I'm having trouble solving this:
Corry collects cube containers. She fills them with water and pours them into a rectangular prism. She was playing with them and discovered something interesting. She had three cube containers. One cube was 1 inch by 1 inch by 1 inch. A second cube was 2 inches by 2 inches by 2 inches and a third cube was 3 inches by 3inches by 3 inches.
She filled all three with water. Then Corry poured all three cubes into a rectangular prism filling it exactly! The rectangular prism has a square base with a side length (1+2+3 = 6) inches and the height is 1 inch.
Corry wonders whether she has found a pattern. Investigate using more cube containers to fill square base prisms with heights of 1 in. Describe any conjectures you discover.

Answer:

8 - (2/x

hope it is helpful

Answer:

Angle L= 53 degrees. Side ML = 4.521 and Side NL= 7.513

Step-by-step explanation:

A stem and leaf plot would best display the following data if you wanted to display the numbers which are outliers as well as the mean. Option C is the correct option.

A stem and leaf plot would be the best choice for displaying the given data if the goal is to show outliers as well as the mean. A stem and leaf plot is a simple and effective way to represent the data distribution while preserving the individual data points.

It organizes the data by separating the leading digit (stem) and the trailing digit (leaf). This plot allows for easy identification of outliers as they would be displayed separately from the main distribution. Additionally, the stem and leaf plot can include a line indicating the mean, providing a visual representation of its position relative to the data points.

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The question is -

Which would best display the following data if you wanted to display the numbers which are outliers as well as the mean?

[4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32]

A. Pie chart.

B. Bar graph.

C. Stem and leaf plot.

D. Venn diagram.

Answer:

4/3

Step-by-step explanation:

Answer:

The slope is 8/6 or 4/3

Step-by-step explanation:

rise over run

The bird will travel a distance of 3.25 meters before it can begin to swerve away from the object.

To calculate the distance the bird will travel before it can begin to swerve, we need to consider the bird's reaction time and its speed. The bird's reaction time is given as 0.25 seconds, and its speed is 13.0 m/s.

In 0.25 seconds, the bird will travel a distance equal to its speed multiplied by the reaction time:

Distance = Speed × Time

Distance = 13.0 m/s × 0.25 s

Distance = 3.25 meters

Therefore, the bird will travel 3.25 meters before it can start to swerve away from the object.

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The formula for the final velocity,\(v_{f}\) , in terms of initial velocity, vi, acceleration, a, and time, t is given by \(V_{f}=at+V_{i}\)

A =\((V_{f}-V_{i} )/t\)  You can put \(1\) under A and then cross multiply.

\(at =V_{f} -V_{i}\)

Get \(V_{f}\)  by adding  \(V_{i}\) in both sides of the equation.

\(at+V_{i} =V_{f}\)

                                                OR

The final speed \(V_{f}\) in terms of other parameters is given by the relation \(V_{f}\)\(=at+V_{i}\)

How to calculate the acceleration of an object?

Mathematically, acceleration is calculated using this formula:

\(a=(V_{f}-V_{i} )/t\)

Where:

Making \(V_{f}\) the subject of the formula, we have:

\(at =V_{f} -V_{i}\)

\(V_{f} =V_{i} +at\)

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Answer:

1. -3145

Step-by-step explanation:

I couldnt solve the other one because they don't have a equal sign. Something like 28x-43= ?

Answer:

-37x85= -3145
28x-43=-1204
-53x-98=5194

those are ur answers

Step-by-step explanation:

The 3.51% compounded quarterly investment is the better investment in terms of higher returns.

We need to compare the effective rates of return for both options in order to determine which investment is superior.

A) For the 3.38% accumulated semiannually, we can work out the successful rate utilizing the equation:

The effective rate is as follows: Effective Rate = (1 + (Annual Interest Rate / Number of Compounding Periods))  Number of Compounding Periods - 1 Annual Interest Rate = 3.38 percent Number of Compounding Periods = 2 (since it is compounded semiannually) Effective Rate = (1 + (0.0338 / 2)) 2 - 1

The 3.38% compounded semiannual investment has an effective rate of approximately 3.59%, which is calculated as follows: Effective Rate = (1 + 0.0169)2 - 1 Effective Rate  0.0359385 or 3.59% (rounded to two decimal places).

B) We can use the same formula to determine the effective rate for the quarterly compound interest rate of 3.51 percent:

Since it is compounded quarterly, there are four compounding periods, and the annual interest rate is 3.51 percent. The effective rate is equal to (1 + (0.0351 / 4))4 - 1.

The compounded quarterly investment at 3.51% has an effective rate of approximately 3.53%, which is calculated as follows: Effective Rate = (1 + 0.008775)4 - 1 Effective Rate  0.0353157 or 3.53% (rounded to two decimal places).

When we look at the effective rates, we can see that the compounded quarterly investment with a rate of 3.51 percent has a slightly higher effective rate (3.53%) than the compounded semiannual investment with a rate of 3.38 percent (3.59%). Consequently, the higher-return investment at 3.51 percent compounded quarterly is superior.

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The zeros for the function f(x) = x(x − 4)(x + 2)^4 are x = 0, x = 4, and x = -2.

To find the zeros of the function f(x), we set each factor equal to zero and solve for x. Therefore, we have x = 0, x = 4, and x = -2 as the zeros.

The end behavior of the function can be determined by analyzing the highest power of x in the equation, which is x^6. Since the power of x is even, the graph of the function is symmetric about the y-axis.

As x approaches positive infinity, the value of x^6 increases without bound, resulting in f(x) approaching positive infinity.

Similarly, as x approaches negative infinity, x^6 also increases without bound, leading to f(x) approaching positive infinity.

In summary, the zeros for f(x) = x(x − 4)(x + 2)^4 are x = 0, x = 4, and x = -2. The end behavior of the function is that as x approaches positive or negative infinity, f(x) approaches positive infinity.

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The situation can be expressed in inequality as: 95x + 0.85y ≤ 500

On solving the maximum amount of miles that can be driven to stay under budget is 253

What is inequality?

If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.

For example, x > 3 (x should be greater than 3)

According to the given question:

Total amount to spend is restricted to $500

Let the number of days be x and extra miles covered be y

The car rental company charges $95 per day to rent the car and charges $0.85 per mile.

Therefore the situation van be expressed as:

95x + 0.85y ≤ 500

If the car is rent for 3 days then the maximum amount of miles that can be driven to stay under budget are

95(3) + 0.85y ≤ 500

285 + 0.85y ≤ 500

0.85y ≤ 215

y ≤ 253

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If we are told that ab=0, then we can infer that either a or b (or both) must be equal to 0.

This is because when the product of two numbers is 0, at least one of the numbers must be 0 according to the zero product property.

One of the most crucial concepts for pupils to understand in maths and science is the zero product property.

The greatest educators, mathematicians, and recognized scientists in the fields of physics and chemistry have worked with Vedantu to provide their insights on the subject.

Their suggestions helped us develop materials for your understanding that would make it simple for you to put these ideas into practice.

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The correct answer is option C which is 5(2a − 3) = (2a − 3) ⋅ 5 showing commutative property.

If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics.

a x b = b x a

So for the expression 5(2a − 3) = (2a − 3) ⋅ 5 suppose 5 is a and ( 2a - 3 ) is b so.

a x b = b x a

5(2a − 3) = (2a − 3) ⋅ 5

Therefore the correct answer is option C which is 5(2a − 3) = (2a − 3) ⋅ 5 showing commutative property.

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a.  The cardinality of the sample space is 30.

b. The cardinality of the event E ∪ F cannot be determined without additional information about the outcomes of the tournament.

a. There are 6 ways to choose the winner and 5 ways to choose the runner-up (as they can't be the same team).

Therefore, the cardinality of the sample space is n(S) = 6 x 5 = 30.

b. The cardinality of the event E is 5 (since the City Slickers can be runners-up in any of the 5 remaining teams).

The cardinality of the event F is 4 (since the Independent Wildcats cannot be the winners or runners-up).

The event E ∪ F is the event that either the City Slickers are runners-up, or the Independent Wildcats are neither the winners nor runners-up.

To find its cardinality, we add the cardinalities of E and F and subtract the cardinality of the intersection E ∩ F, which is the event that the City Slickers are runners-up and the Independent Wildcats are neither the winners nor runners-up.

The City Slickers cannot be both runners-up and winners, so this event has cardinality 0.

Therefore, n(E ∪ F) = n(E) + n(F) - n(E ∩ F) = 5 + 4 - 0 = 9.

There are 9 possible outcomes where either the City Slickers are runners-up, or the Independent Wildcats are neither the winners nor runners-up.

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The cardinality of a set refers to the number of elements within the set. In this case, the set is composed of the six teams participating in Urban University's hockey intramural tournament. Therefore, the cardinality of this set is six.

To find the cardinality, which is the number of possible outcomes, we need to determine the number of ways the winner and runner-up can be selected from the six teams participating in Urban University's hockey intramural tournament.
First, let's find the number of possibilities for the winner. There are 6 teams in total, so any of the 6 teams can be the winner. Now, for the runner-up position, we cannot have the same team as the winner. So, there are only 5 remaining teams to choose from for the runner-up.

To find the total number of outcomes, we multiply the possibilities for each position together:

Number of outcomes = (Number of possibilities for winner) x (Number of possibilities for runner-up)

Number of outcomes = 6 x 5

Number of outcomes = 30

So, the cardinality of the possible outcomes for the winner and runner-up in Urban University's hockey intramural tournament is 30.

In terms of the prizes, there will be awards given to the winner and the runner-up of the tournament. This means that the team that wins the tournament will be considered the "winner," and the team that comes in second place will be considered the "runner-up." These prizes may vary in their specifics, but they will likely be awarded to the top two teams in some form or another.
Overall, the cardinality of the set of teams is important to understand in order to know how many teams are participating in the tournament. Additionally, the terms "winner" and "runner-up" help to define the specific awards that will be given out at the end of the tournament.

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The discount rate raised to nth power.

NPV is defined as Net Present Value. It is mainly used in capital budgeting and investment planning for the purpose of analyzing the project profit. NPV is the difference between  the present value of cash inflows and the present value of cash outflows in a period of time. The occurrence of cashflows in a series at different times is termed as NPV. NPV is a measure widely used in finance and commercial real estate. It is used to help taking decisions in accounting calculation. The cashflow that is discounted can be termed as NPV.

A simple example for NPV is, If a security offers a series of cashflows with an NPV of $30,000 and an investor pays exactly $30,000 for it, then the  investor's, NPV is $0.

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Part A:  The amount of unearned interest is $3,225.

Part B: The amount needed to repay the loan using the Rule of 78 is $8,443.75.

Part C: To support our answers to Part A and Part B, the total interest that Christopher would have paid, which is 3,900$. the amount needed to repay the loan using the Rule of 78, which is $8,443.75.

What is an interest?

To determine the amount of unearned interest, we need to find out how much interest Christopher would have paid if he made all 24 payments.

First, we can calculate the total amount he would have paid if he made all 24 payments:

Total amount paid = 475 x 24 = 11,400$

Next, we can subtract the amount borrowed from the total amount paid to find the total interest:

Total interest = Total amount paid - Amount borrowed

Total interest = 11,400$ - 7,500$

Total interest = 3,900$

Since Christopher paid off the loan after 18 months instead of 24 months, he did not pay the full amount of interest he would have paid if he made all 24 payments. The unearned interest is therefore:

Unearned interest = Total interest - (Number of remaining payments / Total number of payments x Total interest)

Unearned interest = 3,900 - (6 / 24 x 3,900)

Unearned interest = 3,225$

Therefore, the amount of unearned interest is $3,225.

What is repay?

Part B:

To determine the amount needed to repay the loan using the Rule of 78, we need to calculate the proportion of the total interest that has been earned by the lender up to the point when Christopher repays the loan.

The Rule of 78 is a method of allocating interest charges based on the sum of the digits of the loan term. In this case, since the loan term is 24 months, the sum of the digits is:

1 + 2 + ... + 4 + 5 = 15

We can use this sum to calculate the proportion of the total interest earned by the lender up to the point when Christopher repays the loan:

Proportion of earned interest = (Number of payments made / Total number of payments) x (Sum of digits of loan term / Total sum of digits)

Proportion of earned interest = (18 / 24) x (15 / 120)

Proportion of earned interest = 0.09375

The total interest paid is 3,900$, so the amount needed to repay the loan using the Rule of 78 is:

Amount needed to repay loan = Amount borrowed + Total interest x Proportion of earned interest

Amount needed to repay loan = 7,500$ + 3,900$ x 0.09375

Amount needed to repay loan = 8,443.75$

Therefore, the amount needed to repay the loan using the Rule of 78 is $8,443.75.

Part C:

To support our answers to Part A and Part B, we calculated the total interest that Christopher would have paid if he made all 24 payments, which is 3,900$. We also calculated the unearned interest, which is the difference between the total interest and the interest that Christopher actually paid when he paid off the loan early.

Using the Rule of 78, we calculated the proportion of the total interest earned by the lender up to the point when Christopher repaid the loan, which is 0.09375. We then used this proportion to calculate the amount needed to repay the loan using the Rule of 78, which is $8,443.75.

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Answer:

  1) 28,160.33 J

  2) 30.99 m/s

Step-by-step explanation:

Kinetic energy is given by the formula ...

  KE = 1/2mv^2 . . . . . m represents mass

  KE = (1/2)(34 kg)(40.7 m/s)² = 28,160.33 J

__

The potential energy is converted to kinetic energy.

  mgh = 1/2mv² . . . . m represents mass

  v = √(2gh) . . . . . . m cancels when we multiply by 2/m.

  v = √(2·9.8 m/s²·49 m) ≈ 30.99 m/s . . . . . m represents meters

The speed at the bottom is about 30.99 m/s.

_____

Additional comment

Rounding to 2 significant digits, the answers would be ...

  28,000 J

  31 m/s

The equivalent measures to 3 yards are;

108 inches and ; 6 ft 36 inches

Here, we want to get the values of the measurements that are equivalent to 3 yards

To do this, we need to know how to convert between the various measure types

We proceed as follows;

Mathematically, 1 yard is 36 inches; also, 1 yard is 3 feet

So, 3 yards is (3*36) = 108 inches

Also, 3 yards is (3*3) = 9 feet

Also, 1 ft is 12 inches;

So, 6 ft 12 inches is 7 feet

108 inches is as seen above, so 3 yards equal this

3 yards is not 108 feet as calculated above

6 ft 36 inches

36 inches is 3 ft; so by addition; 6 ft 36 inches is 9 ft

So, the correct answers here are 108 inches and 6 ft 36 inches

Answer:

There are 15 Black tokens.

Step-by-step explanation:

If the ratio is 8:5 we divide 24 by 8 to get 3. We then do 5 x 3 for the black tokens and get 15.

The number of black tokens in the bag are 15.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

In the bag, there are 24 green tokens in the bag.

And, The ratio of green tokens to black tokens is 8 to 5.

Now,

There are 24 green tokens in the bag.

And, The ratio of green tokens to black tokens is 8 to 5.

So, Number of green tokens = 8x

And,  Number of black tokens = 5x

Hence, We can formulate;

⇒ 8x = 24

⇒ x = 3

Thus, Number of black tokens = 5x

                                               = 5 × 3

                                               = 15

Therefore, The number of black tokens in the bag are 15.

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Answer:

64

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

number of tiles =(total area/area of one tile)=352÷11/2=352×2/11=32×2=64

Answer:

x=0 is the axis of symmetry of y=x^2 - 16

Answer:

still need it??

Step-by-step explanation:

We can be 99% confident that the true mean score of all bowlers falls within the interval of (187.224, 192.776).

To find the 99% confidence interval of the mean score of all bowlers, we can use the formula:

CI = x ± z×(σ/√n)

where x is the sample mean (190), σ is the population standard deviation (8), n is the sample size (55), and z is the z-score associated with the desired confidence level (99%).

We can find the z-score using a standard normal distribution table or a calculator, which gives us a value of 2.576.

Substituting the values into the formula, we get:

CI = 190 ± 2.576×(8/√55)
CI = 190 ± 2.576×(1.077)
CI = 190 ± 2.776
CI = (187.224, 192.776)

Therefore, we can be 99% confident that the true mean score of all bowlers falls within the interval of (187.224, 192.776).

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The null hypothesis can be rejected at α = 0.01 but not at α = 0.05 level of significance. Hence the correct option is option (c)Fail to reject H, at a=0.05 but reject at a =0.01.

A 95% confidence interval for the proportion of viewers of a certain reality television show who are over age 30 is (0.26, 0.35). The show's producers want to test the hypothesis H.: p=0.25 against H:p=0.25. The appropriate conclusion that the producers can draw is that they can fail to reject H, at a=0.05 but reject at a =0.01.

Hypothesis testing is a systematic procedure for selecting the best feasible hypothesis for a particular set of data. It is a decision-making method for statistical hypothesis testing of the validity of a statement regarding a population parameter.

The following are the hypothesis statements of the problem:

Hypothesis H0: p = 0.25 (Null Hypothesis)Hypothesis Ha: p ≠ 0.25 (Alternative Hypothesis)Hypothesis testing at α = 0.05 level of significance can be performed using the following formula:

Z= (p - Po) / [Po (1 - Po)/ n]Where, Po = 0.25p = (0.26+0.35)/2 = 0.305n = (Zα/2/ E)^2 = (1.96 / 0.04)^2 = 240.1Z = (0.305 - 0.25) / [0.25 (1 - 0.25)/ 240.1] = 3.18For a two-tailed test at α = 0.05, the Z critical values are Zα/2 = ±1.96.The Z value calculated (3.18) is greater than Z critical value (1.96).

Therefore, the null hypothesis can be rejected at α = 0.01 but not at α = 0.05 level of significance. Hence the correct option is option (c)Fail to reject H, at a=0.05 but reject at a =0.01.

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Ans

c=9

Step-by-step explanation:

2 x 9 = 18 +9 = 27

Answer:

13.5

Step-by-step explanation:

Q3 - Q1   is the interquartile range

23- 9.5

The probability of choosing an integer at random from the first 100 positive integers that is exactly divisible by 7 is 7/50.

The probability of choosing an integer from the first 100 positive integers that is exactly divisible by 7 can be calculated by determining the number of integers in the range that are divisible by 7 and dividing it by the total number of integers in the range.

To find the number of integers between 1 and 100 that are divisible by 7, we need to find the largest multiple of 7 that is less than or equal to 100.

By dividing 100 by 7, we get 14 with a remainder of 2. This means that the largest multiple of 7 less than or equal to 100 is 14 * 7 = 98.

So, there are 14 integers between 1 and 100 that are divisible by 7 (7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98).

Now, we can calculate the probability by dividing the number of integers divisible by 7 (14) by the total number of integers in the range (100).

Probability = Number of favorable outcomes / Total number of outcomes

Probability = 14 / 100

Simplifying the fraction, we get:

Probability = 7 / 50

Therefore, the probability of choosing an integer at random from the first 100 positive integers that is exactly divisible by 7 is 7/50.

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Answer:

Option A, x = -3

Step-by-step explanation:

Step 1:  Find the graphed line

x = -3

Answer:  Option A, x = -3

The ordering of the weight from the least to greatest will be 1 1/8, 1.6, 1.625 and 1 5/6.

From the information, Orlando uses 1 5/6 pounds of cashews, 1.6 pounds of sunflower seeds, 1 1/8 pounds of raisins, and 1.625 pounds of pecans..

It should be noted that 1 5/6 will be 1.833.

It should be noted that 1 1/8 will be 1.125

Therefore, it van be seen that the least of the pounds of raisins and the greatest is pounds of cashew.

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The number to multiply with 3 / - 12 to get 5 / 3 is - 20 / 3.

Let's express the expression into an equation before finding the value you can multiply - 3 / 12 to get a product of 5 / 3.

Therefore, let the number be x

Hence,

3 / -12 × x = 5 / 3

multiply both sides of the equation by - 12

3x = 5 / 3 × - 12

3x = - 60 / 3

3x = -20

divide both sides by 3

x = - 20 / 3

Therefore, the number to multiply is - 20 / 3.

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