The difference of twice a number and five is three. Find the number

The volume of the triangular prism is 198 cubic units.

To find the volume of a triangular prism, we need to multiply the area of the base triangle by the height of the prism.

In this case, the base of the triangular prism is a triangle with a base of 11 units and a height of 6 units, so the area of the base is:

Area of base = (1/2) × base × height

Area of base = (1/2) × 11 units × 6 units

Area of base = 33 square units

The height of the prism is given as 6 units.

Therefore, the volume of the triangular prism is:

Volume of prism = Area of base × Height

Volume of prism = 33 square units × 6 units

Volume of prism = 198 cubic units

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To find the largest four-digit value of t such that the expression is an integer, we need to set up an equation and solve for t.

Let's denote the given expression as x:

x = √(t - √(t - √(t - √(t - ...)))

To simplify the expression, we notice that the inner square root can be represented by x itself. So we can rewrite the equation as:

x = √(t - x)

Squaring both sides to eliminate the square root:

x^2 = t - x

Rearranging the equation:

x^2 + x - t = 0

To find the largest four-digit value of t, we can iterate through the values of t starting from 9999 and solve the quadratic equation for x. We are looking for a positive integer solution for x. Once we find the largest value of t that satisfies this condition, we have our answer.

By solving the quadratic equation for different values of t, the largest four-digit value of t that satisfies the condition is 9985.

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Answer:

68

Step-by-step explanation:

Find the scale Factor:

What do you do to 10 to make it 4?

Divide by 2.5 or Multiply by 0.4

Since, Scale factors are always written as multiplications, use x 0.4

Find the area of the smaller pentagon:

Value 1 x Scale Factor = Area of larger pentagon x 0.4 = 68.8 ≈ 68

Hope this helps

Answer:

y = -3x + 3

Step-by-step explanation:

y = mx + b

m is slope

b is y-intercept

substitute slope and y-intercept into the formula

y = -3x + 3

Answer:

{-1, 0, 1, 3}

Step-by-step explanation:

A relation is a set of ordered pairs of numbers. The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. In this case, the relation is (-1,5) , (0,4), ( 1,2) , (3,-2), so the domain is the set of all the x-values in these ordered pairs, which is the set {-1, 0, 1, 3}. Therefore, the domain of the relation is {-1, 0, 1, 3}.

Answer:

63

Step-by-step explanation:

k=y/x

y/x=k

y=k×x

y=7×9

y=63

Answer:

Step-by-step explanation:

To solve first take logarithm to both sides

That's

But

So we have

\(x = log_{10}(1200) \)

Write 1200 as a number with the factor 100

That's

1200 = 100 × 12

So we have

Using the rules of logarithms

That's

Rewrite the expression

That's

x = 3.079

So we have the final answer as

Hope this helps you

The smallest number of eggs that could have been in the box is 1134

The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:

Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:

n ≡ 1 (mod 2)

n ≡ 1 (mod 3)

n ≡ 1 (mod 4)

n ≡ 1 (mod 5)

n ≡ 1 (mod 6)

n ≡ 0 (mod 7)

For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.

Plugging these values into the formula and simplifying modulo 5040, we get:

n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040

n = (−8946) mod 5040

n = (−3906) mod 5040

n = 1134 mod 5040

Therefore, the smallest number of eggs that could have been in the box is 1134

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The probability that a randomly selected squirrel has a weight less than 3 pounds:  P(x < 3) = 0.0139

What is Probability?

Chance is a branch of mathematics that deals with numerical representations of the probability that an event will happen or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 signifies the event's impossibility and 1 denotes certainty.

Given,

μ = 4.1

σ = 0.5

∴ P(x < 3) = P(z < (3 - μ) / σ)

= P(z < (3 - 4.1) / 0.5)

= P(z < -1.1/0.5)

P(x < 3) = P(z < -2.2)

P(x < 3) = 0.0139

As a result, P(x 3) = 0.0139 is the probability that a squirrel chosen at random weighs less than 3 pounds.

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Answer:

$1,255.5 dollars per week

Step-by-step explanation:

40Hr * $2.13 = $85.2 per week from hours alone

$130 * 0.20 = $26 tip per table

$26 * 45 tables = $1,170 in tips

$85.2 + $1,170 = $1,255.2 per typical week

Answer:

0.25 or 1/4

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

Half of half a mile is one quarter mile:  (1/2)(1/2) = 1/4

12. MATLAB code: `f = (-3*t.^2 + 5*t + 20).*(t < 0) + (3*t.^2 + 5*t).*(t >= 0)`

13. MATLAB function: `function random_values = UniGen(n, a, b); random_values = (b - a) * rand(n, 1) + a; end`

MATLAB code to calculate f(t) using the given equation:

t = -9:0.5:9; % Generate values of t from -9 to 9 in steps of 0.5

f = zeros(size(t)); % Initialize f(t) vector

for i = 1:numel(t)

   if t(i) < 0

       f(i) = -3*t(i)^2 + 5*t(i) + 20;

   else

       f(i) = 3*t(i)^2 + 5*t(i);

   end

end

% Display the results

disp('t    f(t)');

disp('--------');

disp([t' f']);

```

This code generates values of `t` from -9 to 9 in steps of 0.5 and calculates `f(t)` based on the given equation. The results are displayed in a tabular format showing the corresponding values of `t` and `f(t)`.

13. MATLAB function UniGen to generate uniformly distributed random values:

function random_values = UniGen(n, a, b)

   % n: Number of random values to generate

   % a: Start of the interval

   % b: End of the interval

   random_values = (b - a) * rand(n, 1) + a;

end

This MATLAB function named `UniGen` generates `n` random values that are uniformly distributed on the interval `[a, b]`. It utilizes the `rand` function to generate random values between 0 and 1, which are then scaled and shifted to fit within the specified interval `[a, b]`. The generated random values are returned as a column vector.

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Answer:

Hi there!

Your answer is:

B) 25/100 × 64

C) .25× 64

Step-by-step explanation:

25% of 64 is

100% is 64

/100

1% is .64

× 25

25% of 64 is 16!

A) 25× 64 = 1600 NO

B) 25/100 × 64 = 16 YES ✓

C) .25 × 64 = 16 YES✓

D) 64 ÷ 25/100= 256 NO

E) 25÷ 64/100= 39.0625 NO

Hope this helps!

Total price paid by Michael for the basket of mangoes is $4.48.

For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -

Total price = 4 + 12%×4

Calculating the percentage of sales tax on Right Hand Side of the equation

Total price = 4 + 12×4/100

Solving the percentage part on Right Hand Side of the equation

Total price = 4 + 0.48

Performing addition on Right Hand Side of the equation

Total price = $4.48

Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.

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Learn more

Answer:

Step-by-step explanation:

20/1.6=12.5

12.5-3.5=9

9=b

Answer:

G: Ms Ruiz

Step-by-step explanation:

She had the lowest slope

The probability that all three of the selected homes have a security system is approximately 7.95%.

To find the probability that all three selected homes have a security system, we need to use the multiplication rule for independent events. Since each home is selected at random, the selection of one home does not affect the selection of the other homes.

The probability that the first home selected has a security system is 7/12.
The probability that the second home selected also has a security system is 6/11 (since there are now only 6 homes with security systems left out of the remaining 11 homes).
The probability that the third home selected also has a security system is 5/10 (since there are now only 5 homes with security systems left out of the remaining 10 homes).

Using the multiplication rule, we multiply these probabilities together to get the overall probability that all three selected homes have a security system:

P(all 3 homes have security systems) = (7/12) x (6/11) x (5/10)

P(all 3 homes have security systems) = 0.0795 or 7.95%

Therefore, the probability that all three of the selected homes have a security system is approximately 7.95%.

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Answer:

-2b and -0.9b and b/12

Step-by-step explanation:

Answer:

3 units

Step-by-step explanation:

I hope it helps you!

Answer:

B. 20x^4-39x^3+26x^2-6x

Step-by-step explanation:

(5x^2-6x+2)*(4x^2-3x)

20x^4 -15x^3 -24x^3 + 18 x^2 +8x^2 - 6x

20x^4 -39x^3 + 26x^2  - 6x

Answer:

The answer to 2 is "acute".

The answer to 6 is "right triangle"

For 10, it actually is possible. An example is 50, 50, 80

Step-by-step explanation:

An acute triangle is when each angle is less than 90 degrees.

Any triangle with 90 degrees for one angle counts as a right triangle.

all angle measures in a triangle must add up to 180 degrees. Hope this helps!

Answer: B. Food

Step-by-step explanation:

Answer:

The domain or x-values are on the horizontal axis, this is what you spend.

The range or y-values are on the vertical axis, this is your bonus.

The points to be indicated:

Plot the points and connect to make a line.

The graph is attached

For the given box plot: The median of the second trip is higher than the median of the first trip.

Box plots, often called box-and-whisker plots, are graphical representations of data sets that highlight essential characteristics and summarise the distribution of the data. A box plot consists of a rectangle (the box) that spans the middle value of the data from the lower quartile (Q1) to the upper quartile (Q3), and a vertical line (the median) inside the box. Any data points outside of this range are displayed as separate dots (outliers), and whiskers (lines) extend from the box to the lowest and highest data points within 1.5 times the IQR (interquartile range). Box plots make it simple to compare several sets of data, and they can highlight variations in central tendency, variability, and skewness.

From the description of the box plots we observe that:

The first trip's range is greater than the second trip's range because the first trip's whiskers are longer than the second trip's whiskers.

Due to the second trip's box being relocated to the right of the first trip's box, the median of the second trip is greater than the median of the first.

Because the box for the first trip is wider than the box for the second trip, the interquartile range (IQR) of the second trip is less than the IQR of the first trip.

Since both trips have a data point at 22, they both have the same highest value.

Hence, The median of the second trip is higher than the median of the first trip.

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Step-by-step explanation:

bicycle cost= 310

initial money in savings account= 50

additional money saved per week = 20

number of weeks = w

you have to set up an equation

The equation is...

bicycle cost = additional money saved × w + initial money

Substitute the values

310 = 20w + 50

Solve for w

310 - 50 = 20w +50 - 50

260 = 20w

260÷ 20 = 20w÷ 20

13 = w

It will take 13 weeks for her to have enough money for her bicycle

I hope this helps!!!

The mean square errors for the three-month and four-month moving average forecasts shown below.

How closely a regression line resembles a set of data points is determined by the Mean Squared Error. It is a risk function that corresponds to the squared error loss's expected value. The average, more particularly the mean, of errors squared from data related to a function is used to determine mean square error.

Given:

According to the Given data we construct a table as

Month   Sales   3- month           4- month      3- month     4- month      

                         moving             moving         squared       squared

                        averages            averages      error           error

1             9.6      

2             9.2

3             9.3

4             9.2     9.367                                        0.111            

5             9.2     9.400                   9.450           0.160        0.123    

6             9.2     9.500                  9.500            0.010        0.140    

7             9.2     9.733                   9.625            0.001         0.006  

8             9.2     9.733                   9.725            0.751          0.776  

9             9.2     10.000                 9.950           0.010           0.002  

10            9.2     10.067                  9.975            0.218          0.141  

11             9.2     10.033                   9.950          0.401           0.322

12            9.2     9.633                   9.975             0.004          0.031

13                       9.567                 9.650    

                                                        MSE             0.185            0.176

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To maximize his employer's matching contribution, Lonnie should contribute at least 5% of his salary each month to his 401(k). This means that he should contribute a minimum of $125 each month (5% of $2,500). However, he is allowed to contribute up to 12% of his salary, which is $300 per month.

While contributing the maximum amount will help him save more for retirement, contributing at least 5% will ensure that he takes full advantage of his employer's matching contribution. It is important to note that contributions to a 401(k) account are tax-deferred, which means that Lonnie's contributions will lower his taxable income, resulting in potential tax savings. it is crucial for employees to take advantage of employer matching contributions, as it is essentially free money that will help them save for retirement.

To maximize his employer's matching contribution, Lonnie should contribute at least 5% of his salary to his 401(k) each month. With a monthly salary of $2,500, this would amount to $2,500 x 0.05 = $125. By contributing this amount, Lonnie ensures that he receives the full 5% matching contribution from his employer, maximizing the benefits of the 401(k) plan.

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Answer:

Step-by-step explanation:

look at picture

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

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

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!