Using relations in a right triangle, it is found that the angle of depression is of θ = 56.31º.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that:
The opposite side to the angle of depression is the top of tower, at a height of 9000 feet.The adjacent side to the angle is the distance to the bird, of 6000 feet.Hence, considering θ as the depression angle, we have that:
tan(θ) = 9000/6000
tan(θ) = 1.5
θ = arctan(1.5)
θ = 56.31º.
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The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day. c(x) = 5x3 7x2 − 14x − 6 c(x) = 4x3 7x2 − 14x 6 c(x) = 4x3 7x2 − 14x − 6 c(x) = 5x3 7x2 − 14x 6
The function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].
What is a function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).To find the function to model the water used by the car wash on a shorter day:
Given that the amount of water used on normal days is given by the equation:
[tex]W(x) =5x^{3} +9x^{2} -14x+9[/tex] ......(1)The amount of decrease in water used is modeled by the equation:
[tex]D(x)=x^{3} +2x^{2} +15[/tex] ......(2)To get the function [tex]C(x)[/tex] that models the water used by the car wash on a shorter day you subtract equation (2) from equation (1).
[tex]5x^{3} +9x^{2} -14x+9-(x^{3} +2x^{2} +15)\\5x^{3} +9x^{2} -14x+9-x^{3} -2x^{2} -15\\4x^{3} +7x^{2} -14x-6[/tex]Therefore, the function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].
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The correct question is shown below:
The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day.
(A) c(x) = 5x3 7x2 − 14x − 6
(B) c(x) = 4x3 7x2 − 14x 6
(C) c(x) = 4x3 7x2 − 14x − 6
(D) c(x) = 5x3 7x2 − 14x 6
Solve for x.
°x = 196
Enter your answers in the boxes. Enter the smallest answer first.
x= ____ and x= ____
4 andfirst find x by finding its smallest factor
The solution to the given system of equation is -7 and 7
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Given:
4x² = 196
4x²/4= 196/4
x² = 49
x=√49
x= ±7
Hence, the solution to the given system of equation is -7 and 7
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Question 7(Multiple Choice)
(05.02 MC)
Which expression is equivalent to 3 log2 x - 4 log2 y + 2 log2 z?
Answer:
C.) [tex]log_2(\frac{x^3z^2}{y^4})[/tex]
Step-by-step explanation:
To find the answer, you need to simplify the expression. To do so, you must combine the logs. You can combine the logs because they all have the same subscript (2).
[tex]3 log_2x - 4log_2y + 2log_2z[/tex] <----- Given expression
[tex]log_2x^3-log_2y^4+log_2z^2[/tex] <----- Raise coefficients to variables
[tex]log_2x^3+log_2z^2-log_2y^4[/tex] <----- Rearrange
[tex]log_2(x^3z^2)-log_2y^4[/tex] <----- Multiply added logs
[tex]log_2(\frac{x^3z^2}{y^4})[/tex] <------ Divide subtracted log
Express the multiplication of a logarithm number of an expression as the logarithm of the power of the expression.
㏒₂ x³ - ㏒₂ y⁴ + ㏒₂ z²Take the product of the arguments
[tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ Log_{2} \frac{x^{3}z^{2} }{y^{4} } } }}}}[/tex]
Therefore, the correct option is alternative "C".
The law of Cosines Is......
Answer: [tex]\Large\boxed{C.~21}[/tex]
Step-by-step explanation:
The goal of the question
Find the value of 2abcosC
Given information
a = 4
b = 3
c = 2
Given formula (Law of Cosine)
[tex]c^2=a^2+b^2-2abcosC[/tex]
Substitute values into the formula (Leave 2abcosC as it is)
[tex](2)^2=(4)^2+(3)^2-2abcosC[/tex]
Simplify the exponents
[tex]4=16+9-2abcosC[/tex]
Simplify by addition
[tex]4=25-2abcosC[/tex]
Add 2abcosC on both sides
[tex]4+2abcosC=25-2abcosC+2abcosC[/tex]
[tex]4+2abcosC=25[/tex]
Subtract 4 on both sides
[tex]4 + 2abcosC-4=25-4[/tex]
[tex]\Large\boxed{2abcosC=21}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
C
Step-by-step explanation:
a² + b² - 2abcosC = c² ( subtract a² + b² from both sides )
- 2abcosC = c² - a² - b² ( multiply through by - 1 )
2abcosC = a² + b² - c²
a, b, c are the sides opposite vertices A, B, C
here a = 4 , b = 3 , c = 2 , then
a² + b² - c²
= 4² + 3² - 2²
= 16 + 9 - 4
= 25 - 4
= 21
If z = 1+ i√3, what is z^5?
Answer:
.....................................
Box a has a volume of 32 cubic meters. box b is similar to box a. to create box b, box a's dimensions were tripled. what is the volume of box b?
The volume of box B is (A) 864 cubic meters.
What is volume?The amount of three-dimensional space enclosed by a closed surface is expressed as a scalar quantity. For example, the space occupied or contained by a substance or 3D object.Volume is frequently mathematically quantified using the SI-derived unit, the cubic meter.To find the volume of box B:
We have been assigned a volume of 32 cubic meters. The cubic root of 32 yields the box's dimensions, which are 3.1748 x 3.1748 x 3.1748 meters. Meters when the dimensions are tripled: 9.5244 x 9.5244 x 9.5244= 864 cubic meters.
Therefore, the volume of box B is (A) 864 cubic meters.
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The complete question is given below:
Box A has a volume of 32 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were tripled. What is the volume of box B?
a. 864 m3.
b. 288 m3.
c. 96 m3.
d. 32 m3
Listed below are systolic blood pressure measurements (in mmHg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05.
The regression equation between the variables is y = 1.03x + 62.12 and the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg is 149.67
How to determine the regression equation?From the table of values, we make use of the following representations:
Represent the Right Arm on the x axisRepresent the Left Arm on the y axisUsing the above representations, we can now plot our data values on a graphing calculator
From the graphing calculator, we have the following summary:
Sum of X = 458Sum of Y = 782Mean X = 91.6Mean Y = 156.4Sum of squares (SSX) = 601.2Sum of products (SP) = 618.8The regression equation is
y = bx + a
Where
b = SP/SSX = 618.8/601.2 = 1.02927
a = MY - bMX = 156.4 - (1.03*91.6) = 62.11843
This gives
y = 1.03x + 62.12
Hence, the regression equation between the variables is y = 1.03x + 62.12
To predict the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg, we have
y = 1.03 * 85 + 62.12
Evaluate
y = 149.67
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Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
According to the developed scale, a radiant day is 16 times brighter than a dim day.
We assume the brightness of a dim day to be x.
According to the developed scale, the brightness of an illuminated day will be 4 times that of a dim day.
Thus, the brightness of an illuminated day = 4*the brightness of a dim day = 4x.
According to the developed scale, the brightness of a radiant day will be 4 times that of an illuminated day.
Thus, the brightness of a radiant day = 4*the brightness of an illuminated day = 4*4x = 16x.
Now, the ratio of the brightness of a radiant day to the brightness of a dim day = 16x:x = 16x/x = 16:1.
Thus, according to the developed scale, a radiant day is 16 times brighter than a dim day.
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The question provided is incomplete. The complete question is:
"Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
Dim=2
Illuminated=3
Radiant=4
Dazzling=5"
A dealer buys oranges for 100000, he sold 60% of them for buying price, he sold 50% of the remaining for profit of 60% then he sold the remaining for a loss of 10%. Find the overall profit
Based on the amount of oranges bought, those sold at a profit and those sold at a loss, the overall profit is 14.2%
What is the overall profit?Assume that the buying price was $1 each.
The amount earned from 60% of them is:
= 60% x 100,000 x 1
= $60,000
The profit from selling 50% of the remaining is:
= (50% x 40,000) x 1.60
= $32,000
The loss from selling the other 50%:
= (50% x 40,000) x 0.90
= $22,222.22
Total selling price:
= 60,000 + 32,000 + 22,222.22
= $114,222.22
Total profit:
= (114,222.22 - 100,000) / 100,000
= 14.2%
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2 Question is down below.
The height of the flagpole is 12.4 meters and the altitude of the balloon is 29.1 meters
How tall is the flagpole?See attachment for the diagram, when redrawn
Start by calculating the length AB using the following tangent function
tan(22) = BC/AB
This gives
tan(22) = 9/AB
Make AB the subject
AB = 9/tan(22)
Evaluate the quotient
AB = 22.3
The length DB is then calculated using:
tan(9) = DB/AB
This gives
tan(9) = DB/22.3
Make DB the subject
DB = 22.3 * tan(9)
Evaluate
DB = 3.35
The height of the flagpole is then calculated as:
Height = DB + BC
This gives
Height = 3.35 + 9
Evaluate
Height = 12.35
Approximate
Height = 12.4
Hence, the height of the flagpole is 12.4 meters
How to determine the altitude of the balloon?The diagram that illustrates the scenario is added as an attachment
Calculate the value of y using the following tangent functions
tan(57) = x/y and tan(72) = (15 + x)/y
Make y the subject in tan(57) = x/y and tan(72) = (15 + x)/y
y = x/tan(57) and y = (15 + x)/tan(72)
Substitute y = x/tan(57) in y = (15 + x)/tan(72)
x/tan(57) = (15 + x)/tan(72)
Evaluate the tangent ratios
x/1.5 = (15 + x)/3.1
Cross multiply
3.1x = 22.5 + 1.5x
Evaluate the like terms
1.6x = 22.5
Divide by 1.6
x = 14.1
The altitude of the balloon is then calculated as:
Altitude = 14.1 + 15
Altitude = 29.1
Hence, the altitude of the balloon is 29.1 meters
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A 2-gallon container of laundry detergent costs $10.24. What is the price per fluid ounce?
Answer:
$0.04
Step-by-step explanation:
The cost per ounce is found by dividing the cost by the number of ounces.
SolutionIn 2 gallons, there are 2×128 fl.oz. = 256 fl.oz. Then the cost per ounce is ...
cost/ounces = $10.24/(256 fl.oz) = $0.04 /fl.oz.
The cost of the laundry detergent is $0.04 per fluid ounce.
__
Additional comment
Keeping the units with the numbers in a calculation can give you confidence that the calculated result has the units you want it to have.
Look at the graph below.
Answer:
B. -1/3
Step-by-step explanation:
Choose 2 points. From the lower points count up until it is in line with the other point. Then count left until you reach the second point.
Rise/Run
Rise=1
Run=-3
[tex]-\frac{1}{3}[/tex]
Hope this helps!
Answer: -1/3 is the answer
Step-by-step explanation:
Your friends and you notice a classmate who always has brand new clothes, shoes, and electronics. What would you need to know in order to tell if this classmate’s family is actually wealthy?
To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.
What is an asset?In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.
Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.
In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.
The asset should more than the debt.
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Louie is trying to find a rectangular canvas for his art project. its height must measure 18 inches and form a 48° angle with the diagonal at the top of the canvas. what is the length of the diagonal of the canvas? round your answer to the nearest inch. 12 inches 14 inches 24 inches 27 inches
The length of the diagonal of the canvas = 27 inches.
The correct option is D.
What is Pythagoras?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem, or Pythagoras' theorem. The area of the square whose side is the hypotenuse is said to be equal to the total of the areas of the squares on the other two sides.
According to the given information:the Hight of the rectangle = 18 inches
the angle it form sinθ = H/P
H = 18
P =
cosθ = 48
cosθ = H/P
cosθ =18/P
P = 18/cosθ
= 29.60
= 27
The length of the diagonal of the canvas = 27 inches.
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Solve the system to answer the questions.
How many premium car washes were ordered?
premium car washes
How many quick car washes were ordered?
quick car washes
The number of quick car and premium car washes ordered are 75 and 50 respectively.
How to find the number of premium and quick car washes ordered?The system of equation models the situation
x + y = 125
5x + 8y = 775
Therefore,
5x + 5y = 625
5x + 8y = 775
3y = 150
divide both sides 3
3y / 3 = 150 / 3
y = 50
Therefore,
x + y = 125
x + 50 = 125
x = 125 - 50
x = 75
Therefore, the number of quick car and premium car washes ordered are 75 and 50 respectively.
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Answer:
50 and 75
Step-by-step explanation:
evaluate 4 + 6 x 6 / 8
Answer:
8.5
Step-by-step explanation:
4 + (6)(6)/8=
17/2 = 8.5
Answer:
8.5
Step-by-step explanation:
6 x 6 = 36/8 = 4.5 + 4 = 8.5
Find the value of z
A. 50
B. 110
C. 65
D. 130
Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=−0. 599, α=0. 01, n=11
Yes, the correlation coefficient is statistically significance
The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.
Given,
Sample size, n = 11
Where ρ is the population correlation.
Then the number of degrees of freedom is, df = n-2 = 11-2 = 9
The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254
Here,
The null hypothesis, = ρ - 0 is rejected
Suppose lr> re 0.254
Because on the sample correlation provided, we know that lrl = 0.599>=0.254.
Here, it is clear that the null hypothesis is rejected.
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Find the total surface area. A. 78 B. 98 C. 69 D. 92
The total surface area of the figure is 92 m².
How to find the surface area of a figure?The surface area of a figure is the sum of the whole sides of the figure.
Therefore,
surface area = 4 × 4 + 4 × 4 + 6 × 4 + 2 × 4 + 1 / 2 (2 + 6)3.5 + 1 / 2 (2 + 6)3.5
Hence,
surface area = 16 + 16 + 24 + 8 + 14 + 14
Therefore,
surface area = 32 + 24 + 8 + 28
surface area = 56 + 8 + 28
surface area = 92 m²
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When the points in a scatter plot cluster closely around the regression line, the correlation can be said to be?
The points in a scatter plot cluster closely around the regression line, the correlation can be said to be the proportion of variance in Y that is determined or explained by X.
It is critical to understand that a correlation coefficient of zero indicates that there is no linear courting, but there can also nonetheless be a strong relationship among the 2 variables.
If one point of a scatter diagram is farther from the regression line than a few other factor, then the scatter diagram has as a minimum one outlier. If two or extra points are the identical farthest distance from the regression line not a commonplace prevalence), then every of those points is an outlier.
When the y variable has a tendency to increase because the x variable increases, we say there may be a high-quality correlation between the variables. when the y variable has a tendency to lower as the x variable increases, we are saying there's a bad correlation between the variables.
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________ is used to describe the relationship between two things of the same type, such as one person being married to another person.
Answer:
"Unary Association" I believe
A spaceship is traveling at a steady rate. The table shows the distance the spaceship travels in a given period of time. Find the distance the spaceship travels in 4 minutes.
Ty.
The distance of the spaceship in discuss as in the task content given can be evaluated as; 800miles.
What is the distance the spaceship travels in 4 minutes?The distance travelled by the spaceship in discuss can be evaluated by means of the slope of the linear relationship as follows;
Hence it follows from ratios that by observation, the linear relationship has a slope of 200mi/min.
Consequently, we can evaluate the distance travelled after 4 minutes as;
Distance = 200 × 4 = 800mi.
Ultimately, the distance travelled per minute by the spaceship is; 800mi.
Remarks:
600 miles
520 miles
800 miles
1,080 miles
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Pick the correct answer
Thanks so much :)
The linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
Line I is decreasing, hence it has a negative slope.Line K is constant, hence it has a slope of zero.Line J is increasing, hence it has a positive slope.Hence the linear functions with their slopes ranked from least to greatest are given as follows:
E. I, K, J.
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Need help ASAP! This is due in an hour and this is the last question!!!
the equation with these solutions is:
0 = x^2 - 6x + 6
How to find an equation with the given solutions?
Remember that a quadratic equation with the solutions a and b is written as:
0 = (x - a)*(x - b)
Here we have the solutions:
x = 3 + √3x = 3 - √3Then we can write a quadratic equation of the form:
0 = (x - (3 + √3) )*(x - (3 - √3) )
0 = (x - 3 - √3)*(x - 3 + √3)
Expanding that, we get:
0 = x^2 - 6x + 9 - 3
0 = x^2 - 6x + 6
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John is 12 meters away from a cliff and looks up to the top of the cliff at an angle of 45. His eyes are 2 meters above the ground. How tall is the cliff?
Answer:
14m
Step-by-step explanation:
Please refer to the attached figure
B is the position where John is standing, His eyes are at point A, 2 meters from the ground
D is the base of the cliff and E is the top of the cliff
∠EAC is the angle at which John looks up to the cliff and is given as 45°
BD is the distance from the cliff given as 12m
So AC is also 12m
∠ACE is 90°
Therefore ∠AEC is 180-(45+90) = 45° since AEC forms a triangle and sum of angles in a triangle = 180°
In the ΔAEC, by the law of sines
12/sin(45) = EC/sin(45) . This means EC = 12 since the denominators cancel out
Since point C is 2 meters above ground(the base of the cliff) add 2 and we get the height of the cliff as 12+2 = 14m
Tanya is 12 years older than Leah. Three years ago, Tanya was five times as old as Leah.
What is the age of Tanya and Leah now?
Answer:
tanya 22
leah12
Step-by-step explanation:
i hope it
help ...
43% of a sample of 100 visitors to a national park believes that additional funds should be used to preserve endangered species. what is the margin of sampling error for a 95% confidence interval?
The margin of sampling error for a 95% confidence interval is 9.7%
How to find the Margin of Error?The formula for margin of error here is;
E = z√(p(1 - p)/N)
where;
n is sample size
z is the z score
p is the sample proportion
z-score for a 95% confidence interval from tables is 1.96.
We are given;
p = 43% = 0.43
n = 100
Thus;
E = 1.96√(0.43(1 - 0.43)/100)
E = 0.097 = 9.7%
Thus, we can conclude that the margin of sampling error for a 95% confidence interval is 9.7%
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A.22
B.183
C.246
D.213
Answer:
B. 183
Step-by-step explanation:
m<L = (1/2)[m(arc)KN - m(arc)KM)]
35 = (1/2)(177x - 107x)
70 = 70x
x = 1
m(arc)KN = 177x = 177
m(arc)NMK = 360 - m(arc)KN
m(arc)MNK = 360 - 177
m(arc)MNK = 183
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
The surface area of the shape is 117.8 km²
Surface area of a coneFrom the question, we are to determine the surface area of the figure
The given figure is a cone.
Total surface area of a cone = Area of circular part + Curved surface area
Total surface area of a cone = πr² + πrl = πr(r + l)
Where r is the radius
and l is the slant height
From the given information,
r = 3 km
l = 9.5 km
The total surface area of the cone = π×3(3+9.5)
The total surface area of the cone = 3π(12.5)
The total surface area of the cone = 117.8 km²
Hence, the surface area of the shape is 117.8 km²
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A company found that an experienced surveyor can survey a roadbed in 7 hours. An apprentice surveyor needs 8 hours
to survey the same stretch of road. If the two work together, find how long it takes them to complete the job.
***
The number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.
Rate of workHours it takes the experienced surveyor = 7 hoursSurveyors rate of work = 1/7Hours it takes the apprentice = 8 hoursApprentice rate of work = 1/8If the two work together;
Time taken for both to complete the task = Surveyors rate of work + Apprentice rate of work
= 1/8 + 1/7
= (7+8) / 56
= 15/56 hours
Therefore, the number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.
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