Basil was shown this enlargement, and he was asked to find the perimeter of the enlarged shape. His work is shown below.

A shape has side lengths 2, 2, 6, 4, 6. A larger shape has corresponding sides, A, A, 24, B, 24.
Figures not drawn to scale.

Basil’s Work
Scale factor
StartFraction 24 over 6 EndFraction = 4
Side A
4 times 2 = 8
Side B
4 times 4 = 16
Perimeter
24 + 16 + 8 + 8 = 56

Where, if any, did Basil first make a mistake in his work?

Answer:

0.0013 probability that at least 6 employees were over 50.

Step-by-step explanation:

The employees were "chosen" to be dismissed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem:

8 employees dismissed means that \(n = 8\)

Had 7 + 17 = 24 employees, which means that \(N = 24\)

7 over 50, which means that \(k = 7\)

What is the probability that at least 6 employees were over 50?

6 or 7, so:

\(P(X \geq 6) = P(X = 6) + P(X = 7)\).

In which

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 6) = h(6,24,8,7) = \frac{C_{7,6}*C_{17,2}}{C_{24,8}} = 0.0013\)

\(P(X = 7) = h(7,24,8,7) = \frac{C_{7,7}*C_{17,1}}{C_{24,8}} \approx 0\)

\(P(X \geq 6) = P(X = 6) + P(X = 7) = 0.0013 + 0 = 0.0013\)

0.0013 probability that at least 6 employees were over 50.

Answer:

1260

Step-by-step explanation:

Tents: 15×54=810

Caravans: 25×18=450

450+810=1260

Answer:

$1260

Step-by-step explanation:

Campsite Fees:

Tent - $15 (per day)

Caravan - $25 (per day)

No. of Tents and Caravans today:

Tents - 54

Caravan - 18

Total fees for Tent = 15 x 54

= $810.

Total fees for Caravan = 25 x 18

= $450.

Fees altogether for Today = Total fees for Tent + Total fees for Caravan

= $810 + $450

= $1260

\(\sqrt{40}=\sqrt{2\cdot2^2\cdot5}=2\sqrt{10}\)

Notice that \(\sqrt{10}\approx3.2\) which means \(\sqrt{40}\approx2\cdot3.2\approx6.4\).

So answer is B.

Hope this helps :)

Answer:

96

Step-by-step explanation:

.............................

Question 3: A

Question 4: D

Question 5: B

Question 6: D

One lb = one pound.

and 11 lb is 11 pound

Is 8 oz the same as 1 lb?

Each pound has 16 ounces or oz.

5,44311

What do you mean by pounds?

a unit for measuring weight: One pound is approximately equal to 454 grams. One kilogram is roughly the same as 2.2 lbs. There are 16 ounces in one pound.

What is a pound and examples?

Image result for What do you mean by pounds?

In simpler words, pounds tell us how heavy an object is. For example, the weight of a soccer ball is about one pound. A pound is expressed as lb or lbs, where “lb” stands for libra. It is a Latin word that means “balance” or “scale”.

Its name derives from the Latin word "poundus" meaning "weight". The £ symbol comes from an ornate L in Libra. The pound was a unit of currency as early as 775AD in Anglo-Saxon England, equivalent to 1 pound weight of silver.

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Answer:

239 eggs

Step-by-step explanation:

We know that a black widow spider laid 346 eggs while a wolf spider laid 107 eggs and we are asked to find how much more eggs were laid by the black widow than the wolf spider.

To solve this, we need to subtract the amount that was laid from the black widow to the amount the wolf laid.

346 - 107

239

The area of the circle is approximately 78.5 square meters.

To determine the area of a figure, we need to know what type of figure it is and what its dimensions are. The formulas for finding the areas of different types of figures are as follows:

Rectangles: Area = length x widthSquares: Area = side x sideTriangles: Area = 1/2(base x height)

Circles: Area = πr² (where π is pi and r is the radius)Problem 1:Let's say we have a rectangle with a length of 6 cm and a width of 4 cm.

To find its area, we use the formula Area = length x width. Substituting in our values,

we get:Area = 6 cm x 4 cm = 24 cm²Therefore, the area of the rectangle is 24 square centimeters.Problem 2:Next, let's look at a circle with a radius of 5 meters.

To find its area, we use the formula Area = πr². Substituting in our values, we get:Area = π(5 m)² = π(25 m²) ≈ 78.5 m²

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Answer:

75

Step-by-step explanation:

a^2+b^2=c^2

plug 21 and 72 for a and b respectively. Once plugged, c will equal 75.

Answer:

The order :

45/90, 5/9,3/1

Step-by-step explanation:

45/90=0.5

5/9=0.555

3/1=3

Then the order :

45/90, 5/9,3/1

Answer:

its actually c

Step-by-step explanation:

6*10=60+40=100

100\(\geq\)100

Answer:

C

Step-by-step explanation:

In order to graph we must first simplify the inequality

40 + 10x ≥ 100

step 1 subtract 40 from each side

40 - 40 cancels out

100 - 40 = 60

we now have 10x ≥ 60

step 2 divide each side by 10

10x/10 = x

60 / 10  = 6

we're left with x ≥ 6

Now to graph

We will start with a closed circled on 6 and because the inequality sign is facing the varibale (x) the line will go in the direction of the right

Thus, the answer is C

According to the solving the Net salary =$2131.92

Before taxes, benefits, and other payroll deductions are taken out of an employee's paycheck, they receive their gross salary.

Acc to given data

Gross pay = $2586.00

Now to find out net salary first find out 28% taxes deducted from her check of 2586.00.

So, 28%of $2586.00 is….

⇒ 28x2586/100=724.08

So the amount deducted is $724.08

Now to find out the net salary use the formula

Net salary= gross salary- taxes

So net salary = $2586.00-$724.08

     Net salary =$2131.92

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Answer:wpeleoe

Step-by-step explanation:

Answer:

F

Step-by-step explanation:

Answer:

x=1 must satisfy both equations.

Step-by-step explanation:

1)Y=X+4

2)Y=3X+2

IT Means x+4=3x+2

3x-x=4-2;

2x=2 ;  x=1 must satisfy both equations

There is no point that is NOT included in the graph of the step function.

The coat check service charges $2 for the first hour and $1 for each additional hour or fraction of an hour.

To determine the point that is NOT included in the graph of the step function, we need to consider the charging scheme and analyze the pattern of charges.

The step function can be represented as follows:

For the first hour, the charge is a flat rate of $2.

For each additional hour or fraction of an hour, the charge is $1.

Let's analyze the points included in the graph:

(1, 2): This point represents the charge for the first hour, which is $2.

Now, let's consider the additional hours:

2. (2, 3): This point represents the charge for 2 hours, which is $2 for the first hour and $1 for the additional hour.

(3, 4): This point represents the charge for 3 hours, which is $2 for the first hour and $2 for the additional 2 hours.

(4, 5): This point represents the charge for 4 hours, which is $2 for the first hour and $3 for the additional 3 hours.

Based on the charging scheme, we can observe a pattern where the charge increases by $1 for each additional hour or fraction of an hour.

Since the charging scheme allows for any additional hour or fraction of an hour, there is no specific point that is excluded from the graph. Any positive value of x greater than or equal to 1 will have a corresponding point on the graph.

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Answer:

-----------------------

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

Answer:

y=mx+b

y=2/3+12.65

Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

Answer:

a

Step-by-step explanation:

the data is represented in the dot plot

Answer:

answer is 77.67

Step-by-step explanation:

explain by the x axis is 68 to y axis is 84 so the median is 77.67

Answer:

Sequence is arithmetic

Common difference = 4

Step-by-step explanation:

All arithmetic sequences have a common difference, so if you can determine a common difference in a given sequence, then the sequence is likely to be arithmetic. To find the common difference, subtract a value from its preceding value, and repeat this step to ensure the difference between all values is the same:

5 - 1 = 9 - 5 = 13 - 9

4 = 4 = 4

The common difference = 4, and because there is a common difference, this sequence is arithmetic.

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63. Option D

To find the relative frequency of students with red hair among the sample population of students with gray eyes, we need to divide the number of students with gray eyes and red hair by the total number of students with gray eyes.

From the given table, we can see that there are 22 students with gray eyes and red hair.

The total number of students with gray eyes is the marginal total for gray eyes, which is 35.

To find the relative frequency, we divide the number of students with gray eyes and red hair by the total number of students with gray eyes:

Relative frequency = Number of students with gray eyes and red hair / Total number of students with gray eyes

Relative frequency = 22 / 35

Simplifying the fraction, we have:

Relative frequency = 0.6286

Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63.

Therefore, the correct answer is option OD) 0.63.

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Answer:

x=34

Step-by-step explanation:

∡PSR=∡TSU

3x+y=4x

y=x

∡PQS=180-2x

180-2x+68=180

2x=68

x=34

Answer:

Angle YXW=Angle VXZ that is 36.6°

Step-by-step explanation:

Vertically opposite angles are equal.

Answer:

3x+9 < 60 where x = Audrey's age

Step-by-step explanation:

Lou says "even if you tripled you age", which means that if Audrey's age is represented by the variable x, then we would multiply it by 3 to get 3x. the next part says "and add 9". We already have the 3x, so we would just tack on a +9 to get 3x + 9. The last part says "you still wouldn't be as old as me." Given that 3x+9 represents Audrey's age, this equation would have to be less than Lou's age, which in this case is 60.

Answer:

36 mph

Step-by-step explanation:

d = rt

d = (x)(3.6)

d = (x-4)(4)

3.6x = 4x - 16

-0.4x = -16

x = 40

Her speed was 40 on Thursday, so 36 on Friday

The speed of Debbie on Friday is 36 miles per hour.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Let d be the distance of her mother's house.

Let x be the speed of Debbie on Thursday.

x = d / 3.6

⇒ d = 3.6x

Speed on Friday = x - 4

Speed on Friday = d / 4

d / 4 = x - 4

⇒ d = 4 (x - 4)

Equating both the equations of d, we get,

4(x - 4) = 3.6x

4x - 16 = 3.6x

4x - 3.6x = 16

0.4x = 16

x = 40

Speed of Debbie on Thursday = 40 mile per hour

Speed of Debbie on Friday = 40 - 4 = 36 mile per hour

Hence the speed of Debbie on Friday is 36 miles per hour.

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One way to do this is to exploit the Pythagorean identity,

\(\cos^2x+\sin^2x=1\)

to rewrite

\(\cos^3(3x)=\cos(3x)\cos^2(3x)=\cos(3x)(1-\sin^2(3x))\)

so that

\(\displaystyle\int\cos^3(3x)\sin^7(3x)\,\mathrm dx=\int\cos(3x)\left(\sin^7(3x)-\sin^9(3x)\right)\,\mathrm dx\)

Then substitute \(u=\sin(3x)\) and \(\frac{\mathrm du}3=\cos(3x)\,\mathrm dx\) to get the integral

\(\displaystyle\frac13\int u^7-u^9\,\mathrm du=\frac13\left(\frac{u^8}8-\frac{u^{10}}{10}\right)+C\)

\(=\boxed{\dfrac{\sin^8(3x)}{24}-\dfrac{\sin^{10}(3x)}{30}+C}\)

which is one correct form of the antiderivative. There's no reason we can't use the identity from before to express the integrand in terms of powers of cos(3x) instead.

Answer:

-11.9

Step-by-step explanation:

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)