Answer:
Step-by-step explanation:
A
solve the inequality -2 / 5 x <-2 show your work in complete sentences describe how solution set a graph on a number line ed
The solution of the inequality will be;
⇒ x > 5
And, The solution is shown on number line.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ - 2/5x < - 2
Now,
Solve the inequality as;
⇒ - 2/5x < - 2
⇒ - 2x < - 2 × 5
⇒ - 2x < - 10
Multiply by - 1,
⇒ 2x > 10
⇒ x > 5
Thus, The solution of the inequality = x > 5
And, The solution is shown on number line in figure.
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If $1743 is invested at 5.45% for 2 years, find the future value if the interest is compounded semi-annually. Round to the nearest
cent.
Do not put the $ in your answer or any units. Only put the number value for your answer.
Add your answer
Answer:
The future value of an investment is calculated by using the formula:
$FV = PV(1 + r/n)^{nt}$
where $FV$ is the future value, $PV$ is the present value (the initial investment), $r$ is the interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the number of years the investment is held.
In this case, we have $PV = 1743$, $r = 5.45% = 0.0545$, $n = 2$, and $t = 2$. Plugging these values into the formula, we get:
$FV = 1743(1 + 0.0545/2)^{2 \cdot 2} = 1743(1 + 0.0273)^{4}$
Now we can calculate the future value by raising $1 + 0.0273$ to the power of 4:
$FV = 1743(1.0273)^{4} \approx \boxed{1956}$
Note that we rounded the result to the nearest cent.
Step-by-step explanation:
three people are asked to throw a fair die. what is the probability that all ofthem get the same number? [10 pts]
The probability that all of them get the same number would be 1/36. Or probability that they will have a chance of get the same number after 36 throws. And the probability concept that use here is theoretical probability.
How to calculate?Theoretical probability It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. The chance that any one die matches another is 1 out of 6.Amount of people whom asked to throw are 3 people.Then everybody will get the some chance to get the same number.And then the probability works out this way:Total out comes in three dice = ( 6 × 6 × 6 = 216 ).
Probability of getting same number = 6 × 1/6 × 1/6 × 1/6
= 6 × 1/6 × 1 × 1/6 × 6
= 6/6 × 1/36
= 1 × 1/36
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NO LINKS!! Help me with the 2-Column Proof Part 4aa
Here is the two column proof:
Statement Reason
AK bisects ∠BAR Givenm∠BAK = m∠BAR/2 Definition of angle bisectorm∠KAR = m∠BAR/2 Definition of angle bisectorm∠BAK = m∠KAR Transitive property of equality∠BAK ≅ ∠KAR Definition of congruent∠1 ≅ ∠2 Substitution property of equalityProvedWhich expression represents 10y(3/5y)?
О 6y
O 53/5y
O 6y^2
O 53/5y^2
Step-by-step explanation:
10y(3/5y) = 3×10y / 5y = 3×2 = 6
since this is not one of the answer options, you must have mistyped something.
probably the real problem is
10y((3/5)y) = 2y×3 × y = 6y²
the 3rd answer option is correct.
Mike took clothes to the cleaners three times last month. First, he brought 3 shirts and 1 pair of slacks and paid
$13.46. Then he brought 7 shirts, 3 pairs of slacks, and 1 sports coat and paid $43.39. Finally, he brought 5 shirts
and 2 sports coats and paid $28.43. How much was he charged for each shirt, each pair of slacks, and each
sports coat?
***
Mike charged for each shirt is $2.49, each pair of slacks is $5.99 and each sports coat is $7.99.
What is system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
Let
Price of shirts = x
Price of slacks = y
Price of sports = z
From the given information,
3x + y = $13.46 ..(1)
7x + 3y + z = $43.39 ..(2)
5x + 2z = $28.43 ..(3)
From equation (1), y = 13.46 - 3x
From equation (3), z = (28.43 - 5x) / 2
Plug the value of x and z in equation (2)
7x + 3(13.46 - 3x) +(28.43 - 5x)/2 = 43.39
7x + 40.38 - 9x + 14.22 - 2.5x = 43.39
-4.5x +54.6 = 43.39
4.5x = 54.6 - 43.39
4.5x = 11.21
x = 2.49
Plug x = 2.49 in equation (1)
3(2.49) + y = 13.46
2.47 + y = 13.46
y = 5.99
Plug x = 2.49 in equation (3),
5(2.49) + 2z = 28.43
12.45 + 2z = 28.43
2z = 15.98
z = 7.99
Hence, Mike charged for each shirt is $2.49, each pair of slacks is $5.99 and each sports coat is $7.99.
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The expression 10ax+14ay+15bx+21by can be factored into two binomials such that all the coefficients are integers. Which is one of the factors
The expression 10ax + 14ay + 15bx + 21by has a coefficient of (2a + 3b)
as a factor.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 10ax + 14ay + 15bx + 21by.
The given expression is in 4 variables namely a, b, x and y we'll combine the x and y terms in the expression.
Now, 10ax + 15bx + 14ay + 21by.
= 5x(2a + 3b) + 7y(2a + 3b).
= (2a + 3b)(5x + 7y)
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Question 1 of 21
Which of the following are solutions to the quadratic equation? Check all that
apply.
x² + 3x-10 = 0
☐ A. 1
B. 2
C. -2
D. -4
OE. -5
OF. 28
Answer:
2 and -5 (B & E)
Step-by-step explanation:
Factor the equation into
(x-2) (x+5)
Thus the zeros are 2 and -5
x=2 and x=-5 are the solutions of the quadratic equation x² + 3x-10 = 0
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given quadratic equation is x² + 3x-10 = 0
We have to find the solutions of the quadratic equation
x² + 3x-10 = 0
Let us factorize the given equation
x² +5x-2x-10=0
x(x+5)-2(x+5)=0
(x-2)(x+5)=0
Now equate both the terms with zero to find the solutions
x=2 and x=-5
Hence, x=2 and x=-5 are the solutions of the quadratic equation x² + 3x-10 = 0
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Write an equation in standard form (1,1) (2,5) Ax+By=-3
The Equation of the Line in Standard form is 4x - y = 3
What is Slope of a Line?
The slope formula is used to compute the inclination or steepness of a line. The slope of the lines is calculated using the x and y coordinates of the lines. It is the ratio of the y-axis change to the x-axis change.
Solution:
Slope of the Line passing through the points (1, 1), (2, 5)
is
m = 5-1/2-1 = 4
Equation of the line = (y - y1) = m(x - x1)
y - 1 = 4(x - 1)
y - 1 = 4x - 4
4x - y = 3
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Can someone pls help me with this last question pls hurry I got 10 mins hurry I’ll do brainliest
Answer:
(12,1)
Step-by-step explanation:
Before the transformation, Point B is at (-8,1).
When it will be reflected, it will be at (8,1)
Then, it shifts 4 points to the right, and so it will be at (12,1)
Solutions
Solve the following.
14.) You and a friend decide to go into business selling bobblehead dolls. The profit p for selling b bobblehead dolls is
given by the equation p(b) = -0.2b² + 15b-150. What will the profit be if you sell 50 bobblehead dolls?
To make more than $100 profit we must make more than 25 bobble heads and less than50. 25 < b < 50 Make between 26 to 49 bobble heads.
Find the solution ?p(b) = -0.2b2 + 15b - 150
-0.2b2 + 15b - 150 > 100
-0.2b2 + 15b - 250 > 0
multiply through by 10 to clear decimal
-2b2 + 150b - 2500 > 0
To find the point where profit is exactly
$100 set the equation equal to zero
-2b2 + 150b - 2500 = 0
b = [-150 ±√(1502 -4(-2)(-2500))]/2(-2)
b = (-150 ±√2500)/(-4)
b = (-150 ± 50)/(-4)
we will have 2 points that work.
b = (-150 + 50)/-4 = 25
b = (-150 - 50)/-4 = 50
To make more than $100 profit we must make more than 25 bobble heads and less than50.
25 < b < 50
make between 26 to 49 bobble heads.
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A researcher collected data on the latitude, in degrees north of the equator, and the average low temperature, in degrees Fahrenheit, for a random sample of cities in Europe. The data were used to create the following equation for the least-squares regression line. predicted average low temperature=65.5−0.70(latitude) Which of the following is the best interpretation of the slope of the line?
The best interpretation of the slope of the linear regression equation is given as follows:
For each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.
What is the slope of a linear function?The slope represents the rate of change of the output variable relative to the input variable of a linear relation.
Hence, it can be said that the slope states by how much the output variable y changes when the input variable x is increased by 1.
The variables in this problem are given as follows:
Input: Latitude.Output: average low temperature.The negative slope of -0.7 means that for each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.
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Answer:
B
Step-by-step explanation:
There are 15 circles and 3 squares What is the simplest ratio of squares to circles?
Answer:
1:5
Step-by-step explanation:
Emrik helped his dad hang lights this weekend around eight windows. Each window is 3 ½ feet wide and 5 feet long. How many feet of lights does he need?
Using mathematical operations, we can say that total of 69 ft of lights is needed to cover all 8 windows.
What are mathematical operations?An operation is a function in mathematics that converts zero or more input values into a clearly defined output value.
The operation's arity is influenced by the number of operands.
The rules that define the order in which we should solve an expression involving many procedures are known as the operation order.
PEMDAS stands for Parentheses, Exponentiation, Multiplication, Division, and Addition and Subtraction (from left to right).
So, we know the dimensions of the window:
3 ½ feet wide and 5 feet long.
And there is a total of 8 windows.
The perimeter of the rectangle: 2(l+w)
Now, the feet of light needed will be:
2(l+w) * 8
2(3 ½+5) * 8
2(7/2+5) * 8
7+5 * 8
12 * 8
96 ft
Therefore, using mathematical operations, we can say that total of 69 ft of lights is needed to cover all 8 windows.
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Divide the polynomials.
Your answer should be a polynomial.
x² - 36
x-6
The polynomial we get after solving this is (x+6).
To simplify this expression, we need to use the rules of algebra. First, we can factor the numerator to get (x-6)(x+6) so the expression becomes:
(x-6)(x+6)÷ (x-6)
Now we can cancel out the (x-6) terms in the numerator and denominator to get:
(x-6)(x+6)÷(x-6) = (x+6)
This is the simplified form of the expression. Note that this result is only valid when x is not equal to 6, since division by zero is undefined.
What is a Polynomial?
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.
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If the determinant of a 5 X 5 matrix A is det(A)=-8, and the matrix C is obtained from A by swapping the second and third rows, then det(C)=If the determinant of a x 5 matrix A is \det\,(A)=9 , and the matrix D is obtained from A by adding 2 times the fourth row to the first, then \det\,(D)=
By using determinant, it can be calculated that-
det(C) = 8
det(D) = 9
What is a determinant?
Determinant of a square matrix is equal to the product of the elements of a square matrix and their cofactors.
Here,
det(A) = -8
The matrix C is obtained from A by swapping the second and third rows
We know if the rows and columns of a matrix are swapped then the value of the determinant of the new matrix changes in sign only
So det(C) = 8
Now,
det(A) = 9
We know that the value of determinant remain unchanged on adding any combination row or column
Matrix D is obtained from A by adding 2 times the fourth row to the first
det(D) = 9
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Determine by direct integration the product of inertia of the given area with respect to the x and y axes.
To evaluate the integral, you will need to define the limits of integration and use appropriate coordinate systems for the given area.
And the area is given as [tex]I_{xy} =\int \limits \int \limits {(y^2 - x^2)} \,dm[/tex]
What is direct integration?
Direct integration is a method of finding the moment of inertia of a body or a region about a given axis by directly integrating the product of the mass of each infinitesimal element of the body or region and the square of its distance from the axis.
To determine the product of inertia of a given area with respect to the x and y axes, you will need to first define the area and its mass distribution. Then, you can use the following formula for the product of inertia:
[tex]I_{xy} =\int \limits \int \limits {(y^2 - x^2)} \,dm[/tex]
Where Ixy is the product of inertia, y is the distance from the y-axis, x is the distance from the x-axis, and dm is the mass of an infinitesimal element of the area.
Hence, To evaluate this integral, you will need to define the limits of integration and use appropriate coordinate systems for the given area.
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Which situation could be represented by the graph shown?
The graph represents the situation Allison purchases lemons for $0.75 each.
What is Slope of Line?The ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane is known as slope of line.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the given graph, we can take two points (4, 3) and (8, 6) to find the slope.
Let us plug in the values in formula of slope.
m=6-3/8-4
m=3/4
m=0.75
Hence, Allison purchases lemons for $0.75 each is represented by the given graph.
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Which ordered pairs are solutions to the inequality y−3x<−8 ? Select EACH correct answer.
(1, −5)
(5, 4)
(−3, −2)
(0, −9)
(2, −1)
Answer:
Step-by-step explanation:
(0,-9)
Points E and F are coplanar. This means that Point E and C _____.
B
Step-by-step explanation:
You are driving on a freeway to a town that Is 300 kilometers from your home. After 30 minutes, you pass a freeway exit that you know is: 50 Kilometers from your home. Assuming that you continue at the same constant speed, how long (in hr) does the entire trip take?
It'll take you 3 hours to reach your destination.
i don’t really know what this means lol so please help i’ll give you brainlist!!!
Answer:
Step-by-step explanation:
A vending machine
The user puts in money, punches a specific button, and a specific item drops into the output slot. (The function rule is the product price. The input is the money combined with the selected button. The output is the product, sometimes delivered along with coins in change, if the user has entered more money than required by the function rule.)
Answer: it is mean to state a real world relationship that consisted a state of a input and output
Step-by-step #hopethishelps
A bag contains 4 red marbles and 6 blue marbles. A marble is drawn and then replaced. This is done 50 times. Round all answers to the nearest hundredth (two decimal places). What is the probability that a red marble is drawn:
a. exactly 15 times:
b. at least 15 times:
c. at most 15 times:
d. less than 15 times:
e. between 17 and 25 times, inclusive:
Answer: e
Step-by-step explanation:
4+6= 10 and then divide by 50 and add 25 so 0.2+25+25.02 so then subtract 4 so about 21 or 21.02
Find the values of x and y in the diagram.
The value of x is 9.
The value of y is 5.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Two triangles in a composite triangle.
We see that,
m∠UST = m∠STR
This means,
x + 4 = 13
x = 13 - 4
x = 9
The sum of the angles in a triangle is 180 degrees.
One triangle is an equilateral triangle.
All three angles are equal.
This means,
The angle has to be 60°.
m∠UTR + m∠URT + m∠TUR = 180
3m = 180
m = 60
Now,
m∠URS = 180
m∠URT + m∠SRT = 180
60 + m∠SRT = 180
m∠SRT = 120
The isosceles triangle has two equal angles.
m∠RTS = m∠RST
m∠SRT + m∠RTS + m∠RST = 180
120 + 6y + 6y = 180
12y = 180 - 120
12y = 60
y = 5
Thus,
The value of x and y are 9 and 5.
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Find the slope of this problem
Answer:
1/9 rise 1 run 9
Step-by-step explanation:
if you graph the y coordinate as 3 and find the x value, x value should be 0. Point (0,3) and (-9,2) and do rise over run
On a standardized test with normal distribution, the mean is 85 and the standard deviation is 3. Within which range should approximately 95% of the scores lie?
Approximately 95% of the scores should lie within the range of 79 to 91.
Approximately 95% of the scores on a standardized test with a normal distribution and a mean of 85 and a standard deviation of 3 should lie within 2 standard deviations of the mean.
Since the standard deviation is 3, 2 standard deviations is : 2 × 3 = 6.
Adding 6 to the mean of 85 gives 91, and subtracting 6 from the mean of 85 gives 79.
Therefore, approximately 95% of the scores should lie within the range of 79 to 91.
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Find the measure of the three missing angles in the parallelogram below
128⁰
Answer: x = 52, y = 128, z = 52
Step-by-step explanation:
On a test that has a normal distribution, a score of 33 falls two standard deviations above the mean, and a score of 24 falls one standard deviation below the mean. Determine the mean of this test.
So our goal is to determine the mean test score, which we don't know, we know to raw scores, we know one raw score is 38 that's one standard deviation below the mean, which by definition of a Z score that Z equals negative one. one
What is meant by mean?Mean is the simple mathematical average of a set of two or more numbers. The mean for a given set of numbers can be computed in more than one way, including the arithmetic mean method, which uses the sum of the numbers in the series, and the geometric mean method, which is the average of a set of products. However, all the primary methods of computing a simple average produce the same approximate result most of the time.The formula for calculating the geometric mean is to multiply all the values in a data set, then take the root of the sum equal to the quantity of values within that data set.To learn more about arithmetic mean refer to:
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There are 25 members. In how many ways can we select a president, a vice president, a secretary and a treasurer?
The number of different ways the club select a president, vice president, treasure, and secretary is 23751.
What is the combination?Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.
The Total number of members in an archeology club = 25 members
Different position to select a member : President , Vice-president, Treasure, and Secretary
The Number of position for selecting a member = 4
Therefore, Number of different ways to select different position
= ²⁹C₄
= (25!)/ (25-4)!4!
= (25× 24×23×23×21!) / (21!) (4×3×2×1)
= 23751
Therefore, the number of different ways the club select a president, vice president, treasure, and secretary would be equal to 23751.
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If you realized your investment account with semi-annual compounding periods (2 per year) had provided you with an effective annual rate of 14.6% over the last 21 years, what would you say its annual percentage rate would be? Your answer should be expressed as a percentage rounded to the 2nd place to the right of the decimal point
The annual percentage rate of the investment account is of:
14.1%.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The effective annual interest rate is given as follows:
[tex]E = \left(1 + \frac{r}{n}\right)^n[/tex]
In this problem we have a semi-annual compounding, hence:
n = 2.
The effective rate was of 14.6%, hence E = 1.146, and thus the interest rate is obtained as follows:
[tex]E = \left(1 + \frac{r}{n}\right)^n[/tex]
[tex]1.146 = \left(1 + \frac{r}{2}\right)^2[/tex]
1 + 0.5r = 1.0705 (applying to square root to both sides).
0.5r = 0.0705
r = 0.0705/0.5
r = 0.141 = 14.1%.
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