To make 30 cupcakes Margaret needs 4.375 cups of vanilla.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Margaret uses 1 3/4 teaspoon of vanilla to make 12 cupcakes
So,
1 3/4 teaspoon vanilla ⇒ 12 cupcakes
(4×1 + 3)/4 teaspoon ⇒ 12 cupcakes
7/4 teaspoon vanilla ⇒ 12 cupcakes
Divide by 12 into both sides,
7/(4×12) teaspoon vanilla ⇒ 1 cupcake
Now multiply by 30 on both sides,
(7 × 30)/(4 × 12)teaspoon vanilla ⇒ 30 cupcake
30 cupcakes ⇒ 4.375 teaspoon vanilla.
Hence "To make 30 cupcakes Margaret needs 4.375 cups of vanilla".
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the probability of an engine's failing during a 30 day acceptance test is 0.3 under adverse environmental conditions. Eight engines are included in such a test. What is the probability of the following?
a) None will fail
b)All will fail
The figure illustrates the apparatus for a tightrope walker. Two poles are set y = 50 feet apart, but the point of attachment P for the rope is yet to be determined. (a) Express the length L of the rope as a function of the distance x from P to the ground.
Equation for the length L of the rope as a function of the distance x from P to the ground is,
⇒ L = √((x-2)²+50²)
Since L is to the second pole, not x, we can't simply say that;
⇒ x² + y²= L² using the Pythagorean Theorem.
Since, due to that we simply increase the original height by 2, decreasing x by 2.
We can, however, say that ;
⇒ (x-2)² + y² = L²
Plugging 50 as y in, we get ;
⇒ (x-2)² + 50² = L².
Square rooting both sides, we get;
⇒ L = √((x-2)²+50²)
Thus, Equation for the length L of the rope as a function of the distance x from P to the ground is,
⇒ L = √((x-2)²+50²)
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The graph of f(x) = log x + 3 is the graph of
g(x) = log x translated 3 units a)up b)down c)left D) right
Answer:
A)up
Step-by-step explanation:
Given : f(x)=log x +3
g(x)= log x
To Find :
The graph of f(x) = log x + 3 is the graph of g(x) = log x translated 3 units
a)up
b)down
c)left
d) right
Solution:
Rule: f(x)→f(x)+b
So, the graph f(x) is translated up by b units
So, on comparing given f(x) with rule , we can say that the graph g(x) is translated up by 3 units
Thus option A is correct.
Hence The graph of f(x) = log x + 3 is the graph of g(x) = log x translated 3 units up
Is the line y = 3x – 7 parallel or perpendicular to 3x + 9y = 9? Explain your answer. Intro Done Go Left Go Right Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 Frame 2 10 of 10
Answer:
the answer is 6.
Step-by-step explanation:
on edge i got my question wrong and the answer was 6 <33.
Simplify b^4c^3d^4/b^3d^3
om class we learned that in 2010 the federal debt (in millions) was $13,561,623 and the population of the U.S. was 309 million. Use this information to compute the federal debt per capita in 2010.
Answer:
$43888.75
Step-by-step explanation:
We have been given that in 2010 the federal debt (in millions) was $13,561,623 and the population of the U.S. was 309 million.
[tex]\text{The federal debt per capita}=\frac{\text{Total debt}}{\text{Total population}}[/tex]
[tex]\text{The federal debt per capita}=\frac{\$13,561,623}{309}[/tex]
[tex]\text{The federal debt per capita}=\$43888.74757[/tex]
[tex]\text{The federal debt per capita}\approx \$43888.75[/tex]
Therefore, the federal debt per capita in 2010 was $43888.75.
What is .58 repeating as a fraction
If Dave drives at a steady speed of 50 mph, how long will it take him to drive 10 miles?
A homeowner plans to hang wallpaper on one wall of a bedroom that is 10 feet long
what is the answer to 72-(-58)-62
The answer to [tex]72 - (-58) - 62[/tex] is 68.
Understanding Double Negatives: When we subtract a negative number, it is equivalent to adding that number. Therefore, [tex]-(-58)[/tex] becomes [tex]+58[/tex].
So, the expression can be rewritten as:
[tex]72 + 58 - 62[/tex]
Performing the Addition: Now we add [tex]72[/tex] and [tex]58[/tex]:
[tex]72 + 58 = 130[/tex]
Performing the Final Subtraction: Next, we subtract [tex]62[/tex] from [tex]130[/tex]:
[tex]130 - 62 = 68[/tex]
Therefore, the final answer is [tex]68[/tex].
highest common factor of 92 and 42
The Greates Common Factor (GCF) is: 2
You can always share this solution
For football tryouts at the local school 12 coaches and 42 players will split into groups each group will have the same number of coaches and players what is the greatest number of groups that can play that can be formed how many coaches and players will be in each of these group
McDonald's has about 210,000 managers and each makes on average 39,000 dollars per year. How much money does McDonald's spend on managers each year?
How do you rewrite 4x24 using the distributive property
The expression 4 × 24 in distributive form will be 4 × ( 20 + 4 ) and the value of 96.
An expression 4x24 is given.
We have to write it using distributive property.
What is the distributive property of multiplication ?
The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
As per the question ;
Expression is 4x24.
Let's rewrite it in form of distributive property ;
4 × 24
= 4 × ( 20 + 4 )
So ,
It is now in form A ( B + C ) , where ; A = 4 , B = 20 and C = 4
⇒ 4 × ( 20 + 4 )
= 80 + 16
= 96
Thus , the expression 4 × 24 in distributive form will be 4 × ( 20 + 4 ) and the value of 96.
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For student spent $12 on school lunch at this rate find the amount 10 students would spend on the same school lunch?
in a mayoral election Jane received 213 more votes than Jack. If Jack received N votes how many votes did Jane receive?
is -8 a solution of -9f=64-f
The Changs updated their bedroom by purchasing a new lamp for $89.95 and a comforter set for $239.99. They paid 2007-03-04-00-00_files/i0120000.jpg% sales tax on their purchases. If the Changs paid $351.72 total, determine if they paid the correct amount. a. The Changs family paid $0.33 too much for their purchases. b. The Changs family paid $0.99 too much for their purchases. c. The Changs family paid $5.94 too much for their purchases. d. The Changs family paid the correct amount for their purchases
In this exercise we will use the knowledge of finance to calculate the total value of the purchase, we have:
Letter D
First, let's organize the information given in the statement as:
$89.95 = New Lamp $239.99 = Comforter 6.6% = Sales Tax $351.72 = Total amount the Chang's paidTaking the percentage over the total amount, we find:
[tex]6.6\% \ of \ 329.94\ is\ \$21.78\\Total= \$351.72[/tex]
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A money box contains only 10-cent and 20-cent coins. There are 27 coins with a total value of $3.60. How many coins of each? No. of 10-cent coins = No. of 20-cent coins =
Answer:
18, 20 cent and 36, 10 cent
Step-by-step explanation:
A baker uses 3/4 cup of honey in one of his cakes. There are 60 calories in 1/8 cup of honey. How many cups of honey will the baker use for 15 cakes.
Jeff prepares meals in the home of his customers. His fixed cost for transportation and supplies is $14.50. The labor and groceries needed for each family meal is $8.80, so the expense function is E=5.7q +8.8
True or false?
The formula for expense is given as:
E = V q + F
where, E = expense, V = variable cost, F = fixed cost
Therefore the equation should be:
E = 8.8 q + 14.50
So the answer is “False”
how many gallons of 80% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 70% antifreeze? use the six step method
To get a mixture that is 70% antifreeze, you would need 600 gallons of 80% antifreeze solution mixed with 100 gallons of 10% antifreeze solution.
Explanation:To solve this problem, we will use the six step method. Let's assign variables to our unknown quantities:
Let x be the number of gallons of 80% antifreeze solution.Now we can set up the equation using the information given:
0.8x + 0.1(100) = 0.7(100 + x)Simplifying the equation:
0.8x + 10 = 70 + 0.7x0.8x - 0.7x = 70 - 100.1x = 60x = 600Therefore, you would need 600 gallons of the 80% antifreeze solution to mix with 100 gallons of the 10% antifreeze solution to get a mixture that is 70% antifreeze.
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How would you write the name of a segment differently than the name of a line
Segments and lines can be named using the letters that represent the points on them, such as AB or line AB.
Explanation:In geometry, segments and lines are fundamental elements. A line is an infinite set of points extending in opposite directions, while a segment is a finite portion of a line with two distinct endpoints. These concepts are essential for understanding geometric shapes, angles, and spatial relationships in mathematics.
In mathematics, the name of a segment and the name of a line can be written differently by using the letters that represent the points on the segment or the line. For example, a segment between points A and B can be written as AB, while a line passing through points A and B can be written as line AB or simply AB. It is important to note that in both cases, the order of the points does not matter, as AB is the same as BA.
If decking cost $5.75 per square feet, how much would it cost to build a deck that is 22 feet by 18.5 feet
It would cost $2338.75 to build a deck that is 22 feet by 18.5 feet at a rate of $5.75 per square foot.
To calculate the cost of building a deck, we need to find the total area of the deck and then multiply it by the cost per square foot.
The area of a rectangle (deck) is given by the formula:
Area = length * width
Given that the deck has a length of 22 feet and a width of 18.5 feet, we can calculate the total area:
Area = 22 feet * 18.5 feet
Area = 407 square feet
Now, to find the total cost of building the deck, we multiply the area by the cost per square foot:
Total cost = Area * Cost per square foot
Total cost = 407 square feet * $5.75/square foot
Total cost = $2338.75
So, it would cost $2338.75 to build a deck that is 22 feet by 18.5 feet at a rate of $5.75 per square foot.
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When you subtract one negative integer from another,will your answer be greater than or less than the integer you started with.
Object a has less thermal energy than object b but heat flows from object a to object begat conditions make this possible
what is -2/3 - (1 1/3)
describe a situation in which a formula could be used more easily if it were rearranged. Include the formula in your description.
Which expression is equivalent to 2^4 ⋅ 2^−7?
The expression 2^4 \u00b7 2^{-7} simplifies to 2^{-3}, which is the same as 1/2^3 or 1/8.
Explanation:The expression 2^4 \u00b7 2^{-7} can be simplified using the properties of exponents, specifically the law that states when multiplying expressions with the same base, you add the exponents. Here, we are multiplying 2 raised to the power of 4 with 2 raised to the power of -7. Therefore, we add the exponents 4 and -7 together to get 2^{4-7} = 2^{-3}.
To simplify further, remember that a negative exponent indicates the reciprocal of the base raised to the positive of that exponent. Hence, 2^{-3} = 1/2^3 = 1/8. Therefore, 2^4 \u00b7 2^{-7} simplifies to 1/8.
a pro-evolution advocate wants to estimate the percentage of people who favor teaching only evolution in schools. She conducts a nationwide survey of 1980 randomly selected adults 18 years and older. The interviewer asks the respondents, "Do you favor promoting science by teaching only evolution in schools?" Which type of bias is this?
The type of bias in the questionnaire is question wording bias or survey question bias, influenced by the way the question is phrased to imply evolution being synonymous with promoting science, potentially leading respondents to answer in line with what they perceive to be the socially desirable response.
The type of bias present in the questionnaire regarding teaching only evolution in schools is an example of question wording bias or survey question bias. When the interviewer asks respondents if they favor promoting science by teaching only evolution, the question implies that evolution is synonymous with science and that alternative perspectives are not scientific. This phrasing can lead respondents to answer in a manner that aligns with what they perceive as the socially desirable response, rather than their true beliefs, which can also be similar to the concept of social desirability bias.
Additionally, using the phrase promoting science might influence the respondents' answers because it frames the question in a way that one answer appears more 'pro-science' than the other, potentially leading to an inflated percentage of respondents in favor of teaching only evolution in schools. This kind of bias prevents the collection of accurate data regarding the population's true stance on the issue being surveyed.