c. 39
Step-by-step explanation:
the answer is 39
Suppose you play a game where you roll a fair six-sided die. If the die lands on an even number, you win $2, and if the die lands on an odd number, you lose $1. What is your expected value for one round of this game?
Show Work and Submit Full Answer
Answer:
1 buck
Step-by-step explanation:
Alright man im not a pro at this, so im not gonna have a professional explanation, but the final answer will be correct.
So listen up a dice has 6 sides labeled 1,2,3,4,5,6
3 of those are even
3 of those are odd
so you have a 50% chance of landing on an evan numbered side
and a 50% chance of landing on an odd-numbered side
So basically, if we play one round, there are 2 possibilities. We get even and win 2 bucks, or we get odd and lose a buck. We dont need to worry about probability as they are both 50%. Therfore, the value is 2-1 = 1 dollar. I found the value by subtracting the possbilities.
If we invest $40,000 at 8% simple interest, how much will we have saved in 20 years?
Answer:
$104,000
Step-by-step explanation:
For simple interest,
I = Prt
where I = interest earned
P = principal, amount invested
r = annual interest rate
t = time in years
I = $40,000 × 0.08 × 20
I = $64,000
The total amount saved is the principal amount plus the interest.
$40,000 + $64,000 = $104,000
Solving Equation with Root and Power. Can someone please step by step explain how to solve this problem please?
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
First, square both sides.
[tex]\left(\sqrt{3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6}}\, \right)^2= 3^2[/tex]
[tex]3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6} = 9[/tex]
This eliminates the square root over the entire left side of the equation.
Next, multiply both sides by 6 to get rid of the fraction on the left side.
[tex]6\left(3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6}\right) = 6( 9)[/tex]
[tex]6(3) + \left(4 + \sqrt{x+3} \, \right)^2 = 6(9)[/tex]
[tex]18 + \left(4 + \sqrt{x+3} \, \right)^2 = 54[/tex]
Then, subtract 18 from both sides to isolate the squared term.
[tex]18 + \left(4 + \sqrt{x+3} \, \right)^2 = 54\\\underline{-18 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \: } \ \ \ \ \ \underline{ - 18}[/tex]
[tex]\left(4 + \sqrt{x+3} \, \right)^2 = 36[/tex]
Now, we can square root both sides.
[tex]\sqrt{\left(4 + \sqrt{x+3} \, \right)^2} = \sqrt{36}[/tex]
[tex]4 + \sqrt{x+3} = \pm 6[/tex]
Remember to use apply the even root property, so that the right side (6) is positive or negative (indicated by the plus or minus sign).
Next, subtract 4 from both sides.
[tex]4 + \sqrt{x+3} = \pm 6 \\ \underline{-4\ \ \ \ \ \ \ \ \ \ \: } \ \ \ \ \ \underline{ - 4}[/tex]
[tex]\sqrt{x+3} = \pm 6 - 4[/tex]
Then, square both sides to get rid of the square root on the left side.
[tex]\left(\sqrt{x+3}\right)^2 = (\pm 6 - 4)^2[/tex]
[tex]x+3 = 2^2[/tex] OR [tex]x+3 = (-10)^2[/tex]
We can see that there are two resulting expressions, each of which we can solve individually.
[tex]x+3 = 4[/tex] OR [tex]x+3 = 100[/tex]
[tex]\boxed{x = 1}[/tex] [tex]\boxed{x\ne97}[/tex]
The reason that x = 97 is crossed out is because when we plug that x-value back into the original equation, it does not come out to be true. Therefore, 97 is an extraneous solution.
Also, see the attached image for another solution (that implores another method).
Answer:
x = 1
Step-by-step explanation:
You want to solve for x:
[tex]\sqrt{3+\dfrac{(4+\sqrt{x+3})^2}{6}}=3[/tex]
SolutionAt any stage where there is a root, you isolate the radical and raise both sides of the equation to a power sufficient to eliminate the radical. Repeat as necessary.
Outer radicalThe radical is already on one side of the equation by itself, so we simply square both sides:
[tex]3+\dfrac{(4+\sqrt{x+3})^2}{6}=9\\\\(4+\sqrt{x+3})^2=6^2\qquad\text{subtract 3, multiply by 6}\\\\|4+\sqrt{x+3}|=6\qquad\text{take the square root}[/tex]
Inner radicalAt this point, we note that the sum cannot be negative, so the absolute value bars are irrelevant. Isolating the radical and squaring both sides, we can finish the solution.
[tex]4+\sqrt{x+3}=6\\\\\sqrt{x+3}=2\qquad\text{subtract 4}\\\\x+3=4\qquad\text{square both sides}\\\\\boxed{x=1}\qquad\text{subtract 3}[/tex]
This is the only solution, as the attached graph shows.
__
Additional comment
Generally, the square root symbol means the positive square root. That is, √z is usually considered to be non-negative. This is why we use ±√z when we want both signs of the root.
In this problem, the only root we're taking as part of the solution is the root of a square. The possibility of a negative value for the term being squared is handled by using the absolute value brackets: √(z²) = |z|.
For solving these using a graphing calculator, we like to rewrite the equation to the form f(x)=0. That way, the solutions are the x-intercepts.
Use the equation y = 1/2x to find out how much money you spent at the carnival if you spent half as much as your friend. If your friend spend $15, you spent
The amount that I spent by using the equation y = 1/2x , according to my friend's expense is $7.5.
What is an equation in mathematics?
In its simplest form in algebra, the definition of an equation is a mathematical statement that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign.
There are two types of equations:
Identities and conditionals. The identity applies to all values of the variable. Constraint expressions apply only to specific values of variables. Equations are written as two expressions separated by an equal sign ("=").
Solution:
Given, amount spent by friend = $15
Equation: y = 1/2x
So, amount spent by me is as follows
y = (1/2)×15
=15/2
y = $7.5
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The amount of money you are spending is $7.50 according to the given equation.
What is an equation?A mathematical equation is a statement that expresses the relationship between two values using mathematical symbols. An equation typically involves a variable, which is a symbol that stands for a number that can change, and an equals sign. Equations can be used to solve a variety of problems in mathematics.
The equation y = 1/2x states that 'y' is equal to one half of 'x'. This equation can be used in many different ways to solve real-life problems. In this case, 'x' represents the amount of money your friend spent at the carnival. 'y' represents the amount of money you spent. To solve for 'y', we divide the value of 'x' by 2.
In the question, your friend spent $15 at the carnival. Therefore, 'x' is equal to 15. We then divide 15 by 2, which gives us 7.5. This means that you spent $7.50 at the carnival.
The equation y = 1/2x is a simple but powerful tool for solving problems. It can be used for a variety of tasks, including finding out how much money you spent at the carnival if you spent half as much as your friend. All you have to do is plug in the value of 'x' and divide it by two.
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What are some numbers that round to 7.8
Answer:
7.75 ; 7.81 ; 7.77 ; 7.84
The shape of the distribution of the time to get an oil change is 15 minute oil change factory is unknown. However records indicate that the mean time is 16.9 and the standard deviation is 4.7 minutes Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical
Saturday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random
sample, at what mean oil-change time would there be a 10% chance of being at or below? This will be the goal
established by the manager.
There would be a 10% chance of being at or below minutes.
(Round to one decimal place as needed.)
The mean oil-change time for which there is a 10% chance of being at or below is approximately 15.92 minutes.
What is the mean oil-change time?We can start by using the Central Limit Theorem.
Data given:
The population mean is μ = 16.9 minutes
population standard deviation is σ = 4.7 minutes
sample size of n = 40 oil changes performed between 10 A.M. and 12 P.M.
The standard error of the mean (SE) is given by:
SE = σ / √n
SE = 4.7 / √40
SE = 0.743
To find the mean oil-change time for which there is a 10% chance of being at or below, we need to find the z-score associated with the 10th percentile of the standard normal distribution, which is -1.28 (using a standard normal distribution table or calculator).
We can use the formula for a z-score:
z = (x - μ) / SE
where x is the desired mean oil-change time.
Substituting the known values and solving for x, we get:
-1.28 = (x - 16.9) / 0.743
x = -1.28 * 0.743 + 16.9
x = 15.92
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The kettle in Keith,s kitchen is 80% full. After 20% of the water in it has been poured out. There are 1152ml of water left. What volume of water does Keith’s kitchen kettle hold when it is full?
The volume of water that Keith's kitchen kettle holds when it is full is 1800 ml.
Assume that Keith's kitchen kettle has a "x" ml capacity when it is full.
The kettle is initially 80% full, which means it holds 0.8x ml of water, according to the problem.
20% of the water is poured out, leaving 80% of the original amount of water in the kettle, which is:
0.8x * 0.8 = 0.64x ml
We are informed that the 1152 ml of water that is left equates to:
0.64x = 1152
By multiplying both sides by 0.64, we obtain:
x = 1800
Consequently, Keith's cooking kettle has an 1800 ml capacity when it is full.
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Please I need help. I don’t understand this.
Answer: πr2h
= π×282×34
= 26656π
= 83742.29377409 centimeters3
Step-by-step explanation:
Answer:
The volume of the composite figure is 12,719 cm³ to the nearest whole number.
Step-by-step explanation:
The composite figure is composed of a cone and a half-sphere.
To calculate the volume of the figure, sum the volume of the cone and the volume of the half-sphere.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a half-sphere}\\\\$V=\dfrac{2}{3} \pi r^3$ \\\\ where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]
Therefore, the equation for the volume of the composite figure is:
[tex]V=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3[/tex]
From inspection of the given diagram:
d = 28 cmh = 34 cmπ ≈ 3.14As the diameter of a circle is twice its radius, r = 14 cm.
Substitute the values of r, h and π into the equation and solve for V:
[tex]\begin{aligned}\implies V&=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3\\\\&=\dfrac{1}{3} (3.14) (14)^2 (34)+\dfrac{2}{3} (3.14) (14)^3\\\\&=\dfrac{1}{3} (3.14) (196) (34)+\dfrac{2}{3} (3.14) (2744)\\\\&=6974.98666...+5744.10666...\\\\&=12719.09333...\\\\&=12719\;\sf cm^3\;\;(nearest\;whole\;number)\end{aligned}[/tex]
Therefore, the volume of the composite figure is 12,719 cm³ to the nearest whole number.
Kathleen begins working and at age 32she invests $6000.0 into a retirement account that pays an APR of 6.4% compounded monthly. She expects to retire at age 65. What will be the size of Kathleen’s total interest when she retires?
By answering the above question, we may state that Hence, when interest Kathleen retires, her total interest will be $10,389.
what is interest ?Divide the principal by the interest rate, the length of time, and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This method makes it easiest to compute interest. The most typical technique to figure out interest is as a portion of the principle sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an annual percentage of the loan total. The interest on the loan is this percentage.
[tex]FV = PV x (r/n + 1)(n*t)[/tex]
where: $6,000 is the initial investment's present value, or PV.
6.4% is the yearly interest rate at zero.
n = 12 is the number of times interest is compounded annually (monthly)
33 years are equal to t. (from age 32 to age 65)
When we enter the values, we obtain:
FV = $6,000 x (1 + 0.064/12)(12*33) FV = $6,000 x (1 + 0.00533)396 FV = $6,000 x 2.7315 FV = $16,389 FV = $6,000 x 2.7315 FV = $16,389.0
As a result, Kathleen's retirement account will be worth $16,389.0 when she turns 65.
The difference between the future value and the initial investment is the total interest that Kathleen will earn:
Total interest is equal to $16,389 minus $6,000
Interest totaled $10,389.0.
Hence, when Kathleen retires, her total interest will be $10,389.
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What do x equal in these?
Answer:
2.-♾️-61/14
3.-♾️-14
4.-♾️4
5.-♾️-10
Find the percent decrease from 498 to 0
As a consequence, the percentage decline from 498 to 0 is equal to 100% of the original value.
what is percentage ?As a fraction of 100, a figure can be expressed as a percentage. For instance, the decimal equivalent of 50% is 50/100 or 0.5. The comparison or representation of changes between two numbers is frequently done using percentages. For instance, a percentage increase or decline indicates how much something has changed from its starting point. Additionally, percentages are frequently used in daily contexts like interest rates, shopping discounts, and academic performance.
given
The formula below can be used to determine the percent reduction from 498 to 0:
(Original value - New value) / 100% of the original value equals the percent decline.
The initial number in this case was 498, and the updated value is 0.
Reduced percentage equals (498 - 0) / (498 x 100%)
% drop equals 100%
As a consequence, the percentage decline from 498 to 0 is equal to 100% of the original value.
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Using the graphs below, select the graph that represents h(x), given that function h(x) = f(x)+g(x).
Answer: h(x) = 8x so choice A.
Step-by-step explanation:
f(x) = (x + 2)² - 1
g(x) = -(x - 2)² + 1
SOLVE:
h(x) = f(x) + g(x)
——————————————
Step 1: Put together
((x + 2)² - 1) + (-(x - 2)² + 1)
Step 2: Positive and Negative 1 add to 0
((x + 2)² - ) + (-(x - 2)² + )
Step 3: Rewrite
(x + 2)² - (x - 2)²
Step 3: Expand the expression
(x + 2)(x + 2) - (x - 2)(x - 2)
Step 4: Distribute
(x² + 4x + 4) - (x² - 4x + 4)
Step 5: Remove Parentheses (don't forget to distribute the negative)
x² + 4x + 4 - x² + 4x - 4
Step 6: Collect Like Terms
x² and -x² add to 0
+ 4 and - 4 add up to 0
Leaving only + 4x and + 4x which add up to 8x
Therefore, h(x) = f(x) + g(x), h(x) = 8x
Graph Letter A:
A bicycle trail is in the shape of a circle has a diameter of 3 miles. Michelle biked around the trail 4 times.About how far did Michelle bike. round
Michelle biked approximately 37.68 miles in the shape of a circle.
What is link between the diameter and radius of a circle?A circle's diameter and radius are connected because the diameter is twice as long as the radius. Mathematically, this connection may be written as d = 2r, where d stands for the diameter and r for the radius. On the other hand, we can alternatively state that the radius is equal to half the diameter's length: r = d/2
The circumference of a circle can be found using the formula:
C = πd
Given that,
Michelle biked around the trail 4 times.
The circumference is:
C = π x 3 = 9.42 miles
Also,
4 x 9.42 = 37.68 miles
Hence, Michelle biked approximately 37.68 miles in the shape of a circle.
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EASY MATH POINTS! Answer from the screenshot :)
Answer: Y = X2
Step-by-step explanation:
A and C aren't proportional and D is increasng
Encuentre el valor de la expresión si a =2, b= -3 y c=-1 ; ab2 -c3
The equivalent expression value when {a} = 2, {b} = -3, {c} = -1 is 19.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is the algebraic expression as -
ab² - c³
For {a} = 2, {b} = -3, {c} = -1, we can evaluate the algebraic expression as -
ab² - c³
2(-3)² - (- 1)³
2 x 9 - (- 1)
18 + 1
19
Therefore, the equivalent expression value when {a} = 2, {b} = -3, {c} = -1 is 19.
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{Question in english -
Find the value of the expression if a =2, b= -3 and c=-1 ; ab2 -c3}
determine which of the following features they have in common.
The common feature of the two functions is given as follows:
Vertical asymptote.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.For this problem, neither of the functions is defined at x = -4, hence x = -4 is the vertical asymptote for both of the functions.
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A spinner has 3 equal sections colored blue, orange, and red. Determine the sample space for spinning the spinner two times.
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Blue Red
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Orange Blue
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Orange Blue
Orange Red
Orange Orange
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Spin 1 Spin 2
Blue Orange
Blue Red
Red Blue
Red Orange
Orange Blue
Orange Red
The sample space for spinning the spinner two times is -
{Blue, Orange} {Blue, Red} {Orange, Red}
{Blue, Blue} {Red, Blue} {Orange, Blue}
{Red, Red} {Orange, Orange}
What is a sample?
A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.
The sample space for spinning the spinner two times can be found by listing all possible outcomes of the two spins.
Each spin has three possible outcomes, so the total number of outcomes for two spins is 3 x 3 = 9.
One way to list the sample space is to use a table where the rows and columns represent the outcomes of the first and second spins, respectively.
The entries in the table represent the ordered pairs of outcomes, with the first entry corresponding to the first spin and the second entry corresponding to the second spin.
Using this method, the sample space for spinning the spinner two times is -
Blue | Blue | (Blue, Blue) | Blue | Orange | (Blue, Orange) | Blue | Red | (Blue, Red)
Red | Blue | (Red, Blue) | Red | Orange | (Red, Orange) | Red | Red | (Red, Red)
Orange | Blue | (Orange, Blue) | Orange | Orange | (Orange, Orange) | Orange | Red | (Orange, Red)
Alternatively, we can list the outcomes as an unordered set of two elements, where the order of the elements does not matter.
In this case, the sample space for two spins would be -
{Blue, Orange} {Blue, Red} {Orange, Red}
{Blue, Blue} {Red, Blue} {Orange, Blue}
{Red, Red} {Orange, Orange}
Therefore, the sample space is obtained.
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London deposits $100 into a savings account that pays a simplete ineterest rate of 3.4%. Chen deposits $200 into a savings account that pays a simple interest rate of 2.2%. Lodon says that she will earn more interest in one year because her interest rate is higher than Pablo's.
According to the given values London's statement is incorrect.
What is Simple Interest?Simple interest is a type of interest that is calculated based on the principal amount of a loan or investment and the length of time for which the money is borrowed or invested. It is called "simple" because the interest is calculated only on the initial principal amount and does not take into account any interest that may have accrued in previous periods.
Let's calculate the interest earned by each person after one year:
London:
The amount deposited by London is $100. The simple interest rate is 3.4%. Therefore, the interest earned by London after one year is:
[tex]$$\text{Interest}[/tex] = [tex]\text{Principal} \times \text{Rate} \times \text{Time}[/tex] = [tex]$100 \times 3.4%[/tex] [tex]\times 1[/tex]= [tex]$3.40$$[/tex]
Chen:
The amount deposited by Chen is $200. The simple interest rate is 2.2%. Therefore, the interest earned by Chen after one year is:
[tex]$$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}[/tex]= [tex]$200 \times 2.2%[/tex] [tex]\times 1[/tex] = [tex]$4.40$$[/tex]
As we can see, even though London's interest rate is higher than Chen's, Chen will earn more interest in one year because he deposited a larger amount of money.
Therefore, according to the given values London's statement is incorrect.
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Michelle made a bead necklace that was 14 inches long. The length of the necklace, in inches, is equal to 4 added to one-fifth the number of beads, b.
How many beads did Michelle use for her necklace?
A. 500
B. 50
C. 15
D. 25
Answer: B. 50
Step-by-step explanation:
To solve this, we will isolate the variable b.
Given:
[tex]\frac{1}{5}[/tex]b + 4 = 14
Subtract four from both sides of the equation:
[tex]\frac{1}{5}[/tex]b = 10
Multiply both sides of the equation by 5:
b = 50
B. 50
Graph the functions f(x)=−2x−6 and g(x)=−2x−6 on the same coordinate plane. What are the solutions of the equation −2x−6=−2x−6? Select each correct answer. Responses x=−1 x equals negative 1 x = 0 x, = 0 x = 1 x, = 1 x = 2 x, = 2 x = 3 x, = 3
The function has an infinite solution.
What is a function?A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values.
The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
Since f(x) and g(x) are the same function, their graphs will be the same and all points on the line are solutions. All x values will be solutions. This means there are infinitely many.
You can see it algebraically too:
-2x-6 = -2x-6
-2x+2x-6 = -2x +2x -6
0-6 = 0-6
-6=-6 True. Infinite solutions.
Hence the function has an infinite solution.
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QUESTION 18
Consider the following argument: If Shaun eats popping candy while drinking a can of soda, soda streams out of Shaun's
nose and he gets embarrassed. It isn't the case that soda streams out of Shaun's nose and he gets embarrassed. So, it
isn't the case that Shaun eats popping candy while drinking a can of soda. What is the logical form of this argument?
O a. Affirming a disjunct
b. Denying the antecedent
O c. Affirming the consequent
d. Modus Tollens
Oe. Modus Ponens
If Shaun eats popping candy while drinking a can of soda, soda streams out of Shaun's nose and he gets embarrassed. It isn't the case that soda streams out of Shaun's nose and he gets embarrassed. So, it isn't the case that Shaun eats popping candy while drinking a can of soda. The logical form of this argument is denying the antecedent. The Option B is correct.
How is "denying the antecedent" a logical form in the statement?If we represent the argument in logical symbols, it would look like this:
P: Soda streams out of Shaun's nose when he eat candy Q: Soda does not streams out of Shaun's nose when he doesnt eat candyThe argument can be summarized as follows:
If P, then Q.
Not P.
Therefore, not Q.
This is the form of denying the antecedent, where the argument asserts that if P is true, then Q must also be true. However, the argument then proceeds to deny the antecedent by claiming that P is not true, and therefore, Q must not be true either.
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a file that is 278 megabytes is being downloaded. if the download is 19.7% complete, how many megabytes have been downloaded? round your awnser to the nearest tenth
If A file that is 278 megabytes is being downloaded and the download is 19.7% complete, then you just need to multiply the 278 megabytes with 19.7%
The calculation would be: 278 megabytes x 0.197 = 54.766 megabytes.
If you round up the answer to nearest tenth it will be 54.8 megabytes.
Please provide steps!
25 pi^2
The circumference is diameter by pi. So you have to divide 50pi by pi, which gives you 50. Then, divide that by 2 to get your radius. 25. A=pi r^2. So you have to multiply 35 by pi, 25pi, and then make it squared.
The room has a width of 8 feet, a length of 12 feet, and a height of 9 feet. What is the greatest possible distance between two points on the walls in the room?
Answer:
The greatest possible distance between two points on the walls in the room is 17 feet.
Step-by-step explanation:
The room can be modelled as a rectangular prism with the following dimensions:
width = 8 ftlength = 12 ftheight = 9 ftThe greatest possible distance between two points on the walls in the room is the line between diagonally opposite corners. This is marked as the blue line (x) on the attached 3D diagram.
This distance is the hypotenuse of a right triangle with a base of the diagonal of the floor and a height of the height of the room.
The diagonal of the floor (marked "y" on the attached diagram) is the hypotenuse of a right triangle with legs of the width and length of the room. To calculate the diagonal of the floor, use Pythagoras Theorem.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Substitute a = 8, b = 12 and c = y into the formula and solve for y:
[tex]\implies 8^2+12^2=y^2[/tex]
[tex]\implies 64+144=y^2[/tex]
[tex]\implies y^2=208[/tex]
[tex]\implies y=\sqrt{208}\; \sf ft[/tex]
Therefore, the diagonal of the floor (y) is √(208) feet in length.
We can now use Pythagoras Theorem again to find the length x.
Substitute a = y, b = 9 and c = x into the formula:
[tex]\implies y^2+9^2=x^2[/tex]
Substitute the found value of y and solve for x:
[tex]\implies (\sqrt{208})^2+9^2=x^2[/tex]
[tex]\implies 208+81=x^2[/tex]
[tex]\implies 289=x^2[/tex]
[tex]\implies x=\sqrt{289}[/tex]
[tex]\implies x=17 \sf \; ft[/tex]
Therefore, the greatest possible distance between two points on the walls in the room is 17 feet.
Calculate the amount of money that the tanker driver receive per day during week days
Steps?
Total amount/Working days
Step-by-step explanation:
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Based on the information, the statements about Josiah's solution that are true are:
He predicted that the number of rock songs on his MP3 player would be 300 songs.He did not multiply the numerator and denominator by the correct number to equal 1500.He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.How do we find this conclusion?Josiah used a proportion to predict the number of rock songs on his MP3 player. He started by setting up the proportion:
10/20 = x/1500He made a mistake when multiplying the numerator and denominator by 30. Instead, he should have multiplied them by 75, which is a common multiple of 20 and 1500. This would have resulted in:
10/20 = x/1500(10 x 75) / (20 x 75) = x/1500750/1500 = x/1500x = 750Therefore, the total number of rock songs on his MP3 player is 750, which is different from his prediction of 300. This means that he made an error in his calculation, and he should have multiplied by 75 instead of 30.
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What is the area of this figure?
___ units 2
The area of the figure is equal to:
A = 28[tex]unit[/tex]² + 7[tex]unit[/tex]² + 7[tex]unit[/tex]² =42[tex]unit[/tex]²
Provide an area example.You could also draw the shape on a grid and count the squares there: The rectangle has a 15 surface area. For instance, if the space is 15 m2 and each square is one meter in size (15 square meters).
Answer:
42[tex]units[/tex]²
Step-by-step explanation:
we know that
The area of the figure is equal to the area of a rectangle plus the area of two triangles
Find the area of rectangle
Observing the graph
The area of rectangle is equal to
A= bh = (2+5)(2+2)= 28[tex]unit[/tex]²
Find the area of the top triangle
A = 1/2bh = 1/2(2+5)(2+2) = 7[tex]unit[/tex]²
Find the area of the bottom triangle
A = 1/2bh = 1/2(2+5)(2+2) = 7[tex]unit[/tex]²
the area of the figure is equal to
A = 28[tex]unit[/tex]² + 7[tex]unit[/tex]² + 7[tex]unit[/tex]² =42[tex]unit[/tex]²
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Given the formula
Profit =Revenue - Cost, that is
P= R- C, find the following
(a) Solve for C.
(b) Find C when
P = $3250 and R= $7200
the electronic grading machine at john adams elementary can grade 52 multiple choice tests in minute. How long will it take to grade 338 tests
It will take 6.5 minutes to grade 338 test by the electronic grading machine.
What are some elements that impact grading system's accuracy?The quality of the answer papers is a key element. The machine might not be able to reliably scan and evaluate the answers if the answer sheets are not filled out completely or if the paper has rips or smudges on it. Similar to this, the computer might not be able to recognize the right answers if the answer sheets are not properly aligned.
Given that, the machine can grade 52 test in 1 minute.
The, we can calculate the time taken to grade 338 test as follows:
time = number of tests / rate of grading
Plugging in the given values, we get:
time = 338 / 52 = 6.5 minutes
Hence, it will take 6.5 minutes to grade 338 test by the electronic grading machine.
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Simplify the expression by combining like terms.
Write the terms from the highest to the lowest
power of the variable.
9b² 10b5b + 4 +7b²-6-15b²-9b
The terms from the highest to lowest power of the variable are 10b⁶, -b², -9b, -9.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
To write the terms from the highest to the lowest power of the variable, we need to first simplify the given expression by combining the like terms.
The given expression can be simplified as follows:
= 9b² + 10b⁵b + 4 + 7b² - 6 - 15b² - 9b
= 10b⁶ + (9b² + 7b² - 15b²) - 9b + (4 - 6)
= 10b⁶ - b² - 9
Now, we can write the terms from highest to lowest power of the variable as follows:
10b⁶ is the term with the highest power of the variable.
The next highest power of the variable is b². Therefore, we have -b².
The next term is -9b, which has the power of the variable 1.
Finally, the constant term is -9, which has no power of the variable.
Therefore, the terms from the highest to lowest power of the variable are 10b⁶, -b², -9b, -9.
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