Answer:
2 cm
Step-by-step explanation:
If x is the length of the sides of the squares, then the height of the box is also x. The length and width of the base are 10−2x and 20−2x. The area of the base is the length times the width.
96 = (10 − 2x) (20 − 2x)
96 = 200 − 20x − 40x + 4x²
0 = 4x² − 60x + 104
0 = x² − 15x + 26
0 = (x − 2) (x − 13)
x = 2 or 13
Since x < 5, x = 2.
So the length of the sides of the squares is 2 cm.
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 95% confidence; n = 349, x = 42
Answer:
0.5705Step-by-step explanation:
Margin of error is expressed as M.E = [tex]z * \sqrt{\frac{\sigma}{n} }[/tex] where;
z is the z score at 95% confidence
[tex]\sigma[/tex] is the standard deviation
n is the sample size
Given n = 349, [tex]\sigma = 42[/tex] and z score at 95% confidence = 1.645
Substituting this values into the formula above we will have;
M.E = [tex]1.645*\sqrt{\frac{42}{349} }[/tex]
[tex]M.E = 1.645*\sqrt{0.1203} \\\\M.E = 1.645*0.3468\\\\M.E = 0.5705 (to\ four\ dp)[/tex]
what is the length of a hypotenuse of a triangle if each of its legs is 4 units
Answer:
[tex]\boxed{c = 5.7 units}[/tex]
Step-by-step explanation:
Using Pythagorean Theorem:
=> [tex]c^2 = a^2+b^2[/tex]
Where c is hypotenuse, a is base and b is perpendicular and ( a, b = 4)
=> [tex]c^2 = 4^2+4^2[/tex]
=> [tex]c^2 = 16+16[/tex]
=> [tex]c^2 = 32[/tex]
Taking sqrt on both sides
=> c = 5.7 units
Answer:
5.65 unitsStep-by-step explanation:
Given,
Base ( b ) = 4 units
Perpendicular ( p ) = 4 units
Hypotenuse ( h ) = ?
Now,
Using Pythagoras theorem to find length of hypotenuse:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
Plugging the values
[tex] {h}^{2} = {4}^{2} + {4}^{2} [/tex]
Evaluate the power
[tex] {h}^{2} = 16 + 16[/tex]
Calculate the sum
[tex] {h}^{2} = 32[/tex]
[tex]h = \sqrt{32} [/tex]
[tex]h = 5.65 \: units[/tex]
Hope this helps..
Best regards !!
Can you draw the reflection Across the y-axis of the attached image.
Answer:
see graph
Step-by-step explanation:
A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.
A heating pad takes 3,030 Watts during each time it is turned on. If you only use it for 34 minutes, how much CO2 was created? Round to 1 decimal.
Answer:
1.7kW/hrStep-by-step explanation:
Using the formula for calculating the energy used up during the process;
Energy used up = Amount of CO₂ created.
Energy used up in the process = Power * Time.
Given Parameters:
Power = 3,030Watts
Converting to Kilowatts, power = 3030/1000 kW
Power (in kW) = 3.03kW
Time taken = 34 minutes
Converting to hour;
Since 60 minutes = 1hr
34minutes = (34/60)hr
34minutes = (17/30)hr
Required:
Energy used up = 3.03 * 17/30
Energy used up = 51.51/30
Energy used up = 1.717 kW/hr
Hence, amount of CO₂ created in kW/hr is 1.7 kW/hr to 1 decimal place.
The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected. a) What is the probability that the sample mean will be larger than 1224
Answer:
the probability that the sample mean will be larger than 1224 is 0.0082
Step-by-step explanation:
Given that:
The SAT scores have an average of 1200
with a standard deviation of 60
also; a sample of 36 scores is selected
The objective is to determine the probability that the sample mean will be larger than 1224
Assuming X to be the random variable that represents the SAT score of each student.
This implies that ;
[tex]S \sim N ( 1200,60)[/tex]
the probability that the sample mean will be larger than 1224 will now be:
[tex]P(\overline X > 1224) = P(\dfrac{\overline X - \mu }{\dfrac{\sigma}{\sqrt{n}} }> \dfrac{}{}\dfrac{1224- \mu }{\dfrac{\sigma}{\sqrt{n}} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{1224- 1200 }{\dfrac{60}{\sqrt{36}} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{\dfrac{60}{6} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{10} })[/tex]
[tex]P(\overline X > 1224) = P(Z > 2.4 })[/tex]
[tex]P(\overline X > 1224) =1 - P(Z \leq 2.4 })[/tex]
From Excel Table ; Using the formula (=NORMDIST(2.4))
P(\overline X > 1224) = 1 - 0.9918
P(\overline X > 1224) = 0.0082
Hence; the probability that the sample mean will be larger than 1224 is 0.0082
Find the surface area of the triangular prism (above) using its net (below).
Answer:
96 square units
Step-by-step explanation:
The surface area of the prism can be calculated using its net.
The net consists of 3 rectangles and 2 triangles.
The surface area = area of the 3 rectangles + area of the 2 triangles
Area of 3 rectangles:
Area of 2 rectangles having the same dimension = 2(L*B) = 2(7*3) = 2(21) = 42 squared units
Area of the middle triangle = L*B = 7*6 = 42 square units.
Area of the 3 triangles = 42 + 42 = 84 square units.
Area of the 2 triangles:
Area = 2(½*b*h) = 2(½*6*2) = 6*2
Area of the 2 triangles = 12 square units
Surface area of the triangular prism = 84 + 12 = 96 square units.
Answer:
It's 96 unit2
Step-by-step explanation:
I just do it in khan and it's correct
A psychologist is studying the effects of lack of sleep on the performance of various perceptual-motor tasks. After a given period of sleep deprivation, a measurement of reaction time to an auditory stimulus was taken for each of 36 adult male subjects.The mean and standard deviation of the reaction times (in seconds) for the fifty adult male subjects were 1.82 seconds and 0.28 seconds respectively. Previous psychological studies have shown that the true mean reaction time for non-sleep-deprived male subjects is 1.70 seconds. Does the sample evidence indicate that the mean reaction time for sleep-deprived adult males is longer than that of non-sleep-deprived adult males.
A. H0:μ=1.82;Ha:μ<1.82
B. H0:μ=1.70;Ha:μ<1.70
C. H0:μ=1.82;Ha:μ>1.82
D. H0:μ=1.70;Ha:μ>1.70
E. None of the above
Answer:
D. [tex]H_{0}[/tex] : μ = 1.70, [tex]H_{a}[/tex] : μ > 1.70
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
√9m^2n^2 + 2√m^2n^2 - 3mn
Answer:
I think it is
Step-by-step explanation:
Answer:
5n√2m^ - 3mn
Step-by-step explanation:
A submarine is moving parallel to the surface of the ocean at a depth of 626 m. It begins a
constant ascent so that it will reach the surface after travelling a distance of 4420 m.
a) What angle of ascent, to the nearest tenth of a degree, did the submarine make? (3
marks)
b) How far did the submarine travel horizontally, to the nearest metre, during its ascent to
the surface? (3 marks)
Answer:
a) the angle of ascent is 8.2°
b) the horizontal distance traveled is 4375 m
Step-by-step explanation:
depth of ocean = 626 m
distance traveled in the ascent = 4420 m
This is an angle of elevation problem with
opposite side to the angle = 626 m
hypotenuse side = 4420 m
a) angle of ascent ∅ is gotten from
sin ∅ = opp/hyp = 626/4420
sin ∅ = 0.142
∅ = [tex]sin^{-1}[/tex] 0.142
∅ = 8.2° this is the angle of ascent of the submarine.
b) The horizontal distance traveled will be gotten from Pythagoras theorem
[tex]hyp^{2}[/tex] = [tex]opp^{2}[/tex] + [tex]adj^{2}[/tex]
The horizontal distance traveled will be the adjacent side of the right angle triangle formed by these distances
[tex]4420^{2}[/tex] = [tex]626^{2}[/tex] + [tex]adj^{2}[/tex]
adj = [tex]\sqrt{4420^{2}-626^{2} }[/tex]
adj = 4375 m this is the horizontal distance traveled.
A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 95% confidence interval for the mean score, , of all students taking the test
Answer:
The 95% confidence interval for the mean score, , of all students taking the test is
[tex]28.37< L\ 30.63[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 59[/tex]
The mean score is [tex]\= x = 29.5[/tex]
The standard deviation [tex]\sigma = 5.2[/tex]
Generally the standard deviation of mean is mathematically represented as
[tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]
[tex]\sigma _{\= x} = 0.677[/tex]
The degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
substituting values
[tex]df = 59 -1[/tex]
[tex]df = 58[/tex]
Given that the confidence interval is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha =[/tex]5%
[tex]\alpha = 0.05[/tex]
Now the critical value at this significance level and degree of freedom is
[tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]
Obtained from the critical value table
So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as
[tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]
substituting value
[tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]
[tex]28.37< L\ 30.63[/tex]
the perimeter of a square flower bed is 100 feet. what is the area of the flower bed in sqaure feet
Answer:
A =625 ft^2
Step-by-step explanation:
The perimeter of a square is
P = 4s where s is the side length
100 =4s
Divide each side by 4
100/4 = 4s/4
25 = s
A = s^2 for a square
A = 25^2
A =625
A point P has coordinates (-5, 4). What are its new coordinates after reflecting
point Pover the y-axis?
A. (-5, -4)
B. (-5, 4)
C. (5, 4)
D. (5, -4)
Answer:
C(5, 4)
Step-by-step explanation:
The rule for a reflection over the y -axis is (x,y)→(−x,y) .
Answer:
(5, 4)
Step-by-step explanation:
when you reflect off the y-axis, you switch (x,y) to (-x,y)
So
(-5, 4) --> (5, 4)
Hope this helps,
Feel free to ask more questions if I need to explain more.
please show on graph (with x and y coordinates) state where the function x^4-36x^2 is non-negative, increasing, concave up
Answer:
[tex] y'' =12x^2 -72=0[/tex]
And solving we got:
[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]
We can find the sings of the second derivate on the following intervals:
[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up
[tex]x=-\sqrt{6}, y =-180[/tex] inflection point
[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down
[tex]x=\sqrt{6}, y=-180[/tex] inflection point
[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up
Step-by-step explanation:
For this case we have the following function:
[tex] y= x^4 -36x^2[/tex]
We can find the first derivate and we got:
[tex] y' = 4x^3 -72x[/tex]
In order to find the concavity we can find the second derivate and we got:
[tex] y'' = 12x^2 -72[/tex]
We can set up this derivate equal to 0 and we got:
[tex] y'' =12x^2 -72=0[/tex]
And solving we got:
[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]
We can find the sings of the second derivate on the following intervals:
[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up
[tex]x=-\sqrt{6}, y =-180[/tex] inflection point
[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down
[tex]x=\sqrt{6}, y=-180[/tex] inflection point
[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up
solve the rational equation 5/x = 4x+1/x^2
Answer:
x = 1
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
Since the expression on each side of the equation has the same denominator, the numerators must be equal
5x =4x+1
Move all terms containing x to the left side of the equation.
Hope this can help you
You change oil every 6000 miles and drive 2000 miles a month; how many times a year do you change oil?
Answer:
you would change it 4 times a year
Step-by-step explanation:
if there is 12 months in a year and 3 mounths equal 6000 then divide 12/3=4
6x-5<2x+11. plz helpppppp
Answer:
x < 4 or x = ( -∞, 4)
Step-by-step explanation:
6x - 5 < 2x + 116x - 2x < 11 + 54x < 16 x < 16/4x < 4or
x = ( -∞, 4)
[tex]\text{Solve the inequality for x:}\\\\6x-5<2x+11\\\\\text{Subtract 2x from both sides}\\\\4x-5<11\\\\\text{Add 5 to both sides}\\\\4x<16\\\\\text{Divide both sides by 4}\\\\\boxed{x<4}[/tex]
I have attached the file
Answer:
sorry i am not able to understood
Step-by-step explanation:
1/2 of a right angle is a? answers: A. reflex angle B. obtuse angle C. acute angle D. straight angle
Answer:
C. acute angle
Step-by-step explanation:
As you know ,right angle is equal to 90 degrees so half of 90 degrees is 45 degree which is an acute angle (acute angles are the angles which are less than 90 degrees)
Hope this helps and pls mark as brainliest :)
Answer: acute
Step-by-step explanation:
An angle that is less than 90 degrees
Sketch the region that corresponds to the given inequality. HINT [See Example 1.] 2x + y ≤ 10 Say whether the region is bounded or unbounded. The region is bounded. The region is unbounded. Find the coordinates of all corner points (if any). (If an answer does not exist, enter DNE.)
Answer:
See the attachment for sketch
Thr region is unbounded
DNE
Step-by-step explanation:
y≤ -2x + 10
The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.
A manufacturer makes plastic wrap used in food packaging and aims to have a minimum breaking strength of 0.5 kg. If the mean breaking strength of a sample drops below a critical value, the production process is halted and the machinery is inspected. Which of the following is a Type 1 error in context?
A) Halting the production process when too many rubber bands break.
B) Halting the production process when the true breaking strength is below the desired level.
C) Halting the production process when the true breaking strength is within specifications.
D) Allowing the production process to continue when the true breaking strength is below specifications.
E) Allowing the production process to continue when the true breaking strength is within specifications
Answer:
Option D
Step-by-step explanation:
A type I error occurs when you reject the null hypothesis when it is actually true.
The null hypothesis in this case is minimum breaking strength is less than or equal to 0.5.
A type one error would be allowing the production process to continue when the true breaking strength is below specifications.
3 is what percentage of 12?
Answer:
25%
Step-by-step explanation:
First you have the fraction of 3/12 and need to turn it into a decimal. So to do that you divide 3 by 12 = 0.25. So your percent is 25%
A circular chicken house has an area of 40m². What length of chicken wire is required to fence the house without any wire left over?
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k. A) 2 B) 3 C) 4 D) 5 IF YOU ANSWER IN 5 MINUTES I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!
Ans k = 4
Step-by-step explanation:
Here g(x) =[tex]\frac{-1}{3}x + 1[/tex] and
f(x) = [tex]\frac{-1}{3} x -3[/tex]
Now, g(x) = f(x) + k
or, [tex]\frac{-1}{3}x + 1[/tex] = [tex]\frac{-1}{3} x -3 + k[/tex]
or, 1 + 3 = k
So, k = 4 Answer.
What is the formula for the area A of a trapezoid with parallel sides of length B and D, nonparallel sides of length A and C and height H?
A. A = 1/2h (a+c)
B. A = 1/2h (b + d)
C. A = a+b + c + d
D. A= abcd
E. A = 1/2h (a+b+c+d)
Answer:
[tex](B) \dfrac12H (B+D)[/tex]
Step-by-step explanation:
[tex]\text{Area of a trapezoid }= \dfrac12 ($Sum of the parallel sides) \times $Height\\Parallel Sides = B and D\\Height =H\\Therefore:\\\text{Area of the trapezoid }= \dfrac12 (B+D) H[/tex]
The correct option is B.
A population is increasing according to the exponential function defined by y = 3e^.04x, where y is in millions and x is the number of years. Which of the following should be done in order to answer the question "When will the population reach 4 million?"
A. Solve 3e^.04x=12
B. Evaluate y = 3e^.04x(4).
C. Evaluate y = 3e^.04x(1/4)
D. Solve 3e^.04x= 4.
Answer:
D. Solve 3e^0.04x= 4.Step-by-step explanation:
Given the population increasing according to the exponential function defined by y = 3e^0.04x, where y is in millions and x is the number of years, to determine when the population will reach 4 million, the following steps must be carried out.
Since y is in millions, we will first substitute y = 4 into the modeled equation as shown;
4 = 3e^0.04x
Therefore to calculate x, we need to solve the expression 3e^0.04x = 4 for the value of x and this is arrived at by simply substituting y = 4 into the given equation.
To get x;
3e^0.04x = 4
e^0.04x = 4/3
taking the ln of both sides
lne^0.04x = ln1.333
0.04x = 0.287
x = 0.287/0.04
x≈ 3.59 years
the petit chef co has 11.7 percent coupon bonds on the market with elven years left to maturtiy. The bonds make annuly payments and have a par value of 1000. If the bonds curtently sell for 1153.60 what is tje ytm
Answer:
9.40%
Step-by-step explanation:
Given:
Annual coupon rate = 11%
Time left to maturity = 11 years
Par value of bond = 1000
Present value of bond = 1153.60
Required: Find Yeild to Maturity (YTM)
To find the yield to maturity, use the formula below:
YTM = [Annual coupon+(Face value-Present value)/time to maturity]/(Face value+Present value)/2
where annual coupon = 1000 * 11% = 110
Thus,
[tex]YTM = \frac{\frac{110+(1000-1139.59}{9}}{\frac{(1000+1139.59)}{2}}[/tex]
YTM = 9.40%
Therefore the approximate YTM is 9.40%
The average college lecture hall (auditorium) can seat 60 students with a standard deviation of 21. Assume that a total of 60 lecture halls are selected for a sample. What is the standard deviation for the sample mean?
Answer:
The standard deviation of the sample mean is [tex]\sigma _ {\= x } = 2.711[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\= x = 60[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
The sample size is [tex]n = 60[/tex]
Generally the standard deviation of the sample mean is mathematically represented as
[tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]
[tex]\sigma _ {\= x } = 2.711[/tex]
PLEASE HELPPP ITS TIMED Consider the following functions. f(x) = x2 – 4 g(x) = x – 2 What is (f(x))(g(x))? a.(f(x))(g(x)) = x + 2; x ≠ 2 b.(f(x))(g(x)) = x + 2; all real numbers c.(f(x))(g(x)) = x3 – 2x2 – 4x + 8; x ≠ 2 d(f(x))(g(x)) = x3 – 2x2 – 4x + 8; all real numbers
Answer:
d(f(x))(g(x)) = x3 – 2x2 – 4x + 8; all real numbersStep-by-step explanation:
(f(x))(g(x)) = (x²- 4)*(x-2) =x³ - 2x² - 4x + 8Choice d. is correct
a.(f(x))(g(x)) = x + 2; x ≠ 2 incorrectb.(f(x))(g(x)) = x + 2; all real numbers incorrectc.(f(x))(g(x)) = x3 – 2x2 – 4x + 8; x ≠ 2 incorrectd(f(x))(g(x)) = x3 – 2x2 – 4x + 8; all real numberscorrectAnswer:
D
Step-by-step explanation:
need help thankssssss
Answer:
301.44
Step-by-step explanation:
V=π r² h
V=π (4)² (12)
V= 603.19
divide by 2 to find half full: ≈ 301
301.44
Question 1
A 16-ounce bag of sugar is supposed to weigh 16 ounces, but it is acceptable for the weight of the bag to vary as much as 0.4 ounce. Which absolute value inequality can be used to find X, the acceptable
weight of a bag of sugar?
Answer: I x - 16ozI ≤ 0.4oz
Step-by-step explanation:
The weight is supposed to be exactly 16 oz.
But we can accept a maximum error of 0.4oz.
Now, if x is the weight of the sugar bag, the error can be calculated as:
E = x - 16oz
if x is larger than 16oz, we have E positive, which means that we have more sugar than 16oz
if x is smaller than 16 oz, we have E negative, which means that we are a little bit short of sugar in the bag.
Now, we know that the maximum error acceptable is 0.4 oz (negative or positive)
So we can write:
-0.4oz ≤ E ≤ 0.4oz
-0.4 ≤ x - 16oz ≤ 0.4oz
Now, if we apply absolute value to the error, we get:
I x - 16ozI ≤ 0.4oz
So the correct option is the fourth one (or the bottom one)
Answer:
D.) |x−16|≤0.4
Step-by-step explanation: