greatest common factor for 90 and 80

The geometric mean of two or more numbers is the same as their average. In this case, we have the numbers 48 and 12.

[tex]\dfrac{48+12}{2}=\dfrac{60}{2}=30[/tex]

Hence, the geometric mean of 48 and 12 is 30. Let me know if you have any questions, thanks!

Kaeya need to save at least $600 for a trip. She ha already saved $45. She plan to save $35 per week she will need 16 week to completely save money for her trip.

Kaeya need to save at least $600 for a trip

She has already saved $45.

so she now has to save 600 - 45 = $555

She plan to save $35 per week

So she have to save 555/35 no of weeks to collect the remaining no of money for her trip

= 555/35

= 15.85

≈ 16 weeks

Therefore, she will need 16 week to completely save money for her trip if  she need to save at least $600 for a trip.

Savings are the funds that remain after subtracting a person's consumer spending from their disposable income during a specific time period. Savings, then, is what's left over after all bills and commitments have been fulfilled for an individual or household.

Cash or cash equivalents (such as bank deposits) are used to store savings since they carry no danger of loss but also offer very low returns. Savings can increase through investing, but doing so involves putting money at risk.

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Let's call the time it takes the fair maiden to sew the border of the tapestry "t". So, her sister can sew the border in t/2 hours.

Working together, they can sew the border in t + t/2 = 1.5t hours.

Since we know the fair maiden can sew the border in 6 hours, we can substitute this into the equation to find t:

6 + 6/2 = 1.5t

Simplifying the right side of the equation:

6 + 3 = 1.5t

9 = 1.5t

Dividing both sides of the equation by 1.5:

t = 6

So the fair maiden can sew the border in 6 hours and her sister can sew the border in 6/2 = 3 hours.

Working together, it would take them 6 + 3 = 9 hours to sew the border of the tapestry.

The value of x in the triangle is 75°

Triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

The sum of angles in a triangle is 180°. Also the sim of angles on a straight line is also 189°

One of the triangle theorem is that the exterior angle of a triangle is equal to the sum of the opposite angles.

Therefore with this, we can say that

120= 57+x

collect like terms

120-57 = x

x = 75°

therefore the value of x in the triangle is 75°

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The slope of this line is m = 1.

An equation of this line is y = x.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

Substituting the parameters, we have:

y - 1 = 1(x - 1)

y = x - 1 + 1

y = x

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In FEM, nodal displacement is calculated using the matrix equation shown below: [K] is the global stiffness matrix, [u] is the displacement (solution) vector, and [F] is the vector of forces.

A function is something that connects an input to an output.

Then, they are interpolated over entire elements using shape functions, which are essentially polynomials of different orders. Although quadratic shape functions, like a quadratic curve, are becoming common, linear shape functions, like a straight line used to approximate a distance between two locations, are the most fundamental. Even higher order shape functions (like cubic) exist, but they are rarely used in practical settings. The calculation of an element's stress uses Gauss Points rather than nodes. You can look up the GP locations for any given kind of element, but for the purposes of this discussion, let's just talk about singles.

Since [K] is the global stiffness matrix, [u] is the displacement (solution) vector, and [F] is the vector of forces, the matrix equation presented below is used to determine nodal displacement.

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Complete question -

Given the tapered bar/axial element below, determine the exact displacement interpolation function and the associated exact shape functions. Show all intermediate steps.

x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

This is the symmetric equation of the line that passes through the point P and is parallel to the vector .

What is symmetric equation?

A line that passes through the point P and is parallel to the vector v can be represented by the parametric equation:

x = -2 + 0t

y = 1 + 2t

z = 0 - 3t

where t is a scalar parameter. To find the symmetric equation of this line, we need to convert the parametric equation to a normal form. We'll start by finding a point on the line other than P, then use those two points to find the direction vector of the line. Let's use t = 1, then the line passes through the point Q(-2 + 01, 1 + 21, 0 - 3*1) = (-2, 3, -3). The direction vector of the line is found by subtracting the position vectors of P and Q:

d = Q - P = (-2 - (-2), 3 - 1, -3 - 0) = (0, 2, -3) = v

So, the direction vector and the vector v are equal, which means the line is parallel to v. Now we have two points on the line, P and Q, which we can use to find the symmetric equation of the line:

(x + 2)/0 = (y - 1)/2 = (z + 3)/(-3) = t

x + 2 = -2t

y - 1 = 2t

z + 3 = 3t

Rearranging the above equations, we get:

x = -2 - 2t

y = 2t + 1

z = 3t - 3

Since t is a scalar parameter, it can be eliminated from the equations to obtain the symmetric equation of the line:

x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

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x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

This is the symmetric equation of the line that passes through point P and is parallel to the vector.

What is the symmetric equation?

A line that passes through the point P and is parallel to the vector v can be represented by the parametric equation:

x = -2 + 0t

y = 1 + 2t

z = 0 - 3t

where t is a scalar parameter. To find the symmetric equation of this line, we need to convert the parametric equation to a normal form. We'll start by finding a point on the line other than P, then use those two points to find the direction vector of the line. Let's use t = 1, then the line passes through the point Q(-2 + 01, 1 + 21, 0 - 3*1) = (-2, 3, -3). The direction vector of the line is found by subtracting the position vectors of P and Q:

d = Q - P = (-2 - (-2), 3 - 1, -3 - 0) = (0, 2, -3) = v

So, the direction vector and the vector v are equal, which means the line is parallel to v. Now we have two points on the line, P and Q, which we can use to find the symmetric equation of the line:

(x + 2)/0 = (y - 1)/2 = (z + 3)/(-3) = t

x + 2 = -2t

y - 1 = 2t

z + 3 = 3t

Rearranging the above equations, we get:

x = -2 - 2t

y = 2t + 1

z = 3t - 3

Since t is a scalar parameter, it can be eliminated from the equations to obtain the symmetric equation of the line:

x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

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On solving the provided question, we can say that  Equivalent Fractions with the LCD 1/8 = 9/72 and 5/12= 30/72

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

LCD = 72

Equivalent Fractions with the LCD

1/8 = 9/72

5/12= 30/72

7/18 = 28/72

Rewriting input as fractions

1/8, 5/12, 7/18

For the denominators (8, 12, 18) the least common multiple (LCM) is 72.

LCM(8, 12, 18)

Therefore, the least common denominator (LCD) is 72.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/8 = 1/8 × 9/9 = 9/72

5/12 = 5/12 × 6/6 = 30/72

7/18 = 7/18 × 4/4 = 28/72

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Answer:

6

Your answer is correct, but since √1 = 1

we can simplify this as 6 · 1 = 6

Step-by-step explanation:

Since the given figure is a square, all four sides are equal.

Each side = 3√2

For a square of side a, the diagonal is given by

d = √(a²+a²) = √(2a²) = a√2

Here we have a = 3√2

So diagonal = x = 3√2 (√2) = 3 · 2 = 6

The volume v of the solid obtained by rotating the region bounded by the curves y = x + 1, y = 0, x = 0, x = 5 about the x-axis is 215π/3.

We have to determine the volume v of the solid obtained by rotating the region bounded by the curves about the specified line.

The line is y = x + 1, y = 0, x = 0, x = 5; about the x-axis.

The volume of the solid disk is;

V = [tex]\int\limits^a_b A(x) \, dx[/tex], where A(x) = π(radius)^2

So, V = [tex]\pi\int\limits^{5}_{0} (x+1)^2 \, dx[/tex]

Now simplifying the value of (x + 1)^2 as x^2 + 2x + 1. So

V = [tex]\pi\int\limits^{5}_{0} (x^2+2x+1) \, dx[/tex]

Now integrating

V = [tex]\pi \left(\frac{x^3}{3}+\frac{2x^2}{2}+x\right)^{5}_{0}[/tex]

V = [tex]\pi \left[\left(\frac{5^3}{3}+\frac{2(5)^2}{2}+5\right)-\left(\frac{0^3}{3}+\frac{2(0)^2}{2}+0\right)\right][/tex]

V = [tex]\pi \left[\left(\frac{125}{3}+\frac{50}{2}+5\right)-\left(0+0+0\right)\right][/tex]

V = π(125/3 + 25 + 5)

V = π(125/3 + 30)

V = π(125 + 90)/3

V = 215π/3

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Answer:

Angle F i= 48 degrees

Step-by-step explanation:

Sum of angles in a triangle= 180°

8x -18+ 6x-4+5x-7= 180

Collect like terms

8x +6x +5x -18 -7-4=180

19x-29=180

19x = 180 +29

19x=209

x=209/19

x= 11

⇒Angle F= 5x-7

= 5(11)-7

= 55-7

=48 degrees

Answer:

48°

Step-by-step explanation:

A/C, 6x - 4 + 8x - 18 + 5x - 7 = 180°

or, 19x - 29 = 180°

or, x = 209 ÷ 19 = 11

So, x equals 11.

Now, Angle F = (5 × x) - 7 = (5 × 11) - 7 = 55 - 7 = 48°

Hence, Angle F measures 48°.

HOPE IT HELPED BUDDY!

Answer:

Angle W is 100 degrees

---------------------------------

Angle W is the exterior angle of the given triangle.

We know that exterior angle is the sum of remote interior angles.

It gives us:

The input values displayed on the x-axis make up the entirety of a graph's domain. The collection of potential output values that make up the range is represented by the y-axis.

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Decreasing the sample size, while holding the confidence level the same, will make the width of your confidence interval bigger. So option a. is correct.

The width of a confidence interval is a measure of the degree of uncertainty in the estimate of the population parameter. It is determined by the sample size, the confidence level, and the standard deviation of the population.

When the sample size decreases, the standard deviation of the sample estimate increases, making the width of the confidence interval larger. This reflects the increased uncertainty in the estimate of the population parameter.

Therefore, decreasing the sample size while holding the confidence level the same will result in a wider confidence interval.

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Decreasing the sample size, while holding the confidence level the same, will make the width of your confidence interval bigger. So option a. is correct.

The width of a confidence interval is a measure of the degree of uncertainty in the estimate of the population parameter. It is determined by the sample size, the confidence level, and the standard deviation of the population.

When the sample size decreases, the standard deviation of the sample estimate increases, making the width of the confidence interval larger. This reflects the increased uncertainty in the estimate of the population parameter.

Therefore, decreasing the sample size while holding the confidence level the same will result in a wider confidence interval.

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There are 100 degrees between the normal freezing and boiling points of water.

On the Celsius temperature scale, the difference between the normal freezing point (0°C) and the normal boiling point (100°C) of water is 100°C - 0°C = 100°C.

On the Kelvin temperature scale, the equivalent temperatures for the normal freezing and boiling points of water are 273.15 K and 373.15 K, respectively. The difference between these two temperatures on the Kelvin scale is 373.15 K - 273.15 K = 100 K.

So, in both Celsius and Kelvin scales, there are 100 degrees between the normal freezing and boiling points of water.

Therefore, there are 100 degrees between the normal freezing and boiling points of water.

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Answer:

False.

Step-by-step explanation:

8154 = eight thousand one hundred and five four

27 = Two seven.

Now we divide.

8154/27 = 302

Now you get 302 if you divide.

So therefore, its false.

Answer:

3/10 or 0.3

Step-by-step explanation:

(9/15)(5/10)

= (3/5)(1/2)

  3x1=3 and 5x2=10

= 3/10 or 0.3

Answer:12(x+18)

Step-by-step explanation:

True , a vector cannot have zero magnitude if one of its components is not zero.

If all of a vector's components are zero, is the vector's magnitude also 0?

A vector's magnitude cannot ever be smaller than any of its components' magnitudes. Only when all of a vector's components are 0 can the vector's magnitude be zero.

                       Their northward components are also equal, and the eastward component of vector A is equal to the westward component of vector B.

What is the vector's magnitude?

A vector's magnitude, represented by the symbol |v|, is used to determine a vector's length. The distance between the vector's beginning point and endpoint is what this amount essentially represents.

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Answer:

it is probably 70° of the triangle

The abiotic factors are Sunlight, oxygen, Carbon Dioxide, Nitrogen, Clouds, Rain, Desert, Snow, Plastic, Dirt and Rock

Abiotic factors are non-living physical and chemical elements and conditions in the environment that influence the survival and growth of living organisms. The abiotic factors in the given list are:

Sunlight: The light energy from the sun that drives photosynthesis and provides energy to living organisms.

Oxygen: A colorless, odorless, tasteless gas essential for respiration in many organisms.

Carbon Dioxide: A colorless, odorless gas that is produced by respiration, combustion and decay of organic material and is used by plants during photosynthesis.

Nitrogen: An odorless, tasteless gas that makes up a major component of the Earth's atmosphere and is essential for plant growth as a component of amino acids and nucleic acids.

Clouds: A visible mass of water droplets or ice crystals suspended in the atmosphere.

Rain: Precipitation that falls from clouds as water droplets.

Desert: An area characterized by little rainfall and high temperature, often with limited vegetation.

Snow: Precipitation that falls from clouds as ice crystals.

Plastic: A synthetic or semi-synthetic material made from various organic polymers.

Dirt: The naturally occurring material that covers the surface of the earth, made up of organic and inorganic matter.

Rock: A naturally occurring solid composed of one or more minerals.

These are all abiotic factors, while the other items in the list are biotic factors, which are living or once-living elements in the environment.

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No, you're incorrect. The tournament lasted from 12:15pm to 4:00pm, which is a duration of 3 hours and 45 minutes. So, the tournament lasted less than 4 hours.

To calculate the duration, you subtract the start time from the end time:

4:00pm - 12:15pm = 3 hours and 45 minutes

Therefore, the tournament lasted for 3 hours and 45 minutes, which is less than 4 hours.

Here's a step-by-step breakdown of the calculation:

Start by calculating the number of whole hours between the start and end time.

4:00pm - 12:15pm = 3 hours

Next, calculate the number of remaining minutes.

4:00pm - 12:15pm = 45 minutes

So the total duration of the tournament was 3 hours and 45 minutes, which is less than 4 hours.

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The value of x is 3.

parallel lines are coplanar infinite straight lines that do not intersect at any point.

The lines l and m are the parallel lines.

3x-18+105=180

3x+87=180

Subtract 87 on both sides

3x=180-87

3x=93

Divide both sides by 3

x=31

Hence, the value of x is 3.

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The definition that justifies the congruence of angle measures GJH and GJI is given as follows:

Definition of Angle Bisector.

A bisection is defined as a segment that splits an angle measure into two equal measures.

Hence an angle bisector means that an angle is divided into two angles of equal measure.

For this problem, we have that segment GJ is the angle bisector of angle G, meaning that the angle measures GJH and GJI are congruent.

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There are 13! x 4 possible sequences where all cards of the same suit are together, and 13! possible sequences where all the clubs are together.

A standard deck of 52 cards contains 4 suits: spades, hearts, diamonds, and clubs.

(a) To find how many sequences have all cards of the same suit together, we need to find the number of sequences where all the cards of the same suit are together.

There are 4 possible suits, and each suit contains 13 cards.

So, the number of sequences where all the cards of the same suit are together is 13! x 4.

(b) To find how many sequences have all the clubs together, we need to find the number of sequences where all the clubs are together.

There are 13 clubs, and each club card can be placed in any order.

So, the number of sequences where all the clubs are together is 13!

Therefore, there are 13! x 4 possible sequences where all cards of the same suit are together, and 13! possible sequences where all the clubs are together.

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Rise divided by run gives you the slope. A line's rise and run can be used to calculate the slope of a line from its graph. A line's continuous slope is one of its defining characteristics. The slope is (-1,3).

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The larger cup can hold 144.51 in³ more water than the smaller cup.

The volume of a cone of radius r and height h is given by one third of the multiplication of pi = 3.14 by the radius squared by the height, hence:

V = 3.14r²h/3

V = 1.0472r²h.

For the smaller cup, the dimensions are r = 2 in and h = 3 in, hence the volume is given as follows:

V = 1.0472 x 2² x 3

V = 12.57 in³.

For the larger cup, the dimensions are r = 5 in and h = 6 in, hence the volume is given as follows:

V = 1.0472 x 5² x 6

V = 157.08 in³.

Then the difference is of:

157.08 - 12.57 = 144.51 in³.

The cones are given by the image presented at the end of the answer.

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The possible measurements for the triangle are given as follows:

The three trigonometric ratios are defined as follows:

For this problem, we have an angle of 45º, which has the same value for sine and cosine, hence:

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Strategy should be, choosing purse A if number of days is less than 10,if it is more than 10 , he should choose purse B.

If there are 10 days, he can choose any of the purse.

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given,

Genie provides friend two purses,

Purse A and Purse B

Graph of Growth in amount to number of days is given.

By the graph,

Intersection point is on 10th day

Till 10th day Amount of purse A is grows more than amount of purse B.

After 10th day amount of purse B starts growing more than amount of purse A

Let no. of days be x

If x < 10, he should choose purse A.

If x > 10 he should choose purse B.

If x = 10, he can choose any purse.

Hence, Friend should choose purse A if number of days is less than 10.

Friend should choose purse B if number of days is greater than 10.

If number of days is 10, he can choose any of the purse.

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There is no value of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by 7.

For d=7, we can see that:

3² - 1 = 8 is divisible by 7, but 5² - 1 = 24 is not divisible by 7.

For larger values of d such as 11, 13, 77, and 1001, we can use a similar approach to see if there are any values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. However, finding an exact value of n for larger values of d may be difficult without using more advanced mathematical methods.

In general, the number of values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by a given integer d will depend on the properties of the numbers 3, 5, and d. For example, if d is a prime number that is not a divisor of either 3 or 5, it is likely that there are only a few values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d.

However, if d is a composite number or a divisor of either 3 or 5, there may be more values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. Whether there are finitely or infinitely many such n will depend on the specific values of 3, 5, and d.

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