Answers
x = 65
Step-by-step explanation:
cos theta = 25/x
cos theta = x/169
25/x = x/169
x² = 169 x 25
x = 65
The missing length x = 65, using the Pythagoras Theorem.
What is the Pythagoras Theorem?
According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
How to solve the question?In the question, we are asked to find the value of x.
In the right triangle ABC, by Pythagoras' Theorem,
AC² + BC² = AB²,
or, x² + BC² = (144 + 25)²,
or, BC² = 169² - x² ... (i).
In the right triangle ACD, by Pythagoras Theorem,
AD² + DC² = AC²,
or, 25² + DC² = x²,
or, DC² = x² - 25² ... (ii).
In the right triangle BCD, by Pythagoras Theorem,
BD² + DC² = BC²,
or, 144² + x² - 25² = 169² - x² {Substituting BC² = 169² - x² from (i) and DC² = x² - 25² from (ii)},
or, x² + x² = 169² + 25² - 144² {Rearranging},
or, 2x² = 28561 + 625 - 20736,
or, 2x² = 8450,
or, x² = 4225,
or, x = √4225 = 65.
Thus, the missing length x = 65, using the Pythagoras Theorem.
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Related Questions
the probability that a customer of a network operator has a problem about you needing technical staff's help in a month is 0.01. This operator installs internet for 500 households in a residential area a, Calculate the average number of households in this residential area having internet problems in a certain month
b, Calculate the probability that in 6 consecutive months there is only one month that no customer in this area has a network problem that needs the help of technical staff
Answers
Answer:
(a) average calls = 5
(b) probability that there is exactly one call in 6 consecutive monts = 0.038
Step-by-step explanation:
Let event of a customer requiring help in a particular month = H
and event of a customer not requiring help in a particular month = ~H
Given
p= 0.01, therefore
Number of households, n = 500.
Binomial distribution:
x = number of households requiring help in a particular month
P(x,n,p) = C(x,n)*p^x*(1-p)^(n-x)
where
C(x,n) = n!/(x!(n-x)!) is the the number of combinations of x objects out of n
(a) Average number of households requiring help = np = 500*0.01 = 5
(b)
Probability that there are no calls requiring help in a particular month
P(0), q= C(0,n)*p^0(1-p)^(n-0)
= 1*1*0.99^500
= 0.006570483
Applying binomial probability over six months,
q = 0.006570483
n = 6
x = 1
P(x,n,q)
= C(x,n)*q^x*(1-q)^(n-x)
= 6!/(1!*5!) * 0.006570483^1 * (1-0.006570483)^5
= 0.038145
Therefore the probability that in 6 consecutive months there is exactly one month that no customer has called for help = 0.038
Assessment
Cymraeg
Isaac plans a hidden treasure game.
Treasure is hidden under the sand in a tray. The tray for the sand is a cuboid: 0.8 m long,
0.6 m wide and 0.1 m deep. Sand comes in 25 kg bags with an approximate volume of
17,000 cm?
How many bags must Isaac buy to completely fill the tray?
3
Isaac needs to buy
bags of sand.
2
Answers
Answer:
So, to fill the tray completely , he needs 3 bags of sand.
Step-by-step explanation:
Tray dimensions,
length = 0.8 m
Width = 0.6 m
height = 0.1 m
Volume of one sand bag = 17000 cm^3
Let the volume of the tray is V.
V = length x idth x height
V = 0.8 x 0.6 x 0.1 = 0.048 m^3
Number of sand bags
[tex]n=\frac{0.048}{17000\times 10^{-6}}\\\\n = 2.82[/tex]
So, to fill the tray completely , he needs 3 bags of sand.
It costs $100 to join a fitness center plus a monthly fee you spent $700 last year at the fitness center how much was the monthly fee
Answers
Answer:
58.3
Step-by-step explanation:
divide 700 by 12
Answer:
$50
Step-by-step explanation:
The equation for this is:
700 = 12m + 100, where $700 is the total cost, m is the monthly fee, 12 is the number of months in a year, and $100 is the starting fee
Solve the equation:
700 = 12m + 100
12m = 600
m = 50
4.27cm rounded to the nearest cm
Answers
Formula: multiply the value in meters by the conversion factor '100'.
So, 4.27 meters = 4.27 × 100 = 427 centimeters.
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]4.27\text{cm} \approx\boxed{4\text{cm}}[/tex]
»»————- ★ ————-««
Here’s why:
We would locate the whole number and look at the number to the right. In this case, we would look at the '2' in the tenths place.Since it is less than or equal to 4, we would round down.⸻⸻⸻⸻
Recall the Rounding Rules:
If the digit to the right is less than or equal to 4, we round down.If the digit is greater than or equal to 5, we round up.⸻⸻⸻⸻
[tex]\underline{4.27cm}\\\\\rightarrow2\leq 4\\\\\boxed{4.27cm \approx 4cm}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 49
1. Find the first term of the progression and the common difference
2. Find the value of n
Answers
Step-by-step explanation:
everything can be found in the picture
he Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the Quality of Management and the Reputation of the Company for over world-wide corporations. Both the Quality of Management and the Reputation of the Company were rated on an Excellent, Good, and Fair categorical scale. Assume the sample data for respondents below applies to this study. Excel File: data12-13.xlsx a. Use level of significance and test for independence of the quality of management and the reputation of the company. Compute the value of the test statistic (to 2 decimals). Do not round intermediate calculations. The -value is - Select your answer - What is your conclusion? - Select your answer - b. If there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer.
Answers
Answer:
Following are the solution to the given question:
Step-by-step explanation:
[tex]H_0:[/tex] Management quality and corporate reputation are independent.
[tex]H_1:[/tex] Management quality and corporate reputation are not independent.
Test statistic:
[tex]\to \chi^2 = \frac{\sum (O-E)^2}{E}[/tex]
[tex]= 0.71429 + 0.0102 +2.8809+0.625+1.75 +0.3333 +0+3.2143+7.5\\\\= 17.02806[/tex]
The critical [tex]\chi^2[/tex] for[tex]df = (r-1)(c-1) = (3-1)(3-1)= 4[/tex] and [tex]\alpha = 0.05[/tex] is [tex]\chi^2= 9.4877[/tex]
Test statistic:
[tex]17.02806 > 9.4877[/tex] therefore rejecting the null hypothesis [tex]H_0[/tex].
p-value[tex]= 0.001909[/tex]
Interpretation:
There is no internal governance quality as well as the reputation of the organization.
Instructions: Find the value of x
I’ll mark brainliest please help
Answers
The little lines theu each section are telling you all those sections are identical, which mean they are the same length.
You are told one section is 10, which means x is also 10
X = 10
A rectangular picture is four times as long as it is wide. The area of the picture is 1024 square inches. Find the
dimensions of the picture.
Width = 16 inches, Length = 64 inches
Width = 64 inches, Length = 64 inches
Width = 16 inches, Length = 16 inches
Width = 64 inches, Length = 16 inches

Answers
find the volume of the cone 3.4 m x 5.5 m
Answers
Answer:
63,5
Step-by-step explanation:
pi r bình pnhân hươnh g
Which ordered pair is a solution to the system of inequalities? y< 3x y< 5
Answers
Answer:
Step-by-step explanation:
Split it into two:
Y<3x
Y<5
X = 1
Y = 3
(1,3)
X = 2
Y = 6
(2, 6)
Plot the line up to y = 4.999999999999999999999 and not higher.
Answer:
Plot the line up to y = 4.999999999999999999999 and not higher
When choosing a four-number PIN.
(personal identification number)
how many different PINS are possible?
(The choice of digits 0-9 are available for each number.)
Answers
Answer:
10,000 different PINS are possible
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
In this question:
Four each digit on the PIN, there are 10 possible outcomes. The digits are independent. So, by the fundamental counting principle:
[tex]T = 10^4 = 10000[/tex]
10,000 different PINS are possible
Q- getting a number greater than 3 or an odd number?
Answers
Step-by-step explanation:
So one's chance of getting a number greater than 3 is 3 chances out of 6 numbers that could be rolled or 1/2. Then we determine what the chances are of getting an ODD number. That includes 1, 3, & 5. So one's chance of getting an odd number is 3 chances out of the 6 numbers on the die, which is also 1/2.
Which is the simplified form of m-8pº?
Answers
Answer:
m-8
Step-by-step explanation:
p⁰ = 1
Help please i will mark brainlist !!!!
Answers
Answer:
You need to add the numbers up
0.4 +0.2+0.1=0.7
1-0.7=0.3
Ans=0.3
How do I solve this and answer?
Answers
Step-by-step explanation:
at first solve first triangle with Pythagorean solving witch it c²=a²+b²
you have to change a bit so it will be c²-b²=a²
you start with 8 and 10 triangle and then you get line which is in the middle and yo udo just the same with triangle 8 and the solved side and you get x in the second triangle you have to use c²-a²=b²
Describe and correct the error in finding DC
Answers
Answer:
DC = 2
Step-by-step explanation:
The wrong equation was used.
The right equation to use based on the midsegment theorem of a trapezoid is:
MN = ½(AB + DC)
MN = 8
AB = 14
Substitute
8 = ½(14 + DC)
Multiply both sides by 2
8*2 = ½(14 + DC)*2
2*8 = 14 + DC
16 = 14 + DC
16 - 14 = 14 + DC - 14
2 = DC
DC = 2
The Madison Cosmetics Company has developed a new women's facial cleanser that they believe is superior to those currently on the market in the $5 - $10 range. They wish to test the cleanser against the two current best-sellers.
A. Identify a potential problem with using a completely randomized experimental design to test the cleanser. Explain.
B. The company executives decide to design and carry out a block design experiment to test the new cleanser against its competition. Choose an appropriate blocking scheme for the experiment and justify your choice.
C. Should the company put a control group into the experiment? Why or why not?
D. Could the experiment be a double-blind experiment? Explain.
Answers
Answer:
a. there could be a problem of high error
b. randomized block design can remove the issue of heterogeneity
c. yes they should
d, yes it could
Step-by-step explanation:
a. if their is a lack of homogeneity among the sample population, then the results that would be obtained are going to be with increased experimental error.
b. given the number of treatment, the randomized block design technique can be done. This would then remove the issue of heterogeneity. It also gives more information and the results from the test are easier. Even in the presence of missing data, the missing plot technique can be employed.
c. when a control group is used, it makes easier the examination of the market research in a more effective way.
d. Yes it could be a double blind one. This would help to take away the problem of bias.
4. Solve the following system of equations for x.
2x + 3y = -14
y = 6x + 22
A. X = -2
B. X = 2
C. X = -4
D. X = 4
Answers
We are given the system of equations -:
[tex] \large{ \begin{cases} 2x + 3y = - 14 \\ y = 6x + 22 \end{cases}}[/tex]
Since the second equation is y-isolated equation. It can be substituted as y = 6x+22 in the first equation.
[tex] \large{2x + 3(6x + 22) = - 14}[/tex]
Expand 3 in the expression so we can combine like terms and isolate x-variable.
[tex] \large{2x + 18x + 66 = - 14}[/tex]
Then combine like terms.
[tex] \large{20x + 66 = - 14}[/tex]
Get rid of 66 from the left side by subtracting both sides by itself.
[tex] \large{20x + 66 - 66 = - 14 - 66} \\ \large{20x = - 80}[/tex]
To finally isolate the variable, divide both sides by 20 so we can leave x only on the left side.
[tex] \large{ \frac{20x}{20} = \frac{ - 80}{20} }[/tex]
Simplify to the simplest form.
[tex] \large{x = - 4}[/tex]
Normally, we have to find the y-value too but since we only find x-value. The answer is x = -4.
Answer
x = -4I hope this helps! If you have any questions or doubts regarding my answer, explanation or system of equations, feel free to ask!
Answer:
A. x = -2
C. x = -4
Step-by-step explanation:
y = 6x + 22
2x + 3•(6x+22) = -14
20x = - 80
x = -4
y = 6x+22
y = 6(-4)+22 = -2
Can someone answer with steps and explanation? Thanks.
Answers
Answer:
A dilation by a factor of three about Point T followed by a translation of two units downwards.
Step-by-step explanation:
When transforming functions, we will reflect/dilate the figure first and then translate it. This is directly from the order of operations.
Since we are trying to determine the transformation that was performed, we can try to map ΔS'T'U' onto ΔSTU. We can start by translating the figure and then determining any reflections/dilations.
First, we can translate ΔS'T'U' up two units to map T' onto T. This is represented by the black triangle in the image below. Let the black triangle be ΔS''T''U''. (T'' and T are the same point.)
Next, notice that from Point T'' to U'', we move nine units right and six units up.
From Point T to Point U, we move three units right and two units up.
Likewise, from Point T'' to S'', we move six units left and nine units up.
From Point T to Point S, we move two units left and three units up.
Therefore, to map ΔS''T''U'' onto ΔSTU, we dilate ΔS''T''U'' about Point T by a factor of 1/3.
Hence, by reversing the transformations, to acquire ΔS'T'U', we can see that we will dilate ΔSTU by a factor of three about Point T and then a perform a translation of two units downwards.
Evaluate 7!
Answers shown are:
A-120
B-40,320
C-5,040
Answers
Answer:
C) 5040
Step-by-step explanation:
[tex]7!=7*6*5*4*3*2*1=5040[/tex]
Answer:
5040
Step-by-step explanation:
! means take multiply that number and all the number down to 1
7! = 7*6*5*4*3*2*1
=5040
Part A: Factor x2b2 − xb2 − 6b2. Show your work.
Part B: Factor x2 + 4x + 4. Show your work.
Part C: Factor x2 − 4. Show your work
Answers
Answer:
A.2b2(x2-x-3)
B.x2+2x+2x+4
=x(x+2)+2(x+2)
=(x+2)(x+2)
C.x2-2^2
=(x+2)(x+2)
Suppose the mean percentage in Algebra 2B is 70% and the standard deviation is 8% What percentage of students receive between a 70% and 94% enter the value of the percentage without the percent sign
Answers
Answer:
49.87
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Suppose the mean percentage in Algebra 2B is 70% and the standard deviation is 8%.
This means that [tex]\mu = 70, \sigma = 8[/tex]
What percentage of students receive between a 70% and 94%
The proportion is the p-value of Z when X = 94 subtracted by the p-value of Z when X = 70. So
X = 94
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{94 - 70}{8}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a p-value of 0.9987.
X = 70
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 70}{8}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5.
0.9987 - 0.5 = 0.4987.
0.4987*100% = 49.87%.
So the percentage is 49.87%, and the answer, without the percent sign, is 49.87.
Based on the Pythagorean theorem , find the missing length for each of the given right triangles
Answers
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the right trianglea are not given. The general explanation is as follows.
Using Pythagoras Theorem, we have:
a² = b² + c²
Where:
a => hypotenuse
Assume that the opposite and the adjacent sides are given as 3 and 4, respectively.
The hypotension becomes
a² = 3² + 4²
a² = 9 + 16.
a² = 25
Take square roots.
a = 5
If any of the other side lengths is missing; you make that side the subject and then solve.
A company manufactures two products. Market research and available resources require the following
constraints:
• The number of units of product A manufactured, 2, is at most 500 units more than twice the number
of units of product B. y.
• The square of the company's profit is equal to the sum of 35 times the number of product A units
sold and 50 times the number of product B units sold.
If the company expects weekly profits to exceed $22,500, which pair of inequalities represents these
constraints?
will give brainliest + 50 points :)
Answers
The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of product A and y represent the number of product B, hence:
x ≤ 500 + 2y (1)
Also:
35x + 50y > 22500² (2)
The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²
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A rectangle has side lengths (x +5) feet and (2x−3) feet. Write a linear expression in simplest form to represent the perimeter. Find the perimeter if the value of x is 6 feet.
Answers
Answer:
6x+4 ft
40 ft
Step-by-step explanation:
The perimeter of a rectangle is
P = 2(l+w)
= 2( x+5 + 2x-3)
Combine like terms
= 2(3x+2)
Distribute
=6x+4
Let x= 6
= 6*6+4
= 36+4
= 40
5a + 4b = 31
5a + 6b = 39
What is a and what is b
Answers
Answer:
a = 3 and b = 4
Step-by-step explanation:
5a + 4b = 31 --(1)
5a + 6b = 39 --(2)
(2) - (1) : 2b = 8
b = 4 -- (3)
Substituting (3) into (1),
5a + 16 = 31
5a = 15
a = 3 -- (4)
Therefore, a = 3 and b = 4
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Have a nie day!
What are some easy ways to find the value of
(2017^4−2016^4)/(2017^2+2016^2) without calculator
Answers
Answer:
Step-by-step explanation:
[tex]\frac{2017^4 - 2016^4}{2017^2 + 2016^2}[/tex]
[tex]= \frac{(2017^2 - 2016^2)(2017^2 + 2016^2)}{2017^2 + 2016^2}[/tex]
[tex]= (2017^2 - 2016^2)[/tex]
[tex]= (2017 - 2016)(2017 + 2016)\\= 4033[/tex]
A man at ground level measures the angle of elevation to the top of the building to
be 87°. If at this point, he is 20 meters away from the building, what is the height of
the building?
Answers
Answer:
The bulding is 381,623 meters high.
Step-by-step explanation:
To dertermine the height of the bulding I would use tanα = rectangulair side / closest rectangulair side.
19,08 = the height/ 20m.
<=> 19,08.20m= the height = 381,623 m
El perro de Antonia debe comer 0,48 kg de alimento cada día. ¿Cuánto alimento necesita para 30 días?
Answers
Answer:
Amount of food need for 30 days = 14.4 kilogram
Step-by-step explanation:
Given information:
Amount of food dog eat each day = 0.48 kilogram
Find:
Amount of food need for 30 days
Computation:
⇔ Amount of food need for 30 days = Amount of food dog eat each day x number of days
⇔ Amount of food need for 30 days = 0.48 x 30
Amount of food need for 30 days = 14.4 kilogram
14.4 kilogram is right answer.
Consider functions f, g, and h.
F(x) = 3x^3 + 9x^2 al- 12x g(x) = x - 1 h(x) = 3x2 + 12x
Which expression defines function h?
Answers
The relation between the functions f(x), g(x), and h(x) will be f(x)/g(x) is equal to h(x). Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The functions are given below.
f(x) = 3x³ + 9x² - 12x
g(x) = x - 1
h(x) = 3x² + 12x
The function f(x) can be written as
f(x) = 3x(x² + 3x - 4)
f(x) = 3x(x² + 4x - x - 4)
f(x) = 3x(x + 4)(x - 1)
f(x) = (x - 1)(3x² + 12)
Then divide the function f(x) by the function g(x), then we have
f(x) / g(x) = (x - 1)(3x² + 12) / (x - 1)
f(x) / g(x) = (3x² + 12)
f(x) / g(x) = h(x)
More about the function link is given below.
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Answer:
B
Step-by-step explanation:
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