[tex]\begin{array}{ccll} \$&hours\\ \cline{1-2} 44 & 6\\ x& 9 \end{array} \implies \cfrac{44}{x}~~=~~\cfrac{6}{9} \\\\\\ \cfrac{ 44 }{ x } ~~=~~ \cfrac{ 2 }{ 3 }\implies 132=2x\implies \cfrac{132}{2}=x\implies 66=x[/tex]
What is the value of 5(y+3)-3 x² when x=4 and y=2 ?
A) -23
B) -10
C) 10
D) 23
Step-by-step explanation:
5(2+3)-3*4²
=5*5-3*16
=25-48
=-23(A)
Use the "at least once" rule to find the probabilities of the following events.
Getting at least one tail when tossing seven
fair coins
The required probability will be 127/128 that getting at least one tail when tossing seven.
We know that the total number of sides on a coin [Tail, Heads] =2
The probability of getting a tail = 1/2
The probability of getting no tail = 1 -1/2 = 1/2
According to the "at least once" rule, when a coin is tossed n times, the chance of obtaining at least one tail is given by:-
P(at least one tail) = 1 - [P(no tail)]ⁿ
In this case, n=7
Then, the probability of getting at least one tail is given by:-
P(at least one tail) = 1 - (1/2)⁷
P(at least one tail) = 1 - (1/128)
P(at least one tail) = 127/128
Thus, the required probability will be 127/128 that getting at least one tail when tossing seven.
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Tom is leading a workshop for 15 people. He wants each person to meet every other person (shake hands once). How many handshakes occur?
The number of handshakes that occur in Tom's workshop is 105
Given: Number of people in the workshop is 15 and Every person shakes hands once with every other person
To find: Number of handshakes
Since every person has to meet the other person only once and shake hands only once. So every handshake has only one possible combination.
Total number of combinations (handshakes) that can be possible with 15 people = [tex]15C_2[/tex]
The formula for a combination is
[tex]nC_r = \frac{n!}{r!(n-r)!}[/tex]
where n is the number of items and r is the unique arrangements.
Plugging in our numbers of n = 15 and r = 2, we get
[tex]15C_2= \frac{15!}{2!(15-2)!}\\= \frac{15!}{2! \times 13!} \\=\frac{15 \times 14 \times 13!}{2! \times 13!}\\[/tex]
On cancelling out 13! from numerator and denominator , we get
[tex]15C_2=\frac{15 \times 14}{2 \times 1}= 15 \times 7=105[/tex]
What is combination?A combination is a method of picking things from a collection in which the order of selection is irrelevant. Assume we have three numbers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.
It is feasible to count the number of combinations in smaller collections, but the possibilities of a set of combination increases with the number of groups of elements or sets. As a result, a formula has been developed to determine the number of things that can be selected.
The formula is
[tex]nC_r = \frac{n!}{r!(n-r)!} \, when \, n > r\\nC_r = 0 \, when \, n < r[/tex]
Where n = number of distinct objects to choose from
C = Combination
r = spaces to fill
The number of handshakes that occur in Tom's workshop is 105
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Explain how to translate the phrase into an algebraic expression. The difference between four times a number and 10
Translating the phrase into an algebraic expression for the difference between four times a number and 10 is 4x - 10.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Let the number be given as x.
Therefore, 4 times will number will be 4x.
Then, difference between four times a number and 10 will be:
= 4x - 10
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Assume that you want to have $ 1900 saved in a sinking fund in 1 year. The account pays 3.5% compounded monthly. What should be your monthly payments?
Monthly Payment =
The monthly payment would be an amount of $163.875.
What exactly is a monthly payment?A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.
As per the given question, we have
Here P = $1900 , r = 3.5%, and T = 1 years
The total payback = P× r/100 × T + P
The total payback = 1900 × 3.5/100 × 1 + 1900
The total payback = 1900 × 0.04 × 4 + 1900
Apply the multiplication operation, and we get
The total payback = $1966.5
The total payback of the borrowings will be $1966.5 over a one-year period. The monthly payment for this will be,
The monthly payment = Total payback / No. of payment
The monthly payment = 1966.5/12
The monthly payment = $163.875
Therefore, the monthly payment would be an amount of $163.875.
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[tex]3x^{2} +x -5=0[/tex]
The two solutions of the quadratic equation are:
x = 1.135
x= -1.468
How to solve the quadratic equation?
A general quadratic equation:
a*x^2 + b*x + c = 0
Has solutions of the form:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Here the quadratic equation is:
3*x^2 + x - 5 = 0
So the values are:
a = 3
b = 1
c = -5
Replacing that in the quadratic formula for the solutions we will get:
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*3*(-5)} }{2*3}\\\\x = \frac{-1 \pm 7.81 }{6}[/tex]
Thus, the two solutions are:
x = (-1 + 7.81)/6 = 1.135
x = (-1 - 7.81)/6 = -1.468
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If Mars travels at 24,126 meters per second in orbit around the Sun and takes 1.88 earth years to complete its orbit, what is the total distance in miles Mars travels throughout its complete orbit? (Round your answer to the nearest whole number and do not include units or commas in your answer.) Note: There are 1,609 meters in a mile.
The total distance in miles Mars travels throughout its complete orbit will be 888 × 10⁶ miles.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, If Mars travels at 24,126 meters per second in orbit around the Sun and takes 1.88 earth years to complete its orbit,
First, we have to convert the unit from earth year to second obtained as,
1.88 earth year= 59287680 second
As we know that the distance is the multiplication of the speed and the time
Distance = speed × Time
Distance =24,126 m/sec × 59287680 second
Distance = 1.4 × 10¹² m
If 1 meter consists of 0,000621371 miles, the obtained distance is in miles.
1 metere = 0,000621371 miles
1.4 × 10¹² m=888 × 10⁶ miles
Thus, the total distance in miles Mars travels throughout its complete orbit will be 888 × 10⁶ miles.
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1. Simplify the following expression which creates an equivalent expression.
7x-8x+14-26-3x
Answer:
-4x-12
Step-by-step explanation:
7x-8x-3x = -4x
14-26 = -12
-4x-12
The FBI determined the true average time between felony acts in the US with a 95% confidence interval of (2.3, 5.7) seconds. Which of the following (if any) are correct? There is a 95% probability that the true average is between 2.3 and 5.7 seconds 95% of all felonies happen in 2.3 seconds to 5.7 seconds We are 95% confident the true average is between 2.3 and 5.7 seconds 95% of the time the true average will be between 2.3 and 5.7 seconds 95% of the time confidence intervals like this capture the true average time between a felony A new confidence interval has a 95% probability of capturing the sample average
95% of the time confidence intervals like this capture the true average time between a felony.
The average of the true ranges throughout the given period is known as the average true range (ATR). ATR calculates volatility by accounting for any gaps in price movement. 14 periods, which can be intraday, daily, weekly, or monthly, are typically used in the ATR calculation. Utilize a shorter average, such as 2 to 10 periods, to gauge recent volatility. Use 20 to 50 periods for volatility over longer time spans.
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1/4(2x + 1.2) = 3(0.7x + 3) - 5 1/2
what is the solution?
show your work please!!
Answer:
Step-by-step explanation:
Simplify parentheses : 0.5x+0.3=2.1x+9-5.5
Combine like terms : 0.5x+0.3=2.1x+3.5
Isolate the variable : -1.6x=3.2
Divide by -1.6 on both sides : x=-2
Answer: the answer is in the picture
have a nice one
Step-by-step explanation:
Find the standard error of the mean for each sampling situation (assuming a normal population).
Standard Error
a. σ = 28, n = 4
b. σ = 28, n = 16
c. σ = 28, n = 64
The standard error is decreasing on increasing number of Sample.
What is the standard error?
The population mean and sample mean are likely to deviate from one another, and the standard error of the mean, or simply standard error, shows how likely this is.
If a study were to be repeated using fresh samples drawn from a single population, it would be possible to calculate how much the sample mean would change.
The standard error is represented by a σ because it is a standard deviation. The subscript (M) indicates that the standard error in question is the standard error of the mean.
Now we will get the standard error for the following situations:
(a) σ_M = 12/√4 = 6
(b) σ_M = 12/√16 = 3
(c) σ_M = 12/√64 = 1.5
Hence from here, we can conclude that the standard error is decreasing on increasing number of Sample.
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Answer fast please.
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
12,18,27,...
Find the 7th term.
The 7th term of the sequence is 136.6875
How to determine the 7th of the sequence?From the question, we have the following sequence that can be used in our computation:
12, 18, 27....
In the above sequence, we can see that the previous term is multiplied by 1.5 to get the current term
Using the above as a guide,
So, we have the following representation
aₙ = 1.5aₙ₋₁
a₄ = 1.5 * 27
Evaluate the products
a₄ = 40.5
Solving further, we have
a₅ = 40.5 * 1.5
Evaluate the products
a₅ = 60.75
Solving further, we have
a₆ = 60.75 * 1.5
Evaluate the products
a₆ = 91.125
Solving further, we have
a₇ = 91.125 * 1.5
Evaluate the products
a₇ = 136.6875
Hence, the 7th term is 136.6875
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What is the domain of the inverse of the function graphed below?
Write your answer as a compound inequality.
The domain of an inverse function, f1, is the domain of a function, f(x) (x). The range of f1 is the scope of f(x) (x).
What's the inverse equation?The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) (= g(f(x)) = x. The initial value is fetched via a function that is its inverse.
What does the math sentence inverse mean?The opposite is called inverse. In mathematics, an inverse operation is one that reverses the effects of a preceding operation. Inverse operations refers to the set of two opposing operations.
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how many ml of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid
10ml of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We need to find how many ml of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid
Let x = number of ml of 20% acid
x mL of 20% acid plus (20 - x )mL of 100% acid = 20 mL of 60% acid
0.20x+1.00(20-x)=0.6(20)
0.20x+20-x=12
20-0.8x=12
Subtract 20 on both sides
-0.8x=12-20
-0.8x=-8
Divide both sides by -0.8
x=10
Hence, 10ml of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid
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Which of the expressions below has a 1 in the ones place of the difference? Select all that apply.
A) 43.45 – 13.22
B) 17.56 – 15.98
C) 7.54 – 6.32
D) 12.54 – 10.67
Answer: D 12.54-10.67
Mathamathics for 9th
The equation of the line is y=3÷5x+4.
How to find the slope of a curve at a given point?A straight line that meets a curve only once and does not pass entirely through it is said to be tangential. The point of tangency is the intersection of the curve and the tangent. We are aware that the slope at any point on the line y=mx+cy=mx+c equals mm. The same is true for curves. When we refer to a curve's slope, we actually mean its point-to-point tangent slope.We employ the subsequent steps to calculate slope:In order to get dy/dx of an equation, we must first differentiate the provided equation.After differentiating, we will have the slope equation.To find the slope, enter the value of x into the equation.Here, we need to figure out the slope of this curve.
if two lines are perpendicular to each other and both of their slopes exist, the product of their slopes is equal to -1.
k1 = -9-6÷1-(-4)
= -5÷3
k2-k1 = -1
∴k2= 3÷5
y-1= 3÷5[x-(-5)]
y= 3÷5÷x+4
Hence, The equation of the line is y=3÷5x+4.
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What equation represents this function?
What is the domain and range of this function?
The equation is [tex]36x-y=145[/tex].
The domain is (∞,-∞), {x,x∈R}.
What is the domain of a function?
The domain of a function is the set of all conceivable values that are acceptable as inputs, or alternatively, it can be interpreted as the full set of potential values for independent variables. The denominator of the fraction is not equal to zero, and the digit under the square root bracket is positive, which is an indicator of the domain.
Let us first take any 2 coordinates of the function, say (-143,-2) and (0,-71).
let us take the slope of these 2 points,
[tex]m=\frac{x_{2}-x_{1} }{y_{2}- y_{1} } \\m=\frac{-71+143}{0+2} \\m=\frac{72}{2} \\m=36[/tex]
Now, using the slope, we can find the required equation:
[tex]y-y_{1} =m (x-x_{1} )\\y+143=36(x+2)\\36x-y=145\\[/tex]
The domain for the function is (∞,-∞), {x,x∈R}.
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Which function could represent the data in
the table below?
X -2 -1 0 1
F(x) 3 1 -1 -3
he data in the table appears to be modeled by the function f(x) = -x^2 + 2.
To see this, let's plug in the values for x in the table and see if the resulting values for f(x) match the values in the table:
f(-2) = (-2)^2 + 2 = 4 - 2 = 2
f(-1) = (-1)^2 + 2 = 1 - 1 = 0
f(0) = 0^2 + 2 = 2
f(1) = 1^2 + 2 = 1 + 2 = 3
We can see that the resulting values for f(x) match the values in the table, so f(x) = -x^2 + 2 is a function that could represent the data.
Mrs. McCoy bought three pieces of cloth. They were 4 yards, 5 yards, and 3 yards long. How many yards of cloth did she buy in all?
Answer:
12 yards
3+4+5=12
3+4=7
7+5=12
Answer:
12, needed to be multiplied ( which I don't think so) 60
Step-by-step explanation:
I really don't have a "step by step explanation" but 4+5=9+3=12
or: 4x5=20x3=60
Stem and leaf plots
And box
Pls help I have no idea what this is
Answer:
61 is the mode.
Step-by-step explanation:
Remember, the mode is the most repeated number in the list. 6|1 is repeated the most times (twice).
Answer:
61 is the correct answer
I need help for a grade
Answer:
36
Step-by-step explanation:
[tex]\frac{1}{4}(12^2)=\frac{1}{4}(144)=36[/tex]
I NEED HELP ASAP PLEASE
v/b - c = d/e make e the subject of the formula
Answer:
[tex]e = \frac{bd}{v - bc} [/tex]
Step-by-step explanation:
[tex] \frac{v}{b } - c = \frac{d}{e } [/tex]
[tex] = > multiply \: bothsides \: by \: e[/tex]
[tex] = > \frac{v}{b} \times e - c \times e = \frac{d}{e} \times e[/tex]
[tex] \frac{ve}{b} - ce = d[/tex]
[tex] = > multiply \: both \: sides \: by \: b[/tex]
[tex] \frac{ve}{b} \times b - ce \times b = bd[/tex]
[tex] = > ve - bce = bd[/tex]
[tex] = > e(v - bc) = bd[/tex]
[tex] = > divide \: both \: sides \: by \: (v - bc)[/tex]
[tex] = > e = \frac{bd}{v - bc } [/tex]
Solve for X
6y = 2x + 10
Answer: x=3y−5
Step-by-step explanation: 6y=2x+10
Swap sides so that all variable terms are on the left hand side.
2x+10=6y
Subtract 10 from both sides.
2x=6y−10
Divide both sides by 2.
2
2x
=
2
6y−10
Dividing by 2 undoes the multiplication by 2.
x=
2
6y−10
Divide 6y−10 by 2.
x=3y−5
[tex]4c^2+10c+4[/tex]
Answer:
Factor for this problem is
2(2c+1)(c+2)
Answer:(c+2)(4c+2)
Step-by-step explanation:
Factor by grouping
(c+2)(4c+2)
Find the probability of royal flush poker hand when 5 cards are dealt from an ordinary deck. Enter your answer as a fraction. P(royal flush) - )
Probability p(Royal flush)= 4/2598960 = 1/649740
What is Probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
A royal rush in Poker Card is five of each of the following: ace, king, queen, jack, and ten.
The ten, Jack, Queen, King, and Ace of a single suit make up a royal flush. These hands come in fours.
Total no. of ways = selecting 5 cards out of 52 cards = 52 C5 = 2598960
So, P(royal flush)= 4/2598960 = 1/649740
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The window frame is a regular octagon. It is made from eight pieces of wood shaped like congruent isosceles trapezoids. What are m∠ A, m∠ B, m∠ C, and m ∠D ?
m ∠A=___
m∠ B=____
m∠ C=___
m ∠D=___
The values of the angles are m∠ A = 112.5°, m∠ B = 67.5°, m∠ C = 67.5°, and m ∠D = 112.5°
How to find the values of m∠ A, m∠ B, m∠ C, and m ∠D?
Considering the regular octagon, the sum of angles in an octagon is 1080°. This implies each angle in the octagon will be 1080/8 = 135°
Thus, you can label the angle as shown in the image attached
c + m<A + 135° = 360° (the sum of angle at a point is 360°)
Since c = m<A (identical sides)
m<A + m<A + 135° = 360°
2 m<A = 360-135
m<A = 225/2 = 112.5°
m<B + m<A = 180° (Between two parallel lines, consecutive interior angles add up to 180°)
m<B + 112.5° = 180°
m<B = 180-112.5 = 67.5°
m<C = <B (base angles of isosceles trapezoids are equal)
m<C = 67.5°
m<D = m<A (base angles of isosceles trapezoids are equal)
m<D = 112.5°
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Tolu, Abram, and Nevis are partners in a
new business. The bank account for the
business currently shows a balance of
-$123, so the partners agree to pay
equal amounts to bring the balance to
$0. Write and solve an equation using
negative numbers to find each partner's
share of the balance.
Please help
Each partner needs to pay $41 to bring the balance to $0.
What is the linear equation in one variable?
The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.
Let x be the amount each partner pays.
We can set up the equation as follows:
(-123) + 3x = 0
To solve for x, we can add 123 to both sides of the equation:
(-123) + 123 + 3x = 0 + 123
This simplifies to:
3x = 123
To solve for x, we can divide both sides of the equation by 3:
(3x)/3 = 123/3
This simplifies to:
x = 41
Therefore, each partner needs to pay $41 to bring the balance to $0.
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Help!
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Slope = -8, passing through (-4,-9)
Answer:
-25
Step-by-step explanation:
The volume of a room is 80 m³. The area of the floor is 20 m². The height of the room is:
Answer:
4
Step-by-step explanation:
Let's think of this as a cube with layers.
(Layer = height)
If the first layer has 20, and the cube has a total of 80, we can use this equation:
80 = 20 × number of layers
Let's figure out how many times we need to multiply 20 to get 80.
20 × 4 = 80
The cubes height is 4.
Answer:
4m
Step-by-step explanation:
The volume of a room is 80 m³. The area of the floor is 20 m². The height of the room is:
Volume = l x w x h (base area times height)
we use the inverse formula
Height = 80 : 20 =
4
Determine which set of side measurements could be used to form a right triangle.
04, 11, 20
16, 21, 25
5, 13, 25
3, 4, 5
Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )
What is the Pythagoras Theorem ?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
For a triangle to be Right Angled , It should obey the Pythagoras Theorem
[tex]c^{2} = a^{2}+b^{2}[/tex]
c = hypotenuse
a = perpendicular side
b = base
Hence
if c = 5 , a = 3 and b = 4
Then
[tex]c^{2} = a^{2}+b^{2}[/tex]
[tex]5^{2}= 3^{2}+4^{2}[/tex]
25 = 3 + 16
25 = 25
So
It obeys the Pythagoras Theorem
Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )
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