For every mile of highway on land, the city needs two truckloads of asphalt and one gallon of paint. For every mile of highway on bridges, the city needs one truckload of asphalt and three gallons of paint. The city has 50 truckloads of asphalt and 80 gallons of paint.

(a)What is the largest total number of miles of highway the city can build?

(b)Suppose the city is on an island and must build at least 25 miles of highway on bridges to reach other islands. Now what is the largest total number of miles of highway the city can build?

The weight of a randomly selected pack of gum that has a z-score of 3.11, is 54.6 grams. So, the right option is D.

A Z-score can be used to calculate how much the data deviates from the mean. It shows how frequently the data is either above or below the mean. According to the formula,

Z = (X - μ)/σ

where, Z is the Z-score, X is the data point, μ is the mean and σ is the standard variable.

Z = 3.11, σ = 2.4, μ = 47.1

Z = (X - μ)/σ

Now putting the value

3.11 = (X - 47.1)/2.4

Multiply by 2.4 on both side

X - 47.1 = 3.11 X 2.4

X - 47.1 = 7.464

Add 47.1 on both side, we get

X = 54.564 grams

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The complete question is:

The weights of a pack of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation of 2.4 grams. What is the weight of a randomly selected pack of gum that has a z-score of 3.11?

39.6 grams

44.7 grams

49.5 grams

54.6 grams

If u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), the derivative of cross product d/dt [u (t) x v (t)] is (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t)).

Formula 5 of the cross product theorem states that the derivative of the cross product of two vectors u and v is equal to the cross product of the derivatives of u and v:

d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt)

Where u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), we can find the derivatives as follows:

du/dt = (d(sin 3t)/dt, d(cos 3t)/dt, dt/dt)

= (3 cos 3t, -3 sin 3t, 1)

dv/dt = (dt/dt, d( cos 3t) /dt, d( sin 3t)/dt)

= (1, -3 sin 3t, 3 cos 3t)

Now, we can substitute these derivatives into the formula to find d/dt [u (t) x v (t)]:

d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt) = (3 cos 3t, -3 sin 3t, 1) x (t, cos 3t, sin 3t) + (sin 3t, cos 3t, t) x (1, -3 sin 3t, 3 cos 3t)

= (-3sin²3t - cos3t, t - 3cos3tsin3t, 3cos²3t + 3tsin3t) + (3cos²3t + 3tsin3t, t - 3cos3tsin3t, -3sin²3t - cos3t)

= (3cos²3t + 3tsin3t - 3sin²3t - cos3t, 2t - 6cos3tsin3t, 3cos²3t + 3tsin3t - 3sin²3t - cos3t)

= (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t))

The cross product of two vectors is a vector, and the result of the above calculation will be a vector that describes the rate of change of the cross product u(t) x v(t).

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The function is not linear because the rate of change in not constant.

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.

Given:

      x                   y

      10                -6

      11                  1

       12                6

       13                12

So, the rate of Change

= 10/ (-6)

= -5/2

and, again = 11/1 = 11

As, the rate of change is not constant.

But, in linear function the rate of change is same.

Hence, the function is not linear.

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Answer:

Step-by-step explanation:

The result of 20 · 34 is 680, and the result of 20 ÷ 34 is approximately 0.588235294117647. Therefore, 20 · 34 is greater than 20 ÷ 34.The symbol "·" is used for multiplication, and the symbol "÷" is used for division. When we multiply 20 and 34, we are finding the total value of 20 items that are each worth 34. While when we divide 20 by 34, we are finding out how many times 34 can fit into 20, which is less than one.In short, Multiplication gives a bigger value than division, that's why 20*34 is greater than 20/34.

Answer:

Step-by-step explanation:

Hello! The way you can figure this question out is by solving each one.  Let's start with 20 x 34.

How you can multiply 20 x 34

     34
   x20
______
     00 - 0 x 4, 0 x 3 both equal 0
+  680 - Put a 0 to the right of the number, 2 x 4 = 8, 3 x 2 = 6
______
680

34 x 20 = 680

Now, divide 20 by 34

20/34 = 10/17  

10/17 is less than 1, while 680 is much greater than 1.  

680 > 10/17

20 x 34 is greater than 20 divided by 34

Fun fact:
If two numbers are greater than 1, are whole numbers, and they are multiplied and divided, the number produced by each equation will always be greater when multiplied.  

We are given that quadrilateral EFGH is a rectangle. If EF=4x−6 and HG=x+3 , then the side EF= -34.

What is a quadrilateral?

A quadrilateral is a four-sided polygon, or a shape with four straight sides. It is a type of closed, two-dimensional shape. The four sides of a quadrilateral can be of equal or varying lengths and angles. Examples of quadrilaterals include squares, rectangles, rhombuses, parallelograms, and trapezoids.

Since quadrilateral EFGH is a rectangle, the opposite sides are congruent and parallel.

Therefore, if EF = 4x - 6 and HG = x + 3, then HG=EF

so, x+3=4x-6

then, x=-9

Therefore, EF=4x-6=4(-9)-6= -34

Hence, EF= -34

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Answer:

The degree is 4 because the term shown has TWO variables, while y has an exponent of 3, x has an exponent of 1, add the exponents of the variables to find the degree

Step-by-step explanation:

The estimate of the product expression is 0.12

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

3.71 * 0.296

From the question, the numbers are to be rounded to the place of its leftmost nonzero digit.

So, when the numbers are rounded, we have

4 * 0.3

Evaluate the product

This gives

0.12

Hence, the solution is 0.12

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The solution of (x³ - 5x² -24x) / (x + 8) using synthetic division is  x² - 3x.

The solution of (x³ - 5x² -24x) / (x + 8) using synthetic division is given below:

(x³ + 5x² -24x) / (x + 8)

The divisor is -8

The coefficients are:

  1    5    -24

Using synthetic division

the first coefficient is 1

the second coefficient = 1 * (-8) + 5

the second coefficient = -3

the third coefficient = -3 * (-8) + (-24)

the third coefficient = 0

Therefore, the solution =  1(x³/x) -3(x²/x) + 0(x/x)

The solution = x² - 3x

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Answer:

halfway between 862350 and 862360

The solution of equation is x=-3

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given

The equation;√x+3=-6

Now,

√x=-6-3

√x=-9

x=-3

Therefore the answer of the given equation will be -3

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a) The circumference of the tire is 7.85 ft

b) About 673 times the tire will have to rotate to travel 1 mile.

The diameter of a tire is 2. 5 ft.

Let r represents the radius of the tire.

r = diameter/2

r = 2.5 / 2

r = 1.25 ft

a)  the circumference of the tire:

We know that the formula for the circumference of circle:

C = 2πr

So, the circumference of the tire would be,

C = 2 × π × r

C =  2 × π × 1.25

C = 7.85 ft

b) Let the tire will have to rotate n times in order to travel 1 mile.

We know that 1 mile = 5,280 ft

So, n = 5280 / 7.85

n = 672.6

n ≈ 673

Thus, the tire will have to rotate 673 times in order to travel 1 mile.

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The estimated age of the tomb of Sneferu is 8,330 years.

The age of the tomb can be estimated using the carbon-14 decay equation, which states that the amount of carbon-14 remaining after time t (in years) is equal to the initial amount of carbon-14 multiplied by 0.5^(t/5730).The decay equation for carbon-14 is A = A₀e⁻kt, where A₀ is the original amount of carbon-14, A is the amount of carbon-14 at time t, k is the decay constant, and t is the amount of time that has passed.

We can rearrange the equation to solve for t: t = -ln(A/A₀)/k. In this equation, A is the amount of carbon-14 found in the cypress beam, and A₀ is the amount of carbon-14 found in living cypress wood.

In this case, the initial amount of carbon-14 was 100%, and the remaining amount was 55%. Solving for t, we get t = (ln(55%)/ln(0.5))*5730 = 8,330 years.

Therefore, the estimated age of the tomb of Sneferu is 8,330 years.

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Answer:

a) The two side lengths of the tenth rectangle in the sequence are 8 + (10 - 1)4 = 32 and 8 + (10 - 2)4 = 28.

b) The area of 576in2 is not possible in the given sequence because it would require a side length of 24, which does not follow the sequence given.

Step-by-step explanation:

The given sequence is represented by the equation an=8+(n−1)4, which means that for each successive rectangle in the sequence, the length of one of the sides will increase by 4. Therefore, in order for the area of a rectangle to be 576in2, the length of one of the sides must be 24, which does not follow the sequence given.

The probability that a random sample of 40 adults would have a mean of at least 7 marshmallows is 0.1943

We know that the formula for the z-score:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

To find: the probability that a random sample of 40 adults would have a mean of at least 7 marshmallows.

This is nothing but the p-value of Z when X = 7

Here the number of marshmallows an adult can fit in their mouth is skewed right with a mean of 6. 5 and a standard deviation of 0. 58

So, mean μ = 6.5

standard deviation σ = 0.58

Also, n = 40,

x = 7,

By central limit theorem,

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{7-6.5}{0.58}\\\\z=\frac{0.5}{0.58}\\\\z = 0.86[/tex]

z = 0.86 has p value 0.1943

Thus, the required probability is 0.1943

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yes it is fair The probability of drawing matching blocks is 1/3

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of drawing matching blocks is 1/3

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.

four main types of probability exist: classical, empirical, subjective and axiomatic. Probability is synonymous with possibility, so you could say it's the possibility that a particular event will happen.

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The line of linear equation y = 8x - 48 is much steeper than the line of linear equation y = -x - 4-.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The table of input and output values are given for the function.

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[16 - 32]/[8 - 10]

(-16)/(-2)

8

So, the slope point is obtained as m = 8.

The equation becomes - y = 8x + b

To find the value of b substitute the values of x and y in the equation -

32 = 8(10) + b

32 = 80 + b

b = 32 - 80

b = -48

So, the value for b is -48.

Now, the equation becomes -

y = 8x - 48

A graph has been plotted for the equation.

Similarly, the points for a line is given as (-6,2) and (-9,5).

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[5 - 2]/[-9 - (-6)]

(3)/(-9 + 6)

3/-3

-1

So, the slope point is obtained as m = -1.

The equation becomes - y = -x + b

To find the value of b substitute the values of x and y in the equation -

2 = -(-6) + b

2 = 6 + b

b = 2 - 6

b = -4

So, the value for b is -4.

Now, the equation becomes -

y = -x - 4

A graph has been plotted for the equation.

It is known that the larger the slope the steeper the line.

In the graph also it can be seen that the graph of line y = 8x - 48 is much steeper.

Therefore, the slope of line y = 8x - 48 is more steeper.

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Length of side of the rhombus is 5cm.

A rhombus can be thought of as a special parallelogram since it satisfies the requirements for one (a quadrilateral with two pairs of parallel sides). Another characteristic of a rhombus is that it has four equal sides, just like a square. It is also known as a tilted square for this reason.

step1

Diagonals of a rhombus bisect each other at right angles.

Let point of intersection of diagonals be O

So, OD = 3cm , OA = 4cm

From Right angled triangle △ AOD,

⇒ AD²  = OA²  + OD²   (Pythagoras theorem)

⇒ AD² =4² + 3²

⇒ AD² = 16+9

⇒AD² =25

step2

⇒ AD² =25

⇒ AD=5 cm

AD is side of the rhombus.

So, length of side of the rhombus is 5cm

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King usually becomes the most emotional during moments of reflection or when he is expressing his views on civil rights and justice. King's message of hope, courage, and resilience encourages individuals to stand up for what is right and to never give up in the face of injustice.

Dr. King utilises passion in his lectures to accentuate his message and to connect with his audience on an emotional level. He frequently speaks about the sorrow and injustice that his people have endured, eliciting an emotional response from his audience. He also inspires his audience to believe in the prospect of a brighter future, which instills hope and motivation. Furthermore, he frequently employs metaphors and analogies to underline his ideas, which may be extremely effective.

King is generally the most emotional when he is reflecting or expressing his ideas on civil rights and justice. In these times, he sends a message of hope, strength, and endurance. King usually uses compelling metaphors and parables to highlight the necessity of equality and justice. He highlights the power of our actions to effect change and the importance of never losing hope in the face of hardship. He frequently urges for unity among all races and sexes and opposes all types of prejudice. He also discusses the power of love, understanding, and mutual respect in bridging gaps and creating a better society.

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Answer:

The equation of a line can be represented in the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

Given that the line has a slope of 5 and passes through the point (-1,1) we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1)

The point (-1,1) can be plugged into the equation:

y - 1 = 5(x + 1)

By simplifying and re-arranging the equation, we get:

y = 5x + 6

So the equation of the line that passes through the point (-1,1) and has a slope of 5 is: y = 5x + 6

Answer:

y = 5x+6

Step-by-step explanation:

Using the slope-intercept form of a line

y = mx+b  where m is the slope and b is the y-intercept

y = 5x+b

Substitute the point into the line.

1 = 5(-1) +b

1+5 = b

6=b

The equation is

y = 5x+6

The better buy for the shrimp based on the information will be the A. 2.24 pound bag.

From the information, Josh paid $11.96 for a 2.24 -pound bag of shrimp at one store and the following week, he paid $17.24 for a 3.12 -pound bag at another store.

The unit price when Josh paid $11.96 for a 2.24 -pound bag of shrimp will be:

= $11.96 / 2.24

= $5.34

The unit price when he paid $17.24 for a 3.12 -pound bag at another store will be:

= $17.24 / 3.12

= $5 53

Therefore, A is cheaper.

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Complete question

Josh paid $11.96 for a 2.24 -pound bag of shrimp at one store. The following week, he paid $17.24 for a 3.12 -pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent.

The percentage of games that Mamadou scores between 136 and 214 is given as follows:

99.7%.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

For this problem, we have that

Hence the percentage is of 99.7%, as the measures are within three standard deviations of the mean.

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Gary would need 15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Bottles   Glue   Glitter

1              3.8       1.9

This means,

1 bottle = 3.8 oz of glue and 1.9 oz of glitter

Now,

1 bottle = 3.8 oz of glue

Multiply 4 on both sides.

4 bottle = 4 x 3.8 oz

4 bottle = 15.2 oz

1 bottle = 1.9 oz of glitter

Multiply 4 on both sides.

4 bottle = 7.6 oz

Thus,

15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.

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Based on the information provided, it can be concluded that for each meal the restaurant used 0.4166 kilograms of potato.

To calculate the quantity of potatoes used, you can use the following formula shown below:

Total of potatoes used / number of meals

2 1/2 kilograms of potatoes/ 6 meals

2 1/2 kilograms of potatoes is equivalent to 2.5 (1/2 = 0.5)

2.5 kilograms of potatoes/ 6 meals

0.4166

Therefore for each meal, the restaurant used 0.4166 kilograms of potatoes.

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Answer:

She was given 1 free apple and paid for 15 apples.

Step-by-step explanation:

0.55x2=1.1

1.1x8=8.8

8.8/.55=16

16-1=15

And you know she paid for 15 apples and got 1 free.

The cups of each items needed will be 9 cups of peanuts, 1.8 cups of chocolate and 7.2 cups of raisins.

From the information, 18 0ne-cup bags of tail mix is needed for the class tripThe recipe includes chocolate, chips and raisins in the ratio of 5:1:4

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number.

5x- peanuts

1x- chocolate chips

4x- raisins

5x + 1x + 4x= 18

10x= 18

x= 18/10

x = 1.8

Chocolate = 1.8 cups

Raisins = 4x

= 4 × 1.8

= 7.2 cups.

Peanut = 5x

= 5 × 1.8

= 9 cups

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A graph of the inequality is shown in the image attached below.

In this scenario, we would solve the given inequality by making m the subject of formula as follows;

-2 > m/6 - 7

By collecting like terms, we have the following:

-2 + 7 > m/6

5 > m/6

Cross-multiplying, we have:

30 > m

By re-writing the inequality, we have:

m < 30

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Also, the circle is open because of the greater than (>) symbol.

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The following is considered a LINEAR table is True .

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The Multiplicative Inverse of postive 146 is  0.00684932.

What is Multiplicative Inverse?

The reciprocal of a particular integer is referred to as the multiplicative inverse. It is employed to make mathematical expressions simpler. The word "inverse" denotes an opposing or opposed action, arrangement, position, or direction. A number becomes 1 when it is multiplied by its multiplicative inverse.

When a number is multiplied by the original number, the result is 1, that number is said to be the multiplicative inverse of that number. A-1, or 1/a, stands for the multiplicative inverse of the letter "a". In other terms, two numbers are said to be multiplicative inverses of one another when their product is 1.

The division of 1 by a number yields the multiplicative inverse of that number. The number's reciprocal is another name for it. According to the multiplicative inverse formula, a number's product with its reciprocal is 1.

Given number for the multiplicative inverse is 146;

so, If the Multiplicative Inverse of 146 is x

then , the problem can be written as a function as follows:

146(x) = 1

Thus, to get the answer, we divide 1 by 146 like this:

1 / 146 = 0.00684932

Therefore,the Multiplicative Inverse of postive 146 is  0.00684932.

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