3) You inherit $2,500 and decide to invest it in an account that earns 1.5% interest
compounded monthly.

a) Write an equation to model this scenario.

b) How much money is in the account 15 years after you first invested?

The lateral surface area of the triangular prism is 364.1 square inches.

The Surace area of any 2D or 3D figure is the outer area of the given figure.

Surface areas are of two types they are lateral surface area when we exclude the areas of top and bottom and total surface area is when we include all the sides.

From the given diagram and the concept of lateral surface area where the base and top are excluded here, it has only the base area as the top results to a point.

Therefore, The lateral surface area of this isosceles triangular prism is,

Two rectangles have a length of 17 inches and a width of 9 inches in addition to two triangles having a base of 7 inches and a height of 8.3 inches which is,

= 2(17×9) + 2[(1/2)×7×8.3) square inches.

= 306 + 58.1 square inches.

= 364.1 square inches.

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Answer:

11.64

Step-by-step explanation:

24.68/2.12=11.64

As the trianlges are SAS congurant the side NK = 1.8.

What is congruent by ASA?

The Angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below. According to the ASA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.

∠LJK=∠LMN

LM =4

MJ=2

LN=3.6

So, As the trianlges are SAS congurant the side NK = 1.8.

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Answer:

-320

Step-by-step explanation:

Use the formula

Tₙ = a + (n - 1)d where

a is the first term (in this case, -2)

n is the required term ( in this case, 54)

d is the common difference (in this case, -6)

54th term = -2 + 53 x -6 = -320

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Answer:

0.4

Step-by-step explanation:

4.00-3.55 = 0.45 = 0.4

The tip she gives is given by approximately 12.7% of the price.

The cost of a medium coffee is given by = $ 3.55

Mary Anne brings $ 4 with her and buy a coffee.

So, the remaining dollars with her is given by = 4 - 3.55 = $ 0.45

According question she gives this remaining amount as tip.

Therefore she gives a tip of $ 0.45 on the price of $ 3.55

The percentage of her tip = (0.45/3.55) * 100% = 12.7 % [Rounding off to one decimal place]

Hence the tip she gives is given by approximately 12.7% of the price.

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Answer:

A) 4 batches

B) 1 1/2 batches

C) 10 batches

D) 1 2/3 batches

Step-by-step explanation:

A) A 1/4 goes into 1, 4 times so it would make 4 batches.

B) 1/4 = 2/8 so 3/8 = 1.5/4 and that would make 1.5 batches.

C) since 1 cup of sugar can make 4 batches, 2 cups can make 8 batches and 1/2 cup makes 2, so 8+2= 10 batches

D) 1/4=3/12 that means 5/12 = 1/4+1/6 and 1/6 divided by 1/4 = 2/3 so that means that it can make 1 2/3 batches.

Answer:

m∠2 = 94°

Step-by-step explanation:

m∠3 and m∠2 are vertically opposite angles meaning they have equal angle. They are of equal measure.

Given that m∠3 = 94°, so m∠2 = 94° as well.

Answer:

94°

Step-by-step explanation:

We know that vertically opposite angles are equal to each other.

Therefore,

<2 = <3

94° = 94°

262 "hyper-texters," or teens who spend more than three hours per day on their smartphones, were found in a sample of 400 youngsters. if North High School enrolls 2,000 pupils.

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The height of the pebble after 2 seconds is 201 feet.

From the question, we have the following parameters that can be used in our computation:

y = 265 − 16t2.

The height of the pebble after 2 seconds is given by

y = 265 - 16 * 2^2.

Plugging in the values:

y = 265 - 16 * 4

y = 265 - 64

y = 201 feet

So, the height of the pebble after 2 seconds is 201 feet.

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Complete question

The deck of a bridge is suspended 265 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by

y = 265 − 16t2. What is the height after 2 seconds

Answer: A rational function is a function that is a fraction and has the property that both its numerator and denominator are polynomials.

Step-by-step explanation:

Answer:

Total people =107

Women =57

Men =50

Men who don't like tea =20

Men who like tea= 30

Women who like tea = (total people who like tea)-(men who like tea)

Women who like tea= 30

Women who don't like tea =27

a=50

b=30

c=20

d=57

e=30

f=27

Number of pounds of banana sold is, 14

And, Number of pounds of grapes sold is, 36

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

Given that;

Each pound of banana sell for $2.

And, Each pound of grapes sell for $1.

Now, Let number of pounds of sell banana = x

And, Number of pounds of sell grapes = y

Since, There are 50 pounds of fruits are sell.

So, We can formulate;

⇒ x + y = 50   .. (i)

And, Each pound of banana sell for $2.

And, Each pound of grapes sell for $1.

Hence, We get;

⇒ $2x + $1y = $64

⇒ 2x + y = 64  .. (ii)

Substitute value of y from (i) in (ii), we get;

⇒ 2x + y = 64

⇒ 2x + (50 - x) = 64

⇒ 2x + 50 - x = 64

⇒ x = 64 - 50

⇒ x = 14

And, From (i);

⇒ x + y = 50

⇒ 14 + y = 50

⇒ y = 50 - 14

⇒ y = 36

So, Number of pounds of sell banana = 14 pounds

And, Number of pounds of sell grapes = 36 pounds

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Answer:

5 people

Step-by-step explanation:

Relay race ---> 3/4 mile

Each runner runs 3/20 miles

3/4÷3/20

3/4×20/3=5

OR

3/4 --> 15/20

3/20 goes into 15/20 5 times

Answer:

5 runners

Step-by-step explanation:

Just multiply 3/20 by 3/4

Answer:

Easy, A is 4.1

Step-by-step explanation:

I just finished this too

Answer:

To find the greatest possible price of the calculator, we can use the information given about the total sales.

We know that the total sales of the calculator on three days are $180, $414, and $306. We can assume that the calculator is sold at a single price p on all three days, and the total number of calculators sold is x, y and z respectively.

So, we can set up the following equation:

px = $180 (1)

py = $414 (2)

p*z = $306 (3)

From (1) and (2) we can say x < y and from (2) and (3) we can say y > z

so the greatest possible price of the calculator will be the one from equation (2)

p = $414 / y

Therefore, the greatest possible price of the calculator is $414 / y.

It is important to note that we don't know the actual numbers of calculators sold, but we know that y is greater than x and z, and that is why we can say that the greatest possible price of the calculator is $414 / y.

A total of 40 nurses do not have a nursing diploma yet

From the question, we have the following parameters that can be used in our computation:

Nurses = 160 nurses

Diploma qualitifications = 75%

The above parameters mean that

No diploma qualification = (1 - Diploma qualitifications) * Nurses

Substitute the known values in the above equation, so, we have the following representation

No diploma qualification = (1 - 75%) * 160

Evaluate

No diploma qualification = 40

Hence, the nurses are 40

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The equations which represent circles whose diameters are 12 units and a center line lies on the y-axis are:

It is noteworthy to know that a center line on the y-axis can be interpreted as a coordinating pair in which case the pair looks like;

( 0, y )

Recall the equation of a circle which takes the form;

(x - h)² + (y - k)² = r²

Hence, since the center that lies on the y-axis, it automatically means that h = 0.

Also, if the diameter of the circle is 12 units

r = 12 / 2 = 6.

On this note, the required equation is;

x² + (y - k) = 6²

where k could be any real number.

Ultimately, the equations which are correct are;

x² + (y – 3)² = 36

x² + (y – 5)²

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The rays in the figure are (b) EA, EF, ED and EG

A ray in geometry is a part of a line that has one endpoint and continues infinitely in one direction.

It is represented by an arrow with the endpoint of the arrow being the endpoint of the ray

Using the above definition as a guide, we have the rays to be

option (b) EA, EF, ED and EG

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Using exponential function, the value of x that makes f(x) = g(x) is x = 6.7 (rounded to the nearest integer).

The value of x that makes f(x) = g(x) is approximately x = 76.

To solve this, you can set f(x) = g(x) and solve for x.

[tex]f(x)=400(0.90)^x\\g(x)=70(1.10)^x\\400(0.90)^x = 70(1.10)^x\\Divide both sides by 400 to get:\\(0.90)^x = (1.10)^x / (400/70)\\[/tex]

Take the logarithm of both sides and use the power rule:

[tex]x(log 0.90) = (log (1.10)) / (log (400/70))\\x = (log (1.10)) / (log (400/70)) / (log 0.90)\\x = 76.3 (round to the nearest integer)\\[/tex]

Therefore, the approximate value of x that makes f(x) = g(x) is x = 76.

To solve this, we can set the two equations equal to each other and solve for x.

[tex]f(x)=400(0.90)^x = 70(1.10)^x\\400(0.90)^x = 70(1.10)^x\\(0.90)^x = 70/400 (1.10)^x\\(0.90)^x / (1.10)^x = 70/400\\(0.90/1.10)^x = 70/400\\(0.81818)^x = 70/400\\[/tex]

Take the logarithm of both sides.

[tex]xlog(0.81818) = log(70/400)\\x = log(70/400) / log(0.81818)\\x = 6.7 (rounded to the nearest integer).[/tex]

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The evaluation of the given fraction is 1 2/19

From the question, we are to evaluate the given fraction

From the given information,

The given fraction is

(11/15 + 2/3) ÷ (1 1/2 - 7/30)

Simplifying

((11 + 10)/15) ÷*(3/2 - 7/30)

(21/15) ÷ ( (45 - 7)/30)

(21/15) ÷ (38/30)

Then,

21/15 × 30/38

(21 × 30) / (15 × 38)

630 / 570

21/19

= 1 2/19

Hence, the evaluation is 1 2/19

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Answer:

A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions correctly.

Step-by-step explanation:

The statement is true because, g(x) = f(x) + 4 is indeed a transformation of f(x) by shifting the graph 4 units up, and because the horizontal asymptote is determined by the highest degree term in the function, which in this case is the same for both functions, so the two functions will have the same vertical asymptote, but the horizontal asymptote is determined by the leading coefficient which is different for both functions, so the two functions will have different horizontal asymptotes.

Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

On solving the provided question we can say that quadratic equation is  y = 3x + 2x^2 => y = 14

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here,

quadratic equation is

y = 3x + 2x^2

y = 6 + 8

y = 14

as x = 2

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Answer:

corresponding

Step-by-step explanation:

<1 and <5 are corresponding angles because they are on the same side of the transversal and on the same side of l and m

Answer:

see explanation

Step-by-step explanation:

∠ 2 and ∠ 5 are on opposite ( alternate) sides of the transversal and are in between ( in the interior of ) the parallel lines.

The pair are then alternate interior angles.

a. The probability that both adults think most celebrities are good role models is 0.0359

b. The probability that neither of adults think that celebrities are good model is 0.6559.

P(adult think most celebrities are good role models) = 209 / 1100

Since the first selected adult is not replaced, there are 1099 total adults left.

P(second adult think most celebrities are good role models) = 208 / 1099

So, P(both adults think most celebrities are good role models) = 209 / 1100 * 208 / 1099

= 0.19 × 0.1893

= 0.0359

b) The probability that neither of adults think that celebrities are good model is,

P(Neither adult) = P(1st adult does not think)P(2nd adult does not think)

= ((1100 – 209)/1100)((1100 – 209– 1)/1099) =0.6559

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Complete question

In a sample of 1100 us adults 209 think the most celebrities are good role models. Two U.S adults are selected from this sample

Calculate the probability that both adults think most celebrities are good role models.

Calculated the probability that neither of adults think that celebrities are good model.

The approximate distance around the outside of the circular field is the circumference = 172.7 feet and the correct option is B.

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π = 3.14).

We shall derive the approximate distance around the outside of the circular field by calculating for the circumference as follows:

Radius of the circular feild = 27.5

circumference of the circular feild = 2 × 27.5 feet × 3.14

circumference of the circular feild = 55 feet × 3.14

circumference of the circular feild = 172.7 feet.

Therefore, the approximate distance around the outside of the circular field is derived as the circumference which is equal to 172.7 feet.

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The fifth term of the arithmetic sequence can be found to be 18.

There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the same" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."

In this arithmetic sequence therefore, you can find the common difference to be:

= 9 - 6

= 3

So the fifth term would be:

= 4th term + common difference

= 15 + 3

= 18

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The fifth term of the arithmetic sequence: 6, 9, 12, 15 is 18.

The formula for the nth term of an arithmetic sequence is expressed as;

aₙ = a₁ + d( n - 1 )

Given the data in the question;

6, 9, 12, 15.

Plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

a₅ = 6 + 3( 5 - 1 )

a₅ = 6 + 3( 4 )

a₅ = 6 + 12

a₅ = 18

Therefore, the fifth term of the sequence is 18.

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From the coordinates we can see the rule for this transformation:

This is a rotation by 180 degrees and translation 5 units down, therefore shape or size remain as is. So this is a congruence transformation.

Answer:

Rotation of 180° about the origin (0, 0) followed by a translation of 5 units down.

Congruence transformation.

Step-by-step explanation:

Given vertices of ΔPQR:

Given vertices of ΔSTU:

From observation, the mapping rule the transforms ΔPQR to ΔSTU is:

Rotation of 180° about the origin (0, 0) followed by a translation of 5 units down.

This is a congruence transformation as the two triangles have the same shape and same size.