Follow the steps to solve the equation.
Solve 3x² -7 = 32x+1. To solve the given equation, _____ both sides.

1.) \(\frac{2n-3}{5} = 5\)

/ 5          /5

(2n - 3) = 1

      +3     +3

2n = 4

/2      /2

n = 2    <--- your answer

Answer:

BC =12

Step-by-step explanation:

use parallelogram law: BC=AD=12

To find the probability of getting 10 or more successes in a binomial experiment with p = 0.63 and n = 11 trials, we can use the cumulative probability function.

P(X ≥ 10) = 1 - P(X < 10)

Using a binomial probability formula, we can calculate the probability of getting exactly k successes:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where C(n, k) represents the binomial coefficient.

Let's calculate the probability for each value from 0 to 9 and subtract it from 1 to get the probability of 10 or more successes:

P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 9)

P(X < 10) = Σ[C(11, k) * p^k * (1 - p)^(11 - k)] for k = 0 to 9

Using this formula, we can calculate the probability:

P(X < 10) ≈ 0.121

Therefore, the probability of getting 10 or more successes in the binomial experiment is:

P(X ≥ 10) ≈ 1 - P(X < 10) ≈ 1 - 0.121 ≈ 0.879

Rounding to three decimal places, the probability is approximately 0.879.

Learn more about Probability here -:brainly.com/question/13604758

#SPJ11

Answer:0.4 as a decimal,2/5 as a fraction

Step-by-step explanation:

The appropriate hypotheses

Н0 = μ = 23.9

HA = μ > 23.9

The first step in hypothesis testing is to state the null hypothesis (H0) and the alternative hypothesis (HA). In this case, the null hypothesis is that the mean age at which men first marry has not changed since 1960. The alternative hypothesis is that the mean age at which men first marry has increased since 1960.

H0 = μ = 23.9

HA = μ > 23.9

If the sample mean age is significantly greater than 23.9 years, we would reject the null hypothesis and conclude that there has been an increase in the mean age at which men first marry in the region since 1960.

If the sample mean age is not significantly greater than 23.9 years, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean age at which men first marry has increased since 1960.

To know more about hypothesis here

https://brainly.com/question/29576929

#SPJ4

Answer:

Mark will travel 300 miles before they meet.

Step-by-step explanation:

Mark leaves 2 hours before Amy, so he will have traveled 120 miles by the time she left. Take 120 from 435: 315 miles to go. Each hour from this point, 105 miles will be closed, because Amy will have started traveling at 45 miles per hour. ( 60 + 45 = 105 ) You can take 105 from 315 3 times evenly ( representing 3 hours ). During those 3 hours, Amy has travelled 135 miles. 2 hours plus 3 hours is 5 hours. Mark has been traveling for 5 hours, and 60 times 5 is 300. 300 miles plus 135 miles equals 435 miles. Let me know if I need to break it down any better :)

Mark travelled a distance of 300 miles before he meet Amy.

Distance is how far one thing is from another thing. It is also a measure of the space between two things. It can be measured along any path. The distance traveled can be measured with speed and time.

For the given question,

The formula to find distance, d=speed(s) × time(t)

Distance between Mark and Amy = 435 miles

Mark's speed = 60 mph

Amy's speed = 45 mph

Amy leaves two hours late than Mark.

If Mark starts at t then Amy starts at (t-2)

Mark's distance = 60t

Amy's distance = 45(t-2)

For the given situation, the equation is

\(st = d\)

⇒ \(60t + 45(t-2)=435\)

⇒ \(60t+45t-90=435\)

⇒ \(105t=435+90\)

⇒ \(105t=525\)

⇒ \(t=\frac{525}{105}\)

Thus distance traveled by Mark's is 60t

⇒ \((60)(5)\)

⇒ \(300 miles\)

Hence we can conclude that Mark traveled a distance of 300 miles before he meet Amy.

Learn more about distance, speed and time here

https://brainly.com/question/21901071

#SPJ2

Answer:

7

Step-by-step explanation:

if a 3-meter tree is casting a shadow of 4 meters than an 8-meter jungle gym is actually 7 meters

The equation of the line parallel to 2x + 2y = -12 that passes through the point (2,-7) is y+7= -(x - 2)  , the correct option is (b)  .

In the question ,

it is given that ,

the equation of the line is parallel to 2x + 2y = -12 ,

2x + 2y = 12

2y = -2x + 12

Dividing both sides by 2  , we get

y = -x + 6

So , the slope of the line is -1 ,

since the required line is parallel , so the slope of the required line is -1 .

So , the equation of the line passing through the points (2,-7) with slope -1 is

(y - y₁) = m(x - x₁)

(y -(-7)) = -1(x - 2)

y + 7 = -1(x - 2)

y + 7 = -(x - 2)

Therefore , The equation of the line parallel to 2x + 2y = -12 that passes through the point (2,-7) is y+7= -(x - 2)    .

The given question is incomplete , the complete question is

Find the equation of a line parallel to 2x + 2y = -12 that passes through the point (2, -7) ?

(a) y+7=x-2

(b) y+7= -(x - 2)

(c) y-7=x+2

(d) y-7= -(x + 2)

Learn more about Equation Of Line here

https://brainly.com/question/28822230

#SPJ1

Answer:

No

Step-by-step explanation:

Plug it in to check. 36 is not equal to 4(11) becuase 4(11)=44.

36 never equals 44.

Answer:

To find the function f(x), we need to use the Remainder Theorem. The Remainder Theorem states that if we divide a polynomial by x - a, the remainder will be equal to the value of the polynomial at x = a.

We know that f(x) divided by 3x + 1 leaves a remainder of 7, so we can set up the equation:

f(x) = (3x + 1)(2x^2 + 2x - 9) + 7

Expanding the left side of the equation, we get:

f(x) = 6x^3 + 2x^2 - 27x - 9 + 7

Simplifying, we get:

f(x) = 6x^3 + 2x^2 - 27x + 2

The function f(x) is in standard form.

Answer:

When the function f (x) is divided by 3x – 1, the quotient is 2x² – 3x + 6 a

Step-by-step explanation:

Step 1 Devisor = 3x - 1Quotient = 2x2 - 3x + 6Remainder = 7Dividend = f(

Option C : At age 32, Angel's intelligence score wil be 110 ,  While  her score at age 16  be 110 .

To calculate IQ, take a person's mental age, divide it by chronological age, then multiply that number by 100 .

An IQ test assesses a variety of cognitive skills and yields a score that is meant to be used as a gauge of a person's potential and intellectual process. Among psychological testing, IQ tests are frequently used. The organisation Mensa International, which serves persons with IQs in the top 2%, defines IQ as "a form of standard score that reflects how far above, or how far below, his/her peer group an individual stands in mental capacity."

There are many different intelligence tests available, and they might have very distinct contents. Three Many medications are made expressly to be given to children, but some are used for adults. There are several uses for IQ tests, including Educational assessment and placement,Assessment and diagnosis of intellectual disability ,Cognitive research,Job candidate evaluation.

For such more questions on IQ test:

brainly.com/question/14986385

#SPJ4

Answer:

100

Step-by-step explanation:

The equation of the line passing through the points (−5,5) and (8,5) will be y = 0x + 5.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation is passing through the points  (−5,5) and (8,5). The equation of the line will be written below,

Y = mx + c

Slope = m  = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = m  =( 5 -5  ) / ( 8 + 5)

Slope = m  = 0

The y-intercept will be calculated as,

Y = 0x + c

5 = 0 + c

C = 5

The equation of the line is,

Y = mx + c

Y = 0x + 5

Therefore, the equation of the line passing through the points (−5,5) and (8,5) will be y = 0x + 5

To know more about an equation of the line follow

brainly.com/question/18831322

#SPJ1

The equation of the parabola that intersects the x-axis at points (-1, 0) and (3,0) is y = 0.

Given that a parabola intersects the x-axis at points (-1, 0) and (3,0).We know that, when a parabola intersects the x-axis, the y-coordinate of the point on the parabola is 0. Therefore, the two x-intercepts tell us two points that are on the parabola.Thus the vertex is given by:Vertex is the midpoint of these x-intercepts=(x_1+x_2)/2=(-1+3)/2=1The vertex is the point (1,0).Since the vertex is at (1,0) and the parabola intersects the x-axis at (-1,0) and (3,0), the axis of symmetry is the vertical line passing through the vertex, which is x=1.We also know that the parabola opens upwards because it intersects the x-axis at two points.To find the equation of the parabola, we can use the vertex form:y = a(x - h)^2 + kwhere (h, k) is the vertex and a is a constant that determines how quickly the parabola opens up or down.We have h=1 and k=0.Substituting in the x and y values of one of the x-intercepts, we get:0 = a(-1 - 1)^2 + 0Simplifying, we get:4a = 0a = 0Substituting in the x and y values of the other x-intercept, we get:0 = a(3 - 1)^2 + 0Simplifying, we get:4a = 0a = 0Since a = 0, the equation of the parabola is:y = 0(x - 1)^2 + 0Simplifying, we get:y = 0Hence the equation of the parabola that intersects the x-axis at points (-1, 0) and (3,0) is y = 0.

Learn more about Parabola here,The vertex of a parabola is (-2,6), and its focus is (-5,6).

What is the standard form of the parabola?

Enter your answe...

https://brainly.com/question/25651698

#SPJ11

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be  normalising the mode shape vectors f1, f2, and f3.

Part (a)

In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.

The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.

The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.

The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.

The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.

Part (b)

The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.

The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.

Learn more about coordinate  from the given link

https://brainly.com/question/17206319

#SPJ11

Answer: Each catalog weighs 0.87 pounds

Step-by-step explanation:

Given: Number of identical catalogs  = 8

Weight of package with the catalogs= 6.96 pounds

Using division operator,

Weight of each catalog  = (Weight of package ) ÷ (Number of identical catalogs)

i.e. Weight of each catalog  =(6.96)÷8 pounds

⇒ Weight of each catalog  = 0.87 pounds

Hence, Each catalog weighs 0.87 pounds

It is important to check that the number of successes and number of failures in each sample is at least 10 because this helps ensure that the normal approximation of the binomial distribution is accurate.

When constructing a confidence interval for the difference between two population proportions, it is important to check that the number of successes and the number of failures in each sample is at least 10 because this helps ensure that the normal approximation of the binomial distribution is accurate. The normal approximation is often used in constructing confidence intervals for proportions because it simplifies the calculations, but it is only accurate if the sample size is large enough.

A common rule of thumb is that each sample should have at least 10 successes and 10 failures in order to ensure that the normal approximation is reasonable. This is because the Central Limit Theorem states that the sum of many independent and identically distributed random variables will approximately follow a normal distribution. When the sample size is large enough, the distribution of the sample proportions will be approximately normal, even if the individual observations are not.

If the number of successes and failures in each sample is less.

Learn more about binomial distribution here: brainly.com/question/9325204

#SPJ4

Answer:

The flow rate of dopamine per hour is 15 mg and the duration is 9.3 hours.

Step-by-step explanation:

It is given that A solution consisting of 70 mg of dopamine in 70 mL of solution is administered at a rate of 15 mL/hr.

A solution consisting of 182 mg of dopamine in 26 mL of solution is administered at a rate of 10 ​mL/hr.

Now, Let's calculate the flow rate of dopamine per hour;

=> Flow rate of dopamine per hour = (70 × 15)/70

=> Flow rate of dopamine per hour = 1050/70

=> Flow rate of dopamine per hour = 15 mg

Further, let's calculate how much the solution should last for a patient that is prescribed to receive 140 mg of dopamine;

=> Prescription = 140 mg

=> Flow rate of dopamine per hour = 15 mg

=> Duration = Prescription/Flow rate of dopamine per hour

=> Duration = 140/15

=> Duration = 9.3 hours

Therefore, the flow rate of dopamine per hour is 15 mg and the duration is 9.3 hours.

To know more about this topic, click here:

https://brainly.com/question/13797070

#SPJ9

Answer:

22.25per person

Step-by-step explanation:

72.50*0.0675=4.89

72.50+4.89=77.39

77.39*.15=11.61=89.00

89.00/4=22.25 per person

Recursive functions produce a string of phrases by iterating over or utilising as input their own previous term.

A recursive function named reverse_string() that reverses a given string

def reverse_string(s):

   if len(s) <= 1:

       return s

   else:

       return reverse_string(s[1:]) + s[0]

Let's break down how this function works:

When the length of the string s is 0 or 1, that is the base case. In these situations, there is no need for reversal, therefore the method simply returns the string as-is.

The function calls itself recursively for strings longer than 1, taking as an input the substring that begins with character two (s[1:]). The string will be cut until the base case is reached by this recursive function.

The recursive call starts returning the sliced strings in reverse order when it reaches the base case and concatenates them with the first character of the original string (s[0]).

Here's an example of how you can use this function:

input_string = "Hello, World!"

reversed_string = reverse_string(input_string)

print(reversed_string)  # Output: "!dlroW ,olleH"

The function recursively reverses the characters in the input string, producing the reversed string as the output.

Learn more about recursive function here:

https://brainly.com/question/30027987

#SPJ11

The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

More can be learned about exponential functions and logarithms at https://brainly.com/question/25537936

#SPJ1

As calculated from the given data set we will get  any value greater than 45 minutes is an outlier.

IQR=Q3-Q1

= 24 - 10 = 14

To calculate the range ,

lower bound = (Q1–1.5*IQR)

= 10 - 1.5( 14)

= -11

upper bound = (Q3+1.5*IQR)

= 24 + 1.5( 14 )

= 45

Clearly , the range is - 11  to 45 , therefore any data which crosses 45 is an outlier.

An observation which gets  deviated from a given range or from a specified range is know as an outlier.

A mild outlier is a point that is outside of an inner barrier on both the side. An extreme outlier is a point that is outside of a barrier.

We can find the outliers with the help of upper and lower limits as shown above.

To learn more about data sets

brainly.com/question/22210584

#SPJ4

Answer:

The numbers are:

5, 12 and 4

Step-by-step explanation:

a + b + c = 21       Eq. 1

b = 2a +2             Eq. 2

b = 3c                   Eq. 3

From Eq. 2:

b - 2 = 2a

(b-2)/2 = a              Eq. 4

From Eq. 3:

c = b/3                     Eq. 5

Replacing Eq. 4 and Eq. 5 in Eq. 1:

(b-2)/2 + b + b/3 = 21

3(b-2)/6 + 6b/6 + 2b/6 = 126/6

3(b-2) + 6b + 2b = 126

(3*b + 3*-2) + 8b = 126

3b - 6 + 8b = 126

11b = 126 + 6

11b = 132

b = 132/11

b = 12

from Eq. 4

(b-2)/2 = a

(12-2)/2 = a

10/2 = a

a = 5

from Eq. 5

c = b/3

c = 12/3

c = 4

Check:

from Eq. 1

a + b + c = 21

5 + 12 + 4 = 21

The graph of f(x)=√x+3+2 is shifted 3 units up and 2 units to the right from the parent graph of f(x)=√x.

We have,

Graph is a type of data structure that consists of a set of nodes (also called vertices) and edges. Each node is connected to other nodes by edges. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. They are also very useful for visualizing relationships between data points in a variety of fields.

The translation of the parent graph of f(x)=√x+3+2 is a vertical shift upward 3 units, followed by a horizontal shift to the right 2 units. This is represented by the bold line in the graph. In terms of the equation, the translation is represented by the addition of the 3 and the 2 to the function. The 3 causes the graph to shift vertically upward and the 2 causes the graph to shift horizontally to the right. As a result, the graph of f(x)=√x+3+2 is shifted 3 units up and 2 units to the right from the parent graph of f(x)=√x.

To know more about graph click-

brainly.com/question/19040584

#SPJ1

complete question:

Below, the graph of f(x) = √x +3 + 2 is sketched in bold. Its parent function f(x)=√x is represented

by the thin curve.

1) Describe the

translation of the parent

graph.

2) How does the translation relate to the equation?

\(y-y_1=m(x-x_1)\)

Given the x1 and y1 = given point.

Substitution x1 = 2 and y1 = -8 in the equation.

\( \begin{cases} x_1 = 2 \\ y_1 = - 8 \end{cases} \\ y - ( - 8) = - 4(x - 2) \\ y + 8 = - 4(x - 2)\)

Hence, the solution is C choice.

\(y + 8 = - 4(x - 2)\)

Answer:

14

Step-by-step explanation:

or 16

Answer:

15

have a good day :)

Step-by-step explanation: