Which number is equivalent to the fraction 15/7? 2
2 1/7
7/15
1 8/7​

Answer:

Domain: input values (x-values)

Range: output values (y-values)

Absolute value: remove negative sign → output becomes positive
eg. |-2| = 2

Squaring a number → output is always positive

\(a(x)=3|x|\)

Domain = all real numbers

Range = all positive numbers and zero

\(b(x)=3x^2\)

Domain = all real numbers

Range = all positive numbers and zero

Answer:

the missing side value is 6.7.

Step-by-step explanation:

so the Pythagorean theorem is a^2+b^2=c^2, but since we are missing the b slide the equation now is 7^2-2^2=b^2. now you may not understand why we are missing the b side. so in the Pythagorean theorem, the a and b slides dont really matter, as long as the c side is the hypotenuse, or the longest slide in a triangle. so 7squared is 49, 2 squared is 4, so 49-4= 45, but its 45squared because the equation is c^2-a^2=b^2 so now we know that 45 is b squared, we just have to square root 45, to get about 6.7.

Answer:

The inequality that describes the problem is given as follows:

x ≤ 75.

How to obtain the inequality?

To describe the inequality in this problem, we need to obtain the upper bound of the total amount that Ted and his friends are expected to spend.

To obtain the upper bound of the total amount, the relevant information is given as follows:

Ted and his friends decided to split the bill evenly among the 5 of them.

Ted figured that each person will pay no more than $15.

Hence the upper bound of the total amount is calculated as follows:

5 x $15 = $75.

The upper bound of $75 means that in total, they are expected to pay at most $75, hence the inequality that describes this problem is given as follows:

x ≤ 75.

Answer:

75

Step-by-step explanation:

You will set the equation up as part/whole = percent/100 and when you replace it with your numbers you get 60/x = 80/100 now you cross multiply and do 60*100 = 80 * x and you get 6,000 = 80x now you divide both sides by 80 then you get 75 was the original price

Answer:

8,201 divided by 59 = 139

Step-by-step explanation:

Hoped this helped.

The sampling technique used for this situation is given by:

c) Cluster.

Samples may be classified as:

In this problem, the population is divided into groups, and each element of the groups are survived, hence cluster sampling was used.

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Answer:

The perimeter of the big rectangle is 38 cm

Step-by-step explanation:

Rectangle 1 and rectangle 2 share the same width, let their width be a cm while Rectangle 3 and rectangle 4 share the same width, let their width be b cm

Rectangle 1 and rectangle 3 share the same length, let their length be x cm while Rectangle 2 and rectangle 4 share the same length, let their length be y cm

The perimeter of a rectangle = 2(length + breadth).

For rectangle 1:

Perimeter = 2(a + x) = 10

a + x = 5            1)

For rectangle 2:

Perimeter = 2(a + y) = 20

a + y = 10          2)

For rectangle 3:

Perimeter = 2(b + x) = 28

b + x = 14         3)

For rectangle 4:

Perimeter = 2(b + y) = 18

b + y = 9         4)

Adding equations 1, 2, 3 and 4 gives:

a + x + a + y + b + x + b + y = 5 + 10 + 14 + 9

a + a + b + b + x + x + y + y  =38

2a + 2b + 2x + 2y = 38

2((a + b) + (x + y)) = 38

For the big rectangle, let its width = c = a + b and its length be d = x + y

The perimeter of the big rectangle = 2 (c + d)

Therefore:

2((a + b) + (x + y)) = 38

2(c + d) = 38 cm = The perimeter of the big rectangle

The perimeter of the big rectangle is 38 cm

Yes, the tangent constraint can be applied between a line and an arc in many CAD (Computer-Aided Design) software programs.

In CAD, a tangent constraint is a geometric constraint that forces two entities (lines, arcs, circles, etc.) to share a common tangent at their point of contact. When you apply a tangent constraint between a line and an arc, the software will ensure that the line and the arc are always tangent to each other at their point of intersection.

This constraint is useful for designing mechanical components, such as gears or cams, where you need to ensure that the contact between two parts is smooth and continuous. It is also commonly used in architecture, where a building's curved surfaces may need to be tangent to adjacent straight lines or walls.

In short, the tangent constraint can be applied between a line and an arc, and it is a useful tool in many different fields of design.

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Answer:

the answer is in point 117.967

Lee Jenkins worked the following hours as a manager for a local Pizza Hut 5 4/1​, 9 4/3​, 7 4/3​ and 8 4/3​.

Now, the above-mentioned hours are not in the proper form that we are required to calculate. Therefore, we need to change them into the proper format .In order to add these hours, we must first convert the hours and minutes to the same format.

We'll need to convert each fraction to a common denominator of 3x3=9.  5 4/1​ in the mixed format is 5 + 4/1,
which is equal to 9. 9 4/3 in the mixed format is 9 + 4/3,
which is equal to 10 1/3.7 4/3​ in the mixed format is 7 + 4/3,

which is equal to 8 1/3.8 4/3​ in the mixed format is 8 + 4/3,
which is equal to 9 1/3.Now that we've converted the times,

we can add them together to get a total of 36 1/3 hours.

Therefore, Lee worked for 36 1/3 hours. the total number of hours Lee worked as a manager for the local Pizza Hut is 36 1/3 hours.

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Answer:

x

Step-by-step explanation:

tan33° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{25}\)

The residential buildings' total assessed land value has the smallest standard deviation.

To determine the standard deviations for the commercial and residential buildings' total assessed land value and total assessed parcel value, we would need access to a specific dataset that includes these values. However, based on general trends and assumptions, residential buildings' total assessed land value is likely to have the smallest standard deviation.

Residential properties typically exhibit more homogeneity compared to commercial properties. Residential neighborhoods often consist of similar types of properties, with comparable land values within a specific area. As a result, the assessed land values for residential buildings are more likely to cluster around a mean value, resulting in a smaller standard deviation.

In contrast, commercial properties can vary significantly in terms of size, location, and intended use. They may be diverse in terms of their land value and parcel value. The assessed land values and parcel values for commercial buildings are more likely to have a wider range of values, leading to a larger standard deviation.  

Therefore, based on these general characteristics, the residential buildings' total assessed land value is expected to have the smallest standard deviation compared to the commercial buildings' total assessed land value and total assessed parcel value.

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The probability of winning the raffle  can be calculated by dividing the number of favorable outcomes  by the total number of possible outcomes (combining all possible sets of four tickets from the given range, which is 25 choose 4).

To calculate the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, the favorable outcome is the selection of tickets 1103, 1111, 1118, and 1122. Since we are choosing four tickets, the order doesn't matter.

The total number of possible outcomes can be calculated using the combination formula "n choose k" (denoted as C(n, k)). In this scenario, we have 25 tickets in total (from 1101 to 1125), and we want to choose 4 tickets. Thus, the total number of possible outcomes is C(25, 4).

To calculate C(25, 4), we can use the formula: C(n, k) = n! / (k! * (n - k)!), where "!" denotes factorial. Plugging in the values, we have: C(25, 4) = 25! / (4! * (25 - 4)!). Simplifying this expression, we get C(25, 4) = 12,650.

The probability of winning the raffle with the specific set of tickets is the ratio of the number of favorable outcomes (1) to the total number of possible outcomes (12,650). Therefore, the probability is 1/12,650, which is approximately 0.00007905 or 0.008%.

So, the probability of winning the raffle with tickets 1103, 1111, 1118, and 1122 out of the given range is very low, approximately 0.008%.

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Answer:

5.099

Step-by-step explanation:

The power series for the function `f(x) = 2/(3x^2)`, centered at `c=3` is given by:`f(x) = 2/27 - 4/243(x-3) + 1/81(x-3)² - 4/243(x-3)³ + ...`

Given the function `f(x) = 2/(3x^2)` and `c=3`.

We are to find the power series for the given function centered at c.

Now, we know that the power series representation for `f(x)` is given by:`

f(x) = ∑(n=0 to ∞) cn (x-c)n`Where `cn = fⁿ(c)/n!`

We will first differentiate the function `f(x)` n times and then substitute `x=c`.`f(x) = 2/(3x²)``f'(x) = -4/(9x³)``f''(x) = 24/(81x^4)``f'''(x) = -96/(243x^5)`

Now, we will substitute `x=3` in the above expressions.

`f(3) = 2/(3(3²))

= 2/27``f'(3)

= -4/(9(3³))

= -4/243``f''(3)

= 24/(81(3^4))

= 8/243``f'''(3)

= -96/(243(3^5))

= -32/243`

Hence, the coefficients `cn` are:`

c₀ = f(3)/0!

= 2/27``c₁

= f'(3)/1!

= -4/243``c₂

= f''(3)/2!

= 8/(2*243)

= 1/81``c₃

= f'''(3)/3!

= -32/(3*243)

= -4/243

`Therefore, the power series representation of `f(x)` is given by:`f(x) = ∑(n=0 to ∞) cn (x-c)n``f(x) = c₀ + c₁(x-c) + c₂(x-c)² + c₃(x-c)³ + ...``f(x) = 2/27 - 4/243(x-3) + 1/81(x-3)² - 4/243(x-3)³ + ...`

Hence, the power series for the function `f(x) = 2/(3x^2)`, centered at `c=3` is given by:`f(x) = 2/27 - 4/243(x-3) + 1/81(x-3)² - 4/243(x-3)³ + ...`

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To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Answer:

140 drummers

Step-by-step explanation:

Let
D = number of drummers
G = number of guitarists

We are given ratio of drummers to guitar players is 35:14

So

\(\dfrac{D}{G}= \dfrac{35}{14}\\\\\)

We are also given G = 56

Therefore
\(\dfrac{D}{56} = \dfrac{35}{14}\)

Multiplying both sides by 56 gets rid of the denominator:
\(\dfrac{D}{56} \times 56 = \dfrac{35}{14} \times 56\\\\\\\begin{aligned}\\D & = 35 \times 4 \\D & = 140\\\end{aligned}\)

Therefore there are 140 drummers

Answer:

Harry has a loan of $9000 in total. Harry obtained a loan from the bank. Explanation Harry's remaining debt, expressed in dollars, is modeled as a function of time t, expressed in months, by the function D(t). The role is played by, This function can be used to determine that $200 is being subtracted each month from the function, meaning Harry is paying $200 toward his loan. Harry has not yet made any payments, therefore we may set t=0 to obtain the total amount of his solo. Therefore, the value of D(t) will reveal the loan's net amount. Harry's borrowing, therefore, equals to $9000.

Answer:

103.125

Step-by-step explanation:

110.00 times 15% = 16.5

16.5 times 6.25% = 103.125

Answer - 103.125

Answer:

With the coupon and sales tax, the bicycle costs $100.38.

Step-by-step explanation:

First, we need to find 6.25% of $110.

110 x 0.0625 = 6.88

Now, let's add this to the total, or $110.

110 + 6.88 = $116.88

After that, we need to find 15% of this total.

116.88 x 0.15 = 17.53

Now, we need to subtract this from the total, which is now $116.88.

116.88 - 16.5 = $100.38

Now, with the coupon and sales tax, the bicycle costs $100.38.

Hope this helps! :D

The approximate y-intercept of the line of best fit given by a regression calculator is around 7.48 (rounded to two decimal places).

In mathematics, a line is a straight, one-dimensional figure that extends infinitely in both directions. It can be thought of as a series of points that are all in a straight line. A line can be described by its slope-intercept form equation, y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line represents its steepness or inclination, and is defined as the change in y divided by the change in x between any two points on the line. If the slope is positive, the line goes uphill as it moves from left to right; if the slope is negative, the line goes downhill as it moves from left to right. If the slope is zero, the line is horizontal. The y-intercept of a line is the point where the line crosses the y-axis, or the value of y when x equals zero. It is often denoted as (0,b) in coordinate notation. Lines can be used to represent many real-world situations, such as the trajectory of a moving object, the trend of data over time, or the relationship between two variables in a mathematical model. They are a fundamental concept in geometry and algebra, and have many applications in science, engineering, and other fields.

Here,

A: Based on the scatterplot, the approximate slope of the line of best fit given by a regression calculator is around 0.93 (rounded to two decimal places).

B: Using the line of best fit, we can estimate the distance traveled after 70 minutes by plugging in x = 70 into the equation of the line and solving for y. From the scatterplot, we can see that the point (70, approximately 76) is close to the line of best fit. Therefore, the approximate distance traveled after 70 minutes is 76 miles.

C: The equation for the line of best fit given by the regression calculator is y ≈ 0.93x + 7.48 (rounded to two decimal places). This equation is in slope-intercept form, where the slope is approximately 0.93 and the y-intercept is approximately 7.48.

D: The approximate y-intercept of the line of best fit given by a regression calculator is around 7.48 (rounded to two decimal places). This represents the estimated distance traveled when the time is zero. However, since the time in this case cannot be zero (it starts at 11 minutes), this value may not have any practical significance.

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Answer:

All are Yes ^^^

Step-by-step explanation:

Got it right

The amount of Type A coffee that was used is 40 pounds.

From the given information;

Type A coffee costs Miguel $5.95 per pound

Type B coffee costs $4.65 per pound.

For this month, the equation can be expressed as:

A + 3A

Thus;

5.95A + 3(4.65)A = 796.00

5.95A +13.95A = 796.00

19.9A = 796.00

A = 796.00/19.9

A = 40

Therefore, we can conclude that the amount of pounds of type A coffee that was used is 40 pounds.

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K = k1 + k2In matrix form, the stiffness matrix is given by: k = [(EIL^-3)(7/3L  2/3L; 2/3L  4/3L)]The above equation represents the stiffness matrix for the beam element with an additional node in the center (higher-order element).

Galerkin’s method is used to derive the stiffness matrix for a given beam element. Here's how to derive the stiffness matrix using Galerkin's method: Derive stiffness matrix using Galerkin's method:

Given, a beam element with an additional node in the center is a higher-order element. It can be represented by the following figure:

The beam element can be divided into two equal sub-elements of lengths L/2 each. Using Galerkin's method, the stiffness matrix of the beam element can be derived. The Galerkin's method uses the minimization principle of the potential energy.

The principle states that the energy of the system is minimum when the potential energy of the system is minimum. Galerkin’s method uses the shape functions of the element to interpolate the unknown displacements. In the Galerkin method, the approximate displacement field is taken as the same as the interpolation functions multiplied by the nodal parameters. Let us assume that there are m degrees of freedom for a beam element.

In matrix form, we have: {u} = [N]{d}Where,{u} is the vector of nodal displacements[N] is the matrix of shape functions[d] is the vector of nodal parameters Thus, the potential energy can be written asV = 1/2∫[B]^T[D][B]dA

where,[B] is the strain-displacement matrix[D] is the matrix of elastic moduli The strain-displacement matrix is given by[B] = [N]'[E]

Where [N]' is the derivative of the shape functions with respect to the axial coordinate The matrix of elastic moduli is given by[D] = (EIL^-3)[l  -l; -l  l]

where E is the Young’s modulus of the beam material, I is the area moment of inertia of the beam, and L is the length of the beam. Using Galerkin's method, the stiffness matrix of the beam element is derived as follows:

Step 1: Determine the shape functions and nodal parameters For this higher-order beam element, there are three degrees of freedom. Thus, there are three shape functions and three nodal parameters. The shape functions are given by: N1 = 1 - 3(ξ - 1/2)^2 N2

= 4ξ(1 - ξ) N3 = ξ^2 - ξ

where ξ is the dimensionless axial coordinate. The nodal parameters are given by: d1, d2, d3

Step 2: Determine the strain-displacement matrix The strain-displacement matrix is given by[B] = [N]'[E]The derivative of the shape functions with respect to the axial coordinate is given by:[N]' = [-6ξ + 3, 4 - 8ξ, 2ξ - 1]Therefore, the strain-displacement matrix is given by[B] = [N]'[E] = [-6ξ + 3, 4 - 8ξ, 2ξ - 1][E]

Step 3: Determine the matrix of elastic moduli The matrix of elastic moduli is given by[D] = (EIL^-3)[l  -l; -l  l]

where E is the Young’s modulus of the beam material, I is the area moment of inertia of the beam, and L is the length of the beam.

Step 4: Determine the stiffness matrix The stiffness matrix can be obtained by integrating the product of the strain-displacement matrix and the matrix of elastic moduli over the element. Therefore, the stiffness matrix is given by: k = ∫[B]^T[D][B]dA Knowing that the beam element can be divided into two equal sub-elements of lengths L/2 each, we can obtain the stiffness matrix for each sub-element and then combine them to obtain the stiffness matrix for the whole element.

The stiffness matrix for the first sub-element can be obtained by integrating the product of the strain-displacement matrix and the matrix of elastic moduli over the sub-element. Therefore, the stiffness matrix for the first sub-element is given by:k1 = ∫[B1]^T[D][B1]dA

where [B1] is the strain-displacement matrix for the first sub-element. The strain-displacement matrix for the first sub-element can be obtained by replacing ξ with ξ1 = 2ξ/L in the strain-displacement matrix derived above. Therefore,[B1] = [-3ξ1 + 3, 4 - 8ξ1, ξ1 - 1][E]The stiffness matrix for the second sub-element can be obtained in the same way as the first sub-element. Therefore, the stiffness matrix for the second sub-element is given by:k2 = ∫[B2]^T[D][B2]dA

where [B2] is the strain-displacement matrix for the second sub-element. The strain-displacement matrix for the second sub-element can be obtained by replacing ξ with ξ2 = 2ξ/L - 1 in the strain-displacement matrix derived above. Therefore,[B2] = [3ξ2 + 3, 4 + 8ξ2, ξ2 + 1][E]The stiffness matrix for the whole element is obtained by combining the stiffness matrices for the two sub-elements. Therefore, k = k1 + k2In matrix form, the stiffness matrix is given by: k = [(EIL^-3)(7/3L  2/3L; 2/3L  4/3L)]The above equation represents the stiffness matrix for the beam element with an additional node in the center (higher-order element).

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At the end of the year, Achley Company's owner's equity is $4,685,000 and can be calculated by starting with the beginning owner's equity, adding the revenues, subtracting the expenses, and subtracting the owner's withdrawals.

To calculate Achley Company's owner's equity at the end of the year, we start with the beginning owner's equity of $5,175,000. We then add the revenues of $225,000 and subtract the expenses of $165,000. This gives us the net income, which is the difference between revenues and expenses, and represents the increase in owner's equity.

So, net income = revenues - expenses = $225,000 - $165,000 = $60,000. Next, we subtract the owner's withdrawals of $550,000 from the net income. Owner's withdrawals are personal expenses or cash withdrawals made by the owner and reduce the owner's equity.

Owner's equity at the end of the year = Beginning owner's equity + Net income - Owner's withdrawals.Owner's equity at the end of the year = $5,175,000 + $60,000 - $550,000. Calculating the above expression, we find that Achley Company's owner's equity at the end of the year is $4,685,000.

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Answer:  Simplify the expression.

12x+6

Step-by-step explanation:

your answer is 12x+6

Answer:

a = -3, b = 6

Step-by-step explanation:

ax + 6 = -3x + b

If a = -3 and b = 6, then the equation would be -3x + 6 = -3x + 6, which would have infinitely many solutions.

If we isolate x, we have (a + 3) x = b - 6. We want the equation to be 0 = 0 for infinitely many solutions, so a has to be -3 and b has to be 6.

Answer:

1

Step-by-step explanation:

-2(-3x-4)=14

6x + 8 = 14

6x= 14-8

6x=6

x=1

A. The fastest bird is the spin-tailed swift and the slowest bird is the mallard.

B. the dive speed of the peregrine falcon is faster than any other birds given in the question.

What is speed?

The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Here, we have

A.  the speed of a spin-tailed swift is 2843.2m/min.

We have to convert the speed to m/sec.

From above we know that,

1 min = 60 sec

2843.2 m/min = 2843.2m/1minm

2843.2/60 = 47.386m/sec

2843.2 m/min = 47.386m/sec            

The speed of a spur-winged goose is 129.1ft/sec.

We have to convert the speed to m/sec.
From above we know that,

1ft = 0.3048m

129.1ft/sec = 129.1/1sec

129.1ft/sec = 39.349m/sec

Hence, from the above, we can say that the fastest bird is the spin-tailed swift and the slowest bird is the mallard.

B. From part (a) we get,

The speed of the different birds in m/sec is given below:

Spine tailed swift

2843.2m/min = 47.386m/sec

Spur-winged goose

129.1ft/sec = 39.349m/sec

Eider duck

31.3m/sec

Mallard

65mi/h = 29.051m/sec

The dive speed of the peregrine falcon is

322km/h = 322km/1h

              = 322(1000)m/1(3600)sec

             = 89.444m/sec

Hence, the dive speed of the peregrine falcon is faster than any other bird given in the question.

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Answer:

I’m fat

Step-by-step explanation:

eat food, then sleep

Answer: √58 or about 7.6

Step-by-step explanation:

use the distance formula: √((x1 - x2)² + (y1 - y2)²)

√((3 - 0)² + (7 - 0)²)

√((3)² + (7)²)

√(9 + 49)

√58

hope this helps!

Answer:

about 7.6

Step-by-step explanation:

right on edge 2021

Answer:

How you would find area of any shape is you would multiply length x width x height.

Step-by-step explanation: