In order to develop a more appealing​ cheeseburger, a franchise uses taste tests with 15 different​ buns, 8 different​ cheeses, 3 types of​ lettuce, and 4 types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each​ cheeseburger, approximately how long would it take the tester to eat all possible​ cheeseburgers?

Answer:

m+p-n

Step-by-step explanation:

given that Jerry manages a local car dealership. At the beginning of the month, his lot had m vehicles. During the month his salesman sold n vehicles, and he purchased p vehicles more

We are to find the number of vehicles did the dealership have at the end of the month

At the end of the month the dealer would have

no of vehicles at the start of the month- sales of the vehicle in that month+Purchase of vechicles during that month

No of vehicles at the start of the month = m

Purchase during month                           =p

Total vehicles including purchase         = m+p

LESS: Vehicles sold in the month         =   n

No of vehicles at the end                      = m+p-n

Answer:

B) x=-3(y+3)^2+4

Step-by-step explanation:

Plug quadratic in for proof

Answer:

The answer to your question is Letter C

Step-by-step explanation:

Data

Vertex (4, -3)

Process

From the image, we notice that it is a horizontal parabola that opens to the left.

So, it formula must be          (y - k)² = 4p(x - h)

-Substitute the vertex

                                             (y + 3)² = 4p(x - 4)

Consider 4p = 1

                                             (y + 3)² = x - 4

Solve for x

                                             x = (y + 3)² + 4

Solution

Letter C

Final answer:

To find the solutions to the system of equations, use the substitution method. The solutions are (1/2, -3/2) and (7, 5).

Explanation:

To find the solutions to the system of equations, we can use the substitution method. First, solve one of the equations for y in terms of x. Let's solve the second equation for y:

y = x - 2

Now substitute this expression for y into the first equation:

x - 2 = 2x^2 - 8x + 5

Now we have a quadratic equation. Rearrange it into standard form:

2x^2 - 9x + 7 = 0

Next, factor the quadratic equation:

(2x - 1)(x - 7) = 0

Set each factor equal to zero and solve for x:

2x - 1 = 0, x - 7 = 0

x = 1/2, x = 7

Now substitute these values of x back into either of the original equations to find the corresponding values of y:

For x = 1/2: y = 1/2 - 2 = -3/2

For x = 7: y = 7 - 2 = 5

So the solutions to the system of equations are (1/2, -3/2) and (7, 5).

cos (a - b) is 56/65

Step-by-step explanation:

Given sin a = 5/13, find cos a.

sin a = opposite side/hypotenuse = 5/13

The adjacent side can be found using Pythagoras Theorem.

Hypotenuse² = Opposite Side² + Adjacent Side²

⇒ Adjacent side² = Hypotenuse² - Opposite Side²

                             = 13² - 5² = 169 - 25 = 144

∴ Adjacent Side = 12

⇒ cos a = adjacent side/hypotenuse = 12/13

Given cos b = 3/5, find sin b.

cos b = adjacent side/hypotenuse = 3/5

The opposite side can be found using Pythagoras Theorem.

Hypotenuse² = Opposite Side² + Adjacent Side²

⇒ Opposite side² = Hypotenuse² - Adjacent Side²

                             = 5² - 3² = 25 - 9 = 16

∴ Opposite Side = 4

⇒ sin b = opposite side/hypotenuse = 4/5

Find cos(a - b).

cos(a - b) = cos a cos b + sin a sin b

               = 12/13 × 3/5 + 5/13 × 4/5

               = 36/65 + 20/65 = 56/65

Answer:

12cm

Step-by-step explanation:

The scoop of Ice Cream is in the shape of a circular solid which is a Sphere.

For the ice cream to fit into the cone, the volume of the cone must be equal to that of the sphere.

Radius of the Sphere=3cm

Volume of a Sphere = [tex]\frac{4}{3}\pi r^3[/tex]

Volume of a Cone=[tex]\frac{1}{3}\pi r^2h[/tex]

[tex]\frac{1}{3}\pi X 3^2h=\frac{4}{3}\pi X 3^3\\\frac{1}{3}h=\frac{4}{3} X 3\\\frac{1}{3}h=4\\h=4 X 3=12cm[/tex]

The Cone of same radius must be 12cm tall.

Answer: the height of the melted candies in the pot is 12.2 mm

Step-by-step explanation:

The formula for determining the volume of a square base pyramid is expressed as

Volume = area of base × height

Area of the square base = 12² = 144 mm²

Volume of each pyramid = 15 × 144 = 2160 mm³

The volume of 100 pyramid shaped chocolate candies is

2160 × 100 = 216000 mm³

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Since the pyramids was melted in the cylindrical pot whose radius is 75 mm, it means that

216000 = 3.14 × 75² × h

17662.5h = 216000

h = 216000/17662.5

h = 12.2 mm

Answer:

The height of the melted candies in the pot is 4.07mm

Step-by-step explanation:

H= 100*1/3(12)^2(15)/π(75)^2=64/5π=4.07

Answer:

B

Step-by-step explanation:

The slope is rise over run, meaning it is 3/4. The y-intercept is 2, making the equation y = (3/4)x + 2

Answer:

The equation representing the scenario is [tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex].

Step-by-step explanation:

Given:

Amount of food in the container = [tex]x \ cups[/tex]

Amount of food added in the container = [tex]2\frac12\ cups[/tex]

We will now convert the mixed fraction into Improper fraction by Multiplying the whole number part by the fraction's denominator and then add that to the numerator  and then write the result on top of the denominator.

[tex]2\frac12\ cups[/tex] can be rewritten as [tex]\frac{5}{4}\ cups[/tex]

Amount of food added in the container =  [tex]\frac{5}{4}\ cups[/tex]

Amount of food removed from container to feed dog  = [tex]\frac34 \ cups[/tex]

Amount of food remaining = [tex]5\frac{1}{4} \ cups[/tex]

[tex]5\frac{1}{4} \ cups[/tex] can be Rewritten as = [tex]\frac{21}{4}\ cups[/tex]

Amount of food remaining =  [tex]\frac{21}{4}\ cups[/tex]

We need to write the equation for above scenario.

Solution:

Now we can say that;

Amount of food remaining is equal to Amount of food in the container plus Amount of food added in the container minus Amount of food removed from container to feed dog.

framing in equation form we get;

[tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex]

Hence the equation representing the scenario is [tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex].

Answer:

2.8 units

You should get 2√(2) or √(8) which is less than 3 and greater than 2.

Answer: 2.8 units

Step-by-step explanation:

The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Where

x2 represents final value of x on the horizontal axis

x1 represents initial value of x on the horizontal axis.

y2 represents final value of y on the vertical axis.

y1 represents initial value of y on the vertical axis.

From the given points

x2 = 5

x1 = 3

y2 = 4

y1 = 2

Therefore,

Distance = √(5 - 3)² + (4 - 2)²

Distance = √2² + 2² = √4 + 4 = √8

Distance = 2.8 units

Answer:

40/13

The decimal form is going to be 3.076

Answer:

A because the linesnever cross.

Step-by-step explanation:

Answer:

There is no solution

Step-by-step explanation:

Answer:

x = 2

y = 2 +  t

z = -20 -20t

Step-by-step explanation:

First, we are going to find the equation for this parabola. We replace x = 2 in the equation of the paraboloid, thus:

[tex]z = 6-x-x^{2} -5y^{2}[/tex]

if x = 2, then

[tex]z = 6-(2)-2^{2}-5y^{2}[/tex]

[tex]z = -5y^{2}[/tex]

Now, we calculate the tangent line to this parabola at the point (2,2,-20)

The parametrization of the parabola is:

x = 2

y = t  

[tex]z = -5t^{2}[/tex]  since [tex]z = -5y^{2}[/tex]

We calculate the derivative

[tex]\frac{dx}{dt}= 0[/tex]

[tex]\frac{dy}{dt}= 1[/tex]

[tex]\frac{dz}{dt}= -10t[/tex]

we evaluate the derivative in t=2, since at the point (2,2,-20) y = 2 and y = t

Thus:

[tex]\frac{dx}{dt}= 0[/tex]

[tex]\frac{dy}{dt}= 1[/tex]

[tex]\frac{dz}{dt}= -10(2)= -20[/tex]

Then, the director vector for the tangent line is (0,1,-20)

and the parametric equation for this line is:

x = 2

y = 2 +  t

z = -20 -20t

The parametric equation of the tangent line is [tex]L(t)=(2,2+t,-20-20t)[/tex]

The equation of Paraboloid is,

                 [tex]z =6-x-x^{2} -5y^{2}[/tex]

Equation of parabola when [tex]x = 2[/tex] is,

       [tex]z=6-2-2^{2} -5y^{2} \\\\z=-5y^{2}[/tex]

The parametric equation of parabola will be,

     [tex]r(t)=(2,t,-5t^{2} )[/tex]

Now, we have to find Tangent vector to this parabola is,

    [tex]T(t)=\frac{dr(t)}{dt}=(0,1,-10t)[/tex]

We get, the point [tex](2, 2, -20)[/tex] when [tex]t=2[/tex]

The tangent vector will be,

 [tex]T(2)=(0,1,-20)[/tex]

The tangent line to this parabola at the point (2, 2, −20) will be,

     [tex]L(t)=(2,2,-20)+t(0,1,-20)\\\\L(t)=(2,2+t,-20-20t)[/tex]

Learn more about the Parametric equation here:

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Answer:

(96π + 160) cm2

Step-by-step explanation:

Mrs. Caldwell will travel 135 miles at an additional 20 mph to catch up to Mr. Caldwell. Therefore, it will take Mrs. Caldwell 6.75 hours to catch up to Mr. Caldwell.

This is a rate time distance problem in mathematics, typically learned in middle school. To calculate how long it will take Mrs. Caldwell to catch up with Mr. Caldwell, we need to compare the distance traveled by each person in the same time. Because rate equals distance over time (r=d/t), we know that the distance each person traveled is rate x time.

Mr. Caldwell left 3 hours before Mrs. Caldwell, so he traveled at 45 mph for 3 hours, or 135 miles. Once Mrs. Caldwell leaves, she needs to cover these 135 miles at a faster speed to catch up. Her speed is 20 mph greater than Mr. Caldwell’s. We divide the distance that Mr. Caldwell has covered (135 miles) by the difference in their speeds (20 mph) to find it will take Mrs. Caldwell 6.75 hours to catch up to him.

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Answer: the Smaller number is 3

The larger number is 60

Step-by-step explanation:

Let x represent the smaller of the numbers.

Let y represent the larger number.

One number is 20 times another number. This means that

y = 20x

The product of the two numbers is 180. This means that

xy = 180- - - - - - - - - -1

Substituting y = 2x into equation 1, it becomes.

x × 20x = 180

20x² = 180

x² = 180/20 = 9

x = √9

x = 3

y = 20x = 20 × 3

y = 60

Answer:

8pi feet per second

Or, 25.1 feet per second (3 sf)

Step-by-step explanation:

C = 2pi×r

dC/dr = 2pi

dC/dt = dC/dr × dr/dt

= 2pi × 4 = 8pi feet per second

dC/dt = 25.1327412287

Answer:

666.667 feet

Step-by-step explanation:

Slope = -1

Intercept = 10

y = -t + 10

y is the acceleration

Integrate y fornv

v = -t²/2 + 10t + c

At t=0, v=0 so c = 0

v = -t²/2 + 10t

Turns when v = 0,

-t²/2 + 10t = 0

t = 0, 20

Integrate v for s

s = -t³/6 + 5t² + c

At t = 0, s = 10

10 = c

s = -t³/6 + 5t² + 10

s at t=30,

-(30³)/6 + 5(30)² + 10

= 10m

(Back to starting point)

At t = 20,

Displacement in

-(20³)/6 + 5(20)² + 10

= 343.333

Total distance = 2(343.333-10)

= 666.6667

The total distance the car travels in this 30 second interval is 1333.34 units

From the graph, we have the following points

(0, 10) and (10, 0).

Start by calculating the slope (m) of the graph

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{0 - 10}{10-0}[/tex]

[tex]m =- \frac{10}{10}[/tex]

[tex]m =- 1[/tex]

The equation is then calculated as:

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

This gives

[tex]y = -1(x -0) + 10[/tex]

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

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

The above equation represents the acceleration (y) as a function of time (x).

Integrate to get the velocity (v)

[tex]v = -\frac{x\²}{2} + 10x + c[/tex]

From the question, we have:

The velocity (v) of the car is 0, when the time (x) is 0.

So, we have:

[tex]0 = -\frac{0\²}{2} + 10(0) + c[/tex]

This gives

[tex]c = 0[/tex]

So, the equation becomes

[tex]v = -\frac{x\²}{2} + 10x + 0[/tex]

[tex]v = -\frac{x\²}{2} + 10x[/tex]

Set v = 0.

So, we have:

[tex]-\frac{x\²}{2} + 10x = 0[/tex]

Multiply through by -2

[tex]x^2 -20x = 0[/tex]

Factorize

[tex]x(x -20) = 0[/tex]

Split

[tex]x = 0\ or\ x -20 = 0[/tex]

Solve for x

[tex]x = 0[/tex] or [tex]x = 20[/tex]  

Integrate velocity (v) to get the displacement (d)

[tex]v = -\frac{x\²}{2} + 10x[/tex]

[tex]d = -\frac{t\³}{6} + 5t\² + c[/tex]

From the question, we have:

The position (d) of the car is 10, when the time (x) is 0.

So, we have:

[tex]-\frac{(0)\³}{6} + 5(0)\² + c = 10[/tex]

[tex]c = 10[/tex]

So, the equation becomes

[tex]d = -\frac{t\³}{6} + 5t\² + 10[/tex]

The position at 30 seconds is:

[tex]d = -\frac{(30)\³}{6} + 5(30)\² + 10[/tex]

[tex]d = 10[/tex]

The position at 20 seconds is:

[tex]d = -\frac{(20)\³}{6} + 5(20)\² + 10[/tex]

[tex]d = 676.667[/tex]

The total distance is then calculated as:

[tex]Total = 2 \times (d_2 -d_1)[/tex]

This gives

[tex]Total = 2 \times (676.667 -10)[/tex]

[tex]Total = 2 \times 666.667[/tex]

[tex]Total = 1333.34[/tex]

Hence, the total distance is 1333.34 units

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Answer: the account that earned compound interest has the greater balance at the end of four years.

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount invested.

P represents the principal or amount invested.

R represents interest rate

T represents the duration of the investment in years.

From the information given,

P = 1000

R = 4%

T = 4 years

I = (1000 × 4 × 4)/100 = 160

Total amount earned is

1000 + 160 = $1160

The formula for determining compound interest is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1000

r = 4% = 4/100 = 0.04

n = 1 because it was compounded once in a year.

t = 4 years

Therefore,.

A = 1000(1+0.04/1)^1 × 4

A = 1000(1.04)^4

A = $1170

Answer:

Answer in explanation

Step-by-step explanation:

The two laws are mathematical laws which are used in navigating problems which involves triangles. While the Pythagorean theorem is used primarily and exclusively for right angled triangle, the cosine rule is used for any type of triangle.

So, why is the cosine rule a stronger statement? The reason is not far fetched. As said earlier, the cosine rule can be used to resolve any triangle type while the Pythagorean theorem only works for right angled triangle. In fact, we can say the Pythagorean theorem is a special case of cosine rule. The reason why the expression is different is that, for the expression, cos 90 is zero, which thus makes our expression bend towards the Pythagorean expression view.

The explanation regarding the law of cosines is the stronger statement if compared with the Pythagorean theorem is explained below.

The Pythagorean theorem is used when there is the right-angled triangle, while on the other hand, the cosine rule is used for any type of triangle. Here the Pythagorean theorem should be considered for the special case of cosine rule. Due to this the cosine law should be stronger if we compared it with the Pythagorean theorem.

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Answer:

B. 1 1/7

Step-by-step explanation:

-9 2/7-(-10 3/7)

=-9 2/7+10 3/7

=1 1/7

Therefore, B. 1 1/7

Answer:

The answer is B

Step-by-step explanation:

B. 1 1/7

Answer:

5000 + x = 23600  

Step-by-step explanation:

a car that cost = 23600

down payment = 5000

So he needs to pay: 23600 - 5000 = 18600 more to get the car

Let x represent the amount he needs to pay more, an equation for his situation:

5000 + x = 23600  

Answer:

3.5x + 15 ≥ 55

Step-by-step explanation:

I think the question below contains the missing information.

Josh has a rewards card for a movie theater. - He receives 15 points for becoming a rewards card holder. - He earns 3.5 points for each visit to the movie theatre. - He needs at least 55 points to earn a free movie ticket. Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his firs free movie ticket?

My answer:

Let x is the number of times he visits = 3.5x

Total points = Points received on becoming a member + Points received on x visits

So,

Total Points = 15 + 3.5x

We know the total points must be at least 55 for a free movie ticket.  This can be expressed as:

3.5x + 15 ≥ 55

Answer:

Tara bought a total of 160 treats.

Step-by-step explanation:

We are given the following in the question:

Number of boxes of dog treats = 3

Number of treats in each dog box = 40

Total number of treats in dog box =

[tex]40 \times 3 = 120[/tex]

Number of boxes of cat treats = 2

Number of treats in each cat box = 20

Total number of treats in cat box =

[tex]20\times 2 = 40[/tex]

Total number of treats Tara brought =

Total number of treats in dog box + Total number of treats in cat box

[tex](40\times 3)+(20\times 2)\\= 120 + 40\\=160[/tex]

Thus, Tara bought a total of 160 treats.

Answer:

i need more context

Step-by-step explanation:

Answer:

the answer is d

Step-by-step explanation:

Answer:

Option C, SAS Postulate

Step-by-step explanation:

I think that it is option C because it does not give you 3 angles or 3 sides, it gives you 2 angles and 1 side.

Answer:  Option C, SAS Postulate

Answer:

b = [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

period = [tex]\frac{2\pi }{b}[/tex], that is

b = [tex]\frac{2\pi }{period}[/tex] = [tex]\frac{2\pi }{\frac{3\pi }{4} }[/tex] = 2π × [tex]\frac{4}{3\pi }[/tex] = [tex]\frac{8}{3}[/tex]

Answer:

f(x) = 4cos(8/3)x - 3.

The missing space is 8/3.

Step-by-step explanation:

The general form is  f(x) = Acosfx + B    where A = the amplitude, f = frequency and B is the vertical shift..

Here A is given as  4,  B is - 3 and the frequency f = 2 π / period  =

2π / (3π/4)

= 8/3.

So the answer is f(x) = 4cos(8/3)x - 3.

Answer:

P =  x³ − 9x² + 36x − 54

Step-by-step explanation:

Complex roots come in conjugate pairs.  So if 3−3i is a zero, then 3+3i is also a zero.

P = (x − 3) (x − (3−3i)) (x − (3+3i))

P = (x − 3) (x − 3 + 3i) (x − 3 − 3i)

P = (x − 3) ((x − 3)² − (3i)²)

P = (x − 3) ((x − 3)² + 9)

P =  (x − 3)³ + 9 (x − 3)

P =  x³ − 9x² + 27x − 27 + 9x − 27

P =  x³ − 9x² + 36x − 54

Answer:

The first zero after decimal point and 4 only

Step-by-step explanation:

Despite having 5 decimal points, the rules of significant figures dictate that unless there is a digit other than zero after, the only significant numbers are those that come before zero. For this case, the significant digits are only 0.04 but if it was 0.0400005 then all the other zeros would have also be considered significant.