Example 49; Jillian saved x dollars so that she could buy her mom a birthday present. Unfortunately, she hadto spend a third of it on lunch, but then she lent $5 to her brother. If she now has $16, how much money didshe begin with?07=750 = 16

Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

Now,

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)

\(\text{Area of pentagon} =52.5\)

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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Answer:

x is greater than or equal to - 8

Step-by-step explanation:

Answer:

Left skewed

Step-by-step explanation:

The distribution displayed in the boxplot Given is negatively skewed, hence, a left tail skweness. Skewness can be determined in a box plot, if the line of the median cuts or divides the box into unequal halves, such that sides relative to the median are longer Than each other. If the longer side is to the left of the median, we have left skewness; to the right we have right skewness. If the sides are equal, then the distribution is symmetric.

For the scenario above, the longwr side is to the left of the median, hence we have left skewness.

Answer:

Since f(-1) = 0 and f(-2) = 0, we can set up two equations:

(-1)³ + p(-1)² - q(-1) - 4 = 0

(-2)³ + p(-2)² - q(-2) - 4 = 0

Simplifying each equation, we get:

-1 + p - q - 4 = 0

-8 + 4p - 2q - 4 = 0

Simplifying further, we get:

p - q = 5

2p - q = 6

Solving for p and q, we can add the two equations together to eliminate q:

p - q + 2p - q = 5 + 6

3p - 2q = 11

Then, we can substitute the value of q from the first equation into this equation to solve for p:

3p - 2(q + 5) = 11

3p - 2q - 10 = 11

3p - 2q = 21

3p - 2(5 + p) = 21

p - 10 = 7

p = 17

Substituting this value of p into either equation for q, we get:

q = p - 5 = 12

Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:

-1 | 1 17 -12 -4

|__ -1 -16 28

1 1 12

This gives us the factorization:

f(x) = (x + 1)(x² + x + 12)

To find the solutions, we can use the quadratic formula on the quadratic factor:

x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)

x = (-1 ± sqrt(1 - 48)) / 2

x = (-1 ± sqrt(-47)) / 2

x1 = (-1 + i(sqrt(47))) / 2

x2 = (-1 - i(sqrt(47))) / 2

Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.

Step-by-step explanation:

give me thanks for more! your welcome bud!

Answer:

Below

Step-by-step explanation:

1. Linear because it is of the form y = mx + b. The variable x  is of the first degree.

The coefficient of x (1/3)  ( = slope) is positive so it is increasing.

2. This is non-linear because the variable x is an exponent.

3. Because  its of the second degree (x^2) - it is non-linear.

Answer:

Option 4

Step-by-step explanation:

The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).

hope this helps :)

Answer:

The Answer is 64 centimeters

Step-by-step explanation:

5/320 = 1/64

Answer:

I think you can answer it with a chart, I guess, of course I'm not sure‍♀️

Answer:

The value is \(\mu_{x} = 5.6 \ years\)

Step-by-step explanation:

From the question we are told that

   The population mean is  \(\mu = 5.6 \ years\)

    The standard deviation is  \(\sigma = 0.9 \ years\)

    The sample size is  n  =  49  

Generally given that the sample size is large enough, the  sampling distribution created using the samples of the ages at which 49 children begin reading is equal to the population mean

i.e

     \(\mu_{x} = \mu\)

=>  \(\mu_{x} = 5.6 \ years\)

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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Answer:3/4

Step-by-step explanation: If you weigh a brick at 2/4 lbs, it will weigh less than a brick that weighs 3/4

Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

350 / 70 = 5km2

5x30 = 150km2

The answer is: 150km2

Answer:

I think there is 140 questions

The the coordinates of Q and T in terms of a and b is -

Q [(3a + b)/4] and T [(5a + 3b)/4].

The mid-point of a line segment is a point on the line segment which divides it into two equal parts.

Given is a line segment AB whose mid-point is M with a and b being the coordinates of A and B respectively. Further, Q is the midpoint of AM and T is the midpoint of QM.

[Refer to the image attached for clear explanation]

Since M is the mid-point of AB, therefore the coordinates of point M will be = M [(a + b)/2]

Now, Q is the mid-point of AM. Therefore, the coordinates of Q will be =

[(a + b)/2 + a]/2 = Q [(3a + b)/4]

and

T is the mid-point of QM. Therefore, its coordinates will be =

(a + b)/2 + (3a + b)/4 = T [(5a + 3b)/4]

Hence, the the coordinates of Q and T in terms of a and b is -

Q [(3a + b)/4] and T [(5a + 3b)/4]

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Answer: This is a biased sample.

Step-by-step explanation:

A biased sample is when there is some kind of "selection" in your sampling process, where in order to avoid this we should have the most random selection that we can make

Here, the sample is "the first 15 students who arrive at a band class"

Here is obviously a bias, because you could think that these students may be more "dedicated" students than the ones that will arrive later to the class, and we also have the fact that all the students in our sample are in the same class, so there is another bias.

Then we can conclude that this is a biased sample.

Answer:

Let's solve for x.

x+y+z=8

Step 1: Add -y to both sides.

x+y+z+−y=8+−y

x+z=−y+8

Step 2: Add -z to both sides.

x+z+−z=−y+8+−z

x=−y−z+8

Answer:

x=−y−z+8

The value of the x is 4.

Given that,

Based on the above information, the calculation is as follows:

x + y + z = 8

y + z = 4

So,

x + 4 = 8

x = 8 - 4

= 4

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Answer:

  half

Step-by-step explanation:

Dividing a number by 2 is the same as multiplying it by 1/2. We can say the result is half the number's value.

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

Brian is constructing figures inscribed in circle C.

Equilateral triangle MNQ inscribed in circle C:

This option is possible since the points M, N, and Q are labeled and they lie on circle C.

Equilateral triangle ANP inscribed in circle C:

This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.

Regular hexagon AMNBPQ inscribed in circle C:

This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.

Square MNPQ inscribed in circle C:

This option is not possible based on the given information. The label points do not form a square.

Square ANBQ inscribed in circle C:

This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

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Answer: 39.62

Explanation: usual speed be x

today's speed = x+4

difference in time = 1/3 hours ( 20 min)

Usual time - today's time = 1/3

144%2Fx+-+144%2F%28x%2B4%29+=+1%2F3

multiply equation by 3x(x+4)

144%2A3%28x%2B4%29-144%2A3%2Ax=+x%28x%2B4%29

432x+1728-432x=x^2+4x

x^2+4x-1728=0

solve this you will get the usual speed which is

Step-by-step explanation:

A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram

Answer:

B. x is less than or equal to 5

Step-by-step explanation:

The dot is on 5 and is also a solid dot which means it is less than or equal to or greater than or equal to

In this case it is less than or equal to because the line goes to the left

Hope this helped!

You would get 23p as change from £1 if you spent 77p.

To find how much change you would get from £1 if you spent 77p, you need to subtract the amount you spent from the total amount you have.

Total amount = £1

Amount spent = 77p

To find the change, we need to convert both amounts to the same unit (pence) before performing the subtraction.

1 pound (£1) is equal to 100 pence, so:

Total amount = 100p

Amount spent = 77p

Now, subtract the amount spent from the total amount to find the change:

Change = Total amount - Amount spent

Change = 100p - 77p

Change = 23p

So, you would get 23p as change from £1 if you spent 77p.

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Answer:

29 inches

Step-by-step explanation:

add all the sides

11+4+3+4+7=29

Answer:

29 inches

Step-by-step explanation:

⇒ Perimeter = Sum of the lengths of the sides

⇒ P = 11 + 4 + 3 + 4 + 7

⇒ P = 18 + 11

⇒ P = 29 inches

Check the picture below.

so the hexagonal prism is really just a hexagon with six 8x27 rectangles, let's simply get the area of all and sum them up.

\(\textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap ~~ \begin{cases} p=perimeter\\ a=apothem\\[-0.5em] \hrulefill\\ p=\stackrel{8\times 6}{48}\\ a=6.9 \end{cases}\implies A=\cfrac{1}{2}(6.9)(48)\implies A=165.6 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{six rectangles} }{(6)(8)(27)}~~ + ~~\stackrel{ \textit{hexgonal face} }{165.6}}\implies 1296+165.6\implies \text{\LARGE 1461.6}~in^2\)

The distance at which the Benson family would be from home after 412 hours of driving according to the task content is; 18,640 miles.

It follows from the task content that the equation which models the distance of the Benson's family from home after a given time t is;

d = 45t +100

Hence, when t = 412 hours.

d = 45(412) + 100

d = 18540 +100

d = 18,640miles.

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