The function f(x) = x + 5x + 1 has exactly one zero in the interval (-1, 0). To prove this, we can use the Intermediate Value Theorem.
This theorem states that if a function f(x) is continuous on an interval [a, b] and if its values at a and b have opposite signs, then there exists at least one root (zero) of the function in the interval (a, b). Therefore, since f(-1) = -6 and f(0) = 1, both of which have opposite signs, the Intermediate Value Theorem can be used to conclude that there exists at least one root of the function in the interval (-1, 0).
Furthermore, since the function is a quadratic function of the form f(x) = ax2 + bx + c, it is known that a quadratic equation can have at most two roots (zeros) (in a given interval). Therefore, since the Intermediate Value Theorem implies that the function f(x) has at least one zero in the interval (-1, 0), it follows that the function has exactly one zero in the interval (-1, 0).
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If the toss of a coin comes down heads, you win two dollars. If it comes down tails, you lose fifty cents. How much would you expect to gain after 16 tosses (in $ dollars)? $______.
The expected gain after 16 tosses of the coin is $400.
State the term equally likely events?Equally likely denotes the probability that each experiment's result will occur. For instance, if you throw a fair, six-sided die, any of the faces (1, 2, 3, 4, 5, or 6) has the same chance of coming up. A fair coin has an equal chance of landing on its head (H) or tail (T).Let x stand in for your entire savings.
There is a 0.5 likelihood of heads and a 0.5 possibility of tails. (equally likely events).
The value of accepting this offer is 1.5. The formula is as follows:
2 heads.
0.5 = P(Heads)
Value anticipated if the coin came out heads: 2x*0.5 = x
Plus
(1 - 0.5)x = 0.5x for tails.
0.5 = P(Tails)
Value anticipated if the coin came up tails: 0.5x*0.5 = 0.25x
Total projected value is equal to 1.25x.
For x = $20
Thus,
Amount = 1.25(20) = $25.
Thus, for the 16 tosses = $25 x 16 = $400.
Therefore, the expected gain after 16 tosses of the coin is $400.
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please someone help me with this problem
In a canoe race, the distance y (in miles) that Team A travels in x hours is represented by y = 5.5x. Team B travels 4 miles per hour and is 3 miles ahead of Team A. The teams continue traveling at their current rates for the remainder of the race. Will Team A catch up to Team B? Use a system to solve and explain your answer.
Answer:
Team A catches up to B in 2 hours, at the 11 mile mark
Step-by-step explanation:
(5.5 mi/hr)(x) = (4 mi/hr)(x) + 3 mi
(1.5 mi/hr)(x) = 3 mi
x = 3/1.5 = 2 hours
Find the equation of the line, given the following information:
Passes through (-9,3) and is perpendicular to
y=1/2x+6
Answer:
y=2/5x + 33/5
Step-by-step explanation:
To find the equation of the line that passes through the point (-9,3) and is perpendicular to y = 1/2x + 6, we can first find the slope of the given line y = 1/2x + 6. The slope of a line is equal to the rise (the change in the y-coordinate) divided by the run (the change in the x-coordinate), so we can find the slope of the line y = 1/2x + 6 as follows:
Slope = (change in y) / (change in x)
= (1/2 - 6) / (1 - 0)
= -5/2
Since the line we are looking for is perpendicular to the line y = 1/2x + 6, its slope must be the negative reciprocal of the slope of y = 1/2x + 6. The negative reciprocal of a number is equal to the negative of the reciprocal of the number, so the slope of the line we are looking for is equal to -1 / (-5/2) = 2/5.
Next, we can use the point-slope form of a line to find the equation of the line that passes through the point (-9,3) and has a slope of 2/5. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Substituting the values for the given point and the slope into this equation, we get:
y - 3 = 2/5(x - (-9))
y - 3 = 2/5(x + 9)
Next, we can distribute the 2/5 on the right-hand side of the equation to get:
y - 3 = 2/5x + 18/5
Finally, we can combine like terms on both sides of the equation to get the final equation of the line:
y=2/5x + 18/5 + 3
y=2/5x + 33/5
Find the distance between the points (0,9) and (6,1).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
______units
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~6 - 0~~)^2 + (~~1 - 9~~)^2} \implies d=\sqrt{(6 +0)^2 + (1 -9)^2} \\\\\\ d=\sqrt{( 6 )^2 + ( -8 )^2} \implies d=\sqrt{ 36 + 64 } \implies d=\sqrt{ 100 }\implies d=10[/tex]
Earth’s distance from the sun is 1.496 x 108 km. Saturn’s distance from the sun is 1.4246 x 109 km. How many times further from the sun is Saturn?
Saturn's distance is 9.5 farther from the Sun than the earth.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Earth's distance from the sun = 1.496 x [tex]10^8[/tex] km
Saturn's distance from the sun = 1.4246 x [tex]10^9[/tex] km
Divide Saturn's distance by Earth's distance.
= 1.4246 x [tex]10^9[/tex] / 1.496 x [tex]10^8[/tex]
= 9.5
We see that,
Saturn's distance from the sun x 0.95 = Earth's distance from the sun.
Thus,
Saturn's distance is 0.95 farther from the sun.
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The amount of a sample remaining after t days is given by the equation P(t)- A
(9) *
the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-
222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?
O 1.5 days
O 2.5 days
O 9.4 days
O 21.1 days
Mark this and return
Save and Exit
where A is the initial amount of
4
Next
Submit
The best estimate for the age of the sample is; 9.4 days
How to solve Exponential decay functions?We are told that;
The amount of a sample remaining after t days is given by the equation; P(t) = A(¹/₂)^(t/h)
Where;
A is the initial amount of the sample.
h is the half-life, in days, of the substance
The equation is:
P(t) = A(¹/₂)^(t/h)
If a sample contains 18% of the original amount of Radon - 222 and h = 3.8, then we have;
0.18 * A = A * (0.5)^(t/3.8)
divide both sides of the equation by A to get;
0.18 = ( 0.5 )^(t/3.8)
(t/3.8)log 0.5 = log 0.18
(t/3.8) = log 0.18/log 0.5
t/3.8 = 2.47
t = 3.8 * 2.47 ≈ 9.4 days
This is the best estimate for the age of the sample
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The complete question is;
The amount of a sample remaining after t days is given by the equation P(t)=A(1/2)^(t/h), where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?
Answer:
It's C
Step-by-step explanation:
Write the fraction below in its simplest form
5(x+6)5 (x-7) 5 (x+8)
15(x+6)⁹ (x−7)(x−8)
Watch video
Answer:
Step-by-step explanation:
Enter the value of x below.
x + 9 = 12
Answer:
x = 3
Step-by-step explanation:
Enter the value of x below.
x + 9 = 12
x = 12 - 9
x = 3
-----------------------------------------------
check
3 + 9 = 12
12 = 12
the answer is good
A baker sells boxes of cookies this table shows the total cast, in dollars, for different numbers of boxes of cookies based on the table what is the total cost in dollars of 7 boxes of cookies
The total cost in dollars of 7 boxes of cookies is; $24.50
How to interpret Function Tables?
From the attached table, we see the following coordinates that represents number of boxes (n) and total cost (c in dollars);
(3, 10.5)
(4, 14)
(5, 17.5)
(9, 31.50)
Now, let us find the slope with two coordinates using the formula;
slope = (y₂ - y₁)/(x₂ - x₁)
Let us use the first two coordinates to get;
Slope = (14 - 10.5)/(4 - 3)
Slope = $3.5
Thus, this is the cost of each box
Thus, for 7 boxes, the cost = 3.5 * 7 = $24.5
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Am cla ha collected 52 can in a food drive. They plan to ort the can into a x bag, with an equal number of can in each bag. Write an expreion to how how many can there will be in each bag
Answer:
Math Expert Answer
Step-by-step explanation:
52 cans in total separated into x number of bags. 52/x with x being the number of bags.
Answer:
c = 52/x
Step-by-step explanation:
We have 52 total cans and x bags of with an equal amount of cans in each.
Thus, we would have c = 52/x cans per bag. This is probably the answer you are looking for.
However, this can evaluate to a fractional number of cans, so you may be looking to round that answer down to an integer. In that case, the answer would be c = ⌊52/x⌋, which is solving for the greatest integer less than the value of 52/x
what is the probability that washing dishes tonight will take me between 15 and 16 minutes? give your answer accurate to two decimal places.
The probability of washing dishes by me tonight will take between 15 and 16 minutes is 14.29%.
The term "uniform distribution" refers to a type of probability distribution in which the likelihood of each potential result is equal.
Let's consider, the lower limit for this distribution as a and the upper limit for this distribution as b.
The following formula gives the likelihood that we will discover a value for X between c and d,
[tex]P(c\leq X\leq d)=\frac{d-c}{b-a}[/tex]
Given the time it takes me to wash the dishes is 11 minutes and 18 minutes. From this, a = 11 and b = 18.
Then,
[tex]P(15\leq X\leq 16)=\frac{16-15}{18-11}=0.1429=14.29\%[/tex]
The answer is 14.29%.
The complete question is -
The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 18 minutes. What is the probability that washing dishes tonight will take me between 15 and 16 minutes?
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The surface area in square units of a cylinder with a volume of 18 cubic units is a function of its radius r in units where s(r)=2pi r^2 + 36/r . What is the surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units?
The surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units is 18π +12.
What is the surface area of the cylinder?
The quantity of space enclosing a three-dimensional shape's exterior is its surface area. The area of the cylinder is determined by adding the areas of its two circular bases and curving surface.
Here, we have
Given
The surface area in square units of a cylinder with a volume of 18 cubic units is a function of its radius r in units
where s(r)=2πr² + 36/r ....(1)
Now, we put the value of r = 3 in equation (1) and we get
s(r)=2π(3)² + 36/3
s(r) = 18π + 12
Hence, the surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units is 18π +12.
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3 x square - 5 x + 2 is equals to zero
Answer:
x=2/3 or x=1
Step-by-step explanation:
Factor 3x² and 2
What is the third quartile of this set?
{-26, -15, -7, 0, 1. 6. 9, 15, 22, 22, 26, 28)
Answer:
22 is the third quartile for this set
What
property is illustrated in: If ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C.a.
Reflexive Propertyb. Symmetric Propertyc. Transitive Propertyd. Addition
Property
The property illustrated in the statement "If ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C" is the Transitive Property.
This property states that if two elements are related by a certain relationship, and another element is related to the second element by the same relationship, then the first and third elements are related by the same relationship.
In this statement, the relationship is that of congruency, meaning that each angle has the same measure. Therefore, the Transitive Property states that if angle A is congruent to angle B, and angle B is congruent to angle C, then angle A is congruent to angle C.
The other three properties listed do not apply to this statement. The Reflexive Property states that a given element is related to itself by a certain relationship, which does not apply to this statement.
The Symmetric Property states that if two elements are related by a certain relationship, then the two elements are related to each other in the same way, which is not applicable in this statement.
Lastly, the Addition Property states that the sum of two elements related by a certain relationship is related to the two elements by the same relationship, which is not applicable in this statement.
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Hannah, Ben, Stephanie, and Brayden bought a gift for their Mom. The total cost of the gift, including tax, was $64.80. Hannah paid $21, Ben paid 1/3 of the cost, Stephanie paid 15% of the cost, and Brayden paid the remaining cost. Who paid the greatest part of the cost?
Answer: Ben paid the most
Step-by-step explanation: Okay, to find the prices of the 4, we need to follow what the problem says. So, we know Hannah paid 21, so we know that is how much she paid. Now, we need to find 1/3 of the total cost ($64.80) So, we do 1/3 divided by $64.80 and get $21.60. For Stephanie, we need to find 15% of $64.80, so we can write it as a proportional relationship, so 15 x $64.80 / 100 is 9.27. (as a decimal) Now, we subtract all of those numbers from the total cost ($64.80) to find Brayden's pay. After I subtracted all of the amounts, I got $12.93. I'll list all the amounts.
Hannah - 21
Ben - 21.60
Stephanie - 9.27
Brayden- 12.93
So, as we see Ben paid the most. I hoped this LONG explanation helped you!
it should be ben.
Hannah paid $21;
ben paid 1/3 of 64.80 and that's $21.6 (64.84÷3);
Stephanie paid 15% of $64.80 and that's $9.72 (15÷100×64.80);
Brayden paid $12.48 [64.80-(21+21.6+9.72)].
hope I helped (btw sorry for any mistake english isnt my forst language)
Can someone help me with Questions 1 and 2 on this assignment? I am not really understanding them. I would deeply appreciate it!
Add 5 to 2 = 2 will make 7 = 7 a true statement and adding 5 to 2 ≠ 3 to make 7 ≠ 8 will make a true statement.
What is a number system?A way to express or represent numbers is through the number system.
We often employ decimal numbers because they are so widely used.
The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.
(1)
As per the given,
2 = 2
Add 5 on both sides of the above equation,
2 + 5 = 2 + 5
7 = 7 (True)
(2)
As per the given
2 ≠ 3
Add 5 on both sides of the above equation,
2 + 5 ≠ 3 + 5
7 ≠ 8 (True)
Hence "It is correct that if you add 5 to 2 = 2, you will get 7 = 7, and if you add 5 to 2 ≠ 3, you will get 7 ≠ 8".
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What is the height and area of the triangle below?
Answer:
height: 27 area: 176
Step-by-step explanation:
Which of the following propositions is tautology?
a. (p v q)→q b. p v (q→p) c. p v (p→q) d. Both (b) & (c)
From the truth table, the values for p v (p→q) are all true. Therefore, this proposition is considered a tautology.
A statement or formula that is true under every scenario is referred to as a tautology. For example, the bag is red or it is not. Whatever the color of the bag, these two statements are true.
Construct a truth table for the given propositions. From the table, we can tell that the proposition p v (p→q) is in tautology. Because whatever the value of p and q, the result is true for this proposition.
Therefore, the correct option is option c.
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How do you measure the size of an angle using a protractor or a compass? Explain the steps and show your work.
The size of the angles is measured in the form of degrees by using a protractor and compass.
The symbol for degrees is a little circle °.
The FULL CIRCLE is 360° (360 degrees). A half circle or a straight angle is 180°.A quarter circle or a right angle is 90°A protractor is a tool that measures the number of degrees in an angle.
To measure an angle with a protractor:
Place the midpoint of the protractor on the VERTEX of the angle.Line up one side of the angle with the zero line of the protractor.Read the protractor to see where the other side of the angle crosses the number scale.Most protractors have two number scales. It's important to use the same number scale for both sides of the angle.
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Translate
What are the x-intercepts of the quadratic function shown?
A
B
C
(3.-4) and (-5-4)
(1.0) and (-3,0)
(0, 1) and (0-3)
D (-1, -2)
Search
A
Answer:
(1,0) and (-3,0)
Step-by-step explanation:
1/2(3x-2/3)+6 less or equal to x+5
The inequality which represents the given phrase is 1/2(3x - 2/3) + 6 ≤ x+5 and the solution are x ≤ -4/3.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
1/2(3x - 2/3) + 6 ≤ x+5
3/2 x - 1/3 + 6 ≤ x+5
3/2 x + 17/3 - x ≤ 5
x/2 ≤ -2/3
x ≤ -4/3
Hence "The inequality 1/2(3x - 2/3) + 6 ≤ x+5 represents the provided sentence, and the answer is x ≤ -4/3.".
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Q. 10. Prove that the sum of the (interior) angles of a pentagon is 540°.
using geometry**
- Like line segments, ray XY, angles etc
please don't answer with (n-2)180 formula.
answer related to proving by lines and angles
like - <ABC + <BCA + <CAB = 180° etc...
Answer:
Step-by-step explanation:
The answer is that yes it is because a pentagon has three triangles inside it and a triangle is equal to 180 degrees so you times 180 times three and you get 540 degrees so yes that is correct!
Work out the urface area of thi olid quarter-cylinder. Give your anwer in term of π
The total surface area of a solid quarter-cylinder is 10(13π + 32) cm².
Given:-
The radius of a solid quarter-cylinder = 10 cm.
Height of solid quarter-cylinder = 16 cm.
To calculate the surface area we have a formula:-
Total surface area of solid quarter-cylinder = (TSA of cylinder / 4) + 2(Area of rectangle)= 2πr(h + r)/4 + 2(r * h) = πr(h + r)/2 + 2rh .
Solution:-
r = 10 cm.
h = 16 cm.
So,
→ Area of rectangle so formed = r * h = 10 * 16 = 160 cm².
then,
→ Area of two rectangles so formed = 2 * 160 = 320 cm².
Therefore,
→ Total surface area of solid quarter-cylinder = πr(h + r)/2 + Area of two rectangles.
→ Total surface area of solid quarter-cylinder = π * 10 * (10 + 16) / 2 + 320
→ Total surface area of solid quarter-cylinder = 5π * 26 + 320
→ Total surface area of solid quarter-cylinder = 5(26π + 64)
→ Total surface area of solid quarter-cylinder = 5*2(13π + 32)
→ Total surface area of solid quarter-cylinder = 10(13π + 32) cm².
Hence, the Total surface area of a solid quarter-cylinder is 10(13π + 32) cm².
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please help thank you!
Answer:
...…...................c = 50
PLEASE HELP!!! Make sure to show your work.
1)How many triangles can be constructed
with angles measuring 16˚, 38˚ and 126˚?
Circle one answer:
A) None
B) One
C) Infinite (More than one)
The angles α = 16°, β = 38° and γ = 126° can construct a triangle. (Correct choice: B)
How many triangles can be made by using three given triangles
In this problem we find the measures of three angles that must be proved to be part of a given triangle. The angles are part of a triangle if and only if the sum of the measures equals 180°. If we know that α = 16°, β = 38° and γ = 126°, then the sum of the measures is:
x = α + β + γ
x = 16° + 38° + 126°
x = 180°
As the sum of the measures of the three angles equals 180°, then the given angles can construct a triangle.
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1. When renting a vehicle from Schrader car rental, a customer pays a fee up front, and is
also charged for miles driven when they return. Henry drove 85 miles and his rental bill
was $77. Marcia drove 115 miles and her rental bill was $83.
The up front payment costs $34.5 while the payment per miles driven is $0.5
How to solve Simultaneous equation word problems?We are told that when renting a vehicle from Schrader car rental, a customer pays a fee up front, and is also charged for miles driven when they return.
Let the amount paid up front be x and let the amount paid per mile driven be y.
Thus, the equation for Henry will be;
x + 85y = 77 -------(1)
The equation for Marcia will be;
x + 115y = 83 ------(2)
Subtract eq 1 from eq 2 to get;
30y = 6
y = 6/30
y = $0.5
Thus;
x + 85(0.5) = 77
x = 77 - 42.5
x = $34.5
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Complete question is;
When renting a vehicle from Schrader car rental, a customer pays a fee up front, and is
also charged for miles driven when they return. Henry drove 85 miles and his rental bill
was $77. Marcia drove 115 miles and her rental bill was $83.
What is the up fronmt cost and the cost per miles driven
Piper invested $990 in an account paying an interest rate of 33% compounded
continuously. Sadie invested $990 in an account paying an interest rate of 3%
compounded monthly. After 14 years, how much more money would Piper have in
her account than Sadie, to the nearest dollar?
Answer:
55
Step-by-step explanation:
that’s if you meant the interest rate is 3 3/8 for compounded continuously and 3 1/8 for compounded monthly
Which of the following sets of ordered pairs represents a function?
Answer: D
Step-by-step explanation:
A function in a set of ordered pairs cannot have repeating x values
A have a repeated x values of -12
B have a repeated x values of 8
C have a repeated x values of 13
D does not have a repeated x value.
D is the correct answer.