Hydrochloric acid (HCl) is combined with cesium hydroxide (CsOH) in a neutralization reaction.
Which ions will combine to form a salt? Check all that apply.
A. H+
B.H3O+
C.Cl-
D.Cs+
E.OH-
Answers
Answer:
HCl + CsOH --> CsCl + H2O
So the ions making up the salt: Cl- and Cs+
Answer:
H+
H3O+
C. Cl-
D.Cs+
OH-
Related Questions
Which ASSUMPTION is specific to the repeated measures ANOVA?
a. homogeneity of variance
b. IV measured on an interval or ratio scale
c. the same participants are tested in each level.
d. spehericity
Answers
The assumption that is specific to the repeated measures ANOVA is c. the same participants are tested in each level.
This is because in a repeated measures design, the same participants are tested multiple times under different conditions, and therefore any differences observed between conditions are assumed to be due to the manipulation of the independent variable rather than individual differences between participants.
The other assumptions listed (homogeneity of variance, IV measured on an interval or ratio scale, and sphericity) are also important for conducting a repeated measures ANOVA, but they are not specific to this type of design.
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The rubber track for a toy digger goes around four circular wheels of diameter 8 cm, as shown. (b) Calculate the length of the rubber track that goes around the four wheels. Give your answer correct to one decimal place.
Answers
Answer:
73.1 cm
Step-by-step explanation:
In the drawing, the rubber track is in black and the wheels are in light gray.
As we can see in the figure, the rubber track will have a length of two halfs of a circunference of radius 8 cm plus six diameters of 8 cm. So the total length is:
Length of rubber track = pi * 8 + 6 * 8 = 25.13 + 48 = 73.133 cm
Rounding to one decimal place, we have that the length is 73.1 cm
This question is incomplete because it lacks the diagram of the 4 circular wheels.
Find attached to this answer the appropriate diagram
Answer:
100.5cm
Step-by-step explanation:
The formula to be used in this calculation is the circumference of a circle.
The circumference of a circle can be defined as the actual length of a circle when it is stretch out(opened up) or the distance around a circle.
The formula for the circumference of a circle is given as 2πr where r = radius of the circle
Or πD where D = Diameter of the circle
In the question, we are given the diameter of the circle = 8cm
So we use the Formula
= πD
The length of the rubber track around one wheel is
= π × 8cm = 25.132741229cm
From the attached diagram, we can see we have 4 wheels.
The length of the rubber track that goes around the four wheels is calculated as
4 × 25.132741229cm = 100.53096491cm.
Approximately to one decimal place = 100.5cm
Therefore, the length of the rubber track that goes around the four wheels to one decimal place is 100.5cm
What is the sampling method that involves taking a random selection of people from a defined population?.
Answers
Simple random sampling is a sort of probability sampling in which a subset of participants from a population is randomly chosen by the researcher. There is an equal opportunity for selection for every person in the population. Then, information is gathered from as much of this random subset as is feasible.
What is simple random sampling, and why is it significant?
One technique researchers employ to select a sample from a broader population is a simple random sampling.
If there is an equal chance that any subject in a population will be chosen, this strategy is effective. In order to draw general conclusions about a group, researchers choose basic random sampling.
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1. The Fibonacci sequence In the 13th century, the Italian mathematician Leonardo Fibonacci-as a way to explain the geometic growth of a population of rabbits-devised a mathematical sequence that now bears his name. The first two terms in this sequence, Fib(0) and Fib(1), are 0 and 1, and every subsequent term is the sum of the preceding two. Thus, the first several terms in the Fibonacci sequence look like this: Fib(0) = 0 Fib(1) = 1 Fib(2) = 1 (0+1) Fib(3) = 2 (1+1) Fib(4)= 3 (1+2) Fib(5)=5 (2+3) Write a program that displays the terms in the Fibonacci sequence, starting with Fib(0) and continuing as long as the terms are less than 10,000. Thus, your program should produce the following numbers: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 This program continues as long as the value of the term is less than the maximum value, so that the loop construct you need is a while, presumably with a header line that looks like this: while term
Answers
To display the terms in the Fibonacci sequence, starting with Fib(0) and continuing as long as the terms are less than 10,000, a program is written with a loop construct. This loop is implemented using a `while` loop with a header line that looks like this: `while term < 10000:`.
Fibonacci sequence is named after the Italian mathematician Leonardo Fibonacci who developed a mathematical sequence in the 13th century to explain the geometric growth of a population of rabbits.
The first two terms in this sequence, Fib(0) and Fib(1), are 0 and 1, and every subsequent term is the sum of the preceding two.
The first several terms in the Fibonacci sequence are:
Fib(0) = 0, Fib(1) = 1, Fib(2) = 1, Fib(3) = 2, Fib(4)= 3, Fib(5)=5.
This program continues as long as the value of the term is less than the maximum
The output is as follows:
```1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765```
The while loop could also be used to achieve the same goal.
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A bleach and water solution with a 2:3 ratio means: A 1/3 part bleach and 2/3 part water B 2 cups of bleach and 3 cups of water C 3 cups of bleach and 2 cups of water
Answers
The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.
A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.
To understand this ratio, let's break it down using different units:
A. 1/3 part bleach and 2/3 part water:
If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.
B. 2 cups of bleach and 3 cups of water:
If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.
C. 3 cups of bleach and 2 cups of water:
If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.
Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.
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Dylan is wrapping a birthday present for his sister. The box the gift is in has a length of 6 inches, a width of 5 inches,
and a height of 3 inches. What is the minimum amount of wrapping paper Dylan will need to completely cover the
box?
TI
Answers
Answer:
126 square inches of wrapping paper
Step-by-step explanation:
To compute for the minimum amount of wrapping paper Dylan will need to completely cover the box, you have to compute the surface area of the box. The formula in getting the surface area of a rectangle is:
A = 2WL + 2LH + 2HW
Substituting the given measurements to the formula:
A = 2(5)(6) + 2(6)(3) + 2(3)(5)
A = 60 + 36 + 30
A = 126 square inches
Therefore, Dylan needs to purchase at least 126 square inches of wrapping paper to completely cover the box.
Answer:
Step-by-step explanation:
Is the sky blue???????
No No the sky is not blue.
A clear cloudless day-time sky is blue because molecules in the air scatter blue light from the sun more than they scatter red light. When we look towards the sun at sunset, we see red and orange colours because the blue light has been scattered out and away from the line of sight.
To understand why the sky is blue you need to remember how color works. Color is largely caused by how well an object absorbs the light spectrum. When you see a blue sky you only see blue because all the other colors were absorbed in the air. Any object with color works that way. For example a red ball is read because all the colors of light are absorbed by the ball except for red. This reflected light is what gives the object color.
This is what happens with the sky. The atmosphere is denser than we imagine and the different gases give the atmosphere unique properties in how it absorbs, diffuses, and reflects light. When sunlight passes through our atmosphere a portion of it is scattered and absorbed. The remainder either reaches the surface or is reflected back. The portion that makes it to us observers is 75 percent.
This process is called diffused sky radiation. So to review, we color because objects due to texture of dyes and surfaces absorb all light wavelengths and reflect back one or more. The reason we see the sky as blue is because the molecules in the air scatter the light absorbing most wavelengths of light except for blue.
In addition to this the sky is gray and overcast because of the water droplets in the atmosphere in the forms of clouds and humidity. water refracts light equally unlike air molecules in the atmosphere. This means we get the entirety of white light only it is dimmer just like when you shine a light through a white sheet.
The fact we see a blue sky is good thing because its shows that are atmosphere is at work shielding us from the full energy of the sun’s rays. While the sun is the largest source of energy to our planet, a lot of its high energy radiation that is deadly for living things. Our atmosphere plays it part by shielding us from that. So when you see a blue sky with your kid you can tell them it means the sky is acting like a huge shade blocking out the bad parts of the sun.
Answers
Answer:
thats cool
Step-by-step explanation:
a survey was given to 350 people asking whether people like dogs and/or cats. 186 said they like dogs 193 said they like cats 42 said they don't like cats or dogs. how many said they liked both cats and dogs?
Answers
By using the principle of inclusion-exclusion, The number of people who said they liked both cats and dogs is 111.
Let's break down the given information:
Total number of respondents (n) = 350
Number of people who like dogs (A) = 186
Number of people who like cats (B) = 193
Number of people who don't like cats or dogs (Neither) = 42
To find the number of people who like both cats and dogs, we can use the principle of inclusion-exclusion. We add the number of people who like dogs (A) and the number of people who like cats (B), and then subtract the number of people who like neither cats nor dogs.
Number of people who like both cats and dogs = A + B - Neither
Number of people who like both cats and dogs = 186 + 193 - 42 = 337 - 42 = 111
Therefore, the number of people who said they liked both cats and dogs is 111.
Out of the 350 people surveyed, 111 of them said they liked both cats and dogs. This indicates that there is a subset of individuals who have an affinity for both types of pets.
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What is 1 19/100 as a decimal?
Answers
Explanation:
Uhh well… 1 19/100 is the same as 119/100 so just do 119 divided by 100…
And then you’ll get 1.19 which is 1 19/100 as a decimal.
Hope this helps!
Answer: 1.19
Step-by-step explanation: To convert this mixed number (fraction) to a decimal just follow these two steps:
Step 1: divide numerator (19) by the denominator (100): 19 ÷ 100 = 0.19
Step 2: add this value to the the integer part: 1 + 0.19 = 1.19. So,
1 19/100 = 1.19
Rounded values:
1 19/100 = 1 rounded to 0 decimal places
1 19/100 = 1.2 rounded to 1 decimal place1
the nth term of a sequence is n²+20
work out the first 3 terms of the sequence
Answers
The first 3 terms of the sequence are 21, 24 and 29
Working out the first 3 terms of the sequenceFrom the question, we have the following parameters that can be used in our computation:
n² + 20
This means that
f(n) = n² + 20
The first 3 terms of the sequence is when n = 1, 2 and 3
So, we have
f(1) = 1² + 20 = 21
f(2) = 2² + 20 = 24
f(3) = 3² + 20 = 29
Hence, the first 3 terms of the sequence are 21, 24 and 29
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How do I solve for number 4 and 5?
Answers
Answer:
i cant really see the words
Step-by-step explanation:
what is the slope of the line that passes through the points (9, 5) and (21, -5)? write your answer in simplest form.
Answers
The slope of the line that passes through the points (9, 5) and (21, -5) is equal to -5/6.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (-5 - 5)/(21 - 9)
Slope, m = -10/12
Slope, m = -5/6.
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find the exact length of the curve. x = 5 12t2, y = 3 8t3, 0 ≤ t ≤ 3
Answers
To find the exact length of the curve defined by the parametric equations x = 5t^2 and y = 3t^3, where 0 ≤ t ≤ 3, we can use the arc length formula for parametric curves.
The arc length formula for a parametric curve defined by x = f(t) and y = g(t) over the interval [a, b] is given by:
L = ∫[a,b] √[ (dx/dt)^2 + (dy/dt)^2 ] dt
In this case, we have x = 5t^2 and y = 3t^3, with the parameter t ranging from 0 to 3.
First, we need to find the derivatives of x and y with respect to t:
dx/dt = d/dt (5t^2) = 10t
dy/dt = d/dt (3t^3) = 9t^2
Next, we substitute these derivatives into the arc length formula:
L = ∫[0,3] √[ (10t)^2 + (9t^2)^2 ] dt
L = ∫[0,3] √(100t^2 + 81t^4) dt
Now, we can integrate the expression inside the square root with respect to t:
L = ∫[0,3] √(100t^2 + 81t^4) dt
L = ∫[0,3] t√(100 + 81t^2) dt
Unfortunately, this integral does not have a simple closed-form solution. We would need to evaluate it numerically using numerical integration techniques or computer software.
So, the exact length of the curve cannot be determined algebraically. However, it can be approximated using numerical methods.
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help me i don’t know how to do this
Answers
Hi!
y = 16
x = 32
In 30-60-90 triangles, the hypotenuse is double the length of the shortest leg, and the longer leg is \(\sqrt{3}\) times the shorter leg.We are given the longest leg. To find the shortest leg, we must divide the longest leg value by \(\sqrt{3}\)
\(\cfrac{16\sqrt{3} }{\sqrt{3} }\)
The radicals cancel out and we are left with 16.
The length of y (the shortest leg) is 16.
Now, we also know that the hypotenuse is double the shortest leg. The shortest leg is 16, so if we double that, it's 32.
Mai runs around a 400-meter track at a constant speed of 200 meters per minute. How many minutes does it take Mai to complete 4 laps of the track?
Answers
Answer:
8 min
Step-by-step explanation:
Answer:
my cheaStep-by-step explanation:
A store sells 4 computers for every 9 printers. There store sells 36 computers on Tuesday, how many printers did it sell? The store sells 44 computers on Wednesday, how many printers did it sell? Create a ratio table
Answers
Answer:
Tuesday=81
Step-by-step explanation:
since 4 x 9 = 36, you have to multiply 9 x 9, which equals 81.
for Wednesday, 4 x 11 = 44, so you have to multiply 9 x 11, which = 99.
for the chart, do something like the photo i am showing for Tuesday (i already made it)
PLEASE HELP ME PLEASEEE I'll give brainliest if correct please help me...
Answers
Answer:
60 mph
50 wpm
$36.25 dollars an hour
Hope this helps :)
Answer:
120 miles in 2 hours = 60 miles per hour.
150 words per 3 min = 50 words per min
145 dollars in 4 hours = 36.25 dollars per hour
Step-by-step explanation:
Hope this helps! :)
Dennis Lamenti wants to buy a new car that costs $15,744.64. He has two possible loans in mind. One loan is through the car dealer; it is a four-year add-on interest loan at 7 3 4 % and requires a down payment of $1,000. The second is through his bank; it is a four-year simple interest amortized loan at 7 3 4 % and requires a down payment of $1,000. (Round your answers to the nearest cent.)
(a) Find the monthly payment for each loan.
dealer $
bank $
b) Find the total interest paid for each loan.
dealer $
bank $
Answers
Cost of the car = $15,744.64 Down payment = $1,000 The rate of interest = 7 3/4%Dealer's loan: Amount to be borrowed = $15,744.64 − $1,000 = $14,744.64Let, "P" be the monthly payment.
Amount to be repaid = P × 48 (four years = 4 × 12 months = 48 months) Let's calculate the total amount to be repaid: Total amount = $14,744.64 + $14,744.64 × 31/400 Total amount = $15,887.618 Let's substitute the values in the formula:Amount to be repaid = P × 48$15,887.618 = P × 48P = $331.41 Therefore, the monthly payment for the dealer's loan is $331.41.Bank's loan.
Let's substitute the values in the formula:Amount to be repaid = P × 48$19,795.69 = P × 48P = $412.07Therefore, the monthly payment for the bank's loan is $412.07.Total interest paid for dealer's loan = Total amount − Amount borrowed Total interest paid for bank's loan = Total amount − Amount borrowed Total interest paid = $19,795.69 − $14,744.64 Total interest paid = $5,051.05 Therefore, the total interest paid for the bank's loan is $5,051.05. Answer:Monthly payment for dealer's loan = $331.41
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I NEED HELP ASAP I WILL GIVE 100 PTS IF YOU HELP ME AND GIVE RIGHT ANSWER AND I NEED EXPLANATION PLS HELP
A student is painting a doghouse like the rectangular prism shown.
A rectangular prism with base dimensions of 8 feet by 6 feet. It has a height of 5 feet.
Part A: Find the total surface area of the doghouse. Show your work. (3 points)
Part B: If one can of paint will cover 50 square feet, how many cans of paint are needed to paint the doghouse? Explain. (Hint: The bottom will not be painted since it will be on the ground.) (1 point)
Answers
Answer:
A: 236 sqaure ft.
B: 4 cans
Step-by-step explanation:
Sure, I can help you with that.
Part A:
The total surface area of a rectangular prism is calculated using the following formula:
Total surface area = 2(lw + wh + lh)
where:
l = lengthw = widthh = heightIn this case, we have:
l = 8 feetw = 6 feeth = 5 feetPlugging these values into the formula, we get:
Total surface area = 2(8*6+6*5+8*5) = 236 square feet
Therefore, the total surface area of the doghouse is 236 square feet.
Part B:
Since the bottom of the doghouse will not be painted, we only need to paint the top, front, back, and two sides.
The total surface area of these sides is 236-6*8 = 188 square feet.
Therefore,
we need 188 ÷ 50 = 3.76 cans of paint to paint the doghouse.
Since we cannot buy 0.76 of a can of paint, we need to buy 4 cans of paint.
Answer:
A) 236 ft²
B) 4 cans of paint
Step-by-step explanation:
Part AThe given diagram (attached) shows the doghouse modelled as a rectangular prism with the following dimensions:
width = 6 ftlength = 8 ftheight = 5 ftThe formula for the total surface area of a rectangular prism is:
\(S.A.=2(wl+hl+hw)\)
where w is the width, l is the length, and h is the height.
To find the total surface area of the doghouse, substitute the given values of w, l and h into the formula:
\(\begin{aligned}\textsf{Total\;surface\;area}&=2(6 \cdot 8+5 \cdot 8+5 \cdot 6)\\&=2(48+40+30)\\&=2(118)\\&=236\; \sf ft^2\end{aligned}\)
Therefore, the total surface area of the doghouse is 236 ft².
\(\hrulefill\)
Part BAs the bottom of the doghouse will not be painted, to find the total surface area to be painted, subtract the area of the base from the total surface area:
\(\begin{aligned}\textsf{Area\;to\;be\;painted}&=\sf Total\;surface\;area-Area\;of\;base\\&=236-(8 \cdot 6)\\&=236-48\\&=188\; \sf ft^2\end{aligned}\)
Therefore, the total surface area to be painted is 188 ft².
If one can of paint will cover 50 ft², to calculate how many cans of paint are needed to paint the doghouse, divide the total surface area to be painted by 50 ft², and round up to the nearest whole number:
\(\begin{aligned}\textsf{Cans\;of\;paint\;needed}&=\sf \dfrac{188\;ft^2}{50\;ft^2}\\\\ &= \sf 3.76\\\\&=\sf 4\;(nearest\;whole\;number)\end{aligned}\)
Therefore, 4 cans of paint are needed to paint the doghouse.
Note: Rounding 3.76 to the nearest whole number means rounding up to 4. However, even if the number of paint cans needed was nearer to 3, e.g. 3.2, we would still need to round up to 4 cans, else we would not have enough paint.
PLSSS HELP IF YOU TURLY KNOW THISSS
Answers
Answer:
x=3
Step-by-step explanation:
2(10x+2)=64
20x+4=64
20x=60
x=60÷20
x=3
Answer:
x=3
Step-by-step explanation:
2
(10x+2)=64
=
20x+4=64
Subtract 4 from both sides
20x=60
Divide both sides by 20
20x/20 = 60/20
therefore x = 3
Father is 20 years older than his son. 5 years ago Father was 3 times as old as his son. Find their present ages?
Answers
The present age of the Father is 35 and the age of the Son is 15 years after solving the given problem.
By examining the given problem we can solve it in the following way:
Present age:
Let x = Son's present age
x + 20 = Father's present age
5 years ago:
x - 5 = Son's age 5 years ago
x + 20 -5 = father's age 5 years ago
Father's age 5 years ago = 3( Son's age 5 years ago )
x + 20 - 5 = 3 (x - 5)
x + 15 = 3x - 15
2x = 30
x = 15
x = 15, Son's present age
x + 20 = 35 = father's present age.
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Mrs. Thornberry wrote three examples of expressions on the board as shown. Using the
examples, write your prediction of what makes something a mathematical expression in the space
below her examples.
-25
30a + 8
-4.2x + 9y - 13x
Answers
When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression
Write an equation of a circle that is centered at (1,-4) with a radius of 10.
Answers
Answer:
\((x-1)^2 + (y+4)^2 = 100\\\\\)
=====================================================
Work Shown:
\((x-h)^2 + (y-k)^2 = r^2\\\\(x-1)^2 + (y-(-4))^2 = 10^2\\\\(x-1)^2 + (y+4)^2 = 100\\\\\)
You could expand terms out and simplify, but I think it's more handy to leave it in this form so you can easily spot the center and radius from a glance.
The solution is, (x - 1)² + (y + 4)² = 100 , is the equation of a circle that is centered at (1,-4) with a radius of 10.
What is circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. The perimeter around the circle is known as the circumference.
here, we have,
we know that,
the standard form of a circle equation is
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle, and r is the radius.
to get r² we simply use the given radius,
here, r = 10
so, we get,
r² = 100
now, circle that is centered at (1,-4)
so, we have,
(x - 1)² + (y + 4)² = 10²
we get, equation in standard form is therefore
(x - 1)² + (y + 4)² = 100
Hence, The solution is, (x - 1)² + (y + 4)² = 100 , is the equation of a circle that is centered at (1,-4) with a radius of 10.
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Ethan is deciding between two different movie streaming sites to subscribe to. Plan A costs $28 per month plus $2. 50 per movie watched. Plan B costs $37 per month plus $1 per movie watched. Let � A represent the monthly cost of Plan A if Ethan watches � x per month, and let � B represent the monthly cost of Plan B if Ethan watches � x movies per month. Write an equation for each situation, in terms of � , x, and determine the interval of movies watched, � , x, for which Plan A is cheaper than Plan B
Answers
If Ethan watches fewer than 6 movies per month, Plan A would be more expensive. If he watches more than 6 movies per month, Plan B would be more expensive.
For Plan A, the monthly cost is composed of a fixed fee of $28 plus a variable fee of $2.50 per movie watched. So, if Ethan watches x movies per month, the monthly cost for Plan A can be represented by the equation:
A = 28 + 2.5x
Here, A represents the monthly cost of Plan A, and x represents the number of movies Ethan watches per month.
For Plan B, the monthly cost is also composed of a fixed fee of $37, but the variable fee per movie watched is only $1. So, if Ethan watches x movies per month, the monthly cost for Plan B can be represented by the equation:
B = 37 + 1x
Again, B represents the monthly cost of Plan B, and x represents the number of movies Ethan watches per month.
To find the number of monthly movies watched, x, that would make the two plans have an equal monthly cost, we need to solve the equation:
A = B
So, we can substitute the equations for A and B to get:
28 + 2.5x = 37 + 1x
Now we can solve for x:
2.5x - 1x = 37 - 28
1.5x = 9
x = 6
So, if Ethan watches 6 movies per month, the monthly cost of Plan A and Plan B would be equal, at $41 per month.
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How many hours did it take Miriam to bike the initial 8 miles?
Answers
Answer:
Step-by-step explanation:
Answer:
45 minutes = 0.75 miles
Step-by-step explanation:
90-45 = 45
Translate the sentence into an inequality. Eight times the sum of a number and 27 is at most "-15." Use the variable y for the unknown number.
Answers
Answer:
8(y + 27) ≤ -15
Step-by-step explanation:
In the given inequality statement, "Eight times the sum of a number and 27 is at most "-15""
The first part, "Eight times the sum of a number and 27" means that 8 is multiplied to the sum of y and 27. While the phrase "at most" means "less than or equal to (≤)" The phrase also implies that the value of y can be -15, or any value less than -15.
Therefore, the correct algebraic expression is: 8(y + 27) ≤ -15
Lines ac and bd intersect at point o. lines ac and bd intersect at point o. if m∠aod = (5x − 4)° and m∠boc = (4x 5)°, what is m∠boc? 9° 10° 41° 82°
Answers
The angle measure of m∠BOC is 41 degrees as per the concept of opposite angles. The correct option is C.
Given lines AC and BD intersect at point O, the angles m∠AOD and m∠BOC are opposite angles.
The property of opposite angles states that when two lines intersect, the angles opposite to each other are congruent.
Applying this property, we equate the measures of these angles: m∠AOD = m∠BOC.
m∠AOD = m∠BOC
5x - 4 = 4x + 5
Now, solve for x:
x = 9
Substitute x back into m∠BOC = (4x + 5)°:
m∠BOC = (4 * 9 + 5)°
m∠BOC = (36 + 5)°
m∠BOC = 41°
So, the angle m∠BOC is 41°. The correct answer is:
C. 41°
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The complete question:
Lines AC and BD intersect at point O. Lines AC and BD intersects at point O. If m∠AOD = (5x - 4)° and m∠BOC = (4x + 5)°, what is m∠BOC?
A. 9°
B. 10°
C. 41°
D. 82°
There are three points on a line, A, B, and C, so that AB = 12 cm, BC = 13. 5 cm. Find the length of the segment AC. Give all possible answers
Answers
The length of the line segment AC is 25.5 cm.
A line segment in geometry is a section of a line that has two clearly defined ends as its boundaries. It may be compared to a straight line that has two points where it begins and ends. Letters or points on the line, such as A and B, are frequently used to represent the two ends of a line segment. In contrast to a line, which extends forever in both directions, a line segment has a limited length. A ruler or other measuring device can be used to determine the length of a line segment.
To find the length of segment AC, we can use the fact that the sum of the lengths of two segments on a line is equal to the length of the entire line. That is:
AB + BC = AC
Substituting the given values, we get:
12 cm + 13.5 cm = AC
Simplifying:
AC = 25.5 cm
Therefore, the length of segment AC is 25.5 cm.
There is only one possible answer for the length of segment AC since it is uniquely determined by the lengths of segments AB and BC.
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Which expression represents the relationship between the step number n and the total number of small squares in the pattern?
A pattern of small squares. Step 1 has 0 squares. Step 3 has 3 squares: 2 by 2 but missing the lower right square. Step 3 has 8 squares: 3 by 3 but missing the lower right square.
A.
B.
C.
D.
Answers
Answer: n squared - 1
Step-by-step explanation:
The relationship between the step number {n} and the total number of small squares in the pattern is -
f(n) = 2ⁿ - 1.
What is expression in mathematics?An expression in mathematics is a combination of terms both constants and variables.
Given is a pattern of small squares as described -
Step 1 has 0 squares.
Step 2 has 3 squares : 2 by 2 but missing the lower right square.
Step 3 has 8 squares : 3 by 3 but missing the lower right square.
We can write the general expression for step {n} as -
Step {n} will have : 2ⁿ - 1 squares with missing the lower right square.
or
f(n) = 2ⁿ - 1
Therefore, the relationship between the step number {n} and the total number of small squares in the pattern is -
f(n) = 2ⁿ - 1.
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If a ball is thrown into the air with a velocity of 40ft/s, its height in feet t seconds later is given by y=40t−16t2.Find the average velocity for the time period beginning when t=2 and lasting 0.5 seconds
Answers
To find the average velocity for the time period beginning when t = 2 and lasting 0.5 seconds, we need to calculate the change in height and the change in time during that period.
Given the equation for the height of the ball as a function of time: y = 40t - 16t^2
Step 1: Determine the height at the initial time t = 2 seconds:
y1 = 40(2) - 16(2)^2
= 80 - 16(4)
= 80 - 64
= 16 feet
Step 2: Determine the height at the final time t = 2 + 0.5 = 2.5 seconds:
y2 = 40(2.5) - 16(2.5)^2
= 100 - 16(6.25)
= 100 - 100
= 0 feet
Step 3: Calculate the change in height:
Δy = y2 - y1
= 0 - 16
= -16 feet
Step 4: Calculate the change in time:
Δt = 2.5 - 2
= 0.5 seconds
Step 5: Calculate the average velocity:
Average velocity = Δy / Δt
Substituting the values:
Average velocity = (-16) / (0.5)
= -32 ft/s
Therefore, the average velocity for the time period beginning when t = 2 and lasting 0.5 seconds is -32 ft/s. The negative sign indicates that the ball is moving downward during this time interval.
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