Given:
The triangle ABC is reflected over the x-axis.
The distance between point A and A’ is 14.
To find:
The distance between the x-axis and A’.
Solution:
If a figure is reflected across the x-axis then the corresponding parts are mirror image of each other about the x-axis.
It means the distance between A and x-axis is same as the distance between x-axis and A'.
The distance between point A and A’ is 14.
Let d be the distance between the x-axis and A’. Then,
[tex]d+d=14[/tex]
[tex]2d=14[/tex]
[tex]d=\dfrac{14}{2}[/tex]
[tex]d=7[/tex]
Therefore, the correct option is 1.
In a class of 20 students, all but 4 of the students put their names on a typed assignment. If the teacher randomly guesses, what is the probability that she correctly guesses which paper belongs to each of the four remaining students
Answer:
4.17%
(1/4)(1/3)(1/2)(1)
alternative you can say that there are 24 permutations of
4 items and that you have to guess 1 of them 1/24 = 4.17%
Step-by-step explanation:
0.25
0.333333333
0.5
1
Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.) 3 217
Using a linear approximation, the estimated cube root of 217 is 6.00925.
Given that the number is,
The cube root of 217
Now, for the cube root of 217 using a linear approximation, use differentials.
So, the derivative of the function [tex]f(x) = x^{(1/3)[/tex] at a known point.
Taking the derivative of [tex]f(x) = x^{(1/3)[/tex], we get:
[tex]f'(x) = (\dfrac{1}{3} )x^{-2/3[/tex]
Now, we can choose a point near 217 to evaluate the linear approximation.
Let's use x = 216, which is a perfect cube.
Substituting x = 216 into the derivative, we get:
[tex]f'(216) = (\dfrac{1}{3} )(216)^{-2/3[/tex]
[tex]= 0.00925[/tex]
Next, use the linear approximation formula:
Δy ≈ f'(a)Δx
Since our known point is a = 216 and we want to estimate the cube root of 217,
since 217 - 216 = 1
Hence, Δx = 1
Δy ≈ f'(216)
Δx ≈ 0.00925 × 1
≈ 0.00925
Finally, add this linear approximation to the known value at the known point to get our estimate:
Estimated cube root of 217 ;
f(216) + Δy = 6 + 0.00925
= 6.00925
Therefore, the estimated cube root of 217 is 6.00925.
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What is the value of x?
30 students in grade 8 finished their summer packet before August 15.
This was 12% of all the students. How many students are in grade 8?
Step-by-step explanation:
12/100=30/x
12x=3000
x=250
hiii! !!
Help please and thanks !!
Answer:
4th option
Step-by-step explanation:
tanZ = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{XY}{ZY}[/tex]
help me plsssssssss:(
Answer:
1: $1200
2: Food ($6000)
3: $3000
4: $1800
5: $3000
Step-by-step explanation:
1: 10%*12000 = 1200
2: Food 50%*12000 = 6000
3: 25%*12000 = 3000
4: 15%*12000 = 1800
5: Food - Education = 6000 - 3000 = 3000
. Which equation represents y = −x2 + 4x − 1 in vertex form?
Answer:
Rewrite in vertex form and use this form to find the vertex
(
h
,
k
)
.
(
2
,
3
)
Step-by-step explanation:
BRAINLIEST HELP ME!!!
Which graph shows the solution to this system of linear Inequalities?
ys2x-3
A. Graph
B. Graph B
C. Graph A
D. Graph D
A box contains 5 orange pencils, 8 yellow pencils, and 4 green pencils.
Two pencils are selected, one at a time, with replacement.
Find the probability that the first pencil is green and the second pencil is yellow.
Express your answer as a decimal, rounded to the nearest hundredth.
Answer:
total pencil = 5 orange pencils + 8 yellow pencils + 4 green pencils
= 17 pencils
P (g n y) = 4/17 + 8/17
= 0.706
Step-by-step explanation:
1. first find the total number of pencils
2. since there is a replacement the demoinator remains the same
3. find the probability of each green and yellow
4. add the two probability
the All-star appliance shop sold 10 refrigerators, 8 ranges, 12 freezers, 12 washing machines, and 8 clothes dryers during January. Freezers made up what part of the appliances sold in January?
Answer:
Freezers made up [tex]\frac{6}{25}[/tex] = 24% of the appliances sold in January.
Step-by-step explanation:
We have that:
10 + 8 + 12 + 12 + 8 = 50 parts were sold in January.
Freezers made up what part of the appliances sold in January?
12 of those were freezers, so:
[tex]\frac{12}{50} = \frac{6}{25} = 0.24[/tex]
Freezers made up [tex]\frac{6}{25}[/tex] = 24% of the appliances sold in January.
Two linear equations are shown in the graph.
#Brainliest award
What are the coordinates of the point where the two lines intersect?
A. (–2, 3)
B. (3, 3)
C. (3, 0)
D. (–3, 3)
Answer:
I am taking this graph because this question looked similar to this one.
Step-by-step explanation:
Answer should be B.
The intersection point is (3,3)
2/5 e +4 = 9
Help please
Answer:
e=12.5 or e=25/2
Step-by-step explanation:
you are making meat loaf with yield: 50, 4oz portions what is the total recipe cost
Answer:
[tex]200oz[/tex]
Step-by-step explanation:
The question says that there are [tex]50[/tex] portions that are [tex]4oz[/tex] each.
Write an equation
[tex](50)4oz[/tex]
Simplify
[tex]200oz[/tex]
A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective. Is it fair to reject the manufacturer's claim based on this observation?
Answer:
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Step-by-step explanation:
A manufacturer of nails claims that only 4% of its nails are defective.
At the null hypothesis, we test if the proportion is of 4%, that is:
[tex]H_0: p = 0.04[/tex]
At the alternative hypothesis, we test if the proportion is more than 4%, that is:
[tex]H_a: p > 0.04[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
4% is tested at the null hypothesis
This means that [tex]\mu = 0.04, \sigma = \sqrt{0.04*0.96}[/tex]
A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.
This means that [tex]n = 20, X = 0.1[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.1 - 0.04}{\frac{\sqrt{0.04*0.96}}{\sqrt{20}}}[/tex]
[tex]z = 1.37[/tex]
P-value of the test and decision:
Considering an standard significance level of 0.05.
The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.
Looking at the z-table, z = 1.37 has a p-value of 0.9147
1 - 0.9147 = 0.0853
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Answer:
Considering an standard significance level of 0.05.
The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.
Looking at the z-table, z = 1.37 has a p-value of 0.9147
1 - 0.9147 = 0.0853
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Step-by-step explanation:
find from first principle the derivative of 3x+5/√x
Answer:
[tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex]Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{3x + 5}{\sqrt{x}}[/tex]
Step 2: Differentiate
Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle \frac{3x + 5}{x^\bigg{\frac{1}{2}}}[/tex]Quotient Rule: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})\frac{d}{dx}[3x + 5] - \frac{d}{dx}[x^\bigg{\frac{1}{2}}](3x + 5)}{(x^\bigg{\frac{1}{2}})^2}[/tex]Simplify [Exponential Rule - Powering]: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})\frac{d}{dx}[3x + 5] - \frac{d}{dx}[x^\bigg{\frac{1}{2}}](3x + 5)}{x}[/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})(3x^{1 - 1} + 0) - (\frac{1}{2}x^\bigg{\frac{1}{2} - 1})(3x + 5)}{x}[/tex]Simplify: [tex]\displaystyle \frac{d}{dx} = \frac{3x^\bigg{\frac{1}{2}} - (\frac{1}{2}x^\bigg{\frac{-1}{2}})(3x + 5)}{x}[/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle \frac{d}{dx} = \frac{3x^\bigg{\frac{1}{2}} - (\frac{1}{2x^{\frac{1}{2}}})(3x + 5)}{x}[/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle \frac{d}{dx} = \frac{3\sqrt{x} - (\frac{1}{2\sqrt{x}})(3x + 5)}{x}[/tex]Simplify [Rationalize]: [tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
How do you solve this problem and what did you do to gain the answer 1/64+5/8-3/32=?
Answer:
the answer is 35/64(in fraction) but in decimals it's 0.55
Assume 10% of Berkeley students are left-handed. If you are in a class of 50 people, what is the probability that exactly 4 of them are left-handed? Round your answer to the nearest hundredth, and omit the leading zero. Enter your answer here.
Answer:
The answer is "0.18"
Step-by-step explanation:
[tex]10\% \ of \ 50= 5 \text{are left handed}\\\\45\ \text{are right handed}\\\\[/tex]
If the probability exactly 4 were heft handed
[tex]=^{50}_{C_4}\times (\frac{5}{50})^4 \times (\frac{45}{50})^{4b}\\\\=^{50}_{C_4} \times (0.1)^4 \times (0.9)^{4b}\\\\=230300 \times (0.1)^4 \times (0.9)^{4b}\\\\=0.181 \approx 0.18[/tex]
I really need help with this problem
Step-by-step explanation:
(x)+(x+1)<832x+1<832x<83-1x<82/2x<41hope it helps.stay safe healthy and happy....Answer:
[tex]x<41[/tex]
Step-by-step explanation:
[tex](x)+(x+1)<83[/tex]
simplify both sides
[tex]2x+1<83[/tex]
subtract one from the both sides to isolate the variable
[tex]2x<82[/tex]
divide both sides by 2 to isolate the variable
[tex]x<41[/tex]
Based on the graph, find the set of all x-values for which the points P(x,y) are on the graph y>0. Enter your answer using interval notation
Answer:
The solution set is: (-1,3)
We want to find the set of the x-values of the points that belong to the given graph and have an y-value larger than zero.
The set is: s = (-1, 3)
To find the set, we need to see the x-values of the points on the graph such that y > 0.
y > 0 means that we only look at the region of the graph that is above the x-axis.
We can see that this region goes from x =-1 to x = 3
Then for all the x-values between x = -1 and x = 3 the points p(x, y) on the graph have an y-value larger than zero.
Notice that because the value must be larger than zero, then the particular x-values:
x = -1 and x = 3 are not in the set.
So the set must be written as:
s = (-1, 3)
This is the set in the interval notation.
If you want to learn more, you can read:
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The sum of two numbers is 44 . One number is 3 times as large as the other. What are the numbers?
Answer:
11 and 33
Step-by-step explanation:
The the smaller number be [tex]x[/tex]. Since the other number is 3 times as large as the other, we can represent the large number as [tex]3x[/tex]. Because they add up to 44, we have the following equation:
[tex]x+3x=44[/tex]
Combine like terms:
[tex]4x=44[/tex]
Divide both sides by 4:
[tex]x=\frac{44}{4}=\boxed{11}[/tex]
Substitute [tex]x=11[/tex] into [tex]3x[/tex] to find the larger number:
[tex]11\cdot 3=\boxed{33}[/tex]
Therefore, the two numbers are 11 and 33.
A city has a population of 350,000 peopleSuppose that each year the population grows by 7.75%What will the population be after 6 years Use the calculator provided and round your answer to the nearest whole number
Answer:
547737
Step-by-step explanation:
So first when know that the equation for exponentinal growth is f(x)=a(1+r)^x
Then you need to substitue so it would be f(x)=350,000(1+0.0775)^6
So then you would add the 1 and 0.0775 to equal 1.0775
So now its f(x)=350,000(1.0775)^6
So after that following PEMDAS, you would basically do 1.0775 to the power of 6 and get 1.56496155465
After you would do 1.56496155465 times 350,000 and that would be 547736.544129 and since its to the nearest whole number the answer would be 547737
Hopefully, that helped. If I did end up making a mistake then just comment on my answer. :)
Someone please help thanks
Answer:
By similar triangles: BE/20 = 18/25 BE 14.4
Also, (ED + 26) / 26 = 18/14.4
ED = 6.5 and AD = 32.5
Find the distance between the two points in simplest radical form. (8,−8) and (−1,−5)
Answer:
Solution given:
[tex]x_{1},y_{1}=(8,-8)[/tex]
[tex]x_{2},y_{2}=(-1,-5)[/tex]
Now
Distance between them is:
d=[tex]\sqrt{(x_{2}-x_{1})²+(y_{2}-y_{1})²}[/tex]
d=[tex]\sqrt{(-1-8)²+(-5+8)²}=3\sqrt{10}[/tex]
Distance between them is [tex]\bold{3\sqrt{10}}[/tex]
Ellis makes some biscuits. For every 200g of flour he uses, he needs 75g of butter
a. Write a ratio for the amount of flour to the amount of butter.
b. Write a formula forf, the amount of flour, in terms of the amount of butter, b.
c. Ellis makes 24 biscuits using 300g of flour.
How many biscuits can he make with 375g of butter?
Answer:
a) 8:3, b) no formula is there, c) 30
Step-by-step explanation:
because 200/75=8:3
because there formula being obtained
because 300/24=12.5
375/12.5=30
Which graph represents the function below?
y= { -x if x > -3
x+6, if x<(or equal to)3
Answer:
second option
Step-by-step explanation:
I'm not sure how to explain but if you really need an explanation please message me
The function that represents the absolute function will be y = -|x + 3| + 3. Then the function is represented by graph A.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = | x - h| + k
The function is given below.
y = -x, if x > -3
y = x + 6, if x ≤ -3
The value of the functions at x = -3 is calculated as,
y = - (-3)
y = 3
y = -3 + 6
y = 3
The capability that addresses the outright capability will be y = - |x + 3| + 3. Then the capability is addressed by diagram A.
The graph is given below.
More about the absolute function link is given below.
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The owners of a baseball team are building a new baseball field for their team and must determine the number of seats to include. The average game is attended by 6,500 fans, with a standard deviation of 450 people. Suppose a random sample of 35 games is selected to help the owners decide the number of seats to include. Identify each of the following and be sure to round to the nearest whole number:
Provide your answer below:
μ =------------
μx=-----------
σx=-----------
σ=------------
n=------------
Answer:
μ = 6500
μx= 6500
σx= 76
σ= 450
n= 35
Step-by-step explanation:
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.
The average game is attended by 6,500 fans, with a standard deviation of 450 people.
This means that [tex]\mu = 6500, \sigma = 450[/tex]
35 games:
This means that [tex]n = 35[/tex]
Distribution of the sample mean:
By the Central Limit Theorem, we have [tex]\mu_x = \mu = 6500[/tex] and the standard deviation is:
[tex]\sigma_x = \frac{450}{\sqrt{35}} = 76[/tex]
The area of a circle is 3.142cm square.find the radius and diameter of the circle
Answer:
50.24 or 50.272
Step-by-step explanation:
Square radius and then times by 3.14 or 3.142
4^2*3.14 = 50.24
4^2*3.142 = 50.272
I need help with these questions
Answer:
1) 6m+8n
4) 21x+14y
7) 14c+16d
10) d+3e
Step-by-step explanation:
Addison drove 960 miles in 16 hours what was her speed in miles per hour
Answer:
60 miles/hour
Step-by-step explanation:
960÷16
=60 hours
Question 20 only plz and thanks
