The equation, A = P(1 + 0.037t), represents the amount of money earned on a savings account with 3.7% annual simple interest. If the amount after 5 years is equal to $1,422, what is the amount of the principal investment? $1,200 $1,422 $274.25 $294.86

The number of possible ways in which we can select 3 elements from 7 elements are  given in option d. 35.

There are a total of 7 elements and we can to select 3 elements out of them.

We have to apply the permutation and combination here in order to find the answer,

The formula is ⁿCₐ

Where, C represents combination,

n is the total number of combination,

a is the number of selections that we have to do,

ⁿCₐ = n!/(n-a)!a!

Now, putting n = 7 and a = 3,

ⁿCₐ = 7!/(4)!3!

ⁿCₐ = 35

So, the total number of ways possible are 35.

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Answer:

Daniel is 8 years old now

Step-by-step explanation:

Let Kevin's age now be K and let Daniel's age now be D

"Kevin is 3 times as old as Daniel"

Translation: K = 3D

"4 years ago, Kevin was 5 times as old as Daniel"
4 years ago Kevin's age = K - 4
4 years ago Daniel's age = D - 4
4 years ago, Kevin was 5 times as old as Daniel.

Translation: K - 4 = 5(D - 4)
K - 4 = 5D - 20

Simplify this equation:
Add 4 to both sides:
K - 4 + 4 = 5D - 20 + 4

K = 5D - 16

Substitute K = #D:
3D = 5D - 16

Subtract 5D from both sides:
3D - 5D = - 16
-2D = -16

or

2D = 16   (multiply by - 1)

D = 16/2 = 8

and

K = 3D = 3 x 8 = 24

Now, Kevin is 24 years old and Daniel is 8 years old

Verify
If Kevin is 3x older than Daniel who is 8 now,
Kevin's age now = 3 x 8 = 24  Check

4 years ago, Daniel was 8 - 4 = 4 years
4 years ago, Kevin was 24 - 4 = 20
Kevin's age 4 years ago = 5 x 4 = 20 Check

Answer: $225. If the price of the coat was $250 last year, then the coat costs $225 this year.

Step-by-step explanation:

Since the coat costed $250 last year, it is 100% of its original.

Now that it has decreased 10%, it is 100%-10%=90% of its original price.

The new price of the coat will be (90% ÷ 100%) × $250 = $225

The p-value can be calculated from the Z-score of the observed result using the Z-table, which is a table of values for the standard normal distribution.

The p-value is the probability of getting a result at least as extreme as the one observed, given that the null hypothesis is true. It is calculated from the Z-score of the observed result, which is a measure of how many standard deviations away from the mean the observed result is. To calculate the p-value from a Z-score, you need to use the Z-table, which is a table of values for the standard normal distribution. The Z-table shows the probability of a given Z-score, or the area under the normal distribution curve to the left of the Z-score. To find the p-value associated with a given Z-score, you simply look up the probability in the Z-table, and subtract this probability from 1. This gives you the p-value, which is the probability of getting a result at least as extreme as the one observed, given that the null hypothesis is true.

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The total surface area of the rectangular prism represented by the net is  174 inch²

A prism is a solid geometric shape with parallelograms for its sides and two comparable, equal, and parallel rectilinear figures for its ends.

Given:

Length of the base = 9 inch

Width of the base = 3inch

Height of the base = 5 inch

Area of the two rectangular base

= 2 x length x width

= 2 x 9 x 3

= 54 inch²

and, Area of lateral surfaces

= 2 lateral surfaces with length 9 inch + 2 lateral surfaces with width 3 inch

= 2 x 9 x 5+ 2 x 3 x 5

= 120 inch²

So, Total surface area = 54+120 = 174 inch²

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The surface area of the rectangular prism is,

⇒ SA = 174 Square units.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The figure is the net for a rectangular prism.

And, Length = 9 in.

Width = 3 in.

Height = 5 in.

Now, We know that;

The surface area of a rectangular prism is given by,

⇒ SA = 2 (lh +wh + lw ) Square units.

Substitute all the values, we get;

⇒ SA = 2 (lh +wh + lw ) Square units.

⇒ SA = 2 (9×5 + 3×5 + 9×3 ) Square units.

⇒ SA = 2 (45 + 15 + 27) Square units.

⇒ SA = 2 × 87

⇒ SA = 174 Square units.

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Answer: The equivalent expression to Sarah's expression is:

6.25(x + y) + 242.78

This expression takes into account the total number of hours worked by James (x) and Sarah (y) and adds it to the sum of their tips, which is $242.78. The expression multiplies the total number of hours worked by 6.25, which is their hourly wage.

Step-by-step explanation:

The required proportional relationship used to evaluate the measure of segment LM is 9/LM = 6/4.5. Option D is correct.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
Since Triangle HJK is similar to triangle LMN.
The property of similar triangle states that the sides of both the triangle will be proportional to each other.
So,
9/6 = LM/4.5

Or

9/LM = 6/4.5

Thus, the required proportional relationship used to evaluate the measure of segment LM is 9/LM = 6/4.5. Option D is correct.

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V(x) = (10 - 2x)(17 - 2x)(x)

To find the volume of an open-top box, we need to find the product of its length, width, and height. In this case, the length and width of the box will be the original dimensions of the cardboard minus twice the side length of the square cutouts, and the height will be the side length of the square cutouts.

a) The expression for V(x) can be written as:

V(x) = (10 - 2x)(17 - 2x)(x)

b) To find the volume of the box when x = 3, we simply need to plug in the value of x into the expression for V(x) and simplify:

V(3) = (10 - 2(3))(17 - 2(3))(3)

V(3) = (10 - 6)(17 - 6)(3)

V(3) = (4)(11)(3)

V(3) = 132

Therefore, the volume of the box when x = 3 is 132 cubic centimeters.

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Answer:

To find f(4), we simply need to substitute 4 for x in the equation for f(x):

f(x) = -x + 2

f(4) = -(4) + 2

f(4) = -2

Therefore, f(4) = -2.

Step-by-step explanation:

1. Answer: The price of Andrea's tacos is $8.

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

Tip amount: $2.0

Percentage: 25% = 0.25 (decimal form, 25/100=0.25)

So, if we multiply the taco's price (x) by the percentage (0.25) we will obtain the amount of the tip (2).

Mathematically speaking:

x (0.25) = 2

Solving for x

x = 2/0.25

x = 8

The price of Andrea's tacos is $8.

2. To solve this problem what you can do is the following rule of three:

40 iris blooms -----> 100%

x iris blooms -------> 115%

Clearing the value of x we have:

x = (115/100) * (40)

x = 46

Then, comparing with last year we have:

40-46 = 6

Answer:

Savanna had this year 6 more iris blooms than last year.

From the given information, by using mass conversion, 156 lbs is equal to approximately 70.76 kg.

Mass conversion is the process of converting a given mass from one unit of measurement to another. It involves using a conversion factor to change the numerical value of the mass while keeping the physical quantity constant.

For example, converting a mass from pounds to kilograms involves using a conversion factor of 0.45359237 kg/lb.

To convert pounds to kilograms, you can use the following conversion formula:

1 lb = 0.45359237 kg

So, to convert 156 lbs to kg, you can multiply 156 by 0.45359237:

156 lbs × 0.45359237 kg/lb = 70.76 kg (rounded to two decimal places)

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Note that the cost of wax that is required to cover the floor is given as = $1.677.39

To arrive at the correct answer, we had to deconstruct the complex shape in regular shapes comprising two rectangles and one right-angled triangle.

When disassembled, a composite form (or complex figure), also known as a compound shape, is made up of several separate regular shapes.

Note that the arrive at the correct answer, we need to deconstruct the complex shape in regular shapes comprising two rectangles and one right-angled triangle.

The objective is to add the area of all the shapes which comprise the irregular floor and multiply by the cost of wax per square foot. (See attached Image for Deconstructed Compound Shape.)

Step 1 - Find the area of the Right-Angled Triangle

Recall that the rea of a Right Angled Triangle = 1/2 B*H;

B = 15ft

H = 35ft

Area of Δ = 1/2 * 15 *35

Area of Triangle = 262.5ft

Step 2 - Find the area of the Two Rectangles
Dimensions of Rectangle a are: L = 30ft; B = 15ft

Area = L*B

Area = 30*15

Area of (a) = 450ft

Dimensions of Rectangle b are: L = 25ft: B= 20ft
Area (b) = 25* 20

Area (b) = 500ft


Step 3 - Find the area of the compound shape
Area of the compound shape = Sum of the area of the individual shapes  =

262.5ft + 450ft + 500ft
= 1212.5 ft

Step 4 - Find the cost of waxing the floor (compound shape)
This is given as:

$1.38 * Area of Compound Shape

⇒ 1.38 * 1212.5
= $1.677.39

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See the images attached for the missing part of the question

The measure of the value of x in the given circle is 27

In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle.

Given that a circle D, having an inscribed angle ∠ EBC measuring 51° and an arc covered by it is arc EC measuring 5x-33, we are to find the value of x,

We know that,

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Therefore,

m ∠ EBC = 2 arc EC

5x-33 = 2×51

5x-33 = 102

5x = 135

x = 27

Hence, the measure of the value of x in the given circle is 27

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The figure is not given, the question is solved for the attached figure.

The mean and standard deviation of the sampling distribution of the difference in sample means xF − xM is 1.5 minutes(mean) and 1.533 minutes(std. dev) approx The probability of getting a difference in sample means xF − xM that is less than 0 is 0.0239 approx.

Suppose that a random variable X is formed by n mutually independent and normally distributed random variables such that:

Xi = N(μi, σ²) ; i = 1, 2,......, n

And if

X = X1 + X2 +........+ Xₙ

Then, its distribution is given as:

X ≈ N (μ1 + μ2+........+ μₙ)

For this case, it's given that

Distribution of time taken for distance ran by lady is Normal distribution and had a mean handling time of = 8.8 minutes with standard divagation of = 3.3 minutes.

Distribution of time taken for distance ran by joker is Normal distribution and had a mean handling time of = 7.3 minutes with standard divagation of = 2.9 minutes.

Samples of size n = 8 are taken from both population.

Estimated sample mean = population mean

Estimated sample standard deviation = population std. dev / √n

where n = sample size

For sample of females, the distribution is

For sample of males, the distribution is

Also, if we take distribution of difference between sample means(, then it would be normal with mean = 8.8-7.3 = 1.5 minutes (as mean for  will be -7.3 but same standard deviation) as factor gets squared for affecting standard deviation and variance)

and standard deviation is:

[tex]\sqrt{s^2f + s^2m } = \sqrt{3.3^2/8 + 2.9^2/8}[/tex]

≈ 1.553 minutes.

The distribution of difference between sample means is  approximately

We need [tex]P(Xf - Xm < 0)[/tex]

Thus, the mean and standard deviation of the sampling distribution of the difference in sample means xF − xM is 1.5 minutes(mean) and 1.533 minutes(std. dev) approx The probability of getting a difference in sample means xF − xM that is less than 0 is 0.0239 approx.

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Number of seconds in a year riddle will be 31,536,000 seconds in a year ((24 x 60 x 60) x 365).

To calculate number of seconds in year riddle, we need to calculate the no. of seconds in each month.

There are a total 12 months and each month consists of 31, 30 and 28 days respectively.

Now, calculating the number of seconds in each month multiplying the count of months with respect to the number of days in that month.

In January, March, May, July, August, October, December : 31x24x60x60=26,78,400x7=1,87,48,800

In Feb: 28X24x60x60=24,19,200

In April, June, September, November: 30x24x60x60=25,92,000x4=1,03,68,000

Now add all the values: No of Seconds in year riddle = 1,87,48,800+24,19,200+1,03,68,000

Totally the value will be equal to 3,15,36,000 seconds.

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Answer:umm

There are no values of

x

that make the equation true.

No solution

Step-by-step explanation:

The value of x is 8 units by using Pythagorean theorem.

If x and 6 are the lengths of the legs of a right triangle and the length of the hypotenuse is 10, then we can use the Pythagorean theorem to find the value of x.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

So in this case:

x^2 + 6^2 = 10^2

Expanding the squares and solving for x:

x² + 36 = 100

x² = 100 - 36

x² = 64

x = [tex]\sqrt{64}[/tex]

x = 8

So the value of one leg of x is 8 units and other which is given is 6 units.

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____ The given question is incomplete, the correct question is given below:

What is the value of x?

Enter your answer in the box.

x=

A right triangle. The legs are labelled x and six, and the hypotenuse is labelled ten.

The original number in the word problem is 77.

Let's call the original two-digit number "x".

Information from the problem

the sum of the digits in x is 14.

So, we can write the number as x = 10a + b,

where a and b are the tens and ones digit, respectively, and a + b = 14.

Reversing and doubling the original number gives us 2(10b + a)

= 20b + 2a.

Adding the original number, x, and the doubled, reversed number, 2(10b + a),

we have 3x = 222.

Substituting x = 10a + b

3(10a + b) = 222

30a + 3b = 222

30a = 222 - 3b

Since the sum of the digits is 14, a + b = 14, so we can substitute for a in the equation:

30(14 - b) = 222 - 3b

420 - 30b = 222 - 3b

198 = 27b

Dividing both sides by 27, we find:

b = 7

So, the original number is x = 10a + b = 10(14 - 7) + 7 = 77.

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The measure of angle number 1 is 69°.

We know that ∠1 + ∠2 = 180°

We also know that the sum of the interior angles of a triangle is always equal to 180°.

Then we can write simple linear equations to find the missing angles, for example we can write:

21° + 38° + ∠2 = 180°

∠2 = 180° - 21° - 38°

∠2 = 121°

Now we can replace that in the original equation  ∠1 + ∠2 = 180°:

∠1 + 121° = 180°

∠1 = 180° - 121° = 69°

∠1 = 69°

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To find the volume of a triangular prism, you will need to use the formula V = (1/2)bhL, where V is the volume, b is the base of the triangular prism, h is the height of the triangular prism, and L is the length of the triangular prism.

Here is a step-by-step explanation on how to find the volume of a triangular prism:

Step 1: Find the base of the triangular prism. This will be one of the sides of the triangular base.

Step 2: Find the height of the triangular prism. This will be the distance from the base to the opposite vertex.

Step 3: Find the length of the triangular prism. This will be the distance between the two triangular bases.

Step 4: Plug in the values for the base, height, and length into the formula V = (1/2)bhL.

Step 5: Simplify the equation to find the volume of the triangular prism.

For example, if the base of the triangular prism is 4, the height is 3, and the length is 6, the volume would be:

V = (1/2)bhL

V = (1/2)(4)(3)(6)

V = 36

So, the volume of the triangular prism is 36.

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The length of the guy wire is 20 feet

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can use the Pythagorean theorem to find the length of the guy wire.

Let's call the length of the guy wire "g".

Then we have a right triangle with hypotenuse g, one leg of length 7 ft, and the other leg of length 19 ft.

Using the Pythagorean theorem, we have:

g² = 7² + 19²

g² = 49 + 361

g² = 410

Take square root on both sides

g = 20.24

Therefore, the length of the guy wire is 20 feet

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The number that is less than 200 and have the prime factors 3, 5, and 13 is 195.

Prime factors are the prime numbers that divide a given positive integer exactly without leaving any remainder. In other words, prime factors are the building blocks of a number.

For example, the prime factors of the number 24 are 2 and 3, because 24 can be written as the product of these prime numbers: 2 × 2 × 2 × 3.

To find the numbers that have prime factors  3,5, and 13, multiply the prime factors together:

3 * 5 * 13 = 195

This is the only number less than 200 that has prime factors 3,5, and 13.

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Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

The outcome is three more than the number, which is 9 if five is taken away from it and the difference is tripled.

Whole Numbers: The collection of natural numbers that include the number 0. Integers are whole integers that are next to their counterparts (negative numbers). Real numbers would be any integers that can be stated as fractions. Any number that cannot be expressed as a fraction is irrational.

Many operations, like measuring, counting, and indexing, require the use of numbers. According to their characteristics, there are several sorts of numbers, including natural numbers, whole figures, rational or irrational numbers, integers, actual values, complex numbers, and even odd numbers, etc.

Let the number be y

5 is subtracted from the number. This can be written as:

y – 5

The difference is tripled. This can be written as:

3(y – 5)

The result of the difference tripled is 23 more than the number. This can be written as:

3(y – 5) = 3 + y

Thus, we can obtain the value of y as follow:

3(y – 5) = 3 + y

Clear bracket

3y – 15 = 3 + y

Collect like terms

3y – y = 3 + 15

2y = 18

y = 18 / 2

y = 9

Thus, the number is 9.

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Answer: 1/2(10+x)

Step-by-step explanation:

"Half the sum of 10 and a number" means 1/2(10+x), where x is the unknown number.

The expression [tex]\frac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex] is equivalent to the expression [tex]\frac{1}{\sqrt[5]{3} }[/tex]. Then the correct option is B.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

[tex]\rightarrow \dfrac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex]

Simplify the expression, then we have

[tex]\rightarrow \dfrac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}\\\\\rightarrow \dfrac{(3)^{1/5 }}{(3)^{2/5}}\\\\\rightarrow \dfrac{(3)^{1/5 }}{(9)^{1/5}}\\\\\rightarrow \dfrac{1}{\sqrt[5]{3} }\\[/tex]

The expression [tex]\frac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex] is equivalent to the expression [tex]\frac{1}{\sqrt[5]{3} }[/tex]. Then the correct option is B.

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The probability of rolling a 9 or higher on the 3rd roll is 4/27, or approximately 14.8%.

Probability is a branch of mathematics that deals with determining the likelihood or chance of an event occurring. It is often expressed as a fraction or a percentage.

Conditional probability is the probability of an event happening given that another event has already happened.

The probability of not rolling a 9 or higher on the first roll is 8/12 or 2/3, as there are 8 numbers on the cube that are less than 9.

The same is true for the second roll, so the probability of not rolling a 9 or higher on the first two rolls is (2/3) * (2/3) = 4/9.

The probability of rolling a 9 or higher on the third roll is 4/12 or 1/3, as there are 4 numbers on the cube that are 9 or higher.

So, the probability of rolling a 9 or higher on the third roll given that the previous two rolls did not result in a 9 or higher is

=> (4/9) * (1/3) = 4/27

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Answer:

If you are asking if y = 4x is proportional, the answer is yes.  It is linear and it goes through the origin.

Step-by-step explanation: