Which statement is true regarding the graphed functions?
141x
12-
10-
g(x)
8-
3)
6
fin
2+
7-6-5-4-3-2-12 1 2 3 4 5 6
-4
-6
-8+
ܘ
-10+
-12+
-14
f(x)
个x
X

The angle subtended at the centre of the circle by a 2.9 centimeter arc is  equal to 15° 38.46'/15° 38' 27.6''.

In this problem we have to determine the measure of a central angle of a circular section in DMS (Degrees - Minutes - Seconds) system, in which a degree is equal to 60 minutes and a minute to 60 seconds. First, we must calculate the radius of the circle by the area formula:

r = √ (A / π)     (1)

r = √ (354 / π)

r ≈ 10.615 cm

Then, the measure of the central angle in radians is found by the equation of circular arc:

θ = s/r

θ = 2.9 cm / 10.615 cm

θ = 0.273 radians

Finally, we convert the angle into DMS system:

θ = 0.273 rad × 180°/π

θ = 15.641°

Degrees: 15°

Minutes and seconds: 0.641° (38.46')

Minutes: 38'

Seconds: (0.46' = 27.6'')

The angle subtended at the centre of the circle by a 2.9 centimeter arc is  equal to 15° 38.46'/15° 38' 27.6''.

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Answer:369

Step-by-step explanation:

all you have to do is multiply 18 and 22 its easy

18 x 22 = 369.

Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.

Hence, option A is the correct answer.

This question is incomplete, the missing diagram is uploaded along this answer below.

Area of a rectangle is expressed as; A = l × b

Given that;

A = l × b

180in² = 20in × x

x = 180in² / 20in

x = 9in

Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.

Hence, option A is the correct answer.

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The Ratio would be 43:100.

Lets simplify the problem,

Expected increase of nurses = 711900

Expected increase of physicians = 168300

Ratio = Expected increase of nurses / Expected increase of physicians

Ratio = 711900 / 168300

= 43/100

Ratio = 43:100

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The area of the actual building lot is 5040 square ft

This factors are used to enlarge or diminish the given figure. Given the  scale model of a rectangular building lot measures 7 feet by 5 feet. If the actual house will be built using a scale factor of 12, the new length and width is expressed as:

Length = 12 * 7 = 84ft

Width = 5*12=60 ft

Determine the area

Area = 84 * 60

Area = 5040 square feet

Hence the area of the actual building lot is 5040 square ft

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Answer:

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m represents the slope and b represents the intercept.

x - 3y = 6

3y = x - 6

y = [tex]\frac{1}{3}[/tex]x - 2

4x - y = 1

y = 4x - 1

6x + 5y = -15

5y = -6x - 15

y = -[tex]\frac{6}{5}[/tex]x - 3

13x - 11y = -12

11y = 13x + 12

y = [tex]\frac{13}{11}[/tex] + [tex]\frac{12}{11}[/tex]

The value of a is 6 and the value of b is 7

The function is given as:

h(x) = a . sin(x - π/2) + b

From the table of values, we have:

x = π/2 when y = 7

So, we have:

a . sin(π/2 - π/2) + b = 7

Evaluate the difference

a . sin(0) + b = 7

Evaluate the value of sin(0)

a . 0 + b = 7

Evaluate the product of a and 0

b = 7

Substitute b = 7 in h(x) = a . sin(x - π/2) + b

h(x) = a . sin(x - π/2) + 7

From the table of values, we have:

x = π when y = 13

So, we have:

a . sin(π - π/2) + 7 = 13

Evaluate the difference

a . sin(π/2) + 7 = 13

Subtract 7 from both sides

a . sin(π/2)  = 6

Evaluate sin(π/2)

a . 1 = 6

Divide both sides by 1

a = 6

Hence, the value of a is 6 and the value of b is 7

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Using relations in a right triangle, it is found that the tree meets the wire at an angle of 56.4º.

The relations in a right triangle are given as follows:

In this problem, we have that:

Hence:

[tex]\sin{\alpha} = \frac{10}{12}[/tex]

[tex]\alpha = \sin^{-1}{\left(\frac{10}{12}\right)}[/tex]

[tex]\alpha = 56.4^\circ[/tex].

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Answer:

404 inches

Step-by-step explanation:

Since a room of 2cm is to be left of either side of the TV, thus, the permissible required length of the TV is 136-2 = 134cm

Use Pythagoras Theorem,

h² = 134² + 86² = 17956 + 7396 = 25352

h = √25352 = 159.22 ≈ 159cm = 404.41 inches ≈ 404 inches.

The length of the shortest side is DC

As a general rule in triangle;

The smallest angle in a triangle is opposite the shortest side.

Similarly, the largest angle in a triangle is opposite the largest side.

From the given figure of triangles, the smallest angle is angle CBD with a measure of 47 degrees.

The side opposite this angle is side length DC

Hence, the length of the shortest side is DC

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The perimeter of the contest area on the judo mat will be 32 meters.

For a square with a side length of a unit, we get:

Perimeter of the square = 4a unit

The side length of square is 8 m.

Then the perimeter of the contest area on the judo mat will be

P = 4 x 8

P = 32 m

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No digit with the format 90x0y07 is divisible by 2017

The given parameters are:

Dividend = 90x0y07

Divisor = 2017

The dividend is a 7-digit number, and the divisor is a 4-digit number

So, the quotient must be 3 to 4 digits.

Comparing the first and last digits of 90x0y07 and 2017;

The first and last digits of the quotient must be 4 and 1, respectively

So, we have:

90x0y07 = 2017 * 4a1

Assume a = 9.

So, we have:

90x0y07 = 2017 * 491

90x0y07 = 990347

The above is 6-digit.

So, we make use of a 4-digit quotient

This gives

90x0y07 = 2017 * 4ab1

Next, we make use of trial by error.

After several attempts, we conclude that no digit with the format 90x0y07 is divisible by 2017

The closest attempt is

90x0y07 = 2017 * 4471

90x0y07 = 9018007

Where:

x = 1, y = 0 and the digit between x and y is 8, not 0

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Answer:

y =x - 2

Step-by-step explanation:

If the slope of the line is  'm', then the slope of the perpendicular to the given line = [tex]\sf \dfrac{-1}{m}[/tex]     (opposite reciprocal)

    y = -x - 3

Compare with equation of line in slope y-intercept form: y = mx +b

 m = -1

[tex]\sf \text{Slope of the perpendicular line = $-(\dfrac{1}{-1})= 1$}[/tex]

This line passes through (2, 0);

Equation of the line in slope - point form:

        [tex]\sf y - y_1 = m(x - x_1)[/tex]

       y  - 0   = 1 (x - 2)

            y = x - 2

The sample size needed to obtain a margin of error of 0.05 for the estimation of a population proportion is 384.

Given margin of error of 0.05 and confidence interval of 95%.

We have to find the sample size needed to obtain a margin of error of 0.5 with confidence level of 95%.

Margin of error is the difference between real values and calculated values.

The formula of margin of error is as under:

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where

z is the critical value of z for given confidence level

n is sample size

σ is population standard deviation

We have not given population standard deviation so we will use the following formula:

Margin of error=z*[tex]\sqrt{p(1-p)}[/tex]/[tex]\sqrt{n}[/tex]

We have to find z value for 95% confidence level.

z value=1.96

We know that [tex]\sqrt{p(1-p)}[/tex]<=1/2

put [tex]\sqrt{p(1-p)}[/tex]=1/2

Margin of error=1.96*1/2/[tex]\sqrt{n}[/tex]

0.05=1.96*0.5/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=0.98/0.05

[tex]\sqrt{n}[/tex]=19.6

squaring both sides

n=384.16

After rounding off we will get

n=384.

Hence the sample size needed to obtain a margin of error of 0.05 is 384.

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The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.

The real rate of return exists at 2.926%.

The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.

The formula for the real rate of return:

R = (1+N)/(1+i) - 1

Where, N exists the nominal rate and i exists the inflation rate, as decimals.

A certificate of deposit offers a nominal interest rate of 5.5 percent annually.

This means that N = 0.055

Inflation exists 2.5 percent

i = 0.025

Substitute the values in the above equation, we get

[tex]$R = [(1+0.055)/(1+0.025)] -1[/tex]

= [1.055/1.025] - 1

= 1.02926 - 1

= 0.02926

0.02926 [tex]*[/tex] 100% = 2.926% ~ 3%

The real rate of return exists at 2.926%.

Therefore, the correct answer is option D. 3%.

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The number of half page advertisements that Michael purchased is 4 while the full page advertisements is 11.

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Let the number of half page ads be represented by h

Let the number of full page ads be represented by f.

Total number of advertisements = 15

h + f = 15 ....... (i)

h = 15 - f

Therefore, the system of equations to represent the situation will be:

60h + 100f = 1340 ........ (ii)

Put the value of h into equation (ii)

60(15 - f) + 100f = 1340

[tex]\Rightarrow[/tex]  900 - 60f + 100f = 1340

Collect like terms

    100f-60f  = 1340-900

[tex]\Rightarrow[/tex]              40f = 440

[tex]\Rightarrow[/tex]                   f = 11

The number of full-page advertisements that Michael purchased is 11.

Since h + f = 15

[tex]\Rightarrow[/tex]    h + 11 = 15

[tex]\Rightarrow[/tex]       h = 15 - 11

[tex]\Rightarrow[/tex]      h = 4

The number of half page advertisements that Michael purchased is 5.

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50^99 is greater than 99!

The numbers are given as:

99! and 50^99

When the above numbers are estimated using a calculator, we have:

99! = 9.332622e+155

50^99 = 1.577722e+168

Next, we compare the exponents

168 and 155

168 is greater than 155

Hence, 50^99 is greater than 99!

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The graph of the rational function is shown below

From the question, we are to graph the given rational function

To determine the graph that corresponds to the given rational function,

First, we will graph the given rational function.

The given rational function is

x²+3x-1/x+1

The graph of the rational function is shown below

Now, we will compare each of the rational graphs in the provided options with the attached graph

The graph that corresponds to the given rational graph in the attachment below is the graph that represents the given rational function.

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Answer:

y=

[tex] - \frac{x {}^{2} + 8x + 16 }{2} - 7[/tex]

Step-by-step explanation:

calculate the product, use (a+b)^2=a^2+2ab+b^2

The answer is D.

The formula to find area of a circle is : πr²

Here, we are given the diameter, but we need the radius. Always remember that the radius is always half the diameter.

Let's find the area.

Based on the given polynomial, the degree of the polynomial can be calculated to be 1.

the degree of the polynomial is defined as the highest exponential degree or power in a polynomial.

from the above, we see that the highest power is 1 from 8x¹.

the degree of the polynomial is therefore 1.

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Using the t-distribution, the upper bound of the 95 percent confidence interval for the gift baskets average shipping weight is of 69.06 ounces.

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

For this problem, the parameters are:

[tex]\voerline{x} = 66, t = 2.0154, s = 10.2, n = 45[/tex]

Hence the upper bound of the interval is:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 66 + 2.0154\frac{10.2}{\sqrt{45}} = 69.06[/tex]

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Stratified random sampling is used to subdivided into groups by volume of sales.

According to the statements

Manufacturers are subdivided into groups by volume of sales. and for this Stratified random sampling is used.

Stratified random sampling is the technique used divide the population can be partitioned into subpopulations.

Thus, Stratified random sampling is used to subdivided into groups by volume of sales.

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The approximate number of minutes that Avery spends on the extra curricular activities are 122 minutes.

Given that Avery spent 10 minutes outside, 64 minutes in riding her bike, 48 minutes on the trampoline.

We have to calculate the approximate time that Avery spends on extra curricular activities.

Time spent by Avery outside=10 minutes

Time spent by Avery in riding her bike=64 minutes

Time spent by Avery on trampoline=48 minutes

Total time spent by Avery on extra curricular activities is equal to 10+64+48

=122 minutes

Hence the total time spent by Avery on extra curricular activities is 122 minutes.

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Question is incomplete as the question should include that Avery spent 10 minutes outside,64 minutes in riding her bike, 48 minutes on trampoline and rest of the time in swimming.

Answer:

4ft^3

Step-by-step explanation:

1.333333*3*1^3=4

To start finding the volume of this sphere, we get the following data:

To find the volume we apply the following formula:

We substitute our data in the formula and solve:

Substituting values into the equation

Calculate exponent cubed

Multiplying

Therefore, the volume of the sphere is 32 ft³.

Using linear functions, the cost will be the same, of $70, when there are 5 students.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the functions are:

The costs are the same when:

45 + 5x = 35 + 7x

2x = 10

x = 5.

The cost is:

y = 45 + 5 x 5 = $70.

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Answer: All real numbers

Step-by-step explanation:

The domain is the set of inputs.

The correct statement about when a scatterplot is constructed is  the independent variable is the input variable and should be represented by the x-axis. Option A

From the given steps, we can see that when a scatter plot is constructed,  the independent variable is the input variable and should be represented by the x-axis.

Hence, the correct statement about when a scatterplot is constructed is  the independent variable is the input variable and should be represented by the x-axis. Option A

The complete question is;

Which statement is correct when a scatterplot is constructed? The independent variable is the input variable and should be represented by the x-axis.

The independent variable is the input variable and should be represented by the y-axis.

The dependent variable is the input variable and should be represented by the x-axis.

The dependent variable is the input variable and should be represented by the y-axis.

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Answer: A; The independent variable is the input variable and should be represented by the x-axis.

Step-by-step explanation:

I just know

The value of x is 4.

Given that diagonals of a rectangle measure x+5 feet and 2x+1 feet as shown in the attached figure.

The diagonal of a rectangle is a line or straight line that connects the opposite corners or vertices of the rectangle.

In the given figure ABCD is a rectangle.

OA=2x+1 and OD=x+5             [Given]

AC and BD are diagonals of a rectangle.

As we know that the diagonals of a rectangle are always equal.

So, AC = BD

We can also write it as,

2×OA=2×OD

2×(2x+1) =2×(x+5)

Apply the distributive property a(b+c)=ab+ac, we get

4x+2=2x+10

Subtract 2x from both sides, we get

4x+2-2x=2x+10-2x

2x+2=10

Subtract 2 from both sides, we get

2x+2-2=10-2

2x=8

Divide both sides by 2, we get

2x/x=8/2

x=4

Hence, the value of x=4 when diagonals of a rectangle measure x+5 feet and 2x+1 feet.

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The answers to the questions are:

1. x = 4

2.  x = 1.5

3. x = 1.875

4. x = 1

1. 4x + 3 = 19

4x = 19 - 3

4x = 16

divide by 4

x = 4

(4/3)x + 5 = 17

= 1.33x + 5 = 7

Take like terms

1.33x = 7-5

1.33x = 2

divide through by 1.33x to get 2

x = 2/1.33

x = 1.5

4x(6 - 2) - 10 = 20

Multiply and open the bracket

24x - 8x - 10 = 20

Take like terms

16x = 20+10

16x = 30

x = 30/16

= 1.875

4.3x + 0.7 = 5

4.3x = 5 - 0.7

4.3x = 4.3

x = 1

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