Answer:
o MDC de 6 e 9 é 3.
O produto de dois números é 54 e o seu MMC é 18. Precisamos encontrar o MDC desses dois números.
Primeiro, encontramos os dois números cujo produto é 54: 6 e 9.
Então, fatoramos cada número em seus fatores primos: 6 = 2 x 3 e 9 = 3 x 3.
O MDC de 6 e 9 é o produto dos fatores primos comuns, elevados à menor potência. Neste caso, o único fator primo comum é 3, elevado à primeira potência.
Portanto, o MDC de 6 e 9 é 3.
The triangle above has the following measures.
q=8 in
m/Q = 37°
Find the length of sider.
Round to the nearest tenth and include correct units.
The triangle above has the following measures. The length of sider is 13.3 inches.
q = 8 inches
m ∠Q = 37°
sin (Q) = q/r
r = q / sin(Q)
= 8 / sin (37°)
= 13.3 inches
In Math, a triangle is a three-sided polygon that comprises of three edges and three vertices. The main property of a triangle is that the amount of the inward points of a triangle is equivalent to 180 degrees. This property is called point total property of triangle.
There are three points in a triangle. These points are framed by different sides of the triangle, which meets at a typical point, known as the vertex. The amount of every one of the three inside points is equivalent to 180 degrees.
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Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 9 1 + 36 Hint By symmetry, you can restrict your attention to the first octant (where 2,4, 20), and assume your volume has the form V = 8zy. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume
The Maximum volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid [tex]9x^2 + y^2 + 36z^2 = 1[/tex]is 4/5.
To find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid [tex]9x^2 + y^2 + 36z^2 = 1:[/tex]
We can use the hint provided.
By symmetry, we can assume that the rectangular box is in the first octant where x, y, and z are all positive.
Let the dimensions of the rectangular box be 2x, 2y, and 2z.
Then the volume of the rectangular box is V = 8xyz.
To maximize V, we need to find the maximum value of xyz that satisfies the equation of the ellipsoid.
Substituting 2x, 2y, and 2z into the equation of the ellipsoid, we get:
[tex](2x/3)^2 + (y/6)^2 + (2z/3)^2 = 1[/tex]
Multiplying both sides by 9/4, we get:
[tex](2x/3)^2 * (9/4) + (y/6)^2 * (9/4) + (2z/3)^2 * (9/4) = 9/4[/tex]
Simplifying, we get:
4x^2/9 + y^2/36 + 4z^2/9 = 1
We can see that this is the equation of an ellipsoid centered at the origin with semi-axes a = 3/2, b = 3, and c = 3/2.
By symmetry, we know that the maximum value of xyz will be achieved when x = y = z. Therefore, we need to find the value of x, y, and z that satisfy the equation of the ellipsoid and maximize xyz.
Substituting x = y = z into the equation of the ellipsoid, we get:
[tex]4x^2/9 + x^2/36 + 4x^2/9 = 1[/tex]
Simplifying, we get:
[tex]x^2 = 9/20[/tex]
Therefore, x = y = z = √(9/20).
Substituting these values into V = 8xyz, we get:
[tex]V = 8(√(9/20))^3 = 4/5[/tex]
Therefore,the Maximum volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid [tex]9x^2 + y^2 + 36z^2 = 1 is 4/5.[/tex]
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suppose you own a restaurant and have a cook whose ability and attitude you are suspicious of. one of the dishes on the menu is duck cassoulet, which uses duck legs that have been slow fried over a couple of hours in oil that does not exceed a temperature of 175 degrees. this is a time consuming and monotonous process, but one that results in excellent meat that you sell for a large mark-up. you suspect your cook is lazy and doesn't properly monitor and maintain the oil temperature. you take a random sample of 12 duck legs and take them to a forensics lab where you are able to discover the maximum temperature the meat has reached. within your sample the mean maximum temperature of the duck legs is 182 degrees with a standard deviation of 5 degrees. meat cooked precisely to 175 degrees is what your cook is supposed to do. test the claim that your employee is capable (meaning he doesn't over-fry the meat) at the 90% confidence level. what is your conclusion? group of answer choices reject the null hypothesis, accept the alternative hypothesis fail to reject the null hypothesis reject the null hypothesis, reject the alternative hypothesis fail to reject the null hypothesis, fail to reject the null hypothesis fail to reject the null hypothesis, reject the alternative hypothesis
The claim of cooking duck legs at given temperature with mean , standard deviation represents reject the null hypothesis, accept the alternative hypothesis.
Confidence level = 90%
Sample mean maximum temperature x = 182 degrees
Hypothesized population mean μ =175 degrees
Sample standard deviation s = 5 degrees)
Sample size n =12
To test the claim that employee is capable of cooking the duck legs within the required temperature range.
Set up the following hypotheses,
Null hypothesis,
The mean maximum temperature of the duck legs is equal to or greater than 175 degrees (μ ≥ 175).
Alternative hypothesis,
The mean maximum temperature of the duck legs is less than 175 degrees (μ < 175).
Testing whether the mean is less than a specific value (175 degrees), this is a one-tailed test.
To reject or fail to reject the null hypothesis,
Use a one-sample t-test with a significance level of 0.1 .
T-test statistic is ,
t = (x - μ) / (s / √n)
Plugging in the values, we get,
t = (182 - 175) / (5 / √(12))
= 4.85
The degrees of freedom for this test is n-1 = 11.
Using a t-distribution table ( attached table) ,
Critical value for a one-tailed test with 11 degrees of freedom and a significance level of 0.1.
The critical value is 1.363.
Since the calculated t-value 4.85 is greater than the critical value (1.363).
Reject the null hypothesis at the 90% confidence level.
⇒Sufficient evidence to conclude that the mean maximum temperature of the duck legs cooked by your cook is less than 175 degrees.
Employee is not capable of cooking the duck legs within the required temperature range.
Therefore, for the given situation of confidence level of 90% reject the null hypothesis, accept the alternative hypothesis.
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In her math class, carla used unit cubes to build a right rectangular prism with a volume of 24 cubic units. The height of the prism was two units. Which figure could be bottom layer of the prism
Carla's right rectangular prism could have either a 3x4 or a 2x6 rectangle as the bottom layer, with a height of 2 units, to achieve the given volume of 24 cubic units.
Carla built a right rectangular prism using unit cubes, with a volume of 24 cubic units and a height of 2 units. To determine the possible figure for the bottom layer of the prism, we need to understand the relationship between the volume, height, and the base area.
The volume of a rectangular prism can be calculated using the formula: Volume = Base Area × Height. In Carla's case, the volume is 24 cubic units, and the height is 2 units. By rearranging the formula, we can find the base area: Base Area = Volume ÷ Height. Substituting the given values, Base Area = 24 ÷ 2, which equals 12 square units.
Now, we need to find a possible figure for the bottom layer with an area of 12 square units. Since the bottom layer is made of unit cubes, it must have whole-number dimensions. There are two possible rectangular figures that meet this requirement: 1) a 3x4 rectangle, and 2) a 2x6 rectangle. Both of these figures have an area of 12 square units (3x4 = 12 and 2x6 = 12) and can be formed using unit cubes.
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what is the measure of the unknown segment? pls help i keep getting bots :(
To determine the measure of the unknown segment, it's essential to first gather information about the given problem, such as the context, any provided measurements, and any relationships between the segments or angles involved. Once you have this information, you can utilize relevant geometric principles and theorems to establish connections and solve for the unknown value.
For example, if the unknown segment is a side in a triangle, you may apply the Pythagorean theorem, triangle inequality theorem, or trigonometric functions such as sine, cosine, or tangent to calculate its length. If the unknown segment is part of a circle, you might use the properties of arcs, chords, or the circumference to determine its measure. In cases where the unknown segment is part of a polygon, you can consider properties like diagonals, perimeter, or area to derive its length.
After identifying the appropriate method and relationships, you can set up equations and solve for the unknown variable. To verify the solution, you can plug it back into the original problem to ensure it satisfies all given conditions. In conclusion, finding the measure of an unknown segment involves understanding the problem's context, applying relevant geometric concepts, and using mathematical techniques to solve for the desired value.
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Unit: Real Numbers
Progress:
Question ID: 501911
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Consider the calculation x – y +( – z) where x and z are positive real numbers and y is a negative real number.
i) What are the directions of motion for this calculation?
ii) Is the final answer positive, negative, or undetermined?
i) Right, right, left
ii) Undetermined
i) Right, right, left
ii) Positive
i) Right, left, left
ii) Undetermined
i) Right, left, left
ii) Negative
The directions of motion for this calculation are:
i) Right, right, left
ii) Undetermined
The first operation is subtraction of y from x, which moves to the right on the number line. The second operation is addition of the opposite of z, which is subtraction of z from the result of the first operation. This also moves to the right on the number line. The final operation is addition of the opposite of z, which is subtraction of z from the result of the second operation. This moves to the left on the number line. Therefore, the directions of motion are right, right, left.
Since we don't know the values of x, y, and z, we cannot determine the sign of the final answer. Therefore, the answer is undetermined.
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The Jones' family experienced a loss of $1,760 in purchasing power last year. If the inflation rate was
3%, find the percentage raise received on the family's $88,000 yearly income. Please explain
Thus, the percentage raise received on the family's $88,000 yearly income is 9.4%.
Explain about the percentage raise:The difference in between final value and the starting value, stated as a percentage, is known as a percentage increase.
The base amount still determines whether a percentage rise or drop by a given percentage occurs. The absolute value change also changes if the basic amount does.
Hence, although the percentage rise or reduction is the same in this instance, the absolute increase is different.
Given data:
Yearly income = $88,000 Inflation rate - 3%From the table, compound interest for the yearly inflation rate of 3% is 1.09417024.
Thus,
amount after compounding:
A = $88,000 * 1.09417024.
A = 96286.98112
A = $96286.98
percentage raise = (96286.98 - 88,000 )/ 88,000
percentage raise = 0.094 * 100
percentage raise = 9.4%
Thus, the percentage raise received on the family's $88,000 yearly income is 9.4%.
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Jim walks 3 miles per hour slower than his friend Steve runs. Steve runs 4 miles per hour slower than his friend Matt rides his bike. Jim walks 25 miles in the same time Matt rides his bike miles. Steve runs 16 miles in the same time Matt rides his bike 24 miles.
Part A: Write an equation to calculate Jim's speed
Let's start by assigning variables to the unknowns in the problem:
- Let j be Jim's speed in miles per hour (in other words, the rate at which he walks).
- Let s be Steve's speed in miles per hour (in other words, the rate at which he runs).
- Let m be Matt's speed on his bike in miles per hour.
From the first sentence of the problem, we know that:
s = m + 4 (Steve runs 4 miles per hour slower than Matt rides his bike)
And from the second sentence, we know that:
j = s - 3 (Jim walks 3 miles per hour slower than Steve runs)
We want to find out how long it takes Jim to walk 25 miles and how long it takes Matt to ride his bike x miles. We can use the formula:
time = distance / rate
For Jim, we have:
time = 25 / j
For Matt, we have:
time = x / m
We also know that Steve runs 16 miles in the same time that Matt rides his bike 24 miles, so we can write:
16 / s = 24 / m
Substituting s = m + 4 and solving for m, we get:
16 / (m + 4) = 24 / m
16m = 24(m + 4)
16m = 24m + 96
8m = 96
m = 12
So Matt rides his bike at a speed of 12 miles per hour.
Now we can use the equations we set up earlier to solve for j and x:
j = s - 3
s = m + 4
j = (m + 4) - 3
j = m + 1
j = 13
x / m = 25 / j
x / 12 = 25 / 13
x = (25 * 12) / 13
x = 300 / 13
x ≈ 23.08
So it takes Jim 25 / 13 ≈ 1.92 hours to walk 25 miles, and it takes Matt 23.08 hours to ride his bike x = 300 / 13 ≈ 23.08 miles.
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Decide whether the triangles are similar. If so, determine the appropriate expression to solve for x.
Triangles ABC and EDF; triangle ABC has angle A measuring 53 degrees, angle C measuring 62 degrees, side AC labeled as y, side AB labeled as w, and side BC labeled as x; triangle EDF has angle D measuring 61 degrees, angle F measuring 53 degrees, side DE labeled z, side EF labeled u, and side DF labeled r.
The triangles are not similar; no expression for x can be found.
ΔABC ~ ΔDEF; x equals r times w over u
ΔABC ~ ΔEFD; x equals r times w over u
ΔABC ~ ΔEFD; x equals r times w over z
The triangles ABC and EDF are similar, and x = r × w/u.
As per the question, we have angle A in triangle ABC congruent to angle F in triangle EDF, angle C in triangle ABC congruent to angle D in triangle EDF, and angle B in triangle ABC congruent to angle E in triangle EDF.
Therefore, the triangles are similar by the Angle-Angle (AA) similarity theorem.
To find the expression for x, we can use the fact that the corresponding sides of similar triangles are proportional.
In this case, we have:
x/w = u/r (corresponding sides of similar triangles)
Solving for x, we get:
x = r × w/u
Therefore, x = r × w/u, and it can use this expression to solve for x in triangle ABC and EDF.
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7. The table shows the linear relationship between the total amount Mrs. Jacobs will be
charged for a skating party and the number of children attending.
Which equation best represents y, the total amount in dollars Mrs. Jacobs will be
charged for
x number of children attending the skating party?
Based on the information given in the table, we can see that there is a linear relationship between the total amount Mrs. Jacobs will be charged for a skating party and the number of children attending. This means that we can use a linear equation to represent this relationship.
To find the equation, we need to determine the slope (m) and y-intercept (b) of the line. We can do this by using two points from the table: (10, 100) and (20, 180).
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
m = (180 - 100) / (20 - 10) = 8
The y-intercept (b) can be found by plugging in one of the points and the slope into the equation:
y = mx + b
Using the point (10, 100) and the slope we just calculated, we get:
100 = 8(10) + b
Solving for b, we get:
b = 20
Therefore, the equation that best represents y, the total amount in dollars Mrs. Jacobs will be charged for x number of children attending the skating party, is:
y = 8x + 20
This equation shows that for every additional child that attends the skating party, Mrs. Jacobs will be charged an additional $8, and the initial cost of the party is $20.
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Solve the following equation for B. Be sure to Take into account whether a letter is capitalized
or not.
G/B=M/n
Answer:
Sure, here is the solution for the equation G/B=M/n:
```
B = Gn/M
```
Here is the step-by-step solution:
1. Multiply both sides of the equation by B.
```
G/B * B = M/n * B
```
2. Simplify both sides of the equation.
```
G = Gn/n
```
3. Divide both sides of the equation by n.
```
G/n = Gn/n * 1/n
```
4. Simplify both sides of the equation.
```
B = Gn/M
```
Therefore, the solution for B is Gn/M.
Step-by-step explanation:
A person places $81200 in an investment account earning an annual rate of 3. 6%,
compounded continuously. Using the formula V = Pent, where Vis the value of the
account in tyears, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 13 years.
If a person places $81200 in an investment account earning an annual rate of 3. 6%, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.
To solve this problem using the formula V = Pent, we need to plug in the given values.
P = $81200 (the principal initially invested)
r = 0.036 (the annual interest rate, expressed as a decimal)
t = 13 years
Using the formula V = Pent, we get:
V = $81200e^(0.036*13)
Using a calculator, we can evaluate e^(0.036*13) to be approximately 1.5498.
So V = $81200*1.5498 = $125689.60
Therefore, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.
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Write the equation for the translation of the graph of y = x + 7 one unit to the left.
Answer:
y=x+8
Step-by-step explanation:
since you are starting with the linear function y=x+7
a translation one unit to the left would be y=x+7(+1)
which gives us the answer y=x+8
What is the value of x?
round to the nearest tenth, if necessary.
x = 6
x = 11
x = 11.5
x = 13.6
right triangle a b c with right angle b. side b c is 8 units long. side a c is 14 units long. side a b is x units long.
Using the Pythagorean theorem, the value of x, rounded to the nearest tenth, is 11.5 units.
In the given right triangle ABC with right angle B, you are given the lengths of sides BC (8 units) and AC (14 units). You are asked to find the length of side AB (x units). To do this, you can use the Pythagorean theorem, which states that the square of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC).
So, the equation for this triangle is:
AC² = AB² + BC²
Plug in the given values:
14² = x² + 8²
196 = x² + 64
Subtract 64 from both sides:
132 = x²
Now, find the square root of 132:
x ≈ 11.5
So, the value of x, rounded to the nearest tenth, is 11.5 units.
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Sandeep's city took a telephone poll about a plan to build a new hotel downtown. 8,000 people took the poll. 92% of them were in favor of the new hotel. How many people were in favor of the new hotel?
Answer: 640
Step-by-step explanation:
????????????????????????
Answer:
[tex] \sqrt{20n} = \sqrt{4} \sqrt{5n} = 2 \sqrt{5n} [/tex]
C is the correct answer.
The height of each cone and the cylinder is 5 (cm) centimeters. The radius of the base of each cone and the cylinder is 4 (cm). What is the volume of the composite figure?
Therefore, the volume of the composite figure is approximately 419.05 cubic cm.
What is volume?Volume is the amount of space occupied by a three-dimensional object or shape. It is measured in cubic units such as cubic centimeters, cubic inches, or cubic meters. The volume of an object can be calculated by multiplying the area of its base by its height, or by using specific formulas depending on the shape of the object. The volume of an object is an important parameter in many areas of science and engineering, such as physics, chemistry, fluid mechanics, and material science, as it allows us to determine how much space an object will occupy or how much material is needed to fill a container or build a structure.
Here,
The composite figure consists of a cylinder and two cones, so we need to find the volume of each of these shapes and add them together.
Volume of cylinder = πr²h
= π(4²)(5)
= 80π cubic cm
Volume of one cone = (1/3)πr²h
= (1/3)π(4²)(5)
= (1/3)(80π)
= 26.67π cubic cm
Volume of both cones = 2(26.67π)
= 53.34π cubic cm
Total volume of composite figure = Volume of cylinder + Volume of both cones
= 80π + 53.34π
= 133.34π
= 419.05 cubic cm (rounded to two decimal places)
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What is the area of triangle hgf? round your answer to the nearest tenth of a square centimeter. recall that you need to
round up if the value of the hundredth is 5 or greater.
The area of triangle HGF is 9.8 cm²
The Sides of the given triangle are 6.5 cm, 3.6 cm and 5.6 cm
We know that the area of the triangle is the half of product of base and height of the triangle.
The base of the triangle = 6.5 cm
Height of the triangle = 3.0 cm
We know that the triangle is
Area = 1/2 × base × height
= 1/2 × HF × GE
= 1/2 × 6.5 × 3.0
= 1/2 × 19.5
= 9.75
Rounding to the nearest tenth
= 9.8 cm²
Hence, the area of triangle HGF is 9.8 cm²
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Given question is incomplete, the complete question is below
What is the area of triangle HGF? Round your answer to the nearest tenth of a square centimeter. Recall that you need to round up if the value of the hundredth is 5 or greater.
PLEASE HELP THIS IS MY LAST QUESTION PLEASEEEEEE
Given PQR with angle P = 42°, angle R = 26°, and PQ = 19, solve the triangle. Round all answers to the nearest tenth.
Angle Q =__
QR =__
PR =__
To solve the triangle, we have;
Angle Q = [tex]112^{o}[/tex]
QR = 30.0
PR = 40.2
What is a sine rule?A sine rule is a trigonometric function that can be applied to determined the unknown side, or angle of a none right triangle.
From the information given in the question, to solve the triangle;
P + R + Q = 180
42 + 26 + Q = 180
Q = 180 - 68
= 112
Q = [tex]112^{o}[/tex]
Applying the sine rule,
QR/Sin P = PR/Sin Q = PQ/Sin R
PR/Sin Q = PQ/Sin R
PR/Sin 112 = 19/ Sin 26
PRSin 26 = 19*Sin 112
= 17.6165
PR = 17.6165/ 0.4384
= 40.1836
PR = 40.2
Also,
QR/Sin P = PQ/Sin R
QR/Sin 42 = 19/ Sin 26
QRSin 26 = 19*Sin 42
= 12.7135
QR = 12.7135/ 0.4384
= 28.9998
QR = 30
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1.47 minutes is how many hours?
(1 hour = 60 minutes)
Answer :
1.47 Minutes = 0.0245 Hours.Step-by-step explanation:
60 minutes = 1 hour
1 minute = 1/60
1 minute = 0.016666666666667 hours
1.47 minutes = 0.016666666666667 × 1.47
1.47 minute = 0.0245 hours
Therefore, 1.47 Minutes is equal to 0.0245 Hours.
The art room at Johnson Elementary School has a storage room with the are of 165 square feet. The length of one wall is 15 feet. What is the width of the storage room? What is the perimeter of the room?
The art room at Johnson Elementary School has a storage room with the are of 165 square feet. The length of one wall is 15 feet. The width of the storage room 11 feet. The perimeter of the room is 52 feet.
Find the width of the storage room, we need to use the formula for area:
Area = Length x Width
We know that the area is 165 square feet and the length is 15 feet, so we can plug those values in and solve for the width:
165 = 15 x Width
Width = 11
So the width of the storage room is 11 feet.
Find the perimeter of the room, we need to add up the lengths of all four walls. We know that one wall is 15 feet, and since the opposite wall must also be 15 feet to maintain the same area, we can add up the remaining two walls:
Perimeter = 2 x (15 + Width)
Perimeter = 2 x (15 + 11)
Perimeter = 2 x 26
Perimeter = 52
So the perimeter of the storage room is 52 feet.
The width of the storage room 11 feet. The perimeter of the room is 52 feet.
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A baker uses 2 lbs of butter to make 7
dozen cookies. How many pounds of
butter would be used to make 132
cookies?
To make 132 cookies 3.14 pounds of butter would be used.
It is given that a bakery make 7 dozen cookies using 2 lbs of butter.
We know that 1 lb=1 pound
We know that 1 dozen = 12
7 dozen =7 × 12
= 84 cookies
We have to find how many pounds of butter would be used to make 132 cookies.
Let x be the number of pounds butter would be used to make 132 cookies
84/2 = 132/x
Apply cross multiplication
84x = 264
Divide both side by 84
x = 264/84
Hence, to make 132 cookies 3.14 pounds of butter would be used .
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Function g is defined as follows:
This function has an inverse.
What is g^-1 (-7)
This solution of g(x) has no real solutions, so g⁻¹ (-7) does not exist.
To find g⁻¹ (-7), we need to solve for x in the equation g(x) = -7.
First, we need to determine which part of the piecewise function to use. Since -7 is less than 5, we know that we need to use the first part of the function: g(x) = 5x² if x ≤ -3.
So, we set g(x) = 5x² equal to -7 and solve for x:
5x² = -7
x² = -7/5
This equation has no real solutions since the square of any real number is always nonnegative. Therefore, g⁻¹ (-7) does not exist in the real numbers.
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The distance traveled by a car based on time, t, in seconds is given by the function of d =3t+1.
identify the independent variable, the dependent variable, rate of change and the initial value
The independent variable is 't' and the dependent variable is 'd' while the rate of change is '3' and the initial value is '1'.
In the given function d=3t+1:
The independent variable here is 't' which represents time in seconds.
whereas the dependent variable is 'd' and it represent the distance traveled by a car in some unit. The rate of change is 3, and it represents the constant speed of the car in units of distance per unit of time.
While the initial value is 1, which represents the distance traveled by the car when time is 0.
Hence this function can be interpreted as if the car is travelling at a constant speed of 3 units of distance and has already travelled 1 unit of distance at the start of the journey.
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The circumference of a circular table is 816.4 centimeters. Determine the radius of the table.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. If the circumference of the circular table is 816.4 centimeters, then we can use this formula to find the radius of the table. Solving for r, we get r = C / (2π) = 816.4 / (2π) ≈ 129.9 centimeters (rounded to one decimal place).
there are 44 green balls, 65 blue balls, 14 yellow balls, and 2 red balls in a basket. a blind man goes to pick balls out of the basket. he does not know this, but all the blue balls and the red balls have a rough surface, and the green balls and yellow balls have a smooth surface. what is the lowest possible number of balls he needs to pick to ensure he has picked two balls of different colors?
The lowest possible number of balls blind man need to pick to ensure that he picked two different colors balls is equal to 48.
Number of green balls = 44
Number of blue balls = 65
Number of yellow balls = 14
Number of red balls = 2
To ensure the blind man picks two balls of different colors.
Maximum number of balls he can pick of a single color before he is guaranteed to have picked two of different colors.
All the blue and red balls have a rough surface.
All the green and yellow balls have a smooth surface.
Treat them as two distinct groups.
Let us consider the worst-case scenario,
where the blind man picks all the balls of one group before picking any ball of the other group.
Here, he could pick all 44 green balls or all 14 yellow balls before picking any blue or red ball.
Similarly, he could pick both red balls before picking any blue ball.
To ensure he has picked two balls of different colors, he needs to pick at least,
(44 green balls + 1 yellow ball) or 3 balls (2 red balls + 1 blue ball)
= 48 balls whichever is higher.
Therefore, the lowest possible number of balls he needs to pick to ensure he has picked two balls of different colors is 48.
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Estimate first, then compute Increase $120 by 160% and give the total. Estimate: Calculate:
The estimate increase for $120 by 160% is 192. The calculated increase for $120 by 160% is 192.
What is percent?Percent is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin phrase "per centum", which means "per hundred". Percentages are often used to describe a part of a whole. Percentages are used in many areas of life, such as finance, business, and statistics. They are used to calculate interest rates, taxes, discounts, and many other important figures.
Here,
Estimate: To estimate 160% of 120, we can first find 10% of 120, which is 12. Then, we can find 100% of 120 by multiplying 12 by 10, which is 120. Finally, we can add 60% of 120, which is 72 (since 60% is 6 times 10%), to get an estimate of 192.
Calculate: To calculate 160% of 120, we can first convert the percentage to a decimal by dividing it by 100, which gives us 1.6. Then, we can multiply 120 by 1.6 to get:
120 x 1.6 = 192
So the total increase is 192.
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At the beginning of spring, jin planted a small sunflower in his backyard. the sunflower's height in inches, h after w weeks, is given by the equation h=18+2.5w. what could the number 18 represent in the equation
After considering all the given data provided by the question we conclude that the number 18 present in the given equation is constant .
The equation for the sunflower's height is h = 18 + 2.5w.
Here, the number 18 shows the height of the sunflower during the time it was planted, so it is the constant term present in the equation and hence it does not relie on the duration of weeks that have passed.
The coefficient of w is 2.5, which represents the rate at which the sunflower grows in height per week.
Therefore, after one week, the sunflower would be 20.5 inches tall (18 + 2.5 x 1), after two weeks it would be 23 inches tall (18 + 2.5 x 2), after four weeks it would be 28 inches tall (18 + 2.5 x 4), and after six weeks it would be 33 inches tall (18 + 2.5 x 6).
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Please help im timed and im stuck
why were the testimonies of nazi officials at the nuremberg trials important?
their testimonies helped clear many nazis of their crimes.
the nazis denied that the events of the holocaust had occurred.
the confessions gave detailed accounts of the nazis’ crimes.
nazi officers got lighter sentences because they confessed.
The testimonies of Nazi officials at the Nuremberg Trials were incredibly important because they provided valuable insight into the atrocities committed by the Nazi regime.
Their testimonies helped to dispel any claims of denial that the events of the Holocaust had occurred. The confessions given by the Nazi officials gave detailed accounts of the crimes committed by the regime, and helped to hold those responsible accountable for their actions. It is important to note that while some Nazis did receive lighter sentences because of their confessions, the vast majority of those involved were held fully responsible for their crimes. Overall, the testimonies of Nazi officials played a crucial role in bringing justice to the victims of the Holocaust and shedding light on the horrific actions of the Nazi regime.
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ON OO
11 At the end of October, Fiona's electricity meter reads 88738 kWh.
At the end of November, her electricity meter reads 89 198 kWh.
Each kWh of electricity Fiona uses costs 16p
Work out how much Fiona had to pay for the electricity she used in November
Answer:
£73.60
Step-by-step explanation:
89198 kWh - 88738 kWh = 460 kWh.
Since each kWh of electricity costs 16p, Fiona’s total cost for electricity in November would be 460 kWh * 16p/kWh = 7360p.
Since there are 100 pence in a pound, this is equivalent to £73.60.
So, Fiona had to pay £73.60 for the electricity she used in November.
The requreid Fiona had to pay £73.60 for the electricity she used in November.
What is arithmetic?It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
To find out how much electricity Fiona used in November, we need to subtract the October reading from the November reading:
89,198 kWh - 88,738 kWh = 460 kWh
So, Fiona used 460 kWh of electricity in November.
To find out how much she had to pay, we need to multiply the number of kWh by the cost per kWh:
460 kWh × 16p/kWh = 7360p
We can convert pence to pounds by dividing by 100:
7360p ÷ 100 = £73.60
Therefore, Fiona had to pay £73.60 for the electricity she used in November.
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