Answer: 61.16 ft
Step-by-step explanation:
We can think in this situation as a triangle rectangle.
where:
The height of the tree is one cathetus
The shadow of the tree is the other cathetus.
We know that the angle of elevation of the sun is 78°, an angle of elevation is measured from the ground, then the adjacent cathetus to this angle is the shadow of the tree. And the opposite cathetus will be the height of the tree.
Now we can remember the relationship:
Tg(A) = (opposite cathetus)/(adjacent cathetus)
Where:
A = 78°
Adjacent cathetus = 13ft
opposite cathetus = height of the tree = H
Then we have the equation:
Tg(78°) = H/13ft
Tg(78°)*13ft = H = 61.16 ft
The centreville city council conducts a survey to find out how many people would be willing to donate money to update the town's library. they randomly select 200 people for the survey, and 80 people say they would donate. if 9,800 people live in centreville, about how many people would likely donate?
a. 122
b. 280
c. 3,920
d. 5,880
(C) 3,920 people would likely donate.
What is the percentage?
A percentage (from Latin per centum "by a hundred") is a number or ratio stated as a fraction of 100 in mathematics. It is frequently symbolized with the percent sign, " percent ". A % is a dimensionless (pure) number; it does not have a unit of measurement.To find about how many people would likely donate:
First, find 80 is what percent of 200.
∴ [tex]\frac{80}{200} * 100 = 40%[/tex]
So, 80 is 40% of 200.
Centreville population is 9,800.
Now, take out 40% of 9,800.
[tex]\frac{x}{9,800} *100 = 40\\\frac{x}{98} =40\\98*40 = 3,920[/tex]
Therefore, (C) 3,920 people would likely donate.
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The Venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet. Enter your answers in the boxes to complete the two-way table based on the given data.
The complete table is
Dog Not Dog Total
Cat 31 10 41
Not cat 24 7 31
Total 55 17 72
Given a venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet as shown in figure which is attached below.
In the figure cat and dog are overlapping which means 31 people like both.
The people that like only dog but not cat are 24 and the people that like only car but not dog is 10.
The people that like not cat not dog is 31-24=7.
The total people that like cats are 31+10=41 and the total people that dont like cat is 24+7=31
The total people that like dogs are 31+24=55 and the people that didn't like dogs are 31+10-24=17 and the total people that like both dog and not dog and also like cat and not cat is 55+17=41+31=72.
Hence, the complete table is shown in attached figure for the given venn diagram.
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(pls help me with this)
4. The points C and D are (4, 5) and (p, q) respectively,
a) Write down, in terms of p and q, the coordinates of the midpoint of CD.
b) Given that the midpoint of CD is (7, 1), find the coordinates of D.
A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]
B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)
A. How to determine the mid pointCoordinate of C = (4, 5)Coordinate of D = (p, q)Mid point =?Mid point = (X , Y)
X = (x₁ + x₂) / 2
X = (4 + p) / 2
Y = (y₁ + y₂) / 2
Y = (5 + q) / 2
Thus,
Mid point = (X , Y)
Mid point = [(4 + p) / 2 , (5 + q) / 2]
B. How to determine the coordinates of DMid point = (7, 1)Coordinates of D =?Mid point = (7, 1) = (X , Y)
X = (4 + p) / 2
7 = (4 + p) / 2
Cross multiply
7 × 2 = 4 + p
14 = 4 + p
Collect like terms
p = 14 - 4
p = 10
Y = (5 + q) / 2
1 = (5 + q) / 2
Cross multiply
1 × 2 = 5 + q
2 = 5 + q
Collect like terms
q = 2 - 5
q = -3
Coordinates of D = (p, q)
Coordinates of D = (10 , -3)
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To study the population of consumer perceptions of new technology, sampling of the population is preferred over surveying the entire population because ______.
Because It is quicker and fast.
Sampling:
Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but it may include simple random sampling or systematic sampling.
Sampling is the selection of a subset of the population of interest in a research study. In the vast majority of research endeavors, the participation of an entire population of interest is not possible, so a smaller group is relied upon for data collection.
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If a skydiver jumps out of an airplane and falls at 212 mph, what is the skydiver's velocity and speed?
The skydiver is falling at a speed of 212 miles per hour.
The speed of the skydiver is 212 mph.
What are Speed and Velocity?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, whereas velocity is a vector, speed is a scalar quantity.
Given:
If a skydiver jumps out of a plane and plummets to the ground while falling at 212 mph.
To Find:
Speed and acceleration of the skydiver.
Velocity is the speed with a direction, whereas speed is only a number with a speed unit at the end.
While velocity refers to the speed and direction of an object's movement, speed refers to the time rate at which an object moves along a path.
212 miles per hour is the descending velocity of the skydiver.
At 212 miles per hour, the skydiver is moving.
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i would appreciate it sm if u anyone responded
x-2(x+1)+3(x-2)+2(x-6)=0
Answer:
x = 5
Step-by-step explanation:
Simplifying the expression:x - 2(x +1) + 3(x -2) + 2(x - 6) = 0
x + (-2)*x + (-2)*1 + 3*x +3*(-2) + 2*x + 2*(-6) = 0
x - 2x -2 + 3x - 6 + 2x - 12 = 0
x - 2x + 3x + 2x - 2 - 6 - 12 = 0
Combine like terms. Like terms have same variable with same power.
4x - 20 = 0
Add 20 to both sides.
4x = 20
Divide both sides by 4
x = 20/4
x = 5
Answer:
x = 5
Step-by-step explanation:
x -2(x+1) + 3(x-2) + 2(x-6) = 0
here, we need to distribute the numbers on the outside of the parentheses to the inside numbers.
As you may know, when two numbers are in parentheses, they are to be multiplied--and it is the same idea here.
When we have a number, say 3, multiplied by parentheses, say (x - 2), we multiply all inside numbers by the outside number, which is called distributing.
We know that 3(x) = 3x, and that 3(-2) = -6, so we distribute
3(x - 2) to be 3x - 6
let's do that for all of our parentheses:
x -2(x+1) + 3(x-2) + 2(x-6) = 0
-2( x + 1 )
-2x - 2
3(x - 2)
3x - 6
2( x - 6)
2x - 12
Now, let's rewrite our problem:
x -2(x+1) + 3(x-2) + 2(x-6) = 0
x - 2x - 2 + 3x -6 + 2x - 12 = 0
First, we should combine like terms:
x - 2x + 3x + 2x - 2 - 6 - 12 = 0
(x - 2x = -x; -x + 3x = 2x; 2x + 2x = 4x)
( - 2 - 6 = -8; -8 - 12 = -20
So, we are left with:
4x - 20 = 0
At this point, we want to get x alone (so that we can find what "x" is)
4x - 20 = 0
+ 20 + 20 ( add 20 to both sides of the equation to isolate x )
4x = 20
÷ 4 ÷ 4 (divide both sides by 4 to find "1"x)
x = 5
So, we know that the value of x is 5, or x = 5
hope this helps! let me know if you need clarification on anything :)
It cost $1031 for a camping trip. You have to pay $231
to park for the entire trip and $200 per day for the
camping site.
Create the equation below to represent this situation.
The equation that represent this situation is as follows:
1031 = 231 + 200d
How to find the equation that represent the situation?It cost $1031 for a camping trip.
You have to pay $231 to park for the entire trip and $200 per day for the
camping site.
Therefore,
let
d = days on the camping site.
Therefore, the equation that represent this situation is as follows:
1031 = 231 + 200d
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determine which two of the three given triangles are similar. Find the scale factor for the pair.
The length of time needed to complete a certain test is normally distributed with mean 44 minutes and standard deviation 8 minutes. Find the probability that it will take less than 34 minutes to complete the test.
The probability that it willtake less than 34 minutes to complete the test is 0.1056
Given mean of 44 minutes and standard deviation of 8 minutes.
We have to find the probability that it will take less than 34 minutes to complete the test.
The probability lies between 0 and 1. The formula to calculate probability is number of items divided by total items but it can also be found through z test calculations.
We are using z test to find the probability.
Z=X-μ/σ
Where μ is sample mean and
σ= standard deviation
Z is z value
First we will find the p value from 34 to 44.
Z=34-44/8
=-10/8
=-1.25
P value for X<34=P(Z<-1.25)
=0.5-0.3944
=0.1056.
Hence the probability that it will take less than 34 minutes is 0.1056.
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Kady and Scott both invest £800.
Kady invests in an account that gives 15.2% compound interest per annum.
Scott invests in an account that gives 15.9% simple interest per annum.
After how many years is Kady's investment worth more than Scott's?
Answer:we smoking fredoooooooooo
Tumbleweed, commonly found in the western united states, is the dried structure of certain plants that are blown by the wind, kochia, a type of plant that turns into tumbleweed at the end of the summer is a problem for farmers because it takes nutrients away from soil that would otherwise go to more beneficial plants. scientists are concerned that ko:hia plants are becoming resistant to the most commonly used herbicide, glyphosate. in 2014, 19.7 percent of 61 randomly selected kochia plants were resistant to glyphosate. in 2017, 38.5 percent of 52 randomly selecteikochia plants were resistant to glyphosate. do the data provide convincing statistical evidence, at the leve of 0.05, that there has been an increase in the proportion of all kochia plants that are resistant to glyphosale?
Since we are dealing with a proportion, it is determined by using the z-distribution that there is insufficient evidence to draw the conclusion that the proportion of all kochia plants that are resistant to glyphosate has increased because the test statistic is less than the critical value for the right-tailed test.
In this problem, we consider that:
[tex]p_{1}[/tex] is the proportion in 2014.[tex]p_{2}[/tex] is the proportion is 2017.What are the hypothesis tested?At the null hypothesis, we test if there has been no increase, that is, the subtraction is of 0.[tex]$H_{0}: p_{2}-p_{1}=0$[/tex]
At the alternative hypothesis, we test if there has been an increase, hence:[tex]$H_{1}: p_{2}-p_{1} \neq 0$[/tex]
What is the distribution of the difference of sample proportions?The proportions and standard errors are given by:
[tex]p_{1}=0.197, s_{1}=\sqrt{\frac{0.197(0.803)}{61}}=0.0509\\p_{2}=0.385, s_{2}=\sqrt{\frac{0.385(0.615)}{52}}=0.0675[/tex]
Hence, the distribution has mean and standard error given by:
[tex]\bar{p}=p_{2}-p_{1}=0.0675-0.0509=0.0166\\s=\sqrt{s_{1}^{2}+s_{2}^{2}}=\sqrt{0.0509^{2}+0.0675^{2}}=0.0845[/tex]
What is the test statistic?It is given by:
[tex]$z=\frac{\bar{p}-p}{s}$[/tex]
In which p = 0 is the value tested at the null hypothesis, hence:
[tex]z=\frac{0.0166}{0.0845}\\$z=0.2$[/tex]
What is the decision?Considering a right-tailed test, as we are testing if the proportion is greater than a value, with a significance level of 0.05, the critical value is of [tex]$z^{*}=1.645$[/tex]There is insufficient information to establish that the fraction of all kochia plants that are resistant to glyphosate has increased because the test statistic is smaller than the crucial value for the right-tailed test.Learn More about the z-distribution here: brainly.com/question/26454209
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Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true? Check all that apply.
x > y
v > x
w = y
y < v
v = w
x < w
The statements that are true about the angle include:
x > y
w = y
y < v
How to illustrate the information?From the information, the first has legs 529m and 229m. Then tan x = 529/229. Also tan y = 529/347.
It can be seen that tan x is greater than tan y. Angles x, v, y, and w are alternate angles. Therefore, the correct options are A, C, avd D.
A weather balloon is 529 meters above the ground. Two weather stations, A and B, monitor the balloon’s progress. Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true
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Lunch costs $6.90. How much change will
Hector get from $20.00?
Answer: 22
Step-by-step explanation:
Kenny wants to fill his attic with insulation. If the insulation costs $16.75 per cubic yard, how much would it cost to fill Kenny's entire attic?
9 yd
3 yd
5 yd
4 yd
A. $904.500
B. $938.00
OC. $1,038.50
D. $1,155.75
The total cost to fill Kenny's entire attic given the cost per cubic yards is $904.50; option A
Triangular prismCost of insulation = $16.75 per cubic yard[tex]V = 1/4h \sqrt{ { - a}^{4} + 2 {ab}^{2} } + 2 {ac}^{2} - {b}^{4} + 2 {bc}^{2} - {c}^{4} [/tex]
= 1/4×9 √-4⁴ + 2(4×5)² + 2(4×3)² - 5⁴ + 2(5×3)² - 3⁴
= 9/4√256 + 2(20)² + 2(12)² - 3125 + 2(15)²- 81
= 9/4√256 + 2(400) + 3(144) - 3125 + 2(225) - 81
= 9/4√256 + 800 + 432 - 3125 + 450 - 81
= 9/4√-1268
= 54 cubic yard
Total cost to fill Kenny's entire attic = 54 × $16.75
= $904.50
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the product of two numbers is 8933. If each of the two numbers is doubled the product of these larger numbers is?
The product of two numbers when doubled, the product of these larger numbers is 35,732
Productlet
The two unknown number = x and yproduct of x and y = 8933
x × y = 8933
If each of the two numbers is doubled2x × 2y = 8933
4xy = 4(8933)
4xy = 35,732
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On a particular vehicle, the front tire makes three revolutions for every one revolution the back tire makes. How many times larger is the radius of the back tire than the radius of the front tire?
Answer:
3 times larger
Step-by-step explanation:
Front tire circumference = pi *d
rear tire is 3 times this = pi 3 d
so rear tire has radius 3x that of the front tire
Write an expression that can be used to produce vector b from vector a, and explain how you determined that expression.
The explanation regarding the vector is illustrated below.
How to illustrate the information?It should be noted that vector A with components a, b, c, can be written as (a, b, c) or in terms of unit vectors as ai + bj + ck.
In this case, the letters I, j, and k are the standard symbols for the unit vectors in the x, y, and z directions.
Therefore, if A = (3,4,5( you can write A = 3i + 4j + 5k.
If B = (1, 1, 1), you can write B = I + j + k.
Then A - B is the vector whose component are the difference in each components.
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PLEASE HELP 50 POINTS
Step-by-step explanation:
The initial velocity of a particle moving along x−axis is u (at t=0 and x=0) and its acceleration a is given by a=kx.Find the value of f(4)?
From the given graph, we can see by tracing that f(4) is -3.5
Graph of a quadratic functionThe given graph is a graph of a quadratic function with a parabola opening upwards.
According to the question, we are to find the value of y where the value of x is 4. From the given graph, we can see by tracing that f(4) is -3.5
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Can someone please help with this question. 20 points up for grabs!!
Based on the railway timetable given, the time the first train reaches Oakengates is 0815.
The time taken to reach Shrewsbury from Telford Central is 22 minutes.
What does the train timetable show?Oakengates is 2 minutes away from Telford Central so when a train leaves the latter and arrives at 0815, this is the first train to Oakengates.
If one left Telford Central at 0852, they would reach Shrewsbury at 0914 to make it:
= 0914 - 0852
= 22 minutes
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On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite
direction. The number b varies directly with the number a. For example b = 22 when a = -22. Which
equation represents this direct variation between a and b?
b=-a
-b=-a
b-a=0
b(-a) = 0
Answer:
b = -a
Step-by-step explanation:
Since a and b are equally distant to zero but in opposite directions, a and b are opposites, or additive inverses.
The sum of additive inverses is zero.
a + b = 0
b = -a
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer: No, they are not similar
Step-by-step explanation:
Similar triangles are triangles with congruent angles.
33° ≠ 32°
These triangles are not similar.
Find the common ratio for 0.1,0.01,0.001
The common ratio of the set of data is 0. 1
How to determine the common ratio
To determine the common ratio of a set of data, we have to
Divide the second term by the first term orDivide the third term by the second termFor the given set of data
0.1,0.01,0.001
Let's divide the second term by the first term
= 0. 01/ 0. 1
= 0. 1
Thus, the common ratio of the set of data is 0. 1
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20 POINTS TO WHOEVER SOLVE THIS !
Applying the linear pair theorem and the sum of interior angles of hexagon, we have:
Angle 7 = 92°
Angle 1 = 107°
What is the Linear Pair Theorem?According to the linear pair theorem/postulate, when two angles lie on a straight line, the sum of their measures equals 180 degrees.
Angle 7 lie on a straight line with 88°, therefore, applying the linear pair theorem, we have:
Angle 7 + 88 = 180
Subtract both sides by 88
Angle 7 + 88 - 88 = 180 - 88
Angle 7 = 92°
Also, using the linear pair theorem, we have:
Angle 5 = 180 - 64
Angle 5 = 116°
Angle 3 = 180 - 57
Angle 3 = 123°
Sum of interior angles of hexagon equals 720°, therefore:
Angle 1 + angle 3 + angle 5 + angle 7 + 118 + 164 = 720°
Plug in the known values
Angle 1 + 123 + 116 + 92 + 118 + 164 = 720
Angle 1 + 613 = 720
Subtract both sides by 613
Angle 1 + 613 - 613 = 720 - 613
Angle 1 = 107°
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When positive integer x is divided by positive integer y, the remainder is 9. If = 96.12, what is the value of y ? 96 75 48 25 12
Y= 75.
Lets try to solve it,
When positive integer x is divided by positive integer y, the remainder is 9
=> x=qy+9;
=> x/y=96.12
=>x=96y+0.12y (so q above equals to 96);
=>0.12y=9
=> y=75.
Hence the value of y would be 75.
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Help please you don’t know how much this means to me
[tex]db {}^{2} - ab {}^{2} = ab {}^{2} - ae {}^{2} \\ db {}^{2} = 2ab {}^{2} - ae {}^{2} \\ (ac + bc) {}^{2} = 2ab {}^{2} - ae {}^{2} \\ ac {}^{2} + bc {}^{2} + 2ac.bc = 2ab {}^{2} - ae {}^{2} \\ 2ac.bc = ab {}^{2} - ae {}^{2} [/tex]
[tex]2ac.bc = ab {}^{2} - (ac {}^{} - ce) {}^{2} \\ 2ac.bc = ab {}^{2} - ac {}^{2} + 2ac.ce - ce {}^{2} \\ 2ac.bc = ab {}^{2} - ac {}^{2} - cb {}^{2} + 2ac.ce \\ but \: ab {}^{2} - ac {}^{2} - cb {}^{2} = 0 \\ 2ac.bc = 2ac.ce \\ bc = ce \\ which \: is \: true[/tex]
can you please help me too
(a) The sample mean for:
Sample 1 is 3.4, Sample 2 is 3.4, Sample 3 is 3.6, and Sample 4 is 3.8.
(b) The range of the sample means is 0.4.
(c) The true statement from the given statements are:
The mean of the sample means will tend to be a worse estimate than a single sample mean, andThe closer the range of the sample means is to 0, the more confident they can be in their estimate.The sample mean, [tex]\bar{x}[/tex], is calculated using the formula, [tex]\bar{x} = \frac{\sum x}{N}[/tex], where N is the sample size.
The range of a data is the difference between the greatest data point and the smallest data point.
(a) Thus, the sample mean for:-
Sample 1:
= (3 + 2 + 6 + 4 + 2)/5 = 17/5 = 3.4.
Sample 2:
= (2 + 2 + 3 + 7 + 3)/5 = 17/5 = 3.4.
Sample 3:
= (6 + 4 + 2 + 2 + 4)/5 = 18/5 = 3.6.
Sample 4:
= (5 + 3 + 2 + 5 + 4)/5 = 19/5 = 3.8.
(b) The range of the sample means is 3.8 - 3.4 = 0.4.
(c) The true statement from the given statements are:
The mean of the sample means will tend to be a worse estimate than a single sample mean, andThe closer the range of the sample means is to 0, the more confident they can be in their estimate.Learn more about means and estimates at
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write the equation of a line this is parallel to y=0.5x-4 and that passes through the point (9,-6).
Answer:
[tex]y=0.5x-10.5[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is 0.5.
Substituting into point-slope form and converting to slope-intercept form,
[tex]y+6=0.5(x-9) \\ \\ y+6=0.5x-4.5 \\ \\ y=0.5x-10.5[/tex]
A sample of 66 observations will be taken from an infinite population. the population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is:_________.
Using the normal distribution, the probability that the sample proportion will be less than 0.1768 is of 0.9222 = 92.22%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].For this problem, the proportion and the sample size are given by:
p = 0.12, n = 66.
Hence the mean and the standard error are:
[tex]\mu = p = 0.12[/tex].[tex]s = \sqrt{\frac{0.12(0.88)}{66}} = 0.04[/tex]The probability that the sample proportion will be less than 0.1768 is the p-value of Z when X = 0.1768, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.1768 - 0.12}{0.04}[/tex]
Z = 1.42
Z = 1.42 has a p-value of 0.9222.
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If tanA+cotA=2, then find the value of tan^2A+cot^2A.
tan45° = cot45° = 1
---> If tanA + cotA = 2, then A is 45°.
---> tan²A + cot²A = 1² + 1² = 2
The correct answer is 2