y=10^x +6
find the inverse

Answer:

0, 3, -6, 7

Step-by-step explanation:

x(x − 3)(x + 6) (x – 7) = 0

so x = 0

or x - 3 = 0, x = 3

or x + 6 = 0, x = -6

or x - 7 = 0, x = 7

Answer: 0, 3, -6, 7

Answer:

The degree of the polynomial is 3.

By the fundamental theorem of algebra, the function has three roots.

Two roots are given, so there must be one root remaining.

By the complex conjugate theorem, imaginary roots come in pairs.

The final root must be real.

Step-by-step explanation:

The number of roots remaining of the polynomial function f(x) = x³ − 7x − 6, with two roots -2, and 3 already given is 1. The nature of the root will be real.

A polynomial function is a function (say f(x)), which is defined over a polynomial expression in x. It is of the form,

f(x) = a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ, where a₀, a₁, a₂, ..., aₙ are constants, x is a variable, and n ≥ 0.

Degree of the polynomial function = n, the highest power of x.

The fundamental theorem of algebra is that the number of roots or solutions of a polynomial function = The degree of the polynomial function.

According to the complex conjugate theorem, if a polynomial function has complex roots, they will always exist in conjugate pairs, that is, if one root is of the form a + bi, the other root will be a - bi.

We are given a polynomial function f(x) = x³ - 7x - 6. Two roots of the equation are given as -2, and 3.

The degree of the equation = 3, so by the fundamental theorem of algebra number of roots = 3.

2 roots are given, so the number of roots remaining = 1.

Since none of the given roots are complex, the third root can not be complex, as complex roots always exist in conjugate pairs, coming from the complex conjugate theorem. So, the remaining root will be real in nature.

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An investment of $6,400 to increase to $14,000 if it is invested at 5% per year compounded continuously is ≈15.6

Define compound interest?

Given that :

P = $ 6,400

Q = $ 14,000

r = 5%

Let P be the initial investment

r be the rate of interest

t be the time

Q be the increase amount

Q = P \(e^{rt} }\)

14,000 = 6,400 (\(e^{0.05t}\))

\(e^{0.05t}\) = \(\frac{14000}{6400}\)

\(e^{0.05t}\)  = 2.187

Taking log on both sides , we get

0.05t = ln (2.187)

0.05t = 0.78

       t = \(\frac{0.78}{0.05}\)

       t ≈ 15.6

An investment of $6,400 to increase to $14,000 if it is invested at 5% per year compounded continuously is ≈ 15.6

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Given:

Sandra Wallace walks at 5 miles per hour

Michael Sanders walks at 3 miles per hour

when Sandra has walked 20 miles

So, the number of hours = 20/5 = 4 hours

Michael starts to walk in a certain direction 2 hours before Sandra

So, the number of waking hours of Michael = 4 + 2 = 6 hours

So, the number of miles that Michael walked = 6 * 3 = 18 miles

So, the difference between them = 20 - 18 = 2 miles

So, the answer will be

Michael will be 2 miles behind Sandra

Since there are 8500 chairs

Since this number id decreases by 6%

Then to find 6% of 8500, multiply 6% by 8500

At first, change 6% to a normal number by dividing it by 100

6% = 6/100

The amount of decreases in the number of chairs produced each month is 510

To find the new number of chairs subtract 510 from 8500

The new number of chairs produced each month is 7990

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)

\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios

\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

Answer:

A.) 5

Step-by-step explanation:

16/3= 5.3333

Round down because it is not a whole serving

answer is: 5 servings

PN = PM

6x + 1 = 10x - 17

Add both sides 17

6x + 1 + 17 = 10x - 17 + 17

6x + 18 = 10x

Subtract both sides 6x

6x - 6x + 18 = 10x - 6x

18 = 4x

Divide both sides by 4

18 ÷ 4 = 4x ÷ 4

9/2 = x

x = 9/2

___________________________

QN = 2x + 5

QN = 2 × ( 9/2 ) + 5

QN = 9 + 5

QN = 14

Answer:

17.1

Step-by-step explanation:

The missing side is x

switch tan 25° and x

Answer:

15

Step-by-step explanation:

Let the probability of picking an orange = P(O), and the probability of picking a strawberry = P(S),

Based on the question, he picked an orange first and the probability of picking that is

P(O) = 12/50

Then he picked a strawberry on the second pick, the probability of picking the strawberry is P(S) and we'll find that later.

The probability of picking orange then strawberry with replacement is

P(O) × P(S) = 9/125

Substitute the P(O)=12/50,

12/50 × P(S) = 9/125

P(S) = 3/10

Then by finding the number of strawberry candies, we'll just have to multiply P(S) with the total number of candies, i.e.

Number of strawberry candy

= 3/10 × 50

= 15

Answer:

15

Step-by-step explanation:

The shape of the parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a square

In order to get the shape using the vertices that we have, we would have to find the length of the diagonals

We have P(−4,0), Q(0,4), R(4,0), and S(0,−4)

The length of the diagonal PQ is given as:

PQ = \(\sqrt{(0-4)^2+(4-0)^2}\)

= \(\sqrt{32}\)

Next we have to solve for the length of the diagonal RS

RS = \(\sqrt{(4-(-4))^2+(0-(-4))^2\)

RS = \(\sqrt{32}\)

Since PQ = RS we would have to conclude that the shape is a square.

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Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

Answer:

412.92

Step-by-step explanation:

\(A = P(1+\frac{r}{n} )^{nt}\)

A: Amount, P: Principal, r: interest, n: no.of times compounded yearly and t: time in years

We have P = 300

r = 4% = 0.04

n = 12 (compounded monthly)

t = 8

\(A = 300(1+\frac{0.04}{12} )^{12*8}\\\\300(\frac{12.04}{12} )^{96}\\\\= 412.92\)

Answer:

1

  The  correct option is  C

2

 The  correct option is C

3

The  correct option is A

4

The  correct option is B

Step-by-step explanation:

From the question we are told that

    The  population mean is  \(\mu = 100\)

     The  standard deviation is  \(\sigma = 15\)

     The  sample size is  \(n = 36\)

     The  sample mean is  \(\= x = 105.1\)

Generally

    The  null hypothesis is  \(H_o: \mu = 100 \ hours\)

     The  alternative hypothesis is  \(H_a : \mu \ne 100\ hours\)

Given that the null hypothesis is  true then the  distribution of sample means  \(\mu_{\= x }\), from a sample size of 36 is  mathematically represented as

        \(\mu_{\= x } = \mu\)

=>     \(\mu_{\= x } = 100\)

According to the Central Limit Theorem the test stated in the question is  approximately normally distributed if the sample size is sufficiently large\((n > 30 )\) so given that the sample size is  large  n =  36

Then the test is normally distributed and hence the standard deviation is 15

Generally the standard error of mean is mathematically represented as

     \(\sigma_{\= x } = \frac{ \sigma }{\sqrt{n} }\)

=>  \(\sigma_{\= x } = \frac{15}{\sqrt{36} }\)

=>  \(\sigma_{\= x } = 2.5\)

Generally  the approximate probability of observing a sample mean of 105.1 or more is mathematically represented as

        \(P( \= X \ge 105.1 ) =1 - P(\= X < 105.1) = 1- P(\frac{\= X - \mu }{\sigma_{\= x }} <\frac{105.1 - 100}{2.5} )\)

=>    \(P( \= X \ge 105.1 ) =1 - P(\= X < 105.1) = 1- P(Z<2.04 )\)

From the z-table (reference calculator dot net )

             \(P(Z<2.04 ) = 0.97932\)

So

  \(P( \= X \ge 105.1 )= 1 - P(\= X < 105.1) = 1- 0.97932\)

 \(P( \= X \ge 105.1 ) =0.02\)    

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer:

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

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

Solution :

1. \($P(\text{ good sales in Asia }) = 0.55+0.15$\)

                                     = 0.7

2. \($P(\text{ good sales in Europe }) = 0.55+0.20$\)

                                     = 0.75

3. \($\text{P(good sales in Asia }| \text{ good sales in Europe}) $\)\($=\frac{\text{P (good sales in Asia and good sales in Europe)}}{\text{P( good sales in Europe)}}$\)

                                         \($=\frac{0.55}{0.75}$\)

                                          \($=\frac{11}{15}$\)

4. \($\text{P(good sales in Asia }| \text{ bad sales in Europe}) $\)

  \($=\frac{\text{P (good sales in Asia and bad sales in Europe)}}{\text{P( bad sales in Europe)}}$\)

  \($=\frac{0.15}{0.25}$\)

  \($=0.6$\)

5. \($\text{P(good sales in Europe }| \text{ good sales in Asia}) $\)

   \($=\frac{\text{P (good sales in Asia and good sales in Europe)}}{\text{P( good sales in Asia)}}$\)

   \($=\frac{0.55}{0.7}$\)

  \($=\frac{11}{14}$\)

6.  \($\text{P(good sales in Europe }| \text{ bad sales in Asia}) $\)

     \($=\frac{0.2}{0.3}$\)

     \($=\frac{2}{3}$\)                              

9514 1404 393

Answer:

  D

Step-by-step explanation:

The inequality symbol is < (not ≤), which means the end point of the graph will be an open circle.

After dividing by the coefficient of x, you have an inequality of the form ...

  x +( ) < ( )

which means the solution will be left of the (open circle) end point of the graph. Only one graph has that form.

__

If you actually work through the numbers, you get ...

  x +8 < 9 . . . . . . divide both sides by 2.9

  x < 1 . . . . . . . . . subtract 8 from both sides

Answer:

u > 7

Step-by-step explanation:

-2u -6 < -20  Add 6 to both sides

-2u - 6 + 6 < -20 + 6

-2u < -14  Divide both sides by -2.  When you multiply or divide both sides by a negative number, you must flig the sign.

\(\frac{-2u}{-2}\) > \(\frac{-14}{-2}\)

u > 7

Helping in the name of Jesus.

The answer is:

u > 7

In-depth explanation:

You haven't told me what the values of u are, but I'll solve the equation for u.

Add 6 on each side:

\(\bf{-2u-6 < -20}\)

\(\bf{-2u < -14}\)

Divide each side by -1 and reverse the sign:

\(\bf{2u > 14}\)

Now divide each side by 2

\(\bf{u > 7}\)

In  linear equation, The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .

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

   x² + y² = 4 ..........1

   x²/4 - y²/9 = 1

⇒ 9x² - 4y² = 36 ..........2

multiply equation (1) is multiply by 9

      9 x²  + 9y² = 36  ..............3

equation (3) - (2)

   13y² = 0

 y = 0

put y =0 in equation 1

     x² + 0 = 4

      x = ± 2

The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .

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Answer:

x=-1 and y=7

Step-by-step explanation:

let s solve the system of equations

(1) 13x+2y=1

(2) 5x-2y=-19

let s do (1) + (2)

13x+2y+5x-2y=1-19=-18

<=>

18x=-18

<=>

x=-1

so x = -1

and then we replace x in (1) it comes

-13+2y=1

<=>

2y-1=1+13=14

<=>

y = 14/2=7

so y =7

The probability of randomly choosing a green marble after you have chosen red is 4.4%

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given

A jar has 20 marbles: 3 green, 12 blue, 5 red.

Probability;

In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.

The total number of marbles = 20

The number of green marbles= 3

The number of blue marbles = 12

The number of red marbles = 5

The probability of choosing a red marble = Number of red marbles / Total number of marbles

= 5/20

The probability of choosing a green marble is =  Number of green marbles / New total number of marbles

= 3/19

Therefore,

The probability of randomly choosing a green marble after you have chosen red is;

= 5/20 * 3/19

= 3/68

percentage = 3/68 * 100 = 4.4%

Hence, the probability of randomly choosing a green marble after you have chosen red is 4.4%

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Answer:

12ft trim

Step-by-step explanation:

assuming that she wants to use the same size on each side (3ft) of the window, we know that the window is a square

and a square has 4 sides

3 + 3 + 3 + 3 = 12ft

She needs 12 ft trim

The correct transformation that describes why rectangles ABCD and A′B′C′D′ are similar is Rectangle ABCD was dilated by a scale factor of 5 to form rectangle A′B′C′D′.

Dilation is a transformation that changes the size of an object while maintaining its shape. In this case, the coordinates of rectangle ABCD were multiplied by a scale factor of 5 to obtain the coordinates of rectangle A′B′C′D′.

This means that each side length of rectangle ABCD was multiplied by 5 to get the corresponding side length of rectangle A′B′C′D′.

The reflection across the y-axis and the rotation of 90° counterclockwise would result in different shapes and orientations, not maintaining the similarity between the two rectangles.

The dilation by a scale factor of 15 or 1/5 would also change the proportions and not result in a similar rectangle.

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Answer:

0.29p + 1.59 = 5.07 where p represents the number of pens

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) 1 7/9 = 9*1+7/9 = 16/9

2) 6 3/4 = 6*4+3/4 = 27/4

3) 11 1/5 = 11*5+1/5 = 56/5

4) 5 2/6 = 5*6+2/6 = 32/6

5) 10 3/7 = 10*7+3/7 = 73/7

Hope you understood!!