a) \($x\approx11.6$\) to the nearest tenth, b) Taking the inverse sine, we get:
\($$\angle K = \sin^{-1}\left(\frac{2}{5}\right) \approx 24.6^\circ$$\), c) the fire is approximately 165.8 feet away from the base of the tower, rounded to the nearest foot.
How to solve each part?a) If the adjacent angle is \($29$\) degrees and the hypotenuse is \($13$\), now use the cosine function to find the length of the adjacent side \($x$\):
\(\cos 29^\circ = \frac{\text{adjacent}}{\text{hypotenuse}}\)
\($$\cos 29^\circ = \frac{x}{13}$$\)
\($$x = 13\cos 29^\circ \approx 11.6$$\)
Therefore, \($x\approx11.6$\) to the nearest tenth.
b) We can use trigonometry to determine the angle if we assume that \($KL$\) is the side opposite \($\angle K$\) and \($KM$\) is the hypotenuse of mentioned right triangle.
Since \($KL$\) is the opposite side, we can use the sine function to find the value of \($\sin{\angle K}$\):
\($$\sin{\angle K}=\frac{KL}{KM}=\frac{2}{5}$$\)
Taking the inverse sine, we get:
\($$\angle K = \sin^{-1}\left(\frac{2}{5}\right) \approx 24.6^\circ$$\)
Therefore, \($\angle K \approx 24.6^\circ$\) to the nearest tenth.
c) We can use trigonometry to find the distance from the fire ranger to the fire. Let \($d$\) be the distance from the base of the tower to the fire. Then, we can set up the following right triangle:
\(\tan(24^{\circ})=\frac{70}{d} = \large \tan(24^{\circ})=\frac{70}{d}\)
Solving for \($d$\) we get:
\(d=\frac{70}{\tan(24^{\circ})}\approx165.8 = \large d=\frac{70}{\tan(24^{\circ})}\approx165.8\)
Therefore, the fire is approximately 165.8 feet away from the base of the tower, rounded to the nearest foot.
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The signed-rank test can be adapted for use in testing H0: μ = hypothesized value, where μ is the mean of a single population (see the last part of this section). Suppose that the time required to process a request at a bank’s automated teller machine is recorded for each of 10 randomly selected transactions, resulting in the following times (in minutes); 1.4, 2.1, 1.9, 1.7, 2.4, 2.9, 1.8, 1.9, 2.6, 2.2. Use the one-sample version of the signed-rank test and a .05 significance level to decide if the data indicate that the mean processing time exceeds 2 minutes.
Answer:
There is not enough evidence suggesting that the mean processing time exceeds 2 minutes.
Step-by-step explanation:
The hypothesis can be defined as follows:
H₀: The mean processing time is 2 minutes, i.e. μ = 2.
Hₐ: The mean processing time exceeds 2 minutes, i.e. μ > 2.
The significance level of the test is, α = 0.05.
Recorded Time (x) (x - μ) + Ranks -Ranks
1.4 -0.6 8
2.1 0.1 1
1.9 -0.1 1
1.7 -0.3 6
2.4 0.4 7
2.9 0.9 10
1.8 -0.2 4
1.9 -0.1 1
2.6 0.6 8
2.2 0.2 4
TOTAL 30 20
Sum of +Ranks = 30
Sum of -Ranks = 20
Test statistic = Min (∑+Ranks, ∑-Ranks)
= Min (30, 20)
= 20
Compute the critical value using the Wilcoxon Signed-rank test table.
Critical value = 11
As the test statistic value is more than the critical value, the null hypothesis was failed to be rejected.
Thus, there is not enough evidence suggesting that the mean processing time exceeds 2 minutes.
in the coordinate plane, ABCD has vertices with coordinates A(1,-1), B(-5,3), C(-3,6),
and D(3,2)
Answer:
C
Step-by-step explanation:
3. Write out the problem 154 x 13 using the multiplication standard algorithm and solve.
Given:
The problem is 154 × 13.
To find:
The solution using the multiplication standard algorithm.
Solution:
In the multiplication standard algorithm, we use partial product to solve the multiplication problem.
Using multiplication standard algorithm, the given problem can be written and solve as
1 5 4
× 1 3
----------------------
4 6 2 (Multiply 154 by 3)
1 5 4 × (Multiply 154 by 1)
----------------------
2 0 0 2 (Adding 462 and 154)
------------------------
Therefore, the value of 154 × 13 is 2002.
A line that describes a proportional relationship between x and y is graphed on a coordinate grid. The line passes through (6, 2). Through what other point must the line pass?
The other point through which a line that describes a proportional relationship must pass is the point (0, 0)
What is a proportional relationship?A proportional relationship is one in which each the ratio of the x and y–values of each point on the line of the function is a constant.
The given relationship described by the line = A proportional relationship
The given point on the line = (6, 2)
Required; The other point through which the line must pass.
Given that the relationship described by the line, the ratio of all points on the line is a constant and each point (x, y) can be expressed in the form;
y = K•x
Which gives;
\( \displaystyle{ K = \frac{y}{x} }\)
Where, K is a constant which is not equal to zero.
From the zero product property, which states that the product of all numbers and zero is also zero, we have;
When x = 0, k × 0 = 0 = y
A point through the line must pass is therefore; (0, 0)
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What is 5.6 x 10⁵ in standard notation
Answer:
560,000
Step-by-step explanation:
5.6 * 100,000 = 560,000
Answer:
560,000
Step-by-step explanation:
Given a mortgage of $48,000 for 15 years with a rate of 11% , what are the total finance charges?
Answer:
$54,576
Step-by-step explanation:
Evaluate. 3(4/5) 64 125 16 25 O 12 15 O I don't know.
When you evaluate \(3(\frac{4}{5})\) you will have \(\frac{12}{5}\)
In this exercise, you're required to evaluate the given whole number and fraction \(3(\frac{4}{5})\)
First of all, you will notice that there is a bracket which signifies multiplication. Therefore, we would open up the bracket by multiplying the two numbers.
Opening the bracket;
\(3 * \frac{4}{5}\)
Multiplying the whole number by the numerator;
\(3(\frac{4}{5}) = \frac{12}{5}\)
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What is the y-intercept of the line representing Beatrice's monthly music subscription bill as a function of the number of songs she downloaded?
$$
The y-intercept of the line representing Beatrice's monthly music is 20
How to determine the y-intercept of the lineFrom the question, we have the following parameters that can be used in our computation:
y = -.95x + 20
To calculate the y-intercept of the line, we set x = 0
So, we have
y = -.95 * 0 + 20
Evaluate
y = 20
Hence, the y-intercept of the line representing Beatrice's monthly music is 20
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Question
What is the y-intercept of the line representing Beatrice's monthly music subscription bill as a function of the number of songs she downloaded?
The equation is y = -.95x + 20
4 +2y+m how many terms?
Answer:
2
Step-by-step explanation:
The equation has 2 terms in it which means 2 is the answer.
Use graphs to find the set.
(-9,-6) n [-7,6]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The set is |_| (Type your answer in interval notation.)
The answer is A since it specifies that the set is [4, -1} in interval notation. Set identification is frequently done with curly brackets.
what is set ?A set is a type of mathematical representation of several different types of objects. The components or concepts that make up a set can be any kind of mathematical object. the use of signs, number, lines, other geometrical shapes, positions in space, variable, and even other values. A proposition is a structured collection of elements that can be stated as a list or perhaps a proposition builder in mathematics. Set identification is frequently done with curly brackets. An example of a set is A = 1, 2, 3, and 4. A set is just a collection of goods that are displayed together. Members or elements of a set are the things that make it up. Any item may make up a set's components, but for practical purposes .
given
According to a number line representation,
the set is [4, -1} ,
where -4 is a part of set B and 1 is not a part of set A.
The answer is A since it specifies that the set is [4, -1} in interval notation.
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The complete question is :- Use Graphs To Find The Set. (-9, 1) Intersection [-4, 4] Select The Correct Choice Below And, If Necessary, Fill In The Answer Box To complete your choice.
A. The set is |_| (Type your answer in interval notation.)
b. The set is an empty .
18 Answer:
Perform the indicated operation. Round the result to the nearest tenth
and then to the nearest hundredth. Separate your answers by a comma.
-49.256 + 17.197
19 Answer:
Perform the indicated operation. Round the result to the nearest tenth
and then to the nearest hundredth. Separate your answers by a comma.
14.357(-2.625)
20 Answer:
Solve the equation. Round the result to the nearest hundredth.
-15x + 73 = 26
21 Answer:
Solve the equation. Round the result to the nearest hundredth.
7y - 27 = 14
22 Answer:
Solve the equation. Round the result to the nearest hundredth.
1.5x + 7.4 = -1.8x - 6.9
23 Answer:
Solve the equation. Round the result to the nearest hundredth.
14.1 - 0.3x = 1.3x - 4.2
24 Answer:
Multiply the equation by a power of 10 to write an equivalent
equation with integer coefficients.
6.2x + 4.5 = 3.8x + 7.9
25 Answer:
Multiply the equation by a power of 10 to write an equivalent
equation with integer coefficients.
4.603y - 1.842 = -3.651y
a) -32.06 (To the nearest hundredth)
b) -37.7 (To the nearest tenth)
c) 3.1 (To the nearest tenth)
d) 5.86 (To the nearest hundredth)
f) -4.33 (To the nearest hundredth)
g) 11.44 (To the nearest hundredth)
h) 62x + 45 = 38x + 79
i) 46y - 18 = -37y
What is an equation?An equation is a mathematical statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=), and shows the relationship between the variables present in the equation. Equations are used to model real-world problems and find solutions to various mathematical problems.
They can be solved for a specific variable by using various mathematical methods and techniques.
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4-7x=25 ? show work please
Answer:
x = -3
Step 1: Rearrange Terms
-7x + 4=25
Step 2: Subtract 4 From Both Sides Of The Equation.
-7x + 4-4 = 25 -4
Step 3: Simplify
Subtract the numbers
-7x = 21
Step 4: Divide both sides of the equation by the same term.
-7x/-7 = 21/-7
Step 5 : Simplify
Cancel terms that are in both the numerator and denominator
-7x/-7=x
Divide Now
x=-3
I HOPE U HAVE A GOOD DAY TODAY HEAR YA GO KID IM IN CLASS RN LOL CYA!
A baker bought a total of 12 pounds of apples and bananas for $10.20.
The system of equations {a+b=120.75a+1.05b=10.20 models this situation, where a is the number of pounds of apples, and b is the number of pounds of bananas.
How many pounds of each did the baker buy?
I need some help! I’m kind of stuck with this problem
Step-by-step explanation:
In March (2) and July (3) , there are a total of 5 flower symbols
each symbol represents THREE flowers = 15 flowers ( March + July)
May has 7 flower symbols = 21 flowers
21 -15 = 6 fewer flowers
Jolene is making a line graph showing that the cost of grain is proportional to the number of pounds purchased. Jolene will plot the number of pounds on the x-axis and the cost in dollars on the y-axis. The coordinates Jolene graphs are shown in the table.
Which coordinate represents the unit rate, in dollars per pound of grain, and why?
Pounds Cost (in dollars)
1.0 0.25
4.0 1.00
Create an equation to represent the cost, y, in dollars, for x pounds of grain.
Answer:
a. \((1,0.25)\)
b. \(y = 0.25x\)
Step-by-step explanation:
Given
The data in the table
Solving (a): The coordinate that represents the unit rate
The unit rate is when its 1 pound
This is so because the unit rate is dollars per pounds.
Hence, the coordinate is \((1,0.25)\)
Solving (b): Equation of the graph
First, we calculate the slope (m)
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Where:
\((x_1,y_1) = (1,0.25)\)
\((x_2,y_2) = (4,1.00)\)
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
\(m = \frac{1.00 - 0.25}{4 - 1}\)
\(m = \frac{0.75}{3}\)
\(m = 0.25\)
The equation is then calculated as thus:
\(y - y_1 = m(x - x_1)\)
This gives:
\(y - 0.25 = 0.25(x - 1)\)
\(y - 0.25 = 0.25x - 0.25\)
Make y the subject
\(y = 0.25x\)
Hence, the equation of the graph is: \(y = 0.25x\)
If 2 pounds of rib steak and 6 pounds of hamburger meat costs $12.30 and 3 pounds of rib steak and 2 pounds of hamburger meat costs $9.70, what is the cost per pound of each type of meat?
The cost per pound of rib steak is $2.40 and the cost per pound of hamburger meat is $1.25.
To find the cost per pound of each type of meat, we can set up a system of equations based on the given information.
Let's denote the cost per pound of rib steak as 'x' and the cost per pound of hamburger meat as 'y'.
From the first statement, we know that:
2x + 6y = 12.30 ---(Equation 1)
From the second statement, we know that:
3x + 2y = 9.70 ---(Equation 2)
Now we can solve this system of equations to find the values of 'x' and 'y'.
Multiplying Equation 1 by 3 and Equation 2 by 2 to eliminate the 'x' term, we get:
6x + 18y = 36.90 ---(Equation 3)
6x + 4y = 19.40 ---(Equation 4)
Subtracting Equation 4 from Equation 3, we get:
14y = 17.50
Dividing both sides by 14, we find:
y = 1.25
Substituting the value of 'y' back into Equation 1, we can solve for 'x':
2x + 6(1.25) = 12.30
2x + 7.50 = 12.30
2x = 4.80
x = 2.40
Therefore, the cost per pound of rib steak is $2.40 and the cost per pound of hamburger meat is $1.25.
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Shown below is a wooden six-sided (hexagon) frame. Which of
the following best approximates the slopes of the six line
segments?
O The slopes are approximately -1.4, 0, and 1.4.
O The slopes are approximately -1.7, 0, and 1.7.
O The slopes are approximately -1.8, 1, and 1.4.
O The slopes are approximately -1.7,0, and 1.4
The slopes are best approximated as: The slopes are approximately -1.7, 0, and 1.7.
How to find the slope between two coordinates?The formula to find the slope between two coordinates is expressed as:
Slope = (y₂ - y₁)/(x₂ - x₁)
The slope of each line above the x-axis are:
Slope 1 = (5 - 0)/(5 - 8)
Slope 1 = -1.7
Slope 2 = (5 - 5)/(5 - (-2))
Slope 2 = 0
Slope 3 = (5 - 0)/(-2 - (-5))
Slope 3 = 5/3 = 1.7
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-8k + 6 = -10k + 10 SOMEONE HELP QUICKKKK
Answer:
k = 2
Step-by-step explanation:
-8k + 6 = -10k + 10
-8k = -10k +4
2k = +4
2k / 2 = 4 / 2
k = 2
According to the histogram of travel times to work from the US 2000 census (Page 6 of "Journey to Work: 2000"), roughly what percentage of commuters travel more than 45 minutes?
Histograms are used to represent data, where the length of each bar represents the frequency of the data element
The histogram is not given; So, I will give a general explanation.
Assume that the number of commuters that travel more than 45 minutes is 450, while the total number of commuters surveyed is 500.
The percentage of commuters that travel more than 45 minutes is the quotient of the commuters that travel more than 45 minutes and the total number of surveyed commuters.
So, we have:
\(\%Percentage = \frac{450}{500}\)
Divide 450 by 500
\(\%Percentage = 0.9\)
Express as percentage
\(\%Percentage = 90\%\)
Hence, the percentage of commuters that travel more than 45 minutes is 90%
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please please help ! will give brainliest points !!
Answer:
The graph will shift 5 units to the left
Write an equivalent fraction with a denominator of 10
1/2 = ?/10
Answer:
5/10
Step-by-step explanation:
An equivalent fraction will have the numerator and denominator multiplied by the same value.
ApplicationThe denominator of 2 must be multiplied by 5 to get a denominator of 10. Then the equivalent fraction is ...
\(\dfrac{1}{2}=\dfrac{1}{2}\cdot\dfrac{5}{5}=\dfrac{1\cdot5}{2\cdot5}=\boxed{\dfrac{5}{10}}\)
Jane wants to win a prize by drawing 2 red marbles from a pot that contains 7 marbles
There are 21 possible ways that Jane can win a prize by drawing two red marbles from the pot.
Jane wants to win a prize by drawing two red marbles from a pot containing seven marbles. She can do this in several ways. However, we will solve the problem by using the combination formula.The combination formula gives us the number of possible ways to choose r items from a group of n items without considering the order.
The formula is given by:\(C(n,r) = n! / r!(n-r)!\)where n is the total number of items and r is the number of items to be selected.To solve Jane's problem, we will find the number of possible ways to choose two red marbles from seven marbles. The number of red marbles in the pot is not given;
we assume that all marbles in the pot are of different colors.Since Jane wants to draw two red marbles, we will consider only the red marbles. We have to find the number of combinations of two red marbles from the total number of red marbles in the pot.
Therefore, n = total number of red marbles in the pot and r = 2 (the number of red marbles to be selected).Thus, using the combination formula;\(C(n,r) = n! / r!(n-r)!C(n,2) = n! / 2!(n-2)!\)We have n = total number of red marbles in the pot = \(7C(n,2) = 7! / 2!(7-2)!C(n,2) = 7! / 2!5!C(n,2) = (7 x 6 x 5!)/ (2!5!)C(n,2) = 21\).
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How is this solved a history class comprised of 3 female and 10 male students , if the instructor of the class randomly chooses 9 students from class for an oral exam what is probation of 2 female and 7 make students selected
Answer:
0.306
Step-by-step explanation:
Using binomial probability,
\(\binom{9}{2}(3/13)^2 (10/13)^7 \approx 0.306\)
Tony left the party early traveling 2 mph. 15 hours later, Pamela decided to head out and catch up with him. She ran 7 mph. How long would she have to run to catch up with him?
Pamela would have to run approximately 4.29 hours to catch up with Tony.
To determine how long Pamela would have to run to catch up with Tony, we need to find the time it takes for Pamela to cover the distance Tony covered during the 15 hours he had already been traveling.
Since Tony traveled at a constant speed of 2 mph for 15 hours, the distance he covered is given by:
Distance = Speed * Time
Distance = 2 mph * 15 hours
Distance = 30 miles
Now, Pamela wants to catch up with Tony, so she needs to cover the same distance of 30 miles. Pamela runs at a speed of 7 mph.
To find the time it takes for Pamela to cover the distance of 30 miles, we can use the formula:
Time = Distance / Speed
Time = 30 miles / 7 mph
Using division, we find:
Time ≈ 4.29 hours
Therefore, Pamela would have to run approximately 4.29 hours to catch up with Tony.
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Find: 11/3 divided by 2/3
The quotient is 5 and ______
Answer:
1/2
Step-by-step explanation:
11/3 divided by 2/3
=5.5
11/3 divided by 2/3 , the quotient is 5 and remainder is 1.
The divisor is the integer that divides a given number. The resultant number is sometimes referred to as the quotient. The residual is the number that the divisor leaves after partially dividing the original integer.
Let, first number is x and second number is y
On dividing given two number
Division=x/y
\(x/y=\frac{11/3}{2/3}\)
\(x/y=11/2\)
It is given that the quotient for dividing two numbers is 5.
Using,
Dividend = Divisor x Quotient + Remainder
Here,
Dividend =11
Divisor =2
Quotient =5
On, substituting these values to get Remainder
11=2 x 5+ Remainder
Remainder=1
Thus, remainder is 1.
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a rectangle has an area of 30 square meters and a permiter of 34 meters what are the dimensions of the rectangle
Answer:
2m by 15m
Step-by-step explanation:
Form a system of equations where x is the length and y is the width.
Area: xy=30
Perimeter: 2x+2y=34
x=2, y=15 (solve by substitution)
Domain and range? Checking my work
My answer:
D:[-7,-1]
R:[-6,-3]
Answer:
Correct numbers, wrong format
Step-by-step explanation:
Remember the figure is continuous so it should be written as an inequality:
D:(-7<x<-1)
R:(-6<x<-3)
the average price of gasoline rose from $2.95 to $3.99 in 6 months. what was the percent increase in the price of gasoline? round to the nearest percent.
Answer:
3.4 and 2.5
Step-by-step explanation:
Answer: 3.4 and 2.5
Step-by-step explanation:
which of the following is a well-dedeffined set?
a. A set of beauteful sceneries
b.A set of good basketball players
c.A set of philipine presidents
d.A set of successfull leaders
Step-by-step explanation:
what kind of industries can be run in local level?
The histogram shows the results of a drivers' education exam.
10
9
8
Frequency
3
2
1
0
0
10
20
30
70
80
90 100
40 50 60
Grade
What percent of the students score between an 80 and 90 othe drivers' education exam?
O 9%
O 10%
45%
90%