Dan went to a craft fair where he spent a total of 16.00 he spent 6.00 on admission and went to 8 tables he spent the same ammount of money (m) at each table the following number sentence can be used to find how much money he spent at each table

Note that:
a) This is a cross-sectional observational study because the data was collected from a single point in time and the observations were made without any manipulation of the variables by the researchers.

b) The explanatory variable in the study is the method of delivery (Caseload midwifery, Standard hospital care, Private obstetric care).

c) The two response variables in the study are the rate of vaginal deliveries (58.5%, 48.2%, 30.8%) and the cost of delivery ($3903.78, $5279.23, $5413.69). The rate of vaginal deliveries is a qualitative variable as it is a categorization of the type of delivery, while the cost of delivery is a quantitative variable as it is a measure of the amount of money spent on delivery.

It is to be noted that a cross-sectional observational study is a type of study in which data is collected from a single point in time without any manipulation of variables by the researchers.

The data collected provides a snapshot of the variables at that point in time.

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The number of 1/5 in a cube required to fill a prism which is 2 2/5 inches x 3 1/5 inches x 2 inches is,  2000 1/5 inch cubes

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

Given that,

The dimensions of a prism  2 2/5 inches by 3 1/5 inches by 2 inches

The volume of the prism = 2 2/5 inches x 3 1/5 inches x 2 inches

                                         = 16  inches³

To find the number of 1/5 inch cubes required to fill the prism,

we need to find the volume of one cube

and then divide the volume of the prism by the volume of one cube:

Volume of one cube = (1/5 inch)³

                                  = (1/5)³ inch³

                                  = 1/125 inch³

Volume of the prism / Volume of one cube = 16 / (1/125)

                                                                        = 16 x 125

                                                                        = 2000 cubes

So, it will take 2000, 1/5 inch cubes to fill the prism.

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Answer:

Step-by-step explanation:

0

The smallest integer is 10, the middle integer is 11, and the largest integer is 12.

What is the consecutive integers in algebra?

In algebra, consecutive integers are a sequence of numbers that follow each other in order, where each number is one more than the previous number.

Let's call the smallest integer "x". Then, the middle integer is "x + 1" and the largest integer is "x + 2".

Now, using the given information, we can set up an equation:

x + 2(x + 1) = 56 - 3(x + 2)

Expanding the equation and simplifying:

3x + 2 = 56 - 3x - 6

6x = 62

x = 10

So, the three consecutive integers are 10, 11, and 12.

Hence, The smallest integer is 10, the middle integer is 11, and the largest integer is 12.

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The required answers are

i) -65.6

ii) -64.8

iii) -64

iv) -64

The pace at which an object's position changes in relation to a frame of reference and time is known as its velocity.

Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.

Its SI equivalent is the metre per second (ms-1). A body is considered to be accelerating if its velocity changes, either in magnitude or direction.

Now in the given question,

1. Average velocity

When t=2

i. [2, 2.1]

= y(2.1) - y(2) / 2.1 - 2

= 205 - 16(2.1)^2 - 205 + 16(2)^2 / 0.1

= 205 - 16*4.41 - 205 +16(4) / 0.1

= -70.56 +64 / 0.1

= -6.56 /0.1

= -65.6

ii. [2, 2.05]

= y(2.05) - y(4) / 4.05 - 4

= 205 - 16(2.05)^2 - 205 +16(2)^2 / 0.05

= 205 - 16*4.2025 - 205 + 16(4) / 0.05

= -3.24 / 0.05

= -64.8

iii. [2, 2.01]

= y(2.01) - y(2) / 2.01 - 2

= 205 - 16(2.01)^2 - 205 + 16(2)^2 / 0.01

= 205 - 16*4.0401 - 205 + 16(4) / 0.01

= -64.64 + 64 / 0.01

= -0.64 / 0.01

= -64

iv. Instantaneous velocity

y = 205 - 16t^2

dy/dx = -32t

Considering t = 2

Instantaneous velocity after 2 seconds = -32(2)

Instantaneous velocity after 2 seconds = -64

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Solving the following expression (4x4-7x3+7x2-12x+15)/(x-1) yields the result -7x2 + 4 + 19/ in the form q(x)+r(x)/b(x) (x-1).

It is permissible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, term, and mathematical operator Three components of a numerical method include numbers, variable, and processes (such as addition, subtraction, multiplication or division etc.) It is possible to oppose expressions and words. An expression, often known as an analytical form, is any mathematics statement that contains variables, values, and an arithmetic procedure between them. For instance, the word m in the balanced formula is separated from the terms 4m and 5 by that of the arithmetic symbol +, as is the term m in the expression 4m + 5.

given

Given expression  is (4x⁴-7x³+7x²-12x+15)/(x-1)

then dividing this

=4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1

=4x³-3x²+4x-8+7/x-1  in form of  q(x)+r(x)/b(x)

= 4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1

= -7x² + 4 + 19/(x-1)

Solving the following expression (4x4-7x3+7x2-12x+15)/(x-1) yields the result -7x2 + 4 + 19/ in the form q(x)+r(x)/b(x) (x-1).

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There are 15 packages in the pile after 30 minutes.

From the question, we have the following parameters that can be used in our computation:

Rate = 2 + 8t packages per hour

To find the number of packages after t minutes, we need to integrate the rate of growth of the pile over time.

We can use the formula:

p(t) = p(0) + ∫_0^t (2 + 8t) dt

where p(0) = 13 is the number of packages in the pile at t = 0.

Evaluate

P(t) = 13 + 2t + 4t^2

For t = 30 minutes, which is equal to 0.5 hours, we have:

P(30) = 13 + 2 * 0.5 + 4 * 0.5^2

P(30) = 15

So, approximately there are 15 packages in the pile after 30 minutes.

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The unit vector with positive first component that is orthogonal to the plane passing through the points is 63i - 63j + 0k.

What is a unit vector?

A measurement that combines magnitude and direction is called a vector. A vector having magnitude 1 is referred to as a unit vector.

We are given three points P, Q and R.

The two vectors PQ and PR will lie on the plane through the three given points P(3, 0, 1), Q(4, -2, 1) & R(5, 3,-1).

The vector PQ = (9, 9, 9) and PR = (9, 9, 16) .

Therefore, the required vector is

N = PQ × PR

N = 63i - 63j + 0k

Hence, the unit vector with positive first component that is orthogonal to the plane passing through the points is 63i - 63j + 0k.

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Answer:

x=4

Step-by-step explanation:

12x+20-4=64

12x+16=64

12x=64-64

12x=48

x=4

the volume of a sphere:

V=[tex]\frac{4\pi r^3}{3} =\frac{4*3.14*13^3}{3}[/tex]≈9198.106

So, the growth rate for each year, x%, can be calculated using the above formula if the population of Nashville for a specific year, f(x)= (ln(f(x) / 10,000) / ln(1.15)) * 100, is known.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Here,

The expression f(x)=10,000(1.15)^x represents the population of Nashville each year, where x is the number of years after a certain reference point. The growth rate for each year can be found by taking the natural logarithm of the factor (1.15) in the expression:

ln(1.15^x) = ln(f(x) / 10,000)

x ln(1.15) = ln(f(x) / 10,000)

x = ln(f(x) / 10,000) / ln(1.15)

The value of x represents the growth rate as a percentage, so we need to multiply it by 100 to get the percentage:

x = (ln(f(x) / 10,000) / ln(1.15)) * 100

So, the growth rate for each year, x%, can be calculated using the above formula if the population of Nashville for a specific year, f(x)= (ln(f(x) / 10,000) / ln(1.15)) * 100, is known.

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The measure of the angle that ladder makes with the ground 41.8°.

Given the data in the question;

This forms a right triangle.

To find the angle, we use trigonometric ratio.

Sine = Opposite / Hypotenuse

sinθ = 20ft / 30ft

sinθ = 2/3

θ = sin⁻¹( 2/3 )

θ = 41.8°

Therefore, the measure of the angle is 41.8°.

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The volume of a sphere of radius 5 yd is 523.33 yd³.

What is the volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

We have given,

the radius of a sphere is 5 yd,

To Find: the volume of the sphere solid

So,

Sphere volume = 4/3 πr³

= 4/3 * 3.14 * (5)³

= 4/3 * 3.14 * 125

= 523.33 yd³

Hence, the volume of a sphere of radius 5 yd is 523.33 yd³.

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The test static value for the stocks is obtained as 3.482.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

It is given that -

The number of stocks n = 76

X = Number of stocks that got increased in price = 36

p = Proportion of stocks that got increased in price.

The formula for p is p = X/n.

Substitute the values in the equation -

p = 76/36 = 2.11111

Now find the value for q -

q = 1 - p

= 1 - 2.11111

= -1.11111

P=0.3

Q = 1 - P

= 1 - 0.3

= 0.7

Now, the values for H0 and H1 are -

H0 : P = 0.3

H1 : P > 0.3

Under H0, the test statistic is given by -

Z = (p - P)/√(PQ/n)

Substitute the values in the equation -

Z = (2.11111 - 0.3)/√(0.3 × 0.7/76)

Z = 1.81111 /√0.002763

Z = 1.81111 /0.052

Z = 3.482

Therefore, test statistic is 3.482.

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The triangles are similar to the AA property.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are items that feature more than two figures that are the same shape but different sizes.

Given triangles ANF and HES

for ΔANF,

∠A = 29°, ∠N = 106°, and ∠F = 45°(from angle sum property)

for ΔHES

∠H = 45°, ∠S = 29° and ∠E = 106°(from angle sum property)

so ∠A  = ∠S

∠N = ∠E

and ∠F = ∠H

so ΔANF ≈ ΔHES

by AA similarity.

Hence option A is correct.

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Nixon's visit to China was intended to advance their relationship and create new trade opportunities.

The President stated on live television that he would visit the PRC in 1972 on July 15, 1971. The American public was able to see photos of mainland China for the first time in more than 20 years during the week-long tour, which took place from February 21 to 28, 1972.

Nixon intended to protect the global populace, which meant he wanted to improve relations amongst the world's superpowers. Nixon's visit to China was intended to advance their relationship and create new trade opportunities.

A significant step in normalizing diplomatic ties with China, Nixon's visit was a big success. The following year, American tourists began to travel there, and American business organizations established a booming trade with China. The United States and China achieved complete diplomatic ties by the year 1979.

Therefore, the correct answer is option B. The Soviet Union was close to falling apart and communism would leave Eastern Europe.

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a) From the given information, [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

be a random sample of size 5 from a normal population with mean 0 and variance 1. Hence,

[tex]W=(\sum_{i=1}^5 Y_{i}^2)\sim X_{5}^2[/tex]

b) From the given information, the random variable is   [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and  [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables. Hence,

.[tex]U=(\sum_{i=1}^5 (Y_{i} - \bar{Y})^2) \sim X_{5}^2[/tex]

c) From the given information,[tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables and moreover, [tex]Y_{6}[/tex]

is independent standard normal variable. Hence,  [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2\sim X_{5}^2[/tex]

and

.[tex]Y_{6}^2\sim X_{1}^2[/tex]

What is Chi-square distribution?

Chi-square distribution with k degrees of freedom is defined as the sum of the k standard normal variables. This is also defined as the square of the deviations taken from the mean. Chi-square distribution is used for testing goodness of fit and independence in contingency tables.

• If  [tex]z_{1}, z_{2},...........z_{k}[/tex]

are independent standard normal variables, then

[tex]\sum_{i=1}^k z_{i}^2\sim X_{k}^2[/tex]

• If   [tex]X\sim X_{m}^2[/tex]

and   [tex]Y\sim X_{n}^2[/tex]

, then

[tex](X+Y)\sim X_{m+n}^2[/tex]

Step: 1

(a)

The distribution of    [tex]\sum_{i=1}^5 Y_{i}^2[/tex]

is obtained below:

From the given information, [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

be a random sample of size 5 from a normal population with mean 0 and variance 1. Hence,

[tex]W=(\sum_{i=1}^5 Y_{i}^2)\sim X_{5}^2[/tex]

The random variable,  [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

representing the sum of squares of standard normal variables and hence, the distribution of   [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

is identified as chi-square distribution.

Hint:

Use chi-square distribution to find the distribution of

.[tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

Step: 2

(b)

From the given information, the random variable is   [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and  [tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables. Hence,

.[tex]U=(\sum_{i=1}^5 (Y_{i} - \bar{Y})^2) \sim X_{5}^2[/tex]

The random variable    [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

representing the sum of squares of deviations taken from the mean for 5 standard normal variables and hence, the distribution of
[tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

is chi-square distribution with 5 degrees of freedom.

Hint:

Use       [tex](X+Y)\sim X_{m+n}^2[/tex]  

to find the distribution of

[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2[/tex]

Step: 3

(c)

From the given information,[tex]Y_{1}, Y_{2},...........Y_{5}[/tex]

representing the standard normal variables and moreover, [tex]Y_{6}[/tex]

is independent standard normal variable. Hence,  [tex]U=\sum_{i=1}^5 (Y_{i} - \bar{Y})^2\sim X_{5}^2[/tex]

and

.[tex]Y_{6}^2\sim X_{1}^2[/tex]

Therefore,

[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2\sim X_{5+1}^2[/tex]

[tex]\sim X_{6}^2[/tex]

The distribution of    [tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2+Y_{6}^2[/tex]

is identified as chi-square distribution with degrees of freedom is obtained by adding the degrees of freedom of[tex]\sum_{i=1}^5 (Y_{i} - \bar{Y})^2[/tex]

and the degrees of freedom of   [tex]Y_{6}^2[/tex].

The distribution of   [tex]W=\sum_{i=1}^5 Y_{i}^2[/tex]

is chi-square distribution with 5 degrees of freedom.

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The probability that a person lives with another person, given that they live in an apartment, is approximately 0.664.

We need to utilise conditional probability to determine the likelihood that a person lives with another person given that they reside in an apartment.

Let's define the subsequent occasions:

A: at least one other person lives with the individual.

B: The resident is an apartment dweller.

The probability that a person shares a home with at most one other person, assuming that they reside in an apartment, is P(A|B).

We are aware of:

The probability that someone resides in an apartment is P(B) = 329/837.

The probability that a person shares a home with at most one other person, given that they reside in an apartment, is given by P(A|B) = 218/329.

P(A|B) can be calculated using Bayes' theorem as follows:

P(A|B) equals P(B|A)*P(A)/P (B)

We may calculate P(B|A), the probability that an individual resides in an apartments given that they share a residence with at most one other person, using the following formula:

P(A and B) = P(B|A) (A)

We are aware of:

The probability that someone lives in an apartment with at most one other person is P(A and B) = 218/837.

The probability that someone lives with at most one other person is P(A) = 629/837.

By entering these values, we obtain:

P(B|A) = (218/837) / (629/837) = 218/629

Now that all the numbers have been entered, we can calculate P(A|B):

P(A|B) = (218/629) * (629/837) / (329/837) = 0.664

Given that they reside in an apartment, the probability that a person lives with another individual is roughly 0.664.

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The required individual functions are given as g(x) = x⁴- 6 and f(x) = [tex]\sqrt[7]{x}[/tex].

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given funciton
h(x) = (f o g) (x)

Where g(x) = x⁴- 6 and h(x) = [tex]\sqrt[7]{x^4-6}[/tex]

Since, put h(x) ⇒ f(x) and  g(x) = x⁴- 6
f(x) =  [tex]\sqrt[7]{g(x)}[/tex]

Again put g(x) ⇒ x
f(x) = [tex]\sqrt[7]{x}[/tex]

Thus, the required individual functions are given as f(x) = x⁴- 6 and g(x) = [tex]\sqrt[7]{x}[/tex].

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The probability that a randomly selected Atlantic cod has a length of 53.68 cm or less is given by the equation P ( x < 53.68 ) = 0.8439

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P

Now , the equation will be

The observed value of x = 53.68 cm

The mean of the sample μ = 49.9 cm

The standard deviation of the sample σ = 3.74 cm

Now , z-score is calculated using the formula:

z = (x - μ)/σ

Substituting the values in the equation , we get

z = ( 53.68 - 49.9 ) / 3.74

z = 1.0107

Now ,the p value from the z table is

P ( x < 53.68 ) = 0.84392

And , the probability is P ( x < 53.68 ) = 84.392 %

Hence , the probability is 84.392 %

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As a result, there is a 52% chance that a pupil chosen at random will be doing homework or playing an activity after school.

By reducing the number of positive outcomes by the overall number of potential outcomes, probability—the chance that a will occur—is determined. The most basic illustration is a coin toss. There are just two results when users flip a coin: either it shows up heads or tails.

We need to discover the sum of the percentage of students who plan to do homework and the percentage of students who plan to engage in a sport in order to calculate the likelihood that a student chosen at random will be doing homework or playing a sport after school.

Therefore, the likelihood that a pupil chosen at random will be working on homework or playing an activity after school is:

24% + 28% = 52%

This is because the two events are not mutually exclusive, and a student may plan to do both activities after school.

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The length of the shorter pipe will be 1.065 meters.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a plumber had two pipes. The ratio of the length of the longer pipe to the shorter pipe was 9:2.

When he cut 1.65m from the longer pipe, the remaining length was 3 times that of the shorter pipe.

L / S = 9 / 2

L - 1.65 = 3S

4.5S - 1.65 = 3S

1.5S = 1.65

S = 1.065 meters

Hence, the measure of the short pipe will be 1.065 meters.

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The measure of ZPQR is approximately 113°. This can be solved usiing the concept of geometry.

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects. A geometer is a mathematician who specializes in geometry.

Therefore, to find the measure of ZPQR, we would follow the following steps:

Let x= measure of <PQR

Hence, the measure of <PQR

296 = x/360 x 3.14 x 2 x 150

Hence, x = 113.12 °

Approximately, the measure of ZPQR is 113 °

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As a result, the answers to the above quadrilateral issue are A.5, B.2, 3, C.-1/5, and D.2/3.

In terms of the geometry, a quadrilateral is really a four-sided polygon with four corners and four corners. Its origins originate from the Latin terms tetra and latus (meaning "side"). A rectangle is a this double form with four sides, 4 vertices, with four corners. Two main types of convex and convex exist. Convex bedbugs or bed bug also have a number of subclasses, such as trapezoids, parallelograms, quarters, rhombuses, and squares. Corresponding points come in many irregular configurations, such as quadrilaterals, trapezoids, rectangles, kites, square, and rhombuses.

given

The vertices of the quadrilateral ABCD are A(-4, -5), B(-3, 0), C(0, 2), and D. (5, 1).

We need to determine whether ABCD is a trapezoidal shape or not.

We are known that a trapezoid has one set of parallel opposed sides, making it a quadrilateral. Moreover, the slopes of two parallel lines are equal.

To start, the slopes of sides AB, BC, CD, and DA will be calculated.

It has

The incline for

AB =0+5/ -3+4

5. In the first step.

Step 2: The slope in BC is

=> 2-0 / 0+3

=> 2/3.

Step 3: The CD's gradient is

1-2/5-0 is equivalent to -1/5.

The gradient of DA is equal to in step four.

=>-5.1/-4.4/2.3

=>2/3.

As a result, the answers to the above quadrilateral issue are A.5, B.2, 3, C.-1/5, and D.2/3.

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The correct measure of variation for best to describe this distribution is,

⇒ interquartile range

Option B is true.

For a data set has outliers and variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.

Given that;

The dot plot shows the ages of the 20 people currently in Ms. Jens classroom.

Hence, To describe this distribution we can use the interquartile range.

Thus, The correct measure of variation for best to describe this distribution is,

⇒ interquartile range

Option B is true.

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Answer:

it takes 0.30769 days or 7.3846 hours for the light bulb to consume 5850 watt-hours.

Step-by-step explanation:

To solve for the time, we can set up a proportion:

1800 watt-hours / day = X / 5850 watt-hours

Cross-multiplying, we get:

1800 watt-hours * 1 day = X * 5850 watt-hours

Simplifying, we get:

X = (1800 watt-hours * 1 day) / 5850 watt-hours

X = 0.30769 days

To convert to hours, we can multiply by 24:

X = 0.30769 days * 24 hours/day

X = 7.3846 hours

Therefore, it takes 0.30769 days or 7.3846 hours for the light bulb to consume 5850 watt-hours.

The equation for w(width of rectangle) is: W = (P - 2L)/2

The correct answer is an option (c)

We know that the formula for the perimeter of the rectangle is:

P = 2L + 2W

where P is the perimeter of the rectangle,

L is the length of the rectangle,

and W is the width of the rectangle.

We need to rearrange this equation for w.

Consider equation,

P = 2L + 2W

P - 2L = 2L + 2W - 2L      ......(subtract 2L from each side of equation)

P - 2L = 2W

(P - 2L)/2 = 2W/2             .....(divide each side by 2)

W = (P - 2L)/2

Therefore, the correct answer is  W equals the quantity P minus 2 times L all over 2

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The complete question is:

Makayla is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her rectangle but wants to solve for the width. Rearrange the following equation for W, where P is the perimeter, L is the length, and W is the width of the rectangle. P = 2L + 2W.

a) W = 2P − 2L

b) W = P/ 2-2 times L

c) W equals the quantity P minus 2 times L all over 2

d) W = 2P + 2L

Answer:

c) W equals the quantity P minus 2 times L all over 2

Step-by-step explanation:i just took the test

In the polynomial f(x) = 3x² - 2x + 5, f(0) is solved to get -2

From the equation of the tangent line

m= -2

b = 5

The derivative of the polynomial f(x) = 3x² - 2x + 5 is solved to be

f'(x) = 2(3)x - 1(2)

f'(x) = 6x - 2

f(0) = -2

Equation of the tangent to the parabola f(x) = 3x² - 2x + 5

f'(x) = 6x - 2 at x = 0, f'(x) = -2 hence the slope, m is -2

Using the point slope formula for (0, 5)

(y - 5) = m (x - 0)

y - 5 = -2x - 0

y = -2x + 5

comparing with y = mx + b

m = -2 and b = 5

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