Answer:
32 inches or [tex]2\dfrac{2}{3}[/tex] feet
Step-by-step explanation:
1 foot = 12 inches
2 feet = 24 inches
Initially, the hole was 2 feet deep, after 3 days, the hole sank 8 inches further, so after 3 days, the hole was 2 feet 8 inches deep.
2 feet 8 inches = 24 inches + 8 inches = 32 inches
Now,
1 inch [tex]=\dfrac{1}{12}[/tex] foot
Then
32 inches [tex]=\dfrac{32}{12}=\dfrac{8}{3}=2\dfrac{2}{3}[/tex] inches
Write an equation of the cosine function with the given amplitude, period, phase shift, and vertical shift. amplitude: 2, period = , phase shift = – , vertical shift = –2
Answer:
[tex]y=2\cos(2x+\frac{1}{4})-2[/tex]
or
[tex]y=-2\cos(2x+\frac{1}{4})-2[/tex]
Step-by-step explanation:
[tex]y=a cos(c(x-b))+d[/tex] has:
1) amplitude=|a|
2) phase shift=b
3) period=2pi/c
d) vertical shift=d
--------------------------------------------------
You are given the amplitude is 2. This means a could either be 2 or -2.
You are given phase shift is -1/8. This means b is -1/8.
You are given the period is pi. So we need to solve pi=2pi/c.
pi=2pi/c
Dividing both sides by pi gives:
1=2/c
Multiply both sides by c gives:
c=2
The vertical shift is -2 so d=-2.
The equation could either be:
y=2cos(2(x-(-1/8)))-2
or
y=-2cos(2(x-(-1/8)))-2
Simplifying a little gives:
y=2cos(2x+1/4)-2
y=-2cos(2x+1/4)-2
Find the unit rate. Round to the nearest hundredth, if necessary.
$210 for 16 ft?
The unit rate is $
Answer:13.125
Step-by-step explanation: divide 210 by 16
Are the sets equivalent? A= {Larry,Moe,Curly,Shemp}. B= {Posh, Sporty,Baby,Scary}
Answer:
yes
Step-by-step explanation:
equivalent sets have the same number of members
Sets A and B are not equivalent, have the same cardinality but no common elements in their intersection.
The sets A and B are not equivalent because they have different members.
The cardinality of set A is 4, and the cardinality of set B is also 4, meaning they have the same number of elements.
The intersection of sets A and B is the empty set, as they have no common elements.
Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three options. The graph of f(x) = x2 is shifted down 50 units. The graph of f(x) = x2 is shifted up 50 units. The graph of f(x) = x2 is shifted left 10 units. The graph of f(x) = x2 is shifted right 10 units. The graph of f(x) = x2 is reflected over the x-axis.
Answer:
The graph of f(x) is shifted up 50 units
The graph of f(x) is shifted right 10 units
The graph of f(x) is reflected over the x-axis
Step-by-step explanation:
we have
[tex]f(x)=x^{2}[/tex]
This is a vertical parabola open upward
The vertex is a minimum
The vertex is the origin (0,0)
[tex]g(x)=-5x^{2}+100x-450[/tex]
This is a vertical parabola open downward
The vertex is a maximum
The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.
Find the vertex of g(x)
Convert to vertex form
[tex]g(x)=-5x^{2}+100x-450[/tex]
Complete the square
[tex]g(x)=-5(x^{2}-20x)-450[/tex]
[tex]g(x)=-5(x^{2}-20x+100)-450+500[/tex]
[tex]g(x)=-5(x^{2}-20x+100)+50[/tex]
[tex]g(x)=-5(x-10)^{2}+50[/tex]
The vertex is the point (10,50)
so
To translate the vertex of (0,0) to (10,50)
The rule of the translation is
(x,y) ------> (x+10,y+50)
That means ----> The translation is 10 units at right and 50 units up
therefore
The transformations are
The graph of f(x) is shifted up 50 units
The graph of f(x) is shifted right 10 units
The graph of f(x) is reflected over the x-axis
the formula K=9/5[F-32]+273.15 converts temperatures from Fahrenheit F to Kelvin K.
a. solve the formula for F
b.The freezing point of water is 273.15 Kelvin. What is the temperature in Fahrenheit?
c.The temperature of dry ice is -78C. Which is colder, dry ice or liquid nitrogen
To solve for F in the conversion formula, subtract 273.15, multiply by ([tex]\frac{5}{9}[/tex]), and add 32. The freezing point of water in Fahrenheit is 32 °F. Liquid nitrogen is colder than dry ice.
Solving the Temperature Conversion Formula
To solve the formula K = [tex]\frac{9}{5}[/tex][F-32] + 273.15 for F (Fahrenheit), we will isolate F in the equation. Here is the step-by-step process:
Subtract 273.15 from both sides: K - 273.15 = [tex]\frac{9}{5}[/tex][F - 32]
Multiply both sides by [tex]\frac{5}{9}[/tex] to get: F - 32 = (K - 273.15) × [tex]\frac{5}{9}[/tex]
Add 32 to both sides to solve for F: F = (K - 273.15) × [tex]\frac{5}{9}[/tex] + 32
Converting Kelvin to Fahrenheit
The freezing point of water is 273.15 Kelvin. To find this temperature in Fahrenheit:
F = (273.15 - 273.15) × [tex]\frac{5}{9}[/tex] + 32 = 32 °F
Comparing Temperatures
Dry ice has a temperature of -78°C, which is equivalent to -108.4°F. Liquid nitrogen boils at 77 K, which is about -196°C or -320.8°F. Therefore, liquid nitrogen is colder than dry ice.
5•3/4 need help ASAP
Answer:
3 3/4
Step-by-step explanation:
5×[tex]\frac{3}{4}[/tex]
5 3
/ × /
1 4
= 15/4
=3 3/4
slope of (8,11) (5,5)
Slope = 2/1
The work is provided in the image attached.
If 10 - y = 7
What is y
Answer:
y = 17
Step-by-step explanation:
-y = 17
y = -17
Answer:3
Step-by-step explanation:
10-7=3
2 Points
At the beginning of this month, Cybil had $185.36 in digital money. So far this
month she has made deposits of $13.74, $58.27, and $69.30 into her
account, while she has made withdrawals of $19.29, $28.19, and $52.55.
How much digital money does Cybil have now?
If f x = x2 + 2x − 5 and g x = 2x + 4, what is (f · g)(x) ?
[tex]\((f \cdot g)(x) = 2x^3 + 8x^2 - 2x - 20 \)[/tex].
To find [tex]\((f \cdot g)(x)\)[/tex], you need to multiply the functions \(f(x)\) and \(g(x)\).
Given:
[tex]\[ f(x) = x^2 + 2x - 5 \]\[ g(x) = 2x + 4 \]To find \( (f \cdot g)(x) \), multiply \( f(x) \) and \( g(x) \):\[ (f \cdot g)(x) = f(x) \cdot g(x) \]\[ (f \cdot g)(x) = (x^2 + 2x - 5) \cdot (2x + 4) \][/tex]
Now, use the distributive property to expand the expression:
[tex]\[ (f \cdot g)(x) = 2x^3 + 4x^2 + 4x^2 + 8x - 10x - 20 \]\[ (f \cdot g)(x) = 2x^3 + 8x^2 - 2x - 20 \][/tex]
So, [tex]\((f \cdot g)(x) = 2x^3 + 8x^2 - 2x - 20 \)[/tex].
I need help with this question please help me...
- 21+3x = -3
Answer:
x=6
Step-by-step explanation:
-21+3x=-3
+21 +21
3x=18
/3 /3
x = 6
Answer:
Step-by-step explanation:
Step one add 21 to each sides of the equal sign the you get
3x = 18
Divide by 3 on each side of the equal sign then your answer is
6
X = 6
Perfume is sold in two different sizes of bottle. The 80ml bottle is priced at £55. The 50ml bottle is usually priced at £45, but is on special offer. If you buy one 50ml bottle of perfume you can get a second for half price.
By calculating the price per ml determine which offers the best value for money the 80ml or two 50ml bottles ? You must show your working .
Answer:
Step-by-step explanation:
Price per ml of 80ml bottle= 0.68
price per ml of 50 ml bottle= 0.9
therefore two 50ml bottles is a better deal.
Given the function f(x) = 3x + 1 and the linear function g(x), which function has a greater value when x = 3?
f(x) is greater.
g(x) is greater.
f(x) and g(x) are the same when x = 3.
g(x) is undefined when x = 3.
Answer:
f(x) is greater.
Step-by-step explanation:
if you replace the x on f(x)=3x+1 with the 3 for x=3 its 3×3+1. 3 times three is 9 plus 9 with one is 10, and the line hits 6.9
The function that has a greater value when x = 3 is option A: f(x) is greater.
What is the functionThe function [tex]\(f(x) = 3x + 1\)[/tex] is a linear function with a slope of 3 and a y-intercept of 1. The function[tex]\(g(x)\)[/tex] is not explicitly provided in your question, so we don't have information about its slope or intercept.
To determine which function has a greater value when x = , we need to evaluate both functions at x = 3 and compare their values.
So, when one replace the x on f(x)=3x+1 with the 3 for x=3 its 3×3+1. 3 times three is 9 plus 9 with one is 10, and the line hits 6.9
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PLEASE HURRY !! The triangles below will be used to construct a polygon.
Which type of polygon could be created?
Answer:
Rectangle
Step-by-step explanation:
The lengths are congruent and the widths are congruent.
Answer: Rectangle (4 sided polygon)
Step-by-step explanation:
The length and breadth in both triangles are equal which can also be said to be congruent. Adding the two triangles since they are both equal would result in a rectangular polygon (Rectangle)
Geometry unit 1 lesson 1
Final answer:
Geometry unit 1 lesson 1 typically covers basic understandings, vocabulary, and objectives related to geometry, such as points, lines, angles, and shapes.
Explanation:
In geometry, unit 1 lesson 1 typically covers basic understandings, vocabulary, and objectives related to geometry. Students learn about concepts such as points, lines, angles, and shapes. They also explore properties and relationships between geometric figures.
For example, students might learn that a point represents a specific location in space, a line is a straight path with no endpoints, and an angle is formed by two rays with a common endpoint.
By studying geometry, students develop spatial reasoning skills and learn to apply geometric principles in problem-solving situations.
write an equation in point-slope form of the line using points D(0,5),E(5,8)
Answer:
8 - 5 = m(5 - 0)
Hope that helps you! :)
7.
Call me maybe? The graph displays the cu
tive relative frequency of the lengths of phone
made from the math department office at Gabalo
High last month.
Cumulative relative
frequency (%)
0
5
10
35
40
45
15 20 25 30
Call length (min)
(a) About what percent of calls lasted 30 minutes or
more?
(b) Estimate the interquartile range (IQR) of the
distribution.
Answer:
a) 35%
b) 19 minutes
Step-by-step explanation:
The graph for this question is attached in the image below.
Part a) Percent of calls that lasted 30 minutes or more
As seen in the graph, the x-axis represent the duration of the call in minutes and y-axis represent the cumulative frequency of the calls.
From the graph we can see that the cumulative frequency against the point 30 minutes is about 65%. This means, 65% of the calls lasted for less than 30 minutes.
Since, out of 100%, 65% of the calls lasted for less than 30 minutes, the percentage of call that lasted for 30% or more would be:
100% - 65% = 35%
This means, 35% of calls lasted 30 minutes or more.
Part b) The interquartile range (IQR) of the distribution.
Interquartile range is defined as the difference of the 3rd Quartile and the 1st Quartile.
3rd Quartile is the point, below which 75% of the data values are present.
1st Quartile is the point, below which 25% of the data values are present.
So, from the cumulative frequency graph we have to look for the values on time axis against the cumulative frequency of 25% and 75%.
The amount of time against 25% cumulative frequency is approximately 13 minutes.
So, 1st Quartile = 13 minutes
The amount of time against 75% cumulative frequency is approximately 32 minutes.
So, 3rd Quartile = 32 minutes
Therefore,
IQR = 3rd Quartile - 1st Quartile
IQR = 32 - 13
IQR = 19 minutes
The interquartile range (IQR) of the distribution is 19 minutes.
Answer:
A,B,E,AND F
Step-by-step explanation:
HOPE THIS HELPS
The expression 146 ÷ 144 is equal to _____.
Answer:1.01
Step-by-step explanation:
The expression 146 ÷ 144 equals 1.0138. This result is obtained by dividing 146 by 144.
Explanation:The expression 146 ÷ 144 equals 1.0138 when rounded to four decimal places. The calculation involves the division of two numbers, in this case, 146 divided by 144. To perform this calculation, you simply take the first number, 146, and divide it by the second number, 144, which gives you 1.0138.
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3649 * 7 use the distributive property to solve
Answer:
Step-by-step explanation:
7(3,649)
=7(3,000+600+40+9)
=(7*3,000)+(7*600)+(7*40)+(7*9)
=21,000+4,200+280+63
=25,480+63
=25,543
The table shows the weight of a newborn infant for its first year. During which three-month period was the infant's weight gain the greatest?
0 Months: 7 1/4 lb
3 Months: 12 1/2 lb
6 Months: 16 5/8 lb
9 Months: 19 4/5 lb
12 Months: 23 3/20 lb
Answer:
12,9,6
Step-by-step explanation:
12=23 3/20. 9=19 4/5. 6=16 5/8.
The infant's weight was gain the greatest during (0 - 3 Months) three-month period.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
The weight gain during (0 - 3 Months) three-month period
⇒ 12 1/2 - 7 1/4 = 25/2 -29/4 = 12.5-7.25 = 5.25 lb
The weight gain during (3 - 6 Months) three-month period
⇒ 16 5/8 - 12 1/2 = 16.625 - 12.5 = 4.125 lb
The weight gain during (6 - 9 Months) three-month period
⇒ 19 4/5 - 16 5/8 = 19.8 - 16.625 = 3.175 lb
The weight gain during (9 - 12 Months) three-month period
⇒ 23 3/20 - 19 4/5 = 23.15 - 19.8 = 3.35 lb
Therefore, the infant's weight was gain the greatest during (0 - 3 Months) three-month period.
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plz help me i will give brainliest and 20 points
Step-by-step explanation:
2x - 12y = 2(x - 6y)2(3x + 1) = 6x + 23x + 12 = 3(x + 4)6(x - 2y) = 6x - 12y6(x + 2) = 6x + 126x + 3y = 3(2x + y) = 1/2(12x + 6y)Write forty two and eight hundredths in decimal form
URGENT
The cost to rent a ballroom is $51 up front plus an additional $23 per hour. If a ballroom is
rented for 2 hours, what is the cost?
Answer:
97
Step-by-step explanation:
Equation:
51+23x, where x = the number up hours
so 51+23(2)=97
51+46=97
(20 Points!!) Which expressions are equivalent?
Answer:
i think it is the last one
Step-by-step explanation:
Check your answer if unsure
Chloe bought 12 chicken wings for $15. What was the cost of the wings in dollars per wing? Express your answer in simplest form.
The cost of the wings in dollars per wing would be $1.25.
To find this, all you need to do is divide the $15 by your amount of chicken wings, which is 12. 15/12 = 1.25.
Answer:
1.25
Step-by-step explanation:
each wings costs 1 $ and 25 cents
The angles of a rectangle are equal.
always
sometimes
never
Answer: A rectangles angles are always equal.
Step-by-step explanation:
Suppose you have a rectangle, four sides, two pairs of parallel lines. in order to be a rectangle, the quadrilateral has to have equal angles, similar to a square, if they didn't, they could be a trapezoid, which is not a rectangle, because it only has one pair of parallel lines.
Hope this helps!
Answer:
They are always equal
Step-by-step explanation:
Because they all have equal sides they can be measured to confirm that the sides are equal.
Write 2,930,365 in expanded notation
Step-by-step explanation: The place value chart can help us write a number in expanded notation. When we put 2,930,365 into the place value chart, we can recognize that our number is equal to 2 millions + 9 hundred thousands + 3 ten thousands + 0 thousands + 3 hundreds + 6 tens + 5 units.
The place value chart is attached in the image provided.
Answer:
Step-by-step explanation:
How do we figure out the value of a variable?
Answer:
To figure out the value of a variable you plug it into an equation solve for it using the equation around it.
Answer:
Step-by-step explanation:
Solve for the unknown variable(number) by moving everything to the other side of the equation.
A vender is loading candybars into a vending machine. Each slot holds 130cm of candy barsand each candy bar is 1.5cm thick, how many bars will fit.
Answer:
86
Step-by-step explanation:
since the slot is 130 cm thick you divide that by the thickness of the candy bar 130/1.5 and then you get 86.6666666.....which rounds to 86 because the slot is not thick enough for another candy bar. good luck on whatever you needed this for!
Harry needs 21 square meters of fabric for every 6 wizard cloaks he makes. How many cloaks could he make with 7 square meters of fabric
Answer: 2
Step-by-step explanation:
First, set up a proportion based on the amount of square meters over the number of cloaks he can make:
21/6 = 7/x
Cross multiply to get your next proportion and result with this:
21x = 42
Divide both sides by 21 (always divide the side with the variable):
21x/21 = 42/21
Cancel out the 21 (it's being divided by 21 so that makes it equivalent to 1 so you wind up with just x)
x = 2
Answer: 2
Step-by-step explanation:
Given : Harry needs 21 square meters of fabric for every 6 wizard cloaks he makes.
Using Unitary method , The number of cloaks can be made in 1 square meter fabric will be :-
[tex]6\div21=\dfrac{6}{21}=\dfrac{2}{7}[/tex]
Now , the number of cloaks made in 7 square meters of fabric will be :-
[tex]\dfrac{2}{7}\times7=2[/tex]
Hence, the number of cloaks made in 7 square meters of fabric =2