Henry is making a corn grits recipe that calls for 1/4 cup of corn grits for every 1/2 cup of water. How much water will he need if he uses 1 1/2 cups of corn grits?

Answer: x = 4

Step-by-step explanation:

[tex]\dfrac{3}{5}(10 + 5x) - \dfrac{1}{3}(6x + 3)=9[/tex]

[tex]\dfrac{3}{5}(10 + 5x)(15) - \dfrac{1}{3}(6x + 3)(15)=9(15)[/tex] multiplied by common denominator

3(10 + 5x)(3) - 1(6x + 3)(5) = 9(15)   reduced all fractions

90 + 45x - 30x - 15 = 135      distributed

15x + 75 = 135      simplified (added like terms)

15x = 60         subtracted 75 from both sides

  x = 4          divided 15 from both sides

[tex]\begin{array}{c|c}18&2\\9&3\\3&3\\1\end{array}\\\\18=\boxed2\cdot\boxed3\cdot\boxed3\\\\\begin{array}{c|c}72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\72=2\cdot2\cdot\boxed2\cdot\boxed3\cdot\boxed3\\\\GCF(18,\ 72)=\boxed2\cdot\boxed3\cdot\boxed3=\boxed{\boxed{18}}[/tex]

The greatest common factor of 18 and 72 can be found through prime factorization, by identifying the prime factors of each number, finding the common factors, and multiplying them together. In this case, the greatest common factor is 18.

To find the greatest common factor (GCF) of 18 and 72 through prime factorization, follow these steps:

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Answer:

hell have 120,000

Step-by-step explanation:

Answer:

2.3 degrees.      

Step-by-step explanation:

Please find the attachment.

We are told that an airplane must clear a 60-foot pole at the end of a runway 500 yards long.

Let us convert 500 yards to feet.

1 yard= 3 feet.

500 yards= 3*500 feet= 1500 feet.

We can see from our attachment pole and runway are in form of a right triangle. The pole is opposite to angle of elevation of plane and length of runway is adjacent.

Since tangent represents the relation between opposite and adjacent of right triangle, So we will use tangent to find angle of elevation that plane must ascend to clear the pole.  

[tex]tan(\theta)=\frac{60}{1500}[/tex]    

[tex]\theta=\tan^{-1}(\frac{60}{1500} )[/tex]

[tex]\theta=\tan^{-1}(0.04)[/tex]

[tex]\theta=2.290610042639[/tex]

Therefore, the airplane must ascend 2.3 degrees to clear the pole.

Put the values of x to the equation y = 2ˣ:

[tex]x=-1\to y=2^{-1}=\dfrac{1}{2}\to\left(-1,\ \dfrac{1}{2}\right)\\\\x=0\to y=2^0=1\to(0,\ 1)\\\\x=1\to y=2^1=2\to(1,\ 2)\\\\x=2\to y=2^2=4\to(2,\ 4)\\\\x=3\to y=2^3=8\to(3,\ 8)\\\\x=4\to y=2^4=16\to (4,\ 16)[/tex]

Answer:

[tex]\left\{\left(-1,\ \dfrac{1}{2}\right);\ (0,\ 1);\ (1,\ 2);\ (2,\ 4);\ (3,\ 8);\ (4,\ 16)\right\}[/tex]

Answer:

a=3.75 un., b=11.25 un.

[tex]x=7.5\ un.[/tex]

[tex]y=\dfrac{15\sqrt{3}}{4}\ un.[/tex]

[tex]z=\dfrac{15\sqrt{3}}{2}\ un.[/tex]

Step-by-step explanation:

Given triangle is special 30°-60°-90° right triangle. The leg that is opposite to the angle of measure 30° is always equal to half of the hypotenuse. The hypotenuse is of length 15 units, the leg that is opposite to the 30° angle is leg with length of x units, then

[tex]x=\dfrac{15}{2}=7.5\ un.[/tex]

In right triangle with hypotenuse x and legs y and a, angle opposite to the leg a is 30°, then

[tex]a=\dfrac{x}{2}=\dfrac{7.5}{2}=3.75\ un.[/tex]

and

[tex]b=15-a=15-3.75=11.25\ un.[/tex]

By the Pythagorean theorem,

[tex]x^2=y^2+a^2,\\ \\7.5^2=3.75^2+y^2,\\ \\y^2=\left(\dfrac{15}{2}\right)^2-\left(\dfrac{15}{4}\right)^2=\dfrac{225}{4}-\dfrac{225}{16}=\dfrac{675}{16},\\ \\y=\dfrac{15\sqrt{3}}{4}\ un.[/tex]

In right triangle with legs y and b and hypotenuse z, leg y is opposite to 30° angle, then

[tex]z=2y=\dfrac{15\sqrt{3}}{2}\ un.[/tex]

Answer:

[tex]a=3.75[/tex]

Step-by-step explanation:

The hypotenuse of the large triangle is 15.

We can see that the side opposite of 30° angle is [tex]x[/tex]

Trigonometric ratio of SINE relates opposite and hypotenuse.

Thus we can write and cross multiply and solve:

[tex]sin(A)=\frac{Opposite}{Hypotenuse}\\sin(30)=\frac{x}{15}\\x=15*sin(30)=7.5[/tex]

Now if you see the smallest triangle, [tex]a[/tex] is the adjacent side and [tex]x[/tex] becomes the hypotenuse of this triangle.

Trigonometric ratio of COSINE relates adjacent and hypotenuse.

Thus we can write and cross multiply and solve:

[tex]cos(A)=\frac{Adjacent}{Hypotenuse}\\cos(60)=\frac{a}{7.5}\\a=7.5*cos(60)=3.75[/tex]

Thus [tex]a=3.75[/tex]

Answer: c is less than zero (third choice)

The parent nth root function (n is some odd number) will look like this sideways S shape, or look like a rotated cubic curve shape. The vertical flat part of the nth root is normally at (0,0); however, it has been shifted down and to the left. Because it has been shifted down, this means c must be negative. The 'c' handles the up and down shifting, depending whether its positive or negative.

Final answer:

The question pertains to the Mathematics subject, specifically within the college-level coursework of precalculus and calculus, with a focus on problem-solving, series expansions, and statistical analysis.

Explanation:

The subject of the question provided falls under the category of Mathematics since it includes discussions of precalculus class scores, calculus problems, concepts of slopes, and statistical analysis regarding the pass rates of calculus courses. The given question pertains at the college level, addressing issues found in a first-year Calculus course (Math 1A and Math 1B). The precalculus scores are likely used to determine statistical measures, such as the mean or median of the data. Problem-solving suggestions hint at understanding mathematical functions and their power series expansions, which are topics covered in calculus. Strategies for solving integrated concept problems involve identifying relevant mathematical principles and applying them correctly.

The issue with the data from precalculus scores and calculus pass rates suggests application of statistical analysis and highlights the importance of accommodation for various mathematical representations, which could include analytical techniques.

In the number game that Valerie and Robbie are playing, based on Valerie's clues, the number she is thinking of can be determined using a mathematical equation: x/4 + 5 - 6 = 6. Solving this equation step-by-step, the number Valerie is thinking of is 28.

In the given scenario, Valerie and Robbie are playing a number game. Valerie tells Robbie that she's thinking of a number which, when divided by 4, then added to 5, and subtracted by 6, equals to 6. This can be translated into a mathematical equation:

x/4 + 5 - 6 = 6

We can simplify this step-by-step. First, we can combine the constants:

x/4 -1 = 6

Next, add 1 to both sides to isolate x/4 on the left:

x/4 = 7

Finally, to find x, multiply both sides by 4:

x = 28

So, the number that Valerie is thinking of is 28.

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By using the simple addition operation, the total number of cups of coffee sold in the coffee shop, counting espressos, cappuccinos, and lattes, is 8,594 cups.

To find the total number of cups of coffee sold, we should add up the number of espressos, cappuccinos, and lattes. This principle is known as simple summation or addition operation in mathematics. As per the numbers given:

When we add these together, we get the total cups of coffee sold as:

1627 (Espressos) + 2741 (Cappuccinos) + 4226 (Lattes) = 8594 cups of coffee in total

So, the coffee shop has sold a total of 8594 cups of coffee.

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Answer:

20

Step-by-step explanation:

Answer:

the father is 40

Step-by-step explanation:

Answer:

35 words per minute

Step-by-step explanation:

To find the unit rate, we divide the number of words  by the number of minutes

70/2

35 words per minute

The unit rate of 70 words per 2 minutes is found by dividing the total words by the minutes, resulting in a unit rate of 35 words per minute.

To find the unit rate, we calculate the number of words that can be written or read per unit of time, which is usually one minute. Given 70 words per 2 minutes, we divide the number of words by the number of minutes to find the unit rate.

Step 1: Divide 70 by 2 to find the number of words per minute.

70 words / 2 minutes = 35 words per minute.

Therefore, the unit rate is 35 words per minute.

Answer:

Option C) 2

Step-by-step explanation:

We are given the following information in the question:

[tex]\displaystyle\frac{a}{b} = 2[/tex]

We have to find the value of [tex]\displaystyle\frac{4b}{a}[/tex].

The solving can be done in the following manner:

[tex]\displaystyle\frac{a}{b} = 2\\\\\RIghtarrow \frac{b}{a} = \frac{1}{2}\\\\\text{Multiplyimg both sides by 4}\\\\4\times \frac{b}{a} =4\times \frac{1}{2}\\\\\frac{4 b}{a} = \frac{4}{2} = 2[/tex]

Option C) 2 is the correct answer.

In the given case, If a/b = 2, the value of 4b/a is 4. Option C is correct.

The answer is C.

The value of an expression in mathematics refers to the result obtained when you perform the specified operations or calculations with the given variables, numbers, or mathematical symbols.

Expressions can be simple or complex and may involve addition, subtraction, multiplication, division, exponentiation, and various mathematical functions.

We are given that a/b = 2.

Solving for b, we get b = a/2.

Substituting this into 4b/a, we get:

4b/a = 4(a/2)/a = 2a/a = 2

Therefore, the value of 4b/a is 2.

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Answer:

see explanation

Step-by-step explanation:

given the geometric sequence then the n th term rule is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] . [tex]r^{n-1}[/tex]

where r is the common ratio and [tex]a_{1}[/tex] the first term

here r = [tex]\frac{192}{48}[/tex] = [tex]\frac{48}{12}[/tex] = 4 and [tex]a_{1}[/tex] = 3, hence

[tex]a_{n}[/tex] = 3 . [tex]4^{n-1}[/tex] ← third option

Answer:

8

Step-by-step explanation:

So solving for x, 1/4x=2. So x=8

Option 2 .The statement that is NOT TRUE is "A is the complement of B"

Let’s analyze each option:

1. A and B are joint sets: Sets A and B are not joint sets (disjoint sets) because they have common elements. Specifically, both sets contain the elements 2, 3, and 4.

2. A is the complement of B: The complement of a set B relative to A would be the set of elements in A that are not in B The complement of B in A is {1, 5\}, not equal to A Therefore, A is not the complement of B.

3. B ⊆ A: Set B = {2, 3, 4} is indeed a subset of A = {1, 2, 3, 4, 5} , meaning all elements of B are contained in A.

4. Ø ⊆ A: The empty set Ø is a subset of any set, including A

5. A ⊆ B: Set A = {1, 2, 3, 4, 5} is not a subset of B = {2, 3, 4}, since A contains elements (1 and 5) that are not in B.

Complete question

Answer:

Product A.

Step-by-step explanation:

The unit price of product A is $1.36/8oz = $0.17/oz.

The unit price of product B is $3.20/16oz = $0.20/oz.

Answer:

not 100% about this answer but I think it is the 8oz bottle

Step-by-step explanation:

take $1.36 and divide it by 8 which gives you .17 which is 17 cents per oz now do the same thing for the 16 oz so take $3.20 and divide it by 16 and you get .2 which is 20 cents per oz so the 8oz has the lowest unit price of the two!

Answer:

The students who never want to travel to another country Y= 7S/10 -40

Step-by-step explanation:

Let's assume the number of students who have never been to another country be Y.

Then as per question 30% percent students have traveled out of the country.

Therefore 70% students out of S have never traveled to another country.

Equation becomes like Y= S×70÷100

                                       Y = 7S/10

Now it is stated that 40 students of the students who have never been out of the country had eventually travel to another country.

Therefore the equation will be Y = 7S/10-40

Answer:

The number of questions in sixth assignment must be less than or equal to 28.

Step-by-step explanation:

The number of questions in first five assignments are 11,10,13,14 and 14.

It is given that Mrs hawk assigns her students an average of no more than 15 questions on each assignment. Therefore the average of six assignments is less than or equal to 15 questions.

Let the number of questions in sixth assignment be x

[tex]\text{Average}=\frac{\text{Sum of observations}}{\text{Number of observations}}[/tex]

Average of six assignments are

[tex]A=\frac{11+10+13+14+14+x}{6}[/tex]

[tex]A=\frac{62+x}{6}[/tex]

Since the average of questions is no more than 15, therefore

[tex]A\leq 15[/tex]

[tex]\frac{62+x}{6}\leq 15[/tex]

[tex]62+x\leq 90[/tex]

[tex]x\leq 28[/tex]

Therefore the number of questions in sixth assignment must be less than or equal to 28.

The distributive property: a(b + c) = ab + ac.

Answer:

d 15+40=5(3+8)

Step-by-step explanation:

Answer: with 11 miles, it can travel 220 miles

Answer:

1) 11h - 25

2) 8

3) C

Step-by-step explanation:

1) 5h-9+-16+6h

+ and - together makes -

5h - 9 - 16 + 6h

Arrange the like terms together

5h + 6h - 9 - 16

= 11h - (9+16)

= 11h - 25

2) 4x+4=9x-36

Subtract 4x from both sides

4x+4-4x = 9x-36-4x

Cancl out 4x and -4x from the left side

4 = 9x - 4x -36

=> 4 = 5x -36

Add 36 to both sides

4+36 = 5x -36 + 36

Cancel out -36 and +36 from the right side

=> 40 = 5x

Flip both the sides of the equation

5x = 40

Dividing both sides by 5

[tex]\frac{5x}{5} = \frac{40}{5}[/tex]

Cancel out the 5's on the top and bottom of the left side

x = 8

3) 7x+5 = 4x+5+3x

Arrange the like terms together on the right side

7x+5 = 4x+3x+5

=> 7x+5 = 7x+5

Subtract 5 from both sides

7x+5-5 = 7x+5-5

Cancel out +5 and -5 on both the sides

7x = 7x

Divide both sides by 7

[tex]\frac{7x}{7} = \frac{7x}{7}[/tex]

Cancel out the 7's from the top and bottom of both sides

x = x

which can be true for infinite value of x like 1=1, 2=2, 3=3,.............

Answer:

you will save 18 dollars

Step-by-step explanation:

Answer:

You would save $18

And your final cost would be $102

Step-by-step explanation:

Answer:

No you can't because just like multiplication, you cant divide anything by zero.

Step-by-step explanation:

You must evaluate the function f first.  Division by 0 is undefined.

Therefore, The composition cannot be evaluated.

Answer:

sample answer on edg2020

Step-by-step explanation:

To evaluate the composition, you need to find the value of function f first. But, f(0) is 1 over 0, and division by 0 is undefined. Therefore, you cannot find the value of the composition.

Answer:

1.61904761905

Step-by-step explanation:

-5 2/3 is equal to -17/3. We then multiply the two fractions: -2/7 *-17/3, the answer is 1.61904761905 as a decimal or 34/21( or 1 13/21).

Hope this helps! <3

The earnings for selling the same number of each type of sandwich, considering both Turkey and Ham with Pretzel Roll and Bagel options, amount to $48. This is derived from a simplified expression of $29.10x, factored by 11, indicating a total revenue of $4.30 per sandwich.

Earnings for Selling Sandwiches

1: Identify the Given Information

We have two types of sandwiches: Turkey and Ham.

Each type comes in two types of bread: Pretzel Roll and Bagel.

Prices are provided for each combination:

Turkey Pretzel: $2.25

Turkey Bagel: $2.00

Ham Pretzel: $1.55

Ham Bagel: $1.30

2: Represent the Number of Sandwiches with a Variable

Let x represent the number of each type of sandwich sold (both Turkey and Ham, regardless of bread).

3: Calculate Earnings for Each Type of Sandwich

Turkey Sandwich: $11 (given price) * x (number sold) = $11x

Ham Sandwich: $11 (given price) * x (number sold) = $11x

Step 4: Calculate Earnings for Each Bread Type (excluding overlapping information)

Pretzel Roll: (Earnings from Turkey Pretzel + Earnings from Ham Pretzel) = ($2.25 * x) + ($1.55 * x) = $3.80x

Bagel: (Earnings from Turkey Bagel + Earnings from Ham Bagel) = ($2.00 * x) + ($1.30 * x) = $3.30x

5: Combine Earnings for Total Revenue

Total Earnings = Earnings from Turkey Sandwiches + Earnings from Ham Sandwiches + Earnings from Pretzel Rolls + Earnings from Bagels

Total Earnings = $11x + $11x + $3.80x + $3.30x = $29.10x

6: Simplify the Expression

Total Earnings = $29.10x

Since we are selling the same number of each type of sandwich, 11 is a common factor in all four terms.

We can factor out 11 to obtain:

Total Earnings = 11 * ($2.65 + $1 + $0.35 + $0.30) = 11 * $4.30 = $48

Therefore, the earnings for selling the same number of each type of sandwich are $48.

Answer:

-2.4

Step-by-step explanation:

The difference between any two consecutive terms (following - preceding) is -2.4. The negative sign corresponds to the observation that the sequence is decreasing.

The common difference in an arithmetic sequence is the consistent difference between consecutive terms of the sequence. It's calculated by subtracting a term from its subsequent term. For example, in the sequence 3, 5, 7, 9, the common difference is 2.

In the field of mathematics, specifically in sequences, the common difference refers to the difference between consecutive terms in an arithmetic sequence. An arithmetic sequence is a list of numbers in which each term is obtained from the previous one by adding a fixed number.

To find the common difference, you simply subtract the second term from the third, or the first from the second. For instance, if your arithmetic sequence is 3, 5, 7, 9, the common difference would be 5-3 or 7-5, which both yield a common difference of 2.

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Answer:-5*5=-25

Step-by-step explanation: If -5=x, since 1=y, then plug it in to the equation to get -25

Answer:

(-1,1) got it right on plato :)

Answer:

The proportional

Step-by-step explanation:

Answer:

There are 25 students in Hannah's class.

Step-by-step explanation:

If 20 students in Hannah's class is 80% of the total amount of students, we can use a variable to figure out the total amount of students.

Let's say x is the total amount of students. We can use this equation to solve the problem:

[tex]20 = .8x[/tex]

This is saying 20 equals 80% (.8 when you move the decimal 2 times) of x, or the total amount of students. Let's solve.

20 = .8x

Divide by .8

25 = x

There are 25 students in Hannah's class.

Percentage of a number is the part of the number in every hundred. The total number of students in Hannah's class is 25.

Given information

Total number of students in Hannah's class voted for the pizza is 20.

The total percent of students in Hannah's class voted for the pizza is 80.

Percentage of a number is the part of the number in every hundred. A percentage of a number is the ratio expressed as fraction of hundred.

Suppose the total number of student in Hannah's class is x.

As total number of students in Hannah's class voted for the pizza is 20 and total percent of students in Hannah's class voted for the pizza is 80.

Therefore the the 80 percent of the total student of the class is equal to the number 20. The 80 percent of a number is 20 thus,

[tex]\begin{aligned}\\\dfrac{80}{100} \times x&=20\\\dfrac{4}{5} \times x&=20\\x&=\dfrac{20\times5}{4} \\x&=25\\\end[/tex]

Thus the total number of students in Hannah's class is 25.

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Answer:

an = -6+n

or

an = 1 + 7(n-1)

Step-by-step explanation:

a(1)=1 and a(n+1)=a(n)+7

The explicit formula is

an = a1+ d (n-1)

we know a1 =1

Looking at a(n+1)=a(n)+7

We are adding 7 each time so the common difference is +7

an = 1 + 7(n-1)

We can simplify this

an = 1 + 7n -7

an = -6+n

You can use either formula