Anthony travels from Newcastle to Manchester at an average speed of 65 miles per hour.
The journey takes him 2 hours and 15 minutes.
Declan makes the same journey in 2 hours and 35 minutes.
(a) Work out Declan's average speed for the journey.

Answer:

[tex]x^2+y^2=64[/tex]

Step-by-step explanation:

So the first important thing in solving this problem, is identifying what the major and minor axis are. The major axis is the bigger one, and we want to find on which axis it is.

So by simply looking at the eclipse, you can see that it's larger on the horizontal axis, so the major axis is on the horizontal axis, and the minor axis is on the vertical axis.

This means the equation will be expressed as:

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1[/tex]

In this equation the major axis, has a length of 2a, and the minor axis has a length of 2b. It's also important to note that (h, k) is the middle of the eclipse, but in the equation you provided, there is no subtraction, so it's just 0, meaning the center is at the origin (0, 0)

So now let's solve for a, and b. I'll look at each individual fraction separately.

[tex]\frac{x^2}{64}[/tex]

The denominator is equal to the value of a^2, so we simply take the square root of this to get the equation: a=8

[tex]\frac{y^2}{36}[/tex]

The denominator is equal to the value of b^2, so we simply take the square root of this to get the equation: b=6

So by just looking at the graph the larger circle appears to have a denominator that is equal to the length of the major axis. The major axis is equal to 2a, and since we know the value of a (8), we simply multiply this by 2 to get a length of 16. This was a bit redundant to do, since in the equation of a circle we need the radius, and the radius is just half the diameter, so now we divide this 16 by 2 to get a radius of 8.

The circle also appears to be centered at the origin so the equation will have (x-0)^2 and (y-0)^2 which is just x^2 and y^2

Plugging in all the values we get the equation:

[tex]x^2+y^2=64[/tex]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

The ellipse shown here is a horizontal ellipse that has major axis parallel to x - axis and minor axis parallel to y - axis. Length of major axis = 2a, and that of minor axis = 2b.

And it has it's centre on origin, it's equation can be written as :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

so, let's equate given equation with the standard equation ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{64} + \cfrac{ {y}^{2} }{36} = 1[/tex]

so we get :

As we know, length of major axis is : 2a = 2 × 8 = 16 units

and, the larger circle has diameter = 2a = 16 units

so, it's radius = 8 units ~

Now, let's write the equation of circle with origin as centre and radius = 8 units

[tex]\qquad \sf  \dashrightarrow \: {(x - h)}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]

[ h = 0, k = 0, since circle has centre at origin ]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + {y}^{2} = 64[/tex]

There are 120 ways to color the 4 rectangles

The given parameters are:

Paints, n = 5

Rectangles, = 4

The number of ways to color the rectangles is

[tex]Ways = ^nP_r[/tex]

This gives

[tex]Ways = ^5P_4[/tex]

Apply the permutation formula

[tex]Ways = \frac{5!}{1!}[/tex]

Evaluate the expression

Ways = 120

Hence, there are 120 ways to color the 4 rectangles

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Answer:

Distance = 15

Step-by-step explanation:

4 - (-11) = 4 + 11 = 15

The required two-digit number is 75.

In mathematics, it deals with numbers of operations according to the statements.

let the number in tenth place be x.
And has two fewer units than tens.
= x - 2

The two-digit number can be given as
= 10x + (x - 2)

= (11x - 2)

Reversing the digits
= (x - 2)10 + x
= 11x -20

The difference between twice the number and the number reversed is 93.

[tex]2(11x - 2) - (11x - 20) = 93\\22x-4-11x+20 = 93\\11x+16 = 93\\11x = 93-16\\11x = 77\\x = 7[/tex]

Now the required two-digit number is,
=  11x -2
=  11*7 - 2
=  77 -2
= 75

Thus the required two-digit number is 75.

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Answer:

Step-by-step explanation:

The radius of the base is the distance between the center of the circle and the edge of the base, therefore in this case it is equal to 3 in.

The volume of a cone is given by:

V = π * r² * h / 3

V = π * (3)² * 10 / 3

V = 94. 25 in³

Therefore, The volume of is 94. 25 in³.

Step-by-step explanation:

6.25 points

Find the GCF for the list.

10m4, 40m⁹

10m5

40m4

10m4

6.25 points

list

Answer: 8 x 10^2

Step-by-step explanation:

scientific notation has to be greater than 1, less than 10

therefore:

0.08 = 8 x 10^2

Answer:

= 5.375

Step-by-step explanation:

Use the algorithm method.

7  9 9 10

8 . 0 0 0

- 2 . 6 2 5

5 . 3 7 5

= 5.375

Answer:

5 3/8

Step-by-step explanation:

change it so that every number is a improper fraction and same denominator

64/8 - 21/8 = 43/8 = 5 3/8

Answer:

See below

Step-by-step explanation:

The derivative of the function is the slope

2x^2 - x -1       take derivative  ( f ' )

4x -1                 equate to 7

7 = 4x -1

x = 2        sub into the original equation to find y = 5

Answer:

[tex] - 3 \times - 1 = 3 \\ \\ 5 - 2 = 3[/tex]

Step-by-step explanation:

3,3

Answer: Second Choice. (3, 3)

Step-by-step explanation:

Given point

(x, y) = (-3, 5)

Given the rule for application

(-x, y - 2)

Determine the new x-value

x = -3

-x = - (-3) = 3

Determine the new y-value

y = 5

y - 2 = (5) - 2 = 3

Therefore, the result is [tex]\Large\boxed{(3,~3)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: TRS is congruent to CSE

Step-by-step explanation:

You can find congruent angles by locating the ones with the same number of lines. You want to start with the angles in the order of TRS.

Angle T has 1 line, so is congruent to C, which also has 1 line.

Angle R has 2 lines, so is congruent to S, which also has 2 lines.

Angle S has 3 lines, so is congruent to E, which also has 3 lines.

You want to keep these in the same order, so TRS, in the order of 1-2-3 lines, is congruent to CSE, also in the order of 1-2-3 lines (aka congruency markings).

Answer:

It's supplementary angle I think

Answer:

one angle is 20° and the other is 70°

Step-by-step explanation:

Complementary angles add up to 90°.

Here it is given that an angle exceeds 3 times its complement by 10. So, we are taking the complement as x. Since it exceeds its complement 3 times, we are multiplying the complement 3 times. so we get [tex]3x[/tex].

Now we also need to add 10, so we get the final equation [tex]3x+10[/tex], which is the second angle.

As of now, first angle = x and second angle =  3x+10.

Since they are complementary angles, both angles add up to 90°

⇒ 1st angle + 2nd angle = 90°

∴ [tex]x+3x+10 = 90[/tex]  [since 3x and x are like expressions, we should add 3x + x = 4x]

⇒ [tex]4x = 90 - 10[/tex]  [by transposing 10 from LHS to RHS]

⇒ [tex]4x = 80[/tex]

⇒ [tex]x = \frac{80}{4}[/tex]  [by transposing 4 from LHS to RHS]

⇒ [tex]x = 20[/tex]

∴The complementary angle is 20° and the given angle is [(3 × 20) + 10)] = 70°

The number paths between c and d of length 2.

Find the number of paths between c and d in the graph of length:

The number of paths between c and d is 0.

There is the number of paths between c and d of length 2.

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Answer:

[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]

Step-by-step explanation:

Given quadratic function:

[tex]f(x)=2x^2-x-10[/tex]

The x-intercepts of the graph are the points at which the curve crosses the x-axis, so when f(x) = 0.

To find these points, factor the quadratic equation, set it to zero, then solve for x.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.

[tex]\implies ac=2 \cdot -10 = -20[/tex]

[tex]\implies b=-1[/tex]

Therefore, the two numbers are -5 and 4.

Rewrite the middle term as the sum of these two numbers:

[tex]\implies 2x^2-5x+4x-10[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x-5)+2(2x-5)[/tex]

Factor out the common term (2x - 5):

[tex]\implies (x+2)(2x-5)[/tex]

Set the factored function to zero:

[tex]\implies (x+2)(2x-5)=0[/tex]

Apply the zero-product property:

[tex]\implies (x+2)=0 \implies x=-2[/tex]

[tex]\implies (2x-5)=0 \implies x=\dfrac{5}{2}[/tex]

Therefore, the x-intercepts of the graph are:

[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]

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The slope of the points on the graph is 4/3

The points on the graph are

(x, y) = (4,3) and (1, -1)

Slope is calculated as:

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

This gives

m = (-1 - 3)/(1 - 4)

Evaluate

m = 4/3

Hence, the slope of the points on the graph is 4/3

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Answer: 9x+4

Step-by-step explanation: We take out the parentheses by multiplying both values by 2 (2 times x and 2 times 3) to get 2x-6. Now our equation is 9x+2x-6-2x+10. We can see that there is a +2x and a -2x so we just take both of them out as they cancel out each other. Now our equation is 9x -6+10. we add 10 to -6 to get +4. The result is 9x+4.

Answer:

9x + 4

Step-by-step explanation:

9x + 2x - 6 - 2x + 10

Rearranging,

=> 9x + 2x - 2x + 10 - 6

=> 9x + 4

Using it's concept, the probabilities are given as follows:

a) C. 7/20.

b) D. 15/22.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For item a, we have that there are 60 students with no curfew, and of those, 21 have no chores, hence the probability is given by:

p = 21/60 = 7/20

Which means that option C is correct.

For item b, we have that there are 66 students with no shores, and of those, 45 have a curfew, hence the probability is given by:

p = 45/66 = 15/22

Which means that option D is correct.

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Answer:

( 2,-3)

Step-by-step explanation:

The solution to the system of equations is where the two graphs intersect

The two graphs intersect at x = 2 and y = -3

( 2,-3)

Based on the calculations, the area of a rectangle to the nearest hundredth is equal to 1143.92 ft².

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

By drawing a line between the points representing wicket 3 and wicket 9, we can logically deduce that wicket 2 forms a perpendicular bisector. Thus, the distance between the points representing wicket 3 and wicket 9 is given by:

Distance = 1/2 × 36.77

Distance = 36.77/2

Distance = 18.39 ft.

For the height of this triangle, we would apply Pythagorean's theorem:

h² = 25.02² - 18.39²

h² = 626.0004 - 338.1921

h² = 287.8083

h = √287.8083

h = 16.97 ft.

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 36.77 × 16.97

Area of triangle = 311.99 ft².

For area of the rectangle, we have:

Mathematically, the area of a rectangle can be calculated by using this formula;

Area = LW

Area = 36.77 × 31.11

Area = 1143.92 ft².

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The events E1 and E2 are not independent events.

The two events are given as:

E1 and E2 such that

P(E1) = 0.27, P(E2) = 0.40 and P(E1 U E2) = 0.58.

The two events E1 and E2 are independent if the following equation is true

P(E1 and E2) = P(E1) * P(E2)

Where

P(E1 and E2) = P(E1) + P(E2) - P(E1 U E2)

Substitute the known values in the above equation

P(E1 and E2) = 0.27 + 0.40 - 0.58

Evaluate the sum in the above equation

P(E1 and E2) = 0.67 - 0.58

Evaluate the difference in the above equation

P(E1 and E2) = 0.09

Substitute P(E1 and E2) = 0.09 in P(E1 and E2) = P(E1) * P(E2)

P(E1) * P(E2) = 0.09

Substitute P(E1) = 0.27 and P(E2) = 0.40 in the above equation

0.27 * 0.40 = 0.09

Evaluate the product

0.108 = 0.09

The above is false because 0.108 and 0.09 are not equal

Hence, the events E1 and E2 are not independent events.

How to solve for x

We  have:

P(A) = x

P(B) = x + 0.2

P(A n B) = 0.15

For independent events, we have:

P(A) * P(B) = P(A n B)

So, we have:

x * (x + 0.2) = 0.15

Expand

x^2 + 0.2x - 0.15 = 0

Using  a graphing calculator, we have:

x = 0.3

Hence, the value of x is 0.3

The value of P(A U B)

This is calculated using

P(A U B) = P(A) + P(B) - P(A n B)

Substitute the known values in the above equation

P(A U B) = x + x + 0.2 - 0.15

Evaluate the like terms

P(A U B) = 2x + 0.05

Substitute 0.3 for x

P(A U B) = 2 * 0.3 + 0.05

Evaluate

P(A U B) = 0.65

Hence, the value of P(A U B) is 0.65

The value of P(A' U B')

This is calculated using

P(A' U B') = P(A') + P(B') - P(A' n B')

Where

P(A') = 1 - x

P(B') = 1 - x - 0.2 = 0.8 - x

P(A' n B') = P(A') * P(B')

P(A' n B') = (1 - x) * (0.8 - x)

Substitute the known values in the equation P(A' U B') = P(A') + P(B') - P(A' n B')

P(A' U B') = (1 - x) + (0.8 - x) - (1 - x) * (0.8 - x)

Substitute 0.3 for x

P(A' U B') = (1 - 0.3) + (0.8 - 0.3) - (1 - 0.3) * (0.8 - 0.3)

Evaluate

P(A' U B') = 0.85

Hence, the value of P(A' U B') is 0.85

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Sis : you : bro

10 : 9 : ?

? ? : 27 : 29

We can get the 9 at the top to 27, by multiplying the whole row by 3 to get:

30 : 27 :?

? : 27 : 29

Your age matches (in the ratios or relation to your sis & bro) now 27 yrs in both ratio. Creating a single ratio, whereby multiplying the top row by 3 to get you to 27 & bottom row by 1 to get you to 27. Knowing when you're 27 in both cases, you know how old your sis & bro is

So, replace the ? with the number above or below it, creating a single ratio, where you are in common with both, by being 27 in both cases.

The ratio of sis : you : bro is now -

The ratio of sis : you : bro is now - 30: 27 : 29

To find what your age is we need to increase the ratio in the same amount to find your maximum age under 70.

So, if we were to double your age to 54, by multiplying your previous age of 27 by 2. We've got to do the same for your sis & bro too, they're aging with you.

We get :

We get :60 : 54 : 58

(30 x 2) : (27 x2) : (29 x2)

Keep increasing the ratio, to the point you're not above 70 years. Now, I'll multiply all ages by 3.

30: 27 : 29

(30 x 3) : ( 27 x 3) : (29 x 3)

We get:

We get:90 : 81 : 87

Right now, you're above the age of 70.

Thus, your maximum age must be 54, where you're under 70 years, but over 40 years.

Answer : 54 years

Hope this helps!

The future value of the savings account, after 18 years when it was withdrawn to help pay for Lois Martin's college expenses, would be $5,816.85.

The future values of the savings account are calculated in two installments.

The first installment is for 10 years when the account earns 6% compounded semiannually.

Using the future value after 10 years, the second installment is for 8 years when the account earns 6% compounded quarterly.

Future values can be determined using the future value formula or an online finance calculator, as follows:

N (# of periods) = 20 (10 years x 2)

I/Y (Interest per year) = 6%

PV (Present Value) = $2,000

PMT (Periodic Payment) = $0

Results:

FV = $3,612.22

Total Interest $1,612.22

N (# of periods) = 32 (8 years x 4)

I/Y (Interest per year) = 6%

PV (Present Value) = $3,612.22 ($2,000 + $1,612.22)

PMT (Periodic Payment) = $0

Results:

FV = $5,816.85

Total Interest $2,204.63

Thus, the value of the account after 18 years was $5,816.85.

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Fraction is a topic that deals with expressing the relationship between two numbers or terms in the form of a ratio. So that the required symbolic language required in the question is: 17 - [tex]\frac{x}{17}[/tex] = [tex]\frac{17}{3}[/tex] + 6

Thus the value of x is 90[tex]\frac{2}{3}[/tex].

Fraction is a topic that deals with expressing the relationship between two numbers or terms in the form of a ratio. Some types of fractions are mixed fractions, proper fractions, and improper fractions.

Thus to express the given question in a symbolic language, let the fraction of 17 taken away be represented by x.

So that;

i. a fraction of 17 is taken away from 17 can be expressed as 17 - [tex]\frac{x}{17}[/tex].

ii. remains exceeds one-third of seventeen by six can be expressed as  [tex]\frac{17}{3}[/tex] + 6

Therefore the required symbolic language to the question is:

                  17 - [tex]\frac{x}{17}[/tex]  =  [tex]\frac{17}{3}[/tex] + 6

So that,

[tex]\frac{289 - x}{17}[/tex] = [tex]\frac{17 + 18}{3}[/tex]

cross multiply to have

3(289 - x) = 17(17 + 180)

867 - 3x = 595

3x = 867 - 595

    =272

x = [tex]\frac{272}{3}[/tex]

  = 90[tex]\frac{2}{3}[/tex]

x = 90[tex]\frac{2}{3}[/tex]

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Answer:

[tex] \frac{27}{8} cm {}^{3} [/tex]

Is the volume of this right rectangular prism.

Step-by-step explanation:

Rectangular prism volume formula is:-

Answer:

[tex]V=\frac{27}{8}\: cm^3[/tex]

Step-by-step explanation:

The formula to find the volume of a rectangular prism is:

V = length × height × width

Let us find now.

[tex]V = length \:* height \:* width\\\\V =\frac{3}{2} *\frac{3}{2} *\frac{3}{2} \\\\V=\frac{9}{4}*\frac{3}{2} \\\\ V=\frac{27}{8}\: cm^3[/tex]

The limit is

[tex]\displaystyle \lim_{x\to\infty} \frac{3x^{7/2} + 7x^{-1/2}}{x^2 - x^{1/2}} = \lim_{x\to\infty} \frac{3x^{3/2} + 7x^{-5/2}}{1 - x^{-3/2}} = \boxed{\infty}[/tex]

since the degree of the numerator exceeds the degree of the denominator.

Given the above information, it is correct to say Yes, since a sample mean number of eggs of 15.1 eggs or less only occurred twice in simulated values, there is evidence that the true mean number of eggs is less than 16. (Option A)

Recall that the mean (statistically speaking) is a measure of central tendency of a probability distribution along median and mode.

You could also state that it is an expected value. Given that samples of actual value taken from the

Hence, since from 100 samples taken, the number of eggs of 15.1 or less occurred, then the true mean or actual mean is less than 16.

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The number of years she had her investment is after 3 years

From the question, the given parameters are:

The number of years (T) is calculated from the following simple interest formula

I = PRT

Substitute the given parameters in the above equation

20.64 = 400 * 1.72% * t

Express 1.72% as decimal without percentage

20.64 = 400 * 0.0172 * t

Evaluate the product

20.64 = 6.88 * t

Divide both sides by 6.88

20.64/6.88 = 6.88/6.88 * t

Evaluate the quotient

3 = t

Rewrite the equation as

t = 3

This means that she had her investment after 3 years

Hence, the number of years she had her investment is after 3 years

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The significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality.

Quote means to cite something as a form of proof. It has several other senses as a verb and a noun. It should be noted that to quote something or someone is to repeat the exact words they said or to recite the exact words written in a book.

Great speakers often quote other inspiring people when making speeches. When you quote, you include the words and ideas of others in your text exactly as they have expressed them.

You signal this inclusion by placing quotation marks (“ ”) around the source author's words and providing an in-text citation after the quotation.

In this case, the significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality. A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written.

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Answer:

[tex]\dfrac{8}{\sin(6^\circ)} \approx 76.53[/tex]

Step-by-step explanation:

[tex]UX \sin(6^\circ) = 8 \Rightarrow \boxed{UX = \dfrac{8}{\sin(6^\circ)} \approx 76.53}[/tex]