Answer:
108347 (srry for not seeing bestay)
Step-by-step explanation:
multiply the polynomials (x^2+4)(x^2-4)
Answer:
x^4-16
Step-by-step explanation:
(x^2+4)(x^2-4)
x^4+4x^2-4x^2-16
x^4-16
Twice the difference of a number and 8 is equal to three times the sum of the number and 7. Find the number.
The number is
Answer:
The number is -37.
Step-by-step explanation:
2(x - 8) = 3(x + 7)
2x - 16 = 3x + 21
x = -37
enter any three different expressions that are equal to \displaystyle \frac{1}{4} \frac{5}{4} 4 1 4 5 .
The three expressions all represent the same value: \(\(\frac{1}{4} \cdot \frac{5}{4} \cdot 4\),\) but they are expressed in different forms.
To express the fraction \(\(\frac{1}{4} \cdot \frac{5}{4} \cdot 4\)\) in different ways, we can use algebraic expressions, decimal numbers, and mixed numbers. Here are three different expressions that are equal to\(\(\frac{1}{4} \cdot \frac{5}{4} \cdot 4\):\)
1. Algebraic expression: \(\(\frac{1}{4} \cdot \frac{5}{4} \cdot 4 = \frac{5}{16} \cdot 4 = \frac{20}{16}\)\)
2. Decimal number:\(\(\frac{1}{4} \cdot \frac{5}{4} \cdot 4 = 0.25 \cdot 1.25 \cdot 4 = 1.25\)\)
3. Mixed number:\(\(\frac{1}{4} \cdot \frac{5}{4} \cdot 4 = \frac{1}{4} \cdot \frac{5}{1} = \frac{5}{4} = 1 \frac{1}{4}\)\)
In the first expression, we simplified the product of the fractions by multiplying the numerators and denominators. Then, we simplified the resulting fraction to its lowest terms.
In the second expression, we converted each fraction to a decimal number and multiplied them together.
In the third expression, we converted the fractions to a mixed number by dividing the numerator by the denominator. This gives us the whole number part and the remaining fraction.
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PLEASE HELP QUESTION IN PICTURE
Answer:
Perimeter= 40
Area= 120.71
Step-by-step explanation:
Daniel says that more than half the students spent 2 1 2 hours or more on homework. Liz says more than half the students spent less than 2 1 2 hours on homework. Who is correct? Explain.
Answer:
Liz is correct
Step-by-step explanation:
Given
See attachment for complete question
Required
Who is correct? Daniel or Liz
From the attached data, we have:
\(Time: 1\frac{3}{4},\ 2\frac{1}{2},\ 2,\ 2\frac{3}{4},\ 1,\ 1\frac{3}{4},\ 1\frac{1}{4},\ 3,3\frac{1}{4},\ 3\frac{3}{4},\ 2,\ 2\)
The total number of students is:
\(n = 12\)
The data that represents \(2\frac{1}{2}\) or more is:
\(Time: 2\frac{1}{2},\ 2\frac{3}{4},\ 3,3\frac{1}{4},\ 3\frac{3}{4}\)
The frequency of this is 5
The frequency that represents \(2\frac{1}{2}\) or less will be 7
This means that less than half spend \(2\frac{1}{2}\) or more
and more than half spend \(2\frac{1}{2}\) or more
Hence, Daniel is incorrect. Liz is correct
a tank holds 4000 liters of water in which 100 grams of salt have been dissolved. saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. write initial the value problem for:
The mass of salt in the tank at time t.
dS/dt = 10 - S/400
S(0) = 100 grams
The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)
A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.
So dS/dt = S(in) - S(out)
S(in) = 1 × 10 = 10 gram/liters
S(out) = S/V × 10 = 10S/V gram/liters
V = V(0) + q(in) - q(out)
V = 4000 + 10t - 10t
V = 4000 liters
dS/dt = 10 - 10S/V
dS/dt = 10 - 10S/4000
dS/dt = 10 - S/400
Now given; S(0) = 100.
Here, p(t) = 1/400, q(t) = 10
\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)
\(\mu=e^{\int p(t)dt}\)
\(\mu=e^{\frac{t}{400}}\)
So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)
S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)
S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)
S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)
S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)
Now solving the bracket
S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)
At S(0) = 100
100 = 4000 + \(e^{\frac{-0}{400}}\) C
100 = 4000 + \(e^{0}\) C
100 = 4000 + C
Subtract 4000 on both side, we get
C = -3900
Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)
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The complete question is:
A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:
The mass of salt in the tank at time t.
dS/dt =
S(0) =
The solution is S(t) =
in the 2002 Winter Olympics in salt lake city , the United States and Canada earned a total of 51 metals. the United States earned twice as many as Canada. how many medals did each country earn?
Answer:
United States:34
Canada:17
Answer:
17 and 34
Step-by-step explanation:
the United States earned 34, while the Canada earned 17
in which of the following problems is a heuristic solution appropriate? group of answer choices find the combination to a lock with n numbers. find the best combination of ingredients for spaghetti sauce. playing chess. find the biggest item in a list.
Based on the information, we can infer that all the options are examples of situations in which the heuristics can be applied.
What is heuristics?Heuristics is a term that refers to a strategy or technique whose main objective is to establish a procedure to advance in the process of solving a problem. In heuristics, the information is usually organized by means of a figure or a scheme to present it in a schematic way and solve it easily.
According to the above, the problems in which it is appropriate to use a heuristic solution are:
Find the combination of a lock with n numbers.Find the best combination of ingredients for the spaghetti sauce.Playing chess.Find the largest element in a list.In this case, they are all problems in which the heuristic method can be applied because they involve different steps to have a solution.
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If all the values in a set of data are the same, which of the following is true? (Check all that apply.)
(A) The median and mode are the same.
(B) The range is zero.
(C) The range and mode are the same.
(D) The low and high values are the same.
The sides of a polygon have lengths 5, 7, 8, 11, and 19 units. The perimeter of a similar polygon is 75 units. Find the lengths of the sides of the larger polygon
The perimeter of small polygon is 50 units. The length of sides of the larger polygon is 7.5, 10.5, 12, 16.5, 28.5 units.
What is polygon?
Polygon in geometry is "any closed curve consisting of set line segments connected such that two segment across".
According to the question,
Lengths of sides of polygon is 5 units, 7 units, 8 units, 11 units, and 19 units.
Formula for Polygon = sum of sides
Perimeter of first polygon = 5 + 7 + 8 + 11 +19
= 50 units.
Perimeter of second polygon = 75 units.
Divide second polygon by first polygon = 75/50 = 1.5 units
This conclude, second polygon is 1.5 units larger than first polygon.
In order to find the length of the sides of larger polygon by given, first polygon and second polygon are similar polygon multiply 1.5 units to the length sides of first Polygon.
5 * 1.5 = 7.5
7 * 1.5 = 10.5
8 * 1.5 = 12
11 * 1.5 = 16.5
19 * 1.5 = 28.5
Hence, the length of sides of the larger polygon is 7.5, 10.5, 12, 16.5, 28.5 units.
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Which number sentence is not true?
A.
B.
C.
D.
3.3g + 6 = 1.3g + 12
Answer:
get smart
Step-by-step explanation:
dont cheat there is no good out of cheating
Answer:
G=3
3.3 x 3 =9.9 9.9 + 6 =15.9
1.3 x 3 =3.9 3.9 + 12 =15.9
So, G=3
Construct a circle with a radius of 8cm, and draw an equilateral triangle inside it. Make sure the length of each side measures to 15.6 cm.
Answer:
Diagram 1
Draw a circle with a radius of 8 cm, ensuring you have clearly marked the center point (black circle with center C1)
Add a point on the circumference of the circle (point C2)
Draw a second circle of radius 8cm with point C2 as its center (red circle with center C2).
Diagram 2
The red circle intersects the black circle at two points (D and E).
Connect these 2 points of intersection with a line segment.
Diagram 3
Draw a third circle with center D and radius DE (shown in blue)
This circle intersects the black circle at point F.
Diagram 4
Draw 2 line segments to connect points D and E with point F - this is your equilateral triangle inside the circle!
How many keys are required to fully implement a symmetric algorithm with 10 participants?
The number of keys required to fully implement a symmetric algorithm with 10 participants is: 45 (Option C)
What is a Symmetric Algorithm?Symmetric encryption or Algorithm is a kind of encryption that uses a single key (a secret key) to encrypt and decode electronic data.
The key must be exchanged between the organizations communicating using symmetric encryption so that it may be utilized in the decryption process.
What is the computation justifying the above result?The formula that determines the number of keys necessary for a symmetric algorithm is given as;
(n*(n-1))/2,
which is 45 in this situation, when n = 10.
That is
(10 * (10-1))/2
= 45.
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Full Question:
How many keys are required to fully implement a symmetric algorithm with 10 participants?
A. 10
B. 20
C. 45
D. 100
336,765=3,14×0.55×(l+0.55) please help
Answer:
l = 194999.45
Step-by-step explanation:
I'm going to assume that you meant 3.14 by 3,14.
336,765 = 3.14 × 0.55 × (l + 0.55)
336,765 ÷ (3.14 × 0.55) = l + 0.55
(336,765 ÷ (3.14 × 0.55)) - 0.55 = l
l = 194999.45
The straight line y = x + 2 rotates 90 degrees clockwise about (0,0) and gets a new line L. The point P is a moving point on the line L. The coordinates of Q is (0,2) What’s the minimum value of PQ?
The minimum value of PQ is 2 units.
To find the minimum value of PQ, we need to determine the position of P that minimizes the distance between P and Q.
The line y = x + 2 represents the original line. To rotate this line 90 degrees clockwise about (0,0), we need to swap the x and y coordinates and negate the new x coordinates. The equation of the new line, L, becomes x = y + 2.
Since Q is given as (0,2), we can substitute these coordinates into the equation of line L:
x = y + 2
0 = 2 + 2
0 = 4
As the equation is not satisfied, the point (0,2) does not lie on line L.
However, we can still find the minimum value of PQ. The minimum value occurs when P is located on the line perpendicular to L and passing through Q. This perpendicular line has the equation x = -2.
Substituting this equation into the distance formula, we get:
PQ = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-2 - 0)^2 + (y - 2)^2)
= sqrt(4 + (y - 2)^2)
= sqrt(4 + y^2 - 4y + 4)
= sqrt(y^2 - 4y + 8)
To find the minimum value of PQ, we can complete the square:
PQ = sqrt((y - 2)^2 + 4)
= sqrt(y^2 - 4y + 4 + 4)
= sqrt(y^2 - 4y + 8)
The minimum value of PQ occurs when the expression inside the square root is minimized. The vertex of the parabola y^2 - 4y + 8 is given by the x-coordinate x = -(-4) / (2*1) = 2. Therefore, the minimum value of PQ is obtained when y = 2.
Substituting y = 2 into the expression for PQ, we get:
PQ = sqrt(2^2 - 4*2 + 8)
= sqrt(4 - 8 + 8)
= sqrt(4)
= 2
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Write an exponential function in the form y = abthat goes through points (0,2)
and (4, 1250).
Answer:
Solve for x.
9x=5x+20
9x=5x+20
9x-5x=20
4x=20
x=5
Mr. drew rides his motorcycle with a constant speed of 72 mi/hr. How far can he travel in 2 ½ hours?
Answer:
180
Step-by-step explanation:
take 72+72 +36 to get your answer .
Answer:
180 miles
Step-by-step explanation:
Assuming that the speed of the motorcycle is constant, the following equation, (\(speed * time = distance\)) can be used to find the distance that a vehicle traveled when one is given the time and speed at which the vehicle operates. Substitute in these values, and solve,
\((72)*(2\frac{1}{2})\\\\= 72 * \frac{5}{2}\\\\= 180\)
Write the fraction 6/2 in simplest form
Answer:
The fraction 6/2 in it's simplest form is simply 3 :)
Step-by-step explanation:
The solution for the fraction 6/2 in simplest form is, 3
We have to given that,
To change the fraction 6/2 in simplest form.
Since, An equal division of a whole number into smaller pieces is called a fraction. Alternately, a fraction is a number that has been represented as a quotient. It may be expressed using the p: q form, which is identical to p/q.
The number is,
⇒ 6 / 2
After divide as,
⇒ 3
Therefore, The solution for the fraction 6/2 in simplest form is, 3
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y= 2x-1 is a tangent to y=x^2. Name the point of tangency,
Answer:
Point of tangency is \(x=1\) or \((1,1)\)
Step-by-step explanation:
You don't really need to use Calculus here. You can just set each equation to each other and solve for x (the point of tangency):
\(x^2=2x-1\)
\(x^2-2x+1=0\)
\((x-1)(x-1)=0\)
\(x=1\)
Therefore, the point of tangency is \(x=1\) or \((1,1)\)
Which equation represents exponential decay?
solve each equation round to the nearest ten-thousandth in (x+21)=7
The solution to the equation (x+21)=7 is x = -14
How to solve the equation?The equation is given as:
(x+21)=7
Remove the brackets
x + 21 = 7
Subtract 21 from both sides
x + 21 - 21 = 7 - 21
Evaluate the expression
x = -14
Hence, the solution to the equation (x+21)=7 is x = -14
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Darryl wants to add enough water to 8 gallons of a 10% bleach solution to make a 5% bleach solution. which equation can he use to find x, the number of gallons of water he should add? original (gallons) added (gallons) new (gallons) amount of bleach 0.8 0 0.8 amount of solution 8 x 8 x startfraction 0.8 over 8 x endfraction times startfraction 5 over 100 endfraction = 1 startfraction 0.8 over 8 x endfraction times = startfraction 5 over 100 endfraction startfraction 0.8 over 8 x endfraction = startfraction 100 over 5 endfraction startfraction 0.8 over 8 x endfraction divided by startfraction 5 over 100 endfraction = 1
0.80 = (x + 8)(0.05) is the equation used to find x.
Given,
Darryl has a solution of bleach with the concentration of 10%.
10% bleach solution means in 100 ml solution amount of bleach is 10 gm
Here,
Darryl wants to change the concentration of this solution to 5%, means he wants to add water so that amount of liquid will change but amount of bleach in grams will remain the same.
Amount of bleach in 8 gallons of 10% solution of bleach will be = (Volume)×(concentration) = 8(.10) gm
Let Darryl adds x gallons of water in 10% solution of bleach to make it 5% solution of bleach.
Amount of bleach in 5% solution of bleach = (x + 8)(0.05) gm
Now in both the concentrations of bleach solution amount of bleach will remain same.
So, 0.8 = (x + 8)(0.05) will be the equation from which he can find the value of x.
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The value of a stock changes from $22 on Monday to $30 on Tuesday. Calculate the percent increase.
Answer:
36.4%
Step-by-step explanation:
You want the percentage change from $22 to $30.
Percentage changeThe percentage change is given by the formula ...
percent change = ((new value)/(old value) -1) × 100%
= (30/22 -1)(100%) ≈ 36.4%
The stock increased in value by about 36.4%.
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Please help!!!!!!!!!!!!!
Answer:
Scenario 1 represents a greater speed
Step-by-step explanation:
scenario 1 - find equation of line on graph to compare
- use the points given to find the slope
rate = slope = (y2-y1)/(x2-x1) = (240-60)/(4-1) = 60
y intercept = 0
line equation -> y = 60x
for every mile, 60 miles are traveled
scenario 2 - interpret the equation
for every mile, 50 miles are traveled
Scenario 1 represents a greater speed
Are there more phones that have between 200 and 249 songs stored on them than have between 150 and 199 songs?
If there are 1,000 phones in total and 100 of them have between 200 and 249 songs while 600 of them have between 150 and 199 songs, then there are more phones with between 150 and 199 songs.
We cannot determine whether there are more phones that have between 200 and 249 songs stored on them than have between 150 and 199 songs without additional information.
For example, if there are 1,000 phones in total and 500 of them have between 200 and 249 songs while 200 of them have between 150 and 199 songs, then there are more phones with between 200 and 249 songs. However, if there are 1,000 phones in total and 100 of them have between 200 and 249 songs while 600 of them have between 150 and 199 songs, then there are more phones with between 150 and 199 songs.
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What are the Slope and Equation of the graph?
Answer:
Slope= -3
Equation: y=-3x-44
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1) Evaluate the following expression. Show your work and EXPLAIN each step needed to determine the value.
Answer:
1/2 x -5/2 = -5/4
-1 1/4 + -1/4
-1 2/4
- 1 1/2
polydactyly is a fairly common congenital abnormality in which a baby is born with one or more extra fingers or toes. it is reported in about one child in every 500 . a young obstetrician celebrates her first 100 deliveries. assuming that these 100 births are unrelated and independent, what is the probability that the obstetrician has delivered no child with polydactyly? (enter your answer rounded to four decimal places, for example, 0.1111.)
The probability that the obstetrician has delivered no child with polydactyly is 0.8187.
To find the probability that the obstetrician has delivered no child with polydactyly, we can use the formula:
P(no polydactyly) = \((1 - P(polydactyly))^{number of births}\)
First, we need to find the probability of a child having polydactyly. This is given as 1 in every 500, which can be expressed as a decimal: 1/500 = 0.002.
Next, we find the probability of a child not having polydactyly: 1 - 0.002 = 0.998.
Now, we can find the probability of the obstetrician delivering no child with polydactyly in 100 unrelated and independent births by raising the probability of no polydactyly to the power of the number of births (100):
P(no polydactyly in 100 births) = (0.998)¹⁰⁰ ≈ 0.8187
So, the probability that the obstetrician has delivered no child with polydactyly is approximately 0.8187.
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