Answers
Answer:
[tex] \large{ \tt{❃ \: SOLUTION}} : [/tex]
The longest side , which is the opposite of side of right angle is the hypotenuse ( h ). There are two other sides, the perpendicular ( p ) and the base ( b ) .In given right triangle , hypotenuse ( h ) = [tex] \sqrt{61} [/tex] , perpendicular ( p ) = 5 & base ( b ) = ?[tex] \large{ \tt{✻ \: USING \: PYTHAGOREAN\: THEOREM : }}[/tex]
[tex] \large{ \tt{❁ {h}^{2} = {p}^{2} + {b}^{2} }}[/tex]
Plug the values and simplify![tex] \large{ ↦( \sqrt{61} })^{2} = {5}^{2} + {b}^{2} [/tex]
[tex] \large{↦ \: 61 = 25 + {b}^{2} }[/tex]
[tex] \large{↦25 + {b}^{2} = 61 }[/tex]
[tex] \large{↦ {b}^{2} = 61 - 25}[/tex]
[tex] \large{↦ {b}^{2} = 36}[/tex]
[tex] \large{↦ {b} = \sqrt{36} }[/tex]
[tex] \large{↦ b = \sqrt{ \underline{3 \times 3} \times \underline{ 2 \times 2} }}[/tex]
[tex] \large{↦b = 3 \times 2}[/tex]
[tex] \large{ \boxed{ \boxed{ \bold{↦b = 6 \: units }}}}[/tex]
Hence , the length of a third side is [tex] \boxed{ \tt{6 }}[/tex] units .✺ Never give up on something that you actually want !
۵Hope I helped! ツ
☼ Have a wonderful day / night ! ☃
# StayInAndExplore ! ☂
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
___________________________________
Problem:Find the length of the third side if necessary right in simplest radical form.Formula:[tex]\quad\quad\quad\quad\boxed{\tt{ {c}^{2} = \sqrt{ {a}^{2} + {b}^{2} }}} [/tex]
Remember:a = perpendicular b = base c = hypotenuseGiven:[tex]\quad\quad\quad\quad\tt{ a = 5 } [/tex]
[tex]\quad\quad\quad\quad\tt{ b = ? } [/tex]
[tex]\quad\quad\quad\quad\tt{ {c = \sqrt{61} }} [/tex]
Solution:[tex]\quad\quad\quad\quad\tt{ {( \sqrt{61}) }^{2} = \sqrt{ {(5)}^{2} + {b}^{2} }} [/tex]
[tex]\quad\quad\quad\quad\tt{ {61}= \sqrt{ {25} + {b}^{2} }} [/tex]
[tex]\quad\quad\quad\quad\tt{ 61 = \sqrt{ 25 + {b}}} [/tex]
Let's convert the "b" like this.[tex]\quad\quad\quad\quad\tt{ {b } = \sqrt{25 - 61 }} [/tex]
[tex]\quad\quad\quad\quad\tt{ {b } = \sqrt{36 }}[/tex]
[tex]\quad\quad\quad\quad\tt{ {b } = 6 }[/tex]
So the final answer is:[tex]\quad\quad\quad\quad \boxed {\boxed{\tt{ \color{magenta} {b } = 6\:units }}}[/tex]
___________________________________
#CarryOnLearning
✍︎ C.Rose❀
Related Questions
This diagram represents 3 batches of light yellow paint. Select a ratio that represents 1 batch of the same shade of light yellow paint. (look at screen shot for full question)
Answers
Answer:
3 white to 5 yellow
the third choice
Step-by-step explanation:
white 9 parts
yellow 15 parts
9 white to 15 yellow
Divide by 3
3 white to 5 yellow
identify the focus and directrix of the graph of the equation x= -1/18^y^2
i don’t get this at all, and need help.
Answers
9514 1404 393
Answer:
B. F(-9/2, 0), x = 9/2
Step-by-step explanation:
One definition of a parabola is that it is all of the points that are equidistant from the focus and the directrix. Among other things, this means the parabola "wraps around" the focus, and opens away from the directrix.
The focus is on the axis of symmetry, so shares a coordinate with the vertex. Since the vertex is a point on the parabola, it is equidistant from the focus and directrix—halfway between them.
The given equation has x get more negative as y increases, so the parabola opens to the left. This means the focus will be a point on the -x axis. Only one answer choice meets that requirement:
focus: (-9/2, 0), directrix: x = 9/2
__
The equation of a parabola with its vertex at the origin can be written as ...
x = 1/(4p)y^2
In this case, we have 4p = -18, so p = -9/2. This is the distance from the vertex to the focus. The negative sign means the focus is to the left of the vertex, and its x-coordinate is -9/2 (as noted above).
Which one hurry
A.9
B.18
C.27
D.33
Answers
Answer:
It’s c I do believe
Answer:
seriously, talk to your teacher. its 21 units squared.
I guess the person who draw this had 18 units squared in mind, but failed to properly draw it.
so none of the options really fit. it's just a badly done problem. not your fault though. its just some of these little things to be just a little mad about.
In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home.
a) Calculate a 99% confidence interval for the proportion of all students who had use of a computer at home and give it in interval notation.
b) Give the value of the point estimate described in this scenario.
c) Give the value of the standard error for the point estimate.
d) Give the value of the margin of error if you were to calculate a 99% confidence interval.
Answers
Answer:
a) The 99% confidence interval for the proportion of all students who had use of a computer at home and give it in interval notation is (0.709, 0.911).
b) 0.81
c) 0.039.
d) 0.101
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home.
This means that [tex]n = 100, \pi = \frac{81}{100} = 0.81[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.81 - 2.575\sqrt{\frac{0.81*0.19}{100}} = 0.709[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.81 + 2.575\sqrt{\frac{0.81*0.19}{100}} = 0.911[/tex]
The 99% confidence interval for the proportion of all students who had use of a computer at home and give it in interval notation is (0.709, 0.911).
b) Give the value of the point estimate described in this scenario.
Sample proportion of [tex]\pi = 0.81[/tex]
c) Give the value of the standard error for the point estimate.
This is:
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.81*0.19}{100}} = 0.039[/tex]
The standard error is of 0.039.
d) Give the value of the margin of error if you were to calculate a 99% confidence interval.
This is:
[tex]M = zs = 2.575*0.039 = 0.101[/tex]
(xii) x^6 - 8 divide by x^2 - 2
Answers
Answer:
1/x^2
Step-by-step explanation:
x^6-8 / x^2-2
x^-2/x^0
x^-2/1
do reciprocal
1/x^2
Note : In division if the power of the base is negative then do its reciprocal then the power will be positive.
Choose the equation and the slope of the line that passes through (3,-2) and is parallel to the x-axis. CHECK ALL THAT APPLY
A. Equation: x= 3
B. Equation: x = -2
C. Slope: undefined
D. Equation: y= 3
E. Slope: 0
F Equation: y= -2
Answers
Answer:
E. Slope: 0
F. Equation: y = -2
Step-by-step explanation:
✔️The x-axis is a horizontal line. Horizontal line does not have any rise, therefore, slope (m) of horizontal line is zero.
The line that is parallel to the x-axis would have a slope of 0 as well.
Therefore, slope (m) = 0
✔️Since the line passes through (3, -2) let's find the y-intercept (b) to enable us write the equation of the line.
Substitute (x, y) = (3, -2) and m = 0 into y = mx + b
-2 = 0(3) + b
-2 = 0 + b
b = -2
✅To write the equation of the line that is parallel to the x-axis, substitute m = 0 and b = -2 into y = mx + b:
y = 0(x) + (-2)
y = 0 - 2
y = -2
The Seattle Space Needle is 605 feet tall. If you are looking down from the top of the Space Needle at your teacher's shoes, how far away from the base of the Space Needle is your teacher standing in feet? You know the angle of depression is 65°
Answers
Answer:
282.12 ft
Step-by-step explanation:
Please find attached a graphical illustration of the question
We are given the value of the opposite side and we are to determine the value of the adjacent side. Thus, tan would be used
Tan 65 = opposite / adjacent
2.1445 = 605 / x
x = 605 / 2.1445
x = 282.12 ft
Find the inverse of the following function. Then prove they are inverses of one another.
f (x)= root 2x-1.
Answers
Answer: [tex]\dfrac{x^2+1}{2}[/tex]
Step-by-step explanation:
Given
[tex]f(x)=\sqrt{2x-1}[/tex]
We can write it as
[tex]\Rightarrow y=\sqrt{2x-1}[/tex]
Express x in terms of y
[tex]\Rightarrow y^2=2x-1\\\\\Rightarrow x=\dfrac{y^2+1}{2}[/tex]
Replace y be x to get the inverse
[tex]\Rightarrow f^{-1}(x)=\dfrac{x^2+1}{2}[/tex]
To prove, it is inverse of f(x). [tex]f(f^{-1}(x))=x[/tex]
[tex]\Rightarrow f(f^{-1}(x))=\sqrt{2\times \dfrac{x^2+1}{2}-1}\\\\\Rightarrow f(f^{-1}(x))=\sqrt{x^2+1-1}\\\\\Rightarrow f(f^{-1}(x))=x[/tex]
So, they are inverse of each other.
The cholesterol levels of a random sample of 250 men are measured. The sample mean is 182 and the sample standard deviation is 32.
a. Give the value of the point estimate of the mean cholesterol level for men in interval notation.
b. Give the value of the standard error of the mean cholesterol level for men.
c. Give the value of the margin of error of the mean cholesterol level for men for a 95% confidence interval.
d. Give the value of the point estimate of the mean cholesterol level for men in interval notation.
Answers
Answer:
182
2.0239
3.97
(178, 186)
Step-by-step explanation:
Given :
Sample mean, n = 250
Sample mean, xbar = 182
Sample standard deviation, s = 32
Point estimate for the mean ;
According to the central limit theorem ; for n > 30, the sample mean equal to the population mean.
Hence, point estimate of mean cholesterol level for men is 182
B.) The standard error = s/√n
s= 32 ; n = 250
Standard error = 32/√250 = 2.0239
C.) Margin of error :
TCritical * standard error
TCritical at 95% ; df =250 -1 = 249 = 1.96
1.969 * 2.0239 = 3.966 = 3.97
D.) The confidence interval :
Point estimate ± margin of error
182 ± 3.97
182 - 3.97 = 178.03
182 + 3.97 = 185.97
(178, 186)
graph y > 1 - 3x whats the answer please
Answers
Answer:
see graph
Step-by-step explanation:
Joseph invested $16,000 in an account paying an interest rate of 5.7% compounded
continuously. Assuming no deposits or withdrawals are made, how much money, to
the nearest cent, wbuld be in the account after 14 years?
Answers
Answer: 34767.2
Step-by-step explanation:
given p = $16,000, n = 14 years, y = 5.7%
amount in bank after 14 years = p ( 1 + </100)
= 16,000 (1 + 5.7/ 100) 14
= 34767.2
Answer:
$35537.51Step-by-step explanation:
Required formula:
P(t) = P₀[tex]e^{rt}[/tex]Substitute values and solve:
P(14) = 16000[tex]e^{0.057*14}[/tex]P(14) = 35537.51would it be the same
Answers
Answers:
a) No, the figure would not look the same. See the diagram belowb) Yes the figure would look the same after a half turnc) Yes the figure would look the same after a full turn==================================================
Explanations:
a) The figure doesn't have 90 degree symmetry, so that's why we have a different looking figure after a quarter turn.b) The figure does have 180 degree symmetry. That's why it looks the same after a half turn (aka 180 degree turn)c) Rotating any figure 360 degrees, aka a full turn, will get everything back where it started. It doesn't matter if the figure has any symmetry or not.3. Evaluate the expression. If k = 3 and h = 2. (Be sure to show each step)
4k+2(5k-2)-h
Answers
Answer:
36
Step-by-step explanation:
Simple:
(4)(3)+2((5)(3)−2)−2
=12+2((5)(3)−2)−2
=12+2(15−2)−2
=12+(2)(13)−2
=12+26−2
=38−2
=36
What is XY? The triangle XZY is right angle triangle. Angle z is right angle and angle X and Y are 45 degree. The side YZ is 5. A. 2–√ B. 5 C. 52–√ D. 10
Answers
9514 1404 393
Answer:
C. 5√2
Step-by-step explanation:
The hypotenuse of an isosceles right triangle is √2 times the length of either leg. The given leg (YZ) is 5 units, so the hypotenuse XY is 5√2 units.
que por qué me va a dar 70
what number x anuder number is =70
Answers
Answer: i didnt really understand what you put but i can help you out. If your saying what _ x _ = 70. You can do 10 x 7 or 7x10
Step-by-step explanation:
Suppose that a histogram of a data set is approximately symmetric and bell shaped. Approximately what percent of the observations are within two standard deviations of the mean?
50%
68%
95%
99.7%
Answers
Answer:a
Step-by-step explanation:
A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 4 types of drinks to choose from, 5 types of sandwiches, and 3 types of chips. How many different value meal packages are possible
Answers
Answer:
60 different meal packages 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:
4 types of drinks
5 types of sandwiches.
3 types of chips.
They are independent events, so, by the fundamental counting principle:
4*5*3 = 60
60 different meal packages are possible.
Dave is helping his grandmother make trail mix. His grandmother ask
him to add 1/5 cup of fruit for every 1/3 cup of nuts. To satisfy his grandmother's request, Dave mix ?? cup of fruit for a single, cup of nuts.
Answers
9514 1404 393
Answer:
3/5 cup of fruit
Step-by-step explanation:
Dave is making 3 times his grandmother's recipe, so for 3 × 1/3 cup of nuts, he needs 3 × 1/5 cup of fruit:
3/5 cup of fruit for 1 cup of nuts
Family Flowers employs 17 people, of whom 14 earn gross pay of $660.00 each and 3 earn gross pay of $700.00 each on a weekly basis. What is the employer's share of total Social Security and Medicare taxes for the first quarter of the year? (Social security tax is 6.2% of wages up to $128,400. Medicare tax is 1.45% of all wages.)A. $660.00B. $700.00 C. $850.68D. $11,277.63
Answers
What is the measure of angle R
Answers
Answer: 37 degrees
Explanation:
We have a right triangle because the tangent is always perpendicular to the radius, at the point of tangency.
That then leads to angles P and R being complementary, ie they add to 90
P+R = 90
R = 90-P
R = 90-53
R = 37
Simplify the expression.
56 ÷ (–7)
–8
8
392
–392
Answers
Answer:
- 8
Step-by-step explanation:
56 ÷ (- 7)
56 ÷ - 7
- 8
Answer:
-8
Step-by-step explanation:
A positive number divided by a negative one results in a negative quotient.
Thus, 56 ÷ (–7) = -8
change the following into mixed fraction 13/5
Answers
Answer:
2 3/5
Step-by-step explanation:
13/5
5 goes into 13 2 time
2*5 =10
13-10 =3
There is 3 left over. This goes over the denominator
2 3/5
2 3/5
Step-by-step explanation:
13/5
5*2=10
reminder=3
divisor = 5
Is there alternative way in solving a arithmetic sequence? yes or no? explain.
Answers
Answer:
Yes there is alternative way in solving and arithmetic sequence .An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
solve for x in parts below:
Answers
Answer:
x=30°
Step-by-step explanation:
50 + x =80 degree (sum of two interior opposite angles is equal to the exterior angles formed)
x=80-50
x=30 degree
PLSSSSSSS ASAPPPPPPPP
A)157
B)67
C)177
D)None of these answers
E)23
Answers
Find value of x? And show work
Answers
Answer:
70
Step-by-step explanation:
X is equal to 70 degrees because angle x and the angle that is 70 degrees are alternate interior angles.
These are alternate interior angles. If two angles are alternate interior angles they are congruent. That means x is also 70 degrees.
Use long division to solve (4x^4-5x^3+2x^2-x+5) ÷ (x^2+x+1)
Answers
Answer:
4x^2-9x+7+\frac{x-2}{x^2+x+1}
Step-by-step explanation:
Here is a hopefully helpful answer! :)
Use any method to multiply (3a + 2b – c)(a – b + 2c).
Question 5 options:
A)
3a2 – 2b2 – 2c2 – ab + 5ac + 5bc
B)
3a2 + 2b2 + 2c2 – ab – 5ac + 5bc
C)
3a2 + 2b2 – 2c2 + ab + 5ac + 5bc
D)
3a2 – 2b2 – 2c2 + ab + 5ac – 5bc
Answers
Answer:
A)
3a2 – 2b2 – 2c2 – ab + 5ac + 5bc
[tex](3a + 2b - c)(a - b + 2c) \\ = (3 {a}^{2} - 3ab + 6ac + 2ab - 2 {b}^{2} + 6bc - ac + bc - 2 {c}^{2} ) \\ = 3 {a}^{2} - ab + 5ac - 2 {b}^{2} + 5bc - {2c}^{2} \\ = 3 {a}^{2} - 2 {b}^{2} - {2c}^{2} - ab + 5ac + 5bc[/tex]
Answer:
option a is correct
Step-by-step explanation:
(3a + 2b - c)(a - b + 2c)
3a(a- b + 2c) +2b(a - b + 2c) - c(a - b + 2c)
multiply the brackets
3a^2 - 3ab + 6ac + 2ab - 2b^2 + 4bc - ac + bc - 2c^2
combine like terms
3a^2 - ab + 5ac - 2b^2 + 5bc - 2c^2
3a^2 - 2b^2 - 2c^2 - ab + 5ac + 5bc
Elsa biked 834 miles. Linda biked 544 miles.
How many miles did they bike together?
Answers
Answer:
they would have bike 544 miles together with each other.
Step-by-step explanation:
since Elsa went more than Linda Linda had to stop while Elsa kept going.
A manufacturer knows that their items have a normally distributed length, with a mean of 15.4 inches, and standard deviation of 3.5 inches. If 16 items are chosen at random, what is the probability that their mean length is less than 16.8 inches
Answers
Answer:
0.9452 = 94.52% probability that their mean length is less than 16.8 inches.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 15.4 inches, and standard deviation of 3.5 inches.
This means that [tex]\mu = 15.4, \sigma = 3.5[/tex]
16 items are chosen at random
This means that [tex]n = 16, s = \frac{3.5}{\sqrt{16}} = 0.875[/tex]
What is the probability that their mean length is less than 16.8 inches?
This is the p-value of Z when X = 16.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{16.8 - 15.4}{0.875}[/tex]
[tex]Z = 1.6[/tex]
[tex]Z = 1.6[/tex] has a p-value of 0.9452.
0.9452 = 94.52% probability that their mean length is less than 16.8 inches.
