Find the value of x in each case
Answer:
x = 69
Step-by-step explanation:
m<M = x
From the triangle we know that
m<M + m<MNQ + m<MQN = 180
From the parallel lines we know that
m<MNQ = m<UQN = x
x + x + 42 = 180
2x + 42 = 180
2x = 138
x = 69
one story with author and summary please
Answer:
The story tells of a plain-looking little bird (the Ugly Duckling) born in a barnyard. His brothers and sisters as well as the other birds and animals on the farm tease him for being plain and ugly, so he runs off to live with a flock of wild ducks and geese until hunters shoot down the flock. Alone again, the Ugly Duckling finds a home with an old woman, but her cat and hen also tease him, so he doesn't stay there long.
In his wanderings, the Ugly Duckling comes across a flock of migrating swans, and he wishes to join them but can't because he's too young and can't fly well enough. When winter sets in, a farmer rescues the Ugly Duckling, but the farmer's children and other animals frighten him with their noise and teasing, so again, he flees. He spends a cold and lonely winter hiding in a cave until springtime, when the flock of swans comes to the lake near his hiding place.
When the Ugly Duckling approaches the swans, he's delighted to find that they accept him and treat him like one of them. When he looks at his reflection in the lake, he realizes, to his astonishment, that he's matured into a beautiful swan himself. When the swans fly off from the lake, he spreads his wings and joins them, finally having found a family who accepts him.
A forestry researcher wants to estimate the average height of trees in a forest near Atlanta, Georgia. She takes a random sample of 18 trees from this forest. The researcher found that the average height was 4.8 meters with a standard deviation of 0.55 meters. Assume that the distribution of the heights of these trees is normal. For this sample what is the margin of error for her 99% confidence interval
Answer:
The margin of error for her confdence interval is of 0.3757.
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 = 18 - 1 = 17
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.8982
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
Standard deviation of 0.55 meters.
This means that [tex]s = 0.55[/tex]
What is the margin of error for her 99% confidence interval?
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]M = 2.8982\frac{0.55}{\sqrt{18}}[/tex]
[tex]M = 0.3757[/tex]
The margin of error for her confdence interval is of 0.3757.
Margin of error is the distance between the mean and the limit of confidence intervals. The margin of error for the given condition is 3.28 approximately.
What is the margin of error for small samples?Suppose that we have:
Sample size n < 30
Sample standard deviation = sPopulation standard deviation = [tex]\sigma[/tex]Level of significance = [tex]\alpha[/tex]Degree of freedom = n-1Then the margin of error(MOE) is obtained as
Case 1: Population standard deviation is knownMargin of Error = [tex]MOE = T_{c}\dfrac{\sigma}{\sqrt{n}}[/tex]
Case 2: Population standard deviation is unknown[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}[/tex]
where [tex]T_{c}[/tex] is critical value of the test statistic at level of significance
For the given case, taking the random variable X to be tracking the height of trees in the sample taken of trees from the considered forest.
Then, by the given data, we get:
[tex]\overline{x} = 4.8[/tex], [tex]s = 4.8[/tex], n = 18
The degree of freedom is n-1 = 17
Level of significance = 100% - 99% = 1% = 0.01
The critical value of t at level of significance 0.01 with degree of freedom 17 is obtained as T = 2.90 (from the t critical values table)
Thus, margin of error for 99% confidence interval for considered case is:
[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}\\\\MOE = 2.9 \times \dfrac{4.8}{\sqrt{18}} \approx 3.28[/tex]
Thus, the margin of error for the given condition is 3.28 approximately.
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What is the value of 3 minus (negative 2)?
A number line going from negative 5 to positive 5.
Answer:
5
Step-by-step explanation:
3-(-2) will become positive 5. so number line will go towards positive 5.
3z+8=12+3x-2
I really need the answer to this asap
Answer:
3z+3x=2
Step-by-step explanation:
3z+8=12+3x-2
collecting like terms
3z-3x=12-2-8
3z-3x=2
3z=2+3x
divide through by three
z= ⅔+x
Midsegments geometry acellus pls helppfpfpff
Answer:
BC = 28
Step-by-step explanation:
The midsegment DF is half the measure of the third side BC , then
BC = 2 × DF = 2 × 14 = 28
when price of indomie noodles was lowered from #50 to #40 per unit, quantity demanded increases from 400 to 600 units per week. calculate the coefficient of price elasticity of demand and determine whether by lowering price this firm has made a wise decision
Answer:
The price elasticity of demand is -10
Step-by-step explanation:
Given
[tex]p_1,p_2 = 50,40[/tex]
[tex]q_1,q_2 = 400,500[/tex]
Solving (a): The coefficient of price elasticity of demand (k)
This is calculated as:
[tex]k = \frac{\triangle q}{\triangle p}[/tex]
So, we have:
[tex]k = \frac{500 - 400}{40 - 50}[/tex]
[tex]k = \frac{100}{-10}[/tex]
[tex]k = -10[/tex]
Because |k| > 0, then we can conclude that the company made a wise decision.
11 Emilio makes metal fences.
He is making a fence using this design.
1.44 m
DO NOT WRITE IN THIS AREA
1.8 m
.
The fence will need
3 horizontal metal pieces of length 1.8m
2 tall metal pieces of length 1.44 m
5 medium metal pieces
6 short metal pieces as shown on the diagram.
The heights of the tall, medium and short metal pieces are in the ratio 9:8:7
.
How many metres of metal in total does Emilio need to make the fence?
Answer:
21.4 m
Step-by-step explanation:
Let x represent the sum of the tall metal, medium metal and short metal heights. Since the tall metal has a length of 1.44 m, and the ratio is in 9:8:7, hence:
(9/24) * x = 1.44
x = 3.84 m
For the medium metal pieces:
(8/24) * 3.84 = medium metal height
medium metal height = 1.28 m
For the short metal pieces:
(7/24) * 3.84 = short metal height
short metal height = 1.12 m
Total horizontal metal piece length = 3 * 1.8 m = 5.4 m
Total tall metal piece length = 2 * 1.44 m = 2.88 m
Total medium metal piece length = 5 * 1.28 m = 6.4 m
Total short metal piece length = 6 * 1.12 m = 6.72 m
Total length of metal = 5.4 + 2.88 + 6.4 + 6.72 = 21.4 m
Suppose a large shipment of televisions contained 9% defectives. If a sample of size 393 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%
Answer:
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose a large shipment of televisions contained 9% defectives
This means that [tex]p = 0.09[/tex]
Sample of size 393
This means that [tex]n = 393[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 3%?
Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812
X = 0.06
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]
[tex]Z = -2.08[/tex]
[tex]Z = -2.08[/tex] has a p-value of 0.0188
0.9812 - 0.0188 = 0.9624
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
In 2006, there were 160 teachers in College A, and three fourth of them had their own vehicles. In 2007, 20 new teachers came to the school and 6 of them had own vehicles. Calculate the percentage increase in the numbers of teacher who had own vehicles.
Answer: 5%
Step-by-step explanation:
In 2006, there were 160 teachers in College A, and ¾ of them had their own vehicles, the number of people who had their own vehicles will be:
= 3/4 × 160
= 120
In 2007, 20 new teachers came to the school and 6 of them had own vehicles. This means the number if people with vehicles will be:
= 120 + 6
= 126
The percentage increase will be:
= Increase / Old vehicle owners × 100
= 6/120 × 100
= 1/20 × 100
= 5%
The Percentage increase is 5%.
An air conditioning system can circulate 310 cubic feet of air per minute. How many cubic yards of air can it circulate per minute? The air conditioning system can circulate about cubic yards of air per minute.
Answer:
310/[tex]3^{3}[/tex] = 310/27 =11.48
Step-by-step explanation:
Answer:
310/ = 310/27 =11.48
Step-by-step explanation:
The data on the box plot describes the weight of several students in sixth grade. Which of the following statements are true about the data set? Select all that apply.
One-fourth of the students weigh between 90 and 101 pounds.
One-half of the students weigh between 75 and 90 pounds.
The median weight of the sixth graders is 85 pounds.
One-fourth of the students weigh less than 75 pounds.
One-fourth of the students weigh more than 75 pounds.
The total range of weight is 40 pounds.
Answer:
Step-by-step explanation:
B
calculate the cost of 4 liters of gasoline if 10 Liters of gasoline cost $8.20 (using proportional relationship).
A . $3.28
B. $4.20
C. $8.20
D.$10
Un automóvil consume 4 galones de gasolina al recorrer 180 kilómetros y para recorrer 900 kilómetros necesita 20 galones ¿cuántos kilómetros recorre por galón? ¿Cuantos galones consumirá en 2700 kilómetros?
Answer:
45 km por galón
60 galones en 2700 Km
Step-by-step explanation:
180 / 4
45 km por galón
900 / 45
20 galones
2700 / 45
60 galones en 2700 Km
will give brainyest (m^2/3 n^-1/3)^6
Step-by-step explanation:
here is the answer to your question
Suppose that 20° of boys opted for mathematics and 40% of girls opted for mathematics. What is the probability that a student opted for mathematics if half of the class is girls?
Answer: 30%
Step-by-step explanation:
Let A be the probability of a student opting for mathematics - it consists of either boy opting for mathematics or girl opting for mathematics. As there is "or" we need to sum these probabilities.
[tex]P(A) = P(B)* P(M|G) + P(G)*P(M|G)[/tex]
[tex]P(A) = \frac{1}{2} * \frac{20}{100} + \frac{1}{2} * \frac{40}{100}[/tex]
[tex]P(A) = 3/10 = 0.3[/tex]
=> 30%
Answer:
30% Chance
Step-by-step explanation:
This one is rather simple. If half the class is girls, split 40 into half. Do the same with 20 if half is boys. Add 10 and 20 and you get 30.
How many students rank themselves as introverts? Demonstrate your work!!
Answer:
36 (maybe...)
Step-by-step explanation:
Technically there is no way to answer this question, it says that 120 ADULTS were surveyed and then asks how many STUDENTS rank themselves as introverts. But if we a supposed to assume that all adults are students:
The ratio of 3:7 means that for every 3 introverts, there are 7 extroverts.
In other words for every 10 people (total introvert+extrovert) there are 3 introverts.
So to find the number of introverts in the group of 120, just multiply by 3/10 or 0.3
The answer would be 36
Find f(4),f(0),f(-1) & f(x)=6x-7
Answer:
f(4) = 31
f(0) = 7
f(-1) = 1
Step-by-step explanation:
f(x) = 6x + 7
f(4) = 6(4) + 7
f(4) = 24 + 7
f(4) = 31
f(0) = 6(0) + 7
f(0) = 0 + 7
f(0) = 7
f(-1) = 6(-1) + 7
f(-1) = -6 + 7
f(-1) = 1
use the figure below to find the answer. find y.
9514 1404 393
Answer:
y = 7√2
Step-by-step explanation:
We are given the side opposite the angle, and we want to find the hypotenuse. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(45°) = 7/y
y = 7/sin(45°) = 7/(1/√2)
y = 7√2
__
Additional comment
In this 45°-45°-90° "special" right triangle, the two legs are the same length. Thus, ...
x = 7
Bob had 10 more cars than Paul. Paul had 15 cars.
Answer:
Bob had 25 cars
Step-by-step explanation:
10+15=25
Points A, B, C, and D lie on a line in that order. If AD/AC = 2/1 and AD/AB = 3/1, what is the value of AC/BD?
9514 1404 393
Answer:
3/4
Step-by-step explanation:
It might be easier to start by expressing the ratios with AD as the denominator.
AD/AC = 2/1 ⇒ AC/AD = 1/2
AD/AB = 3/1 ⇒ AB/AD = 1/3
From the latter, we have ...
(AD -AB)/AD = 1 -1/3 = 2/3 = BD/AD
Then the desired ratio is ...
AC/BD = (AC/AD)/(BD/AD) = (1/2)/(2/3) = (3/6)/(4/6)
AC/BD = 3/4
The area of a square is increasing at a rate of 24 centimeters squared per second. Find the rate of change of the side of the square when it is 4 centimeters. The rate of change of the side is Number cm/sec.
Answer:
3cm/s
Step-by-step explanation:
Area of a square is expressed as:
A = L²
Rate of change of area is expressed as:
dA/dt = dA/dL•dL/dt
Given that
dA/dt = 24cm²/s
L = 4cm
Required
dL/dt
Since dA/dl = 2L
dA/dl = 2(4)
dA/dl = 8cm
Subatitute the given values into the formula
24 = 8 dL/dt
dL/dt = 24/8
dL/dt = 3cm/s
HELP ASAP I WILL GIVE BRAINLIST
Find the length of an arc of a circle with a 8-cm radius associated with a central angle of 240 degrees. Give your answer in exact and approximate form to the nearest hundredth. Show and explain your work
Answer:
33.51 cm
Step-by-step explanation:
240/360 = 2/3 (Arc length is 2/3 of the total circumference)
C = 2[tex]\pi[/tex]r ( Calculate the total circumference)
C = 2(8)[tex]\pi[/tex]
C = 50.265
2/3(50.265) (Take 2/3 of the circumference. times 2 divide by 3)
33.51
Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.
The exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.
The arc length in approximate form is 33.49 radians.
What is the formula for arc length?[tex]s = r\times \theta[/tex]
where r is the radius of the circle and [tex]\theta[/tex] is the central angle in radians.
How to convert angle from degrees to radians?Radians = Degrees ×[tex]\frac{\pi}{180^{\circ}}[/tex]
For given question,
We have been given a circle with a 8-cm radius associated with a central angle of 240 degrees.
[tex]r=8~cm,~\theta=240^{\circ}[/tex]
First we convert angle in radians.
[tex]\theta=240^{\circ}\\\\\theta=240^{\circ} \times \frac{\pi}{180^{\circ}}\\\\ \theta=\frac{4\pi}{3}[/tex]
Using the formula of the arc length,
[tex]s=8\times \frac{4\pi}{3} \\\\s=\frac{32\pi}{3}[/tex]
The exact answer of the arc length is [tex]s=\frac{32\pi}{3}[/tex]
Substitute the value of [tex]\pi = 3.14[/tex]
So, the arc length would be,
[tex]\Rightarrow s=\frac{32\times \pi}{3}\\\\\Rightarrow s=\frac{32\times 3.14}{3}\\\\\Rightarrow s=33.49[/tex]radians
Therefore, the exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.
the arc length in approximate form is 33.49 radians.
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A farmer picks pumpkins from a large field. The farmer makes samples of 260 pumpkins and inspects them. If one in fifty pumpkins are not fit to market and will be saved for seeds, what is the standard deviation of the mean of the sampling distribution of sample proportions?
Answer:
[tex]\mu = 5.2[/tex]
[tex]\sigma = 2.257[/tex]
Step-by-step explanation:
Given
[tex]n = 260[/tex] -- samples
[tex]p = \frac{1}{50}[/tex] --- one in 50
Solving (a): The mean
This is calculated as:
[tex]\mu = np[/tex]
[tex]\mu = 260 * \frac{1}{50}[/tex]
[tex]\mu = 5.2[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\mu * (1-p)}[/tex]
[tex]\sigma = \sqrt{5.2 * (1-1/50)}[/tex]
[tex]\sigma = \sqrt{5.2 * 0.98}[/tex]
[tex]\sigma = \sqrt{5.096}[/tex]
[tex]\sigma = 2.257[/tex]
Find the numerical value of each expression. (Round your answers to five decimal places.) (a) sinh(ln(5)) (b) sinh(5)
sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875
sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992
Value of the expression in which each variable was swapped out with a number from its corresponding domain sinh (l5)
How do you determine an expression's numerical value?sinh (5)
=sinh(1.6094) =2.39990 rad
=sinh(1.6094) =2.3
By doing the following, you may determine the numerical value of an algebraic expression: Replace each variable with the specified number. Then, enter your score in your team's table.
Analyze expressions that are linear.Multi-variable expressions should be evaluated.Analyze expressions that are not linear.Value of the expression in which each variable was swapped out with a number from its corresponding domain. In the case of a number with only one digit, referring to the numerical value associated with a digit by its "value" is a convenient shorthand.
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The sum of the base and height of a triangle is 14 cm. Which of the following equations could be used to find the maximum area of the triangle?
A) A = 0.5x^2 - 15x
B) A = -0.5x^2 + 7x
C) A = -x^2 + 10x
D) A = x^2 - 10x
Answer:
B
Step-by-step explanation:
Let the base of the triangle be b and the height be h.
The sum of the base and height is 14. Thus:
[tex]b+h=14[/tex]
Recall that the area of a triangle is given by:
[tex]\displaystyle A=\frac{1}{2}bh[/tex]
From the first equation, solve for either variable:
[tex]h=14-b[/tex]
Substitute:
[tex]\displaystyle A=\frac{1}{2}b(14-b)[/tex]
Distribute:
[tex]\displaystyle A=\frac{1}{2}(14b-b^2)[/tex]
Distribute:
[tex]\displaystyle A=-0.5b^2+7b[/tex]
Let b = x. Hence:
[tex]A=-0.5x^2+7x[/tex]
Therefore, our answer is B.
Find the volume
h=9cm
8cm
8cm
Answer: (8x8x9)/3=192
Test 21,753 for divisibility by 2,3,5,9 and 10
Answer:
Step-by-step explanation:
21,753
at unit place=3 not an even number,not equal to 5 and not equal to 0
so 21,753 is not divisible by 2,5 and 10
again
2+1+7+5+3=18 divisible by 3 and 9.
so 21,753 is divisible by 3 and 9.
Convert the following 11110011.001 to decimal
Answer:
243.125
Step-by-step explanation:
First do the integral part
11110011
1. From left to right, starting with a zero,
2. add the digit, double, move on to the next digit and repeat step 2 until digits are exhausted.
The successive results are
1
3
7
15
30
60
121
243
For the decimal part, we proceed similarly but
1. From the right-most digit proceed to the left, start with a zero.
2. Add the digit, halve, move on to the next digit and repeat step 2 until the decimal is reached.
Successive results are:
0.5
.25
.125
So the final result is 11110011.001 binary is 243.125 decimal
Question 1 of 10
Estimate the difference of the decimals below by rounding to the nearest
whole number. Enter your answer in the space provided.
46.327
-4.801
Answer:
Step-by-step explanation:
46.327=46 ( neaarest whole number)
-4.801=-5 (nearest whole number)
46-(-5)=46+5=51
