simplify (1/2)³x(1/2)² and write in exponential form​

The probability that the player has all 8 of the number selected by the lottery commission is approximately 1.3 × 10^-9.

There are a total of 40 numbers that can be chosen for the lottery. Out of those 40 numbers, a player must select 8 numbers. The lottery commission will also randomly select 8 numbers from those 40. If a player has all 8 of the numbers selected by the lottery commission, then they will win. The number of ways to choose 8 correct numbers is simply 1, since there is only one set of 8 numbers that the player can choose that matches the 8 numbers selected by the lottery commission.

The number of ways to choose any 8 numbers from 40 is given by the combination formula:

P = (40! / (8! (40 - 8)!) = 769,046,685

Therefore, the probability that the player has all 8 numbers selected by the lottery commission is:

P(all 8 numbers are correct) = 1 / 769,046,685 = 1.3 × 10^-9 (approximately).

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When we can compare the simplified equation to the standard forms of the four main types of conic sections, we get that it has the form of an ellipse with its center at (3,6), a horizontal axis of length 2a = 4, and a vertical axis of length 2b = √(5/4)*4 = 2√5.

Circle: (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is its radius.

Ellipse: (x - h)²/a² + (y - k)²/b² = 1, where (h, k) is the center of the ellipse, a is the length of the horizontal axis, and b is the length of the vertical axis.

Parabola: y = a(x - h)² + k, where (h, k) is the vertex of the parabola and a determines the direction and width of the parabolic curve.

Hyperbola: (x - h)²/a² - (y - k)²/b² = 1, where (h, k) is the center of the hyperbola. The distances between the center and each vertex on the horizontal axis and the vertical axis are denoted by the letters a and b, respectively.

The given equation is in the standard form of a conic section:

5(x − 3)² = 20 − 4(y − 6)²

To identify the type of conic section, we can simplify the equation by dividing both sides by 5:

(x − 3)² = 4 − (4/5)(y − 6)².

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Answer:

[tex] {(x - 3)}^{2} + {(y + 2)}^{2} = 4[/tex]

Answer:

refer the attachment

Step-by-step explanation:

your answers are

2√3 and 2

Answer:

use pythagorean theorem on the lower tri to find its hypotenuse and apply the theorem again to find the base of the upper tri....

Solution to the system of equations is (x, y) = (-7.933, 1.133) by elimination

To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the two equations. In this case, we can eliminate the variable y by multiplying the second equation by 8 and adding it to the first equation.

Here are the steps to solve the system of equations:

Multiply the second equation by 8:

-2x - y = 17 --> -16x - 8y = 136

Add first equation to new equation:

x - 8y = -17 + (-16x - 8y = 136)

-15x = 119

Solve for x:

-15x = 119 --> x = -7.933 (rounded to three decimal places)

Substitute x into an original equation in order to solve for y:

x - 8y = -17 --> -7.933 - 8y = -17

-8y = -9.067

y = 1.133 (rounded to three decimal places)

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Answer:

Step-by-step explanation:

-9+4.8=q-4.8+4.8

-4.2=q-4.8+4.8

-4.2=q

q=-4.2

Required solutions after simplification are 8bz, 1, 3x³/y², 144, x⁹, 1/y⁵ respectively.

7) To simplify the expression:

[tex]\frac{16db {z}^{5} }{ {(2z)}^{4} } \\ = \frac{16}{2} \times \frac{b}{z} \times \frac{ {z}^{5} }{ {z}^{4} } \\ = 8b \times {z}^{5 - 4} \\ = 8bz[/tex]

Therefore, 16dbz⁵/(2z)⁴ simplifies to 8bz.

8)Any non-zero number raised to the power of zero is 1.

Therefore:(15n⁶m²x³/n⁻²m⁻³b⁻⁸)⁰ = 1

9)To simplify the expression:

[tex] \frac{30 {x}^{4} {y}^{ - 3} }{10 {x}^{ - 2} {y}^{5} }

= \frac{3 {x}^{4 - ( - 2)} }{ {y}^{3 - 5} }

= \frac{3 {x}^{6} }{ {y}^{ - 2} }

= \frac{3 {x}^{6} }{ {y}^{2} } [/tex]

herefore, 30x⁴y⁻³/10x⁻²y⁵

[tex]\frac{30 {x}^{4} {y}^{ - 3} }{10 {x}^{ - 2} {y}^{5} } [/tex] simplifies to [tex]\frac{3 {x}^{6} }{ {y}^{2} } [/tex]

13) To solve this expression, we perform the exponentiation first and then perform the multiplication.

6² means 6 multiplied by itself, or 6×6 = 36.

So,4×6² = 4×36

So, 4×6²= 144

Therefore, 4×6² equals 144.

14) To simplify the expression: x³ × x⁻² × x⁷ × x

[tex] = {x}^{3 - 2 + 7 + 1} = {x}^{9} [/tex]

Therefore, x³ * x⁻² * x⁷ * x simplifies to x⁹.

15)To simplify the expression:

[tex] {y}^{ - 11} \times {y}^{6} \times {y}^{0} \\ = {y}^{ - 11 + 6 + 0} \\ = {y}^{ - 5} \\ = \frac{1}{ {y}^{5} } [/tex]

Therefore, Required value is 1/y⁵.

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The magnitude and direction of the resultant vector are 76.158 and 100.496° (rounded to the nearest degree).
So the answer is 76.158; 100°.

To find the magnitude and direction of the resultant vector, we can use the vector addition formula:

R = sqrt(A^2 + B^2 + 2ABcosθ)

Where R is the magnitude of the resultant vector, A and B are the magnitudes of the two vectors, and θ is the angle between them.

First, we can convert the given angles to radians by multiplying by π/180:

40° * π/180 = 0.698 radians
130° * π/180 = 2.268 radians

Then we can plug in the given values and solve for the magnitude of the resultant vector:

R = sqrt(30^2 + 70^2 + 2(30)(70)cos(2.268 - 0.698))
R = 76.158 (rounded to the thousandths place)

Next, we can use the law of cosines to find the angle between the resultant vector and the 30-magnitude vector:

cosθ = (R^2 + A^2 - B^2) / 2RA
cosθ = (76.158^2 + 30^2 - 70^2) / (2 * 76.158 * 30)
cosθ = 0.499
θ = cos^-1(0.499)
θ = 60.496°

Since this angle is between the 30-magnitude vector and the x-axis, we need to add 40° to get the angle between the resultant vector and the x-axis:

60.496° + 40° = 100.496°

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Answer:

2,444,444,442

Step-by-step explanation:

The area of the polygon on the graph is 4 units²

The area of shape is the space enclosed within the perimeter or the boundary of a given shape. Area is measured in unit²

The polygon can be divided into two equal triangles by drawing a line through A to C. The area of the two triangles is then added together to give the area of the polygon.

area of triangle = 1/2 bh

= 1/2 × 2 × 2

= 2 units²

area of the polygon = 2+2

= 4 units²

therefore the area of the polygon is 4 units²

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yeah the nearest is porb 2.6 lol

The value of the triple integral is 1/16(e-1)π.

The region of integration E is defined by the inequalities 0 ≤ r ≤ 1, 0 ≤ θ ≤ π/2, and 0 ≤ φ ≤ π/2. The integrand is f(r, θ, φ) = r^2e^(r^2). Thus, we have:

∭E^xe^(x2+y2+z2) dV = ∫₀¹∫₀^(π/2)∫₀^(π/2) f(r, θ, φ) r^2 sin φ dφ dθ dr

= ∫₀¹∫₀^(π/2)∫₀^(π/2) r^4e^(r^2) sin φ dφ dθ dr

= ∫₀¹∫₀^(π/2) (-e^(r^2))(cos φ)|₀^(π/2) dθ dr [using u-substitution with u = r^2]

= ∫₀¹∫₀^(π/2) (e^(r^2))(sin φ) dφ dθ dr

= ∫₀¹(1-e^(-r^2))dθ dr

= π/2 - ∫₀¹e^(-r^2)dθ

= π/2 - [(1/2)π/2(1-e^(-1))]

= 1/16(e-1)π.

Therefore, the value of the triple integral is 1/16(e-1)π.

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The IQ of students has a mean of 110 and an SD of 18. If 43 students are randomly sampled, the probability that the average IQ of this group is greater than 100 is P(Z > (100-110)/(18/√43)).

Given, that the IQ of students has a mean of 110 and SD of 18.

Number of students randomly sampled, n = 43.

The formula to calculate the probability is:

P(Z > (100-110)/(18/√43))

Now, substituting the values in the above formula:

P(Z > (100-110)/(18/√43))= P(Z > -2.365)= 1 - P(Z < -2.365)

This can be obtained by referring to standard normal tables or using a calculator.

Now, P(Z < -2.365) can be obtained by referring to standard normal tables or using a calculator.

Using a calculator, we get P(Z < -2.365) = 0.009 or 0.01 (rounded off to two decimal places).

So, P(Z > -2.365) = 1 - 0.01 = 0.99.

The probability that the average IQ of this group is greater than 100 is 0.99.

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The compound inequality that produced the given graph is x≤1 and y>2.Therefore the correct option is option (2) x≤1 and y>2.

A compound inequality is an inequality that contains two or more inequalities connected by either the word "and" or "or".

An "and" compound inequality is true only if both inequalities are true, while an "or" compound inequality is true if at least one of the inequalities is true.

The inequality x≤1 and y>2 represents the set of ordered pairs (x,y) that satisfy both conditions simultaneously.

Geometrically, this inequality represents the region in the coordinate plane that is below or on the vertical line x=1 and above the horizontal line y=2.

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The rate at which the shadow of the man is increasing in length is 1/5 m/s.

We can solve this problem using similar triangles. Let x be the length of the shadow, and let y be the distance between the man and the base of the lamppost. Then, we have the following equation:

(1.4 + x)/y = 1/5

Solving for x, we get:

x = (y/5) - 1.4

Differentiating both sides with respect to time t, we get:

dx/dt = (1/5) dy/dt

We are given that dy/dt = 1 m/s, so substituting that in, we get:

dx/dt = (1/5) m/s

Finally, we are asked for the rate at which the shadow length is increasing, which is just dx/dt. Thus, the rate is (1/5) m/s.

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2nd and 4th

(10²)⁹=10¹⁸

10⁵/10¹⁵ = 10^-10

10⁷ × 10⁶ = 10¹³

you cant apply the laws of exponents where you have + or -

The graph has three turns, which is an odd number, and it extends to a negative infinity.

What is the name of a polynomial graph?

A polynomial function's graph is essentially a continuous, smooth curve. You can use a few key features of this kind of graph to assist construct the curve. I'll explain how to use the polynomial function's leading term to analyze the graph's final performance.

If the number of turns is an odd integer, the functions have an even degree.

If the graph's behavior shifts to the negative infinity, the functional does have a negative leading coefficient.

Just this graph met the requirements among the options.

The graph has 3 turns (an odd number) and it goes to the negative infinity.

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The numbers are [tex]\sqrt[3]{-(89)}[/tex], [tex]-\sqrt{30}[/tex], [tex]15-\sqrt{2}[/tex], [tex]\sqrt[3]{43}[/tex], [tex]\sqrt{71}[/tex], 5.2, and 96 in that order.

To order the given numbers from least to greatest, we need to compare them to each other and arrange them in ascending order. Here's how we can do it:

Start with the smallest number: [tex]\sqrt[3]{-(89)}[/tex]. This is a negative number under the cube root, so it is the smallest among the given numbers.

Next, we have [tex]-\sqrt{30}[/tex]. This is a negative number, but its absolute value is smaller than that of [tex]\sqrt[3]{-(89)}[/tex]. So, it comes next.

After that, we have [tex]15-\sqrt{2}[/tex]. This is a number slightly greater than 13. It is greater than [tex]-\sqrt{30}[/tex] but less than [tex]\sqrt[3]{-(89)}[/tex].

The next number is [tex]\sqrt[3]{43}[/tex]. This is a number between 3 and 4, greater than [tex]-\sqrt{30}[/tex] and [tex]15-\sqrt{2}[/tex].

After that, we have [tex]\sqrt{71}[/tex]. This is a positive number, greater than 8 and less than 9.

Then we have 5.2. This is a number slightly greater than 5, greater than [tex]\sqrt{71}[/tex] and [tex]\sqrt[3]{43}[/tex].

Finally, we have the largest number: 96. This is clearly greater than all the other numbers.

Therefore, the order of the given numbers from least to greatest is:

[tex]\sqrt[3]{-(89)} , -\sqrt{30} , 15-\sqrt{2} , \sqrt[3]{43} , \sqrt{71}, 5.2, 96.[/tex]

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The given number, 30, is in the sequence with a position of 6.

The given number, 90, is in the sequence with a position of 29.33.

Number is used to represent a quantity, such as an integer, fraction, or decimal.

The number is 30 and the nth term formula is 5n. To determine whether the given number is in the sequence, we need to solve for n.

Solving for n:

30 = 5n

n = 6

Therefore, the given number, 30, is in the sequence with a position of 6.

The number is 90 and the nth term formula is 3n + 2. To determine whether the given number is in the sequence, we need to solve for n.

Solving for n:

90 = 3n + 2

90 - 2 = 3n

88 = 3n

n = 29.33

Therefore, the given number, 90, is in the sequence with a position of 29.33.

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Answer: 29x +23

Step-by-step explanation: (2x + 4)(3x + 6) = 6[tex]x^{2}[/tex] + 24x + 24.

(3x - 1)(2x - 1) = 6[tex]x^{2}[/tex] - 5x + 1. 6[tex]x^{2}[/tex] + 24x + 24 - (6[tex]x^{2}[/tex] - 5x + 1) = 29x +23.

The answer of the given question based on the finding the size of PRO is angle PRO = 180° degrees.

A circle is a closed two-dimensional shape that is formed by a set of points that are all equidistant from a single point called the center. The distance from the center to any point on the circle is called the radius of the circle. A circle can be defined as the locus of all points that are at a fixed distance from a given point in a plane.

Since P, Q, and R are points on a circle with center O, we know that the measure of angle POQ is equal to 360 degrees (the total angle measure of a circle).

Therefore, we have:

angle ∠POR + angle ∠ROQ + angle ∠OPQ = 360° degrees

Since angle ∠OPQ is given as 36° degrees, we can substitute this value in and simplify:

angle ∠POR + angle ∠ROQ + 36 = 360

angle ∠POR + angle ∠ROQ = 324

Now, we use the fact that angles formed by chords that intersect within a circle are equal.

Since PQ is a chord that intersects chord PR at point O, we know that angle ∠POR is equal to angle ∠OQP. Similarly, angle ∠ROQ is equal to angle ∠OPQ.

Substituting these equalities in, we have:

angle ∠OQP + angle ∠OPQ + angle ∠OPQ = 324

2(angle ∠OPQ) + angle ∠OQP = 324

But we also know that the sum of the angles in triangle OPQ is 180° degrees. Thus:

angle ∠OQP + angle ∠OPQ + angle ∠POQ = 180

angle ∠OQP + 36 + 180 = 180

angle OQP = 144° degrees

Therefore, the measure of angle ∠PRO is:

angle ∠PRO = angle ∠POR + angle ∠OQP

angle ∠PRO = angle ∠OQP + angle ∠POR

angle ∠PRO = 144 + 36

angle ∠PRO = 180° degrees

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The answer of the given question based on the finding the size of PRO is angle PRO = 180°.

A circle is a closed, two-dimensional object made up of a collection of points that are all equally spaced apart from the center. The distance from any point on the circle to its center is known as the radius of the circle. The center of every point in a plane that is isolated from another point by a certain distance is referred to as a circle.

Since P, Q, and R are points on a circle with center O, we know that the measure of ∠POQ is equal to 360° (the total angle measure of a circle).

Therefore, we have:

∠POR + ∠ROQ + ∠OPQ = 360°

Since ∠OPQ is given as 36°, we can substitute this value in and simplify:

∠POR + ∠ROQ + 36 = 360°

∠POR + ∠ROQ = 324°

Now, we use the fact that angles formed by chords that intersect within a circle are equal.

Since PQ is a chord that intersects chord PR at point O, we know that ∠POR is equal to angle ∠OQP. Similarly, ∠ROQ is equal to ∠OPQ.

Substituting these equalities in, we have:

∠OQP + ∠OPQ + ∠OPQ = 324°

2(angle ∠OPQ) + ∠OQP = 324°

But we also know that the sum of the angles in triangle OPQ is 180° degrees. Thus:

∠OQP + ∠OPQ + ∠POQ = 180°

∠OQP + 36 + 180 = 180°

∠OQP = 144°

Therefore, the measure of ∠PRO is:

∠PRO = ∠POR + ∠OQP

∠PRO = ∠OQP + ∠POR

∠PRO = 144 + 36

∠PRO = 180°

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The complete question and circle is attached below,

The probability that it will weigh between 687 grams and 825 grams is 90.47%

Using this formula, we can find the z-scores for the lower and upper bounds of the weight range we are interested in:

z₁ = (687 - 725) / 29 = -1.31

z₂ = (825 - 725) / 29 = 3.45

Next, we use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.

Using the table, we find that the probability of a standard normal distribution up to z₁ = -1.31 is 0.0951, and the probability up to z₂ = 3.45 is 0.9998. To find the probability between these two z-scores, we subtract the smaller probability from the larger one:

P(-1.31 < z < 3.45) = 0.9998 - 0.0951 = 0.9047

Therefore, the probability of picking a fruit that weighs between 687 grams and 825 grams is 0.9047, or 90.47% (rounded to 4 decimal places).

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The sum of the angle measures of a polygon can be calculated using the formula (n - 2) × 180 degrees, where n is the number of sides. For a 31-gon, the sum of the angle measures is 5220 degrees.

To find the sum of the angle measures of a 31-gon, we can use the formula:

sum of angle measures = (n - 2) × 180 degrees

where n is the number of sides in the polygon.

Substituting n = 31 into the formula, we get:

sum of angle measures = (31 - 2) × 180 degrees

sum of angle measures = 29 × 180 degrees

sum of angle measures = 5220 degrees

Therefore, the sum of the angle measures of a 31-gon is 5220 degrees.

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The capacity of the pyramid is 96000 cubic meters.

A pyramid is a three-dimensional geometric shape that consists of a polygonal base and triangular faces that meet at a common vertex, also known as the apex. Pyramids can have different shapes of base, such as square, rectangle, triangle, or any other polygon.

The capacity of a pyramid is given by the formula:

(1/3) x base area x height

The base of the pyramid is a square with side length 60 meters, so its area is:

base area = 60² = 3600 square meters

The height of the pyramid is 80 meters.

Therefore, the capacity of the pyramid is:

(1/3) x 3600 x 80 = 96000 cubic meters

So the capacity of the pyramid is 96000 cubic meters.

pyramids can be studied in terms of their surface area, volume, and other properties.

The volume of a pyramid can be found by using the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.

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There is a building shaped like a square based pyramid. The length of each side of the building' base is 60 meters and the height of the building is 80 meters. What is the capacity of the pyramid?

Answer:

1/2 of her beads are not red, and 3/4 of her beads are not green.

Step-by-step explanation:

If 1/2 of her beads are red, the other half can not be red, therefore meaning 1/2 of her beads are not red. If 1/4 if her beads are green, then the other 3/4 of her beads can not be green.

The average number of bananas Jones's family eats is 11 bananas.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers.

To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.

So, the average number of bananas the Jones family eats is:

We know that there are 52 weeks in a year. Then,

572/52 = 11

Therefore, the average number of bananas Jones's family eats is 11 bananas.

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Option C. An ANOVA examines whether mean differences exist between conditions, whereas a t-test does not is the correct comparison between an ANOVA and a t-test.

What is ANOVA?

ANOVA (Analysis of Variance) is a statistical method that helps to compare three or more means or groups. It is used in behavioral and social sciences research, which determines whether the mean of the dependent variable is significantly different across different levels of an independent variable.

It is used for statistical inference in comparing the means of two or more groups. ANOVA is based on the idea of variance; that is, the variation between the groups' means is compared to the variation within the groups. By assessing the significance of the difference between group means, ANOVA determines whether there is sufficient evidence to conclude that they are not all equal.

What is a t-test?

A t-test is a statistical hypothesis test that compares the means of two independent groups. It is used when the data in each of the groups being compared is normally distributed. The t-test is a parametric test that compares the means of two groups and calculates the standard error of the difference between the means. It compares the difference between the two groups to the variability within each of the groups. The difference between the sample means is examined relative to the variability between the groups. The t-test produces a test statistic that can be compared to a critical value to determine if the means of the two groups differ significantly. It is commonly used to examine if the means of two independent groups are significantly different.

The primary differences between t-test and ANOVA are in terms of the number of groups, and that ANOVA is used for testing the significance of differences between more than two groups while t-tests are used for testing differences between two groups. Hence, ANOVA is used when we want to compare three or more groups, while t-tests are used when we want to compare two groups. Option C. An ANOVA examines whether mean differences exist between conditions, whereas a t-test does not is the correct comparison between an ANOVA and a t-test.

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