in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees. find the length of w, to the nearest centimeter

Answers

Answer 1

The length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.

What is the triangle?

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.

Using cos law:

W = √(41² + 17² - 2×41×17 cos 134)

After solving:

W = 54.20 cm

Thus, the length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.

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Related Questions

a cowboy agreed to work for one year for $\$19{,}200$ plus a horse. he quit after 7 months and was paid $\$10{,}450$ plus a horse. how many dollars was the horse worth, if the paid salary reflects the fair proportion of his yearly salary?

Answers

The horse was worth it for $1800.

What is proportion?

A mathematical comparison of two numbers is called a proportion. Ratios and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers.

Based on the given question condition, where, 'h' denotes the amount for the horse in dollars,  the proportion can be defined as:

or,  [tex]\frac{19200 + h}{12} = \frac{10450+h}{7}[/tex]

or, (19200 + h)7 = (10450 + h)12

or, 134400 + 7h = 125400 + 12h

or, 12h - 7h = 134400 - 125400

or, 5h = 9000

or, h = 9000/5 = 1800

Hence, the horse was worth $1800.

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g what is the probability of flipping at least 3 heads in 4 flips of 2 fair coin given that the first flip is heads?

Answers

The probability is 0.25.

What is probability?

Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To determine how likely an event is to occur, mathematics has created the concept of probability.

Given there are 2 coins flipped 4 times, we get the following sample space

S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

Now, A = event of having at least 3 heads.

A= {HHHH, HHHT, HHTH, HTHH, THHH}

The number of events having the first flip heads is 4.

Therefore, the probability is:

P(A) =

[tex]=\frac{successful \space\ events}{total\space\ sample\space\ events}\\=\frac{4}{16}\\=0.25[/tex]

Therefore, the probability of flipping at least 3 heads in 4 flips of 2 fair coins given that the first flip is heads is 0.25.

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ASAP PLEASE! Complete the square.
[tex]m^2-8m[/tex]

Find the missing term that completes the square.
[tex]m^2-8m+?[/tex]
(Simplify your answer. Type an integer or a fraction.)

Answers

Answer:

16

Step-by-step explanation:

Let us assume the square is (m-a)²
We have to find a


(m-a)² = m² -2am + a²

We are given
m² -8m

Comparing terms
2a = 8

a = 4

so the square is (m-4)²

which is m² - 8m + 16

HELPPP PLEASE ASAP!!!!!!!!

Answers

Answer:

x=6

Step-by-step explanation:

i assume these are similar triangles so we can set them up as fractions

x/9=4/x

cross multiply

9(4)=x(x)

36=x^2

√.    √

6=x

and now we can check if each have the same ratio

6/9= 4/6

2/3=2/3

hopes this helps please mark brainliest

Chris earns $7.00 per hour working on the weekends
He needs at least 210.00 for a new cell phone
Just look at the picture and help please

Answers

it’s d the last one. this is because of the greater than and equal sign

4 a. Graph the following system of equations.
y = -3x
y = x + 4
b. what does the graph show to be the solution of the system?

5 DeAndre and Leah are making origami cranes. their goal is to complete 1,000 cranes by the end of the summer.
- DeAndre already has 30 cranes and makes 5 more each day.
- Leah already has 10 cranes and makes 15 more each day.
The graph shows how many cranes, c, each person has made after d days.
a. what does the graph show to be the solution of the system?
b. what does the solution mean in this context?

Answers

4. a. The graph of the system is attached below.

b. The solution is: (-1, 3).

5. a. (2, 40) is the solution as shown by the graph.

b. (2, 40) means that both will complete 40 cranes after 2 days

How to Graph a System of Equation?

On a graph, when two lines are plotted for different equations, the solution is the coordinates of the point where both lines intersect.

4. a. The graph of y = -3x is the red line in the image attached below, while that of y = x + 4 is the blue line. They both intersect each other at (-1. 3).

b. The solution of the system is therefore, (-1, 3).

5. a. Using the graph given that shows the lines of the equations of DeAndre and Leah, both lines intersect at (2, 40).

We can therefore state that the solution to the system as shown in the graph is: (2, 40).

b. In the context of the scenario given, the solution (2, 40) means that both will have completed equal amounts of 40 cranes after 2 days.

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Graph the following features:

Answers

Hope this helps you

mr. smith has a maximum of $50 to spend at a museum. a ticket to the museum costs $7. he can spend p dollars to buy other things at the museum. write the inequality that can be used to find the values for p and solve for p.

Answers

The inequality that can be used to find the values for p is p + 7 ≤ 50.

Given the information,

Mr. Smith can only spend up to $50 at a museum. The museum admission ticket is $7. He can use his P dollars to purchase other items from the museum.

The total budget is $50.

The cost per ticket is $7

⇒ Total spent ≤  Total Budget

⇒ p + 7 ≤ 50

⇒ p ≤ 43

Therefore, p + 7 ≤ 50 will be the inequality that aids in determining the range of values for p.

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The points given in the table lie on a line. Find the slope of the line.

Answers

Answer:

-4/3

Step-by-step explanation:

We can find the slope of the line using

m = ( y2-y1)/(x2-x1)

m = ( -9 -3)/( 8 - -1)

   = ( -9-3)/( 8+1)

   = -12 / 9

  = -4/3

Answer:

[tex]\sf m=-\frac{4}{3}[/tex]

Step-by-step explanation:

First, select any two coordinates of the line.

( -1, 3 ) ⇒ ( x₁ , y₁ )

( 2, -1 ) ⇒ ( x₂ , y₂ )

And now let us use the below formula to find the slope of the line.

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

Let us find the slope now.

[tex]\sf m= \frac{y_1-y_2}{x_1-x_2} \\\\\sf m= \frac{3-(-1)}{-1-2} \\\\\sf m= \frac{4}{-3}\\\\\sf m=-\frac{4}{3}[/tex]

the actual answer pleaseee hellpp asapp

Answers

Answer:

∠BEC is supplementary to ∠AEB

∠AED and ∠BEC are a pair of vertical angles

Which figure is
misleading?
1) Figure A
2) Figure B

Answers

Answer:

Figure B.

Step-by-step explanation:

Figure A uses what is visually similar in size cylinders to give a detailed image of the amount of money (assumingly as profit). Each given cylinder that is in similar size represents $200, and so it is easy to figure out how the amount of money per store.

In the case of Figure A,

Save Store = $400

Leff's Store = $800

Low Pricer = $1200

In the case of Figure B, however, while it gives a legend for price per cylinder of that proportion, it does not make use of the legend, and does not give a adequate legend to decipher the Figure. In essence, the data given in Figure B is useless as it makes no use of its legend.

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one number added to three times another number is 24 five times the number added to three times the other number is 36 find the numbers

Answers

The required numbers for the given case are 3 and 7 respectively.

How to solve a linear equation?

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

As per the given data the problem can be solved as follows,

Suppose the first number be x and the second be y.

Now, the equations can be formed as,

x + 3y = 24             (1)

5x + 3y = 36           (2)

Solve these equations by multiplying equation (1) by 5 and then subtract from (2) as below,

5x + 3y - 5(x + 3y) = 36 - 5 × 24

3y - 15y = -84

=> -12y = -84

=> y = 7

Substitute y = 7 in equation (1) to get,

x + 3 × 7 = 24

=> x = 3

Hence, the numbers for the given problem are 3 and 7 respectively.

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Secretary of State Roxana Tillerson is worried about malpractice at the 4 processing centers for Green Cards in the country. Green Card applications are given a grade g on a scale 0-100. They are assigned randomly to different centers and thus Tillerson expects all centers to have similar mean scores. She collects the data in the table. #applications g 8g 9360 67.50 14.85 9870 67.17 15.10 0 1 2 3 7020 67.28 14.79 5040 66.77 15.16 4 rows x 3 columns At this point she just wants to decide whether or not to initiate a deeper investigation into malpractice at all sites. Does she have sufficient evidence for this, at 9% significance? SSTr number (rtol=0.01, atol=0.0001) SSE number (rtol=0.01, atol=0.0001) Fx number (rtol=0.01, atol=0.0001) P-val number (rtol=0.01, atol=0.0001) (a) Yes, she has enough evidence (b) No, she cannot make a conclusion Select the key assumptions in the test you used. (a) All the sampled data come from a uniform distribution. (b) The populations are independent and therefore their covariances are one. (c) All the sampled data come from a normal distribution. (d) The populations are independent and therefore their covariances are zero. (e) All sample sizes are equal ? ? ?

Answers

The p-value is 0.0388 at 9% significance, so (a) Yes, she has enough evidence with assumptions used in the test is (c) all the sampled data come from a normal distribution and (d) the populations are independent and therefore their covariances are zero.

How to determine whether the evidence is sufficient or not?

All data in attached table

First, we must calculate the grand mean. So,

Grand mean ([tex]\bar{\bar{g}}[/tex]) = [tex]\frac{\bar{g_{1}} + \bar{g_{2}} + \bar{g_{3}} + \bar{g_{4}}}{k}[/tex]

= (67.5 + 67.17 + 67.28 + 66.77) / 4

= 67.18

Next, we calculate SSTr

SSTr = [tex]\sum n_i(\bar{g_{i}} - \bar{\bar{g}})^2[/tex]

= 9360(67.5-67.18)^2 + 9870(67.17-67.18)^2 + 7020(67.28-67.18)^2 + 5040(66.77-67.18)^2

= 1,876.875

Then, we calculate SSE

SSE = [tex]\sum(n_i-1)Sg_i^2[/tex]

= (9360-1)(14.85^2) + (9870-1)(15.1^2) + (7020-1)(14.79^2) + (5040-1)(15.16^2)

= 7,007,556.804

Before we calculate F test, we first calculate the N value with this formula,

N = [tex]\sum n_i[/tex]

= 9360 + 9870 + 7020 + 5040

= 31,290

Then, for F test use this formula,

F = [tex]\frac{SSTr/(k-1)}{SSE/(N-k)}[/tex]

= [tex]\frac{1876.875/(4-1)}{7007556.804/(31290-4)}[/tex]

= 2.793

Next, for p-value we use p value calculator for f test with following data,

F-ratio value = 2.793

DF-numerator = k - 1 = 4 - 1 = 3

DF-denominator = N - k = 31290 - 4 = 31286

and we get the p-value is 0.0388

Since, 0.0388 < 9% of significance, so she has enough evidence to initiate a deeper investigation.

Thus, assumptions used in the test is all the sampled data is normal distribution and the population are independent with covariances are zero and the result is yes, she has sufficient evidence.

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Jar A contains 4 red marbles and 6 blue marbles. Jar B contains 8 red marbles and 2 blue marbles. (20 points) (a) How many ways are there to choose a marble from Jar A or Jar B? (b) How many ways are there to choose a marble from Jar A and Jar B? (C) How many ways are there to choose a red marble from Jar A and Jar B? (d) If you choose marbles from Jar A and Jar B at random, what is the probability that they are both red?

Answers

The probability of randomly getting the red marbles from both Jar A and Jar B is 8/25.

What do we mean by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, the probability that both marbles will be red is:

Probability formula: P(E) = Favourable events/Total events

We know that:

Jar A: 4 red marbles and 6 blue marbles

The probability of randomly choosing red marble is:

P(E) = Favourable events/Total events

P(E) = 4/10

P(E) = 2/5

Jar B: 8 red marbles and 2 blue marbles

The probability of randomly choosing red marble is:

P(E) = Favourable events/Total events

P(E) = 8/10

P(E) = 4/5

So, the total probability will be:

2/5 * 4/5

8/25

Therefore, the probability of randomly getting the red marbles from both Jar A and Jar B is 8/25.

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Correct question:

Jar A contains 4 red marbles and 6 blue marbles. Jar B contains 8 red marbles and 2 blue marbles. (20 points) If you choose marbles from Jar A and Jar B at random, what is the probability that they are both red?

Find:

11/3÷2/3

the question is five and

Answers

Answer:

[tex]\dfrac{11}{2}[/tex] or [tex]5 \, \dfrac{1}{2}[/tex]

Step-by-step explanation:

Division of fractions can be represented as multiplication by one of the fractions' reciprocal. (Skip, Flip, and Multiply)

So,

[tex]\dfrac{11}{3} \div \dfrac{2}{3} = \dfrac{11}{3} \times \dfrac{3}{2}[/tex]

And we can simplify this to:

[tex]\dfrac{11}{2}[/tex] or [tex]5 \, \dfrac{1}{2}[/tex]

Monique and Tara each make an ice-cream undae. Monique get 2 coop of Cherry ice-cream and 1 coop of Mint Chocolate Chunk ice-cream for a total of 60g of fat. Tara ha 1 coop of Cherry and 2 coop of Mint Chocolate Chunk for a total of 87g of fat. How many gram of fat doe 1 coop of each type of ice cream have?

Answers

 The factors in the word problem for the amount of fat in the ice cream

combination are given by the fat in each constituent.

The amount of fat in Cherry ice-cream is 11 grams.

The amount of fat in the Mint Chocolate Chunk ice-cream is 16 grams.

Reasons:

The given parameters are;

Let C represent the amount of fat in Cherry ice-cream, and let M represent

the amount of fat in Mint Chocolate Chunk ice-cream, we get;

4·C + M = 60...(1)

C + 4·M = 75...(2)

Multiplying equation (1) by 4 and then subtracting equation (2) from the

result gives;

4 × (4·C + M) = 4 × 60

16·C + 4·M = 240...(3)

(16·C + 4·M) - (C + 4·M) = 240 - 75

15·C = 165

The amount of fat in Cherry ice-cream C = 11 grams

4 × 11 + M = 60

M = 60 - 4 × 11 = 16

The amount of fat in the Mint Chocolate Chunk ice-cream, M = 16 grams

the surface area of a rectangular box is given by the polynomial 2hl 2lw 2hw and is measured in square units. a rectangular box is to be constructed for shipping materials. the box is to have dimensions of 5 inches by 3 inches by 7 inches. find the surface area of the box.

Answers

Surface area of the box measuring 5 inches by 3 inches by 7 inches is 142 square inches.

What is surface area ?

The surface area of the object that refers to the overall space that is filled by its surfaces. Different 3D shapes in the geometry have various surface areas, which can be quickly estimated using the formulas. Two categories are used to classify the surface area:

Curved surface area or Lateral surface area

Surface area in total

Surface area of rectangle = 2 ( lb + bh + hl )

Dimensions of box = 5 inches by 3 inches by 7 inches

Hence,

Length = 5 inches

Breadth = 3 inches

Height = 7 inches

By putting it in formula of surface area of rectangle

= 2 ( lb + bh + hl )

= 2 ( 5*3 + 3*7 + 7*5 )

= 2 ( 15 + 21 + 35 )

= 2 * 71

 = 142 square inches

Hence, the total surface area of the box is 142 square inches.

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s It is required to set a stake to mark a grade of 45.49 ft. The Hl of the level is 53.56 ft and the rod on stake reads 4.32 ft. Determine the amount of cut (C) or fill(F) to be marked on the stake. cut 8.07 ft O fill 8.07 ft cut 3.75 Ft fill 3.75 Ft

Answers

The correct option is option C i.e. the amount of cut (C) to be marked on the stake is equivalent to 3.75 Ft.

Given that:

It is required to set a stake to mark a grade of 45.49 ft.

i.e. required grade = 45.49 ft

The Hl of the level is 53.56 ft

i.e. HI =  53.56 ft

the rod on the stake reads 4.32 ft.

i.e. Stake reading =  4.32 ft

We know that,

The formula for cut/fill is:

Cut/Fill = HI – Stake reading – required grade

Cut/Fill = 53.56 ft - 4.32 ft - 45.49 ft

Cut/Fill = 53.56 ft - 49.81 ft

Cut/Fill = 3.75 ft

As the value is positive therefore this amount is for cut and not the amount of fill.

The amount of cut (C) to be marked on the stake is 3.75 Ft.

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a lottery offers one $1000 prize, one $500 prize, and eight $100 prizes. one thousand tickets are sold at $4.00 each. find the expectation if a person buys five tickets.

Answers

Answer:

he would have a 50% chance of getting one of the 10 prizes

Evaluate:
please help fast

Answers

Answer: 256

Step-by-step explanation:

8^8/3 is the same as an 8 square root! We have to factor out and I get 2^8 after finish factor the smallest number and get 256!

american express executives hypothesize that 40% of college students own an american express credit card. testing this hypothesis is an example of

Answers

Testing the hypothesis "Americans express executives hypothesize that 40% of college students own an Americans express credit card." is an example of generalizing.

What is hypothesis?

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge. A straightforward hypothesis only hypothesizes the relationship between two independent and dependent variables.

An example of testing a generalization is "American Express executives' hypothesis that 40% of college students own an American Express credit card."

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which expression is equivalent to (1 tanθ)tan(2θ) for all values of θ for which (1 tanθ)tan(2θ) is defined?

Answers

The given expression of trigonometry is equivalent to cos(2θ).

What is trigonometric function ?

trigonometry capability, in math, one of six capabilities (sine [sin], cosine [cos], digression [tan], cotangent [cot], secant [sec], and co-secant [csc]) that address proportions of sides of right triangles. These six geometrical capabilities comparable to a right triangle.

According to question:

We have,

1 - tan^2(θ)/1 +  tan^2(θ)

Use 1 + tan^2(θ) = sec^2(θ)

1 - tan^2(θ)/ sec^2(θ)

1/ sec^2(θ) - tan^2(θ)/sec^2(θ)

Use tan(θ) = sin(θ)/cos(θ)

cos^2(θ) - sin^2(θ)×cos^2(θ)/cos^2(θ)

cos^2(θ) - sin^2(θ)

Using sin^(θ) + cos^2(θ) = 1

cos^2(θ) - (1 - cos^2(θ))

2cos^2(θ) - 1

Here we have 2cos^2(θ) - 1 = cos(2θ)

Then, simplification of given expression is cos(2θ).

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Correct question:

which expression is equivalent to 1 - tan^2(θ)/1 +  tan^2(θ) for all values of θ for which 1 - tan^2(θ)/1 +  tan^2(θ) is defined?

The radius of a circle is 10 feet. What is the area of a sector bounded by a 180° arc?

Answers

Answer:

50π feet^2

Step-by-step explanation:

area of the circle = 10^2 π = 100π feet^2

A of the sector = 100π/2 = 50π feet^2

(71+9+3)-(9-11+2) I really need help

Answers

Answer:  The correct answer is 83

Step-by-step explanation:

Complete the equations within each set of brackets

(71+9+3)-(9-11+2)

71+9+3 = 83

9-11+2 = 0

Subtract the results

83 - 0 = 83

a 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft . find the side length of the original cube. round your answer to two decimal places.

Answers

The side length of the original cube is, 8.60 feet.

What is volume?

The amount of three-dimensional space that is occupied is measured by volume. It is frequently expressed quantitatively using SI-derived units, other imperial units, or US customary units. Volume and the notion of length are connected.

Given:

A 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft^3.

Let x = the side of the cube then

x^3 = original volume of the cube and

8x^2 = volume of the 8 feet slice

Therefore,

x^3 - 8x^2 = 44

Subtract 44 on both sides,

x^3 - 8x^2 - 44 = 44 - 44

x^3 - 8x^2 - 44 = 0

After solving x ≈ 8.59553

⇒ x = 8.60

Hence, the side length of the original cube is 8.60 feet.

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Problem 9. Find the perimeter of quadrilateral PORS with the vertices P(-2-2), Q(-1,3), R(5,3), and S(4,-2)​

Answers

Answer:

Perimeter is 12+2√26

Step-by-step explanation:

Question:

The perimeter of quadrilateral PQRS with the vertices

P(-2, -2), Q(-1, 3), R(5, 3), and S(4, -2)​

Find distances PS and QR:

Notice the y-coordinates are the same for 2 pairs of points

P(-2, -2), S(4, -2)​ and Q(-1, 3), R(5, 3)

So the distance PS = |-2|+4= 6 and QR = |-1|+5 = 6

Find the distances PQ and SR:

Use the distance formula:

[tex]d= \sqrt{(x_{2}-x_{1} ) ^{2} + (y_{2}-y_{1} ) ^{2} }[/tex]

P([tex]x_{1}[/tex] = -2, [tex]y_{1}[/tex] = -2), Q( [tex]x_{2}[/tex] = -1, [tex]y_{2}[/tex] = 3)

PQ = [tex]\sqrt{(-1--2)^{2} +(3- -2)^{2} } = \sqrt{1^{2} +5^{2} } = \sqrt{26}[/tex]

SR = [tex]\sqrt{26}[/tex], because of PQ and SR are equal.

Find the perimeter of quadrilateral PQRS:

The perimeter is equal to the sum of all sides of the quadrilateral.

P= PS + QR + PQ + SR = 6+6+ √26 +√26 = 12+2√26

Plot the points (0, 6) and (3, 0). What is the slope?
6/-3
O 1/2
-1/2
6/3

Answers

Slope is "change in y over change in x".

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

Using those two points, you'd have

    [tex]m=\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{0-6}{3-0}=\dfrac{-6}{3}=-2[/tex]

Notice that doesn't match any of the listed answers.  The reason is that two of those answers aren't reduced.

If you reduce the first answer of [tex]\dfrac{6}{-3}[/tex], you have  [tex]\dfrac{6}{-3}=-2[/tex].  So that first answer is equivalent to the calculation above.

The answer from your list is the first one.

in the xy-plane, the line x y k   , where k is a constant, is tangent to the graph of 2 y x x    3 1. what is the value of k?

Answers

The value of k is -3.

What is a tangent line?

The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are endlessly close to one another.

Here, we have

Given

x + y = k

y = x² + 3x

slope of tangent line = dy/dx = 2x+3

k is y-intercept of the tangent line

2x+3 = -1

x = -2

y = (-2)^2+3(-2)+1 = -1

The tangent line passes through the point (-2,-1)

k = x+y

k = -2 -1

k = -3

Hence, the value of k is -3.

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Sarah can make 4 cards in 60 minutes. At this rate, how many cards will she make in
300 minutes?

Answers

Answer: 20 cards.

Step-by-step explanation: If Sarah can make 4 cards in 60 minutes, then she can make 1 card in 60/4 = 15 minutes.

Therefore, in 300 minutes, she can make 300/15 = <<300/15=20>>20 cards.

47. refer to exercise 46. suppose the distribution is normal (the cited article makes that assumption and even includes the corresponding normal density curve). a. how likely is it that the sample mean diameter exceeds 71 when n

Answers

The probability that the sample mean diameter surpasses 71 when n = 30 is 0.5 if the distribution is normal (the quoted article makes this assumption and even gives the related normal density curve).

The likelihood that the sample mean diameter exceeds 71 when n = 30 is 0.5, since the normal distribution is symmetric around the mean. This means that there is a 50% probability of the sample mean diameter being above the mean, and a 50% probability that it is below the mean.

The correct question is : suppose the distribution is normal (the cited article makes that assumption and even includes the corresponding normal density curve). a. how likely is it that the sample mean diameter exceeds 71 when n = 30

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