A spherical balloon has a 8-in. diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the balloon remains a sphere.
a. Find the volume of the fully-inflated balloon.
b. Find the volume of the half-inflated balloon.
c. What is the radius of the half-inflated balloon?

The number of standard deviations a score has from the population mean is measured by the z-score, also known as the standard score.

The range of the z-scores is from 3 to 3 on the normal distribution curve, and values outside of this range are called outliers. The z-score's formula is as follows:

Z=X-μ/σ

First, convert the given X value into a Z-score. Keep in mind that equals 50 and equals 360.As a result,

Z = 400-360/50 = 0.80

A measure of how dispersed the data are in relation to the mean is called the standard deviation (or ).Data with a low standard deviation are grouped around the mean, while data with a high standard deviation are more dispersed.

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Answer:

Step-by-step explanation:

1. Area for triangle. Base* Height/2

Here the base it 13 units and height is 11 units. Apply to the formula:

13*11/2=

71.5 sq units

2. Answer: 71.5 sq units

Answer:

4 × v = 60

= 15

Step-by-step explanation:

v represents Victor's savings

4 × v = 60

4v = 60

Divide both sides by 4v

v = 60/4

v = 15

To boost the level of trust in the forecasted values, a balancing point must be attained.

The two phrases confidence interval and precision are intended to provide an accurate estimate of an object's measurability. We can compromise on the confidence level if the precision rises, but if the confidence level rises, the precision of the anticipated value likewise deteriorates.

Therefore, a balance point between these two variables must be reached in order to improve our confidence in the numbers being forecasted without compromising an accurate evaluation of accuracy. ensuring that accuracy and confidence are both upheld.

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The cost of a box of pasta is $2. 64, then what will you be charged for pasta this week is $1,125.

The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function. The average cost function is defined as A(x)=C(x)x, where x > 0. The average cost per unit is calculated by dividing the total cost by the number of units produced.

Given,

Your ending inventories this week for pasta were 35, 41, 32, 19, and 47 boxes. You par value is 120 and a supplier comes each night.

Par level = [(120 - 35) + (120 - 41) + (120 - 32) + (120 - 19) + (120 - 47)]

Par level = [85 + 79 + 88 + 101 + 73]

Par level = 426 units.

Charges = par level × cost

Charges = 426 × 2.64

Charges = 1,124.64

Charges ≈ $1,125

The cost of a box of pasta is $2. 64, then what will you be charged for pasta this week is $1,125.

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Answer:

$1.50

Step-by-step explanation:

first, find the unit rate which is 0.3 (7.2/24)

then multiply that by 5

The slope intercept form of equation of required line is

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

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

Slope of the line = 1.5

The line passes through (21, 32)

Equation of required line =

[tex]y - 32 = 1.5(x - 21)\\y - 32 = \frac{3}{2}(x - 21)\\2y - 64 = 3x - 63\\2y = 3x - 63 + 64\\2y = 3x + 1\\y = \frac{3}{2}x + \frac{1}{2}[/tex]

Putting x = 1 on the line,

[tex]\frac{3}{2} \times 1 + \frac{1}{2}\\[/tex]

[tex]\frac{3 + 1}{2}\\\\\frac{4}{2}\\\\2[/tex]

(1, 2) is coordinate of another point on the line

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Answer: ? = 50, same side interior angles

? = 84, alternate interior angles

Step-by-step explanation:

130 + x = 180

-130   =    -130

x = 50

alternate interior angles are congruent

50° is the value of the missing angle.

Since u and v lines are parallel so the angle asked and the angle with the value of 130° are alternate interior angle.

Alternate interior angles have the following characteristics:

Therefore,

x+130 = 180

x =180-130

x =50°

therefore, the missing angle is 50°.

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Answer:

with what

Step-by-step explanation:

lol

where is the picture..................x1000000000000000000

Answer:

I don't know I just got the app

Step-by-step explanation:

; /

Answer:

395 = 790e^(k*78)

Step-by-step explanation:

Dividing by 790 and taking the natural log

ln ( 395/790 ) = ( kx78 )

-0.6931 = 78k

-0.00888 = k  

Now calculate how much is left after 18 hours:

Amount ( 18 )

= 790e^( -0.00888x18 )

Amount = 673.301 kg

The equation that relates the number of triangles in the figure (n) to the perimeter of the figure (P) is P = 5n + 14.

We are given triangles. The triangles are arranged in a certain pattern. We need to find the relationship between the number of triangles and the perimeter of the figure. Let the perimeter of the figure having "n" number of triangles be represented by the variable "P(n)".

P(1) = 24

P(2) = 30

P(3) = 36

There is an increase of 6 units in the perimeter with every addition of a triangle. We can see and continue the pattern. The relationship between the perimeter and the number of triangles is given below.

P(n) = 18 + 6n

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Answer:

y = -6x - 50

Step-by-step explanation:

y = mx + b

Since it is perpendicular to y=1/6, the slope is -6. (Opposite reciprocal)

y = -6x + b.

Substitute to get: -2 = 48 + b

b = -50

y = -6x - 50

The greatest numbers of these rectangles that can be cut from a piece of paper with width 24 and length 60 is 360 which is option D.

Given:

A rectangle with integer side length has perimeter 10.

If the perimeter of rectangle 2(l+b) = 10

l+b = 10/2

l+b = 5.

Two choices:

1. 2 * 3 rectangle of area 6

2. 1 * 4 rectangle of area 4

The piece of paper has area 24×60 = 1440

This can be divided into rectangles with sides 2×3:

= 24/2 * 60/3

= 12*20

= 240

It can be divided into rectangles with sides 1×4:

= 24/1 * 60/4

= 24*15

= 360

Therefore the greatest numbers of these rectangles that can be cut from a piece of paper with width 24 and length 60 is 360 which is option D.

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Answer: 12

Step-by-step explanation: multiply it all together then divide it by the product.

Using Simple Interest formula ,

The rate percent on amount of Rs.300 is 5.5 .

At same rate, R = 5.5 the principle 800 will be Rs1120 in next 7 years .

In first case we have given that ,

principle = Rs.350

time = 4 years

Amount = Rs 1120

simple interest = 1120-350 = Rs.770

let rate of interest be R% .

Using the formul of simple interest

S.I = P×R×t /100

=> 770 = 350×4×R/100

=> R = 5.5 %

In Second case , rate of interest is same as in first case. So,

Amount = Rs. 1120

Principle = Rs. 800

rate of interest (R)= 5.5

Again simple interest formula Used:

Simple Interest = (P × R × T)/100

Simple interest = 1120 - 800 = Rs. 320

Simple Interest = (P × R × T)/100

⇒ 320 = 800×5.5 ×T/100

=> T = 7.27 ~ 7

∴ In the given principle Rs 800 with same rate of interest will be 1120 in 7 next years .

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Answer:

oh no

Step-by-step explanation:

The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

Pr(C & fewer than 3) = 0.1985

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Here, we are required to find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years.

Let Pr(C) be the number of consumers who believe that cash will be obsolete in the next 20 years.

Therefore, since 39.7% believe so,

Pr(C) = 39.7/100 = 0.397

If 6 consumers are selected randomly, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years will be;

Probability of 2 out 6 to believe so or Probability of 1 out of 6 to believe so.

Pr(2/6) + Pr (1/6)

Therefore the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is;

Pr (fewer than 3) = (2/6) + (1/6)

Pr (fewer than 3) = 3/6

Therefore, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

Pr(C) × Pr (fewer than 3)

i.e 0.397 × (3/6) = 0.1985

Therefore, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

Pr(C & fewer than 3) = 0.1985

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Answer: n=-6

Step-by-step explanation:

1. Make your equation

n-5=-11

2. Solve for n by adding 5 to both sides

n=-6

Answer:

16

Step-by-step explanation:

1) Break down the question

We are told that the difference between a number a 5 is minus -11

As it is a minus we have to be careful we are using the correct operation required!

2) Figure out the number

As the difference is -11 we would need add 11 to 5 to get the final number

3) Check your answer makes sense

It is always best to double check your answer to make sure that your answer is 100% correct!

To do this we just have to work out way backwards.

As we can see we have to minus 11 from 16 to get to 5 meaning our answer is correct and the number is 16!!!

Hope this helps, have a great day!

Using the given information, the volume of the given rectangle is 6/125 cubic units

From the question, we are to determine the volume of the given rectangle.

From the given information,

The dimension of the rectangle is 1/5 by 2/5 by 3/5

To determine the volume of the rectangle, we will determine the product of the length of the sides of the rectangle.

That is,

Volume of the rectangle = 1/5 × 2/5 × 3/5

Volume of the rectangle = 1 ×2×3 / 5×5×5

Volume of the rectangle = 6/125

Hence, the volume is 6/125 cubic units

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Required inequalities are 0.20x=1.20, 0.10y = 1.20 and 0.20x + 0.10y = 1.20. Combination of fruits open to Kojo are (6,0), (1,10), (2,8), (3,6), (4,4), (5,2), (0,12)

Given,

Kojo is given $1.20 to buy some peaches and apples. Peaches cost 20c each, apples 10c each.

He is told to buy at least 6 individual fruits, but he must not buy more apples than peaches.

Let x be the number of peaches Kojo buys.

Let y be the number of apples Kojo buys.

(a)Since Kojo has $1.20 to buy peaches and apples; and each peach and apple costs 20c and 10c respectively.

We have the following inequalitites:

0.20x = 1.20

0.10y = 1.20

0.20x + 0.10y = 1.20

(b)Possible combinations of fruits are as follows:

x = 1.20/0.20 = 6

y = 1.20/0.10 = 12

x = 1,2,3,4,5 ; y = 10,8,6,4,2

Thus, Required inequalities are 0.20x=1.20, 0.10y = 1.20 and 0.20x + 0.10y = 1.20. Combination of fruits open to Kojo are (6,0), (1,10), (2,8), (3,6), (4,4), (5,2), (0,12)

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Answer:

Step-by-step explanation:

The value of x= 110 degrees as it is corresponding to the angle equal to 110 degrees.

As per the given tax percent deduction from Marquis gross pay of $816 , the gross pay is reduced by $174.66.

As given in the question,

Gross pay taken by Marquis is equal to $816

Items withheld from Marquis gross pay are as follow:

1. Federal tax = $92

2. Social security tax = 6.2% of gross pay

6.2% of 816

= (6.2/100) × 816

= $50.592

3. Medicare tax = 1.45% of gross pay

= 1.45% of 816

= (1.45/100) × 816

= $11.832

4. State tax = 22% of federal tax

= 22% of 92

= ( 22 /100) × 92

= $20.24

Total reduced tax amount from Marquis gross pay

= $ ( 92 + 50.592 + 11.832 +20.24 )

= $ 174.664

≈ $174.66

Therefore,  for the given tax percent deduction from Marquis gross pay of $816 , the gross pay is reduced by $174.66.

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the 30% increase is 1,500 comments made on the website.

A music video website received 5,000 comments on a new song they released.

The next day, the artist performed the song on television and an additional 1,500 comments were made on the website.

As we know,

The percentage increase = [(increase value)/(old value)]x100

Divide the increase by the beginning number and multiply by 100 to determine the percentage increase between two numbers:

Increase value = 1500

old value =5000

Percent of increase = (1500/5000)x100

Percent of increase = 0.3x100

Percent of increase = 30%

30% if the next day, the artist performed.

In mathematics, a percentage is various or a ratio expressed as a fragment of one hundred. it is often denoted the use of the percent sign, "%", despite the fact that the abbreviations "pct.", "pct" and sometimes "laptop" is also used. A percent is a dimensionless wide variety; it has no unit of measurement. The calculation of chances is done and taught in special approaches relying on the stipulations and necessities. in this manner, the same old formulas can be acquired with proportions, which saves them from having to remember them. In so-referred to as intellectual arithmetic.

This unfastened percent calculator computes some of the values related to possibilities, consisting of the sharp distinction between two given values. percentages are essentially fractions where the denominator is 100. to reveal that a number is a percentage, we use the percent image (%) besides the range. as instance, if you purchased seventy-five questions proper out of a hundred on a check (seventy-five/100), you would have scored 75%.

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Answer:

B. Subset

Step-by-step explanation:

A(n) subset is a member of a set

The solution of the system of the equations are; x =  -2/3, y = -1/2 and z = 1.

An equation is an expression that shows the relationship between two or more numbers and variables.

The system of equation is given by;

3x − 4y + z = 2 ---- (1)

−9x + 12y − 3z = − 6 -------(2)

4x − 2y − z = -16  -----(3)

Now we add equations 1 from equation 3;

(3x − 4y + z ) + (4x − 2y − z ) =  2 -16

7x - 6y = -14 -----(4)

Further we multiply equation 3 by 3 and subtract from equation 2;

3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6

12x - 6y - 3z + 9x - 12y + 3z = 42

21x  - 18y = 42-----(5)

Now we multiply equation 4 by 3 and add it to equation 4

3(-3x + 3z) + (9x + 4z) = 5×3 - 2

-9x + 9z + 9x + 4z = 15 -2

13z = 13

z = 1

Now we put z = 1 in equation number 5

-3x + 3×1 = 5

-3x + 3 = 5

-3x = 5 - 3

-3x = 2

x = -2/3

y = -1/2

Therefore, the solution of the system of the equations are; x =  -2/3, y = -1/2 and z = 1.

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The person at the 300th number will get a t-shirt and a gift card both.

Given, at the grand opening of a sporting goods store, the store is giving a free shirt to every 12th person who attends.

They give a $25 gift card to every 30th person.

We have to find that which person will get both a t-shirt and a gift card.

To find the person who will get both, we have to find the LCM of 12 and 25.

As, the LCM of 12 and 25 is 300

So, the person at the 300th number will get a t-shirt and a gift card both.

Hence, the person at the 300th number will get a t-shirt and a gift card both.

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Answer:

25 pounds of hamburger meat

Step-by-step explanation:

you need 15 pounds for 60 hamburgers.

We can turn this into a fraction.

15/60

now we need to make the denominator a power of ten.

15/60

=5/20

=25/100

She needs 25 pounds of hamburger meat

Answer:

Step-by-step explanation:

500(108)=54000 i may not be right

30 cars of the delivery company use petrol.

According to the question,

We have the following information:

A delivery company has a total of 160 cars and vans.

The number of cars: the number of vans = 3:7

1/8 of the cars use electricity.

25% of the cars use diesel and rest use petrol.

Let's take the number of cars to be 3x and the number of vans to be 7x.

3x+7x = 160

10x = 160

x = 160/10

x = 16

Number of cars = 3*16

Number of cars = 48

Now, cars that use electricity:

1*48/8

6 cars

Cars that use diesel:

25*48/100

12 cars

Cars that use petrol:

Total number of cars-(number of cars that use electricity and diesel)

48-(6+12)

48-18

30 cars

Hence, 30 cars of the delivery company use petrol.

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