The probability that Jade gets the specific outcome you're interested in when rolling two dice is 1/6.
To find the probability that Jade gets a specific outcome when rolling two dice, we will use the sample space for rolling two dice, which consists of 36 possible outcomes (since there are 6 sides on each die, and we have 2 dice: 6 x 6 = 36).
Step 1: Determine the specific outcome you are interested in (for example, the sum of the numbers on the dice being 7).
Step 2: Count the number of ways this outcome can occur. For example, if we want a sum of 7, there are 6 possible outcomes: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).
Step 3: Calculate the probability by dividing the number of successful outcomes by the total number of possible outcomes in the sample space.
In our example, there are 6 successful outcomes, and there are 36 possible outcomes in the sample space:
Probability = (Number of successful outcomes) / (Total number of possible outcomes) = 6/36
Step 4: Express the probability in its simplest form by reducing the fraction. In our example, 6/36 can be reduced to 1/6.
So, the probability that Jade gets the specific outcome you're interested in when rolling two dice is 1/6.
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Tara wants to prove that a second pair of corresponding angles from KJN and LJM are congruent.
Determine a second pair of corresponding angles from KJN and LJM that are congruent. Then explain how you know that the two angles are congruent
To determine a second pair of corresponding angles from KJN and LJM that are congruent, we can start by identifying the first pair of corresponding angles.
angle JKN is harmonious to angle LJM. thus, we need to find another brace of corresponding angles that involve these same two angles. One possibility is to look at the perpendicular angles formed by the crossroad of KJ and JM. Angle KJM is perpendicular to angle NJL. therefore, angle KJM in KJN corresponds to angle NJL in LJM. thus, these two angles are harmonious.
We can prove that these two angles are harmonious using the perpendicular angles theorem, which states that perpendicular angles are always harmonious. Since KJ and JM cross at point J, angles KJM and NJL are perpendicular angles and must be harmonious. thus, we've shown that the alternate brace of corresponding angles from KJN and LJM that are harmonious are angle KJM and angle NJL.
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Helppppppppppppppppp
Answer:
it would be at point (6,3)
Step-by-step explanation:
If you were to reflect it over the x-axis you would get (-6,3)
simplified ration of squares to total shapes is 6:16 for every 3 squares there are how many total shapes there fore the simplified ratio of squares to total shape is what
For every 3 squares, there are 5 total shapes. Therefore, the simplified ratio of squares to total shapes is 3 : 5.
What is the simplified ratio of squares to total shapes?If the unsimplified ratio of squares to total shapes is 6 : 16, then we can express this as 6/16, then,we can simplify this ratio by dividing both the numerator and denominator by 2, giving us 3/8.
This means that for every 3 squares, there are 5 total shapes. Therefore, the simplified ratio of squares to total shapes is 3 : 5.
Full question "Unsimplified ratio of squares to total shapes: 6 : 16. For every 3 squares, there are ____ total shapes; Therefore, the simplified ratio of squares to total shapes is __ : __.
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The monomial -3xy2z(-2x2yz) has degree of:
The degree of the monomial expression -3xy²z(-2x²yz) is derived to be equal to 8.
What is a monomialA monomial is a type of algebraic expression that consists of only one term. It is an expression in which the variables and their exponents are multiplied together, with no addition or subtraction involved. The degree of a monomial is the sum of the exponents of its variables.
Given the monomial:
-3xy²z(-2x²yz)
We can simplify it by multiplying the coefficients and adding the exponents of the variables:
-3(-2)x^(2+1) y^(2+1) z^(1+1)
= 6x³y³ z²
Therefore, the degree of the given monomial expression is: 3 + 3 + 2 = 8.
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The average first year teacher salary in a certain state is known to be $52,000 with a standard deviation of $1500. A researcher tests this claim by averaging the salaries of 25 first year teachers and finding their average salary to be $52,525. Is there significant evidence to suggest that the claim is wrong at the 5% significance level?
Option C is correct. No, the least value is smaller than the critical value.
Null hypothesis (H₀): The average first-year teacher salary is $52,000.
Alternative hypothesis (Ha): The average first-year teacher salary is not $52,000.
The significance level is 5% (or 0.05), which means we will reject the null hypothesis if the probability of obtaining the observed result is less than 5%.
Calculate the standard error of the mean:
Standard Error = Standard Deviation / √n
where n is the number of samples (n = 25 in this case).
Standard Error = $1500 / √25
= $1500 / 5
= $300
Now, perform the hypothesis test using a t-test since the sample size is relatively small (n < 30) and the population standard deviation is unknown.
t-score = (Sample Mean - Population Mean) / Standard Error
t-score = ($52,525 - $52,000) / $300
t-score = $525 / $300
t-score = 1.75
To find the critical value at a 5% significance level with 24 degrees of freedom (n - 1), we can consult a t-table. At a 5% significance level (two-tailed test), the critical t-value is approximately ±2.064.
Since the calculated t-score (1.75) is not greater than the critical t-value (2.064), we fail to reject the null hypothesis.
Therefore, option C is correct. No, the least value is smaller than the critical value.
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Complete question:
The average first year teacher salary in a certain state is known to be $52,000 with a standard deviation of $1500. A researcher tests this claim by averaging the salaries of 25 first year teachers and finding their average salary to be $52,525. Is there significant evidence to suggest that the claim is wrong at the 5% significance level?
A. Yes, the least value is greater than the critical value
B. No, the least value is larger than the critical value
C. No, the least value is smaller than the critical value
D. yes, the least value is smaller than the critical value
If sin a = -4/5
and sec B =5/3
for a third-quadrant angle a and a first-quadrant angle Ã, find the following
(a)
sin(a + B)
(b)
tan(a + b)
(c) the quadrant containing a + B
O Quadrant I
O Quadrant II
O Quadrant III
O Quadrant IV
Since sin(a) is negative and a is in the third quadrant, we can use the Pythagorean identity to find cos(a):
[tex]cos^2(a) + sin^2(a) = 1[/tex]
[tex]cos^2(a) + (-4/5)^2 = 1[/tex]
[tex]cos^2(a) = 9/25[/tex]
cos(a) = -3/5 (since a is in the third quadrant)
Similarly, since sec(B) = 5/3, we can use the definition of secant to find cos(B):
sec(B) = 1/cos(B) = 5/3
cos(B) = 3/5
(a) To find sin(a + B), we can use the sum formula for sine:
sin(a + B) = sin(a) cos(B) + cos(a) sin(B)
= (-4/5)(3/5) + (-3/5)(4/5)
= -12/25 - 12/25
= -24/25
(b) To find tan(a + B), we can use the sum formula for tangent:
tan(a + B) = (tan(a) + tan(B)) / (1 - tan(a) tan(B))
To find tan(a), we can use the identity: [tex]tan^2(a) + 1 = sec^2(a)[/tex]
[tex]tan^2(a) = sec^2(a) - 1 = (5/3)^2 - 1 = 16/9[/tex]
tan(a) = -4/3 (since a is in the third quadrant)
To find tan(B), we can use the identity: tan(B) = sin(B) / cos(B) = 4/3
Plugging these values into the formula for tan(a + B), we get:
tan(a + B) = (-4/3 + 4/3) / (1 + (-4/3)(4/3))
= 0 / (1 - 16/9)
= 0
(c) To determine the quadrant containing a + B, we need to consider the signs of sin(a + B) and cos(a + B).
From part (a), we know that sin(a + B) is negative. To determine the sign of cos(a + B), we can use the Pythagorean identity:
[tex]sin^2(a + B) + cos^2(a + B) = 1[/tex]
Substituting sin(a + B) = -24/25, we get:
[tex](-24/25)^2 + cos^2(a + B) = 1[/tex]
[tex]cos^2(a + B) = 1 - (-24/25)^2[/tex]
cos(a + B) = ±7/25
Since cos(a + B) is positive in the first and fourth quadrants, and negative in the second and third quadrants, we can conclude that a + B is in the third quadrant, since cos(a + B) is negative and sin(a + B) is negative.
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Consider the expression 16 - y^2/square root of 49 + 12. What is the value of the expression when y=-5?
Answer:
Step-by-step explanation:
16 - (y^2/sqrt(49)) +12
at y = -5
16 - ( (-5)^2 / sqrt(49)) +12
16 - ( 25 / 7) + 12
28 - (25/7)
(28*7 - 5) / 7 (LCM)
(196 - 5) / 7
(191/7)
27.2857 = Ans
Which equation correctly describes the relationship between x and y in the table?
A. y = 2x - 5
B. y = x
C. y = x - 3
D. y = 1/2x + 1
It's "D"
It's self explanatory but y gets 1/2 of whatever x is and adds 1. So if x = 2, then it'll get half of two (which is one) and add one to it, getting two.
Find all solutions of the equation in the interval [0, 2). (Enter your answers as a comma-separated list.)
sec(x) =
2√3
/
3
The whole thing is sec(x) = 2 root 3 and then it’s all over another 3
As an example another question is the same premise but
sec(x) = 2
and then the answer is
x= pi/3 , 5pi/3
So it has to be ordered like that I just don’t understand ty
Therefore, the solutions of the equation in the interval [0, 2) are: x = π/6, -π/6 (in radians) or x = 30°, -30° (in degrees). Note that the solutions are listed in ascending order.
How to Solve the Equation?The equation is:
sec(x) = 2√3/3
First, we can find the values of x for which sec(x) = 2√3/3. Recall that sec(x) = 1/cos(x), so we have:
1/cos(x) = 2√3/3
Multiplying both sides by cos(x), we get:
1 = 2√3/3 cos(x)
cos(x) = 3/(2√3) = √3/2
Now, we can use the unit circle to find the solutions of the equation in the interval [0, 2).
cos(x) = √3/2 when x is π/6 or 11π/6 (in radians), or 30° or 330° (in degrees), since these are the angles in the unit circle where the x-coordinate is √3/2.
However, we need to make sure that these solutions are in the interval [0, 2). Since the period of sec(x) is 2π, we can add or subtract 2π to any solution to get another solution. Therefore, we need to find the solutions in the interval [0, 2π) that correspond to the solutions we found above.
π/6 is already in the interval [0, 2π), so it is a solution in the interval [0, 2). To find the other solution in the interval [0, 2), we can add 2π to 11π/6:
11π/6 + 2π = 23π/6
23π/6 is not in the interval [0, 2), so we need to subtract 2π instead:
11π/6 - 2π = -π/6
-π/6 is in the interval [0, 2), so it is also a solution in the interval [0, 2).
Therefore, the solutions of the equation in the interval [0, 2) are:
x = π/6, -π/6 (in radians) or x = 30°, -30° (in degrees)
Note that the solutions are listed in ascending order.
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Type the correct answer in each box. use numerals instead of words.
lab tests of a new drug indicate a 70% success rate in completely curing the targeted disease. the doctors at the lab created the random data in the table using representative simulation. the letter e stands for "effective," and n stands for "not effective.
the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is ______. the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is ______.
To find the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we can use the geometric distribution. The probability of not curing the disease is 1 - 0.70 = 0.30.
Let X be the number of patients needed to find one patient on whom the medicine would not be effective. Then X follows a geometric distribution with p = 0.30. The probability that it will take at least five patients to find one patient on whom the medicine would not be effective is:
P(X ≥ 5) = (1 - p)^(5-1) = 0.7^4 ≈ 0.2401
Therefore, the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is approximately 0.2401.
To find the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients, we can use the binomial distribution. Let X be the number of patients out of four who are cured by the medicine. Then X follows a binomial distribution with n = 4 and p = 0.70. The probability that the medicine will be effective on exactly three out of four randomly selected patients is:
P(X = 3) = (4 choose 3) * (0.70)^3 * (1 - 0.70)^(4-3) = 4 * 0.343 * 0.3^1 ≈ 0.4116
Therefore, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is approximately 0.4116.
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The thickness of paper manufactured at a manufacturing company is roughly symmetrical with a mean of 0. 0039 inch and a standard deviation of about 0. 00001 inch. A marketing manager wants to divide the values of the thickness of paper by 0. 0001 to make the values easier to manage.
What are the mean and standard deviation of the thickness of paper after dividing by 0. 0001?
The mean is ?
inch.
The standard deviation is ?
inch
The mean of the thickness of paper is 39 inches, and the standard deviation is 0.1 inches.
To find the mean and standard deviation of the thickness of paper after dividing by 0.0001, you should follow these steps:
1. Divide the mean by 0.0001:
Mean after dividing = 0.0039 inches / 0.0001
Mean after dividing = 39 inches
2. Divide the standard deviation by 0.0001:
Standard deviation after dividing = 0.00001 inches / 0.0001
Standard deviation after dividing = 0.1 inches
The mean of the thickness of paper after dividing by 0.0001 is 39 inches, and the standard deviation is 0.1 inches.
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Marcus estimated the mass of a grain of sugar as 6 x 10-4 gram. Based on that
estimate, about how many grains of sugar are there in a small bag of sugar
that weighs 0. 24 kilogram?
There are 400,000 grains of sugar in a small bag of sugar that weighs 0.24 kilograms.
To find out how many grains of sugar are there in a small bag of sugar that weighs 0.24 kilograms, based on Marcus' estimate, follow these steps:
1. Convert the mass of the bag of sugar from kilograms to grams: 0.24 kg * 1000 g/kg = 240 g.
2. Use Marcus' estimate of the mass of a grain of sugar: 6 x 10^-4 g.
3. Divide the total mass of the bag of sugar by the mass of a single grain of sugar: 240 g / (6 x 10^-4 g/grain).
Now, let's perform the calculation:
240 g / (6 x 10^-4 g/grain) = 240 g / 0.0006 g/grain = 400,000 grains.
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Find the solution and also verify your answer , under root 12 x 12 x - 4 is equals under root 4 x + 8
The solution to the given equation is x = -3/4 or x = 1.
What values of x satisfy the equation √(12x² - 4) = √(4x + 8)?In order to find the solution, we start by squaring both sides of the equation to eliminate the square roots:
12x² - 4 = 4x + 8
Next, we simplify the equation by moving all the terms to one side:
12x² - 4x - 12 = 0
Now we can factor the quadratic equation:
4x² - x - 3 = 0
By factoring or using the quadratic formula, we find that the equation can be written as:
(4x + 3)(x - 1) = 0
Setting each factor equal to zero gives us the solutions:
4x + 3 = 0 or x - 1 = 0
Solving for x in each equation yields:
x = -3/4 or x = 1
Therefore, the solution to the given equation is x = -3/4 or x = 1.
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At a print shop reams of printer paper are stored in boxes in a closet. Each box contains 12 reams of printer paper. A worker uses 4 reams from 1 of the boxes. Which function shows the relationship between y, the total number of reams of printer paper remaining in the closet, and x, the number of boxes in the closet?
The function shows the relationship between y, the total number of reams of printer paper remaining in the closet, and x, the number of boxes in the closet is y = 12x - 4
Let's start by considering the initial amount of printer paper in the closet before any boxes are used. Since each box contains 12 reams of printer paper, if there are x boxes in the closet, then the total number of reams of paper is given by 12x.
Now, if a worker uses 4 reams from one of the boxes, then the total number of reams of paper remaining in the closet is (12x - 4). If we define y as the total number of reams of paper remaining in the closet, then we have:
y = 12x - 4
This function shows the relationship between y, the total number of reams of printer paper remaining in the closet, and x, the number of boxes in the closet.
As x increases, the total number of reams of paper in the closet increases as well. However, each time a worker uses 4 reams of paper from a box, the total number of reams of paper in the closet decreases by 4.
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Find an equation in the slope-intercept form for the line: slope = 4, y-intercept = 4
Answer:
y=4x+4
Step-by-step explanation:
The slope formula is:
[tex]y=mx+b[/tex]
with m being the slope and b being the y-intercept
Given: slope=4, y-intercept=4
We can substitute the slope and the y-intercept into the question:
y=4x+4
Hope this helps! :)
The equation of the line in slope-intercept form of a line with slope 4 and y-intercept 4 is [tex]\text{y} = 4\text{x} + 4[/tex].
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\text{m}=\dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}[/tex]
[tex]\text{m}=\dfrac{(\text{y}\bar{\text{a}}-\text{y}\bar{\text{a}})}{(\text{x}\bar{\text{a}}-\text{x}\bar{\text{a}})}[/tex]
It is given that:
A line with slope 4 and y-intercept 4.
The linear equation in one variable can be made:
As we know,
The standard equation of the line is:
[tex]\text{y} = \text{mx} + \text{c}[/tex]
Here m is the slope and c is the y-intercept.
[tex]\text{m} = 4[/tex]
[tex]\text{c} = 4[/tex]
[tex]\boxed{\bold{y = 4x + 4}}[/tex]
Thus, the equation of the line in slope-intercept form of a line with slope 4 and y-intercept 4 is [tex]\text{y} = 4\text{x} + 4[/tex].
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Catering company provides packages for weddings and for showers. The cost per person for small groups is
pproximately Normally distributed for both weddings and showers. The mean cost for weddings is $82. 30 with a
andard deviation of $18. 20, while the mean cost for showers is $65 with a standard deviation of $17. 73. If 9
eddings and 6 showers are randomly selected, what is the probability the mean cost of the weddings is more than
e mean cost of the showers?
The probability that the mean cost of the 9 weddings is more than the mean cost of the 6 showers is approximately 0.0207 or 2.07%.
The probability that the mean cost of the 9 weddings is more than the mean cost of the 6 showers can be found using the Z-score and the difference between the means of two normally distributed variables.
1: Calculate the difference in means and standard deviations.
Δμ = μ_weddings - μ_showers = $82.30 - $65 = $17.30
Δσ = sqrt((σ_weddings²/n_weddings) + (σ_showers²/n_showers)) = sqrt((18.20²/9) + (17.73²/6)) = $8.47
2: Calculate the Z-score.
Z = (Δμ - 0) / Δσ = (17.30 - 0) / 8.47 ≈ 2.04
3: Determine the probability using a Z-table.
P(Z > 2.04) ≈ 0.0207
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I need to know how to solve this equation
Answer:
3/y
Step-by-step explanation:
15x÷5xy
15x/5xy....you will cancel x by x and simplify by 5(GCF)
3/y ...... it is the simplify form of the given equetion.
Find dy/dt at x = – 1 if y = – 2x^2 + 4 and dx/dt = 4. dy/dt =?
Derivative of y w.r.t t is dy/dt = 16 at x = -1.
How to find dy/dt?We need to find dy/dt at x = -1, given y = -2x² + 4 and dx/dt = 4.
Step 1: Differentiate y with respect to x.
Since y = -2x² + 4, we have:
dy/dx = -4x
Step 2: Substitute x = -1 into the dy/dx equation.
When x = -1, we get:
dy/dx = -4(-1) = 4
Step 3: Use the Chain Rule to find dy/dt.
The Chain Rule states that dy/dt = (dy/dx)(dx/dt). We know dy/dx = 4 and dx/dt = 4, so we have:
dy/dt = (4)(4) = 16
Thus, dy/dt = 16 at x = -1.
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Find the following unknowns about the circle. Round all answers to the nearest tenth.
The given circle has a radius of 11.2,
The diameter of the given circle is 22.4The circumference of the given circle is 70.336 The area of the given circle is 393.88Given radius of the circle (r) = 11.2
The diameter of the given circle = 2*r = 2*11.2 = 22.4
The circumference of the given circle = 2πr = 2*3.14*11.2 = 70.336
The area of the given circle = πr² = 3.14*(11.2)² = 393.88
From the above analysis, we can conclude that the diameter of the circle is 22.4 and the circumference of the circle is 70.336 and the area of the circle is 383.88.
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describe the likelihood of the next elk caught being unmarked
The probability of the next elk caught being unmarked is 0.96 when the total number of elks is 5625 and the number of elks marked is 225.
A probability is given by the number of desired outcomes divided by the number of total outcomes.
Total number of elks = 5625
Number of elks marked = 225
We need to find the total number of elks not marked or unmarked we can find it by,
= 5625 - 225
= 5500
Therefore, the total number of elks unmarked is 5500.
We can determine determined the likelihood of the next elk caught being unmarked by using probability. The probability is given by:
P = 5500/5625
= 44 / 45
= 0.96
Therefore, The total number of elks unmarked is 0.96.
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The complete question is,
Describe the likelihood of the next elk caught being unmarked.
A box contains 10 red buttons, 30 green buttons, 40 blue buttons, and 20 yellow buttons. ten buttons were removed, tallied, and then returned to the box. three additional samples were taken in the same way. which sample is the best representation of the buttons in the box?
The best representation of the buttons in the box is the third sample.
To determine which sample is the best representation of the button in the box, we need to examine the samples and compare them to the known ratios of the colors of buttons in the box.
First sample: 6 red, 2 green, 1 blue, 1 yellow (out of 10)
Second sample: 3 red, 3 green, 3 blue, 1 yellow (out of 10)
Third sample: 2 red, 2 green, 5 blue, 1 yellow (out of 10)
To compare the samples to the known ratios, we can calculate the percentage of each color in each sample and compare it to the percentage of each color in the box.
The percentages of each color in the box are:
Red: 10/100 = 10%
Green: 30/100 = 30%
Blue: 40/100 = 40%
Yellow: 20/100 = 20%
First sample:
Red: 6/10 = 60%
Green: 2/10 = 20%
Blue: 1/10 = 10%
Yellow: 1/10 = 10%
Second sample:
Red: 3/10 = 30%
Green: 3/10 = 30%
Blue: 3/10 = 30%
Yellow: 1/10 = 10%
Third sample:
Red: 2/10 = 20%
Green: 2/10 = 20%
Blue: 5/10 = 50%
Yellow: 1/10 = 10%
Based on these percentages, we can see that the third sample is the best representation of the buttons in the box, as it is closest to the known ratios of colors in the box.
The first sample is skewed towards red buttons and away from blue and green buttons, while the second sample has equal percentages of red, green, and blue buttons, which is not reflective of the known ratios in the box.
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What is the area of a triangle with vertices at (5,0), (-3,1) and (2,6)?
6 units squared
54 units squared
22. 5 units squared
36. 5 units squared
Answer:
To find the area of a triangle given its vertices, we can use the formula:
Area = 1/2 * |(x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))|
where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the three vertices.
Using this formula, we can calculate the area of the triangle with vertices at (5,0), (-3,1), and (2,6) as follows:
Area = 1/2 * |(5*(1-6) + (-3)(6-0) + 2(0-1))|
= 1/2 * |-25 - 18 - 2|
= 1/2 * |-45|
= 22.5
Therefore, the area of the triangle is 22.5 units squared. So the answer is option C: 22.5 units squared.
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Consider the parametric equations
x=cos(t)−sin(t);y=cos(t)+sin(t) 0≤t≤2π
a) Eliminate the parameter t to find a Cartesian equation for the parametric curve.
b) Sketch this parametric curve, indicating with arrows the direction in which the curve is traced.
For two parametric equations, x = cos(t)− sin(t) ; y = cos(t) + sin(t) ; 0≤t≤2π
a) Cartesian equation for the parametric curve is represented by x² + y² = 2.
b) The sketch for this parametric curve, with arrows in the direction of curve tracing is present above figure.
A parametric curve in the x-t plane has the equations x=x(t), y=y(t). The curve associates a point of the plane (x,y) to a value of the parameter t. The rectangular form of the curve can be determined by eliminating the parameter t, i.e. determine the parameter in one equation and Substituting this value in the other equation. We have the following parametric equations,
x = cost - sinty = cos(t)+ sint, 0 ≤ t ≤ 2π
(a) we have to eliminate parameter t to determine a cartesian equation for the parametric curve, use x²+ y² = (cos(t) − sin(t))²+ (cos(t) + sin(t))²
=> x² +y² = cos²t + sin²t - 2cost sint + cos²t + sin²t + 2cost sint
=> x² + y² = 2 ( sin²t + cos²t) = 2
which represents a circle curve centered at the origin and having radius √2.
(b) A sketch of this parametric curve is shown above figure and arrows are used to indicate the direction of curve trace.
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A cup has a capacity of 320 ml. It takes 58 cups to fill a bucket and 298 buckets to fill a tank. By rounding to 1 significant figure, estimate the capacity of the tank in litres.
______________________________
Notes: 1L = 1,000ml BUCKET:= 320ml × 58= 18,560mlTANK:= 18,560ml × 298= 5,382,000ml= 5,382,000ml ÷ 1,000= 5,382= ~ 5.4LThe Capacity of The Tank Is Approx. 5.4L_______________________________
Lisa invested money into a bank account. The value of the account after t years can be found using the function f(t)=6320(1.054)t . What is the initial value of the account?
The initial value of the account is: 6320
How to solve compound interest problems?Compound interest is defined as the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 10% interest each year, you'll have $110 at the end of the first year.
The general formula to find compound interest is:
A = P(1 + r/n)^t
where:
A is final amount
P is initial principal balance
r is interest rate
n is number of times interest applied per time period
t is number of time periods elapsed
We are given the equation as:
f(t) = 6320(1.054)^(t)
Thus, the initial value is 6320
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There are ten slips of paper in a box, each numbered 1-10. If Gerard reaches into the box without looking, what is the probability that he will get a number less than 3?
69 ptssssssss
Answer: 1/5
Step-by-step explanation:
There are 10 slips of paper.
The only numbers less than three are 1 and 2
The probability that he will pick up a slip of paper less than three is 2 since only 1 and 2 are less than three.
Therefore the probability is 2/10, and when simplified, it is 1/5.
Therefore the answer is 1/5.
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You get a part time job earning $12.50/hr. Tips are $4.60/hr average. Deductions are FICA (7.65%) and Federal Tax Withholding (10%). You work for 18 hours. What is your gross base pay?
If you are earning $12.50/hr in a part-time job, then your gross "base-pay" after deductions is $253.48.
Your base pay is $12.50/hr and you worked for 18 hours, so the base pay would be:
⇒ $12.50/hr × 18 hrs = $225;
The tips are $4.60/hr on average, so the "total-tips" earned would be:
⇒ $4.60/hr × 18 hrs = $82.80;
To calculate the "total-deductions", we first find the total percentage deducted, which is the sum of FICA and Federal Tax Withholding:
⇒ 7.65% + 10% = 17.65%,
To find the total amount deducted, we multiply the total percentage deducted by the "base-pay" + "tips";
⇒ 17.65% x ($225 + $82.80) = $54.32,
So the pay, before any deductions, is the sum of "base-pay" and "tips";
⇒ $225 + $82.80 = $307.80;
To find the "net-pay", we subtract "total-deductions" from pay;
We have,
⇒ $307.80 - $54.82 = $253.48,
Therefore, your gross base pay is $253.48.
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Answer:
add the tips and pay together , this equals 17.10
then multiply by the 18 hours and you’ll get 307.80
Step-by-step explanation:
Solve for length of segr
6 cm
4 cm
b
18 cm
b = [?] cm
If two segments intersect inside
Answer:
12
Step-by-step explanation:
multiply 4x18 then divide by 6
Peter gets a part-time job cleaning and maintaining his community's swimming pool and spa. 40 Here are some facts about the pool and spa. There is an outlet for a vacuum halfway along the side of the pool. What is the approximate length the hose should be to reach any part of the pool surface from there? Show your work. Answer Between _and _ft.
The length of the hose to reach any part of the pool surface from there will be 22.36 feet.
How to calculate the length:Length of hose = √(L² + W²)
The pool is 20 feet long and 10 feet wide, the length of the hose needed would be approximately:
Length of hose = √(20² + 10²) = √500 = 22.36 feet
Therefore, Peter would need a vacuum hose that is approximately 22.36 feet long to reach any part of the pool surface from the outlet.
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Use the rational expression below to match the variables on the left with their excluded value(s) on the right.
The value of b = 4
How to solveThe function becomes undefined when the denominator goes to 0
3x² - 48 = 0
3x² = 48
x² = 16
x = +/ 4
From the given choices, it's x = 4
Rational expressions that utilize ratios of polynomial expressions are referred to as rational expressions. These can be written in the format p(x)/q(x), where both p(x) and q(x) are polynomials with the constraint that q(x) cannot equal zero.
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