The laptop was marked down from $895 to $720. What was the percentage decrease

\( \: \: \: \: \large\bf\implies \: 4.32\)

\( \longrightarrow \bf \: 1.42 - ( - 2.9) \\ \longrightarrow \bf \: 1.42 + 2.9 \\ \longrightarrow \bf \: 4.32\)

First of all we know that to do this type of question that is ↓

Answer:

the answer is 10,560 feet per minute

Step-by-step explanation:

(176* 60 seconds) / (1 second* 1 minute)

Answer:  The width of the playing field = 45 ft

length of playing fiels =  86ft

Step-by-step explanation:

Step 1

Perimeter of rectangular field is given as 2 ( L+ b)

Let the width be represented as  x

such that the length = 41 ft longer than the width be  x+ 41

To find the length and breadth

Step 2

Perimeter = 2( L+ b)= 2l + 2b

Perimeter =  2 (x+41 ) + 2 x = 262

2x + 82 + 2x= 262

4x+ 82= 262

4x= 262 - 82

4x= 180

x= 180/4

x= 45

width= 45 ft

length = x+ 41= 45+ 41= 86ft

Answer: 45

Step-by-step explanation:

The total profit in all was \(1040-900=\$ 140\).

The total profit per pizza was \((0.50)(8)=\$4\).

This means they sold \(\frac{140}{4}=35\) pizzas.

Adding this to the 10 pizzas held back, there were \(35+10=45\) pizzas in the original order.

The angle from the options given that is shown in the drawing is: D. <LIJ.

An angle is a geometric figure that is formed by two rays that share the same endpoint, called the vertex. The rays are called the sides of the angle, and the endpoint is called the vertex.

In the drawing given,  IJ and LI are two segments that have a common endpoint called vertex I.

Points L, I, and J forms an angle whose vertex is at I, as shown in the image given. Thus, the angle shown in the drawing is: D. ∠LIJ.

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Answer:

x = 40°

Step-by-step explanation:

Two sides are the same length, so the angles opposite them are the same size.

The sum of the angles = 180°. One angle is 100°, so the sum of the remaining two angles is 80°.

Since the remaining two angles are congruent, each is 40°.

Here are the completed tables for each sequence:

Sequence 1 Sequence 2 Ordered Pair

5                    15                   (5, 15)

6                        14               (6, 14)

7                        13             (7, 13)

8                    12                 (8, 12)

9                   11                (9, 11)

The corresponding terms in the two sequences are related by a linear function. The slope of the line is 1, which means that for every 1 increase in y, there is a 1 increase in x.

The corresponding terms in the two sequences are related by a linear function. The slope of the line is 1, which means that for every 1 increase in y, there is a 1 increase in x. This means that the two sequences are increasing at the same rate.

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Answer:

Step-by-step explanation:

it is 1.8

Answer:

Hi there here is the answer!

Step-by-step explanation:

Out of the 3 main chioces there is a total of 15!

so, it would be a probability of 5/15. or 1/3 / 1:3

The volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis is 8π/3 cubic units.

The volume of the solid generated by revolving this region about the x-axis can be found using the method of cylindrical shells. The volume is given by:

V = ∫[0, 2] 2πx(2 - 2√x) dx

Evaluating the definite integral:

V = π ∫[0, 2] (4x - 4x^(3/2)) dx

= π [2x^2 - 4/3 x^(3/2) ] |_0^2

= π [4 - (4/3)(2^(3/2))]

= 8π/3.

Therefore, the volume of the solid generated by revolving the region bounded by the lines y = 2 and y = 2√x and the x-axis about the x-axis is 8π/3 cubic units.

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--The question is incomplete, answering to the question below--

"Find the volumes of the solids generated by revolving the regions bounded by the lines and curves about the x-axis

y=2√x, y=2, x=0"

Answer: B C and D

Step-by-step explanation:

Answer:

first four terms are: 5,11,21,35..

Step-by-step explanation:

The tenth term is 203..

With a mean of $32,500 and a standard deviation of $2,500. The z-score for a sales associate who earns $37,500 is 2.

The z-score, also known as a standard score, is a measure of how many standard deviations a given value is from the mean. It is used to standardize the data and make it easier to compare and interpret. The formula for the z-score is:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

In this case, the mean annual salary for sales associates from a particular store is $32,500 and the standard deviation is $2,500. We want to find the z-score for a sales associate who earns $37,500. Plugging in the values, we get:

z = ($37,500 - $32,500) / $2,500 = 2

This means that the sales associate's salary is 2 standard deviations above the mean.

Interpreting the z-score can help us understand how unusual or typical a given value is in comparison to the mean. In this case, a z-score of 2 indicates that the sales associate's salary is relatively high compared to the mean, but it is not an extremely high salary.

We can use a standard normal table to find the proportion of the data that falls below a given z-score, or to find the corresponding value for a given proportion of the data.

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Answer:

121 is the perfect square between 100 and 144.

Answer:

quarterly N = 4

semi-annually N = 2

Monthly N = 12

annually N = 1

Step-by-step explanation:

Given the following compound interest times :

N = number of times interest is compounded per period :

A period is regarded as a whole year.

Interest compounded;

QUARTERLY = Every 4 months per period = 12/3= 4

SEMI ANNUALLY = Every 6 months per period = 12/6 = 2

MONTHLY = Every month = 12 / 1 = 12

ANNUALLY = Every 12 months = 12 /12 = 1

Step-by-step explanation:

\(x \geqslant - 5\)

from the graph it's seen there's a dot on -5 so it's also considered

and since it considered -5 and greater.

\(x \geqslant - 5\)

Answer:

Step-by-step explanation:

Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods

1/PV (FV) = (PV(1 + r^n)1/PV divide by PV

ln(FV/PV) = ln(1 + r^n) convert to natural log function

ln(FV/PV) = n[ln(1 + r)] by simplifying

n = ln(FV/PV) / ln(1 + r) solve for n

n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually

n = 9

n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly

n = 104 months or 8.69 years

n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily

n = 3163 days or 8.67 years

Alternatively

A = P e ^(rt)

Given that r = 8%

= 8/100

= 0.08

2 = e^(0.08t)

ln(2)/0.08 = t

0.6931/0.08 = t

t= 8.664yrs

t = 8.67yrs

Which ever approach you choose to use,you will still arrive at the same answer.

The total surface area of the cone is 542.592 square mm

The formula for calculating the total surface area of a cone is expressed as:

TSA = πr(r + l)

where

r is the radius of the cone

l is the slant of the cone

Given the following parameter

l = 13.6mm

r = 8mm

Substitute

TSA = π(8)(8+13.6)
TSA = 3.14(8)(21.6)

TSA = 542.592 square mm

Hence the total surface area of the cone is 542.592 square mm

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The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.

The dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.

The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.

The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

The market share of the companies is an illustration of fractions.

The market share of each company in the long run (i.e. after 6 months) is 37/108, 35/216 and 1/108, respectively

The current market shares are:

After 6 months, we have:

Company A:

Company B:

Company C:

The amount of customers lost by each company is

Lost = Market share * [Share retained - Share lost to the other two companies].

So, we have:

A = 2/9 * [3/4 - 1/6 - 1/12] = 1/9

B = 4/9 * [1/2 - 1/3 - 1/6] = 0

C = 1/3 * [3/8 - 1/4 - 3/8] = -1/12

The amount of customers gained by each company is

Gain = Market share of company gained from * Share gained

So, we have:

A = 1/3 * 4/9 + 1/4 * 1/3 = 25/108

B = 1/6 * 2/9 + 3/8 * 1/3 = 35/216

C = 1/12 * 2/9 + 1/6 * 4/9 = 5/54

The total gain in 6 months is:

Total Gain = Gain + Loss.

This gives

A = 25/108 + 1/9 = 37/108

B = 35/216 + 0 = 35/216

C = 5/54 - 1/12 = 1/108

Hence, the market share of each company in the long run (i.e. after 6 months) is 37/108, 35/216 and 1/108, respectively

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Answer:

C

Step-by-step explanation:

i just guessed but it was correct

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

0 < 0.05, which means that we reject the null hypothesis, meaning that the air pressure of the balls is different of the target value of 7.9.

Step-by-step explanation:

The air pressure of a particular ball has a target value of 7.9 PSI.

This means that the null hypothesis is:

\(H_{0}: \mu = 7.9\)

The alternate hypothesis is:

\(H_{a}: \mu \neq 7.9\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

The hypothesis tested means that \(\mu = 7.9\)

Suppose the basketballs have a normal distribution with a standard deviation of 0.20 PSI.

This means that \(\sigma = 0.2\)

When a shipment of basketballs arrive, the consumer takes a sample of 21 from the shipment and measures their PSI to see if it meets the target value, and finds the mean to be 7.3 PSI.

This means that \(X = 7.3, n = 21\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{7.3 - 7.9}{\frac{0.2}{\sqrt{21}}}\)

\(z = -13.74\)

pvalue:

We are testing that the mean pressure is different than the target value of 7.9, and since the test statistic is negative, the pvalue is 2 multiplied by the pvalue of z = -13.74, which we find looking at the z-table.

\(z = -13.74\) has a pvalue of 0.

2*0 = 0

0 < 0.05, which means that we reject the null hypothesis, meaning that the air pressure of the balls is different of the target value of 7.9.

The equation of remaining chocolate C  in terms of t is C = 30 - 3t.

A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C = 30 - 3t.

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Answer:

I didn't want to type it, but it is on the image.

Step-by-step explanation: