the augusta national golf club in augusta, georgia is an 18-hole course that consists of par-3 holes, par-4 holes, and par-5 holes. a golfer who shoots par has a total of 72 strokes for the entire course. there are two more par-4 holes than twice the number of par-5 holes, and the number of par-3 holes is equal to the number of par-5 holes. find the numbers of par-3, par-4, and par-5 holes on the course.

The value of b of the equation is -9/5

Given that: line JK passes through points J(-4,-5) and K(-6,3) and if the equation of the line is written in slope-intercept form, y=mx+b

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

Using the y-y₁/y₂-y₁ = x-x₁/x₂-x₁

where (x₁, y₁) = (-4,-5) and (x₂, y₂) = (-6,3), the equation is:

y-(-5) / 3-(-5) = x-(-4)/-6-(-4)

y+5 / 3+5 = x+4 /6+4

(y+5)/8 =  (x+4)/10       cross multiply:

10(y+5) = 8(x+4)

10y + 50 = 8x + 32

10y = 8x +32 - 50

10y = 8x - 18

y = 8x/10 - 18/10

y = 4x/5 - 9/5

Comparing y = 4x/5 - 9/5 with y=mx+b

b = -9/5

Therefore, the value of b is -9/5

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The probability that their mean length is greater than 20.1 inches is 0.32.

Standard deviation:

The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The given value are:

Mean = 18.8 inches

Standard deviation = 6.2 inches

We have to find the probability that their mean length is greater than 20.1 inches.

Variance of sample mean = 6.2 / 48

                                           = 0.13

S.D of sample mean=   [tex]\sqrt{0.13}[/tex]

                                 = 0.36

Z score for the length of 20.1 is ( 20.1 - 18.8) / 0.36 = 0.468

The p-value for 0.468 in the standard normal table is 0.32.

Therefore 0.32 chance of the sample means is greater than 20.1 inches.

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Using the concepts of probability, we got that  0.0764 is the probability that the sum of the 100 values is greater than 3,908 when a researcher measure the amount of sugar in several cans of the same soda.

The z-score of a measure X of a normally distributed variable with mean  and standard deviation is given by:

                 Z=(X-μ)/σ

For this problem, these parameters are given as follows:

μ=39.01,σ=0.5,n=100,s=0.5/√100=0.05

A sum of  3908 is equivalent to a sample mean of 3908/100 = 39.08, which means that the probability is the p-value of Z when X = 39.08, hence:

Z=(X-μ)/σ

By the Central Limit Theorem:

Z=(X-μ)/s

=>Z=(39.08-39.01)/0.05

=>Z=(0.07)/0.05

=>Z=7/5

=>Z=1.4

Z = 1.4 has a p-value of 0.0764.

Hence, the probability that the sum of the 100 values is greater than 3,908 is 0.0764.

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The scenario describes the stratified random sampling method .

There are many sampling techniques to collect sample from a given population such as Simple random sampling , Systematic Sampling , Cluster Sampling and so on . All of them vary in reliability , accuracy and efficiency .

Stratified Random Sampling : It is a method of  sampling in which division of population is done into smaller subgroups known as strata .The strata are formed based on member's shared attributes or characteristics . It has numerous applications . It is also called proportional random sampling or quota random sampling .

Therefore , the scenario describes the stratified random sampling method .

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The system of equations has its solutions to be (1, -1) and (7, -1)

The system of equations is given as

(x−4)² + (y+1)² = 9

(x−4)²/9 + (y+1)²/81 = 1

Make (y + 1)² the subject in the equation (x−4)² + (y+1)² = 9

So, we have

(y+1)² = 9 - (x−4)²

Substitute (y+1)² = 9 - (x−4)² in (x−4)²/9 + (y+1)²/81 = 1

This gives

(x−4)²/9 + [9 - (x−4)²]/81 = 1

Split

(x−4)²/9 + 9/81 - (x−4)²/81 = 1

Collect the like terms

(x−4)²/9 - (x−4)²/81 = 1 - 9/81

Evaluate the like terms

[9(x−4)² - (x−4)²]/81 = 72/81

So, we have

9(x−4)² - (x−4)² = 72

Evaluate the difference

8(x−4)² = 72

Divide by 8

(x−4)² = 9

Take the square roots

x - 4 = ±3

So, we have

x = 4 ± 3

Evaluate

x = 1 or 7

Substitute x = 1 or 7 in (y+1)² = 9 - (x−4)²

(y + 1)² = 9 - (1−4)² or (y + 1)² = 9 - (7−4)²

This gives

(y + 1)² = 0 or (y + 1)² = 0

This gives

y + 1 = 0

Evaluate

y = -1

Hence, the solution is (1, -1) and (7, -1)

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The greater principal is there for Account A as $400.

Simple interest can be defined as a type of interest where the rate is applied on the same principal.

Given that,

The interest for Account A is $15.75 and Account B is  $28.

The total time for interest is 21 months.

Rate of interest for Account A is  3% and Account B is 4%.

Now, the time period can be written in years as,

21 months = 21 / 12 years

                  = 7 / 4

Suppose the principal for Account A and Account B is P₁ and P₂ respectively.

The formula for simple interest is given as,

(P × r × t) / 100

Substitute the respective values for both the accounts to get,

For Account A,

15.75 = (P × 3 × 7 / 4) / 100

⇒ P = (1575 × 4) / (3 × 7)

⇒ P = 300

For Account B,

28 = (P × 4 × 7 / 4) / 100

⇒ P = 2800 / 7

⇒ P = 400

Hence, Account B had greater principal.

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Answer:

x=12°

Step-by-step explanation:

10x-20+6x+8=180°

16x=180+20-8

16x=192

x=12°

The equation of the line in the given form Ax + By = C is 3x + 4y = 40

The given parameters from the question are given as

Point = (8, 4)

Slope = -3/4

Start by representing the equation in the slope intercept form

This is calculated as

y = m(x - X) + Y

Where

m, Slope = -3/4

(X, Y), Point = (8, 4)

So, we have

y = -3/4(x - 8) + 4

Multiply through by 4

4y = -3(x - 8) + 16

Evaluate the like terms

4y = -3x + 24 + 16

This gives

3x + 4y = 24 + 16

Evaluate

3x + 4y = 40

Hence, the equation is 3x + 4y = 40

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Answer: 27 dogs

Step-by-step explanation: 2 cats + 3 dogs= 5 in total for animals. 2/5x45=18 cats

3/5x45= 27 dogs

27+18=45 animals

There is 27 dogs in the shelter

No , Sydney does not have enough beads to make 15 rings .

beads required for one ring = 60

total rings she have to make is = 15

total beads she has to make rings = 852 beads

now,

60 beads make ring = 1

852 beads make rings = 1/60 x 852

                                     =    14.2 rings

                             OR

                          14 total rings

So , Sydney does not have enough beads to make 15 rings . she can only make 14 beads from the given amount of beads.

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The equation of a line is y = 5x - 6

What is Equation of line ?

A straight line's general equation is y = mx + b, where m denotes the gradient or slope and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.

The given points are (2, 4) and (-4, 6)

The equation of line is given ,

y = mx + b

where, m = slope

b = y - intercept

To find slope , we have formula

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

let, (x1, x2) = (2, 4) and

(y2, y1) = (-4, 6)

Now, put the values in slope formula,

m = ( 6 - (-4) ) / ( 4 - 2)

m = (6 + 4) / 2

m = 10 / 2

m = 5

We get slope, now find y-intercept i,e, 'b'

y = 5x + b

so take any point to find 'b'

Let's take the point (2, 4) which is (x, y) so now put the (x, y) and find 'b'.

4 = 5 * 2 + b

4 = 10 + b

b = 4 - 10

b = -6

so, now put the values of slope and y-intercept in equation of line i.e,        y = mx + b

y = 5x - 6

Hence, the equation of a line is y = 5x - 6

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The ratio when Sophia earned $36 at her job when she worked for 4 hours is 1:9.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

From the information, Sophia earned $36 at her job when she worked for 4 hours.

The equivalent ratio to illustrate the information will be:

= 4 / 36

= 1/9

= 1:9

Note that the coordinates point weren't given in the question.

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The equation of given graph is y = |x - 3| + 5.

The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.

Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.

As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.

So, by putting the value of vertex in general equation we get the equation of the graph,

y = |x - 3| + 5

Therefore, the equation of given graph is y = |x - 3| + 5.

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Answer:

y = [tex]\frac{2}{3}[/tex] x - 6

Step-by-step explanation:

y - [tex]\frac{2}{3}[/tex] x = - 6 ( isolate y by adding [tex]\frac{2}{3}[/tex] x to both sides )

y = [tex]\frac{2}{3}[/tex] x - 6

The equation of given graph is y = |x - 3| + 5.

The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.

Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.

As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.

So, by putting the value of vertex in general equation we get the equation of the graph,

y = |x - 3| + 5

Therefore, the equation of given graph is y = |x - 3| + 5.

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The length of segment DE on the rectangle, considering the midpoint, is given as follows:

DE = 22.67.

The midpoint of a segment divides a segment into two segments of equal length, having half the length of the entire segment.

In this problem, the diagonal of the rectangle represented by segment AC has midpoint E, hence the measure of x is calculated as follows:

EC = AE.

The measures are as follows:

Hence:

7x - 3 = 4x + 8

7x - 4x = 8 + 3

3x = 11

x = 11/3.

Segment DE is also half of a diagonal, hence it's length is obtained with the numeric value of any segment EC or AE, as follows:

DE = EC = 7x - 3 = 7 x 11/3 - 3 = 77/3 - 9/3 = 68/3 = 22.67.

The rectangle is given by the image at the end of the answer.

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The maximum number of hikers who could have walked between 6 miles and 17 miles is 19.

We need to find the maximum number of hikers who could have walked between 6 miles and 17 miles.

When the derivative equals 0, rearrange the function using elementary algebraic principles to find the value for x. The x-coordinate of the function's vertex, which is where the maximum or lowest will occur, is provided in this answer. the solution back into the original function to determine the minimum or maximum.

From the table, we can see

Between intervals 5≤x<10 there are 2 hikers

Between intervals 10≤x<15 there are 9 hikers

Between intervals 15≤x<20 there are 8 hikers

So, total number of hikers = 2+9+8

= 19

Hence, the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.

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Answer: x=10

Step-by-step explanation:

Images below

Help this helps

Answer:

$3.70

Step-by-step explanation:

12 dimes, and dimes are ten cents each. So we will multiply 10*12=120. Which is $1.20.

10 quarters, and quarters are twenty-five cents each. So we will multiply 10*25=250. Which is $2.50

Now we take our two totals and add them together. 1.20+2.50=3.70.

So we have $3.70.

I hope this helps!!!

The statement that cannot be assumed from the figure is

B) BD bisects ∠ADE

What are Supplementary and Complementary Angles?

Supplementary angles are two angles that have a sum of 180°.

Complementary angles are two angles that have a sum of 90°.

Given data ,

From the figure we can arrive at each conclusions

A)

∠ABD and ∠DBE are supplementary

Now , from the figure we can see that point B lies on the line AE

And , ∠ABD + ∠DBE = 180°

Hence , ∠ABD and ∠DBE are supplementary and the statement is TRUE

B)

Bisecting a line means dividing the line into two equal parts

And from the figure BD does not bisect ∠ADE

Hence , BD does not bisect ∠ADE so the statement is FALSE

C)

∠CDA and ∠ADE are complementary

From the figure we can see that ∠EDC is 90°

And , ∠CDA + ∠ADE = ∠EDC

So , ∠CDA + ∠ADE = 90°

Hence , ∠CDA and ∠ADE are complementary and the statement is TRUE

D)

∠EDB and ∠BDA are adjacent and are not complementary

From the figure we can see that ∠EDB and ∠BDA are adjacent

∠EDB + ∠BDA ≠ 90°

Hence , they are not complementary and the statement is TRUE

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Brian has  £63 Initially, by using the ratio and proportion method.

What are Ratio and Proportion?

In this section, the terms ratio and percentage are defined. Both ideas play a significant role in mathematics. Numerous examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.

An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometers per hour is equal to the time it needs to travel 500 kilometers in five hours. Example: 100 km/hr = 500 km/5 hour. The division technique of comparing two amounts can be quite effective in some circumstances. We can argue that a ratio is a comparison or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio may be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol ":".

In the question, It is given that:

The ratio of money in Brian's wallet to Colin's wallet one day was 7:2.

Let 7x denotes the amount in Brian's wallet and 2x denote the amount in  Colin's wallet on that day.

we know that:

Brian spent £39 that day.

Amount left in Brian's wallet = 7x- 39

Brian now had £4 less than Colin.

⇒ 2x -4= 7x- 39

⇒  7x-2x=4+39

⇒  5x=35

⇒  x=7   [Divide both sides by 5 ]

So , The initial amount in Brian's wallet  = 7(7)= £49

The initial amount in Colin's wallet = 2(7)= £14

The amount they had together =  £49+£14 = £63

So, They had £63 altogether initially.

Therefore, Brian has  £63 Initially.

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Answer: £14

Answer:

[tex]\huge\boxed{\sf m = 11}[/tex]

Step-by-step explanation:

-7m + 10m - 8 = 25

3m - 8 = 25

Add 8 to both sides

3m = 25 + 8

3m = 33

Divide 3 to both sides

m = 33/3

m = 11

[tex]\rule[225]{225}{2}[/tex]

The given inequality solved for y is y > 4

From the question, we are to solve the given linear inequality.

To solve an inequality, we will solve for the variable in the inequality.

The given inequality is

-16 > -4y

The variable in the inequality is y.

Now, we will solve for y

-16 > -4y

Divide both sides by -4

-16/-4 > -4y/-4

4 < y

Thus,
y > 4

Hence, the solution is y > 4

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Answer:

[tex]a_{n}[/tex] = n - 5

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence, that is

- 3 - (- 4) = - 2 - (- 3) = - 1 - (- 2) = 1

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 4 and d = 1 , then

[tex]a_{n}[/tex] = - 4 + 1 (n - 1) = - 4 + n - 1 = n - 5

Answer:

-1

Step-by-step explanation:

Given:

[tex]i^{50}[/tex]

Rewrite 50 as the product of 2 and 25:

[tex]\implies i^{(2 \cdot 25)}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies \left(i^2\right)^{25}[/tex]

Apply the imaginary number rule  i² = -1 :

[tex]\implies \left(-1\right)^{25}[/tex]

[tex]\textsf{Apply the exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}:[/tex]

[tex]\implies -1^{25}[/tex]

As 1²⁵ = 1 then:

[tex]\implies -1[/tex]

Answer:

(i)⁵⁰ = -1

Step-by-step explanation:

The problem is,

→ (i)⁵⁰

Formula we use,

→ i² = -1

Let's solve the problem,

→ (i)⁵⁰

→ (i²)²⁵

→ (-1)²⁵

→ -1

Hence, the answer is -1.

Using proportions, the amounts are given as follows:

a) Number of weeks: 17.

b) Number of fortnights: 8.5.

a) Number of days studied: 51.

b) Number of hours studied: 102.

A proportion is a fraction of a total amount, and this fraction is used to build relations, using basic arithmetic operations such as multiplication or division, to obtain the desired measures in the context of a problem.

Using a calendar, the number of weeks between these two dates is of:

17.

A fortnight is composed by two weeks, hence the number of fortnights is:

17/2 = 8.5.

You studied 3 days a week, hence the number of days studying was of:

17 x 3 = 51 days.

You studied 2 hours a hence, hence the number of hours studying was of:

51 x 2 = 102 hours.

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The mean recurrence interval between earthquakes of this magnitude range over the previous 30 years essentially has been 4.769230 in a basically sort of big way in a subtle way.

Given, the earthquake's magnitude literally basically is between 6.0 and 7.0 in a very definitely big way, or so they for all intents and purposes thought. occurrences = 2 earthquakes

Duration: 30 years

particularly Mean Earthquake Recurrence Interval,

T=(n+1) / m

Where m = 6+7 / 2 = 6.5 , n = 30

T = ( 30+1)/6.5

   = 31/6.5

   = 4.769230

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