Answer:
10.7cm
Step-by-step explanation:
x^2= 115
x = √115
x = 10.7
Find an explicit formula for the geometric sequence -3, -12, -48, -192, -768
Answer:
a4 = -3 * 4^(4-1) = -3 * 4^3 = -3*64 = -192
Step-by-step explanation:
A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is always the same. In this case, the given sequence is -3, -12, -48, -192, -768.
To find the explicit formula for this geometric sequence, we can use the following formula:
an = a1 * r^(n-1)
where:
a1 is the first term in the sequence (-3)
an is the nth term in the sequence
r is the common ratio (the ratio between any two consecutive terms)
To find the common ratio, we can divide -12 by -3, -48 by -12, -192 by -48, and -768 by -192, and in all cases we get r = 4
Therefore, the explicit formula for this geometric sequence is:
an = -3 * 4^(n-1)
This formula can generate any term of the sequence given the value of n.
So, for example, the fourth term of the sequence, -192, can be obtained by inputting n = 4 in the explicit formula:
a4 = -3 * 4^(4-1) = -3 * 4^3 = -3*64 = -192
Function g is a transformation of the parent function f(x) = x^2. The graph of g is a translation right 5 units and up 1 unit of the graph of f. Write the equation for g in the form y = ax^2 + bx + c.
Answer: A transformation of a function such as y = f(x) is a way to change the appearance of its graph by applying certain rules to it. In this case, the graph of function g is a translation right 5 units and up 1 unit of the graph of f.
To find the equation of the transformed function g, we can take the equation of the parent function, which is y = f(x) = x^2 and apply the translation rules (right 5 units and up 1 unit) to it.
The translation right 5 units means that the x-coordinate of each point on the graph of f is increased by 5 units. So this can be written as x = x+5
The translation up 1 unit means that the y-coordinate of each point on the graph of f is increased by 1 units. So this can be written as y = y+1
Substituting x = x+5 and y = y+1 in the equation of the parent function y = x^2 gives the equation of g in the form:
y = (x+5)^2 + 1
So the equation of g is y = (x+5)^2 +1
This equation is a parabola with a vertex that
Step-by-step explanation:
[tex]\frac{6y-1}{y} -2=3[/tex]
[tex]\dfrac{6y-1}{y} -2=3[/tex]
Simplify:
[tex]6y-1-2y=3y[/tex]
[tex]4y-1=3y[/tex]
Subtract 3y from both sides:
[tex]4y-1-3y=3y-3y[/tex]
[tex]y-1=0[/tex]
Add 1 to both sides:
[tex]y-1+1=0+1[/tex]
[tex]\fbox{y = 1}[/tex]
Identify the property shown by each statement
1. 4m x 0 x 3m = 0
2. 5 + (a + 17) = (5 + a) + 17
The properties shown in each statement are given as follows:
1. 4m x 0 x 3m = 0 -> neutral element of the multiplication.
2. 5 + (a + 17) = (5 + a) + 17 -> associative property of addition.
What are the properties of each expression?
The first expression is given as follows:
4m x 0 x 3m = 0.
A multiplication by zero will always result in a value of zero, hence the property is of the neutral element of the multiplication.
The second expression is given as follows:
5 + (a + 17) = (5 + a) + 17.
The change is in the order in which the terms are added, which does not change the value of the sum, hence the property is the associative property of addition.
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a rectangule has a preimeter of 446 feet. the rectangle has a length of (13x-1) feet and a width of (9x +4) feet. find the length and width of the rectangle
Answer:
Below
Step-by-step explanation:
Perimeter = 446
446 = (13x-1) + (13x-1) + (9x+4) + (9x+4) ft <====four sides added together
446 = 44x +6
440 = 44x
x = 10 then width = 9(10)+4 = 94 ft Length = (13(10)-1) = 129 ft
What is the name for a line that intersects two or more lines?
Answer:
line that intersects two or more lines at a distinct points is known as transversal line.
You deposit $320 in an account that earns simple interest at an annual rate of 7.5% IS there enough money in the account after 3 years to buy a game console that costs $400?
Answer:
no
Step-by-step explanation:
simple interest formula:
final amount = initial balance * (1 + interest rate * time)
rate = 7.5% = 0.075
initial balance = 320
time = 3
is the final amount of 320 * (1 + 0.075 * 3) greater than or equal to 400?
320 * (1 + 0.075 * 3) = 392 so no
-.Write two different expressions you could use to represent the
combined area of the Description and Small Diagram sections.
What information about the combined area does each
expression show?
Answer:
hey please check my next questioj
Determine whether each question is an example of a statistical question. Drag each question to the correct classification in the table.
Statistical Question:
Not a Statistical Question:
How tall is the Eiffel Tower?
What is the distance from my school to the fire station?
What is the number of days my friends spend at camp every summer?
How many miles do the teachers at our school drive per year?
What is the number of hours sixth graders spend playing sports each week?
Answer: Statistical Question:
What is the number of days my friends spend at camp every summer?
How many miles do the teachers at our school drive per year?
What is the number of hours sixth graders spend playing sports each week?
Not a Statistical Question:
How tall is the Eiffel Tower?
What is the distance from my school to the fire station?
The questions "How tall is the Eiffel Tower?" and "What is the distance from my school to the fire station?" are not statistical questions because they are asking for a single, specific value, rather than a range of values or a pattern among a group of data.
On the other hand, "What is the number of days my friends spend at camp every summer?", "How many miles do the teachers at our school drive per year?" and "What is the number of hours sixth graders spend playing sports each week?" are statistical questions because they are asking for a range of values or a pattern among a group of data.
Step-by-step explanation:
The scatterplot shows the relationship between the number of yards allowed by teams in the National Football League and the number of wins for that team in a recent season, along with the least-squares regression line. Computer output is also provided.
1 . State the equation of the least-squares regression line. Define any variables you use.
Answer:
16.84
Step-by-step explanation:
helping a friend out
Answer:
7.5 hours
Step-by-step explanation:
let t represent time, l represent length and n represent number of painters.
given t varies directly with l and inversely with n then the equation is
t = [tex]\frac{kl}{n}[/tex] ← k is the constant of variation
to find k use the condition t = 5 when l = 200 and n = 3 , then
5 = [tex]\frac{200k}{3}[/tex] ( multiply both sides by 3 )
15 = 200k ( divide both sides by 200 )
0.075 = k
t = [tex]\frac{0.075l}{n}[/tex] ← equation of variation
when l = 500 and n = 5 , then
t = [tex]\frac{0.075(500)}{5}[/tex] = [tex]\frac{37.5}{5}[/tex] = 7.5 hours
Your grandmother tells you a story about a genie that offers two options for rewards.
● Option 1: $1,500,000
● Option 2: A magical $1 coin that triples every day. The coin turns into three coins on the first day. The three coins turn into nine coins on the second day. The nine coins triple to 27 coins on the third day. This doubling will continue for 28 days.
Write an equation that shows the number of coins n that you get when you choose option 2 after d days.
Key: d is the variable
The expression for the magical coin for d days will be [tex]C = (3)^d[/tex].
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that A magical $1 coin that triples every day. The coin turns into three coins on the first day. The three coins turn into nine coins on the second day. The nine coins tripled to 27 coins on the third day. This doubling will continue for 28 days.
The equation can be written as,
[tex]C = (3)^d[/tex]
At d = 28, the value of the coin will be,
C = (3)²⁸
C = $2.28 x 10¹³
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Find the quotient and label the model 14 divide by 54.6
Answer:
On top: 3.9
2nd row: 42
3rd row: 12.6
4th row: 12.6
Top of area model:
3 and .9
Step-by-step explanation:
Long division has a rhythm of four steps. The outside number(divisor) goes into the inside number (dividend, but just a piece of it). Write the answer (quotient) on top. Multiply the top × the outside number. Write it below. Subtract down. Bring down another digit. See image.
The area model is based on length times width. See image.
A circle with a radius of 7 feet is cut into 6 equal pieces. How many square feet are 2 of the pieces? Use 22 over 7 for π.
A. 7 and one third square feet
B. 14 and two thirds square feet
C. 51 and one third square feet
D. 205 and one third square feet
The circle with a 7 feet radius cut into 6 equal sectors, indicates, using 22/7 approximation for pi, that the area of 2 of the pieces is 51 and one third square feet. The correct option is option C.
C. 51 and one third square feet
What is a sector of a circle?A sector of a circle is a pie shaped part of a circle that is bounded by an arc and two radii of the circle.
The specified radius of the circle, r = 7 feet
The number of pieces to which the circle is cut into = 6 equal pieces (sectors)
The area of 2 of the pieces, using 22/7 as an approximation for π are found as follows;
Area of a circle, A = π × The square of the radius
Therefore; A = π × r²
A = (22/7) × 7² = 154
The area of the circle is about A = 154 square feet
The area of one of the pieces into which the circle is cut is therefore;
Area of a piece = A/6
Area of one piece = (154 square feet)/6 = 25 and two thirds square feet
The area of 2 of the pieces = 2 × (A/6) = A/3
Therefore, the area of two of the pieces = (154 square feet)/3 = 51 1/3
The area of 2 of the pieces = [tex]51\frac{1}{3}[/tex] square feet
Option C is correct
C. 51 and one third square feet
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Using the 22/7 approximation for pi, the circle with a radius of 7 feet divided into 6 equal sectors shows that the area of 2 of the sections is 51 and a third square feet. Option C is the one that is right.
51 and a third square feet in C.
[tex]\frac{1}{2}[/tex]x+4=-26
[tex]\dfrac{1}{2} x+4=-26[/tex]
Subtract 4 from both sides:
[tex]\dfrac{1}{2} x+4-4=-26-4[/tex]
[tex]\dfrac{1}{2} x=-30[/tex]
Multiply both sides by 2:
[tex]2\times(\dfrac{1}{2} x)=2\times(-30)[/tex]
[tex]\fbox{x = -60}[/tex]
If you roll 2 dice, what is the probability that you will roll a seven (the numbers on the dice add up to a seven) on or before the 5th roll
Answer:
The probability of rolling a seven on or before the 5th roll is 5/6 or about 83.3%
Step-by-step explanation:
The probability of rolling a seven on any given roll of two dice is 1/6, since there are six ways to roll a seven (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of the 36 possible outcomes (1-6 on the first die and 1-6 on the second die).
To find the probability of rolling a seven on or before the 5th roll, we can use the cumulative probability formula which is the probability of getting a specific event on the first roll plus the probability of getting the event on the second roll plus the probability of getting the event on the third roll and so on.
So the probability of rolling a seven on or before the 5th roll is:
P(rolling a seven on the 1st roll) + P(rolling a seven on the 2nd roll) + P(rolling a seven on the 3rd roll) + P(rolling a seven on the 4th roll) + P(rolling a seven on the 5th roll)
= (1/6) + (1/6) + (1/6) + (1/6) + (1/6)
= 5/6
So the probability of rolling a seven on or before the 5th roll is 5/6 or about 83.3%
It's worth noting that this probability is independent of the previous outcomes of the rolls, so the probability of rolling a seven on or before the 5th roll stays the same even if you already rolled a seven in previous rolls.
Last year, there were d pies baked for the bake sale. This year, there were 231 pies baked. Using d, write an
expression for the total number of pies baked in the two years.
There are 231+d pies baked in two years.
What is expression?expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An equation is made up of two expressions connected by an equal sign.
Since we have given that
Number of pies baked for bake sale last year = 231
Number of pies baked for bake sale this year = d
So, total number of pies baked in two years is given by
231 +d
Hence, there are 231+d pies baked in two years.
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Based on the diagram below, which is closest to the height of the tree?
answer options and picture are below
Using the concept of similar triangles, the height of the tree is; Option D: 38 ft 6 inches.
How to find the side lengths of similar triangles?Similar triangles are defined as triangles that have the same shape, but then their sizes may vary. This means that equilateral triangles and squares are good examples of similar objects. Thus, if two triangles are similar, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.
Thus, applying the principle of similar triangles above to the given image, if the height of the tree is h, then we have;
5/3.25 = h/25
h = (25 * 5)/3.25
h = 38.462 ft = 38 ft + 0.462 ft
Now, conversion of ft to inches gives 0.462 ft approximately 6 inches Thus, our final answer is 38 ft 6 inches.
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True or False:
15 x 32 x 2 = 2 x 15 x 32
The answer is true
15 x 32 x 2 = 2 x 15 x 32
960=960
Answer:
it is true because the answers are the same
Step-by-step explanation:
A grocery store prints coupons on randomly selected receipts.
A coupon was printed on 18 of the last 1,200 receipts. Based on
these results, what is the probability that a coupon will be
printed on the next receipt? Show your work.
Answer:
18/1,200?
Step-by-step explanation:
im not too sure on this
Katie received a sticker each time she picked up her toys. She places some of the stickers on the first page of her scrapbook as shown below. Write an equation to represent the problem using the distributive property.
The number of stickers on the first page of Katie's scrapbook is given by the equation A = 28 stickers
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The number of stickers in Katie's first page of scrapbook is A
The array of stickers is = 4 rows and 7 columns
So , number of stickers in Katie's first page of scrapbook A = 4 x 7
Number of stickers in Katie's first page of scrapbook A = 28 stickers
The total number of stickers in the scrapbook for page 2 and 3 is
A = ( 4 x 4 ) + ( 3 x 4 )
Taking the common factor as 4 , we get
A = 4 ( 4 + 3 )
By using the distributive property , we get
A = 4 x 7
A = 28 stickers
Therefore , the value of A is 28
Hence , the equation is A = ( 4 x 4 ) + ( 3 x 4 )
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There can be no more than 835 people in the concert hall. What inequality represents the number of people, p, allowed in the concert hall? Drag and drop the appropriate symbol to correctly complete the inequality. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.poop
Answer:
p is less than or equal to 835
Step-by-step explanation:
Up to 835 people can fit in the concert, therefore the answer is p<=835.
John and Ben each bought school supplies. John bought three pens, and Ben bought two pens. Ben bought three pencils. If each pen cost $1.10 and each pencil costs $0.75, how many pencils did John buy, if together they spent $10.00?
Answer:
10
Step-by-step explanation:
1.10*2=2.20
10-2.20=7.80
7.80/75=10.4
in total 10 pencils
10. Grapes are on sale for
$2.36 per pound.
Pounds
0.75
1.25
2
2.5
Total Cost
Number 10
Answer:
.75 pounds= $1.77, 1.25 pounds=$2,95, 2 pounds=$4.72, 2.5 pounds= $5.90
Step-by-step explanation:
multiply each number in the pounds column by 2.36 to get the total cost
.75(2.36)=1.77
1.25(2.36)=2.95
2(2.36)=4.72
2.5(2.36)=5.9
Solve the system for w and z.
-4w +3z=-21
3z=w+6
ILL GIVE BRAINLIEST
A man walks 16 miles east and then walks 12 miles due north. How far is the tired man from his starting point?
3/5 is 2/3 of what number?
Answer:
3/5 is 2/3 of 9.
Step-by-step explanation:
Find a parametric equation for the line through the point (-8,10,0) and perpendicular to the plane 7x+5y + 5z=6 which is written using the coordinates of the given point and the
coefficients of x, y, and z in the given equation of the plane.
Let z=5t
The provided equation of the plane contains 60 as the x, y, and z coefficients.
What is the formula for a line that passes through a point and is perpendicular to a plane?The mathematical formula for the line that is parallel to the given plane and passes through the specified point. N is equal to s, which is equal to ai, bj, and ck.
The line's parametric equations are x = x0 + at, y = y0 + bt, and z = z0 + ct, which are obtained by formulating the line's vector equation in terms of its components. The direction numbers of the line are known as the components a, b, and c.
Initially, by solving for y, convert the provided line's equation into slope-intercept form. You obtain y = -2x+5, meaning that the slope is 2. We wish to find the slope of the line, which is 1/2 because perpendicular lines have opposite-reciprocal slopes.
7*-8 + 5*10 + 5*0 = 6
-56 + 50 + 0 = 6
-6 = 6
= 12.
Z = 5*12 = 60.
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The population of a city was 34,000 at the beginning of 1937. Its
population steadily increased by 6.8% every year from 1937 to 1997.
Which of these is the closest to the population of the city at the end of
1970?
Answer:
298078.228074
Step-by-step explanation:
we add 6.8% of the population to the city each year
city population in year x + 1 = city population in year x + 6.8% of city population in year x = city population in year x + 0.068 * city population in year x = 1 * city population in year x + 0.068 * city population in year x = 1.068 * city population in year x
we multiply the population by 1.068 each year to get the next year's population
thus, over a period of y years, we would multiply the population by 1.068 y times.
start = 34000 in 1937
difference in years = 1970 - 1937 = 33
final amount = 34000 * 1.068 33 times = 34000 * 1.068^33 = 298078.228074
The expression √7. √7² is equivalent to
The expression √7. √7² is equivalent to [tex]7\sqrt{7}[/tex].
How to Use the Quadratic Formula to Find the Roots of a Quadratic Equation?According to the quadratic formula, x = (-b (b2 - 4ac)) /2a gives the roots of the quadratic equation ax2 + bx + c = 0. Convert the quadratic equation into standard form, ax2 + bx + c = 0, then find the values of a, b, and c, substitute them in the quadratic formula, and simplify to find the solution to any quadratic equation.
How do you quickly locate roots?Let's say that multiplying 5 by 5 yields the number 25. Therefore, we can state that 5 is equal to 25 squared. Similar to this, the root values of 16, 36, 49, etc. are 4, 6, and 7, respectively.
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