calculate the length of a scarf with sections if each section is 1/2 foot long

Answer:

y = 3x + 12

Step-by-step explanation:

y = mx + b  
The m is the slope and the b is the y intercept.

Slope:

Change in y over the change in x.  The ordered pair is written in the form (x,y)

[tex]\frac{12-3}{8-5}[/tex] = [tex]\frac{9}{3}[/tex] = 3

The slope is 3.

Use the slope of the 3 and the x and y from one of the ordered pairs given.  I am going to use the point (5,3), but either point will work

slope 3

x = 5

y=3  Plug these all in and solve for b

y = mx + b

3 = (3)5 + b

3 = 15 + b  Subtract 15 from both sides

-12 = b

This is the y intercept

y = 3x - 12

Answer:

Slope-intercept form,

→ y = 3x - 12

Step-by-step explanation:

Formula we use,

→ y = mx + b

The value of slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (12 - 3)/(8 - 5)

→ m = 9/3

→ [ m = 3 ]

Then the value of b will be,

→ y = mx + b

→ 12 = (3)8 + b

→ b + 24 = 12

→ b = 12 - 24

→ [ b = -12 ]

Now the slope-intercept form is,

→ y = mx + b

→ [ y = 3x - 12 ]

Hence, the answer is y = 3x - 12.

to be honest ion even know

Answer: 200 Meters

Step-by-step explanation:

a ) The required measure of x = 90°

b ) The height of the right angled triangle = = [tex]\sqrt{244}[/tex]

Given is a triangle with measure 15, 20 and 25

a ) Since a perpendicular is dropped from above

the two angles of x are equal because the angle is bisected by an angle bisector

So to check whether the angle x is a right angled or not

we can use the pythagoras theorem and check if the LHS = RHS or not

LHS = 15² + 20² = 225 + 400 = 625

and RHS = 25² = 625

Since LHS = RHS thus the angle is 90 degrees

b ) The height of the right triangle ;

by using the Pythagoras theorem again

12.5² + h² = 20²  { side 25 is bisected = 12.5 }

h² = 400 - 156.25

h = [tex]\sqrt{244}[/tex]

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Yes, I agree with Jorge.

Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.

Jorge could improve his proof by stating his explanation in terms of mathematics.

He could have used the SAS similarity to show that the given triangles are similar.

What is the similarity test of two triangles?

If the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal, the two triangles are similar.

In the given figures,  the length of side AB is equal to the length of side DE.

                        Side AB = Side DE ----------(I)

Similarly, the length of side BC is equal to the length of side EF.

                        Side BC = Side EF ----------(II)

And the measure of angle  ABC is equal to the measure of angle DEF.

                              ∠ ABC = ∠ DEF -------(III)

From (I), (II), and (III), and by using the SAS test we can say that

                               ΔABC ~ ΔDEF    ----------- SAS test

Hence,

Yes, I agree with Jorge.

Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.

Jorge could improve his proof by stating his explanation in terms of mathematics.

He could have used the SAS similarity to show that the given triangles are similar.

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Since the researcher randomly selected 100 people who exercise regularly and 100 people who do not exercise regularly, and compared how many hours they sleep at night, on average: C. the study is an observational study.

An observational study can be defined as a type of scientific study in which a researcher observes and measures the effect of a diagnostic test, risk factors, and specific treatments on individuals without intervening, manipulating, altering, or changing those who are or aren't exposed to it (controlled conditions).

In Science, a controlled variable must always be held constant and unchanged in an experiment in order to prevent it from affecting or influencing the result, which is not applicable to this research.

In conclusion, we can logically deduce that this research is an observational study because people (participants) were chosen through an appropriate process, however, no attempt was made to control any aspect of the people (participants), even though the variable of interest (exercise) was recorded for one of the group.

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Answer:4/5 : 1/3=4/5 x 3/1=12/5

Step-by-step explanation:

Answer:

12/5

Step-by-step explanation:

If you set it in the calculator 4/5 ÷ 1/3 you get = 12/5

was it helpful?

Answer:

x = 2

Step-by-step explanation:

For the function g(x) to have to equal only 2, that would have to be for the input, x, to be 2 itself considering there's no equation given.

Hope this helps!

Step-by-step explanation:

this creates a right-angled triangle, with the length of the slide being the Hypotenuse (the side opposite of the 90° angle), and height and base are the legs.

so, we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse, a and b being the legs.

length² = 9² + 12² = 81 + 144 = 225

length = sqrt(225) = 15 ft

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex] \textsf{1. Numbers are : 36, 3, 12 } [/tex]

[tex] \textsf{HCF = product of total common factors of} [/tex][tex] \textsf{all three numbers, i.e : 2 } [/tex]

[tex] \textsf{LCM = product of highest power of each factor } [/tex][tex] \textsf{present in any three of them,} [/tex][tex] \textsf{i.e : 2⁵ × 3 = 32 × 3 = 96} [/tex]

Similarly,

[tex] \textsf{2. Numbers are : 6, 54, 12} [/tex]

[tex] \textsf{GCD = 2 × 3 = 6 } [/tex]

[tex] \textsf{[ 2 and 3 are the only ones common} [/tex] [tex] \textsf{among all three ]} [/tex]

[tex] \textsf{LCM = 2² × 3³ = 4 × 27 = 108} [/tex]

[tex] \textsf{3. Numbers are : 16, 8, 12 } [/tex]

[tex] \textsf{GCD = 2 × 2 = 4 } [/tex]

[tex] \textsf{LCM = 2⁴ × 3 = 16 × 3 = 48} [/tex]

Answer:

Numbers are : 36, 3, 12

36 = 2 × 2 × 2 × 2 × 2 × 1

3 = 3 × 1

12 = 2 × 2 × 3

HCF = product of total common factors of all three numbers, i.e : 2

LCM = product of highest power of each factor present in any three of them, i.e : 2⁵ × 3 = 32 × 3 = 96

Similarly,

2. Numbers are : 6, 54, 12

6 = 2 × 3

54 = 2 × 3 × 3 × 3

12 = 2 × 2 × 3

GCD = 2 × 3 = 6

[ 2 and 3 are the only ones common among all three ]

LCM = 2² × 3³ = 4 × 27 = 108

3. Numbers are : 16, 8, 12

16 = 2 × 2 × 2 × 2

8 = 2 × 2 × 2

12 = 2 × 2 × 3

GCD = 2 × 2 = 4

LCM = 2⁴ × 3 = 16 × 3 = 48

A number line which shows -3, 1/2, 3/4, and 1 correctly plotted on a graph is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical value -3 would be plotted on the left hand side of zero (0) while the numerical values 1/2, 3/4, and 1 would be plotted on the right hand side of zero (0) using a number line.

In conclusion, a number line has been used for the comparison of the given numerical values, and they are plotted on the number line shown in the image attached below.

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The function is positive and increasing from 0 to 2.5, at negative and decreasing  from 0 to -2.5,  respectively.

How to find returns to scale?

Returns to scale involves an increase in an output more than when all the inputs increase proportionately.

Using the graph, there is a line segment from the origin to a point. at the middle of the third block making 2.5.  this shows an increase which is positive and on the other hand, there is a line segment from the origin towards left hand side on the number line showing a decrease and a negative from 0 to -2.5.

In conclusion, the line pointing upwards towards right hand side shows both positive and increase while the line pointing leftward shows decrease and negative.

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The mapping of the function f of g(x) will result to 41

A function in mathematics is a rule that defines a relationship between one variable. This is a mapping whose codomain is the set of real numbers.

By mapping of the functions f and g defined as;

f : x » x + 5 and g : x » 8x

then;

f of g(x) = f of 8(4.5)

f of g(x) = f of 36

f of g(x) = 36 + 5

f of g(x) = 41

Hence, with proper mapping of the defined functions of f and g, the correct value for f of g(x) is 41.

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Answer:

The cat is at at  8 north 6 west

Step-by-step explanation:

The cat ran a total of 14 meters

Answer:

12.85

Step-by-step explanation:

hope it helps, pls lmk if it is wrong in comments!

Answer:

12.85

Step-by-step explanation:

64.25÷5

Answer: hours

Step-by-step explanation:

minutes would be way too many

seconds - just self explanatory

days- would be less than one

hours is the only possible solution

The 98% confidence interval limits are given by 1.6 < μ < 33.7.

What is the confidence interval in statistics?

A confidence interval is the mean of your estimate plus and minus its variation. Within a certain confidence level, this is the range of values you expect your estimate to fall between if you redo your test. In statistics, confidence is another word for probability.

Given data: 10, 32, 24, 0, 5, 27, 5, 50, 6.

Sample mean = ∑x/n = 159/9 = 17.66

Sample variance = s² = ∑(x - sample mean)²/n-1

                                   = 2206/8

                                   =  275.75

Sample standard deviation = s = [tex]\sqrt{s^2}[/tex]

                                                    = [tex]\sqrt{275.75}[/tex]

                                                    = 16.60

Significance level = α = 1 - 0.98 = 0.02

Degree of freedom (d.f.) = n - 1 = 9 - 1 = 8

Critical value = [tex]t_{{\frac{\alpha}{2}},d.f}[/tex]

                      = 2.896

Margin of error = E = critical value * [tex]\frac{s}{\sqrt{n} }[/tex]

                                = 16.03

Limits of 98% confidence level are given by:

Lower limit = sample mean - E = 17.66 - 16.03 ≈ 1.6

Upper limit = sample mean + E = 17.66 + 16.03 ≈ 33.7.

Hence, the 98% confidence interval limits are given by 1.6 < μ < 33.7.

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a. The expense function in terms of p is  - 280p + 34, 000

b.  At a price of $10.00, 7, 600 widgets are demanded

c.  It costs  $31, 200 to produce the number of widgets from part b

We have that;

To express the expense function in terms of p, we have to take the following steps;

Substitute the value of q in the demand function into the function for the expense, we get;

Expense function = 2( -140p + 9,000) + 16, 000

Now, expand the bracket, we get;

Expense function = - 280p + 18, 000 + 16, 000

collect and add like terms

Expense function = - 280p + 34, 000

If p = $10. 00

Then,

Demand function is q = -140(10) + 9,000

expand the bracket

q = - 1400 + 9, 000

q = 7, 600

Substitute q in expense function

E = 2.00q + 16,000

E = 2. 00(7600) + 16, 000

E = $31, 200

Hence, the expense function is - 280p + 34, 000

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By using normal distribution of probability, it can be inferred that

For [tex]x_1 = 325[/tex], z = -1.5

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex], z = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-

[tex]f(x) = \frac{1}{\sigma \sqrt{2\pi}}}e^{-\frac{z^2}{2}[/tex]

where  [tex]z = \frac{x - \mu}{\sigma}[/tex], [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

For [tex]x_1 = 325[/tex]

[tex]z = \frac{325 - 496}{114} = -1.5[/tex]

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex]

[tex]z = \frac{366.21 - 496}{114}[/tex] = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

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Answer:

6/7

Step-by-step explanation:

2÷3/7=2*3/7

6/7

Answer:

x is 70°

hopefully this will help u

Answer:  x + 8

Step-by-step explanation:

[tex]f(g(x))=f(\frac{1}{2}x+2) = 4+2(\frac{1}{2}x+2) = 4+x+4 =x +8[/tex]

The number of touchdowns is 4.

The number of extra-point kicks is 4.

and the number of field goals is 2.

What are linear equations in three variables?

If a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables.

How to solve the system of linear equations in three variables?

Select two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. then, solve the system of the two newly obtained equations using the Addition/Subtraction method.

Let the number of touchdowns be "x", the number of extra-point kicks be "y", and the number of field goals is "z".

Total points scored in game = 20+14 =34

Now,

According to the given question,

                                6x + y + 3z = 34 -----------(I)

                                x = y ----------(II)

                                x = 2z

                                z = [tex]\frac{x}{2}[/tex] -----------(III)

Putting the values of "y" and "z" in equation (I), we get

                              6x + x + 3×[tex]\frac{x}{2}[/tex] = 34

                               [tex]\frac{17x}{2}[/tex] = 34

                               x = 4

Now, putting the value of "x" in equations (II) and (III), we get

                               y = 4.

                               z = 2.

Hence, The number of touchdowns is 4. The number of extra-point kicks is 4, and the number of field goals is 2.

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The linear function for the situation is :-

Amount at the end of 3 years = Original investment + original investment*Rate*Time/100

It is given in the question that:-

Investment of George's friend in startup company = $ 500.

Interest percent = 8 %

Time period of investment = 3 years

We have to find the linear function for this situation.

As this interest is on original investment, the interest will be simple.

Hence,

The linear function for the situation will be :-

Amount at the end of 3 years= Original investment + original investment*Rate*Time/100

Amount at the end of 3 years = 500 +  500*8*3/100 = 500 + 120 = $ 620

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It will take 2.5 seconds for the water to hit the nozzle on the way down if the initial velocity is 40 feet per second. The maximum height of the water is 30 feet if the nozzle is 5 feet up.

a) Given equation

h(t) = v₀t - 16t^2

Substitute v₀ = 40, h(t) = 0 in the given equation

40t - 16t^2 = 0

Solve for t

⇒ 16t^2 = 40t

⇒ 16t = 40

⇒ t = 40/16

⇒ t = 2.5 seconds

Hence, water will take 2.5 seconds to hit the nozzle on the way down.

b) The function that represents the given condition

h(t) = -16t^2 + 40t + 5

The maximum value of the function is the y-coordinate of the vertex.

The x-coordinate of the vertex

= -40/2(-16) = 5/4

Find the y-coordinate of the vertex by substituting t = 5/4

⇒ h(5/4) = -16(5/4)^2 + 40(5/4) + 5

⇒ h(5/4) = -25 + 50 + 5

⇒ h(5/4) = 30

Hence, the maximum height of the water is 30 ft.

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The 10 forms 1/8 can be written is as follows;

A fraction refers to a number which consists of a numerator and a denominator.

A numerator is the upper value of a fraction.

A denominator is the lower value of a fraction.

1 over 8 can be written in the following ways;

1/8

1 ÷ 8

1/2³

= 1 / 2×2×2

= 1/8

1/√64

= 1/8

[tex]{8}^{ - 1} [/tex]

= 1/8

1 : 8

= 1/8

[tex]{√64}^{ - 1} [/tex]

= 1/√64

= 1/8

[tex]{2}^{ - 3} [/tex]

= 1/2³

= 1/8

2/16

= 1/8

4 : 32

= 4/32

= 1/8

In conclusion, 1/8 can be written in different forms including using square root and ratios.

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Answer:

Mr. Carson drove 39 more miles in April than in May

Step-by-step explanation:

1027-988=39

The rate of change of the linear functions given in tabular form and equations are found as follows;

1. a. The rate of change of the function is 5

b. The rate of change of the function is 7

c. The rate of then function is 0.75

d. The function has a rate of change of -8

2. The rate of change of the function of -4, indicates that each unit increase in the input value results in 4 unit decrease in the output values

b. The number of days it took for the patients blood sample to have 360 antibodies is 13 days

c. The rate of change of the function is 20, which indicates that the antibody in the patients blood is increasing at a rate of 20 antibodies each day

The rate of change of a function is a measure of how much the output changes per unit change in the input.

1. The rate of change of the functions are as follows;

a. The first difference of the y-values is constant, therefore the function is a linear function

The formula for the rate of change of the linear function is presented as follows;

[tex]m = \dfrac{y_2-y_1}{x_2 - x_1}[/tex]

The rate of change of the function is therefore;

b. The first difference is constant and equal to 7, the rate of change of the straight line function is therefore;

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{49-42}{1-0} = 7[/tex]

c. The function is a linear function, as the first difference is constant and equal to 0.75

The rate of change of the function is therefore;

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{2.25-1.5}{-4-(-5))} = 0.75[/tex]

d. The first difference is constant and equal to -8

The rate of change of the straight line function is therefore;

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{5 - 13}{1 - 0} = -8[/tex]

2. a. The rate of change of the function, y = -4·x + 1 is found by taking the slope of the function

The function is the equation of a straight line, of the form, y = m·x + c with the slope, m = -4

The rate of change of the function is -4, such that for each unit increase in the input value, the output value decreases by 4 units

b. When the number of antibodies is 360, we have;

360 = 20·d + 100

20·d = 360 - 100 = 260

d = 260 ÷ 20 = 13

c. The rate of change of the function means that the number of antibodies the drug produces in the patients body each day is 20 antibodies.

3. The function that gives the amount of antibodies in the body is a = 20·d + 100

d = The number of days

a = The number of antibodies

a. The table is completed as follows;

Data for Medicine A

d    [tex]{}[/tex]                  a

0    [tex]{}[/tex]                  100

1    [tex]{}[/tex]                   120

2    [tex]{}[/tex]                  140

3    [tex]{}[/tex]                  160

4    [tex]{}[/tex]                  180

5    [tex]{}[/tex]                  200

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Answer: a.) 397.5 b.) 1.3333

Step-by-step explanation:

1 cent = £0.75

530 x 0.75 = 397.5

530 / 397.5 = 1.3333

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