3. A(-5,8), B(-2,14), C(12,7), D(9,1)

Given: ,8^2x= 32^x+3

a: (2³)^2x = (2⁵)^x+3

b: Solving, we get

2^6x = 2^5x+15

Since bases are same, we have

=>6x=5x+15

=> x = 15

The answer is 24 when using like terms and the order of operations.

The number would be -4 which is 8 less than the product of 2 and a number is equal to 16.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Let the number would be n

Given that 8 is less than the product of 2 and a number is equal to 16.

According to the statement of the question,

⇒ 8 - (n*2) = 16

⇒  -(n*2) = 16 - 8

Apply the subtraction operation,

⇒  -2n = 8

⇒ n = -8/2

Apply the division operation,

⇒ n = -4

Hence, the number would be -4 which is 8 less than the product of 2 and a number is equal to 16.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ1

Based on the facts behind the scores of Tom, Mary, Hector, and Sue, the players' scores are:

Tom's score is said to be the opposite of Mary's score. The only scores that are the opposites of each other are 2 and -2.

This means that Tom's score is either 2 or -2. However, Tom's score is said to be only larger than Sue's. 2 is greater than -4 and -2 so violates this. Tom's score can therefore only be -2.

Mary's score is then 2. Sue will have the lowest score of -4 and Hector will have the highest score of 3.

Find out more on player scores at https://brainly.com/question/2996032

#SPJ1

The process of writing a = lu is known as the LU decomposition of a matrix.

A matrix A can be decomposed into a lower triangular matrix L and an upper triangular matrix U, such that A=LU. This is called the LU decomposition of a matrix. The lower triangular matrix L has ones on the diagonal, and the upper triangular matrix U has nonzero elements on the diagonal. Here's how you can find the LU decomposition of a matrix:

Step 1: Write the matrix A in the form of an augmented matrix, with an identity matrix on the right-hand side.

Step 2: Use Gaussian elimination to reduce the matrix A to an upper triangular matrix U.

Step 3: The lower triangular matrix L is obtained from the elementary row operations performed on the identity matrix during the Gaussian elimination process.

Step 4: Write the matrix A as the product of the lower triangular matrix L and the upper triangular matrix U.

For example, let's find the LU decomposition of the matrix

                                      \(A = \begin{pmatrix} 2 & 1 & -1 \\ 4 & 2 & 0 \\ -2 & -3 & 8 \end{pmatrix}\)

Step 1: Write the matrix A in the form of an augmented matrix:

                                     \(\begin{pmatrix} 2 & 1 & -1 & 1 & 0 & 0 \\ 4 & 2 & 0 & 0 & 1 & 0 \\ -2 & -3 & 8 & 0 & 0 & 1 \end{pmatrix}\)

Step 2: Use Gaussian elimination to reduce the matrix A to an upper triangular matrix U:

                                    \(\begin{pmatrix} 2 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 2 & -2 & 1 & 0 \\ 0 & 0 & 6 & 2 & 0 & 1 \end{pmatrix}\)

Step 3: The lower triangular matrix L is obtained from the elementary row operations performed on the identity matrix:

                                    \(L = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ -1 & 3 & 1 \end{pmatrix}\)

Step 4: Write the matrix A as the product of the lower triangular matrix L and the upper triangular matrix U:

                         \(A = LU = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ -1 & 3 & 1 \end{pmatrix} \begin{pmatrix} 2 & 1 & -1 \\ 0 & 0 & 2 \\ 0 & 0 & 6 \end{pmatrix}\)

Therefore, the LU decomposition of the matrix A is:

                                         \(L = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ -1 & 3 & 1 \end{pmatrix}\)

                                        \(U = \begin{pmatrix} 2 & 1 & -1 \\ 0 & 0 & 2 \\ 0 & 0 & 6 \end{pmatrix}\)

See more about LU Decomposition at; https://brainly.com/question/30763777

#SPJ11

A pencil consists of a cylindrical body (10 cm long, radius 0.3 cm) with a cone-shaped eraser (1 cm slant height) and a hemisphere-shaped eraser.

A pencil consists of three main parts: a cylindrical body, a cone-shaped eraser, and a hemisphere-shaped eraser. Let's break down the dimensions of each part:

Cylindrical Body:

Length: 10 cm

Radius: 0.3 cm

Cone-shaped Eraser:

Slant height: 1 cm (assumed height of the cone)

Hemisphere-shaped Eraser:

Since the dimensions of the hemisphere-shaped eraser are not specified in detail, we'll assume a few things:

Let's assume that the hemisphere is attached to the cone in such a way that the flat surface of the hemisphere is aligned with the circular base of the cone.

We'll assume that the radius of the hemisphere is the same as the radius of the cylindrical body, which is 0.3 cm.

Please note that the actual dimensions of a pencil can vary, and these assumptions are made for the purpose of explanation.

It's worth mentioning that the cylindrical body of the pencil is the main part used for writing, while the cone-shaped and hemisphere-shaped erasers are located at the opposite end of the pencil, typically used for erasing mistakes.

for such more question on radius

https://brainly.com/question/13689629

#SPJ8

Answer:

See below.

Step-by-step explanation:

A) 3

B) 11

C) 7

-hope it helps

Answer:

a) 3

b) 11

c) 7

Step-by-step explanation:

The factors of 21 are: 1, 3, 7, 21

The factors of 411 are: 1, 3, 137, 411

A common prime factor is 3.

The factors of 77 are: 1, 7, 11, 77

The factors of 242 are: 1, 2, 11, 22, 121, 242

A common prime factor is 11.

The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56

The factors of 63 are: 1, 3, 7, 9, 21, 63

A common prime factor is 7.

Integral calculus is a branch of calculus that deals with the calculation of integrals. In calculus, integration is used to find the area under a curve, known as the definite integral. A definite integral can be used to calculate the area between a function and the x-axis in the range of integration.

When a function is integrated, it gives an anti-derivative of that function. The definite integral is the value of the integral when the range of integration is known. Let us evaluate the given integral step by step, and we use u-substitution to solve this problem.

∫(0 to 1) (x - x²)^(1/2) dxLet u = x - x² ; then du/dx = 1 - 2xdx = du / (1 - 2x) = du/u^(1/2)Substituting the values,∫(0 to 1) u^(1/2) du/u^(1/2) = ∫(0 to 1) du = u (1 to 0) = 1-0 = 1

In the given question, we have to evaluate the integral ∫₀¹√(x-x²)dx using the method of substitution.We know that∫f(x)dx=∫f(g(u))g’(u)duwhere x=g(u).In the given question,

x=x²-x=> x²-x-x=0=> x=0,x=1=> g(0)=0 and g(1)=1.We assume x-x²=u=> 1-2x=du/dx=> dx=du/(1-2x).

Now we substitute these values in the given integral.∫₀¹√(x-x²)dx=∫₀¹√u(1-2x)du/(1-2x)=∫₀¹√udu=√u(1 to 0)=1-0=1

Therefore, the value of the given integral is 1.

To know more about Integral calculus  :

brainly.com/question/24705479

#SPJ11

To find the missing sides and angles of a right triangle with side b = 32 and side c = 51, we can use the Pythagorean theorem and trigonometric ratios.

Let's denote the missing side as a and the angles as A and B, with B being the right angle.

Using the Pythagorean theorem, we know that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c):

a^2 + b^2 = c^2

Plugging in the given values, we have:

a^2 + 32^2 = 51^2

a^2 + 1024 = 2601

a^2 = 1577

a ≈ 39.73

Therefore, the length of the missing side a is approximately 39.73.

Learn more about Pythagorean theorem here: brainly.com/question/14930619

#SPJ11

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.

Learn more about nonlinear problem: brainly.com/question/31457669

#SPJ11

Answer:

The mean travelling time is 25 minutes.

Step-by-step explanation:

add up all of the values and divide by how much values there are. 5+15+25+35+45 equals 125. 125/5 equals 25

what I wrote earlier was cut off sorry, this is what I mean:

You can download Gauthmath if you want to solve your math problems.

Available on Playstore/Appstore

Answer: A

Step-by-step explanation:

Since multiplication is the only operation under the radical, you can apply the root to each term. Im not sure if I worded that correctly, but ill hopefully explain correctly.

First we need to take the cubed root of 648. This number doesn't have a perfect root, but it can be simplified. 648 is the same as 216*3, and 216 has a perfect cubed root of 6. So we can bring the 6 outside of the radical

\(3x*6\sqrt[3]{3x^4y^8}=18x\sqrt[3]{3x^4y^8}\)

The next step is simplifying the variables, which is the easiest part. Just split them up into multiples of 3, again poor explanation but Ill show what I mean.

\(18x\sqrt[3]{3x^3xy^3y^3y^2}\)

The cubed root and the cubed power will cancel and can be brought outside the radical\(18x*xy^2\sqrt[3]{2xy^2} =18x^2y^2\sqrt[3]{3xy^2}\)

Answer: He did not convert the fractions into the like fraction to add.

Step-by-step explanation:Given: The distance Jonah runs on Sunday=  milesThe distance Jonah runs on Monday=  milesThe total distance he ran = Since both the fractions are not like , thus multiply 2 to the numerator and the denominator of the first fraction [to add fractions first convert them into like fractions], we get The total distance he ran = The right answer is "The total distance he ran ="

Answer:

60

Step-by-step explanation:

Answer:

Step-by-step explanation:

a = 2 ; b = 4

4a + 2b² - 2(a -3b) = 4*2 + 2(4)² - 2 (2 - 3*4)

                             = 4*2 + 2*16 - 2(2 -12)

                            = 4*2 + 2*16 - 2* (-10)

                             = 8 + 32 + 20

                             = 60

The given series is of the form Σn^(-5), so we have p = 5. Since p > 1, the series converges. The series ∑(n=5 to infinity) 4/((n-1)^5) diverges.

We can use the integral test to determine whether the series ∑(n=5 to infinity) 4/((n-1)^5) converges or diverges. According to the integral test, if the integral of the function f(x) = 4/((x-1)^5) from 4 to infinity converges, then the series converges. If the integral diverges, then the series diverges.

Let's evaluate the integral:

∫(4 to infinity) 4/((x-1)^5) dx = [-1/4(x-1)^4] (4 to infinity)

= [-1/4((infinity-1)^4 - (4-1)^4)]

= [-1/4(infinity^4 - 81)]

= infinity

Since the integral of f(x) diverges, we conclude that the series ∑(n=5 to infinity) 4/((n-1)^5) also diverges. Therefore, the series is not convergent.

To further illustrate this, let's consider the limit comparison test. We can compare the series to a known divergent p-series, such as the series ∑(n=1 to infinity) 1/n^2. We can then take the limit as n approaches infinity of the ratio of the two series:

lim(n→∞) (4/((n-1)^5)) / (1/n^2)

= lim(n→∞) (4n^2/(n-1)^5)

Applying L'Hopital's rule, we get:

= lim(n→∞) (8n/(n-1)^6)

= 8/lim(n→∞) (n-1)^(-6)

Since the limit of (n-1)^(-6) is zero, the limit comparison test tells us that the series ∑(n=5 to infinity) 4/((n-1)^5) diverges, since it can be compared to the divergent series ∑(n=1 to infinity) 1/n^2.

In conclusion, the series ∑(n=5 to infinity) 4/((n-1)^5) diverges.

Learn more about diverges here

https://brainly.com/question/28452298

#SPJ11

The minimum number of subintervals using the Trapezoidal Rule is 16, and the minimum number of subintervals using Simpson's Rule is 2.

We first need to find the maximum value of the second derivative for Trapezoidal Rule and the fourth derivative for Simpson's Rule over the given interval [0, 2].

Given integral: ∫(3t^3 + 8t)dt from 0 to 2.
First derivative: 9t^2 + 8
Second derivative: 18t
Third derivative: 18
Fourth derivative: 0
The maximum value of the second derivative is 36 (when t=2) and the fourth derivative is 0 over the interval [0, 2].

a. Using the Trapezoidal Rule error estimate formula:
Error <= (b-a)^3 * M / (12*n^2)

Here, Error = 10^-4, a = 0, b = 2, and M = 36 (maximum value of the second derivative).
10^-4 <= (2-0)^3 * 36 / (12*n^2)
10^-4 <= 8 * 36 / (12*n^2)
Solving for n, we get n >= 15.07, and rounding up to the nearest whole number, n = 16.

b. Using Simpson's Rule error estimate formula:
Error <= (b-a)^5 * M / (180*n^4)
Here, Error = 10^-4, a = 0, b = 2, and M = 0 (maximum value of the fourth derivative).
Since the fourth derivative is 0, the error is 0, which is already less than 10^-4. We can use any even number of subintervals, so the minimum number is 2.

The minimum number of subintervals using the Trapezoidal Rule is 16, and the minimum number of subintervals using Simpson's Rule is 2.

Learn more about Trapezoidal and Simpson's rule                                                                                brainly.com/question/14915665

#SPJ11

The likelihood of single adolescent mothers breastfeeding their newborn infants is not statistically significant based on the given p-value of 0.18.

In statistical analysis, p-value measures the strength of evidence against the null hypothesis. A p-value less than 0.05 is typically considered statistically significant, indicating strong evidence against the null hypothesis. Conversely, a p-value greater than 0.05 suggests that there is not enough evidence to reject the null hypothesis.

In this case, the p-value of 0.18 indicates that there is a 18% chance that the observed results occurred by chance alone, assuming the null hypothesis is true. Since this p-value is greater than the commonly used threshold of 0.05, it suggests that there is not enough evidence to conclude a significant association between single adolescent mothers and breastfeeding rates of their newborn infants.

Based on the p-value of 0.18, there is no strong statistical evidence to suggest a significant association between being a single adolescent mother and the likelihood of breastfeeding their newborn infant. However, it is important to consider other factors and conduct further research to gain a comprehensive understanding of the relationship between these variables.

To know more about p-value follow the link:

https://brainly.com/question/4621112

#SPJ11

Answer:

\(y - 8 = \frac{5}{3}(x - 1)\)

Step-by-step explanation:

1) Use the slope formula, \(\frac{y_2 - y_1}{x_2 - x_1}\), and the given points to find the slope. \(x_1\) and \(y_1\) represent the x and y values of one point the line must intersect, and \(x_2\) and \(y_2\) represent the x and y values of another point the line must also intersect:

\(\frac{(3)-(8)}{(-2)-(1)}\)

= \(\frac{-5}{-3}\)

= \(\frac{5}{3}\)

2) Using the point-slope formula, \(y-y_1 = m (x - x_1)\), use the slope you just calculated and substitute it for m. Choose any of the two points given (I chose (1,8)) and substitute its x and y values for \(x_1\) and \(y_1\). Don't worry, the equation of the line is the same no matter which point you choose (unless the question specifies which one you need to choose):

\(y - 8 = \frac{5}{3}(x - 1)\)

Answer:

The answer would be y=3 x=1  

Answer:

Step-by-step explanation:

The awnser to this The 1x4)16 plus 18 and divided by the 3x2 u should be able to get your factor by negative 2, and negative 1 by 2 qnd 3.

Step-by-step explanation:

so 2.3 + 5.7 is 8.0 is the answer

Answer:

Step-by-step explanation:

1yen/0.00747USD

1yen*1000/0.0075USD*1000

1000yen/7.47USD

therfore 1000 yen = 7.47USD

Answer:

8,201 divided by 59 = 139

Step-by-step explanation:

Hoped this helped.

Answer:

(0,6)

Step-by-step explanation:

The y intercept is where the line crosses the y axis or the coordinate where x = 0.

Here, when x is equal to 0, y is equal to 6 meaning that the y intercept is at (0,6)

For the expression to have a true value for x, the limit of k must lie within the range of 4 and 6, inclusive.

The value of x in the formula kx2-6x+4/4x2-6x+x must exist within the range of 4 and 6, inclusive, for k to have a genuine value. Thus, k must be more than or equal to 4 and less than or equal to 6, respectively. When x is real, the expression cannot take on a real value if k is outside of this range. This is because division by zero is illogical because the denominator will be equal to zero. Therefore, x is real for the expression to be capable of the value, k must be between 4 and 6.

Learn more about expression here

https://brainly.com/question/14083225

#SPJ4

Answer:

$6.80

Step-by-step explanation:

1.79 x 3.8 = 6.802

So $6.80

The cartesian coordinates of the centerare (1, 0) and the radius is 1.

The equation r=2cosθ represents a circle with a center located at (a, b) and a radius equal to r.

The center (a, b) can be found by using the following equations:x=a+r cos(θ) and y=b+r sin(θ)Where (x, y) is any point on the circumference of the circle.

The general equation of the circle with center (a, b) and radius r is:(x-a)2 + (y-b)2 = r2Given the equation r = 2 cosθ, we can transform it to rectangular coordinates.

To do that we'll substitute for r with the formula r2 = x2 + y2, and for cosθ with x/r and sinθ with y/r, thus obtaining:(x2 + y2) = 2x => x2 - 2x + y2 = 0

Completing the square yields

(x - 1)2 + y2 = 1We can see that the center is located at the point (1,0), while the radius of the circle is equal to 1.

Given the equation r=2cosθ, we can transform it to rectangular coordinates by substituting r with the formula r2 = x2 + y2, and cosθ with x/r and sinθ with y/r.

Thus, we get(x2 + y2) = 2x => x2 - 2x + y2 = 0

Now, to get the center and radius of the circle, we have to transform the equation into the standard form of the circle equation, which is:(x-a)2 + (y-b)2 = r2(x - 1)2 + y2 = 12

We can see that the center is located at the point (1,0), and the radius of the circle is equal to 1.

Therefore, the cartesian coordinates of the center are (1, 0) and the radius is 1.

Learn more about cartesian coordinates of the center:https://brainly.com/question/4726772

#SPJ11

The correct answer is (c) Only the distribution of pretest scores must be approximately Normal

How is conditions for 99% CI calculation?

In order to construct a 99% confidence interval for the true mean difference in pretest and posttest scores, we need to meet certain conditions. The only condition that must be met is that the distribution of pretest scores should be approximately Normal. This means that the data collected from the pretest should follow a bell-shaped curve, with the majority of the scores being clustered around the mean. This condition is important because it helps us to make accurate statistical inferences about the population mean difference based on the sample data. The distribution of posttest scores or the difference between posttest and pretest scores are not required to be normal for constructing a confidence interval.

Learn more about 99% confidence

brainly.com/question/30762304

#SPJ11

To construct a 99% confidence interval for the true mean difference in pretest and posttest scores, the condition that must be met is only the distribution of differences (post-pre) must be approximately Normal. Thus, the correct option is D.

When constructing a confidence interval for the true mean difference in pretest and posttest scores, it is only necessary for the distribution of the differences to be approximately Normal. The distributions of the pretest and posttest scores themselves do not need to be Normal, as long as the difference between them is approximately Normal.

However, if all three distributions (pretest, posttest, and the difference) are approximately Normal, this can improve the accuracy and precision of the confidence interval.

Therefore, D is the correct option.

To know more about Pretest - Posttest visit:

https://brainly.com/question/31803047

#SPJ11

Answer:

$3.25

Step-by-step explanation:

184-164.50=19.50

19.50÷6=3.25

Answer:1, fractions come in different shapes,2, how to divide fractions and how to simplify mixed fractions. 3, we get to interact with electronics we get a better understanding of the work and more online work

In order to calculate the area of the rhombus, first let's draw the diagonal BD.

This diagonal and the diagonal AC will intersect at point M, which is the midpoint of each diagonal.

Since M is midpoint of AC, we have AM = MC = 7 cm.

Now, let's calculate the length of BM, using the Pythagorean theorem in the right triangle BMC:

Calculating the area of this triangle, we have:

The triangles BMC, BMA, DMC and DMA are all congruent, so the area of the rhombus is:

The volume of water runoff if the parking lot has an area of 1000 square meters is 70 cubic meters.

To calculate the volume of water that runs off the Shoppes at Fremont parking lot after a 7 cm rainfall event, we need to consider the area of the parking lot and the depth of the rainfall.

Given that the rainfall was 7 cm, we first need to convert it to meters to match the unit of the area. We divide 7 cm by 100 to get 0.07 meters.

Let's assume the area of the parking lot is A square meters.

To calculate the volume of water runoff, we can use the formula: Volume = Area × Depth.

Substituting the values, we have: Volume = A × 0.07 cubic meters.

The result of this calculation will give us the volume of water that runs off the parking lot after the 7 cm rainfall event. However, to obtain an exact value, we need to know the specific area of the parking lot in square meters.

Once we have the area of the parking lot, we can multiply it by 0.07 to determine the volume of water runoff in cubic meters.

For example, if the parking lot has an area of 1000 square meters, the volume of water runoff would be 1000 × 0.07 = 70 cubic meters.

It's important to note that this calculation assumes that all the water that falls on the parking lot runs off, without any absorption or infiltration into the ground.

Additionally, this calculation considers only the runoff volume and does not account for any drainage or storm-water management systems that may be present in the parking lot.

Learn more about volume from the given link

https://brainly.com/question/14197390

#SPJ11