Use the information in the illustration to find the distance from the boathouse to the cabin. Round your answer to the nearest yard.

Answer:

Colin will have 421824 pennies after 2 years

Step-by-step explanation:

Given:

Amount invested in bank by Colin (P) = £3900

Rate of interest (r) = 4%

Time period (n) = 2 years

To find: Amount after 2 years (A)

Solution:

Formula for amount (A) is [tex]A=P\left ( 1+\frac{r}{100} \right )^n[/tex]

[tex]A=3900\left ( 1+\frac{4}{100} \right )^2\\=3900\left ( 1+\frac{1}{25} \right )^2\\=3900\times \frac{26}{25}\times \frac{26}{25}\\=4218.24[/tex]

As 1 pound = 100 pennies,

4218.24 pounds = 4218.24 × 100 = 421824 pennies

So,

Colin will have 421824 pennies after 2 years.

Answer:

16

Step-by-step explanation:

The common ratio is 36/54 = 2/3.

So the next term is 2/3 (24) = 16.

Answer:

16

Step-by-step explanation:

sorry no step by step explanation because I was in a rush anyway I did the quiz and here u go anyway have a great day I hope this helps :D

Answer:

[tex]=-8[/tex]

Step-by-step explanation:

[tex]\log _{0.5}\left(256\right)=x\\Switch\:sides\\x=\log _{0.5}\left(256\right)\\\mathrm{Rewrite\:}256\mathrm{\:in\:power-base\:form:}\quad 256=2^8\\x=\log _{0.5}\left(2^8\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\log _{0.5}\left(2^8\right)=8\log _{0.5}\left(2\right)\\x=8\log _{0.5}\left(2\right)\\0.5=2^{-1}\\x=8\log _{2^{-1}}\left(2\right)\\[/tex]

[tex]\mathrm{Apply\:log\:rule\:}\log _{a^b}\left(x\right)=\frac{1}{b}\log _a\left(x\right),\:\quad \mathrm{\:assuming\:}a\:\ge \:0\\x=8\cdot \frac{1}{-1}\log _2\left(2\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1\\x=8\cdot \frac{1}{-1}\\\mathrm{Simplify}\\8\cdot \frac{1}{-1}\\\frac{1}{-1}=-1\\\frac{1}{-1}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{1}{1}\\\mathrm{Apply\:rule}\:\frac{a}{1}=a\\=-1\\=8\left(-1\right)\\[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a\\=-8\cdot \:1\\\mathrm{Multiply\:the\:numbers:}\:8\cdot \:1=8\\=-8\\[/tex]

The value of x for the expression is, - 8.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ [tex]log_{0.5} ( 256) = x[/tex]

Now, We can solve the expression by the logarithmic for the value of x as;

⇒ [tex]log_{0.5} ( 256) = x[/tex]

⇒ [tex]x = log_{0.5} ( 256)[/tex]

⇒ [tex]x = log_{0.5} ( 2^8)[/tex]

Apply log rule,

⇒ [tex]x =8 log_{0.5} ( 2)[/tex]

⇒ [tex]x = 8 log_{2^{-1} } ( 2)[/tex]

⇒ [tex]x = 8 *\frac{1}{-1} log_{2 } ( 2)[/tex]

⇒ [tex]x = - 8 log_{2 } ( 2)[/tex]

We know that; [tex]log_{2} 2 = 1\\[/tex]

Hence, We get;

⇒ x = - 8 × 1

⇒ x = - 8

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Answer:

  1.4

Step-by-step explanation:

Both points are on the vertical line x=4, so the distance between them is the difference of their y-coordinates:

  2.9 -1.5 = 1.4

The points are 1.4 units apart.

Answer:

30 cups

Step-by-step explanation:

mango: 16 cups x 3/4 = 12 cups

pomegranate: 1 pint = 2 cups

cranberry: 1 gallon= 16 cups

Cups of fruit punch: 12+2+16= 30

( Hopefully this helped )

Answer:

Hey mate, I think you forgot to attach photo of sets. Check it.

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

  y > -x -3

Step-by-step explanation:

The graph is shaded above the dashed line, indicating y-values in the solution are greater than those on the line, so your inequality will start with ...

  y >

The y-intercept of the line is (0, -3), so the "b" value in ...

  y > mx +b

will be -3.

The line has a rise of -3 for a run of 3 (between the marked points), so the slope is ...

  m = rise/run = -3/3 = -1

Then the inequality you want is ...

  y > -x -3

Answer:

The volume increases by a factor or 64. When the cube is dilated, each side length is increased by 4, so the volume is increased by 64.

Step-by-step explanation:

Let L represents the Length of the cube before it's dilated.

Volume, V1 = Length * Length * Length

Volume, V1 = L * L * L

Volume, V1 = L³

When the cube is dilated by a factor of 4.

The new Length becomes 4L.

The new volume is calculated as thus.

New Volume, V2 = 4L * 4L * 4L

New Volume, V2 = 64L³

Dividing the new volume by the old volume gives the increment factor.

Factor = New Volume ÷ Old Volume

Factor = V2/V1

Factor = 64L³/L³

Factor = 64.

Hence, when the sides of the cube is dilated by 4, the volume increases by a factor of 64.

Filling the gap of the given sentence;

"The volume increases by a factor or 64. When the cube is dilated, each side length is increased by 4, so the volume is increased by 64"

Answer:

65

Step-by-step explanation:

6 x 5 = 30

6+ 5 = 11

therefore, the answer is 65

Answer:

  0.5 gallons

Step-by-step explanation:

Let x represent the amount of orange juice (in gallons) Gayle must add to the mix. Then the total amount of orange in the mix is ...

  0.25(2) +x = 0.40(2+x)

  0.50 +x = 0.80 +0.40x . . . . eliminate parentheses

  0.60x = 0.30 . . . . . . . . . . . .  subtract 0.50+0.40x

  x = 0.5 . . . . . . . . . . . . . . . . . divide by 0.60

Gayle should add 0.5 gallons of orange juice to make a 40% solution.

Answer:

12,60800000

hope it is not help full

Answer:

12 80000 I hope this helps buddy

Step-by-step explanation:

good luck

Answer:

54 ft^2

(54 in green box; 2 in grey box)

Step-by-step explanation:

We have 2 similar triangles, ABC and DEF.

The area of triangle DEF is given as 6 sq ft.

Side BC of triangle ABC measures 12 ft.

The corresponding side to BC in triangle DEF is EF. It measures 4 ft.

That gives us a scale factor from triangle DEF to triangle ABC.

To find the scale factor between two similar polygons, divide the length of a side of the second polygon by the length of the corresponding side of the first polygon.

scale factor = BC/EF = (12 ft)/(4 ft) = 3

The scale factor of side lengths is 3.

The ratio of the areas is the square of the scale factor.

ratio of areas = 3^2 = 9

Now multiply the area of the first triangle (DEF) by the ratio of areas to get the area of the second triangle (ABC).

area of triangle ABC = 9 * (area of triangle DEF)

area of triangle ABC = 9 * (6 sq ft)

area of triangle ABC = 54 sq ft

Answer: 54 ft^2

(54 in green box; 2 in grey box)

Answer:

b. the ranges of penguin heights are the same.

Step-by-step explanation:

Hello!

Statements:

Which statement correctly compares the spreads of the distributions?

a. the mode of penguin heights at county side zoo is greater than  the mode at city view zoo.

b. the ranges of penguin heights are the same.

c. the range of penguin heights is greater at city view zoo than at  county side zoo.

d. the range of penguin heights is greater at county side zoo than at  city view zoo.

The mode and mean are measurements of central tendency, these indicate the position of a data set but don't show any information concerning the distribution of said data.

The range on the other had is a measurement of variance, it shows the difference between the maximum and minimum values of the data set and indicates its total dispersion.

City view Zoo R= 44-37= 7 cm

County side Zoo: R= 45-38= 7 cm

Both ranges are the same.

I hope this helps!

Formula: r = C/2π

Solve with the given values.

r = 452.16/2(3.14)

r = 452.16/6.28

r = 72

Therefore, the radius is approximately 72 units.

Best of Luck!

Answer: /-2

Step-by-step explanation:

no time to explain but it would make sence using pemdas

Answer:

the answer is B

or

Negative one-half (negative 2) (x + 3) = negative 10 (negative one-half)

Step-by-step explanation:

now give me my brainly plz

I know I wasn't first but the other guy was wrong

Answer:

Step-by-step explanation:

Hello!

Peter is interested in comparing the number of hours adults and teenagers exercise per week, for this selected one random group of adults and a random group of teenagers and surveyed them on their weekly exercise times.

To compare the weekly exercise time of both populations, the best is to use a measure central tendency, so you can compare their positions and see if they are significantly similar or not.

The most common parameters to use for comparing two populations are its population means. So the analysis to do is a two independent sample test.

I hope this helps!

Answer:

AB is mid-segment of this trapezoid, then we have:

2 x AB = DG + EF

=> 2 x 12 = 5x - 4 + 8x + 2

=> 24 = 13x - 2

=>13x = 26

=> x = 2

=> Option A is correct

Hope this helps!

:)

Answer: perfect squares are the squares of the whole numbers: 1, 4, 9,25,36,49,64,81,100...... For example, 9 is a squared number because it can be written as 3x3. However, imperfect squares are numbers whose square roots contain fractions or decimals. For example square root of 20 = 4 1/2

The square number, sometimes known as a perfect square, is an integer that is the square of another integer and numbers with fractional or decimal square roots are considered imperfect squares.

We need to compare and contrast perfect squares and imperfect squares.

Perfect squares: When you multiply an integer by itself, you get a perfect square, which is a positive integer. Perfect squares are sums that are the products of integers multiplied by themselves, to put it simply. A perfect square is typically expressed as x², where x is an integer and x²'s value is a perfect square.

Imperfect squares: Numbers with fractional or decimal square roots are considered imperfect squares.

Therefore, the square number, sometimes known as a perfect square, is an integer that is the square of another integer and numbers with fractional or decimal square roots are considered imperfect squares.

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Answer:

575(1+2.5)^x

Step-by-step explanation:

X represents the number of years since they were first counted.

Answer:

Second option is the correct answer

[tex](x+11)^2+(y+6)^2 = 324[/tex]

Step-by-step explanation:

[tex]x^{2} +12y+22x+y^2-167=0\\x^{2}+22x +y^2 +12y-167=0\\(x^{2}+22x +121)-121 +(y^2 +12y+36)-36-167=0\\(x+11)^2+(y+6)^2-324 = 0\\\huge\red{\boxed{(x+11)^2+(y+6)^2 = 324}}\\[/tex]

Answer:

[tex](x+11)^2+(y+6)^2=324[/tex]

Step-by-step explanation:

[tex]x^2+12y+22x+y^2-167=0\\\mathrm{Circle\:Equation}\\\left(x-a\right)^2+\left(y-b\right)^2=r^2\:\:\mathrm{is\:the\:circle\:equation\:with\:a\:radius\:r,\:centered\:at}\:\left(a,\:b\right)\\\mathrm{Rewrite}\:x^2+12y+22x+y^2-167=0\:\mathrm{in\:the\:form\:of\:the\:standard\:circle\:equation}\\x^2+12y+22x+y^2-167=0\\\mathrm{Move\:the\:loose\:number\:to\:the\:right\:side}\\x^2+22x+y^2+12y=167\\Group\:x-variables\:and\:y-variables\:together\\\left(x^2+22x\right)+\left(y^2+12y\right)=167[/tex]

[tex]\mathrm{Convert}\:x\:\mathrm{to\:square\:form}\\\left(x^2+22x+121\right)+\left(y^2+12y\right)=167+12\\Convert\:to\:square\:form\\\left(x+11\right)^2+\left(y^2+12y\right)=167+121\\\mathrm{Convert}\:y\:\mathrm{to\:square\:form}\\\left(x+11\right)^2+\left(y^2+12y+36\right)=167+121+36\\Convert\:to\:square\:form\\\left(x+11\right)^2+\left(y+6\right)^2=167+121+36\\\mathrm{Refine\:}167+121+36\\\left(x+11\right)^2+\left(y+6\right)^2=324\\Rewrite\:in\:standard\:form[/tex]

[tex]\left(x-\left(-11\right)\right)^2+\left(y-\left(-6\right)\right)^2=18^2\\\mathrm{Therefore\:the\:circle\:properties\:are:}\\\left(a,\:b\right)=\left(-11,\:-6\right),\:r=18[/tex]

Answer:

The correct option is A

Step-by-step explanation:

From the question we are told that

   The average  number of meetings  hours per week is [tex]\mu= 18 \ hours[/tex]

    The standard deviation is  [tex]\sigma = 5.2 \ hours[/tex]

     The sample size is  n=  35

     The sample average per week is  [tex]p = 16.8 \ hours[/tex]

From each solution statement we can deduce that the confidence level is  

    [tex]t = 95[/tex]%

Thus the significance level is  [tex]\alpha = 0.05[/tex]= 5%

The z value for the significance level is gotten as 1.96 from the z-table

    The confidence level interval for the sample mean is mathematically evaluated as

            [tex]\= x = \mu \pm (1.96 * \frac{\sigma }{\sqrt{n} } )[/tex]

 Sustituting values

           [tex]\= x = 18 \pm (1.96 * \frac{5.2 }{\sqrt{35} } )[/tex]

             [tex]\= x = 18 \pm1.7[/tex]

=>               [tex]18 - 1.7 < \= x < 18 +1.7[/tex]

                  [tex]16.3 < \= x < 19.7[/tex]

Answer:

To the nearest tenth = 10.8cm

Step-by-step explanation:

Using the cosine rule

J² = i² + k² + 2ikcosj

J² = 3.4² + 7.7² + 2(3.4)(7.7) cos 30

J² = 11.56 + 59.29 + 52.36cos30

J² = 11.56 + 59.29 + 52.36(0.8660)

J² = 11.56 + 59.29 + 45.35

J² = 116.2

J=√116.2

J= 10.78 cm

To the nearest tenth = 10.8cm

Answer:

its 5.1

Step-by-step explanation:

\text{S.A.S.}\rightarrow \text{Law of Cosines}

S.A.S.→Law of Cosines

a^2=b^2+c^2-2bc\cos A

a  

2

=b  

2

+c  

2

−2bccosA

From reference sheet.

j^2 = 7.7^2+3.4^2-2(7.7)(3.4)\cos 30

j  

2

=7.7  

2

+3.4  

2

−2(7.7)(3.4)cos30

Plug in values.

j^2 = 59.29+11.56-2(7.7)(3.4)(0.866025)

j  

2

=59.29+11.56−2(7.7)(3.4)(0.866025)

Square and find cosine.

j^2 = 59.29+11.56-45.34509

j  

2

=59.29+11.56−45.34509

Multiply.

j^2 = 25.50491

j  

2

=25.50491

Add.

j=\sqrt{25.50491} \approx5.05 \approx5.1

j=  

25.50491

​  

≈5.05≈5.1

Square root and round.

The value of the given equation is 2 and -10.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given is an equation, x²+8x-20 = 0, we need to solve for x,

x²+8x-20 = 0

Solving for x, by using factorization,

x²+8x-20 = 0

Splitting the middle term,

x²+10x-2x-20 = 0

x(x+10)-2(x+10) = 0

(x-2)(x+10) = 0

x = 2 and x = -10

Hence, the value of the given equation is 2 and -10.

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The complete question is attached

Step-by-step explanation:

there are four dogs because each dog at a corner will see the other three dogs at the other corners

Answer:

The third one.

Step-by-step explanation:

Answer:

m=-44

Explanation: distribute the negative and add -1/4 to m and then take the 5 away from 16 and then multiply both sides

Answer:

M = - 44

Step-by-step explanation:

You will start by subtracting 5 on both sides of the equation.

- (1/4)m + 5 =16

            -5     -5

Simplify

- 1/4 m =11

Multiple both sides by - 4

(-1/4m)(-4)= 11 (- 4)

The final result is m equals negitive 4.

M = -44

Answer:

$504

Step-by-step explanation:

In this case you're solving for his checking account. In the beginning due to him withdrawing $358 he was left with -$96, assuming that he grabbed more than he could take. But later, he deposited 3/4 of $800 into his checking account.

So you need to find what 3/4 of 800 is first to see how much money he put into his checking account

3/4x800/1=600

But thats not the answer since thats only how much he put into his checking account, not how much he has.

So according to the question he had -96 left in the checking account. Therefore, you have to add the 600 in.

600+-96=504

In case you are wondering why there was a lower number when adding, it was a negative number which causes you to start from -96, but go more right into the number line 600 times.

If you have any questions please ask and I hope this helped! :)