The average of eight numbers is 56. When one of the numbers was left out, the mean decreased to 54. What number was left out?

Check the picture below.

Answer:

7 muffins in the small box

Step-by-step explanation:

Total: 88 muffins

Each box: 9 muffins

88/9= 9 boxes

9x9=81

88-81=7

Answer:

7

Step-by-step explanation:

To find the proportion of monthly charges between $420 and $580, we can use the standard normal distribution and the properties of the normal curve.

First, we need to standardize the values $420 and $580 using the formula:

z = (x - μ) / σ

where z is the z-score, x is the value, μ is the mean, and σ is the standard deviation.

For $420:

z1 = ($420 - $500) / $80

z1 = -0.875

For $580:

z2 = ($580 - $500) / $80

z2 = 1.00

Next, we can use a standard normal distribution table or a calculator to find the corresponding probabilities for these z-scores.

From the standard normal distribution table, the area/probability between -0.875 and 1.00 is approximately 0.676.

Therefore, the proportion of monthly charges between $420 and $580 is approximately 0.676 or 67.6%.

This means that about 67.6% of the monthly charges fall within the range of $420 and $580 for the customers of the major department store.

Learn more about distribution here:

https://brainly.com/question/29664127

#SPJ11

There are number of 170 seats with folding arm tablets that are not designed for wheelchair users.

1. First we need to identify the total number of seats in the lecture hall which is 200.

2. Then we need to identify the number of seats with folding arm tablets that are designed for wheelchair users which is 30.

3. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats.

4. Therefore, 200 - 30 = 170, which means there are 170 seats with folding arm tablets that are not designed for wheelchair users.

The lecture hall in question has a total of 200 seats, with 30 of those seats having folding arm tablets that are designed for wheelchair users. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats. This means that 200 - 30 = 170, which means there are number of 170 seats with folding arm tablets that are not designed for wheelchair users.

Learn more about number here

https://brainly.com/question/10547079

#SPJ4

Answer:

2/5

Step-by-step explanation:

Answer:

2, 6, 11

Step-by-step explanation:

To evaluate f(- 1) substitute x = - 1 into f(x)

f(- 1) = 2(- 1)³ - 3(- 1)² + 7 = 2(- 1) - 3(1) + 7 = - 2 - 3 + 7 = 2

Similarly

f(1) = 2(1)³ - 3(1)² + 7 = 2(1) - 3(1) + 7 = 2 - 3 + 7 = 6

f(2) = 2(2)³ - 3(2)² + 7 = 2(8) - 3(4) + 7 = 16 - 12 + 7 = 11

Answer:

f(-1) = 2

f(1) = 6

f(2) = 11

Step-by-step explanation:

Got it right on Edge (⌣_⌣”)

Answer:  the cricket chirps about 200 times per minute.

=========================================================

Explanation:

c = number of chirps per minute

T = temperature in Fahrenheit

We're given that T = 93.

Replace T with 93, then solve for c.

T=0.27c+39

93=0.27c+39

0.27c+39 = 93

0.27c = 93-39

0.27c = 54

c = 54/(0.27)

c = 200

When the temperature is 93 degrees Fahrenheit, the cricket chirps about 200 times per minute.

Answer:

x = 11

Step-by-step explanation:

Chords equidistant from the centre , which is the case here are congruent, so

x = 11

A function assigns the values. The function f = xy²-2x² satisfies a conservative vector field F = ∇f.

A function assigns the value of each element of one set to the other specific element of another set.

Given F(x,y) = (y² - 4x) i + 2xy j, and it is needed to be known that,

\(f_x(x,y)=y^2-4x\\f_y(x,y) = 2xy\)

Let's look for a primitive of y²-4x with regard to x. Because we regard y (and y²) as constants, a primitive of y² is xy², just as a primitive of k is xk (because we treat y² as a constant). Because a primitive of x equals x²/2, a primitive of 4x is 2x². As a result, a primitive of y²-4x is xy²-2x². We can get any other primitive by adding constants, but because we considered y as a constant, we have that.

f(x,y) = xy²-2x²+c(y)

where c(y) only depends on y (thus, it is constant respect with x).

To learn more about c(y), we shall deduce the formula in terms of y.

\(2xy=f_y(x,y)\)

      \(=\dfrac{d}{dy}(xy^2-2x^2+c(y))\\\\=2xy-0+\dfrac{d}{dy}c(y)\\\\=2xy+\dfrac{d}{dy}c(y)\)

Thus, d/dy is constant. We can take f(x,y)=xy²-2x². This function f satisfies that  F = ∇f.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ4

Answer:

2.2360679775

Step-by-step explanation:

Answer:

2.2360679775

Step-by-step explanation:

Let's analyze each statement:

There are exactly two planes that contain points a, b.

This statement is true. Given two non-collinear points (a and b), there are infinitely many planes that can contain those points. Any plane passing through points a and b is a valid plane, and there are infinite possibilities for such planes.

There is exactly one plane that contains points e, f.

This statement is true. Given two non-collinear points (e and f), there is exactly one plane that can contain those points. The plane passing through points e and f is unique.

A line that can be drawn through points c and g would lie in a plane.

This statement is true. Any two points in 3D space determine a unique line. Since points c and g are given, the line passing through them is well-defined. Any line in 3D space lies in a plane, so the line passing through points c and g would lie in a plane.

A line that can be drawn through points e and f would lie in plane y.

This statement is not necessarily true. Without additional information about the relationship between points e, f, and plane y, we cannot determine if the line passing through e and f lies in plane y. It depends on the specific positions and orientations of the points and the plane.

The only points that can lie on plane y are points e and f.

This statement is not necessarily true. Without additional information about plane y and its relationship with other points, we cannot determine if only points e and f can lie on plane y. Plane y could potentially contain other points as well, depending on its defined characteristics.

Based on the analysis, the three true statements are:

There are exactly two planes that contain points a, b.

There is exactly one plane that contains points e, f.

A line that can be drawn through points c and g would lie in a plane.

Learn more about vector and 3D here:

https://brainly.com/question/30242211

#SPJ11

Answer:

$8.53

Step-by-step explanation:

because after 2 years she would have $148.53.

I believe the answer is $4.20

The value of annual sales in 9 years is  $309,845.72.

In order to determine the annual sales of the company in 9 years, the formula to be used is:

FV = P (1 + r)^n

Where:

$155,000 x (1.08)^9 = $309,845.72

To learn more about future value, please check: https://brainly.com/question/18760477

The height of plant B growing at a rate of 3.33 centimeters per week should have a height of 19.98 cms.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

First we need two points (x, y) to obtain the slope.

Assuming height to be 'y' and weeks to be 'x'.

Therefore, (0, 0) and (3, 10) are the two points.

Slope(m) = (10 0)/(3 - 0).

Slope(m) = 10/3.

Slope(m) = 3.33

Now, To obtain the y-intercept.

10 = 3(3.33) + b

b = 0.01 Or neglegible.

Therefore y = 3.3x.

Now, In the 6th week, the height of plant B will be,

y = 3.33(6).

y = 19.98 or 20 cm.

learn more about lines and slopes here :

https://brainly.com/question/3605446

#SPJ2

Answer:

base :6 units

height:4units

area of a triangle: 1/2 ×b×h

1/2× 6×4=12

12sqaure units should be the area

To determine whether or not to play this game, the following steps are necessary:

Step 1: Draw up a table that shows the sum of the outcomes when the two cubes are tossed together, as follows:

The table above shows that there are a total of 36 outcomes when the two cubes are tossed together, and shows the sum of the values on the faces of the cubes for each outcome.

Step 2: Use the values in the table to find the probabiity of obtaining a sum greater than or equal to 8, and the probability of obtaining a sum less than 8, as below:

Also:

Step 3: Compute the expectation, using the probabilities and the tokens to be won or lost, as follows:

Now, since the total expectation is -5 tokens, it means that 5 tokens will be lost at the end of this game. Now, would you play a game where you get to lose? Certainly not.

The answer is that you should not play this game

Therefore , the solution to the given problem of trigonometry comes out to be  angle of elevation : 62.3°.

The area of mathematics called trigonometry examines the correlation between triangle length l. The field first came into existence in the Classical world, presumably in the third-century BC, as a result of the integration of geometry with astronomy studies. Precise approaches mathematics deals with certain trigonometric equations and possible uses of them in calculations. There are six common trigonometric functions in trigonometry. They are known by their respective names and abbreviations sine, trigonometry, tangent, secant, etc. cosecant (csc). The studies of triangle aspects, particularly those right triangles, is known as trigonometry. However, studying geometry entails learning about all polygons' characteristics.

Here,

given  :

An aircraft is being followed by two radar stations, which are 4.3 miles apart.

Station A is 9.6 miles away from the plane in a straight line.

Thus,

To find the angle of elevation  from station A to plane :

Using Trigonometric ratios:

=> Sin A  = 8.5 / 9.6

=> Sin A = 85/96

=> A =  \(Sin^{-1}\)(85/96 )

=> A = 62.302840124651483 °

=> A = 62.3°

Therefore , the solution to the given problem of trigonometry comes out to be  angle of elevation : 62.3°.

To know more about trigonometry visit:

https://brainly.com/question/29002217

#SPJ1

1 pound of jelly beans cost $1.75

1 pound of almonds cost $2.75

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

From the table,

We can make two equations:

Cost of jelly beans = x

Cost of almonds = y

First purchased:

9x + 7y = 37

Second purchased:

3x + 5y = 17

Now,

9x + 7y = 37 _____(1)

3x + 5y = 17 ______(2)

Using the elimination method.

Multiply 3 into (2).

9x + 7y = 37

9x + 15y = 51

(-)     (-)      (-)

       -8y = -14

           y = 14/8

           y = 7/4 = 1.75

And,

9x + 7y = 37

9x + 7 x 1.75 = 37

9x + 12.25 = 37

9x = 37 - 12.25

9x = 24.75

x = 2.75

Thus,

Cost of 1 pound of jelly beans = $1.75

Cost of 1 pound of almonds  = $2.75

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The indefinite integral of t ln(\(t^3\)) dt can be evaluated using the simplest method, which is integration by parts. The resulting integral is \((1/4) t^2 ln(t^3) - (3/8) t^2 + c\), where c represents the constant of integration.

To find the indefinite integral of t ln(\(t^3\)) dt, we can use integration by parts. The formula for integration by parts states that the integral of the product of two functions, u and v, can be evaluated using the equation ∫u dv = u v - ∫v du.

In this case, we can choose u = ln(t^3) and dv = t dt. Taking the derivatives and antiderivatives, we have du = (1/t) dt and v = (1/2) t^2.

Applying the integration by parts formula, we get:

∫t ln(t^3) dt =\((1/2) t^2 ln(t^3)\)- ∫(1/2) \(t^2 (1/t)\) dt.

Simplifying the integral on the right-hand side, we have:

∫t ln(t^3) dt =\((1/2) t^2 ln(t^3)\) - (1/2) ∫t dt.

Integrating the second term, we obtain:

∫t ln(t^3) dt = \((1/2) t^2 ln(t^3) - (1/4) t^2 + c\).

Thus, the indefinite integral of t ln(t^3) dt is given by \((1/4) t^2 ln(t^3) - (3/8) t^2 + c\), where c represents the constant of integration.

Learn more about indefinite integral here:
https://brainly.com/question/31617899

#SPJ11

if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

To determine the total amount if the installment option is used, we need to calculate the total repayment over the 240-month term.

The installment amount per month is $4,500, and the repayment term is 240 months.

Total repayment = Installment amount per month * Repayment term

Total repayment = $4,500 * 240

Total repayment = $1,080,000

Therefore, if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

Learn more about installment here:

https://brainly.com/question/11468274

#SPJ11

The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.

A right triangle is a triangle that has an interior angle of 90°, and therefore, it has two sides known as the legs that are perpendicular.

The lengths of the sides of the triangle ΔABC can be found using the Pythagorean formula for finding the distance, d, between two points, (x₁, y₁) and (x₂, y₂) on the coordinate plane as follows;

d² = (x₂ - x₁)² + (y₂ - y₁)²

The vertices of the triangle ΔABC are; A(0, -1), B(6, 5), and C(-4, 3), which gives;

\(\overline{AB}^2\) = (6 - 0)²+ (5 - (-1))² = 72, AB = 6·√2

\(\overline{AC}^2\) = (-4 - 0)² + (3 - (-1))² = 32, AC = 4·√2

\(\overline{BC}^2\) = (-4 - 6)² + (3 - 5)² = 104, BC = 2·√(26)

72 + 32 = 104

Therefore; \(\overline{AB}^2\) + \(\overline{AC}^2\) = \(\overline{BC}^2\)

ΔABC is a right triangle

The slopes of the equation of the lines of the sides of the triangle are;

Slope of side AB = (5 - (-1))/(6 - 0) = 1

Slope of side BC = (3 - 5)/(-4 - 6) = 0.2

Slope of side AC = (3 - (-1))/(-4 - 0) = -1

Therefore;

\(\overline{AB}\) ⊥ \(\overline{AC}\)

Which gives;

Learn more about the Pythagorean theorem in mathematics here:

https://brainly.com/question/343682

#SPJ1

Answer:

The answer is D.

Step-by-step explanation:

The lateral surface area of a 3-D figure is the area of each face that is NOT a base.

Answer:

Line GH or Line HG

Step-by-step explanation:

Hope it help !!

Answer:

Step-by-step explanation:

a point to a point which makes a straight line is called a line segment

The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

To learn more about : radians

https://brainly.com/question/29058626

#SPJ8

Answer:

= 49

Step-by-step explanation:

\(\frac{-7^{7} }{-7^{5} }\)

= -7⁷⁻⁵

= -7²

= -7*-7

= 49

The required operating time, total expense and receipt are 33hours, $759 and $759 respectively.

How to get hours in operation?

It is time taken by worker or operator to operate particular work.

We have given,

Spend money = $594

Average hourly operating cost = $5.

Average hourly receipt = $23

Let time taking in operation be h,

594 + 5h = 23h

18h = 594

h = 33 hours.

and

Total expense = 23h =$23(33) =$ 759

receipt =594 + 5h = 594 + 5(33) = 594 + 165 =$ 759  

To know more about such problems visit:

brainly.com/question/15340173

#SPJ4

Answer:

1,2, and 3

Step-by-step explanation:

1+ (2*2) is equal to 5, so it has to be 1 and 2, and you can figure out that 3 goes after that.

Answer:

1= 66

2= 66

3 = 114

Step-by-step explanation:

If the manufacturer's claim is correct, the probability that the average deviation from perfect accuracy would be 34 seconds or more in the sample obtained by the consumer review website is 0.033

We can use a one-sample t-test to test the manufacturer's claim. The null hypothesis is that the true mean deviation from perfect time is equal to 30 seconds per month, and the alternative hypothesis is that the true mean deviation from perfect time is greater than 30 seconds per month.

The test statistic for this one-sample t-test is calculated as follows

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values given in the problem, we have

x = 34 seconds

μ = 30 seconds

s = 15 seconds

n = 40 clocks

t = (34 - 30) / (15 / √40) = 1.89

Using a t-distribution table with degrees of freedom (df) = n-1 = 39 and a significance level of α = 0.05 (one-tailed test), the critical value is 1.686.

Since our calculated t-value (1.89) is greater than the critical value (1.686), we reject the null hypothesis and conclude that the true mean deviation from perfect time is greater than 30 seconds per month.

To calculate the probability that the average deviation from perfect accuracy would be 34 seconds or more in the sample obtained by the consumer review website, we need to find the area under the t-distribution curve to the right of t = 1.89. Using a t-distribution calculator, we find this probability to be approximately 0.033

Learn more about probability here

brainly.com/question/11234923

#SPJ4