A gold coin has a mass of 45.6 grams and a volume of 2.28 cubic centimeters. Calculate its density. Write your answer to the tenths place. ​

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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The correct answer would be 3. f(x) = -1, so you got to find the -1 in the y row of the table and just say that x =3 if y =-1.

Answer:

x = 3

Step-by-step explanation:

The question is asking for which value of x gives -1

You don't have an equation, however you do have a table of values

Y is similar to f(x) in the sense that it is the output, while x is the input.

All you must do is see where y = -1, this is the same for when f(x) = -1

So, there is only one moment where y = -1, which is when x = 3

With this, we can conclude that for the value of x = 3, f(x) = -1

Answer:

A  54°

Step-by-step explanation:

Sorry if its wrong <3

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation determines how far numbers deviate from the mean. The Standard deviation of the two sets will be the same if the numbers from the respective means are placed in the same order.

This is what 10, 15, and 20 will be on a number line

10_ _ _ _15 _ _ _ _20

(15 is the mean and 10 and 20 are 5 steps away from the mean)

i) Z - X = 10

This is what Z and X will be on the number line

X _ _ _ _ _ Z

ii) Z - Y = 5

This is what Z and Y will on the number line.

Y_ _ _ _ _ Z

Together, their relative placement on the number line:

X _ _ _ _ _  Y  _ _ _ _ _  Z

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

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Answer:

a lot

Step-by-step explanation:

Answer es tu manzana que es comer

Step-by-step explanation: es ella tu mijo no comer la sanda que peso

Answer:

3(x + 5)

Step-by-step explanation:

Answer:

The equation in point-slope form is: y - 5 = 4(x - 2).

The equation in standard form is: 4x - y + 3 = 0.

Answer:

Standard form

4x - y = 3

Step-by-step explanation:

Point slope form of a line equation is:
y - y1 = m(x - x1)

where
(x1, y1) is a point on the line and m is the slope

The standard form of a line equation is:
Ax + Bc = C
where
A, B, C are integers

Slope Point Form

Given
(x1, y1) = (2, 5)
m = 4

The slope-point equation is
y - y1 = m(x - x1)

which is

y - 5 = 4(x - 2)

Expanding the bracket on the right side:
y - 5 = 4x  - 8

Move constant -5 to the right to become +5
y = 4x - 8 + 5 = 4x - 3

Move 4x to left becoming -4x

y - 4x = -3

or

-4x + y = -3

same as

4x - y = 3

This is the standard form with A = -4, B = 1 and C = 13

Answer:

11

Step-by-step explanation:

Answer:11

Step-by-step explanation:

because you have to create the equation and solve

Answer:

y=-2x-10

this is slope-intercept form, if this is what you're asking for?

Step-by-step explanation:

simplify: y-4 = -2x-6

y= -2x -10

A possible unit vector that makes an angle of 45° with 9i + 4j is

\(v = (-9/\sqrt{(97)} )i + (0.933)j\)

Let's call the two unit vectors we're looking for as u and v.

We know that they make an angle of 45° with the vector 9i + 4j.

First, we need to find the unit vector in the direction of 9i + 4j. We can do this by dividing the vector by its magnitude:

\(|9i + 4j| = \sqrt{(9^2 + 4^2)} = \sqrt{(97)}\)

So the unit vector in the direction of 9i + 4j is:

\(u_0 = (9i + 4j) / \sqrt{(97)}\)

Now, we can use the dot product to find two unit vectors that make an angle of 45° with  \(u_0.\)

Let's call the first unit vector u.

We know that the dot product of u and \(u_0\) must be:

u . u_0 = |u| |u_0| cos(45°)

\(= (1)(1/ \sqrt{(97)} )(\sqrt{(2) /2)\)

\(= \sqrt{(2)} / (2 \sqrt{(97)} )\)

We also know that u must be a unit vector, which means its magnitude is We can use this information to solve for the components of u:

\(u . u_0 = (u_x)i + (u_y)j . (9/\sqrt{(97)} )i + (4/\sqrt{sqrt(97)} )j = \sqrt{(2) } / (2 \sqrt{(97)} )\)

Solving for the components of u, we get:

\(u_x = (9\sqrt{(2)} + 4\sqrt{(2)} ) / (2\sqrt{(97)} ) = 0.933\)

\(u_y = (4\sqrt{(2)} - 9\sqrt{(2)} ) / (2\sqrt{(97)} ) = -0.359\)

So one possible unit vector that makes an angle of 45° with 9i + 4j is:

u = 0.933i - 0.359j

To find the second unit vector, let's call it v, we know that it must be orthogonal to u (since the angle between u and v is 90°) and it must also be orthogonal to \(u_0\) (since the angle between \(u_0\) and v is also 90°).

We can use the cross product to find such a vector.

\(v = u_0 * u\)

\(v_x = (u_0)_y u_z - (u_0)_z u_y = (4/\sqrt{(97)} )(0) - (9/\sqrt{(97)} )(1) = -9/\sqrt{(97)}\)

\(v_y = (u_0)_z u_x - (u_0)_x u_z = (1/\sqrt{(97)} )(0.933) - (0/\sqrt{(97)} ) = 0.933\)

\(v_z = (u_0)_x u_y - (u_0)_y u_x = (0/\sqrt{(97)} )(-0.359) - (4/\sqrt{(97)} )(0.933) = -4/\sqrt{(97)}\)

We don't need the z-component of v, since we're working in 2-space.

So a possible unit vector that makes an angle of 45° with 9i + 4j is:

\(v = (-9/\sqrt{(97)} )i + (0.933)j\)

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Answer:

Total Surface Area: 65.97 cm²

Lateral Surface Area: 37.70 cm²

Step-by-step explanation:

You can solve for the surface area without the height or you can solve for the height and then find the surface are, either way is easy.

Lets first solve without the height. We will solve the surface area with the radius and slant height.

Total Surface area of cone formula: πr (r + s)

Curved surface are formula: πrs

Substitute the values in the picture with the formula

Slant height: 4

Radius: 3

πr (r + s)

π(3)(3 + 4)

(3.141593)(3)(3 + 4)

=9.424778(3 + 4)

=(9.424778)(7)

=65.973446

65.973446 rounded to the nearest hundredth is 65.97
TSA = Total Surface Area

TSA = 65.97 cm²

Now to find the curved surface area or some people call it the Lateral Surface Area

Formula: πrs

Radius: 3

Slant Height: 4

π(3)(4)

(3.141593)(3)(4)

=(9.424778)(4)

=37.699112

37.699112 to the nearest hundredth is 37.70

CSA = Curved Surface Area

CSA = 37.70 cm²

If you choose to compute the height (h) the you have to know both the radius (r) and the slant height (s):

Formula: height (h) = √s² - r²

Slant height = s = 4

Radius = r = 3

Height = h = ?

Now substitute the values into the formula

h = √s² - r²

h = √4² - 3²

h = √16 - 9

h = √7

h = 2.64575131

Height: 2.64575131 cm

Now it's time to find the surface area and curved surface area, now that you have the height:

Surface area formula given height and radius: πr(r + √(r² + h²))

Substitute the values

Height: 2.64575131
Radius: 3

πr(r + √(r² + h²))

π(3)(3 + √(3² + 2.64575131²))

TSA = (3.141593)(3)(3 + √(3² + 2.64575131²)

TSA = 9.424778(3 + √(3² + 2.64575131²)

TSA = 9.424778(3 + √(9 + 7)

TSA = 9.424778(3 + √(16)

TSA = 9.424778(3 + 4)

TSA = 9.424778(7)

TSA = 65.973446

TSA = 65.97

Next, time to find the Curved surface area:

Formula: CSA = πr√(r² + h²)

CSA = πr√(r² + h²)

Substitute the values into the formula

Radius: 3

Height: 2.64575131

Slant Height: 4

CSA  = πr√(r² + h²)

CSA = π(3)√(3² + 2.64575131²)

CSA = 9.424778√(3² + 2.64575131²)

CSA = 9.424778√(9 + 7)

CSA = 9.424778√(16)

CSA = 9.424778(4)

CSA = 37.699112

CSA = 37.70

So, we can conclude that the Total Surface Area is 65.97 and the Lateral Surface Area is 37.70.

Answer:

x > -2.5 (-2.5, infinity)

Step-by-step explanation:

Given the inequality expression

5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4

Expand

15.3 + 11.22x > -14.25 - 10.2x - 24

15.3 + 11.22x > -38.25 - 10.2x

Collect the like erms

11.22x + 10.2x > -38.25 - 15.3

21.42x > -53.55

x > -53.55/21.42

x > -2.5 (-2.5, infinity)

This gives the required solution

Answer:

(-2.5, infinity)

Step-by-step explanation:

correct on EDG

The mean would be 35 feet.

The mean tells us that the typical throw of the ball results in a distance of approximately 3.5 feet.

what is Mean?

In arithmetic, mean is the sum of all the added values of all the data in a set divided by the number of data in the set.

To find the mean of the distances, we need to calculate the sum of all the distances and divide by the total number of distances:

(20+25+25+31+33+34+41+41+45+50+56+67) / 12 = 425 / 12 = 35.42

Rounding to one decimal place, we get the mean distance of approximately 3.5 feet.

However, it's worth noting that the stem-and-leaf plot shows some variability in the distances, with some throws going as far as 6.7 feet and some as short as 2 feet.

So while the mean can provide us with a measure of central tendency, it doesn't tell the whole story about the distribution of the distances.

Therefore, The mean would be 35 feet. The mean tells us that the typical throw of the ball results in a distance of approximately 3.5 feet.

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Answer:Translation is when we slide a figure in any direction. Reflection is when we flip a figure over a line. Rotation is when we rotate a figure a certain degree around a point. Dilation is when we enlarge or reduce a figure.

Step-by-step explanation:

Answer:

Translation is when we slide a figure in any direction. Reflection is when we flip a figure over a line. Rotation is when we rotate a figure a certain degree around a point. Dilation is when we enlarge or reduce a figure.

Step-by-step explanation:

Answer:

\(a_{n}\) = 5n + 5

Step-by-step explanation:

The nth term of an arithmetic progression is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 10 and d = a₂ - a₁ = 15 - 10 = 5 , then

\(a_{n}\) = 10 + 5(n - 1) = 10 + 5n - 5 = 5n + 5

The correct answer is:

0.025 P-value < 0.05

In statistical hypothesis testing, the P-value is a measure of the strength of evidence against the null hypothesis. It represents the probability of observing a test statistic as extreme as the one calculated from the sample data, assuming the null hypothesis is true.

In this case, we have a right-tailed test, which means we are interested in the upper tail of the F-distribution. The test statistic is calculated as F = 2.97, with degrees of freedom for the numerator (d.f.N.) = 9 and degrees of freedom for the denominator (d.f.D.) = 14.

Using Table H (which provides critical values for the F-distribution), we can determine the P-value interval. In this table, we find the column for d.f.N. = 9 and locate the row that corresponds to d.f.D. = 14. The intersection of these values gives us the critical value, which is 0.025.

Since the F-value of 2.97 is greater than the critical value of 0.025, the P-value is less than 0.05. Therefore, we can conclude that 0.025 < P-value < 0.05, indicating strong evidence against the null hypothesis.

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The height of the line in a frequency polygon and the height of the bars in a histogram both represent the frequency or count of the data in a particular category or range of values.

What is Polygon?

In two dimensions, a polygon is a closed object made up of segments of straight lines that join at least three points. A polygon in mathematics can be convex or concave and have any number of sides.

The height of the line in a frequency polygon is proportional to the frequency of the data. The frequency value is marked at the highest point of the line, which is drawn between the midpoints of each category or range of values.

The height of the bar in a histogram, which is proportional to the number of data points in that category or range of values, denotes the frequency of the data. To depict the frequency distribution of the data, bars are drawn next to one another with no space in between.

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The height of the line in a frequency polygon and the height of the bars in a histogram both represent the frequency or count of the data in a particular category or range of values.

What is Polygon?

In two dimensions, a polygon is a closed object made up of segments of straight lines that join at least three points. A polygon in mathematics can be convex or concave and have any number of sides.

The height of the line in a frequency polygon is proportional to the frequency of the data. The frequency value is marked at the highest point of the line, which is drawn between the midpoints of each category or range of values.

The height of the bar in a histogram, which is proportional to the number of data points in that category or range of values, denotes the frequency of the data. To depict the frequency distribution of the data, bars are drawn next to one another with no space in between.

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Answer:

y = (-5/6)x - (5/3)

Step-by-step explanation:

The equation of a line in point-slope form is y - y1 = m(x - x1) where (x1,y1) is a point on the line, and m is the slope of the line.

Given that the line passes through the point (6,-8) and has a slope of -5/6, the equation of the line is:

y - (-8) = (-5/6)(x - 6)

y + 8 = (-5/6)x + (-5/6) * 6

y = (-5/6)x - (5/3)

Answer:

(6,-5)

Step-by-step explanation:

(y-y1)=m(x-x1)

(y--8)=-5/6(x-6)

6y=-5x+2

The nth term of the sequence is given as Tn = 64(3/4)^n-1

Given the sequence 64, 48 36, 27...

The given sequence is a geometric sequence. The nth term of a geometric sequence is given as:

Given the following parameters:

a = 64

r = 48/64  = 3/4

Substitute int the formula to get the nth term;

Tn = 64(3/4)^n-1

Hence the nth term of the sequence is given as Tn = 64(3/4)^n-1

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To show that the matrices ab and ba are similar, we need to find an invertible matrix P such that:

P(ab)P^-1 = ba

We can start by rearranging this equation:

P(ab) = baP

Then we can multiply both sides on the left by a^-1 and on the right by b^-1:

(a^-1Pab)(b^-1) = (a^-1ba)(Pb^-1)

Note that a^-1Pab = P', where P' is an invertible matrix because a and b are invertible. Similarly, a^-1ba = b^-1ab = (b^-1a)b, which is also invertible because a and b are invertible.

Substituting P' and (b^-1a)b into the previous equation, we get:

P'(b^-1) = (b^-1a)b(Pb^-1)

Multiplying both sides on the right by a, we get:

P'(b^-1)a = b(Pb^-1)a

Note that b(Pb^-1)a = (ba)(b^-1a)^-1, which is invertible because a and b are invertible. Therefore, we can multiply both sides on the left by (b^-1a)^-1 to get:

(b^-1a)P'(b^-1a)^-1 = ba

This shows that ab and ba are similar, with P = (b^-1a)P'(b^-1a)^-1 being an invertible matrix that relates the two matrices.

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

a) The perimeter of Martin's cat enclosure is 220 inch.

b) Martin need to buy 22 bundles each 10 ft long.

The whole distance that a rectangle's boundaries, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the sum of its four sides.

Given,

Wide = 48 inches

Length = 62 inches

a) Perimeter of enclosure:

2 × (length + width)

2× (48 + 62)

2 × 110

220

The perimeter of Martin's cat enclosure is 220 inch.

b)  Wire mesh is sold in rolls that are each 10 ft long.

Dividing it by perimeter:

220 ÷ 10

22

Martin need to buy 22 bundles each 10 ft long.

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Answer:a I think

Step-by-step explanation:

Answer:

1/ $170 each month

2/ 50 months

Step-by-step explanation:

For the first question

We take 8500 - 6460 = 2040

Then we divided by 12 = $170 each month

For the second question

We take 8500 divided by 170 = 50 months

It takes him 50 months to pay the debt!

Answer:

Step-by-step explanation:

1. If we subtract $6460 from $8500, we get $2040, then we divide $2040 by the 12 months & we get $170, so he pays a fixed amount of %170 per month.

2. We need to multiply $170 by a number to get $8500. $170 times 50 is $8500. So it will take him 50 months or 4 years & 2 months until he pays back all of his debts.

Answer:

C

Step-by-step explanation:

I think I'm not to sure...

Answer:

Assume Gordon got X dollar

Then

sara got = 3*x= 3x

Pip got = 2*3x= 6x

Now,

x + 3x + 6x = 880

10x =880

x= 88

Sara got = 3x = 3*88 = 264

Step-by-step explanation:

Answer:

2 x 2 x 13

Step-by-step explanation:

2 times 26 = 52

You can break 26 up into 2 times 13.

So, you get 2 times 2 times 13.

Answer:

Step-by-step explanation:

to find the bottom base you add the two numbers that make it

5+18=23

now put everything in the formula

\(\frac{1}{2}*12(12+23)\\\)

parathesis first

12+23=35

\(\frac{1}{2} *12*35\)

multiply in order

6*35

210

Step-by-step explanation:

i’m doing my geometry homework with the equation 1/2h(b1+b2) but i can’t figure this one out. please help

1/2h (b1 + b2) is the formula for finding the area of ​​the figure (trapezoid)

1/2 * 12 (18 + 5 + 12)=

6 * 35=

210 units²

Answer:week 3 and week 1

Step-by-step explanation:

Answer:

chicken

Step-by-step explanation: