Identify the Property of Operation that is being used.

3(a – 2) = 3a – 6

Question 1 options:

Distributive Property


Commutative Property


Identity Property


Associative Property
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(5 x 4) x 2 = 5 x (4 x 2)

Question 2 options:

Commutative Property


Distributive Property


Associative Property


Identity Property

-------------------------------
Simplify the expression.

9y + 6 – 7y - 3

Question 3 options:

-2y - 3


2y + 3


2y + 9


-2y + 9

-------------------------------

9y + 6 – 7y - 3

Question 3 options:

-2y - 3


2y + 3


2y + 9


-2y + 9

-------------------------------
a + b + 2a + 2b + 5 − b

Question 5 options:

3a + 2b + 5


3a + 4b + 5


2a + 4b + 5


2a + 2b + 5

The volume of the first and second solid shapes are 3014.4m³ and 360ft³ respectively.

The first shape comprises of a cone and a cylinder, and the volume is derived as follows:

volume of the cone = 1/3 × 3.14 × (8m)² × 5m

volume of the cone = 1004.8m³

volume of the cylinder = 3.14 × (8m)² × 0m

volume of the cylinder = 2009.6 m³

volume of the first solid shape = 1004.8m³ + 2009.6 m³

volume of the first solid shape = 3014.4m³

The second solid shape comprises of a trianglular prism and a cuboid

volume of the trianglular prism = base area × height

base area = 1/2 × 6ft × 4ft = 12ft²

volume of the trianglular prism = 12ft² × 6ft

volume of the trianglular prism = 72ft³

volume of the cuboid = 12ft × 6ft × 4ft

volume of the cuboid = 288ft³

volume of the second solid shape = 72ft³ + 288ft³

volume of the second solid shape = 360ft³

Therefore, the volume of the first and second solid shapes are 3014.4m³ and 360ft³ respectively.

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Answer:

2 terms

Step-by-step explanation:

2

Hope this helps :)))))

Answer:

thanks for tha points

Step-by-step explanation:

Answer:

The interest rate is 8% p.a.

Step-by-step explanation:

Simple interest changes by the same amount each year (per annum)

So in this case, it is $480 per year ($4800/10 years)

480/6000 = is 8%

The interest rate is 8% p.a.

Answer:

hey I hope it helps you

R=8%

Step-by-step explanation:

P=$6,000, T=10yrs and I=$4,800 and R=?

I=PRT/100

4800=6000xRx10/100

cross multiply

60000R=480000

divide both sides by 60000

R=8%

The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

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Answer:

2/5 or 0.4.

Step-by-step explanation:

6/15 = 2/5

The point at (60, 55) represents an item with an original price of $60 that is now being sold at a sale price of $55.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

We are given that;

The point at (60, 55)

Now,

This means that customers who enter the special discount code can save $5 on this particular item.

In general, the point (x, y) on the graph represents an item with an original price of x dollars that is being sold at a sale price of y dollars. The graph is showing how the sale price of items changes as the original price increases.

Therefore, by the graph the answer will be $60 and $55.

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Answer:

there should be value of there sum like

2x+3x=25

Answer:check my profile and answer my question

Step-by-step explanation:

plz

Total number of car repairing jobs is 28 cars

Number of operating hours = 8 hours

Number of total workstation = 7

Average automobile repair job = 2 hours

Total number of car repairing jobs

Total number of car repairing jobs = [Number of operating hours × Number of total workstation] / Average automobile repair job

Total number of car repairing jobs = [8 × 7] / 2

Total number of car repairing jobs = 56 / 2

Total number of car repairing jobs = 28 cars

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Answer:

Step-by-step explanation:

The original equation is \(121y''+110y'-24y=0\). We propose that the solution of this equations is of the form \( y = Ae^{rt}\). Then, by replacing the derivatives we get the following

\(121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)\)

Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that

\(121r^2+110r-24=0\)

Recall that the roots of a polynomial of the form \(ax^2+bx+c\) are given by the formula

\( x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}\)

In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions

\(r_1 = -\frac{12}{11}\)

\(r_2 = \frac{2}{11}\)

So, in this case, the general solution is \(y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}\)

a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations

\(c_1 + c_2 = 1\)

\(c_1\frac{-12}{11} + c_2\frac{2}{11} = 0\)(or equivalently \(c_2 = 6c_1\)

By replacing the second equation in the first one, we get \(7c_1 = 1 \) which implies that \( c_1 = \frac{1}{7}, c_2 = \frac{6}{7}\).

So \(y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}\)

b) By using y(0) =0 and y'(0)=1 we get the equations

\( c_1+c_2 =0\)

\(c_1\frac{-12}{11} + c_2\frac{2}{11} = 1\)(or equivalently \(-12c_1+2c_2 = 11\)

By solving this system, the solution is \(c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}\)

Then \(y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}\)

c)

The Wronskian of the solutions is calculated as the determinant of the following matrix

\(\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2\)

By plugging the values of \(y_1\) and

We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by

\(e^{\int -p(x) dx}\)

In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is

\(e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}\)

Note that this function is always positive, and thus, never zero. So \(y_1, y_2\) is a fundamental set of solutions.

Answer:

both of your answers are b

Step-by-step explanation:

20. difference means subtract

21. assosiative property has to deal with three numbers while communitive is 2 numbers

Answer:

10

Step-by-step explanation:

7+15/5

Answer:

10

Step-by-step explanation:

subsitute

7+15/5=10

The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:

A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.

A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.

A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.

A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.

B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.

B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.

Finally, performing the remaining operations:

(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.

(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.

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Answer:

C

Step-by-step explanation:

Notice how C is the only function that is quadratic. If you expand (2x-1)^2, you get 4x^2-4x+1. Since x is raised to the power of two, it isn't linear, but quadratic.

Answer:

C

Step-by-step explanation:

i used photomath and C was not the linear one!

Answer:

0.45

Step-by-step explanation:

Answer:

LB=12ft

Step-by-step explanation:

Answer:

The country's debt is $ 48,543.68 per person.

Step-by-step explanation:

Given that at the end of a year, the gross debt of a country stood at about $ 15 trillion, to determine this amount in dollars per person, assuming that the population of the country is about 309 million, the following calculation must be done:

15 trillion = 15,000,000,000,000

15,000,000,000,000 / 309,000,000 = X

15,000,000 / 309 = X

48,543.68 = X

Therefore, the country's debt is $ 48,543.68 per person.

Answer:

X=1.66666667 hope this hepled

Step-by-step explanation:

Answer: If 34% of the mixed fruit juice is apple juice, then 66% of it is a combination of other fruit juices. We can assume that the ratio of apple juice to other fruit juices remains the same in the ice cream and mixed fruit juice mixture.

Let the volume of ice cream in each batch be 3x litres and the volume of mixed fruit juice be 2x litres. Then the total volume of mixture in each batch is 5x litres.

If 34% of the mixed fruit juice is apple juice, then the volume of apple juice in each batch is 0.34 × 2x = 0.68x litres. The volume of other fruit juices in each batch is 2x − 0.68x = 1.32x litres.

The ratio of ice cream to mixed fruit juice is 3 : 2, so we have:

3x : 2x = ice cream : mixed fruit juice

Simplifying, we get:

ice cream = 1.5 × mixed fruit juice

Substituting the values we obtained earlier, we have:

3x = 1.5 × 2x

x = 0.75

Therefore, the volume of ice cream in each batch is 3x = 2.25 litres, and the volume of mixed fruit juice is 2x = 1.5 litres.

To make 1.5 litres of mixed fruit juice, we need 0.68 litres of apple juice and 0.82 litres of other fruit juices.

To make 12.5 litres of smoothies, we need 2.25 litres of ice cream and 10.25 litres of mixed fruit juice. Of this, 0.68 litres is apple juice and 9.57 litres is other fruit juices.

Therefore, to make 12.5 litres of smoothies, we need 0.68/1.5 × 12.5 = 5.67 litres of apple juice.

To make 51 litres of apple juice, we can make a maximum of 51/5.67 ≈ 9 batches of smoothies.

The fraction of the library's books are nonfiction biographies is 2/25.

This fraction here describes the quantities of books within the library which are nonfiction biographies. It is given below:

The fraction of the library's books are nonfiction biographies = Number of biographies × Number of nonfiction books at a library

= 1/5 × 2/5

= (1 × 2) / (5 × 5)

= 2/25

So therefore, the fraction of the library's books are nonfiction biographies is 2/25.

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It would be wiser for the couple to stay in the old apartment and save $1400.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation:

If they stay until the end of the lease, total money that will be paid out is $1000 x 6 = $6000,

If they leave, they'll have to forgo $1000.

If they move to their new apartment, they'll pay $900 x 6 = $5400

total expenditure if they move to the new place at the end of the six months period will be, the $1000 that will not be refunded back to them on the old apartment, plus this new $5600 for six month's rent in this new apartment, and that will be a total of $6400.

It would be wiser for the couple to stay in the old apartment and save $1400.

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The entire rectangle is 4 square units because the two triangles on the top put together makes the same shape as the square in the middle, which makes it 1 square unit. And the two bigger triangles on the bottom can create two squares if you break them apart and rearrange them again. So all of those shapes put together equals 4 square units.

G(8) = 40 + 5 - 24 - 4

45 - 28 = 17

G(8) = 17

Answer:

.85x and x-0.15x

Answer: 59

Step-by-step explanation:

Answer: For Y the rate of change is +4

For the rate of x its +5

Step-by-step explanation:

Answer:

Car Value Depreciation Graph

The graph that represents the value of the car, y, in dollars, after x years is the graph that starts at $8,000 on the y-axis and decreases at a steady rate of 25% each year on the x-axis. It would be the graph V.