^2, 4t^3⟩

Acceleration vector: a(t) = d^2r/dt^2 = ⟨-1/t^2, 2/t^3, 12t^2⟩

To find the values at t=2, we plug in t=2 to the expressions for the velocity and acceleration vectors:

Velocity vector at t=2:

v(2) = ⟨1/2, -1/4, 32⟩

Speed at t=2:

|v(2)| = sqrt((1/2)^2 + (-1/4)^2 + 32^2) = sqrt(1025)/4

Acceleration vector at t=2:

a(2) = ⟨-1/4, 1/2, 48⟩

Therefore, at time t=2, the velocity vector is ⟨1/2, -1/4, 32⟩, the speed is sqrt(1025)/4, and the acceleration vector is ⟨-1/4, 1/2, 48⟩.

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Hi there!

\(\large\boxed{\text{ C. } 25\%}}\)

We have the numbers:

0  1  2  3  4  5  6  7  

There are 8 total numbers, and 2 of those numbers (1 and 3) represent a success. Therefore:

\(\text{p(success)} = \frac{\text{number of successes}}{total}\\\\\text{p(success)} = \frac{2}{8} = \frac{1}{4} = \boxed{25\%}\)

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Answer:

one solution

Step-by-step explanation:

that was easy

Answer:

2224.32 cm³

Step-by-step explanation:

La fórmula para el volumen de una pirámide hexagonal = 1/3 (1/2 × P × a) × h

Donde a = Apotema = 9,93 cm

P = Perímetro =

Pirámide hexagonal = 6 × Bordes de la base = 6 × 8 cm = 48 cm

h = Altura = 28 cm

Por eso,

Volumen de la pirámide hexagonal = 1/3 (1/2 (48 × 9.93) × 28 cm

= 1/3 × 238.32 × 28 cm

= 2224.32 cm³

Volumen de la pirámide hexagonal = 2224.32 cm³

The values of x and y by the descriptions in the task content are; 7.5 and 9 respectively.

It follows from the task content that the description in the task content registers the bottom right angle measure of the second intersection as equal to 10y.

Hence, it follows that; 10y = 90 and; y = 9.

From the first intersection; 6x + 5y = 90;

6x + 5(9) = 90

6x + 45 = 90

6x = 45

x = 45/6 = 7.5

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The volume of the solid formed by rotating the region inside the first quadrant enclosed by the curves y = x and y = 5x about the x-axis is (250π/7) cubic units. When finding the volume of a solid of revolution, we use the method of cylindrical shells.

To calculate the volume, we integrate the area of each cylindrical shell formed by rotating an infinitesimally small strip about the x-axis. The height of each shell is the difference between the y-values of the two curves, which is (5x - x²). The circumference of each shell is given by 2πx, and the thickness is dx. Therefore, the volume of each shell is 2πx(5x - x²)dx.

To find the total volume, we integrate this expression over the interval where the two curves intersect. Setting\(y = x^2\)and y = 5x equal to each other, we get x² = 5x. Solving this equation, we find two intersection points: x = 0 and x = 5. Thus, the limits of integration are from 0 to 5.

Integrating the expression \(2\pi x(5x - x^2)dx\) from 0 to 5 gives us the volume of the solid formed by rotating the region inside the first quadrant. Evaluating this integral, we find the volume to be (250π/7) cubic units.

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The annual rate of population growth in the US was about 1.2% in 2015, then the growth factor will be 1.012. The growth factor depends upon annual growth rate.

Growth factor typically refers to a constant multiplier that is used to calculate the growth or decay of a quantity over time. It is given as:

Growth factor = (1 + annual growth rate)

Therefore, the growth factor for the US in 2015 can be calculated as follows:

Growth factor (1+0.012) = 1.012

Therefore, the growth factor for the population of the US in the year 2015 was about 1.012.

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he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Both of these numbers are between 67 and 113, and they are both multiples of 2, 4, and 5.

In mathematics, a multiple is the product of a given integer and another integer. More specifically, an integer b is said to be a multiple of another integer a if there exists an integer c such that b = a * c. Multiples are used in various areas of mathematics, such as in finding common multiples of two or more numbers, or in identifying patterns in sequences of numbers. They also have applications in other fields, such as in physics where multiples of a fundamental frequency are used to describe harmonics in sound waves.

Here,

To find a number between 67 and 113 that is a multiple of 2, 4, and 5, we need to find the smallest common multiple (LCM) of these numbers. The LCM of 2, 4, and 5 is 20.

Next, we need to find the first multiple of 20 that is greater than or equal to 67. We can do this by dividing 67 by 20 and taking the ceiling of the result:

ceil(67/20) = 4

So the first multiple of 20 that is greater than or equal to 67 is 4 x 20 = 80.

Similarly, we need to find the last multiple of 20 that is less than or equal to 113. We can do this by dividing 113 by 20 and taking the floor of the result:

floor(113/20) = 5

So the last multiple of 20 that is less than or equal to 113 is 5 x 20 = 100.

Therefore, the numbers that Henry could choose are: 80, 100

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The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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No  matter what complex number we have, raising it to the power of 0 will always give us 1. Therefore, n must be 0 in this case.

The expression (13 + 4i) raised to the power of n is equal to 0. We need to find the value of n that satisfies this equation.

To solve this, we can set up the equation and use the fact that any number raised to the power of 0 is equal to 1. Therefore, if the expression is equal to 0, then the exponent n must be equal to 0 as well.

So, (13 + 4i)ⁿ = 0 implies n = 0.

In conclusion, n equals 0.

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5