You are a civil engineer designing a bridge. The walkway needs to be made of wooden planks. You are able to use either Sitka spruce planks (which weigh 3 pounds each), basswood planks (which weigh 4 pounds each), or a combination of both. The total weight of the planks must be between 600 and 900 pounds in order to meet safety code. If Sitka spruce planks cost $3.25 each and basswood planks cost $3.75 each, how many of each plank should you use to minimize cost while still meeting building code?

Answer:

v = - 6

Step-by-step explanation:

10 + 3v = - 8 ( subtract 10 from both sides )

3v = - 18 ( divide both sides by 3 )

v = - 6

Answer:

Step-by-step explanation:

10 + 3v = –8

3v=-8-10

3v=-18

v=-18/3

v=-3

The three (3) statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   ....equation 1.

Where:

From the information provided above, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

Comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x – 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:

Max made a mistake in step 5.

He should have used division instead of multiplication.

Step-by-step explanation:

In step #5, he made the mistake of multiply 5/6 by 5/6. The reason why this doesn't work is because y is not a full y. When there isn't a number beside a variable, it is implied that it is 1y. To solve for y, you need 1y or else results or inaccurate.

In reality, 5/6 * 5/6 is equal to 25/36. If you divided 5/6 by 5/6, it is equal to 1, which makes y a full y.

Answer:

he made a lot of mistakes, but i'd say he used division instead of multiplication in step 5

(but the biggest mistake was adding 1/6 to both sides instead of multiplying by it)

Step-by-step explanation:

Answer:

(2, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

2x + y = 5

3x - 2y = 4

Step 2: Rewrite Systems

Manipulate 1st equation

Step 3: Solve for x

Substitution

Step 4: Solve for y

Answer:

Yasmin will spend $6

Nadia will spend $5.9

Step-by-step explanation:

Step one:

the cost of 5 jars at Central market is $3

the cost of 1 jar = 3/5= $0.6

60 cents per jar

we are told that Valley Market sells jars of jam at 59 cents per jar.

$0.59

Step two:

If Yasmin buys 10 jars from Central Market,

Yasmin will spend = 10*0.6= $6

If Nadia buys 10 jars from Valley Market.

Nadia will spend = 10*0.59= $5.9

The market difference is 6-5.9= $0.1

The domain of the function is defined as 0 ≤  x ≤ 4.

option A is the correct answer.

A domain of a function refers to "all the values" that can go into a function without resulting in undefined values.

So the domain of a function is the set of x values, while the range of a function is the set of y values.

From the given statement, the range of the function is defined as;

y = vt

where;

y = 60 mph x 4 hr

y = 240 miles

From the given statement, the domain of the function is defined as;

0 ≤  x ≤ 4

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You would receive $68 in the tenth month based on the given pattern and formula.

To find the amount you receive in the tenth month, we need to identify the pattern in the payments and use it to establish a formula.

From the given information, we can observe that the payments are increasing each month. Let's denote the first month as month 1 and the corresponding payment as \(P_1\), the second month as month 2 with payment \(P_2\), and so on. We have:

Month 1: \(P_1\) = $50

Month 2: \(P_2\) = $52 (an increase of $2 from the previous month)

Month 3: \(P_3\) = $56 (an increase of $4 from the previous month)

Month 4: \(P_4\) = $62 (an increase of $6 from the previous month)

We can see that the increase in payment is consistent, increasing by $2 each month. We can express this pattern with a formula:

\(P_n = P_1 + (n - 1) * d\)

where \(P_n\) represents the payment in the nth month, \(P_1\) is the initial payment, we can see that the pattern is in arithmetical progression, n is the month number, and d is the common difference between the payments.

In this case, \(P_1\) = $50, and the common difference d = $2. Using this formula, we can calculate the payment in the tenth month (n = 10):

\(P_{10} = P_1 + (10 - 1) * d\)

    = $50 + 9 * $2

    = $50 + $18

    = $68

Therefore, you would receive $68 in the tenth month based on the given pattern and formula.

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The length of the triangle's altitude  is 48.5 units

From the question, we have the following parameters that can be used in our computation:

An equiilateral triangle

The side length is then given as

x = 56

For an equilateral triangle, the altitude a is calculated as

a = √(x² - (0.5x²))

Substitute the known values in the above equation, so, we have the following representation

a = √(56² - (0.5 * 56)²)

Evaluate

a = 48.5

Hence, the altitude is 48.5 units

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Based on the numbers that Joe selected, the people selected were D) Alan, Eugene, Martin, Sam.

The 17th person was selected and if we assigned numbers from 1 to 20 to the alphabetized list, we would find that number 17 is Sam.

The 5th person is Eugene and the 1st person is Alan. The 12th person is Nathan.

In conclusion, option D is correct.

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The value of the variable x is 253 degrees

From the question, we have the following parameters that can be used in our computation:

Circle and intersecting tangent lines

Using the theorem of angle between intersecting tangents and arcs, we have the following equation

1/2 * (x - 360 + x) = 73

Multiply by 2

(x - 360 + x) = 146

So, we have

2x - 360 = 146

Evaluate the like terms

2x = 506

Divide by 2

x = 253

Hence, the value of x is 253 degrees

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Answer:3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

CLT

5+7= 4a

12=4a

Divide through by 4

12÷4= 3

Answer:

Length = 7 cm

Width = 2 cm

Step-by-step explanation:

Perimeter of rectangle = 18 cm

Let length of rectangle = \(l\) cm

Let width of rectangle =  \(w\) cm

As per given statement, length is 3 cm more than the twice of its width:

Writing equation:

\(l = 2\times w +3 ....... (1)\)

Formula for perimeter of a rectangle is given as:

\(P = 2 \times (Length + Width)\)

OR

\(P = 2 \times (l + w)\)

Putting values of P as given and \(l\) by using equation (1):

\(18 = 2 \times (2w +3 + w)\\\Rightarrow \dfrac{18}2 = 3w +3 \\\Rightarrow 9 = 3w +3\\\Rightarrow 3w = 9 -3\\\Rightarrow w = \dfrac{6}{3}\\\Rightarrow w = 2\ cm\)

Putting value of \(w\) in equation (1):

\(l = 2\times 2 +3 \\\Rightarrow l = 4+3\\\Rightarrow l = 7\ cm\)

So, the dimensions are:

Length = 7 cm

Width = 2 cm

Answer:

improper fraction

Step-by-step explanation:

im not sure if this is what you're looking for but i hope it helps

Answer: 3.83m^3

Step-by-step explanation:

Use formula for volume of a triangular prism (Area of triangle times length of the figure)

Answer:

6

Step-by-step explanation:

idk i just added them all together

Answer:

53

Step-by-step explanation:

We know the first term and common difference so we can write the explicit formula. The formula is:

aₙ = a₁ + (n - 1)d

aₙ = 8 + (n - 1) * 3

aₙ = 3n + 5

This means that a₁₆ = 3 * 16 + 5 = 53

by using the formula for arithmetic sequence, the 16th term of the progression can be obtained. Given A1 = 8 and d = 3,

A16=A1 + (n-1) d

A16=8 + (16-1) (3)

A16 = 53

I hope I helped! Be safe!

Answer/Step-by-step explanation:

(5 x 10) + ( 5 x -15) or 5 x (10 + -15)

5 x 10 = 50

5 x -15 = -75

50 + -75 = -25

Answer:

-25

Step-by-step explanation:

The volume of water in the ocean is estimated to be approximately 1,332,000,000,000,000,000 liters.

The Earth's oceans cover about 71% of the planet's surface and contain a vast amount of water. To calculate the volume of water in the ocean, we need to consider the average depth and the total surface area of the oceans.

The average depth of the ocean is estimated to be around 3,800 meters. The total surface area of the oceans is approximately 361,900,000 square kilometers. By multiplying the average depth by the surface area, we can find the volume of water.

Volume = Average Depth × Surface Area

Using the given values, we have:

Volume = 3,800 meters × 361,900,000 square kilometers

To convert this volume to liters, we need to consider that 1 cubic meter is equal to 1,000 liters. Therefore, we can multiply the volume in cubic meters by 1,000 to obtain the volume in liters.

Calculating the above expression, we find that the volume of water in the ocean is approximately 1,332,000,000,000,000,000 liters. This is an estimation and may vary slightly depending on the sources and assumptions used for average depth and surface area calculations.

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Answer:

x = 36 degrees, the smaller angle.

4(36) = 144 degrees, The larger angle.

36 + 144 = 180 degrees.

Cleomenius.

Answer:

x = 36 degrees, the smaller angle.4(36) = 144 degrees, The larger angle.36 + 144 = 180 degrees.

Step-by-step explanation:

(1)adjacent- two non-overlapping angles that share a common vertex and a common side

(2)the non-common sides are opposite rays.

(3)adds up to 180

The relationship between the standard deviation and variance is that the standard deviation is the square root of the variance.

The correct option is -C

Hence, the correct option is (c) Standard deviation is the square root of the variance. Variance is the arithmetic mean of the squared differences from the mean of a set of data. It is a statistical measure that measures the spread of a dataset. The squared difference from the mean value is used to determine the variance of the given data set.

It is represented by the symbol 'σ²'. Standard deviation is the square root of the variance. It is used to calculate how far the data points are from the mean value. It is used to measure the dispersion of a dataset. The symbol 'σ' represents the standard deviation. The formula for standard deviation is:σ = √(Σ(X-M)²/N) Where X is the data point, M is the mean value, and N is the number of data points.

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Answer:

1/2 of her book

Step-by-step explanation:

1/6 + 2/6 = 3/6 = 1/2

Answer:

I think that it is 1/2 of her books

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

2/11

Step-by-step explanation:

2 + 4+ 5 = 11

Answer:

The answer is that the ball was in the air for 0.56 seconds when it was 54 feet above the ground. This was determined by using the Quadratic Formula to solve the equation 54 = -16s^2 + 96s for the variable s.

Step-by-step explanation:

To solve this equation, we can use the Quadratic Formula, which states that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

In this case, a = -16, b = 96, and c = -54. Plugging these values into the Quadratic Formula, we get:

s = (-96 +/- sqrt(96^2 - 4 * -16 * -54)) / (2 * -16)

= (96 +/- sqrt(9216 + 4352)) / -32

= (96 +/- sqrt(13,568)) / -32

Since we want the time (in seconds) that the ball was in the air, we need to find the positive solution to this equation. Thus, we have:

s = (96 + sqrt(13,568)) / -32

= (96 + 120) / -32

= 0.5625 seconds

Rounding this value to the nearest hundredth of a second, we get 0.56 seconds. This means that the ball was in the air for 0.56 seconds when it was 54 feet above the ground.

To solve this equation, we used the Quadratic Formula. This method allowed us to find the time (in seconds) that the ball was in the air by solving for the value of the variable s in the given equation. This helped Vue answer his question by providing a numerical value for the amount of time that the ball was in the air when it was 54 feet above the ground.

The confidence interval from the given population is  (25.15, 28.85)

To calculate a confidence interval at the 95% confidence level, we need:

Sample mean (x) = 27

Sample size (n) = 24

Population standard deviation (σ) = 3

Level of significance (α) = 0.05 (since it is a 95% confidence interval, the level of significance is 1 - 0.95 = 0.05)

The critical value of z for a 95% confidence interval is 1.96 (from the z-table)

Using the formula for the confidence interval for the population mean with known standard deviation, we have:

Lower limit = x - z(α/2) * (σ/√n) = 27 - 1.96 * (3/√24) = 25.15

Upper limit = x + z(α/2) * (σ/√n) = 27 + 1.96 * (3/√24) = 28.85

Therefore, the 95% confidence interval for the population mean length of text messages is (25.15, 28.85) characters.

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Answer:

1/6

Step-by-step explanation:

To know what fraction is equal to 50% of 1/3, we have to convert the percentage into a fraction first.

50% = 50/100

So 50% of 1/3 = 1/3 * 50/100

= 50/ 300

= 5/30

= 1/6

Answer:

A, B, D

Step-by-step explanation:

neg * pos = neg

neg * neg = pos

neg / pos = neg

neg / neg = pos

Answer:

195

Step-by-step explanation:

13 x 15 = 195

Answer:

195 cookies

Step-by-step explanation:

13 houses times 15 cookies is 195 divided by 15 is 13