[tex]\text{If k and l are the roots of a polynomial w(x), then}\ w(x)=a(x-k)(x-l).[/tex]
[tex](2-\sqrt3)-a\ root\ of\ a\ polynomial\\\\another\ root\ must\ be\ C.\ (2+\sqrt3),\ because\\\\\ [x-(2-\sqrt3)][x-(2+\sqrt3)]=(x-2+\sqrt3)(x-2-\sqrt3)\\\\=[(x-2)+\sqrt3][(x-2)-\sqrt3]\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=(x-2)^2-(\sqrt3)^2\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=x^2-2(x)(2)+2^2-3=x^2-4x+4-3=x^2-4x+1[/tex]
[tex]Answer:\ \boxed{C.\ (2+\sqrt3)}[/tex]
The correct answer to the question is therefore C. 2 + square root of 3.
If (2 - square root of 3) is a root of a polynomial with integer coefficients, the polynomial must have another root that is the conjugate of (2 - square root of 3), which is (2 + square root of 3). This is due to the Conjugate Root Theorem, which is a result of the fact that the coefficients of the polynomial are real numbers. When you have a non-real root in such a polynomial, its conjugate will also be a root.
The correct answer to the question is therefore C. 2 + square root of 3.
Plz help! 17 points!
2. What is the domain of the function {( 1, 1), {0, 0}, ( 2, -1)} ?
A. {-1, 0, 1}
B. {-1, 0, 1, 2}
C. { 0, 1, 2}
D. {(1, 1), {0, 0}, (1, 0), (2, -1)}
3. Suppose that the function f(x) = 5x + 3 represents the number of cars that drive by in x minutes. How many cars will drive by in 10 minutes?
A. 80
B. 53
C. 50
D. 35
Answer:
2. C. { 0, 1, 2}
3. B. 53
6. P = 14n + 10
Step-by-step explanation:
2. The domain is the input values (or the x values)
The domain is { 0,1,2}
3. f(x) = 5x+3
where x is the number of minutes. We will let x = 10
f(10 ) = 5*10 +3
= 50+3
= 53
53 cars will pass
6. When we have 1 trapezoid, the perimeter is 5+5+8+6 = 24
When we have 2 trapezoids, the perimeter is 5+8+6+5+8+6 = 38
We add 14, when we add a second trapezoid
P = 14n + 10
p(1) = 14+10 Check for 1 trapezoid
p(2) = 14*2 +10 = 28+10 = 38 check for 2 trapezoids
2. You're given a function that maps 1 to 1, 0 to 0, and 2 to -1. The domain is the set of points that are given to the function as inputs, {1, 0, 2}, which is equivalent to the set listed in option C.
3. Evaluate [tex]f(x)[/tex] at [tex]x=10[/tex]:
[tex]f(10)=5(10)+3=50+3=53[/tex]
so the answer is B.
6. Each trapezoid in the chain contributes a copy of 8 and 6 (a total of 14), so that we should expect the total perimeter to contain [tex]14n[/tex]. The remaining two sides contribute a constant 10 regardless of [tex]n[/tex]. So the perimeter is given by the formula in D, [tex]P=14n+10[/tex].
15 points!
1. In how many ways can 3 heads occur when 5 coins are flipped?
2. In how many ways can 3 heads occur when 6 coins are flipped?
Answer: There are 10 possible ways to get 3 heads. The probability of getting 3 heads from 5 flips would possibly be 10/32, or 5/16. I hope this helped! :)
Final answer:
The number of ways in which 3 heads can occur when 5 coins are flipped is 10. The number of ways in which 3 heads can occur when 6 coins are flipped is 20.
Explanation:
To calculate the number of ways in which 3 heads can occur when 5 coins are flipped, we can use the concept of combinations. The number of ways to choose 3 heads out of 5 coins is given by the formula C(5, 3), which is equal to 10. Therefore, there are 10 ways in which 3 heads can occur when 5 coins are flipped.
To calculate the number of ways in which 3 heads can occur when 6 coins are flipped, we can use the same concept. The number of ways to choose 3 heads out of 6 coins is given by C(6, 3), which is equal to 20. Therefore, there are 20 ways in which 3 heads can occur when 6 coins are flipped.
~PLEASE HELP ASAP OFFERING 25 POINTS AND BRAINIEST IF ANSWER IS CORRECT~
Rewrite the quadratic equation in the form y = a(x − h)2 + k.
Y = 5x^2 - 30x + 95
Answer:
Answer is B
Step-by-step explanation:
Answer:
y=5(x-3)^2 +50
Step-by-step explanation:
the units of area are always A. cubic units B. units C. square units
Answer: B
Step-by-step explanation:
The correct option is c.
The units of area are always square units because they are the product of two lengths dimensions. This could be square meters, square centimeters, or any other square unit.
Explanation:The units of area are always square units. This is because area is defined as the product of two lengths dimensions. This applies whether you're calculating the area of a rectangle (length x width), a circle (pi x radius²), or any other shape. In the standard system of international units (SI), the base unit for length is meters, so area would be in square meters (m²). However, this can be adapted to any unit of length, such as centimeters, so area could also be measured in square centimeters (cm²).
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The ratio of boys to girls in homeroom is 2:3if there are 8 boys how many girls are there
The ratio of boys to girls is 2:3, which means for every 2 boys there are 3 girls.
There are 8 boys.
Divide the number of boys by 2 ( their ratio):
8/2 = 4
Multiply that by the part of the ratio for girls:
4 x 3 = 12
There are 12 girls
Two circular ponds at a botanical garden have the following radii. Pond A. 5√(164 ) meters
Pond B. (25√200)/5
Todd simplifies the radius of pond A this way: 5√(164 ) meters
Step 1: 5(√100+√64)
Step 2: 5(10+8)
Step 3: 5(18)
Step 4: 90
One of Todd’s steps is incorrect. Identify which step is incorrect; and rewrite the step so it is correct.
Answer:
The correct step will be [tex]5(\sqrt{164})=5(\sqrt{4*41})[/tex]
Step-by-step explanation:
We have been given that pond A has a radius of [tex]5\sqrt{(164)}[/tex] meters and radius of Pond B is [tex]\frac{(25\sqrt{200)}}{5}[/tex] meters. Todd simplifies the radius of pond A and we are asked to find out error in Todd's steps.
Step 1: [tex]5(\sqrt{100}+\sqrt{64})[/tex]
Since we know that [tex]\sqrt{ab}=\sqrt{a\times b}=\sqrt{a} \times \sqrt{b}[/tex]. We can see that Todd has made error in his very first step by splitting [tex]\sqrt{164}[/tex] as [tex]\sqrt{100+64}[/tex].
The correct step will be,
[tex]5(\sqrt{164})=5(\sqrt{4*41})[/tex]
Therefore, the correct step 1 will be: [tex]5(\sqrt{4*41})[/tex].
Now let us simplify our given radical expression.
[tex]5(\sqrt{4*41})=5(\sqrt{4}*\sqrt{41})[/tex]
[tex]5\sqrt{4}*\sqrt{41}=5*2*\sqrt{41}[/tex]
[tex]5*2*\sqrt{41}=10*\sqrt{41}[/tex]
Therefore, our given radical expression simplifies to [tex]10*\sqrt{41}[/tex] meters.
The incorrect step in Todd's simplification is Step 1, which inaccurately breaks apart the square root of 164.
The step in Todd's simplification of the radius of Pond A that is incorrect is Step 1:
Incorrect Step 1: [tex]5(\sqrt{} 100 + \sqrt{ 64)[/tex]
This is incorrect because it suggests that √164 can be simplifed directly into the sum of the square roots of its components, which is not how square roots work.
The correct step should involve finding the prime factorization of 164 and then simplifying the square root.
Corrected Step 1: [tex]5\sqrt{} (4 x 41)[/tex]
Corrected Step 2: [tex]5(2\sqrt{} 41)[/tex]
Corrected Step 3: [tex]10\sqrt{} 41[/tex]
The fully simplified form of [tex]5\sqrt{} 164[/tex] meters would be [tex]10\sqrt{} 41[/tex] meters.
It is recommended that an adult drink 64 fluid ounces of water everyday Josie has already consumed 700 mL of water how many more liters should he drink today
Answer:
1.2 litres more water should Josie drink.
Step-by-step explanation:
As given
It is recommended that an adult drink 64 fluid ounces of water everyday .
As given
1 ounce = 0.0296 litre .
Now convert 64 ounces into litre.
64 ounce = 64 × 0.0296
= 1.9 litres (Approx)
As
1 litre = 1000 ml
[tex]1\ ml= \frac{1}{1000}\ litre[/tex]
Now convert 700 ml into litre.
[tex]700\ ml= \frac{700}{1000}\ litre[/tex]
[tex]700\ ml= \frac{7}{10}\ litre[/tex]
700 ml = 0 .7 litre
Thus
Recommended amount of water a adult should drink = Amount of water Josie already consumed + More water should Josie drink.
Putting the value
1.9 litres = 0 .7 litres + More water should Josie drink.
More water should Josie drink = 1.9 - 0.7
More water should Josie drink = 1.2 litres .
Therefore 1.2 litres more water should Josie drink.
Wangari plants trees at a constant rate of 1212 trees every 33 hours. Write an equation that relates pp, the number of trees Wangari plants, and hh, the time she spends planting them in hours.
Answer:
[tex]p=4h[/tex]
Step-by-step explanation:
Let p be the number of trees Wangari plants, and h be the time she spends planting them in hours.
We have been given that Wangari plants trees at a constant rate of 12 trees every 3 hours.
Let us find number of trees planted in 1 hour by dividing 12 by 3.
[tex]\text{Number of trees planted in 1 hour}=\frac{12\text{ plants}}{3\text{ hour}}[/tex]
[tex]\text{Number of trees planted in 1 hour}=4\frac{\text{ plants}}{\text{ hour}}[/tex]
We can represent this information as: [tex]p=4h[/tex]
Therefore, the equation [tex]p=4h[/tex] relates the number of trees (p) Wangari plants, and the time (h) she spends planting them in hours.
Answer:
p=4h
Step-by-step explanation:
Calculate the total cost of an item bought at a negotiated price of $17,250 with 7.7 percent sales tax and a $95 registration fee.
$17,250
$17,376.75
$18,673.25
$18,578.25
Answer:
C. $18673.25
Step-by-step explanation:
Let us find cost of item after 7.7% of sales tax. The price after 7.7% of sales tax will be 17250 plus 7.7% of 17250.
[tex]\text{The cost of item after sales tax}=17250+(\frac{7.7}{100}\times 17250)[/tex]
[tex]\text{The cost of item after sales tax}=17250+(0.077\times 17250)[/tex]
[tex]\text{The cost of item after sales tax}=17250+1328.25[/tex]
[tex]\text{The cost of item after sales tax}=18578.25[/tex]
Therefore, the cost of item after 7.7% of sales tax will be $18578.25.
To find the total cost of item let us add registration fee ($95) to $18578.25
[tex]\text{The total cost of item}=18578.25+95[/tex]
[tex]\text{The total cost of item}=18673.25[/tex]
Therefore, the total cost of item is $18673.25 and option C is the correct choice.
Paul is earning money for a new bike. He is paid $3.00 for each car he washes and $1.00 for each bag of leaves he rakes. If he washes 6 cars and fills 12 bags of leaves, how much money will he earn?
Heeeeeelllllllllppppppppppppppppp mmmmmmmmeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!
Considering arithmetic and geometric sequences, would there ever be a time that a geometric sequence does not outgrow an arithmetic sequence in the long run as the number of terms of the sequences become really large?
Yes it is possible for a geometric sequence to not outgrow an arithmetic one, but only if the common ratio r is restricted by this inequality: 0 < r < 1
Consider the arithmetic sequence an = 9 + 2(n-1). We start at 9 and increment (or increase) by 2 each time. This goes on forever to generate the successive terms.
In the geometric sequence an = 4*(0.5)^(n-1), we start at 4 and multiply each term by 0.5, so the next term would be 2, then after that would be 1, etc. This sequence steadily gets closer to 0 but never actually gets there. We can say that this is a strictly decreasing sequence.
If your teacher insists that the geometric sequence must be strictly increasing, then at some point the geometric sequence will overtake the arithmetic one. This is due to the nature that exponential growth functions grow faster compared to linear functions with positive slope.
What is the approximate length of the base of an isosceles triangle if the congruent sides are 3 feet and the vertex angle is 35°?
Answer:
Properties of isosceles triangle:
Two sides are congruent(i.,e equal)Corresponding angles opposite to these sides are equal. A Perpendicular drawn to the third side from the corresponding vertex will bisect the third side. Also the altitude drawn will divide the isosceles triangle into two congruent right triangles.As per the given statement:
Congruent sides(a) = 3 feet And Vertex angle([tex]\angle QPR[/tex]) = [tex]35^{\circ}[/tex]
Let the length of the base(QR) of an isosceles triangle PQR be 2b.
By isosceles properties, in triangle PQR , the median of an isosceles triangle from its vertex angle is also the perpendicular bisector of the base.
Also, this line divides the triangle into two congruent right angled triangles whose hypotenuse is 3 feet,
and [tex]\angle QPS = \frac{\angle QPR}{2} = \frac{35}{2} = 17.5^{\circ}[/tex]
In a right angle triangle QSP
Using sine ratio formula;
[tex]\sin \theta = \frac{\text{opposite side}}{\text{Hypotenuse side}}[/tex]
Hypotenuse sides = PQ = 3 ft and Opposite side = QS = b ft
Solve for b using using sine ratio:
[tex]\sin (17.5^{\circ}) = \frac{b}{3}[/tex]
or
[tex]b = 3 \cdot \sin(17.5^{\circ})[/tex]
[tex]b = 3 \cdot 0.3007057995[/tex]
Simplify:
b = 0.902117398
Length of the base of an isosceles triangle PQR = 2b = 2(0.902117398) = 1.8042348
Therefore, the approximate length of the base of an isosceles triangle is, 1.8 feet
Answer:
1.80 feet.
Step-by-step explanation:
Please see the attachment.
Let c be the length of base of our given triangle.
We have been given that an isosceles triangle's congruent sides are 3 feet the vertex angle is 35 degrees. We are asked to find the length of the base of isosceles triangle.
We will use law of cosine to find the length of our base.
[tex]c=\sqrt{a^2+b^2-2ab\text{ Cos(C)}}[/tex]
Upon substituting our given values in above formula we will get,
[tex]c=\sqrt{3^2+3^2-2\times 3\times 3\times\text{ Cos(35)}}[/tex]
[tex]c=\sqrt{9+9-18\times\text{ Cos(35)}}[/tex]
[tex]c=\sqrt{18-18\times 0.819152044289}[/tex]
[tex]c=\sqrt{18-14.744736797202}[/tex]
[tex]c=\sqrt{3.255263202798}[/tex]
[tex]c=1.8042347970255978\approx 1.80[/tex]
Therefore, the length of base of our given isosceles triangle is approximately 1.80 feet.
What is the solution to the following system?
(2, 3, 4)
(4, 3, –2)
(4, 3, 2)
(6, 7, –2)
Answer:
(4,3,2)
Step-by-step explanation:
We can solve this via matrices, so the equations given can be written in matrix form as:
[tex]\left[\begin{array}{cccc}3&2&1&20\\1&-4&-1&-10\\2&1&2&15\end{array}\right][/tex]
Now I will shift rows to make my pivot point (top left) a 1 and so:
[tex]\left[\begin{array}{cccc}1&-4&-1&-10\\2&1&2&15\\3&2&1&20\end{array}\right][/tex]
Next I will come up with algorithms that can cancel out numbers where R1 means row 1, R2 means row 2 and R3 means row three therefore,
-2R1+R2=R2 , -3R1+R3=R3
[tex]\left[\begin{array}{cccc}1&-4&-1&-10\\0&9&4&35\\0&14&4&50\end{array}\right][/tex]
[tex]\frac{R_2}{9}=R_2[/tex]
[tex]\left[\begin{array}{cccc}1&-4&-1&-10\\0&1&\frac{4}{9}&\frac{35}{9}\\0&14&4&50\end{array}\right][/tex]
4R2+R1=R1 , -14R2+R3=R3
[tex]\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&-\frac{20}{9}&-\frac{40}{9}\end{array}\right][/tex]
[tex]-\frac{9}{20}R_3=R_3[/tex]
[tex]\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&1&2\end{array}\right][/tex]
[tex]-\frac{4}{9}R_3+R_2=R2[/tex] , [tex]-\frac{7}{9}R_3+R_1=R_1[/tex]
[tex]\left[\begin{array}{cccc}1&0&0&4\\0&1&0&3\\0&0&1&2\end{array}\right][/tex]
Therefore the solution to the system of equations are (x,y,z) = (4,3,2)
Note: If answer choices are given, plug them in and see if you get what is "equal to". Meaning plug in 4 for x, 3 for y and 2 for z in the first equation and you should get 20, second equation -10 and third 15.
Answer:
C on edge
Step-by-step explanation:
: )
Given the equation y-4=3/4(x + 8) in point-slope form, identifty the equation of the same line in standard form.
Answer:
The point-slope form is y = 3/4x + 10 and the standard form is -3x + 4y = 40
Step-by-step explanation:
In order to find this equation in point-slope form, simply solve for the y value.
y - 4 = 3/4(x + 8)
y - 4 = 3/4x + 6
y = 3/4x + 10
Now to get to the standard form, solve for the constant, then rationalize the denominator.
y = 3/4x + 10
-3/4x + y = 10
-3x + 4y = 40
The equation of the same line in standard form is 3x - y = -9.
Explanation:The equation of the same line in standard form is 3x - y = -9.
In point-slope form, y - 4 = (3/4)(x + 8). To convert this to standard form, we need to eliminate the fraction by multiplying both sides of the equation by 4. This gives us 4(y - 4) = 3(x + 8).
Simplifying, we have 4y - 16 = 3x + 24. Rearranging the terms, the equation in standard form is 3x - 4y = -40. To make it more standard, we can multiply all the terms by -1 to get -3x + 4y = 40. Finally, we divide all the terms by -1 to get the final equation of the line in standard form: 3x - y = -9.
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Type the correct answer in each box.
Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the equation.
4(px+1)=64
The value of x in terms of p is ____ .
The value of x when p is −5 is____ .
To find the value of x in the equation 4(px+1)=64, you divide by 4, simplify, and then divide 15 by p, resulting in x = 15/p. Substituting p=-5 gives x=-3.
To solve the equation 4(px+1)=64 and find the value of x in terms of p, we follow these steps:
Divide both sides of the equation by 4 to isolate the term with x: (px+1) = 64/4
Further simplify to get px + 1 = 16
Subtract 1 from both sides to get px = 16 - 1
Finally, divide by p to solve for x: x = (16 - 1) / p = 15/p
The value of x in terms of p is 15/p.
Substitute p = -5 into the equation to find the value of x when p is -5:
x = 15 / -5
x equals -3
True or false, by definition, a simple random sample of size n is any sample that is selected in a manner to guarantee every individual in the population has an equal chance of selection. if your answer is false, please clearly explain why it is false.
Answer:
True
Step-by-step explanation:
A simple example would be picking 3 marbles ( of equal size) from a bag of 10 marbles previously shaken.
A simple random sample, by definition, is any sample selected in a manner that ensures every individual in the population has an equal chance of being selected. This method is commonly used in statistical studies and surveys to prevent bias and more accurately represent the larger population.
Explanation:True, by definition, a simple random sample of size n is, indeed, any sample that is selected in a manner that guarantees every individual in the population an equal chance of being selected. This method is akin to drawing names out of a hat or using a random number generator, ensuring that all members of the population have an equal chance of selection. This approach is commonly implemented in statistical studies and surveys to avoid bias and to ensure that the sample accurately represents the broader population.
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How many hours does an employee typically need to work before being eligible for overtime hours?
Wanna try 40?
Step-by-step explanation:
Zoe paid \$18.60$18.60 in sales tax and tips for her dinner. The sales tax rate is 11\%11%, and she tipped 20\%20%. (The sales tax does not apply to the tip, and the tip is based on the price of the dinner before sales tax.) What was the price of Zoe's dinner, before sales tax and tip? \$$
Answer:
The price of dinner before sales tax and tip is $60.
Step-by-step explanation:
Let the price of before sales tax and tip be x.
The amount of tip is 20% of the price of dinner. So, the amount of tip is
[tex]\frac{20}{100}x[/tex]
The amount of sales tax is 11% of the price of dinner. So, the amount of sales tax is
[tex]\frac{11}{100}x[/tex]
It is given that Zoe paid $18.60 in sales tax and tips for her dinner. Therefore the sum of tip and sales tax is $18.60.
[tex]\frac{20}{100}x+\frac{11}{100}x=18.60[/tex]
[tex]\frac{20+11}{100}x=18.60[/tex]
[tex]31x=1860[/tex]
[tex]x=60[/tex]
Therefore the price of dinner before sales tax and tip is $60.
The ratio of the measures of two complementary angles is 7:8 what is the measurement of the smaller angle?
Answer: 42°
Step-by-step explanation: In this problem, we're given that the measures of two complementary angles are in the ratio 7 to 8 and we're asked to find the measure of the smaller angle.
Since our two angles are in the ratio 7 to 8, let's represent the angles as 7x and 8x. We will call 7x an angle and 8x its complement. Now, remember that if two angles are complementary, then the sum of their measures is 90 degrees. So we can set up the equation 7x + 8x = 90.
Simplifying on the left side, we have 15x = 90.
Dividing both sides by 15, we find that x = 6.
So the measure of our first angle, 7x, is 7(6) or 42°.
The measure of its complement, 8x, is 8(6) or 48°.
Finally, notice that if we add our two angles together, we have 42 + 48 which equals 90 so our answer checks. This means that the smaller angle is 42°. Image is provided below.
What is the contrapositive of if a, then b?
A.) if b, then a
B.) if a, then not b
C.) if not b, then not a
D.) if not a, then not b
Answer:
C.) if not b, then not a
Step-by-step explanation:
The formula for a contrapositive is:
a -> b to -b -> -a
Answer: I believe
the answer is C.
Step-by-step explanation:
5 friends go out for pizza. the total bill comes to ?31.35. how much should each of the friends pay
Answer:
the answer is 6.27
Step-by-step explanation:
all you have to do is divide 31.35 by 5
31.35/5 = 6.27
(unless your kind to pay the whole bill ;D)
The Volume of a rectangular prism can be computed by using the formula V=LWH which shows an equation solving for W
Answer:
W = [tex]\frac{V}{LH}[/tex]
Step-by-step explanation:
given the formula V = LWH
to solve for W divide both sides by LH, hence
W = [tex]\frac{V}{LH}[/tex]
Which of the following is the correct factorization of the trinomial below
-7x^2-4x+20
A: (-7x+10)(x-2)
B: -1(7x-10)(x=2)
C: -7(x-5)(x+2)
D: 7(x+10)(-x+2)
Answer:
A: (-7x+10)(x-2)
Step-by-step explanation:
Given trinomial,
[tex]-7x^2-4x+20[/tex]
By middle term splitting,
[tex]=-7x^2-(14-10)x+20[/tex]
[tex]=-7x^2-14x+10x+20[/tex]
[tex]=-7x(x+2)+10(x+2)[/tex]
[tex]=(-7x+10)(x+2)[/tex]
Since, further factorization is not possible,
Thus, the required factorized form of the given trinomial is,
[tex](-7x+10)(x+2)[/tex]
Option A is correct.
do 5,271 x 129 make sure to estimate
Answer:
679959
Step-by-step explanation:
THE ANSWER IS 679959 BUT IF YOU ESTIMATE TO THE LAST DIGIT THE IT WOULD BE 700000 DUE TO 9 ROUNDING THE 7 TO A 8 AND THEN 8 EOUNDS THE 6 TO A 7 EVERYTHING ELSE BECOMES 0
To estimate 5,271 x 129, we round to the closest thousands and hundreds giving us 5,000 x 100, which equals 500,000. This is an estimation, the actual product of 5,271 and 129 is 679,859.
Explanation:To estimate the product of 5,271 x 129, we can round each number to the nearest thousands and hundreds respectively. So, 5,271 can be rounded to 5,000 and 129 can be rounded to 100. Our estimation would then be 5,000 x 100 = 500,000.
Remember that this is an estimation. The actual product of 5,271 and 129 is 679,859, but for quick mental calculations or to get a sense of the size of the result, this type of estimation can be helpful.
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please help on this one?
Answer:
the answer is B 2x-7
Step-by-step explanation:
-1 ║ 2 9 7
-2 -7
----------------------------------------------
2 7 0
⇒ The Quotient is 2x + 7
Which of the following statements represents one of the differences between an experiment and an observational study?
Inclusion of random sample.
Introducing a change to the subgroup.
Ability to calculate the mean.
Ability to draw conclusions.
Answer:
The main difference between an observational study and an experiment is the inclusion of a random sample.
Step-by-step explanation:
In an observational study, the researchers do not interfere with the method the data is collected. In an investigation of how regularly the studying improves marks, the researchers sample people from the population who has studied regularly and those who haven't and then collect the average marks obtained by each of the groups. We can only accomplish an association among the response variable and the explanatory variables because there may be some other variable that may affect both the explanatory and the response variable, thus making it look as if there is a relationship among them.
But in an Experiment, the researchers actually interfere with the method the data is collected. In an experiment, each case is randomly assigned to the treatment groups, i.e. to say that each of the cases has an equal chance of being in both groups. These kinds of studies help us to establish causal connections between the response variable and the explanatory variables because random assignment makes sure that they are equally spread among both the groups.
So, the primary difference between an observational study and an experiment is that in case of an observational study there is no random assignment but in case of an experiment there is a random assignment.
Kia payed $10 for two charms. The price of each charm was a multiple of $2. What are the possible prices of the charms
2,8 2+8=10
4,6 4+6=10
Can’t be more than 10$’s. The multiples of 2 are 2,4,6,8,10. So you’re answering which 2 numbers add up to 10$. If it’s anything higher than that it’s not a possible price and if it’s lower than that then she would have payed less which also isn’t possible.
Company A rents copiers for a monthly charge of $360 plus 12 cents per copy. Company B rents copiers for a monthly charge of $720 plus 6 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?
Final answer:
To find the number of copies above which Company A's charges are higher than Company B's charges, set up an equation and solve for C. The number of copies above which Company A's charges are higher is 6000.
Explanation:
To find the number of copies above which Company A's charges are higher than Company B's charges, we need to set up an equation to represent the total charges for each company. Let C represent the number of copies. For Company A, the total charges can be represented as 360 + 0.12C. For Company B, the total charges can be represented as 720 + 0.06C. We can set these two expressions equal to each other and solve for C to find the number of copies above which Company A's charges are higher.
360 + 0.12C = 720 + 0.06C
0.06C - 0.12C = 720 - 360
-0.06C = 360
C = 360 / -0.06
C ≈ -6000
Since the number of copies cannot be negative, we can conclude that Company A's charges are higher than Company B's charges when the number of copies is greater than 6000.
What is 1.67x10^-4 in standard form?
Answer:
.000167
Step-by-step explanation:
To get 1.67x10^-4 into standard from, we move the decimal to the left (the negative sign means to the left) 4 places. That means we need to add 3 zero's.
.000167
Three ballet dancers are positioned on stage. Monica is straight behind Jodie and directly left of Gina. If Jodie and Monica are 6 meters apart, and Gina and Jodie are 7 meters apart, what is the distance between Monica and Gina? If necessary, round to the nearest tenth.
To find the distance between Monica and Gina, the Pythagorean theorem is used because they form a right-angle triangle with Jodie. Calculating the hypotenuse of this triangle with sides of 6 and 7 meters results in a distance of approximately 9.2 meters between Monica and Gina.
The student has asked to find the distance between Monica and Gina, given the positions of three ballet dancers on stage. This problem can be solved using the Pythagorean theorem because Monica, Jodie, and Gina form a right-angle triangle on stage. Monica is behind Jodie and to the left of Gina, meaning that the line segment between Jodie and Monica is one leg of the right triangle, and the line segment between Jodie and Gina is the other leg of the triangle.
To find the distance between Monica and Gina, which is the hypotenuse of the right triangle, we apply the Pythagorean theorem (where d is the distance between Monica and Gina):
d^2 = Jodie-Monica^2 + Jodie-Gina^2d^2 = 6^2 + 7^2d^2 = 36 + 49d^2 = 85d = \/85d \/= 9.2 (rounded to the nearest tenth)Therefore, the distance between Monica and Gina is approximately 9.2 meters.