The value of sin 45 is 1/ √2
What is angle?An angle is a combination of two rays (half-lines) with a common endpoint.
As per the diagram,
AC= 1 unit, BC= 1 unit
Applying Pythagoras theorem,
AB² = AC² + BC²
AB² = 1²+ 1²
AB² = 2
AB= √2
Now, sine is the ratio between the opposed side and the hypothenuse.
So, sin 45 = 1/ √2 = √2/√2
In radical form = 0.7071
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Final answer:
The sin of 45 degrees is √2/2. This value is found using the properties of an isosceles right triangle and applying the Pythagorean theorem.
Explanation:
In the case of a 45-degree angle in a right triangle, the sine function can be calculated using the properties of an isosceles right triangle. The sin of 45 degrees is equal to the ratio of the opposite side to the hypotenuse. In an isosceles right triangle where the two legs are equal, this ratio is the same for both legs.
By the Pythagorean theorem, we know that in an isosceles right triangle, if each leg is of length 1, the hypotenuse will be √2. Therefore, sin 45 degrees equals the length of the leg (1) divided by the length of the hypotenuse (√2), which simplifies to √2/2 or 1/√2. Expressing this in simplest radical form, we obtain √2/2.
This value is derived from understanding that the sum of the squares of the lengths of the legs equals the square of the hypotenuse, which gives us the equation 1² + 1² = c², where c is the hypotenuse. Simplifying gives us a hypotenuse of √2, and the sine of 45 degrees equals 1/√2, or √2/2 after rationalizing the denominator.
Easy 6th grade math ! Help please :)
Answer:
b 2.50 per 2 bottles of sprite
Step-by-step explanation:
Answer:
The answer is B.
2.50 per 2 bottles of sprite
Step-by-step explanation:
The area of a triangle is 1/2*(base)*(height) or base times height divided by two.
Answer:
both
Step-by-step explanation:
Listed below are student evaluation ratings of courses, where a rating of 5 is for "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a 99% confidence level. What does the confidence interval tell about the population of all college students in the state?
3.6, 3.1, 4.0, 4.9, 3.0, 4.3, 3.6, 4.6, 4.6, 4.0, 4.4, 3.6, 3.3, 4.2, 3.7
What is the confidence interval for the population mean mu?
_ < u < _
nothing (Round to two decimal places as needed.)
Answer:
[tex]3.93-2.977\frac{0.574}{\sqrt{15}}=3.49[/tex]
[tex]3.93+2.977\frac{0.574}{\sqrt{15}}=4.37[/tex]
3.49 < u < 4.37
Step-by-step explanation:
Data provided
3.6, 3.1, 4.0, 4.9, 3.0, 4.3, 3.6, 4.6, 4.6, 4.0, 4.4, 3.6, 3.3, 4.2, 3.7
The sample mean and deviation can be calculated with the following formulas
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex]
[tex]\bar X=3.93[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s=0.574 represent the sample standard deviation
n=15 represent the sample size
Confidence interval
The confidence interval for the true mean is given by:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom, given by:
[tex]df=n-1=15-1=114[/tex]
The Confidence is 0.99 or 99%, the significance is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and the critical value would be[tex]t_{\alpha/2}=2.977[/tex]
Replacing we got:
[tex]3.93-2.977\frac{0.574}{\sqrt{15}}=3.49[/tex]
[tex]3.93+2.977\frac{0.574}{\sqrt{15}}=4.37[/tex]
3.49 < u < 4.37
A recent national survey found that high school students watched an average (mean) of 7.2 movies per month with a population standard deviation of 0.9. The distribution of number of movies watched per month follows the normal distribution. A random sample of 35 college students revealed that the mean number of movies watched last month was 6.2. At the 0.05 significance level, can we conclude that college students watch fewer movies a month than high school students?1. State the null hypothesis and the alternate hypothesis. A. H0: μ ≥ 7.2; H1: μ < 7.2B. H0: μ = 7.2; H1: μ ≠ 7.2C. H0: μ > 7.2; H1: μ = 7.2D. H0: μ ≤ 7.2; H1: μ > 7.22. State the decision rule.A. Reject H1 if z < –1.645B. Reject H0 if z > –1.645C. Reject H1 if z > –1.645D. Reject H0 if z < –1.6453. Compute the value of the test statistic.4. What is the p-value?
Answer:
1) A. H0: μ ≥ 7.2; H1: μ < 7.2
2) D. Reject H0 if z < –1.645
3) [tex]t=\frac{6.2-7.2}{\frac{0.9}{\sqrt{35}}}=-6.573[/tex]
4) [tex]p_v =P(z<-6.573)=2,47x10^{-11}[/tex]
Step-by-step explanation:
Information provided
[tex]\bar X=6.2[/tex] represent the sample mean for the number of movies watched last month
[tex]\sigma=0.9[/tex] represent the population deviation
[tex]n=35[/tex] sample size selected
[tex]\mu_o =7.2[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
1) System of hypothesis
We want to check if college students watch fewer movies a month than high school students, and the best system of hypothesis are:
Null hypothesis:[tex]\mu \geq 7.2[/tex]
Alternative hypothesis:[tex]\mu < 7.2[/tex]
A. H0: μ ≥ 7.2; H1: μ < 7.2
2) Decision rule
For this case we are ocnduting a left tailed test so then we need to find a critical value in the normal standard distribution who accumulates 0.05 of the area in the left and we got:
[tex]z_{crit}= -1.645[/tex]
And the rejection zone would be:
D. Reject H0 if z < –1.645
3) Statistic
Since we know the population deviation the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{6.2-7.2}{\frac{0.9}{\sqrt{35}}}=-6.573[/tex]
4) P value
We have a left tailed test then the p value would be:
[tex]p_v =P(z<-6.573)=2,47x10^{-11}[/tex]
Final answer:
The correct null and alternate hypotheses are H0: μ ≥ 7.2 and H1: μ < 7.2, respectively. Reject the null hypothesis if z < -1.645. The computed test statistic is approximately -7.378, suggesting a p-value near zero and thus, we can conclude that college students watch fewer movies on average.
Explanation:
In order to determine whether college students watch fewer movies a month than high school students, we should set up a hypothesis test comparing the college students' mean number of movies watched to the known population mean for high school students.
Step 1: State the null and alternate hypotheses.
The correct hypotheses would be A. H0: μ ≥ 7.2; H1: μ < 7.2 since we are testing if the college students watch fewer movies, which is a one-tailed test.
Step 2: State the decision rule.
The correct decision rule at the 0.05 significance level for a left-tailed test would be D. Reject H0 if z < – 1.645.
Step 3: Calculate the test statistic.
Using the formula for the z-test, z = (sample mean - population mean) / (population standard deviation / √ sample size), we calculate z = (6.2 - 7.2) / (0.9 / √35) ≈ – 7.378. Thus, the test statistic z is approximately -7.378.
Step 4: Find the p-value.
With a z-score as extreme as – 7.378, the p-value is near zero, implying strong evidence against the null hypothesis.
43. A beam rests against a wall, forming a 65º with the floor. Use the function y = 9 sec 8 to find the
length of the beam to the nearest tenth of a foot.
Answer:
[tex]Length\hspace{3}of\hspace{3}the\hspace{3}beam=y=21.3ft[/tex]
Step-by-step explanation:
Look the picture I attached you. As you can see the beam against the wall form a right triangle. The trigonometry functions on a right triangle are:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\hspace{10}csc(\theta)=\frac{hypotenuse}{opposite}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\hspace{10}sec(\theta)=\frac{hypotenuse}{adjacent} \\\\tan(\theta)=\frac{opposite}{adjacent} \hspace{20}cot(\theta)=\frac{adjacent}{opposite}[/tex]
The problem give us the following data:
[tex]y=9sec(\theta)[/tex]
Using the previous information about the trigonometry functions on a right triangle and the data provided by the problem you can conclude:
[tex]y=Hypotenuse\\Adjacent=9\\\theta=65^{\circ}[/tex]
Therefore:
[tex]y=9sec(65^{\circ})=9*(2.366201583)=21.29581425\approx21.3ft[/tex]
The length of the beam for the given situation is 21.3 ft.
What is Trigonometry?
Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles.
Here, given function
y = 9. sec θ
put, θ = 65⁰
then, y = 9 X sec 65⁰
y = 9 X 2.366
y = 21.294 ft. ≈ 21.3 ft.
Thus, the length of the beam for the given situation is 21.3 ft.
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if £2000 is placed into a bank account that pays 3% compound interest per year how much will be in the account after 2 years
Principal Balance: 2000
Compound Interest: 3%
Type: Yearly
2000 x 1.03 = 2060
Year 1 : £2060
2060 x 1.03 = 2121.8
Year 2: £2121.8
There will be £2,121.80 in the account after 2 years.
Answer:okStep-by-step explanation:
A punch recipe calls for twice as much lemonade as lime soda.
It calls for half as much ice cream as lime soda. If you use 2
gallons of line soda, how much lemonade will you need and
how much ice cream will you need? pls help!! :):):):):)
you will need
2 gallons lime soda
1 gallon icecream
and 4 gallons lemonade
Brandon poured what he estimated to be 32 ounces of oil into his car’s engine. From the markings on the container, he later determined that he had actually poured 36 ounces. What was the percent error in his estimate
Answer:
percentage error = 11.11 %
Step-by-step explanation:
Brandon poured w hat he estimated to be 32 ounces of oil into his car's engine . He later determined that he has actually poured 36 ounces from the marking on the container . The percentage error is computed below.
percentage error = approximate value - exact value/exact value × 100
approximate value = 32 ounces
exact value = 36 ounces
percentage error = |32 - 36| / | 36 | × 100
note we used the absolute value to eliminate negative signs
percentage error = 4/36 × 100
percentage error = 400/36
percentage error = 11.11 %
Two-thirds of a number is equal to 20. What is the number?
Answer:
The number is 30
Step-by-step explanation:
Let x be the number
2/3 x = 20
Multiply each side by 3/2 to isolate x
3/2 *2/3x = 20*3/2
x = 30
What is the shortest possible perimeter for an arrangement with an area of 15 square feet
Answer:
The answer is 16 ft
Step-by-step explanation:
The shape with the smallest possible perimeter for a given area is a circle but among quadrilaterals, it's a square. Given an area of 15 square feet, the length of each side of the square would be approximately 3.87 feet, and the perimeter would be approximately 15.49 feet.
Explanation:The disciplines specified here is Mathematics, and the question is related to the correlation between an area and perimeter of a shape. In this case, the shape with the smallest possible perimeter for a given area would be a circle. However, if we only examine quadilateral shapes, then the shape with the minimum possible perimeter would be a square because a square is the quadrilateral that has the maximum area for a given perimeter.
If the area of the square is 15 square feet, then you can determine each side of the square by taking the square root of the area. The square root of 15 is approximately 3.87 feet. Now, to determine the perimeter of the square, you multiply this value by 4 because a square has four sides of equal length, hence perimeter is ~15.49 feet.
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What do heating systems cooling systems and heat engines have in common
Answer:
is D
Step-by-step explanation:
for egny
Consider the following function. f(x) = (x + 5)2/3 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) x = −5 (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing (−5,[infinity]) decreasing (−[infinity],−5) (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = DNE relative minimum (x, y) = −[infinity],[infinity]
Answer:
See explaination
Step-by-step explanation:
Please kindly check attachment for detailed and step by step solution of the given problem.
a. The critical number of f is -5
b. The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).
c. There is no relative extremum at x = -5.
d. Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).
How to find the critical numbers(a) To find the critical numbers of the function, find where the derivative is 0 or undefined.
To find the derivative of f(x):
[tex]f'(x) = (2/3)(x + 5)^(-1/3)[/tex]
The derivative is undefined at x = -5, since[tex](x + 5)^(1/3)[/tex] would be 0 in the denominator.
So -5 is a critical number of f.
(b) To find the intervals on which the function is increasing or decreasing, examine the sign of the derivative on each interval.
Since f'(x) is always positive (except at x = -5, where it is undefined),
The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).
(c) To apply the First Derivative Test, look at the sign of the derivative near the critical point x = -5.
The derivative is undefined at x = -5, so the test is not applicable
Therefore, there is no relative extremum at x = -5.
Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).
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How many 4 digit numbers can be formed if no two digits are the same?
Carl used some fabric to make a seat cover. Then he used 8 times as much fabric to make a tent. He used 24 yards to make the tent. Write an equation
Answer:
8x = 24
Step-by-step explanation:
[tex]x = \text{The fabric he used to make the seat cover}[/tex]
Then, since he used 8 times as much fabric to make the tent then
[tex]\text{Fabric needed for the tent} = 8x = 24[/tex]
Therefore your equation would be [tex]8x = 24[/tex]
To find the amount of fabric Carl used for the seat cover, the equation is 8x = 24. The variable x represents the amount of fabric for the seat cover, and 24 is the total yards of fabric used for the tent.
Explanation:Carl used some fabric to make a seat cover. Then he used 8 times as much fabric to make a tent. He used 24 yards for the tent. To write an equation to represent this situation, let's designate the amount of fabric used for the seat cover as x.
According to the problem statement, the tent required 8 times more fabric than the seat cover. Therefore, we can write the equation as:
8x = 24
Where:
x = the amount of fabric used for the seat cover8x = the amount of fabric used for the tent24 = the total amount of fabric used for the tent (given)This equation can now be solved to find out the amount of fabric Carl used to make the seat cover.
A survey asked, "How many tattoos do you currently have on your body?" Of the 12311231 males surveyed, 190190 responded that they had at least one tattoo. Of the 10671067 females surveyed, 143143 responded that they had at least one tattoo. Construct a 9090% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval. Let p 1p1 represent the proportion of males with tattoos and p 2p2 represent the proportion of females with tattoos. Find the 9090% confidence interval for p 1 minus p 2p1−p2.
Answer:
[tex](0.154-0.134) - 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=-0.00402[/tex]
[tex](0.154-0.134) + 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=0.044[/tex]
We are confident at 95% that the difference between the two proportions is [tex]-0.00402 \leq p_1 -p_2 \leq 0.044[/tex]
Since the confidence interval contains the value 0 we can conclude that at 10% of significance we don't have enough evidence to conclude that the true proportions for female and male with tattos differs
Step-by-step explanation:
Information given
[tex]p_1[/tex] represent the real population proportion of males with tattoos
[tex]\hat p_1 =\frac{190}{1231}=0.154[/tex] represent the estimated proportion of males with tattos
[tex]n_1=1231[/tex] is the sample size for males
[tex]p_2[/tex] represent the real population proportion of female with tatto
[tex]\hat p_2 =\frac{143}{1067}=0.134[/tex] represent the estimated proportion of females with tattos
[tex]n_2=1067[/tex] is the sample size of female
[tex]z[/tex] represent the critical value
Confidence intrval
The confidence interval for the difference of two proportions would be given by this formula
[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
For the 90% confidence interval the value of [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2=0.05[/tex], and the critical value for this case would be:
[tex]z_{\alpha/2}=1.64[/tex]
Replacing the info given we got:
[tex](0.154-0.134) - 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=-0.00402[/tex]
[tex](0.154-0.134) + 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=0.044[/tex]
We are confident at 95% that the difference between the two proportions is [tex]-0.00402 \leq p_1 -p_2 \leq 0.044[/tex]
Since the confidence interval contains the value 0 we can conclude that at 10% of significance we don't have enough evidence to conclude that the true proportions for female and male with tattos differs
MATHEMATICAL CONNECTIONS What value of x makes the quadrilateral a parallelogram?
3x + 10
***
Answer:
x = 5 (check the diagram included)
Step-by-step explanation:
The question is incomplete, I have included a diagram to aid the understanding of the question
Parallelograms are quadrilaterals which have their opposite sides parallel and equal. This also means that the opposite angles in a parallelogram are equal
From the attached figure, we have:
|FG| = 3x + 10, |HE| = 7x - 30
To calculate for the value of x that makes the quadrilateral a parallelogram, we have:
Remember the opposite sides of a parallelogram are equal
3x + 10 = 7x - 30
3x - 7x = 10 - 30
-4x = -20
x = 20 ÷ 4
x = 5
x = 5 makes the quadrilateral a parallelogram
There are 264 students going on a field trip to the city. If the school is only taking 8 buses, what is the total number of students that will be on each bus?
272
256
33
34
Answer:
Step-by-step explanation:
Answer:
272
Step-by-step explanation:
Every day, you take the elevator from the basement parking lot that is at level -2 . The elevator takes two seconds per level and you find that it takes 46 seconds to reach your floor.
Answer:
you live on the 21st floor
Step-by-step explanation:
46-4=42 (level -2 to ground level)
42÷2=21
10×10 by the power of 2 equal
Answer:
10,000
Step-by-step explanation:
10 x 10 = 100 when you do the power of 2, you multiply that number by itself.
A household goods manufacturer wants to increase the absorption capacity of a dish washing sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge
Answer:
[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
And the p value using the alternative hypothesis is given by:
[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]
Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge
Step-by-step explanation:
Information provided
4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9
We can find the sample mean and deviation with the following formulas:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]\bar X=3.76[/tex] represent the sample mean
[tex]s=0.241[/tex] represent the sample standard deviation
[tex]n=10[/tex] sample size
[tex]\mu_o =3.5[/tex] represent the value to check
[tex]\alpha=0.01[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the new design increased the absorption amount of the sponge (3.5), the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 3.5[/tex]
Alternative hypothesis:[tex]\mu > 3.5[/tex]
Since we don't know the deviation the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
And the p value using the alternative hypothesis is given by:
[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]
Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge
Kermit took out a 4 year loan for $5,500. He had to pay a total of $1,870 in interest payments. What rate did he pay for his loan?
Answer: 8.5%
Step-by-step explanation:
This is simple interest.
The formula fie finding simple interest is
I = principal × rate × time
-------------------------------
100
I = PRT/100
From the given values,
P = $5,500, T = 4years, R = ?, I = $1,870
Now we shall change the formula which is fundamental or in situ to suit the rate R.we now have
I = PRT
----
100
PRT = I × 100
R. = I × 100
---------
P × T
= 1,870 × 100
---------------
5,500 × 4
= 1,870 × 25
------------
5,500
= 187000/4
-----------
5500
= 46750/5500
= 8.5%
Therefore, the imtetest rate at which the loan was calculated is
8.5%.
Five friends are sharing 82 dollars they keep a record of what they do first they split up the ten bills
Answer:
82 divided by 5 = 16.4
Step-by-step explanation:
you divide 82 by 5 and get 16.4 or 82 divided by 10= 8.2
They do first they split up the ten bills and it is 8.0.
We have given that,
Five friends are sharing 82 dollars they keep a record
82 divided by 5
[tex]\frac{82}{5} = 16.4[/tex]
You divide 82 by 5 and get 16.4,
After the split up to ten bills is given by,
What is the split?A split is a situation in a particular frame of a ten-pin bowling game where the player throws the ball and knocks the headpin
82 divided by 10
[tex]\frac{80}{10} =8.0[/tex]
They do first they split up the ten bills.
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A circle with radius 3 3start color #ff00af, 3, end color #ff00af has a sector with a central angle of 1 9 π 9 1 πstart color #9d38bd, start fraction, 1, divided by, 9, end fraction, pi, end color #9d38bd radians . What is the area of the sector? Either enter an exact answer in terms of π πpi or use 3.14 3.143, point, 14 for π πpi and enter your answer as a decimal.
I will give as much points as possible
Answer:
π/2 or 1.57 square units
Step-by-step explanation:
The area of a sector with central angle θ is given by the formula ...
A = (1/2)r²θ
Filling in the given value, we find the area to be ...
A = (1/2)(3²)(π/9) = π/2 . . . . square units
Using 3.14 for π, this is ...
A = 3.14/2 = 1.57 . . . . square units
What is the hinge Theorem in Geomatry
Answer:
In geometry, the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.
Step-by-step explanation:
Answer:
In geometry, the theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.
Step-by-step explanation:
If f(x) = 3x+5 and g(x) = -2x^2-5x+3 fins (f+g)(x)
Answer:
f(x) + g(x) = -2x^2 - 2x + 8
Step-by-step explanation:
Given: f(x) = 3x+5 and g(x) = -2x^2-5x+3
Find f(x) + g(x)
f(x) + g(x) = 3x + 5 + (-2x^2 - 5x + 3)
f(x) + g(x) = 5 + -2x^2 - 2x + 3
f(x) + g(x) = -2x^2 - 2x + 8
Answer:
(f+g)(x) = -2x^2 -2x +8
Step-by-step explanation:
(f+g)(x) = f(x) +g(x)
= (3x +5) +(-2x^2 -5x +3)
(f+g)(x) = -2x^2 -2x +8
A coral reef grows 0.16 meters ever week. How much does it grow in 7 weeks
Answer:
1.12 meters
Step-by-step explanation:
Answer:
1.12
Step-by-step explanation:
each week it grows 0.16 m
so,in 7 weeks it will grow 0.16*7m
The superintendent of a large school district, having once had a course in probability and statistics, believes that the number of teachers absent on any given day has a Poisson distribution with parameter µ.
Use the accompanying data on absences for 50 days to obtain a 95% large sample CI for µ.
Absences: 0 1 2 3 4 5 6 7 8 9 10
Frequency: 2 3 8 11 8 7 6 2 1 1 1
[Hint: The mean and variance of a Poisson variable both equal m, so
Z = (X - µ)/√(µ/n),
has approximately a standard normal distribution. Now proceed as in the derivation of the interval for p by making a probability statement (with probability 1- a) and solving the resulting inequalities for µ.
You first calculate the sample mean, or μ_bar, of the data. Given it's a Poisson distribution, the mean is equal to the variance, giving your standard deviation. Finally, for a 95% CI, you apply the Z score to the formula μ_bar ± Z*(sqrt(μ_bar/n)) to obtain your confidence interval.
Explanation:The subject is related to Poisson distribution and the calculation of a confidence interval (CI) for the population mean (µ).
Firstly, we calculate the sample mean that is the total number of instances divided by the number of days:
(0*2 + 1*3 + 2*8 + 3*11 + 4*8 + 5*7 + 6*6 + 7*2 + 8*1 + 9*1 + 10*1)/50
This gives us the sample mean, µ_bar.
Given the data follows a Poisson distribution, the mean and the variance are equal (µ = variance). For a Poisson distribution, the variance is equal to µ divided by n, hence we get the standard deviation as sqrt(µ/n).
For a 95% CI, Z = 1.96 (from the standard normal table). Our CI will therefore be µ_bar ± Z*(sqrt(µ_bar/n)).
Since n is large, the distribution can be assumed to be approximately normal and the CI can be treated as reliable.
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To calculate a 95% confidence interval for a Poisson distributed data set, first calculate the sample mean. Consider the variance of Poisson equals to its mean, the standard error would be square-root of (mean divided by sample size). Using z-score of ±1.96 for 95% confidence level, solve for mean in both inequalities will give the interval.
The question pertains to deriving a 95% confidence interval for the mean (µ) of a Poisson distributed data set. In this case, the data set provided represents the number of teacher absences in a school district over 50 days.
Firstly, you will need to calculate the sample mean by multiplying each absence by its frequency, sum those up, then divide the sum by the total number of observations. This serves as an estimator for the Poisson mean µ.
Considering that the variance of a Poisson variable equals to its mean µ. The standard error would then be √(µ/n), where n is the number of observations. For a 95% interval, Z should be approximately ±1.96.
The confidence interval can be calculated using the standard formula for a large sample size:
Z = ±1.96 = (X - µ)/√(µ/n)
Solving for µ in both inequalities will give you the confidence interval.
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Time (hours) Number of Bricks
2 100
4 200
6 300
8 400
The time it takes a brick layer to lay bricks varies directly with the number of bricks. The brick layer's data is shown in the table. If x = time, and y = the number of bricks, which equation models the brick layer's direct variation?
Answer:
y=50x
Step-by-step explanation:
For every additional 2 hours (x), there are 100 bricks laid.
This means the slope is 50 (100/2)(200/4)etc.
50*2=100
50*4=200
50*6=300
50*8=400
5 POINTS PLEASE HELP
Alan found the distance between point A(-8,-4) and point B(3,-4), his work is shown below.
-8 to the y-axis=8 units
3 to the y-axis = 3 units
(-8) - (3) = 5 units from A to B
What error did Alan make? What is the actual distnace from point A to point B?
Alan made an error in subtracting the x-coordinates without considering their signs. The correct method to find the distance between two points on the same horizontal line is taking the absolute value of the difference of the x-coordinates. Thus, the actual distance from point A to point B is 11 units.
Alan made an error in calculating the distance between point A(-8,-4) and point B(3,-4). The error is in the subtraction, as he should have taken the absolute value of the difference of the x-coordinates of points A and B because the y-coordinates are the same. To find the distance between two points on a coordinate plane, the correct formula when points lie on the same horizontal line (same y-coordinates) is the absolute difference of the x-coordinates. Therefore, the actual distance is calculated as follows:
|x2 - x1| = |3 - (-8)| = |3 + 8| = 11 units
So, the actual distance from point A to point B is 11 units.
how many feet of outdoor carpet is needed for a hole measuring 6ft,2ft,5ft,2ft,3ft,3ft,and 12ft?