When dividing two numbers written in exponential notation, what do you do with the exponents of 10?

Step-by-step explanation:

the middle one has to be the same for both part ratios.

the best here is to bring the ratio element of B in the first part ratio to 10. we need to double the B element there

for that (as a ratio is a fraction) we also have to adapt the A element in the same way.

so, we get

4×2 : 5×2 : 9 =

= 8 : 10 : 9

and that is also shown in the graphic.

Answer:

X:Y:Z= 8:10:9

Step-by-step explanation:

Let x be the number of students in class A

Let y be the number of students in class B

Let z be the number of students in class C

x:y = 4:5

y:z= 10: 9

x:y:z = ?

Find the LCM of the y terms (5 and 10 ) which is 10

Divide 10 by the first y term (5) = 2

Divide 10 by the second y term(10) = 1

X: y = (4 x 2) :(5 x 2)= 8:10

y:z =(10 x 1) : (9:1)= 10:9

x:y:z= 8:10:9

The angles of the rhombus are m∠ACD = (93 - 4x)°

                                                   m∠ABC= ( 93 - 3x) °

                                                    m∠BEA = 90°

A quadrilateral with four equal sides is known as a rhombus.

The rhombus has an equal number of sides.

In a rhombus, the opposing sides are parallel.

In a rhombus, the opposing angles are equal.

Diagonals in a rhombus cut each other at right angles.

Given ∠BCE = (7x-6)° and ∠EDA = ( 4x - 3)°

Since the diagonals bisect at 90°, the angles ∠BEC,∠CED,∠DEA  and ∠AEB are 90°.

In Δ AED, since total sum of angles in a triangle is 180°,

∠DAE = 180 - ( 90+4x-3) = (93 - 4x)°

The opposite angles in a rhombus are equal. So ∠DAE = ∠DCE

So m∠ACD =∠DCE=(93 - 4x)°

In ΔBEC

∠EBC = 180 - ( 90 + 7x - 6) = (96 - 7x)°

∠ADB = ∠ ABD ( Equal angles)

m∠ABC = ∠ABD + ∠EBC

            = 4x - 3 + 96 - 7x

            = (93 - 3x)°

Therefore m∠ACD = (93 - 4x)°

               m∠ABC= ( 93 - 3x) °

               m∠BEA = 90°

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The distance from the base of the ladder to the wall is approximately 2.9 feet.

To solve for the distance from the base of the ladder to the wall, Walter used the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side of a right triangle.

In this case, the opposite side is the height of the ladder on the wall, and the adjacent side is the distance from the base of the ladder to the wall.

Since the angle between the ladder and the ground is 75 degrees, the other acute angle in the right triangle is 15 degrees. Therefore, Walter used the formula for a tangent:

tangent(15) = height of the ladder on the wall/distance from the base of the ladder to the wall

Solving for the distance, we get:

distance = height of the ladder on the wall/tangent (15)

Substituting the values given, we get:

distance = 12 * sin(75) / tan(15) ≈ 2.9 feet

Therefore, the distance from the base of the ladder to the wall is approximately 2.9 feet.

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Answer:

31.53

Step-by-step explanation:

6% of 525.50 is 31.53

Answer:18°

Step-by-step explanation:

6x3=18

An indirect proof is used to show the negation of a statement. It is a proof by contradiction. The process starts by assuming the opposite of the statement is true. The opposite of the statement is shown to be false, and, as a result, the statement must be true.

The key to an indirect proof is to assume the negation of the statement, and then to use logical steps to derive a contradiction. Here's an indirect proof to prove n intersects k:Given: Coplanar lines j, k, n; n intersects j at P; j || k

To Prove: n intersects k Assume for the purpose of contradiction that n does not intersect k.Draw a line m that is parallel to both j and k such that m intersects n and k at M and K respectively.

This can be done because of the parallel postulate. Thus, line m is a transversal for lines n and k and angles MKP and KPB are alternate interior angles and angles KPB and KPN are corresponding angles. Since alternate interior angles and corresponding angles are congruent, it follows that MKP = KPN.

However, since P lies on line n, it follows that angle KPN is a straight angle. Therefore, MKP is also a straight angle, which implies that M, P, and K are collinear. Since line m intersects both k and n, this contradicts the assumption that n does not intersect k. Therefore, n intersects k.

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Answer:

Hello!!

your answer will be option D.96m^2

Step-by-step explanation:

\(a = 6 \times 10 + \frac{6 \times 12}{2} = 96m ^{2} \)

hope it's helpful

have a great day

Answer: 62.34

Step-by-step explanation:

\(\sum^{5}_{n=0} 3(3/2)^n=3[(3/2)^0 +(3/2)^1 +(3/2)^2 +(3/2)^3 +(3/2)^4 +(3/2)^5] \approx 62.34\)

There will be a total of 1620 four digit numbers having an even second digit and a fourth digit that is atleast twice of the second digit.

Possible second digits allowed = 0,2,4

digits 6 and 8 are also even but cant be included as their twice yeild double digits.

For each of the allowed digits, the possible fourth digit ranges from 0-9(if second digit is zero), 4-9(if second digit is considered as 2) and 8-9(if second digit is 4). Hence the total number of fourth digits allowed            = 10+6+2=18.

The first digit can be any non zero number whereas the third digit can be from 0-9.

Hence the total number of four digits allowed: 9×10×18 = 1620.

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The correct answer is c. frequency polygon.

A chart that contains a continuous line representing the frequencies of scores within a class interval is known as a frequency polygon. Frequency polygons are graphical representations of frequency distributions, which show the number of observations or data points falling within each interval or class.

A histogram, option a, is a graphical representation of data where the data is divided into intervals and displayed as bars. It does not include a continuous line.

Option b, standard deviation, is a measure of the dispersion or spread of a dataset, and it is not directly related to the representation of frequencies.

Option d, frequency distribution, refers to a tabular representation of data that shows the number of observations or data points falling within each interval or class, but it does not include a continuous line plot.

In summary, a frequency polygon is the chart that contains a continuous line representing the frequencies of scores within a class interval.

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The analyst should use the alpha aesthetic. The alpha aesthetic makes some points on a plot more transparent than others to call out specific data points.

A set of points plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of correlation, if any, between the values of observed quantities or phenomena, scatter plots are crucial in statistics (called variables). In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.

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Answer:

CAB

BAC

Step-by-step explanation:

A P E X

A decrease in government purchases of $20 billion will shift the aggregate demand curve to the B. left by about $57.1 billion.

In economics, the marginal propensity to consume (MPC) is defined as the proportion of a pay increase that a consumer spends on goods and services rather than saving. Customers may also save a portion of their extra cash. These tendencies are more than just observations; they serve as the foundation for the marginal propensity to save (MPS) and the marginal propensity to consume.

The marginal propensity to consume is calculated by dividing the change in consumption by the change in income. For example, if a person's spending increases by 90% for every new dollar earned, the equation would be 0.9/1 = 0.9.

Since the MPC is 0. 65. and there's a decrease in government purchases of $20 billion, this will be:

= Purchase / (1 - MPC)

= 20 billion / (1 - 0.65)

= 57.1 billion

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Assume the MPC is 0.65 . Assuming only the multiplier effect matters, a decrease in government purchases of $20 billion will shift the aggregate demand curve to the

a. left by about $30.77 billion.

b. left by about $57.1 billion.

c. right by about $57.1 billion.

d. right by about $30.77 billion

Area will be 2\(r^{2}\)

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form.

Given radius of circle is r

Then area of circle=π\(r^{2}\)

The diagonal of the square is comparable to the diameter (2r) of the circle since two opposing corners of the square contact it.

Now, we will set up Pythagoras' Theorem to determine one side of the square:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

Since it is a square a=b which means all  the sides are same

∴2\(a^{2}\) = \(c^{2}\)

We know c, which is 2r, the diagonal.

∴2\(a^{2}\) = \((2r)^{2}\)

⇒\(a^{2}\) = 2\(r^{2}\)

We can leave it as \(a^{2}\)

since a is one side of the square and \(a^{2}\) would be the area of the square.

So the area of the square =2\(r^{2}\)

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Answer:

The density is the same because both cubes are composed of the same element Iron(Fe).

Answer:

I believe the large cube would be denser.

Step-by-step explanation:

Therefore, The Coordinates of the THIRD VERTEX is:  ( 5, -3 )

        Calculate the midpoint of the given vertices:

        MidPoint = ( -5 + 5/2,  3 + 3/2 )

        MidPoint = ( 0, 3 )

        Distance = √( -5 -5 )^2 + ( 3 - 3 )^2

        Distance = √( -10 )^2  +  (0)^2

        Distance = √100

        Distance =  10

        Side Length =  10/√3

        Side Length = 10/1.7

        Side Length = 5.88

        Height = √3/2  *  Side Length

        Height  = 1.7/2  *  5.88

        Height  =  5

Since the origin lies inside the triangle, The Third Vertex will have a Positive  X-Coordinate and a Negative Y-Coordinate.

       ( x, y )

        x  =  -5 + x/2

        y   =  3 + y/2

       x  =  5

       y  = -3

        Hence, The Coordinate  of the Third Vertex is:  ( 5, -3 )

I hope this helps!

Answer:

b =✓45

Step-by-step explanation:

9^2-6^2

√45

b= ✓45

(i) The meaning of the differential equation dP/dt = kP is that it represents the rate of change of the population (P) with respect to time (t) being proportional to the population size. The constant parameter k determines the growth rate of the population.

(ii) To solve the initial value problem, we can separate variables and integrate:

∫ (1/P) dP = ∫ k dt

ln|P| = kt + C

P = e^(kt+C) = e^C * e^(kt)

Considering the initial condition P(0) = P0, we can determine the value of the constant C:

P0 = e^C * e^(k*0) = e^C

C = ln(P0)

Therefore, the solution to the initial value problem is:

P = P0 * e^(kt)

In the long run, as t approaches infinity, the exponential term e^(kt) becomes very large, leading to unbounded growth of the population. This means that the population will continue to increase without limit.

(iii) The unconstrained growth model is appropriate under the assumption that there are no limiting factors or constraints on population growth, such as limited resources or competition. In reality, most populations are subject to constraints, and their growth cannot continue indefinitely. This model does not align with the situation Thanos is describing because he believes that unchecked growth will lead to the extinction of populations, whereas the unconstrained growth model implies unlimited growth.

(iv) If the population size is suddenly cut in half, we can represent it by changing the initial condition. Let's denote the new initial population size as P1. The model becomes:

P = P1 * e^(kt)

In this case, the parameter P1 would change to represent the new population size, while the growth rate parameter k remains the same. This new model would reflect a population that starts with a reduced size but continues to grow according to the same growth rate as before.

It's important to note that these population models provide a simplified representation of population dynamics and do not account for all the complexities and factors involved in real-world populations.

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Answer:

67.5 kg

Step-by-step explanation:

To determine the weight of 45 books, we need to determine the weight of one book, using the equation (30 books = 45 kg). This can be done by dividing 30 to both sides of the equation. Therefore,

We obtained the following equation;

Now, multiply both sides by 45 to determine the weight of 45 books.

Therefore, the weight of 45 books is 67.5 kg.

Answer:

\(\huge\boxed{\bf{45books = 67.5kg}} \)

Step-by-step explanation:

Given:-

To find:-

Ans:-

30books = 45kg

45books = y kg

Let's find 45 books (y)

\(\sf \to \frac{30}{45} = \frac{45}{y}\)

\(\sf \to 45*45 = 30*y\)

\(\sf \to 2,025 = 30*y\)

\(\sf \to y = \frac{2,025}{30}\)

\(\sf \to y = 67.5kg\)

~therefore 45books = 67.5kg

\(\:\)

\(\huge\colorbox{red}{BlackPain}\)

Answer:

Step-by-step explanation:

Your answer is correct

8 + v = 26

v +8 -8 = 26 - 8

v = 18

Answer: V=18

Step-by-step explanation:

PEMDAS can be used to solve this problem. PEMDAS stands for parentheses, exponents, multiplication, division, addition, and subtraction. You see that there are no parentheses, exponents, or multiplication/division steps so you have addition left. To solve 26=8+v, you have to isolate the variable by subtracting the 8 on both sides of the equation. 26-8 is 18, so, the final equation is v=18.

Answer:

6080 cm OR 60.8m

Step-by-step explanation:

75 x 40 = 3000 cm

77 x 40 = 3080 cm

They are moving in perfectly opposite directions, which makes a straight line.

3000 + 3080 = 6080 cm = 60.8m

Answer:

28 km per hour

Step-by-step explanation:

First determine the amount of time that the trip took

17:55 - 17:40 = :15 or 15 minutes

We need the time in hours

15 minutes * 1 hour/ 60 minutes = 15/60 hours = 1/4 hours

To determine speed, take distance and divide by time

7 km ÷( 1/4 hours)

Copy dot flip

7 * 4/1

28 km per hour

To compute the Galois groups and determine if the field extensions are normal, we need to know the specific field extensions in question. However, I will provide a general method for computing Galois groups and determining normal field extensions.

Step 1: Identify the field extension
Let's say our field extension is given by K/Q, where K is the extension field and Q is the base field (the field of rational numbers).

Step 2: Determine the minimal polynomial
Find the minimal polynomial f(x) of the field extension K/Q. This is the smallest degree polynomial with rational coefficients for which the elements of K are roots.

Step 3: Compute the Galois group
The Galois group, G(K/Q), is the group of automorphisms of the field K that fix the base field Q. To compute G(K/Q), determine the set of automorphisms of K that keep the elements of Q fixed.

Step 4: Check for normality
A field extension K/Q is normal if and only if the minimal polynomial f(x) splits into distinct linear factors over K. If this is true, then K/Q is a normal field extension.

Step 5: Find a normal extension if necessary
If K/Q is not normal, we can find a normal extension L/Q containing K by considering the splitting field of the minimal polynomial f(x) over Q. The splitting field L is the smallest field containing Q and all the roots of f(x), and the extension L/Q will be normal.

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To find the values of z that make the product with the complex number 5-6i a real number, we need to consider the imaginary part of the product.

The product of z and 5-6i can be written as:

z * (5 - 6i)

Expanding this expression, we get:

5z - 6zi

For the product to be a real number, the imaginary part (-6zi) must be equal to zero. This means that the coefficient of the imaginary unit i, which is -6z, must be zero.

Setting -6z = 0, we find:

z = 0

So, one possible nonzero value of z is 0.

However, since we are looking for nonzero values of z, we need to find another value that satisfies the condition.

Let's consider the equation for the imaginary part:

-6z = 0

Dividing both sides of the equation by -6, we have:

z = 0/(-6)

z = 0

Again, we find z = 0, which is not a nonzero value.

Therefore, there are no other nonzero values of z that make the product with the complex number 5-6i a real number. The only value that satisfies the condition is z = 0.

The crease is \($x = \sqrt{15}\text{ cm}$\) long.

Let $x$ be the length of the crease. Then, the visible white area is a triangle with base of length $x$ and height of \($x\sqrt2$.\) The visible black area is also a triangle with the same base and height. Therefore, we have the equation

\($\frac{x^2\sqrt2}{2} = \frac{15}{2}$\)

Solving for $x$, we get

\(x^2=\sqrt{15}\)

Therefore, the crease is \($x = \sqrt{15}\text{ cm}$\) long.

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The position of the ball at t = 2 seconds is -0.8 meters.

The position of a ball rolling in a straight line is given by the equation x = 2.0 - 3.6t + 1.1t^2, where x is the position in meters and t is the time in seconds. To find the position of the ball at a specific time, we can plug in the value of t into the equation and solve for x.

For example, if we want to find the position of the ball at t = 2 seconds, we can plug in 2 for t and solve for x:

x = 2.0 - 3.6(2) + 1.1(2)^2
x = 2.0 - 7.2 + 4.4
x = -0.8

Therefore, the position of the ball at t = 2 seconds is -0.8 meters.

Similarly, we can plug in any value of t into the equation to find the position of the ball at that specific time.

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The total number of social security numbers that are possible are 900,000,000.

In the social security number first digit can only fall between 1 and 9, leaving us only nine options because the first three digits cannot all be zeros. There are still 10 possibilities for each of the second and third digits because they may both still be any integer between 0 and 9.

Therefore, the total number of different social security numbers that can be formed is using the combinations,

= 9 × 10⁸

= 900,000,000

So, there are 900,000,000 different possible social security numbers.

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