In April, Phillipa rode 13 . 5 + 8 . 7 + 11 . 1 miles on her bicycle. In March, she rode ( 13 . 5 + 8 . 7 + 11 . 1 ) ÷ 2 miles, and in May, she rode 4 × ( 13 . 5 + 8 . 7 + 11 . 1 ) miles. Determine the month when she rode the most and the month when she rode the least. How many times farther did she ride in the month when she rode the most than in the month when she rode the least?

Given:

i) 3, -5, -2, 1

ii) -1, -8, -7, -2

iii) -2, -4, 0, 2

To find:

increasing order of the given numbers.

Solution:

Increasing order: We need to start from the smallest number, then write larger number and end with the largest number.

We know that all negative numbers are less than the positive numbers and larger negative value is always the smaller one.

For example: -3 is less than -1.

i) We have,

3, -5, -2, 1

So, the increasing order of these number is -5, -3, -2, 1.

ii) We have,

-1, -8, -7, -2

So, the increasing order of these number is -8, -7, -2, -1.

iii) We have,

-2, -4, 0, 2

So, the increasing order of these number is -4, -2, 0, 2.

Answer:

To solve for x in the equation −12(x + 5) = -10, we will use the following steps:

Distribute the -12 to the terms inside the parentheses:

-12x - 60 = -10

Add 60 to both sides of the equation to isolate the variable term:

-12x = 50

Finally, divide both sides of the equation by -12 to solve for x:

x = -50/12

Simplifying the answer, we get:

x = -25/6 or -4.1667 (rounded to four decimal places)

Step-by-step explanation:

Answer:

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

This is a proportional relationship since it is of the same form:

The constant k represents the rate of change, so:

Answer:

c=68 and b=112

Step-by-step explanation:

Answer:

-77x^2 -84x

Step-by-step explanation:

\( - {77x}^{2} - 84x\)

just multiply -7 by each number within the parentheses.

Answer:

the slope is 6/5, so b

Step-by-step explanation:

The equation for the perimeter is 2(2w + 5) = 70, to calculate the width.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Given the perimeter of a rectangular flower bed = 70 feet

and the length of  the flowerbed is 5 feet more than the width,

let width be w

length = w + 5

perimeter is given by = P = 2(l + b)

P = 2(w + w + 5)

P = 2(2w + 5)

Hence option C is correct to find the width of the rectangular flowerbed.

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Answer:

1&5

Step-by-step explanation:

A pair of corresponding angles from the diagram is ∠1 and ∠5.

The correct option is C.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

We have two parallel lines.

And a line intersects the parallel lines.

The corresponding angles are,

∠1 and ∠5.

∠2 and ∠6.

∠3 and ∠7 etc.

From the given choices,

∠1 and ∠5.

Therefore, from the given choices,

∠1 and ∠5.

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This question asks for the probability of the union of two events A ( pop) and B (had 500 - 1000 plays).

Since we know the probability of each event separately, P(A) = 0.9 and P(B) = 0.6, as well as the probability of their intersection, P(A ∩ B) = 0.5, the probability of their union is given by:

P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.9 + 0.6 - 0.5 = 1

Therefore, the answer is 1.

Car insurance for an 18-year-old typically ranges from $200 to $400 per month.

The cost of car insurance for an 18-year-old can vary significantly depending on various factors. Young drivers, especially those with limited driving experience, are generally considered higher risk by insurance companies, which leads to higher premiums. Insurance providers take into account factors such as the driver's age, gender, location, type of vehicle, driving record, and credit history. Additionally, factors like the level of coverage and deductibles chosen, as well as discounts available, can also impact the cost. It's important for young drivers to shop around and compare quotes from different insurance companies to find the best coverage options at the most affordable rates. Additionally, taking driver's education courses and maintaining a clean driving record can help in reducing insurance costs over time.

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What is the average monthly cost of car insurance for an 18-year-old?

Answer:20.04

Step-by-step explanation: The answer is 20.04 because we have to round in 2 decimal point and 4<5 so 4 is not changed.

Answer:

A. slope of f(x) is 3

B. g(x) has greater y-intercept

Step-by-step explanation:

A.slope of f(x): m = (y2-y1)/(x2-x1)

m = (3 - 0)/(1 - 0) = 3/1 = 3

then y = mx + b => y = 3x + b

then substituting (1,3) => 3 = 3(1) + b => 3 = 3 + b => b = 0

so y = 3x

slope of f(x) is 3

using  y = mx + b

then g(x) = 7x + 2 => slope of g(x) is 7

B. b is the y-intercept

so for f(x) = 3x => b is 0

and for g(x) = 7x + 2 => b is 2

so g(x)'s y-intercept is 2 which is great than f(x)'s

Answer:

13 * 18 = 234 yards of ribbon

Step-by-step explanation:

Each spool has 18 yards of ribbon and Eleanor bought 13 spools. Hence, you can use multiplication to solve it

\(13 \times 18 = 234\)

Answer:

It would be D

Step-by-step explanation:

The distance between the point A and point B is 9.5 units

The formula for calculating the distance between two points is expressed according to the formula shown below;

AB = √(x₂-x₁)²+(y₂-y₁)²

Using the given coordinates points A(5, -3) and B (-4, -6)

Substitute to have:

AB = √(5-(-4))²+(-3-(-6))²

AB = √(5+4)²+(-3+6))²

AB = √81+9

AB =  √90

AB = 9.5 units

Hence the distance between the point A and point B is 9.5 units

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Answer:

0.98 ≤ x ≤ 2.9

Step-by-step explanation:

use graphing calculator

Step-by-step explanation:

I don't know if I got that right

The x-values where f′(x)=0 are x = 0 and x = 2/39.

To find the x-value(s) where f′(x)=0 for the function f(x)=13x^3 - x^2, we need to first find the derivative f′(x):

f′(x) = d(13x^3 - x^2) / dx = 39x^2 - 2x

Now, we need to set f′(x) to 0 and solve for x:

0 = 39x^2 - 2x

Factor out the common factor x:

0 = x(39x - 2)

Now we have two possible solutions for x:

1) x = 0
2) 39x - 2 = 0, which leads to x = 2/39

The x-values where f′(x)=0 are x = 0 and x = 2/39.

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If Q(t)= C/4t - 1 an equation for Q-¹(t) is y = C + t/4t.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Given,

Q(t) = C/4t -1

Put a "y" in place of the "Q(t)":

y = C/4t -1

Change the t and y since each (t, y) has a corresponding (y, t) companion.

t = C/4y -1

Distribute t by multiplying into the bracket to find y.

t × 4y -1 = C

t × 4y - t = C

Add both sides of the equation together now.

t × 4y = C +t

4t divided by both sides

y = C + t/4t

If Q(t)= C/4t - 1 an equation for Q-¹(t) is y = C + t/4t.

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The speed that Jo walked for the first 15 minutes is; 6 km/hr

The distance - time graph is missing and so i have attached it.

Now, the formula for speed is;

Speed = Distance/time

The distance after 15 minutes from the graph is 1.5km.

Now, 15 minutes when converted to hours is 15/60 = ¹/₄ hr

Thus, the speed that Jo walked for the first 15 minutes is;

Speed = 1.5/(¹/₄)

Speed = 6 km/hr

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Largest value can decreased by 49 without affecting the value of median.

The median is the middle score in the set. To find the median, you take these steps:

Step 1: Arrange the scores in numerical order

Step 2: Count how many scores you have

Step 3: Divide the total scores by 2

Step 4: If you have an odd number of total scores, round up to get the position of the median number. If you have an even number of total scores, go to the number in that position and average it with the number in the next higher position to get the median.

For example:

given sets: 5, 4, 3, 6, 8

now rearrange the sets in increasing order: 3, 4, 5, 6, 8

median = ( n + 1 ) / 2 = ( 5 + 1) / 2 = 3

here median = 5

We have given that:

384, 350,  354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.

when we arrange it in increasing order.

here n = 26

median = ( n + 1 ) / 2

median =  average of 13th and 14th element

median = 371

larger value can be decreased by 420 - 371 = 49

Hence,

Largest value can decreased by 49 without affecting the value of median.

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Disclaimer: The question given was incomplete on the portal. Here is the complete question.

Question: A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape:

384, 350,  354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.

By how much could the largest sample observation be decreased without affecting the value of the median?

The largest sample observation could be decreased by 54.5 without affecting the value of the median.

We have given the data:

384, 350,  354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.

Now, we arrange it in increasing order.

321, 329, 330, 339, 350, 354, 354, 359, 361, 363, 365, 366, 369, 370, 374, 376, 376,378, 384, 393, 394, 396, 398,404, 424

Here n = 26

median = ( n + 1 ) / 2

median =  369 + 370 / 2

median = 369.5

Larger value can be decreased by 424 - 369.5= 54.5

Therefore, the largest sample observation could be decreased by 54.5 without affecting the value of the median.

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The question given was incomplete on the portal. Here is the complete question.

A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape:

384, 350,  354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.

By how much could the largest sample observation be decreased without affecting the value of the median?

Answer:

let x represent the number

7x-8=20

7x=20+8

7x=28

x=28/7

x=4

this is the correct answer

Answer:

7x-8=20         or          x=4

Step-by-step explanation:

Let's say the certain number is x

7x-8=20

Add 8 on both sides:

7x-8+8=20+8

Simplify:

7x=28

Divide 7 on both sides:

\(\frac{7x}{7}\)=\(\frac{28}{7}\)

Simplify:

x=4

Answer:

Question 1: b) Find the total distance from A to B

Distance formula:

d=Square root of (x2-x1)^2+(y2-y1)^2+(z2-z1)^2

d=Square root of (6-4)^2+(12-8)^2+(10-2)^2

d= 9.165 = 9.17 units

Answer:

1 a

Use the midpoint formula:

m=x1+x2/2, y1+y2/2, z1+z2/2

m= 4+6/2 ,8+12/2, 2+10/2

m= (5 ,10, 6)

Step-by-step explanation:

Using the concept of independent events, it is found that the correct statement is:

a and b are independent events because p(a∣b) = p(a) = 0.75.

Two events, A and B, are independent if:

\(P(A \cap B) = P(A)P(B)\)

In this problem, the events are:

In this problem, out of 300 students, 225 have surfed, hence:

\(P(A) = \frac{225}{300} = 0.75\)

48 have gone snowboarding, hence:

\(P(B) = \frac{48}{300} = 0.16\)

36 have done both, hence:

\(P(A \cap B) = \frac{36}{300} = 0.12\)

The multiplication is:

P(A)P(B) = 0.75 x 0.16 = 0.12.

That is, the probability of A given B is P(A|B) = P(A) = 0.75, hence they are independent.

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Answer:

the answer is B

Step-by-step explanation:

Answer:

%70

Step-by-step explanation:

percentage can be found by dividing the values than multiplying the values by 100

Formula: (value/totalvalue)100

plug in the formula with what we have;

28/40(100)

→ First step; dividing our value by total value (28/40)

28/40 = 0.7

  → Second step; multiplying our value by 100 (0.7)

0.7 * 100 = 70

Therefore cora got %70 correct on her grammar sheet

Answer:

70% correct

Step-by-step explanation:

We know that there are 40 questions on her grammar worksheet.

Out of those 40 questions, she got 28 right so 28/40 equals 0.7

A bell-shaped probability distribution that is symmetrical about its mean is the student's t-distribution. In the following situations, it is thought to be the distribution that should be used to build confidence intervals when working with little samples that have fewer than 30 components if it is unclear what the population variance is.

When the involved distribution is either normal or nearly normal.

A t-distribution is used to test the following in addition to being used to build confidence intervals:

Individual population mean

The variations in two population means.

The average variation among paired (dependent) populations.

The correlation coefficient for the populace.

If the sample size is high enough for the central limit, a t-distribution may still be viable for usage even in the absence of explicit normality for a specific distribution theorem that must be used. In this scenario, the distribution is regarded as roughly normal.

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a. Less than 25 years: M: 4, F:  5    

25 to 35 years: M: 17, F: 6    

More than 35 years: M: 8, F: 10

b. The probability that the selected employee is male or their age is more than 35 years is 0.44.

a. The given data represents the Health Expenditures of employees by Age and Gender. We can summarize the data in a table by organizing the information based on the age groups and genders.

The summarized table is as follows:

| Age (years)           | Male | Female |

|-----------------------|------|--------|

| Less than 25 years    | 4    | 5      |

| 25 to 35 years        | 17   | 6      |

| More than 35 years    | 8    | 10     |

b. To find the probability that the selected employee is male or his age is more than 35 years, we need to calculate the probabilities of two events and then subtract the probability of their intersection.

1. Event A: The selected employee is male.

  We calculate the probability of Event A by dividing the number of males in the sample by the total number of individuals in the sample:

  P(A) = (Number of males in the sample) / (Total number of individuals in the sample)

       = (4 + 8) / 50

       = 12 / 50

       = 0.24

2. Event B: The selected employee's age is more than 35 years.

  We calculate the probability of Event B by dividing the number of individuals with age more than 35 in the sample by the total number of individuals in the sample:

  P(B) = (Number of individuals with age > 35 in the sample) / (Total number of individuals in the sample)

       = (8 + 10) / 50

       = 18 / 50

       = 0.36

3. Intersection of Event A and Event B: The selected employee is male and has an

age more than 35 years.

  We calculate the probability of the intersection by dividing the number of males with age more than 35 in the sample by the total number of individuals in the sample:

  P(A and B) = (Number of males with age > 35 in the sample) / (Total number of individuals in the sample)

             = 8 / 50

             = 0.16

Finally, we use the formula for the probability of the union of two events to calculate the probability that the selected employee is male or his age is more than 35 years:

P(A or B) = P(A) + P(B) - P(A and B)

         = 0.24 + 0.36 - 0.16

         = 0.44

Therefore, the probability that the selected employee is male or his age is more than 35 years is 0.44.

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In the case of a suspected myocardial infarction (MI) in a client presenting in the Emergency Department, certain medications should be administered as soon as possible to improve outcomes.

When a client presents with a suspected MI, time is of the essence in initiating appropriate treatment to minimize damage to the heart muscle and improve outcomes. The administration of aspirin is a priority as it helps prevent further blood clot formation. Aspirin inhibits platelet aggregation, reducing the risk of thrombus formation in the coronary arteries.

Nitroglycerin is another medication that should be given promptly. Nitroglycerin helps relieve chest pain by dilating coronary arteries and improving blood flow to the heart. It also helps reduce preload and afterload, thereby decreasing the workload on the heart.

In cases where the client experiences severe pain despite aspirin and nitroglycerin administration, morphine can be administered to alleviate pain and reduce anxiety. Morphine also helps dilate blood vessels, which can further improve blood flow to the heart.

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"A client presents in the Emergency Department with a suspected myocardial infarction (MI). Which medications should be given as soon as possible to improve outcomes?"

Answer:

11x-5

Step-by-step explanation: