The distance from town A that they will be, when they will pass each other is 44 4/9 .
How can the distance be calculated?It should be noted that time traveled in each segment is constant, which implies that in this case the average speed can be regarded as the simple mean of speeds. An in the case whereby the distance traveled in each segment is constant, average speed can be described to be the reciprocal of simple mean .
This can be expressed mathematically as
Average speed = Reciprocal [ 1/40 & 1/50].
Average speed = Reciprocal of (1/40 + 1/50)/2
= Reciprocal of [(5+4)/400]
= 44 4/9 .
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(3d). Mary decided to open a uniform cleaning service at GTUC. When she started the business she had to purchase an Ironing Board for $15 and an Iron for $35. Also, she figured it would cost $1.25 in cleaning products for each uniform, so she decided she was going to charge $3.25 for cleaning and pressing one entire uniform i. Write a system of equations that would represent the above scenario. ii. How many uniforms does Mary have to clean in order to break even?
she needs to clean 15 uniforms to break even
There are 6 bottles of water.
Each bottle is 1/2 full. If you
were to combine all the
water, how many full bottles
of water would there be?
Answer:3
Step-by-step explanation: 1/2 X 6 = 3
Answer:
6 x 1/2 = 3 full bottles
Step-by-step explanation:
There are 16 green balls and 4 white balls in a bag. Four balls are drawn randomly from the bag. Let X be the number of white balls drawn.
(a) Find the expectation and variance of X.
Answer:
the variance of X is 0.126.
Step-by-step explanation:
The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:
P(X = k) = (nCk)(N-nCk) / (NCk)
where C denotes the combination function.
(a) Expectation of X:
E(X) = np = nK/N = (4/20) * 4 = 0.8
Therefore, the expected number of white balls drawn is 0.8.
(b) Variance of X:
Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126
Therefore, the variance of X is 0.126.
Answer:
The expected number of white balls drawn is 0.4 and the variance of X is 0.24.
Step-by-step explanation:
The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)
The strength of the beam is proportional to the width and the square of the depth, so we can express it as Strength = k * width * depth²
where k is the proportionality constant.
In the given figures, the beam is cut from a cylindrical log of diameter d = 24 cm, which means the maximum width and depth of the beam are limited by this diameter. We can see from the figures that the width and depth of the beam change depending on the angle at which it is cut from the log.
In Figure 1, the width and depth of the beam are equal, so we can express the strength of the beam as:
Strength = k * width * depth² = k * x² * (d/2 - x)²
where x is the width and depth of the beam.
In Figure 2, the width and depth of the beam are not equal, so we need to express them separately. Let w be the width and d be the depth, then we can express the strength of the beam as:
Strength = k * width * depth² = k * w * d² = k * ((d/2)sinθ)² * ((d/2)cosθ)²
where θ is the angle at which the beam is cut from the log.
In Figure 3, the width and depth of the beam also vary with the angle θ. We can express the width and depth as follows:
w = d sinθ
d = (d/2)cosθ
Then we can express the strength of the beam as:
Strength = k * width * depth² = k * (d sinθ) * [(d/2)cosθ]²
Therefore, depending on the angle at which the beam is cut from the log, the strength of the beam can be expressed using different equations, but in all cases, the strength is proportional to the width and the square of the depth, with a proportionality constant k.
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Complete question is:
The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)
The table describes the quadratic function p(x). x p(x) -4 24 -3 9 -20 -1 -3 0 2 0 What is the equation of p(x) in vertex form? Op(x) = 2(x - 1)² - 3 p(x) = 2(x + 1)² - 3 Op(x) = 3(x - 1)² – 3 p(x) = 3(x - 1)² – 3
The equation of p(x) in vertex form is p(x) = 3(x + 1)² - 3.
Option C is the correct answer.
Since, Polynomial is an equation written as the sum of terms of the form kxⁿ.
where k and n are positive integers.
We have,
From the table,
From p(x) = 24 to p(x) = -3 the value of p(x) is decreasing and from p(x) = -3 to p(x) = 24 it is increasing.
So,
The vertex is (- 1, -3).
The vertex form of p(x).
p(x) = a ( x - h)² + k
Where (h, k) is the vertex.
Now,
(-1, -3) = (h, k)
Make (- 2, 0) = (x, p(x))
0 = a (- 2 + 1)² + (-3)
0 = a x 1 - 3
a = 3
Thus, The vertex equation of p(x).
p(x) = 3(x + 1)² - 3
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Solve by using a system of equations.
A goldsmith has two gold alloys. The first alloy is 30% gold; the second alloy is 80% gold. How many grams of each should be mixed to produce 40 grams of an alloy that is 60% gold?
The amount of grams of each alloy that should be mixed to produce 40 grams of an alloy that is 60% gold are 16 grams and 24 grams respectively.
How to write a system of equations to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the quantity of first alloy (30% gold) and the quantity of second alloy (80% gold) respectively, and then translate the word problem into a linear equation as follows:
Let the variable y represent the quantity of first alloy (30% gold).Let the variable x represent the quantity of second alloy (80% gold).Therefore, a system of linear equations to describe this situation can be written as follows;
x + y = 40 .....equation 1.
0.3x + 0.8y = 0.6(40) .....equation 2.
From equation 2, we have the following:
0.3x + 0.8y = 24
0.3x + 0.8(x - 40) = 24
0.3x + 32 - 0.8x = 24
-0.5x = -8
x = -8/-0.5
x = 16 grams.
y = 40 - x
y = 40 - 16
y = 24 grams.
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Jermaine invested $3,200 in a defined-contribution account. Assuming he is in a 20% marginal tax bracket, how much did he lower his income taxes with the investment
Answer:
$640
Step-by-step explanation:
You want to know the income tax reduction resulting from investing $3200 in a defined-contribution account when the marginal tax rate is 20%.
Tax exemptThe money invested in a defined-contribution account is not subject to income taxes when it is invested. The tax savings is ...
20% × $3200 = $640
Jermaine lowered his taxes by $640.
Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zeros.
-3, √3, 13/3
The other zeros are
(Use a comma to separate answers.)
Answer:
{-3, √3, -√3, 13/3}
Step-by-step explanation:
Since the polynomial has rational coefficients, any irrational zeros must come in conjugate pairs. So, if √3 is a zero, then so is its conjugate, -√3.
We can write the polynomial with these zeros as:
p(x) = a(x + 3)(x - √3)(x + √3)(x - 13/3)
where a is some constant coefficient. Multiplying out the factors, we get:
p(x) = a(x + 3)(x^2 - 3)(x - 13/3)
To find the remaining zeros, we need to solve for x in the expression p(x) = 0. So we set up the equation:
a(x + 3)(x^2 - 3)(x - 13/3) = 0
This equation is true when any of the factors is equal to zero. We already know three of the zeros, so we need to solve for the fourth:
(x + 3)(x^2 - 3)(x - 13/3) = 0
Expanding the quadratic factor, we get:
(x + 3)(x - √3)(x + √3)(x - 13/3) = 0
Canceling out the (x - √3) and (x + √3) factors, we get:
(x + 3)(x - 13/3) = 0
Solving for x, we get:
x = -3 or x = 13/3
Therefore, the other zeros are -3 and 13/3.
The complete set of zeros is {-3, √3, -√3, 13/3}.
Hope it helps^^
Ignatio and his two friends each bought a ticket to play lazer tag and each spent $15 on game tokens at Fun Mountain. Let t represent the cost of a lazer tag ticket. Enter an expression that represents the total amount that Ignatio and his friends spent.
The expression that represents the total amount that Ignatio and his friends spent is 15t
From the question, we have the following parameters that can be used in our computation:
Each spent $15 on game tokens at Fun MountainEach cost = tAfter spending on t games, we have
f(t) = Rate * t
Substitute the known values in the above equation, so, we have the following representation
f(t) = 15 * t
Evaluate
f(t) = 15t
Hence, the expression that represents the total amount that Ignatio and his friends spent is 15t
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The prism below is made of cubes which measure
1
4
of an inch on one side. What is the volume?
A 3D illustration view of a blank tabular with 5 rows and 2 columns.
Note: Figure is not drawn to scale.
A.
15
32
cubic in
B.
5
2
cubic in
C.
30
cubic in
D.
15
2
cubic in
The volume of the prism is B. 2.5 cubic inches.
How to calculate the volumeAccording to the question, the prism measures 1/4 of an inch on one side. Now we will assign values to the length, width, and height of this prism as follows:
Length = 2 × 1/4
Width = 5 × 1/4
Height = 3 × 1/4
= 2/4 + 5/4 + 3/4
= 2 2/4
= 2.5 cubic inches.
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A meter in a taxi calculates the fare using the function f(x) = 2.56x + 2.40. If x represents the length of the trip, in miles, how many miles can a passenger travel for $20?
A passenger can travel 6.875 miles for $20 using the given taxi fare function.
To determine how many miles a passenger can travel for $20 using the taxi fare function f(x) = 2.56x + 2.40, we need to set up an equation and solve for x.
The equation we need to solve is:
2.56x + 2.40 = 20
To solve for x, we can start by subtracting 2.40 from both sides of the equation:
2.56x = 17.60
Next, we can divide both sides by 2.56:
x = 6.875
This calculation assumes that the fare is based solely on distance and that there are no additional fees or charges.
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A population of values has a normal distribution with a mean of 246 and a standard deviation of 89.7. You intend to draw a random sample of size m = 158.
Answer the following, rounding your answers to three decimals where appropriate.
Find the probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4.
P(M>242.4) = ???
The probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4 is 0.751.
How to calculate the probabilityz = (x - μ) / (σ/√n)
where x is the sample mean.
Substituting the values, we get:
z = (242.4 - 246) / (89.7/√158) ≈ -0.670
We want to find the probability of obtaining a sample mean greater than 242.4, which is equivalent to finding the probability of obtaining a standardized sample mean greater than z = -0.670. We can use a standard normal distribution table or calculator to find this probability.
P(z > -0.670) ≈ 0.751
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someone help i really need help with this
Answer:
29
Step-by-step explanation:
she spends $75 on the gift cards, which brings the total down to $175 which is how much money she has left. She then spends $123.5 on the 13 movie passes, she is then left with $51.5 to spend. Then you divide 51.5 by 1.75 to get 29.4 and rounds down to 29.
what is 9v+–3v+–4v–2+1 simplified
Answer:
2v-1
Step-by-step explanation:
9v+-3v+-4v-2+1
=9v-3v-4v-1
=6v-4v-1
=2v-1
Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided.
Lower bound=0.640, upper bound=0.910, n=1200
The point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample are:
margin of error = 0. 135point estimate = 0. 775 x = 930 peopleHow to find the parameters ?The point estimate of the population proportion:
= (lower bound + upper bound) / 2
= (0.640 + 0.910) / 2
= 0. 775
The margin of error for the confidence level :
= p - hat - lower bound
= 0. 775 - 0. 640
= 0. 135
The number of individuals in the sample with the specified characteristic (x ) :
= n x p - hat
= 1, 200 x 0. 775
= 930 people
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3. Find the solution to each equation mentally.
a. 30+ a = 40
b. 500+ b = 200
C. -1+c= -2
d. d +3.567=0
Answer:
[tex]a. \: 30 + a = 40 \\ a = 40 - 30 \\ a = 10 \\ b. \: 500 + b = 200 \\ b = 200 - 500 \\ b = - 300 \\ c. \: - 1 + c = - 2 \\ c = - 2 + 1 \\ c = - 1 \\ d. \: d +3.567=0 \\ d = 0 - 3.567 \\ d = - 3.567[/tex]
hope it helps:)
Identify the null and alternative hypotheses
Statistics!
The null and the alternate hypothesis are:
H₀: p ≤ 0.5H₁: p > 0.5How to write the hypothesisIn hypothesis testing, we take the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis is the opposite of the claim , while the alternative hypothesis states the claim.
In this case, the null hypothesis is that a majority of adults would not erase their personal information online if they could (i.e., 50% or less of them would do so). The alternative hypothesis is that a majority of adults would erase their personal information online if they could (i.e., more than 50% of them would do so). In symbolic form:
H₀: p ≤ 0.5
H₁: p > 0.5
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Denise is designing the seating arrangement for a concert at an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. Explain to Denise how to create an equation to predict the number of seats in any row. Then using your equation. show your work to determine the number of seats in row 18.
Answer:113
Step-by-step Explanation:
To create an equation to predict the number of seats in any row, we need to start by defining a few variables:
Let's call the number of seats in the first row "a".
Let's call the number of additional seats in each row after the first row "d".
Since we know that each row has 6 more seats than the previous row, we can set d equal to 6:
d = 6
We also know that the first row has 11 seats, so we can set a equal to 11:
a = 11
To find the number of seats in any row, we can use the following formula:
number of seats in a given row = a + (n - 1) * d
Where "n" is the number of the row we are interested in.
Using this formula, we can find the number of seats in row 18:
number of seats in row 18 = 11 + (18 - 1) * 6
= 11 + 102
= 113
Therefore, there are 113 seats in row 18.
example of a multi-step combination problem
Answer:
A multi-step-word problem is like a puzzle with lots of pieces. Multi-step word problems are math problems that have more than one operation. An operation is addition, subtraction, multiplication, or division. Multi-step word problems can have any combination of these operations
Describe two trends you can find in the graph below. Use calculations and numbers to support your thinking.
The two trends on the graph are:
Positive correlationNegative correlationDescribing the two trends on the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The two trends on the graph are:
Positive correlationNegative correlationFor the positive correlation, we have
Upward trend from January till August
This is because the function values increase approximately in this domain
For the negative correlation, we have
Upward trend from August till December
This is because the function values decrease approximately in this domain
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For the following exercises,
(a) find the angle between 0 and 2π in radians that is coterminal with the given angle.
(b) find the reference angle of each one.
a)32π/13 b)-17π/6
The reference angle of given angles are -6π/13 and -5π / 6
To get coterminal angles, you simply have to add or subtract 2π.
a) 32π/13 =
= -32π/13 + 2π
= -32π + 26π / 13
= -6π/13
b) -17π/6 + 2π =
= -17π + 12π / 6
= -5π / 6
Hence the reference angle of given angles are -6π/13 and -5π / 6
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please help, due in an hour !!
Answer:
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST
what will the coordinates be if Point A (-4,-5) of the trapezoid was reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction.
Answer:
If point A (-4,-5) of the trapezoid is reflected across the y-axis, the x-coordinate will change sign while the y-coordinate remains the same. This gives us the point A' (4, -5).
Next, if we shift the point A' by -6 units in the x-direction and 7 units in the y-direction, we get the new point A":
A" = (4 - 6, -5 + 7) = (-2, 2)
Therefore, the coordinates of point A after it is reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction are (-2, 2).
Step-by-step explanation:
Answer:
(-2, 2)
Step-by-step explanation:
I did the test
Hope this helps :)
What expression is or is not equivalent, what is the answer?
Answer:
A and B
Step-by-step explanation:
-10/3= -3.33333333333
(- (-10))/(-3)= -10/3, (negative sign being erased)
=-3.33333333333
hope it helped:)
15 POINTS!! ASAP TYYY
Answer:
A
Step-by-step explanation:
She earns $15 per poinsettia.
Using the GCF, what is the factored form of 75 - 3x?
please i need help!!!
u will get 100 points!!!
The GCF (Greatest Common Factor) is the largest number that divides evenly into two or more numbers. In this case, we can find the GCF of 75 and 3 by listing their factors and finding the largest one they have in common. The factors of 75 are 1, 3, 5, 15, 25, and 75. The factors of 3 are 1 and 3. The largest factor they have in common is 3. Therefore, the GCF of 75 and 3 is 3.
We can use the GCF to factor the expression 75 - 3x by dividing each term by the GCF and writing the expression as a product. In this case, we can divide both terms by 3 to get 75/3 - (3x)/3, which simplifies to 25 - x. We can then write the original expression as a product by multiplying this simplified expression by the GCF: 3(25 - x).
Therefore, the factored form of 75 - 3x using the GCF is 3(25 - x).
Answer:
3(25-x)
Step-by-step explanation:
First we find the GCF of 75 and -3x, which is 3
3 is the highest number we can divide both 75 and -3
Hence, the answer is 3(25-x)
the cost of a luna bar is 2 dollars at harmons. what is the cost of 30 luna bars
Answer:
60
Step-by-step explanation:
2$ times 30 luna bars at harmons is $60
Can the following list represent a complete probability model? P(2)= 1/12 P(3) = 2/3 P(4) = 1/4
Therefore , the solution of the given problem of probability comes out to be a complete probability model cannot be represented by this list.
What exactly is probability?The main objective of each considerations technique is to calculate the likelihood that a claim is true or that a particular incident will occur. Anything between 0 and 1, were 0 traditionally denotes a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The probabilities assigned to the outcomes do not add up to 1, hence the following list cannot be a complete probability model.
=> P(2) + P(3) + P(4)
=> 1/12 + 2/3 + 1/4
=> (1 + 8 + 3) / 12
=> 12 / 12 = 1
In a complete probability model, the total of the probabilities should always be equal to 1, indicating that there is a probability of 1 that one of the events will occur.
In this instance, there is a missing probability since the sum of the probabilities assigned to the possible possibilities is less than 1.
Therefore, a complete probability model cannot be represented by this list.
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James answered 14 lems correctly
an a 16-item quiz. what percentage did he answer correctly
Answer:
14/16 = 0.875
Please answer if you know this one with the steps thank you.
Step-by-step explanation:
T = 5200 = .2 ( E - 10600)
5200 / .2 = E - 10600
E = 5200/.2 + 10 600 = 36600 pounds
