We can use the Pythagorean theorem to solve this problem. Let's call the distance from the ball to the center of the green "d". We know that the marker is 150 yards from the center of the green, and the golfer has paced off 35 yards in a direction 110 degrees from the marker.
Let's use x to represent the horizontal distance from the marker to the ball, and y to represent the vertical distance from the marker to the ball. Then, we have:
x = 35 * cos(110)
y = 35 * sin(110)
Using the Pythagorean theorem, we can find the distance "d" from the ball to the center of the green:
d^2 = x^2 + (y + 150)^2
Plugging in the values for x and y, we get:
d^2 = 35^2 * cos(110)^2 + (35 * sin(110) + 150)^2
d^2 = 1225 + (150 + 35 * sin(110))^2
Using a calculator, we can find that sin(110) = 0.939, so:
d^2 = 1225 + (150 + 31.65)^2
d^2 = 1225 + (181.65)^2
d^2 = 1225 + 32762.7225
Taking the square root of both sides:
d = sqrt(1225 + 32762.7225)
d = sqrt(33987.7225)
d = 183.83
Rounding to the nearest yard:
d = 184 yards
So, the ball is 184 yards from the center of the green.
there are c different types of coupon, and each coupon obtained is equally likely to be any one of the c types. find the probability that the first n coupons which you collect do not form a complete se
The probability that the first n coupons which you collect do not form a complete set is (c^n - (c-1)^n) / c^n.
To find the probability that the first n coupons collected do not form a complete set, we need to count the number of ways in which the first n coupons can be collected so that they do not form a complete set and divide it by the total number of ways in which n coupons can be collected, which is c^n.
Let S be the set of all possible complete sets of coupons. The number of ways in which the first n coupons can form a complete set is the number of ways to choose any one of the complete sets in S, multiplied by the number of ways to order the coupons within that set. There are (c choose n) ways to choose n coupons out of c, and for each complete set of n coupons, there are n! ways to order them. Therefore, the number of ways to choose n coupons that form a complete set is (c choose n) * n!.
The total number of ways to choose n coupons out of c is c^n.
So, the probability that the first n coupons collected do not form a complete set is:
P = 1 - [(c choose n) * n! / c^n]
Alternatively, we can count the number of ways in which the first n coupons can be collected so that they do form a complete set. There are (c-1)^n ways to choose n coupons out of c-1 types of coupons, and for each set of n coupons, there is exactly one way to add the missing coupon to form a complete set. Therefore, the number of ways to choose n coupons that form a complete set is c^n - (c-1)^n.
So, the probability that the first n coupons collected do not form a complete set is:
P = (c^n - (c-1)^n) / c^n
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A game lasts 3/8 hours. Tammy played 12 of these games.
The total time that tammy sent in total playing games is; 4.5 hours
How to solve Fraction Word problems?The parameters given for Tammy in playing the game are;
Number of games played = 12 games
Time spent per game = ³/₈ hours
Thus;
Total time she spent playing game will be gotten by multiplying the time per game by number of games played to get;
Total time spent = ³/₈ * 12
= 9/2
= 4.5 hours
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Complete question is;
A game lasts 3/8 hours. Tammy played 12 of these games. For how long did she play in total? Write your answer in simplest form.
Solve this system of linear equations:
4x - 2y = 8
y=-2
Step 1: Plot the x-intercept of the first equation.
Equations by Graphing
d
-6-4-2
6
4
2
-2
4
-6
Y
2
4 6
x+
x
y
A solution to this system of linear equations is (1, -2).
How to graph the solution to this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
4x - 2y = 8 ......equation 1.
y = -2 ......equation 2.
Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant IV and it is given by the ordered pair (1, -2).
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Find the vertex of the parabola y = x2 − 8.
Simplify both coordinates and write them as proper fractions, improper fractions, or integers.
(
,
)
The vertex of the parabola is (0, -8).
What is Parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
We have to find the vertex of the parabola y = x² - 8,
x = -b/2a
where a is the coefficient of the x² term,
b is the coefficient of the x term, and
x is the x-coordinate of the vertex.
a = 1 and b = 0, so:
x = -0/(2.1) = 0
Now let us find the y-coordinate of the vertex, we can substitute x = 0 into the equation for the parabola:
y = (0)² - 8 = -8
Hence, the vertex of the parabola is (0, -8).
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Franny's suitcase weighs 35.7 pounds. Which statement is not true?
A. The 35 represents whole pounds. The 7 represents part of a
pound.
B. The 7 represents more weight than the 5.
OC. The suitcase weighs more than 35 pounds, but less than 36
pounds.
OD. All of these statements are true.
-3k2g - [8kg2 -(6k2g - 2kg2)]
Answer:
Step-by-step explanation:
ghjhkvfgfgnfdgn
what is the standard error? group of answer choices the standard error is the standard deviation of the sampling distribution the standard error is a measure of how representative a sample statistic is likely to be of the population parameter. the standard error is calculated using the standard deviation of the sample all of the options describe the standard error.
The correct option is "the standard error is the standard deviation of the sampling distribution." Correct option is A.
The standard error is a measure of the variability of a sampling distribution, which is the distribution of sample statistics (e.g., mean, proportion) that would be obtained from multiple random samples of the same size from the same population.
The standard error represents the standard deviation of the sampling distribution, and it provides a measure of the precision of the sample statistic in estimating the population parameter.
The standard error is not the same as the standard deviation of the sample, which is a measure of the variability of the individual observations in the sample.
The standard deviation of the sample is typically used to estimate the standard deviation of the population, while the standard error is used to estimate the variability of the sample statistic and to construct confidence intervals or perform hypothesis tests.
While the other options are related to the concept of the standard error, they are not equivalent or fully accurate descriptions of what the standard error represents.
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Complete question is:
What is the standard error?
group of answer choices
A. the standard error is the standard deviation of the sampling distribution
B. the standard error is a measure of how representative a sample statistic is likely to be of the population parameter.
C. the standard error is calculated using the standard deviation of the sample all of the options describe the standard error.
Suppose the water level of a river is 34 feet and that it is receding at a rate of 0.5 feet per day. Write an equation for the water level, y, after x days. In how way days will the water level be 26 feet?
The equation is......
It will take.....days for the water level to be 26 feet.
The equation is y = (-0.5)x + 34 and it will take 16 days for the water level to be 26 feet.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
Let the number of days = x, and the water level = y.
Given that,
Water level of river = 34 ft (initial value/y-intercept)
Rate of change = -0.5 ft per day (slope)
The equation of the line is given as:
y = mx + c
where, m is the slope
c is the y-intercept.
Substituting the values we have:
y = (-0.5)x + 34
The number of days in which the water level will reduce to 26 ft is:
26 = (-0.5)x + 34
26 - 34 = -0.5x
x = 16 days.
Hence, it will take 16 days for the water level to be 26 feet.
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what is the solution to the number sentence k - 1.6 / 6 = 5.4
Answer:
k = 48.4
Step-by-step explanation:
[tex] \frac{k - 16}{6} = 5.4 \\ 6 \times \frac{(k - 16)}{6} = 5.4 \times 6 \\ k - 16 = 32.4 \\ k = 32.4 + 16 \\ k= 48.4 [/tex]
Kingsley knows that 1 inch is about 2. 54 centimeters. He wants to write an equation he can use to convert any given length in inche (I) to centimeters (c)
Kingsley knows that 1 inch is about 2. 54 centimeters.6 inches is equivalent to 15.24 centimeters.
To convert any given length in inches (I) to centimeters (c), Kingsley can use the following equation:
c = I * 2.54
This equation works because we know that 1 inch is equal to 2.54 centimeters. So, to convert any given length in inches to centimeters, we simply multiply the number of inches by 2.54. The result gives us the equivalent length in centimeters.
For example, if we want to convert a length of 6 inches to centimeters, we can use the equation:
c = 6 * 2.54 = 15.24
So, Kingsley knows that 1 inch is about 2. 54 centimeters. 6 inches is equivalent to 15.24 centimeters.
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Find the values of x, y, and z
The values of x, y and z are given as follows:
x = 6.25.y = 6.67.z = 5.What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.There are two similar trapezoids for this problem, hence the proportional relationship for the side lengths is given as follows:
x/15 = 10/24 = y/16 = z/12.
Applying cross multiplication, the value of x is given as follows:
24x = 15 x 10
x = 15 x 10/24
x = 6.25.
The value of y is given as follows:
y = 16 x 10/24
y = 6.67.
The value of z is given as follows:
z = 12 x 10/24
z = 5.
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Reena bought 53. 882 grams of spinach and 49. 883 grams of chili. Did Reena buy more spinach or chili?
Reena bought more spinach as the total weight of spinach is more than chili.
The weight of an object refers to as the force of gravity that is acting on the object. It is the amount of gravitational force applied by the Earth on that object.
Weight of spinach - 53.882 grams or 0.053882 kg
Weight of chili - 49.883 grams or 0.049883 kg
When comparing the above information, we get the weight of spinach to be more than the weight of chili as the weight of spinach is 53.882 grams which is more than the gross weight of chili i.e., 49.883 grams. So, Reena bought more spinach as compared to chili.
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Evaluate3(x-1+2)when x=5
The graph represents the amount of money, in thousands, that you make over a
time period of years. According to the graph, what is the original price you invested?
Answer:
$2,000
Step-by-step explanation:
The initial investment price is given by the y-value where the graph intersects the y-axis
This is at y = 2
Since the scale is in thousands of $, that would mean $2,000 as the original price
Point G is located at -18 on a number line. Point H is 24 more than Point G. Where is Point h?
Point H is located at 6 on the number line, which is 6 units to the right of the zero point.
We know that Point G is located at-18 on the number line, and that Point H is 24 further than Point G. To find the position of Point H, we need to add 24 to the position of Point G
Point H = Point G + 24
Substituting the position of Point G, we get
Point H = -18 + 24
Simplifying the expression, we get
Point H = 6
thus, Point H is located at 6 on the number line.
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If , which equation describes the graphed function? A. y = f(-x) − 3 B. y = -f(x) + 3 C. y = -f(x) – 3 D. y = f(-x) + 3
The equation that describes the graphed function is -
g(x) = - f(x) - 3.
What is root function?A root function in mathematics is given as -
y = [tex]$\sqrt[n]{x}[/tex]
We can further write the function as -
y = [tex]$x^{\frac{1}{n} }[/tex]
Given is the graph of the function as shown in the image attached.
We can write the function f(x) as -
f(x) = √x
Inverting the f(x) across the {x} axis, we can write -
- f(x) = - √x
After downward translation, we can write g(x) as -
g(x) = - f(x) - 3
Therefore, the equation that describes the graphed function is -
g(x) = - f(x) - 3.
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porter is on the swim team. IN addition to swimming he runs as part of his training porterchecks his heart rate halfway through his training session . (swimming 53 beats in 1/3 minute running 42 beats in 1/4 minute). What is porters heart rate when he swims?
Answer: 159 bpm
Step-by-step explanation:
if his rate is 53 beats in 1/3 of a minute, in 3/3 of a minute, (1 full minute), it will be 53 x 3 = 159 beats
so we can say his heart rate is 159 beats/minute, or 159 bpm
A small town has two local high schools. High School A currently has 1000 students and is projected to grow by 35 students each year. High School B currently has 700 students and is projected to grow by 55 students each year. Let A represent the number of students in High School A in t years, and let B represent the number of students in High School B after t years. Write an equation for each situation, in terms of t, and determine after how many years, t, the number of students in both high schools would be the same.
The linear equation for A and B will be A=1000+35t and B=700+55t where t=no. of years and A will be same as B in 15 years.
What exactly is a linear equation?
The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
As given that High School A currently has 1000 students and is projected to grow by 35 students each year. High School B currently has 700 students and is projected to grow by 55 students each year.
Let A represent the number of students in High School A in t years, and
Let B represent the number of students in High School B after t years.
Then A=initial students+35*no. of years and B=initial students+55*no. of years i.e. A=1000+35t and B=700+55t
and for A=B
1000+35t=700+55t
55t-35t=1000-700
20t=300
t=15
hence,
The linear equation for A and B will be A=1000+35t and B=700+55t where t=no. of years and A will be same as B in 15 years.
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Each pair of polygons is similar. Find the value of x.
The value of x for the similar triangles is equal to 13.
How to calculate for x for the similar trianglesWe have the triangles to be similar, this implies that the length 8 of the smaller triangle is similar to the length x - 1 of the larger triangle
and the length 10 of the smaller triangle is similar to the length x + 2 of the larger triangle
so;
10/(x + 2) = 8/(x - 1)
10(x - 1) = 8(x + 2) {cross multiplication}
10x - 10 = 8x + 16
10x - 8x = 16 + 10 {collect like terms}
2x = 26
x = 26/6 {divide through by 6}
x = 13.
Therefore, the value of x for the similar triangles is equal to 13.
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Chloe borrows 800 from the bank for 3 years at simple interest. The interest she is charged after 3 years is 168. Calculate the rate of simple interest charged at this bank. Give the answer as a percentage
After 3 years the rate of simple interest charged at this to Chloe bank is 7%
We can start by using the formula for simple interest:
Simple Interest = Principal * Rate * Time
where the principal is the amount borrowed, the rate is the interest rate as a decimal, and the time is the duration of the loan in years.
Plugging in the given values, we get:
168 = 800 * Rate * 3
Solving for the rate, we get:
Rate = 168 / (800 * 3) = 0.07
Hence,
The rate of simple interest charged at this bank is 0.07, or 7% as a percentage.
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what expressions can be used to calculate the total price of a DVD that cost d dollars if the tax rate is 7.5%
The distance between two towns is 600km,correct to the nearest 10km
A car takes 8 hours 40minute, correct to the nearest 10 minute, to travel this distance
Calculate the lower bound for the average speed of the car in km/h
Answer:
Below
Step-by-step explanation:
rate X time = distance
rate = distance / time <=====we want minimum of this so make denominator as large as possible and numerator as small as possible
distance = 595 KM ( rounds up to 600 km)
time = 8 hr 44 min rounds down to 8 :40 you could make it 8:44.99)
595 km / (8 + 44.99/60) hr = 68 km/hr
1. What must the values of a and b be for PQRS to be a parallelogram?
2. The diagonals of parallelogram ABCD intersect at P. Select all the statements that must be true.
The value of a and b are; a = 2, b = 4
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Given that the diagonals of parallelogram ABCD intersect at P.
4a + b = 2a + 8
4a - 2a + b = 8
2a + b = 8 -----------------(I)
b = 8 - 2a
11b - 10a = 6b
11b - 6b -10a = 0
5b - 10a = 0 ---------(II)
Substitute b = 8 - 2a in equation (II)
5(8-2a) - 10a = 0
40 - 10a - 10a = 0
40 - 20a = 0
-20a = - 40
a = -40/-20
a = 2
Plugin a = 2 in equation (I)
b = 8 -4
b = 4
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A bride-to-be had already finished assembling 15 wedding favors when the maid of honor came into the room to help. The bride assembles at a rate of 2 favors per minute. In contrast, the maid of honor works at a speed of 5 favors per minute. Eventually, they will both have assembled the same number of favors. How many favors will each have made? How long will that take?
The bride-to-be and her maid of honor will each have made __ favors in __ minutes.
Using an equation, the bride-to-be and her maid of honor will each have made 25 favors in 5 minutes.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
Equations are depicted using the equal symbol (=), while mathematical expressions, which combine variables, constants, and values only use mathematical operands.
The total number of wedding favors assembled by the bride-to-be = 15
The bride's assembling rate per minute = 2 favors
The maid of honor's assembling rate per minute = 5 favors
Let x = the number of minutes used
Let the number of favors assembled by the bride = 15 + 2x
Let the total number of favors assembled by the maid of honor = 5x
For the two to assemble the same number of favors, 15 + 2x = 5x
15 = 3x
5 = x
Thus, in 5 minutes the bride-to-be and her maid of honor will have assembled 25 favors each.
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John brings $15 to the candy store. He buys a bag of jelly beans for $4 and plans to buy some chocolate that costs $5 per pound. He wrote the inequality 4+5x≤15 to solve for all the possible values of x , the number of pounds of chocolate John could buy
John can buy any amount of chocolate between 0 and 2.2 pounds (rounded to one decimal place) and still have enough money to buy the jelly beans.
John brings $15 to the candy store and buys a bag of jelly beans for $4. He plans to buy some chocolate that costs $5 per pound. Let x be the number of pounds of chocolate John could buy.
The cost of the chocolate John plans to buy is $5 per pound, so the total cost of x pounds of chocolate is 5x. John's total budget is $15, so he must have enough money to buy the jelly beans and the chocolate. Therefore, the inequality that represents this situation is:
4 + 5x ≤ 15
To solve for x, we can begin by isolating the variable on one side of the inequality. We can do this by subtracting 4 from both sides of the inequality:
5x ≤ 11
Next, we can isolate x by dividing both sides of the inequality by 5:
x ≤ 11/5
Therefore, the possible values of x, the number of pounds of chocolate John could buy, are all real numbers less than or equal to 11/5. However, since John cannot buy a negative amount of chocolate, we must also restrict x to be greater than or equal to 0. Therefore, the solution to the inequality is:
0 ≤ x ≤ 11/5
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Steve repairs elevators. When he is called to a job he uses the stairwell to go to the floor on which the elevator is located. In the Modis building, he climbs 22 steps for every 15 ft of horizontal travel. In Sears Tower, he climbs 17 steps for every 7 ft of horizontal travel
Part A: What is the rate of change for each stairwell?
Part B: Which stairwell will be easier to climb? Explain your reasoning
The rate of change for Modis building stairwell is 0.68 feet per step.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Part A: In the Modis building, he climbs 22 steps for every 15 ft of horizontal travel.
Now, rate = 15/22
= 0.68 feet per step
In Sears Tower, he climbs 17 steps for every 7 ft of horizontal travel
Here, rate 7/17
= 0.41 feet per step
Part B: Sears Tower steps are easy to climb, because rate is lesser than Modis building steps.
Therefore, the rate of change for Modis building stairwell is 0.68 feet per step.
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amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answer:
25 minutes
Explanation:
Subtract the two times to find the duration.
2b (3a – c) + 12 ac –b^{2}[/tex]
The value of the equation is A = 6ab - 2bc + 12ac - b²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 2b ( 3a - c ) + 12ac - b² be equation (1)
On simplifying the equation , we get
A = 2b ( 3a ) - 2b ( c ) + 12ac - b²
On further simplification , we get
A = 6ab - 2bc + 12ac - b²
Hence , the equation is A = 6ab - 2bc + 12ac - b²
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Translate the following sentence into an equation "the sum of 8 times x and 4 is 68"
Answer:
The equation is:
8x + 4 = 68
and the solution is:
x = 8
Step-by-step explanation:
The equation is:
8 time x and 4 is 68
8x+4 = 68
Solve:
8x + 4 - 4 = 68 - 4
8x + 0 = 64
8x = 64
x = 64/8
x = 8
Check:
8*8 + 4 = 68
023) You are the owner of a AT&T store that
has two employees working at all times.
The first employee scheduled to work next
Wednesday makes $10.50 per hour and
averages $50 per day for commision. The
other person that is scheduled earns
$10.50 per hour and averages $60 per day
for commision.
i) Write a function that predicts your
expected payroll for the day.
+12
ii) Next Wednesday the store is going to
be open for 5 hours. How much do you
expect to pay your employees?
(i) The function that predicts your expected payroll for the day is,
For first person; y = $50 + $10.50x
For second person; y = $60 + $10.50x
Where, y is total amount and x is number of working hours.
(ii) In Wednesday; The amount expect to pay your employees is,
For first person;
⇒ y = $102.50
For second person;
⇒ y = $112.50
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The first employee scheduled to work next Wednesday makes $10.50 per hour and averages $50 per day for commission.
And, The other person that is scheduled earns $10.50 per hour and averages $60 per day for commission.
Let total amount earn = y
And, Number of working hours = x
Hence, We can formulate;
The function that predicts your expected payroll for the day is,
For first person;
⇒ y = $50 + $10.50x
For second person;
⇒ y = $60 + $10.50x
And, For 5 hours, the amount is,
For first person;
⇒ y = $50 + $10.50x
⇒ y = 50 + 10.50 × 5
⇒ y = 50 + 52.50
⇒ y = $102.50
For second person;
⇒ y = $60 + $10.50x
⇒ y = 60 + 10.50 × 5
⇒ y = 60 + 52.50
⇒ y = $112.50
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