Question 1 (Multiple Choice Worth 5 points)
(Proportions MC)
Thomas swam 6 laps in 21⁄2 minutes. At this rate, how many laps would he swim in 10 minutes?

The ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.

To represent the gauge readings as rational numbers, we can express them as fractions with a common denominator.

Given readings:

25 psi pressure

13 psi vacuum

6.3 psi vacuum

7.8 psi vacuum

1.9 psi vacuum

2 psi pressure

7.8 psi pressure

Expressed as rational numbers with a common denominator:

25 psi = 25/1

13 psi = 13/1

6.3 psi = 63/10

7.8 psi = 78/10

1.9 psi = 19/10

2 psi = 2/1

7.8 psi = 78/10

Now, let's order these rational numbers from least to greatest:

1.9 psi = 19/10

6.3 psi = 63/10

7.8 psi = 78/10

7.8 psi = 78/10

13 psi = 13/1

25 psi = 25/1

2 psi = 2/1

Ordered from least to greatest:

19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1

Therefore, the ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.

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According to the information, it can be concluded that there is no significant difference in the braking distances of the two models.

To check if there is a wide difference between the braking distances of the two models we can use several alternatives. One of them is to add all the braking distance results of each car and take the average as shown below:

According to the above, it can be concluded that the braking distance of both models only varies by 2 feet, so it is considered that there is not a great difference in braking distances.

Note: This question is incomplete because there is some information missing. Here is the complete information:

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Answer:

We get \(\mathbf{(f-g)(x)= -x^2-3x-8}\)

Step-by-step explanation:

We are given:

\(f(x) = -3x - 3\\ g(x) = x^2 + 5\)

We need to find (f-g)(x) (assuming there is x in the bracket, i.e. (f - g) () should be (f-g)(x))

We would simply subtract f(x) and g(x)

\((f-g)(x)\\= -3x-3-(x^2+5)\\Multiply\:minus\:sign\:with\:terms\:inside\:the\:bracket\\=-3x-3-x^2-5\\Combining\:like\:terms:\\=-x^2-3x-3-5\\=-x^2-3x-8\)

So, We get \(\mathbf{(f-g)(x)= -x^2-3x-8}\)

Answer:

A ; 21

Step-by-step explanation:

Here, the side facing the right angle is the hypotenuse and it has a measure of length 42

The side facing the missing angle is the opposite and it has a length of 15

The trigonometric ratio that connects the hypotenuse and the opposite is the sine

The sine of an angle is the ratio of the opposite to the hypotenuse

Thus;

sine ? = 15/42

sine ? = 0.357

? = arc•sim 0.357

? = 21 degrees

Answer:

Jenny has worked out the area of the whole circle using the formula π × r² where r is the radius length. She has assumed π is 3.14 which leads to her working of 3.14 × 10² = 314 units². She has to divide the total area by 4 to calculate the sector area.

Let's check

Area of sector

Answer:

5.

Step-by-step explanation:

If the first 4 picked are of different colours then the fifth  sock must be a match. for one of the four.

The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

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The verbal expressions A. half of five more than a number, C. five more than half a number, and D. half of five less than a number represent the given algebraic expression when assigned with a variable. The expressions are 1/2(x + 5), 5 + 1/2x, and 1/2(x - 5).

The verbal expressions that represent the algebraic expressions are A. half of five more than a number, C. five more than half a number, and D. half of five less than a number. To convert these expressions into algebraic form, we need to assign a variable, say x, to the unknown number.

A. Half of five more than a number can be expressed algebraically as 1/2(x + 5). B. Twice a number and five can be written algebraically as 2x + 5. C. Five more than half a number can be expressed algebraically as 5 + 1/2x. D. Half of five less than a number can be written algebraically as 1/2(x - 5).

Therefore, the expressions that represent the given algebraic expression are A. half of five more than a number, C. five more than half a number, and D. half of five less than a number. Expression B represents a different algebraic expression altogether.

To summarize, three of the given verbal expressions represent the given algebraic expression, which can be converted to algebraic form by assigning a variable to the unknown number. These expressions are 1/2(x + 5), 5 + 1/2x, and 1/2(x - 5).

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If there are 43,560 square feet in an acre and  3.28 feet in a meter, the there would be approximately 80,937.68 square meters in 20 acres.

First, let's calculate the total number of square feet in 20 acres:

20 acres × 43,560 square feet/acre = 871,200 square feet

Now we can convert this to square meters using the conversion factor given:

Substitute the value of conversion factor in the equation

= 871,200 square feet × (1 square meter / 3.28 feet)^2

Multiply the numbers

= 80,937.68 square meters (rounded to two decimal places)

Therefore, there would be approximately 80,937.68 square meters in 20 acres.

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Answer:

29 units²

Step-by-step explanation:

You could divide this into two triangles and two trapezoids to find the area.  But since the majority of these are either whole or half squares, I‘d count those.  Then you’d just have one triangle in the top right corner.

Whole squares: 21

Half Squares: 10 (so 4 square units)

Triangle: 1/2(b)(h)=1/2(5)(2)=5

TOTAL = 21+4+5= 29 units²

Answer:

2 crusts

2 sauces

4 toppings

2x2x4= 16 combinations

\(y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+\underset{\underset{\textit{\small b }}{\uparrow }}{5}\implies y=-x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

Answer:

8%

Step-by-step explanation:

.08 x 100 = 8%

Answer: 15 - 6i

Step-by-step explanation:

3(5-2i)

3×5+3×(−2i)

Do the multiplications.

15−6i

Answer:

y = -4x + (-3)      or       y = -4x - 3,

Step-by-step explanation:

So the symbol would be negative (-). The rest of the equation is constructed by adding the slope which is -4x to the y intercept which is -3

The circumference of this circle is equal to 20.4 centimeters.

In Mathematics and Geometry, the circumference of a circle can be determined by using the following mathematical equations:

C = πD or C = 2πr

Where:

By substituting the given parameters into the formula for the circumference of a circle, we have the following;

Circumference of a circle, C = 3.14 × 6

Circumference of a circle, C = 20.4 centimeters.

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Answer:

Below

Step-by-step explanation:

y/40 = 5/8    multiply both sides of the equation by 40

y = 40 * 5/8 = 200/8 = 25

You have to find the slope of the line. It will give you the conversion rate from inches to centimetres or the other way around.

Looking closely at the graph, or using a ruler as reference, you can estimate that 30 cm ≈ 12 in. In terms of the graph, the line very nearly passes through the point (12, 30). It also passes through the origin, (0, 0), since 0 cm = 0 in exactly.

The slope of the line is then

\(\dfrac{30\,\mathrm{cm}-0\,\mathrm{cm}}{12\,\mathrm{in}-0\,\mathrm{in}} = \dfrac{30\,\rm cm}{12\,\rm in} = \dfrac{5\,\rm cm}{2\,\rm in} = 2.5\dfrac{\rm cm}{\rm in}\)

which means that 1 in ≈ 2.5 cm.

So, if Sarah's height is 64 in, we convert this to cm and find her height is (approximately)

\(64\,\mathrm{in} \times 2.5\dfrac{\rm cm}{\rm in} = \boxed{160\,\rm cm}\)

In a 6-dimensional data cube with no hierarchies associated with any dimension, the total number of cuboids can be calculated as 63, using a formula based on the inclusion-exclusion principle.

For a 6-dimensional data cube, there are 2^6 - 1 = 63 non-empty subsets of dimensions. Each subset represents a cuboid. Therefore, there are 63 cuboids in a 6-dimensional data cube without any hierarchies associated with the dimensions.

This calculation is based on the concept that each subset of dimensions corresponds to a unique cuboid in the data cube. By summing up the cardinalities of all possible subsets, excluding the empty set, we arrive at the total count of 63 cuboids in the given scenario.

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Answer:

= 11/7

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Assuming we mean biconditional statements. A biconditional must always be true. B is the only answer choice were both p and q are true. A young cow is a calf, and calfs are cows. Hope this helps!

Answer:

385$

Step-by-step explanation:

30% off of 600 is 180. 600-180=420. Then, 35$ off would be 385.

Answer:

42.5° East of South

Step-by-step explanation:

Hope this helps :)

The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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Answer:

The mean increases by 1.4

The equation of the line is y = -3x + 4.

The equation of a line can be represented in slope intercept form as follows:

y - mx + b

where

Hence, using (1, 1) and (0, 4)

Therefore,

m = 4 - 1 / 0 - 1

m = 3 / -1

m = -3

Hence, the y-intercept of the line is as follows:

y = -3x + b

4 = -3(0) + b

b = 4

Therefore, the equation of the line is y = -3x + 4

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The town is approximately 1806.11 feet from the base of the cliff. The opposite side is the vertical distance from the top of the cliff to the town, which is 364 feet.

The angle of depression is an angle formed between a horizontal line and a line of sight to an object below the horizontal line. In this problem, the angle of depression is 19 degrees and the top of the cliff is 364 feet above the town. To calculate the distance from the base of the cliff to the town, we can use the trigonometric function Tangent .Tangent can be expressed as the ratio of the opposite side to the adjacent side in a right triangle. In this problem, the adjacent side is the horizontal distance from the base of the cliff to the town, which we will call x, and the opposite side is the vertical distance from the top of the cliff to the town, which is 364 feet. Therefore, the equation for this problem is tan(19°) = 364ft/x We can solve for x by multiplying both sides by x and dividing both sides by tan(19°).x = (364ft)/tan(19°). Using a scientific calculator, we can find that x is approximately 1806.11 feet. Therefore, the town is approximately 1806.11 feet from the base of the cliff.

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Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.

Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.

So for example, if the salaries of any 5 faculty members are as follows:

$10,000 , $50,000 , $80,000 , $150,000 , $160,000

Mean= (10,000+50,000+80,000+150,000+160,000) / 5

Mean= $90,000

Median= (5+1) / 2

Median= 6/2

Median= 3rd value

As the data is already arranged in ascending order, Median is $80,000

Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.

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The area of water that is open to the atmosphere in acres and square feet, if the water surface elevation is uniformly 45 ft above the reservoir bed and the reservoir is holding 10 billion gallons of water is 436.59 acres and 19,015,471.19 square feet.

The area of water that is open to the atmosphere in acres and square feet, if the water surface elevation is uniformly 45 ft above the reservoir bed and the reservoir is holding 10 billion gallons of water can be calculated as follows:Given data:The surface elevation of water from the reservoir bed is uniformly 45 feet.

The reservoir is holding 10 billion gallons of water.We know that the volume of a rectangular prism can be found by multiplying its length, width, and height. Here, we can consider the reservoir as a rectangular prism whose height is 45 ft. Let's assume that the length and width of the rectangular prism are 'l' and 'w,' respectively. Therefore, the volume of the rectangular prism can be expressed as:l x w x 45 cubic feetAlso, the volume of a rectangular prism can be calculated using the formula:Volume of a rectangular prism = length × width × height= 7.4805 gallons/cubic footHere, the volume of the rectangular prism is 10 billion gallons.

Therefore, we can say:Volume of rectangular prism = 10,000,000,000 gallons= l x w x 45 x 7.4805 cubic feet= 33,660.225 l x w cubic feetWe can also express the area of the water surface by dividing the volume by the height (45 ft).

Therefore:Area of the water surface = (10,000,000,000 gallons) / (7.4805 gallons/ cubic foot × 45 ft)= 19,015,471.19 square feet= 436.59 acres

Hence, the area of water that is open to the atmosphere in acres and square feet, if the water surface elevation is uniformly 45 ft above the reservoir bed and the reservoir is holding 10 billion gallons of water is 436.59 acres and 19,015,471.19 square feet.

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