Hello!
It is given information that this triangle is a right triangle, meaning that the Pythagorean Theorem can apply here.
[tex]a^2+b^2=c^2[/tex]
We can set the length of a leg as an unknown variable [tex]x[/tex].
[tex]x^2+4^2=(3x)^2[/tex]
Remember that it is the whole [tex]3x[/tex] term being squared, meaning that it'll simplify to [tex]9x^2[/tex], not [tex]3x^2[/tex].
[tex]x^2+16=9x^2[/tex]
[tex]8x^2=16[/tex]
[tex]x^2=2[/tex]
[tex]x=\sqrt{2}[/tex]
This means we can plug back in to find the sides.
The hypotenuse would be [tex]3\sqrt{2}[/tex], or 4.2.
And the legs would be 1.4 and 4, respectively.
Hope this helps!
From a random sample of 16 people in a jail, the number of days remaining in each their sentences was noted. The 16 people have a mean remaining sentence of 645 days with a standard deviation of 31 days. Assume the population of remaining sentences is normally distributed. Construct a 95% confidence interval for the mean remaining sentence of all people in the jail. Round final answer to one decimal place.
Answer:
The 95% confidence interval for the mean remaining sentence of all people in the jail is between 628.5 days and 661.5 days.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 16 - 1 = 15
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1315
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.1315\frac{31}{\sqrt{16}} = 16.5[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 645 - 16.5 = 628.5 days
The upper end of the interval is the sample mean added to M. So it is 645 + 16.5 = 661.5 days
The 95% confidence interval for the mean remaining sentence of all people in the jail is between 628.5 days and 661.5 days.
Give the equation of the circle centered at the origin and passing through the point -7 0
Answer: 7.0 because you add 10 to - 3 it makes7.0
Step-by-step explanation:
HELP!!! “Fill in the boxes with the values that make the statement true.”
Answer:
[tex]\sqrt{21m^{17} } = 3m \sqrt[17]{7m}[/tex]
(look attachment)
Helpppppppppppppy pls
Answer:
Step-by-step explanation:
Solve: 2x-3 = 5(x + 6)
Answer:
2x - 3 = 5(x + 6)
2x - 3 = 5x + 30
-33 = 3x
x = -11
Answer:
x= -11
Step-by-step explanation:
1. Expand and distribute.
2x - 3 = 5x + 30
2. Subtract 2x from both sides.
2x - 3 = 5x + 30
-2x -2x
---------------------
-3 = 3x + 30
4 Subtract 30 from both sides.
-3 = 3x + 30
-30 -30
---------------------
-33 = 3x
6. Divide both sides by 33.
-33/3 = 3x/3
-11 = x
7. Switch sides
x = -11
Touch screen maze portfolio if you need more info please comment on the question not answer it all troll answers will be removed
A maze game can be constructed successfully by abiding by the specified guidelines in a systematic manner. Here is a comprehensive guide consisting of multiple steps to create it:
What are the steps?1. Initially, plot the initiation point and conclusion point across different quadrants.
2. Commence the game: Participants must start from the starting point and locate the ending spot through the shortest possible route.
3. Illustrate two sample games through drawing colored paths utilizing pencils or markers which should then be described using coordinates for each route.
4. Compute the overall distance travelled by extracting geographical details available from the used path's coordinates via the distance formula.
5. Finally, determine the most concise path course among all other alternatives.
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What is the surface area of the figure below? Round your answer to the nearest tenth square unit.
Answer: 297 i believe i am a little rusty at this
What is the approximate area of this figure?
A. 25 cm
B. 31 cm
C. 38 cm
D. 42 cm
Answer:
I would say about B. 31 cm
Step-by-step explanation:
if you cut the shape into a triangle and a parallelogram, then you can easily guess that the other side of the square is about 4, and 4 x 4 is 16.. then you will multiply 8 by 4 and get 32 and then divide that by 2 and get 16 again, when you add both 16's together, you get 32, but 31 is closest
Determine the value of w and x in circle M below.
H
w
106
A
Y
M
W=
Answer:
x= 32
w=74
Step-by-step explanation:
my explanation is in the picture
The value of w and x in circle M below mathematically given as
w = 74 , x = 32
What is the value of w and x in circle M below?
Generally, the equation for the sum of angle of a triangle is mathematically given as
w+x+c = 180
w+a = 106
w+x = 106
therefore,
106 +c = 180
c = 180-106
c = 74
w = 74
thus,
w+x+c = 180
74 + x + 74 = 180
x = 180 -148
x = 32
In conclusion, the value of w and x in circle M below is
w = 74 , x = 32
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Evaluate f^-2 g for f = 3 and g = 27.
a) 9
b) 1/3
c) 3
(3)^-2 (27)
the answer is C) 3
Factor this polynomial completely x2-8x+16
Answer:
X^2-8x+16
X^2-4x-4x+16
Factorise by gouping terms
X(x-4)-4(x-4)
=(x-4)(x-4)
There are a couple of formulas that we should know about quadratic functions, and this one utilizes this one:
(x - a)^2 = x^2 -2ax + a^2
Notice how x^2 - 8x + 16 fits into the formula:
x^2 - 8x + 16
x^2 - 2*x*4 + 4^2
(x - 4)^2
(x - 4)(x - 4)
Of course, not all expanded quadratic expressions fit into that formula, so there is a universal method to factor quadratic expressions:
x^2 + x(a + b) + ab —> (x + a)(x + b)
Basically, the middle term is the sum of an and b times x, and the last term is the product of an and b. So, if we are using the expression given in the problem, notice how -4 * -4 is 16, and the sum of -4 and -4 is -8. Thus, a and b are both -4 and the factored form is (x - 4)(x - 4)
1. Which are true of x = log10 31,500? Select all that apply.
a. x < 4
b. x = 4
C. X > 4
d. x < 5
e. X = 5
f.x > 5
I don’t get this
Given:
[tex]x=\log_{10}31,500[/tex]
To find:
Select the true statements from the given options about the given value.
Solution:
We have,
[tex]x=\log_{10}31,500[/tex]
It can be written as
[tex]x=\log_{10}(2^23^25^37)[/tex]
[tex]x=\log_{10}(2^2)+\log_{10}(3^2)+\log_{10}(5^3)+\log_{10}(7)[/tex] [tex][\because \log(ab)=\log a+\log b][/tex]
[tex]x=2\log_{10}2+2\log_{10}3+3\log_{10}5+\log_{10}(7)[/tex]
[tex]x=2\left(0.30105\right)+2\left(0.47712\right)+3\left(0.69897\right)+0.8451[/tex]
[tex]x=4.49835[/tex]
Clearly, the value of x lies between 4 and 5. So, [tex]x>4[/tex] and [tex]x<5[/tex].
Therefore, the correct options are C and D.
The true statements are: (c) x > 4 and (d). x < 5
The logarithmic expression is given as:
[tex]x = \log_{10}(31500)[/tex]
Express 31500 as a product of 100
[tex]x = \log_{10}(315 * 100)[/tex]
Apply the law of logarithm
[tex]x = \log_{10}(315) + \log_{10}(100)[/tex]
Evaluate log 100 base 10
[tex]x = \log_{10}(315) + 2[/tex]
Evaluate log 315 base 10
[tex]x = 2.50 + 2[/tex]
Add the expressions
[tex]x \approx 4.50[/tex]
4.5 is greater than 4 and less than 5
Hence, the true statements are: (c) x > 4 and (d). x < 5
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Each base in this right prism-like figure is a quarter of a circle with a radius of 2 m.
10 m
2 m
2 m
What is the volume of the figure?
Give an exact answer in terms of pi.
Answer:
Volume of the figure = 10π cubic meters
Step-by-step explanation:
Volume of the right prism like figure = Area of the base × Height
Area of the base of the prism = [tex]\frac{1}{4}(\pi r^{2})[/tex]
= [tex]\frac{1}{4}(\pi)(2)^2[/tex]
= π m²
Height of the prism = 10 m
Volume of the prism given in picture = π × 10
= 10π cubic meters
Answer: 10π
Step-by-step explanation:
What is the fraction ⁸⁄₂₀ in its simplest form?
Answer:
2/5
Step-by-step explanation:
dsadsadasddsadsadasddsadsadasddsadsadasddsadsadasd
Step-by-step explanation:
8/20=4/10=2/5
done by cancelling
hope it helps
Can someone please help I really need the answer I give anyone a brainliest
Quadratic vs Exponential Functions
X
- 1000000x y-2
0
1
0
1
1000000
2
2
4000000
4
3
9000000
8
4
16
5
32
16000000
25000000
36000000
49000000
6
64
7
128
Question:
The table shows the behavior of a quadratic and an exponential function near the origin
A. Which function is growing more rapidly?
B. Between which X-values does the table indicate that the functions graphs have crossed?
C. Will the functions graphs ever intersect again? Can you prove this?
1)
Answer:
A) The first function (the quadratic one) is growing more rapidly.
B) Between x=0 and x=1.
C) We can assume that they don't intersect again.
Step-by-step explanation:
A)
The first function (the quadratic one) is growing more rapidly. We can see this because the difference between its y values is so much greater than the difference between the y values for the exponential function.
B)
Between x=0 and x=1. When functions intersect, their y and x values are equal. The y-values are equal at some point over x=0 and x=1 because they both cross over the same range (y=1 and y=2)
C)
We can assume that they don't intersect again because the y-values for the exponential equation will never reach the corresponding values for the quadratic equation; it simply isn't growing rapidly enough.
please help !! A store sells packs of 3 mini-pizzas for $5. Complete the ratio table to show the price for up to 15 mini-pizzas. Mini-Pizzas 6 12 15 Price ($) 5 15 PART B A store sells packs of 3 mini-pizzas for $5. How much would 24 mini-pizzas cost?
Answer:
Step-by-step explanation:
6-$10 12-$20 15-$25
part 2 $40
Review the graph of complex number z. What is the conjugate of z?
7 – 6i
6 – 7i
–7 + 6i
–6 + 7i
Answer: B. 6 - 7i
Step-by-step explanation:
The complex conjugate of the given graph of the complex number is 6-7i.
We have given that,
7 – 6i
6 – 7i
–7 + 6i
–6 + 7i
We have to determine the conjugate of z.
What is the conjugate of complex numbers?
changing the sign of the imaginary part of the complex number. To find the complex conjugate of 4+7i we change the sign of the imaginary part. Thus the complex conjugate of 4+7i is 4 - 7i.
Therefore the complex conjugate of the given graph of the complex number is 6-7i.
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Harry manages a sales force which sells several products in different sales territories. A random sample of 25 territories were selected and the data is provided in an Excel worksheet labelled Harrys. The variables include total sales credited to the sales representative (Sales), the length of time employed in months (time), the market potential (Poten), the advertising expense for the territory (AdvExp), the market share (Share), the change in market share over the previous three years (Change), the number accounts assigned to the sales representative (accounts), an index representing the workload (work), the rating on the last performance review (rating) and whether it is a star territory (star territories have performed well in the past).
Using the methods discussed in this class, determine the “best” regression model to predict Sales. Write a brief report (less than two pages) summarizing your analysis, including key statistical results, conclusions, and recommendations. Include any appropriate technical material in an appendix.
Answer:
13,000 i think
Step-by-step explanation:
Currently, on average, people live 5 years after they retire.
Answer: Thats cool.
Step-by-step explanation:
A quality control inspector has drawn a sample of 11 light bulbs from a recent production lot. Suppose 20% of the bulbs in the lot are defective. What is the probability that less than 7, but more than 4 bulbs from the sample are defective
Answer:
0.04845
Step-by-step explanation:
Probability that less than 7 but more than 4 bulbs from the sample are defective :
P(4 < X < 7) = P(x = 5) + P(x = 6)
Using the binomial probability formula :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
From the question :
p = 0.2 ; 1 - p = 0.8 ; n = 11
P(x =5) = 11C5 * 0.2^5 * 0.8^6 = 0.03876
P(x = 6) = 11C6 * 0.2^6 * 0.8^5 = 0.00969
P(4 < X < 7) = P(x = 5) + P(x = 6)
P(4 < X < 7) = 0.03876 + 0.00969
P(4 < X < 7) = 0.04845
The Holbrooks ordered 25 gallons of orange juice and 16 pints of cranberry juice for their resturant. How much juice do they have in all?
Answers = a- 57 gallons b- 29 gallons
c- 216 gallons d- 164 gallons
Answer:
27gallons
Step-by-step explanation:
First we need to convert 16pints to gallons
Since;
1 pint = 0.125gallons
16 pints = x
Cross multiply
1 * x = 16 * 0.125
x = 2gallons
Since Holbrooks ordered 25 gallons of orange juice and 16 pints of cranberry juice for their resturant, the total juice he has is 25gallons + 2 gallons = 27gallons
If a triangle has a perimeter of 36 inches, which of the following would be the perimeter of the triangle
formed by connecting its midpoints?
(1) 18 inches
(3) 24 inches
(2) 20 inches
(4) 72 inches
Answer:
1) 18 inches
Step-by-step explanation:
By the Midsegment Theorem: A midsegment connecting two sides of a triangle is parallel to the third side and is half as long the third side.
ans: 36/2 = 18
I will mark you brainlist!
How many triangles and rectangles/squares do you need to solve for?
Answer:
8 triangles
Step-by-step explanation:
1 Triangle = 2 needed to be solve. 4 triangle × 2 =8.
PLS HELP!
2x + 4 > 8
2x 4 =- 8
2 x + 4 = 8 2x+4=8 2x+4=8. Subtract 4 from both sides. Simplify 8 − 4 8-4 8−4 to 4. Divide both sides by 2.
Find the area of the figure below, formed from a triangle and a rectangle, in square centimeters.
2 cm
10 cm
6 cm
8 cm
O 68 square centimeters
34 square centimeters
44 square centimeters 58 square centimeters
Answer:68
Step-by-step explanation:
427 × 1,000 jnjnnjnjnnjjjjjjjjjjjjjjjjjj
Answer:
427,000...
Step-by-step explanation:
just search it up. Anywayyysss cute copy and paste☏ ♡ ☆⋆◦★◦⋆°*•°
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HELP THIS IS DUE TODAY. A B C or D. The table shows the relationship of how many pounds of pecans are needed to make a certain number of pies:
Number of Pies
3
6
9
Pounds of Pecans
2
4
6
Which graph below shows plots of equivalent ratios for this situation?
A graph is drawn. The horizontal axis and vertical axis values are 0 to 70 in increments of 10. The horizontal axis label is Number of Pies, and the vertical axis label is Pounds of Pecans. Points are plotted on the ordered pairs 15, 10 and 30, 20 and 45, 30.
A graph is drawn. The horizontal axis and vertical axis values are 0 to 70 in increments of 10. The horizontal axis label is Number of Pies, and the vertical axis label is Pounds of Pecans. Points are plotted on the ordered pairs 10, 15 and 20, 30 and 30, 45.
A graph is drawn. The horizontal axis and vertical axis values are 0 to 70 in increments of 10. The horizontal axis label is Number of Pies, and the vertical axis label is Pounds of Pecans. Points are plotted on the ordered pairs 15, 10 and 25, 10 and 35, 10.
A graph is drawn. The horizontal axis and vertical axis values are 0 to 70 in increments of 10. The horizontal axis label is Number of Pies, and the vertical axis label is Pounds of Pecans. Points are plotted on the ordered pairs 10, 30, and 20, 20 and 30, 10.
17.
Which pair of numbers is relatively prime? *
7 & 21
4 & 15
ОООО
6 & 9
9 & 27
Answer:
9 & 27
Step-by-step explanation:
since all prime numbers above 5 end in 1,3,7 and 9then to find a prime number between say 70 and 80 the only possibilities are 71,73,77,79
Answer:
9 & 27
Step-by-step explanation:
Plz mark as Brainliest...
I need help please.
Answer:
i think the anwser is 2
Step-by-step explanation:
Answer: 24 cubes
Step-by-step explanation:
Tara has two bags of marbles. Bag 1 contains 6 red marbles, 5 blue marbles, and 4 green marbles. Bag 2 contains 3 red marbles, 2 blue marbles, and 4 green marbles. Tara will randomly select 1 marble from each bag. What is the probability that Tara will select a red marble from each bag?
Answer: 26 - 6
Step-by-step explanation: i think sorry if rong