Answers
we know a^2 + b^2 = c^2. However, we only have c^2 and b^2. So we must find in terms of a^2, and so the formula becomes a^2 = c^2 - b^2. When we plug in the numbers, we get 144 - 16 = 128, and so we just find the square root of 128.
Related Questions
At a local restaurant, the amount of time that customers have to wait for their food isnormally distributed with a mean of 12 minutes and a standard deviation of 2minutes. Using the empirical rule, determine the interval of minutes that the middle99.7% of customers have to wait.
Answers
By the empirical rule 99.7% of the customers fall within the interval bounded by
[tex]\bar{x}-3\sigma\text{ and }\bar{x}+3\sigma[/tex]In this case,
[tex]\begin{gathered} \bar{x}=12\min \text{ and} \\ \sigma=2\min \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \bar{x}-3\sigma=12-3(2)=12-6=6\min s \\ \bar{x}+3\sigma=12+3(2)=12+6=18\min s \end{gathered}[/tex]Hence, the interval of minutes that the middle 99.7% of customers have to wait is given by
(6mins, 18mins)
What is the product of 840 and 4.6 x 102 expressed in scientific notation?
Answers
We can rewrite the expression:
[tex]840\times4.6\cdot10^2=8.4\cdot10^2\times4.6\cdot10^2[/tex]The product is,
[tex](8.4\times4.6)(10^2\times10^2)=(38.64)(10^{2+2})=38.64\times10^4[/tex]E Match the corresponding congruent parts.(G.6)(6 point) DE DF / A Lc ZB EF
Answers
By definition:
Congruent figures in geometry are identical in shape and size.
This means that two figures are congruent with each other even if they are rotated, flipped or trasnlated as long as they have the identical shape and size.
For example, look at the following picture
We notice that the triangle has the same size and shaped, hence they are congruent. Furthermore we can say that the side BC is congruent to the side ZY and so on.
pythagorean theorem
Answers
Your answer may need to be rounded depending on what your teacher requires
Step by step
Pythagorean theorem
a^2 + b^2 = c^2
a^2 + 2^2 = 8^2
a^2 + 4 = 64
Subtract 4 from each side
a^2 + 4 - 4 = 64 - 4
a^2 = 60
Take the square root of both side
a= 7.75 units
Answer:
7.75 units squared
Step-by-step explanation:
10. Sydney wants to buy soda and juice for her birthday party. A bottle of soda costs $1.99 each and a jug of juice costs $2.49 each. If Sydney has $30, what equation could be used to find how many soda bottles and how many jugs of juice she can purchase? let x = let y = Equation
Answers
ANSWER
1.99x + 2.49y = 30
EXPLANATION
A bottle of soda costs $1.99 each and a jug of juice costs $2.49.
Sydney has $30.
Let x be the number of bottles of soda she can get.
Let y be the number of jugs of juice that she can buy.
This means that the cost of x bottles of soda is:
1.99 * x = $1.99x
This also means that the cost of y jugs of juice is:
2.49 * y = $2.49y
The total cost must be equal to $30, so this means that the total cost of bottles of soda and jugs of juice she can purchase is:
1.99x + 2.49y = 30
That is the equation that represents it.
I don't understand this at all.
Answers
Answer:
P1V1T2
T1= _______
P2V2
Step-by-step equation:
Pls help I’ll mark brainliest im too tired for this
Answers
Answer:
309.8$
Step-by-step explanation:
450.60 - 35.20*4
= 309.8
:]
Sketch a graph of 6 x + 4 y = 4
Answers
The graph of 6x + 4y = 4 can be sketched as shown in the image attached below.
How to Sketch the Graph of a Linear Equation?A linear equation can be expressed in standard form as Ax + By = C, where A, B, and C are integers. Also, it can be rewritten in slope-intercept form as y = mx + b, where b is the y-intercept and m is the slope of the equation.
In order to graph an equation, we can easily determine what the slope (m) and the y-intercept (m) of the graph would be when we rewrite the equation in slope-intercept form.
Given the equation in standard form as, 6x + 4y = 4, rewrite it in slope-intercept form:
6x + 4y = 4
4y = -6x + 4
y = -6x/4 + 4/4
y = -3/2x + 1
This means that the slope of the graph you'd sketch will be -3/2, and the line must intercept the y-axis at 1, because the y-intercept is 1.
The graph is shown below.
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Writing an equation of a hyperbola give me the Foci and vertices
Answers
Given the Foci of the hyperbola:
[tex]\begin{gathered} (-1,-9) \\ (-1,9) \end{gathered}[/tex]And the Vertices:
[tex]\begin{gathered} (-1,-3) \\ (-1,3) \end{gathered}[/tex]You can plot the Foci on a Coordinate Plane:
Notice that the blue line represents the Vertical Transverse Axis. Then, the equation has this form:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]You need to find the Center using the Midpoint Formula, in order to find the Midpoint between the Foci and the Midpoint between the vertices:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]- For the Foci:
[tex]M=(\frac{-1-1}{2},\frac{-9+9}{2})=(-1,0)[/tex]- For the Vertices:
[tex]M=(\frac{-1-1}{2},\frac{-3+3}{2})=(-1,0)[/tex]Therefore:
[tex]\begin{gathered} h=-1 \\ k=0 \end{gathered}[/tex]Now you need to find "a". This is the distance from the center to the vertices:
[tex]a=3-0=3[/tex]Find "b" with this formula:
[tex]b^2=c^2-a^2[/tex]Knowing that "c" is the distance from the Foci to the center:
[tex]c=9[/tex]You get:
[tex]b^2=9^2-3^2=72[/tex]Therefore, you can write this equation:
[tex]\frac{y^2}{9}-\frac{(x+1)^2}{72}=1[/tex]Hence, the answer is:
[tex]\frac{y^2}{9}-\frac{(x+1)^2}{72}=1[/tex]Consider the steps James uses to solve the equation 2(x – 10) = 24. Equation: 2(x - 10) = 24 Step 1: 2x - 10 = 24 Step 2: 2x = 34 Step 3: x = 17 In which step, if any, did James make an error? A. Step 1 B. Step 2 C. Step 3 D. James did not make an error.
Answers
In the steps that James uses to solve the given equation he made a mistake:
We have:
[tex]2\cdot(x-10)=24\Rightarrow2x-20=24[/tex]James needed to apply the distributive property in the first step. However, he did not.
Therefore, James made an error in Step 1, that is, option A.
22% of the squirrels in Cititon Park are gray. What is the probability that, in a random sample of 322
squirrels, fewer than 71 are gray squirrels? Use a normal approximation to compute your answer.
Round your answer to 4 decimal places.
Answers
The probability is 0.4841 .
Probability theory is the name of the branch of mathematics that deals with probability.
Although there are many ways to interpret the concept of probability, probability theory approaches it in a formal mathematical manner by articulating it through a set of axioms. These axioms typically formalize probability in terms of a probability space, which connects a sample space of possible outcomes to a measure that accepts values between 0 and 1. Statistical mechanics or sequential estimation are two examples of how probability theory approaches can be used to describe complicated systems when only a piece of their state is known. A significant achievement in twentieth-century physics was the description of the probabilistic nature of physical events at the atomic scale in terms of quantum mechanics.Given n = 322
p = 0.22
We know that from probability
μ = n × p = 0.22 ×322 = 70.84
σ = √(p × n×(1-p)) = 7.43
Now (P < 71) = P<70.84
Solving we get
P(z<-0.045)
= 0.48405
Therefore the probability is 0.4841
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find perimeter and area of each triangle round to nearest hundredth
Answers
Given is a right angled triangle. Consider the figure,
Using the trignoetric funcyion tan, we have,
[tex]\begin{gathered} \tan 18=\frac{a}{12} \\ a=12\times\tan 18=3.89 \end{gathered}[/tex]Now, as we have base, a = 3.89 and height c = 12, the perimeter can be calcualted as,
[tex]\begin{gathered} P=a+c+\sqrt[]{a^2+c^2} \\ \text{ =3.89+12+}\sqrt[]{3.89^2+12^2}=28.5=29 \end{gathered}[/tex]Now, the area can be calculated as,
[tex]\begin{gathered} A=\frac{1}{2}ac \\ \text{ =1/2}\times3.89\times12=23.34=23 \end{gathered}[/tex]30 60 90° triangles find the measure of the missing two sides for each figure below leave answer and rationalize and simple light form
Answers
Given : 30 60 90 triangle as shown in the following figure :
As shown : the hypotenuse of the triangle = 28√5
The side length opposite to the angle 30 =
[tex]\frac{1}{2}\cdot28\sqrt[]{5}=14\sqrt[]{5}[/tex]The side length opposite to the angle 60 =
[tex]\frac{\sqrt[]{3}}{2}\cdot28\sqrt[]{5}=\frac{28}{2}\sqrt[]{3\cdot5}=14\sqrt[]{15}[/tex]Please see photo I think it is the first answer but I wanted to confirm
Answers
Hello
The sample which she has to study is 200
The answer to this question is option A
. Fritz spent two days last week writing his report and
another three days this week. In the last ten working
days, what fraction of the time has he been working
on his report?
Answers
Answer:
1/2
Step-by-step explanation:
5/10 which is the same as 1/2
NO LINKS!! Please help me with this probability question
Answers
===========================================================
Explanation:
Define these two events
A = father born in Michigan
B = mother born in Michigan
The notation ~A and ~B represent the opposite of each defined event above.
According to the table
P(A) = 0.48
P(B) = 0.73
If A and B were independent, then P(A and B) = P(A)*P(B) = 0.48*0.73 = 0.3504 = 35.04% but this contradicts the 29% in the "father born in Michigan" column and "mother born in Michigan" row. The table states that P(A and B) = 0.29 should be the case instead of 0.3504.
Because of this contradiction, this means P(A and B) = P(A)*P(B) is false and therefore A and B are NOT independent
--------------------------------------
Another way to look at it:
P(A) = 0.48
P(A given B) = P(A and B)/P(B)
P(A given B) = 0.29/0.73
P(A given B) = 0.39726 approximately
If A and B were independent, then P(A) and P(A given B) would be the same value. However, they are not. This is another way to see why the events are NOT independent
Through similar calculations, P(B given A) = P(A and B)/P(A) = 0.29/0.48 = 0.6042 approximately which doesn't match with P(B) = 0.73; if A and B were independent then P(B) needs to be equal to P(B given A).
Convert 21,510 ft to mi
Answers
Answer:
4.0738636
Step-by-step explanation:
What is a valid conclusion that can be reached by reading the graph?A.Joel and Nancy own 62 cards when you add their cards together.B.Joel and Nancy own more cards than Jim when you add their cards together.C.Nancy and Ricardo own more cards than Jim when you add their cards together.D.Tina owns 350 cards.
Answers
Answer:
C. Nancy and Ricardo own more cards than Jim when you add their cards together.
Explanation:
Taking into account the graph, we can conclude the following:
Nancy and Ricardo own more cards than Jim when you add their cards together
This is because, Nancy and Ricardo have bars with heights that are greater than 40, when we add their cards, we will get a bar with a height greater than 80, and 80 is greater than the height of Jim's bar.
Therefore, the answer is
C. Nancy and Ricardo own more cards than Jim when you add their cards together.
the wholesale price for a pair of shoes is $5.50. A certain department store marks up the wholesale price by 40%. Find the price of shoes in the department store.
Answers
EXPLANATION
Price of shoes = $5.50
Markup= 40%
Let's call x to the unknown final price.
The markup percentage relationship is given by the following formula:
[tex]\text{Markup =( }\frac{Selling\text{ Price}-\text{Cost Price}}{\text{Cost Price}})\cdot100[/tex]Replacing terms:
[tex]\text{40}=(\frac{x-5.5}{5.5})\cdot100[/tex]Multiplying both sides by 5.5:
[tex]40\cdot5.5=(x-5.5)\cdot100[/tex]Dividing both sides by 100:
[tex]\frac{40\cdot5.5}{100}=x-5.5[/tex]Adding 5.5 to both sides:
[tex](\frac{40\cdot5.5}{100})+5.5=x[/tex]Simplifyng the fraction:
[tex]2.2+5.5=x[/tex]Adding numbers:
[tex]\text{7}.7\text{ = x}[/tex]Switching sides:
[tex]x=7.7[/tex]Answer: The final price of the shoes in the deparment store is $7.7
Match the two lines that are parallel and the two lines that are perpendicular. Then, match the equations.
Answers
Step-by-step explanation:
A and C are parallel. equations G and E.
B and D are perpendicular (standing at a right angle = 90° to each other). equations F and H.
parallel means that both lines have the same slope.
the slope is the factor a of x when the equations look like
y = ax + b (slope-intercept form)
or
y - y1 = a(x - x1) (point-slope form)
"a" being the slope, b being the y-intercept (the y- value when x = 0), (x1. y1) being a point on the line.
the slope is specified as ratio (y coordinate difference / x coordinate difference) when going from one point to another.
the perpendicular slope to y/x is the upside down ratio and the sign is flipped.
e.g. the perpendicular slope to 5/4 is -4/5.
equation E is already in point-slope form.
the slope is 2/3, and the point (-9, -2) must be on the line.
only one line goes through the point (-9, -2) : C.
equation H is already in slope-intercept form.
the slope is 3/2, and the y-intercept is 5, meaning the line goes through the point (0, 5).
only one line goes through that point : D
equation F
2x + 3y = -21
3y = -2x -21
y = (-2/3)×x - 7
the slope is -2/3, which is perpendicular to 3/2 (equation H).
the y-intercept is -7, meaning the line goes through the point (0, -7).
only one line goes through that point : B
equation G
-2x + 3y = -6
3y = 2x - 6
y = (2/3)×x - 2
the slope is 2/3 (parallel to equation E).
the y-intercept is -2, meaning the line goes through the point (0, -2).
only one line goes through that point : A
PLS HELP WILL MARK BRAINLIEST
Answers
Answer:
l = [tex]\frac{P-2w}{2}[/tex]
Step-by-step explanation:
P = 2l + 2w ( subtract 2w from both sides )
P - 2w = 2l ( isolate l by dividing both sides by 2 )
[tex]\frac{P-2w}{2}[/tex] = l
Find (f - g)(x)
f(x) = 3x² - 2x
g(x) = 9x²2 - x + 7
A. -6x²-x-7
B. 6x²-x+7
C. 12x²-x-7
D. -6x²-3x - 7
Answers
The solution to the given function is (f-g)(x) = -6x² - x - 7.
What is a function?
Function, in mathematics, an expression, rule, or law that defines a relationship between : one variable (the independent variable) and another variable (the dependent variable).
A function is an equation with a single solution for y for each value of x. Each input of a particular type receives exactly one output when using a function. Instead of y, a function is frequently named f(x) or g(x). When x equals 2, we should determine our function's value because f(2) says to do so.
Given: f(x) = 3x² - 2x
g(x) = 9x² -x + 7
To find: ( f - g )(x)
thus (f-g)(x)= 3x² - 2x - ( 9x² - x + 7)
(f-g)(x) = -6x² - x - 7
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3х2 + 14х — 49 = 0solve for x
Answers
The given expression 3x^2 +14x-49=0
we will de factorization tos solve for x
[tex]\begin{gathered} 3x^2+14x-49=0 \\ 3x^2-7x+21x-49=0 \\ (3x^2-7x)+(21x-49)=0 \\ \text{Taking x common from (}3x^2-7x)=x(3x-7) \\ \text{Taking 7 common from }(21x-49)=7(3x-7) \\ (3x^2-7x)+(21x-49)=0 \\ x(3x-7)+7(3x-7)=0 \\ \text{Taking (3x-7) common} \\ (3x-7)(x+7)=0 \\ \text{ Thus, for} \\ \text{(3x-7)=0} \\ 3x=7 \\ x=\frac{7}{3} \\ \text{and for (x+7)=0} \\ x+7=0 \\ x=-7 \end{gathered}[/tex]The value of x is -7 and 7/3
Answer : x = -7 and x = 7/3
Mr. Rodriquez is purchasing throphies for each trophies for each child that play little ldag
Answers
From the information provided, Mrs Rodriguez wants to spend nothing more than $7.00 per trophy. That means she can spend less than $7.00 if she has to, but she cannot spend anything above that amount.
Therefore, the correct answer is option 2, and that is;
5 trophies for $30.00
With other options given, she would be spending above $7.00 per trophy
The Sugar Sweet Company is going to transport its sugar to market. It will cost $5500 to rent trucks plus $125 for each ton of sugar transported. The total cost,
C (in dollars), for transporting n tons is given by the following.
C=125n+5500
Answer the following questions.
(a) What is the total cost of transporting 11 tons?
(b) If the total cost is $8125, how many tons is the company transporting?
Answers
C=125*11+5500
C=1375+5500
C=$6875
(B) For this part you follow the same concept as part a just change what and where you are substituting since the question gives you total cost C you plus 8125 in for C and solve for n
C=125n+5500
8125=125n+5500 (subtract 5500 from BOTH sides)
2625=125n (divide BOTH sides by 125 to get n alone)
n= 21 tons
kind of confused with this whole probability concept, i just need help with these here
Answers
Solution
For this case we have 0-9 possible digits (10) and 4 spaces for the code
Part a
The number of ways are using the multiplication principle:
10x9x8x7= 5040
Part b
p= 1/5040
Part c
If digits can be repeated we have this:
10x10x10x10= 10000
can you please list 1-6 if they are rational irrational integer whole and natural
Answers
1. -14/2 = -7 Integer, Rational
2. √64 = 8 Natural, Whole, Integer, Rational
3. 0 Whole, Integer, Rational
4. π Irrational
5.
[tex]0.\bar{45}[/tex]can be expressed as a fraction, then it's rational
6. 3/8 Rational
Create your own thought experiment explaining why a negative divided by a negative is a positive.
Answers
Dividing two negative numbers results in a positive number.A negative number divided by a negative number produces a positive result since two negatives equal a positive.
Explaining why a negative divided by a negative is a positive
The quotient is positive when two negative values are divided.The same guidelines apply to multiplication. Divided by another negative integer, a negative number always yields a positive number.divided equally by.The solution cannot be or any other negative number because it is positive. Divide two negative numbers, and you'll always get a positive number as the result.For instance, dividing -4 by -2 yields 2.The negatives cancel out when both numbers are negative, hence the outcome is always a positive number. Consider that you are taking part in a game that uses red and black chips.You will win one dollar (+1) at the end of the game for each black chip you have.You must pay one dollar for every red chip you possess.Assume that at some time throughout the game you have numerous bags of black chips and several bags of red chips. These chips are currently bundled together in bags of five.You make $15 if someone offers you three bags of black chips.(3)(5)=15.You lose 15 bucks if someone steals three of your bags of black chips.(-3)(5)=-15.You lose $15 if someone gives you three bags of red chips.(3)(-5)=-15.You lose $15 if someone gives you three bags of red chips.(3)(-5)=-15.You make 15 bucks if someone steals three of your bags of red chips.(-3)(-5)=15.The crucial concept is that negative numbers signify variations rather than totals.Saying that you have four slices of bread is illogical.However, it makes logical to state that since you had 4 slices of bread, the new number of slices you possess is 4.
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Graph the line that is perpendicular to the line
7x+8y= 16 and passes through the
point (7, 2).
Answers
The general equation of the line is 7x+8y−65=0 when the line equation is 7x+8y=16 and the point is (7,2) and is perpendicular to the given line.
What is line?A line is a one-dimensional figure with no width and only length. A line is made up of a series of points that extend in opposite directions indefinitely. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.
here, the given equation is 7x+8y=16 and point is (7,2).
by the relation y = mx + c we will find the value of slope for the line.
8y=-7x+16
y=(-7/8 ) x+16
on comparing relation,
m=[tex]\frac{-7}{8}[/tex]
y=mx+b
b=y1-m.x1
b=2-(-7/8).7
b=65/8
y=(-7/8)x+65/8
final equation,
7x+8y=65
The required equation of the line is 7x+8y=65 for the given point and line.
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The perimeter of a rectangle is equal to 138. The width of the rectangle is 5 less than the length . What is the area the rectangle?
Answers
Step 1: Concept
Perimeter of a rectangle = 2( L + W)
L = length
W = width
Area of a rectangle = Lenght x Width
Step 2:
Given data
The perimeter of a rectangle = 138
Length L = m
Width W = m - 5
Step 3:
[tex]\begin{gathered} \text{Use the perimeter of the rectangle to find the length(L) and width(W).} \\ \text{Perimeter = 2(L + W)} \\ 138\text{ = 2(m + m - 5)} \\ 138\text{ = 2m + 2m - 10} \\ 138\text{ = 4m - 10} \\ \text{Collect similar terms} \\ 138\text{ + 10 = 4m} \\ 148\text{ = 4m} \\ m\text{ = }\frac{148}{4}\text{ = 37} \end{gathered}[/tex]Step 4:
Length = 37
Width = 37 - 5 = 32
Step 5:
Find the area
Area = length x width
Area = 37 x 32
Area = 1184
Final answer
Area of the rectangle = 1184