1. Calculate the angle between the unit tangent vector at each point of a curve \( X(t)=\left(3 t, 3 t^{2}, 2 t^{3}\right) \) and the plane \( x+z=0 \)

Answer: Trapezium

Step-by-step explanation:

Given

Quadrilateral has only 2 right angles and 1 pair of parallel sides. This is possible in case of trapezoid. Here, 2 non-parallel side are connected with parallel sides which forms right angle. This can be shown by the figure shown below.

If both triangles are similar the ratio of sides will be same

\(\\ \sf\longmapsto \frac{x}{24} = \frac{6}{12} \\ \\ \sf\longmapsto 12x = 6 \times 24 \\ \\ \sf\longmapsto 12x = 144 \\ \\ \sf\longmapsto x = \frac{144}{12} \\ \\ \sf\longmapsto x = 12\)

Answer:

the correct classification and decimal expansion of StartFraction 5 Over 8 EndFraction

=5/8=0.625[irrational number]

Answer:

The correct answer is (b) i believe

Step-by-step explanation:

   Have a great day!

Answer:

x = -2y+77

y =  -x/2+77/2

Step-by-step explanation:

The equation for x variable is x = 77 - 2y and for y variable it is; y =  77- x/2

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

WE have been given linear equation in two variables: 2x + 4y - 31 = 123.

Solve for x and for y

2x + 4y - 31 = 123.

Add 31 to both sides

2x + 4y - 31 + 31 = 123 + 31

2x + 4y = 154

Solving for x then Subtract 4y from both sides

2x + 4y -4y = 154 - 4y

2x = 154 - 4y

Divide by 2

x = 77 - 2y

y =  77- x/2

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Answer:

201.06

Step-by-step explanation:

A=πr2

R= 16/2= 4cm

A= 22/7 x 4 x 4

A= 201.06

The width of the rectangular garden is 21 feet.

A rectangle is a plane shape that have pair of opposite sides equal and parallel.

To calculate the width of the rectangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute into equation 1

Hence, the right option is D. 21 feet.

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Answer:

option a

Step-by-step explanation:

95 +x=180

x=180-95=85

85+31+y=180

116+y=180

y=180-116=64

Answer:

32. C

34.C

36. 2

Answer:

32. C, 34. C, 35. C, 36. 2 miles

Step-by-step explanation:

32. C because you can see the ratio is 7:1. There is only one answer that has a ratio of 7:1 which is C

34. C because the ratio of batches of cookies to cooking oil is \(1:\frac{2}{3}\) since you want 4 batches of cookies, multiply 4 by \(\frac{2}{3}\) to get C

35. C because the ratio of butter to sauce is \(\frac{2}{3}:2\frac{1}{2}\) multiply \(\frac{2}{3}\) by 4 to get C

36. 2 miles because the ratio of miles to hours is \(\frac{1}{2} :\frac{1}{4}\) multiply \(\frac{1}{2}\) by 4 to get 2 miles

144 feet squared

Squares are 4 sided shapes that have an equal length on each side.

Area Formula

The area of a square (or rectangle) is \(l*w\), where \(l\) is the length and \(w\) is the width. Due to the fact that squares have four equal sides, the formula can be rewritten as \(l^2\).

Solving For Area

Plug the length value into the formula.

Then, add the units to the answer. Because the length is multiplied by itself and the original unit is feet, the units are feet squared.

Answer:

First equation: 1/2

Second equation: -1/3

Step-by-step explanation:

We get the following equations:

\(\frac{1}{3}x+\frac{1}{6}y=2\)          first equation

\(\frac{1}{2}x+\frac{3}{4}y=-3\)       2nd equation

Then, to obtain opposite terms for the x variable, we need to identify the coefficient of the x for the 1st equation and the 2nd equation as:

The coefficient for x in the 1st equation is \(\frac{1}{3}\) and the coefficient for x in the 2nd equation is \(\frac{1}{2}\)

Finally, we need to multiply 1st equation with the coefficient of the 2nd equation and multiply the 2nd equation with the negative of the coefficient of the 1st equation.

We multiply by the negative of the coefficient of the 1st equation because we need to find opposite terms for x.

So, the first equation is equal to:

\((\frac{1}{3}x+\frac{1}{6}y)*\frac{1}{2} =2*\frac{1}{2} \\\frac{1}{6}x+\frac{1}{12}y=1\)        

The second equation is:

\((\frac{1}{2}x+\frac{3}{4}y)*\frac{-1}{3} =-3*\frac{-1}{3} \\\frac{-1}{6}x+\frac{-1}{4}y=1\)

Now, the coefficients for x, 1/6 and -1/6, are opposite terms.

Answer:3, -2

Step-by-step explanation:

To find two nonnegative numbers x and y such that xy = 162 and 4x +2y is minimized, we need to use the concept of the Arithmetic-Geometric Mean.The main answer is:x = 9√2y = 9/√2

Explanation: Arithmetic-Geometric Mean: Let a and b be positive numbers.The Arithmetic Mean (AM) is a + b / 2. The Geometric Mean (GM) is √ab.The Arithmetic-Geometric Mean is the following:a_n = (a_n−1 + b_n−1) / 2  b_n = √a_n−1 * b_n−1  a_0 = a  b_0 = b

Let's solve the problem using the Arithmetic-Geometric Mean.√(4xy) = √(4 * 162) = 36xy/36 = 162/36xy = 9√2 * 9/√2xy = 81The numbers that will minimize 4x + 2y are 4x = 36, and 2y = 18. Therefore, x = 9√2, and y = 9/√2

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Answer:

A. All real numbers.

Step-by-step explanation:

\(x + 4 = \frac{2x + 8}{2} \: \: multipling \: both \: sides \: by \: 2 \\ 2(x + 4) = 2x + 8 \\ 2x + 8 = 2x + 8\)

When you end up with a true statement like this, it means that the solution to the equation is “all real numbers”. Any value for x that you can think of will make this equation true.

Answer:

-2x = 4

Step-by-step explanation:

You have 2 negative x tiles on the left side, which is -2x.

You have 4 one tiles on the right side, which is 4.

Hope this helps!

Answer:

The Median is 75

Step-by-step explanation:

median is the middle number in a set of given numbers

arranging in order will be

30,64,70,80,90,110

the middle numbers are 70 and 80

Median=80+70/2

=150/2

Median=75

Answer:

Come on man you are in high school and you can't answer this?

Step-by-step explanation:

To write 0.45 as a common fraction, we can use the fact that the decimal point separates the whole number part from the fractional part. So we have:

0.45 = 45/100

To simplify this fraction, we can divide both the numerator and the denominator by the greatest common factor, which is 5:

45/100 = (45 ÷ 5) / (100 ÷ 5) = 9/20

Therefore, 0.45 written as a common fraction, in its simplest form, is 9/20.

The shortest length of fence that the rancher can use is 6000 ft.

What is meant by length?

The measuring of one thing from finish to finish or on its longest aspect, or a measuring of a selected a part of one thing is known as length.

Main Body:

x = width of rectangle

y = length of rectangle

A = area of rectangle = xy = 1500000 ft^2

L = length of fencing needed = 2(x + y) + x = 3x + 2y

L = 3x + 2(1500000/x) = 3x + 3(10^6)x^(-1)

As x –> 0+, L –> +inf.

As x –> +inf, L –> (3x)+.

Sketch and see that there will be a minimum in Quadrant I.

dL/dx = 3 - 3(10^6)x^(-2)

Extrema occur when dL/dx = 0:

3 - 3(10^6)x^(-2) = 0

(10^6)x^(-2) = 1

x^2 = 10^6

x > 0, so x = 1000 feet for shortest length.

Hence,Shortest L = 3000 + 3(10^6)(10^3)^(-1) = 6000 feet.

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Answer:

2400 inches cubed

Step-by-step explanation:

The formula for the volume of a rectangular prism is:

V=whl

------

So the formula is telling us to multiply the width, height, and length together. So in that case:

10 × 12 × 20 = 2400

------

Have a good day :)

Answer:

6

-1

y+1=2(x-6)

Step-by-step explanation:

Answer:

6

-1

y+1=2(x-6)

Step-by-step explanation:

Answer:

life is possible on earth due to layers of air that surround it

Step-by-step explanation:

as we have a point and the slope, we can start with the point-slope form and then transform.

the point-slope form is

y - y1 = a(x - x1)

(x1, y1) being a point on the line, a being the slope.

the slope-interceot form is

y = ax + b

a being the slope again, b being the y-intercept (the y value for x = 0).

so, we have

y - -5 = 5/2 × (x - -4)

y + 5 = 5/2 × (x + 4) = 5x/2 + 5×4/2 = 5x/2 + 10

y = 5x/2 + 5

or

y = (5/2)x + 5

and this is already the slope-intercept form. all done.

Answer: 50%.

Step-by-step explanation: If someone went shopping for a scooter and it was $49.99 dollars but saw a skateboard for $14.99, they would choose the skateboard because it’s cheaper. If someone else went to the store because they wanted a skateboard but then they saw a scooter for $23.99 and a bike for $19.99 there is a 50% chance they will choose the cheaper one. (I hope this ,add sense

The probability is given by the equation P = 12.3 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability of choosing a person that has a scooter and then choosing another person sequentially who has a skateboard and bicycle be P

Now , the equation will be

Let the probability of selecting a person owing a scooter A = 30 %

Let the probability of selecting a person owing a scooter A = 0.3

Let the probability of selecting a person owing a skateboard and bicylce be B = 41 %

Let the probability of selecting a person owing a skateboard and bicylce be B = 0.41

Now ,

Probability of choosing a person that has a scooter and then choosing another person sequentially who has a skateboard and bicycle P = probability of selecting a person owing a scooter A x probability of selecting a person owing a skateboard and bicylce B

Substituting the values in the equation , we get

Probability of choosing a person that has a scooter and then choosing another person sequentially who has a skateboard and bicycle P = A x B

Probability of choosing a person that has a scooter and then choosing another person sequentially who has a skateboard and bicycle

P = 0.3 x 0.41

P = 0.123

Hence , the probability is P = 12.3 %

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Let's call the length of the rectangle "L" and the width "W". We know that the width is 10 cm shorter than the length, so we can write.

W = L - 10
We also know that the area of the rectangle is 200 cm 2, so we can write:
A = L x W
Substituting W = L - 10, we get:
A = L x (L - 10)
Expanding the brackets, we get:
A = L^2 - 10L
Now we can substitute in A = 200 and solve for L:
200 = L^2 - 10L
0 = L^2 - 10L - 200
We can use the quadratic formula to solve for L:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = -10, and c = -200. Plugging in these values, we get:
L = (10 ± sqrt(10^2 - 4(1)(-200))) / 2(1)
L = (10 ± sqrt(1100)) / 2
L = (10 ± 10sqrt(11)) / 2
L ≈ 19.9 or L ≈ -9.9
We can disregard the negative solution since we're dealing with lengths, so the length of the rectangle is approximately 19.9 cm.
Now we can use W = L - 10 to find the width:
W = 19.9 - 10
W ≈ 9.9 cm
Therefore, the length of the rectangle is approximately 19.9 cm and the width is approximately 9.9 cm.

To find the length and width of a rectangle whose width is 10 cm shorter than its length and whose area is 200 cm², follow these steps:
1. Define the variables: Let the length of the rectangle be L cm, and the width be W cm.
2. Use the given information: Since the width is 10 cm shorter than the length, we can write the equation W = L - 10.
3. Use the formula for the area of a rectangle: The area of a rectangle is given by the formula A = L × W.
4. Substitute the given area and the equation from step 2: In this problem, the area is 200 cm², so we have 200 = L × (L - 10).
5. Solve the equation for L: Expand the equation to get 200 = L² - 10L. Rearrange the equation to L² - 10L - 200 = 0.
6. Factor the quadratic equation or use the quadratic formula: (L - 20)(L + 10) = 0. This gives two possible values for L: L = 20 cm or L = -10 cm.
7. Discard the negative value: Since the length of a rectangle cannot be negative, we discard the value L = -10 cm. So, the length L is 20 cm.
8. Find the width using the equation from step 2: W = L - 10 = 20 - 10 = 10 cm.
Thus, the length and width of the rectangle are 20 cm and 10 cm, respectively.

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Answer:

Keep in mind the rules.

When we multiply terms with same bases we keep one base and add the exponents.

Step-by-step explanation:

The service life that appear to be out of control is 0.0456 as per the given sample service life.

The sample standard deviation is the root-mean square of the discrepancies between observations and the sample mean: A large divergence is defined as two or more standard deviations from the mean.

The sample standard deviation (s) is the square root of the sample variance and a measure of the deviation from expected values.

It is given that,

Rationale:

UCL=520

LCL=480

Mean \(\bar{x}\)=500

The standard deviation of sample(\(S_{n}\))=11.55

Z(for UCL)=(UCL-Mean)/\(S_{n}\)

=(520-500)/10

=2

Similarly, Z(for LCL)=(LCL-Mean)/\(S_{n}\)

==(480=500)/10

=-2

Now, by using the z table for finding the confidence level between the Z value of -2 and 2.

Therefore, confidence level=0.4772+0.4772

=0.9544

Risk(alpha)=1-confidence level

=1-0.9544

=0.0456

The service life that appear to be out of control is 0.0456 as per the given sample service life.

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Answer:

here you go! 36

Step-by-step explanation:

Answer:

I have researched a bit on it and I think the answer is A but if I am wrong I am sorry I really tried and I am just trying to get done with my question and I did not guess I promise.

The value of the two identical charges are 1.19 μC.

In Mathematics, the electrostatic force (F) between two (2) charges can be calculated by using the following formula:

\(F = k\frac{q_1q_2}{r^2}\)

Where:

Since the two charges are identical charges, the electrostatic force would act along the line joining these two charges i.e q₁ = q₂.

By substituting the given parameters into the formula, we have;

\(F = k\frac{q^2}{r^2}\\\\q= \sqrt{\frac{Fr^2}{k} } \\\\q = \sqrt{\frac{0.08 \times (\frac{40}{100}) ^2}{9.0 \times 10^9} }\\\\q = \sqrt{\frac{0.08 \times 0.16 ^2}{9.0 \times 10^9} }\)

q = 1.19 × 10⁻⁹ C.

Note; 1 μ is equal to 1 × 10⁻⁹ C.

q = 1.19 μC.

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Complete Question:

Two identical charges experience a repulsive force on each other of 0.08 N when they are separated in a vacuum by a distance of 40 cm. What is the value of the charges?

Total number of items are 11412.

Let's use the variable s to represent the number of snacks that Hannah bought, and let's use the variable d to represent the number of drinks that she bought.

We can then use this information to set up a system of equations:

s + d = total number of items

2.4s + 3.75d = total cost

We know that the total cost is $47.55, so we can substitute that value in for "total cost" and simplify:

s + d = total number of items

2.4s + 3.75d = 47.55

We also know that each snack costs $2.4 and each drink costs $3.75, so we can set up another equation to represent the total number of items in terms of s and d:

Total number of items = s + d

Now we can substitute the expression for the total number of items into our second equation:

2.4s + 3.75d = 47.55

Simplifying this equation, we can multiply both sides by 100 to get rid of the decimals:

240s + 375d = 4755

Now we have two equations with two variables:

s + d = total number of items

240s + 375d = 4755

We can solve this system of equations by using substitution or elimination.

For simplicity, let's use substitution:

s + d = total number of items

s = total number of items - d (from the first equation)

Substituting the expression for s into the second equation:

240s + 375d = 4755

240(total number of items - d) + 375d = 4755

Expanding and simplifying:

240total number of items - 240d + 375d = 4755

240total number of items + 135d = 4755

240total number of items = 4755 - 135d

Total number of items = (4755 - 135d)/240

We know that,

The total number of items must be a whole number, so we can use this expression to find possible values for d:

Total number of items = (4755 - 135d)/240

Total number of items = s + d

Substituting the expression for s + d:

Total number of items = s + d

(4755 - 135d)/240 = s + d

We also know that,

Each d represents a drink, which costs $3.75.

So the total cost of the drinks is:

Total cost of drinks = 3.75d

We can substitute this expression into the equation for the total cost:

2.4s + 3.75d = 47.55

Substituting the expression for s:

2.4(total number of items - d) + 3.75d = 47.55

Simplifying:

2.4 Total number of items - 2.4d + 3.75d = 47.55

2.4 Total number of items + 1.35d = 47.55

2.4 Total number of items = 47.55 - 1.35d

Total number of items = (47.55 - 1.35d)/2.4

Now we can set these two expressions for the total number of items equal to each other:

(4755 - 135d)/240 = (47.55 - 1.35d)/2.4

Cross-multiplying and simplifying:

(4755 - 135d) x 2.4 = (47.55 - 1.35d) x 240

11412.

Total number of items are 11412.

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Answer:

-4 - (-9) = 5

4- (-3) = 7

Answer:

<P = 56 degrees

Step-by-step explanation:

Given the following

m<R = 90 degrees

QR = 61feet = Adjacent

RP = 90 feet= Opposite

Required

tan<P = opp/adj

Tan<P = 90/61

<P = arc tan (90/61)

<P = arctan 1.4754

<P = 55.9

<P = 56 degrees to the nearest degree