If you have a scoop that holds 2/5 cup, and a recipe calls for 3 3/5 cups of water, then how many scoops would you need to use?

Answers

Answer 1

36/25 scoops needed for the recipe if the we have a scoop that holds 2/5 cup, and a recipe calls for 3 3/5 cups of water.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have given that baker has 2/5 cup, and a recipe calls for 3 3/5 cups of water

3 3/5 = 18/5

we only has a 18/5 cup water.

Scoops we will need for the recipe = (18/5)/(2/5) = 36/25

Thus, we will need 36/25 scoops for the recipe.

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Answer 2

9  scoops would we need to use.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

2/5 cup of water can be hold by a scoop.

So, 1 cup of water hold 5/2 scoop

and, 18/5 cup of water can be hold by

=5/2 x 18/5

=18/2

= 9 scoops

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Related Questions

2. Pequot Lakes, Minnesota has a spherical water tower that is known as “the world’s largest fishing bobber.” The water tower holds 6,684 cubic feet of water. The water tower needs to be repainted, and it will have to be painted twice to get two coats of coverage. One gallon of paint can cover 350 square feet. How many gallons of paint will be needed to paint the water tower?

Answers

Answer:

28.93 gallons of paint

Step-by-step explanation:

The volume of a sphere can be found using the formula:

V = (4/3)πr^3

We are given that the water tower holds 6,684 cubic feet of water, so we can use this to find the radius:

6684 = (4/3)πr^3

(6684 * 3) / (4 * π) = r^3

r = (6684 * 3 / (4 * π))^(1/3) = 35.73 feet

Next, we need to find the surface area of the sphere. The surface area of a sphere can be found using the formula:

A = 4πr^2

So, the surface area of this water tower can be found as:

A = 4π * 35.73^2 = 4π * 1286.13 = 5071.57 square feet

Finally, we need to find the amount of paint needed to paint the surface area twice. One gallon of paint can cover 350 square feet, so we can divide the surface area by 350 to find the number of gallons of paint needed:

Gallons of paint = (5071.57 * 2) / 350 = (10143.14 / 350) = 28.93 gallons

So, 28.93 gallons of paint are needed to paint the water tower twice.

Which of these is the standard form of the polynomial function y=x(x+5)(x−3)

Answers

The standard form of the polynomial function y = x(x + 5)(x - 3) is

y = x³ + 2x² - 15x

What are functions?

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

The polynomial function,

y = x(x+5)(x−3)

To obtain the standard form, we need to multiply out the expression and then arrange the terms in decreasing order of the degree of the monomials. The degree of a polynomial is the highest degree of its monomials.

x(x + 5)(x - 3) = x³ + (5x²) - (3x²) + (5x²) + (-15x) = x³ + 2x² - 15x

In the standard form, the coefficient of the monomial with the highest degree is 1, and the rest of the terms are arranged in decreasing order of the degree.

Thus, the standard form is x³ + 2x² - 15x

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Need help fast. please​

Answers

According to the model, the current population of Algeria is 38 million.

How to find the population ?

The model for the population in t years from now is given by the model P = 38 ( 1 + r ) ^ t.

This means that when given the model, the current population of Algeria is 38 million because the 38 in the model represents the value of population when no years have elapsed.

We can solve for this to get :

= 38 ( 1 + r ) ^ t

= 38 ( 1 + r ) ⁰

= 38 x 1

= 38

= 38 million

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Mrs. Gomez is buying a triangular table for the corner of her classroom. The
side lengths of the table are 5 feet, 3 feet, and 4 feet.
Is this triangular table a right triangle?
OA. No, because 3+ 4+ 5.
B. No, because 3² +4² #5²
C. Yes, because 32 +4² = 5²
D. Yes, because 3² +4² > 5²

Answers

The triangular table that Mrs. Gomez is buying for her classroom is a right triangle table because 3² +4² = 5². That is option C.

What is a right angle triangle?

A right angle triangle is the type of triangle that has one side of its angle perpendicular to another and the value of the three sides can be calculated through the use of the Pythagorean formula.

The Pythagorean formula is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.

Since, 5= c

b= 3

a = 4

Therefore, 3² +4² = 5² shows that the table is a right angle triangle.

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Eric works for a salary of $3,500 per month.

What is Eric’s gross pay for one year?

Answers

Eric’s gross pay for one year if he earns a salary of $3,500 per month is $42,000.

What is Eric’s gross pay for one year?

The total amount of money an employee receives before taxes is referred to as gross pay.

Given  that;

Eric's salary per month = $3,500 Eric’s gross pay for one year = ?

Eric’s gross pay for one year = Eric's salary per month × 12 months

Eric’s gross pay for one year = $3,500 × 12

Eric’s gross pay for one year = $42,000

Therefore, the gross pay is $42,000.

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Find the slope of the line
Slope: m=

Answers

Answer:

Hi there! The answer is 3/5

Step-by-step explanation:

The rise is 3 and the run is 5.

Brainiest, please? Can you click on the crown on my answer?

Answer: 3/5

Step-by-step explanation:

Looks at the points (0,1) and (5,4).

Formula: y2-y1/x2-x1

Substitute: 4-1/5-0 = 3/5

m = 3/5

Let u =(a,7) and v =(4,4)a.find the value of a such that u is parallel to vb.two nonzero vectors u(u1,u2) and v(v1,v2) are perpendicular to each other if 0. find the value of a such that u is perpendicular to v.

Answers

The value of a that makes u parallel to v is a = 4 and  the value of a that makes u perpendicular to v is -7.

How to solve vectors using dot and scalar product?

a. For two vectors to be parallel, their direction ratios must be equal. In other words, their components must have the same ratio. For vectors u = (a, 7) and v = (4, 4), we have:

u1/u2 = a/7 = v1/v2 = 4/4

So the value of a that makes u parallel to v is a = 4.

b. For two nonzero vectors to be perpendicular, their dot product must be equal to zero. The dot product of u = (a, 7) and v = (4, 4) is given by:

u · v = a * 4 + 7 * 4 = 4a + 28

To make this equal to zero, we can solve for a:

4a + 28 = 0

4a = -28

a = -7

So the value of a that makes u perpendicular to v is -7.

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can someone help me please

here is the picture i need step by step

Answers

The picture isn’t there can you try uploading it again (:

Answer:

Can you please post the picture of the question, then I can help.

(25 POINTS) How many solutions does the system of linear equations represented in the graph have?


One solution at (-1, 0)
One solution at (0, -1)
No solution
Infinitely many solutions

Answers

The correct option regarding the solution of the system of equations is given as follows:

One solution at (-1, 0).

What is the solution to the system of equations?

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

For this problem, we have a single equation, hence the solution is obtained when the graph crosses the x-axis.

The graph crosses the x-axis when x = -1 and y = 0, hence the solution is given as follows:

(-1,0).

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Solve for x and y: x=5-2y 6y=5-3x

Answers

Based on the given system of equations, the value of x and y are undefined.

How to solve this system of equations?

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

x = 5 - 2y      .......equation 1.

6y = 5 - 3x            .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

6y = 5 - 3(5 - 2y)

6y = 5 - 15 + 6y

6y = -10 + 6y

6y - 6y = -10 (no solution).

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q1 and q2 are 24m apart. if q2 is 49 times q1, where between the two charges would the net electric field be equal to 0

Answers

The point where the net electric field is equal to zero is located approximately 0.48936m away from q1 and 24m - 0.48936m = 23.51064m away from q2.

Describe charge?

Charge is a fundamental property of matter that describes its electrical state. It is a scalar quantity that can be either positive, negative, or neutral, and is measured in Coulombs (C). The concept of charge is used to explain many of the phenomena that occur in electricity and magnetism, such as electric fields, currents, and voltages. Positive and negative charges are thought to be due to the presence or absence of electrons, which are the smallest negatively charged particles in matter. Neutral objects have an equal number of positive and negative charges, resulting in a net charge of zero. The interaction of charges with each other results in many of the electrical and magnetic phenomena observed in the world around us.

The net electric field at a point is equal to zero if the electric field due to one charge is exactly canceled by the electric field due to the other charge.

Since q2 is 49 times greater than q1, the electric field due to q2 will be 49 times greater than the electric field due to q1 at any given point. In order to cancel the electric field due to q1, we need to place q2 at a point that is 49 times closer to q1 than the original separation of 24m.

Let's call the new separation between the charges x. Then, x = 24m / 49, which is approximately equal to 0.48936m.

So, the point where the net electric field is equal to zero is located approximately 0.48936m away from q1 and 24m - 0.48936m = 23.51064m away from q2.

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Please solve this for me, this is all the info presented in the question.

Answers

About 0.04% percent of quokkas weigh over 15.5 pounds.

What is normal distribution?

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Given that, the weights of quokkas can be described by the Normal model N(10, 2.7).

Let Y the weights of quokkas

Given that, Y~N(μ= 10, σ²=2.7)

So, σ=1.643

a) The probability, P(Y>15.5) denotes chances that quokkas weight over 9.3 pounds, and it is,

P(Y>9.3) = P(Z> (15.5-μ)/σ)

= P(Z> (15.5-10)/1.643)

= P(Z>3.347)

= 0.0004

= 0.0004×100 =0.04%

b) The probability, P(Y<11.9) denotes chances that quokkas weight under 11.9 pounds, and it is,

P(Y>9.3) = P(Z> (11.9-μ)/σ)

= P(Z> (11.9-10)/1.643)

= P(Z>1.156)

= 0.1250

= 0.1250×100 =12.5%

c) The probability, P(11.9≤Y≤15.5) denotes chances that quokkas weight will be between 11.9 and 15.5 pounds, and it is,

P(11.9≤Y≤15.5) = P((15.5-μ)/σ ≤ Z ≤ (11.9-μ)/σ)

= P((15.5-10)/1.643) ≤ Z ≤ (11.9-10)/1.643)

= P(3.347≤ Z ≤1.156)

= P(Z≤3.347)-PZ ≤1.156)

= 0.0004-0.1250

= 0.1246

= 0.1246×100

= 12.46%

Therefore, about 0.04% percent of quokkas weigh over 15.5 pounds.

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In how many ways can a committee of four Democrats and three Republicans be formed from a group of ten
Democrats and eleven Republicans?
A committee of four Democrats and three Republicans can be formed from a group of ten Democrats and eleven
Republicans in
different ways.

Answers

The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.

What is permutation and combination?

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.

Here, the differences between permutation and combination are described in detail.

The number of ways in which we can select a committee of 4 democrats from ten democrats is:

P = 10C 4 = 10! / (4)! (10 - 4)!

P = 210

The number of ways in which we can select a committee of 3 Republicans from 11 Republicans is:

P = 11C 3 = 11! / 3! (11 - 3)!

P = 165

The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is:

P = (210) (165) = 34650

The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.

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Find the imaginary part of (5 - 12i)²​

Answers

(5-12i)^2
Write it twice:
(5-12i)(5-12i)
Distribute:
25-60i-60i+144i^2
Combine like terms:
25-120i+144i^2
Change i^2 to -1, remember the values of i:
25-120i-144
Combine like terms:
-199-120i

Luke has a 65-gallon rectangular aquarium with base 48 inches by 18
inches. He centers it on a rectangular tabletop. There a
re 3 inches
between each side of the aquarium and each side of the tabletop as shown
What is the area, in square inches, of the tabletop?

Answers

The area of the tabletop in square inches is 1071 square inches.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

Given that, there are 3 inches between each side of the aquarium and each side of the tabletop.

The length of the tabletop will be:

l = 48 + 3 = 51 inches.

The width of the tabletop will be:

w = 18 + 3 = 21 inches.

The area of the table top will be:

A = (l)(b)

A = (51)(21)

A = 1071 square inches.

The area of the tabletop in square inches is 1071 square inches.

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SOME ONE HELP! I WILL MAKE BRAINLIST!

Answers

Note that the proof related to the above parallelogram is given as follows:

ΔSVX ≅ ΔUTX                      Given

SV || TU                                 Given

SV ≅ TU                                Corresponding part of congruent triangle

VUTS parallelogram             Definition of parallelogram.

What is a Parallelogram?

A quadrilateral having two pairs of parallel sides is known as a parallelogram. It is possible to demonstrate that the opposing sides of a parallelogram are congruent.

A parallelogram is any quadrilateral having two pairs of congruent opposing sides. Parallelograms contain two congruent opposing angles, thus a quadrilateral with two congruent opposite angles must be a parallelogram.

A parallelogram's diagonals intersect each other, therefore a quadrilateral with diagonals that bisect each other must be a parallelogram. Finally, if a quadrilateral contains two parallel and congruent sides, it must be a parallelogram.

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hello could anyone help me

Answers

I think that answer is yes

the faster the better

Answers

Answer:

1 - [tex]e^{inx}[/tex]

2 - [tex]e^{5in}[/tex]

3 - [tex]e^{in^{3} x}[/tex]

Step-by-step explanation:

List all the subsets of the given set. 0
The subsets are ______
( Use a comma to separate answers as needed .)

Answers

The subsets are {}, {0}.

What is the subset in mathematics?

In mathematics, a subset is a set consisting of elements that are also elements of another set. A set A is said to be a subset of set B if and only if every element of A is also an element of B. In other words, if you have a set A and another set B, and all the elements of set A are present in set B, then set A is considered a subset of set B.

In mathematics, a subset is a collection of elements that belong to a larger set. The elements in a subset can be any type of mathematical objects, such as numbers, vectors, or functions. A set is a subset of itself, and the empty set is a subset of every set.

The subsets of the given set {0} are the empty set {} and the set itself, {0}. So, the subsets of the given set 0 are {}, {0}.

Hence, the subsets are {}, {0}.

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If points F and G are contained in a plane, then is entirely contained in that plane. A. True B. False

Answers

It is true that if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.

What is the two-dimensional plane?

A two-dimensional plane, also known as a plane in two dimensions, is a flat surface that has length and width, but no thickness. It is an abstract mathematical concept that can be represented graphically.

Here,
In geometry, if two points are contained in a plane, then any line segment connecting those two points is also contained in that plane. So, if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.

Thus, it is true that if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.

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True or False: When applying a line of best fit to a data set, you should always set the intercept to zero such that the best fit line passes through the origin (0,0).

Answers

True
Bc the line of best fit dose not have to go through the origin

Solve the initial value problem
dx/dt−4x=cos(5t)
with x(0)=1.
x(t) = ?

Answers

We are given the following differential equation, [tex]\frac{dx}{dt}-4x=cos(5t)[/tex], with the initial condition [tex]x(0)=1[/tex]. This is a linear DE in the form, [tex]\frac{dx}{dt}+P(t)x=Q(t)[/tex], where [tex]\mu(t)=e^{\int\ {P(t)} \, dt }[/tex].

First, finding [tex]\mu(t)[/tex].

[tex]\Longrightarrow\mu(t)=e^{\int\ {P(t)} \, dt }\Longrightarrow\mu(t)=e^{\int\ {-4} \, dt }[/tex]

[tex]\mu(t)=e^{-4t }[/tex]

Multiply the DE by [tex]\mu(t)[/tex].

[tex]\Longrightarrow\frac{dx}{dt}-4x=cos(5t)\Longrightarrow e^{-4t} [\frac{dx}{dt}-4x=cos(5t)][/tex]

[tex]\Longrightarrow (e^{-4t}) \frac{dx}{dt}-(e^{-4t})4x=(e^{-4t})cos(5t)[/tex]

[tex]\Longrightarrow e^{-4t} \frac{dx}{dt}-4e^{-4t}x=e^{-4t}cos(5t)[/tex]

Verify that the L.H.S is a product rule of [tex]e^{-4t}x[/tex].

[tex]\Longrightarrow \frac{d}{dt}[e^{-4t}x ] =(e^{-4t}*-4)x+(e^{-4t})(\frac{dx}{dt} )[/tex]

[tex]\Longrightarrow \frac{d}{dt}[e^{-4t}x ] =-4e^{-4t}x+e^{-4t}\frac{dx}{dt}[/tex]

This matches, so we can move forward by integrating both sides of the DE.

[tex]\int\ {[e^{-4t}x ]'} \, =\int\ {e^{-4t}cos(5t)} \, dt[/tex]

The integral on the R.H.S is pretty nasty to do using integration by parts and u-sub. I will use a table of integrals.

[tex]\int\ {e^{ax}cos(bx) } \, dx=\frac{e^{ax}(acos(bx)+bsin(bx))}{a^2+b^2}[/tex]

Let [tex]a=-4[/tex] and [tex]b=5[/tex]

[tex]\int\ {[e^{-4t}x ]'} \, =\int\ {e^{-4t}cos(5t)} \, dt[/tex]

[tex]\Longrightarrow e^{-4t}x = \frac{e^{-4t}(-4cos(5t)+5sin(5t))}{(-4)^2+(5)^2}+C[/tex]

[tex]\Longrightarrow e^{-4t}x = \frac{e^{-4t}(-4cos(5t)+5sin(5t))}{41} +C[/tex]

Now for the initial condition, [tex]x(0)=1[/tex].

[tex]\Longrightarrow e^{-4(0)}(1) = \frac{e^{-4(0)}(-4cos(5(0))+5sin(5(0)))}{41} +C[/tex]

[tex]\Longrightarrow (1)(1) = \frac{(1)(-4(1)+(0))}{41} +C[/tex]

[tex]\Longrightarrow 1 = -\frac{4}{41} +C[/tex]

[tex]\Longrightarrow 1+\frac{4}{41} = C[/tex]

[tex]\Longrightarrow C=\frac{45}{41}[/tex]

Now we have, [tex]e^{-4t}x = \frac{e^{-4t}(-4cos(5t)+5sin(5t))}{41} +\frac{45}{41}[/tex], solve for x.

[tex]\Longrightarrow x = \frac{\frac{e^{-4t}(-4cos(5t)+5sin(5t))}{41}}{ e^{-4t}} +\frac{\frac{45}{41}}{e^{-4t}}[/tex]

[tex]\Longrightarrow x = \frac{(-4cos(5t)+5sin(5t))}{41}} +\frac{45e^{4t}}{41}[/tex]

Thus, the answer to the given differential equation with an initial condition is, [tex]x = \frac{(-4cos(5t)+5sin(5t))}{41}} +\frac{45e^{4t}}{41}[/tex].

A statistics class suspected that students at their school were getting less than 8 hours of sleep. They took a random sample of 42 students and asked them how many hours of sleep they get per night. The students in the sample reported sleep amounts that had a mean of 7.5 hours and a standard deviation of 1.6 hours. These results produced a test statistic of t -2.03 and a P-value of approximately 0.025. Assuming the conditions for inference were met, what is an appropriate conclusion at the a = 0.05 significance level?
Choose 1 answer: A. Fail to reject the null hypothesis. This isn't enough evidence to conclude that the mean amount of sleep is less than 8 hours. B. Fail to reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours. C. Reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours. D. Reject the null hypothesis. This isn't enough evidence to conclude that the mean amount of sleep is less than 8 hours.

Answers

The correct answer is to Reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours.

The test statistic of t = -2.03 and P-value of approximately 0.025 suggest that the mean amount of sleep for students is significantly less than 8 hours.

The P-value of 0.025 is less than the significance level of 0.05, which means that there is enough evidence to reject the null hypothesis that the mean amount of sleep is 8 hours.

Therefore, the appropriate conclusion at the a = 0.05 significance level is that the mean amount of sleep for students is less than 8 hours.

Hence, the correct answer is C.

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A bicycle has a listed price of 691.95 before tax. If the sales tax rate is 7.75% , find the total cost of the bicycle with sales tax included.

Answers

Answer:

745.57

Step-by-step explanation:

[tex]691.95 \times \frac{7.75}{100} = 53.62[/tex]

[tex]53.62 + 691.95 = 745.57[/tex]

evaluate the function at the given value of the independent variable. simplify the results. (if an answer is undefined, enter undefined.)f(x) = 1/√(x-4)f(x) - f(5) / x - 5

Answers

The function at the given value of the independent variable, f(x) = 1/√(x-4)f(x) - f(5) / x - 5 is (x-5).

Each element of X is given precisely one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealised relationship between two changing quantities.

We have given function as ,

f(x) = 1/√(x-4)

We have to find f(x) - f(5)/x-5

f(x) = f(5)/x-5 = 1/√(5-4)/(x-5)

= 1/√(5-4)/(x-5)

= (x-5)/√(5-4)

= (x-5)

Therefore, The function at the given value of the independent variable, f(x) = 1/√(x-4)f(x) - f(5) / x - 5 is (x-5).

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Find the arc length function for the curve measured from the point P in the direction of increasing t and then reparametrize the curve with respect to arc length starting from P, and (b) find the point 4 units along the curve (in the direction of increasing t) from P. r(f) = (5 - t) i + (4t - 3) j + 3t k. P(4, 1, 3)

Answers

The new arc length function for the curve after reparametrization is as follows

[tex]\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k[/tex]

What is meant by the arc length of a curve?

The distance between two places along a segment of a curve is known as the arc length.

The formula for arc length is used to determine how far something is along the curved line that makes up an arc. The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc.

Given,

Vector equation of curve  r(t) = (5 - t) i + (4t - 3) j + 3t k

    Given P = (4, 1, 3)

5 - t = 4

So, t = 1

Now differentiate r(t)

 r'(t) = -i + 4j + 3k

Magnitude of r'(t) = |r'(t)| = √[(-1)² + 4² + 3²] = √26

The arc length function for the curve

 [tex]s = \int\limits^t_1 { |r'(t)| } \, dt = \int\limits^t_1 { \sqrt{26} } \, dt = \sqrt{26} (t-1)[/tex]

  [tex]t = \frac{s}{\sqrt{26} } + 1[/tex]

Now to reparametrize the curve with respect to arc length, substitute t with (s/√26) + 1 in r(t).

[tex]r(s) = (5 - ( \frac{s}{\sqrt{26} } + 1)) i + (4( \frac{s}{\sqrt{26} } + 1) - 3) j + 3( \frac{s}{\sqrt{26} } + 1) k\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k[/tex]

Therefore the new arc length equation of the curve when  [tex]t = \frac{s}{\sqrt{26} } + 1[/tex] is as follows

[tex]\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k[/tex].

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Omari drives a car that gets 18 miles per gallon of gasoline. The car's gasoline tank holds 15 gallons. The distance Omari drives before refueling is a function of the number of gallons of gasoline in the tank. Identify a reasonable domain for this situation.
(A) 0 to 18 miles
(B) 0 to 270 miles
(C) 0 to 15 miles
(D) 0 to 60 miles

Identify a reasonable range for the function in the question above.
(A) 0 to 18 miles
(B) 0 to 270 miles
(C) 0 to 15 miles
(D) 0 to 60 miles

Answers

a) The domain of the function is 0 to 15 miles

b) The range of the function is 0 to 270 miles

What are domain and range?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the mileage of the car = 18 miles per gallon

The amount of gasoline the car can hold = 15 gallons

Let the distance to empty be a function of mileage of the car × amount of gas in gallons

Now , the domain of a function is the set of values that we are allowed to plug into our function which ranges from 0 to 15

So , distance to empty = 18 x 15 = 270

So , the range of the function is the set of output values which ranges from 0 to 270

Hence , the domain of the function is 0 to 15 miles and the range of the function is 0 to 270 miles

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Daniel invests a lump sum of money in a savings account with a fixed annual interest rate of 5% that is compounded
continuously. After 7 years, the account balance reaches $5,676.27. How much was initially invested?

Answers

Using Compound Interest, The initially invested amount was $5400.

What does compound interest mean?

The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 after the second year is over.

The formula for compound interest is

[tex]C = P(1 + \frac{r}{n})^{nt}[/tex]

Where C is the compound interest value after n years.

P is the principal amount.

I is interest.

n is the number of years.

It is given that percentage of interest is 5% so I=0.05. C=$5676.27.

n=7.

According to the formula of compound interest,

5676.27 = P(1+0.05)7 P = 5676.27 1.051084

P = 5400

Therefore the amount that was invested initially was $5400.

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14. JD is selling high quality bats in his baseball supply store. His new shipment of 30 bats arrives, with a wholesale cost of $80 for each bat. He decides to markup the price by 120% in order to make a good profit. After 3 months he has sold 16 of the bats, but needs to make room for more inventory. He decides to discount the remaining bats by 40%. If he sells all of the remaining bats at the new discounted price, how much profit will he make after selling all of the bats?​

Answers

Answer: JD's markup price is $80 * 120% = $96 per bat.

So, the retail price of each bat is $80 + $96 = $176.

The total revenue from the sale of 16 bats is 16 * $176 = $2,816.

He still has 30 - 16 = 14 bats left.

The discount price of each bat is $176 - ($176 * 40%) = $106.40.

The total revenue from the sale of 14 bats at the discount price is 14 * $106.40 = $1,493.60.

The total revenue from all the bats is $2,816 + $1,493.60 = $4,309.60.

The profit JD makes from selling all the bats is $4,309.60 - ($80 * 30) = $1,039.60.

Step-by-step explanation:

The profit which will he make after selling all of the bats is $1,039.60.

What is Profit?

This is referred to as the amount of money that you gain when you are paid more for something than it cost you to make, get, or do it.

JD's markup price = $80 ×120% = $96 per bat.

Retail price = $80 + $96 = $176.

Revenue of 16 bats is 16 * $176 = $2,816.

Since 30 - 16 = 14 bats which is what we have left.

The discount price of each bat is $176 - ($176 * 40%) = $106.40.

The total revenue from the sale of 14 bats at the discount price is 14 * $106.40 = $1,493.60.

Therefore the total revenue from all the bats is $2,816 + $1,493.60 = $4,309.60.

The total profit = $4,309.60 - ($80 * 30) = $1,039.60.

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The temperature decreasesd by 11 degrees enter a integer that represents this situation in the box

Answers

Step-by-step explanation:

The answer should be -11

Answer:  -11 (negative eleven)

An integer is a real number. Which includes 0, positive numbers, and negative numbers. Since the temperature outside went down by 11 degrees rather than increased, it is negative. Which means our integer is -11.

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