Please give me the answer ASAP The average of 5 numbers is 7. If one of the five numbers is removed, the average of the four remaining numbers is 6. What is the value of the number that was removed Show Your Work

Answers

Answer 1

Answer:

The removed number is 11.

Step-by-step explanation:

Given that the average of 5 numbers is 7. So you have to find the total values of 5 numbers :

[tex]let \: x = total \: values[/tex]

[tex] \frac{x}{5} = 7[/tex]

[tex]x = 7 \times 5[/tex]

[tex]x = 35[/tex]

Assuming that the total values of 5 numbers is 35. Next, we have to find the removed number :

[tex]let \: y = removed \: number[/tex]

[tex] \frac{35 - y}{4} = 6[/tex]

[tex]35 - y = 6 \times 4[/tex]

[tex]35 - y = 24[/tex]

[tex]35 - 24 = y[/tex]

[tex]y = 11[/tex]

Answer 2

Okay, let's slightly generalize this

Average of [tex]n[/tex] numbers is [tex]a[/tex]

and then [tex]r[/tex] numbers are removed, and you're asked to find the sum of these [tex]r[/tex] numbers.

Solution:

If average of [tex]n[/tex] numbers is [tex]a[/tex] then the sum of all these numbers is [tex]n\cdot a[/tex]

Now we remove [tex]r[/tex] numbers, so we're left with [tex](n-r)[/tex] numbers. and their. average will be [tex]{\text{sum of these } (n-r) \text{ numbers} \over (n-r)}[/tex] let's call this new average [tex] a^{\prime}[/tex]

For simplicity, say, sum of these [tex]r[/tex] numbers, which are removed is denoted by [tex]x[/tex] .

so the new average is [tex]\frac{\text{Sum of } n \text{ numbers} - x}{n-r}=a^{\prime}[/tex]

or, [tex] \frac{n\cdot a -x}{n-r}=a^{\prime}[/tex]

Simplify the equation, and solve for [tex]x[/tex] to get,

[tex] x= n\cdot a -a^{\prime}(n-r)=n(a-a^{\prime})+ra^{\prime}[/tex]

Hope you understand it :)


Related Questions


[tex]4x - 2x = [/tex]

Answers

Answer:

2x

Step-by-step explanation:

These are like terms so we can combine them

4x-2x

2x

Answer:

2x

Explanation:

Since both terms in this equation are common, we can simply subtract them.

4x - 2x = ?

4x - 2x = 2x

Therefore, the correct answer should be 2x.

Find the values of x which satisfy the following inequation:
x3 – x² <12x​

Answers

Answer:

x< -3 and 0 < x < 4

Step-by-step explanation:

x^3 – x² <12x​

Subtract 12x from each side

x^3 -x^2 - 12x< 0

Factor

x( x^2 -x-12) <0

Factor

x( x-4) ( x+3) < 0

Using the zero product property

x=0   x=4  x=-3

We have to check the signs regions

x < -3

-( -) (-) < 0   True

-3 to 0

-( -) (+) < 0   False

0 to 4

+( -) (+) < 0   True

x>4

+( +) (+) < 0   False

The regions this is valid is

x< -3 and 0 < x < 4

If x=64 &y=27 Evaluate x½-y⅓÷y-x⅔​

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

-191/162

▹ Step-by-Step Explanation

Answer:

-191/162

Step-by-step explanation:

Substitute the numbers for the variables:

64 1/2 - 27 1/3 ÷ 27 - 64 2/3

Convert the mixed numbers to improper fractions:

129/2 - 82/3 * 1/27 - 194/3

Multiply the improper fractions:

129/2 - 82/81 - 194/3

= -191/162

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

PLS HELP:Find the side length, C.
Round to the nearest tenth.

Answers

Answer:

[tex]\huge\boxed{c = 14.9}[/tex]

Step-by-step explanation:

Using Cosine Rule

[tex]c^2 = a^2 + b^2 -2abCosC[/tex]

Where a = 11 , b = 7 and C = 110

[tex]c^2 = (11)^2+(7)^2-2(11)(7)Cos 110[/tex]

[tex]c^2 = 121+49-154 (-0.34)\\c^2 = 170+52.7\\c^2 = 222.7[/tex]

Taking sqrt on both sides

c = 14.9

Find a vector equation and parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5.

Answers

The normal vector to the plane x + 3y + z = 5 is n = (1, 3, 1). The line we want is parallel to this normal vector.

Scale this normal vector by any real number t to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:

(1, 0, 6) + (1, 3, 1)t = (1 + t, 3t, 6 + t)

This is the vector equation; getting the parametric form is just a matter of delineating

x(t) = 1 + t

y(t) = 3t

z(t) = 6 + t

The vector equation for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5 is v =(1+t)i + (3t)j + (6+t)k

The parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5

x(t) = 1+ty(t) = 3tz(t) = 6+t

The parametric equation of a line through the point A(x, y, z) perpendicular to the plane ax+by+cz= d is expressed generally as:

A + vt where:

A = (x, y, z)

v = (a, b, c) (normal vector)

This can then be expressed as:

s = A + vt

s = (x, y, z) + (a, b, c)t

Given the point

(x, y, z) = (1,0,6)

(a, b, c) = (1, 3, 1)

Substitute the given coordinate into the equation above:

s = (1,0,6) + (1, 3, 1)t

s = (1+t) + (0+3t) + (6+t)

The parametric equations from the equation above are:

x(t) = 1+t

y(t) = 3t

z(t) = 6+t

The vector equation will be expressed as v = xi + yj + zk

v =(1+t)i + (3t)j + (6+t)k

Learn more here: brainly.com/question/12850672

Please help. I’ll mark you as brainliest if correct!

Answers

Answer: x= -1, z=2, y= -4

Step-by-step explanation:

System of equations:

-5x - 4y - 3z= 15  +

-10x + 4y + 6z= 6

-15x         + 3z = 21  ------>  3 (-5x + z) = 7.3

-5x + z = 7

now,

-10x + 4y + 6z= 6

2(-5x + z) + 4y + 4z = 6

14 + 4y + 4z = 6

7 + 2y + 2z = 3

2y + 2z= -4

y+z=-2

Now we were using the equation: 20x + 4y + 4z = -28

20x + 4(y+z) = 20x -8= - 28

20 x = -20

x= -1

With this we can find y and z

X=-1

-5x + z = 7

z= 2

y+z=-2

y=-4

Finally we have: x= -1, z=2, y= -4

I hope this can help you.

Thank you

A soup can has a height of 4 inches and a radius of 2.5 inches. What's the volume of soup in cubic inches that would fill one soup can? Question 3 options: A) 62.8 in3 B) 125.7 in3 C) 78.5 in3 D) 314 in3

Answers

Answer:

C. 78.5 in^3

Step-by-step explanation:

A soup can is in the shape of a cylinder. The volume of a cylinder can be found using the following formula:

[tex]v=\pi r^2h[/tex]

We know that the height is 4 inches and the radius is 2.5 inches.

r= 2.5 in

h= 4 in

[tex]v=\pi (2.5in)^2*4in[/tex]

Evaluate the exponent.

[tex](2.5 in)^2=2.5 in*2.5in=6.25 in^2[/tex]

[tex]v=\pi *6.25 in^2*4 in[/tex]

Multiply 6.25 in^2 and 4 in.

[tex]6.25 in^2*4 in=25 in^3[/tex]

[tex]v=\pi*25 in^3[/tex]

Multiply pi and 25 in^3.

[tex]v=78.5398163 in^3[/tex]

Round to the nearest tenth. The 3 in the hundredth place tells us to leave the 5 in the tenth place.

[tex]v=78.5 in^3[/tex]

78.5 cubic inches can fill one soup can.

I will rate you brainliest Select the best description of what the LCM of a set of polynomials is. a.It is the quotient of all the factors of the polynomials. b.It is the common numerator of a rational expression. c. It is the product of the prime factors that are either unique to or shared by the polynomials. d. It is all the polynomials in the set.

Answers

Answer:

C. It is the product of the prime factors that are either unique to or shared by the polynomials.

Step-by-step explanation:

LCM of polynomials is:

=> Finding the factors of all the numbers and variable in the expression

=> Next, we multiply the unique numbers and the variable of the expression to find the LCM.

So, C is the correct answer.

The LCM of a set of polynomials  is the product of the prime factors that are either unique to or shared by the polynomials.  

What is LCM of polynomial?

To find the lowest common multiple (L.C.M.) of polynomials, we first find the factors of polynomials by the method of factorization and then adopt the same process of finding L.C.M.

Example : The L.C.M. of 4a2 - 25b2 and 6a2 + 15ab.

Factorizing 4a2 - 25b2 we get,

(2a)2 - (5b)2, by using the identity a2 - b2.

= (2a + 5b) (2a - 5b)

Also, factorizing 6a2 + 15ab by taking the common factor '3a', we get

= 3a(2a + 5b)

L.C.M.  is 3a(2a + 5b) (2a - 5b)

According to the question

The LCM of a set of polynomials is

 is the product of the prime factors that are either unique to or shared by the polynomials.  

(from above example we can see that )

Hence,  It is the product of the prime factors that are either unique to or shared by the polynomials.  

To know more about LCM of polynomial here :

https://brainly.com/question/26227783

# SPJ2

1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident​

Answers

Answer:

math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.

The mathematics assessment defines as "the process of gathering evidence about a content performance of capacity to use, as well as comportment away from traditional maths, as well as of making presumptions from that proof for a range of functions". In several inferences could be derived from the information in the Educational section. In order to enhance a program that promotes learning outcomes, assessment involves the use of empirical evidence on student learning. As just a result, students' learning is improved.As per my opinion, the given question is an opinion question and in the education sector some student likes math and some aren't. In this, I will select the "excited and confident" choice because I love maths.

Learn more:

brainly.com/question/13061296

Timothy invested $2,000 in an account earning 3.5% annual interest that is compounded continuously. How long will it take the investment to grow to $3,500?

Answers

Answer: 16 years

Step-by-step explanation:

The exponential function for continuous growth is given by :-

[tex]P=Ae^{rt}[/tex]

, where A = initial amount, r= rate of growth and t = time.

As per given , we have

A= $2,000, =r 3.5%=0.035 and P= $3500

put these vales in equation , we get

[tex]3500=2000e^{0.035t}\\\\\Rightarrow\ \dfrac{3500}{2000}=e^{0.035t}\\\\\Rightarrow\ 1.75=e^{0.035t}[/tex]

Taking log on both sides , we get

[tex]\ln 1.75=0.035t\\\\\Rightarrow\ t=\dfrac{\ln1.75}{0.035}=\dfrac{0.560}{0.035}=16[/tex]

Hence, it will take 16 years to grow to $3,500.

A ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots. After 1 hour, the ship turns 90° toward the south. After 2 hours, maintain the same speed. What is the bearing to the ship from port?

Answers

Answer:

The bearing is N 55.62° W

Step-by-step explanation:

ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots.

It then turns 90° towards the south after one hour.

Still maintain the same speed and direction for two hours.

The bearing is just the angle difference from the ship current location to where it started.

Let the speed be km/h

Distance covered in the first round

= 15*1

= 15km

Distance covered in the second round

=15*2

= 30 km

Angle at C = (90-80)+90

Angle at C = 10+90= 100

Let the distance between the port and the ship be c

C²= a² + b² -2abcos

C²= 15²+30²-2(15)(30)cos 100

C²= 225+900+156.28

C²= 1281.28

C= 35.8 km

Using sine formula

30/sin x= 35.8/sin 100

30/35.8 * sin 100 = sinx

0.838*0.9848= sin x

0.8253= sin x

Sin ^-1 0.8253 = x

55.62° = x

The bearing is N 55.62° W

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.) F(x, y) = (3x2 − 2y2)i + (4xy + 4)j

Answers

In order for F to be conservative, there must be a scalar function f such that the gradient of f is equal to F. This means

[tex]\dfrac{\partial f}{\partial x}=3x^2-2y^2[/tex]

[tex]\dfrac{\partial f}{\partial y}=4xy+4[/tex]

Integrate both sides of the first equation with respect to x :

[tex]f(x,y)=x^3-2xy^2+g(y)[/tex]

Differentiate both sides with respect to y :

[tex]\dfrac{\partial f}{\partial y}=-4xy+\dfrac{\mathrm dg}{\mathrm dy}=4xy+4\implies\dfrac{\mathrm dg}{\mathrm dy}=8xy+4[/tex]

But we assume g is a function of y, which means its derivative can't possibly contain x, so there is no scalar function f whose gradient is F. Therefore F is not conservative.

In this problem, since the condition of equal derivatives does not apply, the vector field is not conservative.

A vector field can be described as:

[tex]F = <P,Q>[/tex]

It is conservative if:

[tex]\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}[/tex]

In this problem, the field is:

[tex]F = <3x^2 - 2y^2, 4xy + 4>[/tex]

Then:

[tex]P(x,y) = 3x^2 - 2y^2[/tex]

[tex]\frac{\partial P}{\partial y} = -4y[/tex]

[tex]Q(x,y) = 4xy + 4[/tex]

[tex]\frac{\partial Q}{\partial x} = 4y[/tex]

Since [tex]\frac{\partial P}{\partial y} \neq \frac{\partial Q}{\partial x}[/tex], the field is not conservative.

A similar problem is given at https://brainly.com/question/15236009

Assume that random guesses are made for ​multiple-choice questions on a test with choices for each​ question, so that there are n ​trials, each with probability of success​ (correct) given by p. Find the probability of no correct answers

Answers

Complete Question

Assume that random guesses are made for 7 ​multiple-choice questions on a test with 5 choices for each​ question, so that there are n=7 ​trials, each with probability of success​ (correct) given by  p=0.20. Find the probability of no correct answers.

Answer:

The  probability is [tex]P(X = 0 ) = 0.210[/tex]

Step-by-step explanation:

From the question we are told that

    The number of trial is  n =  7

    The  probability of  success is  p =  0.20

   

Generally the probability of failure is

       [tex]q = 1- 0.20[/tex]

       [tex]q = 0.80[/tex]

Given that this choices follow a binomial distribution as there is only two probabilities i.e success or failure

Then the probability is mathematically represented as

          [tex]P(X = 0 ) = \left n} \atop {}} \right. C_0 * p^{0} * q^{n- 0}[/tex]    

          [tex]P(X = 0 ) = \left 7} \atop {}} \right. C_0 * (0.2)^{0} * (0.8)^{7- 0}[/tex]

Here   [tex]\left 7} \atop {}} \right. C_0 = 1[/tex]

=>      [tex]P(X = 0 ) = 1 * 1* (0.8)^{7- 0}[/tex]

=>     [tex]P(X = 0 ) = 0.210[/tex]

A 95% confidence interval indicates that:
A. 95% of the intervals constructed using this process based on samples from this population will
include the population mean
B. 95% of the time the interval will include the sample mean
C. 95% of the possible population means will be included by the interval
D. 95% of the possible sample means will be included by the interval

Answers

95% interval would be 95% of the population mean.

The answer should be:

A. 95% of the intervals constructed using this process based on samples from this population will

include the population mean

Answer:

A

Step-by-step explanation:

A 95% confidence interval indicates that 95% of the intervals constructed using this process based on samples from this population will

include the population mean

Michelle is 7 years older than her sister Joan, and Joan is 3 years younger than their brother Ryan. If the sum of their ages is 64, how old is Joan?

16
22
18
19

Answers

Answer:

(C) 18

Step-by-step explanation:

We can create a systems of equations. Assuming [tex]m[/tex] is Michelle's age, [tex]j[/tex] is Joan's age, and [tex]r[/tex] is Ryan's age, the equations are:

[tex]m = j + 7[/tex]

[tex]j = r-3[/tex]

[tex]m+j+r = 64[/tex]

We can use substitution, since we know the "values" of m and j.

[tex](j+7)+(r-3)+r = 64\\(j+7)+(2r-3)=64\\2r + j + 4 = 64\\2r + j = 60\\\\[/tex]

[tex]r = 21, j = 18[/tex]

So we know that Joan is 18 years old.

Hope this helped!

5. What is the solution of the following linear system?
y= 3x + 1
2y = 6x + 2
O A. (5,-2)
OB. (34)
C. Infinitely many solutions
D. No solution

Answers

Answer:

C. Infinitely many solutions

Step-by-step explanation:

First, simplify the second equation by dividing it by 2

2y = 6x + 2

y = 3x + 1

Now, we can see that both equations are the same, both y = 3x + 1.

Since they are the same line, this means that there are infinitely many solutions.

So, the correct answer is C.

f(x) = x^2 + 2x + 1, then for what values of x, f(x)=f(x+2) step by step plz​

Answers

Answer:

x = -2

Step-by-step explanation:

given f(x) = x² + 2x + 1

f(x+2) = (x+2)² + 2(x+2) + 1

= x² 4x+4+2x+4+1

= x² + 6x + 9

for f(x) = f(x+2), simply equate the two expressions and solve for x

f(x) = f(x+2)

x² + 2x + 1 = x² + 6x + 9      (x² terms cancel out)

2x + 1 = 6x + 9  (subtract 1 from both sides)

2x  = 6x + 9 - 1

2x  = 6x + 8  (subtract 6x from both sides)

2x - 6x = 8

-4x = 8 (divide both sides by -4)

x = 8 / (-4)

x = -2

A la propiedad fundamental de las proporcionas, comprueba si las siguientes son o no hay elementos a) 5/7 a 15/21 b) 20/7 a 5/3 c) 16/8 a 4/2

Answers

Answer:

fucuvucybycych tcy bic ttx TV ubtx4 cub yceec inivtxr xxv kb

Step-by-step explanation:

t tcextvtcbu6gt CNN tx r.c tct yvrr TV unu9gvt e tch r,e xxv t u.un4crcuv3cinycycr xxv yctzrctvtcrzecycyvubr xiu nyfex tut uhyh

ASAP Two points ___________ create a line. A. sometimes B. always C. never D. not enough information

Answers

Answer: B. Always

Explanation:

Two points always create a line. The correct answer is option B.

What is a line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.

If there are two points A(x₁,y₁) and B(x₂,y₂) then the distance between the two points will be the length of the line. The formula to calculate the distance is given as below:-

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore, the two points always create a line. The correct answer is option B.

To know more about lines follow

https://brainly.com/question/3493733

#SPJ5

Why is f (x) = (3x + 1/3)^2 + 8/9 not the vertex form of f (x)
not the vertex form of f (x) = 9x^2 +2x +1?
O The expression has a constant outside of the squared term.
O Some of the terms are fractions instead of integers.
O The expression is not the product of two binomials.
O The variable x has a coefficient.

Answers

Answer:

The Variable has a coefficient.

Step-by-step explanation:

Find the measure of a.
A. 60
B. 57
C. 40
D. 80

Answers

Answer:

Option (C)

Step-by-step explanation:

Since angle 'a' is the inscribed angle of the given triangle

Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.

x = 2a ⇒ a = [tex]\frac{x}{2}[/tex]

By the tangent-chord theorem,

"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"

[tex]\frac{x}{2}[/tex] = 40°

Therefore, a = [tex]\frac{x}{2}[/tex] = 40°

Option (C) will be the answer.

Suppose log subscript a x equals 3, log subscript a y equals 7, and log subscript a z equals short dash 2. Find the value of the following expression. log subscript a open parentheses fraction numerator x cubed y over denominator z to the power of 4 end fraction close parentheses

Answers

Answer:

24

Step-by-step explanation:

Given the following logarithmic expressions [tex]log_ax = 3, log_ay = 7, log_az = -2[/tex], we are to find the value of [tex]log_a(\frac{x^3y}{z^4} )[/tex]

[tex]from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}[/tex]Substituting x = a³, y = a⁷ and z = a⁻² into the log function [tex]log_a(\frac{x^3y}{z^4} )[/tex] we will have;

[tex]= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24[/tex]

Hence, the value of the logarithm expression is 24

Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal

Answers

There are [tex]10[/tex] divisions between $3.2$ and $3.3$

so that means each division is $\frac{3.3-3.2}{10}=0.01$

A is the 3rd division after $3.2$, So A is $3.2+3\times0.01=3.23$

similarly, C is 3 division behind $3.2$ so it will be $3.17$

and B is $3.34$

A represents the decimal 3.23

B represents the decimal 3.34

C represents the decimal 3.17

Calculating the decimal values:

We can see that there are 10 divisions between 3.2 and 3.3.

The difference between the two points for 10 divisions is 3.3 -3.2 = 0.1 unit.

Therefore, one division will be equal to 0.1/10 = 0.01 unit

So, point A is 3 divisions after 3.2, thus

A = 3.2 + 0.01×3

A = 3.23

Similarly,

B = 3.3 + 0.01×4

B = 3.34

And,

C = 3.2 - 0.01×3

C = 3.17

Learn more about decimals:

https://brainly.com/question/548650?referrer=searchResults

Simplify the following expression.X^1/3 * X^1/5

Answers

Answer:

[tex] X^{\frac{8}{15}} [/tex]

Step-by-step explanation:

[tex] X^\frac{1}{3} \times X^\frac{1}{5} = [/tex]

To multiply two powers with the same base, write the base and add the exponents.

[tex] = X^{\frac{1}{3} + \frac{1}{5}} [/tex]

[tex] = X^{\frac{5}{15} + \frac{3}{15}} [/tex]

[tex] = X^{\frac{8}{15}} [/tex]

What are the roots for x?

Answers

Answer:

B

Step-by-step explanation:

Use the quadractic equation, x=-b+or-sqrtb^2-4ac/2a, then simplify.

I'm really sorry that it looks messy, I don't know how to make my text look better :(

In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study. Carry answer to the nearest ten-thousandths. (Bonus Question)
a. What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178?
b. What is the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025?

Answers

Answer:

a

  [tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]  

b

  [tex]P( X >0.025 ) = 0.99379[/tex]

Step-by-step explanation:

From the question we are told that

   The  population proportion is  [tex]p = 0.10[/tex]

    The sample size is  [tex]n = 100[/tex]

Generally the standard error is mathematically represented as

       [tex]SE = \sqrt{\frac{ p (1 - p )}{n} }[/tex]

=>   [tex]SE = \sqrt{\frac{ 0.10 (1 - 0.10 )}{100} }[/tex]

=>   [tex]SE =0.03[/tex]

The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178

   [tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} < \frac{ X - 0.10}{SE} < \frac{ 0.178 - 0.10}{0.03} )[/tex]

  Generally  [tex]\frac{ X - 0.10}{SE} = Z (The \ standardized \ value \ of X )[/tex]

    [tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} <Z < \frac{ 0.178 - 0.10}{0.03} )[/tex]

    [tex]P( 0.172 < X < 0.178 ) = P (2.4 <Z < 2.6 )[/tex]

   [tex]P( 0.172 < X < 0.178 ) = P(Z < 2.6 ) - P (Z < 2.4 )[/tex]

From the z-table  

      [tex]P(Z < 2.6 ) = 0.99534[/tex]

     [tex]P(Z < 2.4 ) = 0.9918[/tex]

[tex]P( 0.172 < X < 0.178 ) =0.99534 - 0.9918[/tex]  

 [tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]  

the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as

        [tex]P( X >0.025 ) = P (\frac{ X - 0.10}{SE} > \frac{ 0.0025- 0.10}{0.03} )[/tex]

        [tex]P( X >0.025 ) = P (Z > -2.5 )[/tex]

From the z-table  

        [tex]P (Z > -2.5 ) = 0.99379[/tex]

Thus

      [tex]P( X >0.025 ) = P (Z > -2.5 ) = 0.99379[/tex]

Original price of a soda: $800 tax 7% selling price: $

Answers

Answer:

$856

Step-by-step explanation:

Find 7% of $800 and then add it to $800

Can someone please help me?

Answers

Negative Integers are :

Less than zeroTo the left of zero on a number line.

A person collected ​$700 on a loan of ​$600 they made 5 years ago. If the person charged simple​ interest, what was the rate of​ interest? The interest rate is ​%. ​(Type an integer or decimal rounded to the nearest hundredth as​ needed.)

Answers

Answer:

Rate= 3 1/3%

Or Rate= 3.33%

Step-by-step explanation:

Final amount collected= $700

Initial amount given out= $600

Interest made= Final amount - initial amount

Interest made= $700-$600

Interest made= $100

Type of interest rate = simple

Number of years = 5

PRT/100= interest

R=(100*interest)/(PT)

R= (100*100)/(600*5)

R= 10000/3000

R= 10/3

R= 3 1/3%

Or R= 3.33%

A regression analysis between sales (y in $1000) and advertising (x.in dollars) resulted in the following equation: ỹ= 30,000 + 4x
The above equation implies that an:________
a. increase of $l in advertising is associated with an increase of $4 in sales.
b. increase of $4 in advertising is associated with an increase of $4000 in sales.
c. increase of $1 in advertising is associated with an increase of $34,000 in sales.
d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Answers

Answer:

Correct answer is option d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Step-by-step explanation:

Given the equation of regression analysis is given as:

[tex]y= 30,000 + 4x[/tex]

where [tex]x[/tex] is the cost on advertising in Dollars.

and [tex]y[/tex] is the sales in Thousand Dollars.

To find:

The correct increase in sales when there is increase in the advertising cost.

Solution:

Suppose there is an increase of [tex]\$1[/tex] in the advertising cost.

Let the initial cost be [tex]x[/tex] then the cost will be [tex](x+1)[/tex].

Initial sales

[tex]y= 30,000 + 4x[/tex] ....... (1)

After increase of $1 in advertising cost, final cost:

[tex]y'= 30,000 + 4(x+1)\\\Rightarrow y' = 30,000+4x+4\\\Rightarrow y' = 30,004+4x ..... (2)[/tex]

Subtracting (2) from (1) to find the increase in the sales:

[tex]y'-y=30004+4x-30000-4x = 4[/tex]

The units of sales is Thousand Dollars ($1000).

So, increase in sales = [tex]4 \times1000 = \bold{\$4000}[/tex]

So, correct answer is:

d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Other Questions
what the answer???11x10-12/3 Cmo se organiza la informacin en los diferentes medios de comunicacin antes de entregarla a la audiencia? If R = 20 , what is the equivalent resistance between points A and B in the figure? Write each number in standard notation. 1.057 x 10^3 5.24 x 10^5 3 x 10^8 You purchased 500 shares of Barden Enterprises stock for $55.43 per share at the beginning of the year. The stock is currently priced at $57.48 per share. What is your dividend yield if you received total dividends of $835 over the year? what is meant by oesophagus Name a real world context to describe the sums of rational numbers. Two 1.0 nF capacitors are connected in series to a 1.5 V battery. Calculate the total energy stored by the capacitors. You are making the kite shown at the right fromfive pairs of congruent panels. In parts (a)-(d)below, use the given information to find the sidelengths of the kite's panels. Always use the gross adjustment knob before using the fine adjustment knob when focusing on the microscope 1 2 False True Not every straight line will pass the vertical line test. What is the only typeof straight line that would fail the vertical line test? *A-horizontal lineB-vertical lineC-Option 3 chapter 1 in microscope biology A television screen has a length to width ratio of 8 to 5 and a perimeter of 117 inches. What is the diagonal measure of the screen (to the nearest tenth of an inch)? You recently had to make an important decision.Wite a letter to your friend, telling your friend about the important decision you had to make.In the letter: *you should describe the decision you had to make *explain why it was important *say how you felt after you reached the decision.Your letter should be between 200-300 words long.Igcse English Cambridge (English Language 1123)*Needed today plz* in next 20 mins Please answer this question now In no more than five simple statements, use the kinetic theory to explain why an iron bar expands when it is heated. why do solids have a fixed shape PLEASE HELP ME!!!!!!!!!!!!Read and choose the option with the correct conjugations to complete the dialogue. Pablo, ________ los grados cada da para tu clase en la escuela? S, tengo la tarea de escribir los grados en Celsius y Fahrenheit hoy. contas cuenta conta cuentas Animal migration on savannas is often governed by distance reproduction rainfall fire The business case for why companies should act in a socially responsible manner includes: Select one: a. It generates internal benefits including employee recruiting, workforce retention, training, and improved worker productivity b. It reduces the risk of reputation-damaging incidents c. It is in the best interest of shareholders and offers potential for increased buyer patronage d. All of the above