Write an equation of the line that passes through $\left(-1,\ 7\right)$ and is perpendicular to the line $y=-\frac{1}{8}x-1$ .

The exact value of the trigonometric relation sin(θ/2) is √[(1 + √(17)/5)) / 2]

Given data:

The trigonometric relation is :

sin(θ) = (2√2) / 5 and π/2 < θ< π

Using the half-angle identity for sine:

sin(θ/2) = ± √[(1 - cos(θ)) / 2]

To determine the sign, look at the quadrant in which theta lies. Since π/2 < θ< π, θis in the second quadrant, where the sine function is positive. Therefore, we take the positive sign.

Now, let's calculate the cosine of θ. Using the Pythagorean identity for sine and cosine, we have:

sin²(θ) + cos²(θ) = 1

(2√2/5)² + cos²(θ) = 1

8/25 + cos²(θ) = 1

cos²(θ) = 1 - 8/25

cos²(θ) = 17/25

Taking the square root:

cos(θ) = ± √(17)/5

Since theta is in the second quadrant, take the negative sign:

cos(θ) = -√(17)/5

Now, substituting the values into the half-angle identity, we get:

sin(θ/2) = ± √[(1 - cos(θ)) / 2]

sin(θ/2) = ± √[(1 - (-√(17)/5))) / 2]

sin(θ/2) = ± √[(1 + √(17)/5)) / 2]

Since θ is in the second quadrant, where the sine function is positive, take the positive sign:

sin(θ/2) = √[(1 + √(17)/5)) / 2]

Therefore, the exact value of sin(θ/2) is √[(1 + √(17)/5)) / 2].

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Explanation:

You could use the AC method to factor this, but the quadratic formula is the most efficient route in my opinion. This will avoid any guess-and-check.

Compare the original equation to the form [tex]a\text{x}^2 + b\text{x} + c = 0[/tex]

We have a = 9, b = 6, and c = -8

Those values lead to...

[tex]\text{x} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{x} = \frac{-6\pm\sqrt{(6)^2-4(9)(-8)}}{2(9)}\\\\\text{x} = \frac{-6\pm\sqrt{324}}{18}\\\\\text{x} = \frac{-6\pm18}{18}\\\\\text{x} = \frac{-6+18}{18} \ \text{ or } \ \text{x} = \frac{-6-18}{18}\\\\\text{x} = \frac{12}{18} \ \text{ or } \ \text{x} = \frac{-24}{18}\\\\\boldsymbol{\text{x} = \frac{2}{3} \ \text{ or } \ \text{x} = -\frac{4}{3}}\\\\[/tex]

Side notes:

Using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.

According to the question,

The average household income for a recent year (x₁⁻) = $30,000

The average household income for a recent year (x₂⁻) = $24,500

sample sizes n₁ = n₂ = 34

standard deviation of both samples were $24,500. Thus, s₁ = s₂ = $5928.

Null hypothesis:  There is no evidence to believe that the average household income has increased.

H₀ : μ₁ ≤ μ₂

Alternative hypothesis:  There is evidence to believe that the average household income has increased.

H₁: μ₁ > μ₂  

To check hypothesis we have the formula

Standard error=  [tex]\sqrt{\frac{s_{1} ^{2} }{n_{1} } + \frac{s^{2} _{2} }{n_{2} } }[/tex]

= [tex]\sqrt{2067128.4706}[/tex]

= 1437.7512

Thus, standard error is $1437.7512.

Formula for test statistic = [(x₁⁻ -  x₂⁻) - (μ₁ - μ₂)]/standard error

= [(30000 -  24500) - 0]/1437.7512

= 3.8254

The critical value of z at 5% level of significance is 1.6449.

Here, the calculated value is greater than the critical value so we reject H₀.

Hence using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.

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In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.

Note that by examining the the image if ∠EDA≅∠HCB, the two lines can never intersect even if they go a longer distance.

The reason why is that there are no parallel lines on it and as such, they cannot intercept.

Hence, In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.

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Using an exponential function, it is found that there will be 32,768 bacteria after 3 hours.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

For this problem, the parameters are:

a = 8, b = 4.

3 hours is 6 periods of 30 minutes, hence the amount is:

[tex]y = 8 \times 4^6 = 32768[/tex]

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The primary goal of a data scientist is to create new questions using data.

In the data ecosystem, a data scientist is one who creates new questions using data.

Unlike a data scientist, a data analyst uses existing data questions to find answers through insightful analysis of data.

Data designers design databases and database-specific constructs, and the procedures for storing, retrieving, and deleting persistent objects.

Data engineers build data systems to collect, manage, and convert data into information for both data scientists and analysts.

Thus, the primary goal of a data scientist is to create new questions using data.

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a) scientist

b) engineer

c) designer

d) analyst

Using proportions, it is found that the seismic activity density for this state is of 0.0059 earthquakes per square mile.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the density is the proportion given by the number of earthquakes divided by the area, hence:

424/71,300 = 0.0059 earthquakes per square mile.

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Answer:  Using proportions, it is found that the seismic activity density for this state is of 0.0059 earthquakes per square mile.

Step-by-step explanation:

Answer:

there are 6 people that need to sit down so let's see how we can fill those seeds we will start while finding seats for Alice and bob they can't sit next to each other so will remove one of the seeds them both in the remaining 5 then at a seat between them to ensure that they are not next to each other they are 5 ways to choose seat and 4 ways from those that we make giving 20 ways to seats

Step-by-step explanation:

once a lies and verb are ct we can arrange the remaining people in 4 is equal to 24 west in each other four seats for the total of 20 into 24 4 80 ways to seat everyone

Answer:

Step-by-step explanation:

i think it is c

Answer:

A

Step-by-step explanation:

So let's look at each and determine whether they're true or not.

A. It's vertex is at the origin:

   This is true! The reason for this is because you can express a quadratic in vertex form as such: [tex]f(x)=a(x-h)+k[/tex] where (h, k) is the vertex. If you remember the parent function is simply: [tex]f(x)=x^2[/tex] which we can express as: [tex]f(x) = (x-0)+0[/tex] meaning the vertex is at (0, 0). This also intuitively makes sense, the x^2 will only output positive values for real numbers, so when x<0, f(x) is still going to be positive because it's squaring the negative, so that means when you go from -5 to -4, even though you increased x by 1, the f(x) decreases by 1, since it's squaring the value to get a positive value. The lowest value this can output is 0 because 0^2 = 0. This means you vertex is at the origin.

B. It is not a function:

   So the quadratic parent function only outputs 1 value for each input, although it isn't a one-to-one function, meaning that each output isn't unique, but each input still only outputs 1 output, which makes this a function

C. It is not a parabola:

   parabolas are expressed as quadratic equations, so this is false.

D. It is in quadrants ||| and IV:

   This is not true since the parent function opens upwards and has a vertex at (0, 0) so it will only be in quadrant I and II. I'll provide a diagram showing this.

The expression which expresses the number of square feet of wallpaper needed is 12[tex]x^{2}[/tex]-21.

Given that the length of family room is 3x, breadth be 3x , height be x and the length and breadth of door be 7 feet and 3 feet.

We are required to find the expression which shows the square feet of wallpaper needed for the walls of the family room.

Because the wallpaper is not usually used on the floor and the ceiling and on doors so we will deduct the area of ceiling , floor and door from the surface area of whole room or we will just find the area of four walls one by one and then deduct the area of door from it.

Area of four walls only=2(lh+bh)

=2(3x*x+3x*x)

=2(3[tex]x^{2}[/tex]+3[tex]x^{2}[/tex])

=2*6[tex]x^{2}[/tex]

=12[tex]x^{2}[/tex]

Area of door=length*breadth

=3*7

=21 [tex]feet^{2}[/tex]

Required area=12[tex]x^{2}[/tex]-21.

Hence the expression which expresses the number of square feet of wallpaper needed is 12[tex]x^{2}[/tex]-21.

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Based on the interquartile range, the true statement about the box plots is: D. Number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

The interquartile range is the range of the box, which is the difference between the upper and lower quartile. Interquartile range is a measure of variation. The larger the value, the more the variation of the data.

Interquartile range for cracker = 85 - 75 = 10

Interquartile range for trail mix = 105 - 90 = 15

This means that the variation for trail mix is greater.

Therefore, the statement that is true is: D. Number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

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Answer:d

Step-by-step explanation:

Answer:

n^3 + 1.

Step-by-step explanation:

Each term is 1 more than a perfect cube.

2 = 1^3 + 1

9 = 2^3 + 1

28 = 3^3 + 1

65 =  4^3 + 1

126 = 5^3 + 1

So the explicit formula is n^3 + 1.

The explicit formula that generates the given sequence is indeed aₙ = n³+1.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The nth term of the sequence can be obtained by substituting n = 1, 2, 3, ... into the expression n³+1:

a₁ = 1³+1 = 2

a₂ = 2³+1 = 9

a₃ = 3³+1 = 28

a₄ = 4³+1 = 65

a₅ = 5³+1 = 126

Hence, the explicit formula that generates the given sequence is indeed aₙ = n³+1.

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The circle E, circle F and circle G are the circles which are congruent (similar) to the circle A has a radius of 6.

Let us discuss about the structure of each circles.

The circle D has the secant with the length 12. The secant means the straight line joining two points on the circle. So, we can't conclude that the secant will always be the diameter. Hence, it has different shape compared to circle A.

The circle E has the radius with length 6. The radius is same as the radius of the circle A. So, it is similar to the circle A.

The circle D has the secant with the length 6. Similar to the condition of circle D, it is not congruent to circle A.

The circle F has the diameter with length 12. Which means, the radius of this circle is with length 6. Hence, it is similar to the circle A.

The circle G has the diameter with length 12. Which means, the radius of this circle is with length 6. Hence, it is similar to the circle A.

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Answer:

Circles E and F are congruent to circle A

Answer:

=======================

Any rational number can be written in the form of p/q as per definition of a rational number.

In case with zero, it can be:

So, we'll have:

In the quadrilateral ABCD, in which angle A = 60° and angle B = 50°. The measure of angles C and D are,

∠C = 200° and ∠D = 50°

In the quadrilateral ABCD, it is given that,

A = 60° and angle B = 50°

Now, since AC is the angle bisector of angles A and C, we have,

∠DAC = ∠BAC ......... (1)

And ∠ACD = ∠ACB ............ (2)

Also, AC divides the quadrilateral ABCD into two triangles, ΔABC and ΔACD.

In ΔABC, ∠BAC = 30° [from (2)] and ∠ABC = 50°

Using angle sum property of a triangle, we have,

∠BAC + ∠ABC + ∠ACB = 180°

⇒ 30° + 50° + ∠ACB = 180°

80° + ∠ACB = 180°

∠ACB = 180° - 80°

∠ACB = 100°

From (1), ∠ACD = ∠ACB = 100°

∠C = ∠ACD + ∠ACB

⇒ ∠C = 100° + 100°

∠C = 200°

Now, according to the angle sum property of a quadrilateral,

∠A + ∠B + ∠C + ∠D = 360°

Substituting the values of ∠A, ∠B, and ∠C, we get,

60° + 50° + 200° + ∠D = 360°

310° + ∠D = 360°

∠D = 360° - 310°

∠D = 50°

Hence, in quadrilateral ABCD, ∠C = 200° and ∠D = 50°

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10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit. This can be obtained by multiplying 10 with the tens digit and adding unit digit.

Given that, in a two digit number,

t = the tens digit

u = the ones digit

The expression for the digit will be ,

10×t + u = 10t + u

The value of its reversal,

u = the tens digit

t = the ones digit

10×u + t = 10u + t is the required expression

For example,

37 = 10×3 + 7 = 30 + 7 and its reverse 73 = 10×7 + 3 = 70 + 3

Hence 10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit.

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Answer: 72 square units

Step-by-step explanation:

[tex]A=Bh=6(12)=72[/tex]

Answer:

72 SQUARE UNITS

Step-by-step explanation:

The amount of medication that stays in the bloodstream is the same at 3.04 hours for the two medications

The functions are given as:

[tex]f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}[/tex]

[tex]g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)[/tex]

Next, we represent both functions on a graph.

From the attached graph, we can see that both functions intersect at (11.34, 3.04)

This means that the amount of medication that stays in the bloodstream is the same at 3.04 hours for the two medications

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Complete question

A pharmaceutical scientist studying two medications wonders how long different amounts of each medicine stay in someone's bloodstream. The amount of time (in hours) one medication stays in the bloodstream can be modeled by [tex]f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}[/tex] where x is the initial amount of the medicine (in milligrams). The corresponding function for the other medication is [tex]g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)[/tex]. Here are the graphs of

Answer:

It gives the initial amount + It gives the solution

Step-by-step explanation:

It gives the initial amount + It gives the solution

We know from the graph given and the data provided that the function can automatically be proven true.

It cannot describe the amount of time as the data says X is how much of the medicine is given, not the time.

It can't be the equal ratio because, for example, 1 milligram of medicine doesn't equal 1h of time in the body.

All you need to do for this is educational guessing, reasoning, and the process of elimination. Hope this helped! have a great day :7)

Answer:

Step-by-step explanation:

To solve this equation log both sides and apply log rules.

Substitute the values of logs:

Solve it as linear equation:

Answer:

x = 2 ;   x = -8

Step-by-step explanation:

 [tex]\sf \ log_4 \ x +log_4 \ (x +6) = 2\\\\ log_4 \ (x)*(x +6) = 2\\\\[/tex]

    log₄  ( x² + 6x) = 2

                        4² = x² + 6x

         x² + 6x - 16 = 0

   x² - 2x + 8x - 16 = 0  

   x(x - 2) + 8(x - 2) = 0

       (x - 2) (x + 8)   = 0

x - 2 = 0  or x + 8 = 0

    x  = 2  or      x  = - 8

Answer:

[tex]y=2x+4[/tex]

Step-by-step explanation:

[tex](y-2)= 2(x-(-1))[/tex]

[tex](y-2)=2(x+1)[/tex]

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

[tex]y=2x+4[/tex]

Answer:

AB = 17, x = 6

Step-by-step explanation:

3x - 1 = 34 / 2

3x - 1 = 17

3x = 18

x = 6

AB = 17

x = 6

The percentage change in volume from cylinder A to cylinder B; D: 100%

Formula for Volume of a Cylinder is;

V = πr²h

Thus, volume of Cylinder A is;

V_a = π * 7² * 5

V_a = 245π

Thus, percentage change in volume is;

[245π/(490π - 490π)] * 100%

Percentage change in volume = 100%

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Answer:

100% increase

Step-by-step explanation:

I got it right on the test.

The remaining amount after 4 years is 1.25 kg

The half life of a function is represented as:

[tex]A = A_o * (1/2)^{t/h}[/tex]

Where

Ao represents the initial amount

So, we have:

[tex]A = 5 * (1/2)^{t/2}[/tex]

In 4 years, t = 4.

So, we have:

[tex]A = 5 * (1/2)^{4/2}[/tex]

This gives

[tex]A = 5 * (1/2)^2[/tex]

Evaluate the expression

A = 1.25

Hence, the remaining amount after 4 years is 1.25 kg

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Answer:

Step-by-step explanation:

The volume of the prism is not equal to the volume of the cylinder.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the cross sectional areas of a triangular prism and a right cylinder.

Volume of cylinder = cross sectional area * height = 3 * x = 3x

Volume of triangular prism = cross sectional area * height = 5 * x = 5x

The volume of the prism is not equal to the volume of the cylinder.

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Answer:

m∠1 = 51°

m∠2 = 16°        

Step-by-step explanation:

First ,check the attached photo.

=================

In the right triangle ABC :

m∠1 = 90 - 39

       = 51°

……………………

In the right triangle ABD :

m∠2 = 90 - 74

       = 16°

Answer:

• ∠ 1 = 51°

• ∠ 2 = 16°

Step-by-step explanation:

•  ∠ 1, the 39° angle, and the right angle marked in red are angles of a triangle.

∴  ∠ 1 + 90° + 39° = 180°             [Angles in a triangle add up to 180°]

⇒ ∠ 1 = 180° - 90° - 39°

⇒ ∠ 1 = 51°

• The small triangle on the top-left of the image consists of ∠ 2, a right-angle (marked in red) and a 74° angle.

∴  ∠ 2 + 90° + 74° = 180°            [Angles in a triangle add up to 180°]

⇒ ∠ 2 = 180° - 90° - 74°

⇒ ∠ 2 = 16°

Answer:

Step-by-step explanation:

Let the length be l and the width be y. We have the following:

l + w = 37

lw = 342

From here, we can find the factor pairs of 342, and see which pair has a sum of 37. Our desired pair is 18 & 19, so the dimensions of the field are 18 by 19 feet.

The volume of the cylinder having diameter 12 cm and height of 4 cm is 452 [tex]cm^{3}[/tex].

Given diameter of cylinder be 12 cm and height of cylinder be 4cm.

We are required to find the volume of cylinder.

Volume is the quantity of substance a container can hold in its capacity.

Diameter=12 cm

Radius=6 cm (Radius is always equal to half of diameter)

Volume of cylinder=π[tex]r^{2} h[/tex]

We have to just put the values of r, h and π in the formula to get the volume of the cylinder.

Volume=π[tex](6)^{2} 4[/tex]

=3.14*4*36

=452.57 [tex]cm^{3}[/tex]

After rounding off we will get 452 [tex]cm^{3}[/tex].

Hence the volume of cylinder is 452 [tex]cm^{3}[/tex].

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Question is incomplete as it should include height of cylinder be 4cm.