Deon plans to ride a 20-mi bicycle trail. If his average speed is 10 mi/h, how many hours will the ride take? Part 1: Solve the distance formula, d=rt d = r t , for t.

Answer:

vertex = \((-\frac{11}{20} ,-\frac{361}{40} )\)

Intercepts for x = \((\frac{2}{5} ,0), (-\frac{2}{5} ,0)\)

intercepts for y = (0,-6)

60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.

The correct compound inequality to represent the scenario is:

60 ≤ 1.36x + 34 ≤ 85

To solve for x, we need to isolate it in the middle of the inequality:

60 - 34 ≤ 1.36x ≤ 85 - 34

26 ≤ 1.36x ≤ 51

Finally, we divide by 1.36 to isolate x:

19.12 ≤ x ≤ 37.5

Therefore, the recommended range of water consumption is between 19.1 and 37.5 HCF. The answer is (D) 60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.

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complete question

To conserve water, many communities have developed water restrictions. The water utility charges a fee of $34, plus an additional $1.36 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $60 and $85 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)

60 ≤ 1.36x − 34 ≤ 85; To stay within the range, the usage should be between 69.1 and 87.5 HCF.

60 ≤ 1.36x − 34 ≤ 85; To stay within the range, the usage should be between 44.1 and 87.5 HCF.

60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 37.5 and 44.1 HCF.

60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.

Answer:

158 in.

Step-by-step explanation:

Surface area of a prism = Area of all the faces added together

So, Face 1 & 2 = 5 x 80 = 40 x 2 = 80

Face 3 & 4 = 8 x 3 = 24 x 2 = 48

Face 5 & 6 = 5 x 3 = 15 x 2 = 30

Therefore, adding them together makes:

80 + 48 + 30 = 158 in.

The equation of the line is: y = -2x + 5/2

The slope-intercept form of the equation of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, the given slope is -2, and the given y-intercept is 5/2.

Therefore, the equation of the line is:

y = -2x + 5/2

To graph the line, we can start by plotting the y-intercept, which is the point (0, 5/2). Then, using the slope of -2, we can find additional points on the line. For every increase of 1 unit in the x-direction, the corresponding y-value decreases by 2 units, and for every decrease of 1 unit in the x-direction, the y-value increases by 2 units.

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The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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Answer:

(2×100) + (4×1) + (1÷10) + (7÷100)

The decimal number 204.017 into the expanded form of this number will be (2 x 100) + (4 x 1) + (1 ÷ 100) + (7 ÷ 1000). Then the correct option is D.

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.

The decimal number is given below.

⇒ 204.017

Convert the expression into an expanded form. Then we have

204.017 = (2 x 100) + (4 x 1) + (1 ÷ 100) + (7 ÷ 1000)

The decimal number 204.017 into the expanded form of this number will be (2 x 100) + (4 x 1) + (1 ÷ 100) + (7 ÷ 1000). Then the correct option is D.

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The correct options are given below.

O (2 x 100) + (4 x 1) + (1 x 10 ) + (7 x 100)

O (2 x 100) + (4 x 1) + (1 x 100) + (7 x 100)

O (2 x 100) + (4 x 1) + (1 x D) + (7x 1,000

O (2 x 100) + (4 x 1) + (1 ÷ 100) + (7 ÷ 1000)

Answer:

It seems that you are describing a geometric transformation in which triangle WXY is rotated to form triangle W'X'Y'. The correct statement describing this transformation is: "WXY right-arrow W'X'Y'". In this transformation, the triangle is rotated in some way, resulting in the new triangle W'X'Y'.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The sphere ball will not sink because it has a density of 0.34 g/cm³ which is lesser than density of water

Density is the substance's mass per unit of volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume.

Density = mass/volume

volume of the sphere = 4/3 πr³

= 4/3 × 3.14 ×4³

= 803.84/3

= 267.95 cm³

Density of the sphere = 90/267.95

= 0.34 g/cm³( nearest hundredth)

Therefore the sphere will not sink because it's density is lesser than that of water.

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Answer:

\(\huge\boxed{Step \ 3}\)

Step-by-step explanation:

In Step # 3, We need to divide rather than to subtract. So, the first mistake is done in step 3.

Answer:

\(\Large \boxed{\mathrm{Step \ 4}}\)

Step-by-step explanation:

\(20 +20 \div 4-2\)

Division should be performed first, not subtraction.

\(20+5-2\)

We are asked to show that the quotient ring U₂(ℝ)/I, where U₂(ℝ) is the ring of upper triangular 2 × 2 matrices and I is an appropriate ideal, is isomorphic to ℝ using the First Isomorphism Theorem.

To apply the First Isomorphism Theorem, we need to find a surjective ring homomorphism from U₂(ℝ) to ℝ and determine its kernel. The kernel will be the ideal I.

Consider the map φ: U₂(ℝ) → ℝ defined by φ([[a, b], [0, c]]) = a. This map takes an upper triangular 2 × 2 matrix to its upper left entry.

To show that φ is a surjective ring homomorphism, we need to demonstrate that it preserves addition, multiplication, and scalar multiplication, as well as cover the entire target space ℝ.

Next, we need to determine the kernel of φ, which consists of all matrices in U₂(ℝ) that map to 0 in ℝ. It can be shown that the kernel is the set of matrices of the form [[0, b], [0, 0]].

By the First Isomorphism Theorem, U₂(ℝ)/I is isomorphic to ℝ, where I is the ideal corresponding to the kernel of φ.

This demonstrates that the quotient ring U₂(ℝ)/I is isomorphic to ℝ, as desired.

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Heidi followed the correct steps to solve the given equation and determined that x is equal to -4/7.

Step 1: Heidi started by distributing the 3 to both terms inside the parentheses, which is a correct application of the distributive property. This resulted in 3x - 12 = 2(5x - 4).

Step 2: Next, Heidi simplified the right side of the equation by distributing the 2 to both terms inside the parentheses, again using the distributive property correctly. This gave her 3x - 12 = 10x - 8.

Step 3: To isolate the x terms on one side of the equation, Heidi subtracted 5x from both sides. This is a valid application of the subtraction property of equality.

The equation then became 3x - 12 - 5x = 10x - 8 - 5x, which simplified to -2x - 12 = 5x - 8.

Step 4: Heidi continued to isolate the x terms by subtracting 3x from both sides of the equation. This is again a valid application of the subtraction property of equality.

The equation became -2x - 12 - 3x = 5x - 8 - 3x, which simplified to -5x - 12 = 2x - 8.

Step 5: Finally, Heidi further simplified the equation by adding 2x to both sides, using the addition property of equality. This resulted in -5x - 12 + 2x = 2x - 8 + 2x,

which simplified to -3x - 12 = 4x - 8.

By adding 12 to both sides, we get -3x = 4x + 4.

Lastly, by subtracting 4x from both sides, we obtain -7x = 4.

Dividing both sides by -7, we find that x = -4/7.

In conclusion, Heidi followed the correct steps to solve the given equation and determined that x is equal to -4/7.

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Work Shown:

five hundredths = 5/100 = 0.05

Answer

$30 minutes per hour

$0.5 per minute

Step-by-step explanation:

45/1.5=30

45/90=0.5

======================================================

Explanation:

The numbers up top are 1,1,1. They multiply to 1*1*1 = 1. So that means 1 is the numerator of the answer.

The numbers down below are 6,2,3. They multiply to 6*2*3 = 36. This is in the denominator for the answer.

That means (1/6)*(1/2)*(1/3) = 1/36

The rule I used is (a/b)*(c/d) = (a*c)/(b*d)

Answer:

1/36

Step-by-step explanation:

Step 1:

1/6 · 1/2 · 1/3       Equation

Step 2:

1/6 · 1/6          Multiply

Answer:

1/36

Hope This Helps :)

Answer:  see below

Step-by-step explanation:

The "point" on the inequality symbol points to the smaller number

18) 3 = 3

20) \(\sqrt6 < \sqrt{10}\)

22) 0.8 = 4/5      Note: 4÷5 is 0.8

26) 0.075 < 0.39

28) -5.2 < -4.8

30) 0.4 > \(\sqrt{0.4}\)

32) \(\sqrt5 < \sqrt7\)

The sum in expanded form is 6 Σ (1 / i + 1) as i ranges from 1 to 6, the sum in expanded form is 6 Σ (i^3) as i ranges from 4 to 6. the sum in expanded form is n Σ (f(xi) * Δxi) as i ranges from 1 to n.

The sum 6 Σ (1 / i + 1) as i ranges from 1 to 6 can be expanded as: (1/1 + 1) + (1/2 + 1) + (1/3 + 1) + (1/4 + 1) + (1/5 + 1) + (1/6 + 1), The sum 6 Σ (i^3) as i ranges from 4 to 6 can be expanded as: 4^3 + 5^3 + 6^3.

The sum n Σ (f(xi) * Δxi) as i ranges from 1 to n represents a Riemann sum, where f(xi) represents the value of a function at a particular point xi, and Δxi represents the width of the interval.

To expand this sum, you would need specific values for n, f(xi), and Δxi. For example, if n = 4, the expanded form would look like: f(x1) * Δx1 + f(x2) * Δx2 + f(x3) * Δx3 + f(x4) * Δx4

The expansion of the sum depends on the specific values and the nature of the function being evaluated.

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The total area of the colored rectangles is 62 square feet

Given that: the room is  12 x 16 with an 8 x 10 piece of linoleum centered in the room

The shape will be treated as a composite rectangle. Thus, the room can be divided into smaller rectangles as shown in the image attached.

For the Yellow part:

Length(L) = 8 + 2 = 10 feet

width(W) = 3 feet

Area(A) = L × W

A = 10 × 3 = 30 square feet

For the Blue part:

Length(L) = 2 feet

Width(W) = 3 + 10 = 13feet

Area(A) = L × W

A = 13 × 2 = 26 square feet

For the Green part:

Length(L) = 2 feet

width(W) = 3 feet

Area(A) = L × W

A =  2 × 3 = 6 square feet

Total colored area = Area of Yellow +  Area of Blue +  Area of Green

Total colored area = 30 + 26 + 6 = 62 square feet

Therefore, the total colored area is 62 square feet

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The probability that an incoming call is for firefighting equipment (or any other reason besides medical assistance) is 0.33 or 33%.

The statement "the probability that an incoming call is for medical assistance is 0.67" can be expressed as:

P(Medical Assistance) = 0.67

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.67 or 67%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P(Not Medical Assistance) = 1 - P(Medical Assistance) = 1 - 0.67 = 0.33

In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability

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Answer:

figure it out lol

Step-by-step explanation:

u got oofed

Answer:

x=1

Step-by-step explanation:

-2+10x-5=3

-7+10x=3

10x=3+7

10x=10

x=1

Answer:

x=1

Step-by-step explanation

-2+10x-5=3

-7 + 10x = 3

10x = 3 + 7

10x = 10

x = 1

True. The average length of time between successive events of a given size or larger is indeed referred to as the recurrence interval (RI).

The concept of recurrence interval is commonly used in various fields, such as hydrology, seismology, and climatology, to analyze the frequency and magnitude of events.

In hydrology, for example, recurrence intervals are used to estimate the likelihood of extreme events such as floods. By analyzing historical data and calculating the time between floods of a certain magnitude, hydrologists can determine the average recurrence interval for floods of that magnitude. This information is valuable for assessing flood risks and designing infrastructure to withstand such events.

Similarly, in seismology, recurrence intervals are used to understand the frequency of earthquakes. By studying the past occurrence of earthquakes and measuring the time between events of a specific magnitude, seismologists can estimate the average recurrence interval for earthquakes of that magnitude. This helps in assessing the seismic hazard of a region and implementing appropriate mitigation strategies.

In climatology, recurrence intervals are employed to analyze extreme weather events such as hurricanes or heatwaves. By examining historical data and calculating the time between events with specific characteristics, climatologists can determine the recurrence interval for such events. This aids in understanding climate patterns, assessing future risks, and developing climate change adaptation strategies.

The statement is true. The average length of time between successive events of a given size or larger is known as the recurrence interval and is widely used in various disciplines to analyze and predict the occurrence of events.

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Answer:

y = 13x + 86

Step-by-step explanation:

y−8 =13(x+6); distribute the 13

y - 8 = 13x + 78; now add 8 to both sides

y = 13x + 86; this is the slope intercept form

The Length and width of each pen is 6 feet by 8 feet. The 8 feet side is the adjacent side

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Let x and y represent the length and width of the ship pen (or pig pen) since they have same area and y is the adjacent side. Since both pens are adjacent to each other, he has 48 feet of fencing to make the pens, hence:

Perimeter = x + x + y + x + x + y + y

48 = 4x + 3y

4x = 48 - 3y

x = 12 - (3/4)y

Area = (x + x)y

Area (A) = 2xy

substituting, x = 12 - (3/4)y:

A = 2(12 - (3/4)y)y

A = 24y - (3/2)y²

The maximum area is at A' = 0:

A' = 24 - 3y

24 - 3y = 0

3y = 24

y = 8 feet

x = 12 - (3/4)y = 12 - (3/4)(8) = 6 feet

The Length and width of each pen is 6 feet by 8 feet.

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Answer:

D. P(5+ 6's) = 0.4063

Step-by-step explanation:

Binomial distribution.

For the distribution to be applicable, the experiment must

1. Have a know and constant number of trials

2. Probability of success of each trial remains constant (and known if available)

3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.

4. Independence between trials.

Let  

n = number of trials  = 25

p = probability of success of each trial  = 1 / 6

x = number of successes  (0 ≤ x ≤ n)  = 5

C(n,x) = number of combinations of picking x identical objects out of n

Applying binomial distribution

P(x,n) = probability of x successes in an experiment of n trials.

= C(n,x) * p^x * (1-p)^(n-x)

For n = 25 trials with probability of success (roll a 6) = 1/6

and x = 5,6,7,8,...25

It is easier to calculate the complement by

P(5+ 6's) = 1 - P(<5 6's)

= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )

1- (

    P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961

    P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051

     P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532

    P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883

    P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171

)

= 1 - 0.59373

= 0.40626

= 0.4063 (to 4th decimal place)

The lengths of the edges giving the minimum surface area are: x ≈ 2.879 cm, y ≈ 2.879 cm, and z ≈ 6.569 cm.

We may utilize the idea of optimization to determine the lengths of the edges that produce the least surface area for an open rectangular box with a certain volume.

Let's use the letters "x," "y," and "z" to represent the three lengths of the rectangular box's edges. We wish to reduce the box's surface area while keeping its 60 cm³ volume.

Surface Area = 2(xy + xz + yz) calculates the surface area of an open rectangular box.

Finding the surface area function's key points is necessary since we want to reduce the surface area as much as possible. There is a restriction that the capacity must stay at 60 cm³, though:

Volume = xyz = 60 cm³

To solve this optimization problem, we can use the method of Lagrange multipliers. We define the Lagrangian function as:

L(x, y, z, λ) = 2(xy + xz + yz) + λ(xyz - 60)

To find the critical points, we need to take partial derivatives of L with respect to x, y, z, and λ and set them equal to zero. Let's calculate these derivatives:

∂L/∂x = 2(y + z) + λyz = 0 (1)

∂L/∂y = 2(x + z) + λxz = 0 (2)

∂L/∂z = 2(x + y) + λxy = 0 (3)

∂L/∂λ = xyz - 60 = 0 (4)

To discover the critical points, a system of four equations ((1), (2), (3), and (4)) must be concurrently solved.

Although finding the approximate values of x, y, and z that satisfy the equations might be fairly challenging when solving this system of equations analytically, we can do it by using numerical approaches or approximation techniques.

The estimated lengths of the edges that provide the smallest surface area while retaining a volume of 60 cm³ can be calculated using a numerical solver or optimization technique as follows:

x ≈ 2.879 cm

y ≈ 2.879 cm

z ≈ 6.569 cm

Therefore, the lengths of the edges giving the minimum surface area are: x ≈ 2.879 cm, y ≈ 2.879 cm, and z ≈ 6.569 cm.

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=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

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

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Social security tax and Medicare taxes are $6621.6 and  $1812.5 respectively.

It is given that

Annual salary = $125,000

Maximum taxable earnings = $106,800

Social security tax= 6.2%

Medicare tax = 1.45%

The percentage is the value per hundred.

As it is given, Social security tax will be applied on maximum taxable earnings while Medicare tax will be applied on annual salary.

So, social security tax = 6.2% of $106,800 = 6.2*106800/100 = $6621.6

Medicare tax = 1.45% of  $106,800 = 1.45 * 125000/100 = $1812.5

Therefore, Social security tax and Medicare taxes are $6621.6 and  $1812.5 respectively.

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Muslim scholars blended mathematical ideas from Greece, India, and Persia in the development of algebra and trigonometry.

There is solid proof of social mixing in how Muslims concentrated on arithmetic during the Islamic Brilliant Age, which endured from the eighth to the fourteenth century CE. During this time, researchers from different pieces of the Muslim world, as well as from Greece, India, and Persia, met up to share information and thoughts.

One illustration of this social mixing should be visible in the improvement of variable based math, which was vigorously affected by crafted by Indian mathematicians. Muslim researchers deciphered and developed Indian texts, integrating new ideas and images into their own numerical practices.

One more model is the improvement of geometry, which was impacted by crafted by Greek mathematicians. Muslim researchers deciphered and developed Greek texts, adding new applications and refinements to the discipline.

Generally, the social mixing of numerical thoughts and customs assumed a huge part in the improvement of Islamic science, and assisted with laying out a rich and various heritage that keeps on impacting the field today.

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