Solve this with your work shown. (50 POINTS.)​

Answer:

C) y = ln(x) + 4  

Step-by-step explanation:

The equation can't be A or B, because they are exponential functions, and they can have negative x-values.

It must be one of the two ln functions, because they can't have negative values of x.

To decide between C and D, insert a value of x that makes it easy to calculate the value of y.

Let x = 1.

For Equation C,

y = ln(1) + 4  = 0 + 4 = 4

For Equation D,

y = ln(1) + 5  = 0 + 5 = 5

We draw a vertical line from x = 1 and see where it intersects the graph.

The intersection is at (1, 4), so the correct equation is

y = ln(x) + 4

Using the linear regression equation y = 2.4x + 3.1, substituting '3' for 'x' results in a predicted wait time of approximately 10.3 minutes when there are 3 people in line ahead of you.

To calculate the time it would take to be served at a food stand if there are 3 people in line ahead of you, we will use the given linear regression equation y = 2.4x + 3.1.

Plugging in the value of 3 for x (which represents the number of people in line), we get the result as:

y = (2.4 * 3) + 3.1

y = 7.2 + 3.1

y = 10.3 minutes

Therefore, according to the regression line, it will take approximately 10.3 minutes for you to be served if there are 3 people in line ahead of you.

Final answer:

To determine the service time with 3 people in line, substitute 3 into the regression equation y = 2.4x + 3.1 to get y = 2.4(3) + 3.1, which calculates to approximately 10.3 minutes.

Explanation:

The question involves using a linear regression line to predict the time it would take to be served at a food stand based on the number of people in line ahead. The given linear regression equation is y = 2.4x + 3.1, where y represents the time to be served in minutes and x represents the number of people in line. To find the time it would take to be served when there are 3 people in line ahead, simply substitute 3 for x in the equation:

y = 2.4(3) + 3.1
= 7.2 + 3.1
= 10.3 minutes.

So, it would take approximately 10.3 minutes to be served if there are 3 people in line ahead of you.

Answer:

11 years old

Step-by-step explanation:

If four brothers have the average age 6, then the sum of their ages is

[tex]4\cdot 6=24[/tex]

years.

Let x years be the age of sister. If four brothers and their sister have the average age 7, then

[tex]\dfrac{24+x}{5}=7.[/tex]

Multiply this equation by 5:

[tex]24+x=35\Rightarrow x=35-24=11.[/tex]

The sister is 11 years old.

The answers is:

The first mechanic's rate is $70 per hour.

The second mechanic's rate is $110 per hour.

Let's write the given information in order to make the equations that will help us to solve this problem.

Let be "x" the first mechanic's rate and "y" the second mechanic's rate, so:

If the first mechanic worked for 5 hours and the second mechanic worked for 15 hours, and the together charged a total of $2000.

[tex]5x+15y=2000[/tex]

Also, we know that the sum of the two rates was $170 per hour, so:

[tex]x+y=180[/tex]

Then, isolating "x" and replacing it into the first equation, we have:

[tex]x=180-y[/tex]

[tex]5(180-y)+15y=2000[/tex]

[tex]900-5y+15y=2000[/tex]

[tex]10y=2000-900[/tex]

[tex]10y=1100[/tex]

[tex]y=\frac{1100}{10}=110[/tex]

So, the second mechanic's rate is $110 per hour.

Now, to calculate the first mechanic's rate we need to replace "y" into the second equation:

[tex]x+y=180\\x+110=180\\x=180-110=70[/tex]

So, the first mechanic's rate is $70 per hour.

Have a nice day!

The correct answer is d

The vertex of the graph is at minimum or maximum option (D) (1, -1); the minimum is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have shown a graph of a parabola in the picture.

As the graph opens up and has a vertex at (1, -1)

The minimum value of graph,

At x = 1

y = -1

Thus, the vertex of the graph is at minimum or maximum option (D) (1, -1); the minimum is correct.

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Answer:

See attachment

Step-by-step explanation:

The given parametric equations are;

[tex]x=2t[/tex] and [tex]y=t+5[/tex], [tex]-2\le t\le 3[/tex].

We can graph this by plotting some few points within the given range or eliminate the parameter to identify the type of curve.

Plotting points;

When [tex]t=-2[/tex],

[tex]x=2(-2)=4[/tex] and [tex]y=-2+5=3[/tex]

This gives the point (-4,3).

When [tex]t=0[/tex]

[tex]x=2(0)=0[/tex] and [tex]y=0+5=5[/tex]

This gives the point (0,5).

When [tex]t=3[/tex]

[tex]x=2(3)=6[/tex] and [tex]y=3+5=8[/tex]

This gives the point (6,8).

We plot these points and draw a straight line through them.

Eliminating the parameter.

[tex]x=2t[/tex]

[tex]y=t+5[/tex]

Make t the subject in the second equation;

[tex]t=y-5[/tex]

Substitute into the first equation;

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

This implies that;

[tex]x=2y-10[/tex]

[tex]y=\frac{1}{2}x+5[/tex]

This is an equation of a straight line with slope [tex]\frac{1}{2}[/tex] and y-intercept 5 on the interval

[tex]-4\le x \le 6[/tex]

Answer:

The answer is in attachment

Step-by-step explanation:

First step finde a function t(x) ⇒ t=x/2;

Now we need to finde the limits of that function:

if t=-2 ⇒ x=-4 and t=3 ⇒ x=6. That means -4≤x≤6

Now replace on y(t) ⇒ y(x)= x/2+5, 4≤x≤6

Answer:

-8i

Step-by-step explanation:

To multiply numbers is polar form

z1 = r1 ( cos theta 1 + i sin theta 1)

z2 = r2 ( cos theta 2 + i sin theta 2)

z1*z2 = r1*r2 (cos (theta1+theta2) + i sin (theta1+theta2)

z1 = 2(cos 70° + i sin 70°)

z2 = 4(cos 200+ i sin 200)

z1z2 = 2*4 (cos (70+200) + i sin (70+200)

z1z2 = 8 (cos(270) + i sin (270))

       = 8 (0 + i (-1))

       =-8i

The product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°), is found by multiplying the moduli and adding the angles, resulting in -8i.

To find the product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°), we use the properties of complex numbers in trigonometric form. According to the properties, the product of two complex numbers in this form is given by multiplying their moduli (or absolute values) and adding their angles.

The product is: |z1||z2| e[tex]^{(i(angle1+angle2)),}[/tex] where |z1|, |z2| are the moduli of z1 and z2, and angle1, angle2 are the angles of z1 and z2 respectively.

For z1 and z2, we have:

The product is:

|z1||z2| = 2 * 4 = 8

Sum of the angles: angle1 + angle2 = 70° + 200° = 270°

Therefore, z1z2 = 8(cos 270° + i sin 270°), and since cos 270° = 0 and sin 270° = -1, the product simplifies to z1z2 = 8i(-1) = -8i.

Answer:

A

Step-by-step explanation:

A trinomial can be factored into two binomials, when the discriminant of the trinomial is greater than or equal to 0.

The discriminant for trinomial [tex]ax^2+bx+c[/tex] is he expression [tex]D=b^2-4ac.[/tex]

Check all options:

A.

[tex]D=3^2-4\cdot 1\cdot 2=9-8=1,[/tex]

then

[tex]x_{1,2}=\dfrac{-b\pm\sqrt{D}}{2a}=\dfrac{-3\pm\sqrt{1}}{2}=-2,\ -1.[/tex]

Thus,

[tex]x^2+3x+2=(x-x_1)(x-x_2)=(x-(-2))(x-(-1))=(x+2)(x+1).[/tex]

B.

[tex]D=4^2-4\cdot 1\cdot 5=16-20=-4<0,[/tex]

so this trinomial cannot be factored.

C.

[tex]D=5^2-4\cdot 1\cdot 7=25-28=-3<0,[/tex]

so this trinomial cannot be factored.

D.

[tex]D=6^2-4\cdot 1\cdot 10=36-40=-4<0,[/tex]

so this trinomial cannot be factored.

Answer:

2π/3, 4π/3

Step-by-step explanation:

I interpret your question as asking us to solve the equation

2cos(x) + 1 = 0

2cos(x) = -1

cos(x) = -½x  

x = arccos(-½), 0 ≤ x ≤2π

Since the cosine is negative, x must be in the second or third quadrant.

Referring to the unit circle, we find that

x = 2π/3 (120°) or x = 4π/3 (240°)

Answer:

c) 14

Step-by-step explanation:

The given equation is  [tex]\frac{3v}{7}=6[/tex].

We need to solve this equation for v, so we multiply both sides of the equation by the multiplicative inverse of [tex]\frac{3}{7}[/tex] which is [tex]\frac{7}{3}[/tex] to obtain;

[tex]\frac{7}{3} \times \frac{3v}{7}=6\times \frac{7}{3}[/tex].

We simplify to obtain;

[tex]v=2\times 7[/tex]

[tex]v=14[/tex]

The correct choice is C.

Answer: option c

Step-by-step explanation:

To solve this problem you must apply the following proccedure:

-  Multiply both sides of the equation by 7.

- Divide both sides of the equation by 3.

Therefore, keeping the steps above on mind, you obtain the result shown below:

[tex]\frac{3v}{7}=6\\\\(7)\frac{3v}{7}=6(7)\\\\3v=42\\\\\frac{3v}{3}=\frac{42}{3}\\ v=14[/tex]

Answer:

the answer is 3

Step-by-step explanation:

11-8=3

17-11=6

6/2=3

Answer:the answer is 14 just took the test

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Use the geometric sum formula for in infinite sum. 20 terms of this basic formula is close enough The 20th term is 8.6 * 10^-10 which means this goes out to a number with 9 zeros after the decimal and before the 8.

Put another way, the tenth number of this series is the only one affected.

When you use a spreadsheet, it seems to know that the answer is 3/2 as the solution to the sum.

Solution.

Sum = a / (1 - r)

a = 1

r = 1/3

Sum = 1 / (1 - 1/3)

Sum = 1 // 2/3

sum =  3/2

Now you can worry about the 30.

30 * sum(1/3)^n = 30* 3/2 = 45

If there is something you want more information on, leave a note.

The sum of a finite geometric sequence can be calculated using the formula S = a1(1 - r^n) / (1 - r), where S is the sum, a1 is the first term, r is the common ratio, and n is the number of terms.

The student's question pertains to the summation of a finite geometric sequence. A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. Considering the information provided doesn't match the exact question, we would educate the student on how to find the sum of a finite geometric sequence using the standard formula for such a sum, which is S = a1(1 - r^n) / (1 - r), where S is the sum of the sequence, a1 is the first term, r is the common ratio, and n is the number of terms.

Unfortunately, specific values were not provided in the question. Therefore, to calculate the sum, we'd need the initial term, the ratio, and the number of terms. This formula is only applicable if the common ratio r is not equal to 1. Essential to note is that if the common ratio is greater than 1, the terms in the sequence increase, and if the ratio is between 0 and 1, the terms decrease.

Answer:

(i) Exponential Decay

(ii)linear

(iii)Exponential Growth

Step-by-step explanation:

(i)

Cost of the van=$25,000.

After 2 years, value of van=$17,500.

After 4 years, value of van = $12,250.

Its a decay but to be a exponential decay it must have constant rate.

As its known the exponential decay formula is [tex]C=C_{0} e^{-kt}[/tex]

Now substitute the values in the above formula

[tex]17500=25000 e^{-k*2}[/tex]

Now on simplification, we get

[tex]k=0.1783[/tex]

Now again apply the same formula for the next time interval

[tex]12250=25000 e^{-k*4}[/tex]

Now on simplification, we get

[tex]k=0.1783[/tex]

Since the value of k is constant for both the time interval. Hence the decays is exponential.

(ii)

At the beginning, battery life=100%.

After 3 Hours, battery life=60%.

After 6 Hours, battery life = 20%.

Since the value of battery life decreases by 40% in each interval. Hence the decay of battery life is linear.

(iii)

Initial population=20.

After 5 years, population=30.

After 10 years, population = 45.

Its a growth but to be a exponential growth it must have constant rate.

As its known the exponential growth formula is [tex]P=P_{0} e^{kt}[/tex]

Now substitute the values in the above formula

[tex]30=20 e^{-k*5}[/tex]

Now on simplification, we get

[tex]k=-0.081[/tex]

Now again apply the same formula for the next time interval

[tex]45=20 e^{-k*10}[/tex]

Now on simplification, we get

[tex]k=-0.081[/tex]

Since the value of k is constant for both the time interval. Hence the decays is exponential.

Answer:

Sometimes, but not always.

Step-by-step explanation:

A parallelogram is a quadrilateral with two pairs of parallel sides, but there are no requirements for its interior angles. A rectangle, on the other hand, must have four interior 90 degree angles. So a rectangle is always a parallelogram, but a parallelogram is not always a rectangle.

A parallelogram is usually defined as a quadrilateral with 2 pairs of equal, opposite and parallel sides. It can also form right angles between adjacent sides. Therefore, not all rectangles are squares, not all parallelograms are rectangles.

Hope I could help! :)

Answer:

its 18 inchs in diamatr

Step-by-step explanation:

The area of the figure is 400 in.

Answer:

(3,-5)

Step-by-step explanation:

Answer with explanation:

Perimeter of Square = 36 units

Also, Perimeter of Square =4 × Side

→4 × Side=36

Dividing both sides by ,4 we get

Side of Square = 9 units

Length of Diagonal of square having side a, =√2 a

Length of Diagonal of Square having side , 9 units =9 √2 units

One Vertex of the Square =(3,5)

As , All Interior Angles of Square measures 90°.

So, Other vertices of Square will be, (3,-4),(-6,-4) and (-6,5).

Answer:

Step-by-step explanation:

2 1/4 divided by 1 2/5

8/4 + 1/4 divded by 5/5 +2/5

9/4 divided by 7/5

9/4 times 5/7

9 times 5 over 4 times 7

45 over 28

6, 6 are the solutions of the given equation.

It is a mathematical statement which contains two algebraic expressions on both sides of an ' = ' sign.

Equation shows the equality between the expressions in left hand and right hand side.

The given equation is [tex]6x^{2} -2x+36=5x^{2} +10x[/tex]

Solving the equation, [tex]6x^{2} -5x^{2} -2x-10x+36=0[/tex]

⇒ [tex]x^{2} -12x+36=0[/tex]

⇒ [tex](x-6)^{2} =0[/tex]

∴ The equation have double root, the values of x are 6, 6

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Answer:

a) As x decreases within bound, f(x) increases without bound.  

c) as x increases without bound,f(x) approaches the line y = - 4

Step-by-step explanation:

From the graph, we can see, as x becomes more negative, y gets larger and larger.  

As x→ -∞, y → ∞

As x decreases without bound, y increases without bound

We can also see as x gets larger and larger, y gets closer to -4

As x →∞, y → -4

As x increases without bound, y approaches -4

As x decreases within a limit, f(x) increases without bound.

The correct statement in this question is a) As x decreases within bound, f(x) increases without bound.

To understand this concept better, we can look at the graph of the function y = 1/x. As x approaches zero (within the bound), the value of y increases without bound, meaning it becomes very large and approaches infinity.

Other functions can also exhibit similar behavior where as x decreases within a limit, the corresponding values of f(x) increase without bound.

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ANSWER

All possible solutions are

[tex]k \: > \: 2[/tex]

EXPLANATION

The given inequality is

[tex] - 6k \: < \: - 12[/tex]

Divide both sides by -6 and reverse the inequality sign.

[tex] k \: > \: \frac{ - 12}{ - 6} [/tex]

[tex]k \: > \: 2[/tex]

All real numbers greater than 2.

Answer:

Range

Step-by-step explanation:

The answer is A) 25.5 cm2.

Answer:

it is going to be a

Step-by-step explanation:

but u have to add the number and move your demical

Answer:

Option b 17.2

Step-by-step explanation:

Given is a probability distribution of a random variable say x in table form.We have to find the mean.

All probabilities lie between 0 and 1 and add to 1.

Hence this is a valid prob distribution.

To find mean we multiply the random variable x value with probability and add.

Mean = E(X) = [tex]\Sigma p_i x_i = 15(0.1)+16(0.3)+17(0.2)+18(0.2)+19(0.1)+20(0.1)\\=1.5+4.8+3.4+3.6+1.9+2\\= 17.2[/tex]

Hence option b is right answer.

Answer:

The expression is

y = -17*x + 8

Which is already in the slope intercept form

y = m*x + b

Where m is the slope and b is the y-intercept.

The slope

m = -17

The intercept

b = 8

Please see attached picture for graph

Profit = 8%

If the briefcase was marked down 20% from 1500 you multiply 1500 x .2 = 300 in order to calculate the discount.

Calculate the discounted price:

1500 - 300 = 1200

Calculate 10% discount of 1200:

1200 x .1 = 120

Calculate the sales price:

1200 - 120 = 1080

The last step is to calculate the profit/loss is the cost is 1000.

The briefcase sold for 1080 and the company paid 1000 for it, so there was a profit of 80.

The percentage is calculate by dividing 80/1000 = 8% profit

Final answer:

The briefcase was originally priced at Rs 1500, discounted twice first by 20% and then by an additional 10%, leading to a final selling price of Rs 1080. With a cost of Rs 1000, the profit is Rs 80, resulting in a profit percentage of 8%.

Explanation:

The briefcase was initially selling for Rs 1500 and was marked down by 20%. Therefore, the sale price after the first discount can be calculated as: Rs 1500 - (20% of Rs 1500) = Rs 1500 - Rs 300 = Rs 1200. This briefcase was then marked down by an additional 10% of the promotion sales price, which becomes Rs 1200 - (10% of Rs 1200) = Rs 1200 - Rs 120 = Rs 1080. The cost of the briefcase is given as Rs 1000, so the profit is the final selling price minus the cost: Rs 1080 - Rs 1000 = Rs 80.

To find the profit percentage, we use the formula: (Profit/Cost) x 100. Substituting the values we get: (Rs 80/Rs 1000) x 100 = 8%. So, the profit percentage is 8% after both the discounts.

Answer:

h = 12x^5y^3

Step-by-step explanation:

The area of a parallelogram is found using A = b*h. Substitute the values given and solve for h.

A = b*h

36x^6 y^5 = 3xy^2 * h

36x^6 y^5 ÷ 3xy^2 = h

12x^5y^3 = h

Answer:

[tex]x=\frac{1}{9},-\frac{1}{9}[/tex]

Step-by-step explanation:

[tex]3 + |x*-9|=4\\|x*-9|=1\\|x|=\frac{1}{9}\\ \\x=\frac{1}{9},-\frac{1}{9}[/tex]

The value of x for the given condition will be either 1/9  or -1/9.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers to each other to find a new multiplied number.

Given that 3 + x × (-9) = 4

In the first case  if the value of x is positive

3 - 9x = 4 ⇒ x = -1/9

In the second case if the value of x is negative

3 + 9x = 4 ⇒  x = 1/9

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To find the radius of the circular rug with a circumference of 6.28 yards, the formula r = C / (2π) is used, where π is approximated as 3.14. By substituting the given circumference into the formula, the radius is calculated to be 1 yard.

The question is asking to calculate the radius of a circular rug given its circumference. The formula for the circumference of a circle is C = 2πr, where C is the circumference, π (pi) generally approximated as 3.14, and r is the radius of the circle. To find the radius, we rearrange the formula to solve for r: r = C / (2π).

In this case, the circumference is given as 6.28 yards. Using the formula:

r = 6.28 yards / (2 × 3.14)

r = 6.28 / 6.28

r = 1 yard

Therefore, the radius of the circular rug is 1 yard.

Answer:

i think it is 19 is the whole number 9/40 is the remainder

Step-by-step explanation:

Answer:

B 80 %

Step-by-step explanation:

She wants to reduce the size of the drawing, so the setting should be a proper fraction.

                                                                Setting = 4/5

Multiply numerator and denominator by 20     = 80/100

Convert to percent                                             = 80 %

The setting should be 80 %.

Answer:

80%

Step-by-step explanation:

4/5 multiply them together  and it equals 20

then multiply 4 and 5 by 20 which will get you

80/100 so.. convert it to percentage and you get...

80%