Determine whether the lines
x = 2t + 1, y = t − 2, z = 9t + 1, and x = 2s − 1, y = s − 3, z = s
intersect.

Answer:

-3

Step-by-step explanation:

h(k(2)) = h(k(x=2)) = h(-2) = h(x= -2)= 3/( -2+1) = 3/-1= -3

sorry if I'm wrong.

Answer:

Step-by-step explanation:

Standard form is:

Given

Converting to standard form

Correct option is the first one

In example 4.3, the probability that Gary is not in a glum mood on any of the following three days is 0.729.

The probability of an event occurring is given by:

P(event) = number of favorable outcomes / total number of possible outcomesIn this case, the probability that Gary is not in a glum mood on any of the following three days is the same as the probability that he is in a cheerful mood for all three days.

Since the probability of Gary being in a cheerful mood on any given day is 0.9, the probability that he is in a cheerful mood for all three days is:

P(all 3 days) = 0.9 x 0.9 x 0.9 = 0.729

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However, in some cases, the default location of the click point may be set by default to the top-left corner of the screen or window, which would correspond to the coordinate (0, 0) in a Cartesian coordinate system.

If no coordinates have been assigned to the cursor, the default location of the click point will depend on the program or application being used. In most cases, the default location will be the center or starting position of the screen or window in which the program is running, which could be any location on the screen. Therefore, none of the options provided is necessarily correct.

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Answer:

perpendicular

They are neither parallel nor perpendicular as they have different slopes.

First line equation in form of y = mx +c is:

y = (4x-4)/5

and second line equation is :

y= -((10x+1)/8)

Based on the analysis, none of the given functions are concave down over the set of non-negative real numbers.

To determine which of the given functions are concave down over the set of non-negative real numbers, we need to examine the second derivative of each function.

Let's calculate the second derivative for each function:

Of(x) = 2:

The second derivative of Of(x) = 2 is zero because it is a constant. Therefore, it is neither concave up nor concave down.

f(x) = x²:

The second derivative of f(x) = x² is f''(x) = 2, which is a positive constant. Therefore, it is concave up, not concave down.

Of(x) = 3x + 2:

The second derivative of Of(x) = 3x + 2 is zero because it is a linear function. Therefore, it is neither concave up nor concave down.

Of(x) = x³:

The second derivative of Of(x) = x³ is f''(x) = 6x, which is positive for x > 0. Therefore, it is concave up, not concave down.

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Answer:

7392 pounds

Step-by-step explanation:

22x24x14

multiplication my friend

Answer:

24 pounds of garlic

Step-by-step explanation:

if she spends 3$ per pound, you divide 72 by 3. the answer to that is 24, so if she spends 72 dollars on only garlic, she can buy 24 pounds.

Jennifer can buy 24 pounds of garlic

we see here, that if she spends 3$ per pound, you divide 72 by 3.

The answer would be 24, so if she spends 72 dollars on only garlic,

she can buy 24 pounds.

1: any of various units of mass and weight specifically: a unit now in general use among English-speaking peoples equal to 16 avoirdupois ounces or 7000 grains or 0.4536 kilogram — see Weights and Measures Table

2: the basic monetary unit of the United Kingdom.

In maths, a division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each

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1) Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. 2) The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. 3) trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

1. Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. Therefore, the ratios of the sine, cosine, and tangent of the corresponding angles in similar triangles will also be equal.

2. The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. This means that the sine of an angle is equal to its complement's cosine, and vice versa.

3. Using the appropriate formula based on the given information, trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

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Answer:

This question can be solved using direct and inverse variation. Direct variation can be solved using unitary method that is common sense like if you buy 10 chocolates for 100 rupees how many rupees would you pay for 20 - this is simple as if 10 chocolates is 100 then 20 would be 200. HOWEVER,  Inverse Variation is when one value increase the other value decreases and they are proportional. They have a formula called x1/x2 = y2/y1.

In this problem we can use this formula, x1/x2 = 15/42 and y2/y1 = 30/x

so hence 15/42 = 30/x

= 15x = 30*42

x= 1260/15

 = 84

Therefore 84 is the answer.

Answer: t = 7.85seconds

Step-by-step explanation:

Given that :

Height of tower = 986 Feets

Function s(t) = 16t^2

To find the time t 8 in Seconds taken for an object to fall to the ground from the top of the​ building

16t^2 = 986

t^2 = 986/16

t ^2 = 61.625

Take the square root of both sides

t = sqrt(61.625)

t = 7.85seconds

Answer:

7.85sec

Step-by-step explanation:

Given that,

s(t)=16t squared​, where t is time in seconds. The height of a certain tower is 986 feet.

s(t) = 16t²

so when s = 986feet

16t² = 986 feet

t² = 986 /  16

t² = 61.625

t = √61.625

t= 7.85 seconds

Answer:

$6

Step-by-step explanation:

Answer:

826

Step-by-step explanation:

82.6 x 10 to the power of 2 :

8.26 * 10^2

8.26 * (10 * 10)

8.26 * (100)

= 826

Answer:

Shaded area= 5.14 cm² (3 s.f.)

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

$2278.50

Step-by-step explanation:

Answer:

9.3%

Step-by-step explanation:

10/50= 0.20 or 20%

14/30= 0.4667 or 46.6%

0.20•0.4667=0.09333 or 9.3%

(i) The dual of the given LP problem can be found by following these steps:

1. For each constraint in the primal problem, create a dual variable. In this case, we have three constraints, so we'll have three dual variables: y1, y2, and y3.
2. The objective function of the dual problem will be the sum of the products of the primal variables and their corresponding dual variables. So, the dual objective function is:
  Maximize w = 3y1 + 2y2 + y3.
3. For each primal variable x, create a constraint in the dual problem with the coefficient of the corresponding dual variable equal to the coefficient of x in the primal objective function. So, the dual constraints are:
  y1 + 2y2 - y3 ≤ -2
  y1 + y2 + y3 ≤ -1
  y1, y2, y3 ≥ 0.

(ii) To find the optimal solution to the dual problem, we need to solve the optimal tableau of the dual problem. From the given information, we know that Row 0 of the optimal tableau is:
  w = 4x1 + e2 + (M-1)a2 + (M+2)a3 = 0.
 
  However, the given information does not provide any details about the values of x1, e2, a2, or a3. Therefore, without this information, we cannot determine the specific optimal solution to the dual problem.

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The recipe for the waffles presented using rational numbers are as follows;

1. The recipe for 2 waffles is as follows;

\( \displaystyle \frac{3}{5} \) cups of flour

\( \displaystyle \frac{2}{15} \) teaspoon of salt

\( \displaystyle \frac{4}{5} \) teaspoons of baking powder

\( \displaystyle \frac{7}{20} \) Cups of milk

\( \displaystyle \frac{1}{15} \) Cup of butter

2. The recipe for 5 waffles is as follows;

\( \displaystyle 1\frac{1}{2} \) cups of flour

\( \displaystyle \frac{1}{3} \) teaspoon of salt

\( \displaystyle 2 \) teaspoons of baking powder

\( \displaystyle \frac{7}{8} \) Cups of milk

\( \displaystyle \frac{1}{6} \) Cup of butter

3. The recipe for 300 waffles is as follows;

900 cups of flour

200 teaspoon of salt

1200 teaspoons of baking powder

525 Cups of milk

100 Cup of butter

4. The required number of waffle irons is 50

5. It would take approximately 6 servers

It would take 34 trips

A rational number is one that can be expressed as a fraction.

From the given table, we have;

The recipe for 10 waffles includes;

3 cups of flour

\( \displaystyle \frac{2}{3} \) teaspoon of salt

4 teaspoons of baking powder

\( \displaystyle 1\frac{3}{4} \) Cups of milk

\( \displaystyle \frac{1}{3} \) Cup of butter

1. To make 2 waffles, we have;

\( \displaystyle 2 = \frac{10}{5} \)

Dividing each of the quantities required to make 10 waffles by 5 gives;

\( \displaystyle \frac{3}{5} \) cups of flour

\( \displaystyle \frac{2}{3 \times 5} = \frac{2}{15} \) teaspoon of salt

\( \displaystyle \frac{4}{5} \) teaspoons of baking powder

\( \displaystyle \frac{1\frac{3}{4}}{5} = \frac{7}{20} \) Cups of milk

\( \displaystyle \frac{\frac{1}{3}}{5} = \frac{1}{15} \) Cup of butter

2. If each person gets 1 waffle, we have;

Number of waffles = 1 + 4 = 5

\( \displaystyle 5 = \frac{10}{2} \)

Dividing the recipe for 10 waffles by 2 gives;

\( \displaystyle \frac{3}{2} = 1\frac{1}{2} \) cups of flour

\( \displaystyle \frac{2}{3 \times 2} = \frac{1}{3} \) teaspoon of salt

\( \displaystyle \frac{4}{2} = 2 \) teaspoons of baking powder

\( \displaystyle \frac{1\frac{3}{4}}{2} = \frac{7}{8} \) Cups of milk

\( \displaystyle \frac{\frac{1}{3}}{2} = \frac{1}{6} \) Cup of butter

3. When each of 300 people can have one, the number of waffles is 300, which gives;

30 × 10 = 300

Multiplying the quantity of each ingredients required to make 10 waffles by 300 gives;

300× 3 = 900 cups of flour

\( \displaystyle 300 \times \frac{2}{3} = 200 \) teaspoon of salt

300 × 4 = 1200 teaspoons of baking powder

\( \displaystyle 300 \times 1\frac{3}{4} = 525 \) Cups of milk

\( \displaystyle 300 \times \frac{1}{3} = 100 \) Cup of butter

4. Time it takes to cook a waffle = 10 minutes

Number of waffles required = 300

Time allowed = 1 hour = 60 minutes

The number of waffle iron is therefore;

\( \displaystyle {n = \frac{300 \times 10}{60} = 50} \)

The number of waffle irons required is 50 waffle irons

5. Number of waffles each server can deliver = 9 waffles

The time it takes each server per trip = 10 minutes

Number of waffles to be delivered = 300

Time in which to deliver the 300 waffles = 1 hour

The number of servers is therefore;

\( \displaystyle {n = \frac{300}{9 \times 6} = 5. \overline 5 \approx 6} \)

The number of trips is therefore;

5 servers will deliver 5×9×6 = 270

The sixth server will deliver the remaining 300 - 270 = 30 waffles in 30 ÷ 9 = 3.3 ≈ 4

The number of trips all together is therefore; 5×6 + 4 = 34 trips

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The product of the radii of two circles tangent to a common external line can be determined from the length of the line.

Let the radii of the two circles be r1 and r2, where r1 > r2. When a common external line is tangent to both circles, it forms two right triangles with the radii of the circles as their hypotenuses. The length of the common external line is the sum of the hypotenuse lengths, which is given as 8. Therefore, we have r1 + r2 = 8.

To find the product of the radii, we need to eliminate one of the variables. We can square the equation r1 + r2 = 8 to get (r1 + r2)^2 = 64. Expanding this equation gives r1^2 + 2r1r2 + r2^2 = 64.

Now, we can subtract the equation r1 * r2 = (r1 + r2)^2 - (r1^2 + r2^2) = 64 - (r1^2 + r2^2) from the equation r1^2 + 2r1r2 + r2^2 = 64. Simplifying, we get r1 * r2 = 64 - 2r1r2.

Therefore, the product of the radii of the circles is given by r1 * r2 = 64 - 2r1r2.


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Answer:

7/5

Step-by-step explanation:

If he starts with 3/5 of the new set, then he begins with 3/5

After adding 4/5 of the new set, you add his current stamps with the new stamps, 3/5 + 4/5 , which results in 7/5

\(\\ \tt\Rrightarrow 15^2\times 3^2\div \sqrt[3]{125}+9^3\)

\(\\ \tt\Rrightarrow 3^25^2\times 3^2\div 5^1+3^33^3\)

\(\\ \tt\Rrightarrow 3^45^1\div 3^6\)

\(\\ \tt\Rrightarrow 3^{-2}5\)

\(\\ \tt\Rrightarrow \dfrac{1}{3^2}5\)

\(\\ \tt\Rrightarrow \dfrac{5}{9}\)

N(x, y, z) = [-1, √3, 2] . [x - √3/2, y + 1/2, z - √3] = 0and O(x, y, z) = [-2√3, -2, 4√3] . [x - √3/2, y + 1/2, z - √3] = 0 respectively.

The equations of the normal plane and osculating plane of the curve at the given point are given by N = 0 and O = 0.

Here is the step-by-step explanation for finding equations of the normal plane and osculating plane of the curve at the given point for X= sin 2t, y=-c0s 2t, z =(0, 1, 2x) and 150:

Given that X= sin 2t, y=-c0s 2t, z =(0, 1, 2x) and t = 150.

Let us first find the first derivative of the given function.

f (t) = [X(t), Y(t), Z(t)] = [sin 2t, -cos 2t, 2 sin 2t]f'(t) = [2 cos 2t, 2 sin 2t, 4 cos 2t]

Again, let us find the second derivative of the given function.

f''(t) = [-4 sin 2t, 4 cos 2t, -8 sin 2t]At t = 150, we have

f'(t) = [2 cos 300, 2 sin 300, 4 cos 300] = [-1, √3, 2]f''(t) = [-4 sin 300, 4 cos 300, -8 sin 300] = [-2 √3, -2, 4 √3]

At the given point [X(150), Y(150), Z(150)] = [sin 300, -cos 300, 2 sin 300] = [√3/2, -1/2, √3]

The equation of the normal plane can be found as

N(x, y, z) = [f'(150)] . [x - X(150), y - Y(150), z - Z(150)] = 0[-1, √3, 2] . [x - √3/2, y + 1/2, z - √3] = 0

The equation of the osculating plane can be found as

O(x, y, z) = [f''(150)] . [x - X(150), y - Y(150), z - Z(150)] = 0[-2√3, -2, 4√3] . [x - √3/2, y + 1/2, z - √3] = 0

Hence, the equations of the normal plane and osculating plane of the curve at the given point are given by

N(x, y, z) = [-1, √3, 2] . [x - √3/2, y + 1/2, z - √3] = 0and O(x, y, z) = [-2√3, -2, 4√3] . [x - √3/2, y + 1/2, z - √3] = 0 respectively.

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Answer:

part A . 61.5$

Step-by-step explanation:

total amount = $2400+$385-$940

= 1845$

average change per day = 1845÷

30

answer is 61.5

Answer:

  about 3.08 L

Step-by-step explanation:

You want the number of litres in the volume of a cylindrical can 14 cm in diameter and 20 cm high.

A litre is a cubic decimeter, 1000 cubic centimeters. As such, it is convenient to perform the volume calculation using the dimensions in decimeters:

The volume of the cylinder is given by the formula ...

  V = (π/4)d²h . . . . . . . where d is the diameter and h is the height

  V = (π/4)(1.4 dm)²(2.0 dm) ≈ 3.079 dm³ ≈ 3.08 L

The cylindrical can will hold about 3.08 litres.

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The nth term rule for the given sequence is -2n - 0.6.

In the given sequence, we observe that each term is decreasing by 1.8 as we move from one term to the next. The common difference between consecutive terms is -1.8.

To find the nth term rule, we can express the general term as a function of n. Let's denote the nth term as Tn. We can express the relationship between the term number (n) and the value of the term (Tn) as:

Tn = an + b

Since the common difference between consecutive terms is -1.8, we have a = -1.8. To determine the value of b, we can substitute any term from the sequence. Let's use the first term (-0.6):

-0.6 = -1.8 * 1 + b

Solving for b, we find b = 1.2.

Therefore, the nth term rule for the given sequence is Tn = -1.8n + 1.2, which can be simplified as -2n - 0.6.

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Answer:

o {5, 6, 7, 8}

Step-by-step explanation:

To find P'

P' = U - P

P' = {1, 2, 3, 4, 5, 6, 7, 8} - {1, 2, 3, 4}

P' = {5, 6, 7, 8}  ANS.

The chance of the event B is 0.4 when using the probability for the two independent two event formula.

In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).

Events classified as independent do not depend on other events for their occurrence.

Event A's likelihood of happening is P(A)=0.65.

The likelihood of the two events A and B intersecting is P(A∩B)=0.26.

Given that the likelihood of the two independent events is:

P(A∩B) = P(A)⋅P(B)

Then the probability of the event B will be,

P(B) = P(A)/P(A∩B)

P(B) = 0.65/0.26

P(B) =0.4

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