Answer:
-7
Step-by-step explanation:
Because picture y with a 1 in front of it the divide -7 by 1 and you get -7
An airline company wants to provide service to San Francisco, Los Angeles, Chicago, Dallas, Washington D.C., and New York City. The company's president draws lines between each pair of cities in the list on a map. No three of the cities are collinear How many lines did the president draw?
The president draw 15 lines on map.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
here, it is given that :
there are 6 cities
No three of the cities are collinear that is are not in a straight line.
Now, to find the lines did the president draw use the formulae :
n(n-1)/2
where, n = number of cities
lines did the president draw = 6 x 5/ 2
= 15
Therefore, The president draw 15 lines on map.
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Enter the values needed to find thelength CB. (Simplify your answer.)A(-3a, b)IFB(3a, b)ECB = V(4a)2 + ([?])2C(-a, -5b)Distance Formula: d = (x2 – xı)2 + (y2 - yı)2
We are asked to find the values needed for the length CB
The coordinates of points C and B are given as
C(-a, -5b)
Recall that the distance formula is given by
[tex]d=\sqrt{\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1 } \right)^2 }[/tex]For the given case,
[tex]\begin{gathered} (x_1,y_1)=\mleft(-a,-5b\mright) \\ (x_2,y_2)=\mleft(3a,b\mright) \end{gathered}[/tex]Let us substitute these coordinates into the above distance formula
[tex]\begin{gathered} CB=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ CB=\sqrt[]{({3a_{}-(-a)})^2+({b_{}-(-5b)_{}})^2} \\ CB=\sqrt[]{({3a_{}+a})^2+({b_{}+5b})^2} \\ CB=\sqrt[]{({4a})^2+({6b})^2} \end{gathered}[/tex]Therefore, the required values are
[tex]CB=\sqrt[]{({4a})^2+({6b})^2}[/tex]Which multiplication problem can be used to determine how many possible combinations there are for a lock consisting of 3 digits from 0–9, if the digits can be repeated?
___________________
900
___________________
in a survey of u.s. cities it is discovered there is a positive correlation between the number of paved streets in the city and the number of registered cars.does this mean that paving more streets will result in the increase of registered cars?
Yes if there is a positive correlation existing between the paving of streets and the number of registered cars then paving more streets would result in the increase in the registered cars.
What does a positive correlation mean?This is the term that is used to tell us that there is the presence of a correlation that would make the two variables that we are talking about to move in the same direction. That is when one increases, the other would have to increase as well.
Such that we would have the increase in the number of paved street to cause an increase in the number of registered cars in the place.
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Three times the middle integer of three consecutive integers equals four less than twice the sum of the smallest and largest. find the integers
Integers are 3, 4 and 5.
What are integers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.
Given Data
Let the three consecutive integers are :
x, x+1 and x+2
According to question
3(x+1) = 4 - 2(x+x+2)
3x + 3 = 4 - 2(2x + 2)
3x + 3 = 4 - 4x - 4
3 = 4x-3x
x= 3
Integers are 3, 4 and 5.
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An architect
makes a model
of a new house
with a patio
made with
pavers. In
the model, each
paver in the
1
patio is in.
4
1
long and in.
6
wide. The actual
2
9
ft
1
The constant of proportionality is
(Type the ratio as a simplified fraction.)
3
ft
a. What is the constant of proportionality that relates the length of
a paver in the model and the actual length? Write an equation that
represents this relationship.
Answer - The constant proportionality constant of proportionality between the actual dimensions of the pavers and the model is 9. The proportionality constant for the area is 81.
Step-by-step explanation: To solve this problem, let's transform all quantities to the same units (inches)
The actual dimensions of the pavers are:
Then we divide the real dimensions between those of the model:
Width:
Long =
Then, the constant of proportionality between the actual dimensions of the pavers and the model is 9.
Actual length = model length * (9)
The "A" area of a paver is the product of its width multiplied by its length.
So:
(real width) * (real length) = ((9) Model width) * ((9) model length)
(real width) * (real length) = * (Model width) * (model length)
(real area) = 81 * (Model area)
The proportionality constant for the area is 81.
Find the distance between each pair of points
The distance between each pair of points (-1,4) and (1,-1) exists √29 units after utilizing the distance formula.
What is meant by distance formula?It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]$\mathrm{d}=\sqrt{\left(\mathrm{x}_2-\mathrm{x}_1\right)^2+\left(\mathrm{y}_2-\mathrm{y}_1\right)^2}[/tex]
It is given that:
The distance between each pair of points (-1,4) and (1,-1)
Two points are (-1,4) and (1,-1)
To estimate the distance between the above two points utilize the distance formula:
[tex]$\mathrm{d}=\sqrt{(1-(-1))^2+(-1-4)^2}$$[/tex]
[tex]$\mathrm{d}=\sqrt{(1+1)^2+(-1-4)^2}$$[/tex]
The arithmetic operation can be described as the operation in which we do the addition of numbers, subtraction, multiplication, and division
d = √[(2)² + (-5)²]
simplifying the above equation, we get
d = √(4 + 25)
d = √29 units
Therefore, the distance between each pair of points (-1,4) and (1,-1) exists √29 units after utilizing the distance formula.
The complete question is:
Find the distance between each pair of points (-1,4) and (1,-1)
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(6.4 × 103) ÷ (3.2 × 102)
Express your answer in scientific notation.
The required solution in scientific notation is 2 × 10¹ .
Scientific notation can be used to indicate values that are either too large or too little to be conveniently written in decimal form (typically would result in a long string of digits).
In the UK, it is also known as standard form, scientific form, and standard index form.Because it can simplify numerous mathematical operations, this base ten notation is frequently used by scientists, mathematicians, and engineers.Scientific notation for non-zero numbers takes the form m × 10n, or m times ten raised to the power of n, where n is an integer and m is a non-zero real number.The given expression is (6.4 × 10³) ÷ (3.2 × 10²)
Simplifying we get :
(6.4 × 10³) ÷ (3.2 × 10²) = 20
This can be written in the scientific notation as : 2 × 10¹
Therefore the required solution is 2 × 10¹
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What is the solution to the given equation 2(y-5)=14
Answer: y=12
Step-by-step explanation:
Distribute
Add 10 to both sides
Simplify.
Answer: y = 12
Step-by-step explanation:
2 ( [tex]y\\[/tex] - 5 ) = 14
2[tex]y\\[/tex] - 2 · 5 = 14
2[tex]y\\[/tex] - 10 = 14
(2[tex]y\\[/tex] - 10) + 10 = 14 + 10
2[tex]y\\[/tex] = 24
[tex]\frac{2y}{2} = \frac{24}{2}[/tex]
solve for x
pls hurry
Answer:
12
Step-by-step explanation:
Answer:
x = 19
Step-by-step explanation:
Alternate Exterior Angles Theorem
When a transversal line intersects two parallel lines, the resulting alternate exterior angles are congruent.
Therefore:
⇒ 8x + 11 = 5x + 68
⇒ 8x + 11 - 5x = 5x + 68 - 5x
⇒ 3x + 11 = 68
⇒ 3x + 11 - 11 = 68 - 11
⇒ 3x = 57
⇒ 3x ÷ 3 = 57 ÷ 3
⇒ x = 19
Find the area and perimeter of each composite figure
The perimeter and area of each of the composite figure is:
a. Area: 138.6 mm²; Perimeter = 50.27 mm.
b. Area: 120.5 cm²; Perimeter = 42.7 cm
c. Area: 521.1 mm²; Perimeter: 95.8 mm
What is the Area of a Circle, Triangle, and a Rectangle?Area of a circle = πr²
Area of a triangle = 1/2(base)(height).
Area of a rectangle = (length)(width).
What is the Perimeter of a Composite Figure?The perimeter of a composite figure = the sum of all lengths of the sides surrounding the composite figure.
a. The area of the composite figure = area of rectangle + area of two semicircles
Two semicircles = 1 circle
Area of the rectangle = (15)(5) = 75 mm²
Area of the two semicircles = πr² = π(4.5²) = 63.6 mm²
The area of the composite figure = 75 + 63.6 = 138.6 mm².
Perimeter = 5(2) + 4(3) + (perimeter of 1 circle)
Perimeter = 5(2) + 4(3) + (2πr)
Perimeter = 5(2) + 4(3) + (2π(4.5))
Perimeter = 50.27 mm.
b. Area = area of triangle + area of square + area of half circle
Area = 1/2(base)(height) + s² + 1/2(πr²)
Base = 5 cm
Height = 7 cm
s = √(7² + 5²) = 8.6 cm [Pythagorean theorem]
r = 8.6/2 = 4.3 cm
Area = 1/2(5)(7) + 8.6² + 1/2(π(4.3²))
Area = 120.5 cm²
Perimeter = 5 + 7 + 8.6 + 8.6 + (perimeter of half circle)
Perimeter = 5 + 7 + 8.6 + 8.6 + 1/2(2πr)
Perimeter = 5 + 7 + 8.6 + 8.6 + (2π(4.3))
Perimeter = 42.7 cm
c. Area = area of triangle + area of rectangle + area of half circle
Area = 1/2(base)(height) + (length)(width) + 1/2(πr²)
Base = 32 - 20 = 12 mm
Height = 14 mm
Length = 20 mm
Width = 14 mm
r = 1/2(20) = 10 mm
Area = 1/2(12)(14) + (20)(14) + 1/2(π(10²))
Area = 521.1 mm²
Perimeter = 14 + 32 + hypotenuse of the triangle + (perimeter of half circle)
Hypotenuse = √(12² + 14²) = 18.4 mm
Perimeter of half circle = 1/2(2πr) = 1/2(2π(10)) = 31.4
Perimeter of the composite figure = 14 + 32 + 18.4 + 31.4
Perimeter of the composite figure = 95.8 mm
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The quadratic function − 0.379 ( x − 46 ) 2 + 2.62 ( x − 46 ) − 3.61 gives the percentage (in decimal form) of puffin eggs that hatch during a breeding season in terms of x , the mean sea surface temperature of the surrounding area, in degrees Fahrenheit.
a
.
What is percentage of puffin eggs that will hatch at
51°F? Round your answer to the nearest tenth of a percent.
b
.
For what mean temperature is the percentage of hatched puffin eggs a maximum? Round your answer to the nearest tenth of a degree.
°F
Find the percentage of hatched eggs at this temperature. Round your answer to the nearest tenth of a percent.
The percentage of puffin eggs that hatch given in decimal form by the quadratic function, f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61, gives;
a. At 51 °F, 1.5% of the eggs will hatch
b. The temperature at which the maximum percentage of puffin eggs will hatch is approximately 49.5 °F
The maximum percentage of eggs that hatch is approximately 91.8 %
What is a quadratic function?A quadratic function is a polynomial of the second degree (degree 2) such that the highest power of the variables in a quadratic function is 2
The quadratic function is presented as follows;
f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61
Where;
f(x) = The percentage of the eggs that hatch
x = The mean sea surface temperature of the area in degrees Fahrenheit
a. The percentage of the eggs that will hatch at 51° is therefore;
f(51) = -0.379•(51 - 46)² + 2.62•(51 - 46) - 3.61 = 0.015
The percentage of the eggs that hatch at 51° d is f(51) = 0.015 × 100% = 1.5%
b. The temperature for which the percentage of hatched puffin eggs is a maximum, is given by the maximum value of the quadratic function as follows;
At the maximum value of the quadratic function, f(x) = a•x² + b•x + c, we have;
x = -b/(2•a)
Therefore, where we have;
f(x) = -0.379•(x - 46)² + 2.62•(x - 46) - 3.61
At the maximum value;
x - 46 = -2.62/(2×(-0.379)) = 1310/379
x = 46 + 1310/379 ≈ 49.5°Which gives;
The mean temperature at which the percentage of hatched puffin eggs is a maximum is approximately 49.5°Second part;
The percentage of eggs that hatch at the temperature that gives the maximum percentage of eggs is the maximum percentage of eggs, which is found as follows;
f(46 + 1310/379) = -0.379•(1310/379)² + 2.62•(1310/379) - 3.61 ≈ 0.9179683
The maximum percentage of puffin eggs is therefore;
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The diameter of
one species of bacteria is shown. Bonnie
approximates this measure as 3 × 10-11 meter.
Is she correct? Explain.
No, i don't think she is correct as she didn't rounded-off correctly while measuring the diameter of bacteria.
What is rounding- off?Rounding off is a type of estimation. Estimation is used in everyday life and also in subjects like Mathematics and Physics. Many physical quantities like the amount of money, distance covered, length measured, etc are estimated by rounding off the actual number to the nearest possible whole number.
According to the picture it shows the diameter of the bacteria is 0.00000025691m
So , [tex]2.5691 * 10^-^7m[/tex] is rounded off and will be equal to [tex]3*10^-^7m\\[/tex]
As, The digit right to 2 is 5 and which already passed halfway up
So, the number 2 will be rounded off to 3 as it being the nearest digit.
Therefore, Bonnie is wrong as she did mistake while rounding - off measurments.
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Anyone know the answer for this
Can someone help me pleaseeeeee
Answer:
a) 225 meters
b) -162°C
Step-by-step explanation:
a) 5 meters per second for 45 seconds. 5*45 = 225 meters
b) cooled by 18°C per hour over a 9 hour period. -18*9 = -162°C
Answer:
a) 225 meters.
B) -2 °
Step-by-step explanation:
a If it is moving 5 meters per second, then in one second it moves 5 meters, in 2 seconds it move 10 meters, in 3 seconds it move 15 minters.
So to find how much it moved in 454 seconds we would multiply 45 x 5 = 225
B) In 9 hours it cooled 18 degrees 18/9 = 2. This means that is cooled 2 degrees per hour.
QR = 5x - 15, and QS = 100
The value of x if R is the midpoint of QS is 31 units.
How to find value of x using midpoint?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
The midpoint is halfway between the two end points.
Therefore, R is the midpoint of QS
Hence,
QS = QR + RS
QR = 5x - 15
QS = 100
Therefore, QR and RS are congruent because R is the midpoint of QS
QR = RS
Hence,
100 = 5x - 15 + 5x - 15
100 = 10x - 30
100 + 30 = 10x
130 = 10x
divide both sides by 10
x = 130 / 10
x = 13
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Liz had 140 pens and inna had 100 pens. after inna gave some of her pens to liz,liz had 3 times the amount of pens that inna had. how many pens did inna give
Answer:
40
Step-by-step explanation:
140 + x = 3*(100-x)
140 + x = 300 - 3x
x + 3x = 300 - 140
4x = 160.
x = 40.
Water is leaking from the bottom of a conical cup that is 20 inches across and 20 inches deep. Given that the cup loses 0. 5 cubic inches of water per minute, at what rate is the water level changing when the water is 8 inches deep?.
If water is leaking from the bottom of a conical cup that is 20 inches across and 20 inches deep. The rate that the water level changes when the water is 8 inches deep is: 3 /32π.
Rate of change of water leveldv/dt = rate of cup loss water per minutes=0.5
r = radius when the water is 8 inches deep
Hence,
20/10 = 8/r
r = 4
Volume of conical cup
v= 1/3πr²h
dv/dt=1/3πr² dh/dt
0.5 = 1/3π × (4)² dh/dt
dh/dt =3 /32π
Therefore the rate is 3 /32π.
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water is leaking from an inverted conical tank at a rate of . water is also being pumped into the tank at a constant rate. the tank has height and the diameter at the top is . if the water level is rising at a rate of when the height of the water is , find the rate at which water is being pumped into the tank. hint: let denote the rate (in ) at which the tank is being filled, and let denote the volume (in ) of water in the tank. then rate in - rate out , so it suffic
The rate of the water being pumped into the tank is 289,753 cm3/min
d = 4m
∴ r = 2m
h = 6m
Therefore r = h/3
The formula for the volume of the cone is:
V=(1/3)π•r2h
substitute:
V=(1/3)π (h/3)2h
V=(1/27)π h3
Derive both sides with respect to time:
dV/dt = (1/9) π h2• dh/dt
When h= 2 meters = 200 cm when dh/dt = 20
dV/dt = (1/9) π (200)2• (20)
dV/dt = (800,000/9) π ~ 279,252.68
Meaning the volume of water is increasing at a rate of 279,252.68 cm3/min.
However, it's leaking out at a rate of 10,500 cm3/min. Therefore the rate of the water being pumped into the tank is:
279,252.68 + 10,500 = 289,752.68 ~ 289,753 cm3/min
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I need the answer asapplease and thank you!!!
In mathematics, a line's slope, also known as its gradient, is numerical representation of line's steepness and direction. The equation will be [tex]y= \frac{-1}{3}x +5[/tex].
What is a slope?In mathematics, a line's slope, also known as its gradient, is numerical representation of line's steepness and direction. The letter m is the frequently used to represent slope; the reason for this usage is unclear, although it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for the straight line as "[tex]y = mx + b[/tex]" and "[tex]y = mx + c[/tex]," respectively.
The ratio of "vertical change" to "horizontal change" between the (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or design.
Let, x= -3, x1= -2, y= 5, y1= 2
Then,
slope= [tex]\frac{x-x1}{y-y1} = \frac{-3-(-2)}{5-2} =\frac{-1}{3}[/tex]
now,
y= mx+c
y= [tex]\frac{-1}{3}[/tex]x+ 5
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How is a line segment different from a line? How is a line segment different from a ray?
Answer:
ray:
Part of a line, containing one endpoint and extending to infinity in one direction.
line segment
Two points on a line, and all the points between those two points.
Step-by-step explanation:
Create a division problem where both the divisor and the dividend are decimals. the quotient must be a whole number greater than 1. step by step please!
The Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.
As per the question we need to create a division problem where both the divisor and the dividend are decimals and the quotient must be a whole number greater than 1.
So, Let us suppose divisor as 1.5 . Now the dividend must be a decimal number which is greater than 1.5, let's say 5.5.
Now on dividing 5.5 by 1.5,
Divisor = 1.5
Dividend = 4.5
(Dividend/Divisor) = ( 4.5 / 1.5 ) = 3
Quotient = 3
On dividing dividend by divisor the quotient is 3 which is a whole number greater than 1.
So, we can conclude that the Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.
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–3d = 5.7
ANSWER ASAP!!!!!!!!!!
Answer:
D = 1.9
You can find for d by using the associative property of division (divide instead of multiply):
5.7 divided -3 = 1.9
Step-by-step explanation:
Hope it helps! =D
Choose the multiplication problem that matches this model: I Dan studied for of an hour for 4 days in a row. How many hours did he study? Dan studied for 2 hours for 4 days in a row. How many hours did he study? O Dan studied for of an hour for 4 days in a row. How many hours did he study? O Dan studied for of an hour for 4 days in a row. How many hours did he study?
The number of bars of the same color could be used to show the number of hours that Dan studies hence he studied for 2/3 hours in four days.
What is multiplication?The term multiplication refers to the number of times that a number is added to itself. For instance, if I add four three times, I could shorten the expression as four multiplied by three.
If we look at the diagram, we can see that in each tile, there are always two bars of the same color out the whole three bars. The bars that are of the same color shows the number of hours that Dan studied.
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HELP WITH MATH PLEASE
Answer: 5 and the power is 2
the power used is 2
Step-by-step explanation:
Find the discriminant of
The discriminant of the quadratic equation is 11.1.
What is the discriminant?The discriminant is the expression that we could use to deduce the kind of roots that a quadratic equation would have. Note that when we say the roots of the equation, we are talking about the solutions of the quadratic equation. We shall now try to obtain the discriminant of this equation as we can see below.
The discriminant is given as;
√b^2 - 4ac
Given;
3x^2 - 10x + 2 = 0
a = 3
b = -10
c = 2
We have;
√(-10)^2 - 4(-3) (2)
√100 + 24
11.1
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marlena surveyed classmates and found that the ratio of the numbers of text messages sent by girls varies directly with the number of texts sent to boys. The girls sent 27 texts for 9 texts sent by the boys.How Many texts did the girls send if the boys sent 7 texts
Select the correct answer. paula used these steps to solve an equation: step 1: step 2: step 3: step 4: step 5: between which two steps did paula use the division property of equality? a. steps 1 and 2 b. steps 2 and 3 c. steps 3 and 4 d. steps 4 and 5
In linear equations, x = 9.5 Paula use the division property of equality.
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.
That is, if a, b, and c are real numbers such that a = b and c ≠0, then
a/b = c/d
The equation was -6x = 57
To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below
-6x = 57 ( Divide both sides by -6)
-6x/6 = 57/-6
x = 9.5
Hence, we can conclude that the division property of equality.
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The complete question is -
Paula used these steps to solve an equation:
Step 1: -4(7 + 8) - 21 = 25
Step 2: -4r – 32 - 2x = 25
Step 3: -61 – 32 = 25
Step 4: -6x = 57
Step 5: x = -95
Between which two steps did Paula use the division property of equality?
consider a spinner that, after a spin, will point to a number between 0 and 1 with uniform probability. 1. what is the probability that the spinner will land on something less than 0.75? 2. determine p(1/5
Hence the probability that the spinner will land on something less than 0.75 is 37/50
As we know in between 0 and 1 the decimal numbers are ( 0.1, 0.2, 0.3, 0.4 _ _ _ _ _ 0.95, 0.96, 0.97, 0.98, 0.99, 1.00)
So,
To find the probability = favorable outcomes/ total numbers of outcomes
Favorable outcomes = 0.74 / 1.00
solve the decimal numbers in the simplified form
The probability that the spinner will land on something less than the decimal number 0.75 is 37/50.
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PLEASE HELP ASAP math isn’t going so well
Answer:
b
Step-by-step explanation:
The graph was reflected over the y-axis.