You started a savings account by depositing $4,200. The savings account earns 2.1% APY, compounded monthly. What was the balance in the account after 2 months?
1=Prt

The simplified ratios are shown below:

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

We have ratios

1. 30: 45

= 30/45

= 2 /3

2. 350 : 400

= 350/400

= 7/8

3. 600g : 4 Kg

= 600 / 4000

= 6/ 40

= 3/20

4. 65:91

= 5 / 7

5. 12 cm  : 1 m

= 12 / 100

= 3 /25

6. 3 Km: 50 m

= 3000 / 50

= 60

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Answer:

The probability of picking the first boy is 14/26 and the probability of picking another boy is 13/25.

Step-by-step explanation:

The sample taken by Sam is Biased sampling.

A subset of a population is chosen at random in a basic random sampling. Each person in the population has an exact equal probability of getting chosen using this sampling technique.

Given:

Sam asked 15 of his friends what they thought about the pizza they just had.

Sam here chooses his friend that means the people are selective already.

He already chooses the people which were known to him.

So, the selection here is biased sample.

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The percent probability that Isabella will roll a 14 is 0%, since the dice she is using has a sample space of 1 through 12 and there is no 14 on the dice. Therefore, the probability of her rolling a 14 is 0%.

The probability of Isabella rolling a 14 with a 12-sided dice is 0%. This is because the sample space of the dice is 1 through 12, and there is no 14 on the dice. In order to calculate the probability, you would need to take the number of possible outcomes (the sample space) and divide it by the number of outcomes you are looking for. In this case, the sample space is 12 and the outcome being searched for is 1, giving you 12 divided by 1 which is 0. This means that the probability of Isabella rolling a 14 is 0%. This is because the sample space does not contain a 14, thus making it impossible for Isabella to roll a 14.

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Answer:

Step-by-step explanation:

(f - g) (x) = f(x) - g(x)

Given that f(x) = 7x + 5 and g(x) = 6x - 8, we can substitute these values into (f - g) (x):

(f - g) (x) = (7x + 5) - (6x - 8)

(f - g) (x) = 7x + 5 - 6x + 8

(f - g) (x) = x + 13

So, the answer is (f - g) (x) = x + 13

To find how many more texts were sent this week than last week we use,

(f − g)(x) = x + 13.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

From the given information, The number of more texts sent this week than last week is the difference between the functions f(x) - g(x).

= (f - g)x.

= (7x + 5) - (6x - 8).

= 7x + 5 - 6x + 8.

= x + 13.

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Answer: 25 sessions

Step-by-step explanation:

Set up an equation.

50+10x=12x

50=2x

x=25

She will have to take 25 sessions for both gym costs to be the same.

You can check this too. 50 plus 10*25 is $300, and 12*25 is $300.

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Hope this helps.

MM4343

Answer: We can start by setting the cost of the two gyms equal to each other and then solving for the number of sessions. Let's call the number of sessions Macy takes x. The cost of Avery's gym is 50 + 10x, and the cost of Gabe's gym is 12x. Setting these two equal to each other, we have:

50 + 10x = 12x

Subtracting 12x from both sides:

50 = -2x + 10x

Simplifying:

50 = 8x

Dividing both sides by 8:

x = 6.25

So, Macy would need to take 6.25 sessions for the cost of both gyms to be the same. However, since she can only take whole number of sessions, she would need to take 7 sessions to make both gyms cost the same.

Step-by-step explanation:

The value of z in the triangle using trigonometric ratio is; z = 10.90

The three basic trigonometric ratios from which others are derived are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

From the diagram, we can easily see that z is the opposite side of the given angle and 13 is the hypotenuse. Thus;

z/13 = sin 57

z = 13 * sin 57

z = 13 * 0.83867

z = 10.90

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The scientist poured 17 ounces of chemical out of the beaker, calculated from the total and remaining amount of chemical.

We are aware of the conversion unit that 1 pint is equal to 16 fluid ounces. So, total amount of chemical in the beaker is -

Chemical in beaker in points = 5/4

Chemical in beaker in ounces = 16×1/14

Chemical in beaker = 20 ounces

Now, the expression to calculate poured amount of chemical will be -

Total amount = poured chemical + remaining chemical

20 = poured chemical + 3

Poured chemical = 20 - 3

Performing subtraction on Right Hand Side of the equation

Poured chemical = 17 ounces

Therefore, 17 ounces of chemical was poured.

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The correct question is -

A beaker contains 1 1/4 pints of a chemical. A scientist pours the chemical out of the beaker until only 3 fluid ounces remain. How many fluid ounces of the chemical did the scientist pour out of the beaker?

A. The functions are not inverse of each other.

B.  The domain of the composition using interval notation is (-∞, ∞)

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

A. To show that two functions are inverses of each other, we need to show that their compositions are equal to the identity function, which is denoted as f(x) = x.

That is, we need to show that:

(f ∘ g)(x) = x

(g ∘ f)(x) = x

where ∘ denotes function composition.

First, we'll find the composition (f ∘ g)(x):

(f ∘ g)(x) = f(g(x))

             = f(9x+1)

             = (9x+1) - 3

             = 9x - 2

Next, we'll find the composition (g ∘ f)(x):

(g ∘ f)(x) = g(f(x))

             = g(x-3)

             = 9(x-3) + 1

             = 9x - 26

Since (f ∘ g)(x) ≠ x and (g ∘ f)(x) ≠ x, the functions f(x) and g(x) are not inverses of each other.

B. To find the domain of (f ∘ g)(x), we need to ensure that the input to g(x) is within its domain, which it is for all real numbers. To find the domain of (g ∘ f)(x), we need to ensure that the input to f(x) is within its domain, which it is for all real numbers.

Therefore, the domains of (f ∘ g)(x) and (g ∘ f)(x) are both all real numbers, and we can express this using interval notation as:

Domain of (f ∘ g)(x) and (g ∘ f)(x):

(-∞, ∞)

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Step-by-step explanation:

sorry for the wait I hope this helps you with you're problem

The probability of selecting a student who is wearing a yellow shirt is 36 %

The total number of students is 45 students and out of these, 3 / 7 are wearing blue shirts while 2 / 9 are wearing red shirts.

This means that the number of students wearing yellow is:

= 45 - ( 45 x 3 / 7 ) - ( 45 x 2 / 9 )

= 45 - 19 - 10

= 16 students

The probability of selecting a student who is wearing yellow is :

= 16 / 45

= 36 %

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The full question is:

A class has 45 students of the students are wearing 3/7 blue shirts, of

them are 2/9  wearing red shirts, and the rest are wearing yellow shirts.

What is the probability of selecting a student who is wearing a yellow

shirt?

If lines A, B and C shows proportional relationships, then the line A has a constant of proportionality between y and x is 5

Given the line A, B and C

The constant of proportionality is the ratio of the y coordinates to the x coordinate

k = y /x

Where k is the constant of proportionality

Consider the line A

One point on the line = (1, 5)

Constant of proportionality K = 5/1

= 5

Consider the line B

One point on the line = (3, 5)

Constant of proportionality k = 5/3

Consider the line C

One point on the line = (7, 5)

Constant of proportionality = 5/7

Therefore, the line A has the constant of proportionality of 5

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The given question is incomplete, the complete question is

Lines A, B, and C show proportional relationships. Which line has a constant of proportionality between y and x of 5?

Answer:

Therefore, the correct answer is (a) 24.52 cm^2.

Step-by-step explanation:

To find the area of the figure, we need to find the area of the two triangles and the trapezoid and add them together.

The top triangle has a base of 5 cm and a height of 2.7 cm, so its area can be found by multiplying the base by the height and dividing by 2: (5 * 2.7) / 2 = 13.5 cm^2.

The bottom triangle has a base of 3 cm and a height of 2.7 cm, so its area can be found by multiplying the base by the height and dividing by 2: (3 * 2.7) / 2 = 4.05 cm^2.

The trapezoid has a base of 5 cm, a top length of 6.8 cm, and a height of 3.4 cm, so its area can be found using the formula for the area of a trapezoid: ((5 + 6.8) / 2) * 3.4 = 20.06 cm^2.

The total area of the figure is the sum of the areas of the three shapes: 13.5 + 4.05 + 20.06 = 37.61 cm^2.

Therefore, the correct answer is (a) 24.52 cm^2.

Answer:

1

Step-by-step explanation:

everything to power of 0 is 1, except for 0^0 is undefined

The transformation that fully transforms Shape A to Shape C is reflected in the x =6.5

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

The line x = 2, x = 6, and x = 6.5 is given on the graph below.

Shape A is reflected in the line with equation x = 2 to get Shape B.

Shape B is reflected in the x = 6 to get Shape C.

Now,

Shape A is reflected in the x =6.5 to get Shape C.

Thus,

The transformation that fully transforms Shape A to Shape C is reflected in the x =6.5

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Step-by-step explanation:

Since it varies directly, we can set up a ratio and solve for x

[tex] \frac{ - 4}{ - 2} = \frac{x}{12} [/tex]

Next we would cross multiply... multiply the numbers diagonally

[tex]( - 4)(12) = ( - 2)(x)[/tex]

Simplifying

[tex] - 48 = - 2x[/tex]

Now to get X alone, we would divide by the number attached to it, so -2. We'd do -2 on the -48 also

[tex]x = 24[/tex]

Part(a), An inequality to show the number of additional minutes required to get at least 80% battery life will be 3m + 40 ≤ 80.

Part(b) The number of minutes will be 13 minutes and 20 seconds.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that according to a survey, students often have 40% of their cell phone batteries left at the end of the school day when utilizing the newest fast charger, which charges phones at a pace of 3% per minute.

Part(a) The inequality can be written as:-

3m + 40 ≤ 80.

Part(b), The number of minutes will be:-

3m + 40 ≤ 80.

3m ≤ 40

m ≤ 40 / 3

m ≤ 13.33

The time can also be written as 13 minutes and 20 seconds.

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Hi there, here's your answer:

Given two trapeziums, ABCD and WXYZ, where ABCD ~ WXYZ.

To find:

Value of v.

Solution:

We see that 2 sides are equal for both the trapeziums and it appears that

when comparing these sides, the bigger sides which are equal are always a multiple of 5 of the smaller side.

Applying this to find the similarity of the other two sides which are not equal, we find that on comparing the sides that are known, the similar side for AB is WX and AB = 5 × WX.

Thus, using this we can find the value of v to be YZ × 5 = 10 × 5 = 50m

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Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex]  => AC = [tex]\sqrt{115}[/tex]

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.

Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.

Here, in this triangle by Pythagorean theorem

[tex]A^2 = B ^2 + c^2[/tex]

AC = [tex]\sqrt{14^2- 9^2}[/tex]

AC = [tex]\sqrt{196- 81}[/tex]

Ac = [tex]\sqrt{115}[/tex]

Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.

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The graph that best models the situation of the home value increasing every year is Graph A

To find the graph, use the percentage increase to find the value of the house in two different time periods and then check which graph coincides with this prediction.

After 5 years, the value of the house should be:

= 200, 000 x ( 1 + 6 % ) ⁵

= $ 267, 645

After 10 years :

= 200, 000 x ( 1 + 6 % ) ¹⁰

= $ 358, 170

The best graph for the situation is therefore Graph A which starts from $ 200, 000 and passes through the above points.

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The probability of a person dying of renal failure if neither of their parents had renal failure is 0.056 or about 5.6%.

To solve this problem, we can use Bayes' theorem, which states that:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this case, we want to find the probability of a person dying of renal failure given that neither of their parents had renal failure. Let's define the following events:

R: death due to renal failure

P: at least one parent with renal failure

NP: neither parent has renal failure

We are given the following information:

Total deaths = 1000

Deaths due to renal failure (R) = 321

People with at least one parent with renal failure (P) = 460

Deaths due to renal failure among people with at least one parent with renal failure = 115

Using this information, we can calculate the probabilities as follows:

P(R) = 321/1000

P(P) = 460/1000

P(R|P) = 115/460

To find the probability of a person dying of renal failure given that neither of their parents had renal failure (i.e., P(R|NP)), we need to use Bayes' theorem. We can start by finding the probability of neither parent having renal failure (i.e., P(NP)):

P(NP) = 1 - P(P) = 1 - 0.46 = 0.54

Next, we can use the law of total probability to find the probability of dying of renal failure among people with neither parent having renal failure:

P(R|NP) = P(R) * P(NP|R) / P(NP)

We can find P(NP|R) using the formula:

P(NP|R) = P(NP ∩ R) / P(R)

To find P(NP ∩ R), we can use the formula:

P(NP ∩ R) = P(R|NP) * P(NP)

Substituting the values, we get:

P(R|NP) = P(R) * P(NP|R) / P(NP)

= 321/1000 * (1 - 115/460) / 0.54

= 0.056

This calculation shows how conditional probabilities can be calculated using Bayes' theorem and the law of total probability.

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Answer:

hey there here's your answer !!!!

Step-by-step explanation:

For two-digit numbers, there is the TENS place and the ONES place. Let's take a closer look at the place value for the number 12. The 1 is in the TENS place, and the 2 is in the ONES place. That's because the number 12 is made up of 1 ten and 2 ones.

The probability expressed as P(x ≥ 92) in the normal distribution is; C: 0.84

We are given that the normal distribution has;

Population mean: μ = 98

Population standard deviation; σ = 6

Sample mean; x' = 92

Thus, z-score is;

z = (x' - μ)/σ

z = (92 - 98)/6

z = -1

Thus, from z-score tables we have;

P(z ≥ -1) = 0.84

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Answer:

x = 1/3

Step-by-step explanation:

64^2x+1 = 1024
4^3(2x+1) = 4^5

Since the bases are the same, two expressions are only equal if the exponents are also equal.

3 (2x + 1) = 5

Divided each term by 3

2x + 1 = 5/3

2x = 2/3

x = 1/3

The greatest whole number that divides both 372 and 324 without a remainder is 4.

To find the greatest whole number that divides both 372 and 324 without a remainder, we can use the concept of the greatest common divisor (GCD).

One method to find the GCD is to factor each number into its prime factors and then find the product of the common prime factors.

372 can be factorized as 2 * 186, and 324 can be factorized as [tex]2^2 * 3^4[/tex]

The greatest common divisor is [tex]2^2[/tex], which is equal to 4.

So, the greatest whole number that divides both 372 and 324 without a remainder is 4. This means that 4 is the largest number that can divide both 372 and 324 evenly, leaving no remainder.

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Using the table of measurement,  0.4970969  is equivalent to 800 meters

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. To convert a mile measurement to a centimeter measurement, multiply the length by the conversion ratio.

1 inch = 2.54 centimeters

1 foot = 0.3048 meters

1 mile = 1.60 kilometers

Recall that 1 mile is 1609.344 meters

Therefore, the equivalence is 800/1609.344

Therefore 800 meters is equivalent to 0.4970969 miles

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The solution of the expression for the value of k is [tex]\dfrac{8}{3^{15}}[/tex].

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

The given expression is,

[tex]\dfrac{3^8}{2}\times \dfrac{3^8}{4}\times k = 3[/tex]

The given expression will be solved as below,

[tex]\dfrac{3^8}{2}\times \dfrac{3^8}{4}\times k = 3[/tex]

Apply the properties of exponents which say that the number with the same base its exponents will be added.

[tex]\dfrac{3^{16}}{8}\times k = 3[/tex]

Now cross-multiply the number 3 by the ratio of 8 and the 3¹⁶ and solve for the value of k,

[tex]k = \dfrac{8}{3^{15}}[/tex]

Therefore, the value of k will be calculated as the ratio  [tex]\dfrac{8}{3^{15}}[/tex].

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a. The flagpole is 5 feet away from the building.

b. The height of the flagpole is 8 feet.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

The distance from the building to the flagpole is,

tan35° = 3.5/x.

x = 3.5/0.7.

x = 5 feet.

Now, tan48° = x/5.

x = 5/1.11.

x = 4.5 feet.

Therefore, The height of the flagpole is 4.5 + 3.5 = 8 feet.

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