Answer:
130 ft
Step-by-step explanation:
The distance across the canyon is 130 feet.
When Christian moved 100 feet from the tree on his side, the angle formed by the tree on his side and the tree on the other side was 70°. This means that the distance across the canyon is the length of the opposite side of the right triangle formed by Christian's position, the tree on his side, and the tree on the other side.
To find the length of the opposite side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is the distance across the canyon, and the other two sides are 100 feet and the length of the opposite side of the triangle.
We can write this as an equation: (distance across the canyon)^2 = (100 feet)^2 + (opposite side of the triangle)^2.
To solve for the distance across the canyon, we can take the square root of both sides of the equation: distance across the canyon = √((100 feet)^2 + (opposite side of the triangle)^2).
Since the length of the opposite side of the triangle is equal to the length of the adjacent side (100 feet) divided by the tangent of the angle formed by the tree on his side and the tree on the other side, we can substitute this value into the equation above: distance across the canyon = √((100 feet)^2 + (100 feet / tan 70°)^2).
To calculate the value of tan 70°, we can use a calculator or look up the value in a table of trigonometric functions. The value of tan 70° is approximately 1.73. We can substitute this value into the equation above to get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2).
We can now use a calculator to evaluate this expression and find the distance across the canyon. When we do this, we get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2) ≈ 130 feet.
Therefore, the distance across the canyon is approximately 130 feet.
Evaluate:
10 Σn=1 8(1/4) n -1= [?]
The evaluation is 10.67 of given geometric progression.
What is Geometric progression series?A geometric progression is a set of elements where each succeeding element is created by multiplying the one before it by a number called the common ratio. The standard representation for a geometric progression series is a, ar, ar²,..., where an is the first term and r is the common ratio of the sequence.
The ratio between two consecutive numbers, or a number divided by the number before it in the sequence, is known as the common ratio since it is the same for all numbers or common.
The sum of a finite geometric series can be found using the formula:
[tex]a (1-r^{n}) / (1-r)}[/tex].
Where a is the first term and r is the common ratio between successive terms.
To find the ratio of successive terms by plugging into the formula
r = aₙ +1 / (aₙ)
Simplifying,
r =1/4
And the first term is;
when n=1, a = 8
Substituting all the values to the formula,
The summation of GP
= 8 x { 1 - (1/4)¹⁰ } / {1- (1/4)}
= 8 { 1 - (1/1048576) / (3/4)
= 8 x {(1048576 - 1) / 1048576} x (4/3)
= 8 x (1048575 / 1048576) x (4/3)
= 8 x 349525 / 262144
= 2796200 / 262144
= 10.6666
The decimal form is 10.67.
Therefore, the evaluation is 10.67.
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Can someone help? Please?
Answer:
D. 66 cm
Step-by-step explanation:
You have parallelogram MNPR with diagonals that cross at E, and ME = 7x-30, and PE = 5x-12. You want to know the length of MP.
DiagonalsThe diagonals of a parallelogram bisect each other this means point E is the midpoint of diagonal MP, and ...
ME = PE
7x -30 = 5x -12
2x = 18 . . . . . . . . . add 30-5x
x = 9
Then the length of the half-diagonal is ...
ME = 7x -30 = 7(9) -30 = 33
So, the full diagonal is ...
MP = 2·33 = 66 . . . . . cm
PLEASE HEP ASAP GOT TEN MINS LEFT TILL DUE
Answer:
a ≈ 3.009075116
Step-by-step explanation:
cos(α) = adj/hyp
cos(53°) = a/5
a = 5 * cos(53°)
a ≈ 3.009075116
Decrease by
15 %
Increase by
85 %
Determine the Input
A number went into this machine and 50 came out.
What number went in?
To determine the input number, we can use the following steps:
Calculate the change in the input number as a percentage of the input number. In this case, the input number decreased by 15%, so the change is -0.15 * input number.
Add the change to the output number to find the input number. In this case, the output number is 50, so the input number is 50 + (-0.15 * input number).
Solve for the input number. In this case, we can solve for the input number by rearranging the equation and solving for x:
input number = 50 / (1 - 0.15)
input number = 50 / 0.85
input number = 58.82
Therefore, the input number is 58.82.
Note that this process can also be used to determine the output number given the input number and the percentage change. For example, if the input number is 100 and it increases by 85%, the output number would be:
output number = 100 * (1 + 0.85)
output number = 100 * 1.85
output number = 185
Answer:
[tex]x \times \frac{85}{100} \times \frac{185}{100} = 50[/tex]
[tex]x = 50 \times \frac{ {100}^{2} }{85 \times 185} [/tex]
[tex]31.8[/tex]
it seems to be a long number so I rounded
There might be a mistake because I wasn't able to check.
Please help me answer this question
Step-by-step explanation:
5x - 3 = 5
5x = 8
x = 8/5 = 1.6
5x = 2
x = 2/5 = 0.4
both equations are vertical lines.
the first one (x = 1.6) was moved (translated) left by 1.2 units to become x = 0.4.
Read the following statement: If A is an acute angle, then m2A = 30°. This statement demonstrates:
the substitution property.
the reflexive property. the symmetric property. the transitive property.
Answer:
Its been a minute since I've done this math
Step-by-step explanation:
This statement demonstrates the substitution property.
The substitution property states that if two expressions are equal, then we can substitute one expression for the other in any equation or inequality. In this case, "A" is an acute angle, and "m2A" is the measure of twice that angle. The statement says that if we double the measure of an acute angle, the result will be 30 degrees. Therefore, we can substitute "m2A" for 30 degrees in any equation or inequality.
The reflexive property states that any number or object is equal to itself. The symmetric property states that if a = b, then b = a. The transitive property states that if a = b and b = c, then a = c. None of these properties are demonstrated in the given statement.
What transformation took place to get from triangle ABC to triangle A’B’C’? Be specific.
What transformation took place to get from triangle A’B’C’ to triangle A”B”C”? Be specific.
We can see two transformations.
1) ΔABC → ΔA'B'C', it is a translation 10 units left and 2 units up.
T(-10, 2)2) ΔA'B'C' → ΔA''B''C'', it is a reflection across the x-axis.
R(x-axis)Convert 1 1/8 to a decimal….
Answer:
1.375
Step-by-step explanation:
11/8=1.375
Need help also stepbystep
Answer: -81
Step-by-step explanation: So, when finding exponents, you have to multiply the # in parentheses (in this case, -3) and multiply it by itself 4 times, so once is 3 x 1, twice is 3 x 3 = 9, three times is 9 x 3 = 27, and finally, 27 x 3 = 81. Oh, and a positive times a negative is ALWAYS negative. I hoped this explains why this is the rule for exponents.
This bar chart shows the average monthly expenditure, by category, of
households in a particular town in 2010 and 2020.
Average monthly expenditure (£)
600
500
400
300
200
100
Clip 15
Key:
2010
2020
I
Transport Utility Food Housing Leisure
bills Category
a) Which category shows a decrease
in the average monthly expenditure
between 2010 and 2020?
leisure
b) How much more was the average
monthly expenditure on Food in
2020 than in 2010?
c) The total average monthly
expenditure in 2010 was £1200.
What was it in 2020?
View One Minute Version
£
Find a Clip
£
a) The category that shows a decrease in the average monthly expenditure between 2010 and 2020 is Leisure.
b) The average monthly expenditure on food was 175 euros more in 2020 than in 2010.
c) The total expenditure in 2020 is of: 1,625 euros.
What is shown by the bar chart?The bar chart shows the average monthly expenditure in five categories, considering that:
The blue bar represents the year of 2010.The gray bar represents the year of 2020.
Then a decrease happens for the category which the blue bar is greater than the gray bar, which is Leisure.
The averages on Food are given as follows:
2010: 150 euros.2020: 325 euros.Hence the difference is of:
325 - 150 = 175 euros.
From the gray bars, the 2020 total is given as follows:
250 + 425 + 325 + 550 + 75 = 1,625 euros.
Missing InformationThe bar graph is given by the image shown at the end of the answer.
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Kala's parents give her simple interest on any money she saves for college. Which equation and solution represents the total interest, T, earned when the principal amount is $100, the
annual simple interest rate is 1%, and the number of years is 10
Answer:
The interest earned is $10.00
Step-by-step explanation:
Interest = principal x rate x time
I= 100(.01)(10)
I = 10
What is the slope of the line that passes through the points (-7,-2) and
(-15, -14)? Write your answer in simplest form.
Answer:
Step-by-step explanation:
To find the slope of a line that passes through two points, we can use the slope formula, which is written as follows:
slope = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
Given the points (-7, -2) and (-15, -14), we can substitute their coordinates into the slope formula to find the slope of the line:
slope = (-14 - (-2)) / (-15 - (-7))
= -12 / -8
= 3/2
Therefore, the slope of the line that passes through the points (-7, -2) and (-15, -14) is 3/2. In simplest form, this is equal to 1.5.
*URGENT*
The sin (theta) = -2/5, and theta lies in quadrant IV. Find the exact values of the sine and cosine of 2 theta.
Answer: first choice!
sin2Theta= -4rt21/25
cos2Theta = 17/25
Step-by-step explanation:
Use Double Angle Formulas.
You can find cos2Theta immediately because one of the formulas needs only sin(theta) and that was given.
Cos2Theta =
1 - 2(sinTheta)^2
= 1 - 2(-2/5)^2
= 1 - 2(4/25)
= 1 - 8/25
= 25/25 - 8/25
= 17/25
The only answer with cos2theta=17/25 is the first choice.
Use a simple graph and Pythagorean Theorem to find cos(theta). Then you can use the Double Angle Formula for sin2theta. This would kinda be a double check if you have time. Since the first part of the solution eliminated all choices except the first choice, if you're pressed for time just do cos2theta calculation and pick the first choice.
See image for sin2theta calculation.
Can someone please help me
The equivalent expressions of 9/7x-3/4 are 9/7x+(-3/4) and -3/4+9/7x.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 9/7x-3/4.
Nine by seven times of x minus three by four.
x is the variable of expression.
The equivalent expression is an expression whose value is same but looks different.
9/7x-3/4.
By commutative property
-3/4+9/7x is an equivalent expression of 9/7x-3/4.
9/7x+(-3/4).
When we simplify we get 9/7x-3/4.
-9/7x+3/4 is also a equivalent expression we get it by multiplying with negative.
Hence, 9/7x+(-3/4) and -3/4+9/7x are equivalent expressions of 9/7x-3/4.
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Draw a line PQ and take a point A outide it. Uing ruler and compa , draw a line through A parallel to PQ
Using a ruler and compass, draw a line through point A parallel to line PQ by first drawing a line segment from A to any point on PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. Finally, use the ruler to draw a line through the arc, parallel to PQ.
Drawing a line parallel to an existing line can be done using a ruler and compass. First, draw a line segment from point A to any point on line PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. This arc should intersect with the first line segment. Finally, use the ruler to draw a line through the arc, parallel to PQ. This line will be parallel to PQ since it is the same distance from each point on the original line. The use of the compass ensures that the resulting line is the same distance away from the original line throughout, thus resulting in a line parallel to PQ.
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uppose we wanted the margin of error for the 90% confidence level to be about 1.5%. how large of a survey would you recommend?
confidence level to be about 1.5%. Then the survey would you recommend is 1537
The first thing is to apply the corresponding formula of this case, it is the calculation of a sample size without knowing the population. The equation is as follows, let n be the sample size:
n = (z * s / E) ^ 2
We know that z the corresponding z score of 95% of the confidence level, that this case is 1.96.
s, is the standard deviation and has a heat of 10.
Finally E, would be the error that is 0.5.
Now it's just replace in the formula:
n = (1.96 * 10 / 0.5) ^ 2 = 1536.64, that is approximately the sample must be 1537.
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if a vehicle is going 75 mph, how many feet does it travel in one second? 110 feet 660 feet 330 feet 550 feet
The vehicle travels 110 feet distance in 1 second duration.
What is mean by mph?mph expresses the speed or velocity in miles per hour. Speed means rate of change of distance with respect to time.
speed = distance/time
hence, distance = speed x time
the above equation is the relationship between distance, speed and time
How can we calculate distance in feet?we will use the above equation and convert miles to feet and second to hour.
given, speed of vehicle = 75 mph
time = 1 second =1/3600 hour as 1 hour = 3600 second
distance travel by vehicle = speed x time
= 75 mph x 1/3600 hour
distance = 0.020833333 miles
we know, 1 mile =5280 feet
distance in feet = 110 feet
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
[tex] \sf \: x = 25[/tex]
Step-by-step explanation:
Given equation,
→ (x - 7)2 = 36
Now the value of x will be,
→ 2(x - 7) = 36
→ (2 × x) - (2 × 7) = 36
→ 2x - 14 = 36
→ 2x = 36 + 14
→ 2x = 50
→ x = 50/2
→ [ x = 25 ]
Hence, the value of x is 25.
Answer:
x = 25
Step-by-step explanation:
(x-7)2 = 36
divide both sides by 2
x-7 = 18
add 7 to both sides
x = 25
how would including a control group be useful in this experiment? responses it would provide a reference for the effects of random environmental factors. it would provide a reference for the effects of random environmental factors. it would provide a number against which percentages can be computed. it would provide a number against which percentages can be computed. it would provide a value for which the standard ph can be measured. it would provide a value for which the standard ph can be measured. it would provide a standard number to test for statistical uncertainty. it would provide a standard number to test for statistical uncertainty.
It would provide a reference for the effects of random environmental factors.
What is control group?A control group is a statistically significant subset of experiment participants who are not exposed to factors. For example, in a pharmaceutical medication research, the control group is given a placebo, which has no impact on the body. Assume you want to put a new ADHD medicine to the test. One group would be given the new drug, while the other would be given a tablet that looked precisely like the one given to the others, but it would be a placebo. The control group would be the group that receives the placebo.
Here,
It would serve as a reference for the effects of uncontrollable environmental elements.
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I need help on this geometry probability question
Answer:
83% to (rare photos) becaheyhw euehem e the same time of 6year and I was in a group with my wife and a daughter and my daughter in the night and I was so happy 4and was a 4ship 4in who 5is and my daughter and my husband were so young that I was in the same 5 year olds and I was in the
a new chemotherapy drug was tested in a randomized controlled trial (rct) on 822 cancer patients. of the 344 patients randomly assigned to receive the new drug, 101 survived for at least five years. of the 478 patients randomly assigned to the placebo, 299 survived for at least five years. determine the conditional probability of randomly selecting a study participant who survived for at least five years, given drug assignment.
We determined the conditional probability of drug assigned people who survived at least 5 years = 101/344
What is conditional probability?The possibility of occurring an event connected to the previous other event. That means occurring of two events is related to each other.
How to determine conditional probability of the question?We determine the probability by the following way.
At first, we will make a chart with the given data.
survived 5yrs get other result total
Drug assign 101 243 344
placebo 299 179 478
total 400 422 822
We need to determine the probability of 5 years survived persons from drug assigned
Let, it is denoted by P(Sr/Dr)
As per conditional probability P(Sr/Dr) = P(Sr and Dr)/P(Dr)
= 101/344
As from the above chart, we find P (Sr and Dr) =101 and
P(Dr) = total drug assigned = 344
hence, P(Sr/Dr) = 101/344
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I need help!!!
BC.
AB.
BD.
CD.
Given all angle information, the assumption that sides [tex]\overline {BC}[/tex] must not be congruent to [tex]\overline{DA}[/tex] to give an appropriate answer. (Right choice: None)
How to determine what side is the shortest one in a quadrilateral
Any quadrilateral can be divided into two triangles by adding a diagonal. By Euclidean geometry, the sum of the measures of internal angles equals 180°. Likewise, we can determine how short or long a side is in terms of side BD by law of sine:
AD / sin 60° = AB / sin 63° = BD / sin 57°
1.155 · AD = 1.122 · AB = 1.192 · BD
AD = 0.971 · AB = 1.032 · BD
BC / sin 57° = CD / sin 55° = BD / sin 68°
1.192 · BC = 1.221 · CD = 1.079 · BD
BC = 1.024 · CD = 0.905 · BD
By direct inspection and use of equality properties, we find the existence of an absurdity, because 1.032 · BD = 0.905 · BD, then [tex]\overline {BC}[/tex] must not be congruent to [tex]\overline{DA}[/tex] to satisfy all angle conditions.
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Rida writes a fitness blog. At a certain point, she has 6,218 followers. Then the following events happen, in order:
92 people stop following Rida's blog.
417 people start following Rida's blog.
The number of followers doubles.
Use the drop-down menus to answer the questions below.
CLEAR CHECK
An expression that models this series of events is
.
Zuberi also writes a fitness blog. His current number of followers is equal to 3(945−120)+312. A possible series of events that led to this number of followers would be:
An expression that models the series of events is 2(6,218 - 92 + 417).
The possible events are:
120 followers stop following Zuberi's blog.
The number of followers triples.
312 followers start following Zuberi's blog.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
At a certain point, she has 6,218 followers.
Events happened in order:
92 people stop following Rida's blog.
417 people start following Rida's blog.
The number of followers doubles.
An expression that models this series of events.
= 2(6,218 - 92 + 417)
The current number of followers.
= 3 (945 - 120) + 312
The possible events.
120 followers stop following Zuberi's blog.
The number of followers triples.
312 followers start following Zuberi's blog.
Thus,
An expression that models the series of events is 2(6,218 - 92 + 417).
The possible events are given above.
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WILL GIVE 50 POINTS
Which statement can be used to prove that the two triangles are congruent? the SAS Postulate the SSS Postulate the HL Theorem the ASA Postulate
Answer:
the HL Postulate
Step-by-step explanation:
The diagram gives us the information that 2 sides and 1 angle are congruent. Since the sides we know are a leg and the hypotenuse, and it is a right angle- we know to use the HL (Hypotenuse-Leg) Postulate.
If the angle given was the angle between the hypotenuse and the leg, we could use the SAS (Side-Angle-Side) Postulate. But, since it is the right angle instead- we know to use the HL Postulate!
question a polynomial p(x) has a relative maximum at (-2,4) , a relative minimum at (1,1) , a relative maximum at (5, 7) and no other critical points. how many zeros does p(x) have?
The polynomial p(x) must have at least two zeros, since it has three relative extrema.
What is polynomial?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x²- 4x + 7 is an illustration of a polynomial with a single indeterminate x.
Here i would think that since there are only 3 critical points given and no other information other than that those are the only critical points that p(x) would not have any real zeros.
At each of the relative extrema, the value of the function changes from increasing to decreasing or vice versa, meaning that the function crosses the x-axis at that point, which is a zero. Therefore, p(x) must have at least two zeros.
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what is an equation of the line that passes through the point (1,6)(1,6) and is perpendicular to the line x 3y
The equation of the line that passes through the point (1, 6) and is perpendicular to the line x + 3y = 27 is y = 3x + 3.
What is a perpendicular line?
If two geometrical objects overlap at a right angle, they are perpendicular. It can be defined between two planes, two lines, or two planes and another line.
Here, we have
Given
The point (1, 6) and is perpendicular to the line x + 3y = 27
The slope of the line x + 3y = 27
m = -1/3
The slope of the line perpendicular to the line x + 3y = 27
M = 3
The equation of the line:
y - 6 = 3(x - 1)
y = 3x + 3
Hence, the equation of the line that passes through the point (1, 6) and is perpendicular to the line x + 3y = 27 is y = 3x + 3.
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what is sue's position x if her home is the origin? assume the positive direction is to the right.
If Sue's home is the origin and the positive direction is assumed to the right, then her position is 2 mi.
Therefore, the answer is 2mi.
Origin depends on the frame of reference, it depends on from where the observer is viewing.
From the figure, distance between home and Sue = 2 - 0 = 2mi
and the distance between Cinema and Sue = 5 - 2 = 3mi
Sue's position is 2mi right to her home and 3mi left to the Cinema. So if her home is the origin and positive direction is to the right x is +2 mi.
--The question is incomplete without the figure, answering to the figure attached--
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Lucy wants to plant 218 flowers in her garden. If there are 32 flowers in a box, how many boxes of flowers will Lucy need to order?
Answer:
Step-by-step explanation:
She could order 7 boxes. if each box has 32 flowers, then you would multiply 6 by 32 which is 192. If you subtract 218 from 192 you get 26. meaning that if she orders 6 boxes of 32 flowers then she would only have 192 flowers and there would be 26 flowers remaining, so then it's better for her to order 7 boxes it's better to have more than what she wants instead of having less than what she wants... that way she is able to plant 218 flowers even if there are some left.
PLEASE HELP 5 QUESTIONS MUST BE GOOD AT MATH
DO NOT ANSWER THE QUESTION ASKING A QUESTION COMMENT THE QUESTION PLEASE WILL GIVE BRAINLY ONLY IF ALL QUESTONS CORRECT
Answer:
1. B
2. A
3. B
4. D
5. C
6. The discount price of a hat is $18. What is the regular price?
The store offers a 20% discount btw .
Answer:$22.50 regular price
Step-by-step explanation: RP=Regular Price
RP-20%of RP=18
RP-0.20RP=18........RP =1RP
1RP-0.20RP=18
0.80RP=18
RP=18/0.80
RP=$22.50
Answer:
22.50
Step-by-step explanation:
other answer is cryptic so here is a full explaination
To find the regular price of the hat, we need to determine the amount of the discount and then add that amount to the discount price.
The discount on the hat is 20% of the regular price, or 20/100 * regular price. The discount price is $18, so we can set up the equation:
discount price = regular price - (20/100 * regular price)
Substituting the known values into the equation, we get:
$18 = regular price - (20/100 * regular price)
Solving for the regular price, we find that the regular price is $22.50. This is the price of the hat before the discount.