The point where he buried his treasure is (6.28,9.84)
First of all, we are going to find the equation of the line which describes the first path crossed by the horseman. In order to find it we have to take into account that the vector V provides us with the direction of this path. We can associate the direction with the slope of the line. The slope is defined by the ratio of vertical changes to horizontal changes between two points.
According to the V=6i+5j, we can determine that:
Vertical change (y)= 5
Horizontal change (x)=6
Slope=\frac{5}{6}
Now, using the point-slope form:
y-y₁=m(x-x₁)
The chosen point is the point where the horseman began riding (-2,5). Therefore:
m=5/6
y1=5
x1=-2
y-5=5/6(x+2)
y=5x/6-10/3
Since the horseman at some point turned at a right angle towards village B and he unchanged his direction until arrived in village B, the second path must be described by a line perpendicular to the first path.
We should know that two lines are perpendicular if and only if their slopes are negative reciprocals This means m1*m2=-1
m₁=5/6
m₂=-1/m₁=-6/5
In order to find the equation of the second path, we will use again the point-slope form.
The chosen point is the point where is located Village B (2,11)
y-11=-6/5(x-2)
y=-6x/5+13.4
The coordinates of the point where the horseman buried a jar full of silver coins correspond to the intersection of path 1 and path 2. Therefore we are going to equal the two equations of each path.
5x/6-10/3=-6x/5+13.4
Solving this equality for x
X=6.28
Replacing this value in any of the equations of the paths
Y=9.84.
Finally, the point where he buried his treasure is (6.28,9.84).
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Rewrite in simplest form -10(2g-7)+6g
Answer:
70-14g
Step-by-step explanation:
-20g+70+6g = 70-14g
A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 47 type I ovens has a mean repair cost of $75. 51, with a standard deviation of $23. 53. A sample of 54 type II ovens has a mean repair cost of $71. 32, with a standard deviation of $18. 43. Conduct a hypothesis test of the technician's claim at the 0. 01 level of significance. Let μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens
The value of test statistics z=1.04
First, state the null and alternative hypotheses:
[tex]H_o=u_1=u_2\\H_a=u_1 > u_2[/tex]
Use z-statistics:
[tex]z=\frac{x_1-x_2}{y} ------(1)[/tex]
where x₁ and x₂ are the means and:
[tex]y=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} }[/tex]
Calculating the value of test statistics:
[tex]y=\sqrt{\frac{(23.53)^2}{47}+\frac{(71.32)^2}{54} }[/tex]
[tex]y=\sqrt{\frac{533.6609}{47}+\frac{5086.542}{54} }[/tex]
[tex]y=\sqrt{11.780+7.460}[/tex]
[tex]y=\sqrt{19.24}[/tex]
y = 4.386
Now substitute the y value in equation (1)
[tex]z=\frac{75.57-71.32}{4.386}[/tex]
z = 1.04
The test statistics is z = 1.04
The decision rule for rejecting the null hypothesis is: α≤ test statistics
Using the z-score table, it is possible to determine the p-value, which is:
value = 0.877
Comparing the p-value with the level of significance (α = 0.05):
0.877 > 0.05
Therefore, we fail to reject the null hypothesis.
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C The triangles in this picture are similar. Find the height of the tree.
Answer:
30 ft
Step-by-step explanation:
h/(40 + 8) = 5/8
h = 30
John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Which inequality shows the constraint on the amount of flour John has to make pies and cobblers?
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
An inequality which shows the constraint on the amount of flour John has to make pies and cobblers is: B. 3x + 3y ≤ 16
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pies John makes.Let the variable y represent the total number of cobblers John makes.Since a pie uses 4 cups of apples and 3 cups of flour while a cobbler uses 2 cups of apples and 3 cups of flour, the constraint on the amount of flour is given by:
3x + 3y ≤ 16
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A square-shaped painting has a length and a width of 1 foot. A line painted
diagonally on the painting has a length of V2 feet. About how long is the length of
the diagonal line, to the nearest tenth of a foot?
The diagonal V2 of the square will be √2 feet.
What are squares?
A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.
The most important properties of a square are listed below:
All four interior angles are equal to 90°.All four sides of the square are congruent or equal to each other.The opposite sides of the square are parallel to each other.The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other.The square has 4 vertices and 4 sides.The diagonal of the square divides into two similar isosceles triangles.The length of diagonals is greater than the sides of the square.Area of square=(side)²
Perimeter of square=4*side
Now,
as side=1 foot
By applying Pythagorean theorem,
Diagonal²=side²+side²
therefore,
V2²=1²+1²
=2
V2= √2 feet
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Segment AB is tangent to ⊙T at B. What is the radius of ⊙T? Triangle ABT where T forms the centre of a circle. B is a point on the circumference of the circle. The side AT intersects the circumference at the point C. AC equals 25 and Ab equals 45.
Answer:
28
Step-by-step explanation:
AB and TB are perpendicular because the tangent and radius are perpendicular. So you have a right triangle. Triangle ABT is a right triangle.
Also, TB is a radius of the circle, but so is TC. They are the same length.
Use Pythagorean Theorem to solve this problem.
AB^2 + TB^2 = AT^2
see image.
Emily filled up her car with gas before embarking on a road trip across the country.
Let G represent the number of gallons of gas remaining in her gas tank after driving
for thours. The table below has select values showing the linear relationship between
t and G. Determine the number of hours driven until the tank is empty.
Answer:
7 hours
Step-by-step explanation:
So you know in the second to third row of boxes how a hour and a half later the car loses 3 gallons of gas let's says another hour and a half goes by and the car has 1 gallon of gas left so each 30 minutes the car lost gas so now that we have that 1 gallon of gas left 30 minutes went by and now we are out gas
A three-column table is given.
Part A C D
Part 14 28 63
Whole 50 40 B
What is the value of B in the table?
12
36
68
90
The value of B in the table will be D. 90
How to explain the proportional relationship!The equation y = kx represents a proportional relationship between two quantities y and x that have the same proportionality constant, k.
The ratios between the two variables should be considered in order to determine whether a relationship is proportional. The relationship is proportional if the ratio remains constant. The relationship is not proportional if the ratio changes.
In this case, the relationship between part and whole is 7:10.
Therefore, the value of B will be:
= 10 / 7 × 63
= 10 × 9
= 90
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The height of a vase is 45. 7 centimeters when rounded to the nearest tenth of a centimeter. What is the shortest possible height of the vase?
The shortest possible height of the vase would be 45.650 centimeters.
Rounding to the nearest tenth of a centimeter, the height of a vase is 45.7 centimeters. The vase's height can be as short as possible. Include three digits in your response.
Rounding to the nearest tenth, the vase's height is 45.7.The vase's smallest possible height will be 45.65 due to the fact that the figure is rounded to a tenth digit of 7 after the tenth digit.Using the, we can determine that the tenth digit is 7 - 1 = 6 before rounding.In order for the hundredth digit to be rounded to 1, the smallest value that could be assigned to it is 5.The value placed at 1,000 could take the smallest digit value up to three decimal places.To know more about height of vase here
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question 6
Match each number that is in scientific notation to its calculator shorthand representation
The calculator short hand notations are;
a) -4E3
b) -3E4
c) 3E4
d) 4E3
What is the calculator short hand notation?We have to note that the calculator short hand notation has to do with the manner in which the calculator would show an exponential function when we are solving the mathematical problem using the calculator.
It is common to see that the calculator would display the letter E to stand in for the mathematical figure * 10^n. The letter that is depicted by n would then be written at the right hand side of the letter E.
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Basil has 5 numbered cards. Two of the numbers are hidden. The mode of the 5 is 8. The mean of the 5 is 6. Work out the two hidden numbers
Two hidden cards out of five numbered cards with 8 as mode and 6 as mean of five numbers is equal to 8 and 1.
Total number of numbered cards is equal to 5
Number of hidden cards are two.
Let us consider two hidden cards be 'a' and 'b'.
Mode of the five numbered cards is 8
Three numbers are 4 , 9 , a, b, 8.
Mode represents the number with higher frequency.
4, 9, 8 only one time as 8 is the mode one of the number should be equal to 8.
let b = 8
Mean of five numbers is 6
Mean = ( Sum of all the numbers ) / total numbers
⇒ 6 = ( 4 + 9 + a + 8 + 8 ) / 5
⇒ 30 = 29 + a
⇒ a = 30 -29
⇒ a = 1
Therefore, two hidden numbers for the given mode and mean is equal to 8 and 1.
The above question is incomplete , the compete question is:
Basil has five numbered cards.
Two of the numbers are hidden. 4 9 ? ? 8
The mode of the five numbers is 8.
The mean of the five numbers is 6
c) Work out the two hidden numbers.
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The circle graph below represents the number of students at a middle school who buy lunch. If 624 students go to the school, about how many students do not buy lunch? Students who do not buy lunch Students who buy lunch 255⁰
The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.
Approximately what percentage of pupils skip lunch at school?In comparison to only 4% of children aged 6 to 13 years old, nearly one in ten adolescents (aged 14 to 17) admitted to skipping lunch.The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022. Comparatively, the cost of the national school lunch program in the prior year was about 7.9 billion dollars.The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.Comparatively, the cost of the national school lunch program in the prior year was about 7.9 billion dollars.To learn more about percentage refer to:
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The number of students who do not buy lunch is 624 students - 420 students = 204 students.
Approximately how many pupils skip lunch at school?The circle graph represents the proportion of students who buy lunch and those who don't. To find the number of students who don't buy lunch, we need to subtract the number of students who buy lunch from the total number of students.
Since 255° represents the proportion of students who buy lunch, we can use this to find the number of students who buy lunch. To do this, we divide the number of degrees by 360° and multiply by the total number of students, 624:
(255° / 360°) x 624 students = 420 students
Therefore, the number of students who do not buy lunch is 624 students - 420 students = 204 students.
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Find the greatest common factor 12 of and 48.
Answer: I believe the answer is 12
Given cot A = 8 5 cotA= 5 8 and that angle A A is in Quadrant I, find the exact value of csc A cscA in simplest radical form using a rational denominator.
The exact value of csc A is (√89) /5
How to find the exact value of csc A?Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.
Since cot A = 8 /5 and that angle A is in Quadrant I.
tan A = 5/8 (Remember: tan = 1/cot and tan = opposite/adjacent)
opposite = 5 and adjacent = 8
hypotenuse = √(5² + 8²) = √89
sin A = 5/(√89) (sin = opposite/hypotenuse)
csc A = (√89) /5 (csc = 1/sin)
Thus, the exact value of csc A is (√89)/5
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Elizabeth rode her bike 6 1/2 miles from her house to the library And then another 2 2/5 miles to his friend Milo's house, how far would she travel from her house to Carsons house?
Elizabeth would travel a distance of [tex]11\frac{2}{5}[/tex] miles.
The distance between Elizabeth's house and Carson's house = Sum of (the distance between Elizabeth's house and the Library + the distance between the library and Millo's house + the distance between Millo's House and Carson's House). That is:
Total Miles = [tex]6\frac{1}{2}[/tex] + [tex]2\frac{2}{5}[/tex] + [tex]2\frac{1}{2}[/tex]
To calculate the total miles, we need to transform the mixed numbers into fractions. We can do that as:
[tex]6\frac{1}{2}[/tex] = [(6 × 2) + (1)]/2 = 13/2
[tex]2\frac{2}{5}[/tex] = [(2 × 5) + (2)]/5 = 12/5
[tex]2\frac{1}{2}[/tex] = [(2 × 2) + (1)]/2 = 5/2
So, the distance from Elizabeth's house to Carson's House has 57/5 miles, and it is calculated as:
13/2 + 12/5 + 5/2 = 57/5
Then, convert 57/5 into a mixed number, and we get:
57/5 = [tex]11\frac{2}{5}[/tex]
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creating a historgram algebra
The way that algebra can help in the creation of a histogram is that it helps organize and analyze the data in the histogram.
How does algebra help with histograms ?Algebra can be used to determine the range of values in the data set, and to create bins or intervals for the histogram. Algebra can be used to calculate the frequency of data points in each bin. This is important for creating the histogram, as it will determine the height of each bar.
Algebra can also be used to calculate the mean, median, mode, and standard deviation of the data set, which can provide a summary of the distribution of the data.
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Full question is:
Creating a historgram algebra. How does algebra help in creating a histogram ?
when finding the reflection of a fraction do you convert it to a decimal or just reflect the fraction
A fraction can be converted to a decimal number by dividing the numerator—the piece at the top of the fraction—by the denominator, which can be done with a calculator. A decimal number that represents the value of the fraction is the answer.
What exactly is reflection fraction?The geometry and location of the primary source of radiation directly affect the ratio of flux between direct and reflected radiation, known as the "reflection fraction."
What does "reflection" in math mean?Flip is the mathematical term for reflection. An image of the shape reflected in a mirror. A line, called the line of reflection, is where an image will reflect. When one figure "reflect[s]" another, that phrase is used.
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) Lea plots a point at a number on this number line. The number rounded to the nearest thousand is 30,000. What must be true about the point? +) 31:000 28,000 29. 000 30,000 ?) It is closer to 30. 000 than 29,000. D)) It is between 30,000 and 31,000. It is closer to 28,000 than 31,000. It is between 29,000 and 30,000.
As number is rounded off to 30,000, the correct option is A i.e, it is closer to 30,000 than 29,000.
We look at the last three digits and round to the closest thousand. If these digits total 500 or more, the thousands digit is rounded up; if they total less than 500, the thousands digit is rounded down while remaining the same.
For example, to solve this question we have to check whether 16796 is closer to 16000 or 17000 in the counting. In this case, 16796 is closer to 16000, hence 17000 is the round figure of 16796.
In this problem, as the number is said to be rounded off to the nearest thousand is 30,000, this means that, the number is closer to 30,000 than 29,000.
The question is incomplete. The picture of number line is missing. It is placed in the attachment below.
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Use logarithms to solve: 9x=4
The value of given expression 9x=4 equals to 4/9.
What is Algebraic expression ?
Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The basics of algebra taught us how to express an unknown fee using letters which includes x, y, z, and so forth. these letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any price that is placed before and accelerated through a variable is a coefficient.
Given expression ,
log 9x = log 4
log 9 + log x = log 4
log x = log 4 - log 9
log x = log 4 / 9
x = 4 /9.
Hence, The value of given expression 9x=4 equals to 4/9.
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true or false: if the median of a data set is larger than the mean, then the histogram of the data will likely have a longer right tail.
The given statement about Histogram that , " if median of a data set is larger than mean, then the histogram of data will likely have a longer right tail" is FALSE .
A histogram is a graph in which most of data falls to the right of graph's peak and is known as a right-skewed histogram. This type of histogram is also known as a positively skewed histogram.
The relation between the mean , median and mode in a right-skewed histogram is denoted as : mean > median > mode .
A distribution is called skewed Right if, in histogram , the right tail (smaller values) is much longer than the left tail (larger values).
Therefore , For histogram to have longer right tail , the median should be less than the mean .
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a) A rhombus of side 5cm has acute angles of
840 Find the
the length
Of the diagonals of the rhombus
The length of the diagonals of the rhombus is 3.5cm.
A rhombus's diagonals are always perpendicular to one another and always the same length. It contains four right angles, hence an acute angle of 840 is an obtuse angle. We are aware that in a rhombus, the diagonal is the hypotenuse of a right triangle, and the other two sides make up each half of the side.
Consequently, we can use the Pythagorean theorem to determine the diagonal's length:
c = √(a² + b²)
where an is the rhombus's half-length side and b is the other half, and c is the length of the diagonal. So we have:
a = (5cm) / 2 = 2.5cm
b = (5cm) / 2 = 2.5cm
c = √(2.5² + 2.5²) = √(6.25 + 6.25) = √12.5 = 3.5cm
Therefore, the length of the diagonals of the rhombus is 3.5cm.
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solve for x 4x+23=x+2
Answer: x = -7
Step-by-step explanation: Subtract 23 from both sides. 4x + 23 - 23 = x + 2 - 23, than simplify and subtract x from both sides
Please Help me On this Question thank you if you do!
Answer:
3rd one
Step-by-step explanation:
Answer:
3rd one
Step-by-step explanation:
NGC 5866
is about 44 million light years, or 13.5 megaparsecs, from
the Milky Way. How fast is NGC 5866 receding?
It has a diameter of about 60,000 light-years (18,400 parsecs).
Size of NGC 5866?A distance of 44 million light-years separates NGC 5866 from Earth in the Northern constellation Draco (13.5 Megaparsecs). Even though it has a diameter only around two-thirds that of the Milky Way and a mass similar to our galaxy, it has a diameter of about 60,000 light-years (18,400 parsecs).NGC 5866, a lenticular galaxy, contains many intricate dust lanes that appear black and red, but its disk is largely composed of brilliant stars, giving it a more subtly blue undertone.Numerous globular clusters—gravitational groups of nearly a million stars—that are gravitationally bound are scattered throughout the outer halo. Through the halo, it is also possible to detect background galaxies that are millions to billions of light-years away from NGC 5866.To learn more about diameter refer to:
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The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the face value of a 10-year term insurance policy on a 25-year-old female given that the annual premium for the insurance policy is $384. 59. If need be, round your answer to the nearest cent.
a. 80,290. 19
b. 86,038. 03
c. 85,274. 94
d. 79,296. 69
The correct option is Option C - 85.274.94.
The face value of the 10-year term insurance policy on a 25-year-old Female given that the annual premium for the insurance policy of $384.59 is 85,274. 94.
Given:
Annual premium for the insurance policy = $384. 59
According to the chart at the conclusion of the answer, the amount paid per $1,000 of coverage for a female 25 year old for a 10 year policy is 4.51.
Face value = (1,000 x Annual premium) / Amount paid for 25 year old female for 10 year policy)
Face value = (1000 x 384.59) /4.51
Face Value = 384590 / 4.51
Face Value = 85274.94
Therefore the face value is 85274.94.
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The table is given by the image shown at the end of the answer.
-10 + 17 < 2x - 10
solve the equality
Answer: x>17/2
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
7<2x−10
Step 2: Flip the equation.
2x−10>7
Step 3: Add 10 to both sides.
2x−10+10>7+10
2x>17
Step 4: Divide both sides by 2.
2x/2 > 17/2
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
Let's solve your inequality step-by-step.
−10+17<2x−10
Step 1: Simplify both sides of the inequality.
7<2x−10
Step 2: Flip the equation.
2x−10>7
Step 3: Add 10 to both sides.
2x−10+10>7+10
2x>17
Step 4: Divide both sides by 2.
[tex]\frac{2x}{2} > \frac{17}{2} \\\\ x > \frac{17}{2}[/tex]
Hope this helped :0
proofs in geometry transversal angels please help me
Following are the different types of angles:
In the 1 figure, ∠1 and ∠2 are same - side interior anglesIn the 2 figure, ∠1 and ∠2 are Alternate interior anglesIn the 3 figure,∠1 and ∠2 are corresponding anglesWhat is an angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The unit circle's sixteen unique angles, each indicated at the terminal point and measured in radians. These angles are frequently used as a parameter in trigonometric functions like the sine or cosine.
In the 1 figure,
∠1 and ∠2 are same - side interior angles
In the 2 figure,
∠1 and ∠2 are Alternate interior angles
In the 3 figure,
∠1 and ∠2 are corresponding angles
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Find X and Y.
TEACHING TEXTBOOKS GEOMETRY
The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.
The equations are given below.
2y = 180° - 126°
2y = 54°
y = 27°
2x + 1 = 180° - 85°
2x + 1 = 95°
2x = 94°
x = 47°
The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.
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The complete question is attached below.
Show that the following recurring decimal are rational. (1) 0,4 (2) 0,21 (5) 0,124 (6) 0,124 (3) 0,14 (7) -1,124 (4) (8) 19,45 -2,35
The given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.
(1) 0.4 is a rational number because it can be written as 4/10 which is a fraction with a denominator that is not zero.
(2) 0.21 is a rational number because it can be written as 21/100 which is a fraction with a denominator that is not zero.
(3) 0.14 is a rational number because it can be written as 14/100 which is a fraction with a denominator that is not zero.
(4) 0.124 is a rational number because it can be written as 124/1000 which is a fraction with a denominator that is not zero.
(5) -1.124 is a rational number because it can be written as -1124/1000 which is a fraction with a denominator that is not zero.
(6) 19.45 is a rational number because it can be written as 1945/100 which is a fraction with a denominator that is not zero.
(7) -2.35 is a rational number because it can be written as -235/100 which is a fraction with a denominator that is not zero.
In conclusion, all the given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.
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two people are picked at random from a group of 50 and given $10 each. after that, independently of what happened before, three people are picked from the same group - one or more people could have been picked both times - and given $10 each. what is the probability that at least one person received $20?
The probability that at least one person received $20 is 0.3
In math the term called probability is defined as a number that reflects the chance or likelihood that a particular event will occur.
Here we know that two people are picked at random from a group of 50 and given $10 each.
Here we have also know that three people are picked from the same group - one or more people could have been picked both times - and given $10 each.
Then the probability is calculated based on the binomial distribution is written as,
=> P = (50 3) 10³ (1 - 10) ⁵⁻³
When we simplify this one then we get the value of p as 0.3.
Then the following values are calculated through it,
μ = 15
σ = 3.24
σ² = 10.5
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