Answer:
0.80
Step-by-step explanation:
The hundredth is 2 digits after the decimal.
Rounding 0.799, we want 0.xx
Look at the third digit, 9, meaning we round up.
However, since the second digit after the decimal is also a 9, we can make that a 0 by adding 1 to the first digit after the decimal.
We get 0.80
If −2≤f(x)≤5 on [−1,3] then find upper and lower bounds for ∫−13f(x)dx
Answer:
Answer is attached as a photo. I will be honest I am not familiar with a calculus problem being set up that way. I am guessing that is what they are looking for...
Step-by-step explanation:
The upper bound of the given function is 20 while the lower bound of the given function is -8.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given function,
-2 ≤ f(x) ≤ 5
At the upper bond, f(x) = 5
[tex]\int\limits^{3}_{-1} {f(x)} \, dx[/tex] = [tex]\int\limits^{3}_{-1} {5} \, dx[/tex]
⇒ 5(3 + 1) = 20
At the lower bond f(x) = -2
[tex]\int\limits^{3}_{-1} {f(x)} \, dx=\int\limits^{3}_{-1} {-2} \, dx[/tex]
⇒ -2(3 + 1) = -8
Hence "The upper bound of the given function is 20 while the lower bound of the given function is -8".
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What are the 7 types of triangles?
The 7 names of triangles:
Scalene, Isosceles, Equilateral, Equiangular triangle, Acute triangle,
Right triangle, Obtuse triangle
What are triangles?
Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.
Equiangular triangle: All angles are equal.
Acute triangle . . . all three angles are less than 90°
Right triangle . . . one angle is 90°
Obtuse triangle . . . one angle is greater than 90°
Equilateral triangle . . . all three sides are the same length
Isosceles triangle . . . two sides are the same length
Scalene triangle . . . all three sides are different lengths
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André planted a cedar hedge 15 years ago (currently it's the start of the 16th year). The
hedge is now 3 metres high. The cedars grew an average of 12 cm per year. How tall were
the cedars when he planted them?
The height of the cedars when they were planted by André, found using the formulas for arithmetic progression is 1.32 meters
What is an arithmetic progression?An arithmetic progression is a number sequence that consists of numbers that have a constant or common difference between consecutive term of the sequence.
The year André planted the cedar hedge tree = 15 years ago
The present height of the hedge = 3 meters = 300 cm
The average rate at which the cedars grew = 12 cm per year
The height of the cedar hedge when André initially planted the them can be found by representing the situation using an arithmetic progression formula or as follows;
The nth term of an arithmetic progression, aₙ, can be found using the formula; aₙ = a₁ + (n - 1)·d
Where;
a₁ = The initial height of the tree
d = The amount the tree grows each year = 12 cm
n = The number of years ago, the tree was planted
When n = 15, we get;
a₁₅ = 3 meters = 300 cm
Therefore;
300 = a₁ + (15 - 1) × 12
a₁ = 300 - (15 - 1) × 12 = 132
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Question 3: Multiply: 0.33.10⁵
330
330000
33000
3300
Answer:
33,000
Step-by-step explanation:
0.33 x 10^5 is 33,000
The sum of two numbers is 66. Two times the lesser number is 15 more than the greater number. What are the numbers
If x is a lesser number, the equation is
Answer:
See below!
Step-by-step explanation:
Let the two numbers be x and y
Condition # 1:x + y = 66 ----------------(1)
Condition # 2:2x = y + 15
2x - y = 15 ---------------(2)
Add both equations
x + y + 2x - y = 66 + 15
x + 2x = 66 + 15
3x = 81
Divide both sides by 3
x = 27Put x = 27 in Eq. 1
27 + y = 66
Subtract 27 to both sides
y = 66 - 27
y = 39[tex]\rule[225]{225}{2}[/tex]
You read 6 chapters. Each chapter has 8 pages. Your brother reads the same number of pages. His chapters have 12 pages. How many chapters does your brother read?
The sixth chapter's Brother 0.66 pages were read.
How to calculated the chapters in 12 pages?According to the order of operations, you should perform multiplication and division first, going from left to right, before adding and subtracting.
Add and subtract from left to right while continuing to multiply and divide. the next step is to add and subtract from left to right.
Assumed the question is how many pages are in each chapter.
Let it be x:
6x + 8 = 12
6x = 4
x = 4 /6
x = 0.66.
The sixth chapter's Brother 0.66 pages were read.
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Chelsey puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
problem A: What is the probability that Chelsey will draw out three pieces of candy in this order: red, green, yellow?
Problem B: What is the probability that Chelsey will draw out three pieces of candy in this order: green, yellow, red?
problem C: What is the probability that Chelsey will draw out three pieces of candy in this order: yellow, red, green?
problem D: Make a conclusion about how the order in which she draws out the red, green, and yellow pieces affects the probability.
The probability for each event are
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
What is a expression? What is a mathematical equation? What is Probability?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes
We have Chelsey who puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
[A] -
{3/12} x {3/11} x {4/10} =
36/1320
[B] -
{3/12} x {4/11} x {3/10}
36/1320
{C} -
{4/12} x {3/11} x {3/10}
36/1320
D) The probability doesn’t change in any order.
Therefore, the probability for each event are -
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
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WHAT WILL YOU WEAR?
You are getting ready for Thanksgiving dinner and trying to find the perfect outfit. You want to wear your new sweater from Infinity21. The manufacturer advertises that this sweater is most comfortable to wear when the temperature satisfies |t-56| ≤6 degree: Fahrenheit. The weaather report says it will be 53°F on Thanksgiving Day at mealtime.
Can you wear your new sweater comfortably?
By solving a linear inequation, it can be concluded that
The sweater can be worn comfortably
What is a linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by > . < , ≤, ≥
A one degree inequation is known as linear inequation.
Here, the given linear inequation is
[tex]|t - 56| \leq 6\\t - 56 \geq -6 \ or \ t - 56 \leq 6\\t \geq 56 - 6 \ or \ t \leq 56+6\\t \geq 50 \ or \ t \leq 62\\50 \leq t \leq 62[/tex]
As 53° F lies between 50 and 62, the sweater can be worn comfortably
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EVALUATE ₈C₇ and ₁₁P₅
₈C₇=
₁₁P₅=
The permutation and combination expressions have their values to be ⁸C₇ = 8 and ¹¹P₅ = 55440
How to determine the permutation and combination expressions?From the question, we have
⁸C₇ and ¹¹P₅
The combination expression: ⁸C₇
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 8 and r = 7
Substitute the known values in the above equation
Total = ⁸C₇
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
⁸C₇ = 8!/7!1!
Evaluate
⁸C₇ = 8
(b) The permutation expression: ¹¹P₅
The number of ways of selection could be drawn is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 11 and r = 5
Substitute the known values in the above equation
Total = ¹¹P₅
Apply the permutation formula
ⁿPᵣ = n!/(n - r)
So, we have
¹¹P₅ = 11!/6!
Evaluate
¹¹P₅ = 55440
Hence, the values are 8 and 55440
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0 x ≤-21
0 x ≤21
0 x ≤-15
0 x ≤15
21. 2z>-28 (I point)
O z>-56
O z>-14
O z<-14
O z<14
Answer: [tex]z > -14[/tex]
Step-by-step explanation:
Divide both sides by 2.
A certain triangle has a 30° angle and a 60° angle. Which must be a true
statement about the triangle?
OA. The longest side is 3 times as long as the shortest side.
OB. The second-longest side is twice as long as the shortest side.
OCTwo sides of the triangle have the same length.
Sons
D. The longest side is twice as long as the shortest side.
Answer:
D. The longest side is twice as long as the shortest side.
Step-by-step explanation:
Given one angle is 30° and another is 60°, the third must be 90°, making a Special 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (longest side) is twice (two times) as long as the shortest side.
help me i dont get this at all
Answer: 18
D
Step-by-step explanation:
The constant of proportionality is y/x, not x/y, which is what your friend found.
X= 1
y=18
18/1=18
What does it mean when the discriminant is greater than 0?
We are interested in values that make the quadratic expression negative if the quadratic expression is less than, equal to, or greater than 0. We are interested in numbers that make our quadratic expression positive if the quadratic expression is more than, greater than, or equal to 0.
An discriminant value definition ?
The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.
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if somthing costid 64 dolers and thay sold it for 90% of the originol price how much wold it be
?
Answer:
6.40
Step-by-step explanation:
For this we will divide,
look below for a explanation
Purchase Price:
$64
Discount:
(64 x 90)/100 = $57.60
Final Price:
64 - 57.60 = $6.40
Write an expression to represent: 8 less than the product of 2 and x.
A recipe for flapjacks uses only syrup, butter and oats, in the ratio 1: 2: 3
a) Trevor makes some flapjacks using this recipe and uses 200g of syrup.
(i) What quantity of butter should he use? _________g
(ii) What quantity of oats should he use? _________g
b) Using this recipe, 150g of syrup are needed to make 8 flapjacks. Find the quantity of oats needed to make 16 of these flapjacks.
Answer: _____g
By using Unitary method, it can be calculated that
a) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g
Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g
b) 900 g of oats is required to make 16 flapjacks
What is Unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here Unitary method will be required
a) Let Trevor use x g Syrup, 2x g butter and 3x g oats
Trevor uses 200 g syrup
So x = 200
i) Quantity of butter Trevor uses = 200 [tex]\times[/tex] 2 = 400 g
ii) Quantity of oats Trevor uses = 200 [tex]\times[/tex] 3 = 600 g
b) To make 8 flapjacks 150 g of syrup is used
To make 1 flapjack [tex]\frac{150}{8}[/tex] g of syrup is used
To make 16 flapjacks [tex]\frac{150}{8} \times 16[/tex] g of syrup is used
To make 16 flapjacks 300g of syrup is used
To make 16 flapjacks 300 [tex]\times[/tex] 3 g of oats is used
To make 16 flapjacks 900 g of oats is used
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Graph -7x+5y=35−7x+5y=35minus, 7, x, plus, 5, y, equals, 35.
Answer:
835786543225644323567
cards and chips are being created for a board game by company the number of cards produced is proportional to the number of chips that are produced over a short period of time the company produced 32 cards and four chips what is the ratio of cars the chips produce State and simplest form as a unit rate in cards per chip (I NEED ANSWERS FAST)
Answer:
8 cards per chip
Step-by-step explanation:
So 32:4 is the ratio.
Divide by 4 to get 8 cards per chip.
Luke and Cade have started running. Luke runs 15 more than three times the number of miles Cade runs. Together they run a total of 63 miles. Write an equation to determine the number of miles Luke and Cade ran.
*
1 point
3x + 15 = 63
x + 15 + 3x = 63
x - 15 + 3x = 63
3x - 15 = 63
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
Linear Equation:A linear Equation is a Mathematical expression that is used to calculate an unknown number of values or any unknown quantity. Here we use variables to represent the unknown numbers.
Here given that
Luke and Cade have started running
Luke runs 15 more miles than thrice of that of number of miles Cade runs
Since we don't know the number of miles run by Cade
Let us assume that Cade runs x miles
=> Number of miles run by Cade = x miles
From the given data,
The number of miles run by Luke will be = 3x + 15
=> Number of miles run by Luke and Cade = x + 3x + 15
Given that the total mile run by Luke and Cade = 63 miles
=> x + 3x + 15 = 63
Therefore,
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
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The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 3.50 minutes. To make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 41 randomly selected calls. The mean wait time was calculated to be 3.94 minutes. Assuming the population standard deviation is 1.30 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes with a 95% level of confidence?
Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
The value of the test statistic is given as follows:
z = 2.17.
There is sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes.
How to obtain the value of the test statistic?The value of the test statistic is obtained using the z-distribution, as the population standard deviation is known in the context of this problem.
The equation that gives the test statistic is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which the parameters of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value claimed at the test of the hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]\overline{x} = 3.94, \mu = 3.50, \sigma = 1.30, n = 41[/tex]
(all values are taken from the text).
Then the numeric value of the test statistic is obtained as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.94 - 3.50}{\frac{1.30}{\sqrt{41}}}[/tex]
z = 2.17.
There is sufficient evidence to say that the mean wait time for customers is longer than 3.50 minutes, as the critical value for the right-tailed test with 95% confidence is of z = 1.645, and the test statistic is greater than this.
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if I can vaccinate 10 people in 2 hours. how many people will I get vaccinated in 5 hours?
y=the number of people being vaccinated
x= the number of hours
Answer:
25 people
Step-by-step explanation:
10 people will be vaccinated for 2hrs
10 = 2
y people will be vaccinated for 5hrs
y = 5
(To find y we need to cross multiply)
10 = 2
y = 5
2y= 50
y=50/2
y=25
:- 25 people will be vaccinated in 5hrs.
Lets check if our answer is correct let us make 5 hrs our unknown x
10 = 2
25 = x
(cross multiply)
25×2=10x
50=10x
x=5hrs
so our answer is correct.
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which number line represents the solution set for the inequality 4x 3 2 2x
The solution to the inequality expression is x ≥ - 5
what is inequality expressions ?
Both equations and inequalities are mathematical phrases created by connecting two expressions. The two expressions are regarded as being equivalent in an equation.
solution:
The given expression - 4(x + 3) ≤ –2 – 2x
- 4x - 12 ≤ -2 - 2x
-4x + 2x ≤ -2 + 12
-2x ≤ 10
-x ≤ 5
Multiply both sides by - 1
Then x ≥ - 5
Hence the solution to the inequality expression is x ≥ - 5
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Annika is comparing two companies based on the costs for renting a bike for the . Company A charges a $20 rental fee plus $4.50 the bike is rented. Company B charges a 9 rental fee plus $6.50 per hour the bike is rented.
Answer:
depends on how long u need it for
Step-by-step explanation:
Rewrite sin(x-7pi/4) in terms of sin(x) and cos(x)
The expression written in terms of sinx and cosx is
sinx· cos7π/4 - cosx ·sin7π/4
What is an algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given expression is sin(x - 7π/4).
Use the formula for sin(A-B) to rewrite the expression:
sin(x - 7π/4)
= sinx· cos7π/4 - cosx ·sin7π/4
Hence, the expression written in terms of sinx and cosx is sinx· cos7π/4 - cosx ·sin7π/4
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Lydia and Claudia have the same number of charms in their collections. Lydia started with 6 charms and bought 3 more packs. Claudia started with 9 charms and bought 2 more packs. If each pack had x charms, which equation be used to find x?
A. x=(2+3)-(6+9)
B. x=6+3+9+2
C. 6x+3=9x+2
D. 3x-2x=6+9
E. 3x+6=2x+9
The equation that can be used to find x is
3x + 6 = 2x + 9
Option E is the correct answer.
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,
Lydia started with 6 charms and bought 3 more packs.
Claudia started with 9 charms and bought 2 more packs.
If each pack had x charms.
This can be written as,
Lydia:
Number of charms = 6 + 3x
Claudia:
Number of charms = 9 + 2x
Now,
Lydia and Claudia have the same number of charms in their collections.
This can be written as,
6 + 3x = 9 + 2x
3x + 6 = 2x + 9
Thus,
The equation that can be used to find x is
3x + 6 = 2x + 9
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I need help on this Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
{3, 4, 6, 7, 8}
Step-by-step explanation:
For sets U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 5, 6}, and C = {1, 2, 3, 4, 5}, you want the set {A∩C}'.
A∩CThe set A∩C contains the elements that are common to both sets. Those are {1, 2, 5}.
{A∩C}'The set of interest contains the elements of U that are not in A∩C. Those are ...
{3, 4, 6, 7, 8}
__
Additional comment
DeMorgan's theorem tells us the desired set is equivalent to A'∪C', or {3, 4, 7, 8}∪{6, 7, 8}. That, too, is ...
(3, 4, 6, 7, 8}
What is the graph of the system of inequality?
Graph of the system of inequality is a solid line and a portion of area is shaded which satisfy the condition of the inequality.
What is inequality?
When left hand side is not exactly equal to the right hand side of an equation then it is known as inequality. For system of inequality, there are four types of inequalities <, >, [tex]\le[/tex], and [tex]\ge[/tex].
Using following steps anyone can graph the inequality:
1. Get y alone on one side of a linear inequality in two variables (like x and y) before graphing it. Then, take into account the associated equation that was created by switching the inequality sign for an equality sign. This equation has a line as its graph.
2. The graph is a dashed line if the inequality is strict ( < or >). The graph is a solid line if the inequality is not strict ([tex]\le[/tex] or [tex]\ge[/tex] ).
3. The last step is to choose a point that is not on either line (typically (0, 0) is the simplest) and determine whether or not these coordinates fulfil the inequality. If so, shade the portion of the half-plane that contains that point. If not, shade the opposite half-plane.
Hence, the graph of the system of inequality is a solid line and a portion of area is shaded which satisfy the condition of the inequality.
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After a 20% discount, you purchase a television for $240. What was the television's
price before the reduction? (Define a variable, create an equation, solve using algebra,
and answer in a sentence.)
===========================================
Work Shown:
x = price of the TV before the discount
20% of x = 0.20x = discount, aka amount saved
x - 0.20x = 0.80x = price after discount
0.80x = 240
x = 240/0.80
x = 300
The TV was $300 before the discount.
-------------
Check:
20% of 300 = 0.20*300 = 60 dollars is the amount saved
300-60 = 240 is the price after the discount, which matches the given info. The answer is confirmed.
NO LINKS!! Use tests for symmetry to determine which graphs from the list below are symmetric with respect to the y-axis, the x-axis, and the origin. (Select all that apply.) Part 1
Answer:
[tex]\begin{aligned}\textsf{(a)} \quad y&=-6x^2\\y&=4x^2-2\end{aligned}[/tex]
[tex]\textsf{(b)} \quad x=\dfrac{1}{4}y^2[/tex]
Step-by-step explanation:
Part (a)A graph is symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph.
Linear functions are not symmetric with respect to the y-axis.
Quadratic functions are symmetric with respect to the y-axis if the y-axis is their axis of symmetry, so when the variable x is squared.
Cubic functions are not symmetric about the y-axis.
Square root functions are not symmetric about the y-axis.
There are two quadratic functions with x² in the given answer options.
Test to see if they are symmetric with respect to the y-axis.
Test for symmetry
To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.
Given function:
[tex]y=-6x^2[/tex]
Replace x with (-x):
[tex]\implies y=-6(-x)^2[/tex]
[tex]\implies y=-6x^2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.
Given function:
[tex]y=4x^2-2[/tex]
Replace y with (-y) and x with (-x):
[tex]\implies y=4(-x)^2-2[/tex]
[tex]\implies y=4x^2-2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.
Part (b)A graph is symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, -b) on the graph.
Linear functions are not symmetric with respect to the x-axis.
Quadratic functions are symmetric with respect to the x-axis if the x-axis is their axis of symmetry, so when the variable y is squared.
Cubic functions are not symmetric about the x-axis.
Square root functions are not symmetric about the x-axis.
There is one quadratic functions with y² in the given answer options.
Test to see if it is symmetric with respect to the x-axis.
Test for symmetry
To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.
Given function:
[tex]x=\dfrac{1}{4}y^2[/tex]
Replace y with (-y):
[tex]\implies x=\dfrac{1}{4}(-y)^2[/tex]
[tex]\implies x=\dfrac{1}{4}y^2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the x-axis.
3. Represent and Connect Write 2,857 using only hundreds and ones.
By using a linear combination, we can write our number using only hundreds and ones as:
2,857 = 28*100 + 57*1
How to write the number using only hundreds and ones?To write the number using only hundreds and ones we need to write our number as a linear combination of ones and hundreds, so we can write:
2,857 = a*100 + b*1
There are multiple solutions for this, we can use b to cover the ones and the tens, so:
57 = b*1
57 = b
And we can use a to cover the hundreds and thousands, so:
2,800 = a*100
2,800/100 = a
28 = a
Then we can write our number using only hundreds and ones as:
2,857 = 28*100 + 57*1
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