Answer: 36
Step-by-step explanation:
This is a geometric progression. The formula for a geometric progression is given as:
= ar^n-1
where
a = first term = 16
r = common ratio = 24/16 = 1.5
n = 3
Therefore, the 3rd term will be:
= ar^n-1
= 16 × 1.5^3-1
= 16 × 1.5²
= 36
Therefore, the third term of the progression is 36.
Please need help ASAP, 50 points!!!!!!!!!!!!!!!!!!!!!!!!!!
Decide whether the triangles can be proven congruent by the given postulate or theorem. If not, state what information is needed.
(1). ΔIJH ≅ ΔKHJ, by SSS criterion,
and (2) we need, ΔTNS and ΔUHS are right-triangles and S is the mid-point to prove ΔTNS ≅ ΔUHS, by HL criterion.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
We have the triangle:
ΔIJH ≅ ΔKHJ.
To prove the congruent by SSS:
We have to show that three sides of the triangle are congruent to three sides of the other triangle.
Here,
IJ ≅ KH.
IH ≅ JH, Given.
And both triangles share the same side JH.
So,
JH ≅ JH
So, ΔIJH ≅ ΔKHJ, by SSS criterion.
ΔTNS ≅ ΔUHS.
To prove the congruent by HL:
We have to show that the triangles are right-triangle and one leg and hypotenuse of the triangle is congruent to one leg and hypotenuse of the other triangle.
So, we need;
ΔTNS and ΔUHS are right-triangles.
S is the mid-point.
So,
SN ≅ SH.
ST ≅ US
So, ΔTNS ≅ ΔUHS, by HL criterion.
Therefore, ΔIJH ≅ ΔKHJ, by SSS criterion and we need;
ΔTNS and ΔUHS are right-triangles and S is the mid-point.
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Determine whether the relation is a function.
Carlos has chosen 12 different CDs he would like to buy: 4 are rap music, 5 are country, and 3 are heavy metal. He has only enough money to buy 5 of them (each CD costs the same price). So he selects 5 of them at random. What is the probability that his purchase includes at least one CD from each of the three genres.
Answer:
The probability is 0.7449
Step-by-step explanation:
Given
[tex]n = 12[/tex] ---- total
[tex]r = 5[/tex] --- selection
[tex]Genre =\{Rap(4), Country (5), Heavy\ metal (3)\}[/tex]
Required
Probability of buying at least 1 of each genre
First, we calculate the total possible selection.
To select 5 CDs from a total of 12, we use:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
[tex]^{12}C_5 = \frac{12!}{(12 - 5)!5!}[/tex]
[tex]^{12}C_5 = \frac{12!}{7!5!}[/tex]
Expand
[tex]^{12}C_5 = \frac{12*11*10*9*8*7!}{7!*5*4*3*2*1}[/tex]
[tex]^{12}C_5 = \frac{12*11*10*9*8}{5*4*3*2*1}[/tex]
[tex]^{12}C_5 = \frac{95040}{120}[/tex]
[tex]^{12}C_5 = 792[/tex]
So, the total selection is:
[tex]Total = 792[/tex]
To select at least 1 from each genre, there are 6 possible scenarios.
And they are:
[tex]\begin{array}{ccc}{Heavy\ Metal (3)} & {Rap (4)} & {Country(5)} & {3} & {1} & {1} & 2 & {1} & {2} & {2} & {2} & {1}& {1} & {2} & {2}& {1} & {3} & {1}& {1} & {1} & {3} \ \end{array}[/tex]
The possible selections for the given scenario is:
[tex]Possible = ^3C_3* ^4C_1 * ^5C_1 +^3C_2* ^4C_1 * ^5C_2 +^3C_2* ^4C_2 * ^5C_1 +^3C_1* ^4C_2 * ^5C_2 +^3C_1* ^4C_3 * ^5C_1 +^3C_1* ^4C_1 * ^5C_3[/tex]
Using a calculator, we have:
[tex]Possible = 1*4*5 +3*4*10 +3*6*5 +3*6*10+3*4*5+3*4*10[/tex]
[tex]Possible= 20 +120 +90 +180+60+120[/tex]
[tex]Possible = 590[/tex]
The probability is then calculated using:
[tex]Pr = \frac{Possible}{Total}[/tex]
[tex]Pr = \frac{590}{792}[/tex]
[tex]Pr = 0.7449[/tex]
Suppose that you want to begin saving money to buy a house valued at $300,000. The bank recommends that you have a 20% down payment before it approves a loan for the remaining difference. How much money do you need to save before you will be approved for a loan? What is the remaining difference that you will need to borrow?
Answer:
$60,000 as down payment and remaining difference for loan is 300,000 - 60,000 = $240,000.
The money you need to save before you will be approved for a loan is $60,000 and the remaining difference that you will need to borrow is $2,40,000
What is a percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
What is a loan?A loan is money, property, or other material goods given to another party in exchange for future repayment of the loan value amount with interest.
Given value of the house is $300,000.
The bank recommends that you have a 20% down payment before it approves a loan i.e. is $300,000× 20% = $60,000
The remaining difference that you will need to borrow is $300,000 - $60,000= $2,40,000
Thus the money you need to save before you will be approved for a loan is $60,000 and the remaining difference that you will need to borrow is $2,40,000
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At a state fair, there are 10 animal exhibits, 12 gardening exhibits, and 8 farm equipment exhibits. Describe a model that you could use to simulate randomly choosing an exhibit to visit.
Answer:
10:12:8
Step-by-step explanation:
so, there are 10 animal exhibits, 12 gardening exhibits, and 8 farm equipment exhibits. so it would look like this 10:12:8
SOMEONE HELP! I don’t understand
Answer:
Step-by-step explanation:
That is not possible.
express a decade as a percentage of a century
PLEASE HELP ME ASAP NOW PLEASE
The lines with a slope larger than f(x) are:
option 4) y = (25/3)*x - 1/2
option 5) (4/5)*y - 16x = -1/2
Which one is the linear equation shown on the graph?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
First, you can see that the line crosses the y-axis at y = -4, so the line is something like:
y = a*x - 4
And we can see that it crosses the x-axis at x = 2, then we can write the equation:
0 = a*2 - 4
4 = a*2
4/2 = a
2 = a
So the linear equation on the graph is:
y = 2*x - 4
The slope is 2, the linear equations with a slope larger than that are:
option 4) y = (25/3)*x - 1/2
option 5) (4/5)*y - 16x = -1/2
Which can be rewritten as:
y = (5/4)*16x - (5/4)*(1/2)
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convert 84 min into fraction
Answer:
84/60
Step-by-step explanation:
1 hour is 60 minutes so 84 minutes /60 gives how much it is in hours
A tourism website claims travelers can see Europe for $75 a day. If a tourist saved $1,875 for a vacation, how many days can he spend in Europe?
hello- need help on this :)
What is the equation of a line with the slope of 3 that goes through the
point (0,-7)?
9514 1404 393
Answer:
y = 3x -7
Step-by-step explanation:
The given point is the y-intercept, so we can write the equation in slope-intercept form.
y = mx + b . . . . . line with slope m through point (0, b)
For your slope and point, the equation is ...
y = 3x -7
1. choices : never. always. sometimes
2. choices: never. always. sometimes
3.choices: variables. coefficient. exponents
4:choices: variables. coefficient. exponents
5. choices: not closed. closed
please help
The product of f(x) and g(x) is always a polynomial. By the definition of
polynomials the product of polynomials is always a polynomial because
the coefficient are real numbers and the exponents are whole
numbers. Real numbers and whole numbers are closed under addition
and subtraction.
What is Polynomial?A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) with coefficients, that is either a constant or the indeterminates (also called variables or x's). The most common examples are the quadratic equation, cubic equation, and so on. The degree of a polynomial is the highest power of the indeterminate in the polynomial. For example, a polynomial with three indeterminates to the power of 2 is said to have a degree of 2.
Here f(x) and g(x) are two given polynomial,
let f(x) = x+1 ang g(x) = x-1
f(x).g(x) = (x+1)(x-1).
f(x).g(x) = x²-1.
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Alice reads a scatterplot that shows data for nine schools. It relates the percentage of students receiving free lunches to the percentage of students wearing a bicycle helmet. The plot shows a strong negative correlation. Alice recalls that correlation does not imply causation. In this example, Alice sees that increasing the percentage of free lunches would not cause children to use their bicycle helmets less.
Identify the confounding variable that is causing Alice's observed association.
a. The number of bike helmets available
b. Parents' income
c. School funding
d. The number of free lunches available
Answer:
Parents' income
Step-by-step explanation:
The confounding variable also called the third or lurking variable is usually an unaccounted for variable or factor which may creep into our research, Hence, causing an association or relationship which does not actually exists between the two correlated variables. In the experiment abive, there is no really any actual relationship between increasing percentage of free lunch and less usage of bicycle helmets.
However, We may attribute the change in bicycle helmets used by the children to a swerve or change in the income of the parents of the students, being able to afford a bicycle helmet will depend in the income of the parent and this mightvhave caused the observed association between the variables.
Answer:
parents income
Step-by-step explanation:
Which property is demonstrated below?
a times c = c times a
A.
associative property
B.
distributive property
C.
commutative property
D. identity property
Answer:
distributive property is your answer
The graphs of lines a and b are shown on the coordinate
plane. Write the equation on the line provided for each line.
Then solve the system of equations using any method.
The equation of line a is.
The equation of line b is.
Solution
From the graph we got two equations of line -3x+ y -9 =0 and x+y-7 =0
and solution of these equations are x = -1/2 and y= 15/2
what is equation of line?An algebraic expression that represents a number of points which creates a line in the XY coordinate system or another coordinate plane.
What is the equation of lines shown in the graph?
we are given a graph containing two equations of line named a and b. The lines are plotted in XY coordinate system.
From the graph, we can detect two locations of point (5, 6) and (1, -6) for line a and detect two location of point (1, 6) and (6, 1) for line b.
As per the formula for equation of straight line, a line passes through two points can be written as y-y₁ = [(y₂-y₁) / (x₂-x₁)] × (x- x₁)
hence, line a can be written as (y- 6) = [(-6 -6) / (1-5)] × (x- 5)
y-6 = 3(x-5)
y-6 = 3x -15
y-3x -9 = 0
In the next, line b can be written as (y-6) = [(1-6) / (6-1)] × (x-1)
y-6 = -1(x-1)
y-6 = -x+1
x+ y -7 =0
now, we get two equations, -3x+ y -9 =0
x+ y - 7 =0
Solving these two equations by addition method, we get x= -1/2 and y = 15/2
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Which expression is equivalent to -3(x+4)(x-6)-(x^2+8x-10)?
Answer:-4x^2-2x+46.
Step-by-step explanation:
To simplify this expression, you can start by distributing the negative sign to the first set of parentheses:
(-3)(x+4)(x-6)-(x^2+8x-10)
Then, you can distribute the -3 to the terms inside the first set of parentheses:
(-3x-12)(x-6)-(x^2+8x-10)
Then, you can combine like terms:
-3x^2+6x+36-x^2-8x+10
This simplifies to:
-4x^2-2x+46
Therefore, the expression that is equivalent to -3(x+4)(x-6)-(x^2+8x-10) is -4x^2-2x+46.
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Jamie has 18/5 cups of frosting she uses 2/5 cups of frosting for each cupcake how many cupcakes will Savannah be able to frost
Answer:
9
Step-by-step explanation:
18/5 ÷ 2/5 = 18/5 x 5/2 = 9
Jessie is building a cabinet door, which is pictured below. The center of the cabinet door is 12 inches by 16 inches, and the border of the cabinet door has a width of x inches. The entire cabinet door has an area of exactly 396 square inches.
Clockwise from the top, the picture reads, x, 12 inches, 16 inches, x, Figure not drawn to scale.
Write an equation in standard form that can be used to find x , the width of the border.
Answer:
[tex]x^2+14x-51=0[/tex]
Step-by-step explanation:
Since the entire cabinet door is a rectangle, its area is given by:
[tex]A=w\ell[/tex]
The center of the cabinet door measures 12 inches by 16 inches.
And the border of the cabinet door has a width of x inches.
Therefore, the total width of the cabinet door will be (12 + 2x).
Likewise, the total length of the cabinet door will be (16 + 2x).
Thus, the area of the entire cabinet door will be:
[tex]A=(2x+12)(2x+16)[/tex]
We are given that this entire area is 396 square inches. Thus:
[tex]396=(2x+12)(2x+16)[/tex]
Simplify. We can factor out a two from both of the factors on the right-hand side:
[tex]396=2(x+6)(2)(x+8)[/tex]
So:
[tex]396=4(x+6)(x+8)[/tex]
Dividing both sides by four yields:
[tex]99=(x+6)(x+8)[/tex]
Distribute the right-hand side:
[tex]x^2+14x+48=99[/tex]
Therefore, our equation in standard form is:
[tex]x^2+14x-51=0[/tex]
Edit:
We want to find the width of the board. So, we simply have to solve for x. We previously obtained:
[tex]x^2+14x-51=0[/tex]
We can factor:
[tex](x+17)(x-3)=0[/tex]
By the Zero Product Property:
[tex]x+17=0\text{ or } x-3=0[/tex]
Solve for both cases:
[tex]x=-17\text{ or } x=3[/tex]
Length/width cannot be negative. So, we can reject the first solution.
Thus, our only solution is:
[tex]x=3[/tex]
The width of the border of the cabinet door is 3 inches.
This means that the total length of the cabinet is 16 + 2(3) = 22 inches, and the total width of the cabinet is 12 + 2(3) = 18 inches.
Please helppp can’t figure this one out. Keep getting 8.1
In the algebraic expression, 6x + 10, x is the (blank), 6 is the (blank), and 10 is the (blank)?
In the algebraic expression, 6x + 10, x is the variable, 6 is the coefficient and 10 is the constant.
What are algebraic expressions?
Algebraic expressions are mathematical phrases that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. They can be used to represent mathematical operations and relationships between numbers.
Examples of algebraic expressions include:
2x + 3 (This is an expression that represents the sum of 2 times the value of x plus 3)
A letter or symbol that denotes an unknowable value is called a variable. The variable here is represented by x.
A coefficient is a number that is multiplied by a variable in an algebraic expression. In this case, 6 is the coefficient of x.
A constant is a value that does not change in an algebraic expression. In this case, 10 is the constant.
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write a word problem and make and explain a math drawing for 4×3/4=?
Answer:u cheating like a mfka lol
Step-by-step explanation:dwd
The price of premium fuel has increased from 289.7 cents per litre to 297.9 cents per litre. Calculate the percentage increase
Answer:
≈ 2.76%
Step-by-step explanation:
Price increase
297.9 - 289.7 = 8
% increase
8/289.7 * 100 = 2.7614773904%
≈ 2.76%
Population Growth
What is the growth rate of the function y = 3 · 2×?
a. 3 c. 1
b. 2 d. 6
Please select the best answer from the choices provided
Answer:
C. 1
Step-by-step explanation:
I calculated it logically
Step-by-step explanation:
The correct choice is C
C.1
BRAINILIEST PLEASESolve the system of equations -x-y=-2 and 5x + 7y= 28 by combining the
equations.
Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.
What is equation?The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.
Here,
Given :
=> -x-y=-2
=> 5x + 7y= 28
So ,
=>x = 2-y
thus,
=> 5(2-y) + 7y =28
=> 10 -5y + 7y =28
=> 10 -2y = 28
=> -2y = 18
=> y =-9
and
=> x = 2 - (-9)
=> x = 11
Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.
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A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses 1 2/3 pounds of gravel. For each pound of gravel, he uses 2/5 pound of cement. He is making enough concrete that he needs to use 3 pounds of sand. How many pounds of cement does he use? PLEASE HELP DUE NOW !! TYYY
A. 1 pound
B. 1 4/15 pounds
C. 2 pounds
D. 2 1/15 pounds
Answer:
C
Step-by-step explanation:
1 pound sand for 1 2/3 pounds gravel.
1 pound gravel for 2/5 pound cement.
3 pounds sand = 3× 1 2/3 = 3 6/3 = 3+2 =
= 5 pounds gravel.
5 pounds gravel = 5 × 2/5 = 2 pounds of cement
A woman leaves home at 7 am and drives to New York City 200 miles away. If she averages 50 miles per hour, what time will she arrive at the city
Find time needed to drive 200 miles:
50 miles = 1 hour
1 mile = 1/50 hour
200 miles = 1/50 x 200 = 4 hours
Find time of arrival:
7:00am + 4 hours = 11am
Answer: She will arrive at 11am
Answer:
The woman will arrive at New York City at 11 am.
Step-by-step explanation:
At an average speed of 50 miles per hour, it will take the woman 4 hours to reach New York City. If she leaves at 7 am, she will arrive at 11 am. Here's the math:
200 miles / 50 miles per hour = <<200/50=4>>4 hours
7 am + 4 hours = 11 am
So the woman will arrive at New York City at 11 am.
(30 points easy) write the equation of side B seat inside AC to determine if the three points could form a right triangle
write the equation of the line for side B C, and side AC, If the points were connected, could this be a right triangle explain why
(use the graph in the photo)
Answer:
Side BC: y = -2x + 10
Side AC: y = 2x + 4
Yes, these three points could form a right triangle. This is because the slopes of the two lines, Side BC and Side AC, are opposite reciprocals of each other. This means that when the two lines intersect, they will form a right angle.
What is the probability of rolling a 5 on a fair number cube 5 times in a row?
Answer:
Impossible
Step-by-step explanation:
Answer:
1/7778
Step-by-step explanation:
We multiply each event
1/6 x 1/6 x 1/6 x 1/6 x 1/6 =
1/36 x 1/36 x 1/6
= 1/7776
Prove that if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0
The proof that if if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0 is made by contradiction in this problem.
What is a proof by contradiction?Proof by contradiction is different of traditional proof because it accepts a single example showing that a statement is false, instead of having the need to derive a general relationship for all input values.
For this problem, we must assume the case in which at least one of the terms is non-zero, hence we assume that A is non-zero, hence the expression would be given as follows:
A² + B² + C² = 0
A² = -(B² + C²)
This means that the square of A would be negative. However, the square of a number is always a non-negative number, hence this equation above is a contradiction.
This contradiction was used to prove that if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0.
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