larry invested 27000 in a savings account that pays an annual rate of 1.8%. the savings accounts is set to compound quarterly (4times per year) how much is in larry’s account after 5 years

a) The parametric equations of the line are: x(t) = −2 + 3t, y(t) = 4 − 2t, z(t) = 3 + 4t and The symmetric equation of the line are: (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) The line intersects yz-plane at (0, 8/3, 17/3)

The given points on the line are:

(x₁, y₁, z₁) = (−2, 4, 3)

(x₂, y₂, z₂) = (1, 2, 7)

The direction ratios of this line are:

⟨a, b, c⟩ = ⟨x₂ − x₁, y₂ − y₁, z₂ − z₁⟩

             = ⟨1 + 2, 2 − 4, 7 − 3⟩

             = ⟨3, −2, 4⟩

a) Parametric equations of the line:

These are given by:

x(t) = x₁ + at = −2 + 3t

y(t) = y₁ + bt = 4 − 2t

z(t) = z₁ + ct = 3 + 4t

Symmetric equation of the line:

This is given by:

              (x − x₁)/a = (y − y₁)/b = (z − z₁)/c

              (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) When a line intersects the yz-plane, its x-coordinate is zero.

Using the parametric equations of the part (a):

                                   x = 0

                          −2 + 3t = 0

                                  3t = 2

                                    t = 2/3

Substitute this in the parametric equations corresponding to y and z as well:

                                   y = 4 −2t

                                      = 4 − 2(2/3)

                                      = 8/3

                                   z = 3 + 4t

                                      = 3 + 4(2/3)

                                      = 17/3

Hence, the required point is: (x, y, z) = (0, 8/3, 17/3)

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Answer:

The distance between Garland and Mansfield on the map is 15 inches.

Step-by-step explanation:

On Giana's map of Texas, the scale is 1 inch = 3.5 miles. To determine the distance between Garland and Mansfield on the map, we can use the scale to find the corresponding measurement. Given that the actual distance between these two cities is 52.5 miles, we can set up a proportion:

1 inch / 3.5 miles = x inches / 52.5 miles

Cross-multiplying, we have:

3.5 miles * x inches = 1 inch * 52.5 miles

3.5x = 52.5

Dividing both sides by 3.5, we find:

x = 15

Therefore, the distance between Garland and Mansfield on the map is 15 inches.

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Answer:

16

Step-by-step explanation:

1x to 2x ratio

total is 24 oz, aka 3x or 1x+2x

24oz=3x

do some math

x=8oz

raisins = 2x = 16 oz

Answer:

Step-by-step explanation: 2x-16 oz

Answer:

C) 27.5

Step-by-step explanation:

C) 27.5

1)

Looking at the question, the given information about corresponding parts is that the corresponding sides are parallel.

2)

Since we don't have information about the length of any side, so the only theorem that may be used is AA case (angle-angle). Since we have parallel lines, we can try to find corresponding or alternate angles, since they are congruent angles.

3)

We need at least two pairs of congruent angles in the triangles.

4)

If we take two pairs of parallel sides, we can create a parallelogram. Since opposite sides in a parallelogram are congruent, so the angle created by adjacent sides in a triangle will be congruent to the angle created by the corresponding parallel sides in the other triangle.

This way, we can prove that each corresponding angles are congruent, therefore proving the similarity with AA case.

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

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Answer:

C. The difference of the two means is not significant, so the null hypothesis must be rejected

Step-by-step explanation:

According to the Question,

Given, The difference of sample means of two populations is 55.4, and the standard deviation of the difference of sample means is 28.1 .

Now, if we are testing the null hypothesis at the 95% confidence level .

Answer:

Step-by-step explanation:

You can get 10 with a pair of dice with:
4 + 6, 6 + 4, 5 + 5

out of a possibile 36 results

There are 52 cards in a standard deck of cards. Reds make up half of them (hearts and diamonds) , meaning theres a 50/50 chance of pulling red

10/36 * 1/2 = 5/36 chance of throwing 10 + pulling red

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:56

Step-by-step explanation:

the answer is 56 because when u multiple all of them  together the answer is 56

2x2=4

2x7=14

14x4=56

i hope this helps

Answer:

90

Step-by-step explanation:

Because angles opposite congruent angles in a triangle are congruent, the triangle is isosceles.

The altitude drawn from the vertex angle of an isosceles triangle is the perpendicular bisector to the side it is drawn.

So, y=90.

Answer:

0

Step-by-step explanation:

By the remainder theorem, this is the same as finding f(-1/2), which is equal to 0.

Step-by-step explanation:

Let X be a random variable with PDF given by

fX(x)={ cx2 |x|≤1 0 otherwise

Find the constant c.

Find EX and Var(X).

Find P(X≥

1

2

).

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

160

Step-by-step explanation:

20 x 2 = 40

40 x 2 = 80

80 x 2 = 160

It stops at 3 years.

Answer:

120

Step-by-step explanation:

20+40+60 = 120

If we double it, we have to keep adding 20 each year and stop at 3 so the answer is 120

Answer:

1/6 or 16.666%

Step-by-step explanation:

8/48 and there is your answer.

Number of shoppers per hour (during business hours) = 84

Time spent by each shopper (average) = 5 minutes.

→ 60 mins (1 hour) = 84 shoppers

→ 60 = 84

→ 84/60

→ 1.4

→ 1.4 × 5 = 7

→ 7 shoppers on an average, are waiting in the checkout line to purchase at the "Good Deals store"

The number of shoppers, on average waiting in the checkout line to make a purchase at the Good Deals Store is 7 shoppers.

The given parameters:

The average number of shoppers per minute at the Good deals store is calculated as follows;

\(n = \frac{84 \ }{hr} \times \frac{1 \ hr}{60 \min} \\\\n = 1.4 \ shoppers/ \min\)

The number of shoppers, on average waiting in the checkout line to make a purchase at the Good Deals Store is calculated as follows;

\(number \ of \ shoppers = 1.4 \ \frac{shoppers}{\min} \ \times \ 5 \min\\\\number \ of \ shoppers = 7 \ shoppers\)

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Answer:

0.0359 approximately 0.0360

Step-by-step explanation:

Mean = 7% = p

N = 527

We find The standard deviation

√p(1-p)/n

√0.07(1-0.07)/527

= √0.0651/527

= 0.01111437889

We are now to get z score

x = 0.09

U = 0.07

Sd = 0.01111437889

Z = x-u/sd

= 0.09-0.07/0.1111437889

= 1.799470775

Going to the statistical table,

P(z>1.799470775)

= 0.035972123

This is in the right tailed area

We approximate to 0.036.

The two case given below are disjoint and cover all the cases for n length strings, hence the numbers add up to give \(a_{n} =a_{n-1}+a_{n-2}\).

In the given question we have to find a recurrence relation for the number of n-digit binary sequences with no pair of consecutive.

Be sure to include the initial conditions Solution an \(a_{n-1}+ a_{n-2}\) Initial condition: \(a_{1}=2,a_{2}=3\)

Clearly \(a_{1}\) = 2 (0,1) and \(a_{2}\) = 3 (00,10,01). Now for the case of n. Suppose we are given a string with no consecutive 1's. There are two cases:

Case 1: the given string starts with a 0. In this case the n-1 length string after the first bit can be any string without consecutive 1's of length n-1. Hence there are n-1 of those.

Case 2: the given string starts with a 1. In this case the second bit has to be a 0 since we don't want consecutive 1's. Not the last n-2 length string can be any string without consecutive 1's of length n-2. Hence there are \(a_{n-2}\) of those.

These two case are disjoint and cover all the cases for n length strings, hence the numbers add up to give \(a_{n} =a_{n-1}+a_{n-2}\).

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Answer:

Step-by-step explanation:

Given the simultaneous equation

4x-5y+16 =0  ....... 1

2x+y-6 =0  ...... 2

Let us solve to get the variable x and y:

The equation becomes

4x-5y =-16   ........ * 1

2x+y =6 ...... *2

Using Elimination method

Multiply eqn 1 by 1 and eqn 2 by 2

4x-5y =-16

4x+2y =12

Subtract resulting equation

-5y-2y = -16-12

-7y = -28

solve for y

-7y/-7 = -28/-7

y = 4

Substitute y = 4 into equation 2 to get x

2x+y =6

2x + 4 = 6

2x = 6-4

2x = 2

x = 2/2

x = 1

hence x is 1, y is 4

Given:

F varies inversely with d²

So,

Where (k) is the proportionality constant

We will find the value of (k) using the given condition

When F=21, d= 7

Substitute with (F) and (d):

So, the answer will be:

The general formula to describe the variation is:

Answer:

C. 7

49 square rooted would be 7 and the 4 in (x+4) would be negative and not positive like the answer shows.

By using the substitution method, the value for (x,y) = (-2, 2)

The substitution method for solving a system of algebra equations is a process where by we make a variable (say variable x) the subject of the formula and substitute it into the second equation to solve for the other variable.

In essence, from the given system of equations; let's make x the subject of the formula in the first equation.

5x + 3y = -4

5x = -4 - 3y

Divide both sides by 5;

x = -4/5 - 3y/5

Now, we are going to substitute this value for x into the second equation. The second equation says:

y - 2x = 6

y - 2(-4/5 - (3y/5)) = 6

By solving for y;

y = 2

Now, let's replace the value of y with any of the given equation (2);

y - 2x = 6

2 - 2x = 6

-2x = 6 - 2

-2x = 4

Divide both sides by -2

-2x/-2 = 4/ -2

x = -2

Therefore, we can conclude that by using the substitution method, the value for (x,y) = (-2, 2)

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Answer:

hhhhhhhhghhhgggghhhhhhhhhhhhhhhhh

The values of the variables are;

x = 7

y = -9

From the information given, we have that;

5x−y=44

−3x−y=−12

Using the elimination method of solving simultaneous equations

Subtract equation (2) from equation (1), we get;

5x - y - (-3x - y) = 44 - (-12)

Now, expand the bracket

5x - y+ 3x + y = 56

collect the like terms

5x + 3x = 56

add the terms

8x = 56

Make 'x' the subject of formula

x= 7

Now, substitute the value of x in equation (2)

-3x - y = -12

-3(7) - y = -12

expand the bracket

-21 - y= - 12

collect like terms

-y = 9

y = -9

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The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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Answer:

Ok, so with this problem, you would start with the equation 6/10=x/38.

Then, cross multiply:

38(6)=10x

After, you would:

38 x 6 = 228

Then:

228/10

Lastly:

x=22.8m which when rounded equals 23 ft.

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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step 1

Find out the area of the closet

The area is equal to the area of a right triangle plus the area of a semicircle

so

step 2

Find out the total charge

40.2325*5.60+150=$375.30

therefore

In both cases, the sample proportion is very likely to be within a certain range of the population proportion, with a probability of 1.0000 or 100%.

What is probability?

Probability is a measure of the likelihood that an event will occur, it is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In this case, we are interested in the probability that the sample proportion (p) will be within a certain range of the population proportion (0.30).

a. To find the probability that the sample proportion will be within ±0.03 of the population proportion, we can use the standard normal distribution (z-table). The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

The formula for the standard normal distribution is:

z = (p - 0.30) / (standard deviation of p)

The standard deviation of p is given by the formula:

(population proportion * (1 - population proportion)) / sample size

In this case, we have:

(0.30 * (1 - 0.30)) / 150 = 0.0006

So, the standard deviation of p is 0.0006

The probability that the sample proportion will be within ±0.03 of the population proportion is the same as the probability that the sample proportion will be between 0.27 and 0.33.

Therefore, we can calculate the z-score for the lower and upper bounds of the range:

z1 = (0.27 - 0.30) / 0.0006 = -5

z2 = (0.33 - 0.30) / 0.0006 = 5

Using the z-table, we can find the probability that a z-score falls between -5 and 5.

The probability that the sample proportion will be within ±0.03 of the population proportion is:

P(z1 <= z <= z2) = P(-5 <= z <= 5) = 1 - 0.0000 = 1.0000

b. To find the probability that the sample proportion will be within ±0.08 of the population proportion, we can use the same formula as before. The probability that the sample proportion will be within ±0.08 of the population proportion is the same as the probability that the sample proportion will be between 0.22 and 0.38.

Therefore, we can calculate the z-score for the lower and upper bounds of the range:

z1 = (0.22 - 0.30) / 0.0006 = -10

z2 = (0.38 - 0.30) / 0.0006 = 10

Using the z-table, we can find the probability that a z-score falls between -10 and 10.

The probability that the sample proportion will be within ±0.08 of the population proportion is:

P(z1 <= z <= z2) = P(-10 <= z <= 10) = 1 - 0.0000 = 1.0000

Hence, In both cases, the sample proportion is very likely to be within a certain range of the population proportion, with a probability of 1.0000 or 100%.

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