Alec invested $1500 in an account with annually compounded interest. The account earns 4% annual interest. How much will Alec have in his account after 4 years?

Answer:

There is no picture or diagram so add them and i can edit this answer, look at paperclip sign first take picture screen shot then add pic on paperclip edit button here.

Step-by-step explanation:

For missing sides of a triangle we do the following.

Does it have a right Angle determine other angle measures, say if an external angle on a straight line showed 145 then its adjoing interior would be 180-145=35 degree.

Are the measure of the lengths congruent with a larger or smaller triangle shown.

If yes then if one triangle showed 4 and same triangle showed 6 and had ne missing, then the other had 8 and 10 and had one missing we would compare and if 8 was the same as 4 we would recognise the congruent triangle is x2 (scale factor 2) so measure 6 woyuld also be measure 12 for the other triangle. and then to find the smaller missing side we see 10 is left over and 10/2 = 5

Other ways to find length is through Pythagoras  we use the squares a^2 + b^2 = c^2 for missing slant

and c^2 - b^2 = a^2 for any missing side

so a represents any missing side for the second equation and c represents the missing side if it is a slant only.

Answer:

y = 15x + 65, or y = 15(9) +65

Step-by-step explanation:

So first, subtract $65 from $200 because Brittany is already using $65 for a plantar.  For y = mx+b, $65 would be the b, because b is the fixed number, the number that cannot be changed. At this point, you are at y = mx + 65.

Now you are left with $135. Brittany wants to buy flowers with the remaining money. What you can do is division to see how many times $15 will go in $135  because with one flower = $15, we want to see the maximum number we can spend. If you do the division, you will see that $15 goes into $135 9 times, meaning you can buy 9 flowers, because each flower is $15, maxing out the remaining money you have.

In equation form, $15 would be the m, because m is what you multiply by and x is the independent variable, or the number of flowers Brittany will buy.  

y = 15x + 65, or y = 15(9) +65

The value of f(g(2)) from the given functions f(x) and g(x) is 3.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=2x²+1 and g(x)=3x-5.

We need to find f(g(2)).

Put x=2 in the function g(x)=3x-5, we get

g(2)=3×2-5

= 6-5

= 1

So, g(2)=1

Put x=1 in the function f(x)=2x²+1, we get

f(g(2))=2(1)²+1

= 2+1

=3

Therefore, the value of f(g(2)) is 3.

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If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.

Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².

So, we have:

lw = 114

Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.

So, we have:

2l + 2w = 50

We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:

l = 114/w

We can then substitute this expression for l in the second equation:

2(114/w) + 2w = 50

Multiplying both sides by w to eliminate the fraction, we get:

228 + 2w² = 50w

Rearranging and simplifying, we get a quadratic equation:

2w² - 50w + 228 = 0

We can solve for w using the quadratic formula:

w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5

Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:

l(5) = 114

l ≈ 22.8

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The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.

An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.

In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.

Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.

The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.

In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.

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Answer:

19 adults were questioned

10.5% of adults had five children

Step-by-step explanation:

Add all of the hights of the bars

Divide the amount of persons having five children by the amount of persons in total.

The approximate surface area of the package is approximately 245.05 square inches.

The best model for the package is a cylinder.

To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.

The lateral surface area of a cylinder can be calculated using the formula:

Lateral Surface Area = 2πrh

where r is the radius of the base and h is the height.

The area of the circular base can be calculated using the formula:

Area of Base = \(πr^2\)

Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.

Using the given height of 13 inches, we can now calculate the surface area:

Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches

Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches

To find the total surface area, we add the lateral surface area and the area of the base:

Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches

Therefore, the approximate surface area of the package is approximately 245.05 square inches.

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Answer:

x = 9

Step-by-step explanation:

Move all terms that don't contain x to the right side and solve.

The solution to the equation 4x - 6 = 30 is x = 9.

Given the equation in the question:

4x - 6 = 30

To solve the equation 4x - 6 = 30, first, isolate the term with the variable:

4x - 6 = 30

Add 6 to both sides of the equation to isolate the term with the variable:

4x - 6 + 6 = 30 + 6

Add -6 and 6

4x + 0 = 30 + 6

4x = 30 + 6

Add 30 and 6

4x = 36

Divide both sides of the equation by 4 to solve for x:

(4x)/4 = 36/4

x = 36/4

x = 9

Therefore, the value of x is 9.

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Answer:

0.0793 > 0.01, which means that we have a result in line with the manufacturer's claim.

Step-by-step explanation:

Manufacturer’s claim that the average nicotine content does not exceed 3.5 mg

This means that the null hypothesis is given by:

\(H_{0}: \mu = 3.5\)

And the alternate hypothesis is:

\(H_{a}: \mu > 3.5\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

3.5 is tested at the null hypothesis

This means that \(\mu = 3.5\)

A random sample of 8 cigarettes of a certain brand has an average nicotine content of 4.2 milligrams and a standard deviation of 1.4 milligrams.

This means that \(n = 8, X = 4.2, \sigma = 1.4\)

Value of the z-statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{4.2 - 3.5}{\frac{1.4}{\sqrt{8}}}\)

\(z = 1.41\)

Pvalue of the test:

We are testing if the mean is higher than 3.5.

The sample mean found is of 4.2, and we have to find the probability of finding a sample mean at least as large as this, which is 1 subtracted by the pvalue of z = 1.41.

z = 1.41 has a pvalue of 0.9207

1 - 0.9207 = 0.0793

0.0793 > 0.01, which means that we have a result in line with the manufacturer's claim.

Answer:

1

Step-by-step explanation:

1 increased by 3=1+3=4

Twice of 1=1+1=2

4 is two more than 2.

Therefore, the number=1

The area of the circle with radius 33 cm is 3419.5 square centimeters.

According to the question,

We have the following information:

Radius of the circle = 33 cm

We know that the following formula is used to find the area of the circle:

Area of the circle = π\(r^{2}\) where r is the radius of the circle

There are two approximate values of π which are 22/7 and 3.14. In this case, we will use the value of π as 3.14.

So, we have the following expression:

Area of the circle = 3.14*33*33

Area of the circle = 3419.46 square centimeters

Rounding it off to one decimal point:

3419.5 square centimeters

Hence, the area of the circle with radius 33 cm is 3419.5 square centimeters.

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Answer:

I hope this will help you :)

The width of the river using the similar triangle is 43.3 metres.

The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.

Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Hence, let's find the width of the river.

Therefore,

18.6 / 34.2 = AB / 79.6

cross multiply

18.6 × 79.6 = 34.2 AB

34.2 AB = 1480.56

divide both sides of the equation by 34.2

AB = 1480.56 / 34.2

AB = 43.2912280702

AB = 43.3 metres

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Answer:

p: x = 4  

q: y = -2

If p happens then q will also happen

Step-by-step explanation:

Given two propositions, we want to rearrange them in a conditional statement.

The correct answer is:

p → q

First, a conditional statement is something of the form:

If [Hypothesis] then [Conclusion]

So, if the first part is true, then the second part must be true.

Now, here we have two propositions:

p: "x  = 4"

q: "y = -2"

We want to write:

"if x = 4, then y = -2"

this is just written as: "p implies q" or:

p → q

Where "→" means "then", and the initial "if" is tacit.

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Using limits the value of k is c √2

The limit of a function is the valuer the function tends to as the dependent variable tends to a particular value.

Given that the limit lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1, we desirte to find the value of k.

So, we proceed as follows

lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1

Factorizing out √2x, we have that

lim n → ∞ [x√(x + 1)[1 - √(2x√(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√(x + 1)√(2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

Also, factorizing out √x, we have that

lim n → ∞ [x√x√(1 + 1/√x)√2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

Factorizing x² from the denominator, we have that

lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/x²(7/x² - 6/x + k) = - 1

lim n → ∞ [√2√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7/x² - 6/x + k) = - 1

Now substituting x = ∞ into the equation, we have that

[√2√(1 + 1/√∞)[1/√(2∞ - √(1 + 3/√(2∞)]/(7/∞² - 6/∞ + k) = - 1

[√2√(1 + 0)[0 - √(1 + 0]/(0 - 0 + k) = - 1

[√2√(1)[- √1]/k = - 1

[√2(1)[- 1]/k = - 1

-√2/k = - 1

k = -√2/-1

k = √2

So, the value of k is c √2

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Answer:

1: by using this equation x*y=96, or just list out 96's factors

2: 3 by 32

3: no, unless you want to use decimals.

4: finding the surface area  

Answer:

$483.75

Step-by-step explanation:

32.25 x 15 = 483.75

If I'm wrong, please kill me ;-;

Аnswer is in а photo. I couldn't аttach it here, but I uploаded it to а file hosting. link below! Good Luck!

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Answer:

y= -2/3x+6

Step-by-step explanation:

Answer:

Step-by-step explanation:

You got 91% of the questions right out of 175. In math words, this is saying that:

\(\frac{91}{100}*175=x\)

\(x=159.25\)

So, you got 175 - 159 = 15.75 questions wrong. The decimal could be from getting only part of a question wrong. So you got partial credit for one question

Answer: 15

Step-by-step explanation:

160/175

=0.914285714285 or 0.91

175-160

=15

...And there you go

Answer: 36˚

Step-by-step explanation:

180 - 3x = 2x

180 = 5x

.: x = 36˚

In linear equation , 240 liters of 90% solutions will be used.

What are a definition and an example of a linear equation?

Let x be the quantity of 75% antifreeze solution and y be the quantity of 90% antifreeze solution,

Since, the total quantity of the mixture = 360,

⇒ x + y = 360 ----- (1),

Also, the resultant solution is of  85% antifreeze solution,

⇒ 75 % of x + 90% of y = 85% of 360

0.75x + 0.90y = 0.85 × 360

0.75x + 0.90y = 306

75x + 90y = 30600 -----(2),

Equation (2) - 75 × equation (1),

We get,

15y = 3600

⇒ y = 240

Hence, 240 liters of 90% solutions will be used.

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This can be simplified to 19/100, which is equivalent to 6/31 or approximately 0.19 or 19%. The answer is: 6 over 31.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain. Probability can be expressed as a fraction, decimal, or percentage.

The question asks for the experimental probability of drawing a 3, 5, or 7 from a deck of cards, given the frequency table provided.

The frequency table tells us how many times each card was drawn out of a total of 100 draws.

To calculate the frequency of drawing a 3, 5, or 7, we add the frequencies of these cards: 4 (for 3) + 6 (for 5) + 6 (for 7) = 16. Note that we do not include the frequencies of any other cards.

To calculate the probability of drawing a 3, 5, or 7, we divide the frequency of these cards (16) by the total number of draws (100): 16/100 = 0.16. This means that in our experiment, we drew a 3, 5, or 7 approximately 16% of the time.

The total number of draws is 100, and the frequency of cards 3, 5, and 7 is 7+6+6=19.

Therefore, the experimental probability of drawing a 3, 5, or 7 is:

19/100 = 0.19

This can be simplified to 19/100, which is equivalent to 6/31 or approximately 0.19 or 19%.

Therefore, the answer is: 6 over 31.

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Answer:

33.67

Step-by-step explanation:

BODMAS (Bracket of Division Multiplication Addition Subtraction)

bracket then divide and so on

Answer:

33.67

Step-by-step explanation:

hope this helps have a wonderful day

The author uses paragraph 12 to create tension because of D.The author increases a feeling of discomfort with descriptions of conflict and disagreement.

Tension is a storytelling technique to ensure that readers do not drop a novel but keep readers engaged.

Creating tension helps the readers of a story to emotionally invest in the story, the characters, and the scenes.

Some authors use the following strategies to create tension?

Thus, the author increases a feeling of discomfort with descriptions of conflict and disagreement.

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Answer:

Infinetly many (d)

Step-by-step explanation:

The graphs are the same, so they will all have the same solutions.

hope this helps!

ibrahim

Answer:

y= -3x+1

Step-by-step explanation:

Let's start with the y-intercept (initial value). The y-intercept is where the line intersects the y-axis, so the x value should be 0. Here, the y-intercept is (0,1).

The slope is equivalent to the rise over run. We rise three and go to the left 1 which gives us a slope of negative 3 since we went to the left instead of the right.

Equation for a line:

y=mx+b where m is the slope and b is the y-intercept.

We plug in the slope and y-intercept in and get...

y= -3x+1

Answer:

Step-by-step explanation:

Slope

To find the slope of the line, it is useful to find two grid intersections that the line passes through. If one of those is on the y-axis, that is a good place to start. Here, that one is (0, 1).

Another can be see up and to the left, at (-1, 4).

The slope formula can be used to find the slope between these points:

  m = (y2 -y1)/(x2 -x1)

  m = (4 -1)/(-1 -0) = 3/-1 = -3

The slope of the line is -3.

__

Initial value:

This is the value that the function has when x=0. It is the y-intercept. We identified that value in the previous section as 1.

The initial value is 1.

__

Equation:

The slope-intercept equation of the line is of the form ...

  y = mx + b . . . . . . . where m is the slope (-3) and b is the y-intercept (1).

Filling in the values we know, the equation is ...

  y = -3x +1

__

Variation:

The line represents "direct variation" only if the y-intercept is zero. That is, the equation will be of the form ...

  y = kx

with no added constant. The value "k" is called the constant of proportionality, or "rate of change."

You will notice the equation for the line on this graph has a y-intercept of 1, so does not represent direct variation. Of the two answer choices, the appropriate one is ...

  Partial Variation

To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.

To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.

What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).

What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.

To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value

step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)

Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)

Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11

Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)

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The amount of water in each pool at a particular time are illustrations of linear functions

For the first pool, we have the following parameters

So, the equation of the amount of water in the pool is:

y = 2164 + 31.75x

For the second pool, we have the following parameters

So, the equation of the amount of water in the pool is:

y = 2500 + 21.25x

When both pools have the same amount of water, we have:

2164 + 31.75x = 2500 + 21.25x

Collect like terms

31.75x - 21.25x = 2500 - 2164

Evaluate the like terms

10.5x = 336

Solve for x

x = 32

This means that they will have the same amount of water after 32 minutes

Substitute 32 for x in y = 2164 + 31.75x

This gives

y = 2164 + 31.75 * 32

y = 3180

Both pools will have 3180 liters at 32 minutes

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