15 POINTS!!!!
What is the difference (2 x - 3) - (x - 1)
A. x - 4
B. x - 2
C. x + 2
D. x + 4

Option A, which states that the ordered pair of point P' will be, is the appropriate response (-8.75, 5.25).

Given,

A scaling factor of 7/4 is used to enlarge the pentagon in the OPQRS.

In order to generate O'P'Q'R'S, we must identify the ordered pair of point P'.

Here,

To obtain the coordinates of P', multiply the coordinates of point P by the scale factor 7/4.

P(-5,3)

P' (x, y) = P (-5 x 7/4, 3 x 7/4).

= P(-8.75, 5.25) 

As a result, option A, which states that the ordered pair of point P' will be, is the appropriate response (-8.75, 5.25).

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The question is improper. Proper question is given below;

If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’?

A. (-8.75, 5.25)

B. (-1.25, 0.75)

C. (-3.5, 8.75)

D. (-1.75, 3.5)

The acceleration function is a(t) = 6(t - 3).

Acceleration is the rate at which an object changes its velocity. The acceleration function is a mathematical function that gives the acceleration of an object at any given time

To find the acceleration function, we need to take the second derivative of the given velocity function f(t).

f(t) = (t - 3)^3 + t

First, let's find the first derivative of f(t)

f'(t) = 3 × (t - 3)^2 + 1

Now, let's find the second derivative of f(t) ( the acceleration function )

a(t) = f''( t )

= d/dt [3 × (t - 3)^2 + 1]

Do the derivation

= 6(t - 3)

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The given question is incomplete, the complete question is:

The velocity (in meters per second) with which a roller coaster moves can be given by the function f(t) = (t - 3)^3 + t. find the acceleration function a(t).

Answer:

586

Step-by-step explanation:

You can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 4102 and 7 using

GCF(4102,7) = 7

4102÷7

-------------  =5861 / 1

7÷7=5861

We know that

5861 / 1

Is equal to

5861 ÷ 1

Then using Long Division for 586 divided by 1 and rounding to a Max of 3 Decimal Places gives us

5861

Hopefully this helped! :D

-LavenderVye

The sample mean of the median ages in the given states is approximately 39 years.

To compute the sample mean, we need to find the average of the given median ages in the six states.

First, let's list the median ages provided:

Mississippi: 37

South Carolina: 39

Florida: 42

Wyoming: 38

New Mexico: 38

Ohio: 39

To find the sample mean, we sum up all the median ages and divide by the number of observations (in this case, six).

Sum of median ages = 37 + 39 + 42 + 38 + 38 + 39 = 233

Now, we divide the sum by the number of observations:

Sample mean = Sum of median ages / Number of observations

= 233 / 6

≈ 38.83

Rounding the sample mean to the nearest whole number, we get:

Sample mean ≈ 39

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\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Let's solve ~

Calculate discriminant :

\(\qquad \sf  \dashrightarrow \: 3 {x}^{2} + 6x - 1\)

\(\qquad \sf  \dashrightarrow \: discriminant = {b}^{2} - 4ac\)

\(\qquad \sf  \dashrightarrow \: d = (6) {}^{2} - (4 \times 3 \times 1)\)

\(\qquad \sf  \dashrightarrow \: d = 36 - 12\)

\(\qquad \sf  \dashrightarrow \: d = 24\)

\(\qquad \sf  \dashrightarrow \: \sqrt {d} = 2 \sqrt{6} \)

Now, let's calculate it's roots ( x - intercepts )

\(\qquad \sf  \dashrightarrow \: x = \cfrac{ - b \pm \sqrt{d} }{2a} \)

\(\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{2 \times 3} \)

\(\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{6} \)

So, the intercepts are :

\(\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6 - 2 \sqrt{6} }{6} \)

and

\(\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6 + 2 \sqrt{6} }{6} \)

Answer:

\(\left( \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ 0\right), \ \left(\dfrac{ -3 - 2\sqrt{3}}{ 3}, \ 0\right)\)

Explanation:

Given expression:

f(x) = 3x² + 6x - 1

Use quadratic formula:

\(\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ where \ ax^2 + bx + c = 0\)

Here after finding coefficients:

Applying formula:

\(x = \dfrac{ -6 \pm \sqrt{6^2 - 4(3)(-1)}}{2(3)}\)

\(x = \dfrac{ -6 \pm \sqrt{48}}{6}\)

\(x = \dfrac{ -6 \pm 4\sqrt{3}}{6}\)

\(x = \dfrac{ -6 \pm 4\sqrt{3}}{2 \cdot 3}\)

\(x = \dfrac{ -3 \pm 2\sqrt{3}}{ 3}\)

\(x = \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ \dfrac{ -3 - 2\sqrt{3}}{ 3}\)

Prism means two bases of equatorial triangle

So

Total area of bases

Total Lateral surface area

So

TSA:-

Relly made error in LSA

Answer:

Given:

Question 1

Total surface area = 2 x base area + 3 x lateral face area

                              = 2 x 73.2 + (3 x 104)

                              = 146.4 + 312

                              = 458.4 cm²

Question 2

Riley calculated the area by adding 2 base areas and only one lateral face.

The degrees of freedom for the chi-square test based on the two-way table provided are (r-1) times (c-1), where r is the number of rows and c is the number of columns in the table.

Here, the table has 3 rows and 4 columns, the degrees of freedom will be(3-1) times (4-1) = 2 times 3 = 6. The chi-square test is used to determine if there is a significant association between two categorical variables. In a two-way table, the rows represent one variable and the columns represent the other variable.

The degrees of freedom for the chi-square test is calculated by subtracting 1 from the number of categories in each variable and then multiplying these values. In this case, there are 3 categories (A, B, C) for one variable and 4 categories (D, E, F, G) for the other variable.

Therefore, the degrees of freedom would be (3-1) times (4-1) = 2 times 3 = 6. The degrees of freedom represent the number of independent pieces of information available for the chi-square statistic, which is used to determine the likelihood of the observed association occurring by chance.

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Step-by-step explanation:

3x-3(20)=12

3x=72

x=24.

24 stickers on each sheet

the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.

A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.

Given the mean is 121 while the standard deviation of the women is 9. Therefore, Using the z-table, the probability can be found.

(a) The probability that a woman selected at random has blood pressures greater than 136.

\(P(x > 136) = 1 - P(x < 136)\\\\P(x > 136) = 1 - P(z < \dfrac{x-\mu}{\sigma})\)

                  \(=1 - P(z < \dfrac{136-121}{9})\\\\=1 - P(z < 1.667)\\\\=1-0.9515\\\\=0.0485\)

(b) The probability that a woman selected at random has a blood pressure less than 114.

\(P(x < 114)= P(z < \dfrac{114-121}{9})\\\\\)

                  \(= P(z < -0.77)\\\\= 0.2206\)

(c) The probability that a woman selected at random has a blood pressure between 114 and 128.

\(P(114 < x < 128)= P(\dfrac{114-121}{9} < z < \dfrac{128-121}{9})\\\\\)

                  \(= P(-0.77 < z < 0.77)\\\\= P(z < 0.77)-P(z < -0.77)\\\\= 0.7794 - 0.2206\\\\=0.5588\)

Hence, the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.

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The given expression is

First, we solve the powers and the root

We solve the products on each side of the fraction

Now, we divide whole numbers each other and powers each other

a) The linearized function is 2x - 1. b) The linearized function is ex. c) The linearized function is 1. d) The linearized function is 5x - 5.

To linearize the given functions around the specified points, we can use the first-order Taylor series expansion. The linearized function will be in the form f(x) ≈ f(a) + f'(a)(x - a), where a is the specified point.

a) f(x) = \(x^1\) + x', around x = 2

To linearize this function, we evaluate the function and its derivative at x = 2:

f(2) = \(2^1\) + 2' = 2 + 1 = 3

f'(x) = 1 + 1 = 2

Therefore, the linearized function is f(x) ≈ 3 + 2(x - 2) = 2x - 1.

b) f(x) = \(e^x\), around x = 1

To linearize this function, we evaluate the function and its derivative at x = 1:

f(1) = \(e^1\) = e

f'(x) = \(e^x\) = e

Therefore, the linearized function is f(x) ≈ e + e(x - 1) = e(1 + x - 1) = ex.

c) f(x) = cos(x), around x = 0

To linearize this function, we evaluate the function and its derivative at x = 0:

f(0) = cos(0) = 1

f'(x) = -sin(x) = 0 (at x = 0)

Therefore, the linearized function is f(x) ≈ 1 + 0(x - 0) = 1.

d) f(x) = sin(x)(cos(x) - 4), around x = 0

To linearize this function, we evaluate the function and its derivative at x = 0:

f(0) = sin(0)(cos(0) - 4) = 0

f'(x) = cos(x)(cos(x) - 4) - sin(x)(-sin(x)) = \(cos^2\)(x) - 4cos(x) + \(sin^2\)(x) = 1 - 4cos(x)

Therefore, the linearized function is f(x) ≈ 0 + (1 - 4cos(0))(x - 0) = 5x - 5.

To compare the linearized functions with the actual functions, we can use MATLAB's "taylor" and "plot" commands. Here is an example of how to perform the comparison for the given functions:

% Part (a)

syms x;

f = x^1 + diff(\(x^1\), x)*(x - 2);

taylor_f = taylor(f, 'Order', 1);

x_vals = -0.5:0.2:0.5;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (a):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

% Part (b)

syms x;

f = exp(x);

taylor_f = taylor(f, 'Order', 1);

x_vals = -0.5:0.2:0.5;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (b):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

% Part (c)

x_vals = 0:0.1:1;

actual_f = cos(x_vals);

linearized_f = ones(size(x_vals));

disp("Part (c):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

figure;

plot(x_vals, actual_f, 'r', x_vals, linearized_f, 'b');

title("Comparison of Actual and Linearized f(x) for Part (c)");

legend('Actual f(x)', 'Linearized f(x)');

xlabel('x');

ylabel('f(x)');

grid on;

% Part (d)

syms x;

f = sin(x)*(cos(x) - 4);

taylor_f = taylor(f, 'Order', 1);

x_vals = 0:0.1:1;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (d):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

This MATLAB code snippet demonstrates the calculation and comparison of the actual and linearized functions for each part (a, b, c, d). It also plots the actual and linearized functions for part (c) using the "plot" command with the "hold" command to combine the graphs in one plot.

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Answer:

$47.25

Step-by-step explanation:

When the price goes down by 30%, you pay 70% of the original price.

When the price goes down by 10%, you pay 90% of the original price.

0.9 × 0.7 × $75 = $47.25

Answer:

76%

Step-by-step explanation:

number of girls is 6

number of boys is 25-6=19

percentage of boys = number of boys ÷ total no of students * 100

so... (19÷25)*100=76%

Answer:

the chances of her picking a yellow one is 6 in 35

Step-by-step explanation:

The probability distribution at each point x along the horizontal axis.

For a Normal distribution with mean 0 and standard deviation 1,

the following Python line outputs the probability p(-0.15 < x < 1.88):

print(st.norm.cdf(1.88, 0, 1) - st.norm.cdf(-0.15, 0, 1))

Probability is the likelihood or chance that an event will occur. It is a number between 0 and 1, with 0 indicating that an event will never occur and 1 indicating that an event will always occur.

Probability values range from 0 to 1, with a value of 0 indicating that the event will never occur and a value of 1 indicating that the event will always occur.

The probability is the value between 0 and 1 that indicates the likelihood of an event occurring. The probability is obtained by dividing the number of ways an event can occur by the total number of possible outcomes.

Scipy.stats.norm is the normal distribution's probability density function (pdf) in SciPy.

The PDF function is a part of the scipy.stats library in Python. The probability density function of the normal distribution is the function scipy.stats.norm.pdf(x, loc=0, scale=1). It is the height of the probability distribution at each point x along the horizontal axis.

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Answer:it

Step-by-step explanation:

it should be 10 i think

a) The right distribution law holds for S.

b) (1,0) is the multiplicative identity element for S.

c) The multiplicative identity law holds for S.

To find the multiplicative identity element for S, we need to find an element (x,y) in S such that (a,b) * (x,y) = (a,b) and (x,y) * (a,b) = (a,b) for all (a,b) in S. Let (x,y) be (1,0). Then:

(a,b) * (1,0) = (b-a-0, a-a-0) = (b-a, 0) = (a,b)

and

(1,0) * (a,b) = (0b-0a-0b, 0a-0b-0a) = (0,0) = (a,b)

To prove the multiplicative identity law for S, we need to show that for any (a,b) in S, (a,b) * (1,0) = (1,0) * (a,b) = (a,b). We have already shown that (1,0) is the multiplicative identity element for S, so we can use the definition of the identity element to compute:

(a,b) * (1,0) = (b-a-0, a-a-0) = (b-a, 0) = (a,b)

and

(1,0) * (a,b) = (0b-0a-0b, 0a-0b-0a) = (0,0) = (a,b)

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The value of the function (f.h)(x) is 96x⁵ + 132x⁴ + 78x³ + 18x²

f(x) = 3x² + 4x³ + 8x⁴

g(x) = -3x + 12x² - 5x³

h(x) = 12x + 6

Therefore,

(f.h)(x) = f(x).h(x)

Hence,

f(x).h(x) = (3x² + 7x³ + 8x⁴)(12x + 6)

f(x).h(x) = 36x³ + 18x² + 84x⁴ + 42x³ + 96x⁵ + 48x⁴

(f.h)(x) = 96x⁵ + 84x⁴ + 48x⁴ +  36x³ + 42x³ + 18x²

(f.h)(x) =  96x⁵ + 132x⁴ + 78x³ + 18x²

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Let's start with triangle RST. This is a 30-60-90 triangle, which means it has the relationship x - x sqrt(3) - 2x.

If RS is 2 sqrt(3), then ST must be 2 and RT must be 4.

Triangle QRT is a 45-45-90 triangle, which means it has the relationship x - x - x sqrt(2).

If RT is 4, then RQ must also be 4.

Answer: x = 4

Hope this helps!

Using the formula of margin of error for the confidence interval, the minimum sample size is 120

We can use the formula for the margin of error for a confidence interval:

margin of error = z* (standard deviation/√n)

where z* is the z-score for the desired confidence level.

For a 95% confidence interval, z* = 1.96. We want the margin of error to be 5, and we are given that the standard deviation of the population is 28. So we can solve for n:

5 = 1.96 * (28 / √n)

√n = 1.96 * 28 / 5

n = (1.96 * 28 / 5)²

n = 120.47

n = 120

The minimum sample size that will give a margin of error of 5 minutes with 95% confidence is 120.

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The rate charged per hour by the first mechanic = $105,

And the rate charged per hour by the second mechanic = $110.

Use the concept of ratio defined as:

A ratio indicates how many times one number contains another number. The ratio of two numbers is written as x: y, which is equivalent to x/y.

Where x and y are individual amounts of two quantities.

And, the Total quantity gives after combining as x + y.

Given that,

Two mechanics worked on a car.

The first mechanic worked for 10 hours.

The second mechanic worked for 5 hours.

Together, they charged a total of $1600.

The sum of the two rates charged per hour is $215.

Assume that,

The rate charged per hour by the first mechanic is = x dollars,

The rate charged per hour by the second mechanic is = y dollars.

The first mechanic worked for 10 hours,

The total amount earned by the first mechanic would be 10 times their hourly rate = 10x dollars.

Similarly,

The second mechanic worked for 5 hours,

The total amount earned by the second mechanic would be 5 times their hourly rate =  5y dollars.

Set up two equations based on the given information:

The first equation is the sum of the two rates, which is,

x + y = 215  ......(i)

The second equation is the total amount earned by both mechanics,

10x + 5y = 1600  .....(ii)

Use substitution to find the values of x and y:

From the first equation, we can express x in terms of y as,

x = 215 - y

Substitute this value of x into the second equation:

10(215 - y) + 5y = 1600

Expanding the equation, we get,

2150 - 10y + 5y = 1600

Combining like terms, we have:

-5y = 1600 - 2150

-5y = -550

Dividing both sides of the equation by -5, we get:

y = 110

Now that we have the value of y,

Substitute it back into the first equation to find x:

x + 110 = 215

Subtract 110 from both sides, and we get:

x = 105

Hence,

The rate charged per hour by the first mechanic is $105, &  the rate charged per hour by the second mechanic is $110.

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Answer:

Step-by-step explanation:

If the lengths of two sides of a triangle are given the third side must be less than the sum of those two sides, but more than the value of the difference between the given two sides.

So for #9, the answer is 4 (which is 12-8) <x<16 (which is 12+8)

#10. 10<x<16

#11. 19<x<61

#12. 6<x<16

Below are what would happen if the 3rd side was too big (left) or too small (right)

Answer:

HERE YOU GO

Step-by-step explanation:

x2 - 4x + 2 + y2 - 4y + 2 = 4 : expand equation of first circle

x2 - 2x + 1 + y2 - 2y + 1 = 4 : expand equation of second circle

-2x - 2y - 6 = 0 : subtract the left and right terms of the above equations

y = 3 - x : solve the above for y.

2x2 - 6x + 1 = 0 : substitute y by 3 - x in the first equation, expand and group like terms.

(3/2 + √(7)/2 , 3/2 - √(7)/2) , (3/2 - √(7)/2 , 3/2 + √(7)/2) : solve the above for x and use y = 3 - x to find y.

Answer:

5/3 hours   or 1 hour and 40 minutes

Step-by-step explanation:

The statement is true. If a matrix B can be expressed as B = PDP^T, where P is an invertible matrix and D is a diagonal matrix, then B is a symmetric matrix.

This can be proven as follows:
First, let's take the transpose of B:

B^T = (PDP^T)^T = (P^T)^TD^T P^T

Since D is a diagonal matrix, its transpose is equal to itself:

D^T = D

Therefore, we can substitute D^T with D in the above equation:

B^T = PDP^T = B

Since B is equal to its transpose, it is a symmetric matrix.

In other words, if a matrix B can be diagonalized by an orthogonal matrix P, which means that P^T=P^-1, then B is a symmetric matrix. This is because orthogonal matrices preserve the dot product and the symmetry of a matrix. The diagonal matrix D represents the eigenvalues of B, which can be either positive, negative, or zero. Therefore, if all the eigenvalues of B are non-negative, then B is positive definite, and if they are non-positive, then B is negative definite. If some eigenvalues are positive and some are negative, then B is indefinite.

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a) -5/-6

b) 5/-6

c) -5/6

d) 4/-6

From the format of -4/9 and -7/8 you can deduct that it is either A or C, -5/-6 (a) will be a positive decimal so therefore the answer is C because it is the only fraction in the correct format that has an answer on between the two in the problem.

C.) -5/6

The Variable d in the equation represents the time per minute Lilianna spends walking to the park

The equation:

d(3/4 + 1) = 12 1/4

d(3+4/4) = 12 1/4

d(7/4) = 49/4

d = 49/4 ÷ 7/4

= 49/4 × 4/7

= 49/7

d = 7

Complete question:

Lilianna uses 3/4 calories per minute just by sitting. She uses 1 more calorie per minute by walking. Liliana uses a total of 12 1/4 calories walking to the park. Lilianna uses the equation, d(3/4+1)=12 1/4 to represent the situation. What does the variable d represent in the equation?

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So, the inputs for which the output of function f(x) is 2 are x = 3√2 or x = -3√2.

an equation is a mathematical statement that asserts the equality of two expressions. it typically consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=). the expressions on both sides can contain variables, constants, operations, and functions, and the equation is usually solved by finding the values of the variables that make both sides of the equation equal to each other. equations can be used to model real-world phenomena, analyze data, and solve problems in various fields such as physics, engineering, finance, and statistics.

To solve for x when \(y = f(x) = 1/2 x^2 - 7\), we can set y to 2 and solve for x:

\(2 = 1/2 x^2 - 7\)

Adding 7 to both sides, we get:

\(9 = 1/2 x^2\)

Multiplying both sides by 2, we get:

\(18 = x^2\)

Taking the square root of both sides (remembering to consider both the positive and negative roots), we get:

x = ±√18 = ±3√2

So, the inputs for which the output of f(x) is 2 are x = 3√2 or x = -3√2.

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the value of a is -7/4.

Simply change x in the original equation to -1/4 to determine the value of a:

y = 4x² - 7x - 2

y = 4(-1/4)² - 7(-1/4) - 2

y = 1 - (-7/4) - 2

y = 1/4 - 2

y = -7/4

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

from the question:

We must discover a solution for x before we can find the solutions to the equation y = 4x2 - 7x - 2. By calculating the quadratic equation while putting y equal to zero, we can achieve this:

4x² - 7x - 2 = 0

(4x + 1)(x - 2) = 0

This quadratic equation has two solutions:

4x + 1 = 0 or x - 2 = 0

4x = -1 or x = 2

x = -1/4 or x = 2

As a result, the equation has solutions a = -1/4 and b = 2, where a b.

Simply change x in the original equation to -1/4 to determine the value of a:

y = 4x² - 7x - 2

y = 4(-1/4)² - 7(-1/4) - 2

y = 1 - (-7/4) - 2

y = 1/4 - 2

y = -7/4

Therefore, the value of a is -7/4.

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