What is the exact situation to the equation e^4x-1=3
(In picture)

Answer: D

Step-by-step explanation:

x - 2 = 0   -->   x = 2

Using synthetic division:

2   |   4   -5   3   -1

    |   ↓    8   6   18

        4    3   9   17  ← this is the remainder!

Using remainder theorem:

f(x) = 4x³ - 5x² + 3x - 1

f(2) = 4(2)³ - 5(2)² + 3(2) - 1

     =   32   - 20    +  6    - 1

    = 17

[tex]\sin^2q+\cos^2q=1\to \cos^2q=1-\sin^2q\to\cos q=\pm\sqrt{1-\sin^2q}\\\\q\ \text{terminates in the fourth quadrant, therefore}\ \cos q > 0.\\\\\sin q=-\dfrac{3}{5}\to\cos q=\sqrt{1-\left(-\dfrac{3}{5}\right)^2}\\\\\cos q=\sqrt{1-\dfrac{9}{25}}\\\\\cos q=\sqrt{\dfrac{25}{25}-\dfrac{9}{25}}\\\\\cos q=\sqrt{\dfrac{16}{25}}\\\\\cos q=\dfrac{4}{5}[/tex]

[tex]\tan q=\dfrac{\sin q}{\cos q}\\\\\sin2q=2\sin q\cos q\\\\\cos2q=\cos^2q-\sin^2q\\\\\text{therefore}\\\\\tan2q=\dfrac{\sin2q}{\cos2q}=\dfrac{2\sin q\cos q}{\cos^2q-\sin^2q}\\\\\text{substitute}\\\\\tan2q=\dfrac{2\left(-\dfrac{3}{5}\right)\left(\dfrac{4}{5}\right)}{\left(\dfrac{4}{5}\right)^2-\left(-\dfrac{3}{5}\right)^2}=\dfrac{-\dfrac{24}{25}}{\dfrac{16}{25}-\dfrac{9}{25}}=\dfrac{-\dfrac{24}{25}}{\dfrac{7}{25}}=-\dfrac{24}{25}\cdot\dfrac{25}{7}=-\dfrac{24}{7}[/tex]

[tex]Answer:\ \boxed{B:\ -\dfrac{24}{7}}[/tex]

The exact value of tan 2θ will be –24/7. Then the correct option is B.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

If sin θ = -3/5.

Then the value of cos θ will be

cos² θ = 1 – sin² θ

cos² θ = 1 – (-3/5)²

cos² θ = 1 – 9/25

cos² θ = 16/25

 cos θ = 4/5

Then the value of tan 2θ will be

[tex]\tan 2\theta = \dfrac{\sin 2\theta }{ \cos 2\theta}\\\\\\\tan 2\theta = \dfrac{2 \sin \theta \cos \theta }{ \cos^2 \theta - \sin ^2 \theta}\\\\\\\tan 2\theta = \dfrac{2 * \frac{-3}{5} * \frac{4}{5} }{( \frac{4}{5})^2 - ( \frac{-3}{5}) ^2 }[/tex]

Simplify the equation, we have

tan 2θ = (–24/25) / (7/25)

tan 2θ = –24/7

Then the correct option is B.

More about the trigonometry link is given below.

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Answer:

130m

Step-by-step explanation:

Let the ocean be the origin (0,0)between the the bird flying and the shark swimming. If the distance between a bird flying and the ocean is 100m and the distance between the ocean above and a shark swimming below the sea is 30 m, the distance between the flying bird and the shark will be calculated by adding the two distances to give;

=(100-0)+(30-0)

= 100+30

= 130m

Note that the ocean serves ad the origin(0,0) therefore the distance between each animal and the sea will be known first and the two values will be added as shown above to get the distance between the two animals.

Answer:

yes you are right

Step-by-step explanation:

d=50t

Answer:

Yes. It is :

D=50t

Step-by-step explanation:

Answer:

$6.    

Step-by-step explanation:

Let x be the new price of ticket.

We have been given that a ticket cost $4.80. The new ticket price will be 1.25 times the old price.  

We can represent this information as:

[tex]x=1.25\times 4.80[/tex]  

[tex]x=6[/tex]      

Therefore, the cost of new ticket will be $6.

Final answer:

The new ticket price will be $6.00

Explanation:

Increased Price: The problem states that the new ticket price will be 1.25 times the old price. This means the new price will be 25% higher than the old price.

Calculating the Increase: To calculate the new price, we need to find 1.25 times the old price. Mathematically, this is done by multiplying the old price by 1.25.

Old ticket price: $4.80

Calculation: New ticket price = Old ticket price × 1.25

Calculation: New ticket price = $4.80 × 1.25 = $6.00

Therefore, the new ticket price will be $6.00

Answer:

First choice is correct ∠A ≅ ∠D, ∠B ≅ ∠E, ∠c ≅ ∠F, AB = DE, BC = EF, AC = DF

Step-by-step explanation:

Given that triangles ABC and DEF are congruent. Now we need to choose correct congruency statements from the given choices.

We know that corresponding angles of congruent triangles are equal so we can write:

∠A ≅ ∠D

∠B ≅ ∠E

∠c ≅ ∠F

We know that corresponding sides of congruent triangles are equal so we can write:

AB = DE

BC = EF

AC = DF

comparing these with given choices we see that, First choice { ∠A ≅ ∠D, ∠B ≅ ∠E, ∠c ≅ ∠F, AB = DE, BC = EF, AC = DF} is correct.

Answer: A

Step-by-step explanation:

[tex]V = 32,000(.8)^{t}[/tex]

   [tex]= 32,000(.8)^{2}[/tex]

   [tex]= 32,000(.64)[/tex]

  = 20,480

Answer:

Batting average = 0.382

Step-by-step explanation:

In the 1918 baseball season Ty cobb had 421 at bats and 161 base hits.

number of bat hits= 161

Number at bats = 421

Batting average = [tex]\frac{base \ hits}{at \ bats}[/tex]

Plug in the values in the formula

Batting average = [tex]\frac{161}{421}=0.382422802[/tex]

Now round the answer to three decimal places

Batting average = 0.382

Answer:

89 feet

Step-by-step explanation:

First of all, we will make a diagram to demonstrate the given scenario as shown in the attached picture.

Now we will use similar triangles to set the ratios as shown below to figure out the height of the building.

[tex]\frac{x}{130} =\frac{5.5}{8}[/tex]

Now we will solve for x from this equation by cross multiplying.

[tex]8x=130\cdot5.5[/tex]

[tex]8x=715[/tex]

[tex]x=89.375[/tex]

Therefore, height of the building is approximately 89 feet.

Answer:

5.83 units

Step-by-step explanation:

We write the coordinate points of Maple Station (-3,5) and Town Center (0,0). We label the points left to right as [tex](x_{1}, y_{1}) and (x_{2}, y_{2})[/tex] and substitute the values.  

[tex](x_{1}, y_{1}) = (-3, 5)\\(x_{2}, y_{2})=(0,0)[/tex]

[tex]d=\sqrt{(0-5)^{2} + (0-(-3) })^{2}}[/tex]

[tex]d=\sqrt{(0-5)^{2} + (0+3) })^{2}}[/tex]

[tex]d=\sqrt{(-5)^{2} + (3) }^{2}}[/tex]

[tex]d=\sqrt{25 +9}}[/tex]

[tex]d=\sqrt{34}}[/tex]

5.83 units

Answer:

E.

Step-by-step explanation:

Even though we have a sample of 40 units, we cannot determine that the units that are not in the sample will have the same or similar quality as the units that are in the sample. Thus none of the conclusions can be true.

Answer: Choice B) 100 pieces must be defective

Assuming the sample selected is representative of the population, we have two copies of "25" in that list (row 4; row 8) out of 40 total. So 2/40 = 1/20 = 0.05 = 5% of the items should be defective out of the entire population. Again this is assuming the sample is representative.

So we take 5% of 2000 and we end up with 0.05*2000 = 100 items we expect to be defective from a sample of 2000 items. Keep in mind that the true count will probably not be 100 items but some value close around it (eg: 98 or 101). This value is an estimate and not always perfect.

If choice B said "around 100" or "about 100" or "approximately 100" then I think it would be more technically correct. I think this is what your teacher is after.

Answer:

Option a is correct.

Exponential functions exhibit exponential growth (or decay) which mean the graph will rise or fall more dramatically than a polynomial graph

Step-by-step explanation:

An exponential function is in the form of [tex]y =ab^x[/tex] where a≠0  is a y-intercepts and  b is a positive number other than 1, multiplier this base is constant  , x  is the independent variable  and y is the dependent variable.

Exponential growth:

Exponential decay:

therefore, the graph will rise or fall more dramatically than a polynomial graph

Answer: y = (-1/2)*x + 1

Step-by-step explanation:

In the graph we can see a linear equation, the first thing we know is that a linear equation has the shape of:

y = ax + b

first, to find the slope we can use two pairs of the graphed ones, in the notation (x,y) we can select the pairs: (0, 1) and (2, 0)

we have that a = (y2 - y1)/(x2 - x1)

a = (0 - 1)/(2- 0 ) = -1/2

so the slope is -1/2

now, b is the y-intercept, this is the value of y when x = 0, and we can see that this value is 1 (the point where the graph intercepts the y-axis) so b = 1.

then the equation is y = (-1/2)*x + 1

Answer:21

Step-by-step explanation:

Answer:

21 stacks of 30

Step-by-step explanation:

630 divided into 30 stacks:

630/30= 21

Answer:

y+3= 8(x+2)

Step-by-step explanation:

original eq

y-y1=m(x-x1)

then you plug in given numbers

Answer:

[tex]y+3=8(x+2)[/tex]

Step-by-step explanation:

The point slope form:

[tex]y-y_1 = m(x-x_1)[/tex]

[tex]m=8\\(-2, -3)\\x_1=-2\\y_1=-3[/tex]

[tex]y-(-3)=8(x-(-2))[/tex]

[tex]y+3=8(x+2)[/tex]

Answer:

a) -4 mult. 2

b) [tex](x+4)^2[/tex]

c) 2, quadratic

Step-by-Step Explanation:

A polynomial graph has several features we look for to determine the equations.

In this graph, there is one real zero: -4

We can write them in intercept or factored form as (x+4) since x+4=0 gives x=-4.

Because the graph never crosses the x-axis it has an even multiplicity of at least 2.

The graph is facing up and is a U shape. This can only be a quadratic of degree 2. It is positive.

This means the function has a degree of 2.

Answer:

550

Step-by-step explanation:

We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other. Since we know the population increased to 200% of last year and is 1,100.

[tex]\frac{200}{100}=\frac{1100}{y}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

200y=100(1100)

200y=110,000

y=550

There was 550 rabbits last year.

By applying percentages and division, we find that there were 550 rabbits last year, as this year's population of 1,100 rabbits is 200% or twice the amount of last year's.

The rabbit population in a certain area is 200% of last year's population. This year, there are 1,100 rabbits. It means that 1,100 is double the population from last year because 200% is equal to 2 times the original number. To find the population of rabbits last year, we need to take this year's total and divide it by 2. So, 1,100 rabbits divided by 2 equals 550 rabbits. Therefore, last year, the population of rabbits was 550.

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The first hexagon: 2, 2, 3, 4, 6, 7

The second hexagon: 3, 3, a, b, c, d

The hexagons are similar. Therefore the sides are in proportion.

[tex]\dfrac{a}{3}=\dfrac{3}{2}[/tex]     multiply both sides by 3

[tex]a=\dfrac{3}{2}=4.5[/tex]

[tex]\dfrac{b}{4}=\dfrac{3}{2} [/tex]   multiply both sides by 4

[tex]b=\dfrac{3}{2}\cdot4=6[/tex]

[tex]\dfrac{c}{6}=\dfrac{3}{2}[/tex]     multiply both sides by 6

[tex]c=\dfrac{3}{2}\cdot6=9[/tex]

[tex]\dfrac{d}{7}=\dfrac{3}{2}[/tex]    multiply both sides by 7

[tex]d=\dfrac{21}{2}=10.5[/tex]

The perimeter:

[tex]P=4.5+6+9+10.5=30[/tex]

Answer:

Width of the store = 15 feet.

Step-by-step explanation:

Area = length * width

Plugging in the given dimensions:-

325 =  21 2/3 * x

x = 325 / 21 2/3

= 325 /  65/3

= (325 * 3) / 65

= 15 feet    (answer)

Answer:

Let x be the number of mile.

Total cost is no more than 130.

As per the given statement: if the car rental 94 a week plus 12 cent a mile.

12 cent a mile means 12x

then the equation become:

[tex]94 + 12x \leq 130[/tex]

Subtract 94 to both sides we get;

[tex]94 + 12x-94 \leq 130-94[/tex]

Simplify:

[tex]12x \leq 36[/tex]

Divide both sides by 12 we get;

[tex]x \leq 3[/tex]

Therefore, 3 miles she drive  if the car rental 94 a week plus 12 cent a mile.

Answer:

3 boxes.    

Step-by-step explanation:

We are told that Janice bought juice packets for the 15 players on the soccer team. The juice packets come in boxes of 6.

To find the number of boxes that Janice need to buy for 25 players, we will divide 15 by 6.

[tex]\text{Number of boxes that Janice needs to buy}=\frac{15}{6}[/tex]

[tex]\text{Number of boxes that Janice needs to buy}=2.5[/tex]

Since the juice packets come in boxes of 6, so we will round our answer to nearest whole number.

[tex]\text{Number of boxes that Janice needs to buy}=2.5\approx 3[/tex]

Therefore, Janice will buy 3 boxes of juice packets for 15 players.

The question entails a simple division operation of 15 players divided by 6 juice packets per box which gives 2.5. However, since Janice can't buy half a box, she ends up buying 3 boxes of juice packets.

To answer your question, we need to perform a simple division arithmetic operation. This involves taking the total number of players which is 15 and dividing that by the number of juice packets in one box, which is 6 .  The calculation is as follows: 15 ÷ 6 = 2.5. However, Janice cannot purchase half of a box so she would need to round up to the nearest whole number. Hence, Janice bought 3 boxes of juice packets for the soccer team.

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Answer:

An equation with a slope of -3 and an intercept of -4 is y = -3x - 4

Step-by-step explanation:

To find this we start with the base form of slope-intercept.

y = mx + b

Now we know that the slope goes in for m and the intercept goes in for b. Simply input those values.

y = -3x - 4

Answer:

 The population at the end  of 2017 is 65,550

Step-by-step explanation:

 step 1; find the  population   at the end  of 2016

if 60,000   increases by 15% therefore final % = 100 +15 =115%

Therefore  60,000   = 100%

                         ?      =    115%

by cross multiplication

={ (115 % x 60,000) /100}  =69,000

Step 2:  find the population at the end  of 2017  

if  69,000   decrease by 5% therefore the final% = 100 -5 =95%

Therefore 69000  = 100%

           ?    =  95%

by cross multiplication

= 69000 x 95/100 = 65,550

Answer:

FALSE

Step-by-step explanation:

Area of triangle is given by formula :

[tex]Area\ =\ \frac{1}{2}\left(base\right)\left(Altitude\right)[/tex]

From picture we see that Altitude = 60 m

Base = 52 + 71 = 123 m

Now plug these values into above formula:

[tex]Area\ =\ \frac{1}{2}\left(123\right)\left(60\right)[/tex]

[tex]Area\ =\ \frac{1}{2}\left(15129\right)[/tex]

[tex]Area\ =\ \frac{15129}{2}[/tex]

[tex]Area\ =\ 7564.5[/tex]

Which is different than given area 1560 m^2.

Hence answer is FALSE.

Answer:600 miles apart

Step-by-step explanation: one inch is 100 miles multiply that by 6 you get 600 miles

Answer:

Question 1 (5 points)

Correlation implies causation.

False

Question 2 (5 points)

A correlation between two variables means...

that a change in one variable is matched by a change in the other variable

Question 3 (5 points)

A negative correlation between two variables means...

when one variable goes up, the other goes down

Question 4 (5 points)

A strong linear correlation means...

the graph of data points stay close to a line

Question 5 (5 points)

Standard deviation is a measure of...

the spread of data.

Question 6 (5 points)

The formula for standard deviation uses which average?

mean

Question 7 (5 points)

According the the fundamental counting principal for multiplication, if event A has m possible outcomes and event B has n possible, then even A followed by event B has....

m x n outcomes

Question 8 (5 points)

What is the value of 4! ("four factorial")

24

Question 9 (5 points)

If the probability of passing an exam is 80%, what is the probability of not passing it?

20%

Question 10 (5 points)

Given that when flipping a coin, there is 1/2 chance of getting a heads:

What is the probability of flipping a coin and getting heads twice in a row?

1/4

Step-by-step explanation:

These are just facts you should know.

A correlation between two variables means that a change in one variable is matched by a change in the other variable. Standard deviation is a measure of the spread of data. The probability of flipping a coin and getting heads twice in a row is 1/4 or 25%.

A correlation between two variables means that a change in one variable is matched by a change in the other variable. For example, if there is a positive correlation between studying time and test scores, it means that as the studying time increases, the test scores also increase.

A negative correlation between two variables means that when one variable goes up, the other variable goes down. For instance, if there is a negative correlation between temperature and ice cream sales, it means that as the temperature increases, the ice cream sales decrease.

A strong linear correlation means that the data points on a graph stay close to a line. This indicates a strong relationship between the variables being measured.

Standard deviation is a measure of the spread of data. It tells us how much the individual data points differ from the mean (average) of the data set.

The formula for standard deviation uses the mean as the average.

According to the fundamental counting principal for multiplication, if event A has m possible outcomes and event B has n possible outcomes, then event A followed by event B has m x n outcomes.

The value of 4! (four factorial) is 24. Factorial represents the product of all positive integers from 1 to the given number.

If the probability of passing an exam is 80%, the probability of not passing it would be 20%.

The probability of flipping a coin and getting heads twice in a row is 1/4 or 25%.

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Answer:

27 children.

Step-by-step explanation:

We are told that at the newest animated movie, for every 9 children, there are 4 adults. There are a total of 39 children and adults at the movie.

We can see that number of children is proportional to number of adults. So we will use proportions to solve for number of children at the movie.

[tex]\frac{\text{Number of children}}{\text{Number of children + Adults}}=\frac{9}{4+9}[/tex]

[tex]\frac{\text{Number of children}}{\text{Number of children + Adults}}=\frac{9}{13}[/tex]

Let us substitute number of children and adults in our proportion.

[tex]\frac{\text{Number of children}}{39}=\frac{9}{13}[/tex]

Multiply both side of equation by 39.

[tex]39*\frac{\text{Number of children}}{39}=39*\frac{9}{13}[/tex]

[tex]\text{Number of children}=39*\frac{9}{13}[/tex]

[tex]\text{Number of children}=3*9[/tex]

[tex]\text{Number of children}=27[/tex]

Therefore, 27 children are at the movie.