Cedric deposited $796.00 in a savings account that earned 2.5% simple interest annually. Determine the amount of interest Cedric's account earned after 1 year and 9 months. (4 points)
$37.81
$34.83
$348.25
$295.56

Recall that the sum of the interior angles of a convex polygon with n sides is:

Therefore:

12) If the sum of the interior angles of a convex polygon is 3240 degrees, then we can set the following equation:

Dividing the above equation by 180 we get:

Adding 2 to the above equation we get:

13) If the sum of the interior angles of a convex polygon is 6660 degrees, then we can set the following equation:

Dividing the above equation by 180 we get:

Adding 2 to the above equation we get:

Answer:

12) 20.

13) 39.

The lateral surface area of the triangular base prism is 288 m².

The lateral area of the triangular base prism can be found as follows:

Lateral area of the triangular base prism = (a + b + c)h

where

Therefore,

a = 7 m

b = 8 m

c = 9 m

h = 12 m

Therefore,

Lateral area of the triangular base prism = (7 + 8 + 9)12

Lateral area of the triangular base prism = 24 × 12

Lateral area of the triangular base prism = 288 m²

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Answer:

280 m³

Step-by-step explanation:

Volume of a Triangular Prism

Solving

Answer:

280

Step-by-step explanation:

So first lets establish the formula for a Triangular Prism :

1/2 * b * h * l

now lets use the mesurements given to substitute into the formula :

1/2 * 7 * 8 * 10

now lets solve it by first multiplying all the whole numbers together!

7 * 8 = 56

56 * 10 = 560

Finally lets multiply 560 by 1/2 or in other words, divide 560 by 2 :

560/2 = 280

The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1

To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.

Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.

Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.

On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.

Option 1 is correct.

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Answer:

its B

Step-by-step explanation:

Answer:

14 ft = 4 yd 2 ft

Explanation:

1 yd is equivalent to 3 ft, so first, we need to convert 5 yds to ft as follows

Therefore, the given expression is equal to

5yd - 1 ft = 15 ft - 1 ft = 14 ft

Now, we need to convert 14 ft to yards and ft. First, we can write 14 ft as

14 ft = 12 ft + 2 ft

Then, 12 ft to yd is equal to

Therefore, the answer is

14 ft = 12 ft + 2t

14 ft = 4 yd 2 ft

The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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Answer:

32÷8=4

Step-by-step explanation:

1 pack of sugar is 8 and he needs 32 so 32 divided by 8 of 1 pack will then get you 4 packs he will need.

Answer:

74

Step-by-step explanation:

84+84=168

316-168=148

148/2=74

Answer:

y = 2x+1

Step-by-step explanation:

The slope-intercept form is given by y = mx + c

where m is the slope, and c is the y-intercept.

Let's apply the point-slope form,

that is: \(\frac{y-y{__1}}{x-x{__1}}} = m\)

Given \(({x__1},{y__1}) = (2,5)\) and \(m = 2\)

Let plug in all these values into the point-slope form.

\(\frac{y-5}{x-2}} = 2\)

y-5 = 2x-4

y = 2x-4+5

y = 2x+1

Answer:

Yes they are congruent

Step-by-step explanation:

let the triangle as ABC

and let the median of BC is point D

Now,

in triangles ABD and ACD

90° is common

side AB and AC is common

and AD is common

so by A-S-S property they are congruent.

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The diameter of the circle is given 40 cm,

Consider that the radius 'R' of the circle is half its diameter,

Thus, the radius (JK)) of the circle is 20 centimeters.

Consider that the circumference 'C' of the circle is given by the formula,

Substitute the value,

The scenarios that can be considered a seller-based discount are:

A. The offer by Wire and Cable

B. Carfna's Fine Foods

C. Mouser Electronics offer

E. Carchex Car Maintenance

A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.

The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.

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Answer:

A

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

0.8 * x = 40

40/0.8=50

Answer: 2.63

Step-by-step explanation:

Using the formula \(A=\frac{1}{2} ab \sin C\),

\(6\sqrt{2}=\frac{1}{2}(2x-1)(x+3) \sin 45^{\circ}\\\\6\sqrt{2}=\frac{(2x-1)(x+3)}{2} \cdot \frac{\sqrt{2}}{2}\\\\6=\frac{(2x-1)(x+3)}{4}\\\\24=(2x-1)(x+3)\\\\24=2x^2 +5x-3\\\\2x^2 +5x-27=0\\\\x=\frac{-5 +\sqrt{5^2 -4(2)(27)}}{2(2)} \text{ } (x > 0)\\\\x=\frac{\sqrt{241}-5}{4} \approx 2.63\)

Answer: The answer is 1.62.

Explanation: It is in the image.

The selling prices of the sculpture, painting, and photograph were 166.5 million, 107.0 million, and 57.6 million respectively.

Let's call the selling prices of the sculpture, painting, and photograph as S, P, and Ph respectively.

From the first sentence, we know that:

S + P + Ph = 308.0 million

From the second sentence, we know that:

P = Ph + 49.4 million

And from the third sentence, we know that:

P + Ph = S + 24.4 million

Now we can substitute the second equation into the third equation:

(Ph + 49.4 million) + Ph = S + 24.4 million

Simplifying:

2Ph + 49.4 million = S + 24.4 million

2Ph = S - 25 million

Substituting this into the first equation:

S + P + Ph = 308.0 million

S + (Ph + 49.4 million) + Ph = 308.0 million

2Ph + S = 258.6 million

Now we can substitute the equation we derived earlier:

S + 2Ph - 49.4 million = 258.6 million

S + 2Ph = 308.0 million

Substituting 2Ph = S - 25 million:

S + S - 25 million = 308.0 million

2S = 333.0 million

S = 166.5 million

Now we can use this value to find P and Ph:

P = Ph + 49.4 million

P + Ph = S + 24.4 million

Substituting S = 166.5 million in both equations:

P + Ph = 190.9 million

P = Ph + 49.4 million

Solving these two equations simultaneously:

Ph = 57.6 million

P = 107.0 million

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Answer:

14w 2 − 4w

Step-by-step explanation:

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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The points that represent this data are shown in the image attached below.

A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

Based on the information provided in table above, the points that represent this data are shown in the image attached below.

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Answer:

please look at the picture

Their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

To determine the day of the week on which Kai and Finley's exam was scheduled, we need to consider the information provided about the trail being closed on Mondays, Wednesdays, and weekends.

If they had planned to hike to the log cabin for two days after the exams, and the trail is closed on weekends, it means they cannot start hiking on Saturday or Sunday.

Since they cannot start hiking on Saturday or Sunday, the two possible options for the exam day would be Monday or Wednesday, as they have not specified whether the hike starts immediately after the exams or the day after.

However, we can conclude that their exam was not scheduled on Monday, as the trail is closed on Mondays, and they had planned to hike immediately after the exams.

Therefore, their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

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If one person received 25 messages. Then the number of messages received by each friend will be 26.

The division of something into distinct portions, or the sharing of something among other persons, locations, or things, is referred to as division.

A group of 9 friends received a combined total of 233 text messages in two hours. One person received 25 messages.

Then the number of the remaining messages will be

→ 233 - 25

→ 208

Then the number of the text messages that each of the other 8 friends receives is the same number of the messages. Then we have

Let each friend has an equal number of the messages be x. Then

\(\rm x = \dfrac{208}{8}\\\\x = 26\)

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Answer:

i think probably x = 10

Step-by-step explanation:

sin(60°) = 5√3/x

√3/2 = 5 √3/x

√3 x = 10√3

x = 10

Answer:

a) 4ABC such that LA is obtuse

c) AABC such that C is acute

Step-by-step explanation:

An angle is obtuse if it measures more than 90 degrees and acute if it measures less than 90 degrees. In statement a), the angle LA is obtuse, which means it measures more than 90 degrees. In statement c), the angle C is acute, which means it measures less than 90 degrees. These two statements contradict each other because they cannot both be true at the same time.

Answer:

3:7

Step-by-step explanation:

Let x = pounds of the $10 rice in the mixture

Let y = pounds of the $30 rice in the mixture

Total cost of the $10 rice = 10x

Total cost of the $30 rice = 30y

(10x + 30y) / (x + y) = 24

Solve this equation for y/x:

10x + 30y = 24(x + y)

10x + 30y = 24x + 24y

30y - 24y = 24x - 10x

6y = 14x

y/x = 6/14  simplify the fraction

y/x = 3/7

So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.

It looks like the vector field is

F(x, y) = 3x ^(2/3) i + e ^(y/5) j

Find a scalar function f such that grad f = F :

∂f/∂x = 3x ^(2/3)   =>   f(x, y) = 9/5 x ^(5/3) + g(y)

=>   ∂f/∂y = e ^(y/5) = dg/dy   =>   g(y) = 5e ^(y/5) + K

=>   f(x, y) = 9/5 x ^(5/3) + 5e ^(y/5) + K

(where K is an arbitrary constant)

By the fundamental theorem, the integral of F over the given path is

∫c F • dr = f (0, 1) - f (1, 0) = 5e ^(1/5) - 34/5

Answer:

0.0143 = 1.43% probability that first 4 digits of the code are even numbers.

Step-by-step explanation:

Arrangements of n elements:

The number of possible arrangements of n elements is given by:

\(A_{n} = n!\)

Probability:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

Desired outcomes:

First four digits are even(2, 4, 6 and 8 are even, so arrangements of 4 elements).

Last four digits are odd(1, 3, 5 and 7 are odd, so the last four elements are also arrangements of 4 elements). So

\(D = 4!*4! = 24*24 = 576\)

Total outcomes:

Arrangements of 8 digits. So

\(T = A_{8} = 8! = 40320\)

Probability:

\(p = \frac{D}{T} = \frac{576}{40320} = 0.0143\)

0.0143 = 1.43% probability that first 4 digits of the code are even numbers.