Step-by-step explanation:
Functions can be represented as equations, and equations can be represented as functions.
The number of people that started the rumor is 10
The function is represented as:
To calculate the number of people that started the rumor, we simply set t to 0.
So, we have:
Evaluate the exponent of e
Express e^0 as 1
Multiply 39 and 1
Add 1 and 39
Divide 400 by 40
When t = 0, N(t) = 10
This means that 10 people started the rumor.
Hence, the number of people that started the rumor is 10
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Daryl walks 10.5 miles in 3.5 hours. How many miles does he walk per hour?
Answer: 3
Step-by-step explanation: Daryl is walking 3 miles in 1 hour. When you divide 10.5 by 3.5 you get. So 3 miles in one hour. For example if you walk 12 miles in 4 hours, you divide and get 3. That three becomes the miles in one hour.
Lester bought 8 t-shirts. The shirts came in p packages. Write an expression that shows how many t-shirts were in each package.
Expression for Number of t shirts in each package = [tex]\frac{8}{p}[/tex]
What is Unitary Method ?The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Total number of shirts bought = 8 T- shirts
Total number of packages = p
So,
According to unitary method
In p packages we have t shirts = 8
In one package number of t shirts we will have = [tex]\frac{8}{p}[/tex]
Expression for Number of t shirts in each package = [tex]\frac{8}{p}[/tex]
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Average employee salary?
Answer:
$67,680
Step-by-step explanation:
average is calculated as
average = [tex]\frac{sum}{count}[/tex]
Denver
[tex]\frac{sum}{137}[/tex] = 67,013 ( multiply both sides by 137 )
sum = 9,180,781
Anchorage
[tex]\frac{sum}{25}[/tex] = 71,332 ( multiply both sides by 25 )
sum = 1,783,300
total sum for both = $9,180,781 + $1,783,300 = $10,964,081
then average salary across both companies is
average = [tex]\frac{10,964,081}{162}[/tex] = $67,680 ( to the nearest dollar )
Ru buy three cake for £1. 60 each. He pay with a £20 note. How much change doe he get
We know that Ru will get back £15.2 when she buys 3 cakes for £1.60 each using simple mathematical operations.
What are mathematical operations?The process of calculating a value using operands and a math operator is known as a mathematical "operation."
The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.
The rules that determine how to solve an expression with several operations are referred to as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).
So, we know that:
Ru buys 3 cakes for £1.60 each.
She was given £20 not.
The money she will get back is:
20 - (1.60*3)
20 - 4.8
£15.2
Therefore, we know that Ru will get back £15.2 when she buys 3 cakes for £1.60 each using simple mathematical operations.
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If 8% of a liquid is 56 mL, what is the whole
amount?
Please help
Answer:
700 mL
Step-by-step explanation:
You want to know the whole amount if 8% of it is 56 mL.
RelationThe problem statement tells you ...
8% × whole = 56 mL
Divide by the coefficient ...
whole = (56 mL)/(0.08) = 700 mL
The whole amount is 700 mL.
write an eqation of the line that passes throught the points (0,-2), (4,-2),
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line is y = -2.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of the line is given as,
y = mx + c
The line passes through the points (0, -2) and (4, -2).
Now,
Slope = m
m = (-2 + 2) / (4 - 0)
m = 0 / 4
m = 0
Now,
(x, y) = (0, -2)
y = mx + c
-2 = 0 x 0 + c
c = -2
Now,
m = 0 and c = -2
y = 0x -2
y = -2
Thus,
The equation of the line is y = -2.
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PLEASE I NEED HELP!!!!!!!!
Answer:
161 square inches.
Step-by-step explanation:
The surface area of a pyramid is the sum of the areas of all of its faces. Since the base of the pyramid is a square with an edge length of 7 inches, the area of the base is 49 square inches (7 inches x 7 inches).
To find the surface area of the pyramid, you also need to find the area of the lateral faces of the pyramid. The lateral faces of a pyramid are the triangular faces that are not the base. The lateral faces of a pyramid are all congruent, meaning that they are all the same size and shape.
To find the area of a lateral face of the pyramid, you can use the formula for the area of a triangle: A = 1/2bh, where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle.
In this case, the base of the triangle is 7 inches (the edge length of the base of the pyramid) and the height of the triangle is 8 inches (the slant height of the pyramid). The area of each lateral face of the pyramid is therefore 1/2 x 7 inches x 8 inches = 28 square inches.
Since there are 4 lateral faces on the pyramid, the total area of the lateral faces is 4 x 28 square inches = 112 square inches.
To find the surface area of the pyramid, add the area of the base to the area of the lateral faces: 49 square inches + 112 square inches = 161 square inches. Therefore, the surface area of the pyramid is 161 square inches.
What is the distance from the origin to pint A graphed on the complex plane below
Answer: it's [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Cindy had $660 in a savings account when Erika opened a savings account with zero dollars.
Cindy deposited $60 into her account each month for x months.
Erika deposited $100 into her account each month for x months.
• The accounts did not earn interest.
Which inequality represents this situation when the amount of money in Cindy's account was greater than the amount of money in Erika's accour
Answer: To represent the situation where the amount of money in Cindy's account is greater than the amount of money in Erika's account, you can set up the inequality as follows:
Cindy's account balance + (Cindy's monthly deposit * number of months) > Erika's account balance + (Erika's monthly deposit * number of months)
Substituting the known values, we get:
660 + (60 * x) > 0 + (100 * x)
Combining like terms, we get:
660 + 60x > 100x
Subtracting 60x from both sides, we get:
660 > 40x
Dividing both sides by 40, we get:
16.5 > x
Therefore, the inequality that represents the situation when the amount of money in Cindy's account is greater than the amount of money in Erika's account is 16.5 > x. This means that for the number of months (x) to be greater than 16.5, the amount of money in Cindy's account must be greater than the amount of money in Erika's account.
50 POINTS IF ANSWERED PLS!!!!
Which angle is the biggest based on the sides of the triangles below? Explain your reasoning.
Answer:
angle c
Step-by-step explanation:
since the largest angle will be across from the longest side, angle c is the right answer because it is across from the longest side which measures 35 cm.
hope this helps
Two piece of metal meaure one and one fifth yard and three tenth yard each. Three time the amount of metal i needed for a project. How many total yard of metal i needed? one and one half yard one and nine fifteenth yard four and one half yard four and one fifth yard
As per the area of the rectangle, the amount of metal need for the total yard is 4.68
Area of rectangle
In geometry, the area of rectangle is written as,
A = l x b
where l refers the length and b refers the breadth of the rectangle.
Given,
Here we have given that the 1 1/5 and 3 1/10 is the measure of yard.
While we looking into the given question, we have identified that,
3 time of metal is need for the project,
So, as per the area of the rectangle formula, it can be written as,
=> 3 x 1 1/5 x 3 1/10
=> 3 x 6/5 x 13/10
=> 234/50
=> 4.86
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Answer:
4 1/2
Step-by-step explanation:
add 1 1/5 and 3/10 and then multiply your answr by 3
Given vector u = ⟨−3,−2⟩ and v = ⟨1,−5⟩,determine the value of u - 2v in component form.
The component form of the linear combination of the two vectors is u - 2v = < -5, 20>
How to find the vector u - 2v?Here we have the two vectors: u = <-3, -2> and v = <1, -5> We want to determine the value of the linear combination:
u - 2v
To do that we just add the correspondent components, then we get:
u - 2v = <-3, -2> - 2*<1, -5>
= <-3, -2> - <2*1, 2*-5>
= <-3, -2> - <2, -10>
= < -3 - 2, -2 -(-10)>
= < -5, 20>
That is the component form of the linear combination.
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Find the measure of angle f given the information below. please help !!
The measure of Angle f from the the figure is [tex]53^{o}[/tex].
What is the relation between Angles and Parallel lines ?On a shared plane, parallel lines do not cross one another. Now, if a transversal crosses two parallel lines at two separate sites, four angles are created at each location. The characteristics of parallel lines with respect to transversals are therefore listed below.
Angles that coincide are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that alternate are equal.Exterior angles that alternate are equal.On the same side of the transversal, a pair of internal angles are additional.The pair of alternative internal angles are equal when two parallel lines are crossed by a transversal.
When a transversal cuts between two parallel lines, the interior angles on the same side of the transversal are additional.
In the problem angle
a = [tex]119^{o}[/tex]
e = [tex]66^{o}[/tex]
Now , c = e ( alternate angles, interior)
⇒ c = [tex]66^{o}[/tex]
a + b = [tex]180^{o}[/tex] ( as sum of angles on a straight line is [tex]180^{o}[/tex] )
b = [tex]180^{o}[/tex] - [tex]119^{o}[/tex] = [tex]61^{o}[/tex]
f + b+ c = [tex]180^{o}[/tex] [sum of angles of a Triangle is [tex]180^{o}[/tex] ]
f = [tex]180^{o}[/tex] - [tex]61^{o}[/tex] - [tex]66^{o}[/tex] = [tex]53^{o}[/tex].
The measure of Angle f from the the figure is [tex]53^{o}[/tex].
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In the diagram below, OQ = 25, PM = 9, and QN = 15. Find the length of OP.
Round your answer to the nearest tenth if necessary.
0
Answer: OP |
P
M
Q
N
Submit Answer how do I come up with the number
In the diagram, the length of OP to the nearest tenth is 5.4
How to determine the length?We are to determine the ratio of the sides of the diagram.
The ratio of the sides using the given sides is
Let the unknown side be x
The ratio of the sides is given as follows
25:34 = 15:x+15
Put into fraction we have
25/(25+9)= 15/(x+15)
Cross multiplying we have
25x+375 = 375+135
Collecting like terms
25x=510-375
Simplify further to have
25x=135
Making x the subject
x=5.4
Therefore the length OP is 5.4 units
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Given: ∠BCD is right; BC ≅ DC; DF ≅ BF; FA ≅ FE
Triangles A C D and E C B overlap and intersect at point F. Point B of triangle E C B is on side A C of triangle A C D. Point D of triangle A C D is on side C E of triangle E C D. Line segments B C and C D are congruent. Line segments B F and F D are congruent. Line segments A F and F E are congruent.
Which relationships in the diagram are true? Select three options.
△ACF ≅ △ECF by HL
ΔCBF ≅ ΔCDF by SSS
ΔBFA ≅ ΔDFE by SAS
ΔCFD ≅ ΔEFD by SSS
ΔCBE ≅ ΔCDA by HL
SAS
The three relationships in the diagram that are true include the following;
B. ΔCBF ≅ ΔCDF by SSS
C. ΔBFA ≅ ΔDFE by SAS
E. ΔCBE ≅ ΔCDA by HL
What is the Right Triangles Similarity Theorem?In Mathematics, the Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two (2) triangles that are formed would be similar to each other, as well as the original triangle.
Based on the Right Triangles Similarity Theorem, we have the following;
ΔCBF ≅ ΔCDF by side, side, side (SSS).ΔBFA ≅ ΔDFE by side, angle, side (SAS).What is HL?In Mathematics, HL is an abbreviation for hypotenuse leg and it can be defined as a theorem which states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent.
By applying the hypotenuse leg (HL) theorem across right-angle BCD (∠BCD), we have the following;
ΔCBE ≅ ΔCDA
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Emma had to finish her 366-page novel by Friday. She had already read 244 pages. Write and solve an equation to show how many pages Emma had left to read by Friday.
p − 244 = 366; p = 610 pages
p + 244 = 366; p = 122 pages
122p = 244; p = 2 pages
p over 244 equals 2; p = 488 pages
Answer: Its b my guy :)
Step-by-step explanation: 244 + 122 = 366
and the only answer with 366 is b! hope this helps!
Your grocery bill before taxe wa $265. 24. You have to pay 7. 3 ale tax. How much i your grocery bill?
If the grocery bill before tax is $265.24 and you have to pay 7.3% tax, then he has to pay $284.6 for the grocery bill
The amount of the grocery bill before tax = $265.24
The percentage of tax = 7.3%
The amount of tax = The price of the grocery bill before tax × (7.3/100)
Substitute the values in the equation
= 265.24 × (7.3/100)
= 265.24 × 0.073
= $19.36
The final bill including tax = The price of the grocery bill before tax + The amount of tax
Substitute the values in the equation
= 265.24 + 19.36
= $284.6
Therefore, the grocery bill including tax = $284.6
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How much compound interest will $50,000 have earned in 10 years at
6.4% annual interest compounded quarterly?
The compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly would be $28,167.50.
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
Compound Interest =P(1+r/n)^rt
We are given that
Principal amount = $50,000
Time = 10 year
Rate = 6.4%
Determine the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly, we can use the formula:
Plugging in the given values, we get:
compound interest = $50,000 (1 + 0.064/4)^(4 x 10) - $50,000
= $50,000 (1.016)^40 - $50,000
= $50,000 x 2.6335 - $50,000
= $78,167.50 - $50,000
= $28,167.50
Therefore, the compound interest is $28,167.50.
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Evaluate f(x)=2x+5 when x=0, x=1, x=5
Answer:
f(0)=5
f(1)=7
f(5)=15
Step-by-step explanation:
f(0)=2x+5
=2(0)+5
=5
f(1)=2x+5
=2(1)+5
=2+5
=7
f(5)=2x+5
=2(5)+5
=10+5
=15
There are 4 chocolate chip cookies and 3 oatmeal cookies in a cookie jar. If a child randomly takes 2 cookies, what is the probability that both are chocolate chip?
when the philies play the dodgers, the tickets for three adults and three children are $75. for two adults and four children the total admission cost is $62. find the cost of each adult and each child ticket.
when the philies play the dodgers, the tickets for three adults and three children are $75. for two adults and four children the total admission cost is $62. So, by using equation formula:
the cost of each adult is $19
and each child ticket is $6
What is an equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
The relationship between the two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.
Let us assume,
tickets for adults = a
tickets for children = c
Now,
3a + 3c = $75 ........ (i)
2a + 4c = $62 ......... (ii)
Multiply the equation (i) ×2 and equation (ii) × 3, we get -
6a + 6c = $150 ........ (iii)
6a + 12c = $186 .........(iv)
Now, subtract equation (iv) from (iii) we get -
or, 6c = $36
or, c = $6
Now, putting the value of c in equation (iii) we get -
6a + 6×6 = $150
6a = $114
a = $19
Thus, the cost of each adult is $19
and each child ticket is $6
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What is the equation of the blue line
Answer:
y = -1/2 x + 2
Step-by-step explanation:
A (0,2)
B (4,0)
(y-2)/(0-2) = (x-0)/(4-0)
(y-2)/-2 = x/4
(-y+2)/2 = x/4
4 * (-y+2)/2 = x/4 * 4
-2y+4 = x
-2y = x -4
2y = -x + 4
y = - 1/2 x + 4/2
y = -1/2 x + 2
A pet store sells a large dog kennel 98.50 the wholesale cost o the kennel is 63.55 what is the percent of markup round to the nearest percent.
Rounded to the nearest percent, the markup is approximately 55%.
What is the percent markup?
Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus its cost to make or purchase for resale) by the cost of that unit.
To find the percent markup, you can use the following formula:
percent markup = (retail price - wholesale price) / wholesale price * 100
Plugging in the values given, we have:
percent markup = (98.50 - 63.55) / 63.55 * 100 = 34.95 / 63.55 * 100 = approximately 55%
Hence, rounded to the nearest percent, the markup is approximately 55%.
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let lines x and y be parallel, and let lines z and w be parallel. if angle a is the angle formed by lines y and z, and angle b is the angle formed by lines w and x, if the measure of angle a is 25 degrees, what is the measure of angle b?
155° is the measure of angle b .
What is an example of parallel lines?
Two lines that are equally spaced apart from one another and never cross each other are said to be parallel lines.
Both horizontal and vertical shapes are possible. In our daily lives, parallel lines can be seen in the form of zebra crossings, rows of notebooks, and the nearby railroad tracks.
from the figure , we understand that ∠1 and ∠3 together from a straight line.
thus, ∠1 + ∠3 = 180°
25° + ∠3 = 180°
∠3 = 155°
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Rewrite 15x^4y^3 − 45x^3y^4 using a common factor
15x^4y^3 − 45x^3y^4 Can be rewritten using a common factor as 15x^3y^3(x - 3y)
What is a common factor?common factors are defined as factors that are common to two or more numbers. In other words, a common factor is a number with which a set of two or more numbers will be divided exactly.
In the algebraic expression 15x^4y^3 − 45x^3y^4,
15x^4y^3 is a term and 45x^3y^4, is another term.
if we take each variable and constant and compare
15 is common factor between 15 and 45
x^3 is a common factor between x^4 and x^3
y^3 is a common factor between y^3 and y^4
so multiplying the common factors together we have 15x^3y^3
what is left in the first term is x and second term is 3y
so that the rewritten form becomes 15x^3y^3(x - 3y)
In conclusion the other form of 15x^4y^3 − 45x^3y^4 is 15x^3y^3(x - 3y)
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(10)
Write the equation
of the line in
Slope-Intercept
Form.
Answer:
y = -x
Step-by-step explanation:
The slope of this line is -1 (rise/run = -1/1 = -1). We can plug this value into the slope-intercept form equation:
y = mx + b
y = -1x + 0
and simplify.
y = -x
Perpendicular lines form angles that are how many degrees at their intersection?
O a. 45 dregrees
O b. 90 degrees
O c. 135 degrees
O d. 225 degrees
Answer:
Step-by-step explanation:135 degrees
help due tomm!!! suppppper easyy!!
Answer: b/-3<a/-3
Step-by-step explanation:
a/-3<b/-3
b/-3<a/-3
A new Youth Activity Center is being built in Ook Valley. The perimeter of the rectangular playing field is 272 yards. The length of the field is 8 yards less than double the width. What
are the dimensions of the playing field?
Answer:
w = 48 and l = 88
Step-by-step explanation:
A new Youth Activity Center is being built in Ook Valley. The perimeter of the rectangular playing field is 272 yards. The length of the field is 8 yards less than double the width. What are the dimensions of the playing field?
P = 2w + 2l
w = w
l = 2w - 8
272 = 2w + 2(2w - 8)
272 = 2w + 4w - 16
272 = 6w - 16
288 = 6w
w = 48
remember that: l = 2w - 8
l = 2w - 8 when w = 48
l = 2(48) - 8
l = 96 - 8
l = 88
CHECK: w = 48 and l = 88
P = 2w + 2l
272 = 2(48) + 2(88)
272 = 96 + 176
272 = 272
so: w = 48 and l = 88
given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line. State True or False your answer:
a. True
b. False
It is true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
A parabola is a quadratic function graph .A parabola is a curve equation in which a point on the curve is equidistant from a fixed point and a fixed line.
The fixed point is known as the parabola's focus, and the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie on the fixed line.
A parabola is a locus of any point that is equidistant from a given point (focus) and a given line (directrix). The parabola is a significant curve of the coordinate geometry's conic sections.
The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h,k) denotes the vertex.
The standard equation of a regular parabola is y² = 4ax.
It's true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
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