a frozen yogurt factory makes 100 quarts of frozen yogurt in 5 hours. how many quarts could be made in 36 hours

Answer:

to find the answers for the chart, just multiply 2 with the number of kites purchased and add twenty to the total. For example for 4, it would be 4x2 and then add 20 to the total.

For the equation, x stands for the amount of kites purchased. So, it would be 2(x) + 20.

Step-by-step explanation:

Answer: 324

Step-by-step explanation: Take 25% and enter it into a calculator with the percentage sign and times it by 480 and then subtract the number you get from 480, which is 360. Take 10% and enter it and times it by 360 and subtract that number from 360 and you should get 324. :)

11,160 cubes can be fit in the prism.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given:

Cube edge length = 1/2 cm

We have a rectangular prism that measures

= (7 + 1/2)cm by 12cm by (15 + 1/2) cm.

So, the volume is

V = (7 + 1/2)cm x 12cm x (15 + 1/2)cm

   = 1,395 cm³

Now, a cube with an edge length of 1/2 cm has a volume of:

V' = (1/2cm)³

   = 0.125 cm³

Now, the number of cubes fitted

V/V' = ( 1,395 cm³)/(0.125 cm³)

       = 11,160

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The diameter in inches of the small tire on the toy tractor is; 6 inches

The diameter is defined as the length of the line through the center that touches two points on the edge of the circle.

The parameters are;

Diameter of large tire = 5 ft

Diameter of small tire = 3.75 ft

The sizes are proportional, and as a result we have;

Toy size / actual size = (8 in)/(5 ft) = x/(3.75 ft)

Multiply both sides by 3.75 ft to get;

x = (8 in)(3.75/5)

x = (8 in)(0.75)

x = 6 in

The small tire on the toy is 6 inches in diameter.

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Complete question is;

On tractor,the diameter of the large tire is 5 feet and the diameter of the small tire is 3.75 feet.

A toy tractor is made to scale from the actual tractor. On the toy tractor, the diameter of the large tire is 8 inches

What is the diameter in inches of the small tire on the toy tractor?

The value of an angle in radians that corresponds to a given trigonometric function value can be found using the inverse trigonometric functions.

In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied.

In this case, since sinθ = 1/2, we can use the inverse sine function, denoted as sin^-1, to find the value of θ:

θ = sin^-1 (1/2)

Note that the inverse sine function returns an angle in the range of [−π/2, π/2].

The actual value of the angle may also lie in other ranges, depending on the context in which it is used.

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A jar has 1000 coins, of which 999 are fair and 1 is double-headed. pick a coin at random, and toss it 8 times. given that you see 8 heads,  the probability that the next toss of that coin is also a head  1.

Since the coin is double-headed, each toss will always result in a head. Therefore, the probability of getting a head on the next toss is 1, or 100%.   This is because the coin has been identified as having two heads, and thus it can never land on a tail.

The coin is still subject to the laws of probability, so it is not guaranteed that it will always land on a head, but it does make the probability of getting a head on the next toss one hundred percent.   It is important to note, however, that this probability is only true for the specific coin, and not for any other coin in the jar. The other 999 coins in the jar are all fair coins, meaning that the probability of getting a head on the next toss is still 50-50.

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Answer:

143.2 L

Step-by-step explanation:

1 pm: 1870 L

Each hour, 14% is drained.

x - 14% of x = x - 0.14x = 0.86x

To decrease a number by 14%, multiply the number by 0.86

2 pm: 0.86 × 1870 L = 1608.2 L

3 pm: 0.86 × 1608.2 L = 1383.052 L

4 pm: 0.86 × 1383.052 L = 1189.4247 L

5 pm: 0.86 × 1189.4247 L = 1022.9052 L

6 pm: 0.86 × 1022.9052 L = 879.69847 L

From 5 pm to 6 pm, the volume decreased from 1022.9052 L to 879.69847 L:

1022.9052 L - 879.69847 L = 143.2068 L

Answer: 143.2 L

Answer:

see below

Step-by-step explanation:

Put first equation into second

18x+3*(-6x+7) =21

open up the bracket

18x -18x+21=21

21 = 21

so infinite many solutions

By using the unitary method and dividing the time into equal intervals, the number of bacteria doubled every 3 hours, the final total of 32,000 bacteria after 14 hours.

Unitary method involves dividing the time interval into equal parts, and calculating the growth for each unit of time before adding them all up to get the total growth.

To start, let's divide the 14 hours into 3 hour intervals. We have

=> 14 hours / 3 hours = 4 intervals.

Next, we need to calculate the growth in each 3 hour interval. Since the number of bacteria doubles every 3 hours, we can find the growth by multiplying the initial number of bacteria by 2.

Starting with the first interval, we have 2000 bacteria * 2 = 4000 bacteria.

We can now repeat this calculation for each interval, multiplying the previous total by 2 each time.

For the second interval, we have 4000 bacteria * 2 = 8000 bacteria.

For the third interval, we have 8000 bacteria * 2 = 16,000 bacteria.

Finally, for the fourth interval, we have 16,000 bacteria * 2 = 32,000 bacteria.

So, at the end of 14 hours, there will be 32,000 bacteria in the culture.

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The expression is solved with x = 6 to 62

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, factors and constants.

They are also composed of mathematical operations

From the information given, we have that;

1/2 x + 7.5 (x) + 11.4 + 2.6

Now, expand the bracket

1/2x + 7.5x + 11.4 + 2.6

Substitute the value of x as 6 , we get;

1/2(6) + 7.5(6) + 11.4 + 2.6

Multiply the values

3 + 45 + 11.4 + 2.6

Add the values

62

Hence, the value is 62

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Answer:

To solve the inequality - 3x ≤ 3, using the table provided, we can see that when x = -2, the value of 3x is -6, which is less than 3. So the solution of the inequality -3x ≤ 3 is x ≤ 1.

The probability that the average final exam grade of a sample of 45 students selected from this class is between 80 and 83 is approximately 0.0922.

The standard error of the mean is given by the formula: [tex]standard error=standard deviation / \sqrt{sample size}\\\\ = 8.2/\sqrt{45} \\\\ = 1.935[/tex]

Next, we can calculate the Z-scores for 80 and 83:

Z1 = (80 - 79.8) / 1.935 = 0.512

Z2 = (83 - 79.8) / 1.935 = 2.056

Finally, we can use a Z-score table or calculator to find the cumulative probability of a standard normal distribution between Z1 and Z2:

P(80 < Xbar < 83) = P(0.512 < Z < 2.056) = 0.0922

So the probability that the average final exam grade of a sample of 45 students selected from this class is between 80 and 83 is approximately 0.0922.

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The required probability P(x< 75) is given as 0.8943, as of the given condition.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

here,
z = x - μ / σ

where, μ = mean and σ = standard daviation

From the question put the value in the above expression,
z = 75 - 60 / 12
z = 1.25

From z score table,
P(x < 75) = p(z < 1.25)
P(x< 75) = 0.8943

Thus, the required probability P(x< 75) is given as 0.8943.

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Step-by-step explanation:

I don't understand explain further

The side WX is perpendicular to side XY,

similarly,  XY is perpendicular to side YZ, YZ is perpendicular to side WZ, and side WX is parallel to size YZ.

so WXYZ is a square.

A line's slope is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Given the slope of WX = [4 - 1] / [3 - (-1)] = 3/4

the slope of XY = [0 - 4] / [6 - 3]

slope of XY = -4/3

the slope of YZ = [-3 - 0] / [2 - 6]

the slope of YZ = 3/4

slope of WZ = [-3 - 1] / [2 - (-1)] = -4/3

for the perpendicular slope, m₁m₂ = -1

or m₁ = -1/m₂

where m₁ is perpendicular to m₂

so the slope of WX = -1/(the slope of XY)

so WX is perpendicular to side XY,

similarly,  XY is perpendicular to side YZ, YZ is perpendicular to side WZ, and side WX is parallel to size YZ.

so the coordinates form a square.

Hence WXYZ is a square.

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The value of x is  x€ {( x1=- 3/4+(√151)/4 i), (- 3/4  - (√151)/4 i)}

2X^2 + 3X + 20 = 0

Here we will use the Quadratic formula:

Once in standard form, identify a,b and c from the original equation and plug them into the quadratic formula.

2x∧2+ 3x +20=0

Give:

Here,

a= 2

b= 3

c= 20

x= (-3±√(3^2-4.2.20))/2a

x= (-3±√(3^2-4.2.20))/2.2

x= (-3±√(9-160))/(      2^(1+1) )

Now take x1 and x2 , as we have two signs + and -.

x1  = (-3+√(9-160))/(      2^2 )

x2   =   (-3-√(9-160))/(      2^2 )

x1  = (-3+√(-151))/(      2^2 )

x2  = (-3-√(-151))/(      2^2 )

x1   =   (-3+√(-151).  √(-1))/(      2^2 )  

x2   =   (-3-√(-151).  √(-1))/(      2^2 )

x1   =   (-3+√151.  i)/(      2^2 )  

x2   =   (-3-√151.  i)/(      2^2 )

x1   =   (-3+√151.  i)/(      4)  

x2   =  - (3+√151.  i)/(      4)

x1= - 3/4+(√151)/4 i

x2= - 3/4  - (√151)/4 i

x€ {( x1=- 3/4+(√151)/4 i), (- 3/4  - (√151)/4 i)}

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Answer:

Step-by-step explanation: what you have to do is 36 divided by 3 because he used 3 scoops = 12 now 12 x 4( amount of how many scoops he used)= 48

* you times 4 by 12 because that's the amount he makes with 1 scoop

The value of [tex]i^5[/tex] is i.

The correct option is (A).

Complex Numbers in Maths. Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”.

Given:

[tex]i^5[/tex]

Now, we have to expand the complex number

[tex]i^5[/tex] = i x i x i x i x i

   = (i)² x (i)² x i

As, the value of i² = -1

[tex]i^5[/tex] = (i)² x (i)² x i

   = (-1) x (-1) x i

   = 1 x i

   = i

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If the right triangle has side lengths of 12 feet and 5 feet then the length of hypotenuse is 13 feet.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that a right triangle has side lengths of 12 feet and 5 feet

We need to find the length of the hypotenuse.

By using pythagoras theorem we find hypotenuse.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

12²+5²=x²

144+25=x²

169=x²

Take square root on both sides

x=13

Hence, if the right triangle has side lengths of 12 feet and 5 feet then the length of hypotenuse is 13 feet.

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Option B is correct, the missing length is 12.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

We know that the corresponding sides are in proportion .

Let x be the missing length

9/6=x/8

Apply cross multiplication

72=6x

Divide both sides by 6

x=72/6

x=12

Hence, Option B is correct, the missing length is 12.

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The claim that a random sample is representative of the population of interest is only true under certain conditions.

The concept of population and sample is crucial in conducting a survey. In a survey, a sample is a smaller group of individuals selected from a larger group, also known as the population.

When a sample is selected randomly from a population, it is said to be representative of the population of interest.

However, just because a sample is selected randomly does not guarantee that it is representative of the population.

Therefore, the claim that the sample of 500 students selected from the statistics classes is representative of the population of interest (all the students enrolled in the university) is only partially true.

If the population of all students enrolled in the university is homogeneous with respect to their opinions on foreign language classes, and if the random sampling process was carried out correctly, then it is possible that the sample is representative of the population.

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Answer:

.

Step-by-step explanation:.

The stated statement indicates that the item's new cost of goods sold is $37.7.

Exempt and non-exempt workers are the two basic categories into which employees fall. Your business may need to hire a variety of workers in order to function effectively and complete the task. This varies according to the type of organization.

A store manager gives his staff the order to mark up every item by 30%. The retailer paid $29 for the item, and 30% is shown in decimal form.

30/100 = 0.30

30% of the $29 = 0.30 × 29

                         = $8.7

Selling price of the item = Original price of item + 30% of the $29

                                       = $29 + $8.7

                                      = $ 37.7

Consequently, the item's new selling price is $37.7.

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The value of cos(a - B) is 63/65.

option C.

The value of cos(a - B) is calculated by applying the following formula as shown below.

sina = 3/5,

sinb = 5/13

The values of cos(a) and cos(b) is determined by applying Pythagoras tipple.

sin = opp/hypo

third side = adj

if sin (a) = 3/5, cos (a) = 4/5

if sin (b) = 5/13, cos (b) = 12/13

cos (a - b) = cos(a)cos(b) + sin(a)sin(b)

cos (a-b) = (4/5 x 12/13)  +  ( 3/5 x 5/13)

cos ( a -b ) = ( 48 / 65 )  +  ( 3/13 )

cos ( a - b ) = ( 63/65)

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So the image of the point (-9, -3) under the translation is (-7, -1).

Every point in the plane is translated by shifting it a predetermined distance in one direction to a new position. The translation moves the point (x1, y1) by the same horizontal and vertical distances to reach to point (x2, y2) if the image of the point (x1, y1) under a translation is (x2, y2) (x2, y2).

We can observe that the translation shifts the point -2 units to the right and 2 units up if we consider that the image of point (-3, -6) under a translation is (-1, -8).

By shifting the point -9 units to the right and -3 units up by 2 units, the image of the point (-9, -3) under the same translation may be found:

(-9 + 2, -3 + 2) = (-7, -1) (-7, -1)

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The probability of getting exactly two heads when three coins are tossed is 25%, and the probability of getting one heads and one tail when three coins are tossed is 37.5%.

The probability of getting exactly two heads when three coins are tossed is 1/4 or 25%. This can be calculated using the formula for probability of an event: P(E) = Number of favorable outcomes / Total number of outcomes. In this case, the favorable outcome is two heads, and the total number of outcomes is 8 (2^3) since each coin has two possible outcomes (head or tail). So P(E) = 1/8 = 0.125 = 25%.

The probability of getting one heads and one tail when three coins are tossed is 3/8 or 37.5%. This can be calculated using the same formula as above. In this case, the favorable outcome is one heads and one tail, and the total number of outcomes is 8 (2^3). So P(E) = 3/8 = 0.375 = 37.5%.

The probability of getting exactly two heads when three coins are tossed is 25%, and the probability of getting one heads and one tail when three coins are tossed is 37.5%.

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The number of whole numbers that are less than n are n.

A horizontal line with uniformly spaced numerical increments is referred to as a number line.

The way the number on the line can be replied will depend on the numbers on the line.

The number's intended use is described in the question that goes with it, such as when graphing a point.

Locating numbers, comparing numbers, fractions and mixed numbers, decimals, integers, absolute value, addition, subtraction, inequalities, multiples, common denominators, and other mathematical concepts may all be taught using number lines, which are incredibly versatile manipulatives.

Here, we do not have the bounds of n.

Let the number n = m.

Then the number of whole number is m.

Example - the number is 5.

Then,

n > 5.

The whole numbers are 4, 3, 2, 1, 0.

Therefore, the explanation is given above.

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Answer:x = 7

Step-by-step explanation:

To solve the equation 9x = 7(x + 2), we can first expand the expression inside the parentheses:

9x = 7x + 14

Next, we can isolate x by subtracting 7x from both sides:

2x = 14

Finally, we can divide both sides by 2 to find the solution:

x = 7

Answer:

Step-by-step explanation:

A cake recipe says to bake the cake until the center is 180°F, then let the cake cool to 120°F. The table shows

temperature readings for the cake.

a. Given a room temperature of 70°F, what is an

exponential model for this data set?

b. How long does it take the cake to cool to the desired

temperature?

Time (min)

a. The exponential model is y= 114.910(0.854) +70

(Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)

b. The cake takes about ____ min to cool to 120°F

(Use the answer from part a to find this answer. Round to one decimal place as needed.)

Mar 7, 2019 · Do you know how to solve this? A cake recipe says to bake the c

ata set? How long does it take the cake to cool to the desired temperature? Follow • 1

Mar 7, 2019 · Do you know how to solve this? A cake recipe says to bake the cake until the center is 180° F, then let the cake cool to 100°F. The table shows temperature readings for the cake. Given a room temperature of 69 ° F, what is an exponential model for this data set? How long does it take the cake to cool to the desired temperature? Follow • 1