Jean-Luc deposits $625 in a savings account which pays 1.6% interest, compounded continuously (A = Pe^rt). How much will his account be worth in 5 years?

Answer:

8x^2-4x-15

Step-by-step explanation:

To find the sum of the functions, we add them together:

f(x) + g(x) = (5x + 4) + (3x² - 9)

Simplifying, we get:

f(x) + g(x) = 3x² + 9x - 5

Therefore, the sum of the functions is 3x² + 9x - 5, which is option D.

a) At least one of the two games? - 300 members

b) Exactly one of the games? - 240 members

c) The Summer Olympic Games only? - 150 members

d) None of the games? - 60 members

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The number of squares wide needed is 7 squares and the number that can be used to replace A is 0.1 km.

Grid squares are a way to represent two-dimensional space using a grid of squares, with each square representing a unit of length.

Grid squares are often used in various fields, such as computer graphics, geographic information systems, and mathematics, to represent and manipulate two-dimensional data.

Here we have

The table shows the distance traveled in a time period

The maximum time is shown in a table = 35 minutes

Let 1 unit = 5 minutes

Number of squares used to represent 35 minutes = 35/5 = 7

Therefore, the number of squares wide needs = 7 blocks

Given that the grid is 20 squares tall

The maximum distance in a table = 1.8 km  

Let's take the total distance = 2 km

The number of squares along length = 2 km/20 = 0.1

Therefore,

The number of squares wide needed is 7 squares and the number that can be used to replace A is 0.1 km.

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The next marble's experimental probability of being blue, according to an experiment, is: 23/25.

Based on empirical data, experimental probability is the likelihood that an event will occur. A theoretical probability would be obtained by dividing the number of different ways to achieve the desired result by the total number of outcomes.

The next marble's likelihood of being blue, according to an experiment, is:

Experimental probability = Number of time blue appears / Total outcomes

Experimental probability = 23/25

Thus, the next marble's experimental probability of being blue, according to an experiment, is: 23/25.

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Answer:

Step-by-step explanation:

We separate into 2 congruent triangles. Both have a base of 3.5 and a height of 9 inches. Using pythagoran theorum, we will square 9 and 3.5

81 and 12.25

Add them up and it's 93.25

[tex]\sqrt{93.25}[/tex]=9.65660395791

Now since it's isosceles, the other side will also be 9.65660395791.

9.65660395791 + 9.65660395791 + 7 =26.3132079158

You want it rounded to the nearest tenth, so 26.3

The probability that the first two bulbs are of the same colour and the last two are of different colours is 25/48.

The probability that the first two bulbs are of the same colour and the last two are of different colours is calculated as follows:

Given:

n(B) = 3 (Number of blue bulbs)

n(G) = 4 (Number of green bulbs)

n(R) = 5 (Number of red bulbs)

Formula: P(A) = n(A) / n(S)

Where,

P(A) = Probability of event A

n(A) = Number of favorable outcomes

n(S) = Number of possible outcomes

The probability of selecting two bulbs of the same colour is calculated as:

P(SS) = n(B) * n(B) / n(S)

= 3 * 3 / 12

= 1/4

The probability of selecting two bulbs of different colour is calculated as:

P(DD) = n(B) * n(G) * n(R) * n(R) / n(S)

= 3 * 4 * 5 * 5 / 12

= 25/12

Therefore, the required probability is calculated as:

P(SSDD) = P(SS) * P(DD)

= 1/4 * 25/12

= 25/48

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10[4-(3-2x)]+4x=3(8x+4)-2   is an identity equation.

To determine whether the equation is a conditional, an identity, or a contradiction, we need to simplify the equation and see if it is true for all values of x, true for some values of x, or false for all values of x.

First, let's simplify the equation:

10[4-(3-2x)]+4x=3(8x+4)-2

10[4-3+2x]+4x=24x+12-2

10[1+2x]+4x=24x+10

10+20x+4x=24x+10

24x-24x=10-10

0=0

Since the equation is true for all values of x, it is an identity equation. An identity equation is an equation that is true for all values of the variable.

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The present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.

The present value of an annuity is calculated using the following formula:

PV = A[((1+i)n-1)/(i(1+i)n)]

where A = amount of each annuity payment, i = interest rate, and n = number of payments.

For this problem, A = $500, i = 6%, and n = 15 years.

Therefore, the present value of the annuity necessary to fund the withdrawal is:

PV = $500[((1+0.06)15-1)/(0.06(1+0.06)15)]

PV = $500[5.72982/0.105638]

PV = $5,354.82

Therefore, the present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.

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The correct description for best represents the end behavior of the

function f (x) = - x⁴ + 5x³ - 2x + 5 is,

⇒ The right-end is  y → - ∞ as x → ∞ . The right-end is rising.

The left-end is y → - ∞  as x→ - ∞ . The left-end is falling.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = - x⁴ + 5x³ - 2x + 5

Now, We have;

Degree of the polynomial = 4

Hence, We get;

⇒ The right-end is  y → - ∞ as x → ∞ . The right-end is rising.

The left-end is y → - ∞  as x→ - ∞ . The left-end is falling.

Thus, The correct description for best represents the end behavior of the

function f (x) = - x⁴ + 5x³ - 2x + 5 is,

⇒ The right-end is  y → - ∞ as x → ∞ . The right-end is rising.

The left-end is y → - ∞  as x→ - ∞ . The left-end is falling.

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The value of [tex](5 - x)/(2)[/tex] is [tex]2[/tex] when[tex](5x - 1)/(2)[/tex] is equivalent to [tex](3x - 6)/(3)[/tex].

The given expression is [tex](5x - 1)/(2)[/tex] and it can be written in the equivalent form [tex](3x - 6)/(3)[/tex].

To find the value of [tex](5 - x)/(2)[/tex], we can use the property of equivalent fractions, which states that if two fractions are equivalent, then the cross products are equal.

So, we can cross multiply the given equivalent fractions to get:

[tex](5x - 1)(3) = (3x - 6)(2)[/tex]

Simplifying the equation, we get:

[tex]15x - 3 = 6x - 12[/tex]

[tex]9x = 9[/tex]

[tex]x = 1[/tex]

Now, we can substitute the value of x into the expression [tex](5 - x)/(2)[/tex] to find the value of the expression:

[tex](5 - 1)/(2) = 4/2 = 2[/tex]

Therefore, the value of [tex](5 - x)/(2)[/tex] is 2 when [tex](5x - 1)/(2)[/tex] is equivalent to [tex](3x - 6)/(3)[/tex].

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The probability that a person chosen at random from this group will either seek further assistance or merely study at home is 5/6, or roughly 0.833. (rounded to three decimal places).

Typically, the probability is defined as the ratio of favourable events to all other outcomes in the sample space. The formula for probability of an occurrence is P(E) = (Number of favourable outcomes) (Sample space).

The formula is as follows:

P(AorB) = P(A)+P(B)-P(AandB)

where A and B are two events.

Then, we have:

P(A) = 30/60 = 1/2 (since 30 out of 60 students go for extra help)

P(B) = 22/60 (since 22 out of 60 students study at home only)

Using the formula, we can then find:

P(AorB) = P(A)+P(B)-P(AandB)

= 1/2 + 22/60 - 0

= 5/6

Hence, the probability that someone chosen at random from this group will either seek further assistance or merely study at home is 5/6, or roughly 0.833. (rounded to three decimal places).

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The slide does not meet safety requirements.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

As per the given data:

maximum average slope = 30°

height of the slide = 6 ft

length of the slide = 11.7 ft

For calculating slope (θ):

sinθ = (P/H) {P is perpendicular and H is hypotunese}

sinθ = (height/length)

sinθ = (6/11.7)

sinθ = 0.512

Using sin inverse:

θ = 30.8°

θ > maximum average slope

Hence, the slide does not meet safety requirements.

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The empirical norm therefore states that 68% of 7-year-old kids are between 47 and 51 inches tall.

A column in a table is a collection of cells which are arranged vertically. A field, like the received field, is a sort of element that contains only one item of data. A column in a table usually contains the values for just a single field.

The empirical rule states that in a normal distribution, 68% of the data fall within one average standard deviation. In this instance, the mean difference is 2 inches, while the average height of 7-year-old kids is 49 inches.

We must identify the range among heights that is within one average standard deviation in order to apply the scientific rule. To accomplish this, we can add and subtract the standard variance from the median as follows:

Mean ± (Standard Deviation) = 49 ± 2

As a result, the height range which falls within the standard deviation from the average is between 47 and 51 inches.

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There are 14 books on the bookshelf as a result.

Assume that there are x total books on the bookshelf. Neil has read 7 out of a total of 7 + (x-7) = x-0 books, which means that he has read 7/14 of the books, according to the problem. This is reduced to 1/2.

Now that he has read 8 out of 15 books, his percentage of books read will be 8/15 if he reads one more (the original 7 books he read plus the one he read now). This implies:

8/15 = 8/(x+1)

In order to find x, we can cross-multiply:

8(x+1) = 15(8) (8)

8x + 8 = 120

8x = 112

x = 14

There are 14 books on the bookshelf as a result.

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Answer: slope of the line

Step-by-step explanation: I'm not sure if we're talking about the same thing though

Answer: The slope (stands in for m)

Step-by-step explanation:

In a direct variation, the variable m (slope) is swapped for k.

Answer:

Step-by-step explanation:

its 190 because you started on page 4 and you add 186

The expression √9−9x2 can be written as a trigonometric expression 3sin(θ) using the substitution x = cos(θ).

To write the expression as a trigonometric expression using the suggested substitution, we can substitute x = cos(θ) into the expression and simplify:

√9−9x2 = √9−9(cos(θ))^2

= √9−9(cos^2(θ))

= √9(1−cos^2(θ))

= √9(sin^2(θ))

= 3sin(θ)

Therefore, the expression √9−9x2 can be written as a trigonometric expression 3sin(θ) using the substitution x = cos(θ).

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The solution of linear equations is (x, y) = (-0.8905, 0.708).

To solve this system of linear equations by elimination, first multiply both equations by the same number so that when you add the equations together, one of the variables is eliminated. In this case, we'll multiply the first equation by 3 and the second equation by 8.

8(8x+3y=-5)

3(3y=x+4)

24x + 9y = -15

24y = 8x + 32

Now add the two equations together:

24x + 24y = -15 + 32

24x + 24y = 17

Simplifying this equation, we get:

24y = 17

y = 17/24

y = 0.708

Now, plug in the value of y into one of the original equations to solve for x. We'll use the first equation:

8x + 3(0.708) = -5

8x + 2.124 = -5

8x = -7.124

x = -7.124/8

x = -0.8905

Therefore, the solution to the system of linear equations is (x, y) = (-0.8905, 0.708).

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The intersection point on the graph has an approximate x-value of 1a.

Making the curve that represents a function on a coordinate plane is the process of graphing a function. If the curve (or graph) represents the function, then each point on the curve will satisfy the function equation.

The line, also called the "curve," has a point at each point that fulfils the function.

The three lines are contemporaneous if they all cross at the same point.

From the second equation,

x = 8y + 19

Putting value of x,

2(8y + 19) + 3y = 0                              9(8y + 19) + 5y = 17

16y + 38 + 3y = 0                                 72y + 171 + 5y = 17

19y = -38                                                77y = -154

 y = -2                                                      y = -2

You'll see that the y value for the answer is the same for the two equations. Simply evaluate the second equation now to find x. Hence, we are aware that the y-coordinate is negative two at some x number.

x = 8(-2) + 19

x = -16 + 19

x = 3

The single point that these three equations share is (3, -2).

4x - 3y = 13                     eq1

-6x + 2y = -7                   eq2

Use the elimination method. Multiply eq1 by eq2 and multiply eq2 by eq3.

8x - 6y = 26                eq1

-18 + 6y = -21              eq2

Adding the equations to eliminate the y terms.

-10x = 5

 x = -1/2

Substituting this value of x into any of the equations to solve for the value of y.

Substituting the first equation into the second equation. In terms of x, this will translate the second equation. From that freshly created equation, find x. Once you solved for x, substitute that value of x into the first equation to solve for y.

You have a vertical line that passes all points that have the x coordinate 7 and you have a horizontal line that passes all point that have the y coordinate -5.

If you were to graph these two lines, they will be intersecting at (7, -5).

Now, draw the following lines on a coordinate system:

i) A vertical line passing through the points (3, 0).

ii) A horizontal line passing through the point (0, 6).

iii) A line passing through the points (0,0) and (1, -3).

Once you have drawn these lines, look for 3 points of intersection.

Area = (base × height) / 2

Lines that have the same slope never intersect.  Put both equations in y=mx+b  form where the slope is the coefficient of x.

2x + 3y = > 3y = -2x + 23

y = (-2 / 3) x + 23/3

7x + py = 8

py = -7x + 8

y = (-7 / p) x + 8/p

Set the slopes equal to each other.

-2 / 3 = -7 / p

Cross-multiply.

-2p = -21

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Answer:

=35

Step-by-step explanation:

5d - 25/5

5(8) -25/5

40 - 5

=35

Answer:

the answer is 35

Step-by-step explanation:

d=8, therefore plug 8 into the equation

5d - [tex]\frac{25}{5}[/tex]

5(8)-  [tex]\frac{25}{5}[/tex]

40-5

35

The number "4" in the expression 4x - 5 represent the number of days Gerard worked.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Gerard worked the same number of hours, x, on Monday, Tuesday, and Wednesday, but on Thursday, he worked 5 hours less than the previous day.

The total number of hours Gerard worked can be found using the expression, 4x − 5

Hence:

The number "4" in the expression 4x - 5 represent the number of days Gerard worked which is Monday, Tuesday, and Wednesday and Thursday

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The equation of the volume of the box in terms of x is 4x³ - 40x² +100x.

The set of all conceivable values of x that make sense in the context of the issue constitutes the domain of the function V(x). This time, x must be a positive value less than or equal to 5, as it reflects the length of the side of the square that was cut out of each corner of the cardboard. The range of V(x) is thus 0 x 5.

Given that, the squares cut at the end are x inches.

Thus the dimension of the rectangular box are:

The length of the box will be (10-2x).

The width of the box will be (10-2x).

The height of the box will be x inches.

The volume of the rectangular box is given by:

V = (l)(w)(h)

Substituting the values we have:

V(x) = (10-2x)(10-2x)x = x(100-40x+4x^2) = 4x³ - 40x² +100x.

Hence, the equation of the volume of the box in terms of x is 4x³ - 40x² +100x.

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Answer:

Option B

See below

Step-by-step explanation:

Two simultaneous equations:

[tex]7x - 4y - 8 = 0[/tex] —————- (equation i)

[tex]2x^{2} + x + 4y + 8 = 0[/tex]   ——- (equation ii)

Step 1:

Rearrange (equation i):

[tex]7x - 4y = 8[/tex] ———- updated (equation i)

Step 2:

Substitute the updated (equation i) into (equation ii) and bring like terms together to simplify them in reduced forms:

[tex]2x^{2} + x + 4y + (7x - 4y) = 0[/tex]

[tex]2x^{2} + x + 4y + 7x - 4y = 0[/tex]

[tex]2x^{2} + x + 7x + 4y - 4y = 0[/tex]

[tex]2x^{2} + 8x = 0[/tex]

Step 3:

Factorize:

[tex]2x(x + 4) = 0[/tex]

Either [tex]2x = 0[/tex]        
∴ [tex]x = 0[/tex]

Or [tex]x + 4 = 0[/tex]

∴ [tex]x = -4[/tex]

Step 4:

Substitute these values of x in (equation ii) to determine their corresponding values of y:

For x = 0:

[tex]2(0)^{2} + 0 + 4y + 8 = 0[/tex]

[tex]4y + 8 = 0[/tex]

[tex]4y = -8[/tex]

[tex]y = \frac{8}{-4}[/tex]

∴[tex]y = -2[/tex]

For x = -4:

[tex]2(-4)^{2} + (-4) +4y + 8 = 0[/tex]

[tex]2(16) - 4 + 4y + 8 = 0[/tex]

[tex]32 - 4 + 4y + 8 = 0[/tex]

[tex]32 - 4 + 8 + 4y = 0[/tex]

[tex]36 + 4y = 0[/tex]

[tex]4y = -36[/tex]

[tex]y = \frac{-36}{4}[/tex]

∴ [tex]y = -9[/tex]

∴The values of y are [tex]-2[/tex] and [tex]-9[/tex]

∴Option B

To prove that EVPI > 0 for the simple decision sapling, we need to understand what EVPI is. EVPI stands for Expected Value of Perfect Information, and it is the difference between the expected value of the decision with perfect information and the expected value of the decision without perfect information.

For the simple decision sapling, we have two options: a sure thing of value r, and a risky gamble with a random payoff G. The expected value of the decision without perfect information is simply the maximum of the two options:
EV = max(r, EG)
The expected value of the decision with perfect information is the maximum of the two options, knowing the outcome of the gamble:
EVPI = max(r, G) - max(r, EG)
Since we know that G is a random variable, the expected value of G is simply the average of all possible outcomes. Therefore, the expected value of the decision with perfect information is simply the maximum of the two options, knowing the average outcome of the gamble:
EVPI = max(r, EG) - max(r, EG) = 0
Therefore, EVPI > 0 for the simple decision sapling.

To prove that the EVPI will be larger if the random payoff of the gamble is replaced by a noisy version of the original gamble, we need to understand how the expected value of the decision changes with the addition of the noise variable Y. The expected value of the decision without perfect information is now:
EV = max(r, EG + EY) = max(r, EG)
Since EY = 0, the expected value of the decision without perfect information does not change. However, the expected value of the decision with perfect information now becomes:
EVPI = max(r, G + Y) - max(r, EG)
Since Y is a random variable with mean 0, the expected value of Y is 0. However, the variance of Y is not necessarily 0, which means that the addition of Y adds variability to the decision. This means that the expected value of the decision with perfect information is now larger, because we have more information about the possible outcomes of the gamble. Therefore, the EVPI will be larger when the random payoff of the gamble is replaced by a noisy version of the original gamble.

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The possible values of x are 2 and 17

The complete question is added as an attachment

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

Similar triangles

In the triangles, we have the following possible equations

15/18 = 10/(10 + x)

10/18 = 15/(10 + x)

Solving the equations, we have

15/18 = 10/(10 + x)

150 + 15x = 180

15x = 30

x = 2

10/18 = 15/(10 + x)

100 + 10x = 270

10x = 170

x =17

Hence, the values of x are 2 and 17

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Complete Question

The two triangles in the diagram are similar there are 2 possible values for x

See attachment for image of the triangle

Answer:

6.74

Step-by-step explanation:

100 - 93.26

Answer:

$6.74

Step-by-step explanation:

100.00 - 93.26 = 6.74

Helping in the name of Jesus.

The three equations that have the same value of x as the original equation are:

18x - 15 = 72

3(6x - 3) = 72

x = 4.5

What is an equation?

An equation is a statement that two expressions are equal. It typically contains one or more variables (represented by letters) and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to represent relationships between quantities or to solve for unknown values.

The correct options are:

18x - 15 = 72

18x - 9 = 72

x = 4.5

To see why, we can start by simplifying the original equation:

Three-fifths (30x - 15) = 72

(3/5)(30x - 15) = 72

18x - 9 = 72

18x - 15 = 72 + 15

18x = 87

x = 87/18

So we see that x = 87/18 is the solution to the original equation.

Now let's check each of the answer choices:

18x - 15 = 72

Solving for x, we get x = 87/18, which is the same as the solution to the original equation. This equation is equivalent to the original equation.

50x - 25 = 72

Solving for x, we get x = 97/50, which is not the same as the solution to the original equation. This equation is not equivalent to the original equation.

18x - 9 = 72

Solving for x, we get x = 81/18 = 9/2, which is not the same as the solution to the original equation. This equation is not equivalent to the original equation.

3(6x - 3) = 72

Simplifying, we get 18x - 9 = 72, which is equivalent to the second equation listed above. So this equation is also equivalent to the original equation.

x = 4.5

This is the same solution as the original equation, so this equation is also equivalent to the original equation.

Therefore, the three equations that have the same value of x as the original equation are:

18x - 15 = 72

3(6x - 3) = 72

x = 4.5

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Answer:

The difference between the LCM and the GCF of 30 and 55 are that the LCM is the smallest positive integer that is divisible and the GCF is the largest positive integer that divides each of the integers.

Step-by-step explanation:

We need to pour 250 ml of liquid from container B to container A so they can be equal in volume.

To make container A and B equal in volume, we need to pour some liquid from container B into container A. Let's call the amount of liquid that we need to pour from container B to container A as "x" ml.

After pouring x ml of liquid from container B to container A, the total volume of liquid in container A will be (750 + x) ml, and the total volume of liquid in container B will be (1250 - x) ml.

Since we want the volumes of both containers to be equal, we can set up the equation:

750 + x = 1250 - x

Solving for x:

2x = 500

x = 250

Therefore, we need to pour 250 ml of liquid from container B to container A so they can be equal in volume.

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