the price of an article is Marked 25% above the cost price .if it is solid the profit of Rs.500 after allowing 15% discount .what will be it's selling price​

The required volume of the given shape is given as 432 cubic feet.

Given that,
A 3-dimensional shape with a hexagonal profile is given with dimension,
a = 6 in, H = 6 in and h = 4 in as shown in figure.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

here,
The volume of the given shape is,
Volume = 6/2[ah] × H
Substitute the value in the above expression,
Volume = 3 [4×6] × 6
Volume = 432 cubic feet,

Thus, the required volume of the given shape is given as 432 cubic feet.

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The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

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Answer:

Step-by-step explanation:

You probably should check for silly mistakes.

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:

14 students have to retake the test

Step-by-step explanation:

to calculate the mean mark as

sum of ( product of mark and frequency ) ÷ total

mean = \(\frac{14(2)+15(10)+16(2)+17(3)+18(13)}{30}\)

        = \(\frac{28+150+32+51+234}{30}\)

       = \(\frac{495}{30}\)

      = 16.5

students who score less than 16.5 will retake the test , that is

2 scored 16 , 10 scored 15 , 2 scored 14

number who have to retake test = 2 + 10 + 2 = 14

Answer: 3600

Step-by-step explanation: N= 3,600

3,600/12= 300

Answer:

n=0, or n=3600

Step-by-step explanation:

If your question is n/12 = 300n, n=0

Otherwise n/12=300, n=3600

Multiply both sides by 12 to isolate variable

The curves of the labor market are illustrations of demand and supply, and the curves are all linear functions

The equations are given as:

D = 36 - 2W

S₁ = 9 + W ---- domestic (i.e. without immigrants)

S₂ = 10 + 2W ---- total (i.e. including immigrants)

See attachment for the graph

This is the point of intersection between the curves of S₁ and D.

From the graph, we have:

(W, D) = (9,18)

Hence, the equilibrium wage rate before immigration is $9, and the number of workers that would be hired is 18

This is the point of intersection between the curves of S₂ and D.

From the graph, we have:

(W, D) = (6.5,23)

Hence, the equilibrium wage rate after immigration is $6.5, and the number of workers that would be hired is 23

Substitute 6.5 for W in S₁ = 9 + W

S₁ = 9 + 6.5

S₁ = 15.5

Remove decimal

S₁ = 16

Hence, the number of domestic workers that would be hired is 16

Substitute 6.5 for W in S₂ = 10 + 2W

S₂ = 10 + 2 * 6.5

S₂ = 23

Subtract S₁ = 16 from S₂ = 23

Immigrants = 23 - 16

Immigrants = 7

Hence, the number of immigrants that would be hired is 7

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Solution :

Let x, y, z be the dimensions of the rectangle.

Volume of the rectangle (V) = xyz

Given that the vertex should lie on ellipse \($4x^2 + y^2+4z^2=4$\) .......(i)

So here the volume xyz must be maximum with constraints above.

We solve this using Lagranches method with variable λ

Lagranches function is

\($F : xyz + \lambda(4x^2+y^2+4z^2-4)=0$\) .....(ii)

To find λ, \($\frac{dF}{dx}=0; \frac{dF}{dy}=0;\frac{dF}{dz}=0$\)

\($\frac{dF}{dx}=0 \Rightarrow yz+\lambda(16x)=0 \Rightarrow \lambda = -\frac{yz}{16x}$\) .............(iii)

\($\frac{dF}{dy}=0 \Rightarrow xz+\lambda(2y)=0 \Rightarrow \lambda = -\frac{xz}{2y}$\) ..................(iv)

\($\frac{dF}{dz}=0 \Rightarrow xy+\lambda(16z)=0 \Rightarrow \lambda = -\frac{xy}{16z}$\) ...............(v)

Equating (iii) and (iv)

\($-\frac{yz}{16x}=-\frac{xz}{2y} \Rightarrow y^2=8x^2 \Rightarrow y = \sqrt8 x$\) ...............(vi)

Equating (iii) and (v)

\($-\frac{yz}{16x}=-\frac{xy}{16z} \Rightarrow z^2=x^2 \Rightarrow z = x$\) ....................(vii)

Substitute (vi) and (vii) in (i),

From (i),

\($4x^2 + (\sqrt8 x)^2+4x^2 = 4$\)

\($\Rightarrow 4x^2 +8x^2+4x^2 = 4 \Rightarrow x = \frac{1}{4}$\)

From (vi),

\($y = \sqrt8 x$\)

\($\Rightarrow y= \sqrt8 \times \frac{1}{4} \Rightarrow y =\frac{\sqrt8}{4}$\)

\($\Rightarrow y =\frac{\sqrt{2\times4}}{4} \Rightarrow y = \frac{1}{\sqrt2}$\)

From (vii),

z = x

\($z =\frac{1}{4}$\)

Therefore, for maximum volume the dimensions of a rectangle box are

\($x =\frac{1}{4} ; y = \frac{1}{\sqrt2} ; z =\frac{1}{4}$\)

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

The most reasonable unit of measurement for 3) is option (C): \(m^2\), 4) is option (B): \(km^2\), 5) is \(in^2\).

3) The most reasonable unit for the measurement of the baseball field is \(m^2\) because the baseball field covers a large distance which is not accurately measured by small units  \(cm^2\) or \(mm^2\)  where it is not that big to be measured in large units like \(km^2\). So option C is the correct option.

4) The most reasonable unit for the measurement of a lake is \(km^2\) because lakes are generally very large water bodies that cover a large distance and are not accurately measured by small units like \(cm^2\) , \(mm^2\) , and \(m^2\). So option B is the correct option.

5) The most reasonable unit for the measurement of the area of a door is \(in^2\) because doors are relatively small compared to the other options and are often measured in square inches or square feet. So option B is the correct option.

Therefore the correct answers question-wise are:

3) \(m^2\)

4) \(km^2\)

5) \(in^2\)

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Answer:

5.5 or 5 1/2

Step-by-step explanation:

Jane because she has a higher credit score.

Given,

Jane and Stephanie both borrow $15,000 from the same bank to purchase the same make and model car. Jane's credit score is 732 and Stephanie's credit score is 588 .

Now,

For taking loan from the bank the most important thing is the credit score of the individual. If the individual has higher credit score than the person gets loan more easily and will pay less finance charges.

In our case,

Jane has a credit score of 732 which is higher than that of Stephanie .

So, jane will pay less finance cost as compared to Stephanie.

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The value of n, considering the intersecting chords in the circle, is given as follows:

n = 6m.

A chord of a circle is a straight line segment that connects two points on the circle. Specifically, it is a line segment whose endpoints are on the circle. A chord is often denoted by drawing a line segment between the two endpoints, with the segment passing through the interior of the circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Considering the two intersecting chords for the circle in this problem, the value of n is obtained as follows:

5n = 15 x 2

5n = 30

n = 30/6

n = 6m.

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25% of the students in the seminar are shorter than 65 inches.

To find the percentage of students who are shorter than 65 inches, we first need to find the number of students whose height is less than 65 inches:

There are three students who are shorter than 65 inches: 62, 60, and 58.

Therefore, the percentage of students who are shorter than 65 inches is:

(3 students / 12 students) × 100% = 25%

Note that the value given for 1% × 5 does not appear to be relevant to this question, and is not necessary for the calculation of the percentage of students who are shorter than 65 inches.

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At the given point,

\(f(5,0) = \dfrac1{\sqrt{5^2 + 0^2 - 9}} = \dfrac1{\sqrt{16}} = \dfrac14\)

Then the level curve is

\(\dfrac1{\sqrt{x^2 + y^2 - 9}} = \dfrac14 \\\\ \implies \sqrt{x^2 + y^2 - 9} = 4 \\\\ \implies x^2 + y^2 - 9 = 4^2 \\\\ \implies x^2 + y^2 = 25 = 5^2\)

which is a circle centered at the origin with radius 5 - quite easy to sketch.

The value of 6315 ×41 is 260391.

Multiplication is a method of finding the product of two or more numbers

We have to find the product of 6315 times of forty one

 6351

×     41

_______

    6351

25404+

__________

260391

Hence, the value of 6315 ×41 is 260391.

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Answer:

x = 27 , ∠ EAF = 27°

Step-by-step explanation:

∠ GAF = 90° , then

∠ GAC + ∠ CAF = ∠ GAF , that is

x + 63 = 90 ( subtract 63 from both sides )

x = 27

∠ DAE = 90°

since CD is a straight angle of 180° , then

∠ CAE = 90° , so

∠ CAF + ∠ EAF = ∠ CAE , that is

63° + ∠ EAF = 90° ( subtract 63° from both sides )

∠ EAF = 27°

Answer:

The answer is 7.1cm to 1d.p

Step-by-step explanation:

Area of square =L²

25=L²

√L²=√25

L=5cm

hyp²=opp²+adj²

x²=5²+5²

x²=25+25

x²=50

√x²=√50

x=7.1cm to 1d.p

The monthly Payment for the loan is approximately $271.24.

To calculate the monthly payment for the loan, we can use the formula for calculating the monthly payment on an intermediate-term loan. The formula is:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Given:

Loan Amount = $50,000

Interest Rate = 6.5% per year

Number of Years = 5

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is:

Monthly Interest Rate = (6.5% / 100) / 12 = 0.00541667

Plugging in the values into the formula, we get:

Monthly Payment = ($50,000 * 0.00541667) / (1 - (1 + 0.00541667)^(-5 * 12))

              = $271.24

Therefore, the monthly payment for the loan is approximately $271.24.

The owners of the restaurant want to use the loan to renovate the kitchen and expand the dining room, which they expect will generate additional monthly revenue between $2,000 and $5,000.

If we assume a conservative estimate of $2,000 per month in additional revenue, the loan payment of $271.24 represents approximately 13.56% of the additional revenue. This means that the owners would still have a significant portion of the additional revenue available for other expenses or profit.

On the other hand, if we consider the higher estimate of $5,000 per month in additional revenue, the loan payment would represent only about 5.42% of the additional revenue, leaving a substantial amount of money for other purposes.

Considering these calculations, it appears that taking this loan is a smart business decision. The monthly payment is manageable and leaves a significant portion of the additional revenue for the restaurant's operation and potential profit. However, it is essential for the owners to ensure that the projected additional revenue is realistic and sustainable to cover the loan payment and other business expenses.

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Answer:

5

Step-by-step explanation:

12$:3 =4$ a pints of raspberries

20$:4$=5 pints of raspberries

The percent increase of the profit is 15%

In this question, the figures are given as

Profit in March = £2750

Profit in April = £3162.50

The percentage of the increase of the profit is then calculated using the following equation

Increase percentage = (Profit in April - Profit in March)/Profit in March * 100%

Substitute the known values in the above equation, so, we have the following representation

Increase percentage = (3162.50 - 2750)/2750 * 100%

Evaluate

Increase percentage = 15%

Hence, the increase in percentage is 15%

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The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

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Answer:

(-2,-4) or (2,4) depending on which one you start on.

Step-by-step explanation:

if you start from the highest point it is (-2,-4)

And if you start from the lowest point (2,4)

Answer:

< BAD and < CAD

Step-by-step explanation: line AD bisects <BAC. When a bisector bisects an angle, it splits it into 2 equal halves

Answer:

Danny has the better deal.

Step-by-step explanation:

26 x 2 = 52

Danny charges $52 for 4 hours while Martin charges $60.

Answer:

y+6=-3/4(x-4)

Step-by-step explanation:

the point slope form is (y-y1)=m(x-x1) so you just have to plug in the numbers for the formula

Answer:

Given that triangle RSP is a right triangle, then using the Pythagorean Theorem, RP = 5.  (3²+4²=5²)

Plugging the 5 in to triangle RPQ, we find that the Theorem still works for that one, which means it is a right triangle (5²+12²=13²)

Step-by-step explanation:

Given that triangle RSP is a right triangle, then using the Pythagorean Theorem, RP = 5.  (3²+4²=5²)

Plugging the 5 in to triangle RPQ, we find that the Theorem still works for that one, which means it is a right triangle (5²+12²=13²)

Answer:

see explanation

Step-by-step explanation:

Using Pythagoras' identity in Δ PRS

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, then

PR² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )

PR = \(\sqrt{25}\) = 5

Using the converse of Pythagoras in Δ PQR

If the longest side squared is equal to the sum of the squares on the other 2 sides then the triangle is right.

QR² = 13² = 169

PR² + PQ² = 5² + 12² = 25 + 144 = 169

Thus Δ PQR is a right triangle, with right angle at P

0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.

Given that,

Standard deviation (σ) = 5.2 oz

mean (μ) = 10 oz

Number of students (n) = 120

As we know,

P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ\(\sqrt{n}\)}/σ])

                        = P (z > [{12.7 - 10\(\sqrt{120}\)}/5.2])

                        = P (z > 1.86)

                        = 1 - P ( z < 1.86)

                        = 1 - 0.862394

                        = 0.137606

Thus, P( z > 12.7 oz.) = 0.137606

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