5^3 x 2^5 x 10^2 as a product of prime

Answer:

C. populations are non normal and the sample sizes are large.

Step-by-step explanation:

To test hypotheses about the difference between two populations means we deal with the following three cases.

1) both the populations are normal with known standard deviations.

2)both the populations are normal with unknown standard deviations.

3) both the populations are non normal in which case both the  sample sizes are necessarily large.

So option C is the correct answer.

Answer:

The last option y<4. Y is less than 4 since the shaded region is below 4 on the y Axis.

Answer: D  y <4

Step-by-step explanation:

The line is horizontally passing through the 4 which is the y intercept and all the solutions are less than 4.

Answer:

0.1198 < p < 0.1802

Step-by-step explanation:

Percentage who had, or intended to cheat (p) = 15% = 0.15.

1 - p = 1 - 0.15 = 0.85

Confidence interval = 95%, z = 1.96 = 2

number of observation= 560

p ± z * √(p * (1 -p)/n)

Lower limit:

0.15 - 2 * √0.15 * 0.85/560

0.15 - 0.0301780 = 0.119822

= 0.1198

Upper limit:

0.15 + 2 * √0.15 * 0.85/560

0.15 + 0.0301780 = 0.180178

= 0.1802

0.1198 < p < 0.1802

Answer:

Step-by-step explanation:

Hello, first of all we can divide by 2.

[tex]7n^2+16n+17=0\\\\\Delta=b^2-4ac= 16^2-4*7*17=-220 < 0 \ \ !![/tex]

The discriminant is negative so there is no real solutions.

Thank you.

Speed = distance / time

Speed = 4/3 / 1/10

When dividing fractions flip the second fraction over and multiply:

Speed = 4/3 x 10/1 = (4 x 10)/(3 x1) = 40/3 miles per hour

Answer:

The cost of a chicken shawarma wrap is $10.99 and the cost of one order of spiced potatoes is $4.99.

Step-by-step explanation:

X denotes the cost of a chicken shawarma wrap and Y denotes the cost of an order of spiced potatoes.

From the provided information we can form two equations for the total price paid by Ms. Ironperson and Mr. Thoro.

[tex]3x+2y=42.95...(i)\\5x+4y=74.91...(ii)[/tex]

Multiply (i) by 4 and (ii) by 2 and subtract the two resulting equations:

[tex]3x+2y=42.95\ \ \ ]\times 4\\5x+4y=74.91\ \ \ ]\times2\\\\\Rightarrow\\\\12x+8y=171.80\\10x+8y=149.82\\\\\text{subtract}\\\\2x=21.98\\\\x=10.99[/tex]

Substitute x = 10.99 in (i) and solve for y as follows:

[tex]3x+2y=42.95\\\\(3\times 10.99)+2y=42.95\\\\2y=9.98\\\\y=4.99[/tex]

Thus, the cost of a chicken shawarma wrap is $10.99 and the cost of one order of spiced potatoes is $4.99.

Answer:

1/2

Step-by-step explanation:

The value of the given expression is 1 / √3.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

The given values are  cos60=sin30=1/2 and cos30=sin60=√3/2.

Divide sin30 and cos30,

[tex]\dfrac{sin30}{cos30}=tan30 = \dfrac{\dfrac{1}{2}}{\dfrac{2}{\sqrt{3}}}=\dfrac{1}{\sqrt{3}}[/tex]

Divide sin60 and cos60.

[tex]\dfrac{sin60}{cos60}=tan60 = \dfrac{\dfrac{2}{\sqrt{3}}}{\dfrac{1}{2}}= \sqrt3[/tex]

The value of the expression is.

[tex]\dfrac{ tan60-1}{1-tan30}=\dfrac{\sqrt{3}-1}{\sqrt{3}-1}}\times \dfrac{1}{\sqrt{3}}=\dfrac{1}{\sqrt{3}}[/tex]

Therefore, the value of the given expression is 1 / √3.

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Answer:

The question is not complete, below is a complete question with the accompanying diagram:

Instructions: Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

AB is parallel to CD, and EF is perpendicular to AB

The number of 90° angles formed by the intersections of Ef and the two parallel lines AB and CD is ____

Answer:

The number of 90° angle formed = 8 angles

Step-by-step explanation:

From the question and attached diagram, the following information is given:

AB is parallel to CD

EF is perpendicular to AB

Required: number of 90° angles formed by the intersection of the perpendicular line and the parallel lines.

Note, the angle formed between a line and a perpendicular line = 90°

From the diagram:

Number of 90° angle formed by intersection of perpendicular line EF and line AB = ∠1, ∠2, ∠3 and ∠4 = 4 angles

Number of 90° angle formed by intersection of perpendicular line EF and line  CD = ∠5, ∠6, ∠7 and ∠8 = 4 angles

Total 90° angles formed by perpendicular line with lines = ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 = 8 angles

Answer:

Step-by-step explanation:

We can observe that x coordinate increases on line segment JL from J and y coordinate decreases.

The difference in x:

The difference in y:

Point K is at 3/7 distance from J, so it's coordinates will be:

So K = ( -9, 5)

Answer:

log(16) + log(14)

Step-by-step explanation:

Answer:

  D. The input force is equal to the output force

Step-by-step explanation:

A pulley changes the direction of the applied force, but does not change its magnitude. The mechanical advantage is the ratio of output force to input force, so must be 1 when the force magnitude does not change.

Answer:

The answer is

Step-by-step explanation:

Cross multiply

We have

f(6 + y) = rw

6f + fy = rw

Move 6f to the right side of the equation to make fy stand alone

That's

fy = rw - 6f

Divide both sides by f to isolate y

That's

We have the final answer as

Hope this helps you

Differentiate both sides implicitly:

[tex]\dfrac{\mathrm d}{\mathrm dt}[e^y+x^3y^2+\ln x]=\dfrac{\mathrm d[1]}{\mathrm dt}[/tex]

[tex]e^y\dfrac{\mathrm dy}{\mathrm dt}+3x^2y^2\dfrac{\mathrm dx}{\mathrm dt}+2x^3y\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm dx}{\mathrm dt}=0[/tex]

Solve for [tex]\frac{\mathrm dx}{\mathrm dt}[/tex]:

[tex]\left(3x^2y^2+\dfrac1x\right)\dfrac{\mathrm dx}{\mathrm dt}=-(e^y+2x^3y)\dfrac{\mathrm dy}{\mathrm dt}[/tex]

[tex]\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{e^y+2x^3y}{3x^2y^2+\frac1x}\dfrac{\mathrm dy}{\mathrm dt}[/tex]

[tex]\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{xe^y+2x^4y}{3x^3y^2+1}\dfrac{\mathrm dy}{\mathrm dt}[/tex]

Plug in [tex]x=1[/tex], [tex]y=0[/tex], and [tex]\frac{\mathrm dy}{\mathrm dt}=2[/tex]:

[tex]\dfrac{\mathrm dx}{\mathrm dt}=\boxed{-2}[/tex]

Answer:

$64,800

Step-by-step explanation:

First, we calculate the total she pays all three employees in 1 month.

$2300 + $1700 + $1400 = $5400

Since there are 12 months in 1 year, we multiply the total monthly wages by 12 to find the total yearly wages.

12 * $5400 = $64,800

Answer: $64,800

Answer:

79

Step-by-step explanation:

Σ is a summation symbol. It means you need to add all values of x1 through x5.

19 + 13 + 20 + 10 + 17 = 79

Answer:

the answer is 7

Step-by-step explanation:

7+(-3)=4

7-3=4

hence shown so missing number is 7

Answer:

The answer is 1 4/7

Step-by-step explanation:

First you will want to take the mixed number and make it unmixed which will make it 11/3 divided by 7/3. Then you do the keep change flip method to divide fraction which makes it 11/3 times 3/7 then you multiply across and get 33/21 which as a mixed number is 1 12/21 but you can simplify it to be 1 4/7.

Answer:

Remainder

Step-by-step explanation:

Remainder is a number that's left over after division.

For example:

Hope this helps ;) ❤❤❤

Answer:

[tex]\Large \boxed{\mathrm{D) \ remainder}}[/tex]

Step-by-step explanation:

The remainder is the amount left over after performing division.

For example when we divide 7 by 5:

7/5 = 1 and remainder 2. 2 is the amount left after dividing.

Answer:

65000

Step-by-step explanation:

Answer:

7x + 3

Step-by-step explanation:

Answer:

I think Its 4hrs

Step-by-step explanation:

8400m÷ 35m = 240mins

240mins= 4hrs

Answer:  12) 34°     13) 90°

Step-by-step explanation:

[tex]\text{Law of Sines:}\quad \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

12) Given: a = 10.2,  b = 6.8, A = 122°

[tex]\dfrac{\sin 122^o}{10.2}=\dfrac{\sin B}{6.8}\\\\\\\dfrac{6.8\sin 122^o}{10.2}=\sin B\\\\\\\sin^{-1}\bigg(\dfrac{6.8\sin 122^o}{10.2}\bigg)=B\\\\\\34.4^o=B[/tex]

*****************************************************************************

Law of Cosines: a² = b² + c² - 2bc · cos A

Note: The letters can be swapped

13) Given: a = 3,  b = 4,  c = 5, C = ???

3² = 4² + 5² - 2(4)(5) · cos C

9  = 16 + 25 - 40 cos C

9 = 41 - 40 cos C

-32 = -40 cos C

0.8 = cos C

90° = C

Answer:

B: -6+2i

Step-by-step explanation:

Answer:

Final amount of customers =30141.44

Step-by-step explanation:

Amount of customer remaining

A= p(1-r/n)^(nt)

P= initial amount of customers

R= rate but it's a negative rate

N= number of times

T= number of years

A= final amount of customers

A= p(1-r/n)^(nt)

A= 51200(1-0.038/14)^(14*14)

A= 51200(1-0.0027)^196

A= 51200(0.9973)^196

A= 51200(0.5887)

A= 30141.44

Answer:

Dimensions are 350/9 ft and 17.5 ft

Step-by-step explanation:

We are given the cost per ft of all the 4 sides. Let the horizontal be x and the vertical be y.

Now, we will set up the constraint and equation that we are being asked to maximize.

Thus;

700 = 10y + 10y + 7x + 2x

700 = 20y + 9x

Maiking y the subject, we have;

y = (700 - 9x)/20

y = 35 - 9x/20

Now,area of a rectangle is: A = xy

Thus, A = x(35 - 9x/20))

A = 35x - 9x²/20

We can get the critical points by finding the derivatives and Equating to zero

Thus;

dA/dx = 35 - 0.9x

At dA/dx = 0,we have; x = 350/9

At d²A/dx², we have;

d²A/dx² = -0.9

This is negative, thus we will disregard and use the one gotten from the first derivative.

Thus, we will use x = 350/9 ft

Plugging this into the equation y = 35 - 9x/20, we have;

y = 35 - ((9 × 350/9)/20)

y = 17.5 ft

The dimensions of the field that will maximize the enclosed area are 350/9 ft and 17.5 ft and this can be determined by forming the linear equation.

Given :

Let 'x' be vertical, and 'y' be horizontal. So, the linear equation becomes:

700 = 10y + 10y + 7x + 2x

Simplify the above expression.

700 = 20y + 9x

Now, solve the above equation for 'y'.

[tex]\rm y = \dfrac{700-9x}{20}[/tex]    --- (1)

Now, the formula of the area of the rectangle is:

A = xy

Now, substitute the value of 'y' in the above formula.

[tex]\rm A = x \times \dfrac{700-9x}{20}[/tex]

[tex]\rm A = 35x -\dfrac{9x^2}{20}[/tex]  

Now, differentiate the above equation with respect to 'x' and then equate to 0.

[tex]\rm \dfrac{dA}{dx}=35-0.9x[/tex]

Now, equate the above equation to zero.

35 - 0.9x = 0

x = 350/9

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

[tex]\rm y = \dfrac{700-9\times \dfrac{350}{9}}{20}[/tex]

y = 17.5 ft

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Answer :

Step by Step explanation :

Take the given equation :

⇒2 + x = 6

Now, start solving it

⇒x = 6 - 2

⇒x = 4

Hence, Solution of given equation is 4. And only one solution exists.

Answer:

one

Step-by-step explanation:

the answer is 4 and there is only one solution there

Answer:

8.51%

Step-by-step explanation:

Let us assume the radius of the sphere is r. The surface area of a sphere is:

Surface area = 4πr².

There is a 4% error in the measurement of the radius, therefore the radius being measured = (100% - 4%)r = (96%)r = 0.96r

The surface area as a result of error is:

Surface area after measurement = 4π(0.96r)² = 3.6864πr²

The percentage error is the ratio of the difference between the actual and measured value to the measured value. It is given as:

[tex]Percent\ error =\frac{Actual\ area-Measured\ area}{Measured \ area}*100\%\\ \\Percent\ error =\frac{4\pi r^2-3.6864\pi r^2}{3.6864\pi r^2}*100\%\\ \\Percent\ error =\frac{0.3136\pi r^2}{3.6864\pi r^2}*100\%\\ \\Percent\ error =0.0851*100\%\\\\Percent\ error =8.51\%[/tex]

Answer:

It does not show variation

Step-by-step explanation:

Given

[tex]x = y + 2[/tex]

Required

Determine if there's direct variation between x and y

The general form of direct variation is:

[tex]y = kx[/tex]

Make y the subject of formula in the given parameters;

[tex]x = y + 2[/tex]

[tex]y = x - 2[/tex]

Compare [tex]y = x - 2[/tex] to [tex]y = kx[/tex]

Since they are not of the same form, then the given equation do not show direct variation