please help soon, i can't seem to figure this one out!!

Consider the following equation. -2x + 6 = -(2/3)^x + 5. Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point.

A. x = 3/4
B. x = 13/16
C. x = 7/8
D. x = 15/16

The graph that represents \(f(x) = 3(2)^x\) is graph (d)

The function is given as:

\(f(x) = \frac 32(2)^x\)

The given function is an exponential function.

An exponential function is represented as:

\(f(x) = ab^x\)

Where a and b represent the initial value and the rate, respectively.

So, by comparison:

\(a = \frac32\)

\(b =2\)

This means that, the graph of \(f(x) = \frac 32(2)^x\) has an initial value of 3/2, and rate of 2

Hence, the graph that represents \(f(x) = 3(2)^x\) is (d)

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Answer:

\(x^3+\frac{-x^2-x}{4}+x+x^2-5\)

Step-by-step explanation:

\((x^3-(\frac{x}{2})^2 +x) + (x^2-\frac{x}{4} -5)\)

The addition sign between the sets of parentheses means to add the two equations together by combining like terms

There is only one term raised to the 3rd power so that remains the same.

Next you have -1/2x ^2 + x ^2 = 1/2x ^2

Then x + -x/4 = 3/4x

And -5 is the only term with no variable so that remains the same.

Now combine into one line:

X ^3 +1/2x^2 + 3/4x -5

The average rate of change of the total cost as his shirt production increases from 10 to 20 is 150.

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing.

Given that, the total cost to produce by James shirts is represented by a function, f(x) = 5x²+6.

We are to find the average rate of change of the total cost as his shirt production increases from 10 to 20.

The average rate of change is given by =

f(b) - f(a) / b-a, where a and b are given intervals,

Here, we have, a = 10 and b = 20

f(b) = 5(20)²+6 = 2006

f(a) = 5(10)²+6 = 506

The rate of change =

2006 - 506 / 20-10

= 1500 / 10

= 150

Hence, the average rate of change of the total cost as his shirt production increases from 10 to 20 is 150.

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Answer:

Q (- 1, 6 )

Step-by-step explanation:

use the midpoint formula to find the coordinates of M then equate the x and y coordinates with the actual coordinates of M

P (11, - 10) and let Q = (x, y ) , then

\(\frac{11+x}{2}\) = 5 ( multiply both sides by 2 )

11 + x = 10 ( subtract 11 from both sides )

x = - 1

and

\(\frac{-10+y}{2}\) = - 2 ( multiply both sides by 2 )

- 10 + y = - 4 ( add 10 to both sides )

y = 6

coordinates of Q = (- 1, 6 )

Answer:

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

The sum is 105

n+n+2+n+4=105

3n+6=105

minus 6 both sideds

3n=99

divide both sides by 3

n=33

n+2=35

n+4=37

If a transformation was performed on the following figure, the transformation applied to ΔSRT is given as translation

Translation is a transformation in which a figure or shape is moved without rotating, flipping, or resizing it. This movement is in a straight line, either horizontally, vertically, or diagonally. The figure's orientation changes but its size, shape, and angles remain the same. In other words, a translation moves a figure to a new location without changing its appearance. It is also called a slide. The direction and distance of the slide are specified by a vector.

For example, if we translate a triangle to the right by 3 units and up by 2 units, we will obtain the same triangle, but at a different location on the coordinate plane.

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Answer:

100,000,000,000.90987

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

Just sustitute the z for -4

z+z+z

-4+(-4)+(-4)

=-12

I hope this help :)

Steps to solve:

z + z + z when z = -4

~Substitute

-4 + (-4) + (-4)

~Simplify

-4 - 4 - 4

~Subtract

-8 - 4

~Subtract

-12

Best of Luck!

Answer: I can’t really see 4 but 7 is B and 10 is C

Step-by-step explanation:

ANSWER:

1st option: The y-intercept of f(x) is equal to the y-intercept of g(x).

STEP-BY-STEP EXPLANATION:

The y-intercept can be determined when x = 0, therefore:

For f(x):

In the function g(x), we can see that when x = 3, g(x) = -3, which means that the y-intercept is (0,-3)

Which means that the intercept is the same for both functions.

The correct answer then would be:

The y-intercept of f(x) is equal to the y-intercept of g(x).

Answer:

6 games and 3 rides

Step-by-step explanation:

Let the number of games Brianna played be x,

and the number of rides she went on be y.

Total cost for games= 1.25x

Total cost for rides= 3.75y

Since number of games is twice the number of rides,

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

Total costs= cost of games +cost of rides

\(18.75= 1.25x +3.75y\)

Multiply the whole equation by 4 to remove the decimals:

\(75= 5x +15y\)

Simplify by dividing the whole equation by 5:

\(15 = x + 3y\)

Label the equation:

x +3y= 15 -----(2)

Although we can solve these 2 equations by substitution, since the question requires us to graphically solve, we have to graph 2 linear lines.

I will choose 3 points to plot on the graph for each equation:

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

\(\begin{tabular}{|c|c|c|c|}

\cline{1-4}x & 2(1) = 2&2(2) = 4&2(3) = 6\\

\cline{1-4}y & 1 &2&3\\

\cline{1-4}

\end{tabular}\)

x +3y= 15 -----(2)

x= -3y +15

\(\begin{tabular}{|c|c|c|c|}

\cline{1-4}x & -3(1)+15= 12& -3(2)+15= 9& -3(3)+15= 6\\

\cline{1-4}y & 1 &2&3\\

\cline{1-4}

\end{tabular}\)

Let's plot these points on a graph paper. Then, join them with a straight line for each straight line graph. Please see the attached picture for the graph.

From (1): y= ½x

From (2): 3y= 15 -x

y= 5 -⅓x

From the graph, the solution of the equation is (6,3). The solution is the point on the graph in which the 2 lines intersect.

x- coordinate: 6

y- coordinate: 3

Thus, Brianna played 6 games and went on 3 rides.

Answer:

6 games=$7.5  3 rides=$11.25

1.25*6=7.5

3.75*3=11.25

7.5+11.25=18.75

To parameterize the plane in R^3 containing the point (1,2,3) and parallel to the given lines, we first need to find the normal vector to the plane. Since the plane is parallel to both lines, its normal vector must be perpendicular to both of their direction vectors.

The direction vector of the first line is (1,2,3), and the direction vector of the second line is (1,-1,1). To find a vector perpendicular to both of these, we can take their cross product:
(1,2,3) x (1,-1,1) = (5,2,-3)
This vector (5,2,-3) is perpendicular to both lines and therefore is the normal vector to the plane.
Now we can use the point-normal form of the equation for a plane:
ax + by + cz = d
where (a,b,c) is the normal vector and (x,y,z) is any point on the plane. We know that (1,2,3) is a point on the plane, so we can plug in these values
5x + 2y - 3z = d
To find the value of d, we can plug in the coordinates of the given point:
5(1) + 2(2) - 3(3) = -4
So the equation of the plane is:
5x + 2y - 3z = -4
To parameterize the plane, we can choose two variables (say, s and t) and solve for the remaining variable (say, z) in terms of them. Then we can plug in any values of s and t to get points on the plane.
Solving for z in terms of s and t:
5x + 2y - 3z = -4
5x + 2y + 4 = 3z
z = (5/3)x + (2/3)y + (4/3)
We can choose any values of s and t to get points on the plane, so a possible parameterization is:
x = s
y = t
z = (5/3)s + (2/3)t + (4/3)
Alternatively, we can write this in vector form:
(r,s,t) = (s,t,5s/3 + 2t/3 + 4/3)
where (r,s,t) represents a point on the plane.

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Evaluating the step function we will get:

For the step function:

f(x) = [x]

For any input x, the output is the whole number that we get when we round x down.

So, for the first input x = 1.1

We need to round down to the next whole number, which is 1, then:

[1.1] = 1

b) (here we have x = 1.1 again, maybe it is a typo).

[1.1] 0 1

c) [-0.1]

The next whole number (rounding down) is -1, so:

[-0.1] = -1

e [2.99]

Does not matter how close we are to 3, we always round down, so in this case, the output is 2.

[2.99] = 2

g) I assume the input here is 1/2 = 0.5

So:

[1/2] = [0.5] = 0

We round down to zero.

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Answer:

29

Step-by-step explanation:

Hi,

f(5) = 7 * 5 - 6 = 35 - 6 = 29.

For the function f(z) = z² + z - 2, the poles are found, and the residues at each pole z = -3/2 is a pole of order 6.

In part (a), we will evaluate the integral of the function x²+x+1. To do this using contour integration, we need to find a contour C that encloses the singularities of the function. However, this particular function is a polynomial, which means it is entire and has no singularities. Therefore, the integral of x²+x+1 over any closed contour C is zero.

In part (b), we are given the function f(z) = (3+2sinθ)/(2z+3)^6 and asked to evaluate the integral of f(z) over a circle with radius 4 (|z| = 4). To accomplish this, we can use the residue theorem. First, we need to find the poles of the function, which occur when the denominator (2z+3)^6 is equal to zero. Solving this equation, we find that z = -3/2 is a pole of order 6.

To determine the residues at each pole, we can expand the function f(z) in a Laurent series around the pole z = -3/2. The residue can be found by taking the coefficient of the (z - (-3/2))^-1 term. Once the residues are calculated, we can apply the residue theorem, which states that the integral of f(z) over the circle C is equal to 2πi times the sum of the residues. By substituting the values into the formula, we can evaluate the integral over the given contour.

In conclusion, using contour integration, we evaluated the integral of x²+x+1 and found it to be zero. We also determined the poles and residues for the function f(z) = z² + z - 2 and used the residue theorem to evaluate the integral of f(z) over a circle with radius 4.

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Answer:

The slope is -2.

Good Luck

In a right triangle, the tangent of an angle is defined as the quotient between the length of the side opposite to the angle and the length of the side adjacent to the angle.

Nevertheless, that is only true when the triangle is a right triangle. If BCA is a right angle, then all the reasoning is correct. But we cannot assume that BCA is a right angle unless it is given or there is a way to prove it.

Therefore, the mistake resides in assuming that the triangle is a right triangle without prior proof.

Answer:

24 or 12

Step-by-step explanation:

The area of the right triangle that is given would be = 60.

To calculate the area of the given triangle, the base of the triangle should first be calculated using the Pythagorean theorem.

That is ;

C² = a²+b²

c = 17

a = 8

b = ?

make b the subject of formula;

b² = c²-a²

= 17²-8²

= 289-64

= 225

b = √225 = 15

The area = ½ base ×height

= 1/2× 15 × 8

= 60

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Using the fundamental counting principle, it is found that there are 24 different combinations she can wear.

The sweaters and the pants are independent, and this is why the fundamental counting principle is used.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

Thus:

T = 6 * 4 = 24

There are 24 different combinations.

A combination in mathematics is a selection of items from a fixed that have amazing members, making the order of selection irrelevant (not like permutations). For instance, given a set of three fruits—say let's an apple, an orange, and a pear—one can choose between three combinations: an apple and a pear, an apple.

A hard and fast S's ok aggregate is, more precisely, a subset of S's ok amazing components. As a result, two combinations are equal if and best if each contains the same players. (The ties between the people in each group are not considered.)

(n/k) ={ n(n - 1) . . . (n – k + 1)}/{k(k - 1) . . . 1}

n!/{k!(n - k)!}

k > n.

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Answer:

Common ratio=1/2

Sum of first 6 terms of an A.P=31.5

Step-by-step explanation:

Let a be the first term and d be the common difference of an A.P

a=4

nth term of an A.P

\(a_n=a+(n-1)d\)

Using the formula

\(a_4=a+3d=4+3d\)

\(a_{10}=a+9d=4+9d\)

According to question

We know that

For G.P

\(\frac{a_n}{a_{n-1}}=r\)=Common ratio

\(r=\frac{4+3d}{4+9d}=\frac{4}{4+3d}\)

\(\frac{4+3d}{4+9d}=\frac{4}{4+3d}\)

\((4+3d)^2=\frac{4}{4+3d}\)

\(16+9d^2+24d=16+36d\)

\(9d^2+24d-36d-16+16=0\)

\(9d^2-12d=0\)

\(3d(3d-4)=0\)

\(d=0, d=4/3\)

Substitute the value of d

When d=0

\(r=\frac{4}{4+3d}=\frac{4}{4+0}=1\)

When d=4/3

\(r=\frac{4}{4+3\times \frac{4}{3}}=\frac{1}{2}\)

But we reject d=0 because  if we take d=0 then the terms are not consecutive terms of G.P

Sum of n terms of an A.P

\(S_n=\frac{n}{2}(2a+(n-1)d)\)

Using the formula

Substitute n=6 and d=1/2

\(S_6=\frac{6}{2}(2(4)+5\times \frac{1}{2})\)

\(S_6=31.5\)

The reason for why the confidence intervals help researchers attain their purpose of using a sample to understand a population is given below .

In the question ,

we have been asked how does the confidence interval help researchers to attain the purpose of using a sample to understand a population ,

we know that , the confidence interval is calculated from an estimate of how far away our sample mean is from actual population mean .

the confidence interval are useful because ,

(i) by calculating the confidence intervals around any data we collect, we have additional information about the likely values we are trying to estimate .

(ii) they make data analyses richer and help us to make more informed decisions about the research questions .

Therefore , the reason how confidence interval helps is mentioned above.

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The value of k⁻¹(8) in for k(x) = 4 ÷ 5x - 6 is 2/35.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, k(x) = 4 ÷ 5x - 6.

k(x) = (4/5x) - 6.

Let, y = k(x).

y =  (4/5x) - 6.

(4/5x) = y + 6.

1/x = 5(y + 6)/4.

x = 4/{5(y + 6)}.

y = 4/{5(x + 6)}.

k⁻¹(x) = 4/{5(x + 6)}.

k⁻¹(8) = 4/{5(8 + 6)}.

k⁻¹(8) = 4/{5(14)}.

k⁻¹(8) = 4/70.

k⁻¹(8) = 2/35.

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Answer: ≈37.8 m

Step-by-step explanation:

The sum of the angles of a triangle is equal to 180°.

⇒ х+32°+83°=180°

х+115°=180°

x+115°-115°=180°-115°

x=65°

The sine theorem goes like this: the sides of a triangle are proportional to the sines of the opposing angles.

\(\displaystyle\\\frac{22}{sin32^0} =\frac{S}{sin65^0} \\\\Multiply\ both \ parts\ of \ the \ equation\ by\ sin65^0:\\\\S=\frac{22(sin65^0)}{sin32^0} \\\\S\approx\frac{22(0.91)}{0.53}\\\\ S\approx37.8 \ m\)

Answer:

8

Step-by-step explanation:

if one tree equals 700 bags, then you would divide the amount of bags that were used, 5600, by 700 to get answer. 5600 divided by 700 = 8

Answer:

Angel Fall is 3091 ft taller.

Step-by-step explanation:

Height of Angel fall = 3281 ft

Height of Niagara falls in the United States = 190 ft

Angel fall is taller than Niagara Fall by

==> 3281 - 190 = 3091 ft

Answer:

20÷ 8 = 2.5

you have to divide 20 by 8 hope it's right

Answer:

15

Step-by-step explanation:

74.75 divided by 5 is 14.95 so when you add to the nearest whole number it will be 15.

Sixteen randomly selected engines were tested, and their maximum horsepower values are provided. Assuming the data is normally distributed and using a significance level of 0.05, the test statistic is computed to assess the hypothesis.

To perform the hypothesis test, we will use a t-test for the mean. The null hypothesis (H0) assumes that the average maximum horsepower for the experimental engines is equal to the calculated maximum horsepower of 630HP. The alternative hypothesis (Ha) assumes that the average maximum horsepower is significantly different from 630HP.

Using the provided data, we calculate the sample mean of the maximum horsepower values:

(643 + 641 + 598 + 621 + 644 + 601 + 649 + 652 + 671 + 653 + 666 + 654 + 670 + 670 + 666 + 654) / 16 = 651.0625

Next, we calculate the sample standard deviation to estimate the population standard deviation:

s = √[((643 - 651.0625)^2 + (641 - 651.0625)^2 + ... + (654 - 651.0625)^2) / (16 - 1)] ≈ 24.663

Using the formula for the t-test statistic:

t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size)

t = (651.0625 - 630) / (24.663 / √16) ≈ 2.027

Finally, comparing the calculated t-value of 2.027 with the critical t-value at a significance level of 0.05 (using a t-distribution table or software), we determine whether to reject or fail to reject the null hypothesis. If the calculated t-value falls outside the critical region, we reject the null hypothesis and conclude that there is a significant difference between the average maximum horsepower and the calculated maximum horsepower.

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