Different arrangements of the display are possible is 2520.
Given:
the artist r. locklen jones selects 5 paintings from a collection of 7 to display in a row.
Permutation :
A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order.
= [tex]7_P_5[/tex]
we know that,
[tex]n_P_r[/tex] = n! / ( n - r ) !
[tex]7_P_5[/tex] = 7! / ( 7 - 5 ) !
= 7! / ( 2 ) !
= 7! / 2!
= 7 * 6 * 5 * 4 * 3 * 2! / 2!
= 42 * 20 * 3
= 840 * 3
= 2520
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√3 + (4 + √x + 3)² / 6 = 3
Answer: x = 1
Step-by-step explanation:
6x^3+2x^2+3x -(3x^3-2x^2-3x)
The simplest form of the given expression is 3x³+4x²+6x
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical operation, and extraction of roots.
Main body:
according to question ,
6x³+2x²+3x -(3x³-2x²-3x)
we need to simplify the given equation.
firstly opening the bracket and taking care of sign,
⇒6x³+2x²+3x -3x³ +2x² +3x
taking like terms seperately,
⇒6x³ -3x³ +2x²+2x²+3x+3x
⇒3x³+4x²+6x
Hence the simplest form of the given expression is 3x³+4x²+6x
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Find the slope of the line that passes through all of the points on the table.
I need help badly.
0.000236 to 3 significant figures.
Answer:
It is rounded to 3 sig figs already
Step-by-step explanation:
The formula A=23.1 е⁰⁰¹⁵²⁺ models the pollution of US state, a, in millions ,t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was million.
The population of the state is 23.1 million
The population of the state will reach 28.3 million in 13.5 years
What is population ?
Any whole group that shares at least one trait is referred to be a population. People do not make up all populations. Populations can include, but are not limited to, individuals, animals, organizations, structures, buildings, cars, farms, objects, or occasions.
The population state is:
A = 23.1*e^(0.0153*t)
In millions.
Where t represents the number of years after 2000.
a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).
A(0) = 23.1*e^(0.0153*0) = 23.1
The population at year 2000 was 23.1 millions.
b) Now we want to solve:
A(t) = 28.3 = 23.1*e^(0.0153*t)
28.3/23.1 = e^(0.0153*t)
1.23 = e^(0.0153*t)
Now we can apply the natural logarithm to both sides:
ln(1.23) = ln( e^(0.0153*t) )
ln(1.23) = 0.0153*t
ln(1.23)/0.0153 = t = 13.5
So 13.5 years after 2000 the population will be 28.3 million.
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One angle measures 160°, and another angle measures (3k + 61)°. If the angles are vertical angles, determine the value of k.
k = 14
k = 33
k = 74
k = 160
Answer:
Therefore, the value of k is 1.
Step-by-step explanation:
Vertical angles are pairs of angles that are opposite each other and are formed by two intersecting lines. If one angle measures 160°, the other angle must measure 180° - 160° = 20°. Therefore, if the other angle measures (3k + 61)°, we can set up the equation 20 = 3k + 61. Solving for k, we get k = -41. However, since the value of k must be a positive integer, the only possible value of k is k = 1. Therefore, the value of k is 1.
Answer:
k = 33
Step-by-step explanation:
8x³ +16x² + 12x+13)÷(2x+2)
Find quotient and remainder
The degree of the remainder is less than the degree of the divisor, we have found the complete remainder. Therefore, the quotient is 4x² + 8x + 6, and the remainder is -16x² -16x.
What is the quotient?
The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.
To find the quotient and remainder when dividing 8x³ +16x² + 12x+13 by 2x+2, we can use polynomial long division.
First, we divide the leading coefficient of the dividend (8x³) by the leading coefficient of the divisor (2x). This gives us a quotient of 4x². We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the first term of the remainder:
8x³ +16x² + 12x + 13
(2x+2)(4x²)
8x³ - 8x³ -8x² -8x² +12x+13
This leaves us with 12x+13 as the first term of the remainder.
Next, we bring down the next term of the dividend (16x²) and divide it by the leading coefficient of the divisor (2x). This gives us a quotient of 8x. We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the next term of the remainder:
12x+13
(2x+2)(8x)
12x+13 - 16x² - 16x
-4x² -4x
This leaves us with -4x² -4x as the next term of the remainder.
Finally, we bring down the last term of the dividend (12x) and divide it by the leading coefficient of the divisor (2x). This gives us a quotient of 6. We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the final term of the remainder:
-4x² -4x
(2x+2)(6)
-4x² -4x -12x -12
-16x² -16x
This leaves us with -16x² -16x as the final term of the remainder.
Hence, the degree of the remainder is less than the degree of the divisor, we have found the complete remainder. Therefore, the quotient is 4x² + 8x + 6, and the remainder is -16x² -16x.
We can write the result of the division as:
(8x³ + 16x² + 12x + 13) ÷ (2x+2) = (4x² + 8x + 6) + (-16x² -16x)/(2x+2)
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20 + 4 (3x - 5) + 2x = 28
How can I get the answer and please explain step by step!
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
Equation
[tex]20 + 4(3x-5)+2x=28[/tex]
Expand the brackets
[tex]20 + 12x- 20 + 2x=28[/tex]
Combine like terms
[tex]14x=28[/tex]
Solve
[tex]x=2[/tex]
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Q1 - Similar shapes and area
Work out the missing area in each pair of similar shapes.
The answer for the first shape would be 24cm^2.
The answer for the second shape would be 20cm^2.
The answer for the third shape would be 30cm^2. "30".
What are Shapes?
A shape in geometry can be characterized as an object's form, outline, outer border, or outer surface.
Every object we notice in the world has a form. The objects we see around us may be broken down into several fundamental forms, such as the two-dimensional square, rectangle, and oval, or the three-dimensional rectangular prism, cylinder, and sphere few types of Shape.Shapes establish an object's perimeter and may be distinguished in a variety of ways depending on their characteristics. In a Shape a border that is created by merging the curves, points, and line segments surrounds these forms. The name of each form depends on the structure. Circle, square, rectangle, triangle, and other simple forms are few types of Shape.The first shape seems to be scaling up. From 3cm to 12cm. So for this you need to multiply. Using the formula that I gave you last time.
3cm times ___ = 12cm. 4 fits in there,
therefore 6cm^2 times 4 = 24cm^2.
The answer for the first one would be 24cm^2. "24" in the blank.
The second shape seems to be scaling down. From 16cm to 8cm. So for this you need to divide.
16cm divided by ___ = 8cm. 2 fits in there,
therefore 40cm^2 divided 2 = 20cm^2.
The answer for the second one would be 20cm^2. "20" in the blank.
The third shape seems to be scaling up.
From 3cm to 4.5cm.
So for this you need to multiply. 3cm times ___ = 4.5cm.
Now since we're dealing with decimals, not whole numbers this time you can't really use guess and check as efficiently. So you do the opposite operation, which in this case the opposite of multiplication is division.
You take 3cm (the original shape's number) and divide it into 4.5cm. So 4.5cm divided by 3cm = 1.5. 1.5 fits in there,
therefore 20cm^2 times 1.5 = 30cm^2.
The answer for the third one would be 30cm^2. "30" in the blank.
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El primer término en una serie geométrica es 64 y la razón común es 0.75
Answer:
Si...
En una progresión geométrica se conocen a1 = 64 y r = 0,75
Xavier is riding on his bike at a constant speed of 15
miles per hour. What is the closest approximation of
how long it will take Xavier to ride 5 miles?
A. 0.15 hour
B. 0.2 hour
C. 0.33 hour
D. 0.5 hour
Answer:
C. 0.33 hour
Step-by-step explanation:
15 miles = 1 hr
5 miles = x hr
cross multiply
5 = 15x
x = 5/15
x = 0.333 hr
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4. Which statement best describes the relationship in the table?
Months 12 24 36 48
Years 1 2 3 4
a. The constant of proportionality is 0.
b.The constant of proportionality is 4.
c. The number of months is proportional to the number of years?
d. The number of months is not proportional to the number of years?
On solving the provided question, we got that the number of months is proportional to the number of years
What is proportionality>When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.
What do you think about proportionality?We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
Here,
12/1 = 12
24/2 = 12
36/3 = 12
48/4 = 12
So, They are proportional to each other.
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PLEASE HELP ASAP!!!! FULL ANSWER ONLY!!!
A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The quadratic function h = − 16 t^2 + 84 t + 72 models the ball's height above the ground, h , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? ____________ feet
b) How many seconds does it take until the ball hits the ground? ____________ seconds
What is the maximum height of the ball 182.25 feet
How many seconds does it take until the ball hits the ground 6 seconds
How to find the maximum height of the ballThe maximum height will occur at the vertex v(h', k)
h' = -b/2a
From the equation h = − 16 t^2 + 84 t + 72
a = -16
b = 84
h' = -84/(2 * -16)
h' = t = 2.625
k = h = − 16 t^2 + 84 t + 72 at t = 2.625
= − 16 * 2.625^2 + 84 * 2.625 + 72
= 182.25 feet
The ball hits the ground when h = 0
0 = − 16 t^2 + 84 t + 72
solving the quadratic equation gives
t = 6 OR -3/4
Use the positive value
t = 6 seconds
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fhyyyyyyyyyyyyyyyyyyyyytttttttttttttttttttttttttttttttttttttttttgsdddddddddddddtttttttt
Answer:
Step-by-step explanation:
there is no answer it just a bunch of f,h,y and t this is not math this is something
(a) Complete this synthetic division table.
-2√-1 2 12 0 -16
(b) Write your answer in the following form: Quotient + Remainder / x+2
-x⁴+2 x³+12 x²-16 / x+2= ____+ _____ / x+2
a) The synthetic division table is given by the image shown at the end of the answer.
b) The result of the division is given as follows:
-x³ + 4x² + 4x - 8 + 0/x + 2.
How to apply the synthetic division algorithm?In the synthetic division algorithm, the coefficients of a polynomial, which is the dividend, are each divided by a value.This divisor is the goes into the far left box.In this problem, the dividend is given as follows:
-x^4 + 2x³ + 12x² - 16.
Hence the coefficients are given, respectively, by:
-1, 2, 12, 0 and -16.
The divisor is of:
x + 2.
Hence the term on the left box is of:
x + 2 = 0 -> x = -2.
Then the procedure goes as follows:
-1 is multiplied by -2 and added to 2, result of 4.4 is multiplied by -2 and added to 12, result of 4.And the same logic follows until the last term.From the coefficients of the bottom box, we have that:
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for any relation r, if, for every valid instance of a, that value of a uniquely determines the value of b:
"In a relation r, for every instance of a, that value of a uniquely determines the value of b then a primary dependency exists in the relation.
Relation:
In math relation means the relationship between sets of values of ordered pairs.
Given,
Here we need to find if for every valid instance of a, that value of a uniquely determines the value of b in the relation.
As per the definition of relation, for every relation has two set of data ad each of the element in one set is uniquely refers the other one's element.
Here we have to identify the type of relation between a an b.
Here we have given that the relation a uniquely determines the value in b.
So, this type primarily refers the dependency of the relation.
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changing tne value of m in f(x)=mx+b resulst in a (translation or rotation) of the graph
?????
Answer:
Rotation
Step-by-step explanation:
The function [tex]f(x)=mx+b[/tex] , is the equation of a line given in slope-intercept form. Where m is the slope of the line and b is the y-intercept of the line. If you were to change the value of m, while keeping the value of b the same, that would result in a rotation. If you were to change the value of b, while keeping the value of m the same, that would result in a translation (specifically a vertical translation).
If 3000 dollars is invested in a bank account at an interest rate of 10 per cent per year, Find the amount in the bank after 10 years if interest is compounded annually:
Find the amount in the bank after 10 years if interest is compounded quaterly:
Find the amount in the bank after 10 years if interest is compounded monthly:
Answer:
Step-by-step explanation:
100%-10%=90%
90/100=0.9%
3000*0.9^10 years= 1046.04
Step-by-step explanation:
For annually,
3000×(1.10)^10= 7781.23
For quarterly,
3000×(1.10)^40= 135777.77
For montly,
3000×(1.10)^120=278127206.5
Consider the equation 5y + 9 =
Which value or expression can you write in the blank so the equation
has no solution?
0
9
5y
+2.
7y
The equation has no solution if the blank is filled with 5y, so option c is correct.
What is equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.
Given equation:
5y + 9 = _
Use the hit and trial method and put the value zero,
5y + 9 = 0
y = -9 / 5
So the equation has a solution,
Again put
5y + 9 = 5y
9 = 0, which is not possible
Therefore, the equation has no solution if we fill the blank with 5y.
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Help help help help help help
Answer:
Andre walks more steps
Step-by-step explanation:
Step-by-step explanation:
dawn step rate=8400/60=140step/he
dawn step=140×240=33600 steps
teddl step=142 ×240 =34080
Help Please!!!!!!!!!!!!
The packages a and b together weigh 6kg
Package a is twice as heavy as package b
Find the weight of package a and find the weight of package b
The Bateria in a culture increases according to the law [tex]\frac{ds}{dt} = \frac{N}{4}[/tex]
if intially N = 200, then what is thevalue of N when t = 200
The required value of N when t = 200 is given as 10,000.
Given that,
The Bateria in culture increases according to the law ds/dt = N/4
if intially N = 200, then what is the value of N when t = 200 is to be determined.
Rate of change is defined as the change in value with rest to the time is called rate of change.
Here,
ds/dt = N/4 = 200/4 = 50
Now,
N = 50t
N = 50[200]
N = 10,000
Thus, the required value of N when t = 200 is given as 10,000.
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A garden table and a bench cost $821 combined. The garden table costs $71 more than the bench. What is the cost of the bench?
X
The cost of the bench is $ 375 and the Cost of the garden table is $ 446.
Calculating Unknown Quantity:We can Calculate unknown quantities mathematically using Algebra Expressions. Unknown values in an equation are represented by variables, which are often represented by a letter of the alphabet like x, y, and z or a, b, and c, etc.
Here we have
A garden table and a bench cost $ 821 combined
Let x, and y be the cost of the garden table and bench
Given that
The garden table costs $71 more than the bench.
=> x = y + $ 71 ---- (1)
It is also given that
The total cost of the garden table and a bench = $ 821
=> x + y = 821
=> y + 71 + y = 821
=> 2y = 821 - 71
=> 2y = 750
=> y = 375
=> Cost of bench, y = $ 375
=> The cost of the garden table, x = $ 375 + $ 71 = $ 446
Therefore,
The cost of the bench is $ 375 and the Cost of the garden table is $ 446.
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Find the measure of angle b.
59°
A) 69°
C) 21°
B) 121°
D) 159
Answer:
he answer is B
Step-by-step explanation:
Total angle is 180°
angle a=59°angle b=180°-59°=121°
need help!!! with geometry
The value of r is 45 and the value of s is 29
Calculating value of missing variablesFrom the question, we are to solve the parallelogram for the missing variables.
The missing variables are r and s
Since opposite angles of a parallelogram are equal, we can write that
(r - 10)° = (3r - 100)°
Solve for r
r - 10 = 3r - 100
-10 + 100 = 3r - r
90 = 2r
r = 90/2
r = 45
Also,
We can write that
(5s)° = (4r - 35)°
Substitute the value of r and solve for s
5s = 4(45) - 35
5s = 180 - 35
5s = 145
s = 145/5
s = 29
Hence, r = 45, s = 29
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Consider the conversion facts 1 inch = 2.54 centimeters and 1 centimeter = 0.39 inch.
a. Write an expression for the exact number of inches in 1 centimeter.
1 cm = -in.
b. Use a calculator to evaluate your expression in part (a). Round to the nearest ten thousandths if necessary.
1 cm =
in.
he clightly different when converting botung
The expression for the exact number of inches in 1 centimeter is 2.54/2.54 cm = 1/2.54 in and the number of inches is 0.39
How to determine the expression?From the question, we have the following parameters that can be used in our computation:
1 inch = 2.54 centimeters and 1 centimeter = 0.39 inch.
To calculate the number of inches expression, we make use of the following equation
1 inch = 2.54 centimeters
Divide both sides of the equation by 2.54
So, we have the following representation
1/2.54 inch = 2.54/2.54 centimeters
Rewrite the expression as
2.54/2.54 centimeters = 1/2.54 inch
So, we have
2.54/2.54 cm = 1/2.54 in
So, the expression is 2.54/2.54 cm = 1/2.54 in
The value of the expressionIn (a), we have'
Expression: 2.54/2.54 cm = 1/2.54 in
This implies that
2.54/2.54 cm = 1/2.54 in
Evaluate the quotients
1 cm = 0.39 in
Hence, the value is 0.39 inches
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The length of rectangle is twice its width.How many times long as the width of the rectangle is the perimeter of the rectangle.
Step-by-step explanation:
w=x
l=2x
p=2(l+w)
p=2(2x+x)
p=6x
Station 2: Unit 3 and Unit Linear Functions given the table x 9,3,-3,-9 y 2,-2,-6,-10 ,
Find equation slope form answer the following questions.
Answer:
y = (2/3)x - 4
Step-by-step explanation:
To find the equation of the line in slope-intercept form given a table of values, you will need to calculate the slope of the line and the y-intercept. The slope of a line is a measure of its steepness, and it is calculated as the rise (change in y-values) divided by the run (change in x-values) between two points on the line. The y-intercept is the point at which the line crosses the y-axis.
Given the table x: 9, 3, -3, -9 and y: 2, -2, -6, -10, you can use any two points to calculate the slope. For example, you could use the points (9, 2) and (3, -2) to calculate the slope:
slope = (y2 - y1) / (x2 - x1) = (-2 - 2) / (3 - 9) = -4 / -6 = 2/3
To find the y-intercept, you can use the slope and one of the points from the table to substitute into the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Using the slope and the point (9, 2), you can solve for b:
y = mx + b
2 = (2/3) * 9 + b
2 = 6 + b
b = -4
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 4.
To answer the other questions, you can use this equation to determine the y-value for a given x-value or the x-value for a given y-value. You can also use the equation to graph the line on the coordinate plane.
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42