(Q4) Which values of a and b in the exponential function y = a (bx) would result in the following graph?

Answer:

D) Over $4,000,000

Step-by-step explanation:

On the last day, the worker is paid $0.07*2²⁵ (it's by the power of 25 because it's 0 on the first day), which is $2,348,810.24. That means that the amount of money earned on all other days are $2,348,810.37, since 2⁰ + 2¹ + 2² + 2³... + 2ⁿ⁻² + 2ⁿ⁻¹ = 2ⁿ + 1.

That totals to approximately $4.6 million dollars, which is larger than $4 million.

To find the worker's total pay over 26 days, the pay is calculated as a geometric series with a first term of $0.07 and a common ratio of 2, using the geometric series sum formula.

The worker's pay is doubling each day. This pattern represents a geometric sequence where the first term a is $0.07 and the common ratio r is 2. To find the total pay after 26 days, we need to calculate the sum of the first 26 terms of the sequence.

The formula for the sum S of a geometric series is S = a(1 - r^n) / (1 - r), where n is the number of terms. Plugging in our values, we get S = 0.07(1 - 2^26) / (1 - 2).

Performing the calculation yields a sum that we can evaluate to determine the worker's pay over the 26-day period. This result would fall into one of the ranges provided in the original question.

Answer:

[tex]S_3=39[/tex]

Step-by-step explanation:

The nth term of the sequence is

[tex]a_n=3(3)^{n-1}[/tex]

To get the first term, substitute n=1,

[tex]a_1=3(3)^{1-1}=3[/tex]

To get the second term, substitute n=2,

[tex]a_2=3(3)^{2-1}=9[/tex]

To get the third term, substitute n=3,

[tex]a_3=3(3)^{3-1}=27[/tex]

The sum of the first three terms is

[tex]S_3=3+9+27=39[/tex]

We could also use the formula

[tex]S_n=\frac{a_1(r^n-1)}{r-1}[/tex] to get the same result.

Answer:

The correct answer is last option   39

Step-by-step explanation:

It is given that,

aₙ = 3(3)ⁿ⁻¹

To find a₁

a₁ = 3(3)¹⁻¹ = 3(3)°

= 3 * 1 = 3

To find a₂

a₂ = 3(3)²⁻¹ = 3(3)¹

= 3 * 3 = 9

To find a₃

a₃ = 3(3)³⁻¹ = 3(3)²

= 3 * 9 = 27

To find the value of S₃

S₃ = a₁ + a₂ + a₃

 = 3 + 9 + 27 = 39

Therefore the correct answer is last option   39

Answer:

Step-by-step explanation:

Graphs of quadratics are symmetrical about the vertex (minimum or maximum point).  

The x value of the point (-3, 11) is 3 units to the left of the vertex (0, 2), the x value that is 3 units to the right of the vertex will have the same y value, so the point

(3, 11) is also on the graph

The quadratic function has a minimum at (0, 2) and includes the point (-3, 11). Solving for the function's equation, we find y = x² + 2, and another point on the graph is (1, 3).

Since the quadratic function has a minimum at (0, 2), it means the vertex form of the quadratic function is y = a(x - 0)² + 2, or simply y = ax² + 2. We know another point on the graph is (-3, 11), so we can use this point to find the value of 'a'.

So, the equation of the quadratic function is y = x² + 2. To find another point on the graph, choose any x-value and compute the corresponding y-value. For example, let x = 1:

Thus, another point on the graph is (1, 3).

Answer:

[tex]C(h)=\$30+xh[/tex]

Step-by-step explanation:

Let

C-----> the cost of having a plumber spend h hours at your house

h----> the number of hours

x----> the cost per hour of labor

we know that

The linear equation that represent the cost C is equal to

[tex]C(h)=\$30+xh[/tex]

In this linear equation in the slope-intercept form (y=mx+b)

the slope is equal to [tex]m=x\frac{\$}{hour}[/tex]

the y-intercept b is equal to [tex]b=\$30[/tex] ---> charge for coming to the house

Answer:

Option A. 10

Step-by-step explanation:

we know that

Applying the Intersecting Secants Theorem

[tex]QS*RS=CS*TS[/tex]

substitute the values

[tex](11x-1+8)*(8)=(9+7)*(9)[/tex]

solve for x

[tex](11x+7)*(8)=(16)*(9)[/tex]

[tex]88x+56=144[/tex]

[tex]88x=144-56[/tex]

[tex]88x=88[/tex]

[tex]x=1[/tex]

Find the measure of QR

[tex]QR=11x-1=11(1)-1=10[/tex]

Answer:

6/11

Step-by-step explanation:

We are not told which number cube shows a 4; it can be the first one or the second one.

If the first number cube is a 4, this gives us the options of:

4 and 1; 4 and 2; 4 and 3; 4 and 4; 4 and 5; 4 and 6.

However if the second number cube is a 4, this gives us

1 and 4; 2 and 4; 3 and 4; 4 and 4; 5 and 4; 6 and 4.

We cannot count "4 and 4" twice; this leaves us with 11 total possibilities.

Out of these 11, only the sum of 4 and an odd number will be odd:

1 and 4; 3 and 4; 5 and 4; 4 and 1; 4 and 3; 4 and 5.

There are 6 ways to have an odd sum out of 11 total possibilities; this gives us a probability of 6/11.

Answer:

8.28 units

Step-by-step explanation:

The formula for the circumference of a circle is [tex]C=\pi d[/tex]

where

[tex]C[/tex] is the circumference of the circle

[tex]d[/tex] is the diameter of the circle

We know form our problem that the circumference of our circle is 26.28 units, so [tex]C=28.26[/tex]. Let's replace that value in our formula and find [tex]d[/tex]:

[tex]C=\pi d[/tex]

[tex]26=\pi d[/tex]

Divide both sides of the equation by [tex]\pi[/tex]

[tex]\frac{26}{\pi } =\frac{\pi d }{\pi }[/tex]

[tex]\frac{26}{\pi } =d[/tex]

[tex]d=\frac{26}{\pi }[/tex]

[tex]d=8.28[/tex]

The diameter of the circle that has a circumference of 28.26 units is 8.28 units.

Answer:

The diameter of a circle is 9 units

Step-by-step explanation:

A circle has a circumference of 28.26

Let diameter of a circle be d unit.

Formula:

[tex]C=\pi d[/tex]

where, C=28.26

[tex]28.26=\pi d[/tex]

[tex]d=\dfrac{28.26}{\pi}[/tex]

[tex]d=8.995\approx 9[/tex]

Hence, The diameter of a circle is 9 units

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point form:

(3,2), (3-2), (-3,2), (-3,-2)

Equation Form:

x = 3, y = 2.

x = 3, y = -2.

x = -3, y = 2.

x = -3, y = -2.

Hope this is helpful. <33

The point estimates for the mean and standard deviation of the given data is respectively; 68 and 17.6

A) To find the point estimate of the mean, we add all up all the data and divide by the number of values.

Thus;

∑x = 57 + 61 + 86 + 87 + 72 + 73 + 19 + 56 + 81 + 79 + 83 + 75 = 816

n = 12 numbers

Thus;

mean = ∑x/n = 816/12

Mean = 68

B) To find the estimate of the standard deviation, we would get it from the formula;

s = √[(n*(∑x²) - (∑x)²)/n(n - 1)]

∑x² = 572 + 612 + 862 + ... + 742 = 59,010

s = √[ (12*(59,010) - (816)²)/(12)(11)]

s = 17.6

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Answer:

A mere 15 years back, navigators would have scoffed at the idea of Paperless Navigation on big ocean going ships. After all, since centuries, navigational paper charts had been the heart and soul of ship navigation. Imagining that a day would come where we’d no longer have them onboard was nothing short of blasphemy.

Step-by-step explanation:

The advantages of technology versus old-school methods for determining the position at sea include ease of navigation and safety.

The ECDIS is the abbreviated form Electronic Chart Display and Information System. It is a modern technology used for navigation through waters.

With ECDIS as the dominant source of sailing, the Navigating Officer can plan and summarise the transition much more speedily than on Paper Charts.

This is the background that will sound an alarm if the ship is inside the limit stated.

This scene displays the non-traversable field and marks the confine save that the container can harmlessly cross.

Therefore, we have found that the advantages of technology versus old-school methods for determining the position at sea include ease of navigation and safety.

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The   Answer    is     frequency

= (pi)/(2pi)

= 1/2 freq  

Answer:

Step-by-step explanation:

The easiest way to do this is to get the period correct first.

If the function f(x) = cos(B * x) then the period is

P =  2*pi/B  In this case B = 5

P = 2* pi/5

The frequency is the reciprocal of the period

f = 1/p

f = 1/(2pi/5) Now all you do is turn 2p/5 upside down.

f = 5/2*pi <<<< Answer

I don't know how simple your marker considers this, but it is the answer.

Answer:

The difference is in which in way that they can be separated.

Step-by-step explanation:

While all three of these include mixtures of two or more things, a suspension can typically be re-separated by using a centrifuge and a solution can be filtered out. A colloid on the other hand, cannot typically be separated after it is put together.  

Answer:

3 miles

Step-by-step explanation:

1)

x + 2y = 21

+ -x + 3y = 29

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

5y = 50

y = 10

x + 2(10) =21

x = 1

2)

6x + 6y = 30

+ 15x - 6y = 12

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

21x = 42

x = 2

6(2) + 6y = 30

6y = 18

y = 3

1.  The solution to the system of equations is (x, y) = (1, 10)

2. the solution to the system of equations is (x, y) = (-2, 7)

3. the solution to the system of equations is (x, y) = (5, 3)

4.  the solution to the system of equations is (x, y) = (6, 4)

5.  the solution to the system of equations is (x, y) = (2, -3)

1. To solve the system of equations using elimination, you need to add the two equations to eliminate one of the variables. Here's how you can do it:

x + 2y = 21

-x + 3y = 29

Add the two equations together:

(x + 2y) + (-x + 3y) = 21 + 29

Now, simplify the equation:

(2y + 3y) = 50

Combine like terms:

5y = 50

Now, divide both sides by 5 to solve for y:

5y/5 = 50/5

y = 10

Now that you've found the value of y, substitute it back into either of the original equations to solve for x. Let's use the first equation:

x + 2(10) = 21

x + 20 = 21

Subtract 20 from both sides:

x = 21 - 20

x = 1

So, the solution to the system of equations is (x, y) = (1, 10). The correct answer is (1, 10).

2. 15x + 6y = 12

To solve this system of equations using elimination, you can follow these steps:

Multiply both sides of the second equation by 2 to make the coefficients of y in both equations equal:

2(15x + 6y) = 2(12)

30x + 12y = 24

Now you have the system:

6x + 6y = 30

30x + 12y = 24

Multiply the first equation by -5 to make the coefficients of x in both equations equal:

-5(6x + 6y) = -5(30)

-30x - 30y = -150

Now you have the system:

-30x - 30y = -150

30x + 12y = 24

Add the two equations to eliminate the x variable:

(-30x - 30y) + (30x + 12y) = (-150 + 24)

-18y = -126

Divide both sides by -18 to solve for y:

-18y / -18 = -126 / -18

y = 7

Now that you've found the value of y, substitute it back into the first equation to solve for x:

6x + 6(7) = 30

6x + 42 = 30

6x = 30 - 42

6x = -12

x = -12 / 6

x = -2

So, the solution to the system of equations is (x, y) = (-2, 7). The correct answer is (-2, 7).

3. Subtract the first equation from the second equation to eliminate the x variable:

(2x + 6y) - (2x + 2y) = 28 - 16

This simplifies to:

4y = 12

Divide both sides by 4 to solve for y:

4y / 4 = 12 / 4

y = 3

Now that you've found the value of y, substitute it back into the first equation to solve for x:

2x + 2(3) = 16

2x + 6 = 16

Subtract 6 from both sides:

2x = 16 - 6

2x = 10

Divide both sides by 2 to solve for x:

2x / 2 = 10 / 2

x = 5

So, the solution to the system of equations is (x, y) = (5, 3). The correct answer is (5, 3).

4. Multiply the second equation by -3 to make the coefficients of x in both equations equal:

-3(2x + y) = -3(8)

-6x - 3y = -24

Now you have the system:

2x - 3y = 0

-6x - 3y = -24

Add the two equations to eliminate the y variable:

(2x - 3y) + (-6x - 3y) = 0 - 24

This simplifies to:

-4x = -24

Divide both sides by -4 to solve for x:

-4x / -4 = -24 / -4

x = 6

Now that you've found the value of x, substitute it back into the first equation to solve for y:

2x - 3y = 0

2(6) - 3y = 0

12 - 3y = 0

Subtract 12 from both sides:

-3y = -12

Divide both sides by -3 to solve for y:

-3y / -3 = -12 / -3

y = 4

So, the solution to the system of equations is (x, y) = (6, 4). The correct answer is (6, 4).

5. To solve the system of equations using elimination, you can follow these steps:

Subtract the second equation from the first equation to eliminate the y variable:

(5x + 5y) - (5x - 5y) = -5 - 25

This simplifies to:

10y = -30

Divide both sides by 10 to solve for y:

10y / 10 = -30 / 10

y = -3

Now that you ve found the value of y, substitute it back into either of the original equations to solve for x. Let's use the first equation:

5x + 5(-3) = -5

5x - 15 = -5

Add 15 to both sides:

5x = -5 + 15

5x = 10

Divide both sides by 5 to solve for x:

5x / 5 = 10 / 5

x = 2

So, the solution to the system of equations is (x, y) = (2, -3). The correct answer is (2, -3).

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B. R>2 because to win the game they must have had more runs than the losing team

Final answer:

The inequality that represents the number of runs the winning baseball team could have scored is r > 2, since the winning team must score more than the losing team, which scored 2 runs.

Explanation:

The student is asking for the inequality that represents the number of runs, r, that the winning team could have scored in a baseball game, given that the losing team scored 2 runs. The condition to win a game is that the winning team must score more runs than the losing team. Therefore, if the losing team scored 2 runs, the inequality that represents the number of runs the winning team scored is r > 2. This is because the winning team must have scored more than 2 runs to win.

360°=18

120°=x

x=120*18/360=6

Answer:

Negative 8 plus negative 6 equals negative fourteen.

Answer:

Negative eight plus negative six equals negative fourteen

Answer:

im not 100% sure but to me it looks like it could be 225

Answer:

The correct option is 3.

Step-by-step explanation:

From the given figure it is clear that the vertices of preimage are A(-4,-2), B(-2,1) and C(-2,-2).

Center of rotation is origin, i.e., (0,0).

Triangle ABC is rotated counterclockwise about the origin.

We need to find the angle of rotation.

Draw line segments OC and OC'. From the below figure it is clear that the angle of rotation counterclockwise about origin is

[tex]45^{\circ}+90^{\circ}+90^{\circ}=225^{\circ}[/tex]

Therefore the correct option is 3.

Here is your answer

[tex]\bold{x=12}[/tex]

REASON:

[tex]<font color="blue" size=5>Concept used</font>[/tex]: The opposite sides of a parallelogram are equal.

So, in above given figure

[tex] 3x+7=5x-17 [/tex] (measures of opposite sides)

[tex] 5x-3x= 17+7 [/tex]

[tex] 2x= 24 [/tex]

[tex] x= 24/2 [/tex]

[tex] x= 12 [/tex]

HOPE IT IS USEFUL

Answer:

The two triangles may be congruent, but additional information is needed about the sides of each triangle.

Step-by-step explanation:

Given that Samantha measured two of the angles in PQR and found that they had measures of 65° and 70°. Then, she measured two of the angles in XYZ and found that they had measures of 65° and 45°.

We have by using properties of sum of angles of triangles, angles of PQR are 65, 70, 45 and also same for XYZ

Hence there is a chance that these triangles may be congruent depending on the sides.  We are sure that the angles are congruent hence triangles are similar.  But to prove congruence we must have additional information about sides.

The two triangles may be congruent, but additional information is needed about the sides of each triangle.

Answer:The two triangles may be congruent, but additional information is needed about the sides of each triangle

Step-by-step explanation:

Answer:

The solution is (-2,-11)

Step-by-step explanation:

The given system is

[tex]-5x+y=-1[/tex]

and

[tex]y-4x=-3[/tex]

Make y the subject in the first equation to get;

[tex]y=5x-1[/tex]

Put [tex]y=5x-1[/tex] into the second equation.

[tex]5x-1-4x=-3[/tex]

Group similar terms;

[tex]5x-4x=-3+1[/tex]

[tex]x=-2[/tex]

Put [tex]x=-2[/tex] into [tex]y=5x-1[/tex].

This implies that;

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

[tex]y=-10-1[/tex]

[tex]y=-11[/tex]

The solution is (-2,-11)

Answer:

(-2, -11)

Step-by-step explanation:

We are given the following two equations:

[tex]-5x + y = -1[/tex] --- (1)

[tex]y - 4x = -3[/tex] --- (2)

From equation (2):

[tex]y=4x-3[/tex]

Substituting this value of y in equation (1) to get:

[tex]-5x + y = -1[/tex]

[tex]-5x + (4x-3) = -1[/tex]

[tex]-5x+4x=-1+3[/tex]

[tex]x=-2[/tex]

Now substituting the value of x in equation (2) to get:

[tex]y - 4(-2) = -3[/tex]

[tex]y+8=-3[/tex]

[tex]y=-8-3[/tex]

[tex]y=-11[/tex]

Therefore, the solution of the equations as an ordered pair is (-2, -11).

Answer:

Option d.

Step-by-step explanation:

For this problem we have 2 sides of a triangle (a and b) and the angle between them C = 160 °.

We have a triangle of type SAS.

We have:

a=25

b=30

C= 160°

Then we use the law of cosine.

[tex]c = \sqrt{a^2 +b^2 - 2abcos(C)[/tex]

Now we substitute the values in the formula to find c

[tex]c = \sqrt{25^2 +30^2 - 2(25)(30)cos(160\°)}\\\\c = 54.2[/tex]

Now we use the cosine theorem to find B. (You can also use the sine)

[tex]b = \sqrt{a^2 +c^2 - 2accos(B)}\\\\b^ 2 = a^2 +c^2 - 2accos(B)\\\\b^ 2 -a^2 -c^2 =- 2accos(B)\\\\\frac{a^2 +c^2 -b^2}{2ac} =cos(B)\\\\B = arcos(\frac{a^2 +c^2 -b^2}{2ac})\\\\B = arcos(\frac{25^2 +54.2^2 -30^2}{2(25)(54.2)})\\\\B = 10.9\°[/tex]

Finally:

[tex]A=180\° - B- C\\\\A = 180\° - 10.9\° - 160\°\\\\A = 9.1\°[/tex]

Answer:

The ball will hit the ground in 2 seconds

Step-by-step explanation:

The formula for throwing a baseball in the air is represented by :

h = -16t² + 12t + 40

where h is the height of the ball and t is the time in seconds

Now we need to find after how many seconds will the ball hit the ground

When the ball hits the ground the height of the ball is 0

⇒ -16t² + 12t + 40 = 0

⇒ 4t - 3t - 10 = 0

⇒ 4t² - 8t + 5t - 10 = 0

⇒  4t(t - 2) + 5(t - 2) = 0

⇒ t cannot be negative so t = 2

Hence, The ball will hit the ground in 2 seconds

The ball will hit the ground after 2 seconds.

The formula for the height of a thrown baseball is given by:

h = -16[tex]t^{2}[/tex] + 12t + 40

where h is the height (in feet) and t is the time (in seconds).

To find the time when the ball hits the ground, we need to determine when the height h is equal to zero:

0 = -16[tex]t^{2}[/tex] + 12t + 40

Solving this quadratic equation using the quadratic formula:

The quadratic formula is: t = (-b ± √(b² - 4ac)) / 2a

For our equation, a = -16, b = 12, and c = 40. Plugging these values in:

Thus, the ball will hit the ground at t = 2 seconds.

Note that we ignore the negative time value as it doesn’t represent a meaningful physical solution.

Answer:

Correct choice is D). -4.

Step-by-step explanation:

Given the following relation is a function where the relation is :

{(6,3),(-4,1),(8,-5),(x,1)}

Now we need to decide about which of the following cannot be a value for x.

Where given choices are:

A). 3

B). 1

C). -5

D). -4

E). 4

We know that a relation is called function if doesn't contains repeated values in domain or doesn't have repeated x-values.

In given relation, {(6,3),(-4,1),(8,-5),(x,1)}, we see that x-values are 6, -4 and 8.

So to prevent repetition, x can't be any of 6, -4 and 8.

Hence correct choice is D). -4.

Total discount will be of $14.85.

To calculate the total discount Jennifer received on her purchase of music CDs, each original price must be multiplied by the discount rate of 33 percent (or 0.33 in decimal form).

Let's calculate the discount for each CD first:

For the $9.99 CD: $9.99 × 0.33 = $3.30

For the $14.99 CD: $14.99 × 0.33 = $4.95

For the $19.99 CD: $19.99 × 0.33 = $6.60

Next, add up the discounts to find the total discount:

$3.30 + $4.95 + $6.60

= $14.85

Answer:

It is B.

Step-by-step explanation:

Substitute x = 0 into the function

y = -2(0) - 4 = -4

x = 1:

y = -2(1) - 4 = -6.

x = 2 and 3 give y = -8 and - 10.

Answer:

The correct answer is B.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A=l•w

=5/6•1/3

=5/18

A=0.28 mi²

Answer:

D & E

Step-by-step explanation:

1/ they're the only ones in the right format

2/ they're both highlighted on the graph

(im not completely confident in my answer, so don't drag me if im wrong.)

Answer:

it is a and b

Step-by-step explanation:

Answer:

4 and -21

Step-by-step explanation:

When you factor it (x-4)(x+21)

You get 4 and -21