Joe wants $75,000 in 18 years to give his grandkids for college. How much must he deposit now at 3.75% interest, compounded monthly?

The daily percent οf decrease is 12.94%.

Sο the cοrrect οptiοn is: 12.94%.

Percentage decrease is the percentage by which a quantity οr value has decreased cοmpared tο its οriginal οr previοus value. It is calculated by taking the difference between the οriginal value and the new value, dividing that difference by the οriginal value, and then multiplying by 100 tο cοnvert the result intο a percentage. The fοrmula fοr percentage decrease is:

Percentage decrease = [(Original value - New value) / Original value] x 100%

The fοrmula fοr the amοunt οf radiοactive element remaining, r, in a 100-mg sample after d days is given as:

[tex]r = 100(1/2)^{(d/5)[/tex]

Tο find the daily percent οf decrease, we need tο find the difference between the amοunt οf the element at the start οf a day and the amοunt at the end οf that day, and then express this as a percentage οf the starting amοunt.

Let's assume that we start with 100 mg οf the radiοactive element. After οne day, the amοunt remaining is:

[tex]r = 100(1/2)^{(1/5)[/tex] ≈ 87.06 mg

The difference between the starting amοunt and the amοunt at the end οf the day is:

100 - 87.06 = 12.94

Tο express this as a percentage οf the starting amοunt, we divide this difference by the starting amοunt and multiply by 100:

12.94/100 * 100% = 12.94%

Therefοre, the daily percent οf decrease is 12.94%.

Sο the cοrrect οptiοn is: 12.94%.

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Answer:

7:6

Step-by-step explanation:

...

Answer:

Below

Step-by-step explanation:

154 : 132      the GCF of these two numbers is 22.   Divide them both by 22

7:6    Done

The total fluid intake for the meal is 493.04 mL.

We first need to convert the volume of each beverage to ounces, and then to milliliters.

1/3 glass of orange juice = (1/3) x 8 oz = 2.67 oz = 79.01 mL (assuming 1 oz = 29.57 mL)

1/2 cup of tea = (1/2) x 6 oz = 3 oz = 88.72 mL

1/2 pt milk = (1/2) x 16 oz = 8 oz = 236.59 mL (assuming 1 pt = 16 oz and 1 oz = 29.57 mL)

1 popsicle (3oz) = 3 oz = 88.72 mL

The total fluid intake for the meal is

79.01 mL + 88.72 mL + 236.59 mL + 88.72 mL = 493.04 mL

Therefore, the fluid intake for the meal is approximately 493.04 mL.

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When lines A and B are cut by a transversal, then ∠1 and ∠4 fοrm a pair οf vertical angles.

In geοmetry, a transversal line intersects twο lines in the same plane at twο different lοcatiοns. In the Euclidean plane, transversals help establish the parallelism οf twο οr mοre οther straight lines. It crοsses twο lines at separate lοcatiοns. Transversal intersectiοn results in numerοus angles.

Twο parallel lines are A and B are drawn.

They are cut by a transversal C.

The angles ∠1 and ∠2 are fοrming a pair οf alternate exteriοr angles.

The angles ∠3 and ∠4 are fοrming a pair οf alternate interiοr angles.

The angles ∠2 and ∠3 are verticals angles.

Similarly, the angles ∠1 and ∠4 fοrm a pair οf vertically οppοsite angles.

Therefοre, the angles fοrm vertical pair.

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The distance between Dallas, TX and Austin, TX is 312 kilometers.

To convert miles to kilometers, we need to multiply the distance in miles by the conversion factor, which is 1.6.

So, to find the distance between Dallas, TX and Austin, TX in kilometers, we need to multiply 195 miles by 1.6:

Distance in kilometers = 195 miles * 1.6 = 312 kilometers

Therefore, the distance between Dallas, TX and Austin, TX is 312 kilometers.

To understand how this conversion works, we need to understand what a mile and a kilometer represent. A mile is a unit of length that is used primarily in the United States and is defined as 5,280 feet. A kilometer, on the other hand, is a unit of length that is used in most other countries and is defined as 1,000 meters.

Since the conversion factor between miles and kilometers is 1.6, it means that for every 1 mile, there are 1.6 kilometers. This conversion factor is derived from the fact that 1 mile is approximately equal to 1.60934 kilometers.

Therefore, to convert any distance in miles to kilometers, we need to multiply the distance in miles by 1.6. Conversely, to convert a distance in kilometers to miles, we need to divide the distance in kilometers by 1.6.

Therefore, the distance between Dallas, TX and Austin, TX is 312 kilometers.

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Answer:

slope is undefined

Step-by-step explanation:

We have 2 coordinates (-4,0) and (-4,1)

Slope m = (y2 - y1)/(x2 - x1) = (1 - 0)/(-4 - -4) = 1/0 or undefined

The undefined slope is the slope of a vertical line

The linear dependence between the vectors is -3[10 02] + 1[21 3−1] + 2[11 3−3] = 0.

The linear dependence between the following vectors in Mat 2×2 (R) [10 02],[21 3−1],[11 3−3] can be found by solving the equation a[10 02] + b[21 3−1] + c[11 3−3] = 0 for a, b, and c. This gives us the following system of equations:10a + 21b + 11c = 02a + 3b + 3c = 02b - c = 0Solving this system of equations, we get a = -3, b = 1, and c = 2. Therefore, the linear dependence between the vectors is -3[10 02] + 1[21 3−1] + 2[11 3−3] = 0. This means that the vectors are linearly dependent and can be written as a linear combination of each other.

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An example of a compound interest problem and the solution problem is:

"Sarah deposits $10,000 into a savings account with a 5% annual interest rate compounded annually. How much will she have in the account after 3 years?"

Solution: Sarah will have $11,576.25 in the account after 3 years.

The compound interest on the same sum at the same rate for the same period, compounded annually, is:

$6,646.34

Sarah deposits $10,000 into a savings account with a 5% annual interest rate compounded annually. How much will she have in the account after 3 years?

To solve this problem, we can use the formula for compound interest: A = P(1 + r)^n, where A is the final amount, P is the principal amount, r is the annual interest rate, and n is the number of years.

To find the compound interest on the same sum at the same rate for the same period, we can use the same formula for compound interest: A = P(1 + r)^n.

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Answer:

a) x = 132

b) x = 125

Step-by-step explanation:

Angles in a quadrilateral sum to 360 degrees. Given this, we can determine the missing angles by subtracting the known angles from 360:

a) 360 - 48 - 48 - 132 = 132

b) 360 - 108 - 68 - 59 = 125

Answer:

x=18

Step-by-step explanation:

Being that the angles are corresponding they are going to equal the same thing.

(7x+7)=133

Now just follow the laws of PEMDAS

7x+7=133

-7 -7

7x=126

÷7 ÷7

x=18

Answer: bro hear me out rq in the explanation

Step-by-step explanation: Jim hands the cashier the $20 bill and, if necessary, provides his identification to purchase the item. The cashier will then record the purchase, give Jim his change, and thank him for his business.

Diameter of flu virus particle is 8.1 × 10⁻⁸ meter

Scientific notation is a way of representing numbers that are too large or too small to be easily written in decimal form because they require very long strings of digits to  be written. This is sometimes called scientific or standard exponential format, or British standard format.

Given,

Diameter of water molecule = 2.7 × 10⁻¹⁰ meters

Flu virus particle is 300 times bigger than water molecule

Diameter of flu virus

= 300 × 2.7 × 10⁻¹⁰

= 810 × 10⁻¹⁰

= 8.1 × 10⁻⁸ meter

Hence, 8.1 × 10⁻⁸ meter is the diameter of the Flue virus particle.

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The zero vector [0, 0, 0], the length would be √(0^2 + 0^2 + 0^2) = 0.

Examples of 3 element vectors include:
- [1, 2, 3]
- [-1, 0, 5]
- [3, -2, 1]
- [0, 0, 0]
- [4, 4, 4]
- [-2, -2, -2]

There are infinitely many 3 element vectors that have a length of 0. A vector with a length of 0 is called the zero vector, and it has all of its components equal to 0. In the case of a 3 element vector, the zero vector would be [0, 0, 0].

Examples of 3 element vectors include:
- [1, 2, 3]
- [-1, 0, 5]
- [3, -2, 1]
- [0, 0, 0]
- [4, 4, 4]
- [-2, -2, -2]

Remember that the length of a vector is calculated using the formula √(x1^2 + x2^2 + x3^2), where x1, x2, and x3 are the components of the vector. So, for the zero vector [0, 0, 0], the length would be √(0^2 + 0^2 + 0^2) = 0.

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Answer:

C

Step-by-step explanation:

The leading coefficient of f(x) is positive, which means that the graph will be pointing upwards on both ends. The graph is attached below.

Graphs are a not unusual place technique to visually illustrate relationships within side the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately within side the textual content and in much less space.

To sketch the graph of f(x) = x^4 - 3x^3 + x - 3, we can use the information gathered from analyzing the function:

Using this information, we can sketch the graph of f(x) as follows:

Putting all of this information together, we can sketch the graph of f(x) as shown below:

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The value of 8#(8#8) is (A) 1/2

An operation \# for positive real numbers is defined by the equation a#b=ab/a+b. The value of 8#(8#8) is (A) 1/2. To solve, use the equation given:

8#(8#8) = (8*8)/(8+8)

= 64/16

= 1/2

Hope this helps!

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Answer:

Step-by-step explanation:

Bob was on the top rung of his ladder (rung 30) and Roy was on the 15th rung of his ladder when they were at the same height.

Two or more expressions with an Equal sign is called as Equation.

Let's assume that Bob started at the top of his ladder and Roy started at the bottom of his ladder.

If both ladders have 30 rungs, then they have a total height of 30 - 1 = 29 rungs.

If Bob went down two rungs every second and Roy went up one rung every second, then they were changing their height at a rate of -2

Let's use "t" to represent the time they had been climbing. Then, we can write an equation to represent the heights of Bob and Roy at this moment:

Bob's height = 30 - 2t

Roy's height = t

30 - 2t = t

Solving for "t", we get:

t = 15

This means that Bob and Roy were at the same height after 15 seconds of climbing.

Bob's height = 30 - 2t = 30 - 2(15) = 0

Roy's height = t = 15

Therefore, Bob was on the top rung of his ladder (rung 30) and Roy was on the 15th rung of his ladder when they were at the same height.

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By trigonometric formulas, there are two solution sets for the trigonometric equation 2 · cos β = - √(3 · cos β) + sin β + 2 · cos β: β₁ ≈ 0.402π + 2π · k, β₂ = - 0.402π - 2π · k, where k is an integer.

In this problem we find the case of a trigonometric equation, whose roots must be found by algebra properties and trigonometric formulas. First, write the complete expression:

2 · cos β = - √(3 · cos β) + sin β + 2 · cos β

Second, simplify the expression by algebra properties:

√(3 · cos β) = sin β

Third, square both sides and simplify the expression:

3 · cos β = sin² β

3 · cos β = 1 - cos² β

cos² β + 3 · cos β - 1

Fourth, factor the resulting expression:

(cos β - 0.303) · (cos β + 3.303)

Fifth, determine the set of solutions:

cos β = 0.303

β₁ ≈ 0.402π + 2π · k, β₂ = - 0.402π - 2π · k, where k is an integer.

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The length of the arc intercepted by a central angle of 6 radians in a circle of radius 53 is:

Arc length = radius x central angle

Arc length = 53 x 6

Arc length = 318

Therefore, the length of the arc intercepted by a central angle of 6 radians in a circle of radius 53 is 318.

The length of the arc intercepted by a central angle of 97° in a circle of radius 8 is:

First, we need to convert 97° to radians:

97° = (97/180) x π radians

97° = 1.69 radians (rounded to two decimal places)

Arc length = radius x central angle

Arc length = 8 x 1.69

Arc length ≈ 13.52 (rounded to two decimal places)

Therefore, the length of the arc intercepted by a central angle of 97° in a circle of radius 8 is approximately 13.52.

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The fraction of the euro is 8/100

one Euro will cost in 8 rands

When we talk about exchange rates, we're essentially talking about the value of one currency compared to another. In this case, we're comparing the South African rand to the euro.

We know that one South African rand is valued at 0.125 of one euro. To figure out what fraction of the euro one South African rand is worth, we can simply divide the value of one rand by the value of one euro:

1 rand ÷ 0.125 euro = 8/100 euro

So, one South African rand is worth 8/100 or 0.08 (which is equivalent to 8%) of one euro.

To calculate what one euro would cost in rands, we can use the inverse of the exchange rate we were given:

1 euro ÷ 0.125 rand/euro = 8 rand

So, one euro would cost 8 South African rand.

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Answer:

Yes

What is horizontal distance ?

The distance between two points is understood to mean the horizontal distance, regardless of the relative elevation of the two points.

How to calculate horizontal distance?

Horizontal distance can be expressed as x = Vtx = Vtx=Vt. Vertical distance from the ground is described by the formula y = – 1 2 g t 2 y = – \frac{1}{2}g t^2 y=–21gt2, where g is the gravity acceleration, and h is an elevation.

Step by step explanation:

As long as the ramp is no more than .9965 feet high, then yes

If the ramp is .9965 feet high then its horizontal distance is 12 X .9965 feet or 11.958 feet

Using Pythagoras’ Theorem, the actual length of the ramp would be the square root of (11.958 X 11.958 + .9965 X .9965)

Or the square root of (142.9934 + .9930)

Or SQRT (143.987)

= 11.999 feet

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The number of laps increases by 50 percent.

The number of laps Jane can run has increased by 50%. To find this, we can use the formula:

Percentage Increase = (New Value - Old Value) / (Old Value) × 100

In this case, the new value is 6 (the number of laps Jane can now run) and the old value is 4 (the number of laps Jane used to be able to run). Plugging these values into the formula gives us:

Percentage Increase = (6 - 4) / (4) × 100
Percentage Increase = 2 / 4 × 100
Percentage Increase = 0.5 × 100
Percentage Increase = 50%

Therefore, the number of laps Jane can run has increased by 50%.

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Answer:

V=103.

Step-by-step explanation:

V=πr2h

=π·2.82

·4.2≈103

.44636

Answer:

Step-by-step explanation:

the correct answer is 10.39 cubic feet

(a) Stratified random sampling ensures a representative sample, and Ys is an unbiased estimate of the population mean y.

(b) Proportional allocation allocates sample size in each stratum proportionally to its size, while optimum allocation determines sample size based on variance and cost in stratified random sampling.

(a) Stratified random sampling is a method of sampling that involves dividing the population into smaller groups or strata, and then randomly selecting a sample from each stratum. This is done to ensure that the sample is representative of the population as a whole. The formula for the expected value of the sample mean, E(Ys), in stratified random sampling is:
E(Ys) = Σ wi * E(Yi)
where wi is the weight of the ith stratum, and E(Yi) is the expected value of the sample mean in the ith stratum.
Since Ys is an unbiased estimate of the population mean y, we can prove that E(Ys) = y by substituting y for E(Yi) in the formula:
E(Ys) = Σ wi * y
= y * Σ wi
= y * 1
= y
Therefore, E(Ys) = y, proving that Ys is an unbiased estimate of the population mean y.

(b) Proportional allocation is a method of allocating the sample size in stratified random sampling, where the sample size in each stratum is proportional to the size of the stratum in the population.

This ensures that each stratum is represented in the sample in proportion to its size in the population.

Optimum allocation is another method of allocating the sample size in stratified random sampling, where the sample size in each stratum is determined based on the variance of the stratum and the cost of sampling from the stratum.

This ensures that the sample size in each stratum is optimized to minimize the variance of the sample mean and the cost of sampling.

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The line of reflection that produces Z′(10, 7) is y - axis.

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is a Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).

The rule for a reflection over the y -axis is (x, y) → (−x, y). We can write the reflection as -

Z(- 10, 7) → Z'(10, 7)

Therefore, the line of reflection that produces Z′(10, 7) is y - axis.

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The line of reflection that produces Z′(10, 7) is y - axis.

What is a triangle?

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is a Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Z′(10, 7).

The rule for a reflection over the y -axis is (x, y) → (−x, y). We can write the reflection as -

Z(- 10, 7) → Z'(10, 7)

Therefore, the line of reflection that produces Z′(10, 7) is y - axis.

The simplified expression is 14+a.

Using the commutative and associative properties, we can simplify the expression (7+a)+7.

First, let's use the commutative property to rearrange the terms. The commutative property states that the order of addition or multiplication does not matter. In other words, a+b = b+a and a*b = b*a.

So, we can rearrange the terms in the expression to get:

(7+7)+a

Next, let's use the associative property to simplify the expression. The associative property states that the way we group terms in an addition or multiplication problem does not matter. In other words, (a+b)+c = a+(b+c) and (a*b)*c = a*(b*c).

So, we can group the terms in the expression to get:

14+a

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[tex]PQ = 2 - (-3) = 2 + 3 = 5 \ cm[/tex]

[tex]RS = PQ \implies RS = 5 \ cm[/tex]

the perimeter of rectangle PQRS is 20 centimeters ⇒

[tex]QR = SP = 5 \ cm[/tex]

⇒ PQRS is square

[tex]x_{R} = x_{Q} - 5 = -1-5 = -6[/tex]

[tex]y_{R} = y_{Q} = 2[/tex]

[tex]\implies R(-6,2)[/tex]

[tex]x_{S} = x_{R} = -6[/tex]

[tex]y_{S} = y_{P} = -3[/tex]

[tex]\implies Q(-6,-3)[/tex]

The proof that ∠B ≅ ∠C is:

D is the midpoint of of BC - Given...................(1)
Thus
BD = DC ................................................................(2)

∠EDC ≅ ∠FDB  - Given......................................(3)

DE ⊥ AB - Given...................................................(4)
DF ⊥ AC - Given ..................................................(5)
∠AED = ∠DEB = 90° - perpendicular bisector theorem  ....(6)

∠AFD = ∠DFC = 90° - perpendicular bisector theorem ....(7)
∠EAF = ∠EDF = 90° - Properties of the angles of a Quadrilateral

Since ∠EDC ≅ ∠FDB, as in   (3) above, and

Both comprise of ∠EDF,

thus,
(∠EDC - ∠EDF) ≅ (∠FDB - ∠EDF)

Since

∠EDB = (∠FDB - ∠EDF); and

∠FDC = (∠EDC - ∠EDF)

Thus,

∠EDB ≅ ∠FDC

thus,
∠EDB = ∠FDC = 45° (Sum of Angles on a Straight line) that is
∠EDB =  ∠FDC = (180° -∠EDF)/2

Since  ∠EDF = 90°
∠EDB =  ∠FDC = (180° -90°)/2

∠EDB =  ∠FDC = 90/2
∠EDB =  ∠FDC = 45°

Since
∠DEB = 90° (5); and

∠DFC = 90° (7)
ΔBED ≅ ΔDFC

Thus, by Sum of Angles in a Triangle,
∠B ≅ ∠C.

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-6x+25y+66z=232 is the equation of the plane and distance between the point D and the plane is  157/70.

lets find the equation of the line AB and BC and equations of the lines will be of the form

[tex]  \text{ $\frac{x-a}{l}$ = $\frac{y-b}{m}$ = $\frac{z-c}{n}$ } [/tex]

So, the equation of AB is

[tex]  \text{ $\frac{x}{2}$ = $\frac{y-4}{18}$ = $\frac{z-2}{7}$ } [/tex]

So, the equation of AB is

[tex]  \text{ $\frac{x-3}{-1}$ = $\frac{y+2}{24}$ = $\frac{z}{9}$ } [/tex]

let b1 andb2 are the direction vectors of the two above lines.

b1= 2i + 18j + 7k

b2= -1i + 24j + 9k

now n= Det( i       j       k)

                   2      18     7

                  -1       24    9

or, n= -6i + 25j + 66k

the point (0,4,2) lies on the plane. the equation of the plane passing through (0,4,2) and perpendicular to a line with a direction ratio (-6, 25, 66) is

-6x+25(y-4)+66(z-2)=0

or, -6x+25y+66z=232.

now formula of distance between the point (x0,y0,z0) and the plane is

[tex] \frac{Ax0+By0+Cz0+D}{√A^2+B^2+C^2} [/tex]

so for the point D and the plane is

( -6*0 + 25*1 + 66*2 - 132)/√5017 = 157/70.

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