Answers
The rule that makes the machine work is *-5 + 6 * -5
How to make the machine work for the pair of input and outputFrom the question, we have the following parameters that can be used in our computation:
4 -50
-8 10
-3 -15
A linear equation is represented as
y = mx + c
Using the points, we have
4m + c = -50
-8m + c = 10
Subtract the equations
So, we have
12m = -60
m = -5
Next, we have
-8 * -5 + c = 10
So, we have
c = 10 - 40
c = -30
This means that the operation is
-5x - 30
When expanded, we have
*-5 + 6 * -5
Hence, the rule that makes the machine work is *-5 + 6 * -5
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Related Questions
The veterinarian has prescribed carprofen 2.2 mg/kg BID x30d. Weight of patient is 34kg. Concentration is 75mg tablet. What is the amount of medication needed for 30 days?
Answers
The amount of medication needed for 30 days is approximately 59.84 tablets of carprofen.
To calculate the amount of carprofen medication needed for 30 days, we need to consider the prescribed dosage, the weight of the patient, and the concentration of the tablets.
The prescribed dosage is 2.2 mg/kg BID x 30d. This means that the patient should take 2.2 milligrams of carprofen per kilogram of body weight, twice a day, for 30 days.
The weight of the patient is 34 kilograms. So, we need to calculate the total amount of carprofen needed for the entire treatment period.
First, we calculate the daily dosage by multiplying the weight of the patient (34 kg) by the prescribed dosage (2.2 mg/kg).
Daily dosage = 34 kg * 2.2 mg/kg = 74.8 mg/day.
Since the medication is prescribed twice a day, we multiply the daily dosage by 2 to get the total dosage per day.
Total dosage per day = 74.8 mg/day * 2 = 149.6 mg/day.
Finally, to find the total amount of medication needed for 30 days, we multiply the total dosage per day by the number of days.
Total medication needed = 149.6 mg/day * 30 days = 4488 mg.
Since the concentration of the tablets is 75 mg, we divide the total medication needed by the tablet concentration to find the number of tablets required.
Number of tablets needed = 4488 mg / 75 mg = 59.84.
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Quiz: Equations of Lines - Part II
Question 9 of 10
The slope of the line below is 2. Which of the following is the point-slope form
of the line?
OA. y-1 -2(x+1)
B. y-1=2(x+1)
OC. y+1 -2(x-1)
D. y+1=2(x-1)
-10
10-
(1,-1)
10
Answers
Answer:
We have the slope of the line, which is 2 and a point that is (1, -1).
To find the point-slope form of the line, we use the equation:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Substituting in the values we have, we get:
y - (-1) = 2(x - 1)
Simplifying this equation, we get:
y + 1 = 2(x - 1)
Therefore, the answer is option C: y + 1 - 2(x - 1).
9497 ÷ 16 _R_ please
Answers
So, 9497 ÷ 16 = 593 remainder 9. Month
1/2 (6m - 12n)
helpp!!
Answers
(03.01 MC)
Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)
three to the fourth power all over nine equals three squared
By simplifying 9 to 32 to make both powers base three and adding the exponents
By simplifying 9 to 32 to make both powers base three and subtracting the exponents
By finding the quotient of the bases to be one third and simplifying the expression
By finding the quotient of the bases to be one third and cancelling common factors
Answers
The correct answer is By finding the quotient of the bases to be one third and canceling common factors. Option D.
The Quotient of Powers Property states that when dividing two powers with the same base, you can subtract the exponents. In the given expression, we have three to the fourth power divided by nine.
To simplify this expression using the Quotient of Powers Property, we first need to recognize that nine can be written as three squared, since 3 multiplied by itself gives 9.
So, we have (3^4) / (3^2). According to the Quotient of Powers Property, we subtract the exponents: 4 - 2.
This gives us 3^(4-2), which simplifies to 3^2. Therefore, the expression three to the fourth power all over nine equals three squared.
It states that we find the quotient of the bases to be one third and cancel common factors. In this case, the bases are 3 and 3, and their quotient is indeed one third. Additionally, there are no common factors that can be canceled, as the expression does not contain any variables or additional terms.
Therefore, By finding the quotient of the bases to be one third and canceling common factors. accurately describes the steps involved in simplifying the expression using the Quotient of Powers Property.
We find the quotient of the bases (one third) and cancel common factors (which is not applicable in this case). Option D is correct.
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Note the complete question is
Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)
Three to the fourth power all over nine equals three squared
A.) By simplifying 9 to 32 to make both powers base three and adding the exponents
B.) By simplifying 9 to 32 to make both powers base three and subtracting the exponents
C.) By finding the quotient of the bases to be one third and simplifying the expression
D.) By finding the quotient of the bases to be one third and cancelling common factors
Please answer ASAP I will brainlist
Answers
Answer:
There is one solution. The solution is 2, 18, 19.
Step-by-step explanation:
If you want me to show working tell me in the comments and I'll edit the answer
Answer:
A. (2, 18, -19)
Step-by-step explanation:
To solve:
Z is the most suitable variable to remove first
Add the first equation to the second equation: (this conveniently removes both y and z)
(x+y-z) + (4x-y+z) = 1+9
Simplify
5x = 10
Solve
x = 2
Multiply the second equation by 2 and minus it to the third equation: (Solve for y)
2(4x-y+z) - (x-3y+2z) = 2(9) - (-14)
Simplify
8x-2y+2z-x+3y-2z=18+14
7x+y=32
Substitute using x=2
7(2) + y = 32
y = 32 - 14
y = 18
Now substitute x and y for their respective values into Equation 1
2 + (-18) - z = 1
Simplify
-z = 19
z = -19
So :
x = 2, y = 18 , z = -19
The diagram shows the curve y = √8x + 1 and the tangent at the point P(3, 5) on the curve. The tangent meets the y-axis at A. Find:
(i) The equation of the tangent at P.
(ii) The coordinates of A.
(iii) The equation of the normal at P.
Answers
The tangent and normal lines of the curve:
Case (i): y = (4 / 5) · x + 13 / 5
Case (ii): (x, y) = (0, 13 / 5)
Case (iii): y = - (5 / 4) · x + 35 / 4
How to determine the equations of the tangent and normal lines
In this problem we have the representation of a curve whose equations for tangent and normal lines must be found. Lines are expressions of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.Both tangent and normal lines are perpendicular, the relationship between the slopes of the two perpendicular lines is:
m · m' = - 1
Where:
m - Slope of the tangent line.m' - Slope of the normal line.The slope of the tangent line is found by evaluating the first derivative of the curve at intersection point.
Case (i) - First, determine the slope of the tangent line:
y = √(8 · x + 1)
y' = 4 / √(8 · x + 1)
y' = 4 / √25
y' = 4 / 5
Second, determine the intercept of the tangent line:
b = y - m · x
b = 5 - (4 / 5) · 3
b = 5 - 12 / 5
b = 13 / 5
Third, write the equation of the tangent line:
y = (4 / 5) · x + 13 / 5
Case (ii) - Find the coordinates of the intercept of the tangent line:
(x, y) = (0, 13 / 5)
Case (iii) - First, find the slope of the normal line:
m' = - 1 / (4 / 5)
m' = - 5 / 4
Second, determine the intercept of the normal line:
b = y - m' · x
b = 5 - (- 5 / 4) · 3
b = 5 + 15 / 4
b = 35 / 4
Third, write the equation of the normal line:
y = - (5 / 4) · x + 35 / 4
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Algebra Question
Jasmine played outside today. She asked her mother if she could play outside tomorrow. Her mother said she could play outside only if the difference between today’s temperature and tomorrow’s temperature is less than 10 degrees. If today’s temperature was 93, what is the range of temperatures that would allow Jasmine to play outside tomorrow?
Address each of these parts:
a. Define the variable for the situation.
b. Write an absolute value inequality to represent the situation (tolerance).
c. Solve the inequality.
Referring back to the last question, using words, write the interpretation of the solution in terms of the range of temperatures that will allow Jasmine to play outside. Then, graph the solution.
Answers
Answer:
a. Let tomorrow's temperature be x
b.
[tex] |93 - x | < 10[/tex]
c.
[tex] - 10 < 93 - x < 10 \\ - 103 < - x < - 83 \\ 103 > x > 83[/tex]
answer the question submitted
Answers
The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.
To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:
Step 1: Divide the coefficient of x by 2 and square the result.
(Coefficient of x) / 2 = -28/2 = -14
(-14)² = 196
Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.
g(x) = 4x² - 28x + 49
= 4x² - 28x + 196 - 196 + 49
Step 3: Rearrange the terms and factor the perfect square trinomial.
g(x) = (4x² - 28x + 196) - 196 + 49
= 4(x² - 7x + 49) - 147
= 4(x² - 7x + 49) - 147
Step 4: Write the perfect square trinomial as the square of a binomial.
g(x) = 4(x - 7/2)² - 147
Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.
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The probable question may be:
Rewrite the function by completing the square.
g(x)=4x²-28x +49
g(x)= ____ (x+___ )²+____.
NO LINKS!! URGENT HELP PLEASE!!
Answers
Answer:
[tex]\text{a.} \quad m\angle NLM=93^{\circ}[/tex]
[tex]\text{c.} \quad m\angle FHG=31^{\circ}[/tex]
Step-by-step explanation:
The inscribed angle in the given circle is ∠NLM.
The intercepted arc in the given circle is arc NM = 186°.
According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc.
Therefore:
[tex]m\angle NLM=\dfrac{1}{2}\overset{\frown}{NM}[/tex]
[tex]m\angle NLM=\dfrac{1}{2} \cdot 186^{\circ}[/tex]
[tex]\boxed{m\angle NLM=93^{\circ}}[/tex]
[tex]\hrulefill[/tex]
According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore:
[tex]m\angle HFG=\dfrac{1}{2}\overset{\frown}{HG}[/tex]
[tex]m\angle HFG=\dfrac{1}{2}\cdot 118^{\circ}[/tex]
[tex]m\angle HFG=59^{\circ}[/tex]
As line segment FH passes through the center of the circle, FH is the diameter of the circle. Since the angle at the circumference in a semicircle is a right angle, then:
[tex]m\angle FGH = 90^{\circ}[/tex]
The interior angles of a triangle sum to 180°. Therefore:
[tex]m\angle FHG + m\angle HFG + m\angle FGH =180^{\circ}[/tex]
[tex]m\angle FHG + 59^{\circ} + 90^{\circ} =180^{\circ}[/tex]
[tex]m\angle FHG +149^{\circ} =180^{\circ}[/tex]
[tex]\boxed{m\angle FHG =31^{\circ}}[/tex]
Question #4
Find the measure of the indicated angle.
20°
161°
61°
73°
H
G
F
73° E
195°
Answers
The measure of the outside angle F indicated in the figure is 61 degrees,
What is the measure of angle GFE?The external angle theorem states that "the measure of an angle formed by two secant lines, two tangent lines, or a secant line and a tangent line from a point outside the circle is half the difference of the measures of the intercepted arcs.
Expressed as:
Outside angle = 1/2 × ( major arc - minor arc )
From the figure:
Major arc = 195 degrees
Minor arc = 73 degrees
Outside angle F = ?
Plug the value of the minor and major arc into the above formula and solve for the outside angle F:
Outside angle = 1/2 × ( major arc - minor arc )
Outside angle = 1/2 × ( 195 - 73 )
Outside angle = 1/2 × ( 122 )
Outside angle = 122/2
Outside angle = 61°
Therefore, the outside angle measures 61 degrees.
Option C) 61° is the correct answer.
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Suppose we have two equations and they are both equal to each other. Equation A is "y = x^2 - 9" and Equation B is "y = x + 3". If we had to solve this system of equations, what quadratic equation do we have to solve in order to get our x values?
a. x^2 - x - 12 = 0
b. x^2 + x + 3 = 0
c. x^2 - x - 6 = 0
Answers
Answer:
a) x² - x - 12 = 0
Step-by-step explanation:
We have equation A = equation B
⇒ x² - 9 = x + 3
⇒ x² - 9 - x - 3 = 0
⇒ x² - x - 12 = 0
How many gallons of a 90% antifreeze solution must be mixed with 100 gallons of 25% antifreeze to get a mixture that
is 80% antifreeze? Use the six-step method.
You need gallons.
(Round to the Question Viewer ber.)
answer
Answers
Answer:
550 gallons
Step-by-step explanation:
Let [tex]x[/tex] be the number of gallons for the 90% antifreeze solution and [tex]x+100[/tex] be the total number of gallons that will contain 80% antifreeze solution:
[tex]\displaystyle \frac{0.90x+0.25(100)}{x+100}=0.80\\\\0.90x+25=0.80x+80\\\\0.10x+25=80\\\\0.10x=55\\\\x=550[/tex]
Therefore, you would need 550 gallons of the 90% antifreeze solution.
a) Write a linear system to model the situation:
For the school play, the cost of one adult ticket is $6 and the cost of one student ticket is $4. Twice as many student tickets as adult tickets were sold. The total receipts were $2016.
b) Use substitution to solve the related problem:
How many of each type of ticket were sold?
Answers
Answer:
There were 126 student tickets sold and 252 adult ticket sold.
Step-by-step explanation:
Let x be the number of adult tickets sold
y be the number of students tickets sold
Twice as many student tickets as adult tickets were sold
a.
x = 2y ---equation 1
6x + 4y = 2016 ---equation 2
b.
Substitute equation 1 to equation 2
6(2y) + 4y = 2016
12y + 4y = 2016
16y = 2016
Divide both sides of the equation by 16
16y/16 = 2016/16
y = 126
Substitute y = 126 to equation 1
x = 2y
x = 2(126)
x = 252
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answers
The number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) is option C: A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3, and a bold line starts at negative 3 and is pointing to the left.
To determine the solution set for the inequality 3(8 – 4x) < 6(x – 5), we need to solve it step by step:
Simplify the inequality:
24 - 12x < 6x - 30
Combine like terms:
-12x - 6x < -30 - 24
-18x < -54
Divide both sides of the inequality by -18, remembering to flip the inequality sign:
x > (-54) / (-18)
x > 3
The inequality tells us that x must be greater than 3. To represent this on a number line, we place an open circle at the value 3 and draw a bold line pointing to the right to indicate that the solution set includes all values greater than 3.
Therefore, option C accurately represent the solution set for the inequality 3(8 – 4x) < 6(x – 5).
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Find the solution to the equation below.
2x2+3x-20=0
Answers
Answer:
[tex]x = 5.3 \: or \: 5 \frac{1}{3} [/tex]
Step-by-step explanation:
[tex]2 \times 2 + 3x - 20 = 0 \: \: \: \: \: \: 4 + 3x - 20 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:3x = 20 - 4 = 16 \: \: \: \: \: \: \: \: 3x = 16 \: \: divide \: both \: side \: by \: 3 = \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 5.3[/tex]
find AB using segment addition prostulate 2x-3 24 5x+6
Answers
Answer:
To find the length of AB using the segment addition postulate , we need to add the lengths of segments AC and CB.
AC + CB = AB
Substituting the given lengths:
2x-3 + 24 = 5x+6
Simplifying and solving for x:
21 = 3x
x = 7
Now that we know x, we can substitute it back into the expression for AB:
AB = 2x-3 + 24 = 2(7)-3 + 24 = 14-3+24 = 35
Therefore, the length of AB is 35.
Step-by-step explanation:
Question 4Multiple Choice Worth 5 points)
(Dilations MC)
Polygon ABCD with vertices at A(1,-1), B(3, -1), C(3, -2), and D(1, -2) is dilated to create polygon ABCD with vertices at A(4, -4), B(12,-4), C(12, -3), and D(4, -3). Determine the scale factor used to
create the image
0 1/4
0 1/2
0 2
0 4
Answers
The scale factor used to create the image of polygon ABCD is 4.
To determine the scale factor, we need to compare the corresponding side lengths of the original polygon ABCD and the image polygon ABCD. Let's denote the scale factor as k.
Original polygon ABCD:
Side AB: length = 3 - 1 = 2
Side BC: length = -2 - (-1) = -1
Side CD: length = 1 - 3 = -2
Side DA: length = -2 - (-1) = -1
Image polygon ABCD:
Side AB: length = 12 - 4 = 8
Side BC: length = -3 - (-4) = 1
Side CD: length = 4 - 12 = -8
Side DA: length = -3 - (-4) = 1
Comparing the corresponding side lengths, we can set up the following equations:
k * 2 = 8 (for side AB)
k * (-1) = 1 (for side BC)
k * (-2) = -8 (for side CD)
k * (-1) = 1 (for side DA)
From the equations, we can see that k = 4 satisfies all of them.
Therefore, the scale factor used to create the image of polygon ABCD is 4.
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Select all the correct answers.
Third
B.
90 feet
A. 16, 200 feet
√180 feet
C. √16, 200 feet
180 feet
D.
The area of a baseball field bounded by home plate, first base, second base, and third base is a square. If a player at first base throws the ball to a
player at third base, what is the distance the player has to throw?
First
90 feet
Home
Reset
Next
Answers
The diagonal distance from home plate to third base is approximately √16,200 feet.
The correct answers are:
B. 90 feet
C. √16,200 feet
D. 180 feet.
In baseball, the bases are arranged in a square shape.
The distance between each base is 90 feet.
Therefore, the correct answer for the distance a player at first base has to throw to a player at third base is 90 feet (option B).
To find the diagonal distance from home plate to third base, we can use the Pythagorean theorem.
Since the area of the baseball field is a square, the diagonal distance represents the hypotenuse of a right triangles.
The two legs of the right triangle are the sides of the square, which are 90 feet each.
Using the Pythagorean theorem [tex](a^2 + b^2 = c^2),[/tex] we can calculate the diagonal distance:
a = b = 90 feet
[tex]c^2 = 90^2 + 90^2[/tex]
[tex]c^2 = 8,100 + 8,100[/tex]
[tex]c^2 = 16,200[/tex]
c = √16,200 feet (option C)
Therefore, the diagonal distance from home plate to third base is approximately √16,200 feet.
The options A, √180 feet, and 180 feet are incorrect because they do not represent the correct distances in the given scenario.
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what is the value of m
Answers
The value of m<RQS as required to be determined in the task content is; 70°.
What is the value of m<RQS as required to be determined?It follows from the task content that the measure of angle RQS is to be determined as required.
Recall, the measure of the central angle subtended by an arc is twice that which it subtends at any point on the circumference.
Therefore, m<RPS = 2 • m<RQS.
m<RQS = 140°/2
m<RQS = 70°.
Ultimately, the measure of angle RQS are; 70°.
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For which values is this expression undefined?
Answers
The values x = -5 and x = 3 make the second expression undefined. The correct answers are:
x = -5
x = 3
x= -3
To determine the values for which the given expressions are undefined, we need to find the values that make the denominators equal to zero.
First expression: [tex]\frac{3x}{(x^2 - 9)}[/tex]
For this expression, the denominator is (x^2 - 9). It will be undefined when the denominator equals zero:
x^2 - 9 = 0
Factoring the equation, we have:
(x - 3)(x + 3) = 0
Setting each factor equal to zero, we get:
x - 3 = 0 --> x = 3
x + 3 = 0 --> x = -3
So, the values x = 3 and x = -3 make the first expression undefined.
Second expression: [tex]\frac{(x + 4)}{(x^2 + 2x - 15)}[/tex]
For this expression, the denominator is (x^2 + 2x - 15). It will be undefined when the denominator equals zero:
x^2 + 2x - 15 = 0
Factoring the equation, we have:
(x + 5)(x - 3) = 0
Setting each factor equal to zero, we get:
x + 5 = 0 --> x = -5
x - 3 = 0 --> x = 3
So, The second expression is ambiguous because x = -5 and x = 3.
Consequently, the right responses are x = -5, x = 3 and x= -3.
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Pls help I beg thank you
Answers
Answer:
8cm
Step-by-step explanation:
perimiter A = 11+11+4+4=30
perimiter B = 4+4+8+8=24
24+30=54
perimeter c =4+8+8+4+11+7+4=46
so perimiter of c is 8cm shorter than A and B total
hope this helps
Evaluate |x - y| + 4 if x = -1, y = 3, and z = -4.
Answers
Answer:
8
Step-by-step explanation:
Substitute the values in the expression, we have:
[tex]\displaystyle{|-1-3|+4}[/tex]
Evaluate:
[tex]\displaystyle{|-4|+4}[/tex]
Any real numbers in the absolute sign will always be evaluated as positive values. Thus:
[tex]\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}[/tex]
Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.
PLSS HELP HURRYYY
ILL GIVE BRAINLIST
Answers
Answer:
hope you understand it and please follow me
find surface area and volume
Answers
The surface area and volume of the composite solid is are 1720ft² and 3563.33 ft³ respectively.
What is volume and surface area of composite solid?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of the solid = lateral area of pyramid + surface area of cuboid
lateral area of pyramid = 4 × 1/2 bh
= 4 × 1/2 × 10× 12
= 120×2 = 240 ft²
Surface area of the cuboid = 2( 100+ 320+ 320)
= 2( 740)
= 1480 ft²
Surface area of the composite solid = 240 + 1480
= 1720 ft²
Volume of the composite solid = volume of cuboid + volume of pyramid
volume of cuboid = 10×10×32 = 3200ft²
volume of pyramid = 1/3base area × height
height of the pyramid is calculated as;
diagonal of base = √ 10²+10²
= √200
= 14.14
h² = 13²-7.07²
h² = 169 - 49.98
h² = 119.02
h = 10.9 ft
Volume of pyramid = 1/3 × 100 × 10.9
= 363.33 ft³
Volume of the composite solid = 3200+363.33
= 3563.33 ft³
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Roger can run one mile in 9 minutes. Jeff can run one mile in 6 minutes. If Jeff gives Roger a 1 minute head start, how
long will it take before Jeff catches up to Roger? How far will each have run?
They each will have run of a mile.
Answers
It will take approximately 5.33 minutes for Jeff to catch up to Roger. Both Jeff and Roger will have run a distance of 1 mile.
Let's calculate the time it takes for Jeff to catch up to Roger and the distance each will have run.
First, we need to determine how much distance Roger covers during the 1-minute head start. Since Roger runs one mile in 9 minutes, in 1 minute, he would cover 1/9 of a mile.
Now, let's set up an equation to represent the time it takes for Jeff to catch up to Roger:
Distance covered by Jeff = Distance covered by Roger + Distance covered during the head start
Let's denote the time it takes for Jeff to catch up as t minutes. During this time, Jeff runs a distance of 1 mile, while Roger runs a distance of 1/9 of a mile (from the head start).
Distance covered by Jeff = Distance covered by Roger + Distance covered during the head start
1 mile = (1/9) mile + (6 minutes) × t × (1 mile/6 minutes)
Now, let's solve this equation to find the time it takes for Jeff to catch up:
1 = (1/9) + (1/6)t
Multiplying the equation by the least common multiple (LCM) of 9 and 6, which is 18, to clear the fractions:
18 = 2 + 3t
Subtracting 2 from both sides:
16 = 3t
Dividing by 3:
t = 16/3 = 5.33 minutes (rounded to two decimal places)
Therefore, it will take approximately 5.33 minutes for Jeff to catch up to Roger. Both Jeff and Roger will have run a distance of 1 mile.
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A total of 90 groom's guests and 85 bride's guests attended a wedding. The bride's guests used 100 tissues. The groom's guests used 180 tissues. Calculate approximately how many tissues each groom's guest used.
Answers
Approximately 2 tissues were used by each groom's guest at the wedding.
The calculation is as follows:
180 tissues ÷ 90 guests = 2 tissues per guest.
To determine how many tissues each groom's guest used, we need to find the average number of tissues per guest. We start by adding up the number of tissues used by the groom's guests, which is 180.
Then, we divide this total by the number of groom's guests, which is 90. This division gives us an average of 2 tissues per guest.
By dividing the total number of tissues used by the total number of guests, we can find the average number of tissues per guest. In this case, each groom's guest used approximately 2 tissues.
It's important to note that this calculation assumes an equal distribution of tissues among all the groom's guests.
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Identify the algebraic rule that would translate a figure 3 units left and 2 units up.
Answers
The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). Option B.
To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.
When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.
Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.
Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.
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What is the slope of the line shown below?
-6
10
(-3,-7) 5
-10
AY
(9, 1)
10
15
X
O A.-²2/
3
OB.
NIM
O c. 3
2
O D.
3
MIN
Answers
Answer:
[tex]m = \frac{1 - ( - 7)}{9 - ( - 3)} = \frac{8}{12} = \frac{2}{3} [/tex]
B is the correct answer.
The time (in minutes) between volcanic eruptions was measured along with the duration (in minutes) of the eruption.
Use the data to answer the following question.
Time Between Eruptions 12.17 11.63 12.03 12.15 11.30 11.70 12.27 11.60 11.72
Duration of Eruption 2.01 1.93 1.97 1.99 1.87 1.99 2.11 1.96 2.03
Your answers should be numerical values. If necessary, round to four decimal places. Use rounded
answers for subsequent questions parts.
The value of the linear correlation coefficient is
The value of the coefficient of determination is
The regression line is y =
The predicted duration of an eruption is
The residual for x = 12.03 is
x+
minutes if the time between eruptions is 12.03 minutes.
Answers
The actual duration of eruption for x = 12.03 is 1.97 minutes, so the residual is 1.97 - 3.8431 = -1.8731 minutes.
The value of the linear correlation coefficient, also known as the Pearson correlation coefficient, measures the strength and direction of the linear relationship between two variables.
In this case, it represents the correlation between the time between eruptions and the duration of the eruption. To calculate the linear correlation coefficient, we can use the given data. The linear correlation coefficient is 0.8404.
The coefficient of determination, denoted as R-squared, represents the proportion of the variance in the dependent variable (duration of eruption) that can be explained by the independent variable (time between eruptions).
It is calculated by squaring the linear correlation coefficient. In this case, the coefficient of determination is 0.7055.
The regression line represents the best-fit line that approximates the relationship between the independent and dependent variables.
It can be expressed in the form of y = mx + b, where y represents the predicted duration of the eruption, x represents the time between eruptions, m represents the slope of the line, and b represents the y-intercept.
To determine the regression line, we can perform linear regression analysis using the given data. The regression line is y = 0.1608x + 1.8305.
The predicted duration of an eruption can be calculated by substituting the given time between eruptions value into the regression line equation. For x = 12.03 minutes, the predicted duration of an eruption is y = 0.1608 x 12.03 + 1.8305 = 3.8431 minutes.
The residual for x = 12.03 is the difference between the actual duration of eruption and the predicted duration. It can be calculated by subtracting the predicted value from the actual value. The actual duration of eruption for x = 12.03 is 1.97 minutes, so the residual is 1.97 - 3.8431 = -1.8731 minutes.
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