Answers
9514 1404 393
Answer:
x = (8/9)(4 +√7) ≈ 5.9073
Step-by-step explanation:
Maybe you want to know the value of x.
The Pythagorean theorem can be used to find the length of the bottom side of the right triangle. It is ...
bottom = √((5x)² -(3x)²) = √(16x²) = 4x
Then the cosine of the angle at lower left is ...
cos(α) = Adjacent/Hypotenuse
cos(α) = 4x/5x = 4/5
Now, the law of cosines can be used to find x. Using the angle whose cosine we just found, we have ...
(4x)² = (5x)² +8² -2(5x)(8)cos(α)
16x² = 25x² +64 -80x(4/5)
9x² -64x +64 = 0 . . . . . put in standard form
The quadratic formula can be used to find the solutions.
x = (-(-64) ±√((-64)² -4(9)(64)))/(2(9))
x = (64 ±√1792)/18 = (32 ±8√7)/9 ≈ {1.204, 5.907}
In this context, only the larger solution makes sense.
x = (8/9)(4 +√7) ≈ 5.9073
_____
Formulas used
Law of Cosines
For sides a, b, c and angle C opposite side c, ...
[tex]c^2=a^2+b^2-2ab\cdot\cos(C)[/tex]
Quadratic formula
For quadratic ax²+bx+c=0, the solutions are ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Pythagorean theorem
For legs a, b, and hypotenuse c of a right triangle, ...
c² = a² + b²
_____
Alternate solution
As an alternative to using the Law of Cosines, you can define "y" to be the length of the dashed bottom leg of the triangle whose hypotenuse is 4x. Two equations can be written using y and the Pythagorean theorem for the right triangles in which y is all or part of a leg. This set of equations can be solved for x to get the same result as the one shown above.
Related Questions
I've been asking since yesterday :(
Candace is designing a rectangular garden. The garden's diagonal must be 37.7 feet, and the ratio between the garden's base and height must be 12:5. Find the length of the garden's base and height. The garden's base is feet and its height is
Answers
Answer:
Step-by-step explanation:
let the base=12x
and height=5x
(12x)²+(5x)²=37.7²
144x²+25x²=37.7²
169x²=37.7²
(13x)²=37.7²
13x=37.7
x=37.7/13=2.9
base=12×2.9=34.8 ft
height=5×2.9=14.5 ft
Ms. Clark is building a patio that is 4 yards long and 3 yards wide. She has enough bricks to cover an area of 14 square yards. Does Ms. Clark have enough bricks to build the patio? Explain.
Answers
Answer:
DONT CLICK THE LINK!!!! IT IS A BOT. THEY WILL. HACK.
Step-by-step explanation:
Given, we know that she has 14 bricks.
We also know that the patio is 4 yards long and 3 yards wide. If we multiply those two numbers together we get 12.
So, if we do the math 14-12=2 bricks left over.
Therefore, she will have enough bricks to build the patio.
What is the surface area of the right prism below? A 432 sq units B. 448 sq units C. 480 sq units D. 400 sq units
Answers
[tex]\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}[/tex]
D. 400 sq units
ThanksHope it helpsThe surface area of the right prism given below is 432 square units.
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Given a right prism.
The right prism consists of three rectangular faces and two triangular faces.
Area of a triangular face = 1/2 × 8 × 6 = 24
Area of two triangular faces = 2 × 24 = 48 square units
Area of rectangular faces = (10 × 16) + (8 × 16) + (6 × 16)
= 384 square units
Total area of the prism = 48 square units + 384 square units
= 432 square units
Hence the total area of the prism is 432 square units.
Learn more about Surface Area here :
https://brainly.com/question/29298005
#SPJ7
What are the values of the coefficients and constant term of 0 = 4 - 7x2 + x in standard form?
a =
b =
C=
Answers
Answer:
a = -7
b = 1
c = 4
Step-by-step explanation:
0 = 4 - 7x²+ x
-7x²+x+4 = 0
But
ax²+bx + c = 0
a = -7
b = 1
c = 4
Answer:
-7, 1, 4
Step-by-step explanation:
WILLL MARK BRAINLIEST IF GOTTEN RIGHT
Answers
Sorry for the changing answers, did the question too fast and misinterperted the diagram. The answer below is the correct one.
Answer:
mUC=70°
Step-by-step explanation:
The angle (87) formed by two chords (US and TS) is half the sum of the intercepted arcs(104 and mUC):
87=(1/2)(104+mUC)
174=104+mUC
mUC=70°
Find the median of the dot plot below 5 6 7 8 9 10 11 12 13
Answers
Answer:
The median is 9
Step-by-step explanation:
Answer:
Hey love! Answer: 9
Step-by-step explanation:
these are the numbers 5 6 7 8 (9) 10 11 12 13
the median is simply just the one in the middle so this one is 9 because it has 4 numbers in front and 4 numbers after
Hope this helps!
Explain how you found your answer
Answers
Answer:
29°
Step-by-step explanation:
151° + a=180°
We know the sum of angles in a straight line is 180°
a= 180°-151°
The sign changed as it changed sides
a= 29°
does the graph of this equation widen or narrow from the parent function? g(x)=3/4(x-5)^2+12
Answers
9514 1404 393
Answer:
widen
Step-by-step explanation:
The vertical scale factor is 3/4, so the vertical extent is shortened at a given x-value distance from the axis of symmetry. That will give the appearance of making the parabola (slightly) wider.
Answer:
Widen is the answer.Step-by-step explanation:
#CarryOnLearningWhat’s the slope???? Please help meee!
Answers
Answer:
The slope is 0.
Step-by-step explanation:
Suppose we have two points in a data set, the slope is given by the change in the output divided by the change in the input.
In this question:
Two points: (0,-20) and (1,-20)
Change in the output: -20 - (-20) = -20 + 20 = 0
Change in the input: 1 - 0 = 1
Slope: 0/1 = 0
The slope is 0.
What is the slope of the line graphed below? (-1,3) (-2,-1)
Answers
Answer:
the slope of (-1,3) (-2,-1) is 4
At the beginning of the school year, Jamie had $500 in her savings account. She wants to have at least $200 left in the account at the end of the school year. Each week, she withdraws $30 for spending money. To determine how many weeks she can spend $30, Jamie wrote and solved this inequality.
500 − 30x ≥ 200
−500 −500
−30x ≥ −300
x ≥ 10
Review Jamie’s work. What was her error?
Answers
Her error was that she misplaced the numbers
-30x ≥ -300
its supose
to be -30x ≥ 200
Answer:
Jamie should have reversed the inequality when using the division property of inequality.
Step-by-step explanation:
The cost of a spa treatment is $42 and there is sales tax of 6%. What is the total cost of the spa treatment?
Answers
Answer:
$52.92 has been spent in total for spa treatment and this amount includes a sales tax of $2.52 and a tip of $8.40.
Step-by-step explanation:
Cost of the spa treatment = $42
Percentage of sales tax = 6%
Percentage of tips = 20%
Normally the tips amount is calculated before adding sales tax.
Then
Amount of tips given = (20/100) * 42
= (1/5) * 42
= 8.40 dollars
Amount of sales tax taken = (6/100) * 42
= 252/100
= 2.52 dollars
Then
The total amount spent for spa treatment = (42 + 8.40 + 2.52) dollars
= 52.92 dollars
In triangle ABC, m∠A=(2x+2)∘, m∠C=54∘, and the exterior angle at B is (4x)∘.
Triangle A B C. Angle A is 2 X plus 2 degrees, angle C is 54 degrees, & the exterior angle at B is 4 X degrees.
© 2020 StrongMind. Created using GeoGebra.
What is the measure of angle A?
58∘
112∘
28∘
68∘
Answers
Answer:
112 ^0
Step-by-step explanation:
cant explains it very well
jada uses a pitcher to fill a pot of water. the pitcher holds 8/10 liter of water. it takes 12 full pitchers of water to fill the pot. what is the total amount of water that the pot holds?
Answers
Answer:
The pot can hold 9 6/10 liters of water
Step-by-step explanation:
Since you know that the pitcher can hold 8/10 liters of water and that Jada has to fill the pitcher 12 times to fill the pot you would first convert the 8/10 liters that the pitcher can hold to a decimal so that would become 0.8 liters of water and then you would multiply the 0.8 by 12 to get 9.6 liters of water and then you can convert that back to a fraction which would be 9 6/10 liters of water. So the pot can hold 9 6/10 liters of water
You have been given the task of designing a study concerning the lifetimes of five different types of electric motor. The initial question to be addressed is whether there are differences in mean lifetime among the five types. There are 20 motors, four of each type, available for testing. A maximum of five motors can be tested in a day. The ambient temperature differs from day to day, and this can affect motor lifetime.
a. Describe how you would choose the five motors to test each day. Would you use a completely randomized design? Would you use any randomization at all?
b. If X;j represents the measured lifetime of a motor of type i tested on day j, express the test statistic for testing the null hypothesis of equal lifetimes in terms of the Xir
Answers
Answer:
a-As the only factor of interest is type of electric motor, thus instead of using 1-factor randomization, a randomized block design is used where at maximum one motor of each type is tested every day.
b- The test statistic is given as
[tex]F_{I-1,(I-1)(J-1)}=\dfrac{12\left(\Sigma^{5}_{i=1}\bar{X}^{2}_{i.}-IJ\bar{X}^2_{..}\right) }{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}[/tex]
Step-by-step explanation:
a-
This is done such that the days are considered as blocks and the randomization is only occuring within the block. The order of testing is random. However the condition is implemented such that one motor of each type is tested each day.
b-
The F-Value is given as
[tex]F-Value=\dfrac{MSA}{MSAB}[/tex]
Here MSA is given as
[tex]MSA=\dfrac{J\Sigma^I_{i=1}(\bar{X}_{i.}-\bar{X}_{..})^2}{I-1}[/tex]
Here
I is the number of types which is 5J is the number of motors of each type which is 4[tex]\bar{X}_{i.}[/tex] is the row-wise mean which is given as [tex]\bar{X}_{i.}=\dfrac{1}{J}\Sigma^J_{j=1}X_{ij}[/tex][tex]\bar{X}_{..}[/tex] is the sample grand mean which is given as [tex]\bar{X}_{..}=\dfrac{1}{IJ}\Sigma^I_{i=1}\Sigma^J_{j=1}X_{ij}[/tex]Similarly MSAB is given as
[tex]MSAB=\dfrac{\Sigma^I_{i=1}\Sigma^J_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{(I-1)(J-1)}[/tex]
Here
I is the number of types which is 5J is the number of motors of each type which is 4[tex]\bar{X}_{i.}[/tex] is the row-wise mean which is given as [tex]\bar{X}_{i.}=\dfrac{1}{J}\Sigma^J_{j=1}X_{ij}[/tex][tex]\bar{X}_{..}[/tex] is the sample grand mean which is given as [tex]\bar{X}_{..}=\dfrac{1}{IJ}\Sigma^I_{i=1}\Sigma^J_{j=1}X_{ij}[/tex][tex]\bar{X}_{.j}[/tex] is the column-wise mean which is given as [tex]\bar{X}_{.j}=\dfrac{1}{I}\Sigma^I_{i=1}X_{ij}[/tex][tex]X_{ij}[/tex] is the any motor j of type iBy putting these values and simplifying, equation becomes:
[tex]F-Value=\dfrac{MSA}{MSAB}\\\\F-Value=\dfrac{\dfrac{J\Sigma^I_{i=1}(\bar{X}_{i.}-\bar{X}_{..})^2}{I-1}}{\dfrac{\Sigma^I_{i=1}\Sigma^J_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{(I-1)(J-1)}}\\\\F-Value=\dfrac{\dfrac{4\Sigma^5_{i=1}(\bar{X}_{i.}-\bar{X}_{..})^2}{5-1}}{\dfrac{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{(5-1)(4-1)}}\\\\[/tex]
This is further simplified as
[tex]F-Value=\dfrac{\dfrac{4\Sigma^5_{i=1}(\bar{X}_{i.}-\bar{X}_{..})^2}{4}}{\dfrac{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{12}}\\\\F-Value=\dfrac{\Sigma^5_{i=1}(\bar{X}_{i.}-\bar{X}_{..})^2}{\dfrac{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{12}}\\\\[/tex]
The numerator can be written as
[tex]F-Value=\dfrac{\Sigma^{5}_{i=1}\bar{X}^{2}_{i.}-IJ\bar{X}^2_{..}}{\dfrac{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{12}}\\\\F-Value=\dfrac{12(\Sigma^{5}_{i=1}\bar{X}^{2}_{i.}-IJ\bar{X}^2_{..})}{{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}}\\[/tex]
what is the measure of angle a enter your answer as a decimal in the box round only your final answer to the nearest hundredth
Answers
ANSWER.
The measure of angle A is 53.13°.
STEP BY STEP
Given,
ABC is a triangle,
In which m∠CBA = 90°, AB = 3 cm, BC = 4 cm and CA = 5 cm,
By the law of sine,
( By cross multiplication )
By substituting the values,
( sin 90° = 1 )
Hence, the measure of angle A is 53.13°.
which equation is equivalent to xy (3x + 2y) = 4
Answers
Answer:
the value x is 0 and the value of y is 2
which equation represents a line that passes through (5,4) with a slope of 2/5
Answers
Answer:
y = 2/5x +2
Step-by-step explanation:
y - 4 = 2/5(x -5)
y-4 = 2/5x -2
y = 2/5x +2
How many solutions are there to the system
{y = 1/3x + 5
{x + 3y = 6
Answers
Answer:
there are 3 solutions which can be done by substitution method, elimination method,graphical method, 9f you need solution than contact me 8n comments I can show solutions
app 19.study
Tools
Tools
Probability
Jacob performed an experiment with a weighted die, numbered 1 to 6. He rolled the die 125 times and recorded the results.
Complete the table below.
0.232
37
24
0.176
18
0.048
0.104
22
Result of Roll
Frequency
Experimental
Probability
1
2
13
3
0.144
4
29
5
0.296
6
Reset
Submit
Answers
Answer:
[tex]1 \to 22 \to 0.176[/tex]
[tex]2 \to 13 \to 0.104[/tex]
[tex]3 \to 18 \to 0.144[/tex]
[tex]4 \to 29 \to 0.232[/tex]
[tex]5 \to 37 \to 0.296[/tex]
[tex]6 \to 6 \to 0.048[/tex]
Step-by-step explanation:
Given
[tex]n = 125[/tex]
See attachment for proper table
Required
Complete the table
Experimental probability is calculated as:
[tex]Pr = \frac{Frequency}{n}[/tex]
We use the above formula when the frequency is known.
For result of roll 2, 4 and 6
The frequencies are 13, 29 and 6, respectively
So, we have:
[tex]Pr(2) = \frac{13}{125} = 0.104[/tex]
[tex]Pr(4) = \frac{29}{125} = 0.232[/tex]
[tex]Pr(6) = \frac{6}{125} = 0.048[/tex]
When the frequency is to be calculated, we use:
[tex]Pr = \frac{Frequency}{n}[/tex]
[tex]Frequency = n * Pr[/tex]
For result of roll 3 and 5
The probabilities are 0.144 and 0.296, respectively
So, we have:
[tex]Frequency(3) = 125 * 0.144 = 18[/tex]
[tex]Frequency(5) = 125 * 0.296 = 37[/tex]
For roll of 1 where the frequency and the probability are not known, we use:
[tex]Total \ Frequency = 125[/tex]
So:
Frequency(1) added to others must equal 125
This gives:
[tex]Frequency(1) + 13 + 18 + 29 + 37 + 6 = 125[/tex]
[tex]Frequency(1) + 103 = 125[/tex]
Collect like terms
[tex]Frequency(1) =- 103 + 125[/tex]
[tex]Frequency(1) =22[/tex]
The probability is then calculated as:
[tex]Pr(1) = \frac{22}{125}[/tex]
[tex]Pr(1) = 0.176[/tex]
So, the complete table is:
[tex]1 \to 22 \to 0.176[/tex]
[tex]2 \to 13 \to 0.104[/tex]
[tex]3 \to 18 \to 0.144[/tex]
[tex]4 \to 29 \to 0.232[/tex]
[tex]5 \to 37 \to 0.296[/tex]
[tex]6 \to 6 \to 0.048[/tex]
The waiting time W for accessing one record from a computer database is a random variable uniformly distributed between 0 and 28 milliseconds. The read time R for moving the information from the disk to the main memory is 7 milliseconds. The random variable X milliseconds is the total access time (waiting time + read time) to get one block of information from the disk. Before performing a certain task, the computer must access 6 different blocks of information from the disk. (Access times for different blocks are independent of one another.). Compute the followings:
a. E[X]
b. Vae[X]
c. E[A]
Answers
Solution :
Let
Waiting time for accessing one record = W
Read time for moving the information = R
Total time for accessing to get one block of information = X
So, the random variable X is defined as :
X = W + R
= W + 7
a). Calculating E(X)
E(X) = E(W+7)
= E(W) + 7
[tex]$=\int_{0}^{28}\frac{1}{28-0}w dw +7$[/tex]
[tex]$=\frac{1}{28}\int_{0}^{28}w dw +7$[/tex]
[tex]$=\frac{1}{28}\left[\frac{w^2}{2}\right]_0^{28}+7$[/tex]
[tex]$=\frac{1}{56}\left[28^2\right]+7$[/tex]
[tex]$=\frac{28}{2}+7$[/tex]
= 14 + 7
= 21
b). Calculating Var(X)
V(X) = V(W+7)
= V(W)+0
= V(W)
= [tex]$E(W^2)-[E(W)]^2$[/tex]
[tex]$=\int_0^{28}\frac{1}{28}w^2 dw-[14]^2$[/tex]
[tex]$=\frac{1}{28}\left[\frac{w^3}{3}\right]_0^{28}-196$[/tex]
[tex]$=\frac{1}{28\times 3}\times 28^3-196$[/tex]
[tex]$=\frac{28\times 28}{3}-196$[/tex]
= 65.33
c). Considering A is the random variable that can be defined as follows:
A = 6(W+7)
=6W + 42
So calculating E(A)
E(A) = E(6W + 42)
= E(6W) +42
= 6E(W) + 42
= 6(14) + 42
= 84 + 42
= 126
I need help please tell the right answer
Answers
Answer: 47.6 is your answer hope this helped
plz make brainly
Step-by-step explanation:
Answer:
36 - 4
Step-by-step explanation:
(6x - 2)(6x + 2)
= (6x)(6x) + (6x)(-2) + (2)(6x) + (-2)(2)
= 36 - 12x + 12x - 4
= 36 - 4Step-by-step explanation:
PLEASE HELP PLEASE (dont do links)
Answers
Answer:
B
-2(0)²+24(0)-54
= -54
Answer:
I think its C
Step-by-step explanation:
y intercepts (0,-54)
The number of hours per week that the TV is turned on is determined for each family in a sample.
The mean of the data is 37 hours.
The median is 33.2 hours.
Twenty four of the families in the sample watched TV for less than 22 hrs per week.
The 16th percentile is 22hrs.
150 families participated in the study.
The first percentile is greater than or equal to 22 hours: True or False?
Answers
Answer:
False, the first percentile is less than 22 hours.
Step-by-step explanation:
xth percentile:
If a measure is said to be in the xth percentile, it means that x% of the measures are smaller than it, and (100-x)% are larger.
Twenty four of the families in the sample watched TV for less than 22 hrs per week. In the sample, there are 150 families.
This means that 22 is the:
24*100%/150 = 16th percentile.
The first percentile is greater than or equal to 22 hours: True or False?
The first percentile is less than the 16th percentile, which is 22. This means that this is false, the first percentile is less than 22 hours.
For which value of k does Limit as x approaches kf(x) = 4?
0
2
6
8
Answers
Answer:
2
Step-by-step explanation:
on Edge
Answer: 2
Step-by-step explanation:
have a great day!
What is the answer to this
Answers
Answer:
5 f
Re-order terms so that constants are on the left
. 5
5 f
solution
5 f
What is the answer to this problem?
Answers
Answer:
Surface area = 24in
Step-by-step explanation:
I think its 6in x 4in
so like since the green cylinder is 6in i think you multiply it with the purple (sorry if I’m wrong)
Tori's Burgers cooks its burgers either well done or medium. Last night the restaurant served
25 burgers in all, 5 of which were well done. What percentage of the burgers were well done?
Write your answer using a percent sign (%).
Answers
5/25 = .2
.2 x 100 = 20%
As reported in Trends in Television, the proportion of US households who have at least one VCR is 0.592. If 8 households are selected at random, without replacement, from all US households, what is the (approximate) probability that the number having at least one VCR is exactly 4. Be sure to use many decimal places in your calculations (at least 4), but report your answer to three decimal places.
Answers
Answer:
0.23825
Step-by-step explanation:
Given :
p = 0.592 ; number of trials, n = 8
x = 4 ; q = 1 - p = 1 - 0.592 = 0.408
Using the binomial probability relation :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 4) = 8C4 * 0.592^4 * 0.408^4
P(x = 4) = 70 * 0.592^4 * 0.408^4
P(x = 4) = 0.23825
You need a 70% alcohol solution. On hand, you have a 40 mL of a 35% alcohol mixture. You also have 75% alcohol mixture. How much of the 75% mixture will you need to add to obtain the desired solution?
Answers
Answer:
250 ml of the 75% mixture are needed to obtain the desired solution.
Step-by-step explanation:
Since I need a 70% alcohol solution, and on hand, I have a 40 mL of a 35% alcohol mixture, and I also have 75% alcohol mixture, to determine how much of the 75% mixture will you need to add to obtain the desired solution, the following calculation must be performed:
100 x 0.75 + 0 x 0.35 = 75
90 x 0.75 + 10 x 0.35 = 71
89 x 0.75 + 11 x 0.35 = 70.6
87.5 x 0.75 + 12.5 x 0.35 = 70
12.5 = 40
87.5 = X
87.5 x 40 / 12.5 = X
3,500 / 12.5 = X
280 = X
Therefore, 250 ml of the 75% mixture are needed to obtain the desired solution.