Answer: -1
Step-by-step explanation:
Evaluate 4x if x = -1/4
4(-1/4) = -1
Answer: -1
Step-by-step explanation:
4x and x = -1/4
plug x into the expression
[tex]4(-\frac{1}{4} )[/tex]
simplifies to:
[tex]-\frac{4}{4}[/tex]
4 divided by 4 is just 1, but it is negative so your final answer is
-1
There are 48 people coming to a family reunion. One fourth of them live out of state. How many live in-state?
Step-by-step explanation:
1/4×48
=12
So if 12people are out of state
48-12=36,is the number of people living in the state
A COUPLE PLAN TO HAVE THREE CHILDREN.
A) LIST ALL THE POSSIBILITIES FOR THE SAMPLE SPACE.
B) WHAT IS THE PROBABILITY THAT THEY HAVE AT MOST TWO BOYS?
C) WHAT IS THE PROBABILITY THAT THEY HAVE AT LEAST TWO GIRLS?
D) WHAT IS THE PROBABILITY THAT THEY ARE ALL OF THE SAME SEX?
Researchers wanted to study if having a long beak is related to flight and birds they surveyed a total of 34 birds the data are shown in the contingency table below what is the relative risk of flying for those birds that have long beaks
The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.
What is an odds ratio?An odds ratio is a measure of the strength of an association with the exposure and outcome.
The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).
Flies Does not fly Total
Long beak 11 7 19
Not a long beak 3 13 15
Total 14 20 34
Probability of long beaks flying = 0.79 (1/14)
Probability of not having long beaks flying = 0.21 (3/14)
Odds ratio = 3.76 (0.79/0.21)
Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.
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Complete question
Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.
Long beakNot a long beakTotalFlies11719Does not fly31315Total142034
What percent of 50 is 15?
A. 0.3%
B. 7.5%
C. 30%
D. 35%
Answer:30%
Step-by-step explanation:
10% of 50 is 50/10 so 10% is 5
15/5=3 so its three lots of 10%
3*10%=30%
Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive?
(–∞, –3)
(–∞, 3)
(–3, ∞)
(3, ∞)
The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)
on what interval is the function positive?The function is positive when g(x) > 0.
Then we need to solve:
∛(x - 3) > 0
We can directly remove the cubic root, because it does not affect the sign of the argument, then:
x - 3 > 0
x > 3
The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)
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The interval which the function is positive is (3, ∝)
How to determine the positive interval?
The equation of the function is given as:
g(x) =∛x - 3
Set the radical greater than 0
x - 3 > 0
Add 3 to both sides of the inequality
x > 3
Express as an interval notation
(3, ∝)
Hence, the interval which the function is positive is (3, ∝)
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When it is Noon (12 pm) in London, it is 10pm in Sydney, Australia. Dan in London rings his friend Boski in Sydney at 15:30pm on Christmas Day. What time is it in Sydney?
A. 1am
B. 1:30am
C. 2am
S. 2:30am
The time at Sydney when Dan rings his friend is 1 : 30 am (option B).
What is the time at Sydney?The first step is determine the time difference between London and Sydney.
Time difference = time at Sydney - time at London
( 12 + 10pm) - 12pm
22pm - 12pm = 10 hours
The second step is to add the time difference to the time it was when Dan rang.
15 : 30 pm + 10pm = 25 : 30
We know that there are only 24 hours in day, so subtract 24 hours from 25 : 30
25 : 30 - 24 = 1 : 30 am
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A glass inform of frustrum of cone
The volume of the cone illustrated will be 117.2 unit³.
How to illustrate the information?From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.
It should be noted that the volume of a cone is calculated as:
= 1/3 πr²h.
where,
π = 3.142
r = radius = 4cm
h = height = 7cm
In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:
= 1/3πr²h
= 1/3 × 3.14 × 4² × 7
= 117.2 unit³
Therefore, the volume of the shape is 117.2 unit³.
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Complete question:
A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.
Suppose the length and width of the box double. Does the surface area S double? Complete the explanation.
Help!
A recent food drive distributed 6,298 pounds of stoneground cornmeal to 1,007 people. Approximately how many pounds did each person receive? Round to the hundredths.
Answer: 6.25
Step-by-step explanation: Here, you want to find how much of 6,298 pounds of food each person got. You can do this by dividing. 6,298/1,007 should get you the answer because it shows how the 6,298 pounds were distributed amongst the 1,007 people.
The points
(−1.2,2.9) and (2.9,9.46) are on the graph of a linear relationship between two variables, x and y
Write a formula that expresses
y in terms of x
What is the value of y when x=115
[tex](\stackrel{x_1}{-1.2}~,~\stackrel{y_1}{2.9})\qquad (\stackrel{x_2}{2.9}~,~\stackrel{y_2}{9.46}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9.46}-\stackrel{y1}{2.9}}}{\underset{run} {\underset{x_2}{2.9}-\underset{x_1}{(-1.2)}}}\implies \cfrac{6.56}{2.9+1.2}\implies \cfrac{6.56}{4.1}\implies 1.6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2.9}=\stackrel{m}{1.6}(x-\stackrel{x_1}{(-1.2)}) \\\\\\ y-2.9=1.6(x+1.2)\implies y-2.9=1.6x+1.92\implies \boxed{y=1.6x+4.82} \\\\\\ \textit{when x = 115, what is "y"?}\qquad y=1.6(115)+4.82\implies y=188.82[/tex]
Please need help fast
Instructions: Match the following data with the correct histogram.
The histogram that correctly shows the data in the table is the histogram number four.
What is a histogram?This a type of graph that allows people to visually represent data by using bars and gathering the data they have in different categories.
How should the data in the table be represented?This data can be represented using ranges of temperature and the number o elements or substances in these ranges.
0-500°C = 5 elements500 - 1000°C = 1 element1000-1500°C = 1 element1500-2000°C = 1 element2000-2500°C= 2 elements2500-3000°C= 2 elements3000-3500°C= 2 elements3500-4000°C= 1 elementThis data matches the fourth graph
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Thirty-two percent of workers in Troberca City are college graduates. You randomly select 50 workers and ask them is he or she is a
college graduate. Find the probability that less than 18 workers are college graduate. (Approximating a Binomial Distribution)
(A) 32.6%
B 67.4%
64.0%
36.0%
The correct option is B) 67.4%
What is the z- score table?A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.
Given here, P(probability that a worker is a college graduate) = 32%
= 0.32
q (probability that a worker is not a college graduate) is 1-0.32 = 0.68
now μ(mean) = n×p
= 50×0.32
= 16
Again standard deviation σ = [tex]\sqrt{npq\\}[/tex]
σ = [tex]\sqrt{50\cdot 0.32\cdot 0.68}[/tex]
σ = 3.2985
now P(x<17.5) = P((x-μ)/σ <(17.5-16)/3.2985)
= P(z<0.45)
= 0.674 [using z table]
= 67.4%
Hence option 2 is the correct answer
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a) Find the perimeter of a rectangle whose length is 10 10²/3 cm and breadth is 6 cm.
please need fast I will make brilliant
Answer:
40
Step-by-step explanation:
P=2(l+w)
2·(10+10)
=40
Could you please help me solve this question?
Find the common ratio: 64, -16, 4, -1, ...
The common ratio of the given sequence is -1/4. In a geometric sequence, the common ratio is the value that is in between each number in the sequence.
What is the common ratio?The ratio of the value of a term in the sequence to the value of the previous term in the sequence is said to be the common ratio. I.e.,
C.R = (nth term)/(n - 1)th term
Calculation:The given sequence is 64, -16, 4, -1, ...
Taking the ratio of the second term to the first term, we get
-16/64 = -1/4
Similarly, the ratio of the third term to the second term,
4/16 = -1/4
Since the ratios are equal, then the common ratio of the sequence is -1/4.
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Divide. write your answer in simplest form. 7/9 divided by 8/15
Answer:
Step-by-step explanation:
7/9 * 15/8 = 105/72 = 35/24
Suppose 45% of the population has a college degree.
If a random sample of size 437 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%? Round your answer to four decimal places.
Using the normal distribution, there is a 0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The proportion estimate and the sample size are given as follows:
p = 0.45, n = 437.
Hence the mean and the standard error are:
[tex]\mu = p = 0.45[/tex][tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.45(0.55)}{437}} = 0.0238[/tex]The probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3% is 2 multiplied by the p-value of Z when X = 0.45 - 0.03 = 0.42.
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (0.42 - 0.45)/0.0238
Z = -1.26
Z = -1.26 has a p-value of 0.1038.
2 x 0.1038 = 0.2076.
0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.
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What is the standard form equation of the ellipse that has vertices (-15, 4) and (5, 4) and co-vertices (-5, -3) and
(-5, 11)?
Step-by-step explanation:
Notice that the main vertices (-15,4) and (5,4) both have the same y coordinate. This means that the focal axis is horizontal so we have a horizontal ellispe.
Equation of a horizontal ellipse is
[tex] \frac{(x - h) {}^{2} }{ {a}^{2} } + \frac{(y - k) {}^{2} }{ {b}^{2} } = 1[/tex]
I'll explain the variables.
Step 1: Find the center.
The center (h,k) is the midpoint of either the main or co vertices. It doesn't matter because of the definition of an ellipse.
So using the midpoint formula, let find the midpoint of the main vertices.
[tex]( \frac{ - 15 + 5}{2} ) = - 5[/tex]
[tex] \frac{4 + 4}{2} = 4[/tex]
So our center is (-5,4) so as of right now we have
[tex] \frac{(x + 5) {}^{2} }{ {a}^{2} } + \frac{(y - 4) {}^{2} }{ {b}^{2} } = 1[/tex]
Step 2: The variable a represents the semi major axis. This
basically means what is the distance from the center to either main vertex.
Here, let use (5,4). Using (5,4), our main vertex and (-5,4), our center.
Use the distance formula
[tex]a= \sqrt{(5 - ( - 5) {}^{2} + (4 - 4) {}^{2} } [/tex]
[tex]a = \sqrt{100} [/tex]
[tex]a= 10[/tex]
So our distance is 10, this means a=10
Step 3: The variable b represent the semi minor axis. This basically the distance from the center to either co vertex.
Using the distance formula,
[tex]b = \sqrt{ (- 5 - ( - 5) {}^{2} + (4 - 11) {}^{2} } [/tex]
[tex]b = \sqrt{49} [/tex]
[tex]b = 7[/tex]
So b=7, so finally we plug a=10, b=7
[tex] \frac{(x + 5) {}^{2} }{100} + \frac{(y - 4) {}^{2} }{49} = 1[/tex]
Work with your teacher/tutor. Match each inequality with its graph. Use the online tool to complete this
activity. The first one Is done for you.
The inequalities are matched with the respective graphs as shown in the attached image.
What is an inequality?In mathematics, inequality is the relationship between two non-equal expressions, denoted by a sign such as 'not equal to,' > 'greater than,' or 'less than.'
Roads feature speed limits, some movies have age limitations, and the time it takes to go to the park are all instances of inequalities in the real world.
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If A= {1,2,3,4,5},B= {1,3,5,7}and C= {2,4,6,8}
Step-by-step explanation:
Intersection of A and B={1,3,5}Intersection of B and C={ }B - A={1,3,5,7} - {1,2,3,4,5} ={1,7}
19. At a boardroom meeting, the sales manager is happy to announce that sales have risen from $850,000 to $1,750,000 at a
rate of 4.931998% per year. How many years did it take for the sales to reach $1,750,000?
The number of years it would take sales to reach $1,750,000 is 14.65 years.
What is the number of years?The formula that can be used to determine the number of years it would take for the sales to reach $1,750,000 is:
Number of years : In (FV / PV) / r
Where:
FV = future level of sales - $1,750,000PV = present level of sales = 850,000r = rate of growth - 4.931998%Number of years : In ($1,750,000 / 850,000) / 0.04931998
Number of years : In (2.06) / 0.04931998
Number of years : 14.65 years
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Please help me I’m stuck
Answer:
-1/3
5
Step-by-step explanation:
We need to complete
y = mx + b
with a slope, m, and with the y-intercept, b.
From the graph, we see that the line intersects the y-axis at y = 5, so the y-intercept, b, is 5.
We now have y = mx + 5.
Now we need the slope.
We pick two points that are easy to read, (0, 5) and (3, 4).
m = slope = rise/run
To go from (3, 4) to (0, 5), we go up vertically 1 unit. The rise is 1.
Then we go left horizontally 3 units. The run is -3.
m = slope = rise/run = 1/(-3) = -1/3
Now we have the slope, so we can finish.
y = -1/3 x + 5
Answer:
-1/3
5
HELPPPPPP PLSSSSSSSSSS
Answer:
wait ewiai twia it i ti i got this soon
(1+3) x (2 x 3)
please help with question
Applying precedence of operations, the result of the expression is of 161.
What is the precedence of operations?Power operations are done before multiplication/division, which are also done before addition/subtraction.
Operations inside brackets or parenthesis also take precedence.
In this problem, the operation is:
[3 x 2^5 + 13 x (-2)] + 7[8 - (4 - 9)]
First the power:
[3 x 32 + 13 x (-2)] + 7[8 - (4 - 9)]
Now the multiplications on the first bracket, and the subtraction on the second:
[96 - 26] + 7[8 - (-5)]
Then, applying the parenthesis to the negative number, we have that:
[96 - 26] + 7[8 - (-5)] = 70 + 7 x 13 = 161.
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[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3 \times 2^5 + 13(-2)] + 7[8 - (4 - 9)]}[/tex]
[tex]\mathsf{= 3\times32 + 13\times -2 + 7[8 - (4 - 9)] }[/tex]
[tex]\mathsf{= 96 + 13\times -2 + 7(8 - (4 - 9))}[/tex]
[tex]\mathsf{= 96 - 26 + 7(8 - (4 - 9))}[/tex]
[tex]\mathsf{= 70 + 7(8 - (4 - 9))}[/tex]
[tex]\mathsf{= 70 + 7(8 - (-5))}[/tex]
[tex]\mathsf{= 70 + 7\times13}[/tex]
[tex]\mathsf{= 70 + 91}[/tex]
[tex]\mathsf{= 161}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{161}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
? km
2.6 km
Area = 20.8 km²
What is the height of Thai rectangle?
A cereal box filling machine is designed to release an amount of 16 ounces of cereal into each box, and the machine’s manufacturer wants to know of any departure from this setting. The engineers at the factory randomly sample 150 boxes of cereal and find a sample mean of 15.75 ounces. If we know from previous research that the population is normally distributed with a standard deviation of 1.46 ounces, is there evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance? State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.
Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is not different to 16 ounces, that is:
[tex]H_0: \mu = 16[/tex]
At the alternative hypothesis, it is tested if the mean is different, hence:
[tex]H_1: \mu \neq 16[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are:
[tex]\overline{x} = 15.75, \mu = 16, \sigma = 1.46, n = 150[/tex].
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{15.75 - 16}{\frac{1.46}{\sqrt{150}}}[/tex]
z = -2.1
What is the p-value and the conclusion?Using a z-distribution calculator, for a two-tailed test, as we are testing if the mean is different of a value, with z = -2.1, the p-value is of 0.0357.
Since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.
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Add 10/12 and 6/10 as a mixed number
Answer:
1 13/30
Step-by-step explanation:
10/12 + 6/10 =
= 5/6 + 3/5
= 25/30 + 18/30
= 43/30
= 30/30 + 13/30
= 1 13/30
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Equation:}[/tex]
[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]
[tex]\huge\textsf{Solving:}[/tex]
[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]
[tex]\mathsf{= \dfrac{10\div2}{12\div2} + \dfrac{6\div2}{10\div2}}[/tex]
[tex]\mathsf{= \dfrac{5}{6} + \dfrac{3}{5}}[/tex]
[tex]\mathsf{= \dfrac{5\times5}{6\times5} + \dfrac{3\times6}{5\times6}}[/tex]
[tex]\mathsf{= \dfrac{25}{30} + \dfrac{18}{30}}[/tex]
[tex]\mathsf{= \dfrac{25 + 18}{30-0}}[/tex]
[tex]\mathsf{= \dfrac{25 + 18}{30}}[/tex]
[tex]\mathsf{= \dfrac{43}{30}}[/tex]
[tex]\approx\mathsf{1\dfrac{13}{30}}[/tex]
[tex]\huge\textsf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{1\dfrac{13}{30}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Derive Integral equation for dy/dv
By the fundamental theorem of calculus,
[tex]\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}[/tex]
In general,
[tex]\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}[/tex]
The price of an item has risen to $187 today. Yesterday it was $110. Find the percentage increase.
Answer:
Percent increase is 70%.
Step-by-step explanation:
The original price was $110. That will go on the bottom (denominator) in our calculation. On the top (numerator) we put the change in the dollar amount. The new price is $187. So we'll subtract:
187 - 110
= 77
The change in price was $77.
change/original
= 77/110
= 0.7
Change the decimal answer to a percent by multiplying by 100.
0.7 × 100
= 70%
The percent increase is 70%.
Which of the triangles in the diagram are congruent?
Triangle 1, triangle 3 and triangle 4 are congruent triangles bases on side-side-side and side-angle-side congruency.
What are congruent triangles?Triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, equilateral and scalene triangle.
Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other. Also, their corresponding angles are congruent.
Triangle 1, triangle 3 and triangle 4 are congruent triangles bases on side-side-side and side-angle-side congruency.
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