Graph by writing equations in slope intercept form.

Graph By Writing Equations In Slope Intercept Form.

Answers

Answer 1

Answer:

1) y = -1x+-1 and 2) y = -1x+-1

Step-by-step explanation:

Slope Intercept Form: y = mx+b (m is slope and b is y-intercept)

1) 8x+8y=-8

8y = -8x+-8

y = -1x+-1

2) 3x+3y =-3

3y = -3x+-3

y = -1x+-1


Related Questions

Solve this system of equations by substitution or by linear combination

Answers

Answer:

No solution

Step-by-step explanation:

2x - 4y= -6 ----- eq(1)

-x + 2y = -2 ----- eq(2)

Simplifying eq(1) by taking 2 as common,

2(x-2y) = 2(-3)

x - 2y= -3 -----eq(1)

from eq(1)

x - 2y = -3

x = -3 + 2y ---eq(3)

substituting eq(3) into eq(2)

-(-3 + 2y) + 2y = -2

3 - 2y + 2y = -2

3 = -2

Therefore This pair of linear Equations Has No Solution

a marketing manager tells her assistant that she wants to use only primary data in her market research. which of the following data would be most applicable for this research?

Answers

Primary data is usually designed to collect original data which is required for a specific kind of research. This data is tailored according to what is the focus of the research and what outcome are the people looking for.

Interviews: This is type of primary data in which we conduct interview of our target segment. The information exchange is mostly based out of questions and answers, and in-depth information regarding customer experience or product feedback could be easily done. This is collection of qualitative data instead of quantitative one. Only con is its high costs.Surveys and Questionnaire: This is the most common form of primary data collection, the main reason being this is not cost intensive and helps with getting large quantitative data for the research. Observation. This is most less likely to be used as primary data, as this mostly relates to behaver sciences. Thus, this is least conducted form of data collection. In products this would be used to observe the customer reaction to product packaging or their prices.Focus groups. Focus groups is collection of target segment and allowing them exchange of their thoughts. This helps with understanding customer behaver or understanding any pain-point that customer has. Experiment. This is the most basic form of primary data collection, here a controlled environment is designed and a determined process is followed in order to understand the causality of process with outcome.

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Complete Question:

A marketing manager tells her assistant that she wants to use only primary data in her market research. Which of the following data would be most applicable for this research?

Interviews

Observation

Focus groups

Experiment

Surveys and Questionnaire

qualitative research

market research

Find the missing dimension of the triangle. A=13.5 b=6.75 h = __ in.

Answers

The height of the given triangle having an area of 13.5in.² and a base length of 6.75 in. is 4 in.

What is a triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. Any three points in Euclidean geometry, when they are not collinear, produce a distinct triangle.

In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.

In this question, we are given,

Area of triangle A = 13.5 in.²

Base of triangle b = 6.75 in.

We are asked to find the height h of the triangle.

Now formula of the area is:

A = 1/2 * b * h

13.5 = 1/2 * 6.75 * h

h = 13.5 *2 / 6.75 = 4 in.

Therefore the height of the given triangle is 4 in.

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the length of each side of a square was decreased by 2 inches, so the perimeter is now 48 inches. What was the orginal length of each side of the square?

Answers

The original length of each side of the square was 14 inches.

Define a square.

A square is a geometric form with two dimensions that has four equal sides and four angles that are each 90 degrees (also known as right angles). With all sides being the same length and all angles being right angles, it is a particular case of a rectangle and a parallelogram. A square's sides are all perpendicular to one another, and its diagonals are at right angles to one another. Squares exhibit rotational symmetry of order 4 because they are symmetrical in both their vertical and horizontal axes.

Let's assume that the original length of each side of the square was "x" inches.

When each side of the square is decreased by 2 inches, the new length of each side will be (x-2) inches.

The perimeter of the new square is given as 48 inches. Since a square has four equal sides, the perimeter of a square is given by the formula:

Perimeter = 4 * Side

So, for the new square, we have:

48 = 4 * (x-2)

Simplifying the above equation, we get:

12 = x-2

Adding 2 to both sides, we get:

x = 14

Therefore, the original length of each side of the square was 14 inches.

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Hello I’m having a hard time with question

Answers

[-1.5, 3.5] and [-2, infty) are the range and domain of the equation.

Determining the domain and range of a quadratic function

Quadratic function are functions that have a leading degree of 2.

The domain of the function are values that lies along the x-axis of the graph. Hence the domain of the curve will be [-1.5, 3.5]

The range of the function are values that lies along the y-axis of the graph. Hence the domain of the curve will be [-2, infty)

Hence the range and domain of the graph are [-1.5, 3.5] and [-2, infty)

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The proportion of people who respond to a certain mail-order solicitation is a random variable X having the following density function 2(x+3) 0

Answers

The question you have indicated appears incomplete. However, here is a very similar example that uses the same logic and principles of probability and proportion. In this case, the proof is given below.

What is the rationale for the above response?

a.

Given: f(x) = 2(x+2)/5 , 0 <x< 1

Calculating P(0 <X< 1)

P(0 <X< 1) = ∫ f(x) dx {0.1}

Substitute 2(x+2)/5 for f(x)

P(0 <X< 1) = ∫ 2(x+2)/5 dx {0.1}

P(0 <X< 1) = 2/5 ∫(x+2) dx {0.1}

Integrate with respect to x

P(0 <X< 1) = 2/5 (x²/2+2x) {0.1}

P(0 <X< 1) = 2/5 (1²/2+2(1))

P(0 <X< 1) = 2/5 (½+2)

P(0 <X< 1) = 2/5 * 5/2

P(0 <X< 1) = 1 ----- Proved

b.

Here we're to solve for P(¼<X< ½)

P(¼<X< ½) = ∫ f(x) dx {¼,½}

Substitute 2(x+2)/5 for f(x)

P(¼<X< ½) = ∫ 2(x+2)/5 dx {¼,½}

P(¼<X< ½) = 2/5 ∫(x+2) dx {¼,½}

P(¼<X< ½) = 2/5 (x²/2+2x) {¼,½}

P(¼<X< ½) = 2/5 [ (½²/2+2(½)) - (¼²/2+2(¼))]

P(¼<X< ½) = 2/5 [(⅛+1)-(1/32 + ½)]

P(¼<X< ½) = 0.2375

The probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation is 0.2375

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Full Question:

The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function f(x) = 2(x+2)/5 , 0 <x< 1, 0, elsewhere.

(a) Show that P(0 <X< 1) = 1.

(b) Find the probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation.

You’re trying to save to buy a new $230000Ferrari. You have $31000 today that can be invested at your bank. The bank pays 4.5 percent annual interest on its accounts. How long will it be before you have enough to buy the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answers

We can use the formula for compound interest to find the time it will take to reach the target amount:

FV = PV * (1 + r)^t

where FV is the future value (target amount), PV is the present value (amount you have today), r is the interest rate, and t is the time (in years).

Substituting the given values, we get:

230000 = 31000 * (1 + 0.045)^t

Simplifying and solving for t, we get:

t = log(230000/31000) / log(1 + 0.045)

t ≈ 14.09

Therefore, it will take approximately 14.09 years to save enough to buy the Ferrari.

How much more interest to your parents have to pay at the end of the first month because their rating is good rather than excellent?

Answers

The interest to pay at the end of the first month C. $18.71.

How to find the monthly interest?

To calculate the monthly interest rate, divide the annual percentage rate by 12. For excellent credit, the monthly rate is 4.75% / 12 = 0.3958%, and for good credit, the monthly rate is 5.00% / 12 = 0.4167%.

The total cost of the mobile home including sales tax is $92,738 ($89,000 x 4.2% sales tax). With a $3,000 down payment, the amount financed is $89,738.

For excellent credit, the monthly interest rate :

= 4.75% / 12

So, the interest charged in the first month is $89,738 x  4.75% / 12 = $355.21

For good credit, the monthly interest rate is 0.4167%. So, the interest charged in the first month is $89,738 x 0.004167 = $33.91.

The difference in interest charged between good and excellent credit is $373.91 - $355.21 = $18.71.

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The complete question is:

Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment. How much more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent?

Secured Unsecured

Credit APR (%) APR (%)

Excellent 4.75 5.50

Good 5.00 5.90

Average 5.85 6.75

Fair 6.40 7.25

Poor 7.50 8.40

Options:

$29.39

$21.10

$18.71

$19.02

For an acute angle θ, the equation sin(θ) = cos(6) is true. what is the value of θ? Show or explain your answer​

Answers

Answer:

84 deg

Step-by-step explanation:

cos(x)=sin(90-x)

90-x=6

x=84

Select the correct equation in the list PLSS HELP

Answers

3x - 8y = -19 would be -6x + 16y = 38. Option A is correct when we multiply the equation by factor -2

How to solve the equation

The systems of equation that would be equivalent to

3x - 8y = -19 can be gotten by using a common factor that can get us the solution

3x - 8y = -19 we would multiply this by 2

6x - 16y = -38 this is not in the solution

Then we have to multiply the first equation by -2

-2(3x - 8y = -19)

-6x + 16y = 38

Therefore the first option is equivalent to the first equation in the system

proof using 7 and 5

- 6 * 7 + 16 * 5 = 38

-42 + 80 = 38

Also 3x - 8y = -19

= 3 * 7 - 8 * 5 = -19

21 - 40 = -19

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Gage stocks two ponds with bass and bluegill.
He stocks Pond A with 60 fish and Pond B with
300 fish. Gage stocks Pond B with twice the
amount of bass and six times the amount of
bluegills as Pond A. How many bass and
bluegills does Gage stock in Pond A?

Answers

The requried, Gage stocks Pond A with 15 bass and 45 bluegills.

What is equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let x be the number of basses in Pond A.

Then the number of bluegills in Pond A is 60 - x.

According to the problem, Pond B has twice the number of bass as Pond A, so there are 2x bass in Pond B.

Similarly, Pond B has six times the number of bluegills as Pond A, so there are 6(60 - x) bluegills in Pond B.

The total number of fish in Pond B is 300, so we can set up an equation:

2x + 6(60 - x) = 300

Simplifying and solving for x, we get:

2x + 360 - 6x = 300

-4x = -60

x = 15

Therefore, Gage stocks Pond A with 15 basses and 45 bluegills.

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A small-scale model of a submarine is being designed with the stabilizing wings and rudder to be added later. The fuselage is a cylinder of length 30 inches with a radius of 5 inches. The bow (front) is a semi sphere ( half of a sphere) that fits on one end of the cylinder. The stern (back) is a cone on the tail end that has a height of 6 inches. Calculate the volume and surface area of the new solid.

If a medium-scale model was required at 8x the scale of the small model, What is the overall length from back to the tip? What is the new surface area? What is the new Volume?

Answers

The Volume of Solid is 2,773.66 inch³ and Surface Area is

2,552.82 inch².

What is Surface Area?

Surface area is the amount of space covering the outside of a three-dimensional shape.

Given:

Cylinder: Height = 30 inch, Radius = 5 inch

Semi sphere: radius = 5 inch

Cone: Height = 6 inch, radius = 5 inch, l= √r² + h² = 7.81 inch

Now, The Volume solid

= Volume of Semi sphere  + Volume of Cylinder + Vol. of Cone

= 2/3 πr³ + πr²H + 1/3 πr²h

= πr² (2/3 r + H + 1/3 h)

= 3.14 x 5 x 5 (2/3(5) + 30 + 1/3 (6))

= 78.5 x ( 10/ 3 + 30 + 2)

= 2,773.66 inch³

Now, the Surface Area of Solid

= SA (Cylinder+ S. Sphere + Cone)

= πr²H + 2πr² + 1/3 πrl

= πr (rH + 2r + 1/3l)

= 3.14 x 5 (150 + 10 + 2.60)

= 2,552.82 inch²

Now, the model is increased by 8 times then the dimensions are:

Cylinder: Height = 240 inch, Radius = 40 inch

Semi sphere: radius = 40 inch

Cone: Height = 48 inch, radius = 40 inch, l= √r² + h² = 62.48 inch

and, Now, The Volume solid after dilation

= Volume of Semi sphere  + Volume of Cylinder + Vol. of Cone

= 2/3 πr³ + πr²H + 1/3 πr²h

= πr² (2/3 r + H + 1/3 h)

= 3.14 x 40 x 40 (2/3(40) + 240 + 1/3 (48))

= 78.5 x ( 10/ 3 + 30 + 2)

= 1,420,117.33 inch³

Now, the Surface Area of Solid

= SA (Cylinder+ S. Sphere + Cone)

= πr²H + 2πr² + 1/3 πrl

= πr (rH + 2r + 1/3l)

= 3.14 x 5 (1200 + 80 + 20.82)

= 163, 382. 992 inch²

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Find the area of the irregular figure. Use 3.14 for π. Show your work. Round to the nearest tenth

Answers

The area of the irregular figure to the nearest tenth is 8.12 sq. ft.

What are irregular figures?

Shapes classified as irregular lack both equal sides and equal angles. The entire area occupied by an irregular shape on a two-dimensional plane is referred to as the shape's area. An irregular form can be split into a number of regular shapes, such as triangles, squares, and rectangles, to determine its area. The area of those smaller shapes can then be added to determine the total area.

Given that, the diameter of the semicircle= 2.8 ft.

The radius of the semicircle = 1.4 ft.

The area of the semicircle is:

A = πr² / 2

A = (3.14)(1.4)²/2

A= 3.077 sq. ft

The area of the triangle is given as:

A = 1/2(b)(h)

A = 1/2(2.8)(3.6)

A = 5.04 sq. ft

The area of the irregular figure is:

A = Area of semicircle + area of triangle

A = 3.077 + 5.04

A = 8.117 sq. ft

Hence, the area of the irregular figure to the nearest tenth is 8.12 sq. ft.

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The perimeter of a rectangular parking lot is 274m. If the width of the parking lot is 62 m, what is its length?

Answers

The required length of the parking lot is 75 meters.

What is the perimeter?

Perimeter is the measure of the figure on its circumference.

Here,
Let's call the length of the parking lot "L". The perimeter of a rectangle is given by the formula:

Perimeter = 2 × (length + width)

We know that the width is 62 m and the perimeter is 274 m, so we can plug these values into the formula and solve for the length:

274 = 2 × (L + 62)

Dividing both sides by 2, we get:

137 = L + 62

Subtracting 62 from both sides, we get:

L = 137 - 62

L = 75

Therefore, the length of the parking lot is 75 meters.

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find the coordinates of all points where the lines x + y = 8, y = 5, and x = 1 intersect

Answers

Intersection points for the lines are,

⇒ (3, 5) (1, 7) and (1, 5)

What is Line segment?

Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.

Given that;

The equation of lines are,

x + y = 8  .. (i)

y = 5 .. (ii)

x = 1  .. (iii)

Now, Intersect point for equation (i) and (ii);

x + y = 8  .. (i)

y = 5 .. (ii)

⇒ x + 5 = 8

⇒ x = 3

Hence, The intersection point = (3, 5)

And, Intersect point for equation (i) and (iii);

x + y = 8  .. (i)

x = 1  .. (iii)

⇒ x + y = 8

⇒ y = 8 - 1

⇒ y = 7

Hence, The intersection point = (1, 7)

And, Intersect point for equation (ii) and (iii);

⇒ (1, 5)

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Hiking Trails The Farina family spent a week at the state park. Christine hiked the Evergreen trail twice and the Yellow River trail once. Brian hiked each of the three longest trails once. How many more miles did Brian hike than Christine?​

Answers

Answer:

Brian hiked 6 1/2 more miles than Christine.

Step-by-step explanation:

Ok. 5.25+4.75+6-2*4.75=6.5 or 6 1/2 more miles.

The Spirit Club buys shirts in bulk for $8 each. They mark up the shirts 75% to sell in the school store. At the end of the year, they sell the shirts for 25% off. How much profit does the Spirit Club make on each shirt at the end of the year? Show your work


Write the work down step by step, math involved.

Answers

The Spirit Club makes $2.5 profit on each shirt at the end of the year.

What is profit?

Cost price and selling price are better ways to explain profit. Cost price is the actual cost of the good or service, whereas selling price is the price at which it is offered for sale. In this case, the business has made a profit if the selling price of the good is higher than the cost price. Consequently, the profit calculation formula is;

Selling price minus cost price equals profit or gain.

Given that the cost of a shirt for the Spirit Club is $8.

They mark up the shirts 75% to sell in the school store.

The amount that is up on each shirt is $8×75%

= $8×(75/100)

= $8×(3/4)

= $6.

The marked price of each shirt is  $8 + $6 = $14.

They sell the shirts for 25% off at the end of the year.

The discount amount is $14×25%

= $14×(25/100)

= $14×(1/4)

= $3.5

The selling price of each shirt at the end of the year is $14 - $3.5 = $10.5.

The profit is Selling price - cost price = $10.5 - $8 = $2.5

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which polynomial represents the difference below 12x^3+7x+3-(3x^7+4x)

Answers

Answer:

The polynomial that represents the difference of 12x^3+7x+3 and 3x^7+4x is 12x^3-3x^7+7x-4x.

Please help me
Thank you

Answers

The solution for x in the given equation (x-c)/2 = d is x = 2d + c.

What is the solution for x in the given equation?

Given the equation in the question;

(x-c)/2 = d

x = ?

To solve for x, cross multiply and simplify.

(x-c)/2 = d

x - c = d × 2

x - c = 2d

Add +c to both sides

x - c + c = 2d + c

x = 2d + c

Therefore, the solution for x in the given equation (x-c)/2 = d is x = 2d + c.

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please help me with this

here is the picture is just one question

Answers

Note that the equation for the parent function y=x² stretched horizontally by a factor of 4 and shifted down 5 units is given as follows: y = (1/16)x² - 5

What is the rationale for the above response?

Note that a parent function is a simple, basic function from which other more complex functions can be derived by applying transformations.

To stretch the graph horizontally by a factor of 4, we divide x by 4, which gives:

y = (1/16)x²

To shift the graph down 5 units, we subtract 5 from the whole function, which gives:

y = (1/16)x² - 5

Therefore, the equation for the parent function y=x^2 stretched horizontally by a factor of 4 and shifted down 5 units is:

y = (1/16)x² - 5

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I can’t get this right!!!!

Answers

Answer:

[tex]\csc \theta=\dfrac{\sqrt{61}}{6}[/tex]

[tex]\sin \theta=\dfrac{6}{\sqrt{61}}=\dfrac{6\sqrt{61}}{61}[/tex]

[tex]\cot \theta=\dfrac{5}{6}[/tex]

Step-by-step explanation:

Use Pythagoras Theorem to calculate the length of the hypotenuse of the given right triangle:

[tex]\implies a^2+b^2=c^2[/tex]

[tex]\implies 5^2+6^2=c^2[/tex]

[tex]\implies 25+36=c^2[/tex]

[tex]\implies c^2=61[/tex]

[tex]\implies c=\sqrt{61}[/tex]

Therefore:

The side opposite angle θ is 6 units.The side adjacent angle θ is 5 units.The hypotenuse is √(61) units.

[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric ratios}\\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\\\$\sf\csc(\theta)=\dfrac{H}{O}\quad\sec(\theta)=\dfrac{H}{A}\quad\cot(\theta)=\dfrac{A}{O}$\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]

Substitute the given values into each ratio:

[tex]\csc \theta=\dfrac{\sqrt{61}}{6}[/tex]

[tex]\sin \theta=\dfrac{6}{\sqrt{61}}[/tex]

[tex]\cot \theta=\dfrac{5}{6}[/tex]

Note: The sin θ ratio can also be written as:

[tex]\implies \sin \theta=\dfrac{6}{\sqrt{61}}\cdot \dfrac{\sqrt{61}}{\sqrt{61}}[/tex]

[tex]\implies \sin \theta=\dfrac{6\sqrt{61}}{61}[/tex]

An installment loan is made for 36 monthly payments of $160.43. The loan carries an APR of 11%, and the finance charge associated with the loan is $875.48. Instead of making the twenty-fourth payment, the borrower decides to pay the remaining balance and terminate the loan. (Refer to an APR table as necessary.)
a. Use the actuarial method to determine how much interest will be saved by repaying the loan early.
b. By using the actuarial method, what is the total amount due on the day of the loan's termination?
c. Use the rule of 78 to determine how much interest will be saved by repaying the loan early.
d. By the rule of 78, what is the total amount due on the day of the loan's termination.

Answers

A is the answer and if it’s wrong then i’m sorry

To indirectly measure the distance across a lake, Mia makes use of a couple
landmarks at points Vand W. She measures UX, XV, and XY as marked. Find
the distance across the lake (VW), rounding your answer to the nearest hundredth
of a meter.
W
70 m
120.25 m
130 m
U

Answers

The distance across the lake VW is 185m.

Define the term similar triangle?

Triangles that are similar but not necessarily the same size are called similar triangles. This indicates that their sides are proportional and that their angles are the same.

We can see there are two similar triangles with interior parallel line.

So, apply the Side Angle Side (SAS) rule for ΔUVW ≈ ΔUXY;

⇒   [tex]\frac{VW}{XY} = \frac{UV}{UX}[/tex]

⇒   [tex]\frac{VW}{120.25}=\frac{(130+70)}{130}[/tex]

Cross multiply both sides,

⇒   VW  =  [tex]\frac{200}{130}*120.25[/tex]

⇒    VW = 185 m

Therefore, the value of VW is 185m.

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n environmental agency frequently samples the water in a region to ensure that the levels of a certain contaminant do not exceed 30 parts per billion (ppb). From 12 randomly selected samples of the water, the agency constructed the 99 percent confidence interval (22.5, 28.7).
We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb

Answers

The correct interpretation of the interval is " We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb "

What is confidence interval?

In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as the confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations.

We need to find correct interpretation of the interval.

Among all answer choices given, the correct  option is :

We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb

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3. Which of the following are true? The universe for each statement is given in parentheses.
a) (Vx) (x+xzx). (R)
b) (3x) (2x+3=6x+7). (N)
c) (3x) (3*=x²). (R)
d) (3) (3x). (R)
e) (3x) (3(2-x)=5+8(1-x)). (R)
f) (Vx)(Vy) [x

Answers

The statement that are true are:

a) (Vx) (x+xzx). (R)

c) (3x) (3*=x²). (R)

d) (3) (3x). (R)

f) (Vx)(Vy) [x<y -> (3x<3y)]. (R)

What are the statement that are true?

a) (Vx) (x+xzx). (R) - This statement is true. It is a vacuously true statement, meaning it is true because the predicate (x+xzx) is never satisfied for any element x in the universe (R).

b) (3x) (2x+3=6x+7). (N) - This statement is false. There is no value of x in the universe (N) that satisfies the equation 2x+3=6x+7.

c) (3x) (3*=x²). (R) - This statement is true. For every value of x in the universe (R), 3 times x is equal to x squared.

d) (3) (3x). (R) - This statement is true. For any value of x in the universe (R), multiplying x by 3 will always result in a real number, which means 3x is also in the universe (R).

e) (3x) (3(2-x)=5+8(1-x)). (R) - This statement is false. There is no value of x in the universe (R) that satisfies the equation 3(2-x)=5+8(1-x).

f) (Vx)(Vy) [x<y -> (3x<3y)]. (R) - This statement is true. For any two elements x and y in the universe (R) where x<y, 3x is always less than 3y, so the implication (3x<3y) is true. Since this is true for all x and y, the universal quantifiers (Vx)(Vy) make the statement true.

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Please help I need help so badly

Answers

Step-by-step explanation:

area

3.14×18×18

1017.36ft²

circumference

2×3.14×18

113.04ft

Data from www.centralhudsonlabs.com determined the mean number of insect fragments in 225-gram chocolate bars was 14.4, but three brands had insect contamination more than twice the average. Assume the number of fragments follows a Poisson distribution.
a. If you consume a 225-gram bar from a brand at the mean contamination level, what is the probability of no insect contaminants?
b. Suppose you consume a bar that is one-fifth the size tested (45 grams) from a brand at the mean contamination level. What is the probability of no insect contaminants?
c. If you consume seven 28.35 gram (one-ounce) bars this week from a brand at the mean contamination level, what is the probability that you consume one or more insect fragments in more than one bar?
d. Is the probability of contamination more than twice the mean of 14.4 unusual, or can it be considered typical variation? Explain.

Answers

a. The probability of no insect contaminants in a 225-gram bar from a brand at the mean contamination level can be found using the Poisson probability formula:


[tex]P(X = 0) = \frac{ (e^{-λ})(λ^0)}{0!} = \frac{(e^{-14.4})(14.4^0)}{0!}= 0.000000831[/tex]


b. If you consume a bar that is one-fifth the size tested (45 grams) from a brand at the mean contamination level, the mean number of insect fragments would be one-fifth of 14.4, or 2.88. The probability of no insect contaminants can be found using the Poisson probability formula:


[tex]P(X = 0) = \frac{(e^-λ)(λ^0)}{0!} = \frac{(e^-2.88)(2.88^0)}{0!} = 0.056032[/tex]

c. If you consume seven 28.35 gram (one-ounce) bars this week from a brand at the mean contamination level, the mean number of insect fragments would be (7 * 28.35/225) * 14.4 = 5.4336.

The probability of consuming one or more insect fragments in more than one bar can be found using the Poisson probability formula and the complement rule:


[tex]$$\begin{aligned}& P(X>1) \\& =1-P(X \hat{a} 1) \\& =1-\left[\left(e^{-} \hat{I}\right)\left(\hat{I}^0\right) / 0 !+\left(e^{-} \hat{I}\right)\left(\hat{I}^1\right) / 1 !\right] \\& =1-\left[\left(e^{-} 5.4336\right)\left(5.4336^0\right) / 0 !+\left(e^{-} 5.4336\right)\left(5.4336^1\right) / 1 !\right] \\& =0.994784\end{aligned}$$[/tex]

d. The probability of contamination more than twice the mean of 14.4 can be found using the Poisson probability formula and the complement rule:

[tex]P(X > 28.8) = 1 - P(X ≤ 28.8) \\= 1 - ∑(e^-λ)(λ^x)/x!\\ = 1 - 0.999999999999999 \\= 0.000000000000001[/tex]


This probability is extremely small, so it can be considered unusual and not typical variation.

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Find the perimeter of the triangle whose vertices are (−2,−2)
, (4,−2)
, and (4,6)
. Write the exact answer. Do not round.

Answers

When the triangle's vertices are (2, 2), (4, 2), and (2, 2), its circumference is 28. (4,6).

what is perimeter ?

An closed path that surrounds, distinguishes, or comprises a multiple shape or a three-dimensional length is spoken to as a boundary. The perimeter of either an ellipse or circle refers from its outermost area. The perimeter calculation had several practical uses. Discover how to determine the perimeter by adding the measurements of the vertices of various forms. You can still find the perimeter of a shape by multiplying its side lengths. The peripheral of an object is the space around it. At your house, a covered garden is one illustration. The circumference of anything is all area encircling it. For a 50 feet x 50 feet yard, a 200 yard fence is required.

given

d=√(x2−x1)2+(y2−y1)2

d1=√(4+1)2+(−5−6)2=√146≅12

For the second two;

d2=√(−2−4)2+(−4+5)2=√37≅6

And for the last pair;

d3=√(−2+1)2+(−4−6)2=√109≅10

So the sum of the three sides is roughly;

12+6+10=28

When the triangle's vertices are (2, 2), (4, 2), and (2, 2), its circumference is 28. (4,6).

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Can someone help me with this problems with an explanation please? Thank you.

Answers

The values and heights obtained using the trigonometric ratios are as follows;

4. The six trigonometric ratios are;

cos(θ) = 15/17sec(θ) = [tex]1\frac{2}{15}[/tex]sin(θ) = 8/17csc(θ) = [tex]2\frac{1}{8}[/tex]tan(θ) = 8/15cot(θ) = [tex]1\frac{7}{8}[/tex]

5. The two other ways to write cot(θ) are;

cot(θ) = 1/tan(θ)cot(θ) = cos(θ)/sin(θ)

6. The six trigonometric function values are;

cos(x) = -3/5sec(x) = [tex]-1\frac{2}{3}[/tex]sin(x) = -4/5csc(x) = [tex]-1\frac{1}{4}[/tex]tan(x) = [tex]1\frac{1}{3}[/tex]cot(x) = 3/4

7. The function for the height of the tree is; H = 100·tan(θ)

The completed table is presented as follows;

θ   [tex]{}[/tex]               10°                 15°              20°                 25°

H[tex]{}[/tex]               17.63             26.79          36.4               46.63

What are trigonometric ratios?

Trigonometric ratios are functions that relate the ratio of two of the sides of a right triangle to an interior angle of the right triangle.

4. The length of the adjacent side to the angle θ according to the Pythagorean Theorem is; Adjacent = √(17² - 8²) = 15

The six trigonometric ratios are;

cos(θ) = 15/17, sec(θ) = 17/15 = 1 2/15

sin(θ) = 8/17, csc(θ) = 17/8 = 2 1/8

tan(θ) = 8/15, cot(θ) = 15/8 = 1 7/8

5. The 2 other ways to write cot(θ) are;

cot(θ) = 1/(tan(θ))

cot(θ) = cos(θ)/sin(θ)

6. The location of the point on the terminal side of the angle is; (-3, -4)

Length of the hypotenuse side = √((-3)² + (-4)²) = 5

Let x represent the angle, we get;

The six trig functions of the angle are;

cos(x) = -3/5sec(x) = -5/3 = -1 2/3sin(x) = -4/5csc(x) = -5/4 = -1 1/4tan(x) = -4/(-3) = 4/3 = 1 1/3cot(x) = 3/4

7. The length of the shadow of the tree = 100 m

Angle of elevation of the Sun = θ

Let h represent the height of the tree, we get;

tan(θ) = h/100

Therefore, the height of the tree, h = 100·tan(θ)

The values of the height of the tree at the different angle of elevation in the table are;

θ = 10°, h = 100 feet × tan(10°) ≈ 17.63 feet

θ = 15°, h = 100 feet × tan(15°) ≈ 26.79 feet

θ = 20°, h = 100 feet × tan(20°) ≈ 36.4 feet

θ = 25°, h = 100 feet × tan(25°) ≈ 46.63 feet

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A cylinder has a volume of 155.43m3 and a radius of 3m. What is the height of the cylinder to the nearest tenths of a meter??

Answers

V = r²h where,

V is the volume of the cylinder

r is the radius of the cylinder

h is the height of the cylinder

in this case, h is the value we want to find, h, r is 3m and V is 155.43m³ !!

155.43 = × (3)² × h

17.27 = × h

h = 5.4972117...

= 5.50m (3.s.f) = height of cylinder

hope this helped, if you have any questions feel free to ask !! :D

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