The equation that could be used to represent the whole pizza is 4/8 + 2/8 = 6/8 = 3/4.
We are given that;
Pizza ate by children= 4/8
Pizza ate by Jonus= 2/8
Now,
4/8 + 2/8 + x = 1
where x is the fraction of the pizza that was saved for later. This equation shows that the sum of the fractions of the pizza that were eaten and saved is equal to 1, which represents the whole pizza. To solve for x, we can simplify the fractions and subtract them from both sides:
4/8 + 2/8 = 6/8 = 3/4
3/4 + x = 1
x = 1 - 3/4
x = 1/4
Therefore, the equation will be 4/8 + 2/8 = 6/8 = 3/4
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Multiply.
x²+3x+2
x 2x²+3x-1
OA. 2x¹ +9x² + 12x² + 3x-2
OB. 2x¹ +9x2 - 2
OC. 3x2 + 6x +1
OD. 2x¹ +21x² + 3x-2
The multiplication of the expression (x² + 3x + 2) (2x² + 3x + 1) is 2x⁴ + 9x³ + 14x² + 9x + 2
Multiplication(x² + 3x + 2) (2x² + 3x + 1)
= 2x⁴ + 3x³ + x² + 6x³ + 9x² + 3x + 4x² + 6x + 2
collect like terms= 2x⁴ + 3x³ + 6x³ + x² + 9x² + 4x² + 3x + 6x + 2
= 2x⁴ + 9x³ + 14x² + 9x + 2
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For what values of x is the expression below defined?
√x+3 ➗√1-x
A. 3≤x≤1
B. 3>x>1
C. -3
D. 3> x≤-1
Answer: [tex]-3 \leq x < 1[/tex]
Step-by-step explanation:
[tex]\sqrt{x+3} \geq 0 \longrightarrow x \geq -3\\\\\sqrt{1-x} > 0 \longrightarrow 1-x > 0 \longrightarrow x < 1\\\\\therefore -3 \leq x < 1[/tex]
What are the values of a₁ and r of the geometric series?
2-2+2-2+2
O
a₁ = 2 and r=-2
O a₁ = -2 and r = 2
O
a₁ = -1 and r = 2
a₁ = 2 and r=-1
Answer:
Step-by-step explanation:
Therefore, the values of
a
1
and r are 2 and -1, respectively.
The values of a₁ and r of the geometric series are 2 and -1 respectively.
What is Geometric Sequence?Any term divided by the preceding term is a constant in a geometric series. The common ratio of the sequence is the name given to this constant. Any term in the sequence can be divided by the prior term to determine the common ratio.
We have the series 2, -2, 2, -2, ......
Here, The first term is 2.
and, the Common Ratio = -2 / 2
= 2/(-2)
= -1
So, the first term is 2 and r is -1.
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What are the steps you would need to take to find slope from data?
3⁵.2⁴.2¹.3⁶.(3²)⁴ and down (2³)².3⁶
Answer:
[tex]\dfrac{3^{13}}{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot (3^2)^4}{(2^3)^2 \cdot 3^6}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \dfrac{3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot 3^8}{2^6 \cdot 3^6}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies \dfrac{3^{(5+6+8)} \cdot 2^{(4+1)}}{2^6 \cdot 3^6}[/tex]
[tex]\implies \dfrac{3^{19} \cdot 2^{5}}{2^6 \cdot 3^6}[/tex]
[tex]\implies \dfrac{3^{19} \cdot 2^{5}}{3^6 \cdot 2^6}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 3^{(19-6)} \cdot 2^{(5-6)}[/tex]
[tex]\implies 3^{13} \cdot 2^{-1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{3^{13}}{2^1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]
[tex]\implies \dfrac{3^{13}}{2}[/tex]
Answer:
The result is 3¹³ /2
Step-by-step explanation:
Greetings
A cellular network transmits its signals in a circular pattern. The tower is considered the origin, (0,0), of the signal and there is a house located on the edge of the circle at (2, 4). Which of the following coordinates could represent the location of another house that is also on the edge of the circle?
A.(1.3)
B.(-2,-4)
C.(3,3)
D.(4,4)
Answer:
B
Step-by-step explanation:
because at origin they are both positive and when it rotates about 270 both will change to negative
Find the shortest distance from A to B in the diagram below. A. 505‾‾‾‾√ m B. 17 m C. 329‾‾‾√ m D. 10 m
The shortest distance from A to B in the diagram is 17 m.
How to find the shortest distance?The shortest distance from D to B can be found as follows:
using Pythagoras theorem,
c² = a² + b²
where
c is the hypotenusea and b are the other legsTherefore,
DB² = 15² + 8²
DB² = 225 + 64
DB² = 289
DB = √289
DB = 17 m
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Answer:
B, 17 m
Step-by-step explanation:
Founders 23
Use properties of operations to find the quotient. -10.2/6
A. 1.7 B. -1.7 C. 4.2 D. -4.2
Answer:
B, -1.7
Step-by-step explanation:
-10.2 divided by 6 is -1.7.
I hope this helps!
A board is 59.69cm long. How long is the board in inches ? Use the following conversion 1in is 2.54cm
Answer:
Given,
1in= 2.54cm
59.69cm=
[tex] \frac{59.69}{2.45} in[/tex]
=23.5 in
The princess of the Kingdom of Abundance accidentally drops her magic salamander's feeding bowl into a fire. She orders a new feeding bowl to be made out of Dragon Alloy #18, which is 86% magic steel and the rest titanium. The
dwarfs have a lot of Dragon Alloy #33, which is 28% titanium. How much of
that alloy and how much magic steel should they combine to make 700 grams of Dragon alloy #18?
350 grams of magic steel and 350 grams of dragon alloy #33 is needed to make 700 grams of Dragon alloy #18.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of magic steel and y represent the amount of alloy #33, hence:
(0 * x) + (y * 0.28) = 700(1 - 0.86) (1)
Also:
x + (1 - 0.28)y = 0.86(700) (2)
From both equations:
x = 350, y = 350
350 grams of magic steel and 350 grams of dragon alloy #33 is needed to make 700 grams of Dragon alloy #18.
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`H_0: p = 0.63`
`H_1: p > 0.63`
Your sample consists of 150 subjects, with 96 successes. Calculate the test statistic, rounded to 2 decimal places
`z=`
The test statistic, rounded to 2 decimal places is equal to
How to calculate value of the test statistic?For this sample, the hypothesis is given by:
H₀: μ₁ ≤ μ₂
H₁: μ₁ > μ₂
Assuming this sample has a normal distribution, we would use a pooled z-test to determine the value of the test statistic:
Substituting the given parameters into the formula, we have;
[tex]z = \frac{\frac{96}{150} \;-\;0.63}{\sqrt{0.63\; +\; \frac{1\;-\;0.63}{150}} }\\\\z = \frac{0.64 \;-\;0.63}{\sqrt{0.63\; +\; \frac{0.37}{150}}}\\\\z = \frac{0.01}{\sqrt{0.63\; +\; 0.0025}}\\\\z = \frac{0.01}{\sqrt{0.6325}}\\\\[/tex]
z = 0.01/0.7953
z = 0.013.
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You have nine line segments with the lengths of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.
How many ways are there to form a square by connecting the ends of some of these
line segments? No overlapping of the line segments is allowed.
The number of ways to forma a square by connecting the ends of some of the line segments is 3, 024 ways
What is permutation?From the given information, we should use the formula for permutation without repetition.
The formula is given as;
Permutation = [tex]\frac{n!}{n -r !}[/tex]
Where n = number of set = 9
r = 4, this is so because, the sides of a square a four
Permutation = [tex]\frac{9!}{9 - 4!}[/tex]
Permutation = [tex]\frac{9!}{5!}[/tex]
Permutation = [tex]\frac{362, 880}{120}[/tex]
Permutation = 3, 024 ways
Thus, the number of ways to forma a square by connecting the ends of some of the line segments is 3, 024 ways
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Tim wants to build a rectangular fence around his yard. He has 42 feet of fencing. If he wants the length to be twice the width. What is the largest possible length
Answer: The largest he can possibly build is x = 14
Step-by-step explanation:
I need this answered please and thank you! ASAP
Answer:
Greetings!
The answer for the first figure is attached but the second diagram is not clear.
Also use the image i attached horizontally.
and also it TD subject not Mathematics.
R = 15 when m = 6 s= 4 inversely when m=24 s =4
The value of r If r varies directly with the square of m and inversely with s is 240
Variation
Suppose r varies directly with the square of m and inversely with s.
If r varies directly with the square of m and inversely with s, then;
r = km²/s
Given that R = 15 when m = 6 s= 4
15 = k(6)²/4
60 = 36k
k = 60/36
k = 5/3
If the value of m = 24 and s = 4, hence;
r = 5/3*24²/4
r = 240
Hence the value of r If r varies directly with the square of m and inversely with s is 240
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An issue of Taunton's Fine Woodworking included plans for a hall stand. The total height of the stand is 5912 59 1 2 inches. If the base is 25716 25 7 16 inches, how tall is the upper portion of the stand?
The length if the upper portion of the stand is 33. 56 inches
How to determine the lengthThe formula for the finding the length is given thus;
Total height = length of upper portion + length of base
Where
Length of base = 257/16
Total height = 591/2
Length of upper portion = total height - length of base
= 118/2 - 407/16
= 59 - 25. 44
= 33. 56 inches
Thus, the length if the upper portion of the stand is 33. 56 inches
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A bag contains 3 red balls, 4 green balls, and 2 yellow balls. Deborah reaches into the bag and pulls out the following 4 balls: red, red, green, yellow Deborah reaches into the bag to pick out another ball. What's the probability that the ball she picks is green?
The probability that the ball Deborah picks is green is; 3/5.
What is the probability that the ball picked last is green?Since the bag initially contains; 3 red balls, 4 green balls, and 2 yellow balls, after Deborah pulls out the 4 balls: red, red, green, yellow.
The balls remaining are; 1 red ball, 3 green and 1 yellow.
Hence, the probability that the final ball she picks is green is; 3/(3+1+1) = 3/5.
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13)
Medical officials want to determine if birth weights are lower than usual in Southeast Asia. They randomly weigh 100 babies, and they determine that the average birth weight is 6 pounds 8 ounces.
State the variable.
What are the units for the variable?
State the population.
State the sample.
POINTS Out OF
7
What is the individual.
What is the Parameter.
What is the statistic.
See below for the response to each question
The variableThis is the item that is being surveyed.
The surveyed item is birth weights
Hence, the variable is birth weights
The units of the variableFrom the question, we have:
Average birth weight is 6 pounds 8 ounces.
Hence, the units of the variable are pounds and ounces
The populationThis is the total number of babies in Southeast Asia
Hence, the population of interest is the babies in Southeast Asia
The individualThis is the people in the survey
Hence, the individual in the study is the 100 babies that were randomly surveyed
The parameter of interestThis is the value that gives the required information.
Hence, the parameter of interest is the average birth weight
What is the statistic involvedThe statistic is the average
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If a person rows to his favorite fishing spot 21 miles downstream in the same amount of time that he rows 7 miles
upstream and if the current is 7 mph, find how long it takes him to cover 28 miles.
28 miles upstream requires 28/7 = 4 hours.
28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.
How long does it take him to cover 28 miles?Apply the distance formula:
d = rt
where
d is distance
r is rate or speed
t is time
21 = t*(r+7) = rt+ 7t
7 = t *(r-7) = rt - 7t
28 = 2rt
14 = rt
21 = rt + 7t
21 = 14 + 7t
7 = 7t
t=1
21 = (r+7)*1 = r+7
r = 14
The speed of the boat is 14 mph. With the current (downstream), the speed is 14+7 = 21 mph, so 21 miles are traveled in 1 hour. Against the current (upstream), the speed is 14-7 = 7 mph, which means 7 miles are traveled in the same 1-hour time frame.
28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.
28 miles upstream requires 28/7 = 4 hours.
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What is the completely factored form of f(x) = x3 – 2x2 – 5x + 6?
f(x) = (x + 2)(x – 3)(x + 6)
f(x) = (x + 2)(x – 3)(x – 6)
f(x) = (x – 2)(x + 3)(x – 1)
f(x) = (x + 2)(x – 3)(x – 1)
Answer:
The last option, (x+2)(x-3)(x-1)
Step-by-step explanation:
The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,
⇒ f (x) = (x - 1) (x - 2) (x - 3)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
Function is,
⇒ f (x) = x³ - 2x² - 5x + 6
Now, We can factor the function as;
Since, 1 is a root of function as it satisfy the function.
So, One factor is,
⇒ (x - 1)
Find another roots as;
(x - 1) ) x³ - 2x² - 5x + 6 ( x² - x - 6
x³ - x²
----------
- x² - 5x
- x² + x
-------------
- 6x + 6
- 6x + 6
------------
0
Hence,
⇒ f (x) = x³ - 2x² - 5x + 6
⇒ f (x) = (x - 1) ( x² - x - 6 )
⇒ f (x) = (x - 1) ( x² - 3x - 2x - 6)
⇒ f (x) = (x - 1) ( x (x - 3) - 2 (x - 3))
⇒ f (x) = (x - 1) (x - 2) (x - 3)
Hence, The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,
⇒ f (x) = (x - 1) (x - 2) (x - 3)
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Find the value of t; log3y=2 and log3ty=6
Answer: [tex]10^4[/tex]
Step-by-step explanation:
Assuming we are using the common log (base 10),
[tex]\log 3ty=6\\\\\log 3y +\log t=6\\\\2+\log t =6\\\\\log t=4\\\\t=10^4[/tex]
Would the horizontal translations shift the square root right or left? Sort each into the appropriate category.
f(x)=√x+0.8
f(x)=√x-4.7
f(x)=√x-25
f(x)=√x+6
f(x)=√x-11
Answer:
Step-by-step explanation:
Shift right
f(x)=√x-4.7
f(x)=√x-25
f(x)=√x-11
Shift left
f(x)=√x+0.8
f(x)=√x+6
Find the sum of the arithmetic series given a1=45, an=85, and n=. 5
The sum of the arithmetic series is 325
How to determine the sum?The given parameters are
a1 = 45
an = 85
n = 5
The formula for the sum of arithmetic series is:
[tex]S_n = \frac n2 * (a_1 + a_n)[/tex]
Substitute the values of a1, an and n in the above equation
[tex]S_5 = \frac 52 * (45 + 85)[/tex]
Add 45 and 85
[tex]S_5 = \frac 52 * 130[/tex]
Divide 130 by 2
[tex]S_5 = 5 * 65[/tex]
Multiply
[tex]S_5 = 325[/tex]
Hence, the sum of the arithmetic series is 325
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Construct a 96% confidence interval if a sampling distribution has a mean of 20, a standard deviation of 5, and a size of 100.
Using the t-distribution, the 96% confidence interval is given as follows:
(18.96, 21.04).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 96% confidence interval, with 100 - 1 = 99 df, is t = 2.0812.
The parameters are given as follows:
[tex]\overline{x} = 20, s = 5, n = 100[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 20 - 2.0812\frac{5}{\sqrt{100}} = 18.96[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 20 + 2.0812\frac{5}{\sqrt{100}} = 21.04[/tex]
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Kaitlin,Scott and bill served a total of 81 orders on Monday .Kaitlin served 9 fewest orders than Scott .bill served 3 times as many orders as Scott . How many orders did they each serve?
Answer: Scott - 18, Kaitlin - 9, Bill - 54
Step-by-step explanation:
Let's view this as units. There are a total of 81 units. If we solve for Scott's orders:
Kaitlin served 9 fewer orders than Scott. We add 9 to 81 --> 9 + 81 = 90.
Now if we view Scott's orders as one unit:
Scott - 1 unit
Kaitlin (after adding 9) - 1 unit
Bill - 3 units (he served 3 times as many orders as Scott)
In total there are 3 + 1 + 1 = 5 units.
90 / 5 = 18.
Therefore, Scott served 18 orders.
18 - 9 = 9.
Kaitlin served 9 orders.
18 x 3 = 54.
Bill served 54 orders.
And to check our answer, 54 + 18 + 9 is 81.
Given the graph of g(x), describes the transformation of the parent function f(x)=2^x
Answer:
The transformation being described is from g(x)=x2 g ( x ) = x 2 to f(x)=x2 f ( x ) = x 2 . The horizontal shift depends on the value of h . The horizontal shift is described as: f(x)=f(x+h) f ( x ) = f ( x + h ) - The graph is shifted to the left h units
The roots of the quadratic function describing the relationship between number of products produced and
overall profit margin are x = 0 and 26. The vertex is (13, -50).
The vertex is a minimum at (13, -50). The company actually loses money on their first few products as it
costs them more to make them, but once they hit 26 items they break even again.
The worst case scenario is that they produce
first root tells us that the profit will be 0 when
Check
items, as they will have a profit of
products are sold.
dollars.
In Economics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.
This ultimately implies that, all producers of any product generally work to maximize their profits and make them as large as possible, in order to enable them break even and successful.
Based on the information provided, we can logically deduce that this function has its roots at x = 0 and x = 26 and its vertex is a minimum. Thus, this quadratic function which describes the relationship between the number of products produced and the overall profit margin is an increasing function:
0 < x < 26, f(x) < 0, which implies a negative profit is generated when between 0 and 26 items are produced.x > 26, f(x) > 0, which implies a positive profit is generated when more than 26 items are produced.x is equal to 26 is the break even point.Therefore, once they hit 26 items they break even again. The worst case scenario is that they produce 13 items, as they will have a profit of -50 dollars because the minimum point is at (18, -35). Also, the first root tells us that the profit will be 0 when 0 products are sold.
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mangleR = 120° and mangleS = 100°. Find mangleT. The diagram is not drawn to scale.
) Explain why the expression x2 + (p + q )x + pq leads to the need to determine integers that add to b and have a product c when factoring a trinomial of the form x2 + bx + c.
The reason why the expression x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c is because they follow the FOIL Technique
How to factorize Quadratic Equations?We want to explain why x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c.
Now, using the FOIL Technique we can say that the factors are;
(x + p)(x + q)
Expanding this gives;
x² + px + qx + pq
⇒ x² + (p + q)x + pq
Now, applying that to the trinomial; x² + 6x + 8, we can say that;
p + q = 6, and pq = 8
Thus, solving simultaneously gives;
p = 2 and q = 6.
Thus;
x² + 6x + 8 = (x + 2)(x + 6)
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Find an equation for the plane that contains the line
v=(-3,4,5)+t(3,2,4)
and is perpendicular to the plane
2x+y-3z+4=0
(Use symbolic notation and fractions where needed.)
The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.
How to find the equation of a plane that contains a line and is perpendicular to another plane
From the equation of the plane 2 · x + y - 3 · z = - 4 we know that its normal vector is (2, 1, - 3). Hence, we have found two direction vectors and already know a point, which are part of this parametric equation:
(x, y, z) = (- 3, 4, 5) + t · (3, 2, 4) + u · (2, 1, - 3) (1)
The normal vector of the plane is equal to the cross product of the direction vectors of (1):
[tex]\vec n = (3, 2, 4) \,\times\,(2, 1, -3)[/tex]
[tex]\vec n = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\3&2&4\\2&1&-3\end{array}\right|[/tex]
[tex]\vec n = (-6-4,8+9, 3-4)[/tex]
[tex]\vec n = (-10, 17, -1)[/tex]
Since the plane contains the point (x, y, z) = (- 3, 4, 5), then we find that the independent constant of the equation of the plane is:
- 10 · x + 17 · y - z = k
- 10 · (- 3) + 17 · 4 - 5 = k
30 + 51 - 5 = k
k = 76
The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.
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