Emilia invests $10,000 in an account that compounds continuously. She plans to leave it in the account untouched. The table shows the balance of the account over 30 years. Enter the data into the graphing tool to plot these values on a scatter plot, with x representing the number years invested and f(x), or y, representing the account balance. Time Invested (years) Account Balance 5 $12,840 10 $16,487 15 $21,170 20 $27,183 25 $34,903 30 $44,817 Which equation most likely represents the curve of best fit for this data set? Select the correct answer.

The mistake Matt made in calculating the distance the mouse travelled each hour was that Matt should have divided the numerator but not the denominator of 3/24 by 3

The distance the mouse travelled per hour is calculated by comparison

If the mouse covers 3/24 miles in in 3 hours then in an hour the mouse will cover

3/24 = 3

? = 1

cross multiplying

3 * ? = 1 * 3/24

? = 3/24 ÷ 3

? = 3/24 * 1/3

? = 1/24

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Answer: log(10)

Step-by-step explanation:

Based on the laws of logarithm attached below, the expression can be rewritten as:

[tex]log(5)+log(18)-log(9)=log(5*18)-log(9)\\\\=log(90)-log(9)=log(\frac{90}{9})=log(10)[/tex]

The remainder is 8 in the given synthetic division problem. which is the correct answer would be option (B).

In mathematics, divides left-hand operands into right-hand operands in the division operation.

In the given synthetic division, the coefficients of terms are 4,6, and -2.

Fill in the first coefficient as it appears on the bottom line.

Now multiply 1 by 4 and write the result (i.e., 4) underneath the second coefficient in the center line.

Now multiply 6 by 4 and write the result (i.e., 10) in the bottom row.

Now multiply 1 by 10 and write the result (i.e., 10) below the third coefficient in the center line.

Now add -2 with 10 and write the result (i.e., 8) in the bottom row.

The first two terms now indicate the polynomial coefficient, while the last term shows the remainder.

Therefore, the remainder is 8 in the given synthetic division problem.

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Answer:  80.44 meters/seconds/ to 179.9391553 miles/hours

Step-by-step explanation:  Example:  80.44X2.2369362921=

1 m/s = 2.3469362921 that gives you the above answer.

Answer:

(a)  x = 2

(b)  7 + 5√2

Step-by-step explanation:

Given terms of a geometric sequence:

The common ratio of a geometric sequence is found by dividing consecutive terms.  Therefore:

[tex]\implies \dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}[/tex]

Substitute the given terms into the equation and solve for x:

[tex]\implies \dfrac{\sqrt{x}+1}{1}=\dfrac{1}{\sqrt{x}-1}[/tex]

[tex]\implies (\sqrt{x}-1)(\sqrt{x}+1)=1[/tex]

[tex]\implies x+\sqrt{x}-\sqrt{x}-1=1[/tex]

[tex]\implies x-1=1[/tex]

[tex]\implies x=2[/tex]

General form of a geometric sequence:

[tex]\boxed{a_n=ar^{n-1}}[/tex]

where:

Substitute the found value of x into the expressions for the given terms:

Find the common ratio:

[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{\sqrt{2}+1}{1}=\sqrt{2}+1[/tex]

Therefore, the equation for the nth term is:

[tex]\boxed{a_n=(\sqrt{2}-1)(\sqrt{2}+1)^{n-1}}}[/tex]

To find the 5th term, substitute n = 5 into the equation:

[tex]\implies a_5=(\sqrt{2}-1)(\sqrt{2}+1)^{5-1}[/tex]

[tex]\implies a_5=(\sqrt{2}-1)(\sqrt{2}+1)^{4}[/tex]

[tex]\implies a_5=(\sqrt{2}-1)(\sqrt{2}+1)^2(\sqrt{2}+1)^2[/tex]

[tex]\implies a_5=(\sqrt{2}-1)(3+2\sqrt{2})(3+2\sqrt{2})[/tex]

[tex]\implies a_5=(\sqrt{2}-1)(9+12\sqrt{12}+8)[/tex]

[tex]\implies a_5=(\sqrt{2}-1)(17+12\sqrt{2})[/tex]

[tex]\implies a_5=17\sqrt{2}+24-17-12\sqrt{2}[/tex]

[tex]\implies a_5=7+5\sqrt{2}[/tex]

Answer:

The weight of oranges growing in an orchard is normally distributed with a mean weight of 6.5 oz. and a standard deviation of 1 oz. Using the empirical rule, determine what interval would represent weights of the middle 99.7% of all oranges from this orchard

Step-by-step explanation:

bran leist ple

Answer:

1954

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ²:

[tex]\boxed{X \sim \textsf{N}(\mu,\sigma^2)}[/tex]

Given:

First find the probability that the weight of an orange is less than 5 oz.

[tex]\text{If \;$X \sim \textsf{N}(4,0.5^2)$,\;\;find\;\;P$(X < 5)$}.[/tex]

Method 1

Using a calculator:

[tex]\implies \text{P}(X < 5)=0.977249868[/tex]

Method 2

Converting to the z-distribution.

[tex]\boxed{\text{If\;\;$X \sim$N$(\mu,\sigma^2)$\;\;then\;\;$\dfrac{X-\mu}{\sigma}=Z$, \quad where $Z \sim$N$(0,1)$}}[/tex]

[tex]x=5 \implies Z=\dfrac{5-4}{0.5}=2[/tex]

Using the z-tables for the probability:

[tex]\implies \text{P}(Z < 2)=0.9772[/tex]

To find the expected number of oranges that will weigh less than 5 oz from a batch of 2000, multiply the total number of oranges by the probability calculated:

[tex]\begin{aligned}2000 \times \text{P}(X < 5)&=2000 \times 0.977249868\\&=1954.499736\\&=1954\end{aligned}[/tex]

Therefore, 1954 oranges would be expected to weigh less than 5 oz.                                

Answer:

v = 9√2 ; u = 18

Step-by-step explanation:

angle 45 degrees = the legs are congruent

v = 9√2

u = [tex]\sqrt{(9\sqrt{2} )^2+{(9\sqrt{2})^2}} = \sqrt{2(9\sqrt{2)}^2} = \sqrt{2 (81 *2) }= \sqrt{4 * 81}= 2 * 9 = 18[/tex]

Answer:

Step-by-step explanation:

a triangle with an angle of 90° and an angle of 45° is an isosceles right triangle, so V equals 9√2.

to find u we use the Pythagorean theorem

u = √(9√2)²+(9√2)²

u = 9 + 9

u = 18

A probability is given by the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes when a pair of dice is rolled is given by:

6² = 36.

As each throw has six outcomes.

The outcomes with a sum of 5 are given as follows:

(1,4), (2,3), (3,2), (4,1).

Hence 4 outcomes, and the probability that player A wins is of:

p = 4/36 = 1/9.

The outcomes with a sum of 4 are given as follows:

(1,3), (2,2), (3,1).

Hence the probability that B wins is given by:

p = 3/36 = 1/12.

Then the probability that a player wins on each trial is given by:

p = 4/36 + 3/36 = 7/36.

Then the expected number of rolls is given as follows:

E(X) = 1/(7/36) = 36/7 = 5.1 rolls.

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Answer:

41.6 km/h

Step-by-step explanation:

Nao drives 95mi/2.5hr or 38 miles per hour, or 60.8 km/h

1 hr 15 min is the same as 1.25 hours

Arban drives 128km/1.25hr or 102.4 km/h

The difference is 102.4-60.8 = 41.6

Differentition of [tex]y=log_{2}x^{3}.(5x^{4}+2)[/tex] is [tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}[/tex]

A differential equation is an equation that contains one or more functions with its derivatives.

Given,

[tex]y=log_{2}x^{3}.(5x^{4}+2)[/tex]

We have to differentiate with respect to x.

y'=xy'+yx'

[tex]x=log_{2}x^{3}[/tex]

[tex]y=5x^{4}+2[/tex]

[tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x^{3}} .3x^{2}[/tex]

[tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}[/tex]

Hence, differentiation of [tex]y=log_{2}x^{3}.(5x^{4}+2)[/tex] is [tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}[/tex]

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Answer:

The total of 100 breakfasts that cost $7.50 would be $750  and the placement of the decimal point would be moved 2 spaces to the right.

Step-by-step explanation:

Breakfasts cost $7.50. Find the customer's total cost for ordering 100 breakfasts. Explain the number of zeros and the placement of the decimal in your answer using a place value chart.

7.50(100)

Brainliest Please?

Step-by-step explanation:

4x + 3y = -10

9x + 2y = 6

we have 2 general options :

substitution or elimination.

in substitution we use one equation to express one variable by the other, then use that equality in the second equation and solve for the remaining variable.

like in our case

4x = -10 - 3y

x = (-10 - 3y)/4

in elimination we multiply one or both equations by some factors and then subtract one equation from the other resulting in one equation in one remaining variable.

this is the better method, if substitution leads to more complex fractions.

like in our case.

so, I would multiply equation 1 by 2 and equation 2 by 3, and then subtract e.g. equation 2 from 1 (we could also do it the other direction, it gives the same solutions) :

8x + 6y = -20

- 27x + 6y = 18

------------------------

-19x 0 = -38

-19x = -38

19x = 38

x = 2

and then we pick any of the original equations to get the other variable :

e.g.

4x + 3y = -10

4×2 + 3y = -10

8 + 3y = -10

3y = -18

y = -6

Answer:

30 days

Step-by-step explanation:

Look at you z-score table to find the value closest to .6400  (64%)

 my table shows this corresponds to z-score + .36   standard deviation ABOVE the mean of 22 days

    .36  * 22 = ~ 8 days

  added to the mean   8  + 22 = 30 days      

The event that is least likely to occur among the given events after finding their probabilities is; Event number 4

1) From 1 to 12, the multiples of 3 are;

3, 6, 9 12. They are 4 in number and so;

P(roll a multiple of 3) = 4/12 = 0.333

2) Spinner is divided into 4 equal sized sections made up of red/green/yellow/blue. Thus probability that it lands on red or blue.;

P(red) = 1/4

P(blue) = 1/4

Thus;

P(red or blue) = (1/4) + (1/4)

P(red or blue) = 1/2 = 0.5

3) Total number of tickets = 100

Number bought = 62

Thus, probability of winning = 62/100 = 0.62

4) Number of strawberry chews = 15

Number of cherry chews = 65

Total number of chews = 15 + 65 = 90

Probability of pulling out a strawberry chew is;

P(Strawberry chew) = 15/90 = 0.167

The least likely to occur has the least probability which is number 4.

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Answer:

(-1,4)

Step-by-step explanation:

to find out we just fill in the values to see if it’s true

(x,f(x))

4=-1^2+3

4=1+3

4=4

True

-4=-1^2+3

-4=1+3

-4=4

Not true

-4=1^2+3

-4=1+3

-4=4

Not true

-1=-4^2+3

-1=16+3

-1=19

Not true

Hopes this helps please mark brainliest

The required greatest rate of change is at x = 7 to x = 10. Option A is correct.

Given that,
The function is graphed. On which interval of a is the average rate of change of the function the greatest is to be determined.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
The average rate for,
x = 7 tot x = 10
Rate = 56 - 8 / 10 -7
Rate = 16
While the other pair has an average rate of 4, 4.46

Thus, the required greatest rate of change is at x = 7 to x = 10. Option A is correct.

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Answer:

1.522756e+12

Step-by-step explanation:

The equation of the line that passes through (-1, -6) and (5,0). is y = x - 5.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's find the equation of the line that passes through  (-1, -6) and (5,0).

m = 0 + 6 / 5 + 1

m = 6 / 6

m = 1

Therefore, let's find the y-intercept using (5, 0)

y = x + b

0 = 5 + b

b = -5

Therefore, the equation is y = x - 5

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Answer:

25 advance tickets and 20 same day

Step-by-step explanation:

Answer: Advanced tickets:25
Same Day tickets: 20

The required quadratic inequality whose graph is given below is

[tex]y > -\frac{1}{4}x^2 -4x +2[/tex]

What is graph of a function?

At first it is important to know about function

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Graph of a function f(x) is the collection of all point of the form (x, f(x))

Let the equation be  [tex]y = ax^2 + bx + c[/tex]

The graph passes through (0, 2)

Putting x = 0 and y = 2

c = 2

[tex]y = ax^2 + bx + 2[/tex]

The graph passes through (-12, 14) and (-4, 14)

[tex]14 = (-12)^2a + (-12)b+2\\144a - 12b = 14 - 2\\12(12a- b) = 12\\12a - b = \frac{12}{12}\\12a - b = 1 ... (1)[/tex]

Also

[tex]14 = (-4)^2a + (-4)b + 2\\16a - 4b = 14 - 2\\16a - 4b = 12\\4(4a - b) = 12\\4a - b = \frac{12}{4}\\4a - b = 3 .... (2)[/tex]

Subtracting (2) from (1),

8a = -2

[tex]a = -\frac{2}{8}[/tex]

[tex]a = -\frac{1}{4}[/tex]

Putting the value of a in (2)

[tex]4 \times -\frac{1}{4} - b =3\\-1 - b = 3\\b = -3 - 1\\b = -4[/tex]

The required equality is

[tex]y = -\frac{1}{4}x^2 -4x +2[/tex]

Since the shaded region is the outer region and the line is given dotted,

The required quadratic inequality is

[tex]y > -\frac{1}{4}x^2 -4x +2[/tex]

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Answer:

1) 5

2) 3
3) 2
4) 10
5) 7
6) 36
7) 110
8) 100
9) 40
10) 8
11) 30
12) 60
13) 12
14) 63
15) 77
16) 5

Step-by-step explanation:

Answer:

1) x=5; 2) x=3; 3) x=2; 4) x=10; 5) x=7; 6) x=36; 7) x=110; 8) x=100; 9) x=40; 10) x=8; 11) x=30; 12) x=12; 13) x=12; 14) x=63; 15) x=77; 16) x=5

Step-by-step explanation:

I can't explain every problem, but I will do the first three.

1) We divide the sides by 4 to get x=5

2)We divide by 3 to get x=3

3)Divide by 4 to get x=2

Answer: its gonna be D

Step-by-step explanation:

its just zeros

Answer:

The answer to  your question is,

D. Reflect over the x-axis and reflect over the y-axis

Step-by-step explanation:

I Hope this helps :)

Answer:

C. Reflect over the X axis and translate 6 units left

Step-by-step explanation:

That is the only one that works

A, B, and D are close but don't line up. For one rectangle to line up with another, it had to be in the same place with the same letters at the same corners. For option C, a reflection across the X axis means that rectangle ABCD will flip across the horizontal line. (it matches A'B'C'D now) then a translation 6 units left just moves it six boxes left. It should match A"B"C"D now :)

The required proof by Mathematical Induction of 1 / 1 ×2 + 1 / 2 ×3 + 1 / 3 × 4 + ... + 1 / n ( n + 1 ) = n / n + 1 has been in the solution.

To begin, we suppose that the assertion is correct for some integer k.

⇒ 1/1. 2 + 1/2 . 3 + . . . + 1/k . (k+1)  = k/(k+1)    ....(i)

As per Mathematical Induction, the required solution would be as:

Let the LHS be Sk.

Consider the series with one more term, when k = k+1.

We must demonstrate that Sk+1 has the same form as equation (i) but with k substituted by k+1.

Then,

Sk+1 = Sk + 1/(k+1)(k+2)

       = k/(k+1) + 1/(k+1)(k+2)

       = [k(k+2) + 1] / (k+1)(k+2)

       = (k2+2k +1) / (k+1)(k+2)

       = (k+1)2 / (k+1)(k+2)

       = (k+1) / (k+2)

       = (k+1) / ((k+1)+1)

And this has the same form as equation (i) but with k+1 in place of k.

As a result, if it is true for n=k, it must also be true for n=k+1.

When n=1, S1 = 1/1. 2 = 1/2 = 1/1(1+1), hence the assertion is correct.

As a result of the preceding demonstration, it must be true for n= 1+1 = 2.

as well as for n=2+1=3 and so forth for all n numbers.

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The line x1 = b/2a serves as the axis of symmetry for the graph of a quadratic equation with the form y1 = ax1²+bx1+c.

A parabola is the name for a quadratic function's graph.

Finding the vertex for the given equation is the first step in drawing a parabola graph. To accomplish this, use the formulas x=-b/2a and y=f(-b/2a). When the quadratic equation is stated in the vertex form, f(x) = a(x-h)2 + k, where (h, k) is the parabola's apex, the graph is plotted.

Let y equal the phrases on both sides of the equal sign as the first step.

Step 2: Graph the two newly formed functions.

Step 3: Estimate the location(s) where the function graphs intersect.

Hence a quadratic equation with the form y1 = ax1²+bx1+c is graphed, and the line x1 = b/2a acts as the axis of symmetry.

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The number of permutation and number of combination of 10 objects taken 4 at a time are

10P₄ = 5040

10C₄ = 210

The permutation of 10 objects taken 4 at a time is given by the formula

= 10! / (10 - 4)!

= 10! / 6!

= 10 * 9 * 8 * 7 * 6! / 6!

= 10 * 9 * 8 *7

= 5040

The combination of 10 objects taken 4 at a time is given by the formula

= 10! / (4!(10 - 4)!)

= 10! / (4! * 6!)

= 10 * 9 * 8 * 7 * 6! / (6! * 4!)

= 10 * 9 * 8 *7 / 4!

= 210

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Answer:

13200

Step-by-step explanation:

7.5 x 1760 = 13200

The Center of the circle is (5, -17) and radius of the circle is 29 units.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

We have given circle in the x, y-plane has the equation;

x² + y² -10x + 34y - 527 = 0

Now we will convert this equation to the standard form of the circle as;

x² -10x + y² + 34y = 527

[x² - 2(5)x] + [y² + 2(17)x] =527

[x² - 2(5)x + 5²] + [y² + 2(17)y + 17²] = 5² + 17² +527

(x - 5)² + (y + 17)² = 25 + 289 +527

(x - 5)² + (y + 17)² = 841

(x - 5)² + (y + 17)² = 29²

By comparing this equation with the standard equation of the circle →

That is;  (x - h)² + (y - k)² = r²

The Center of the circle is (5, -17) and radius of the circle is 29 units.

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1.2.1 There are 18 houses in the neighborhood.

1.2.2 The building located next to the park is the hospital.

1.2.3 The business which appears more than all the other businesses in the neighborhood is the Cafe.

1.2.4. The bar scale measures 25 centimeters.

1.2.5 Based on the above measurement, the scale of this street map has a scale factor of 0.005468, compared to the original distance of the neighborhood.

1.2.6 There are 3 more houses in the street at the top than the street at the bottom.

The scale factor is the ratio between two scales of an object.

The scale factor shows how larger or smaller the new scale is compared to the old scale (original measurement).

The formula for the scale factor is as follows:

Scale factor = Dimension of the new scale ÷ Dimensions of the original scale.

1 yard = 91.44 centimeters

50 yards = 4,572 centimeters (91.44 x 50)

The original (larger) dimension of the neighborhood = 50 yards or 4,572 centimeters

Scale (smaller) dimension of the map = 25 centimeters

Scale factor = Smaller dimension/Larger dimensions

= 25/4,572

= 0.005468

The number of houses at the top street = 8

The number of houses at the center street = 5

The number of houses at the bottom street = 5

The total number of houses in the neighborhood = 18

The difference between the top street houses and the bottom street houses = 3 (8 - 5)

The number of cafes = 2

The number of parks = 1

The number of other businesses = 1 each

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Answer: Rational

Step-by-step explanation:

The function is not continuous, so the function cannot be exponential, logarithmic, or exponential.

This means the only possibility is that the function is rational.