Question 13
Write (but DO NOT SOLVE) an equation for x based on the picture below.
2x523

Answer:

70°

Step-by-step explanation:

Sum of angles in a parallelogram is 360°

Opposite angles are equal

2(16x - 2) + 2(8x + 14) = 360°

32x - 4 + 16x + 28 = 360°

32x + 16x + 28 - 4 = 360°

48x + 24 = 360°

48x = 360 - 24

48x = 336

x = 7

m< E = 8x + 14

Substitute for x

= 8(7) + 14

= 56 + 14

= 70°

In conclusion, a) it is an odd permutation, b) it is an even permutation, c) it is an even permutation, d) it is an even permutation and e) it is an odd permutation.

To determine whether a permutation is even or odd, we need to count the number of transpositions it can be written as.
a) (1235)(24567): This permutation can be written as (12)(13)(15)(24)(25)(26)(27), which consists of 7 transpositions. Therefore, it is an odd permutation.
b) (345)(245): This permutation can be written as (34)(35)(24)(25), which consists of 4 transpositions. Therefore, it is an even permutation.
c) (1243)(3521): This permutation can be written as (12)(14)(13)(24)(35)(51)(52)(21), which consists of 8 transpositions. Therefore, it is an even permutation.
d) (12345)(123)(45): This permutation can be written as (15)(14)(13)(12)(45)(23), which consists of 6 transpositions. Therefore, it is an even permutation.
e) (13)(24567): This permutation can be written as (13)(24)(25)(26)(27), which consists of 5 transpositions. Therefore, it is an odd permutation.

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Answer:

y=3x+14

Step-by-step explanation:

Well you already know that the slope is 3

parallel lines always have the same slope.

so then you plug in the point (-6,-4) into y=3x+b

-6 is x and -4 is y

-4=3(-6)+b

-4=-18+b

14=b

so your equation is y=3x+14

Hope this helps :D

Answer:

No

Step-by-step explanation:

Option (d) An explicit formula representing the sequence is f(x) = 4(3/2)^x and option (e) The sequence shows exponential growth, are correct for the given geometric sequence.

A geometric sequence is a sequence of numbers where the ratio between any two neighboring terms is a constant. This constant ratio is called the common ratio. If the first term of the geometric sequence is a and the common ratio is r, then the n-th term (the last term) is given by a * r^(n-1). The first term is denoted by a, while the common ratio is denoted by r. Here, we are given that the recursive formula representing the sequence is f(x + 1) = 3/2(f(x )) when f(1) = 4.

By using the formula and considering f(1) = 4, we can find the first few terms in the sequence. So, the first few terms are 4, 6, 9, 27/2, …Now, let’s check each statement one by one.(a) The domain is the set of natural numbers. False.

The domain is {1, 2, 3, …} because the first term of the sequence is given and we need to use the recursive formula to find all the other terms.(b) The range is the set of natural numbers. False.

The range is not just the set of natural numbers as the sequence has decimals and fractions in it.(c) The recursive formula representing the sequence is f(x + 1) = 3/2(f(x )) when f(1) = 4.True.

This is given in the question.(d) An explicit formula representing the sequence is f(x) = 4(3/2)^x. True.

We can find the common ratio by dividing any term by its preceding term, and we get 3/2. Since the first term is 4, we can write the nth term as 4(3/2)^(n-1).(e) The sequence shows exponential growth. True.

The sequence is increasing and the ratio between any two consecutive terms is constant, which means it’s an exponential sequence.

Therefore, the answers are options (d) An explicit formula representing the sequence is f(x) = 4(3/2)^x and (e) The sequence shows exponential growth..

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B) m is the independent variable and p is the dependent variable.

Its given in question,

The number of people they will be able to serve depends on the number of meals they prepare. p = the number of people Florence and Anna will be able to serve m = the number of meals Florence and Anna prepare.

Which means people served depends on the meals prepared.

Therefore, p depends on m.

Hence, m is the independent variable and p is the dependent variable.

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Answer:

46

Step-by-step explanation:

turn the percentage into a fraction

so 20% is equal to 2/10.

230 is the whole number so multiply is by the numerator which is 2

230 x 2=460

and divide it by the denominator which is 10

460/10=46

Answer:

9*10^7 is 90000000. 3*10^7 is 30000000. So it is 3 times as large

Answer:

10 is B and D

9 is B,C, and D

Answer:

AB || CE, so we have triangle DEO, two of whose angles are 100° and 26° (from point D, draw DE such that CD + DE = CE intersects BO). The third angle of this triangle measures 54°, so

x = 180° - 54° = 126°.

Answer: 4.7 gallons

Step-by-step explanation:

The range is the difference in the highest number and the smallest number, so 2.8 - -1.9 = 4.7

The total playground area is 280 square meter, if the dome cover an area of 1+2/3 = 5/3 square meter.

The area covered by the dome = 5/3 square meter

The area covered by the dome is 5/840 times of the total playground area.

Let the total area of the playground = A

5/3 = 5/840 × A

A = (5 × 840)/(3 × 5)

A = 280 square meter

--The given question is incomplete, the complete question is " Ben like to go in the covered dome, when he feels overexcited. The dome covers an area of 5/3 square meter, which is 5/840 of the total playground area. What is the total playground's area?"--

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The value of n is 25  according to standard deviation in the question.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

s = 30 minutes

C.I. = 99%

mean = 15 minutes

z value for 99% = 2.58

mean = z*s/√n

15  = 2.58 * 30 / √n

√n = 5.06

n = 25

Hence the value of n is 25 .

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Answer:

3/16 or 0.1875

Step-by-step explanation:

Since she remembers the first two digits, she only has to guess the last two digits. If both digits are greater than 5, there are 4 possible alternatives for each digit (6, 7, 8 or 9).

In three tries, the probability that she will get it right is:

\(P=\frac{3}{4*4}\\P=\frac{3}{16}=0.1875\)

The probability she will get access to her account is 3/16 or 0.1875.

Answer:

55x + 148/24

Explanation:

Answer:

volume of a cylinder = 536.9 cm³

Step-by-step explanation:

volume of a cylinder, V = πr²h

where π = 3.14

h = 19 cm

r = ?

given is diameter = 6 cm

as we know, r = d/2 = 6/2 = 3 cm

by substituting the values in the formula,

V = 3.14 * 3² * 19

= 536.94 cm³

by rounding off to the nearest tenth place,

volume of a cylinder = 536.9 cm³

Answer:

v = 537.2 cm3

Step-by-step explanation:

volume:

\(v=\pi r^{2} h\)

\(r=d/2=6/2=3cm\)

\(h=19cm\)

\(v=\pi (3)^{2} (19)=171\pi\)

\(v=537.21\)

Rounded nearest tenth:

\(v=537.2cm^{3}\)

Hope this helps

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

1+1+1+1=4

Converges; the series is a constant multiple of a geometric series. Option A.

The given series can be written as:

\(\sum n=1 to \ \infty 2^{(n+1)} * 3^{(-n)\)

= 2 * ∑n=1 to ∞ (2/3)^n

This is a geometric series with first term a=2 and common ratio r=2/3. The series converges if and only if |r| < 1. Here, |r| = 2/3 < 1, so the series converges.

The sum of a convergent geometric series with first term a and common ratio r is given by:

sum = a / (1 - r)

Applying this formula, we get:

sum = 2 / (1 - 2/3) = 2 * 3 = 6

Therefore, the given series converges to 6.

The correct answer is option (a) Converges; the series is a constant multiple of a geometric series.

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Answer:

\(3n + 7 = 52 \\ 3n = 52 - 7 \\ 3n = 45 \\ n = \frac{45}{3} \\ n = 15\)

Graph is not inserted.

The surface area of the sphere is 132 ft². Thus, the correct answer choice is H.

The surface area of the sphere can be calculated using the formula \(A = 4\pi r^2\), where \(A\) represents the surface area and \(r\) is the radius of the sphere.

Given that the area of the great circle of the sphere is 33 ft², we can use this information to find the radius of the sphere.

The area of the great circle is equal to the area of the base of the sphere, which is a circle. The formula for the area of a circle is \(A = \pi r^2\). Since the given area of the great circle is 33 ft², we have:

\(\pi r^2 = 33\)

To find the radius \(r\), we divide both sides of the equation by \(\pi\):

\(r^2 = \frac{33}{\pi}\)

Now, we can find the surface area of the sphere by substituting the radius into the formula for surface area:

\(A = 4\pi r^2 = 4\pi \left(\frac{33}{\pi}\right)\)

The \(\pi\) in the numerator and denominator cancels out, giving:

\(A = 4 \times 33 = 132\) ft²

Therefore, the surface area of the sphere is 132 ft². Thus, the correct answer choice is H.

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Answer:

1/2=20/40 19/20=38/40

Step-by-step explanation:

so the first option

The fee charged for the R 2, 500 withdrawal from TownBank would be R 33. 30.

To find the total fee charged to withdraw the sum of R 2, 500 from TownBank, the formula is :

= 3. 30 + R 1, 20 per R 100

The amount withdrawn was R 2, 500 so the total fee charged would be :

= 3. 30 + 1, 20 x ( 2, 500 / 100 )

= 3. 30 + 1. 20 x 25

= 3. 30 + 30

= 33. 30

= R 33. 30

In conclusion, the total fee charged was R 33. 30.

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First part of the question :

The TownBank current account charges R3,30 plus R1,20 per R100 or part thereof for a cash withdrawal from a TownBank ATM. The first five withdrawals in a month are free. Determine the bank charges for a withdrawal of:

Answer:

\(x = 6\)

Step-by-step explanation:

Given

\(2y-x=-6\)

Required

Determine the x intercept

To get the value of x intercept; we simply substitute 0 for y;

i.e. y = 0

\(2y-x=-6\) becomes

\(2(0)-x=-6\)

\(0-x=-6\)

\(-x=-6\)

Multiply both sides by -1

\(-1 * -x=-6 * -1\)

\(x=-6 * -1\)

\(x = 6\)

Hence, the x intercept is 6

More accurate predictions are associated with correlations is (c) having higher absolute value .

Any statistical association between two random variables or bivariate data, whether causal or not, is referred to as correlation or dependence. Although "correlation" can mean any kind of association in the broadest sense, in statistics it typically refers to the strength of a pair of variables' linear relationships. Examples of common dependent phenomena include the relationship between parent and child height and the relationship between a good's price and the number of units buyers are prepared to buy, as shown in the so-called demand curve.

From the above question we can justify that In order to anticipate solar activity, a correlation as high as possible has been sought after and used because larger correlations tend to produce predictions that are more correct.

So the more accurate predictions are associated with correlations is having higher absolute value is the correct answer .

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Answer:

3/15 x 12/14 = 36/210 = 6/35

Step-by-step explanation:

3 + 12 = 15

3/15 = black

12/15 = green

the probability Lila selects the black ribbon first is 12/15

Lila has taken one away so the total now decreases by one to 14

There are 3/14 black ribbons now, and hence the probability that Jessica takes one is 3/14.

Then you just multiply the two together:

3/15 x 12/14 = 36/210 = 6/35

So as a result, The simplified answer is 6/35

The point prevalence of brilliance at the end of Week 1 is 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 is 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 is 0.33 or 33%.

Using person-weeks as denominator, the incidence of brilliance over the course of the 10-week course is 0.017 or 1.7%

In epidemiology context, brilliance can be calculated through calculating point prevalence, cumulative incidence, and incidence rate. The provided data table can be used to determine the point prevalence, incidence, and incidence rate of brilliance among PHE 450 students. So, the calculations of point prevalence, cumulative incidence, and incidence rate based on the provided data are as follows:

The point prevalence of brilliance at the end of Week 1 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #8 was the only existing case of brilliance at the beginning of Week 1, so the point prevalence of brilliance at the end of Week 1 is; Point prevalence = 1 ÷ 12 = 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3 and Student #8 were existing cases of brilliance at the beginning of Week 2, so the point prevalence of brilliance at the end of Week 2 is; Point prevalence = 2 ÷ 12 = 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3, #4, #6, and #8 were existing cases of brilliance at the beginning of Week 3, so the point prevalence of brilliance at the end of Week 3 is; Point prevalence = 4 ÷ 12 = 0.33 or 33%.

The incidence of brilliance can be calculated by the following formula; Incidence = Total number of new cases ÷ Total person-weeks of observation

Student #5 and Student #7 developed brilliance during the 10-week course, so the incidence of brilliance over the course of the 10-week course is; Incidence = 2 ÷ 120 = 0.017 or 1.7%.

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Answer:

You have to show the table, not enough information is given here

Step-by-step explanation:

The size of each section in a graph tells in relation to the portion of the data :

The magnitude of a graphic's segment indicates a specific attribute of the data being presented. In charts like pie charts or stacked bar graphs, each component's size denotes the relative frequency or proportion of data points in a particular category.

This implies that larger fragments reflect an increased number of data points for its associated categories whereas smaller ones represent categories with lesser data points.

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