In a round of mini-golf , Clare records the number of strokes it takes to hit the ball into the hole of each green. She said that, if she redistributed the strokes on different greens, she could tell that her average number of strokes per hole is 3. ​

Answer:

x = 10

Step-by-step explanation:

All angles in a triangle must add up to 180. We know one angle is 68 and another is 90 because there is a right angle (which are always 90).

180 = 90 + 68 + (2x + 2)

180 = 158 + (2x + 2).      subtract 158 from both sides

22 = 2x + 2.     subtract 2 from both sides

20 = 2x.       divide both sides by 2

10 = x

Answer:

x = 10

Step-by-step explanation:

2x + 2 + 68 + 90 = 180

2x + 160 = 180

2x = 20

x = 10

9. The solution is (x, y) = (4/3, -5/3).

10. The solution is (x, y) = (1, 2).

The coefficient matrix is:

| -1  5 |

|  1 -2 |

The determinant of the coefficient matrix is:

|-1  5 |      |-2  5 |

| 1 -2 |  = (-1)(-2) - (5)(1) = 3

The matrix formed by replacing the first column of the coefficient matrix with the constants on the right side of the equation is:

| 2  5 |

|-2 -2 |

The determinant of this matrix is:

| 2  5 |      | -2  5 |

|-2 -2 |  = (2)(-2) - (5)(-2) = -4 + 10 = 6

|-1  2 |

| 1 -2 |

The determinant of this matrix is:

|-1  2 |     | 1  2 |

| 1 -2 | = (-1)(-2) - (2)(1) = 2

Using Cramer's rule:

x = |2  5| / 3 = 4/3

   |-2 -2|

y = |-1 2| / 3 = -5/3

   |1 -2|

10.The coefficient matrix is:

| -5 -5 |

| -2 -4 |

The determinant of the coefficient matrix is:

|-5 -5 |      |-2 -5 |

|-2 -4 |  = (-5)(-4) - (-5)(-2) = -10

The matrix formed by replacing the first column of the coefficient matrix with the constants on the right side of the equation is:

| 25 -5 |

| 16 -4 |

The determinant of this matrix is:

| 25 -5 |     | 16 -5 |

| 16 -4 | = (25)(-4) - (-5)(16) = -100 + 80 = -20

|-5 25 |

|-4 16 |

The determinant of this matrix is:

|-5 25 |     |-4 25 |

|-4 16 | = (-5)(16) - (25)(-4) = -80 -(-100) = 20

Using Cramer's rule:

x = |-5 -5| / -10 = 1

   |-2 -4|

y = |-5 25| / -10 = 2

   |-4 16|

For such more questions on solution

https://brainly.com/question/24644930

#SPJ8

Answer:

23

Step-by-step explanation:

Using an online calculator and plugging the values in, we get our equation of y=mx + b to become y = 1.2x - 17.8 .

Plugging 34 in for x, we get 1.2(34) - 17.8 = 23 for their projected test grade

Answer:

The answer is b and helping for higer points

Step-by-step explanation:

Answer: D

Step-by-step explanation:

y intercept is at 2 and the slope is 1/5

The triple integral f(x, y, z)dV for the following function f is 256π(256 - x - y)² as an iterated integral in cylindrical coordinates.

In two-dimensional space R2, a point with rectangular coordinates (x, y) can be identified with (r, θ) in polar coordinates and vice versa, where x=rcosθ, y=rsinθ, r2=x2+y2 and tanθ=(y.x) are the relationships between the variables.

In three-dimensional space R3, a point with rectangular coordinates (x, y, z) can be identified with cylindrical coordinates (r,θ,z) and vice versa. We can use these same conversion relationships, adding z as the vertical distance to the point from the x y-plane

According to the question:

The integrated integral in cylindrical coordinates is given by:

∫∫∫f(ρ, θ, z)dV = ∫∫∫xρcos(θ)ρsin(θ)zdρdθdz

Evaluating the integral yields:

∫∫∫f(ρ, θ, z)dV = 256π∫zdz

= 256πz²

= 256π(256 - x - y)²

Learn more about Triple Integral:

https://brainly.com/question/2289273

#SPJ4

Answer:

False

Step-by-step explanation:

When a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

It's important to note that pressure increases as depth increases under water. The pressure in pounds per square foot, P, at a depth of d feet is given by the equation:

P = 0.433d + 14.7 where 0.433 is a constant for water, and 14.7 is the pressure at the surface.

In order to find the depth at which the pressure is 159 pounds per square foot, we need to solve the equation for

d.P = 0.433d + 14.7

Substitute P = 159 and solve for

d.159 = 0.433d + 14.7

Subtract 14.7 from both sides.

144.3 = 0.433d

Divide both sides by 0.433 to isolate d.

d ≈ 333.06

Hence, when a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

Learn more about volume here:

https://brainly.com/question/28058531

#SPJ11

Answer:

I used a chip bottle and it was 3.5 inches

Step-by-step explanation:

I hope this helps sorry if its wrong

Answer:

(-2, -3)

(3, 12)

Step-by-step explanation:

To solve this, we're gonna get rid of the y's with substitution

x² + 2x - 3 = 3x + 3

Let's make this equation equal to zero

Subtract 3 from both sides

x² + 2x - 3 = 3x + 3

            - 3         - 3

x² + 2x - 6 = 3x

Subtract 3x from both sides

x² + 2x - 6 = 3x

    - 3x        - 3x

x² - x - 6 = 0

Factor the equation

(x - 3)(x + 2) = 0

This means x can be -2 or 3

Let's solve it with -2 first, plug the new x in y = 3x + 3

y = 3(-2) + 3

y = -6 + 3 = -3

Do the same for x = 3

y = 3(3) + 3

y = 9 + 3 = 12

The question asks to estimate the rainfall at station D in the year 1980 based on the rainfall data of other stations. The answer is that station D's rainfall in 1980 can be estimated by comparing the rainfall patterns of all stations in the basin.

To estimate the rainfall at station D in 1980, we can analyze the relationship between the rainfall at different stations. In this case, we can observe that there is a correlation between the annual rainfall at stations A, B, C, and D. By comparing the rainfall patterns of these stations, we can make an estimation for station D.

In the given data, station D is inoperative in 1980, but the rainfall data for stations A, B, and C are available. By analyzing the rainfall patterns in previous years and considering the correlation between the stations, we can estimate the rainfall at station D in 1980 based on the rainfall data of the other stations in the basin.

Learn more abut inoperative here: brainly.com/question/30889685

#SPJ11

The error is that vertical angles are congruent, and don't necessarily add to 180°. Vertical angles only add to 180° if they are right angles.

\(13x+45+19x+3=180 \\ \\ 32x+48=180 \\ \\ 32x=132 \\ \\ x=33/8\)

Answer:

x = 7

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent.

Angles on a Straight Line Theorem

The sum of angles formed on a straight line is equal to 180°.

The error made is confusing the Vertical Angle Theorem with the Angles on a Straight Line Theorem.  To find x, we should either:

Applying the Vertical Angle Theorem:

\(\boxed{\begin{aligned} (13x+45)^{\circ} &=(19x+3)^{\circ} \\13x+45&=19x+3\\13x+42&=19x\\42&=6x\\x&=7\end{aligned}}\)

Applying the Angles on a Straight Line Theorem:

\(\boxed{\begin{aligned}(6x+2)^{\circ}+(19x+3)^{\circ}&=180^{\circ}\\6x+2+19x+3&=180\\25x+5&=180\\25x&=175\\x&=7\end{aligned}}\)

Therefore, the value of x is \(\boxed{x=7}\) .

The probability that she makes correct guesses 14 times or more is 0.0582 and this probability does not seem to verify her claim

Number of tosses of coin  n = 20

probability she guesses correctly p = 0.5

Probability she guesses incorrectly q = 1- p = 0.5

P(X < A) = P( z*σ + μ < A) = P(z < (A-μ)/σ)        (1)      ( ∵ we know z = x - μ/σ)

Mean = μ  = np = 20 * 0.5 = 10

Standard deviation = σ

Standard deviation σ = √npq = √(20 *0.5*(1-0.5) = √5 = 2.236

Probability of being correct 14 times or more

P(X ≥ 14) = 1 - P(X < 13.5)      

              = 1 - P(Z < (13.5 - 10)/2.236)         (using 1)

              = 1 - P(Z < 1.57)

               = 1 - 0.9418

               = 0.0582

Here, the probability of getting 14 or more is 0.0582 and it is usually as the probability is more than 0.05. Thus this probability does not verify her claim

Problem based on normal distribution

brainly.com/question/14919097

#SPJ4

Answer:

144 000

Step-by-step explanation:

960 000 × 0.15

= 144 000

Answer:

144,000

Step-by-step explanation:

\( \frac{15}{100} \times 960000 \\ 15 \times 9600 \\ 144000\)

Answer:

The answer is the equation for the function describing the movement of the buoy:

f(x) = 5 * sin(2 * pi * x / 16) + 8

Step-by-step explanation:

To graph the function, we need to find an equation that describes the buoy's movement. Since the buoy bobs up and down 5 meters from the ocean's depth, we can use the sine function. The amplitude of the function is 5, since the buoy moves 5 meters from the normal ocean depth. The period of the function is 16 seconds, since it takes 16 seconds for the buoy to go from its highest point to its lowest point.

Using this information, we can write the equation for the function as:

f(x) = 5 * sin(2 * pi * x / 16) + 8

where x is the time in seconds.

The first point on the graph would be (0, 8), since at x = 0 the buoy is at normal ocean depth. The second point would be either a maximum or minimum value on the graph closest to x = 0, which can be found by finding the derivative of the function and setting it equal to zero.

The graph of the function would look like a wave that oscillates up and down, with a maximum value of 5 meters above the normal ocean depth and a minimum value of 3 meters below the normal ocean depth.

isiaiisjjajsihajaihaiahshushsu a habja uahabja ha ha a ha ha Janna j Jabjaban an aka. na a ha ha ha ha a ja aja naja ha. ha aub ah ah ah ha ahahaha a ahba ahbahabhaba babav aha ha ha answer a

Step-by-step explanation:

you earned $43.88 for 6.5 hours of work.

an hourly rate means how much money you get for 1 hour of work.

to get that we need to divide now both by 6.5, as 6.5/6.5 = 1 hour.

and

43.88/6.5 = $6.750769231... per hour ≈ $6.75/ hour

Answer:

4x-3

Step-by-step explanation:

9+4x-12

9-12 = -3

4x-3

Answer:

4x - 3

Step-by-step explanation:

You can first take out 9 and solve for 4 (x - 3) which is 4x - 12. Now, you can put 9 back into the equation so it will be 9 + 4x - 12. We can simplify a bit further which will give us 4x - 3.

Answer:

900

Step-by-step explanation:

4500/5

The category in the Excel Options dialog box that contains the option to change the user name is "General".

In the Excel Options dialog box, the category that contains the option to change the user name is the General category.

Excel graphing methods, Go to Insert > Line after selecting the data. The type of line chart you want may be chosen from a dropdown menu that appears when you click the icon.

We'll use the fourth 2-D line graph (Line with Markers) for this illustration. Your line graph for the chosen data series will be added by Excel.

What are the primary three graphs?

How to Use Graphs in Science

Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph may be used to display a certain kind of data.

To know more about graph click here

brainly.com/question/30934484

#SPJ11

If we use a 95% confidence level instead of a 90% confidence level, the confidence interval calculation from the same data will produce an interval wider than (0.26, 0.30).

In this question we have been given that a random sample of 1000 mosquitoes, 280 of them carried west nile virus. the 90% confidence interval for the true proportion of west nile virus infected mosquitoes is (0.26, 0.30).

We need to determine if we use a 95% confidence level instead of a 90% confidence level, whether the confidence interval calculation from the same data produce an interval wider than (0.26, 0.30) or not.

We know that the greater the confidence level, the wider the confidence interval.

This means, if we use a 95% confidence level instead of a 90% confidence level, the confidence interval calculation will produce the wider interval.

Therefore, for given sample 95% confidence interval calculation will produce the wider interval.

Learn more about the confidence interval here:

https://brainly.com/question/24131141

#SPJ4

Answer:

sorry i cant read it

Step-by-step explanation:

The equations are solved to w = 0 and z = -2. Option B

From the information given, we have the simultaneous equations as

3w-4z=8

2w+3z=-6

Make w the subject from equation 1

w = 8 + 4z/3

Substitute the value into equation 2, we have that;

2(8 + 4z/3) + 3z = -6

expand the bracket, we get;

16 + 8z/3 + 3z = -6

find the LCM, we have;

16 + 8z + 9z/3 = -6

cross multiply

16 + 17z = - 18

add the values

19z = -34

Make 'z' the subject

z =-2

Substitute the value

3w - 4z = 8

3w = 8 - 8

w = 0

Learn about simultaneous equations at: https://brainly.com/question/16863577

#SPJ4

Answer: 6 boys

Step-by-step explanation:

To find the number of boys in the class, we start by dividing the number of girls (18) by the first number in the ratio (which is 3):

This tells us that there are 6 sets of 3 girls in the class.

Since the ratio of girls to boys is 3:1, we know that for every 3 girls, there is 1 boy. So, for the 6 sets of girls we just found, there must be 6 sets of boys as well:

So, there are 6 boys in the class.

________________________________________________________

Answer:

yes

Step-by-step explanation:

The final expression after collecting terms is: 19zx^(2) - 3z^(2)x + 2z^(2)y

Explanation: To collect terms in an expression, we need to combine like terms. Like terms are terms that have the same variables with the same exponents. In the given expression, the like terms are 13zx^(2) and 6zx^(2). We can combine these terms by adding their coefficients:

13zx^(2) + 6zx^(2) = 19zx^(2)

The other terms, 2z^(2)y and -3z^(2)x, do not have any like terms, so we cannot combine them with any other terms. Therefore, the final expression after collecting terms is:

19zx^(2) - 3z^(2)x + 2z^(2)y

Learn more about expression

brainly.com/question/13947055

#SPJ11

The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.

The ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.

12⅝ = 101/8 = 12.645

12.62 = 12.62

√146 = 12.0830

12.39 = 12.39

12¾ = 51/4 = 12.75

Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.

Read more about numbers here:https://brainly.com/question/1094377

#SPJ1

Answer: Rectangle 2 and Rectangle 3 have the greatest difference in area

Therefore, the sum of the series is 5050.

To find the sum of the series 1 + 2 + 3 + 4 + ... + 97 + 98 + 99 + 100, we can use the formula for the sum of an arithmetic series:

\(S_n = (n/2)(a_1 + a_n)\)

where \(S_n\) is the sum of the series, n is the number of terms, \(a_1\) is the first term, and \(a_n\) is the last term.

In this case, the first term \(a_1\) is 1 and the last term \(a_n\) is 100, and there are 100 terms in total.

Substituting these values into the formula, we have:

\(S_n\) = (100/2)(1 + 100)

= 50(101)

= 5050

To know more about series,

https://brainly.com/question/28584903

#SPJ11

Answer:

I'm not sure though but this is what I got

Step-by-step explanation:

surface area of a sphere is 4 pi r square

4×22÷7×5×5

314.3

It takes 1 hour 43 minutes to finish mowing the lawn.

The rate of work done by Gregory and Jennifer finish mowing the lawn in

1 hour 43 minutes.

According to the question

Gregory can mow the family's lawn in 3 hours, she mows at a rate of 1/3 of the lawn per hour(1/3 lawn/hour)

Jennifer can mow it in 4 hours, which means her rate is 1/4 lawn/hour.

Together , their rates are 1/3 + 1/4.

This equals 7/12 lawns/hr.

We want to know how many hours they have to mow in order to mow 1 lawn.

This can be represented by the equation : \(\frac{7}{12} \times x = 1\)

To solve for x, we would divide both sides by 7/12.

This leaves us with x = 12/7 which is 1.714.

Convert 1.714 to minutes by multiplying 60.

This gives you a final answer of about 1 hour 43 minutes.

Hence, It takes 1 hour 43 minutes to finish mowing the lawn.

The rate of work done by Gregory and Jennifer finish mowing the lawn in

1 hour 43 minutes.

Find out more information about rate of work here

brainly.com/question/14305692

#SPJ4