At 8am Sunday morning, the temperature was 35 degrees Fahrenheit. A student recorded the change in temperature at 8:00am for the next three days. Which number line shows a point representing the temperature on Wednesday morning at 8:00am? *
Answer:
B. 28 degrees
Step-by-step explanation:
ok so,
the starting temperature is 35 degrees then the temperature dropped 4 degrees. making the temp 31 degrees. next the temperature rose 2 degrees, making it 33 degrees. lastly, the temperature dropped another 5 degrees making it 28 degrees out on wednesday.
so the number line showing this would be B.
Final answer:
After a cold front caused the temperature to drop by 40 degrees from the initial 35 degrees Fahrenheit, the resulting temperature would be -5 degrees Fahrenheit on the number line for Wednesday morning at 8:00am.
Explanation:
The student originally observed a temperature of 35 degrees Fahrenheit on Sunday morning. If we suppose a cold front blows in and drops the temperature by 40.0 Fahrenheit degrees, the temperature change can be calculated by subtracting 40 from the initial temperature:
35 °F - 40 °F = -5 °F
Therefore, the number line that shows the temperature on Wednesday morning at 8:00am should have a point at -5 degrees Fahrenheit, representing the new temperature after the cold front.
y=6x-7 and find the x intercept
Answer:
x-intercept
= 7/6
= 1.16667
if 3 popsicles cost $5.25. at this rate how much would 1 popsicle cost?
Which number is greatest?
2.89 x 10^-8
1.997 x 10^2
8.9×10^-6.
5×10^-6
Answer:
1.997 x 10²
Step-by-step explanation:
The number with the highest exponent is the greatest value.
10² is bigger than 10⁻⁶ and 10⁻⁸, so 1.997 x 10² is your answer.
Simplify -12x^4/x^4+8x^5
Answer:
OPTION A: [tex]$ \frac{12}{1 + 8x} $[/tex], where [tex]$ x \ne - \frac{1}{8} $[/tex].
Step-by-step explanation:
Given: [tex]$ \frac{- 12x^4}{x^4 + 8x^5} $[/tex]
Taking [tex]$ x^4 $[/tex] common outside in the denominator, we get:
[tex]$ = \frac{-12x^4}{(x^4)(1 + 8x)} $[/tex]
[tex]$ x^4 $[/tex] will get cancelled on the numerator and denominator, we get:
[tex]$ = \frac{-12}{1 + 8x} $[/tex]
we know that the denominator can not be zero.
That means, 1 + 8x [tex]$ \ne $[/tex] 0.
[tex]$ \implies 8x \ne -1 $[/tex]
[tex]$ \implies x \ne \frac{-1}{8} $[/tex]
So, the answer is: [tex]$ \frac{-12}{1 + 8x} $[/tex], where [tex]$ x \ne \frac{-1}{8} $[/tex].
A.
discrete
B.
continuous
C.
linear
D.
nonlinear
E.
increasing
F.
decreasing
G.
both increasing and decreasing
H.
neither increasing nor decreasing
A 4.15 percent TIPS has an original reference CPI of 182.1. If the current CPI is 188.3, what is the par value of the TIPS?
Answer:
par value of the TIPS is $1034.05
Step-by-step explanation:
Given:
- original reference CPI = 182.1
- current CPI = 188.3
Assume face value of tips = $1000
par value of the TIPS = [tex]face\ value\ of\ tips\times \frac{current\ CPI}{original\ reference\ CPI}[/tex]
par value of the TIPS = [tex]1000\times \frac{188.3}{182.1}\approx $1034.05[/tex]
Final answer:
The par value of a TIPS adjusts with the CPI's inflation rate. To find the adjusted par value of a 4.15% TIPS, multiply the original par value by 1 plus the inflation rate, which is determined by the percentage increase from the original to the current CPI.
Explanation:
A student asked about the par value of a Treasury Inflation-Protected Security (TIPS) given an original reference Consumer Price Index (CPI) of 182.1 and a current CPI of 188.3. The par value of TIPS adjusts with inflation to protect investors, with the adjustment based on the change in the CPI.
First, we need to calculate the percentage increase in the CPI by using the formula:
(Current CPI - Original CPI) ÷ Original CPI x 100%.
Plugging in the given CPI values:
(188.3 - 182.1) ÷ 182.1 = 0.0340 or 3.40%
This percentage tells us how much the CPI has increased since the TIPS was issued. To find the adjusted par value, you would multiply the original par value of the TIPS (which is typically $1,000) by 1 plus the inflation rate. Since we do not have the original par value, we can only provide the formula for its calculation.
The adjusted par value would be:
Original Par Value x (1 + Inflation Rate).
Input value of which f (x)=3
Answer:
y = 3
Step-by-step explanation:
A sandbox has an area of 26 square feet . The length is 6 1/2 feet. What is the width of the sandbox
Answer:
The width of the sandbox is 4 feet
Step-by-step explanation:
Area = Length x Width
Fill in known values
26 sq ft = 6.5 ft x w
Divide by 6.5 on both sides
4 ft = w
Width = 4 ft
:)
-2/3, -4/5, -4/6, -5/4
The slope is -4/5
Step-by-step explanation:
We have to observe the graph to find two points to find slope.
The graph has two points
(-5,0) and (0, -4)
The formula for slope is given by:
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\[/tex]
Here
(x1,y1) = (-5,0)
(x2,y2) = (0,-4)
Putting the values
[tex]m = \frac{-4-0}{0+5}\\=-\frac{4}{5}[/tex]
Hence,
The slope is -4/5
Keywords: slope, steepness
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(-6) x (3) = (3 x 6) x 3 =-1 x-1 =
Answer:
They are not equal? I don't get what you're trying to ask.
f(x) = 1/x
g(x) = x - 4
Can you evaluate (gof)(0)? Explain why or why
not.
(gof)(0) cannot be evaluated
Solution:
Given that,
[tex]f(x) = \frac{1}{x}\\\\g(x) = x - 4[/tex]
A composite function is denoted by (g o f) (x) = g (f(x)).
The notation g o f is read as “g of f”
Therefore, let us find whether (gof)(0) can be evaluated or not
To find (gof)(0):
(g o f) (x) = g (f(x))
Now substitute the given value of f(x)
[tex](g o f) (x) = g(\frac{1}{x})[/tex]
[tex]\text{ Substitute } x = \frac{1}{x} \text{ in } g(x) = x - 4[/tex]
[tex](g o f) (x) = \frac{1}{x} - 4[/tex]
Now to find (gof)(0), substitute x = 0
[tex](g o f) (x) = \frac{1}{0} - 4[/tex]
Since 1 divided by 0 is undefined, because any number divided by 0 is undefined
(gof)(0) cannot be evaluated
Answer:
You must evaluate the function f first.
Division by 0 is undefined.
The composition cannot be evaluated.
Step-by-step explanation:
Which religious settlement was reached with the Peace of Augsburg?
Final answer:
The Peace of Augsburg allowed rulers to establish either Lutheranism or Roman Catholicism as the official religion in their lands, giving birth to the principle 'whose realm, their religion' but excluded other religious groups such as Calvinists and Anabaptists.
Explanation:
The religious settlement reached with the Peace of Augsburg in 1555 allowed rulers within the Holy Roman Empire to choose either Lutheranism or Roman Catholicism as the official religion of their territories. This principle, known as cuius regio, eius religio ('whose realm, their religion'), meant that a ruler's subjects were obliged to follow the same religion.
The Peace of Augsburg formally recognized the division between Catholics and Protestants, mainly Lutherans, and ended the religious conflict within the empire at that time. However, other religious groups, such as Calvinists and Anabaptists, were not accommodated, and the agreement failed to resolve underlying tensions leading to future wars, including the devastating Thirty Years' War.
Two sides of a triangle have the following measures: 15 and 39. What is the range of possible measures for the third side?
A) 15 < x < 24
B) 24 < x < 39
C) 24 < x < 54
D) 39 < x < 54
Answer:
Option C) 24 < x < 54
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Let
x ----> the measure of the third side
Applying the triangle inequality theorem
1) [tex]15+39 > x[/tex]
[tex]54 > x[/tex]
Rewrite
[tex]x < 54\ units[/tex]
2) [tex]x+15> 39[/tex]
[tex]x > 39-15[/tex]
[tex]x > 24\ units[/tex]
therefore
The range of possible measures for the third side is the interval (24,54)
Can anyone solve the 8th question given below??? Urgent!!
Answer:
AY = 10 cm.
Step-by-step explanation:
Given that, ΔABC is similar to ΔAXY
and [tex]\frac{AB}{AX } = \frac{5}{3}[/tex]
⇒ [tex]\frac{AC}{AY } = [tex]\frac{BC}{XY } = \frac{5}{3}[/tex]
⇒ BC = XY× \frac{5}{3}[/tex] = \frac{20}{3}[/tex] (as XY = 4 cm given)
Now, check the attached figure,
given, BY bisects ∠XYC
let ∠XYB = ∠BYC = x
⇒ ∠AYX = 180-2x (angle on a straight line)
and also ∠AYX = ACB (similar triangle properties)
⇒ ∠ACB = 180-2x
Now, sum of angles in ΔBYC = 180°
⇒ ∠YBC = x
⇒ BC = YC (as two sides of equal angles are equal in a triangle)
⇒ YC = \frac{20}{3}[/tex]
And also [tex]\frac{AC}{AY } = \frac{5}{3}[/tex]
AC = AY + YC
⇒ [tex]\frac{AY+YC}{AY } = \frac{5}{3}[/tex]
⇒ [tex]\frac{AY+\frac{20}{3}[/tex]}{AY } = \frac{5}{3}[/tex]
⇒ 5AY = 3AY + 20
⇒ AY = 10 cm
Danny needs to buy a lawn mower and 3 wheelbarrows for his business. The lawn mower cost $1500. If Danny has $2000 to spend, what is the most each wheelbarrow can cost?
Answer:
the most it could cost would be $83 dollars
Step-by-step explanation:
2000-1500=500
500/3=83.33
Is 6 15/28 or 6 5/9 bigger?
Answer:
[tex]6 \frac{5}{9} [/tex]
is greater than
[tex]6 \frac{15}{28} [/tex]
Answer:6 5/9 is greater than 6 15/28
Step-by-step explanation: positive proper fractions: 15/28, 5/9;
1 positive integer number: 6; Any positive proper fraction is smaller than
any positive integer number Sort the positive proper fractions:
15/28 and 5/9 15/28 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
15 = 3 × 5;
28 = 22 × 7;
5/9 already reduced to the lowest terms;
the numerator and the denominator have no common prime factors:
5 is a prime number;
9 = 32; 15 = 3 × 5;
5 is a prime number;
Multiply all the unique prime factors, by the largest exponents:
LCM (15, 5) = 3 × 5 = 15 Divide LCM by the numerator of each fraction:
For fraction: 15/28 is 15 ÷ 15 = (3 × 5) ÷ (3 × 5) = 1;
For fraction: 5/9 is 15 ÷ 5 = (3 × 5) ÷ 5 = 3; Build up all the fractions to the same numerator (which is LCM).
Multiply the numerators and the denominators by their expanding number:
15/28 = (1 × 15)/(1 × 28) = 15/28;
5/9 = (3 × 5)/(3 × 9) = 15/27;
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What are the 3 undefined terms of geometry?
Point, polygon and parallel
Point, line and plane
Line, ray and segment
Measure, draw, and construct
Answer: point, line, and plane.
Step-by-step explanation:
Answer:
Hope it helps In Geometry, we have several undefined terms: point, line and plane. From these three undefined terms, all other terms in Geometry can be defined. A line is defined as something that extends infinitely in either direction but has no width and is one dimensional while a plane extends infinitely in two dimensions.
Step-by-step explanation:
Solve for x: 6/x = 4/8
Answer: x = 12
Step-by-step explanation:
[tex]\frac{6}{x}[/tex] = [tex]\frac{4}{8}[/tex]
cross multiply
4x = 6 × 8
4x = 48
divide through by 4
x = 12
A deck of cards contains 52 cards. These cards consist of four suits (hearts, spades, clubs, and diamonds) of each of the following: 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace. If a card is chosen from a deck of cards, find the probability of drawing the 8 of spades.
The probability of drawing the 8 of spades from a deck of cards is 1/52, or approximately 0.0192, which can also be expressed as 1.92%.
Explanation:The probability of drawing the 8 of spades from a deck of cards is calculated as the number of favorable outcomes divided by the total number of possible outcomes. In this case, there is only 1 8 of spades card in the deck, and there are a total of 52 cards. Therefore, the probability is 1/52, or approximately 0.0192, which can also be expressed as 1.92%.
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These is 1/3 gallon of water in a 3-gallon container. What fraction of the container is filled? Write a multiplication and division equals to represent the situation.
Final answer:
The fraction of a 3-gallon container filled with 1/3 gallon of water is 1/9. This is found by dividing the amount of water by the total capacity of the container. It can be represented through multiplication and division, both yielding the result 1/9.
Explanation:
The question asks what fraction of a container is filled if there is 1/3 gallon of water in a 3-gallon container. To represent this situation, we can simply realize that the fraction filled is equal to the amount of water in the container (1/3 gallon) divided by the container's total capacity (3 gallons).
Identify the fraction of the container that is filled with water: 1/3 gallon.Identify the total capacity of the container: 3 gallons.Divide the amount of water by the total capacity to find the fraction of the container that is filled: (1/3) ÷ 3 = 1/9.So, 1/9 of the container is filled with water.
To set up a multiplication and division equation to represent the situation:
Multiplication: 1/3 gallon * 1/3 = 1/9Division: 1/3 gallon ÷ 3 = 1/9These representations show how to derive the fraction of the container that is filled using multiplication and division.
If h is an angle bisector of the given isosceles triangle, what is the measure of ∠a if ∠c = 55°?
Answer:
[tex]\angle a=35^o[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
An isosceles triangle has two equal sides and two equal interior angles
The angles opposite to the equal sides of an isosceles triangle are equal.
[tex]\angle b=\angle c[/tex]
we have
[tex]\angle c=55^o[/tex] -----> given problem
so
[tex]\angle b=55^o[/tex]
Remember that
The sum of the interior angles in any triangle must be equal to 180 degrees
[tex]\angle b+\angle c+2\angle a=180^o[/tex]
substitute the given values
[tex]55^o+55^o+2\angle a=180^o[/tex]
[tex]110^o+2\angle a=180^o[/tex]
[tex]2\angle a=180^o-110^o[/tex]
[tex]2\angle a=70^o[/tex]
[tex]\angle a=35^o[/tex]
The sum of two numbers is 278. One number is 52 more than the other number. What are the two numbers
Answer:
The numbers are 165 and 113
Step-by-step explanation:
Let
x ----> one number
y ----> the other number
we know that
[tex]x+y=278[/tex] ----> equation A
[tex]x=y+52[/tex] ----> equation B
substitute equation B in equation A
[tex](y+52)+y=278[/tex]
solve for y
[tex]2y=278-52[/tex]
[tex]2y=226[/tex]
[tex]y=113[/tex]
Find the value of x
[tex]x=y+52[/tex]
[tex]x=113+52=165[/tex]
therefore
The numbers are 165 and 113
how to solve this please
Answer:
Step-by-step explanation:
If (3, 5) is a solution of both y= 4x + 7 and y=5, what is the solution of 4x + 7=5?
Answer:
Step-by-step explanation:
X=-1/2
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Yes, -1/2 will be the x-coordinate for the solution. We can also find the y-coordinate by subbing in -1/2 for x in the equation y=4x+7.
y=4(-1/2)+7
y=-2+7
y=5
The intersection point would be (-1/2,5).
write an equation for the line that passes through the given point and is parallel to the graph of the given equation.
(10, -5) y= 3/2x-7
(6,2) y= 2/3x+19
Answer:
[tex]\displaystyle 2x - 3y = 6\:OR\:y = \frac{2}{3}x - 2 \\ \\ 3x - 2y = 40\:OR\:y = \frac{3}{2}x - 20[/tex]
Step-by-step explanation:
2 = ⅔[6] + b
4
[tex]\displaystyle -2 = b \\ \\ y = \frac{2}{3}x - 2[/tex]
If you want it in Standard Form:
y = ⅔x - 2
- ⅔x - ⅔x
_________
−⅔x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid it.]
−3[−⅔x + y = −2]
[tex]\displaystyle 2x - 3y = 6[/tex]
_______________________________________________
−5 = 3⁄2[10] + b
15
[tex]\displaystyle -20 = b \\ \\ y = \frac{3}{2}x - 20[/tex]
If you want it in Standard Form:
y = 3⁄2x - 20
- 3⁄2x - 3⁄2x
__________
−3⁄2x + y = −20 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]
−2[−3⁄2x + y = −20]
[tex]\displaystyle 3x - 2y = 40[/tex]
* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so ⅔ and 3⁄2 remain the way they are.
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On Monday morning, Susan bought 2.5 pounds of grapes at the supermarket.That day,Susan ate some grapes and had 1.75 pounds of grape left. What is the percent decrease of pounds of grapes on Monday?
Answer:
30%
Step-by-step explanation:
Use formula to find percent decrease
[tex]\text{Percent Decrease}=\dfrac{\text{Old Value}-\text{New Value}}{\text{Old Value}}\cdot 100\%[/tex]
In your case,
Old Value = 2.5 pounds
New Value = 1.75 pounds
Hence,
[tex]\text{Percent Decrease}=\dfrac{2.5-1.75}{2.5}\cdot 100\%\\ \\=\dfrac{0.75}{2.5}\cdot 100\%\\ \\=\dfrac{75}{250}\cdot 100\%\\ \\=\dfrac{3}{10}\cdot 100\%\\ \\=30\%[/tex]
A triangle has an area of 52 square meters. and a height of 13 meters. Find the length of the base.
Answer:
Length of the base = 8
Step-by-step explanation:
Area of a triangle = 1/2(h*b)
h = height
b = base
52 = 1/2 (13 * b)
Rearrange the equation to get b on it's own
52 * 2 = 13 * b
104 = 13 * b
104/13 = b
b = 8
A = 1/2(bh)
in this case, b = 2a/h. plug in the values:
steps
b = 2a/h
b = 2(52)/13
b = 104/13
b = 8 meters
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Find the area. You answer will be a decimal.
_________ ft²
Answer:
26.4 ft^2 (1 d.p.)
Step-by-step explanation:
[tex]area \: of \: circle = \pi {r}^{2} [/tex]
Since it is given that r, the radius of the circle, is 2.9 ft,
area of circle= π(2.9)^2= 8.41π= 26.4 ft^2 (1 d.p.)
In which of the following functions would it be appropiate to use only positve integers for the domain?Select all that apply.
Complete Question:
As you may have unintentionally forgotten to add the answer choices in your question, but I was able to find the complete the question and answering your question based on this as it may surely clear your concepts. Here is the complete question.
In which of the following functions would it be appropriate to use only positive integers for the domain? Select all that apply.
The function c(p) represents The cost for P people to attend the movies. The function m(t) represents the miles driven over T hours. The function t(m) represents the average high temperature for a given number of months. The function p(w) represents the prophet of a farmer who sells whole watermelons. The function h(n) represents the number of person-hours it takes to assemble n engines in a factory.
Answer Explanation:
Domain is termed as all the input values on a certain interval that define the function.
Here are the appropriate function scenarios where it is appropriate to use only positive integers.
The function c(p) represents The cost for P people to attend the movies.
As the function c(p) contains people. And People are not counted as negative, although they can be zero. So, only positive integers should be appropriate to use in this scenario.
The function m(t) represents the miles driven over T hours
As the function m(t) contains miles. And miles are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.
The function t(m) represents the average high temperature for a given number of months.
As the function t(m) contains months. And months are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.
The function p(w) represents the prophet of a farmer who sells whole watermelons.
As the function p(w) contains the number of watermelons. And watermelons are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.
The function h(n) represents the number of person-hours it takes to assemble n engines in a factory.
As the function h(n) contains the number of engines. And engines are not counted as negative. They normally initiate with 1. So, only positive integers should be appropriate to use in this scenario.
Keywords: domain, function, positive integer
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