please help!!
my problems are in the photo.

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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The value of surface area is,

SA = 570 cm²

Given that;

Base of house = 6 cm

And, Height of house = 19 cm

Since, The shape of house is like a prism.

We know that;

Area of Prism is,

SA = 2B + ph,

where B, stands for the area of the base, p represents the perimeter of the base, and h stands for the height of the prism.

Hence, We get;

SA = 2 × (1/2 x 6 × 19) + 2 (6 + 6) × 19

SA = 114 + 456

SA = 570 cm²

Hence, The value of surface area is,

SA = 570 cm²

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The 95% confidence interval for the population proportion of members who vote yes is (0.782, 0.818).

A choice that is made at random (purely by chance, with no predictability). They tapes of samples are:

Convenient: Sample taken from a pool that is easily accessible.

Random: Put all the possibilities into a hat, then pull some of them at random. Every kth element is taken in a systematic manner. If you wanted to survey anything on the street, for instance, you may interview every fifth person.

Cluster: The population is divided into groupings, or clusters, and every component of each cluster is surveyed.

Stratified: Additionally stratifies the people into several groupings. But only a small portion of the group is questioned after that.

Now, finding the sample proportion,

\(p=\frac{x}{n} \\\\=\frac{1600}{2000}\\\\ =0.8\)

The confidence level is given as,

\(C=p\pm[z(\frac{\alpha}{2})\times\sqrt{\frac{p(1-p)}{n} } ]\)

The value of \(z(\frac{\alpha}{2})\) is 1.96

Putting the values, we get

\(C=0.8\pm[1.96\times\sqrt{\frac{0.8(1-0.8)}{2000} } ]\\\\C=0.8\pm[1.96\times\sqrt{\frac{0.8(0.2)}{2000} } ]\\\\C=0.8\pm0.018\\\\C=(0.782,0.818)\)

Therefore, the 95% confidence interval is (0.782,0.818).

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The given question is incomplete. Here is the complete question.

a random sample of 2,000 members of a union reveals that 1,600 would vote yes on a merger proposal. what is the 95% confidence interval for the population proportion of members who would vote yes?

a) 0.782 to 0.818

b) 0.754 to 0.799

c) 0.690 to 0.713

d) 0.799 to 0.951

Answer:

ok and ty oof

Step-by-step explanation:

Step-by-step explanation:

area= (pi)r^2

a = (pi)×16^2

a= 256pi square units

To prove the given identities:

(a) cos(x+2π) = cos(x)
We know that cos(x+2π) = cos(x) because the cosine function has a period of 2π. This means that the value of the cosine function repeats every 2π radians. Adding 2π to the angle x doesn't change the value of the cosine function, so cos(x+2π) is equal to cos(x).

(b) sin2x = 2tanx/sec^2x
To prove this identity, we'll use the trigonometric identities sin2x = 2sinxcosx, tanx = sinx/cosx, and sec^2x = 1/cos^2x.

Starting with sin2x = 2sinxcosx, we'll replace sinx with tanx/cosx (using the identity tanx = sinx/cosx):
sin2x = 2(tanx/cosx)cosx
sin2x = 2tanx

Now, we'll replace tanx with sinx/cosx and sec^2x with 1/cos^2x:
sin2x = 2tanx
sin2x = 2(sinx/cosx)
sin2x = 2(sinxcosx/cosx)
sin2x = 2sinxcosx/cosx
sin2x = 2sec^2x

So, sin2x is equal to 2tanx/sec^2x.

In conclusion, we have proved the given identities:
(a) cos(x+2π) = cosx
(b) sin2x = 2tanx/sec^2x

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Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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Answer:

r= -4

Step-by-step explanation:

-208/-8=26

26+2=28

28/-7=-4

Answer:

-1+1

Step-by-step explanation:

cause takes out one gallon then adds one

Answer:

its not -1+1 NOT HELPFUL

Step-by-step explanation:

hi how is your day

Answer:

35

Step-by-step explanation:

Since you know that a triangle must have a total of 180 degrees and a right triangle is 90 degrees then you just subtract 90 from 180 and you get 90. Then subtract 55 from 90 and you get 35 which is the only possible answer.

Answer:

= -4(2.3x + 0.7)

Step-by-step explanation:

=(3x + 5.1) + (-12.2x - 7.9)

= 3x + 5.1 - 12.2x - 7.9

= -9.2x - 2.8

= -4(2.3x + 0.7)

The equations that represent the line are:

B. 2x + 3y = –3

D. y + 3= –2/3(x – 3)

E. y – 1 = –2/3(x+3)

An equation that represents a line whose slope is given as m, and it intercepts the y-axis at b, is expressed in slope-intercept form as y = mx + b.

To find the equation of the given line above, pick two points on the line, (0, -1) and (-3, 1) and find the slope (m):

Slope of the line (m) = change in y / change in x = (1 - (-1)) / (-3 - 0)

Slope of the line (m) = 2 / -3

Slope of the line (m) = -2/3.

The line intercepts the y-axis at -1. This means the y-intercept of the line is b = -1.

To write the equation of the line, substitute m = -2/3 and b = -1 into y = mx + b:

y = -2/3x - 1

It can be rewritten as 2x + 3y = –3 in standard form, or as y + 3= –2/3(x – 3) or y – 1 = –2/3(x+3) in point-slope form.

Therefore the answers are:

B. 2x + 3y = –3

D. y + 3= –2/3(x – 3)

E. y – 1 = –2/3(x+3)

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Answer:

e then m 4

Step-by-step explanation:

cause thats how it goes

Answer:

0.25

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

To solve this expression, we need to remember that division should be done before multiplication or addition/subtraction.

So we first simplify the expression by dividing 1/2 by 6:

1/2 ÷ 6 = 1/2 × 1/6

Next, we multiply the two fractions by multiplying their numerators and denominators:

1/2 × 1/6 = (1 × 1)/(2 × 6) = 1/12

Therefore, the value of the expression 1/2 ÷ 6 is equal to 1/12.

Answer:

5 pounds

Step-by-step explanation:

54.89 - 49.75 = 5.14

Then once that was rounded is turned to 5 pounds

Answer:  5.14 pounds, A

Step-by-step explanation:

54.89 - 49.75 = 5.14 pounds

The formula for the circumference of a circle is C = 2πr, where r is the radius and C is the circumference. The equation solved for r is r =c/π2 .

The exact value of the expression 4cos²(60)24csc²(45) is 12.

To find the exact value of the expression 4cos²(60)24csc²(45), we need to evaluate each trigonometric function separately and then substitute the values into the expression.

Let's start with cos²(60). The cosine of 60 degrees is equal to 1/2, so we have:

cos²(60) = (1/2)² = 1/4

Next, let's consider csc²(45). The cosecant of 45 degrees is equal to the square root of 2 divided by 2, so we have:

csc²(45) = (√2/2)² = 2/4 = 1/2

Now, we can substitute these values into the original expression:

4cos²(60)24csc²(45) = 4(1/4)24(1/2) = 1(24)(1/2) = 12

Therefore, the exact value of the expression 4cos²(60)24csc²(45) is 12.

It's important to note that we used the specific values of the trigonometric functions at the given angles (60 degrees and 45 degrees) to evaluate the expression. The final result is a numerical value without any variables.

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The standard deviation of conductance for the baby dolphin group is 0.94 watts per square meter per degree Celcius.

The standard deviation of conductance for the baby dolphin group can be calculated using the formula:

s = √[ Σ (\(x_{i}\) - x)² / (n - 1) ]

where s is the standard deviation, \(xi\) is each individual conductance value, x is the mean conductance for the baby dolphin group, and n is the sample size.

Plugging in the given values, we get:

s = √ [ (10.44 - 10.44)² + (9.13 - 10.44)² + (11.79 - 10.44)² + (11.15 - 10.44)² + (10.16 - 10.44)² + (9.13 - 10.44)² / (6 - 1) ]

s = √ [ 0 + 1.6916 + 2.2936 + 0.5376 + 0.1764 + 1.6916 / 5 ]

s = √ [ 0.8756 ]

s = 0.94 (rounded to two decimal places)

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Answer:

20

Step-by-step explanation:

240 divided by 12 = 20

Answer:

Translation?

Step-by-step explanation:

The largest palindrome made from the product of two 3-digit numbers is 906609.

To find the largest palindrome made from the product of two 3-digit numbers, we can start by considering all possible products of two 3-digit numbers, ranging from 100 to 999. We can then check if each product is a palindrome.

A palindrome is a number that reads the same forwards and backwards. We can iterate through the products in decreasing order and check if each product is a palindrome. If we find a palindrome, we compare it with the current largest palindrome found and update it if necessary.

Starting from 999 and iterating downwards, we multiply each number by all the 3-digit numbers below it. For example, we multiply 999 by 999, 998, 997, and so on. We continue this process until we find the largest palindrome.

After checking all possible products, we find that the largest palindrome made from the product of two 3-digit numbers is 906609. This palindrome is obtained by multiplying 993 by 913.

Therefore, the largest palindrome made from the product of two 3-digit numbers is 906609.

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Answer:

3 1/8

Step-by-step explanation:

simplified.

Answer:

The answer would be 10.

Step-by-step explanation:

10 is the number that has the most number of dots above it.

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

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Answer:

The area of triangle VZX is 210 cm^2

Step-by-step explanation:

Here, we want to get the measure of the area of triangle VZX

From the given diagram, we have two explicit triangles making up triangle VWX

These are triangles VWZ and VZX

By adding the areas of both triangles, we can get the area of VWX

Mathematically, the area of VZX is the difference between the area of VWX and VZW

To get the area of VZW, we can use the formula for the area of a triangle

We have this as 1/2 * base * height

base = 35 cm and height = 28 cm

The area of VWZ is 1/2 * 35 * 28 = 490 cm^2

The area of triangle VZX is thus;

700 cm^2 - 490 cm^2 = 210 cm^2

Step-by-step explanation:

Slope of the line:

\(m = \frac{8 + 6}{7} = 2\)

know that:

\(y - y 0 = m(x - x0)\)

Using m=2 and A(0, —6):

\(y + 6 = 2(x) \\ y = 2x - 6\)

So y-intercept is —6

Slope:-

\(\\ \rm\rightarrowtail m=\dfrac{8+6}{7-0}=\dfrac{14}{7}\)

\(\\ \rm\rightarrowtail m=2\)

Equation in point slope form

\(\\ \rm\rightarrowtail y+6=2(x)\)

\(\\ \rm\rightarrowtail y=2x-6\)

The number for which the sample standard deviation is exceeded with a probability of 0.01 is approximately 29.143.

To find the probability that the sample standard deviation is bigger than a certain number, we can use the chi-square distribution.

Given:

Sample size (n) = 15

Standard deviation of the population (σ) = 1.8%

Significance level (α) = 0.01 (1%)

To find the critical chi-square value, we need to determine the degrees of freedom. For a sample standard deviation, the degrees of freedom are (n - 1).

Degrees of freedom (df) = 15 - 1 = 14

Using a chi-square distribution table or calculator with 14 degrees of freedom and a significance level of 0.01, we find the critical chi-square value to be approximately 29.143.

The probability that the sample standard deviation is bigger than a certain number can be interpreted as the probability of having a chi-square value greater than that number.

Therefore, the probability that the sample standard deviation is bigger than the critical chi-square value of 29.143 is 0.01 or 1%.

In summary, the probability is 0.01 that the sample standard deviation is bigger than 29.143.

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