The equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.
What is the equivalent of the expression?
Given the expression; (z−3)4z−6
First, we apply distributive property.
(z−3)4z−6
(z−3)4z−6
z(4z) - 3(4z) - 6
We remove the parentheses
4z² - 12z - 6
Therefore, the equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.
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Why is it important for the world to have an order of operations
Answer:
Well a sovial reason is that no one would no what order yo do it in, which would cause arguments
Answer:
without the order of operations, maths literally doesn't work.
Step-by-step explanation:
like whilst some equations don't rely on a particular order for solving, if you for example, don't solve brackets first, then try to multiply them by something else basically the equation breaks and you get the wrong answer. So... kids remember your BODMAS :)
Information about a play took up 1/3 of the pages in the program. Information about the actors took up 1/4 of the remaining pages. Information about the director, the producer, and the designer took up 2 pages, the same number of pages devoted to the actors. How many pages were there in the program?
Answer:
Step-by-step explanation:
Comment
Let the number of pages = x
Play = 1/3x
Actors = 1/4(x - 1/3 x)
Actors = 1/4(2/3x)
Actors = 2/12 x
Producer Director etc = 2 pages
Equation
Actors = 2 pages
2/12 x = 2
Solution
2x/12 = 2 Multiply both sides by 12
12*2x/12 = 2*12 Combine
2x = 24 Divide by 2
2x/2 = 24/2 Combine
x = 12
Answer
The program had 12 pages.
Which inequality in vertex form represents the region less than the quadratic function with vertex (-2, 2) and includes the point (-4, 14) on the boundary?
The inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)
What is the inequality associated to a given statement
The standard form of the equation of the parabola is defined by the following expression:
y - k = C · (x - h)² (1)
Where:
h, k - VertexC - Vertex constantNow we proceed to find the vertex constant: (h, k) = (- 2, 2) and (x, y) = (- 4, 14)
14 - 2 = C · [- 4 - (- 2)]²
12 = C · (-2)
C = - 6
The equation of the parabola in vertex form is
y - 2 = - 6 · (x + 2)²
y = - 6 · (x + 2)² + 2
Then, the inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)
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Answer:
y < 3(x + 2)2 + 2
Step-by-step explanation:
just do it
Expand 4(6)to the 8th power
4(6)^8
The expanded form of the given exponential equation is 6718464
Exponential equationsExponential equations are inverse of logarithmic equations. The standard exponential equation is expressed as. y = ab^x
where
a is the base
x is the exponent
Given the expression below;
a = 4(6)^8
Expand to have:
a = 4 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6
a = 4 * 1679616
a = 6718464
Hence the expanded form of the given exponential equation is 6718464
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What is the equation of the line that passes through the point (6,-3) and has an undefined slope?
Answer:
x=6
Step-by-step explanation:
This is a vertical line going through (6,0). If you take this point and the point given and calculate the slope you find the change in y over the change in x.
0-(-3)/6-6 The slope is undefined because the denominator of the slope would be zero.
a. How many bushels of corn, if any, will the United States export or import at the prices below?
At $1, it will (import, export, or neither import or export )
___bushels.
b. How many bushels of corn, if any, will the United States export or import at the prices below?
At $2, it will (import, export, or neither import or export )
____bushels.
c. How many bushels of corn, if any, will the United States export or import at the prices below?
At $3, it will (import, export, or neither import or export )
____ bushels.
d. How many bushels of corn, if any, will the United States export or import at the prices below?
At $4, it will (import, export, or neither import or export )
____ bushels.
e. How many bushels of corn, if any, will the United States export or import at the prices below?
At $5, it will (import, export, or neither import or export )
____ bushels.
2.
a. Use this information to construct the U.S export supply curve and import demand curve for corn
b. Suppose that the only other corn-producing nations is France, where the domestic price is $4. Which country will export corn and which country will import it
The United Stated will import corn France will export it
The United States will export corn and France will import it
Neither country will import or export corn.
Based on the graph which depicts the United States domestic market for corn at different prices, we can logically deduce the following information:
At $1, the United States will import 15,000 bushels of corn.At $2, the United States will import 7,000 bushels of corn.At $3, the United States will neither import nor export any bushels of corn.At $4, the United States will export 6,000 bushels of corn.At $5, the United States will export 10,000 bushels of corn.Assuming France is the only other corn-producing nations at a domestic price of $4, we can reasonably infer that the United States will export corn while France will import it.
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Which of these numbers is in the solution set of x-15=5?
Answer:
x=20
Step-by-step explanation:
x-15=5
x=5+15
x=20
please fill in the blanks of the question i sent a pic of
The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.
What is the center and the radius of the circle?
In this question we must determine the location of the center and the measure of the radius of a circle. According to Euclidean geometry, diameters are the longest possible chords of a circle. First, we determine the location of the center by definition of midpoint:
(h, k) = (1/2) · (4, 5.5) + (1/2) · (4, 10.5)
(h, k) = (4, 8)
And the radius is found by Pythagorean theorem:
[tex]d = \sqrt{(4 - 4)^{2}+(10.5-5.5)^{2}}[/tex]
d = 5
r = 0.5 · 5
r = 2.5
The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.
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Which statement correctly describes the diagram?
On a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C.
1. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A..
2. Triangle B is a reflection of triangle A across the y-axis. Triangle C is a reflection of triangle A across the line y = x + 3.
3. Triangle B is a reflection of triangle A across the y-axis. Triangle C is not a reflection of triangle A.
4. Triangle B is a reflection of triangle A across the x-axis. Triangle C is a reflection of triangle A across the line y = x + 3.
The correct statement is Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A.
Given that in a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C.
From the given figure , it says that Triangle B is a reflection of triangle An across the x-pivot. Triangle C isn't a reflection of triangle A" in light of the fact that Triangle A is in the main quadrant and its appearance with x-axis makes the triangle-B in the fourth quadrant and the triangle C which is in second quadrant can not be a reflection and annot be a rotation of triangle-A. Triangle C is drawn by taking firstly the reflection of triangle A and then rotate on the same place and increased x+3 units in above direction.
Hence, the statement correctly describes the diagram is "Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A".
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Answer:
A. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A..
Step-by-step explanation:
goodluck
There are 7 roses and 8 daisies in a vase. (a) What is the ratio of daisies to all flowers in the vase? 1 (b) What is the ratio of roses to all flowers in the vase?
Answer:
a. 8:15
b. 7:15
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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Evaluate the sum (for math nerds)
[tex]i {}^{0!} + i {}^{1!} + i {}^{2!} + i {}^{3!} + ... + i {}^{100!} [/tex]
Note that :
[tex]i = \sqrt[]{ - 1} [/tex]
Answer: i+96
Step-by-step explanation:
Note that [tex]i^{4k}[/tex], where k is an integer, is equal to 1.
This means that [tex]i^{4!}=i^{5!}=i^{6}=\cdots=i^{99!}+i^{100!}=1[/tex]
So, we can rewrite the sum as [tex]i^{1}+i^{1}+i^{2}+i^3+97(1)=i+i-1-i+97=i+96[/tex]
[tex]n![/tex] is divisible by 4 for all [tex]n\ge4[/tex]. This means, for instance,
[tex]i^{4!} = \left(i^4\right)^{3!} = 1^{3!} = 1[/tex]
[tex]i^{5!} = \left(i^4\right)^{5\times3!} = 1^{5\times3!} = 1[/tex]
etc, so that [tex]i^{n!} = 1[/tex] for all [tex]n\ge4[/tex].
Meanwhile,
[tex]i^{0!} = i^1 = i[/tex]
[tex]i^{1!} = i^1 = i[/tex]
[tex]i^{2!} = i^2 = -1[/tex]
[tex]i^{3!} = i^6 = (-1)^3 = -1[/tex]
Then the sum we want is
[tex]i^{0!} + i^{1!} + i^{2!} + i^{3!} + 97\times1 = i + i - 1 - 1 + 97 = \boxed{95+2i}[/tex]
Use the following triangle to find Sec theta.
Note: enter the exact, fully simplified and rationalized answer
Answer:
[tex]\frac{\sqrt{41}}{4}[/tex]
Step-by-step explanation:
sec(theta) is defined as: [tex]sec(\theta)=\frac{1}{cos(\theta)} = \frac{hypotenuse}{adjacent}[/tex]
In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
So this gives us the equation where a=adjacent side:
[tex]a^2+5^2=\sqrt{41}^2[/tex]
[tex]a^2+25=41[/tex]
Subtract 25 from both sides
[tex]a^2=16[/tex]
Take the square root of both sides
[tex]a=4[/tex]
So now plug this into the definition of sec(theta) and you get: [tex]\frac{\sqrt{41}}{4}[/tex]. This is in most simplified form since 41, has no factors besides 41 and 1.
The number 27 is ___?
-prime
-composite
Answer:
the number 27 is a composite
Step-by-step explanation:
Yes, since 27 has more than two factors . 1, 3, 9, 27. In other words, 27 is a composite number because 27 has more than 2 factors
Answer:
The number 27 is composite.
Find the value of x.
helllppp
tysm
Answer:
Step-by-step explanation:
t
Use the table to the right, which shows the age distribution of those who earned less than
minimum wage in a recent year. If a worker is randomly selected from those surveyed, what
y is the probability that the person is younger than 65?
na
Ci
20
ar
The probability that the person is younger than 65 is
(Type a decimal rounded to three decimal places as needed.)
CID
Age
16-19
20-24
25-34
35-44
45-54
55-64
65 and older
Working Below Minimum
Wage (thousands)
350
412
318
200
107
51
49
The probability that a person chosen at random is younger than 65 is 0.967.
What is the probability?Probability calculates the odds that a random event would happen. The odds that the random event happens lie between 0 and 1.
The probability that a person chosen at random is younger than 65 = (total number of people younger than 65 / total number of respondents)
(350 + 412 + 318 + 200 + 107 + 51 ) / (350 + 412 + 318 + 200 + 107 + 51 + 49)
1438 / 1487 = 0.967
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Two friends, Jamie and Devin, are working together at the Sparrowtown Cafe today. Jamie works every 2 days, and Devin works every 7 days. How many days do they have to wait until they next get to work together?
Using the least common factor, they need to wait 14 days until they next get to work together.
How to find the time it takes for periodic events to repeat at the same time?To find the time that passes between the events happening at the same time, we need to find the least common multiple of the periods.
In this problem, the periods are of 2 days and 7 days, which already are prime numbers, hence:
lcm(2,7) = 2 x 7 = 14.
They need to wait 14 days until they next get to work together.
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The vertices of a triangle are P (-6,1), Q(-2,5) and R (8,1) - what is the slope of the median of the triangle that passes through point R?
What is the slope of the altitude of the triangle that passes through point Q?
The slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.
Given that vertices of triangle is P(-6,1),Q(-2,5),R(8,1) and there is a median which passes through R.
Median of a triangle is a line segment which originates from a vertex of triangle and divides the opposite side in two equal parts. let median touches the line at L point.
When line passes through R then it must be a perpendicular on PQ. The coordinates of L is {(-2-6)/2,(5+1)/2}=(-4,3)
Now because median passes through R,it will be LR and we know that the formula of calculating slope of line from two points is [tex](y_{2} -y_{1} )/(x_{2} -x_{1} )[/tex] where [tex](x_{1} ,y_{2} ),(x_{2} ,y_{2} )[/tex] are the points of the end points of line.
Slope=(1-3)/(8+4)
=-2/12
=-1/6
Hence the slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.
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Alvin wants to know what his average paddling rate was for a canoe trip to a campsite. On the way there it took him 10 hours against a river current of 3 km/ hr. On the way back, the same distance took him 5 hours with the same 3 km/hr current.
The paddling rate of Alvin is 9km/hr
Given time against the river current is 10 hours , speed is 3km/hr
and time with the river current given is 5 hours and the speed is 3km/hr
We need to calculate the paddling rate of Alvin
Let us assume that
r =Alvin's average paddling rate in km/hour
y = speed of the current in km/hour
we know that
speed= distance/time
∴ distance=speed*time
Now,
To Campsite against the current
Speed=(r-y)
∴ Speed=(r-3) ---- (1)
Time=8 hours
Distance=(r-3)*10------ (2)
10r - 30
From Campsite with the current
Speed=(r+y)
∴Speed=(r+3)*5
Time=3 hours
Distance=(r+3)*5----(1)
Equate equation 1 and equation 2
5r +15
because is the same distance
5r + 15 = 10r - 30
5r = 45
r = 9
Hence ,The rate of the paddling rate is 9km/hr
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Membership selection. A town council has members, Democrats and Republicans.
(A)
If the president and vice-president are selected at random, what is the probability that they are both Democrats?
(B)
If a 3-person committee is selected at random, what is the probability that Republicans make up the majority?
The probability that they are both Democrats is approximately
enter your response here.
(Type a decimal. Round to three decimal places.)
Using the hypergeometric distribution, the probabilities are given as follows:
a) 0.2 = 20%.
b) 0.5539 = 55.39%.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.Researching this problem on the internet, it is found that the council has 15 members, of which 7 are Democrats and 8 are Republicans.
Item a:
The parameters are:
N = 15, n = 2, k = 7.
The probability is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]
Item b:
At most one Democrat, with n = 3, hence:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which:
[tex]P(X = 0) = h(0,15,3,7) = \frac{C_{3,0}C_{8,3}}{C_{15,3}} = 0.1231[/tex]
[tex]P(X = 1) = h(1,15,3,7) = \frac{C_{3,1}C_{8,2}}{C_{15,3}} = 0.4308[/tex]
Then:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1231 + 0.4308 = 0.5539[/tex]
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What numbers are the arrows pointing to?
a)
b)
c)
60
∞
2.5
70
3.5
Using proportions, the numbers that the arrows are pointing to are:
a) 62.
b) 8.8.
c) 2.8.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In item a, the arrow is 2/10 of the way from 60 to 70, hence the number is:
60 + 0.2(70 - 60) = 60 + 2 = 62.
In item b, the arrow is 8/10 of the way from 8 to 9, hence the number is:
8 + 0.8(9 - 8) = 8.8.
In item c, the arrow is 3/10 of the way from 2.5 to 3.5, hence the number is:
2.5 + 0.3(3.5 - 2.5) = 2.8.
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A coin is flipped 10 times where each flip comes up either heads or tails. How many possible outcomes
a. Contain no heads?
b. Contain exactly three heads?
c. Contain at least three heads?
d. Contain more heads than tails?
Answer:
a.1
b.10
c.120
Step-by-step explanation: don't know that last one
Two ares are congruent if they have the same measure and ?
Two ares are congruent if they have the same measure and lengths
How to complete the statement?The statement is given as:
Two ares are congruent if they have the same measure and ?
The conditions for congruent shapes in geometry are;
Congruent angleCongruent lengthThis means that the angle and the length must be equal
Hence, the term that completes the blank is length
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10 points please answer correctly (due soon)
Let’ pretend that in an American city there were 2000 new cases on Monday which is a 12% decrease from two weeks ago.
1. Write a linear/exponential equation that
models this situation (consistent with the data
provided). Time is the explanatory variable, and
New Cases is the response variable.
B) Explain what the slope/multiplier (consistent
with your choice above) means in this context
of the problem. Be sure to use units.
The exponential equation of the model is A(t) = 2583 * 0.88^t and the multiplier means that the number of new cases in a week is 88% of the previous week
The function that models the dataThe given parameters are:
New, A(t) = 2000
Rate, r = 12%
The function is represented as:
A(t) = A * (1 - r)^t
So, we have:
2000 = A * (1 - 12%)^t
This gives
2000 = A * (0.88)^t
2 weeks ago implies that;
t = 2
So, we have:
2000 = A * 0.88^2
Evaluate
2000 = A * 0.7744
Divide by 0.7744
A = 2583
Substitute A = 2583 in A(t) = A * 0.88^t
A(t) = 2583 * 0.88^t
Hence, the exponential equation of the model is A(t) = 2583 * 0.88^t
The interpretation of the multiplierIn this case, the multiplier is 88% or 0.88
This means that the number of new cases in a week is 88% of the previous week
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The table shows preferences of dancing or playing sports for male and female students:
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 18 16 34
Female students 18 35 53
Column totals 36 51 87
Mason mistakenly calculated the conditional relative frequency for female students who prefer playing sports to be 21%. What statistic did Mason actually calculate, and what should he have done differently?
The conditional relative frequency for female students who prefer playing sports is 34%.
How to determine the statistic calculated?The table of values is given as:
Sports Dancing Row totals
Male students 18 16 34
Female students 18 35 53
Column totals 36 51 87
Mason's calculation is given as:
P = 21%
This is gotten by
18/87 = 21%
The above represents the joint relative frequency of female students who prefer playing sports.
To calculate the conditional relative frequency, he should divide 18 by the row total.
So, we have
18/53 = 34%
Hence, the conditional relative frequency for female students who prefer playing sports is 34%.
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Pls hellp
A small bowl of candy has a piece of chocolate, cinnamon, and butterscotch candy. Over the course of a few days, the three candies were eaten. Determine the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order.
Please show work.
Using the arrangements formula, the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order is:
[tex]\frac{1}{6}[/tex].
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, there are 3 candies, hence the number of ways they can be eaten is:
[tex]A_3 = 3! = 6[/tex]
The desired order is only one, hence the probability is:
[tex]\frac{1}{6}[/tex].
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Engineers must design a process for producing ammonia in amounts large enough to ensure a reasonable profit. Which criterion would the process need to meet? A. The process must make large amounts of product at a low cost? B. The process must be based on a technology that has long been used.C.The process must use only small amounts of reactants.D.The process must use the safest and most natural materials
Need this fast please
The process needs to meet the following criterion:The process must make large amounts of product at a low cost. That is option A.
What is ammonia?Ammonia is defined as a gas compound that is made up of nitrogen and oxygen in the ratio of 1:3 respectively.
The industrial and modern method constructed by Engineers for ammonia production is called steam reforming.
The natural resources used for industrial production of ammonia can be gotten from natural gas such as methane.
To make profit, natural products are used which costs less to acquire but will lead to the production of large ammonia quantity.
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A rectangle has a length of x-8 and a width of x-9. Which equation below describes the perimeter, P, of the rectangle in terms of x?
a. P=x² - 17x+72
b. P=x-17
c. P = 2x-17
d. P = 4x - 34
*show your work*
Answer:
d.
Step-by-step explanation:
Given a length [tex]l[/tex] and a width [tex]w[/tex], we can express the perimeter of a rectangle as [tex]2(l+w)[/tex].
Therefore the perimeter [tex]P[/tex] can be expressed as
[tex]2\times[(x-8)+(x-9)]\\=2\times(2x-17)\\=4x-34[/tex]
14) Write the scientific notation.
12 million
Answer:
1.2 × 107 this is the sciencetific notation for 12 million
..
12480 es divisible de 6
Doy 50
12,480 es par y la suma de sus digitos da un multiplo de 3, por ello concluimos que es divisible por 6.
¿Como saber si un número es divisible por 6?Para que un número sea divisible por 6 debe cumplir dos condiciones.
Ser par.La suma de sus digitos debe ser multiplo de 3.En este caso tenemos 12,480, que sabemos que es par.
La suma de sus digitos da:
1 + 2 + 4 + 8 + 0 = 15
15 es multiplo de 3.
Entonces este número cumple ambas condiciones, por lo que concluimos que 12,480 es divisible por 6.
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