Solve for b.
a−b+c−−−−−−−√=3

b=−9+a√+c√
b=−9+a+c
b=3−a−c
b=−3+a√+c√

Answer:

y = -2x + 7

Step-by-step explanation:

Given: (0, 7) and (2, 3)

Using the slope-intercept formula: y2-y1/x2-x1

3-7/2-0 = -4/2 = -2

Y-intercept:

Use y= mx + b to find the y-intercept (b). For this, I will be using the coordinates (2, 3). Plug 2 into x and 3 into y, then solve.

3 = -2(2) + b

3 = -4 + b

7 = b

Form the equation together:

y = -2x + 7

Answer:

x ≤ 9

Step-by-step explanation:

Answer:

.......................o.-ppppppppppppp

Step-by-step explanation:

Answer:

mile

Step-by-step explanation:

The volume of the solid obtained by rotating the region bounded by the curves x = 3 + (y − 7)² and x = 12 about the x-axis is 504π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves x = 3 + (y - 7)² and x = 12 about the x-axis, we can use the method of cylindrical shells. This method involves integrating the circumference of each cylindrical shell and summing up all the shells to find the total volume.

Let's set up the integral for calculating the volume:

V = ∫[a,b] 2πy * h(y) dy

Where [a, b] is the interval of y-values that defines the region, 2πy is the circumference of each cylindrical shell, and h(y) is the height or the difference in x-values for each y.

First, let's find the interval of y-values. The curves x = 3 + (y - 7)² and x = 12 intersect at two points. We need to find those points of intersection.

Setting the two equations equal to each other:

3 + (y - 7)² = 12

(y - 7)² = 9

Taking the square root of both sides:

y - 7 = ±3

y = 7 ± 3

So we have two y-values: y = 4 and y = 10.

Therefore, the interval of y-values is [4, 10].

Next, let's find the height, h(y), for each y-value. The height is the difference in x-values between the curves.

h(y) = (12 - (3 + (y - 7)²))

Simplifying:

h(y) = 12 - 3 - (y - 7)²

h(y) = 9 - (y - 7)²

Now we have all the components needed to set up the integral:

V = ∫[4,10] 2πy * (9 - (y - 7)²) dy

= ∫[4,10] 2πy * (9 - (y² + 49 -14y)²) dy

= 2π ∫[4,10] y * (9 - y² - 49 + 14y) dy

= 2π ∫[4,10] y * (14y - y² - 40) dy

= 2π ∫[4,10] (14y² - y³ - 40y) dy

= 2π [14y³/3 - y⁴/4 - 40y²/2]₄¹⁰

= 2π [14(10)³/3 - (10)⁴/4 - 20(10)² - 14(4)³/3 + (4)⁴/4 + 20(4)²]

= 2π [252]

= 504π

Therefore, the volume of the solid obtained by rotating the region bounded by the curves x = 3 + (y − 7)² and x = 12 about the x-axis is 504π cubic units.

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Answer:

80% son perros,

Step-by-step explanation:

Se considera que el total corresponde al 100%

Por tanto:

100% - 20% = 80%

The remainder when \(5^{400}\) is divided by 19, the remainder is 17.

Remainder

The Remainder is the value left after the division. If a number (dividend) is not completely divisible by another number (divisor) then we are left with a value once the division is done. This value is called the remainder.

We can write,

\(5^{400} = (5^4)^{100} = 625^{100}\)

We know that,

19*33 = 627

Hence, we can write 625 as 627 - 2

It will become,

\(\frac{(627-2)^{100}}{19}=\frac{(-2)^{100}}{19}\)

We know that, even power of any number and its negative counterpart will be same.

Hence, we can write,

\(\frac{(-2)^{100}}{19}=\frac{(2)^{100}}{19} = \frac{2*2^{99}}{19}\)

We know that 99 = 11*9

Hence, we can write,

\(\frac{2*({2^9})^{11}}{19} =\frac{2*512^{11}}{19}\)

We know that,

19*27 = 513

Hence, we can write, 512 as 513 - 1

\(\frac{2*(513-1)^{11}}{19}=\frac{2(-1)^{11}}{19}\)

2*(-1)/19 = -2/19

It means the remainder will be 19 - 2 = 17.

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In this scenario, we are given three functions: f, g, and h, where the input and output for each function are natural numbers. Additionally, we are given the condition that f(n) < g(n) < h(n) for all natural numbers n.

The objective is to determine the relationship between the three functions based on this condition.Based on the given condition, we can conclude that the output of function g is greater than the output of function f for all natural numbers. Similarly, the output of function h is greater than the output of function g for all natural numbers. This implies that the functions f, g, and h are ordered in increasing order.

In other words, for any input value n, the value of f(n) is the smallest, followed by g(n), and then h(n) is the largest. This order is maintained consistently for all natural numbers. This information allows us to establish the relative magnitudes of the outputs of the three functions and the overall ordering of the functions themselves.

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Answer:

a × a × a × a × a × a is the answer

Answer:

The answer would be a × a × a × a × a × a

Step-by-step explanation:

This is because a² is just a × a, and a² to the power of ³ is going to be \(a^6\). And \(a^6\) is just a × a × a × a × a × a

Answer:

7.5x = total cost

As the cost is 7.5 dollars for each person, multiple the cost by the amount of people for the total cost of the whole party.

The 95% of regular grade gasoline sells for between $3.23 & $3.63 and per gallon (to decimal) and 85% of regular grade gasoline sells for between $3.23 & $3.53 and per gallon (to decimal) and 16% percentage of regular grade gasoline sells for less than $3.53 per gallon (to decimal).

Suppose that mean retail price per gallon of regular grade gasoline 3.43.

empirical rule explains that  approximately 68%,95% and 99.7% of data lies between (µ ± 1*σ) ,(µ ± 2*σ) and (µ ± 3*σ) respectively.

⇒If some data {x} are normally distributed, the corresponding {z} will be normal with mean 0 and standard deviation 1 where the correspondence between the {x} and {z} is given by

Such z's are called z-scores.

(µ ± 1*σ)=68%

(µ ± 2*σ)=95%

(µ ± 3*σ)=99.7%

a)

P(3.23<x<3.63) =\(P[ \frac{(x1- \mu)}{\sigma} < z < \frac{(x2- \mu)}{\sigma}} ]\)

=P[( \(\frac{3.23-3.43}{0.10}\) < z < \(\frac{3.63-3.43}{0.10}\) ]

=P[-2 < z < 2 ]

=0.95

=95.0 %

b)

P(3.23<x<3.53) =\(P[ \frac{(x1- \mu)}{\sigma} < z < \frac{(x2- \mu)}{\sigma}} ]\)

=P[( \(\frac{3.23-3.43}{0.10}\) < z < (\(\frac{3.53-3.43}{0.10}\) ]

=P[-2 < z < 1 ]

=0.815

=81.5 %

c)

P(x>3.53) =\(P[ z > \frac{x-\mu}{\sigma} ]\)

=P[ z > \(\frac{3.53-3.43}{0.10}\) ]

=P[ z > 1 ]

=0.16

=16.0 %.

Therefore, 95% of regular grade gasoline sells for between $3.23 & $3.63 and per gallon (to decimal) and 85% of regular grade gasoline sells for between $3.23 & $3.53 and per gallon (to decimal) and 16% percentage of regular grade gasoline sells for less than $3.53 per gallon (to decimal).

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Given:-

To find the value of x.

Since the corresponding opposite angles are equal and also the sum of angles inside a triangle is 180 degrees. we get,

So the required value of x is 5.

You need to work out the volume to know how much batter you need to pour. For any shape, the volume is width x length x height. In this case it would be 9 x 8 x 1.5 which would be 108 inch³. So the maximum batter is C.

C = 108.

The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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The Upper Control Limit (UCL) and Lower Control Limit (LCL) are calculated for different data sets, as specified in the given values.

The UCL and LCL are statistical control limits used in process control to determine if a process is in a stable and predictable state. These limits define the range within which data points should fall if the process is under control.

In each case provided (A, B, C, D, E), the UCL and LCL values are given. These values represent the calculated control limits for the respective data sets.

To calculate the control limits, a specific statistical method such as the ± 3σ (sigma) method may have been used. This method sets the UCL and LCL at three standard deviations above and below the mean.

The UCL represents the upper threshold or upper boundary, while the LCL represents the lower threshold or lower boundary. These limits help identify any potential deviations or out-of-control situations in the data.

By applying the given values, the corresponding UCL and LCL for each data set can be calculated. These limits are important for quality control and process monitoring, ensuring that the data falls within acceptable ranges.

To calculate the UCL and LCL using ±3σ limits, we use the following formulas:

UCL = Mean + 3σ
LCL = Mean - 3σ

Here, σ represents the standard deviation of the data set. The ±3σ limits provide a range that encompasses most of the data points in a normal distribution, with approximately 99.7% of the data falling within this range.
A) For data set A:
UCL = 7.437
LCL = -2.237

B) For data set B:
UCL = 7.82
LCL = 0

C) For data set C:
UCL = 8.382
LCL = 0

D) For data set D:
UCL = 7.82
LCL = -2.22

E) For data set E:
UCL = 9.112
LCL = 0

The ±3σ limits are derived from the standard deviation (σ) of the data set. Unfortunately, the standard deviation is not provided in the given information. If you have the standard deviation available, we can proceed to calculate the UCL and LCL using the formulas UCL = Mean + 3σ and LCL = Mean - 3σ.

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Question - What are the upper control limit (UCL) and lower control limit (LCL) using a ±3σ limit for the given data sets?

A) For data set A, the UCL is 7.437 and the LCL is -2.237.
B) For data set B, the UCL is 7.82 and the LCL is 0.
C) For data set C, the UCL is 8.382 and the LCL is 0.
D) For data set D, the UCL is 7.82 and the LCL is -2.22.
E) For data set E, the UCL is 9.112 and the LCL is 0.

Answer: D

Step-by-step explanation: The line of best fit is a straight line that passes through as many points as possible and has around the same number of points above and below it. D meets those requirements the best.

Answer:

Line D

Step-by-step explanation:

Line D is most fit because it intercepts more of the dots on the graph, if not, comes close to touching the majority of them.

Answer: 93

suppose: the grade we need on the next exam is x (x > 0)

to have an average of 90, we have the equation:

\(\frac{85+88+94+x}{4}=90\\\\<=>267+x=360\\\\<=>x=360-267\\\\<=>x=93\)

so the grade we need on the next exam is 93

Step-by-step explanation:

\(suppose: the grade we need on the next exam is x (x > 0)

to have an average of 90, we have the equation:

\begin{gathered}\frac{85+88+94+x}{4}=90\\\\ < = > 267+x=360\\\\ < = > x=360-267\\\\ < = > x=93\end{gathered}485+88+94+x=90<=>267+x=360<=>x=360−267<=>x=93

so the grade we need on the next exam

\)

296 quarters is equal in value to 74 dollars.

To determine the value of 296 quarters in dollars using dimensional analysis, we need to convert the number of quarters to dollars. Since 4 quarters are equivalent to 1 dollar, we can set up a conversion factor:

1 dollar = 4 quarters

To cancel out the unit "quarters" and end up with "dollars," we multiply the given quantity (296 quarters) by the conversion factor:

296 quarters × (1 dollar/4 quarters) = 74 dollars

Therefore, 296 quarters is equal in value to 74 dollars.

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The possible roots of √9 are +3 and -3.

What is root of a number?

In mathematics, a number's root is the number that, when multiplied by itself, yields the original number. For instance, since 7 x 7=49, the square root of 49 is 7. In this instance, 7 is referred to as the square root of 49 since it must be multiplied twice to produce the number. 3 because

3 x 3 x 3 = 27 is the cube root of 27.

We have to find the possible roots of √9.

The number 9 is not a prime number and is an odd number.

The multiple of nine can be expressed as follows:

1 x 9 = 9

3 × 3 = 9

9 × 1 = 9

You are aware that the number 9 is a multiple of three or that the result of multiplying three times itself is nine. Consequently, the square root of 9 can be expressed as;

\(\sqrt{9} = \sqrt{3*3} = \sqrt{3^2}\)

The square root of a number is cancelled by the square. As a result, when we square the above expression's square root, we obtain.

√9 = ±3

In essence, taking a number's square root yields two root values, one with a +ve symbol and the other with a -ve symbol.

Therefore, we can say that the roots of 9 are +3 and -3, or that the value of the square root of 9 can be expressed as +3 and -3.

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Answer: 64=s3

Step-by-step explanation: V=s3

64=s3

find the cubic root of each side

3√ 64=s4=s

so the side of the cube is 4 cu in.

The surface area of a cube is

SA=nA

where SA

is surface area, n

is the number of faces, and A

is the area of one face.

Te area of one face (A) is s2 so

Answer:

6.   A    5c + 3e + 2

7.   A    w = P/2 - 125

8.   D   point S

Step-by-step explanation:

6.

3 triangles + 5 hexagons + 2 squares =

= 3e + 5c + 2(1)

= 5c + 3e + 2

7.

perimeter = P

length = 250 m

width = w

P = 2L + 2W

P = 2(250) + 2w

2w = P - 500

w = (1/2)(P - 500)

w = (P - 500)/2

w = P/2 - 250

Incorrect expression: w =  P/2 - 125

8.

X = 5

Y = -25

X - Y = 5 - (-25) = 5 + 25 = 30

S = 30

This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

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Answer:

-8, -6, -4, -2

Step-by-step explanation:

This is the only sequence that is using constant repetition of addition, either adding positive numbers or adding negative numbers (the same positive or negative number). This one that you answered is always adding 2 from the prior number, so -6 = -8+2, -4=-6+2, and so on.

The first one is an odd combo where you add and subtract different values different signs each time, it is not constant addition of the same number.

The second one is multiplication which is not arithmetic, so that means it is constantly being multiplied by 2 each time.

Answer:-8,-6,-4,-2

Step-by-step The last one because it is consistent by adding 2 the other ones ad then subtract or multiply and you can do that so the last on

Answer:

10 cookies

Step-by-step explanation:

10 x 3 = 30

15 x 2 = 30

30 + 30 = $60

The number of cookies sold by Linda will be 10 cookies.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Linda sells cookies for $2 and hamburgers for $3. She sold 25 items and made $60.

The number of cookies sold by Linda will be calculated as below:-

10 x 3 = 30

15 x 2 = 30

30 + 30 = $60

Therefore, the number of cookies sold by Linda will be 10 cookies.

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Answer:

-6.8

Step-by-step explanation:

Since the number line goes by 0.1, if you count down from -6.5, the blue dot would be at -6.8.

Hope this helped!

Answer:

-6.8

Step-by-step explanation:

There are 10 ticks between -7 and -6, so we know each tick is -0.1

So, -6.5-0.3 is -6.8

The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine.

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