The truck is 32.22m away from the base of the building
As a 1.5m long man is standing on the 42m long building,
=>the height of man's site= 42+ 1.5= 43.5m
If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle produced between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.
As given, the angle of depression = 53.5°
We know that,
tan ∝= perpendicular* base
so, ∝=53.5:
tan(53.5 )= 43.5/y
[where y= distance of the truck from the base of the building]
1.35= 43.5/y
y=43.5/1.35= 32.22m
Hence, the truck is 32.22m away from the base of the building.
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*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.
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 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.
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
an agriculturalist working with australian pine trees wanted to investigate the relationship between the age and the height of the australian pine. a random sample of australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the australian pine based on the age, in years, of the tree. Predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?
The height increases by 0.48 meters each year.
The available regression equation is: Predict height= 0.29 + 0.48 (age).
Here, the predict height is dependent variable and the age is in-dependent variable.
Intercept = 0.29
Slope = 0.48
The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.
The height increases, an average, by 0.48 m per year.
Because co-efficient of slope variable indicate the positive sign and we increase 1 year in age then automatically height increased is 0.48 m.
The height increases, on average, by 0.48 meter each year.
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The available regression equation is: Predict height= 0.29 + 0.48 (age).
Here, the predict height is dependent variable and the age is in-dependent variable.
Intercept = 0.29
Slope = 0.48
The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.
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
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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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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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
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)What is the answer to this question
Answer:
Step-by-step explanation:
a because if you divide everything under the fraction number you get answer a
The solution for the given expression is x = 4³/₅. The correct option is B.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is x - 17⁴/₅ = -13¹/₅. The given expression will be solved as,
x - 17⁴/₅ = -13¹/₅
x = 17⁴/₅ -13¹/₅
x = 89 / 5 - 66 / 5
x = 23 / 5
x = 4³/₅
The expression will be equivalent to x = 4³/₅.
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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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If f(x)=|x−5| 2, find f(3). responses 10 10 6 6 4 4 0
If the function f(x) = |x-5| + 2, then the value of f(3) is 4
The function
f(x) = |x-5| + 2
The function is defined as the mathematical statement that shows the relationship between the independent variable and the dependent variable. The function consist of different variables, numbers and mathematical operators
Here the function consist of the absolute value symbol.
|-a| = a
The absolute value of the positive and the negative number will be always positive.
The function is f(x) = |x-5| + 2
Then,
f(3) = |3-5| + 2
= |-2| + 2
= 2 + 2
= 4
Therefore, the value of f(3) is 4
I have answered the question in general, as the given question is incomplete
The complete question is:
If f(x)=|x−5| + 2, find the value of f(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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What is a written description of x − 14?
Answer: The written description of x - 14 is given as the difference of variable x and integer 14 gives x -14.
Step-by-step explanation:
Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
Let x be a variable,
And 14 is an integer.
By using mathematical operations,
The difference of x and 14 can be given as,
x - 14.
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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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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PLS HELP
What is the range of f(x) = |x| + 7?
−7 ≤ y < ∞
−∞ < y ≤ −7
0 ≤ y < ∞
7 ≤ y < ∞
The range of the function f(x) = |x| + 7 is given by the option presented as follows:
7 ≤ y < ∞.
How to obtain the range of a function?The range is composed by the set containing all the values assumed by the output of the function, that is, all the numeric values assumed by the function.
In the context of this problem, the function is defined as follows:
f(x) = |x| + 7.
The parent function is the absolute value function g(x) = |x|, which gives the distance of a point x from the origin, assuming real values of at least 0, as a distance cannot be negative.
The addition by 7 means that the parent function was translated up seven units, meaning that the minimum value assumed by the range is seven, and the range of the function is given by the last option given as follows:
7 ≤ y < ∞.
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PLEASE HURRY!
Write and solve the inequality that represents negative one eighth is less than the product of negative two thirds and a number.
A: negative one eighth is less than negative two thirds y where y is less than three sixteenths
B: negative one eighth is less than or equal to negative two thirds y where y is greater than negative three sixteenths
C: negative two thirds is less than negative one eighth y where y is less than one twelfth
D: negative two thirds is greater than negative one eighth y where y is greater than negative one twelfth
The solution to the inequality statement is x < 3/16
How to determine the solution to the inequality?From the question, we have the following parameters that can be used in our computation:
negative one eighth is less than the product of negative two thirds and a number.
Express as numbers and operators
So, we have
-1/8 < -2/3x
Divide both sides by -2/3
So, we have the following representation
1/8* 3/2 > x
Evaluate the produdts
3/16 > x
Rewrite as
x < 3/16
Hence, the solution is x < 3/16
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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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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.
Three years ago Joseph was three times older than Agnes in 2 years times the sum of their ages will be 75 years. Determine their present ages
Answer:
Hey, answer is attached.
Step-by-step explanation:
Hope this helps.
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.
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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Graph the image of this figure after a dilation with a scale factor of 3 centered at
(−7, −6). Use the polygon tool to graph the dilated figure. *picture Below*
Answer:
See the picture below
Step-by-step explanation:
You start from the center given (-7,-6), then count how many spaces from the center to that point. Take that number and triple it to find the new point. I drew lines so that you could see the path of two of the points.
The path that I did not draw was from the point (-3,-2). If you start at (-7,-6) you will have to move 4 spaces to the right and 4 spaces up to get to (-3,-2) Now triple that. You will move 12 spaces to the right and 12 spaces up for the new point of (5,6)
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.
Solve the inequality 3(x-2) + 1 ≥x + 2(x + 2).
O A. x≤ 4
OB. x ≥-5
OC. no solution
OD. all real numbers
Answer: no solution
Step-by-step explanation:
1. distribute through both sides to get 3x-6+1 ≥ x+2x+4
2. then combine like terms to get 3x-5 ≥ 3x+4
3. then make sure like terms are together on either side -> 3x -3x ≥ 4+5 ->
4. since the 3x-3x = 0, there are no solutions
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