Olivia entered a baking contest. As part of the contest, she needs to demonstrate how to measure a gallon of milk if she only has a teaspoon measure. She converts the measurement using the ratios below: 4 quarts 1 gallon ⋅ 2 pints 1 quart ⋅ 2 cups 1 pint ⋅ 1 4 cup 4 tablespoons ⋅ 3 teaspoons 1 tablespoon 1 gallon 4 quarts ​ ⋅ 1 quart 2 pints ​ ⋅ 1 pint 2 cups ​ ⋅ 4 tablespoons 4 1 ​ cup ​ ⋅ 1 tablespoon 3 teaspoons ​ Which ratio is incorrectly written in Olivia's conversion?

For the equation [tex]8^{2x-y} = 5^{x-y+8}[/tex], the value for sum of integers x and y is option A: 24.

What is integer?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

The given equation is [tex]8^{2x-y} = 5^{x-y+8}[/tex].

The first step is to make the base same-

Multiply the left-hand side with 5 and right-hand side with 8.

[tex]5(8)^{2x-y} = 8(5)^{x-y+8}\\40^{2x-y} = 40^{x-y+8}[/tex]

Since, the bases are same, the power values can be taken into consideration -

2x - y = x - y + 8

Collect the like terms -

2x - x = - y + y + 8

x = 8

Substitute the value of x in any one side of the equation -

2x - y = 0

2(8) - y = 0

16 - y = 0

-y = -16

y = 16

So, now the value of expression x + y is -

8 + 16 = 24

Therefore, the final value is obtained as 24.

To learn more about integer from the given link

brainly.com/question/26009132

#SPJ1

Tracie net pay is,

⇒ $1,967.1

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Tracie works for a salary of $2,666 per month.

Here, She has federal income tax withheld at the rate of 15%

Hence, The amount for federal income tax is,

⇒ 15% of $2666

⇒ 15/100 × 2,666

⇒ $399.9

And, Social Security tax at the rate of 6.2%

Hence, The amount for Social Security tax is,

⇒ 6.2% of 2,666

⇒6.2/100 × 2666

⇒ $165.3

And, Medicare tax at the rate of 1.45%.

Hence, The amount of Medicare is,

⇒ 1.45% of $2,666

⇒ 1.45/100 × 2,666

⇒ $38.7

And, She have health insurance premiums of $95 per month.

Thus, The net pay is,

⇒ $2,666 - ($95 + $38.7 + $165.3 + $399.9)

⇒ $1,967.1

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ1

Oh yeah definitely, two lines don't have to be parallel or intersect. There are many examples. I'll give you one. Imagine two lines right now, one is flat horizontal, 180 degrees. Another line is above the horizontal line, at like 30 degrees. But they do not touch. So therefore, these lines are neither parallel or intersecting. The answer is true.

The runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.

What is the coefficient?

A coefficient is a number multiplied by a variable. Examples of coefficients: In the term 14 c 14c 14c, the coefficient is 14. In the term g, the coefficient is 1.

A) The mechanical energy lost due to friction can be calculated as follows:

Initial kinetic energy of the runner: KE = 0.5 * m * v² = 0.5 * 80 kg * (4.7 m/s)² = 140.29 J

The force of friction acting on the runner is given by:

[tex]friction_{force} = friction_{coefficient} * normal_{force}[/tex]

where,

[tex]friction_{coefficient} = 0.70[/tex]

[tex]and normal_{force} = m * g (g = 9.8 m/s^{2} )[/tex]

The normal force is given by:

[tex]normal_{force} = m * g = 80 kg * 9.8 m/s^{2} = 784 N[/tex]

Therefore, the force of friction acting on the runner is: [tex]friction_{force} = 0.70 * 784 N = 548.8 N[/tex]

The work done by friction is given by:

[tex]W = friction_{force} * distance[/tex]

Since the speed of the runner is reduced to zero, the work done by friction is equal to the change in kinetic energy:

[tex]W = KE_{final} - KE_{initial}[/tex]

= 0 - 140.29 J = -140.29 J

So, the mechanical energy lost due to friction is 140.29 J.

B) The distance the runner slides can be calculated using the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.

The work done by friction is given by: W = friction_force * distance

Since the friction force is constant, the work done by friction is equal to the change in kinetic energy:

[tex]W = KE_{final} - KE_{initial}[/tex]

= 0 - 140.29 J = -140.29 J

Rearranging this equation and substituting in the known values, we get:

[tex]distance = -W / friction_{force}[/tex]

= -140.29 J / 548.8 N = 0.255 m or 25.5 cm

Hence, the runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.

To learn more about the coefficient visit,

https://brainly.com/question/26250153

#SPJ4

36/25 scoops needed for the recipe if the we have a scoop that holds 2/5 cup, and a recipe calls for 3 3/5 cups of water.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have given that baker has 2/5 cup, and a recipe calls for 3 3/5 cups of water

3 3/5 = 18/5

we only has a 18/5 cup water.

Scoops we will need for the recipe = (18/5)/(2/5) = 36/25

Thus, we will need 36/25 scoops for the recipe.

Learn more about the fraction here:

brainly.com/question/1301963

#SPJ1

9  scoops would we need to use.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

2/5 cup of water can be hold by a scoop.

So, 1 cup of water hold 5/2 scoop

and, 18/5 cup of water can be hold by

=5/2 x 18/5

=18/2

= 9 scoops

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ1

Answer: Y = 23

Step-by-step explanation: -5 x -4 = positive 20 then add 3 which equals 23. 23 is the value of y

If 6 is an element in the domain of f(x) = (8x - 16)/2, the corresponding element in the range include the following: [16].

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Based on the information provided, we have the following function rule:

Function, f(x) = y = (8x - 16)/2

When the domain x = 6, the range (y) of this function is given by;

Range, y = (8(6) - 16)/2

Range, y = (48 - 16)/2

Range, y = 32/2

Range, y = 16.

Read more on range here: https://brainly.com/question/16678516

#SPJ1

The solutions to the equations are

a) The percentage of quokkas that weigh over 15.5 pounds is 2.1 %

b) The percentage of quokkas that weigh uncer 11.9 pounds is 75.9 %

c) Percentage of quokkas that weigh between 15.5 and 11.9 pounds 22.0 %

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

The weights of the quokkas are described by the normal model as

N ( 10 , 2.7 )

So , the mean μ = 10

And , the standard deviation σ = 2.7

a)

The percentage of quokkas that weigh over 15.5 pounds is given by the equation P ( x > 15.5 )

On simplifying the equation , we get

From the z-score formula ,

P ( z > ( 15.5 - 10 ) / 2.7 )

P ( z > 2.037 ) = 0.020825

0.020825 = 2.0825 %

Hence , the percentage of quokkas that weigh over 15.5 pounds is 2.1 %

b)

The percentage of quokkas that weigh uncer 11.9 pounds is  given by the equation P ( x < 11.9 )

On simplifying the equation , we get

From the z-score formula ,

P ( z < ( 11.9 - 10 ) / 2.7 )

P ( z < 0.7037 ) = 0.020825

0.75919 = 75.919 %

Hence , the percentage of quokkas that weigh uncer 11.9 pounds is 75.9 %

c)

Percentage of quokkas that weigh between 15.5 and 11.9 pounds is

P ( 11.9 < x < 15.5 )

On simplifying the equation , we get

From the z-score formula ,

P ( 11.9 < x < 15.5 ) = 1 - P ( x < 11.9 ) - P ( x > 15.5 )

P ( 11.9 < x < 15.5 ) = 1 - 0.020825 - 0.75919

P ( 11.9 < x < 15.5 ) = 0.219985

P ( 11.9 < x < 15.5 ) = 22.0 %

Hence , the equations are solved using z-score

To learn more about z-score click :

https://brainly.com/question/25638875

#SPJ1

In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

aX1 + bX2 ≤ c

where a, b, and c are constants.

The first constraint, 1.5X1 + 2.5X2 ≤ 80, is already in standard form.

The second constraint, 2X1 + 1.5X2 ≤ 70, can be rewritten in standard form as follows:

-2X1 - 1.5X2 ≤ -70

You can now write the problem in the following standard form:

Maximize Z = 5X1 + 4X2

Subject to:

1.5X1 + 2.5X2 ≤ 80

-2X1 - 1.5X2 ≤ -70

X1, X2 ≥ 0

In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200.

This means that if you produce 40 units of X1 and 0 units of X2, you will achieve the highest possible value of Z.

To learn more on inequality click:

brainly.com/question/24853349

#SPJ1

Answer:

see below

Step-by-step explanation:

1. XZ = √(200²+200²) =√2*200 = 282.8m

2. if the man started from 0,0 point & walks 120° meaning he's walking towards the northwest, so he'll be 400m west and 400√3 = 693m north from his starting point, because 120° -90° = 30° you are basically solving a problem of 3 sides length of a special straight triangle with an angle of 30. this type of triangle has a property of shorter side = 1/2 of the long side.  2nd shorter side = √3/2 of the long side.  this, you should memorize.  which will make lots of problems a piece of cake. good luck

Answer:

1. XZ = √(200²+200²) =√2*200 = 282.8m

2. Not sure

Step-by-step explanation:

The depreciable cost,

$1,800,000

The straight-line rate,

5%

The annual straight-line depreciation,

90,000

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

If a building acquired the beginning of the year at a cost of 2,200,000 has an estimated residual value of 400,000 and an estimated useful life of 20 years.

The depreciable cost,

= cost - residual value

= 2,200,000 - 400,000

= $1,800,000

The straight-line rate,

=100/20

= 5%

The annual straight-line depreciation,

= 1,800,000 x 5/100

= 90,000

Therefore, all the required values are given above.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ1

Answer:

6 scarves

Step-by-step explanation:

So he has $90 and spends $35 so: [tex]90-35=55[/tex]

The scarves cost 8 dollars each so we need to divide: [tex]55[/tex]÷[tex]8=6.875[/tex]

You can't buy have .875 of the scarves so he can only buy 6 scarves

Answer: 6

Step-by-step explanation: 90-35=55  55-8-8-8-8-8-8=7

Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup

To determine how much water Ella should add to make a specific concentration of syrup, you need to use the formula:

Syrup Concentration = (Mass of Sugar) / (Mass of Sugar + Mass of Water)

50% syrup: In this case, the syrup concentration is 0.50, so you can use the formula as follows:

0.50 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.5 - 0.5 lbs of sugar

Mass of Water = 0.5 lbs

The total amount of syrup will be 0.5 lbs of sugar + 0.5 lbs of water = 1.0 lbs

5% syrup: In this case, the syrup concentration is 0.05, so you can use the formula as follows:

0.05 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.05 - 0.5 lbs of sugar

Mass of Water = 9 lbs

The total amount of syrup will be 0.5 lbs of sugar + 9 lbs of water = 9.5 lbs

75% syrup: In this case, the syrup concentration is 0.75, so you can use the formula as follows:

0.75 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.75 - 0.5 lbs of sugar

Mass of Water = 0.33 lbs

The total amount of syrup will be 0.5 lbs of sugar + 0.33 lbs of water = 0.83 lbs

1.5% syrup: In this case, the syrup concentration is 0.015, so you can use the formula as follows:

0.015 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.015 - 0.5 lbs of sugar

Mass of Water = 33 lbs

The total amount of syrup will be 0.5 lbs of sugar + 33 lbs of water = 33.5 lbs

So, to summarize, Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup.

Learn more on Calculatng  lbs of  syrup: https://brainly.com/question/14536269

#SPJ1

Answer:

Step-by-step explanation:

Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup

Calculatng  lbs of  syrup

To determine how much water Ella should add to make a specific concentration of syrup, you need to use the formula:

Syrup Concentration = (Mass of Sugar) / (Mass of Sugar + Mass of Water)

50% syrup: In this case, the syrup concentration is 0.50, so you can use the formula as follows:

0.50 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.5 - 0.5 lbs of sugar

Mass of Water = 0.5 lbs

The total amount of syrup will be 0.5 lbs of sugar + 0.5 lbs of water = 1.0 lbs

5% syrup: In this case, the syrup concentration is 0.05, so you can use the formula as follows:

0.05 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.05 - 0.5 lbs of sugar

Mass of Water = 9 lbs

The total amount of syrup will be 0.5 lbs of sugar + 9 lbs of water = 9.5 lbs

75% syrup: In this case, the syrup concentration is 0.75, so you can use the formula as follows:

0.75 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.75 - 0.5 lbs of sugar

Mass of Water = 0.33 lbs

The total amount of syrup will be 0.5 lbs of sugar + 0.33 lbs of water = 0.83 lbs

1.5% syrup: In this case, the syrup concentration is 0.015, so you can use the formula as follows:

0.015 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)

Rearranging the formula, we get:

Mass of Water = (0.5 lbs of sugar) / 0.015 - 0.5 lbs of sugar

Mass of Water = 33 lbs

The total amount of syrup will be 0.5 lbs of sugar + 33 lbs of water = 33.5 lbs

So, to summarize, Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup.

Answer:

B

Step-by-step explanation:

The statement isn't true because when you multiply or divide different signs the answer is always negative.

Both B and C are false.

Answer:

Tip=7.47

Total bill=57.24

Step-by-step explanation:

tip=15/100×49.77=7.47(to nearest cent)

total bill=115/100×49.77=57.24(to nearest cent)

Answer:

The common difference is -12

Step-by-step explanation:

Finding the common difference:

11, - 1, - 13, - 25, . . .

The difference between the first and second terms

-1 -11 = -12

The difference between the second and third terms

-13 - -1 = -13 + 1 = -12

The common difference is -12

Probability that it is Saturday is 1/2 as it is on weekend. We can calculate this using Conditional Probability formula.

Given that a day of the week is randomly selected and that it is on the weekend, the probability of it being Saturday can be calculated as follows:

There are two days in a week that are on the weekend: Saturday and Sunday.

If we know that a day is on the weekend, the probability of it being Saturday is equal to the number of Saturdays on the weekend divided by the total number of weekend days. This is because there are two equally likely outcomes for the weekend (Saturday and Sunday), and we are interested in only one of them.

We can find this out by using formula:

P(A|B) = P(A and B) / P(B), where A and B are two events.

So, the probability of selecting Saturday, given that it is on the weekend, is 1/2. In other words, if we randomly select a day of the week and it is on the weekend, there is a 50% chance that it will be Saturday.

This can be written as P(Saturday|Weekend) = 1/2.

Therefore, probability = 1/2

Learn more about Probability here:

https://brainly.com/question/15590961

#SPJ4

Answer: divide $39857

Step-by-step explanation:

Answer:

The perimeter of the triangle is 30.5.

Step-by-step explanation:

To find the perimeter of the triangle, we need to find the length of the other leg.

We can use the equation of the line that defines the hypotenuse, y = 3x + 2, to find the coordinate of the endpoint of the shorter leg. The endpoint has x-coordinate equal to 3 (since the length of the leg is 3), and the y-coordinate can be found by substituting x = 3 into the equation:

y = 3x + 2

y = 3 * 3 + 2

y = 11

So the endpoint of the shorter leg is (3, 11).

Next, we can use the Pythagorean theorem to find the length of the other leg:

a^2 + b^2 = c^2

where a is the length of the shorter leg (which we know is 3), b is the length of the other leg, and c is the length of the hypotenuse (which is also on the line y = 3x + 2).

We can use the coordinates of the endpoint of the shorter leg to find the length of the hypotenuse:

c = √((3 - 0)^2 + (11 - 2)^2)

c = √(3^2 + 9^2)

c = √(9 + 81)

c = √90

So the length of the hypotenuse is √90.

Using the Pythagorean theorem, we can now find the length of the other leg:

3^2 + b^2 = (√90)^2

9 + b^2 = 90

b^2 = 81

b = 9

So the length of the other leg is 9.

Finally, the perimeter of the triangle is 3 + 9 + √90, which is approximately 12 + 9 + 9.5 = 30.5.

Answer:

48 minutes

Step-by-step explanation:

Why did the ant cross the road?

Speed of ant = 7 inches per minute
Width of road = 28 feet

28 feet = 28 x 12 inches = 336 inches

At 7 inches per minute, to cross 336 inches , it would take 336/7 or 48 minutes

Answer: [tex]4\sqrt{3}[/tex]

Step-by-step explanation:

We can use the pythagorean theorem to solve this.

We will call the length of the unknown side x for now.

Using the theorem, we will get to:
[tex]8^2-4^2=x^2[/tex]

[tex]64 - 16 = x^2[/tex]

[tex]48 = x^2[/tex]

[tex]x = \sqrt{48}[/tex]

In simplest radical form, it will be:

[tex]4\sqrt{3}[/tex]

Answer:

4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x represent the third side, then

x² + 4² = 8²

x² + 16 = 64 ( subtract 16 from both sides )

x² = 48 ( take square root of both sides )

x = [tex]\sqrt{48}[/tex] = [tex]\sqrt{16(3)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]

The correlation between age and price is -0.94. It indicates a strong negative correlation. Hence, as the age increases the price of the car decreases.

A procedure for determining the connections between two variables is referred to as correlation. You discovered that plotting two variables on a "scatter plot" can help you determine whether or not they are generally connected. Correlation is the most widely applied strategy even though there are other measures of association for variables measured at the ordinal or higher level of measurement.

The data was collected in 2005. So, to obtain the age we subtract the data collection year from the make year:

Age (x): 1,1, 3,3,4,4,5,5,5,5,6,7,10

Now, the array of price given is:

Price (y): 26900,23000,17500,18999,17200,18995,13900,15250,13200,11000,13900,8350,5800.

Using the correlation equation in excel sheet we see that the correlation coefficient between the age and the price is: - 0.94.

-0.94 indicates a strong negative correlation. Hence, as the age increases the price of the car decreases.

Learn more about correlation here:

https://brainly.com/question/28898177

#SPJ4

Answer:

m+1p4 =mp5

1p4= mp5-m

m=p5

Answer:

The answer is 313° degrees.

The region has a 318.0863 square foot size, as stated in the sentence.

The diameter or extent of a circular is its circumference. A straight line connecting a spot on one length of the circular to a position at the other end, going through the middle, is the diameter.

Diameter of the circle is 26 feet , so radius of the circle is r

= 26/2

= 13 feet

Central angle of the sector is [tex]\frac{5 \pi}{8} \text { radians. }[/tex]

We know that area of a sector of circle of radius r and central angle θ is

[tex]A=\frac{1}{2} \theta r^2[/tex]

Therefore, area of the sector is

A = 1/2 × 5π/8 × 13² = 318.0863 square feet

To know more about Diameter visit:

https://brainly.com/question/23220731

#SPJ1

Answer:

It might be "C"

Step-by-step explanation:

Answer:

63, 69, 75, 81

Step-by-step explanation:

to find the first 4 terms substitute n = 1, 2, 3, 4 into the explicit rule.

a₁ = 63 + (1 - 1) × 6 = 63 + 0 × 6 = 63 + 0 = 63

a₂ = 63 + (2 - 1) × 6 = 63 + 1 × 6 = 63 + 6 = 69

a₃ = 63 + (3 - 1) × 6 = 63 + 2 × 6 = 63 + 12 = 75

a₄ = 63 + (4 - 1) × 6 = 63 + 3 × 6 = 63 + 18 = 81

the first four terms are 63, 69, 75, 81

Answer:

B

Step-by-step explanation:

12 long 9 wide = 12*9 =108 sqft

$5/sqft

so she'll need 108*5 =540

but she rounded to 100 sqft