Which of the following is an example of an exponential function?
A. f(x) = 2x + 1
C. f(x) =
2x2-1
B. f(x) = 2x2 - 1
D. f(x) = 2× ​

The equation for  regression line is ŷ = -0.0192X + 39.288,

The  correlation coefficient is  -0.9817,

The population of Detroit in 2008 is 0.73 millions.

A line that, using the bivariate data gathered, summarises the linear relationship (or linear trend) between the two variables in a linear regression study.

An estimate of the line that depicts the actual, but the unidentified, linear relationship between the two variables is called a regression line. When the value of the explanatory variable is known, the regression line's equation is used to predict (or estimate) the value of the response variable.

Given table showing the population of Detroit each decade.

year                                1960   1970   1980   1990    2000

Population (millions)      1.67     1.51     1.20     1.03       0.95

A. equation for regression line,

X - Mx     Y - My     (X - Mx)²   (X - Mx)²       (X - Mx)(Y - My)

-20          -20               400          0.158              -7.96

-10           -10               100          0.057              -2.38

0              0               0          0.005                   0

10      10               100          0.059               -2.42

20     20               400           0.104               -6.44

                             Sum: 1000.00   Sum: 0.382 Sum: -19.200

Sum of X = 9900

Sum of Y = 6.36 millions

Mean X = 1980

Mean Y = 1.272

Sum of squares (SSX) = 1000

Sum of products (SP) = -19.2

Regression Equation = ŷ = bX + a

b = SP/SSX = -19.2/1000 = -0.0192

a = MY - bMX = 1.27 - (-0.02*1980) = 39.288

ŷ = -0.0192X + 39.288

B. correlation coefficient,

X Values

∑ = 9900

Mean = 1980

∑(X - Mx)² = SSx = 1000

Y Values

∑ = 6.36

Mean = 1.272

∑(Y - My)² = SSy = 0.382

X and Y Combined

N = 5

∑(X - Mx)(Y - My) = -19.2

r Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -19.2 /√((1000)(0.382)) = -0.9817

Meta Numerics

r = -0.9817

The value of R is -0.9817.

High X variable scores correlate negatively with low Y variable scores because of this strong negative connection (and vice versa).

C. population in 2008

y  = -0.0192X + 39.288  

substitute x = 2008

y = -0.0192(2008) + 39.288

y = 0.7344

population in 2008 is  0.73 millons.

Hence the equation is ŷ = -0.0192X + 39.288,

the correlation coefficient is r = -0.9817

and population of Detroit in 2008 is  0.73 millions.

Learn more about regression line;

https://brainly.com/question/7656407

#SPJ1

Answer:

6y - 14

Step-by-step explanation:

simplify the expression

2y - 6 + 4 (y -2)

Distribute the 4 to each term in the parentheses.

2y - 6 + 4y -8

Combine like terms

2y+4y-6-8

6y - 14

Answer:

[tex] \sf \: 6y - 14 [/tex]

Step-by-step explanation:

Given expression,

→ 2y - 6 + 4(y - 2)

Let's simplify the expression,

→ 2y - 6 + 4(y - 2)

→ 2y - 6 + 4(y) - 4(2)

→ 2y - 6 + 4y - 8

→ (2y + 4y) + (-6 - 8)

→ (6y) + (-14)

→ 6y - 14

Hence, the answer is 6y - 14.

Answer:

70⁰ is the correct answer.

Answer:

i have no clue big dawg you gonna have to cheat somewhere else

These identities are not true and cannot be derived from the first identity.

What is trignomentry ?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of angles and circles, and to solve problems involving geometric shapes and measurements. Trigonometry is used in many fields such as physics, engineering, and navigation.

The statement "sin 0 + cos 0 = 1" is a correct foundational trigonometric identity. However, it is not possible to derive the identities "1+cot^2(0) = csc^2(0)" or "tan^2(0)+1 = sec^2(0)" by dividing through by cot^2(0) or by tan^2(0) respectively. These identities are not true, and are not a direct consequence of the first identity.

These identities are not true and cannot be derived from the first identity.

To learn more about trignomentry visit : brainly.com/question/29002217

#SPJ4

The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides. Since the perimeter is a linear measure, therefore, the unit of the perimeter of rectangle will be in meters, centimeters, inches, feet, etc.

Perimeter of rectangle = 42 cm.

2 × (l + b) = 42

l + b = 21

So l + b = 2 + 19 ; 3+ 18; 4+17; 5+16; 6+ 15 ; 7+14 ; 8+13 ; 9+12; 10 +11:

Area for l × b =  2× 19= 38 sq.cm

Area for second case = 3* 18=54sq.cm

Area for third case = 4* 17=68sq.cm

Area for fourth case = 5* 16=80sq.cm

Area for fifth case = 6* 15=90sq.cm

Area for sixth case =7* 14=98sq.cm

Area for seventh case =8* 13=104sq.cm

Area for eighth case =9* 12=108sq.cm

Area for ninth case =10* 11=110sq.cm

To know more about area of rectangle  visit brainly.com/question/20693059

#SPJ4

On solving the provided question we can say that in this triangle 6 blocks separate the bus stop from his house.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon.

The graph of the provided data is included below. 10 blocks separate his residence from the park.

His friend's home is 15 blocks away from his home. 9 blocks separate the grocery shop from his home.

The sides are in proportions according to Side-Angle-Side Similarity. Consequently, we calculate a ratio using the corresponding triangles.

= distance from home to friend's home / distance from home to park

= distance from home to grocery / distance from to bus stop

= 15/10 = 9/x

x = 6

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ4

Answer:

His friend's house, grocery store, and his home

Step-by-step explanation:

Had this question on a test and got it right.

Answer:

Step-by-step explanation:

A polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 1, 3 is (x- -2)(x-1)(x-3) = x^3 - 6x^2 + 11x - 6

Answer:

Step-by-step explanation:

Answer:

5x = y

10x= 5y

20x= 15y

50x= 45y

A function f for f'(0) = 3 it means that the slope of the line tangent to the point x = 0 is 3.

An easy definition of a function?

As a set of inputs with one output for each, a function is defined as a relationship between them.

              A function, expressed simply, is an association between inputs where each input is connected to one and only one output.

when it says something like f(1) = 0 it means that when x = 1, y = 0

so we know one point on the graph is (0,0)

when it says something like f'(0) = 3 it means that the slope of the line tangent to the point x = 0 is 3

here is a picture of the tangent lines, then what a sketch of the function would be.

Learn more about function

brainly.com/question/12431044

#SPJ4

Answer: [tex]y-1=\frac{1}{4}(x-5)[/tex]

Step-by-step explanation:

The median from vertex [tex]A[/tex] passes through [tex]A[/tex] and the midpoint of [tex]\overline{BC}[/tex].

Using the midpoint formula, the midpoint of [tex]\overline{BC}[/tex] has coordinates [tex]\left(\frac{3+7}{2}, \frac{5-3}{2} \right)=(5, 1)[/tex].

Therefore, we need the equation of the line passing through [tex](-3,-1)[/tex] and [tex](5,1)[/tex].

The slope of this line is [tex]\frac{-1-1}{-3-5}=\frac{1}{4}[/tex].

Using point-slope form, the equation is y[tex]y-1=\frac{1}{4}(x-5)[/tex].

The value of x is x = 25 and the measure of angle ∠2 = 60°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the transversal line be represented as t

Now , the measure of angles on a straight line = 180°

So , the measure of angle 1 + angle 2 = 180°

The measure of angle 1 = 5x - 5

The measure of angle 2 = 2x + 10

Substituting the values in the equation , we get

5x - 5 + 2x + 10 = 180°

7x + 5 = 180

Subtracting 5 on both sides of the equation , we get

7x = 175

Divide by 7 on both sides of the equation , we get

x = 25

Substitute the value of x in measure of angle 2 , we get

The measure of angle 2 = 2x + 10

The measure of angle 2 = 2 ( 25 ) + 10

The measure of angle 2 = 50 + 10

The measure of angle 2 = 60°

Hence , the measure of angle 2 is 60°

To learn more about parallel lines cut by transversal click :

https://brainly.com/question/28182928

#SPJ1

The smallest possible sum of the two perfect squares is 205.

Now, According to the question:

The data is given as:

The difference between two perfect squares is 133.

Let the 'x' and 'y' be the difference between two perfect squares.

Now,

The difference between two perfect squares is 133.

[tex]x^{2} -y^2=133[/tex]

[tex]-y^2=-x^2+133[/tex]

[tex]y^2=x^{2} -133[/tex]

[tex]y = \sqrt{x^2-133}[/tex]

First integer solution to this equation

x=13, y=6

Sum = [tex]13^2 + 6^2 = 205[/tex]

Hence, The smallest possible sum of the two perfect squares is 205

Learn more about Squares at:

https://brainly.com/question/14198272

#SPJ4

Ratio grade 7 is a mathematical concept that involves comparing two or more quantities using a ratio. It is a common part of mathematics curriculums for middle and high school students.

1. A ratio is a comparison of two or more numbers.

2. Ratios can be expressed as a fraction, a decimal, or a percentage.

3. Ratios are used to compare quantities of different kinds and are used to find relationships between them.

4. In grade 7, students will learn about ratios and how to use them to solve various problems. They will also learn about proportionality, rates, and unit rates.

5. Ratios can also be used to compare measurements, such as lengths, weights, and areas.

6. Students will also use ratios to calculate proportions, which can be used to solve problems involving proportional relationships.

Learn more about ratio here

https://brainly.com/question/13419413

#SPJ4

The amount the  family spend on items other than food and housing is PhP25000 over the time.

You should understand that budget involves the summary of income and expenditure of a person or individual over a period of time

If total expense is $50,000 and the spend 20% on food 30% on housing

Which make is 50% on both hosing and food leaving 50% on other expenses

Which makes half of the total budget

You have to work out 50% of 50000 to get

50/100* $50000 =PhP25000

This therefore means that the family spends PhP25,000 on items other than food and housing

Study more about percentage of spending on https://brainly.com/question/28627592

#SPJ1

Complete question

The circle graph represents a family's monthly budget. If the total monthly budget is $50,000,

how much does the family spend on items other than food and housing?

According to algebra, the square binomial (6 · x + 5 · y)² has the following equivalent expression: 36 · x² + 60 · x · y + 25 · y².

According to algebra, we find the case a square binomial, whose equivalent form is shown below by following rule:

(a + b)² = a² + 2 · a · b + b²

Where a, b are real coefficients.

If we know that a = 6 · x and b = 5 · y, then the equivalent form of the square binomial is:

First, write the entire expression:

(6 · x + 5 · y)²

Second, use power properties:

(6 · x)² + 2 · (6 · x) · (5 · y) + (5 · y)²

Third, perform associative and commutative properties:

6² · x² + (2 · 6 · 5) · (x · y) + 5² · y²

Fourth, multiply similar terms:

36 · x² + 60 · x · y + 25 · y²

To learn more on square binomials: https://brainly.com/question/29142274

#SPJ1

By applying the first derivative of distance with respect to time, it can be concluded that the person is walking 4/3 meters per second.

Instantaneous velocity or rate is the first derivative of distance with respect to time. Mathematically it is written v = ds/dt, where v is the velocity, s is the distance and t is the time.

First, we make a simple drawing using the given information:

The walking person = 2 meters tall

The street light = 8 meters above the ground

The walking rate is constant

The person's shadow lengthening rate = 4/9 meter per second = dy/dt

We want to know the walking rate, dx/dt.

We determine the value of y:

8 / 2 = (x + y) / y

  8y = 2x + 2y

  6y = 2x

    y = x / 3

Then we substitute the value of y into the equation:

dy/dx = d(x/3) / dx

         = 1/3

Finally, we can get the rate dx/dt:

dx/dt = dy/dt * dx/dy

         = 4/9 * 3

         = 4/3

Thus, it can be concluded that the person is walking 4/3 meters per second.

To learn more about Instantaneous Velocity, click here: https://brainly.com/question/10518017

#SPJ4

the height of six glasses (24 / 6 = 4). Finally, we can multiply this by six to get the final answer, which is 30 cm.

30 cm

For two glasses, the height is 18 cm.

For eight glasses, the height is 42 cm.

Therefore, for six glasses, the height would be (42 - 18) / (8 - 2) * 6 = 30 cm.

To answer the question, we need to first determine the height of two glasses, which is 18 cm. Next, we need to find the height of eight glasses, which is 42 cm. Once we have these two values, we can calculate the height of six glasses. We can do this by finding the difference between the two heights (42 - 18 = 24), which will give us the height of six glasses (24 / 6 = 4). Finally, we can multiply this by six to get the final answer, which is 30 cm.

Learn more about height here

https://brainly.com/question/10726356

#SPJ4

The probability for an aircraft to experience crosswinds upon takeoff or landing is generally greatest during the months of spring and fall, specifically in March, April, September and October.

During these months, the transition from winter to summer or summer to winter can lead to greater temperature and pressure differences between the air masses, which can create stronger winds. Additionally, these seasons are also associated with increased storm activity, which can also lead to stronger winds.

However, the probability of experiencing crosswinds upon takeoff or landing can also be affected by regional weather patterns and location, and it's always best to consult with local weather forecast and airport meteorological services before planning any flight.

To know more on crosswinds

https://brainly.com/question/2043739

#SPJ4

Answer:

23.8

Step-by-step explanation:

Solve for the missing side, x, by using the pythagorean theorem:

5² + 3² = x²        **(8-5=3)

x² = 25+9 = 34

x = √34 = 5.831

P = sum of all sides = 5 + 5 + 8 + 5.831 = 23.8

Answer:

(x-1)^3.

Step-by-step explanation:

To find the least common multiple (LCM) of two polynomials, you can factor them and take the highest exponent of each variable that appears. In this case, the LCM is (x-1)^3 because it has the highest exponent of x that appears in both polynomials. It also contains all the other terms of both polynomials.

If vec SD, vec SE, and vec SG and if m angle DSE = 5x – 4, m angle E5G = 3x + 4, and m angle DSG = 72, m angle DSE = 90.

Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

An angle is a figure created by two rays or lines that have the same termination in plane geometry. The Latin word "angulus," which meaning "corner," is where the term "angle" originates. The common terminal of the two rays—known as the vertex—is referred to as an angle's sides.

To learn more about angle refer to :

https://brainly.com/question/25716982

#SPJ1

All of the conditions for inference are met, so it is appropriate to construct a 99% confidence interval for the true proportion of all magazine subscribers who do not read the magazine they subscribe to.

Random sample: The sample of 100 magazine subscribers was selected randomly, so this condition is met.

10% condition: The sample size is 100, which is less than 10% of the population of all magazine subscribers, so this condition is met.

Large counts condition: To check the large counts condition, we need to calculate the expected number of subscribers who do not read the magazine they subscribe to, which is n × p = 100 × 0.38 = 38. Since this number is greater than 5, the large counts condition is met.

To know more on confidence interval

https://brainly.com/question/29680703

#SPJ4

Answer:

Random condition:

✔ met

10% condition:

✔ met

Large counts condition:

✔ met

Are the conditions for inference met?

✔ yes

An absolute value is defined as , | y | = | − y | for all y , we can thus say that their absolute value is even.

The definition of h in the equation is given as given next ,  | f (x) | = h (x).  The logic when checking for an equation to be even or odd is defined as , if  g (x) is an even function whereas f (x) is an odd function , then the value of g (f (x)) is even and f (g (x)) will also be even.

A function is known as an odd function is that ,

f(x) = f(−x) for all the value of x

A function is known as an even function is that ,

f(x) = f(−x) for all x

To learn more about even functions

brainly.com/question/11268126

#SPJ4

The lengths of q and r are 2.5 , 2.5 respectively if the perimeter of an isosceles triangle pqr is 9 cm.

A triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.

here, Given that,

The perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm.

the length of side p is 4 cm

Let the lengths of q and r are x and y respectively.

The perimeter of an isosceles triangle  =  (p+2q)

So,

p+2q = 9

4+2q = 9

2q = 9-4

2q = 5

q = 5/2

q = 2.5 cm

Hence , the lengths of q and r are 2.5 , 2.5 cm respectively .

To learn more about triangle from the given link.

brainly.com/question/2773823

#SPJ1

Answer: 14.7

Step-by-step explanation:

The remaining interior angle is [tex]135^{\circ}[/tex].

[tex]\frac{x}{\sin 19^{\circ}}=\frac{32}{\sin 135^{\circ}}\\ \\ x=\frac{32 \sin 19^{\circ}}{\sin 135^{\circ}} \\ \\ x \approx 14.7[/tex]

The possible percentage of the marks the students will have is (D) 83%.

A percentage, often known as percent, is a division by 100.

Percentage, which means "per 100," designates a portion of a total sum.

45 out of 100 is represented by 45%, for instance.

Finding the percentage of a whole in terms of 100 is what percentage calculation is.

Both manual calculation and the use of internet calculators are options.

So, we know that:

When we find the percentage, after division, we multiply the answer by 100 to get the answer in percentage.

Similarly,

0.83 * 100 = 83%

Therefore, the possible percentage of the marks the students will have is (D) 83%.

Know more about percentages here:

https://brainly.com/question/9553743

#SPJ4

Complete question:
A student added all her grades together and then divided by the total points possible to figure out her grade, as her instructor had said to do, and the result was 0.83. What percent of the possible points does she have?

a) 8.3%

b) 0.83%

c) Can't tell, but she has 83 total points.

d) 83%

The formula for work is force multiplied by displacement.

Work done refers to the amount of energy used by a force to move an object. It is also a physical quantity. Its SI unit is Joule. Every time a force is applied to an object and it moves from one location to another, work has been done. The displacement is what needs to be taken into account and not the distance. Displacement is the smallest distance or straight line that connects the object's initial and final positions. Work is therefore equivalent to force times its displacement. Force is measured in newtons, and the displacement is measured in meters. Therefore, if a force of 1N is used to move a body by a displacement of 1m, then 1J of work has been completed.

                                        [tex]W=F.S[/tex]

                                         [tex]1J=1m.1N[/tex]

Learn more about displacement here:

https://brainly.com/question/29545897

#SPJ4

Answer:

(6-squarre root 8)^2 = 10.058874