solve for T. pls help this is literally the last one i need to finish
The solution of the given linear inequality will be -10/3 <= t <= -2.
What are linear inequalities?
Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.
The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.
e.g. y>x+2
Now,
Given inequality is -2 I-3t-8I <=-4
So there are two inequalities 1. -2+3t+8<=-4 2. -2-3t-8<=-4
1. 3t+6<=-4 2.-3t-10<=-4
1. t>=-10/3 2. t<=-2
Hence,
The solution of the given linear inequality will be -10/3 <= t <= -2.
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write the equation of the line satisfying the given conditions in slope-intercept form. (let x be the independent variable and y be the dependent variable.) slope = −4, passes through (1, 3)
The equation of the line is y = -4x + 7.
The slope of a line is determined by the formula m = (y2 - y1) / (x2 - x1). Therefore, the slope of the line in question is -4, as given. To find the equation of the line, we must use the slope-intercept form, y = mx + b.
We know that the line passes through the point (1, 3). We can use this point to solve for b, the y-intercept. To do so, we will substitute the x- and y-coordinates of the point into the equation, and solve for b. We get 3 = (-4)(1) + b, so b = 7.
Therefore, the equation of the line is y = -4x + 7.
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suppose that 20% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?
Suppose that 20% of people own dogs, if you pick two people at random, the probability that they both own a dog is 0.04.
Suppose that 20% of people own dogs.
So the probability of selecting own dogs = 0.20
The probability that a population unit will be included in a sample obtained through probability sampling is known as probability of selection. Each subset of a population has a probability of being chosen in the sample, which is determined by the sampling design.
If you pick two people at random, then the probability that they both own a dog = 0.20 × 0.20
If you pick two people at random, then the probability that they both own a dog = 0.04
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5. Mr. Jones donates 1/5 of his paycheck to the animal shelter. Half of that money goes to rescue puppies. How much of Mr. Jones' paycheck helps rescue puppies?
Answer:
1/10 or 0.1 or 10%
Step-by-step explanation:
[tex] \frac{1}{5} \times \frac{1}{2} = \frac{1}{ 10 } [/tex]
i dont understand this
Answer:
C
Step-by-step explanation:
Hi there and welcome to brainly!
By looking at the number line, we want to identify which point represents the approximate value of 5π
We know that π has an approximate value of 3.14 so the approximate value of 5π = 5 × 3.14 = 15.7
Looking at the number line, 15.7 falls in between 15 and 16 which correlates to point C
Jamal depoited $4000 into an account with 2. 5% interet, compounded quarterly. Auming that no withdrawal are made, how much will he have in the account after 10 year? Do not round any intermediate computation, and round your anwer to the nearet cent
Jamal will have the amount of $5132.10 in the account after 10 years.
As per the given data:
Jamal deposited the principal amount of $4000 into an account.
P = $4000
Amount brought with 2. 5% interest which is compounded quarterly.
Convert the rate percent to the decimals.
We get:
2. 5% = [tex]$\frac{25}{100}[/tex]
2. 5% = 0.025 = r
Also given that no withdrawals are made.
Here we have to determine that how much will he have in the account after 10 years.
t = 10 years
As the interest is compounded quarterly the value of n is 4
n = 2
Compound interest is the type of interest that is added to the principle amount before the next compounding period begins.
According to compound interest formula:
[tex]$ A=P\left(1+\frac{r}{n}\right)^{n t} \\[/tex]
[tex]$\Rightarrow & A=4000\left(1+\frac{0.025}{4}\right)^{4 \times 10} \\[/tex]
[tex]\Rightarrow \quad & A=4000(1+0.00625)^{40} \\[/tex]
[tex]\Rightarrow \quad & A=4000 \times(1.00625)^{40} \\[/tex]
A = 4000 × 1.2830268206
A = 5132.1072824
A = 5132.10 (After rounding to the nearest cent)
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Determine the point P that
partitions the line segment AB
into the ratio 1:3 when A(2, 4)
and B(10, 8).
Answer:
[tex]\left(\dfrac{14}{3}\;, \;\dfrac{16}{3}\right)[/tex]
Step-by-step explanation:
We have two points A(2, 4) and B(10, 9)
P divides the segment AB, it is located 1/3 of the distance from A to B
Lets use the following notation
[tex]\textsf {x_{AB}$= x-distance from A to B}[/tex]
This is the absolute difference between the x-coordinates of A and B
[tex]\textsf {y_{AB}$= y-distance from A to B}[/tex]
This is the absolute difference between the y-coordinates of A and B
[tex]\textsf {x_{AP}$= x-distance from A to P}[/tex]
This is the absolute difference between the x-coordinates of A and P
[tex]\textsf {y_{AP}$= y-distance from A to P}[/tex]
This is the absolute difference between the y-coordinates of A and P
To find the coordinates of P:
Find the x-distance between A and B:Answer: The coordinates of point P are:
[tex]\left(\dfrac{14}{3}\;, \;\dfrac{16}{3}\right)[/tex]
If you actually calculate the distances AB and AP using the distance formula: [tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
you will find
AB has length 8.944272 and AP has length 2.9829
2.9829/8.944272 ≅ 0.333 which is 1/3
An 8 unit x 8 unit x 8 unit cube is composed of smaller 1 unit cubes and is painted blue. How many of the 1 unit cubes have exactly 1 face painted blue?
A. 72
B. 296
C. 216
D. 512
solve the equation 4(x/8 - 2) = 1/4(2x - _) so that it has infinitely many solutions. NEED HELP ASAP
Answer:
Solution:
4 (x/8-2)
= 4 times 1/16 (16 x x/8 - 2x 16)
= 1/4 (2x-32)
Hence 4, (x/8-2) = 1/4 (2x-32) and it has infinitely many solutions
Step-by-step explanation:
Erin i making banana bread to erve 20 guet. He want each guet to have 1 1\6 of a loaf. If he bake 3 loave pf banana bread,will Erin have enough banana bread? Show your work and jutify your anwer
If he bake 3 loave pf banana bread. Since 23 1/3 wants a lot of bread, Erin's banana bread is not enough.
Will Erin have enough banana breadThese are the specified parameters:
Erin's number of guests = 20 people.
Each guet to have 1 1\6 of a loaf.
If he bake 3 loave pf banana bread.
Much to be desired bread
= number of guests × bread per guest
= 20 × 1 1/6
= 20 × 7/6
= 70/3
= 23 1/3
He baked 3 banana loaves, whereas the desired number of loaves was 23 1/3.
Thus Erin's banana bread is not enough for the guest.
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List the key features of comparative bar graph and segmented bar graph:
CONNECTING CONCEPTS Find the value of x such that the quadrilateral is a parallelogram. Then find the perimeter of the parallelogram.
2x+1
x²-5
x²-7
3x - 1
x =
Perimeter:
Answer:
To find the value of x such that the quadrilateral is a parallelogram, you need to solve for x in the equation 2x+1 = 3x - 1. This gives x = 1. The perimeter of the parallelogram is then 2x + x² - 5 + x² - 7 + 3x - 1 = 4x² - 13. Substituting x = 1 gives the perimeter as 4 - 13 = -9.
x is less than or equal to 8, y is more than -3. Graph the solution of the system of linear inequalities. (and fill in)
Answer:
The solution to the system of linear inequalities x <= 8 and y > -3, represented on a coordinate plane, is a region that satisfies both inequalities. It is the half-plane formed by the line x=8 and above the line y=-3 .
Step-by-step explanation:
The solution to the system of linear inequalities x <= 8 and y > -3 can be represented on a coordinate plane as a region that satisfies both inequalities.
To graph the solution, we first plot the line x = 8 on the coordinate plane. Since x <= 8, this line represents the boundary of the solution. Everything to the left of the line x = 8 is included in the solution.
Next, we plot the line y = -3. Since y > -3, everything above the line y = -3 is included in the solution.
The final graph will be a half-plane formed by the line x=8 and above the line y=-3 .
order the following values from least to greatest 13 hundredths 0.03
Evaluate the expression when a=2, b=4, c= -5, and d= -5. 1/4b^3 - 1/5d^3
When a = 2, b = 4, c = -5, and d = -5, the expression for 1/4b^3 - 1/5d^3 is 11.
How do you evaluate this expression?
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations solve the equation for the variable. Then plug that variable value into the expression and simplify to get the answer. Follow this same process anytime you need to use an equation to evaluate an expression.When a = 2, b = 4, c = -5, and d = -5, the expression becomes:
1/4 * 4^3 - 1/5 * (-5)^3
= 1/4 * 64 - 1/5 * -125
= 16 - 25/5
= 16 - 5
= 11
So the expression evaluates to 11.
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if the simple multiplier is 5, the required reserve ratio must be group of answer choices 0 50 percent 20 percent 5 percent 10 percent
The required reserve ratio is 20 percent
What is Ratio?
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
A ratio is the relationship or comparison of two numbers belonging to the same unit to determine how much larger one number is than the other.
Given,
If the simple multiplier is 5
Multiplier = 1 / Required Reserve Ratio
5 = 1 / RR
5 = RR
The required reserve ratio = 1/5 = 20%
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Refer to the following scenario to solve the next four problems: A spinner that is divided into six (6) congruent regions, numbered “one” through “six”, is spun once. Let “A” be the event “odd” and “B” be the event “5”. Find each of the given probabilities.
Answer:
To solve this problem, we first need to determine the probability of events A and B. Event A is the event "odd", so the probability of event A is 3/6, or 1/2. Event B is the event "5", so the probability of event B is 1/6.
Next, we can use the rules of probability to determine the probability of the given events. The probability of A and B occurring is the probability of event A multiplied by the probability of event B, so the probability of A and B occurring is 1/2 x 1/6 = 1/12.
The probability of either A or B occurring is the probability of event A plus the probability of event B minus the probability of A and B occurring, so the probability of either A or B occurring is 1/2 + 1/6 - 1/12 = 5/12.
The probability of A or B not occurring is the probability of the complement of A or B, which is the probability of neither A nor B occurring. The probability of neither A nor B occurring is 1 - (1/2 + 1/6 - 1/12) = 1/12.
The probability of A given B is the probability of A and B occurring divided by the probability of B occurring, so the probability of A given B is 1/12 / 1/6 = 1/2.
Therefore, the probabilities of the given events are 1/2, 5/12, 1/12, and 1/2 respectively.
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The distance to Star A is 4x10^7 about light years. The distance to Star B is about 5x10^4 light years. Choose which star is farther away. Then fill in the blank with a number written in standard notation.
Answer:
Star is is further away
3.995 x [tex]10^{7}[/tex]
Step-by-step explanation:
(4 x [tex]10^{7}[/tex]) - ( 5 x [tex]10^{4}[/tex]) To subtract we need to have the same powers of 10
(4 x [tex]10^{7}[/tex]) - (.005 x [tex]10^{7}[/tex])
(4 - .005)x [tex]10^{7}[/tex]
3.995 x [tex]10^{7}[/tex]
36.
Volume of a Bird Cage. A company makes rectangular shaped bird cages with height b inches and square bottoms.
The volume of these cages is given by the function V= 6³-66b²+ 9b.
(i) Find an expression for the length of each side of the square bottom.
Use the function to find the volume of a cage with a height of 18 inches.
(iii) Use the remainder theorem to find the volume of a cage with a height of 15 inches.
(iv) Verify the result of (iii) using function ?
The expression for side of square bottom = b - 3, volume of rectangle is 4050 and the volume of a cage with a height of 15 inches is 2160.
What is a function ?
Function can be defined as which relates an input to output.
Given,
Volume of a Bird Cage. A company makes rectangular shaped bird cages with height b inches and square bottoms.
Height = b
Volume V = 6³-6b²+9b.
Length of each side (s) :
V = 6³-6b²+9b.
s^2 b = b (b^2 - 6b + 9 )
s^2 = b^2 - 6b + 9
(a - b ) ^2 = a^2 + b^2 -2ab
s^2 = (b-3) ^2
s = b-3
height is 18 inches and height is given as b
Hence, b = 18
s= b-3 (from i)
= 18 - 3
s = 15
Therefore volume:
volume of rectangle = l x b x h
V= 18 x15 x15= 4,050
(If height = 15
then, b = 15
b -15 = 0
Definition of remainder theorem:
we divide a polynomial P(x) by a factor ( x – a); to find a smaller polynomial along with a remainder. The factor doesn't have to be a part of the polynomial.
b^3 - 6b^2 + 9b / b-15 = 2160
Therefore Volume with b = 15 is 2160
Therefore, The expression for side of square bottom = b - 3, volume of rectangle is 4050 and the volume of a cage with a height of 15 inches is 2160.
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justify why the function with f ′ = 2cosx 2cosxsinx is decreasing from pi over 2 to 3 pi over 2. (1 point)
The statement that the function is decreasing in the given interval is incorrect.
We have,
To justify why the function with f' = 2cos(x)sin(x) is decreasing from π/2 to 3π/2, we need to analyze the sign of the derivative in that interval.
The derivative f' represents the instantaneous rate of change of the function f(x) at any given point.
When f' is positive, it indicates that the function is increasing, and when f' is negative, it indicates that the function is decreasing.
In this case,
f' = 2cos(x)sin(x).
To determine the sign of f' in the interval [π/2, 3π/2], we can examine the behavior of cos(x) and sin(x) in that range.
In the interval [π/2, 3π/2], cos(x) is negative, and sin(x) is negative as well. When both factors in the expression 2cos(x)sin(x) are negative, their product is positive.
Since f' = 2cos(x)sin(x) is positive in the interval [π/2, 3π/2], it indicates that the function f(x) is increasing in that interval.
Therefore, the function is not decreasing from π/2 to 3π/2.
Thus,
The statement that the function is decreasing in the given interval is incorrect.
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Y’all please help me with this
Answer:
C = .40n
Step-by-step explanation:
The line shows that the graph is proportional. I know this because the graph is linear and goes through the origin (0,0). This means that I can take any point and put it in the form y/x to find the slope.
I took the point (10,4) on the graph. I put that in the form y/x = 4/10. 4/10 = .40 which is my slope.
C= .40n
scenario 2, continued next, you prepare for the question-and-answer session that will follow your presentation. what methods help you consider any limitations of your data? select all that apply. 1 point look at the context eliminate the outliers critically analyze the correlations understand the strengths and weaknesses of the tools
The concept is Data Analysis, which is the process of totally applying statistical tools to dissect data. The answer is options B, C, and D.
To help you consider data limitations, critically dissect correlations, examine the environment, and understand tool strengths and sins. Data analysis applies statistical and/ or logical ways to describe, illustrate, epitomize, and estimate data.
Data analysis helps individualities and associations make sense of data. Data analysts typically analyze raw data for insights and trends.
Limitations include:
Lack of alignment within teamsLack of commitment and patienceLow quality of dataPrivacy concernsComplexity & BiasQuestion
You're preparing a question-and-answer session that will follow your donation. Which styles help you to consider data limitations? elect everything that suits you.
A) exclude the outliers
B) Understand the strengths and sins of the tools
C) Critically dissect the correlations
D) Look at the environment
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Is W a subspace of the vector space? If not, state why. (Select all that apply.)
W is the set of all nonnegative functions in C(−[infinity], [infinity]).
W is a subspace of C(−[infinity], [infinity]).W is not a subspace of C(−[infinity], [infinity]) because it is not closed under addition.W is not a subspace of C(−[infinity], [infinity]) because it is not closed under scalar multiplication.
W satisfies both conditions and is closed under addition and scalar multiplication.
What is vector space?In mathematics, a vector space is a fundamental concept in linear algebra.
It is a mathematical structure that consists of a set of objects called vectors, along with operations for vector addition and scalar multiplication.
These operations follow certain axioms, which define the properties of a vector space.
The statement "W is the set of all nonnegative functions in C(−∞, ∞)" does not specify the vector space C(−∞, ∞) correctly.
To determine if W is a subspace of a given vector space, we need to define the vector space correctly.
However, assuming C(−∞, ∞) refers to the set of all continuous functions defined on the interval (−∞, ∞), we can analyze whether W is a subspace of this vector space.
To be a subspace, W must satisfy two conditions:
W must be closed under addition.
W must be closed under scalar multiplication.
Let's evaluate these conditions for W, the set of all nonnegative functions in C(−∞, ∞):
W is closed under addition:
If we take two nonnegative functions from W, their sum will also be nonnegative.
Thus, the sum of any two functions from W will remain in W. Therefore, W is closed under addition.
W is closed under scalar multiplication:
If we multiply a nonnegative function from W by a positive scalar, the result will still be a nonnegative function.
Thus, scalar multiplication by a positive scalar preserves the nonnegativity of the function.
Therefore, W is closed under scalar multiplication.
Based on the above analysis, W satisfies both conditions and is closed under addition and scalar multiplication.
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A convex hexagon's six interior angles are as follows: x°. x°, (2x - 3)°, (3x +7)°, (7x - 12)° and (6x +28)°. Solve for x.
A. 35
B. 37
C. 53
D. 55
35⁰
To solve for x, we need to find the sum of the interior angles of the hexagon and equate it to the known sum for a convex hexagon, which is 720°.
The sum of the interior angles is:
x° + x° + (2x - 3)° + (3x + 7)° + (7x - 12)° + (6x + 28)° = 720°
Expanding:
20x + 20 = 720
Subtracting 20 from both sides:
20x = 700
Dividing both sides by 20:
x = 35
So the value of x is 35.
The polygons are similar. Find the value of x.
Answer:
24
Step-by-step explanation:
18/3=6 6*4=24
The value of x for the similar triangles is equal to 24.
How to calculate for x for the similar trianglesThe triangles are similar, this implies that the length x cm of the bigger triangle is similar to the length HJ = 18 cm of the smaller triangle
and the length DF = 16 cm of the bigger triangle is similar to the length JG = 12 cm of the smaller triangle
so;
x/18 = 16/12
12x = 18 × 16 {cross multiplication}
12x = 288
x = 288/12 {divide through by 12}
x = 24 cm
Therefore, the value of x is equal to 24 cm for the similar triangles.
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Please mark the graph for this equation
The points to be graphed are (0, 3.5) and (-2.8, 0). The graph of the equation is shown in the attached image
How to graph the equation of a line?Given y = x/8 + 3.5
In order to graph the equation of the line:
First, find the value of x when y = 0:
y = x/8 + 3.5, when y = 0:
0 = x/8 + 3.5
x/8 = -3.5
x = -28
Thus, x-intercept is (-28, 0)
Also, find the value of y when x = 0:
y = x/8 + 3.5, when x = 0:
y = 0/8 + 3.5
y = 3.5
Thus, y-intercept is (0, 3.5)
Therefore, the values to be plotted on our graph are (0, 3.5) and (-2.8, 0). The image of the graph is attached
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the length of a rectangular land is 10 m long then that of its breadth . the cost of fencing around it with three rounds at rs 50 per metre is rs 13800 find the length and breadth of the land
The breadth and length is 64m and 74m
What is perimeter?A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter.There are numerous practical uses for calculating the perimeter. The complete length of a shape's boundary, as used in geometry, is referred to as the shape's perimeter. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet. The perimeter is the space surrounding a shape's edge. Find the perimeter of various forms by multiplying their side lengths.breadth=x
length=x+10
perimeter for 3 rounds=3y
3y*50=13800
y(perimeter)=276
2(l+b)=286
2(x+10+x)=276
2(2x+10)=276
4x+20=276
4x=276-20
x=256/4
x=64
breadth=64m
length=74m
The complete question is,
rectangular land is 10m longer than its breadth cost of fencing around it is 3 rounds at rs 50 per meter is rs 13800. find length and breadth
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The breadth and length of the land is 64m and 74m.
Define rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It is also known as an equiangular quadrilateral because all of its angles are equal; or a parallelogram with a right angle. A square is defined as a rectangle with four equal-length sides.A four-sided polygon with four right angles and each pair of opposite sides parallel and the same length.A rectangle is a type of quadrilateral with equal and parallel opposite sides. It is a four-sided polygon with four 90-degree angles. A rectangle is a two-dimensional shape. The diagonals in a rectangle are equal, but not in a parallelogram.To learn more about rectangle refer to:
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when $0.\overline{36}$ is expressed as a common fraction in lowest terms, what is the sum of the numerator and denominator?
When 0.36 is expressed as a common fraction in lowest terms, the numerator is 9 and the denominator is 25. The sum of the numerator and denominator is 34.
To calculate the sum of the numerator and denominator when 0.36 is expressed as a fraction in lowest terms, follow these steps:
Express 0.36 as a fraction by writing 0.36 as the numerator and 10, 100, 1000, or any other power of 10 as the denominator.Reduce the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor.Add the numerator and denominator together to get the sum.In this case, 0.36 can be expressed as 9/25. The greatest common factor of 9 and 25 is 1, so the fraction is already in its lowest terms. The sum of the numerator and denominator is 9 + 25 = 34.
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One serving of a crispy cereal has 8 grams of fiber, which is 25% of the recommended daily amount. What is the total recommended daily amount of fiber? Give your answer in grams.
The Recommended daily amount of fiber from the expression 8x is 32g.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given Fiber in one serving of cereal=8gm which is 25% of one day need.
Let 8x be the fiber in cereal where x is multiple of 25%.
So, for one day need fiber needed is 100% i.e. x=4.
Therefore, Fiber needed =8*4=32g
Hence,
The Recommended daily amount of fiber is 32g.
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Solve the following inequalities; a. 4x+15 >27
Answer:
X>3
Step-by-step explanation:
So we're solving for X
Since it's an inequality, let's make it = 27 instead
4x+15=27
Now we can subtract 15
4x = 12
x = 3
Now that it's saying > 27, that means the same for x, it's has to be > too, concluding x>3... all x's greater than 3
