A lion can run 1.89 miles in distance. If 1 mile is the
same as 5,280 feet, what is the distance that a lion
can run in feet?

The graph of the inequality y ≤ (5/2)x - 5 is a downward-sloping line with shading below the line.

To graph the inequality 5x - 2y ≥ 10, we need to convert it to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Let's go step by step:

Step 1: Start with the original inequality:

5x - 2y ≥ 10

Step 2: Move the 5x term to the other side of the inequality by subtracting 5x from both sides:

-2y ≥ -5x + 10

Step 3: Divide the entire inequality by -2 (since we want to isolate y and have a positive coefficient for y):

y ≤ (5/2)x - 5

Now we have the inequality in the desired form. The graph of y ≤ (5/2)x - 5 represents all the points below or on the line y = (5/2)x - 5.

To graph this inequality, follow these steps:

Step 1: Plot the y-intercept, which is -5. This point is (0, -5).

Step 2: Find a second point by using the slope (5/2). The slope is the ratio of the change in y to the change in x. Starting from the y-intercept, move up 5 units (numerator of the slope) and move right 2 units (denominator of the slope). This gives us the point (2, 0).

Step 3: Draw a solid line passing through the two points (0, -5) and (2, 0). This line represents the equation y = (5/2)x - 5.

Step 4: Since the inequality is "y ≤ (5/2)x - 5," we need to shade the region below the line (including the line itself) to represent all the points that satisfy the inequality.

The graph should resemble a downward-sloping line passing through the points (0, -5) and (2, 0), with the shaded region below the line.

To know more on inequality

brainly.com/question/12189350

#SPJ1

The amount of paint needed to cover the walls of a room, you can use the area of the walls to estimate the amount of paint required.

The area of a two-dimensional shape is the amount of space inside its boundaries, while the perimeter is the length of its outer edge.

These concepts are often related, as the perimeter of a shape can be used to calculate its area.
For example, consider a square with sides of length 5cm.

The perimeter of the square would be 4 x 5cm = 20cm, while the area would be 5cm x 5cm = 25cm².

We can see that the area is greater than the perimeter, as there is more space inside the square than around its edges.
Another way that area and perimeter can be related is through similar shapes. Similar shapes have the same shape, but different sizes.

For example, a small square and a large square are similar shapes, but the large square has longer sides and therefore a larger area and perimeter.

The ratio of the areas of two similar shapes is equal to the square of the ratio of their corresponding side lengths.

Similarly, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.
Understanding the relationship between area and perimeter can be helpful in a variety of situations.

For example, if you need to calculate the amount of fencing needed to enclose a rectangular garden, you can use the perimeter of the garden to determine the length of the fencing required.
For more related questions on amount of paint:

https://brainly.com/question/13672761

#SPJ11

Answer:

The number of discharge days for a patient admitted January 23 to February 15 is 31 - 23 + 15 = 23

The length of the golden rectangle is 49 cm.

A rectangle is a quadrilateral (a polygon with four sides) in which each angle is a right angle (90 degrees). It is a type of parallelogram in which opposite sides are parallel and congruent (equal in length). Rectangles have four sides and four vertices (corners).

The length of a rectangle is the distance between its two longer sides, while the width is the distance between its two shorter sides. The perimeter of a rectangle is the sum of the lengths of all its sides, while the area is the product of its length and width.

A golden rectangle has sides in the proportion of the golden ratio, which is approximately 1:1.618. Therefore, if the width is 30cm, the length can be found by multiplying 30 by 1.618.

Length ≈ 48.54 cm

The length of the rectangle is 49 cm.

To know more about rectangles follow

https://brainly.com/question/27954648

#SPJ1

The family would need to bring home an additional $2400 annually to cover the increased cost of housing.

The family would need to bring home annually to cover the cost of increased housing need to calculate the total cost of housing for a year and subtract the current annual cost of housing.

The current monthly cost of housing is $1600 so the annual cost is:

$1600/month x 12 months = $19,200/year

Let's assume the family needs to cover an increased housing cost of $200 per month.

The new monthly cost of housing would be:

$1600/month + $200/month = $1800/month

The new annual cost of housing would be:

$1800/month x 12 months = $21,600/year

The family would need to bring home annually to cover this increased cost need to subtract the current annual cost of housing from the new annual cost of housing:

$21,600/year - $19,200/year = $2400/year

For similar questions on cost of housing

https://brainly.com/question/28669349

#SPJ11

To solve this problem, we can use the formula:

Total = n(A) + n(B) + n(C) - n(A and B) - n(A and C) - n(B and C) + n(A and B and C)

where:

n(A) = number of people who liked Nepali

n(B) = number of people who liked English

n(C) = number of people who liked Hindi

n(A and B) = number of people who liked both Nepali and English

n(A and C) = number of people who liked both Nepali and Hindi

n(B and C) = number of people who liked both English and Hindi

n(A and B and C) = number of people who liked all three languages

From the given information in the problem, we have:

n(A) = 50

n(B) = 40

n(C) = 30

n(A and B) = 11

n(A and C) = 19

n(B and C) = 13

n(A and B and C) = 6

We can now substitute these values into the formula:

Total = 50 + 40 + 30 - 11 - 19 - 13 + 6

Total = 73

ANSWER: Therefore, there were a total of 73 people who liked at least one of the three languages.

The probability that the husband has more than $150,000 of insurance is 1.4577

Looking at the row where the husband's insurance is between $50,000 and $100,000, we can see that there are a total of 329 policies.

Out of these policies, the number of policies where the husband has more than $150,000 of insurance is 249+30+25+176 = 480.

Therefore, the probability that the husband has more than $150,000 of insurance given that his insurance is between $50,000 and $100,000 is:

480/329 ≈ 1.4577

Rounded to four decimal places, the probability is 1.4577.

Learn more about probability at https://brainly.com/question/13604758

#SPJ1

The required perimeter of the equilateral triangle is 12.72 cm.

An equilateral triangle has all three sides equal in length. Therefore, if the edge of an equilateral triangle is 4.24 cm, then all three sides are 4.24 cm.

To find the perimeter of the equilateral triangle, we need to add the length of all three sides together:

Perimeter = 4.24 cm + 4.24 cm + 4.24 cm

Perimeter = 12.72 cm

Therefore, the perimeter of the equilateral triangle is 12.72 cm.

Learn more about equilateral triangles here:

https://brainly.com/question/3461022

#SPJ1

number 4

studied this before if no correct must be a error

The future value of the emergency fund after 6 years will be approximately $159,321.50.

To calculate the future value of the emergency fund using annuity due tables, we need to break down the given information and apply the appropriate formulas.

Given:

Sienna health and fitness deposits $5000 at the beginning of each three months.

The deposits have been made for the last 6 years.

The interest rate is 8% compounded quarterly.

To calculate the future value of the emergency fund, we need to determine the number of compounding periods and the interest rate per period.

Number of compounding periods:

Since the deposits are made every three months for 6 years, we have:

6 years * 4 quarters/year = 24 compounding periods.

Interest rate per period:

The interest rate is 8% per year, compounded quarterly. To find the interest rate per quarter, we divide it by 4:

8% / 4 = 2% per quarter.

Now, using the annuity due tables 12-1, we can find the future value factor for 24 periods at an interest rate of 2% per quarter. Let's denote this factor as FV.

Using the annuity due table, we find that the future value factor for 24 periods at 2% per quarter is 31.8643.

To calculate the future value of the emergency fund, we multiply the quarterly deposit amount ($5000) by the future value factor (31.8643):

Future Value = $5000 * 31.8643 = $159,321.50

For more such questions on annuity due tables

https://brainly.com/question/15293360

#SPJ8

The first derivative of the parametric curve is:

dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]

1. To find the first derivative of the parametric curve x = 1/(t-1) and [tex]y = t^2/(t-1)[/tex], we can use the chain rule.

2. Let's differentiate each component separately.

3. Differentiating x with respect to t, we have:

dx/dt = [tex]-1/(t-1)^2[/tex]

4. Differentiating y with respect to t, we have:

dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2[/tex]

5. Therefore, the first derivative of the parametric curve is:

dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]

Read more about derivative here:

https://brainly.com/question/28376218

#SPJ1

The division expressions to the quotients and remainders are

Expression (a)

The expression is given as

(x² - x - 30) ÷ (x - 6)

The synthetic set up is

6 |   1  -1  30

   |__________

Bring down the first coefficient, which is 1 and repeat the process

6 |   1  -1  30

   |___6_-30_____

      1   -5   0

This means that

Quotient = x - 5 with no remainder

Expression (b)

The expression is given as

(x³ - 2x² - 7x - 4) ÷ (x² + 2x + 1)

Using a graphing tool, we have

(x³ - 2x² - 7x - 4) ÷ (x² + 2x + 1) = x - 4 with no remainder

This means that

(x³ + 2x² - 1) ÷ (x² - x + 1) = x + 3 R 2x - 4

Read more about synthetic method at

brainly.com/question/13820891

#SPJ1

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-7 -6}{0 +4} \implies \cfrac{ -13 }{ 4 } \implies - \cfrac{13}{4}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{13}{4}}(x-\stackrel{x_1}{(-4)}) \implies y -6 = - \cfrac{13}{4} ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(y-6)=4\left( - \cfrac{13}{4} ( x +4) \right)}\implies 4y-24=-13(x+4) \\\\\\ 4y-24=-13x-52\implies 13x+4y-24=-52\implies \boxed{13x+4y=-28}[/tex]

The derivative of the function is f'(x)=4(3x²−4x+1)³ (6x-4)

The given function is  f(x)=(3x²−4x+1)⁴

We have to find the derivative of the function

By using chain rule we find the derivative

f'(x)=4(3x²−4x+1)³ d/dx(3x²−4x+1)

=4(3x²−4x+1)³ (6x-4)

Hence, the derivative of the function is f'(x)=4(3x²−4x+1)³ (6x-4)

To learn more on Differentiation click:

https://brainly.com/question/24898810

#SPJ1

The probability that the first person will be seated at a plastic table is 0.8

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

Plastic tables = 12

Composite tables = 3

Using the above as a guide, we have the following:

Total tables = 12 + 3

Evaluate the sum

Total tables = 15

So, we have the probability to be

P = Plastic tables/Total tables

Substitute the known values in the above equation, so, we have the following representation

P = 12/15

Evaluate

P = 0.8

Hence, the probability that the first person will be seated at a plastic table is 0.8

Read more about probability at

https://brainly.com/question/31649379

#SPJ1

That's quadratic.

y=x^2

It's a very simple version of y=ax^2+bx+c. Just in this case, a = 1, b = 0 and c = 0.

The expression has no solution when k < - 5.

Hence, option B is correct.

The given inequality is

|2x + 7|-k ≤ 5

We know that,

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count.

A function with absolute values is another name for it.

No matter what input was provided to this function, the outcome is always favorable.

Now adding k both sides of inequality,

⇒ |2x + 7| ≤ 5 + k

When we take value of k less than -5

Then the expression |2x + 7| becomes negative.

Since it always gives absolute value,

Therefore,

There is no any solution when k < -5.

To learn more about inequality visit:

https://brainly.com/question/30231190

#SPJ1

The probabilities are given as follows:

a) x is less than 60: 0.9495 = 94.95%.

b) x is greater than 16: 0.9909 = 99.09%.

c) x is between 16 and 60: 0.9404 = 94.04%.

d) x is greater than 60: 0.0505 = 5.05%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 42, \sigma = 11[/tex]

The probability of a value less than 60 is the p-value of Z when X = 60, hence:

Z = (60 - 42)/11

Z = 1.64

Z = 1.64 has a p-value of 0.9495.

Hence the probability of a value greater than 60 is of:

1 - 0.9495 = 0.0505 = 5.05%.

The probability of a value greater than 16 is one subtracted by the p-value of Z when X = 16, hence:

Z = (16 - 42)/11

Z = -2.36

Z = -2.36 has a p-value of 0.0091.

1 - 0.0091 = 0.9909 = 99.09%.

The probability of a value between 16 and 60 is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 16, hence:

0.9495 - 0.0091 = 0.9404 = 94.04%.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

The value of P(B) is simply the conditional probability of B given A, which is 0.3.

Given that events A and B are independent with P(A) = 0.63 and P(B|A) = 0.3, we can use the formula for the probability of independent events to find P(B).

P(B|A) = P(B)

Therefore, P(B) = 0.3.

Since events A and B are independent, the probability of B occurring is not affected by whether or not A occurs. Therefore, the value of P(B) is simply the conditional probability of B given A, which is 0.3.

Rounding to the nearest thousandth, P(B) is 0.300.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

Answer: 9530

Step-by-step explanation: It has to be 9 in the thousands place to start of. And for it to round to 10,000, it would have to be 5 since it would round up one more thousand. And I would just say 3 because its bigger. Then 0

Since angles M and P are complementary, if m∠M = 3x - 45 and m∠P = 2x + 15, the value of x is 24
and the value of M and P are   27° and 63°   respectively.

Since M and P are complimentary, that means the sum of them is = 90°

So
3x - 45 + 2x + 15 = 90

Taking like terms

3x + 2x = 90 + 45 -15
5x = 120
x = 120/5

x = 24

to find M and P

since m∠M = 3x - 45

m = 3(24) -45

m = 27°

m∠P = 2x + 15

since x = 60

P = 2(24) + 15

P = 63°

Learn more about complementary angles at:

https://brainly.com/question/15592900

#SPJ1

Full Question:

Although part of your question is missing, you might be referring to this full question:

Angles M and P are complementary. If m∠M = 3x - 45 and m∠P = 2x + 15, what is the value of x? What is the measure of each angle?

The requried domain and range of the given graph are a set of all real values i.e. (-∞, ∞).

Consider the given figure,
The domain is said to be the values of the set of dependent variables, in the given case the value on the x-axis, represents the domain.
The domain is given as all real value i.e. (-∞, ∞)

Similarly, the range is represented by the y-axis and given as (-∞, ∞).

Learn more about the domain and range here:

https://brainly.com/question/29452843

#SPJ1

The coordinates of the point in the graph is (3, 2)

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

The graph

On the graph, we have the following

Represent the point with x

So, we have

X = (3, 2)

Hence, the coordinates of the point in the graph is (3, 2)

Read more about coordinates at

https://brainly.com/question/32144496

#SPJ9

Answer:12 faces and 20 vertices

Step-by-step explanation:

Dodecahedron:- The three-dimensional geometric geometry of a dodecahedron comprises 20 vertices, 30 edges, and 12 flat faces.

Each face is a regular pentagon, with five equal-length sides and five equal-sized angles. One of the five Platonic solids, regular, convex polyhedrons with identical regular polygon faces and equal angles between them, the dodecahedron is one of these regular, convex polyhedrons. The dodecahedron is frequently utilised in architecture, design, and the arts because of its great degree of symmetry.

A dodecahedron has 12 faces.

To learn more about dodecahedron

brainly.com/question/32074764

The statement thet complete the proof of the congruent triangles is (a) SAS criterion

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

The incomplete proof

In the proof, we have

AD ≅ BC --- side length

DC ≅ DC --- side length

∠ADC ≅ ∠BCD -- angle

This means that the triangles are congruent by the SAS theorem

The SAS theorem is defined by "If two sides in one triangle are congruent to two sides in another triangle and the included angle in both are congruent, then the two triangles are congruent"

This means that they are congruent by the SAS congruent

Read mroe about triangles at

brainly.com/question/31898026

#SPJ1

Answer: A. SAS criterion.

Step-by-step explanation: Angle : ∠ADC ≅ ∠BCD                                         Side length : AD ≅ BC                                                                                       Side length : DC ≅ DC                                                                                                

Because of this △ADC ≅ △BCD by SAS criterion.

Answer:

perimeter = 12.72 cm

Step-by-step explanation:

an equilateral triangle has 3 congruent sides

the perimeter is the sum of the 3 sides , that is

perimeter = 4.24 + 4.24 + 4.24 = 12.72 cm

The relation is a function because (d) Yes because for each output there is exactly one input.

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

The graph

The graph can be represented as

x  g(x)

-5  1

-2  0

-1   -1

0  2

1  3

5   1

The above table of values is a function

This is so because each output values have different input values.

i.e. it would pass the vertical line test when represented on a graph

Read more about functions at

brainly.com/question/22340031

#SPJ1