1. Construction workers build 54 feet of a bridge each day for 9 days. To determine whether the bridge is at least 490 feet long, can you use an estimate, or is an exact answer required? Explain.​

Answer:

128 miles

Step-by-step explanation:

If 48 miles equals 12 minutes ,and every 4 minutes equals 12 miles,then 32 minutes equals 128 miles

Answer:

Given the expression x2 + 16x.

If the quadratic equation is of the form ax2 + bx + c then to complete square

Step1: Take coefficient of x2 common from ax2 + bx + c,

⇒ a[x2 + (b/a)x + (c/a)]

Step2: Add and subtract (1/2 coefficient x)2 to quadratic term then,

⇒ a [(x + 1/2 coefficient x)2) + (c/a) - (1/2 coefficient x)2

⇒ a [(x + b/2a)2 + c/a - (b/2a)2]

Note that if the coefficient of x2 is 1 then we have to add (1/2 coefficient x)2 to convert it into perfect square expression.

Thus, in the given problem x2 + 16x.

1/2 coefficient of x = (1/2) × 16 = 8

We have to add 82 = 64, to convert it into a perfect square.

Therefore, 64 must be added to the expression to make it a perfect-square trinomial.

Andrew needs to score 99 on his fifth science test in order to have an average of 93 across all five tests.

To find out what score Andrew needs to earn on his fifth science test, we can use the concept of averages. The average of a set of numbers is calculated by adding up all the numbers and then dividing the sum by the total number of values.

Andrew has already taken four science tests, and their scores are given as 87, 89, 97, and 95. To calculate the average, we add up these four scores: 87 + 89 + 97 + 95 = 368.

Now, we need to consider the fifth test score that Andrew needs to achieve. Let's call it x. To have an average of 93 across all five tests, we need to divide the sum of all the scores (including the fifth test score) by 5 (the total number of tests): (368 + x) / 5 = 93.

We can solve this equation for x by isolating it on one side. Multiplying both sides by 5 gives us 368 + x = 465. By subtracting 368 from both sides, we find x = 465 - 368 = 97.

Therefore, Andrew needs to score 97 on his fifth science test to have an average of 93 across all five tests.

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The maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD is 434 kips.

The maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD,

where

D = 100k,

L = 140k, L < 100psf,

Lr = 40k,

W = +160k or −100k, and

E = +180k or −125k is given below:

Design load = 1.2D + 1.6(Lr or S or R) + 0.5(L + Lr or R) + (W or E)

Here, D is the weight of dead load, L is the weight of live load, Lr is the weight of the roof live load, W is the weight of wind load and E is the weight of earthquake load.

Therefore, for the given loads,

D = 100k

L = 140k

Lr = 40k

W = +160k or −100k

E = +180k or −125k

Max load = 1.2D + 1.6(Lr) + 0.5(L + Lr) + W

= 1.2 (100) + 1.6 (40) + 0.5 (140 + 40) + 160

= 120 + 64 + 90 + 160

= 434 kips

Therefore, the maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD is 434 kips.

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Answer:

324.27

Step-by-step explanation:

3,891.24/12=324.27

Answer:

x=-3,-4

Step-by-step explanation:

math

Answer:

x = -3 or x = -4

Step-by-step explanation:

x^2 + 7x + 12 = 0

(x + 3)(x + 4) = 0

x + 3 = 0  or  x + 4 = 0

x = -3 or x = -4

Answer: A. 33

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given

3 < 5 + 6h < 10 ( subtract 5 from each interval )

- 2 < 6h < 5 ( divide each interval by 6 )

- \(\frac{1}{3}\) < h < \(\frac{5}{6}\)

Answer:

14

Step-by-step explanation:

evaluate multiplication first

14

hope this helped :l

Answer:

y= -2x +2.5

Step-by-step explanation:

The expressions formed are,

Formation of expressions in 1, 2 and 3:

In 1, twelve times f is, 12f

Taking away 5, it becomes (12f-5)

In 2, sum of k and 6 is, (k+6)

One-half of the above quantity is, (k+6)/2

In 3, sum of 5 with x is, (x+5)

Now, x squared minus the above expression indicates (x²-x+5)

Formation of expressions in 4 and 5:

In 4, product of a and b, is ab and 3 times c is 3c

Sum of the expressions evaluated in the previous statement = ab+3c

In 5, 24 times the product of x and y is, 24xy

Adding, g in the above computed expression, we get, 24xy+g

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Answer:

5.6

Step-by-step explanation:

4 ÷ 5/7

is 4 divide 5 over 7

which is 5.6

Answer:

72

Step-by-step explanation:

24 times 3 is 72

Answer:

The volume of the new model of Pluto is 195,432.20 cm^3

Step-by-step explanation:

new radius: 12 * 3 = 36 cm

volume: V=4/3 * π * r^3

volume of new mode is 195,432.20 cm^3

The standard equation of a hyperbola with a vertical transverse axis, centered at the origin, and values of a = 9 and b = 4 is y^2/81 - x^2/16 = 1.

The standard equation of a hyperbola centered at the origin with a vertical transverse axis is given by (y^2/a^2) - (x^2/b^2) = 1. In this case, we are given that a = 9 and b = 4, so substituting these values into the equation, we get:

(y^2/81) - (x^2/16) = 1

This is the standard equation of the hyperbola in question. It tells us that the center of the hyperbola is at the origin (0,0), the transverse axis is vertical (parallel to the y-axis), and the distance from the center to the vertices is 9 units (which is the value of a).

The distance from the center to the foci is given by c = sqrt (a^2 + b^2), which in this case is sqrt (81 + 16) = sqrt (97). The asymptotes of the hyperbola are the lines y = (a/b) x and y = -(a/b) x, which in this case are y = (3/4) x and y = -(3/4) x.

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Answer: The actual height of the house is 17 feet.

Step-by-step explanation:

The actual height of the house can be found by multiplying the model's height (4.25 inches) by the scale factor.

4.25 inches * 4 (3 feet/1/4 inch) = 17 feet.

So the actual height of the house is 17 feet.

If x - 1 is a factor of ƒ(x), then we can write the function as ƒ(x) = (x - 1) * g(x), where g(x) is another polynomial. This means that whenever x - 1 equals zero, the function ƒ(x) will also be equal to zero. Therefore, x - 1 is a zero of the function ƒ(x).

To find the other zeros of ƒ(x), we can use the factor theorem, which states that if a polynomial ƒ(x) has a factor (x - a), then a is a zero of ƒ(x). In this case, we know that x - 1 is a factor of ƒ(x), so 1 is a zero of ƒ(x).

To find the other zeros of ƒ(x), we can divide ƒ(x) by (x - 1) using polynomial long division. This will give us the quotient g(x), which will be a polynomial of degree 2. Since a polynomial of degree 2 can have at most 2 zeros, we know that the other zeros of ƒ(x) must be the zeros of g(x).

To find the zeros of g(x), we can use the quadratic formula, which states that the zeros of a quadratic polynomial ax² + bx + c are given by x = (-b ± √(b² - 4ac)) / (2a). In this case, we can plug in the coefficients of g(x) to find its zeros:

g(x) = x² - 10x + 15

x = (-(-10) ± √((-10)² - 4 * 1 * 15)) / (2 * 1)

x = (10 ± √(100 - 60)) / 2

x = (10 ± √40) / 2

x = (10 ± 2√10) / 2

Therefore, the zeros of ƒ(x) are 1, (10 + 2√10) / 2, and (10 - 2√10) / 2. These are the only values of x for which ƒ(x) equals zero.

dm_C/dt = k_B × m_B(t),  k_A represents the decay constant for the decay of element A into B, and k_B represents the decay constant for the decay of element B into element C. m_C(t) = (k_B/4) ×∫m_B(t) dt

To solve this problem, we need to set up a system of differential equations that describes the decay of the elements over time. Let's define the masses of the three elements as follows:

m_A(t): Mass of element A at time t

m_B(t): Mass of element B at time t

m_C(t): Mass of element C at time t

Now, let's write the equations for the rate of change of mass for each element:

dm_A/dt = -k_A × m_A(t)

dm_B/dt = k_A × m_A(t) - k_B × m_B(t)

dm_C/dt = k_B × m_B(t)

In these equations, k_A represents the decay constant for the decay of element A into element B, and k_B represents the decay constant for the decay of element B into element C.

We can solve these differential equations using appropriate initial conditions. Given that we start with 3 kg of element A and no element B or C, we have:

m_A(0) = 3 kg

m_B(0) = 0 kg

m_C(0) = 0 kg

Now, let's integrate these equations to find the expressions for the masses of the elements as a function of time.

For element C, we can directly integrate the equation:

∫dm_C = ∫k_B × m_B(t) dt

m_C(t) = (k_B/4) ×∫m_B(t) dt

Now, let's solve for m_B(t) by integrating the second equation:

∫dm_B = ∫k_A× m_A(t) - k_B × m_B(t) dt

m_B(t) = (k_A/k_B) × (m_A(t) - ∫m_B(t) dt)

Finally, let's solve for m_A(t) by integrating the first equation:

∫dm_A = -k_A × m_A(t) dt

m_A(t) = m_A(0) ×\(e^{-kAt}\)

Now, we have expressions for m_A(t), m_B(t), and m_C(t) based on time.

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x is present in the algebraic expression, therefore, option A is correct.- x is present in the expression, therefore, option B is correct.- x + y is present in the expression, therefore, option D is correct.

The given expression is: 3x[3(x + y)]^3x[3(x + y)]^3 × (x + 3)(x + y)

To simplify the given expression, we will first solve the expression within the brackets as follows:

(3(x + y))^3 = (3)³(x + y)³ = 27(x + y)³

Now, we will substitute the above value in the expression:

3x[3(x + y)]^3 = 3

x × 27(x + y)³ = 81x(x + y)³

Multiplying both terms of (x + 3)(x + y), we get:

(x + 3)(x + y)

= x(x + y) + 3(x + y) + 3y

= x² + xy + 3x + 3y + yx + 3y

= x² + 4xy + 6y + 3x

The final expression after substituting the value of 3x[3(x + y)]^3 and (x + 3)(x + y) is:

81x(x + y)³ × (x² + 4xy + 6y + 3x)

= 81x(x + y)³x² + 81xy(x + y) + 6xy + 27x(x + y)

= 81x³ + 189xy² + 81x²y + 6xy + 27x² + 81xy

Now, let's check which options are correct:- 3x is present in the expression, therefore, option A is correct.- x is present in the expression, therefore, option B is correct.- x + y is present in the expression, therefore, option D is correct.

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Answer:

the third one

Step-by-step explanation:

8x + 40 ≥ 0

8x ≥ -40

x ≥ -5

The larger the group of answer choices, the less likely our data represent the model due to larger differences between the expected frequencies.

Based on the terms provided, we want to know the relationship between the size of a group of answer choices, differences between expected frequencies, and how likely the data represents a model.

The larger the group of answer choices, the larger the differences between the expected frequencies, and the less likely our data represent the model.

This is because a larger group of answer choices increases the complexity of the dataset, which may lead to more significant deviations from the expected frequencies, ultimately making it less likely that the data represents the given model.

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Answer:

x = y − 4

Step-by-step explanation:

y=x+4

Step 1: Flip the equation.

x+4=y

Step 2: Add -4 to both sides.

x+4+−4=y+−4

x=y−4

Answer:

x=y−4

The answer is the independent variable

Here, we want to select the choice that can impact the dependent variable

A dependent variable is one which has its value depending on an input

This input is called the independent variable

In clear terms, we are sourcing the values of the dependent varaible from the independent

In a well designed experiment, the control, constant and the extraneous variable will not affect the dependent variable. Only the independent variable has an effect or impact on the activities, values or actions of the dependent variable

A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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Answer:

1200

Step-by-step explanation:

since there are 30 in each package, and 40 packages in total, then you would just multiply the two together.

True, a researcher wants to compare performance scores for men versus women on a motor skills task. it would not be possible to use a repeated measures design for this study.

What is a performance comparison?

They are frequently used while benchmarking, which is the practice of evaluating an organization's performance versus that of the best-performing businesses.

                 The measures are employed in productivity improvement projects to monitor changes in productivity over time.

Why is performance measurement important?

Comparing is one of the most important growth drivers. Only when we contrast our development with that of our rivals or our current performance with our former performance do we get motivated to advance and accomplish greater feats.

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Step-by-step explanation:

It takes 73 pounds of seed to completely plant an 11 -acre field. How many pounds of seed are needed per acre?

73 / 11 = 6.6363636 pounds per acre

rounded to two decimal places: 6.64 pounds per acre

Answer:

\(x + x + 4 + 3x - 9 =90 \\ 5x = 95 \\ x = 19 \\ \\ gjh = 19 + 4 = 23\)

Answer:

The model is made in a 1:40 ratio

Step-by-step explanation:

How many times is 4 multiplied to be equal to 160?

4(x) = 160

X = 160 / 4

X = 40

The proportion, rate, and ratio are almost the same.

They represent the correspondence between the parts and the whole since they all express a binary relationship between the quantities, that is, objects, people, tablespoons.

If the ratio is 1: 2 it could be read that for every 1 there are 2.

For example 1: 2 cups; For every cup of something there are 2 cups of something else.

In this case, 1:40; For every inch of the model, there are 40 feet in the playground.

Answer:

137°

Step-by-step explanation:

By the exterior angle theorem, \(m\angle JKX=93^{\circ}+44^{\circ}=137^{\circ}\).