A light in a park can illuminate effectively up to a distance of 100 m. A point on a bike path is 150 m from the light. The sight line to the light makes an angle of 23° with the bike path. What length of the bike path, to the nearest metre, is effectively illuminated by the light?
Answers
The length of the bike path, to the nearest meter, is effectively illuminated by the light is 138 m
The missing diagram is attached with the answer.
What is Angle of elevation ?The angle formed between the horizontal line and line of sight is called Angle of Elevation.
It can be seen in the diagram that
It is a right angled triangle if extended and
cos 23 degree = (length of the bike path)/Hypotenuse
Hypotenuse here is the point on a bike path is 150 m from the light
Therefore
cos 23 ° = x / 150
x = 0.92 * 150
x = 138 m
Therefore The length of the bike path, to the nearest meter, is effectively illuminated by the light is 138 m.
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Related Questions
the the radius of a sphere is 8 cm. find the volume. round off to nearest tenth if necessary. use 3.14 for pi
Answers
radius of sphere , r = 8cm
We know that,
Volume of sphere = 4/3 pi r^3 cubic units
=> Volume of sphere , V = 4/3 x 3.14 x 8 x 8 x 8
=> Volume of sphere , V = 2143.573 units
Rounding of to nearest tenth , V =2143.58 units
The volume of the given sphere.
Solution:[tex]\large\boxed{Formula:V = \frac{4}{3} \pi {r}^{3}}[/tex]
[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]
Let's solve
Substitute the values according to the formula.
[tex]V = \frac{4}{3} \times 3.14 \times {8}^{3} [/tex]
[tex]V = 2143.573333 \: {cm}^{3} [/tex]
[tex]\large\boxed{= 2143.6 \: {cm}^{3} \: (nearest \: tenth)}[/tex]
Hence, the volume of the given sphere is 2143.6 cubic centimeters.
Without plotting the function
y = f(x) on a graph paper, find the coordinates of the common points of the axes when
a) f(x) = 4x² - 25
b) f(x) = 3x² - 5x
Answers
The outside of a rectangular picture frame has length 4x + 5 centimeters and width 2x + 3 centimeters. The picture window inside the frame is a rectangle that is 4x - 2 centimeters long and x + 1 centimeters wide.
a. Write a polynomial to describe the area (in square centimeters) of the picture window.
b. The picture frame, not including the window, is made of flat pieces of wood. Write a polynomial that describes the area (in square centimeters) of the wooden part of the frame. Explain your reasoning
Answers
The area of the wooden part of the frame is 4x² +20x +17 sq.cm , Area of a Rectangle is 4x² +2x-2 sq.cm .
What is a Rectangle ?A rectangle is a polygon with four sides . The opposite sides are parallel and equal.
It is given that the outside length and breadth is 4x + 5 centimeters and width 2x + 3 centimeters.
inside the frame has length and breadth 4x - 2 centimeters long and x + 1 centimeters wide.
The polynomial to describe the area of the picture window
The dimension of the inner picture frame is the dimension of the picture window
Area of a Rectangle = Length * Breadth
Area of a Rectangle = (4x-2) (x+1) = 4x² +4x -2x-2 = 4x² +2x-2 sq.cm
The picture frame area without the window =
Area of the total picture frame - Area of the inner picture frame
= (4x+5)(2x+3) - (4x-2)(x+1)
= 8x² + 12x +10x+15 -4x²-2x +2
= 4x² +20x +17
The area of the wooden part of the frame is 4x² +20x +17 .
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Suppose a nuclear power plant disaster occurs. How could GDP be a "false beacon" in this case?
Answers
If there was a nuclear plant disaster, then GDP would be a false beacon because it would account for government spending but not for the pollution caused.
Why would GDP be a false beacon?Two of the components of GDP are government spending and private investment.
If there is a nuclear plant disaster, either the government will spend a lot to clean it up, or a private company will depending on if the plant is public or private.
GDP would therefore increase.
This would be a false beacon however, because this increase would not take into account the nuclear pollution that would have occurred that would negatively impact future production.
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Celia simplified the expression Negative 4 x (1 minus 3) minus (2 x + 2). She checked her work by letting x = 5 in both expressions. Her work for the original expression is shown below.
Negative 4 x (1 minus 3) minus (2 x + 2) = negative 4 (5) (1 minus 3) minus (2 (5) + 2) = negative 20 (negative 2) minus 12 = 40 minus 12 = 28.
Celia knows that the simplified expression should also equal 28 when x = 5. Which shows Celia’s simpllifed expression?
–6x – 1
–6x + 2
6x + 1
6x – 2
Answers
Answer:
6x-2
Step-by-step explanation:
-4x(1-3)-(2x+2)
= 4x+12x-2x-2
6x-2
(simplify)
Answer:
6x - 2
Step-by-step explanation:
Edge
**Find the perimeter of the region.**
The circle are congruent to each other.
The circles are tangent to each other, and the straight
segments are tangent to the circles.
The straight
segments are 5 units long.
Answers
Find the perimeter of the region.**
The circle are congruent to each other.
The circles are tangent to each other, and the straight
segments are tangent to the circles.
The straight
segments are 5 units long
Determine whether these two ratios make a proportion 5/9, 56/99. True or False
Answers
Answer: The answer is True .
The statement is false, these two ratios don't make a proportion.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
here, we have,
5/9, 56/99
we know, that, two ratios make a proportion if, a:b=c:d
but, here,
5/9= 5:9
56/99 = 56: 99
Hence, The statement is false, these two ratios don't make a proportion.
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Sergio is creating a college fund for his son Diego, who is now 4 years old. Sergio put $1600 in a CD that will earn 8.25% simple interest. How much will be in the account when Diego turns 18?
Answers
well, Diego is 4 now, so by his 18th birthday that'll be 14 years later.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1600\\ r=rate\to 8.25\%\to \frac{8.25}{100}\dotfill &0.0825\\ t=years\dotfill &14 \end{cases} \\\\\\ A=1600[1+(0.0825)(14)]\implies A=1600(2.155)\implies A=3448[/tex]
1) Write an equation in point slope form
that passes through the point (1, 2) & slope
of -5
Answers
Answer:
y - 2 = -5 (x - 1)
Step-by-step explanation:
Formula for point-slope equation :
y - y₁ = m (x - x₁)
============================================================
Given :
⇒ Point (x₁, y₁) = (1, 2)
⇒ Slope (m) = -5
=============================================================
Solving :
⇒ y - 2 = -5 (x - 1)
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Equation of line can be written in point - slope form as :
[tex]\qquad \sf \dashrightarrow \:y - y_1 = m(x - x_1)[/tex]
y1 = y - coordinate of point = 2 x1 = x - coordinate of point = 1m = slope = -5So, required equation is ~
[tex]\qquad \sf \dashrightarrow \:y - 2 = - 5(x - 1)[/tex]
What is the volume of the solid?
Answers
Answer:
V≈314
Step-by-step explanation:
* means times
volume of a cone
it's a right circular cone
formula
volume =
π * radius squared * (height ÷ 3)
π * 5 squared * (12 ÷ 3)
π * 25 * (4)
π * 100
3.14 * 100 = 314
factoid
pi or π in fraction form is 22/7
5 and 12 means the length of that
cone is 13
because it's a right circular cone
that means there's a right triangle
one of the special triangles is a
5,12,13 right triangle where
13 is the hypotenuse
moomoomath
Determine the probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more. Then complete the statements.
The significance level is set at 5%, and the probability of the result is
%, which is
the significance level. The result is
.
Answers
The probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more is 0.036.
How to calculate the probability?The probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more will be:
= (26 + 8 + 2)/1000
= 36/1000
= 0.036
The significance level is set at 5%, and the probability of the result is statistically significant because the probability of the difference is less than 5% significance level.
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110- (5x) 70, 110- What is the value of x? 14 15 16 17
Answers
The value of x is 14 because the sum of all angles in kite is 360 degree option first 14 is correct.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The question is in the picture please refer to the attached picture.
We know the sum of all angles in a kite is 360 degree
110 + (5x) + 110 + 70 = 360
290 + 5x = 360
5x = 70
x = 14
Thus, the value of x is 14 because the sum of all angles in kite is 360 degree option first 14 is correct.
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3(5z - 7) - 2 (9z - 11) = 4 (8z - 13) - 17
Answers
Answer z=2
See picture attached for the math
The box plot shows the number of home runs hit by 43 players during a baseball season.
Which statement best describes the data?
The number of data values between the lower
quartile and the median is less than the
number of data values between the upper
quartile and the median.
2
9
15 19
28
The number of data values between the lower
quartile and the median is greater than the
number of data values between the upper
quartile and the median.
|++++++
0 4 8 12 16 20 24 28 32
The spread between the lower quartile and
the median is less than the spread between
the upper quartile and the median.
The spread between the lower quartile and
Answers
The statement fourth "The spread between the lower quartile and the median is greater than the spread between the upper quartile and the median" is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
The box plot is missing.
The box plot is shown (please refer to attached picture)
The given options are:
The number of data values between the lower quartile and the median is less than the number of data values between the upper quartile and the median.The number of data values between the lower quartile and the median is greater than the number of data values between the upper quartile and the median.The spread between the lower quartile and the median is less than the spread between the upper quartile and the median.The spread between the lower quartile and the median is greater than the spread between the upper quartile and the median.As we know the property of box plot the difference between the lower and higher quartiles is greater than the difference between the upper and lower quartiles.
The spread between the lower quartile and the median:
= 15 - 9 = 6
= 19 - 15 = 4
Thus, the statement fourth "The spread between the lower quartile and the median is greater than the spread between the upper quartile and the median" is correct.
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Which of the following solutions to the inequality -7x+14>-3x -6? Select all that apply
-10
10
-5
5
-3
3
0
Answers
I went thru it and im pretty sure that only these work
-10
-5
-3
Help asap immediately
Answers
[tex] \frac{9}{8 \: } = 1 \frac{1}{8} [/tex]
HOPE THIS HELPS :)[tex] \sf \frac{9}{8} [/tex]
Step-by-step explanation:
[tex] \sf9 \div 8 = 1(1left)[/tex]
[tex]1 \frac{1}{8} [/tex]
#Hopethishelp
_______
Moumocl!
please help! easy! it is due right now!!
Answers
Answer:
3 Cups of flour.
Step-by-step explanation:
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
36, 27,
81
4
Find the 10th term.
Answers
Answer:
T10=108
Step-by-step explanation:
TN=bn+c
27,36,81=constant difference is 9
Tn=bn+c
Tn=9n+18
T10=9(10)+18
T10=90+18
T10=108.
hope it helps.
Answer: 2.703
Step-by-step explanation:
I NEED HELP ASAP!!!
Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y=2.5 + 1.25rMULTIPLE CHOICE Question 7 Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y= 2.5 + 1.25x
X = the number of weeks that have passed
= the height of the plant
They want to use the equation to estimate when the height of the plant will be 10
Amalia's estimate is after 6 weeks.
Alec's estimate is after Week 15.
Is either student correct?
Answers
Amalia would be correct. They are guessing when the height would be 10, and you are given an equation that will 'predict' that. Height is y, so substitute 10 in the equation and solve for x. You will get x=6
Question 1 of 10
f(x) = 3x³ - 2x² + 4x - 5
g(x) = 6x - 7
Find (f + g)(x).
Answers
Done!
Answer:
[tex](f+g)(x)=3x^3-2x^2+10x-12[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=3x^3-2x^2+4x-5\\g(x)=6x-7 \end{cases}[/tex]
[tex]\begin{aligned}(f+g)(x) & = f(x)+g(x)\\& = (3x^3-2x^2+4x-5)+(6x-7)\\& = 3x^3-2x^2+4x-5+6x-7\\& = 3x^3-2x^2+4x+6x-5-7\\& = 3x^3-2x^2+10x-12\end{aligned}[/tex]
Question 2: Find the equation of the line that has an x intercept of 2 and a y intercept of -6
Answers
Answer:
[tex]y = 3x - 6[/tex]
Step-by-step explanation:
Hello!
With an x - intercept of 2, the coordinate is (2, 0). With a y - intercept of -6, the coordinate is (0, -6).
We have to find the equation of the line that goes through these points.
The equation of a line is written in slope-intercept format: [tex]y = mx + b[/tex]
y = ordinate, y - valuem = slope, rate of changex = abscissa, x - valueb = y-interceptSlopeFirst let's find the slope using the slope formula: [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]. Remember that a coordinate is written in (x, y) format.
[tex]\frac{-6 - 0}{0 - 2}[/tex][tex]\frac{-6}{-2}[/tex][tex]3[/tex]So, we have the slope and the y - intercept. We can plug those into the equation.
[tex]y = mx + b[/tex][tex]y = 3x - 6[/tex]The equation of the line is [tex]y = 3x - 6[/tex]
A dentist has 420 male and female patients that range in ages from 10 years old to 50 years old and up as shown in the table.
What is the experimental probability that the next patient will be female and in the age range 22-39?
Answers
The experimental probability that the next patient will be female and in the age range 22-39 is 56/420
What is the experimental probability?Probability is the odds that a random event would happen. The odds usually lie between 0 and 1.
The experimental probability = number of female in the age range 22-39 / total number of patients
= 56/420
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The annual profits for a company are given in the following table, where x represents the number of years since 2014, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the calendar year in which the profits would reach 144 thousand dollars.
Answers
The linear regression equation that represents this data set is equal to y = 11.7x + 48.2 and an estimate of the calendar year is 2022.
How to write the linear regression equation?First of all, we would determine the slope of the given data set by using this formula:
[tex]Slope = \frac{\sum (x-\bar x)(y-\bar y)}{\sum (x-\bar x)^2}[/tex]
For the sample mean (years), we have:
∑x = 0 + 1 + 2 + 3
∑x = 6.
∑x² = 0² + 1² + 2² + 3²
∑x² = 14.
For the sample mean (profits), we have:
∑y = 46 + 57 + 84 + 76
∑y = 263.
∑xy = (0 × 46) + (1 × 57) + (2 × 84) + (3 × 76)
∑xy = 453.
Now, we can determine the slope:
[tex]Slope = \frac{4(453) - 6(263)}{4(14) - 6^2} \\\\Slope = \frac{234}{20}[/tex]
Slope, m = 11.7.
For the intercept, we have:
[tex]Intercept = \frac{14(263) - 6(453)}{4(14) - 6^2} \\\\Intercept = \frac{964}{20}[/tex]
Intercept, c = 48.2.
Therefore, the linear regression equation is given by:
y = 11.7x + 48.2.
Since the profit would reach 144,000 dollars, the calendar year would be calculated as follows:
144 = 11.7x + 48.2
11.7x = 144 - 48.2
11.7x = 95.8
x = 95.8/11.7
x = 8.2.
For the calendar year, we have:
Year = 2014 + 8.2
Year = 2022.2 ≈ 2022.
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willams bought piece of woods that is 3 feet long.he cuts it in to two pieces.one piece is 14 in long how long is the other piece
Answers
Answer:
22 inches
Step-by-step explanation:
3 feet = 36 inches
36-14=22
The other half is 22 inches long
pls help me this is important
Answers
Using the Charles law, the following are the solutions to the problems;
1) 16 dm3
2) 170 K
3) 2.4 L
What is Charles law?Charles law states that, the volume of a given mass of gas is directly proportional to the temperature at constant pressure.
For problem 1;
T1 = 20 + 273 = 293 K
V1 = 15 dm3
T2 = 318 K
V2 = ?
V1/T1 = V2/T2
V1T2 =V2T1
V2 = V1T2/T1
V2 = 15 dm3 * 318 K/293 K
V2 = 16 dm3
Problem 2
V1 = 250cm3
T1 = 10 + 273 = 283 K
V2 = 150cm3
T2= ?
T2 = V2T1/ V1
T2 = 150cm3 * 283 K/250cm3
T2 = 170 K
Problem 3
V1 = 2.3 L
T1 = 25 + 273 = 298K
V2 = ?
T2 = 40 + 273 = 313 K
V2 = V1T2/T1
V2 = 2.3 L * 313 K/298K
V2 = 2.4 L
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Please solve these questions!! preferrably today since the quarter locks today!!
Answers
Answer:
131
Step-by-step explanation:
X÷ 5+1 = 11
X =
What does X =
Answers
Answer:
x = 2
Step-by-step explanation:
x/5 + 1 = 11
x/5 = 10
x = 50
Select the correct answer. Which expression is equivalent to the complex number 10 + 3i?
Answers
The expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)
Complex numbersComplex numbers are square root of negative numbers. They are expressed as a + bi
Using the expression
(4+7i)-2i(2+3i)
Expand
4 + 7i - 4i -2i(3i)
4 + 3i - 2(-3)
4 + 6 + 3i
10 + 3i
Hence the expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)
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A
ABCD FECG
2
B
F
6
4
5
E
100°
120°
G
W
D
w = [?]°
5
60°
C
Answers
Answer:
120
Step-by-step explanation:
Corresponding angles of similar figures are congruent.
The measure for w is 120 degree.
We have ABCD ~ FECG
If two quadrilaterals are similar, it means that their corresponding angles are congruent, and their corresponding sides are proportional.
Then, we can write as
AB/ FE = CB/ EC = CD/ CD = AD/ FG
and, <A= <F,
<B = <E,
<C= <C,
<D= <G
So, the measure for w is same as angle G.
Thus, the measure for w is 120 degree.
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A card is drawn from a deck of 52 cards what is the probability that it is a number 2?
Answers
Answer:
Step-by-step explanation:
Remark
The deck is divided into 4 different kinds of cards
clubs
diamonds
Hearts
Spades
Each kind of card has a 2
So there are 4 twos in a standard deck of cards.
Answer:
P(2) = 4/52P(2) = 1/13P(2) = 0.07692