The letters in the word MIAMI are rearranged at random so that every possible anagram is equally likely. The probability that it still spells MIAMI is 1/5.
Let us count the total number of ways MIAMI can be arranged regardless of condition.
There are 2 M’s 2 I’s 1 A in word.
Total ways of arrangement will be = 5!/2!2!
Total ways of arrangement will be = (5 × 4 × 3 × 2!)/2! × 2 × 1
Total ways of arrangement will be = 5 × 2 × 3
Total ways of arrangement will be = 30 ways
Now, ways in which all similar words are together, thus we have to consider 2M's as one unit, similarly 2 I's as a unit, so number of ways will be 3!.
Thus, the probability will be = 3!/30
The probability will be = (3 × 2 × 1)/30
The probability will be = 6/30
The probability will be = 1/5
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What are the coordinates of R on QS such that the ratio of QR
to RS is 1:4?
The coordinate of the point R of the line segment QS will be (-3.8, -0.4). Then the correct option is A.
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
The endpoints are Q(-6, -2) and S(5, 6). And m:n is 1:4. Then the coordinate of the point R is given as,
x = (5 · 1 + (-6) · 4) / (1 + 4)
x = -3.8
y = (6 · 1 + (-2) · 4) / (1 + 4)
y = -0.4
The coordinate of the point R of the line segment QS will be (-3.8, -0.4). Then the correct option is A.
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A salesperson at a car
dealership earns 2%
commission. If the
salesperson had sales of
$135,000 in one week, how
much did they earn in
commission?
Answer:
2700
Step-by-step explanation:
turn 2% into a decimal and multiply by 135,000.
i need the slope of (5, -3) and (8,-3)
first off, let's notice that the y-coordinates are the same for both points, meaning is really just a horizontal line, and its slope is 0, however, let's go through the rigamarole
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{5}}} \implies \cfrac{-3 +3}{3} \implies \cfrac{ 0 }{ 3 } \implies \text{\LARGE 0}[/tex]
4. For dessert you can choose
apple, cherry, blueberry, or peach pie to
eat, and milk or juice to drink. How
many different combinations of one
pie and one beverage are possible?
Then you have 6 different combination to choose from.
"Information available from the question"
For dessert you can choose
Apple, cherry, blueberry, or peach pie to eat, and milk or juice to drink.
To find the how many different combinations of one pie and one beverage are possible?
Now, According to the question:
To eat: Apple pie, Cherry pie, or peach pie = 3 desserts
To drink: milk or juice = 2
Then you can choose one from each:
Then your choices are:
(apple, milk) (apple, juice) (cherry, milk)(cherry, juice) (peach, milk) and (peach, juice)= 6
Then you have 6 different combination to choose from.
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Two lamp posts are of equal height. A boy standing mid-way between then observes the elevation of the top of either post to be 30∘. After walking 15 m towards one of them, he observes the elevation of it stop to be 45∘. Find the heights of the posts and the distance between them.(Ans:20.49m,70.98m)
Answer:
The height of the lamp posts is 20.49 m and the distance between them is 70.98 m.
Step-by-step explanation:
Draw a diagram using the given information (see attachment).
The lamp post is at point C (the top of the lamp post is at point D).The height of the lamp post is labelled "h".The boy is at point A.After walking 15 m towards one of the lamp posts, the boy is at point B.The distance between both lamp posts is 2x.[tex]\boxed{\begin{minipage}{7 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]
Use the tan trigonometric ratio to create two equations for h.
Triangle ACD:
[tex]\implies \tan 30^{\circ}=\dfrac{h}{x}[/tex]
[tex]\implies h=x\tan 30^{\circ}[/tex]
[tex]\implies h=\dfrac{\sqrt{3}}{3}x[/tex]
Triangle BCD:
[tex]\implies \tan 45^{\circ}=\dfrac{h}{x-15}[/tex]
[tex]\implies h=(x-15)\tan 45^{\circ}[/tex]
[tex]\implies h=(x-15)\cdot 1[/tex]
[tex]\implies h=x-15[/tex]
Substitute the second equation into the first equation and solve for x:
[tex]\implies x-15=\dfrac{\sqrt{3}}{3}x[/tex]
[tex]\implies x-\dfrac{\sqrt{3}}{3}x=15[/tex]
[tex]\implies \dfrac{3-\sqrt{3}}{3}x=15[/tex]
[tex]\implies (3-\sqrt{3})x=45[/tex]
[tex]\implies x=\dfrac{45}{3-\sqrt{3}}[/tex]
[tex]\implies x=35.4903810...[/tex]
To find h, substitute the found value of x into the second equation and solve for h:
[tex]\implies h=x-15[/tex]
[tex]\implies h=35.4903810...-15[/tex]
[tex]\implies h=20.4903810...[/tex]
[tex]\implies h=20.49\; \sf m\;\;(2\;d.p.)[/tex]
As the distance between the two lamp posts is 2x:
[tex]\implies 2x=2 \cdot 35.4903810...[/tex]
[tex]\implies 2x=70.9807621...[/tex]
[tex]\implies 2x=70.98\; \sf m\;\;(2\;d.p.)[/tex]
Therefore:
The height of the lamp posts is 20.49 m.The distance between them is 70.98 m.solve for x
60 < 5 (x + 8)
60<5x+40
60-40<5x
20<5x
x>4
A system of two linear equations is shown on the coordinate plane.
Which of the following is the BEST estimate for the x-coordinate of the solution to this
system?
-1.8
-0.8
4.5
5.5
The BEST estimate for the x-coordinate of the solution to this system is -4
How to determine the estimate of the solutionFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that the lines intersect at
Approximately (-4, 3)
This means that the x-cooridnate of the solution is
x = -4
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Answer:
Step-by-step explanation:
look at where they cross that your point so -4 so none of those answers!
Solve the following Recurrences by iteration method
T(1)= 1 and T(n) = 2T(n/2) + n/logn (Help:- ∑_(i=1)^n▒〖1/i〗 is ϴ(log n) )
The time complexity is O(1) as the recurrence reduces to a constant.
T(n) = 2T(n/2) + n/log n
T(1) = 1
T(2) = 2T(1) + 2/log 2
= 2 + 2/log 2
T(4) = 2T(2) + 4/log 4
= 2(2 + 2/log 2) + 4/log 4
T(8) = 2T(4) + 8/log 8
= 2(2(2 + 2/log 2) + 4/log 4) + 8/log 8
T(n) = 2^k T(1) + (2^k + 2^(k-1) + ... + 2 + 1)*n/log n
= 2^k + (2^k + 2^(k-1) + ... + 2 + 1)*n/log n
= 2^k + n*Σ_(i=1)^k▒2^i/log n
= 2^k + n/log n*(2^(k+1) - 1)
= 2^k + n/log n*(n/2 - 1)
= (2^k + n/2 - n/log n)*n/log n
= (2n - n/log n)*(log n/n)
= 2 - 1/log n
The time complexity is O(1) as the recurrence reduces to a constant.
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There are about 10 ^ 4 different species of birds on Earth. Just over 10 ^ 3 of them are threatened. Evaluate both expressions.
The values of the expressions when evaluated are 10000 and 1000
How to evaluate both expressions.From the question, we have the following parameters that can be used in our computation:
There are about 10 ^ 4 different species of birds on Earth. Just over 10 ^ 3 of them are threatenedThis means that
Species = 10^4 = 10000
Threatened = 10^3 = 1000
Hence, the values are 10000 and 1000
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Distribute and match the following values to the correct terms.
(8k+k2−6)−(−10k+7−2k2)
(8k+k26) after matching, (10k+72k2) because a trinomial cannot be factored 3k2 + 18k - 13
what is coefficient ?In maths, a coefficient is a cubic, a sequence, or the exponential coefficient of a descriptive word in an expression. Any phrase is acceptable, though digits are frequently used. If the equations are variables, and so the word "parameter" also could refer to the variables themselves. A coefficients is the product of either a number and then a variable. Some occurrences of correlations are: The coefficient as in sentence . The variable is multiplied by it amount when word g has a coefficient of 1. example Since "z" is a factor and the term's interpretation is 6z, the multiplier is 6. The square root of x has a score of one.
given
((8k + (k2)) - 6) - ((7 - 10k) - 2k2)
The first term is 3k2 and it has a 3 coefficient.
The coefficient of the middle word, +18k, is 18.
"The constant," the final term, is -13.
Step 1: Add the constant 3 • -13 to the coefficient of the first term to get -39.
Step 2 is to identify two -39 factors whose combined value is equal to the middle term's coefficient of 18, which is 18.
-39 + 1 = -38
-13 + 3 = -10
-3 + 13 = 10
-1 + 39 = 38
(8k+k26) after matching, (10k+72k2) because a trinomial cannot be factored 3k2 + 18k - 13 .
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The space program has 23 astronauts in outer space and 7 astronauts on Earth. What is the ratio of the number of astronauts on Earth to the total number of astronauts?
The ratio of the number of astronauts on Earth to the total number of astronauts is 7 : 30.
A ratio is a mathematical expression that compares two or more values by dividing the size of one value by the size of another.
Ratios can be expressed in several different forms, including fractions, decimals, or percentages, and can be used to compare quantities, measurements, or other values in a meaningful way.
Ratios provide a way to express the relationship between two or more values in a compact and concise format, and can be used in a variety of fields, including mathematics, science, finance, and engineering.
If the space program has 23 astronauts in outer space and 7 astronauts on Earth, then the ratio of the number of astronauts on Earth to the total number of astronauts is:
7 : (23 + 7) = 7 : 30
You can simplify the ratio to 7/30 or approximately 0.23 or 23%.
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A kite is flying 98 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 57°. Find the length of the string. Round your answer to the nearest tenth.
Answer:
224.7
Step-by-step explanation:
sin 57 = 98/ ?
? = 98/sin57° = 224.7
PLEASE HELP IM TIMED.
How does increasing the amount of charge on an object affect the electric force it exerts on another charged object? The electric force increases because the amount of charge has an indirect relationship to the force. The electric force increases because the amount of charge has a direct relationship to the force. The electric force decreases because the amount of charge has an indirect relationship to the force. The electric force decreases because the amount of charge has a direct relationship to the force.
The way that increasing the amount of charge on an object affects the electric force it exerts on another charged object is; The electric force increases because the amount of charge has a direct relationship to the force
How to interpret the Electric Force on an object?The amount of charge on an object due to the effect of the force that is exerted on it can be calculated by using the formula :
F = E × q
Where;
F is the electric force.
E is the energy.
q is the charge.
The electric force between charged particles at rest is known as electrostatic force.
The magnitude of the electric force between point charges is directly proportional to the multiplication of the charges and inversely proportional to the distance between them.
Therefore, we conclude that increasing the amount of charge on an object would increase the electric force because the amount of charge has a direct relationship with the force.
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Find x
3(x-4)=5(x+1)
Give answer in improper fraction in simplest form
Answer:
[tex] \frac{ - 17}{2} [/tex]
Step-by-step explanation:
[tex]3(x - 4) = 5(x + 1)[/tex]
first expand the brackets[tex]3x - 12 = 5x + 5[/tex]
Subtract 5x from both sides[tex]3 - 12 - 5x = 5x + 5 - 5x [/tex]
[tex]3x - 12 - 5x = 5[/tex]
Add 12 to both sides[tex]3x - 12 - 5x + 12 = 5 + 12[/tex]
[tex]3x - 5x = 5 + 12[/tex]
Combine the like-terms[tex]3x - 5x = - 2x[/tex]
[tex]5 + 12 = 17[/tex]
[tex] - 2x = 17[/tex]
Divide both sides by -2[tex] \frac{ - 2x}{2} = \frac{17}{ - 2} [/tex]
[tex]x = \frac{17}{ - 2} [/tex]
[tex]x = \frac{ - 17}{2} [/tex]
Please I need answers for 5/6 and 7/8pleaeeeeeeee
The sum of the interior angles of polygon A is 1260°.
The sum of angles of the exterior angles of a polygon A is 360°
How to find sum of interior and exterior angles of a polygon?Polygon A
A polygon with 9 sides is called a nonagon. The sum of interior angles of a Nonagon is 1260°. This can be calculated using the formula (n -2) * 180, where n is the number of sides.
Thus, the sum of the interior angles of polygon A is 1260°.
The sum of the exterior angles of a polygon is 360°.Thus, the sum of angles of the exterior angles of a polygon A is 360°.
Polygon B
Polygon B has 7 sides i.e. n = 7
sum of angles of the interior angles of polygon B = (7-4) * 180 = 900°
Thus, y = 900- 135 - 140 - 150 - 120 - 135 - 120 = 100°
x = 180 - 100 = 80° (sum of angles on a straight line is 180°)
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ABCD is a kite, AC DB and DE = EB. Calculate the length of AC, to the nearest tenth of a centimeter.
Answer:
7.8 cm
Step-by-step explanation:
One tenth of a centimeter = [tex]\frac{1}{10} (1 cm)[/tex] = 0.1 cm . This means the answer has to be rounded to 1 decimal place.
Length of BE = Length of ED = [tex]\frac{6}{2}[/tex] = 3 cm
Focus on the triangles AED and CED. These two are right-angled triangles.
In both triangles, sides AE and CE are perpendicular sides, whose lengths will be calculated using Pythagorean Theorem:
Triangle AED:
[tex]AD^{2} = AE^{2} + ED^{2}[/tex]
[tex]AD^{2} - ED^{2} = AE^{2}[/tex]
[tex]AE^{2} = 6^{2} - 3^{2}[/tex]
Taking square root on both sides of the equation to get rid of the square:
[tex]AE = \sqrt{6^{2} -3^{2} }[/tex]
[tex]AE = \sqrt{36 - 9}[/tex]
[tex]AE = \sqrt{27}[/tex] cm
Triangle CED:
[tex]CD^{2} = CE^{2} + ED^{2}[/tex]
[tex]CE^{2} = CD^{2} - ED^{2}[/tex]
[tex]CE^{2} = 4^{2} - 3^{2}[/tex]
Taking square root on both sides of the equation to get rid of the square:
[tex]CE = \sqrt{4^{2} -3^{2} }[/tex]
[tex]CE = \sqrt{16 - 9}[/tex]
[tex]CE = \sqrt{7}[/tex] cm
Length of AC = Length of AE + Length of EC
∴ Length of AC = [tex](\sqrt{27} + \sqrt{7})[/tex] cm
= 7.841 cm
Length of AC = 7.8 cm (Rounded to the nearest tenth of a centimeter)
Calculate the rate of change for each linear function. Determine which linear function has a greater rate of change.
a. Rate of change for linear function A:
Question Blank 1 of 3
type your answer...
b. Rate of change for linear function B:
Question Blank 2 of 3
type your answer...
Answer:
Step-by-step explanation:
The rate of change is just the slope of the equation and/or graph.
for the linear function A, y = 2/3x + 5, the slope (therefore rate of change) is 2/3. For B (I can't make it out that clear), 3/2. That gives the answer for C: 3/2 is greater than 2/3.
Could anyone solve both and say how they did it? asked my teacher and she didnt help
The values of x in the triangles are x = 17 and x = 52
How to determine the values of xTriangle 1
From the question, we have the following parameters that can be used in our computation:
The triangle
Using the law of cosines to solve for x, we have
x^2 = 7^2 + (8√2)^2 - 2 * 7 * (8√2) * cos(135 degrees)
Evaluate the like terms and multiply
x^2 = 289
Take the square roots
x = 17
Triangle 2
Here, we have"
Using the law of cosines to solve for x, we have
x^2 = 28^2 + 32^2 - 2 * 28 * 32 * cos(120 degrees)
Evaluate the like terms and multiply
x^2 = 2704
Take the square roots
x = 52
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plsss help me
thanks
Answer:
y = -3(x + 0.5)² - 45.25
Step-by-step explanation:
a = -3
b = -3
c = -47
h = -b/2a = -(-3)/2(-3) = -1/2
k = c - b²/(4(-3)) = -46 - (-3)²/(-12) = -45.25
f(x) = -3(x - (-1/2))² - 45.25
y = -3(x + 0.5)² - 45.25
-7
standard form of 9.4359 × 10
The standard form of the given exponent is 0.00000094359.
What are Exponents?
A number's exponent demonstrates how many times we are multiplying a given number by itself. 3⁴, for instance, indicates that we are multiplying 3 by four. 3 × 3 × 3 × 3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.
[tex]9.4359 \times 10^{-7}[/tex]
Use [tex]10^{-7} = 1/10^7[/tex] Because a⁻ᵇ = 1/aᵇ
= 9.4359 ×1/10⁷
= ( 9.4359)/10⁷
= ( 9.4359)/10000000
= 0.00000094359
The standard form of the given exponent is 0.00000094359
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NEED HELP ASAP !!!!! Find the missing values. Leave answers in simplified radical form. (#5, 6: 2 points each; #7: 4 points)
The value of t is 8 and the value of r is 8√2. The solution has been obtained by using trigonometry.
What is trigonometry?
The study of triangle sides, angles, and relationships is the focus of the mathematical field of trigonometry.
We are given a right angled triangle with an angle 45° and the perpendicular measuring 8.
Using trigonometry,
We know that tan theta = opposite side/ adjacent side
So,
⇒tan 45° = 8/t
⇒1 = 8/t (tan 45° = 1)
⇒t = 8
Similarly,
We know that cos theta = adjacent side/hypotenuse
So,
⇒cos 45° = 8/r
⇒1/√2 = 8/r (cos 45° = 1/√2)
⇒r = 8√2
Hence, the value of t is 8 and the value of r is 8√2.
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Since, there are multiple questions so, the question answered above is attached below.
Mrs. Battle is designing a brick walkway to install in her front yard. How many square feet of bricks will be needed for the walkway?
The area of the brick walkway in the front yard is 122 square feet.
What is a trapezoid?An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.
A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the measurement of the angle perpendicular to the parallel sides.
We know, The area of a trapezoid is,
(1/2)×(sum of the two parallel sides)×height, And The area of a rectangle is (length×width).
From the given, Diagram the total area would be the sum of the area of a rectangle and a trapezoid which is,
= [(15×6) + (1/2)(10 + 6)×4] square feet.
= [90 + 32] square feet.
= 122 square feet.
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IT'S DUE TODAY I NEED HELP PLEASE!!!
Answer:
Rise over run for the first one is x=300 and y=600
Find the total surface area of a cylindrical tank of height 2.1m and diameter 0.7 m. Also find the cost of painting at the rate of $9.5 per sq metre.
Answer:
$ 56.34
Step-by-step explanation:
Total surface area of cylindrical tank:height = h = 2. 1m
diameter = 0.7m
radius = diameter ÷2
r = 0.7 ÷ 2 = 0.35 m
Substitute the values of r and h in the below mentioned formula and find the surface area of the tank.
[tex]\boxed{Area \ of \ cylindrical \ tank = 2\pi r((r + h)}[/tex]
= 2 * 3.14 * 0.35 (0.35 + 2.1)
= 2 * 3.14 * 0.35 * 2.45
= 5.39 square meter
To find the cost of painting the surface area of tank, multiply the cost of painting per square meter by the total surface area of tank.
Cost of painting = 5.93 * 9.50
= $ 56.34
Help me with questions 7-8 pls urgent hurry my bed time is in 10 mins and I have to get my homework done
what is adding and subtracting rational expressions calculator ?
The Adding and Subtracting Rational Expression Calculator is a free online tool that displays the results of rational number arithmetic operations.
What is rational expression?A rational expression is nothing more than the product of two polynomials. In other words, it is a fraction with polynomial numerator and denominator. Rational expressions resemble fractions with variable denominators (and often numerators too).
Adding or subtracting rational expressions involves four steps: All fractions must be written as equivalent fractions with a common denominator. Combine the fractions to form a single fraction with a common denominator. Reduce the complexity of the expression at the top of the fraction. Reduce the fraction to its simplest terms.
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I have a mixture of 135 M&Ms. They come in the colors, red, blue, yellow and brown. There are five more blue M&Ms than red ones. The number of yellow M&Ms is nine less than the number of red ones. The number of brown M&Ms is thirteen more than half the number of red ones. Find the number of red, blue, yellow and brown M&Ms.
Answer:
Let x be the number of red M&Ms.
Then the number of blue M&Ms is x + 5, the number of yellow M&Ms is x - 9, and the number of brown M&Ms is (1/2)x + 13.
The total number of M&Ms is 135, so we can write an equation:
x + (x + 5) + (x - 9) + (1/2)x + 13 = 135
Simplifying this equation, we get:
3.5x + 9 = 135
Subtracting 9 from both sides, we get:
3.5x = 126
Dividing both sides by 3.5, we get:
x = 36
So there are 36 red M&Ms, 41 blue M&Ms (36 + 5), 27 yellow M&Ms (36 - 9), and 31 brown M&Ms (1/2 * 36 + 13).
Answer:
Step-by-step explanation:
r: the number of red M&Ms
b: the number of blue M&Ms
y: the number of yellow M&Ms
br: the number of brown M&Ms
We can translate the given information into equations:
r + b + y + br = 135 (the total number of M&Ms is 135)
b = r + 5 (there are five more blue M&Ms than red ones)
y = r - 9 (there are nine less yellow M&Ms than red ones)
br = 13 + (1/2)r (there are thirteen more brown M&Ms than half the number of red ones)
We can use equations 2, 3, and 4 to substitute for b, y, and br in equation 1:
r + (r + 5) + (r - 9) + (13 + (1/2)r) = 135
Simplifying this equation, we get:
3.5r + 9 = 135
Subtracting 9 from both sides, we get:
3.5r = 126
Dividing both sides by 3.5, we get:
r = 36
Now that we know the value of r, we can use equations 2, 3, and 4 to find the values of b, y, and br:
b = r + 5 = 36 + 5 = 41
y = r - 9 = 36 - 9 = 27
br = 13 + (1/2)r = 13 + (1/2)(36) = 31
Therefore, the number of red, blue, yellow, and brown M&Ms in the mixture are 36, 41, 27, and 31, respectively.
Please explain, everytime I try I get it wrong. Thank you
Answer:
[tex]slope = - \frac{8}{5} [/tex]
Step-by-step explanation:
So it looks like on the line, we have two dots.
Let's find those points, starting from the left one.
The left point is: (-1, 4) --- (x1, y1)
The right point is: (4, -4) --- (x2, y2)
**These are in (X, Y) form**
Now to find the slope, you use this equation
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Now let's plug our numbers into this equation
[tex]m = \frac{ - 4 - 4}{4 - ( - 1)} = \frac{ - 8}{5} = - \frac{8}{5} [/tex]
Two negatives make a positive, so 4-(-1) is the same as 4+1.
Select the addition problem that is shown from the fraction strips below
Answer:
C
Step-by-step explanation:
You are able to simplify both of the 2/8ths and it comes to be 2/8 + 2/8 = 4/8
Please help me asap!!
Answer:
1 and 10
Step-by-step explanation:
Account #1: one year (because it doubles each year)
Account #2: ten years (100 * 10 = 1000)