please answer this question ​

Answer:

The bicycle that originally cost $375 is the best to be sale at 285. a discount of $88 unlike the discount of an electric scooter.

By using the concept of maxima, it can be calculated that

Length of the  rectangle of perimeter 72 m with maximum area is 18 m

Breadth of the  rectangle of perimeter 72 m with maximum area is 18 m

What is maxima of a function?

Maxima of a function gives the maximum value of the function in a given interval or in the whole domain.

Let the length of the rectangle be l m and width of the rectangle be w m

Perimeter (P) = 2(l + w)

By the problem,

2(l + w) = 72

l + w = [tex]\frac{72}{2}[/tex]

l + w = 36

w = 36 - l

Area (A) = l [tex]\times[/tex] w

A = l [tex]\times[/tex] (36 - l) = [tex]36l - l^2[/tex]

Differentiation with A with respect to l

[tex]\frac{dA}{dl} = 36 - 2l[/tex]

For maximum area,

[tex]\frac{dA}{dl} = 0[/tex]

36 - 2l = 0

2l = 36

l = [tex]\frac{36}{2}[/tex]

l = 18 m

[tex]\frac{d^2A}{dl^2} = -2 < 0[/tex]

Hence area is maximum

w = 36 - 18 = 18 m

Length of the  rectangle of perimeter 72 m with maximum area is 18 m

Breadth of the  rectangle of perimeter 72 m with maximum area is 18 m

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Cartlon's score is 4.5434.

Given that,

Carlton has a z-score 1.74 on the achievement test.

From the z-table we get the value 0.959.

We know the formula for standard deviation,

z = (x - μ) / σ

where x = score, σ = standard deviation, μ =  mean

Now z-score corresponding to 98th percentile is 2.06

substituting the values in the above equations,

2.06 = (x - 0.959) / 1.74

i.e. x - 0.959 = 2.06 * 1.74

                    x = 3.5844 + 0.959

                    x = 4.5434

Therefore carlton's score is 4.5434.

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Answer:

Step-by-step explanation:

The amount of something that needs to be bought will be $2,875.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

If there is a 15% increase in the aggregate price level, a consumer who had been looking to purchase something that cost $2,500.

Let 'x' be the amount that needs to pay. Then the amount of something that needs to be bought will be given as,

x = (1 + 15%) of $2,500

x = (1 + 0.15) x $2,500

x = 1.15 x $2,500

x = $2,875

The amount of something that needs to be bought will be $2,875.

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Answer:

Step-by-step explanation:

(1/2)(1/2)=1/4

The pressure is assessed through the ideal gas equation and Dalton's law

Partial Pressure of hydrogen gas in the gas collecting tube can be calculated as:

According to Dalton's law, the total pressure of the system will be the sum of partial pressure of all gases

In the system, the pressure is exerted by the water and  gas.

Total pressure = P(water) + P(Hydrogen)

P(hydrogen) = 746 mm Hg (given) = 19.8 mm Hg +

P(hydrohen) = = 746 mm Hg - 19.8 mm Hg

= 726.2 mm Hg

So, the partial pressure of Hydrogen was found to be 726.2 mm Hg.

To calculate the volume of hydrogen at STP, ideal gas equation is used.

For this, we calculate the moles of Hydrogen in given conditions:

Pressure = 726.2 mm Hg

 = 726.2/760

= 0.955 atm

Therefore, The pressure is assessed through the ideal gas equation and Dalton's law

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Answer:

The correct answer is 5.672 x 10^3

Step-by-step explanation:

change the exponent for 3.28 x 10^2, and you get 0.328 x 10^3, and then subtract normally, which gets you 5.672 x 10^3

Answer:

[tex]SA = 2.94 \, \textrm{units}^2[/tex]

Step-by-step explanation:

The surface area of a regular 3D figure can be represented as:

[tex]SA = A_{\textrm{\,1 side}} \cdot (\# \textrm{ of sides})[/tex].

Therefore, the surface area of a cube is:

[tex]SA = s^2 \cdot 6[/tex]

where [tex]s[/tex] is the length of a side.

To solve this problem, simply input the given side length into the above formula:

[tex]SA = 0.7^2 \cdot 6[/tex]

and simplify.

[tex]SA = 0.49 \cdot 6[/tex]

[tex]SA = 2.94 \, \textrm{units}^2[/tex]

The rule of dilation can be defined as to  enlarge or reduce any shape or graph of any function, to create a new graph or shape.

We have to write a rule for the dilation,

A transformation is termed as an operation that moves, flips, and create a new shape.

Dilation is also a type of transformation that enlarges or reduces any shape or graph of any function, to create a new graph or shape.

The scale factor, k determines how much large or small the dilation figure will be as compared to the previous shape or figure.

So, the rule of dilation can be defined as to  enlarge or reduce any shape or graph of any function, to create a new graph or shape.

Hence, the rule of dilation can be defined as to  enlarge or reduce any shape or graph of any function, to create a new graph or shape.

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The solutions of x in the interval [0°, 360°) are 3[tex]\pi[/tex]/4 and 5[tex]\pi[/tex]/4 respectively.

What is a quadrant?

The quadrant is the area that is bounded by the point where the X and Y axes connect.

A plane is split into four sections in the cartesian system, the X-axis, a horizontal line, and the Y-axis, a vertical line. The term "quadrant" refers to these four areas.

Given, 2cos x + √2 = 0

       or, 2cos x = -√2

       or, cos x = -√2/2 = -1/√2 = - cos ([tex]\pi /4[/tex] )

As the given cos(x) is negative, then it must lie in quadrants II and III respectively for the given interval  [0°, 360°).

Then, cos x = cos ([tex]\pi[/tex] - [tex]\frac{\pi}{4}[/tex])             and, cos x = cos ([tex]\pi +\frac{\pi }{4}[/tex])

       or, x = 3[tex]\pi[/tex]/4                                 or, x = 5[tex]\pi[/tex]/4

Hence, the required solutions of x are 3[tex]\pi[/tex]/4  and 5[tex]\pi[/tex]/4.

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The upper limit of blood pressure is 123.4.

The lower limit of blood pressure is 116.6..

The applicant's blood pressure limit does not meet the standards limit of blood pressure to qualify for study.

we have given that,

mean , μ = 120

standard deviation , σ = 4

The z - distribution of the 60% is,

P( -z < Z < z ) = 0.60

P( Z < z ) - P( Z < -z ) = 0.60

2× P(Z < z ) - 1 = 0.60

2× P(Z < z ) = 1 + 0.60

P( Z < z ) = 1.60 / 2

P( Z < z ) = 0.80

P( Z < -0.84) = 0.80

z = -0.84 and z = 0.84

let X be the required mean of sample .

Using z - score formula,

X = (z × σ )+ μ

= -0.84 × 4 + 120

= 116.6

and

X = z × σ + μ

= 0.84 × 4 + 120

= 123.4

Hence , Lower blood pressure limit = 116.6

Upper blood pressure limit = 123.4

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Complete question:

To qualify for a medical study, an applicant must have a systolic blood pressure in the 60% of the middle range. If the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 4, find the upper and lower limits of blood pressure a person must have to qualify for the study. Round final answers to 1 decimal place and intermediate-value calculations to 2 decimal places. Applicants must have a lower blood pressure limit of 118.48 and an upper blood pressure limit of 124.16 to qualify for the study.

P-value for the test is 0.011.

(a) We have two samples

y₁₁ = μ₁ + e₁₁

...

y₁,₁₀ = μ₁ + e₁,₁₀

y₂,₁ = μ₂ + e₂₁

...

y₂,₁₀ = μ₂ + e₂,₁₀

with unknown means μ₁ and μ₂. The total number of observation n = 20,

number of parameters p = 2.

First, we estimate the means of both samples:

û₁ = [tex]\frac{1}{10}[/tex] ∑ y₁i = 9.97, û₂ = [tex]\frac{1}{10}[/tex] ∑ y₂i = 10.4

The residual sum of squares

SSres = ∑(y₁i - û₁)^2 + ∑(y₂i - û₂)^2 = 2.081.

The unbiased variance estimate is

[tex]s^{2}[/tex] = [tex]\frac{1}{n - p}[/tex]SSres

  = [tex]\frac{2.081}{18}[/tex]

[tex]s^{2}[/tex]= 0.116

In testing the null hypothesis H₀ : μ₁ = μ₂, the test statistic of the t-test is defined as

T = |û₁ - û₂|/([tex]\sqrt{s^{2}(\frac{1}{10}+\frac{1}{10} ) }[/tex])

T= 2.83.

Since t18(0.05/2) = 2.1

the hypothesis H₀ is rejected, at the significance level 5%. In other words, under the standard assumptions, the data do not support the claim that the mean each rate is the same for both solutions, at the level of significance 5%.

(b)  

p = P(|T18| > T)

  = 2P(T18 > T)

p = 0.011.

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Agile promotes innovation, speeds up product delivery, and motivates workers in a world that values technology above everything else

What is enterprise ?

Despite being another word for a for-profit business or organization, the word "enterprise" is most frequently related to entrepreneurial endeavors. Those who are successful in business are frequently referred to as "enterprising." Legal businesses come in a variety of shapes and sizes, but the most popular ones in the US.

Industry goliaths can no longer win by virtue of their size and market power. Today, adapting to a constantly shifting corporate environment and quickly changing client demands requires speed and agility.

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The equation of parabola in vertex form is [tex]y=-3(x-3)^2+1[/tex].

What is the vertex form of the parabola?

The equation of parabola in vertex form is as follows:

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

Here, (h,k) is the coordinate of vetex and a is the constant. From this form of parabola, vertex can be easily determined.

In the above equation, (h,k) is known and a can be determined by sustituting (2,-2) for (x,y).

Substitute (3,1) for (h,k) in the above equation.

[tex]y=a(x-3)^2+1[/tex]               .. (1)

Since the point (2,-2) lies on the parabola hence, it must satisfy the above equation. Substitute (2,-2) in the above equation.

[tex]-2=a(2-3)^2+1\\-2=a+1\\a=-3[/tex]

Now, substitute the value of a in equation (1).

[tex]y=-3(x-3)^2+1[/tex]

Hence, the equation of parabola in vertex form is [tex]y=-3(x-3)^2+1[/tex].

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The solution of the expression will be;

⇒ - 1/30

What is Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Given that;

The expression is,

⇒ - 7/12 + 11/20

Now,

Simplify the expression as;

⇒ - 7/12 + 11/20

LCM of [12, 20] = 60

⇒ - 35/60 + 33/60

⇒ (- 35 + 33) / 60

⇒ - 2/60

⇒ - 1/30

Thus, The solution of the expression will be;

⇒ - 1/30

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The given Fibonacci sequence ,

b)  First term of the Fibonacci sequence is 8.

c) First term = y-x.

Fourth term = x+y

Fifth term = y+30.

What is Fibonacci Sequence?

 A series in which each number is the sum of the two numbers before it is known as the Fibonacci Sequence. We must specify values for the first two terms in order to complete the Fibonacci Sequence. In the Fibanocci sequence we can find next term by adding previous terms.

Here the given Fourth term = 30 and Fifth term = 49.

Here second and third terms are x and y. Let us take first term as a.

We know that the Fibonacci sequence is sum of previous terms.

The sequence are,

=> a , x , y , 30 ,49 ,...

Here Fourth term = 30

=> second term + third term = 30

=> x+y = 30----->1

Now the fifth term is third term + fourth term = 49

=> y+30 =49

=> y =19.

Put y=19 into 1 then,

=> x+19=30

=> x = 30-19 =11

Now third term is first term+second term = third term

=> a+x =y

=> a+11=19

=> a =19-11 =8.

b) First term of the Fibonacci sequence is 8.

c) Third term = first term+second term

=> y = first term +x

=> First term = y-x.

Fourth term = Second term+third term

=>Fourth term = x+y

Fifth term = third term+fourth term

=> Fifth term = y+30.

Therefore the given Fibonacci sequence ,

b)  First term of the Fibonacci sequence is 8.

c) First term = y-x.

Fourth term = x+y

Fifth term = y+30.

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Each person will pay $516.44.

To split an expense means to divide it into equal parts among the data given.

Over here we have, three friends so we will split the amount among them.

Here, sharing the cost of living means first calculating their total expenses (rent and other costs), which must then be divided among them.

They spend $859.32 on additional expenses in addition to their $690 rent payment.

Their total expenses are rent and other costs.

$690 + $859.32 = $1549.32.

We must now divide the money among the three friends 1554.32/3 =$516.44.

Therefore each individual will pay $516.44.

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The length of the line segment x equals half the height of the triangle.

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a right triangle  is a triangle in which one angle is a right angle, i.e., two sides are perpendicular. Trigonometry is based on the relationship between the sides and various angles of a right triangle.

Side an is the side adjacent to angle B that is opposed to angle A, whereas side b is the side adjacent to angle A that is opposed to angle A.

If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle, and its side lengths are referred to as a Pythagorean triple.

The triangle's designated length is L.

The triangle's designated height is h.

Take a look at the angle

The diagram is provided below.

Consider the little triangle in the diagram as

tan=x/L.

Take a look at the huge triangle; the angle is given as

tan=h/(L+L).

tanθ=h/2L

Both equations (1) and (2) can be written as

x/L=h/2L

x=h/2.

As a result, line segment x is half the height of the triangle.

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The correct answer is 'in statistical hypothesis testing, the null hypothesis and the alternative hypothesis are stated in terms of population parameter.

A population parameter is always used to express a statistical hypothesis: The null hypothesis is true if the test statistic's value is within the nonrejection zone.

We look for evidence supporting the null hypothesis when testing a statistical hypothesis. The null hypothesis and the alternative hypothesis are the two variants of the hypothesis that are typically used in research (called the experimental hypothesis when the method of investigation is an experiment).

According to the alternative hypothesis, a population parameter does not equal the given value. Usually, this number is zero, which is the null hypothesis value for an effect of zero.

You can reject the null hypothesis and favour the alternative hypothesis if your sample includes enough evidence to support it.

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The quadratic function f(x) = 3x^2 + 6x – 144  displays the y-intercept of the function.

In the given question, four equivalent forms of a quadratic function are given.

We have to choose which form displays the y-intercept of the function.

The given quadratic functions are:

f(x) = 3(x^2 + 2x - 48)

f(x) = 3(x + 1)^2 - 147

f(x) = 3x^2 + 6x – 144

f(x) = 3(X + 8)(x-6)

As we know that in y intercept form x=0.

A quadratic equation's Y intercept is the location where the graph's Y-axis is broken. This implies that the x axis's coordinates must be zero.

Put x = 0 in the equation to determine the Y intercept in a quadratic equation. You will also receive the Y interception.

Since we have to find the y intercept in the given form so the function

f(x) = 3x^2 + 6x – 144 given in a standard form and y intercept is clearly seen in this function.

So, the function f(x) = 3x^2 + 6x – 144  displays the y-intercept of the function.

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The right question is

Four equivalent forms of a quadratic function are given. Which form displays the y-intercept of the function?

f(x) = 3(x2 + 2x - 48)

f(x) = 3(x + 1)2 - 147

f(x) = 3x2 + 6x – 144

f(x) = 3(X + 8)(x-6)

The rate of change of the volume of sphere when is decreasing at a constant rate is found as  3319.16 cm³/min.

For the stated question-

Thus, the volume of sphere is found by the equation.

Volume of sphere V = 4/3 πr³

V =  1611 cm³.

1611 = 4/3 πr³

On solving,

r = 7.27 cm

Rate change of the volume;

dV/dt = 4/3 πr² × 3

dV/dt =  4 πr²

Put r = 7.27 cm and π = 3.14

dV/dt =   4 x 3.14 x 7.27²

dV/dt = 3319.16 cm³/min.

Thus, the rate of change of the volume of sphere when is decreasing at a constant rate is found as  3319.16 cm³/min.

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(A + B)3's binomial expansion has (D) 1, 3, 3, 1 coefficients.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression.

It is typically a number, but it can also be any expression.

They may also be referred to as parameters if the coefficients are variables in and of themselves.

A coefficient is, in other words, the numerical factor of a term that contains both constants and variables.

For instance, the coefficient in the expression 2x is 2.

So, we have: (a + b)3

Since we have nothing before (a + b)3.

Then the coefficient will be 1 here.

If we have 3 after (a + b) then the coefficient will be 3.

Therefore, (A + B)3's binomial expansion has (D) 1, 3, 3, 1 coefficients.

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Correct question:
What are the coefficients for the binomial expansion of (a + b)3?

a. 1, 4, 6, 4, 1

b. 1,1

c. 1, 2,1

d. 1,3,3, 1

μ1 <= μ2,

 mean score on campus 1 is higher than on campus 2

There is also a competing theory put forth by the researcher, according to which test results are unrelated and the advanced learning program has minimal bearing on students' academic performance. Because the researcher wants to know if the scores are greater or lower than the state average, this is an illustration of a two-sided hypothesis.

 μ1 <= μ2,

 mean score on campus 1 is higher than on campus 2.

Because the researcher wants to know if the scores are greater or lower       than the state average, this is an illustration of a two-sided hypothesis.

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The correct answer is the equation of the line is y = [tex]-\frac{2}{3} x - 2[/tex]

Given the equation of the parallel line is 2x + 3y = 3

and the required line passes through the point (3, -4) where x is 3 and y is -4

We can write the given equation  as:

⇒ 3y = 3 - 2x

Dividing both sides by 3

[tex]y = 1 - \frac{2x}{3}[/tex]

On comparing this equation with y= mx+b, thus m = [tex]-\frac{2}{3}[/tex] and the slopes of parallel lines are always equal.

Using the point slope form, we will derive the equation of line

⇒ [tex]y-y_1 =m ( x- x_1)[/tex]

⇒ [tex]y- (-4) = -\frac{2}{3} (x-3)[/tex]

⇒ [tex]y+4= -\frac{2}{3} (x) - \frac{2}{3} (-3)[/tex]

⇒ [tex]y = -\frac{2}{3} (x) +2-4[/tex]

⇒ [tex]y = -\frac{2}{3} (x) - 2[/tex]

Hence, the equation of the required line is [tex]y = -\frac{2}{3} (x) - 2[/tex]

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Answer:  The correct answer is (3x−y)(2a−b)

Step-by-step explanation:

Factor 3x(2a−b)−y(2a−b)

6ax−2ay−3bx+by

=(3x−y)(2a−b)

The estimated age of the archaeological sample  as calculated from the given data is  = 2622.58333 years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 73 % of the 14C remains

then |A1|/|A2|  = 0.73

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.73)= -0.00012t

t = -0.31471/ -0.00012

 = 2622.58333 years

Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, non-exponential) decay.

For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time.

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the value of a1 of the geometric series sigma-summation underscript n = 1 overscript infinity endscripts 12 (negative one-ninth) superscript n minus 1negative twelve-ninthsnegative one-ninths112 is a1 = 12

Given the geometric series

Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 12 (negative one-ninth) Superscript n minus 1

From the series given, the nth term of the sequence is given as;

an = 12(1/9)^n-1

To get a1, we will substitute the value of n=1 into the nth term of Tue geometric series.

Given the nth term of the series as;

an = 12(1/9)^n-1

When n=1

a1 = 12(1/9)^1-1

a1 = 12(1/9)^0

Since anything raise to power of zero is 1, then;

(1/9)^0 = 1

a1 = 12{1}

a1 = 12

The value of a1 of the geometric series is 12.

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