A tortoise and a hare run in the NYC marathon (26.2 miles). The hare crosses the finish line first in a time of 4 hours and 30 minutes. How fast did the hare run?

The function's y = 3(x + 5)² +11 width will be narrower.

In mathematics, a function from a set x to a set y assigns each element of x precisely one element of y. The subsets x and y are referenced to as the function's domain and codomain, correspondingly. A relationship between a number of inputs and one output per input is referred to as a function. Simply described, a function is an association between inputs in which each piece of data is connected to exactly one output. There is a domain and a codomain, or range, for every function. A function is a type of rule that produces one output from one input. y = x² is a good illustration of this. Any information for x yields a single output for y.

A parabola is made narrow by a large positive value of a and wide by a large positive value of a that is close to 0.

Compare the given equation y = 3(x + 5)² + 11 with y = x² + c

So, a = 3

Therefore, the function will be narrower.

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3√2x is the simplified form of the given expression by rationalizing the denominator.

In the form p q, where p and q are integers and q0, rational numbers can be expressed. The distinction between fractions and rational numbers is that the numerator or denominator of a fraction cannot be negative.

In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.

A common factor is a whole number that is a factor of at least two other numbers. The greatest common factor is the biggest factor that may be divided into two or more integers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).

Make the denominator simpler.

12/2√2x

Reject the 12/2 common factor.

6/√2x

Multiply the numerator and denominator by √2x

(6√2x⋅√2x/√2x)

Combine and make the denominator simpler.

6√2x/2x

= 3√2x

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The factors of the expression (x³ - 6x² + 3x + 10) are (x + 1), (x - 2), and (x - 5).

We are given a mathematical expression. The expression is cubic in nature. We need to find the factors of the algebraic expression. Let the expression be represented by the variable "E". The expression consists of three terms. Hence, the expression is trinomial. The expression is given below.

E = x³ - 6x² + 3x + 10

One of the factors in the expression is already given. The given factor is (x + 1).

Now we will perform the long division method on the expression to break it into the given factor and a quadratic expression.

E = (x + 1)(x² - 7x + 10)

Now we will factorise the quadratic expression.

E = (x + 1)[x² - 2x - 5x + 10]

E = (x + 1)[x(x - 2) - 5(x - 2)]

E = (x + 1)(x - 2)(x - 5)

We cannot simplify and factorise the expression any further.

Hence, the factors of the expression are (x + 1), (x - 2), and (x - 5).

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The x-intercept of the given graph of the function is (10,0) while the y-intercept is (0,15).

A graph is a diametrical representation of any function between the dependent and independent variables.

The graph is easy to understand the behavior of the graph.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

As per the given equation,

y = (-3/2)x + 15

At y-intercept,

x = 0 so, y = 0 + 15 = 15 thus, (0,15)

At x-intercept

y = 0

0 = (-3/2)x + 15

x = 10 thus, (10,0)

Hence "The x-intercept of the given graph of the function is (10,0) while the y-intercept is (0,15)".

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For the complete question and graph image attached below,

Answer:

B

Step-by-step explanation:

Use the slope-intercept form to find the slope and y-intercept.

Slope: 5

y-intercept: (0,-10)

Answer:

Step-by-step explanation:

The slope is 5

The arrangement of the points in increasing order of the slopes are (27, 2) and (243, 18),  (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40),  (12, 32) and (18, 48), (18, 63) and (24, 84)

Slope is defined as the change in y divided by the change in x. Mathematically:

Slope = (y2 - y1) / (x2 -x1)

To arrange the pair of points. You need to find the slope:

For (15, 30) and (20, 40):

x1 = 15, y1 =30 and x2 =20, y2=40

slope = (40-30)/(20-15) = 10/5 =2

For (12, 32) and (18, 48):

slope = (48-32)/(18-12) = 16/6 = 2.67

For (27, 12) and (72, 32):

slope = (32-12)/(72-27)  = 20/45 = 0.44

For (45, 15) and (60, 20):

slope = (20-15)/(60-45) = 5/15 = 1/3 = 0.33

For (27, 2) and (243, 18):

slope = (18-2)/(243-27) = 16/216 = 0.07

For (18, 63) and (24, 84):

slope = (84-63)/(24-18) = 21/6 = 7/2 = 3.5

For (63, 9) and (84, 12):

slope = (12-9)/(84-63) = 3/21 = 1/7 = 0.14

Therefore, the pairs of points in increasing order of the slopes are (27, 2) and (243, 18),  (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40),  (12, 32) and (18, 48), (18, 63) and (24, 84)

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The sale price of an item normally priced at £90 is £67.5            

What is the percentage?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100.

Given :

A shop is having a sale. all items are reduced by 25%.

To Find:

Work out the sale price of an item normally priced at £90.

Price of an item = £90

Price is reduced by 25%

Reduction in price = 25%*90=25/100= 22.5

Reduced price = 90-22.5=67.5

Hence, the sale price of an item normally priced at £90 is £67.5                              

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Answer:

The line meeting the criteria is y = (1/2)x + 6 does not match any of the answer options.

Step-by-step explanation:

Let's use the slope-intercept form of a linear equation:  y = mx + b, where m is the slope and b the y-intercept (the value of y when x = 0).  We are given the slope, (1/2), so let's put that into the equation:

   y = (1/2)x + b

It is the value we choose for b that will make the line pass through point (6,-3).  We can determine that value by entering the given point in the equation and then solving for b:

y = (1/2)x + b

-3 = (1/2)*(6) + b for point (6,-3)

-3 = 3 + b

b = -6

The full equation is thus y = (1/2)x + 6

See the attached graph.

===

The `list of options doesn't have an equation that matches this conclusion.  The first two aren't even equations.  Assuming for the moment they are mistyped and should have an "=" sign after the y, we will change the list as follows:

Original   New

y-2x+6     y=2x+6

y-1x-6       y=1x-6

y=2x-3     y=2x-3

y=x+3      y=x+3

The slopes are either +1 or +2.  None have the required slope of (1/2)

Answer:

14.

Step-by-step explanation:

The interquartile range (IQR) contains the second and third quartiles or the middle half of your data set.

Please give brainliest, will be appreciated.

Answer:

The interquartile range (IQR) measures the spread of the middle half of your data.

Answer:

120,000

Step-by-step explanation:

To estimate the product of 283 × 416, first round each number so that each number contains only 1 non zero digit.

In this case, we will round 283 to the nearest hundred and we will also round 416 to the nearest hundred. To round 283 to the nearest hundred, the number next to two is higher than 5 so we round up. 283 rounds to 300.

416 rounded to the nearest hundred is 400 because the digit to the right of 4 is less than 5 which means we round down. 416 rounds down to 400.

Now we have 300 × 400 which equals 120,000

This means that 283 x 416 is approximately 120,000.

The p-value for a Z of 1.34 for a two-tailed test is 0.18025. Since the worth of p is greater than 0.05, we has fail to reject the null hypothesis.

What is hypothesis testing?

In hypothesis testing, we'll find to know whether we should reject or fail to reject some hypothesis.

To hold the decision, we should always compare the p-value in the test statistic to the significance level we have chosen to use the test. If the p-value is a smaller amount than the significance level, we'll reject the null hypothesis. Otherwise, we'll fail to reject the null hypothesis.

This calculations will tells you whether you ought to reject or fail to reject a null hypothesis based on the value of the test , the format of the test are going to be (one-tailed or two-tailed), and therefore the significance level you have chosen to use.

One-tailed or two-tailed ?

Value of the test statistic

1.34

Decision Rule say that : fail to reject the null hypothesis

The p-value for a Z of 1.34 for a two-tailed test is 0.18025. Since the worth of p is greater than 0.05, we has fail to reject the null hypothesis.

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Answer:

P=(2.25 x 10^4)(1 + 0.051)(1 +0.051)

Step-by-step explanation:

The length of the table is 1.51 meters.

Allan is measuring his dining room table to make a tablecloth. The table is 0.45 meter longer than it is wide. The width of the table is 1.06 meter. We need to find out the length of the table.

Let the length of the table be represented by the variable "L". In the context of a mathematical problem or experiment, a variable is a quantity that may vary. The length of the table is the sum of the width of the table and the difference between the two quantities.

L = 1.06 + 0.45

L = 1.51

Hence, the length of the table is 1.51 meters.

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Answer: A 22-ounce package costs $7.26 is best to buy

Step-by-step explanation:

A 9-ounce package costs $3.15 = 35 cents an ounce

A 12-ounce package costs $4.44 = 37 cents an ounce

A 22-ounce package costs $7.26 = 33 cents an ounce making it the cheapest by ounce

Answer:

Step-by-step explanation:

1. Put the variable as numbers in the computation. m=6 and n=6

SO:

6+6*6

2. Compute using Pemdas( Parentheses, exponets,multiplication, division, addition, subtraction)! Or order of operations!

6+36= 42

Answer: 42

The fraction that is equivalent to the fraction expression given as 5/8 is 40/64

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

Fraction = 5/8

The above expression is a fraction and at the same time it is a rational number

The denominator of the fraction is 8

So, we start by rationalizing the expression by the fraction

This is represented as

5/8 = 5/8 * 8/8

Evaluate the products of the numerator

So, we have the following representation

5/8 = 40/8 * 1/8

Evaluate the products of the denominator

So, we have the following representation

5/8 = 40/64

The above expression cannot be further simplified

Hence, the equivalent expression of the fraction is 40/64

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Possible question

Which of the following is equal to the fraction below? (5/8)

40/64

0.556

2/5

Answer:

1. y=2x+3

2. y=5x+3

Step-by-step explanation:

1. to find equation of the line we need the gradient and y-intercept

gradient=2

y=mx+c where m is gradient,x and y are coordinates and c is the y-intercept

input given coordinates and gradient in the equation to find c:

9 = 2(3)+c

9 = 6+c

9-6 = c

c = 3

to write the equation we only input gradient and y-intercept:

y=2x+3

2. to find the equation of the line we need the gradient and y-intercept

gradient=5

y=mx+c where m is gradient,x and y are coordinates and c is the y-intercept

input given coordinates and gradient in the equation to find c:

8 = 5(1)+c

8 = 5+c

8-5 = c

c = 3

to write equation we only input gradient and y intercept:

y=5x+3

Answer:

We can do it by using the format tab

Step-by-step explanation:

We can change the background of a group of cells by selecting the cell or range of cells we want to format. We should Click Home > Format Cells dialog launcher, or press Ctrl+Shift+F from the keyboard. Then on the Fill tab, under Background Color, we pick the color we want. To use a pattern with two colors, we pick a color in the Pattern Color box, and then pick a pattern in the Pattern Style box. In this tab we can also select gradient or single color

Answer: 13

Step-by-step explanation: 5, 12, and 13 is a Pythagorean Triple so if 12 were replaced with 13 in the word problem the answer would be 12 because all these numbers "travel" together.

Tony would require 13 meters of garland to reach from one corner to the opposite corner of the rectangular ceiling.

The ceiling of the ballroom is rectangular in structure.

The dimensions of the rectangle are 12 by 5 meters.

So we have to find the length of the diagonal of the ceiling which is the length from one corner to the other.

We will use Pythagoras theorem to calculate the length of the diagonal.

12² +5 ² = D²

or, D² = 144 + 25

or, D =√169

or, D = 13

Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares on the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

The hypotenuse in this case is the longest side because it is located across from the 90° angle. A right triangle's positive integer sides are squared to produce a Pythagorean triple equation.

Hence Tony will need 13 meters of garland.

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The cycle in order is D, E, F, B, C then A.

Define life cycle.

An organism goes through a series of shape changes in a biological life cycle before reverting to its original state. The notion contrasts with those of life history, development, and ontogeny in that it emphasizes renewal. Life cycles are common to all animals and plants.

The stages, which frequently entail beginning as a seed, egg, or live birth, then growing up and reproducing, are best shown visually using diagrams. Life cycles keep repeating themselves.

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The number of general public and students are 175 and 215 respectively.

Based on the information given:

Let p = general public

Let s = students/staff

390 people attended the concert. This will be:

p + s = 390 .... i

Tickets sold for $8.00 to the general public and for $5.50 for students and staff. Ticket sales brought in $2,582.50. This will be:

8p + 5.5s = 2582.5 .... ii

From equation i

p = 390 - s

8p + 5.5s = 2582.5 .... ii

8(390 - s) + 5.5s = 2582.5

3120 - 8s + 5.5s = 2582.5

Collect like terms

- 8s + 5.5s = 2582.5 - 3120

-2.5s = - 537.5

Divide

s = 537.5 / 2.5

s = 215

Students = 215

Note that p + s = 390

p + 215 = 390

P = 390 - 215

P = 175

Public = 175

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We are 90% certain that the average number of  hamsters per litter is between 7.1077 and 8.3323.

A confidence interval is a range of values that includes a population value with a high degree of certainty. When a population mean falls between an upper and lower interval, it is frequently expressed as a percentage. The confidence level is the long-run proportion of corresponding CIs that contain the parameter's true value. For example, 95% of all intervals computed at the 95% level should contain the true value of the parameter.

Given, n=47

[tex]\bar{x}[/tex]=7.72

s=2.5

c=90%=0.90

To find the t-value, look in the row that starts with degrees of freedom.

df=n-1

df=47-1

df=46>45 and in the column with c=90% in the table

=1.679

Now, the margin of error is then:

E=[tex]t_{\alpha/2}\times \dfrac{s}{\sqrt{n}}=1.679\times \dfrac{2.5}{\sqrt{47}}\approx 0.6123[/tex]

The confidence interval's boundaries are thus:

[tex]\overline{x}-E[/tex]=7.72-0.6123=7.1077

[tex]\overline{x}+E[/tex]=7.72+0.6123= 8.3323

The average number of hamsters per litter is between 7.1077 and 8.3323, and we are 90% certain of this.

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The vertex of the curve is at (-2, -4) and the axis of symmetry is at -2

The curve opens downward.

from, the graph, the roots of the equation are -4 and 0

so if -4 is a root, (x + 4) is a factor and if 0 is a root, then x is a factor.

The equation of the curve is the product of the factors of the curve which is y = x(x + 4)

y = [tex]x^{2}[/tex] + 4x

the x coordinate of the vertex = -b/2a = axis of symmetry

where a is the coefficient of [tex]x^{2}[/tex] and b is the coefficient of x

so a = 1, b = 4

x coordinate of vertex = -4/2 = -2

substitute x = -2 into y =  [tex]x^{2}[/tex] + 4x to find the y-coordinate of the vertex

y = [tex](-2)^{2}[/tex] + 4(-2)

y = 4 -8

y = -4

vertex  = (-2, -4)

The axis of symmetry is -b/2a which is -2

The curve opens downward as the vertex is at -4

In conclusion, the vertex of the parabola is (-2, -4) and the axis of symmetry is -2 and the parabola opens downward

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Step-by-step explanation:

x + y = 17

x = 17 - y

xy = 20

(17 - y)y = 20

-y² + 17y = 20

-y² + 17y - 20 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

y = (-17 ± sqrt(17² - 4×-1×-20))/(2×-1) =

= (-17 ± sqrt(289 - 80))/-2 =

= (-17 ± sqrt(209))/-2

y1 = (-17 + sqrt(209))/-2 = 1.271583853...

y2 = (-17 - sqrt(209))/-2 = 15.72841615...

the 2 numbers are

1.271583853...

15.72841615...

Answer:

Step-by-step explanation:

To find Mr.Santos's age subtract morgan's age from their combined age

44-15=29

Therefore Mr. Santos age is 29 years

Hope that helps

Answer: 600$

Step-by-step explanation:

2/5 of 600 is 240

The slope of the line is 0.393.

Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").

Given,

A data set has an r- value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772.

We'll use the following formula for slope if the r- value (or Pearson's coefficient) and the standard deviations of the x and y coordinates are provided:

m = 8ₓ/8ₐ

where m is the slope of the best-fit line.

8ₓ = Standard deviation of the x-coordinates is 5.591,

8ₐ =  the standard deviation of the y-coordinates is 2.772.

Slope is:

m = 8ₐ/8ₓ

m = (0.793)(2.772)/5.591

m = 0.393

The slope of the line is 0.393.

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