The recipe makes 20 portions of potato soup. Richard follows the recipe but wants to make 4 portions. Complete the amounts of each ingredient that he needs. 120 ml oil 280 g onion 1.8kg potatoes 2.2 l milk

Final answer:

The stone is approximately 583 feet high 4 seconds later.

Explanation:

To find the height of the stone 4 seconds later, we can use the equation of motion for an object in free fall:

h = h0 + v0t + (1/2)gt^2

Where:

h = height at time t

h0 = initial height

v0 = initial velocity

g = acceleration due to gravity

t = time

Substituting the given values:

h = 775 + 16(4) + (1/2)(-32)(4)^2

h = 775 + 64 - 256

h = 583 feet

Therefore, the stone is approximately 583 feet high 4 seconds later.

∠A = ∠B

6x + 12 = 3x + 63

6x - 3x = 63 - 12

3x = 51

x = 51 ÷ 3

x = 17

6(17) + 12

102 + 12

∠A = 114°

Answer:

114

Step-by-step explanation:

Answer:

B) x + y = 3

Step-by-step explanation:

This is a specific way to give details without a detailed written explanation of the function. There will be NO exponents when trying to find out information about something:

[tex]\displaystyle x + y = 3 → y = -x + 3[/tex]

I am joyous to assist you anytime.

Answer:

option C) (7, -2)

Step-by-step explanation:

By the graph, the initial coordinates of point A are ( -5, -4)

first reflection along the line x=1, only the x coordinate will change.

the new x coordinate is = x = 7

thus the point becomes (7, -4)

similarly, reflection along y= -3, only the y coordinate will change.

the new y coordinate is = y = -2

thus the final coordinates are (7, -2)

Answer:

The time it takes for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.

Step-by-step explanation:

Given the equation

[tex]d = 11cos( \frac{8\pi}{5}*t)[/tex]-----------Equation 1

where d, in inches of the pendulum of a grandfather clock from the center.

Comparing with the standard equation of an oscillating pendulum bob.

[tex]d = Acos (wt + \alpha )[/tex] ----------Equation 2

         where ω =  angular velocity

                     t =  time taken

                     α =  The angular displacement when t = 0

Comparing equation 1 and 2,

α = 0

[tex]w =\frac{8\pi }{5}[/tex]

Recall that [tex]w = 2\pi f

Therefore,

[tex]2\pi f = \frac{8\pi }{5} \\\\f = \frac{4}{5}[/tex][/tex]

f = 0.8 Hertz

Recall that [tex]f = \frac{1}{T}[/tex]

[tex]T = \frac{1}{0.8}[/tex]

T = 1.25 seconds

Therefore, the time it takes for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.

Answer:

Option D.

Step-by-step explanation:

Cost of truck = $16000

Residual value after 5 years = $1000

Depreciated value of a truck in 5 year is

[tex]Depreciation=16000-1000=15000[/tex]

In straight-line method, the value of a fixed asset depreciate by a constant rate.

Since depreciation of truck in 5 years is $15000, therefore, the depression of one year is

1 year Depreciation = [tex]\dfrac{15000}{5}=3000[/tex]

From July 3 to end of fist year = 1/2 year

1/2 year Depreciation = [tex]\dfrac{3000}{5}=1500[/tex]

So, the value at the end of year 1 using straight-line rate is

[tex]Value=16000-1500=14,500[/tex]

Therefore, the correct option is D.

Answer:

Step-by-step explanation:

We have four equations here.  Let's actually solve them, using factoring if possible and some other method if factoring is not possible.

A)  x^2 + 5x + 4 factors into (x + 1)(x + 4), but x^2 + 5x - 4 does not.

B)  x^2 + 6x + 9 factors into (x + 3)^2.

C) x^2 + 3x - 4 factors into (x + 4)(x - 1).

D) x^2 - x - 6 factors into (x - 3)(x + 2)

x^2 + 5x - 4 = 0 can be solved, but not by factoring.

The rate of change of the volume of a ball when the radius is 5cm is -300π cubic centimeters per second.

To find the rate of change of the volume of a ball, we can use the formula for the volume of a sphere, which is V = (4/3)πR³. We are given that the radius is decreasing at a constant rate of 3 cm per second. So, the rate of change of the volume can be found using the derivative of the volume function with respect to time.

First, we differentiate the volume function with respect to time:

dV/dt = (4/3)π×3R²×(-3)

dV/dt = -12πR²

Then we substitute the given value of the radius when it is 5 cm:

dV/dt = -12π×5²

dV/dt = -12π×25

dV/dt = -300π

Therefore, the rate of change of the volume of the ball when the radius is 5 cm is -300π cubic centimeters per second.

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Answer:

a)550

b)910

c)730

Step-by-step explanation:

The given model is

[tex]v(t) = 10t^2 ft/s[/tex]

Use the interval [0,6], with n=6 rectangles

Then, the interval width is

[tex]\Delta t = \frac{b-a}{n}[/tex]

[tex]\Delta t = \frac{6-0}{6}[/tex]= 1

so, the sub intervals are

[0,1], [1,2], [2,3], [3,4],[4,5],[5,6]

Now evaluating the function values

[tex]f(t_0)= f(0) = 0[/tex]

[tex]f(t_1)= f(1) = 10[/tex]

[tex]f(t_2)= f(2) = 40[/tex]

[tex]f(t_3)= f(3) = 90[/tex]

[tex]f(t_4)= f(4) = 160[/tex]

[tex]f(t_5)= f(5) = 250[/tex]

[tex]f(t_6)= f(6) = 360[/tex]

a) left hand sum is

L_6 = [tex]\Delta t [f(t_0)+ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)][/tex]

=[tex]1 [0+ 10+40+90+160+250][/tex]

= 550

b) right hand sum

R_6 = [tex]\Delta t [ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)+f(t_6)][/tex]

= [tex]1 [10+40+90+160+250+360][/tex]

= 910

c) average of two sums is

[tex]\frac{L_5+R_5}{2}[/tex]

= [tex]\frac{550+910}{2}[/tex]

=730

If the coefficient of determination is a positive value, then the regression equation could have either a positive or a negative slope.

If the coefficient of determination is a positive value, then the regression equation could have either a positive or a negative slope.

The coefficient of determination, denoted as r², is equal to the square of the correlation coefficient, r. It represents the percentage of variation in the dependent variable, y, that can be explained by variation in the independent variable, x, using the regression line. When r² is positive, it indicates a positive relationship between x and y, but it does not specify the direction of the slope.

Therefore, if the coefficient of determination is positive, the regression equation could have either a positive or a negative slope.

Kyle is correct in saying that 3/5 is equal to 60% because 3/5 is equivalent to 60/100.

Kyle says that 3/5 is equal to 60%. This statement can be explained by saying that 3/5 is equivalent to 60/100. To convert a fraction to a percentage, you multiply the top number (numerator) by 100 and then divide by the bottom number (denominator). In this case, multiplying 3 by 100 gives you 300, and when you divide 300 by 5, it equals 60. Hence, 3/5 is indeed equivalent to 60%, which makes Kyle's statement correct.

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Answer:

Step-by-step explanation:

If you plot the vertex and the point that it goes through, the point it goes through is above the vertex, so the vertex is a positive one that opens upwards.  The general vertex form of a parabola of this type is

[tex]y=a(x-h)^2+k[/tex]

We have the x, y, h, and k.  We will plug all those in and solve for a.  That looks like this:

[tex]-5=a(6-4)^2-13[/tex] which simplifies to

-5 = 4a - 13 and

8 = 4a so

a = 2

That means that the paraobola in vertex form is

[tex]y=2(x-4)^2-13[/tex]

Answer:

a)[tex]P(X\geq 11) = 0.198[/tex]

b)[tex]P(X\leq 2) = 0.000565[/tex]

c) Mean = 8.8

Step-by-step explanation:

1) Previous concepts

Binomial Distribution is a "discrete probability distribution which is used to calculate the probabilities for the independent trials and for each trial there is only two outcomes success or failure and probability for each success remains constant throughout each trial".

The Binomial distribution is a type of Bernoulli experiment with following properties:

a)There are two possible outcomes; success or failure.

b) Outcomes are independent on preceding result of a trial.

c) The probability of success remains constant throughout the experiment.

d)The number of successes are fixed.

The probability mass function for the Binomial distribution is given by:

[tex]P(X=a)=(nCa)(p)^x (1-p)^{n-x}[/tex]

Where [tex]p[/tex] is the probability of success, n the number of trials and x the number of successes that we want on the n trials.

[tex]X[/tex] represent the number federal inmates that are serving time for drug dealing

[tex]p=0.55[/tex] represent the proportion of federal inmates that are serving time for drug dealing

[tex]n=16[/tex] random sample selected

2) Part a

The random variable X follows this distribution [tex]X \sim Binom(n,p)[/tex]

On this case we want the following probability, and since says greater or equal than 11 we can express like this:

[tex]P(X \geq 11)=P(X=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)+P(x=16)[/tex]

[tex]P(X=11)=(16C11)(0.55)^{11} (1-0.55)^{5} =0.112[/tex]

[tex]P(X=12)=(16C12)(0.55)^{12} (1-0.55)^{4} =0.0572[/tex]

[tex]P(X=13)=(16C13)(0.55)^{13} (1-0.55)^{3} =0.0215[/tex]

[tex]P(X=14)=(16C14)(0.55)^{14} (1-0.55)^{2} =0.00563[/tex]

[tex]P(X=15)=(16C15)(0.55)^{15} (1-0.55)^{1} =0.000918[/tex]

[tex]P(X=16)=(16C16)(0.55)^{16} (1-0.55)^{0} =0.00007011[/tex]

[tex]P(X \geq 11)=0.112+0.0572+0.0215+0.00563+0.000918+0.00007011=0.198[/tex]

3) Part b

[tex]P(X \leq 2)=P(X=0)+P(x=1)+P(x=2)[/tex]

[tex]P(X=0)=(16C0)(0.55)^{0} (1-0.55)^{16} =0.00000283[/tex]

[tex]P(X=1)=(16C1)(0.55)^{1} (1-0.55)^{15} =0.0000552[/tex]

[tex]P(X=2)=(16C2)(0.55)^{2} (1-0.55)^{14} =0.000507[/tex]

[tex]P(X \leq 2)=0.00000283+0.0000552+0.000507=0.000565[/tex]

4) Part c

The expected value for the binomial distribution is given by the following formula:

[tex] E(X)=np=16*0.55=8.8[/tex]

So then the average number of federal inmates that are serving time for drug dealing on a sample of 16 is approximately 9.

Answer:

1: C(n) = 2.50 + 16n

2: $66.50

Step-by-step explanation:

Part 1

Each ticket costs $16 per person. If tickets for n persons were purchased, the total cost would be 16n.

There is also a one-time service fee of $2.50 that must be paid. Thus, for n tickets the total cost is

C(n) = 2.50 + 16n

Part 2

For n = 4, the expression evaluates to

C(4) = 2.50 + 16 (4) = $66.50

Answer:

A

Step-by-step explanation:

Given:

- The original function is:

                               f(x) = x^3

Find:

How does the graph of g(x) = (x − 1)3 + 5 compare to the original function.

Solution:

- We have a general form of the new function relating to parent function.

                               g(x) = a*( x +/- b )^n + c

Where; a, b and c are constants.

- The constant a magnitude denotes steepness of the graph relative to 1 and the sign of a will determine the mirror image of the graph about line y = 0.

- The constant b magnitude denotes shifts of the graph of every x value sign of b will determine the direction of shifts. + b : shift left , - b shift right.

- The constant c magnitude denotes shifts of the graph of every y value. sign of c will determine the direction of shifts. + c : shift up , - b shift down.

- In our g(x).   a = 1 , b = -1 , c = + 5

Hence, g(x) is shifted 1 unit to the right and 5 units up.

The graph of g(x) = (x - 1)^3 + 5 is shifted 1 unit to the right and 5 units up compared to the parent function f(x) = x^3.

The graph of g(x) = (x - 1)3 + 5 is obtained by shifting the graph of f(x) = x3 one unit to the right and five units up. Shifting a function horizontally is done by replacing x with (x - h), where h is the amount of units you want to shift.

In this case, g(x) = (x - 1)3 + 5 is equivalent to f(x - 1) + 5. So the graph is shifted 1 unit to the right. Shifting a function vertically is done by replacing f(x) with f(x) + k, where k is the amount of units you want to shift.

Since f(x - 1) + 5 is obtained by shifting f(x) one unit to the right and five units up, the correct answer is: g(x) is shifted 1 unit to the right and 5 units up.

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Answer:

The worth of the automobile after an year with 15% depreciation  is $22,100.

Step-by-step explanation:

The current cost of the automobile car = $26,000

The percentage of depreciation  = 15%

Now, calculating the depreciated amount:

15% of $26,000  = [tex]\frac{15}{100}  \times 26,000 = 3,900[/tex]

So, the depreciated amount of the car in the next year = $3,900.

Now, the worth of the car after an year

= CURRENT WORTH - THE DEPRECIATED AMOUNT

= $26,000 - $3,900.

= $22,100

Hence, the worth of the automobile after an year  is $22,100.

Answer:

The value of x is 3 cm.

Step-by-step explanation:

Given,

Total surface area of cuboid = 112 cm^2

Height of cuboid = 10 cm

Breadth of cuboid = 2 cm

Length of cuboid = x cm

Solution,

Formula for total surface of cuboid = [tex]2\times(length\times breadth +breadth\times height+height\times length)[/tex]

∴[tex]112=2(x\times2+2\times10+10\times x)\\112=2(2x+20+10x)\\112=2(12x+20)\\12x+20=\frac{112}{2}\\12x+20=56\\12x=56-20\\12x=36\\x=\frac{36}{12}=3[/tex]

Thus the length of cuboid is 3 cm.

Answer:

the answer is (-4,2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is (-4,2)

Answer:

four bouquets

Step-by-step explanation:

The way of solving this problem is tell Abigail to keep the relation between flowers constant, that is

We have  16 roses   and 20 carnations

16  2       16  =  2⁴      20  2     20 = 2² * 5

8   2                           10   2

4   2                            5   5

2   2                             1

1

So we will make bouquets of 4 roses and 5 carnations

so we will have  4 bouquets using all flowers

Answer:

A. pay for each individuals tipping fee at landfills with taxes

Step-by-step explanation:

Because it is a recyclic methodology .It is a service provide to household for dispose of the waste and recycled it. So as a  municipality wanting to waste management so Curbside recycling can be used.

Municipal should attract business that utilize source reduction in their manufacturing.

They should offer much to its resident.

They maintain a hazardous waste collection site for its residents as well.

Answer: No

Step-by-step explanation:

X does not represent the cost of fabric. X represents the number of yards of fabric used.

15x + 250

Could be read as ($15 × # of yards) + $250

So she has to pay $15 per yard of fabric plus an additional $250 base amount for having them made and hung in the first place.

She could use an additional variable to represent the cost of fabric.

Example: Y

Y= 15x

Cost of fabric is equal to $15 per yard × # of yards.

The equation for the total cost depending on the number of students in Emma's Extreme Sports classes is C = 50 + 20x.

C = 50 + 20x

Where C represents the total cost, 50 is the fee per class, and 20 is the cost per student.

Answer:

Part 1 : Figure show the graph of triangle

Part 2 : The area of triangle is 4 sqaure units

Step-by-step explanation:

Given points A(1, -3), B(3, -1) and C(5, -3) make triangle.

Part 1:

Figure show the graph of triangle with A(1, -3), B(3, -1) and C(5, -3)  as vertices.

Part 2: Find the area of the triangle.

The area of triangle is given by A=[tex]\frac{(Base)(height)}{2}[/tex]

From figure, Take base as length of AC

Length of line is given by L=[tex]\sqrt{(X1-X2)^{2}+(Y1-Y2)^{2} }[/tex]

Now, Base = length of AC

Base =[tex]\sqrt{(X1-X2)^{2}+(Y1-Y2)^{2} }[/tex]

        =[tex]\sqrt{(1-5)^{2}+((-3)-(-3))^{2}}[/tex]

        =[tex]\sqrt{(-4)^{2}+(0)^{2}}[/tex]

        =[tex]\sqrt{16}[/tex]

        =4units

and Height as difference of y-component of point A and point B

Height = (y of component of point B)- (y of component of point A)

           = (-1)- (-3)

           = 2units

Therefore, The area of triangle is given by A=[tex]\frac{(Base)(height)}{2}[/tex]

A=[tex]\frac{(4)(2)}{2}[/tex]

A=4 sqaure units

Answer:

Part a) [tex]120\pi\ \frac{rad}{min}[/tex]

Part b) [tex]960\pi\ \frac{in}{min}[/tex]

Step-by-step explanation:

we have

60 rev/min

Part a) Find the angular speed in radians per minute

we know that

One revolution represent 2π radians (complete circle)

so

[tex]1\ rev=2\pi \ rad[/tex]

To convert rev to rad, multiply by 2π

[tex]60\ \frac{rev}{min}=60(2\pi)=120\pi\ \frac{rad}{min}[/tex]

Part b) Find the linear speed in inches per minute

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=8\ in[/tex] ----> given problem

substitute

[tex]C=2\pi(8)[/tex]

[tex]C=16\pi\ in[/tex]

Remember that

One revolution subtends a length equal to the circumference of the circle

so

[tex]1\ rev=16\pi\ in[/tex]

To convert rev to in, multiply by 16π

[tex]60\ \frac{rev}{min}=60(16\pi)=960\pi\ \frac{in}{min}[/tex]

Final answer:

The angular speed of the pulley is 120π radians per minute, and the linear speed is 960π inches per minute.

Explanation:

The question pertains to angular and linear speeds related to circular motion. Given that a belt runs a pulley with a radius of 8 inches at 60 revolutions per minute (rpm), we are tasked with finding both the angular speed in radians per minute and the linear speed in inches per minute.

Calculating the Angular Speed

The angular speed (ω) in radians per minute can be calculated using the formula ω = 2π×rpm, where rpm is the number of revolutions per minute and 2π radians is the equivalent of one full revolution.

ω = 2π × 60 = 120π radians/minute

Calculating the Linear Speed

The linear speed (v) can be determined from the radius (r) and angular speed (ω) using the formula v = r×ω. The radius of the pulley is 8 inches, so:

v = 8 inches × 120π radians/minute = 960π inches/minute

Answer:

easey

Step-by-step explanation:

Answer:

a) 95% confidence interval estimate of the true weight is (3.026, 3.274)

b) 99% confidence interval estimate of the true weight is (2.944, 3.356)

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

And margin of error (ME) can be calculated using the formula

ME=[tex]\frac{t*s}{\sqrt{N} }[/tex] where

Using the numbers 95% confidence interval estimate of the true weight is:

3.150±[tex]\frac{2.776*0.1}{\sqrt{5} }[/tex]≈3.150±0.124

And 99% confidence interval estimate of the true weight is:

3.150±[tex]\frac{4.604*0.1}{\sqrt{5} }[/tex]≈3.150±0.206

Answer:

The answer to your question is x = 4

Step-by-step explanation:

                                   2x² - bx - 20 = 0

One root is -2.5

Process

Get the value of the equation when x = -2.5

                                   2(-2.5)² - b(-2.5) - 20 = 0

                                   2(6.25) + 2.5b  - 20 = 0

                                   12.5 + 2.5b - 20 = 0

                                   2.5b = 20 - 12.5

                                   2.5b = 7.5

                                   b = 7.5 / 2.5

                                  b = 3

Then

                                  2x² - 3x - 20 = 0

Factor the polynomial

                                  2 x -20 = -40

                                  2x² -8x + 5x - 20 = 0

                                  2x(x - 4) + 5(x - 4) = 0

                                  (x - 4)(2x + 5) = 0

                                  x₁ - 4 = 0               2x₂ + 5 = 0

                                 x₁ = 4                     x₂ = -5/2

                                                               x₂ = -2.5

Answer:

The "other" or "second" root is 4.

Step-by-step explanation:

We are told that -2.5 is a root of the equation.  The coefficient b of the x term is unknown, and must be determined.  Because -2.5 is a root, synthetic division with -2.5 as divisor must return a remainder of zero.

Setting up synthetic division, we arrive at:

-2.5    /    2    -b    -20

                     -5     +12.5 + 2.5b

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

                2   -5-b    -7.5 + 2.5b

The remainer, -7.5 + 2.5b, must be zero (0).  Thus, 2.5b = 7.5, and b = 3.

Then the other factor has the coefficients {2, -5-b}, and because b = 3, this comes out to coefficients {2, -8}.

The other factor is 2x - 8, which, if set equal to 0, yields x = 4.  This is the "other root."

Answer:

  C)  28√17

Step-by-step explanation:

The perimeter is twice the sum of the two given side lengths, so is ...

  P = 2(L +W) = 2(2√153 +4√68)

  = 2(6√17 +8√17) = 2(14√17)

  P = 28√17 . . . . . matches choice C

_____

This is about simplifying radicals. The applicable rules are ...

  √(ab) = (√a)(√b)

  √(a²) = |a|

__

  153 = 9×17, so √153 = (√9)(√17) = 3√17

  68 = 4×17, so √68 = (√4)(√17) = 2√17

_____

Comment on the problem presentation

It would help if there were actually radicals in the radical expressions. We had to guess based on the spacing and the answer choices.

In any event, this problem can be worked with a calculator. Find the perimeter (≈115.45) and see which answer matches that. (That's what I did in order to verify my understanding of what the radical expressions were.)

Answer:

  y(x) = e^(-2x +3)

Step-by-step explanation:

The graphed line has a "y-intercept" of 3 and a slope of -2, so its equation is ...

  ln(y) = -2x +3

Taking antilogs, we get ...

  y(x) = e^(-2x +3)