Answer:
a) t₀ = 1.73205 s
b) 1.0 C
Step-by-step explanation:
(A)
The time dilation (t) observed by an observer at rest relative to the time (t₀) measured by observer in motion is;
[tex]t = \frac{t_0}{\sqrt{1 - \frac{V^2}{C^2}}}[/tex]
[tex]t_0 = t \sqrt{1 - \frac{V^2}{C^2}}[/tex] time measured by captain
⇒ [tex]t_0 = 2.0 \sqrt{1 - \frac{0.5^2C^2}{C^2}}[/tex] V = 0.5 c
⇒ t₀ = 1.73205 s
(B)
Speed of the light never exceeds by its real value. The speed of the light in any frame of reference is constant.
∵ It will be "1.0C" or just "C"
Your bank offers free access to online banking, but they charge you $.02 for each online e-check you send. They charge you $.10 for each paper check you write. You have chosen to write all future checks online. Over the year you have sent an average of 18 checks per month. What have you saved in a year with online checking?
Answer: 17.28
Step-by-step explanation:
18*12 =216*.02=4.32
18*12=216*.10=21.6
21.6-4.32=17.28
In a year, by opting for online e-checks at a rate of $.02 per check instead of paper checks at $.10 per check for an average of 18 checks per month, your savings amount to $17.28.
Explanation:The subject of your question is a practical application of mathematics, specifically an area often referred to as personal finance. To find out how much you've saved over a year by sending e-checks online instead of writing paper checks, we first need to calculate the cost of each method and then compare the two.
First, let's calculate how much it would cost for the e-checks. The bank charges you $0.02 for each e-check you send. If you send an average of 18 checks per month over a year (12 months), that's 18 checks/month x 12 months/year = 216 checks/year. At $0.02 a check, that comes out to 216 checks/year x $0.02/check = $4.32/year.
Now let's calculate the cost if you were writing paper checks. The bank charges $0.10 for each paper check you write, so that would have been 216 checks/year x $0.10/check = $21.60/year.
So, by choosing to send e-checks online instead of writing paper checks, you've saved $21.60/year - $4.32/year = $17.28/year.
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Which of the following rational functions is graphed below a. F(x)=(x-1)/x(x-2)
The equation of the graphed rational function is f(x) = (x + 1)/(x + 2)(x - 2)
How to determine the graphed rational function
From the question, we have the following parameters that can be used in our computation:
The graph
From the graph, we have vertical asymptotes at
x = 2 and x = -2
This means that the denominator of the function is
(x + 2)(x - 2)
Looking through the list of options, we have the function with a denominator of (x + 2)(x - 2) to be f(x) = (x + 1)/(x + 2)(x - 2)
Hence, the graphed rational function is f(x) = (x + 1)/(x + 2)(x - 2)
The rational functions is graphed below is [tex]F(x) = \frac{(x - 1)}{x(x - 3)},[/tex] (after dividing both the numerator and denominator by (x)). The correct answer is C.
1. Analyze the graph's behavior:
The graph has vertical asymptotes at x = -3 and x = 2. This means the denominator of rational function must have factors (x + 3) and (x - 2).
The graph intersects y-axis at (0, -1). when x = 0, function value is -1.
As x approaches positive / negative infinity, graph approaches line y = 0. The numerator's degree must be smaller than denominator degree.
2. Consider the answer choices:
Only option C, [tex]F(x) = \frac{(x - 1)}{x(x - 3)},[/tex] has correct vertical asymptotes and a numerator degree of 1.
3. Verify the answer choice:
Let's substitute x = 0 into option C:
[tex]F(0) = \frac{(0 - 1)}{(0)(0 - 3)} = \frac{-1}{0} = -\infty[/tex]
This doesn't match the graph's behavior at x = 0. However, this is a common issue with rational functions when the numerator and denominator have a common factor. In this case, both the numerator and denominator have a factor of (x). Dividing both the numerator and denominator by (x) gives:
[tex]F(x) = \frac{\cancel{(x - 1)}}{\cancel{x}(x - 3)} = \frac{1}{(x - 3)}[/tex]
Now, let's substitute x = 0:
[tex]F(0) = \frac{1}{(0 - 3)} = -\frac{1}{3}[/tex]
This matches the graph's behavior at x = 0.
Complete and correct question:
Which of the following rational functions is graphed below?
[tex]A. F(x)=\frac{(x+1)}{(x+3)(x-2)}\\\\B. F(x)=\frac{(x-1)}{(x+2)^{2}}\\\\C. F(x)=\frac{(x-1)}{x(x-3)}\\[/tex]
A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the cost to make the can if the metal for the sides will cost $1.25 per 2 cm and the metal for the bottom will cost $2.00 per 2 cm ?
Answer:
Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.
Step-by-step explanation:
Given that, the volume of cylindrical can with out top is 25 cm³.
Consider the height of the can be h and radius be r.
The volume of the can is V= [tex]\pi r^2h[/tex]
According to the problem,
[tex]\pi r^2 h=25[/tex]
[tex]\Rightarrow h=\frac{25}{\pi r^2}[/tex]
The surface area of the base of the can is = [tex]\pi r^2[/tex]
The metal for the bottom will cost $2.00 per cm²
The metal cost for the base is =$(2.00× [tex]\pi r^2[/tex])
The lateral surface area of the can is = [tex]2\pi rh[/tex]
The metal for the side will cost $1.25 per cm²
The metal cost for the base is =$(1.25× [tex]2\pi rh[/tex])
[tex]=\$2.5 \pi r h[/tex]
Total cost of metal is C= 2.00 [tex]\pi r^2[/tex]+[tex]2.5 \pi r h[/tex]
Putting [tex]h=\frac{25}{\pi r^2}[/tex]
[tex]\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}[/tex]
[tex]\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}[/tex]
Differentiating with respect to r
[tex]C'=4\pi r- \frac{62.5}{ r^2}[/tex]
Again differentiating with respect to r
[tex]C''=4\pi + \frac{125}{ r^3}[/tex]
To find the minimize cost, we set C'=0
[tex]4\pi r- \frac{62.5}{ r^2}=0[/tex]
[tex]\Rightarrow 4\pi r=\frac{62.5}{ r^2}[/tex]
[tex]\Rightarrow r^3=\frac{62.5}{ 4\pi}[/tex]
⇒r=1.71
Now,
[tex]\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0[/tex]
When r=1.71 cm, the metal cost will be minimum.
Therefore,
[tex]h=\frac{25}{\pi\times 1.71^2}[/tex]
⇒h=2.72 cm
Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.
The radius should be approximately 1.7 cm, and the height should be approximately 2.77 cm.
We are to find the dimensions of a cylindrical can without a top that will minimize the cost while containing 25 cubic centimeters (cm³) of liquid.
The volume of a cylinder is given by the formula:
V = πr²h
where r is the radius and h is the height.
Given V = 25 cm³, we can express the height h in terms of the radius r:
h = V / (πr²) = 25 / (πr²)
The cost involves the lateral surface area (sides) and the bottom area:
Lateral surface area: As = 2πrh
Bottom area: Ab = πr²
Cost of the sides: $1.25 per square cm (let's denote the lateral cost by Cs)
Cs = 1.25 * 2πrh = 2.5πrh
Cost of the bottom: $2.00 per square cm (let's denote the bottom cost by Cb)
Cb = 2.00 * πr² = 2πr²
Total cost C is given by:
C = Cs + Cb = 2.5πrh + 2πr²
Substituting h = 25 / (πr²) into the total cost formula,
C = 2.5πr(25 / πr²) + 2πr² = 62.5 / r + 2πr²
To minimize the cost, we take the derivative of C with respect to r and set it to zero:
dC/dr = -62.5 / r² + 4πr = 0
Simplifying, we get:
4πr³ = 62.5
r³ = 62.5 / 4π = 4.978
r = ∛(4.978) ≈ 1.7 cm
Now, calculate the height h:
h = 25 / (π * 1.7²) ≈ 2.77 cm
Thus, the dimensions of the can that minimize the cost are approximately: radius = 1.7 cm and height = 2.77 cm.
What is the answer for Two step equations 5n+3=18
Answer: n=3
Step-by-step explanation: 5n+3=18
18-3=15
15/5=3
Answer:
Step-by-step explanation:
5n +3 =18
5n = 18- 3
5n = 15
Dividing through with 5
n =15/5
n = 3
A company that produces laundry detergent is interested in the level of consumer awareness concerning the unique properties of their product. Historical data indicated that among the consumers who buy this detergent, the proportion who purchased it because they had seen it advertised on TV is 0.80. The marketing manager feels that decreases in the TV advertising budget over the years has caused a decrease in sales. She decides to conduct a survey to determine if there is sufficient evidence to conclude that the population proportion is less than 0.80. In a random sample of 400 consumers who bought this detergent, 296 indicated that they bought it because they saw it advertised on TV. What is the value of the test statistic for the test described above and what is the type of alternative hypothesis?
Answer:
The value of test statistic is -2.736.
The type of alternate hypothesis is Left- tailed.
Step-by-step explanation:
We are given that Historical data indicated that among the consumers who buy this detergent, the proportion who purchased it because they had seen it advertised on TV is 0.80. In a random sample of 400 consumers who bought this detergent, 296 indicated that they bought it because they saw it advertised on TV.
We have to test the hypothesis to determine if there is sufficient evidence to conclude that the population proportion is less than 0.80.
Let p = population proportion of people who purchased the detergent because they had seen it advertised on TV.
SO, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 0.80 {means that the population proportion of people who purchased the detergent because they had seen it advertised on TV is greater than or equal to 0.80}
Alternate Hypothesis, [tex]H_a[/tex] : p < 0.80 {means that the population proportion of people who purchased the detergent because they had seen it advertised on TV is less than 0.80}
The test statistics that will be used here is One-sample z-proportion test;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = proportion of people who bought detergent because they saw it advertised on TV in a sample of 400 customers = [tex]\frac{296}{400}[/tex] = 0.74
n = sample of customers = 400
SO, test statistics = [tex]\frac{0.74-0.80}{\sqrt{\frac{0.74(1-0.74)}{400} } }[/tex]
= -2.736
Therefore, the value of the test statistic for the test described above is -2.736.
And the type of alternative hypothesis is left-tailed because we have to determine whether the population proportion of people who purchased the detergent because they had seen it advertised on TV is less than 0.80.
Final answer:
To test if the population proportion is less than 0.80, a hypothesis test can be conducted using the sample data. The test statistic can be calculated using the formula (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size). Using the given information, the test statistic is approximately -5.00.
Explanation:
To test whether there is sufficient evidence to conclude that the population proportion of consumers who purchased the detergent because of TV advertisements is less than 0.80, we can conduct a hypothesis test using the sample data.
Null Hypothesis:
The proportion of consumers who bought the detergent because of TV advertisements is 0.80 or higher.
Alternative Hypothesis:
The proportion of consumers who bought the detergent because of TV advertisements is less than 0.80.
We can calculate the test statistic, which is also known as the z-score, using the formula:
test statistic = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size)
Using the given information, the sample proportion is 296/400 = 0.74. The hypothesized proportion is 0.80, and the sample size is 400.
Plugging these values into the formula, we get:
test statistic = (0.74 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 400)
Calculating this expression, we find that the test statistic is approximately -5.00.
Mr. Thompson wants to tile his living room which measures 15.7 feet in length and 12.2 feet in width. What is the area of Mr. Thompson’s living room?
b) If tile costs $10.50 per square foot, how much will it cost Mr.Thompson to tile his living room.
Answer:
A. 191.54 ft²
B. $2011.17
Step-by-step explanation:
Part A involves multiplying to find the area of the living room using the formula to find the area of a rectangle.
A = b*h (original formula)
A = 15.7*12.2 (substitute values)
A = 191.54 (multiply)
The area of his living room is 191.54 ft²
Next, you need to multiply the number of ft² by the cost per ft² to find the cost to tile the living room
Cost = $10.50*191.54 (equation)
Cost = $2011.17 (multiply)
The total cost of tiling the living room would be $2011.17
Answer:
Step-by-step explanation:
Which unit rate is the lowest price per ounce? 5 ounces for $1.49 or 12 ounces for $3.59.
Answer:
5 ounce for $1.49 is you're answer.
Step-by-step explanation:
1.49/6 = 0.248 per oz
3.59/13 = 0.276 per oz
What is the linear equation x×3y=6
Answer:
Find the degree of the equation to determine if linear.
"Not Linear"
Step-by-step explanation:
Answer:
not linear, degree 2
Step-by-step explanation:
The degree of this equation is the highest sum of the exponents of the variables in any given term.
Here, there is one variable term. The variables are x and y. They each have an exponent of 1, so the degree of the variable term is 1+1 = 2.
Since the degree of the equation is not 1, it is not a linear equation.
que valor tiene los numeros que van ala izquierda del punto decimal
Answer:
A decimal number can be divided in a decimal part, a whole part and the decimal point which separates the first two.
So, all numbers that are placed leftside of the decimal point can be classified in units, tens, hundreds, thousands, and so on. Basically, each value depends on a base of 10. This means that thousands are ten times more than hundreds, hundreds are ten times more than tens, tens are ten times more than units.
If we want to a specific value of the whole part in a decimal number, we just need to look units, tens, hundreds, thousands or millions.
For example, if we have the number 1235.8456, the whole part would be 1235, and the value of the numbers that are leftside of the decimal point is 1235 units.
Answer:
The name of the numbers that go to the left of the decimal point is INTEGERS. This is the whole number part of the decimal number.
Step-by-step explanation:
The english translation is
What is the name of the numbers that go to the left of the decimal point?
A number with decimal numbers has 3 parts.
- The whole number part that are to the left of the decimal point. This whole number part is called the INTEGER part.
- The decimal point. The decimal point separates the whole numbers part of the number on the left and the mantissa part that has numbers to the right of the decimal point.
- The numbers to the right of the decimal point constitute a value less than 1. This part of a decimal is called the MANTISSA.
Hope this Helps!!!
7/10 = 350/x
Please help cross multiply
Answer:
x=500
Step-by-step explanation:
7/10=350/x
cross-multiply by multiplying 350 to 10 and multiply 7 to x.
example:
7•x
350•10
7x=3500
divide both sides by 7
-------------
x=500
-------------
Complete the sentence below. The standard deviation of the sampling distribution of x overbar, denoted sigma Subscript x overbar, is called the _____ _____ of the _____. The standard deviation of the sampling distribution of x overbar, denoted sigma Subscript x overbar, is called the ▼ standard population sample ▼ mean error deviation distribution variance of the ▼ mean. sample. error. distribution.
Answer:
The standard deviation of the sampling distribution of x overbar, denoted sigma subscript x overbar, is called the Standard Error of the Mean.
Step-by-step explanation:
Standard deviation of the sampling distribution, or sigma Subscript x overbar, is also known as the standard error of the mean. It represents how much the sample means deviate from the population mean. The standard error can be calculated by dividing the population standard deviation by the square root of the sample size.
Explanation:The standard deviation of the sampling distribution, represented by the symbol sigma Subscript x overbar is also known as the standard error of the mean. This term refers to the standard deviation of the population of all possible sample means from samples of a specific size.
The basic formula to calculate the standard deviation is Σ(x – μ)2 / N for the population and Σ(x – x)² / (n-1) for the sample. Greek symbol µ represents the population mean while 'x' is the sample mean.
The standard error can be calculated by dividing the population standard deviation (σ) by the square root of the sample size (n). Thus, lesser the standard error, closer are the sample means to the population mean and vice versa. This is a very important concept in statistics as it allows one to estimate an unknown population parameter using sample data.
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If tan0= 3/4, find csc0
Answer: 5/3
Step-by-step explanation:
This is a trigonometry ratio. Tangent of a right angle triangle
Tan0° = opposite
------------
adjacent.
Now from the question
Tan0° = 3/4 meaning that the opposite side is 3 while the adjacent side is 4. Going by the triple coordinate, when two of the sides of a right angle triangle are, 3 and 4, the third side should be 5, in other words you could as well use the Pythagoras theorem to find the other side which I believed you should be familiar with. Since the third side is known, the cosec could be calculated.
Cosec of an angle =
1/sine. From the question now,
Sine0° = opposite side
-----------------
Hypothesis
= 3/5
Therefore
Cosec0° = 1/3/5
= 1
---
3/5
= 5/3
What bearing and airspeed are required for a plane to fly 700 miles due north in 3.5 hours if the wind is blowing from a direction of 338 degrees at 10 mph? The plane should fly at nothing mph at a bearing of nothing degrees. Calculator
Answer:
1. Airspeed = 201.17 mph
2. Bearing = 358.93⁰
Step-by-step explanation:
Given Data:
d = 700 mi
t = 3.5 hrs
speed of wind Vx = 10 mph
velocity of plane Vy = d/t
= 700/3.5
= 200 mph
1. Air speed (V) is calculated using the formula;
V² = V²x + V²y -2*Vx *Vy*cos∝
But ∝ = 338 - 180 = 158°
Substituting into the equation, we have
V² = 10² + 200² - 2*10*200*Cos 158
= 40100 - 400 *(-0.92718)
= 40100 + 370.872
V² = 40470.872
V = √40470.872
V = 201.17 mph
2. calculating the bearing using cosine rule, we have;
sin∅/Vx = sin∝/V
sin∅/10 = sin158/201.17
sin∅ = 10*sin 158/201.17
= 3.746/201.17
= 0.0186
∅ = sin⁻¹ 0.0186
= 1.07
Therefore,
Bearing = 360 - 1.07
= 358.93⁰
The airspeed is 201.17 mph and bearing is [tex]358.93^\circ[/tex] and this can be determined by using the vector form of velocity.
Given :
Plane to fly 700 miles due north in 3.5 hours if the wind is blowing from a direction of 338 degrees at 10 mph.
To determine the airspeed the following formula can be used.
[tex]\rm V^2 = V^2_x +V^2_y-2V_xV_y cos \theta[/tex] ---- (1)
where, [tex]\theta = 338-180 = 158^\circ[/tex], [tex]\rm V_y[/tex] is the velocity of the plane and [tex]\rm V_x[/tex] is the velocity of the wind.
Now, put the value of [tex]\rm V_y[/tex], [tex]\rm V_x[/tex] and [tex]\theta[/tex] in the equation (1).
[tex]\rm V^2 = 10^2+200^2+2\times 10\times 200\times cos158[/tex]
[tex]\rm V^2= 100 + 40000+4000(-0.9271)[/tex]
V = 201.17 mph
Now, using cosine rule:
[tex]\rm \dfrac{sin \alpha}{V_x}=\dfrac{sin \theta }{V}[/tex]
[tex]\rm \dfrac{sin\alpha }{10}=\dfrac{sin158}{201.17}[/tex]
[tex]\rm sin\alpha =10\times \dfrac{sin158}{201.17}[/tex]
[tex]\rm sin \alpha = \dfrac{3.746}{201.17}[/tex]
[tex]\rm sin\alpha =0.0186[/tex]
[tex]\alpha = 1.07^\circ[/tex]
Therefore, the bearing is given by 360 - 13.07 = [tex]358.93^\circ[/tex]
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I am not understanding this question.
Answer:
boardgamegeek.com/boardgame/245655/kings-dilemma
Step-by-step explanation:
NEED HELP ASAP PLZ
which of the following are rational numbers select three that apply
Square root 3
Square root 9
Square root 5
Square root 4
Square root 8
Square root 1
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 3 years of the actual mean with a confidence level of 98%, how many citizens should be included in your sample
Answer:
list all the statistics
Step-by-step explanation:
What the value 0 in degrees
Answer:
45 degrees
Step-by-step explanation:
38:27
The cost table shows the average cost, a(x), of producing x
number of earbuds.
When verifying that a function represented in another table
is the inverse of the given cost function, which ordered pair
can be expected?
x
a(x)
20 25
52 67.5
30
84
(20, 20)
(52, 20)
(20,52)
(52, 52)
What’s the answer
Answer:
(52,20)
Step-by-step explanation:
Answer: B
(52, 20)
Step-by-step explanation:
Please help me !!☹️❤️
Answer:
(x-10) (x+1) =0
x=10 x=-1
Step-by-step explanation:
x^2 -9x-10 =0
Factor
What two numbers multiply to -10 and add to -9
-10*1 = -10
-10+1=-9
(x-10) (x+1) =0
Using the zero product property
x-10 = 0 x+1=0
x-10+10=0+10 x+1-1=0-1
x=10 x=-1
These are the x intercepts
The guidance counselor of a large high school reports that 48.5% of Junior Pre-Calculus students signed up to take AP Statistics next year, 52.5% signed up to take AP Calculus next year and 10% of Junior Pre-Calculus students signed up to take both AP Statistics and AP Calculus next year.
If one Junior Pre-Calculus student is selected at random, what is the probability that they did not sign up to take AP Statistics or AP Calculus next year?
(A) 0.09
(B) 0.11
(C) 0.19
(D) 0.91
(E) Not enough information is given to determine the probability
Answer:
A. 0.09
Step-by-step explanation:
which is equal to 5 exponent of -4
Answer:
[tex]\frac{1}{5^{4}}[/tex] = [tex]\frac{1}{625}[/tex] = 0.0016
Step-by-step explanation:
I'm assuming you mean [tex]5^{-4}[/tex] (which could also be written as 5^-4, for future reference).
Negative exponents actually mean you'd use the term in the denominator, taking away the negative portion. It's difficult to explain in words, and is easier to see.
[tex]5^{-4}[/tex] = [tex]\frac{1}{5^{4}}[/tex]
Notice how the -4 changes to 4, and it becomes the denominator.
[tex]5^{4}[/tex] is also 625, so [tex]5^{-4}[/tex] is also 1/625, or the decimal version (0.0016).
I hope this helps!
What is the equation of the circle with center (0, 0) that passes through the point (-3, -5)
A) x2+y2=34
B) x2+y2=64
C) x2+y2=16
D) x2+y2=31
Answer:
A
Step-by-step explanation:
(x - h)² + (y - k)² = r²
x² + y² = r²
(-3)² + (-5)² = r²
r² = 34
x² + y² = 34
How can models and equation help me subtract like fractions?
Answer:
You don't need "models and equations"; if the denominator is the
same, just subtract the numerators.
Step-by-step explanation:
in how many distinct ways can the letters of the word READERS be arranged?
Answer:
The letters of the word readers can be arranged in 1260 distinct ways.
Step-by-step explanation:
A word has n letters.
The are m repeating letters, each of them repeating [tex]r_{0}, r_{1}, ..., r_{m}[/tex] times
So the number of distincts ways the letters can be arranged is:
[tex]N_{A} = \frac{n!}{r_{1}! \times r_{2}! \times ... \times r_{m}}[/tex]
In this question:
Readers.
Has 7 letters.
E repeats twice.
R repeats twice.
So
[tex]N = \frac{7!}{2! \times 2!} = 1260[/tex]
The letters of the word readers can be arranged in 1260 distinct ways.
The word 'READERS' can be arranged in 1260 distinct ways, considering the repetition of letters.
Explanation:The problem involves finding the number of distinct ways the letters in the word 'READERS' can be arranged. This is a topic in combinatorics, or counting, in mathematics.
The formula for the number of ways of arranging n objects where some objects are identical is n!/r1!r2!... where r1, r2, ... are the numbers of each type of similar object.
In the word 'READERS', there are 7 letters in total (n=7). Three of these letters are 'E', 'R' and 'R' (r1=2) and two of these letters are 'E' (r2=2).
The remaining letters 'A', 'D' and 'S' are all distinct (r3=1, r4=1 and r5=1). So, applying the formula, we get the number of distinct arrangements as 7!/(2!2!1!1!1!) = 1260.
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please help best answer gets BRAINLIEST!!!
Lily’s car used 5 gallons of gas to drive 230 miles. At what rate does her car use gas in gallons per mile? Answer in simplest form.
____ Gallons per mile
Answer:
0.0217391304
Step-by-step explanation:
Answer:
1/46 gallons per mile
Step-by-step explanation:
Take the gallons used and divide by the number of miles driven
5 gallons /230 miles
1/46 gallons per mile
in a 45-45-90- triangle what is the length of the hypotenuse when the leg is 22 cm
Answer:
[tex] 22\sqrt 2 [/tex] cm
Step-by-step explanation:
[tex] in \: a \: 45 \degree - 45 \degree - 45 \degree \: \triangle \\ leg = \frac{1}{ \sqrt{2} } \times hypotenuse \\ \\ \therefore \: 22 = \frac{1}{ \sqrt{2} } \times hypotenuse \\ \\ \purple{ \bold{ \therefore \: hypotenuse = 22 \sqrt{2} cm}}[/tex]
(b) 3m - 2n=19
5m + 7n=11
3m-2n=19
5m+7n=11
21m-14n=133
10m+14n=22
Now add equations
31m=155
m=5
Now let's find n
3×5-2n=19
-2n=4
n=-2
Answer: (5; -2)
The question is about solving a system of two linear equations with two variables, m and n, using substitution method. First, solve one of the equations for one variable and substitute this into the other equation. Solve the resulting equation to find the value of one variable and substitute this value into the first equation to find the value of the second variable.
Explanation:The question represents a system of linear equations. Such system contains two equations with two variables, namely m and n. To solve such a system, we can use various methods, such as substitution, elimination, or matrix methods. Let's use the substitution method in this case.
From the first equation, isolate variable m: m = (19 + 2n) / 3. Substitute m into the second equation: 5 * ((19 + 2n) / 3) + 7n = 11. Solve the second equation, you will find the value of n. Substitute the value of n into the first equation to find the value of m. Learn more about System of Linear Equations here:
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Find the probability of rolling factors of 8
The probability of rolling a factor of 8 with a six-sided die is 0.5 or 50%, as there are 3 favorable outcomes (1, 2, 4) out of 6 possible outcomes when rolling the die.
Explanation:To find the probability of rolling factors of 8 with a fair, six-sided die, we first need to identify the factors of 8, which are 1, 2, 4, and 8. Of these, only 1, 2, and 4 are possible outcomes on a six-sided die. There are six possible outcomes when rolling a die (1, 2, 3, 4, 5, 6), so the probability of rolling a factor of 8 is the number of favorable outcomes (where the result is a factor of 8) divided by the total number of possible outcomes.
The favorable outcomes for this probability event are {1, 2, 4}, hence there are 3 favorable outcomes. Thus, the probability of rolling a factor of 8 is:
P(rolling a factor of 8) = Number of favorable outcomes / Total number of possible outcomes
P(rolling a factor of 8) = 3 / 6
P(rolling a factor of 8) = 0.5
Therefore, the probability of rolling a factor of 8 is 0.5 or 50%.
Tim has to mow his lawn in under two hours. If "t" represents the time it takes to mow the lawn, how can you express this as an inequality? At > 2 incorrect answer Bt < 2 incorrect answer C2 ≠ t incorrect answer Dt = 2
Answer:
B. t<2 hours
Step-by-step explanation:
If Tim has to mow his lawn in under two hours.
It means:
Tim cannot spend more than two hours mowing the lawn, therefore t>2 is not correct.2[tex]\neq[/tex]t means that Tim can spend less or more than 2 hours which is not what is required.Tim cannot spend exactly two hours mowing the lawn, therefore t=2 is not correct.Tim must finish mowing the lawn before two hours, therefore t<2 is the correct option.
To express that Tim must mow his lawn in under two hours, the correct inequality is t < 2. This indicates that the time, t, must be less than two hours to complete the task. Option B.
To express the condition that Tim has to mow his lawn in under two hours as an inequality, we represent the time it takes to mow the lawn with the variable t. The inequality that represents the situation is t < 2, meaning the time must be less than two hours. This is conveyed using the less than symbol (<).
In the context of other example inequalities, such as t=0, which represents a starting time, and t=t+1, which indicates an increment of time, these are used to express discrete points or changes in time. However, to represent a range of time under a specific amount, we use an inequality like t < 2 to denote that the time taken should not exceed two hours, option B.
In the number 49,869 there are how many tens?
Answer:
The number at tenth place is 6. Therefore, I guess there's 6 tens.
Step-by-step explanation:
There are 6 tens in the number 49,869.
To find the number of tens, we look at the digit in the tens place, which is the second digit from the right.
4 is in ten thousand place.
9 is in thousand place.
8 is in hundred place.
6 is in ten place.
As the digit in the tens place is 6.
The digit 6 represents six groups of ten in the number.
So, in the number 49,869, there are 6 tens.
Therefore, the correct answer is that there are 6 tens in the number 49,869.
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