The following is a list of grades that students received on a recent math exam:

77, 78, 81, 62, 63, 65, 81, 92, 93, 89, 91, 78, 66, 75, 78, 80, 91, 93, 95, 93, 91, 88, 76, 89, 91, 96.

The teacher wants to list all test scores. Which of the following displays would represent the data in this way?

Box plot
Circle graph
Histogram
Stem-and-leaf plot

The solution to the compound inequality is 1 ≤ x < 21

Compound inequality are  type of inequality that has two or more parts.

In order to solve these simultaneous inequalities, we need to write them as two separate inequalities, and find the values of x that satisfy both of them

(-4x [tex]\leq[/tex]x-5 -------------------------------Equation  1

(x-5< 16) --------------------------------Equation  2

Move all the term to the left side

(-4x +(-x+5) ≤ (x-5) +(-x+5) ---------Equation 3

(x-5) +(-16) < 16+(-16)------------------Equation  4

We need to get rid of expression interval. If there is a negative sign in front of it, each term within the expression changes sign

(-4x -x +5 ≤x-5-x+5)-------------------Equation 5

( X-5 -16 < 16 -16) ----------------------Equation 6

Rearrange and Simplify equation (5 & 6)

(-5x+5 ≤ ) ---------------------------------Equation 7

(x -21 < 0)----------------------------------Equation 8

We need to get rid of expression interval and subtract 5 from equation (7) and add 21 to equation (8)

(-5x ≤ -5) ---------------Equation (9)

(x  <  21)------------------Equation (10)

Divide equation (9) by 5 on both sides and flip the sign because of the negative

5x/ 5 ≥ 5/ 5  

( x  ≥  1 )  

(x  <  21 )

Therefore the solution to the compound inequality is 1 ≤ x < 21

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0.21 inches of rain for one hour for ratio of 5 inches of rain in 24 hours

A division is a process of splitting a specific amount into equal parts.

Given,

5 inches of rain in 24 hours

We need to find the unit rate.

For this we need to use the division.

Divide five by twenty four

5/24

Zero point two zero eight

0.208

Zero point two one

0.21

Hence 0.21 inches of rain for one hour for ratio of 5 inches of rain in 24 hours

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The factors of the given expression are [tex]\frac{(x-1)^{2}}{x^{\frac{3}{2} }}[/tex]  .

In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftovers. We may employ a variety of techniques, including the division method and the multiplication method, to determine the factors of a given integer. When we need to split anything into equal rows and columns, compare prices, exchange money, and other real-world scenarios, we employ factors.

The given expression is [tex]x^{\frac{-3}{2}} -2x^{\frac{-1}{2} }+ x^{\frac{1}{2} }[/tex]

Apply the exponential rule [tex]a^{b+c}= a^{b}a^{c}[/tex], so we can write

= [tex]x^{\frac{-3}{2}} -2x^{\frac{-1}{2} }+ x^{\frac{-1}{2}}(x^{2\times\frac{1}{2}})[/tex]

Factor out the common term [tex]x^{\frac{-1}{2} }[/tex]

= [tex]x^{\frac{-3}{2}} + x^{\frac{-1}{2}}(-2+x^{2\times\frac{1}{2}})[/tex]

Apply the exponential rule [tex]a^{b+c}= a^{b}a^{c}[/tex],

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

Factor out the common term [tex]x^{\frac{-3}{2} }[/tex]

= [tex]x^{\frac{-3}{2} }(1-2x+x^{2})[/tex]

= [tex]x^{\frac{-3}{2} }(x-1)^{2}[/tex]

= [tex]\frac{(x-1)^{2}}{x^{\frac{3}{2} }}[/tex]

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As per the statement the function which is best suited for this calculation is averageif.

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Answer: 55 rounded to the nearest tenth is 60.

Step-by-step explanation: Hope this helps!!!

Answer: 60

Step-by-step explanation

Answer:

The answer is [tex]\frac{4}{13}[/tex].

Step-by-step explanation:

Additive rule:

According to this rule, the probability that events A or B will occur is given by the formula,

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Here,

We know that there are 13 spades and 4 queens in a deck of 52 cards. Also, there is only one queen of a spade.

Then,

[tex]\begin{aligned}P(S)&=\frac{13}{52}\\P(Q)&=\frac{4}{52}\\P(S\cap Q)&=\frac{1}{52}\end{aligned}[/tex]

Therefore, the probability that the card you select is a spade or queen is given by,

[tex]\begin{aligned}P(S\cup Q)&=P(S)+P(Q) -P(S\cap Q)\\&=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}\\&=\frac{16}{52}\\&=\frac{4}{13}\end{aligned}[/tex]

Therefore, the answer is [tex]\frac{4}{13}[/tex].

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Part A: The length (number of hours) of each CD is 0.875 hours.

Part B: The Hernandez family can listen each for 0.875 hours

Given that,

The Hernandez family is on a road trip. They have been driving for 3 1/2 hours. They have listened to 4 CDs of equal length.

What is an equation?

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Part A

Let the length (number of hours) of each CD be x.

Now, x = 7/2 = 3.5/4 = 0.875

= 0.875 hours

Part B

If the family has 1 hour of their drive left, still they can listen 4 CDs.

Therefore, the Hernandez family can listen each for 0.875 hours.

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Answer:

D.  8

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}\dfrac{1}{3}x+\dfrac{1}{4}y=1\\\\2x-4y=-30\end{cases}[/tex]

Multiply the first equation by -6:

[tex]\implies -6 \cdot \dfrac{1}{3}x+-6 \cdot \dfrac{1}{4}y=-6 \cdot 1[/tex]

[tex]\implies -2x-\dfrac{3}{2}y=-6[/tex]

Add this to the second equation to eliminate x:

[tex]\begin{array}{rrcccl}&2x &- &3y& = &-30\\\phantom{\dfrac12}+ &(-2x& - &\frac{3}{2}y &= &\;\;-6)\\\cline{2-6} \phantom{\dfrac12}&0&-&\frac{9}{2}y&=&-36\\ \cline{2-6}\end{array}[/tex]

Solve the equation for y:

[tex]\implies -\dfrac{9}{2}y=-36[/tex]

[tex]\implies \dfrac{9}{2}y=36[/tex]

[tex]\implies 9y=72[/tex]

[tex]\implies y=\dfrac{72}{9}[/tex]

[tex]\implies y=8[/tex]

Answer:

[tex]y=\frac{\pi}{6}[/tex]

Step-by-step explanation:

Given that:

[tex]\sin(\frac{2\pi}{3})=\cos y[/tex]

Substitute the value [tex]\frac{2\pi}{3}=\frac{\pi}{2}+\frac{\pi}{6}[/tex].

[tex]\sin(\frac{\pi}{2}+\frac{\pi}{6})=\cos(y)[/tex]

(Using the formula: [tex]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta[/tex])

[tex]\sin\frac{\pi}{2}\cos\frac{\pi}{6}+\cos\frac{\pi}{2}\sin\frac{\pi}{6}=\cos y[/tex]

Using [tex]\sin\frac{\pi}{2}=1, \cos\frac{\pi}{2}=0[/tex], we obtain:

[tex]1\times\cos\frac{\pi}{6}+0\times \sin\frac{\pi}{6}=\cos y[/tex]

This is equivalent to:

[tex]\cos\frac{\pi}{6}=\cos y[/tex]

Applying cos inverse on both sides, we get:

[tex]y=\frac{\pi}{6}[/tex]

The required equation of a parabola expressed in vertex form is f(x) = (x + 2)² - 1.

The equation of a parabola expressed in vertex form is

y = a(x - h)² + k

Where a is a multiplier and (h, k) are the coordinates of the vertex

The expression is given in the question as

f(x) = x² + 4x + 3

To complete the perfect square:

We have to add/subtract ( half the coefficient of the x- term )² to x² - 4x

f(x) = x² + 2(2)x + 4 - 4 + 3

f(x) = (x + 2)² - 1

Thus, the required equation of a parabola expressed in vertex form is f(x) = (x + 2)² - 1.

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Answer:

How I got the answer:

93 doesn't have an exact square root. So, we need to try numbers that fit with the equation.

x will be less than the square root of 93. Since the square root of 93 is between 9 and 10. The largest perfect square that we can try is 9. Let us see if that number works.

x + x² + √x = 93

9 + 9² + √9 = 93

9 + 81 + 3 = 93

93 = 93 ✔

It does work.

So the number is 9.

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Answer:

She purchased 5 boxes

Step-by-step explanation:

17.40 ÷ 3.48 = 5

You could use

2x((2x5)+5+2)+1

The evaluation of the quadratic equations are as follows;

Question 5

Question 6

Question 7

Sometimes; Factoring

Always; Quadratic formula

Always; Completing the square

Sometimes; Square root method

Sometimes; Factoring by group

Question 8

The numerator are;

(a) 8

4

(b) The denominator value;

4

(c) The roots are;

2

1

A quadratic equation is an equation of the form; a·x² + b·x + c = 0

Question 5

The quadratic equation, x² + 6·x + 10 = 0

The discriminant is 6² - 4×1×10 = -4

The discriminant < 0, therefore, the equation does not have solution

Question 7

Factoring;

Method of solving equations work more when the coefficient of x and the constant can be expressed as a + b and a·b

Where;

a·b = The constant

a + b = The coefficient of x

Therefore, factoring works sometimes

Sometimes; Factoring

Quadratic formula

The quadratic formula is an equation that involves the use of the constant and the coefficients of x

The quadratic formula therefore works all the time

Always; Quadratic formula

Complete the square

The completing the square method works by rearranging the equation in the form;

a·x² + b·x + c ⇒ a·(x + m)² + n

Where;

m = b/(2·a),

n = c - (b²/(4·a))

The method therefore works all the time

Always; Completing the square

Square root method

The square root method involves placing the square term of the equation on one side of the equation and the constant term on the other side

The square root method  works for equations that can be expressed in the form x² = b

The method  works sometimes

Sometimes; Square root method

Factoring by group

The method involves finding the common factors and grouping based on the common factors

The method only works when there are common factors

Sometimes; Factoring by group

Question 8

The  equation is 2·x² - 5·x = x - 4,

Writing the equation so that we have;

2·x² - 5·x - x + 4 = 0

2·x² - 6·x  + 4  = 0

x = (6 ± √((6² - 4× 2 × 4))/(2×2) =

Therefore;

x = 8/(2×2)  or x =  4/(2×2)

The numerators are 8 and 4

8

4

(b) The denominator is (2 × 2) = 4

(c) The two roots of the quadratic equation are;

x = 8/4 = 2 and x = 4/4 = 1

2

1

Question 6

The equation, x² - 16·x + 64 = 4

The left side of the equation can be factored as follows;

x² - 16·x + 64 = 4

x² - 8·x - 8·x + 64 = 4

(x² - 8·x) + (64 - 8·x) = 4

x·(x - 8) - 8·(x - 8) = 4

(x - 8)·(x - 8) = (x - 8)² = 4

Yes; (x - 8)² = 4

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The value of the sum of the arithmetic sequence from a₃ to a₆ is 38

An arithmetic sequence is a sequence in which the difference between two consecutive terms is a constant.

The first term of the sequence is 20, the common difference is 17 - 20 = 14 - 17 = 11 - 14 = 8 - 11 = 5 - 8 = 2 - 5 = -3

The sum from n = 3 to n = 6 of aₙ is found as follows;

The sequence is an arithmetic progression of the form aₙ = a + (n - 1)·d

Where;

aₙ is the value of the nth term

a = The first term

d = The common difference

From the sequence, we have;

a = 20, d = -3, from which we have;

aₙ = 20 + (n - 1) × (-3) = 20 - 3·(n - 1)

aₙ = 20 - 3·(n - 1)

From which we have;

a₃ = 20 - 3×(3 - 1) = 14

a₄ = 20 - 3×(4 - 1) = 11

a₅ = 20 - 3×(5 - 1) = 8

a₆ = 20 - 3×(6 - 1) = 5

a₃ + a₄ + a₅ + a₆ = 5 + 8 + 11 + 14 = 38

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Answer:√(9) is a rational number.

Step-by-step explanation:

Answer:This is a rational numer because it can be expressed in the form of p/q

Step-by-step explanation:If a number can be expressed int he form of p/q then its rational.

The coordinates of the midpoints of GH are M (4,3) and the coordinates of one endpoints are G (5,-6) the coordinates of the other endpoints are

The co - ordinates of another end point is

(x,y) = (3, 12)

mid point formula:-

Let [tex](x_{1}, y_{1}) and (x_{2}, y_{2})[/tex] be any two end points

Mid point of two given points are

[tex](\frac{x_{1}+ x_{2}}{2}, \frac{y_{1}+ y_{2}}{2} )[/tex]

let (x,y ) be the another end point

given one end point is (5,-6)

now by using mid-point formula , we get

 [tex](\frac{x+5}{2} ,\frac{y-6}{2})[/tex]  this is equating to given mid-point is M(4,3)

now [tex](\frac{x+5}{2}, \frac{y-6}{2}) = (4,3)[/tex]

simplify , we get

[tex]\frac{x+5}{2} = 4 and \frac{y-6}{2} = 3[/tex]

cross multiplication and simplify

x+5 = 8 and y-6 = 6

so x = 3 and y = 12

Hence the another point is (x,y) = (3,12)

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to calculate the total price for car wash services. A base car wash is $10. A dictionary with each additional service and the corresponding cost has been provided. Two additional services can be selected. A '-' signifies an additional service was not selected. Output all selected services, according to the input order, along with the corresponding costs and then the total price for all car wash services.

"""

Python version: 3.6

Python program to calculate the total price for car wash services

"""

# dictionary containing the services as keys and their price as values

services = {'Air freshener' : 1, 'Rain repellent' : 2, 'Tire shine' : 2, 'Wax' : 3, 'Vacuum' : 5}

# variable to store the base car wash price

base_wash = 10

# variable to store the total price

total = 0

# read the 2 services

service_choice1 = input()

service_choice2 = input()

print("ZyCar Wash")

# display the base wash price

print("Base car wash -- ${}".format(base_wash))

total += base_wash # add base_wash to total

# first service read is in services dictionary

if service_choice1 in services:

   total += services[service_choice1] # add the price for the service to total

   # display the service and its price from dictionary

   print("{} -- ${}".format(service_choice1, services[service_choice1]))

# second service read is in services dictionary    

if service_choice2 in services:

   total += services[service_choice2] # add the price for the service to total

   # display the service and its price from dictionary

   print("{} -- ${}".format(service_choice2, services[service_choice2]))

# display the total price  

print("----")

print("Total price: ${}".format(total))    

# end of program

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A total of 676 different three-letter initials combinations end with the letter Z using the uppercase characters in English alphabets.

We have three letters which have to be filled in.

English alphabets consist of 26 letters (A-Z). Let's suppose A1, A2 & A3 are the three initials.

For A1, we have 26 alphabets to choose from i.e. A-Z

For A2, we again have 26 alphabets to choose from i.e. A-Z

For A3, we have only one option i.e. Z

Thus, total different three-letter initials combinations for "**Z" pairings are:

26 x 26 x 1 = 676

Please note that combinations allow repetition of values. If one wants to avoid repetition, permutation needs to be calculated.

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The margin of error is approximately 0.3

To answer the question, we must figure out what margin of error corresponds to a 90% confidence level. The definition of the margin of error used to create confidence intervals for the population mean is as follows;

Mean = μ = 20.6

Standard deviation = σ = 2.7

Number of students = n = 225

the result of the sample mean's standard error and the accompanying z-score. The formula used to compute the sample mean's standard error is;

⇒  σ / √n

The z-score associated with a 90% confidence level:

From the given table z-score is 1.645

Therefore, the margin of error;

σ / √n * 1.645 = 2.7/√225 * 1.645

                      = 0.296

Hence, the margin of error is approximately 0.3

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Answer:

Approximately 0.3 of an error is allowed.

Given data in question

Confidentialevel=90%

Mean = μ = 20.6

2.7 as the standard deviation

N = 225 students are enrolled.

the outcome of the standard error of the sample mean and the corresponding z-score. The formula used to determine the standard error of the sample mean is;

⇒ σ / √n

The z-score for a 90% degree of confidence is:

Z-score for the provided table is 1.645.

Consequently, the error margin;

σ / √n * 1.645 = 2.7/√225 * 1.645

= 0.296

Consequently, the margin of error is roughly 0.3.

The number of small rooms reserved is 13 and the number of large rooms reserved is 12.

Given, Nolan is blocking off rooms for the guests. We will solve the problem using the linear equation. The number of small rooms is x and number of large rooms is y.

There are total of 25 rooms, which can be written as,

x+y=25 ------(1)

Small room can accommodate 3 people and large room 5 people, which can be written as follows,

3x+5y=99 --------(2)

Multiplying the equation 1 by 3, we get

3x+3y=75

Substracting equation 1 and 2, we get

3x+5y=99

3x+3y=75

-    -       -

---------------

0x+2y=24

2y=24

y=12

x+12=25

x=25-12

x=13

Therefore, the number of small rooms is 13 and large rooms is 12.

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The number in scientific notation is 2.1×10⁵.

Adjusting a number's digits so that it produces an approximation of a result is known as rounding.

The given number is 2.085×10⁵.

Round the number 2.085 to the nearest tenth:

2.085 ≈ 2.1

Therefore, the number in scientific notation is 2.1×10⁵.

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Caspian Sea is elevated at 92 feet (or 28 meters) below sea level. (globally preferred unit is meters)

On the scale of sea levels, a certain height has been assigned zero elevation. This acts as a reference point for rest of the measurements and is called Mean Sea Level (MSL). It is also known as still water level.

Caspian Sea at 92 feet below sea level means it is 92 feet below MSL. Thus, its elevation is considered 92 feet below sea level.

Global MSL is calculated using the spatial average of the complete ocean's level.

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Answer:

534,000

Step-by-step explanation:

12 days pass from may 10 to may 22 so we replace x with 12

190,000(1.09)^12
190,000(2.81266)

534406.309

But rounded to the nearest thousands

534,000

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We can see that the p-value for above test is less than α=0.05 and it indicates that we have very strong evidence against H(0) to reject it and we can conclude that there is highly significant relationship between money spent on advertising and sales.

In the given question we have to find is there a statistically significant relationship between money spent on advertising and sales.

Here we have Sales(in $1000) as dependent variable (y) and spend on Advertising (in $1000) as independent variable (x).

The significance of relationship between x and y is given by the significance of regression coefficient of regression of y of x.

So we have to test

H(0): β1=0

H(1): β1≠0

From the table that is given below, we have;

b(1)=3.778221987

se(b(1)) =0.563520732

The test statistic to test the above hypothesis is

t=b(1)/se(b(1))

From the given output, we already have

t=6.704672556

p-value=0.0000146

We can see that the p-value for above test is less than α=0.05 and it indicates that we have very strong evidence against H(0) to reject it, so we reject the H(0) and we can conclude that there is highly significant relationship between money spent on advertising and sales.

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James bond should come ashore 3.464 miles from point A to reach B in least time.

Calculus  is defined as a branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus).

Let's say the James bond travels x miles from point A.

We are aware that time = distance / speed

Total time taken by James bond to reach B is

t(x) = √(x^2+36)/6 + (10-x)/12

dt/dx = x/(6√(x^2+36)) - 1/12

for critical point dt/dx =0

= x/(6√(x^2+36)) - 1/12 = 0

√(x^2+36) = 2x

Squaring on both sides we get

X2 + 36 = 4x2

X2 = 12

X2 = 2√3

T(0) = √(0^2+36)/6 + (10-0)/12 = 41/6

= 6.833 hours

T(2√3) = √(12+36)/6 + (10-2√3)/12 = (5+3√3)/6

= 1.699 hours

T(0) = √(10^2+36)/6 + (10-10)/12 = √34/3

= 1.94 hours

Therefore James bond should come ashore 3.464 miles from point A to reach B in least time

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The equation to represent the area of the.large office is 3.5l = 42.

An equation is simply used to illustrate the relationship between the variables given.

In this case, the large office desk has an area of 42ft² anz the width is 3.5 feet. It should be noted that the area is calculated as:

= Length × Width

Therefore, l × w = 42

where w = 3.5

l × 3.5 = 42

3.5l = 42

Therefore, the equation is 3.5l = 42

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The average acceleration is -3.71m/s². Any procedure where the velocity varies is referred to as acceleration.

acceleration = change in velocity / Time taken

a = 0 - 15.6 / 4.2

= -15.6 / 4.2

=  -3.71

The average acceleration is -3.71m/s²

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Answer:

Step-by-step explanation:

The slope is determined with two points.

Take the pairs (0, - 9) and (1, - 5).

The slope is:

Answer:

Slope = 4

Step-by-step explanation:

Formula we use,

→ Slope = (y2 - y1)/(x2 - x1)

Then required slope will be,

→ (y2 - y1)/(x2 - x1)

→ (-5 -(-9))/(1 - 0)

→ (-5 + 9)/(1 - 0)

→ 4/1 = 4

Therefore, the slope is 4.