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.
The time that it takes to fold 1,000 origami cranes varies inversely with the number of people folding the cranes. If a class of 25 students work together to fold the 1,000 cranes, it will take 3 hours. Write an equation to show the relationship between time (t) and the number of people (n) folding cranes.
ASAP!!!!
Answer:
t = [tex]\frac{75}{n}[/tex]
Step-by-step explanation:
Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]
Replace y with t, and replace x with n, since those are the variables in this situation:
t = [tex]\frac{k}{n}[/tex]
Plug in 3 as t and 25 as n, and solve for k:
3 = [tex]\frac{k}{25}[/tex]
75 = k
Create the equation by plugging in 75 as k:
t = [tex]\frac{75}{n}[/tex]
So, the equation is t = [tex]\frac{75}{n}[/tex]
is the equation x^3 - 2x^2 + 1 = 0 a quadratic equation?
Answer:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
STEP
1
:
Equation at the end of step 1
(((x3) - 2x2) + 2x) - 1 = 0
STEP
2
:
Checking for a perfect cube
2.1 x3-2x2+2x-1 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3-2x2+2x-1
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 2x-1
Group 2: -2x2+x3
Pull out from each group separately :
Group 1: (2x-1) • (1)
Group 2: (x-2) • (x2)
The sum of an a.p is 340. the first term is 7 and the common difference is 6. Cal the number of terms in the sequence.
anyone?
Common difference: 6
First term: 7
Second term: 13
Third term: 19
Fourth term: 25
Fifth term: 31
I hope this is correct and helps!
Answer to the following question is as follows;
Number of term in AP (N) = 10
Step-by-step explanation:
Given:
Sum of arithmetic progression (Sn) = 340
First term of AP (a) = 7
Common difference of AP (d) = 6
Find;
Number of term in AP (N)
Computation:
Sn = [n/2][2a + (n-1)d]
340 = [n/2][2(7) + (n-1)6]
340 = [n/2][14 + 6n - 6]
680 = n[6n + 8]
6n² + 8n - 680
Using Quadratic Formula
n = 10
Number of term in AP (N) = 10
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The distribution of the number of children for families in the United States has mean 0.9 and standard deviation 1.1. Suppose a television network selects a random sample of 1000 families in the United States for a survey on TV viewing habits.
Required:
a. Describe (as shape, center and spread) the sampling distribution of the possible values of the average number of children per family.
b. What average numbers of children are reasonably likely in the sample?
c. What is the probability that the average number of children per family in the sample will be 0.8 or less?
d. What is the probability that the average number of children per family in the sample will be between 0.8 and 1.0?
Answer:
a) By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.
b) Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.
c) 0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less
d) 0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0
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.
Mean 0.9 and standard deviation 1.1.
This means that [tex]\mu = 0.9, \sigma = 1.1[/tex]
Suppose a television network selects a random sample of 1000 families in the United States for a survey on TV viewing habits.
This means that [tex]n = 1000, s = \frac{1.1}{\sqrt{1000}} = 0.035[/tex]
a. Describe (as shape, center and spread) the sampling distribution of the possible values of the average number of children per family.
By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.
b. What average numbers of children are reasonably likely in the sample?
By the Empirical Rule, 95% of the sample is within 2 standard deviations of the mean, so:
0.9 - 2*0.035 = 0.83
0.9 + 2*0.035 = 0.97
Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.
c. What is the probability that the average number of children per family in the sample will be 0.8 or less?
This is the p-value of Z when X = 0.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8 - 0.9}{0.035}[/tex]
[tex]Z = -2.86[/tex]
[tex]Z = -2.86[/tex] has a p-value of 0.0021
0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less.
d. What is the probability that the average number of children per family in the sample will be between 0.8 and 1.0?
p-value of Z when X = 1 subtracted by the p-value of Z when X = 0.8.
X = 1
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1 - 0.9}{0.035}[/tex]
[tex]Z = 2.86[/tex]
[tex]Z = 2.86[/tex] has a p-value of 0.9979
X = 0.8
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8 - 0.9}{0.035}[/tex]
[tex]Z = -2.86[/tex]
[tex]Z = -2.86[/tex] has a p-value of 0.0021
0.9979 - 0.0021 = 0.9958
0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0
Find the measure of XY
Answer:
70
Step-by-step explanation:
the answer is 35*2=70
Answer:
70
yhsdhjbfjdfjdfhdfh
Jan is as old as Gary was 15 years ago. Six years from now, Gary will be twice as old as Jan will be then. How old is Gary now?
Answer:
Gary is now 24years
Step-by-step explanation:
let the age of Jan be x and that of Gary be x+15
in six years time they will be as follows
Jan =x+6
Gary=x+15+6=x+21
2(x+6)=x+21
2x+12=x+21
collect the like terms
2x-x=21-12
x=9
Gary =9+15=24years
Step by step solution help me pls
Step-by-step explanation:
Recall that
[tex]1 + \tan^2 x = \sec^2 x[/tex]
and
[tex]\dfrac{d}{dx}(\tan x) = \sec^2 x[/tex]
so that
[tex]\displaystyle \int \tan^2 x = \int (\sec^2 x - 1)dx[/tex]
[tex]\:\:\:\:\:\:\:\:\:=\int \sec^2 xdx - \int dx[/tex]
[tex]\:\:\:\:\:\:\:\:\:=\tan x - x + C[/tex]
where C is the constant of integration.
Complete this sentence: The longest side of a triangle is always opposite the
• A. angle with the smallest measure
O B. angle with the greatest measure
O C. shortest side
D. second-longest side
Answer:
B. angle with the greatest measure
opposite the largest angle
What is the product of x(x + 1)?
1. 2x + x
2. x2+ 2x
3. 212 + x
4. x2 + x
Answer:
4. x²+x
Step-by-step explanation:
the product of x(x + 1) = (x)(x) + (x)(1)
= x²+x
Which of the following are not polynomials?
Answer:
A, C and D are not polynomials
Step-by-step explanation:
A because the variable has a negative power.
C because the variable is in the denominator
D because the variable has a root.
When a variable has a root, it's power is 1/2 which does not count as an ideal polynomial. You might be wondering then that why E is a polynomial?
E is a polynomial because because the root is not on the variable but on the constant.
B and E are polynomials while A,C and D are not.
Please mark me as brainliest.
solve for the solution of each linear equation.
1. 3x+1=4
2. 7x-6=0
3. 4x-5=19
4. 9x+6=8
5. 8x-7=15
Answer:
no.1 answer 0
Step-by-step explanation:
3x + 1= 4
or; 3x = 4 - 1
or; x = 3 ÷ 3
x = 0
help pls i don't get the question
Answer:
pretty sure it could
Step-by-step explanation:
Answer:
What it's asking is for 2 angles at different angles of attack, are parallel
Step-by-step explanation:
for example, // these two slashes are parallel because they wont ever touch, it wants you to find if the angles are parallel or not.
Identify the dependent and independent variable in y = 12x - 30.
Step-by-step explanation:
guess
Dependent variable: y and Independent variable: x
gauthammath dot com
Express 20% as a decimal number
Answer: 0.2
Step-by-step explanation: 20/100=1/5
and 1/5 equals 1 divided by five so it is 0.2
There are 100 cars in a car pack.28 of them are blue and 34 are red. If a car is selected at random from the cars. What is the probability that it is neither red nor blue
Answer:
0.38 = 38% probability that it is neither red nor blue.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
100 cars.
Of those, 28 + 34 = 62 are either blue or red.
100 - 62 = 38 are neither blue of red.
What is the probability that it is neither red nor blue?
38 out of 100, so:
[tex]p = \frac{38}{100} = 0.38[/tex]
0.38 = 38% probability that it is neither red nor blue.
Which triangle must be a right triangle and why?
O AA'B'C' is right because it is the image of AABC.
O AADC is right because AA' intersects AC at A.
O ABCC' is right because B lies of the line of
reflection.
O ABGC is right because G. CC')
Answer:
it would be the last one.
Step-by-step explanation:
its looking for a right triangle, a right triangle has one 90 degree angle. all of the other triagles have acute angles making them smaller than 90 degrees
Triangle BGC is the right triangle, because BG is perpendicular to CC'.
The line passing through points E, F, and G in the image is now perpendicular to the lines is DF and CG.
So we know that our triangle will be made with some of these lines.
For example, the right triangles in the figure are:
BFD, BGC, B'FD', and B'GC'.
Then, the concluded statement is ΔBGC, because BG ⊥CC.
There says that "Triangle BGC is the Right because BG is perpendicular to CC.
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A random sample of size 36 is to be taken from a population that is normally distributed with mean 72 and standard deviation 6. The sample mean of the observations in our sample is to be computed. The sampling distribution of the sample mean is
Answer:
The sampling distribution of the sample mean is approximately normal with mean 72 and standard deviation 1.
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.
Normally distributed with mean 72 and standard deviation 6.
This means that [tex]\mu = 72, \sigma = 6[/tex]
A random sample of size 36
This means that [tex]n = 36, s = \frac{6}{\sqrt{36}} = 1[/tex]
The sampling distribution of the sample mean is
By the Central Limit Theorem, it is approximately normal with mean 72 and standard deviation 1.
One number is 1/4 of another number. The sum of the two numbers is 5. Find the two numbers. Use a comma to separate your answer
Answer: 1, 4
Step-by-step explanation:
Number #1 = xNumber #2 = [tex]\frac{1}{4} x[/tex][tex]\frac{1}{4} x+x=5\\\\\frac{1}{4} x+\frac{4}{4} x=5\\\\\frac{5}{4} x=5\\\\5x=4*5\\5x=20\\x=4[/tex]
Number #1 = x = 4Number #2 = [tex]\frac{1}{4} x[/tex] = [tex]\frac{1}{4} *4=\frac{4}{4} =1[/tex]What is the range of the function shown in the graph?
у
A
8
6
2
2
X
8
- 6
2
4
6
8
2
4
6
ce
I
OA. -5 < y < 0
OB -00
O c. - < y < -5
-
5
Answer:
-∞ <y<5
Step-by-step explanation:
The range of the graph is the values that y can take. The graph can go from negative infinity to 5
-∞ <y<5
Indicate the method you would use to prove the two 's . If no method applies, enter "none".
Answer:
AAS
Step-by-step explanation:
It will be angle angle side because you are given a side and two angles, and when you put them in the correct order, you will get AAS, or SAA (not the correct way to say it)
A(n) _____ is an expression that uses variables to state a rule.
plz help asap
Answer:
A FORMULA is an expression that uses variables to state a rule.
The graphs below have the same shape. Complete the equation of the blue
graph. Enter exponents using the caret (-); for example, enter y as x^3. Do
not include "G(x) =" in your answer.
Answer:
The graphs below have the same shape. What is the equation of the blue graph? A. G(x) = (x + 3)^3 B. G(x) = x^3 + 3 C. G(x) = x^3 - 3 D. G(x) = (x - 3)^3
The blue graph is a horizontal shift to the left by 3 units of F(x) = x³.
G(x) = (x + 3)³.
What is translation?In mathematics, translation is the process of moving an object from one position to another without changing its shape, size, or orientation.
It involves sliding the object in a particular direction by a certain distance.
We have,
From the graph, the blue graph is G(x) = (x + 3)³.
The function f(x) = (x + 3)³ is a transformation of the function f(x) = x³.
Specifically, it is a horizontal shift to the left by 3 units.
To see why,
Let's consider the effect of replacing x with x + 3 in the original function f(x) = x³.
f(x + 3) = (x + 3)³
Notice that f(x + 3) is equal to f(x) translated horizontally to the left by 3 units.
For example, when x = 0, we have:
f(0) = 0³ = 0
f(0 + 3) = 3³ = 27
So the point (0, 0) on the graph of f(x) = x³ is transformed to the point
(-3, 27) on the graph of f(x) = (x + 3)³.
Similarly, we can see that every point on the graph of f(x) = x³ is shifted horizontally to the left by 3 units to obtain the graph of f(x) = (x + 3)³.
Therefore,
The blue graph is G(x) = (x + 3)³.
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WILL MARK BRAINLIEST PLEASE HELP
Answer:
Step-by-step explanation:
evaluate the expression when x= -3 and y=3
y-8x
Answer:
27
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
x = -3
y = 3
y - 8x
Step 2: Evaluate
Substitute in variables: 3 - 8(-3)Multiply: 3 + 24Add: 27[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{y - 8x}\\\\\large\textsf{= 3 - 8(-3)}\\\\\large\textsf{8(-3) = \bf -24}\\\\\large\textsf{= 3 - \bf 24}\\\\\large\textsf{= \bf 27}\\\\\boxed{\boxed{\large\textsf{\huge\textsf{Answer: \bf 27}}}}\huge\checkmark\\\\\\\\\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
22/24 Marks
51%
The diagram shows a star made by surrounding a
regular octagon with triangles.
Explain why angle a must be 135º.
+
I
Answer:
Step-by-step explanation:
shape Sides Sum of interior angles Each Angle
Triangle 3 180° 60°
Quadrilateral 4 360° 90°
Pentagon 5 540° 108°
Hexagon 6 720° 120°
Heptagon 7 900° 128.57...°
Octagon 8 1080° 135°
Nonagon 9 1260° 140°
A right rectangular prism has a length of 5 centimeters, a width of 8 centimeters, and a height of 4 centimeters. What is the volume of the prism?
Answer:
volume of prism is 160 cm
Solve the inequality. |X+19|<7
Answer:
x<-12
Step-by-step explanation: hope this helps!
What is equivalent to 3(5x-4)
Answer:
15x - 12
Step-by-step explanation:
3(5x-4)
We can find an equivalent expression by distributing the 3 to what's inside of the parenthesis (5x and -4)
3(5x-4)
* Distribute *
3 * 5x = 15x
3 * -4 = -12
An equivalent expression would be 15x -12
Joaquin drew the triangle below.
On a coordinate plane, triangle K L J has points (3, 6), (4, 0) and (negative 5, 0).
Which statement must be true about a figure that is congruent to Joaquin’s triangle?
It has two angles on the x-axis.
It has a side that is 9 units long.
It has a side that lies on the x-axis.
It has an obtuse angle.
Answer:
It has a side that is 9 units long.
Step-by-step explanation:
Answer:
B) It has a side that is 9 units long.
Step-by-step explanation:
Since it does not have two angles on the X-axis, a side that lies on the X-axis, or an obtuse angle the reasonable answer would be B as it is true, and all of the others are false.
Sara is working on a Geometry problem in her Algebra class. The problem requires Sara to use the two quadrilaterals below to answer a list of questions.
Part A: For what one value of are the perimeters of the quadrilaterals the same? (Hint: The perimeter of a quadrilateral is the sum of its sides.)
Part B: For what one value of are the areas of the quadrilaterals the same? (Hint: The area of a quadrilateral is the product of its base and height.)
Answer:
For the perimeters, x must be equal to 2.
For the areas, it is either undefined, or something.
Step-by-step explanation:
You can first find the perimeters for both sides.
For the left shape, we add the two sides of 6 and x + 4 to get x + 10.
Then we multiply x + 10 by 2 because there are 4 sides, and we only got 2 sides.
The perimeter of the first shape is 2x + 20.
The second shape can be solved by doing the same thing by adding 2 and 3x + 4 to get 3x + 6.
3x + 6 times 2 is 6x + 12.
The second perimeter is 6x + 12.
If both sides are supposed to be equal, then we can write these two expressions we solved for like:
6x + 12 = 2x + 20.
Subtraction property of equality
6x + 12 - 12 = 2x + 20 - 12
Simplify
6x = 2x + 8
Again
6x - 2x = 2x - 2x + 8
Simplify
4x = 8
Division property of equality
4/4x = 8/4
Simplify
x = 2
So if x = 2, the perimeters will be the same.
You can confirm this by plugging it back into either equation.
For the areas, we just multiply the length and width for both shapes, so we get
6(x+4) = 2(3x+4)
Since they are supposed to be equal.
We simplify and get
6x + 24 = 6x + 8
We know this is false and is not possible, since we can remove the 6x because it is on both sides.
We also know that 24 is not equal to 8 (who thought!)
:D
24 ≠ 8
So it is undefined or whatever you call it.
