2-2+5+1-3*55+12-33*98​

Let's assume the cost of one package of chicken is represented by 'C' and the cost of one case of barbecue sauce is represented by 'B'.

From the given information, we can form the following equations:

Equation 1: 3C + 4B = 40 (Three packages of chicken and four cases of barbecue sauce cost $40)

Equation 2: 5C + 2B = 34 (Five packages of chicken and two cases of barbecue sauce cost $34)

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using the elimination method. Multiply Equation 1 by 5 and Equation 2 by 3 to make the coefficients of 'C' in both equations equal:

5 * (3C + 4B) = 5 * 40

3 * (5C + 2B) = 3 * 34

This gives us:

15C + 20B = 200

15C + 6B = 102

Now, subtract the second equation from the first equation:

(15C + 20B) - (15C + 6B) = 200 - 102

15C - 15C + 20B - 6B = 98

14B = 98

B = 98 / 14

B = 7

Substituting the value of B back into Equation 1:

3C + 4(7) = 40

3C + 28 = 40

3C = 40 - 28

3C = 12

C = 12 / 3

C = 4

Therefore, the cost of one package of chicken is $4, and the cost of one case of barbecue sauce is $7.

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For this we can use an equation of y=mx+b, b will equal what she started with, and m will be how much she saves each week

Using this, we now can use the equation Y=15x+30, y equals the total she has saved, and x equals the weeks.

You should be able to use this equation to solve the rest now!

The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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Answer:

10w+6 is the difference between the two areas

Step-by-step explanation:

for the old room:

l=2w

wich mean

 Area_old=l*w=2w*w=2w²

for the new room:

L=l+2 since l=2w => L=2w+2

W=w+4

so

Area_new=L*W=(w+4)*(2w+2)= 2w² +10w+6

the difference is :

Area_new - Area_old= 10w+6

Answer:

It should be 80% Hope this helps! ^^

The total surface area of the pyramid is: 208.88 m²

The surface area of the pyramid is simply the sum of the areas of all the given surfaces.

Formula for the area of a triangle is:

Area = ¹/₂bh

where:

b is base

h is height

Area of four side triangles = 4(¹/₂ * 8 * 12) = 192 m²

Using Pythagoras theorem, the height of the base triangle is:

x = 4.22

Area of base = ¹/₂ * 8 * 4.22 = 16.88 m²

Total surface area = 192 + 16.88

= 208.88 m²

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Answer:

We can use FOIL to solve this:

F - First

O - Outer

I - Inner

L - Last

\( = (x \times x)+(x \times - 7)+(3 \times x)+(3 \times - 7)\)

\( = {x}^{2} + - 7x + 3x - 21\)

\( = {x}^{2} - 4x - 21\)

Answer:

\(x^2-4x-21\)

Step-by-step explanation:

\(\left(x+3\right)\left(x-7\right)\)

Apply FOIL method:-

\(\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\)

\(\left(x+3\right)\left(x-7\right)\)

\(xx+x\left(-7\right)+3x+3\left(-7\right)\)

\(=x^2-4x-21\)

OAmalOHopeO

Answer:

3

Step-by-step explanation:

72÷8=9

3×y=9

3=y

I hope this helps

Answer:

The choice B.

\(f(x) ^{ - 1} = 7 - 21x\)

I hope I helped you^_^

There are two terms in the given expression 5xy²+ 35xy².

What is meant by term?

Terms comprise expressions. A term may be a constant, a variable, or a combination of variables and constants.

What is an example of a term?

It could be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase. Single-word examples: A single phrase is 3x.

There are two terms in the equation 5xyA ^2 + 35xyA^2 that is separated by an arithmetic operator +.

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Answer:

  (a)  $810.45

Step-by-step explanation:

You want the value of an investment of $300 earning 5% interest compounded quarterly for 20 years.

The compound interest formula tells you the value is ...

  A = P(1 +r/n)^(nt)

where P = 300, r = 0.05, n = 4, t = 20.

Using the given parameters in the given equation, you find the account value to be ...

  A = $300(1 +0.05/4)^(4·20) ≈ $810.45

__

Additional comment

The "rule of 72" tells you the account value will approximately double in a number of years equal to 72 divided by the interest rate percentage: 72/5 = 14.4 years. After 20 years, it will be worth more than that doubled amount, $600. This only leaves one reasonable answer choice.

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Answer:

The range is greater than or equal to -3

Step-by-step explanation:

The range is y.

At y  = -6, x doesn't have values.

At y = -3, x stops; therefore, y is greater or equal to -3.

At y = 2, x has values.

Answer:

3x - 18

Step-by-step explanation:

There are 55,440 possible 5-permutations of 11 distinct objects.

There are 55 5-permutations of 11 distinct objects.

To find the number of 5-permutations of 11 distinct objects, you need to use the formula for permutations, which is n!/(n-r)!, where n represents the total number of objects and r represents the number of objects to be arranged.

In this case, n = 11 (total number of distinct objects) and r = 5 (number of objects to be arranged).

Calculate (n-r)!
(11-5)! = 6!

Calculate 6!
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Calculate n!
11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 39,916,800

Divide n! by (n-r)!
39,916,800 ÷ 720 = 55,440

So, there are 55,440 possible 5-permutations of 11 distinct objects.

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There are a few different ways to approach this question, but one possible explanation is based on the fact that the sine function is periodic, meaning it repeats itself over certain intervals.

The sine function has a period of 2π, which means that sin(x + 2π) = sin(x) for any value of x.Now, let's consider the interval [-2, 2] and imagine that we want to evaluate sin(x) for some value of x outside of this interval. Without loss of generality, suppose that x &gt; 2 (similar arguments can be made for x &lt; -2). Then, we can write x as x = 2πn + y, where n is some integer and y is a number in the interval [0, 2π) that represents the "extra" amount beyond the interval of [-2, 2]. (Note that this decomposition is possible because the period of the sine function is 2π.)

Now, we can use the fact that sin(x + 2π) = sin(x) to rewrite sin(x) as sin(2πn + y) = sin(y). Since y is in the interval [0, 2π), we can evaluate sin(y) using any method that works for that interval (e.g., a lookup table, a series expansion, a graph, etc.). In other words, we can always "wrap" any value of x outside of [-2, 2] into the interval [0, 2π) using the periodicity of the sine function, and then evaluate sin(x) for that "wrapped" value.

Now, why did we choose the interval [-2, 2] in particular? One reason is that this interval is convenient for many practical purposes, such as approximating the sine function using polynomial or rational functions (e.g., Taylor series, Chebyshev polynomials, Padé approximants, etc.). These approximations often work best near the origin (i.e., when x is close to 0), and the interval [-2, 2] contains the origin while still being small enough to be computationally tractable.

Another reason is that many real-world applications that involve trigonometric functions (e.g., physics, engineering, statistics, etc.) often involve angles that are small enough to be within the interval [-2, 2] (e.g., angles in degrees or radians that are less than or equal to 180 degrees or π radians). In these cases, evaluating sin(x) within the interval [-2, 2] is often sufficient for practical purposes.

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Answer:

B. 6x + 8y = z , x represents the calzones sold; y represents grinders sold; z represents total sales.

Answer:

22.5 mins

Step-by-step explanation:

To find what that video's length must be, subtract the previous videos' lengths from the requirement, 5 hours. (x is the video length of her fourth video)

7/8 + 1 1/4 + 2 1/2 + x = 5

To make adding these fractions easier, find a common denominator.

7/8 + 1 2/8 + 2 4/8 + x = 5

4 5/8 + x = 5

x = 3/8, or 22.5 minutes.

Answer:

\(\frac{3}{8} \text{ hours.}\)

Step-by-step explanation:

Her first three videos totalled up to

\(\frac{7}{8} + 1\frac{1}{4} + 2\frac{1}{2}\\=\frac{7}{8} + \frac{5}{4} + \frac{5}{2}\\=\frac{7}{8} + \frac{5}{4} \cdot \frac{2}{2} + \frac{5}{2} \cdot \frac{4}{4}\\=\frac{7}{8} + \frac{10}{8} + \frac{20}{8}\\=\frac{7+10+20}{8}\\=\frac{37}{8}\)hours. To meet the \(5 = \frac{40}{8}\) hour goal the shortest fouth video she can make is \(\frac{40}{8} - \frac{37}{8} = \frac{3}{8}\) hours, because if the fourth video was any shorter, she'd end up with less than \(\frac{37}{8} + \frac{3}{8} = \frac{40}{8} = 5\) hours in total (this is called a proof by contradiction). We are now done.

The system of linear equations that can be formed to find x and y is 3x + 2y = 15.12 and 2x + 4y = 19.36. Then one can of chili costs $2.37 and one jar of salsa costs $4.005.

Let us consider  x being  the cost of one can of chili and y be the cost of one jar of salsa.
Then we can write two equations
3x + 2y = 15.12
2x + 4y = 19.36

We can multiply the first linear equation by 2 and subtract it from the second  linear equation in order to  eliminate x
(2x + 4y = 19.36) - 2(3x + 2y = 15.12)
= -4x + 0y
= -9.48

Applying Simplification to this equation
-4x = -9.48
Dividing both sides by -4 gives us:
x = 2.37

Now we can place this value of x into either of the original equations to find y
3(2.37) + 2y = 15.12
7.11 + 2y = 15.12
Subtracting 7.11 from both sides
2y = 8.01
Dividing both sides by 2
y = 4.005
Then, one can of chili costs $2.37 and one jar of salsa costs $4.005.

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Answer:

B- The volume of the basketball when the radius is r

Step-by-step explanation:

I took the 10 question test

Answer:

b

Step-by-step explanation:

b

The solution to the system of equations is d = 300m, which means that after Jada starts, both Hasina and Jada will be 300m away from home.

The solution to the system of equations is d = 300m. This means that after Jada starts, both Hasina and Jada will be 300m away from home. This is because the equation for Hasina states that she is 300m + 1500m away from home. Since Jada is starting second, she will only be traveling 300m from home. Therefore, the solution of the system of equations is d = 300m.

To solve the system of equations, we can use substitution. First, we can substitute 300m for d in Jada's equation. This gives us 300m = 300m, which is a true statement. We can then substitute this value for d in Hasina's equation, which gives us 300m + 1500m = 300m. To solve for m, we can subtract 1500m from both sides, giving us 0 = -1500m. To isolate m on one side, we can divide both sides by -1500, giving us -1 = m. This means that after Jada starts, both Hasina and Jada are 300m away from home.

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Answer:

1440°

Step-by-step explanation:

Each exterior angle of a 10 sided regular polygon =360/10=36°  

Each interior angle = 180°-36° =144°.  

Sum of all interior angles = 144°×10. = 1440°.

Answer:

Step-by-step explanation:

if the ant travels 980 every 5 minutes

980/5=196 inch/min

in 7 min

196*7=1372 inches

Answer:

Step-by-step explanation:

X axis intercept (y=0)

3x+2(0)=5

3x=5

x=5/3

Y axis intercept (x=0)

3(0)+2y=5

2y=5

y=5/2

so, the interception points are: (5/3,0) and (5/2,0)

The average is 3.71, range is 57, median is 7, mode is bimodal (3 and 50), and the sample standard deviation is 26.93.

The given ungrouped data is: 3.0, 7.0, 3.0, 5.0, 50, 50, and 60 minutes.Average:Average can be calculated using the formula:Average = sum of all values/ total number of valuesAverage = (3.0 + 7.0 + 3.0 + 5.0 + 50 + 50 + 60)/7 = 26/7Therefore, the average is 3.71.Range:

Range is the difference between the highest and the lowest value.Range = Highest value - Lowest valueRange = 60 - 3.0 = 57Median:Median is the central value in the data when arranged in ascending or descending order.

Therefore, the given data arranged in ascending order is:3.0, 3.0, 5.0, 7.0, 50, 50, and 60There are 7 observations in the data set. The median is the fourth observation in the data set.The fourth observation is 7.0.Therefore, the median is 7.

Mode:Mode is the value which occurs most frequently in the data set.The given data set has two modes, 50 and 3. Therefore, the data set is bimodal.Sample standard deviation:Sample standard deviation can be calculated using the formula:S = √((∑(x-µ)²)/(n-1))where S is the sample standard deviation, x is the value, µ is the average of the values, and n is the total number of values.The value of µ = 3.71.

Using the above formula:S = √(((3-3.71)² + (7-3.71)² + (3-3.71)² + (5-3.71)² + (50-3.71)² + (50-3.71)² + (60-3.71)²)/(7-1))= √((4356.32)/6)= √(726.05)Therefore, the sample standard deviation is 26.93.Hence, the Annwert Average is 3.71, Range is 57, Med is 7 and the Mode is bimodal (3 and 50). The sample standard deviation is 26.93.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:

58

Step-by-step explanation:

x= points in 2nd game

x+8= points in 1st game

42= points in third game

x+x+8+42>150

2x+50>150

2x>100

Therefore x must be greater than 50.

50+8=58, which is the least amount of points in the second game.

Answer:

Answers below

Step-by-step explanation:

1. The value 550 represents the initial balance in the account, which means the account started with $550.

2. 528.28

425.00 x  2.7% x 9 = 103.275

Then we add 103.275 to the initial deposit of $425.00

425.00 + 103.275 = 528.275

Therefore the answer is $528.28

3. The answer for this one is  f(n) = 56 + 3(n − 1)

So, as we can see the first value is 56 and the common difference is 3 and the rule for the nth term is \(a_{n} =a_{1} +d(n-1)\)

Therefore, its 56 + 3(n − 1)

4. For this one we solve for r and using a calculator its r = 0.04

The value of r from the given equation is 0.04. Therefore, option A is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

1) The given equation is 687.5=550(1+0.05t)

Here, amount=$687.5, principal (initial balance)=$550 and rate of interest =0.05×100 =5%

So, the value 550 represents the initial balance in the account, which means the account started with $550.

2) Given that, principal=$425.00, time period=9 years and rate of interest=2.7%

We know that, S.I=(P×T×R)/100

= (425×9×2.7)/100

= 103.275

Amount=103.275+425

= 528.275

≈ $528.28

3) The given arithmetic sequence is 56, 59, 62, 65, 68,.…

Here, first term (a)=56 and common difference=59-56=3

We know that, general form of arithmetic sequence is aₙ=a+(n-1)d

Now, f(n)=56+(n-1)3

4) The given equation is 816=600(1+9r)

1+9r =816/600

1+9r =1.36

9r=0.36

r=0.04

The value of r from the given equation is 0.04. Therefore, option A is the correct answer.

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The probability that a person chosen at random has run a red light in the last year can be calculated by taking the number of people who said “yes” to running a red light and dividing it by the total number of people in the group.

For example, if 10 people said “yes” and 20 said “no”, the probability of a person chosen at random running a red light in the last year is 10/30, or 1/3.

The probability of an event happening is calculated using the formula:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

In this case, the favorable outcome is running a red light in the last year, and the total number of outcomes is the total number of people asked.

To calculate the probability, we take the number of people who said “yes” to running a red light in the last year and divide it by the total number of people in the group. In our example, 10/30 = 1/3, so the probability that a person chosen at random has run a red light in the last year is 1/3.

In conclusion, the probability of a person chosen at random having run a red light in the last year is calculated by taking the number of people who responded “yes” and dividing it by the total number of people in the group.

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