When a ladder of length 2.5 m leans against the
of 55° with the ground. When the ladder leans
top edge of a window of a building, it forms an
angle
against the lower edge of the same window,
it forms an angle of 38° with the ground. Find the
height of the window, giving your answer in
centimetres.
Answers
Answer: window = 0.50 m
Step-by-step explanation:
First, draw a picture (see image below).
Then set up two equations that eventually you can set equal to each other.
Given: Ladder (hypotenuse) = 2.5
Angle to Top edge of window = 55°
Angle to Lower edge of window = 38°
[tex]\sin \text{Top}=\dfrac{opposite}{hypotenuse}\qquad \qquad \sin \text{Lower}=\dfrac{opposite}{hypotenuse}\\\\\\\sin 55^o=\dfrac{h+y}{2.5}\qquad \qquad \qquad \sin 38^o=\dfrac{y}{2.5}\\\\\\\underline{\text{Solve both equations for y:}}\\2.5\sin 55^o-h=y\qquad \qquad 2.5\sin 38^o=y\\\\\\\underline{\text{Set the equations equal to each other and solve for h:}}\\\\2.5\sin 55^o-h=2.5\sin 38^o\\2.5\sin 55^0-2.5\sin 38^o=h\\\large\boxed{0.50=h}[/tex]
Related Questions
Find the midpoint of AB when A=(1,-2) B=(1,-1)
Answers
Answer:
Midpoint Of AB = ( 1+1/2 , -2-1/2)
= (2/2 , -3/2)
= ( 1 , -1.5)
Hope this helps
Please mark Branliest.
Answer:
-2,0
Step-by-step explanation:
Im stuck on this question
Answers
Answer:
well the shape is acute so it will be quite low work out the opposite angles and you will find out that the lines are parallels there for meaning the answer is the lowest angle
Step-by-step explanation:
What's the measure of Z1 if Z CBD = 75° and ZABC = 135°?
Answers
Answer:
60°
Step-by-step explanation:
∠ABC-∠CBD=∠1
[tex]135-75[/tex]
[tex]=60[/tex]
Answer:
Brainliest goes to me!
Step-by-step explanation:
angle abc = 135 degrees
part of it is angle 1 and the other part is angle cbd
<abc (135) = cbd (75) + <1
angle 1 = 60 degrees
Which has the lowest value: 1/20, 1/80, or 1/100?
Answers
Answer:
1/100
Step-by-step explanation:
Since the numerators are all the same, the lowest value will depend on the denominators. The greater the denominator, the lower the value. Thus, the answer is 1/100
Lily is cutting a piece of yarn into 3 (three) pieces. The 2nd piece is 3 times as long as the 1st piece, while the 3rd piece is 6 centimeters longer than the 1st piece. When the yarn has a total length of 211 centimeters, calculate the length of the first piece.
Answers
Answer:
The length of the first piece = 41 cm
Step-by-step explanation:
Let the length of the first piece = a
Let the length of the second piece = b
Let the length of the third piece = c
we are given the following:
b = 3a . . . . . (1) (The 2nd piece is 3 times as long as the 1st piece)
c = 6 + a . . . . (2) (the 3rd piece is 6 centimeters longer than the 1st piece)
a + b + c = 211 . . . . . (3) ( the yarn has a total length of 211 centimeters)
Next, let us eliminate two variables, and this can easily be done by substituting the values of b and c in equations 1 and 2 into equation 3. this is done as follows:
a + b + c = 211
a + (3a) + (6 + a) = 211 ( remember that b = 3a; c = 6 + a)
a + 3a + 6 + a = 211
5a + 6 = 211
5a = 211 - 6 = 205
5a = 205
∴ a = 205 ÷ 5 = 41 cm
a = 41 cm
Therefore the length of the first piece (a) = 41 cm
now finding b and c
substituting a into equation 1 and 2
b = 3a
b = 3 × 41 = 123
∴ b = 123 cm
c = 6 + a
c = 6 + 41 = 47
∴ c = 47 cm
Evaluate the expression. 8! − 5!
Answers
Answer:
40200
Step-by-step explanation:
(8x7x6x5x4x3x2x1) - (5x4x3x2x1)
Or simply plug 8! - 5! into the calc.
Answer:
Step-by-step explanation:
40200
The owner of Limp Pines Resort wanted to know the average age of its clients. A random sample of 25 tourists is taken. It shows a mean age of 46 years with a standard deviation of 5 years. The width of a 98 percent confidence interval for the true mean client age is approximately:_______.
A. ± 2.492 years.
B. ± 1.711 years.
C. ± 2.326 years.
D. ± 2.797 years.
Answers
Answer:
C. ± 2.326 years.
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.01 = 0.99[/tex], so [tex]z = 2.326/tex]
Now, find the width of the interval
[tex]W = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]\sigma = 5, n = 25[/tex]
So
[tex]W = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]W = 2.326*\frac{5}{\sqrt{25}}[/tex]
The correct answer is:
C. ± 2.326 years.
6) The average Mathematics mark for Amin, Azman and Aziz is 73. Azman's mark is 35 more than
Amin while Aziz's is twice of Amin's. What is the Mathematics mark of Amin?
Answers
Answer:
46
Step-by-step explanation:
Azman=35+amin
Aziz=3×amin
therefore;35+amin+2amin+amin/3=73
219=35+4amin
219-35=4amin
184=4amin
Amin's mark=184÷4
=46
If the price of a product is p (dollars), the number of units demanded is given by the equation q-pe-3p
(a) Find the price elasticity of demand by using the differentials definition of elasticity. Fully simplify your answer.
(b) Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.
Answers
Answer:
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%
Step-by-step explanation:
Given that:
the number of units demanded [tex]q = pe^{-3p}[/tex]
Taking differentiations ; we have,
[tex]\dfrac{dq}{dp}=e^{-3p}+p(-3e^{-3p})[/tex]
[tex]\dfrac{dq}{dp}=(1-3)e^{-3p}[/tex]
Now; the price elasticity of demand using the differentials definition of elasticity is:
[tex]E(p) = \dfrac{dq}{dp}*\dfrac{p}{q}[/tex]
[tex]E(p) =[(1-3)e^{-3p}]*[\dfrac{p}{pe^{-3p}}][/tex]
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
(b) Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.
The estimate of the percentage change in price is :
[tex]=\dfrac{2.10-2.00}{2.00}*100 \%[/tex]
= 5%
From (a)
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
Now at p = $2.00
E(2) = 1 - 3 (2.00)
E(2) = 1 - 6
E(2) = -5
The percentage change in q = -5 × 5%
The percentage change in q = -25%
Thus; we can conclude that the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%
There are five faculty members in a certain academic department. These individuals have 4, 6, 7, 10, and 15 years of teaching experience. Two of these individuals are randomly selected to serve on a personnel review committee. What is the probability that the chosen representatives have a total of at least 16 years of teaching experience
Answers
Answer:
3/5Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given 5 individuals with 4, 6, 7, 10, and 15 years of teaching experience.
Since two of these 5 individuals are randomly selected to serve on a personnel review committee, total possible outcome = 5C2 (randomly selecting 2 personnel out of 5 )
5C2 = [tex]\frac{5!}{(5-2)!2!}[/tex]
[tex]= \frac{5!}{3!2!}\\ = \frac{5*4*3!}{3!*2} \\= 10\ possible\ selections\ can\ be\ done[/tex]
To get the probability that the chosen representatives have a total of at least 16 years of teaching experience, first we need to find the two values that will give a sum of years greater that or equal to 16 years. The possible combination are as shown;
4+15 = 19years (first reps)
6+10 = 16years (second reps)
6+15 = 21years (third reps)
7+10 = 17 years (fourth reps)
7+15 = 22 years (fifth reps)
10+15 = 25 years (sixth reps)
This shows that there are 6 possible ways to choose the representatives that have a total of at least 16 years of teaching experience
Total outcome = 10
expected outcome = 6
Probability that the chosen representatives have a total of at least 16 years of teaching experience = [tex]\frac{6}{10} = \frac{3}{5}[/tex]
Safety by-laws state that for a ladder to be stable, the angle the base of the ladder makes with the ground should be between 70° and 80'. A safety inspector at a construction site notices a painter on a 10-m ladder that is leaning against a wall. The base of the ladder is 1.5 m away from the wall. Does the inspector have cause to be concerned? Explain.
Answers
Cos(angle) = adjacent/hypotenuse
Cos(angle) = 1.5/10
Angle = arccos(1.5/10)
Angle = 81.37 degrees
Although the angle is close, it is over the 80 degrees, so the inspector should be concerned.
If a company's cost function is C(x) = 15x + 100. What price should the company sell each unit, x, to break even after selling 10 units.
Answers
on monday, it took 3 builders 5 1/2 hours to build a wall. an identical wall needs to be built on tuesday and 5 builders are available. each builder is paid £8.90 for each hour they work. work out how much each builder will be paid for the work completed on tuesday
Answers
Answer:
£29.37
Step-by-step explanation:
→ First step is to find the amount of hours it takes for 5 builders
[tex]\frac{3*\frac{11}{2} }{5} =\frac{33}{2} /5=\frac{33}{2} *\frac{1}{5} =\frac{33}{10} =3\frac{3}{10}[/tex]
→ Now we know how long 5 builder takes we need to multiply the hourly rate by their time worked
[tex]3\frac{3}{10} *8.90=\frac{33}{10} *8.90=3.3*8.90 = 29.37[/tex]
Answer:
Step-by-step explanation:
When the number of builders is increased, the hours worked will be reduced.
So, this is inverse proportion.
Number of hours worked by 5 builders = [tex]\frac{3*\frac{11}{2}}{5}\\\\[/tex]
[tex]=3*\frac{11}{2}*\frac{1}{5}\\\\=\frac{33}{10}\\\\=3\frac{1}{10}[/tex]
Amount received by each builder= 33/10 * 8.90
= £ 29.37
The 3 by 3 grid below shows nine 1 cm x 1 cm squares and uses 24 cm of wire.
What length of wire is required for a similar 20 by 20 grid?
Answers
Answer:
840 cm
Step-by-step explanation:
From the diagram attached, the 3 by 3 grid is made up of nine 1 cm x 1 cm squares. The the length of wire needed to make this grid consist of four rows each row having a length of 3 cm and four columns with each column having a length of 3 cm.
The length of wire required by the 3 by 3 grid = 4 column (3 cm / column) + 4 row (3 cm / row) = 12 cm + 12 cm = 24 cm
The 20 by 20 grid is made up of twenty 1 cm x 1 cm squares. The the length of wire needed to make this grid consist of twenty one rows each row having a length of 20 cm and twenty columns with each column having a length of 20 cm.
The length of wire required by the 20 by 20 grid = 21 column (20 cm / column) + 21 row (20 cm / row) = 420 cm + 420 cm = 840 cm
last one haha ill give 20 points
Answers
The type of triangle drawn is an isosceles triangle.
Base angles ∠ACB and ∠CAB are equal.
What is an isosceles triangle?This is a type of triangle with base angles and opposite sides equal.
Analysis:
∠DCA = ∠CAB ( alternate angles are equal)
∠CAB + ∠ACB + ∠CBA = 180°( sum of angles in a triangle)
50 + ∠ACB + 80 = 180
130 + ∠ACB = 180
∠ACB = 180 - 130 = 50°
Since ∠ACB = ∠CAB = 50°. The triangle drawn is an isosceles triangle.
In conclusion, the triangle is isosceles because the base angles are equal.
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Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean. See Attached Excel for Data. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.
Answers
Answer:
The 99% confidence interval for the mean germination time is (12.3, 19.3).
Step-by-step explanation:
The question is incomplete:
Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.
We start calculating the sample mean M and standard deviation s:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(18+12+20+17+14+15+13+11+21+17)\\\\\\M=\dfrac{158}{10}\\\\\\M=15.8\\\\\\[/tex]
[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((18-15.8)^2+(12-15.8)^2+(20-15.8)^2+. . . +(17-15.8)^2)}\\\\\\s=\sqrt{\dfrac{101.6}{9}}\\\\\\s=\sqrt{11.3}=3.4\\\\\\[/tex]
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=15.8.
The sample size is N=10.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{10}}=\dfrac{3.4}{3.162}=1.075[/tex]
The degrees of freedom for this sample size are:
df=n-1=10-1=9
The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=3.25 \cdot 1.075=3.49[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 15.8-3.49=12.3\\\\UL=M+t \cdot s_M = 15.8+3.49=19.3[/tex]
The 99% confidence interval for the mean germination time is (12.3, 19.3).
The moon is 2.4 X 10^5 miles from Earth. Assume the speed of the fastest spacecraft is 3.6 X 10^4 miles per hour. How many hours would it take this spacecraft to fly to the moon from Earth? Write your answer in standard form, rounded to the nearest hour. The solution is
Answers
Answer: . x 10^5 miles from the earth. How long does it take light to from a source on earth to reach a reflector on the moon and then return to earth? The speed of light is 3.0 x 10^8 m/s. ... sec. to give us our final answer of 1.28 seconds (the time required for light to travel 2.4 x 105 miles). and the fastest spaceship goes 153,454 miles per hour
Step-by-step explanation:
The number of hours that should be taken to fly to the moon from Earth is 7 hours.
Given that
Distance between earth and moon is [tex]2.4 \times 10^5\ miles[/tex]The speed is [tex]3.6 \times 10^4\ miles\ per\ hour[/tex]Now we know that
[tex]Time = \frac{Distance}{Speed} \\\\= \frac{2.4 \times 10^5 }{3.6 \times 10^4} \\\\= \frac{240}{36}[/tex]
= 6.66 hours
= 7 hours
Therefore we can conclude that The number of hours that should be taken to fly to the moon from Earth is 7 hours.
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Simplify 5^2 · 5^9 1. 5^11 2. 5^18 3. 25^11 4. 25^18
Answers
Answer:
Answer choice 1
Step-by-step explanation:
[tex]5^2\cdot 5^9= \\\\5^{2+9}= \\\\5^{11}[/tex]
Therefore, the correct answer choice is choice 1. Hope this helps!
a line has an x-intercept of (4,0) and a y-intercept of (0,12).Find the slope of the line
Answers
Answer:
m = -3
Step-by-step explanation:
Slope Formula: [tex]m = \frac{y2-y1}{x2 - x1}[/tex]
All you have to do is plug in 4 for x1, 0 for x2, 0 for y1, and 12 for y2 and you should be able to calculate your answer!
Answer:
-3
Step-by-step explanation:
→ Utilise the gradient formula
[tex]\frac{y2-y1}{x2-x1}[/tex]
→ Substitute in the values from the coordinates (4,0) and (0,12)
[tex]\frac{12-0}{0-4}=\frac{12}{-4} =-3[/tex]
→ The gradient of the line is -3
What is the repeating digit in the decimal equivalent of 49?
Answers
Answer:
49/99
Step-by-step explanation:
I'm assuming you want to find the fraction that gives the decimal 0.494949...
If that is the case, the 49/99 is your answer.
Answer:
4
Step-by-step explanation:
2/3 divided by 3/4 and for answer of 8/9. Which statement is true
Answers
Answer: true
Step-by-step explanation: reciprocal of 3/4 is 4/3
Hence, 2/3 × 4/3 = 8/9
A piece of wire 30 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
(a) How much wire should be used for the square in order to maximize the total area?m
(b) How much wire should be used for the square in order to minimize the total area? m
Answers
The length of wire used for the square in order to minimize the total area is 9.42m.
We are given that;
Length of wire= 30m
Now
Let the length of the wire used for the square x. The length of the wire used for the circle is 30-x.
The perimeter of the square is 4x and the perimeter of the circle is 2πr=2π(30-x)/(2π)=15-x/π.
The area of the square is [tex]x^2/16[/tex] and
the area of the circle is π(15-x/π)2/4π=225/π-(15x)/π2+[tex]x^2[/tex]/4π.
The total area is A=x2/16+225/π-(15x)/π2+[tex]x^2[/tex]/4π.
To maximize A, we take its derivative with respect to x and set it equal to zero: d[tex]A/dx=x/8-15/π^2+1/(4π)(x)=0[/tex]
Solving for x, we get x=120/(8+4π).
Therefore, 30-x=120/(8+4π)(3-π).
To minimize A, we take its derivative with respect to x and set it equal to zero:
[tex]dA/dx=x/8-15/π^2+1/(4π)(x)=0[/tex]
Solving for x, we get x=120/(8+4π)(3+π).
So, 30-x=120/(8+4π)(3-π).
Therefore, by area the answer will be approximately 9.42 m.
Learn more about the area;
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Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that of the respondents did not provide a response, said that their experience fell short of expectations, and of the respondents said that their experience met expectations.A. If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations?B. If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?
Answers
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that 4% of respondents did not provide a response, 26% said that their experience fell short of expectations, 65% of the respondents said that their experience met expectations (Clarkson Magazine, Summer, 2001). If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations? If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?
Solution:
Probability = number of favorable outcomes/number of total outcomes
From the information given,
The probability that respondents did not provide a response, P(A) is 4/100 = 0.04
The probability that a respondent said that their experience fell short of expectations, P(B) is 26/100 = 0.26
The probability that a respondent said that their experience met expectations, P(C) is 65/100 = 0.65
A) Adding all the probabilities, it becomes 0.04 + 0.26 + 0.65 = 0.95
Therefore, the probability,P(D) that a respondent said that their experience surpassed expectations is 1 - 0.95 = 0.05
B) The event of a randomly chosen respondent saying that their experience met expectations and that their experience surpassed expectations are mutually exclusive because they cannot occur together. It means that P(C) × P(D) = 0
Therefore, the probability of P(C) or P(D) is 0.65 + 0.05 = 0.7
If n is an even integer such that 5≤n≤12, then what is the mean of all possible values of n?
Answers
Answer:
9
Step-by-step explanation:
5≤n≤12
List all the even integers
6,8,10,12
Then find the mean
(6+8+10+12) /4
36/4
9
The mean is 9
[tex]{f}^{4} = - 1[/tex]
O True
O False
?
Answers
Answer:
False.
Step-by-step explanation:
This statement is false, for any value of F because the power function with an even exponent is always positive or 0.
Please answer this correctly
Answers
Answer:
14.3%
Step-by-step explanation:
There is only one four out of 7 total numbers.
1/7 = 0.142857 = 14.29%
We are given 7 numbers.
4 is only one card in that 7 card set so, 1/7.
1/7 = 0.1428
0.1428 * 100% = 14.28%
Therefore, the answer is roughly 14.3%
Best of Luck!
What is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point (4, 32)?
y = 2 x + 33
y= *x+36
y = 4x - 16
y = 4x + 16
Answers
Answer:
y = 4x +16
Step-by-step explanation:
The given equation is in "point-slope" form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
The slope of the given line is m=4. This is the same slope as any parallel line.
__
The line you want can be written in the same point-slope form as ...
y -32 = 4(x -4)
Rearranging, we have ...
y = 4x -16 +32 . . . . . add 32, eliminate parentheses
y = 4x +16 . . . . . . . . collect terms
Boys to girls ratio is 2 to 3. There are 18 girls. What is total number of students
Answers
[tex]\frac{2}{3}=\frac{boys}{18}[/tex]
3*boys=2*18
3*boys=36
boys=12
12+18=30
total number of students: 30
Answer:
30 students
Step-by-step explanation:
2:3 = x:18
X = number of boys
[tex]\frac{2}{3} = \frac{x}{18}[/tex]
multiply 18 by both sides
18 × [tex]\frac{2}{3} = X[/tex]
X = 18 × [tex]\frac{2}{3} = 12[/tex]
18 + 12 = 30
A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, then what is the computed value of the test statistic?
Answers
Answer:
Th computed value of the test statistic is 3.597
Step-by-step explanation:
The null and the alternative hypothesis is as follows:
Null Hypothesis:
[tex]\mathbf{H_o:}[/tex] the population correlation coefficient is equal to zero
[tex]\mathbf{H_a:}[/tex] the population correlation coefficient is not equal to zero
The test statistics for Pearson correlation coefficient is thus computed as :
[tex]t =\dfrac{r \sqrt{(n-2)}} { \sqrt{(1-(r)^2)} }[/tex]
where;
r = correlation coefficient = 0.60
n = sample size = 25
So;
[tex]t =\dfrac{0.60 \sqrt{(25-2)}} { \sqrt{(1-(0.60)^2)} }[/tex]
[tex]t =\dfrac{0.60 \sqrt{(23)}} { \sqrt{(1-0.36} }[/tex]
[tex]t =\dfrac{0.60 *4.796} {0.8}[/tex]
t = 3.597
Comparing to a critical value of t (23 degrees of freedom two-tailed value) = 2.069
Decision Rule:
Since computed value of t is greater than the critical value of t; We reject the null hypothesis and accept the alternative hypothesis.
Conclusion:
We conclude that the population correlation coefficient significantly differs from 0 at 5% (0.05) level of significance.
Please answer this correctly
Answers
Answer:
64
Step-by-step explanation:
There are only pink and yellow sections of the circle, so every spin will land on pink or yellow.
Answer: 64
Answer:
Brianliest!
Step-by-step explanation:
since there are only the colors pink and yellow and the prediction for the number of times it will land on pink or yellow, it will have a 100% probability
64