An equation of the line in slope-intercept form that passes through the coordinates (6, -5) and (8, -6) is: B. y = -1/2(x) - 2; y is equal to negative 1 half x minus 2
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (6, -5), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-5) = (-6 - (-5))/(8 - 6)(x - 6)
y + 5 = (-6 + 5)/(8 - 6)(x - 6)
y + 5 = -1/2(x - 6)
y = -1/2(x) + 3 - 5
y = -1/2(x) - 2
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in a study of environmental lead exposure and iq, the data was collected from 221 221 children in cincinnati, ohio. their iq scores at age of 7 7 approximately follow a normal distribution with mean of 87.0 87.0 and standard deviation of 11.4. 11.4 . suppose one child had an iq of 55. 55 . the researchers would like to know whether an iq of 55 55 is an outlier or not. calculate the lower fence for the iq data, which is the lower limit value that the iq score can be without being considered an outlier. keep a precision level of two decimal places for the lower fence.
The lower fence is 56.2428
As the Iq score < lower fence, Iq score is outlier
What is average/mean?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
data was collected from 221 children
iq scores at age of 7 approximately follow a normal distribution with mean of 87.0 and standard deviation of 11.4.
Let X=iq scores
distribution is
X ~ [tex]N( \mu=87, \sigma=11.4)[/tex]
If one child has iq of 55,
To find outlier, find the lower fence
lower fence = [tex]Q_{1}-1.5( Q_{3} - Q_{1} )[/tex]
[tex]Q_{1} = \mu + Z_{0.25}\sigma[/tex]
[tex]Q_{3} = \mu + Z_{0.75}\sigma[/tex]
Using excel function,
[tex]Z_{0.25} = -0.67[/tex]
[tex]Z_{0.75} = 0.67[/tex]
[tex]Q_{1} = \mu + Z_{0.25}\sigma[/tex]
=87+(-0.6745)11.4
= 79.3107
[tex]Q_{3} = \mu + Z_{0.75}\sigma[/tex]
= 87+(0.6745)11.4
= 94.6893
lower fence = [tex]Q_{1}-1.5( Q_{3} - Q_{1} )[/tex]
= 79.3107 -1.5(94.6893 - 79.3107 )
= 56.2428
So, the lower fence is 56.2428
As the Iq score < lower fence, Iq score is outlier
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John is creating a Thanksgiving display at the store where he works, using only canned pumpkin and canned green beans. He needs to maintain a ratio of pumpkin to green beans of 4 to 2. If he wants to use a total of 102 cans, how many cans of green beans should he use?
Using the ratios we know that out of 102 cans, 34 cans will be of green beans that John will use.
What is the ratio?In mathematics, a ratio shows how frequently one number appears in another.
For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.
Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.
If you enter this into a calculator, the result will come out as 0.6 decimal.
In other words, 3/5 is equal to any two numbers that divide to provide the same result.
So, the total cans that John wants to use:
102
Then, the ratio of pumpkin to green beans:
4:2
Sum: 4+2 = 6
Then, out of 102 cans, the cans of green beans would be:
= 102 * 2/6
= 102 * 1/3
= 34
Therefore, using the ratios we know that out of 102 cans, 34 cans will be of green beans that John will use.
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A cone with a volume 1,780.38 and a height of 7. What is the radius
Answer:
15.585 is the radius of the cone
A town is designing a rectangular park that will be 600 feet by 1000 feet. A rectangular area of the park for swing sets will be 25 feet by 100 feet. On a scale drawing of the park the swing set area is 0. 5 inch by 2 inches. What is the dimensions of the park on the scale drawing?
The dimensions of the park on the scale drawing are 2 inches by 0.5 inches
The dimensions of the park on the scale drawing can be determined by using the scale factor between the actual dimensions and the scale drawing dimensions. The scale factor can be found by dividing the actual dimensions by the scale drawing dimensions.
Scale factor for length = Actual length / Scale drawing length = 1000 feet / 2 inches = 500 feet per inch
Scale factor for width = Actual width / Scale drawing width = 600 feet / 0.5 inches = 1200 feet per inch
Now, we can use the scale factor to determine the dimensions of the park on the scale drawing.
Length of park on scale drawing = Actual length / Scale factor for length = 1000 feet / 500 feet per inch = 2 inches
Width of park on scale drawing = Actual width / Scale factor for width = 600 feet / 1200 feet per inch = 0.5 inches
Therefore, on the scale drawing, the park measures 2 inches by 0.5 inches.
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Which table of value represents the linear function y=4x+1
The required value table is
x -1 0 1 2 3
y -3 1 5 9 13
Value table of a function:To find the value table of a linear function take, any values for 'x' and from that find the 'y' values for each corresponding value of 'x'.
Here in this problem, we are taking x values as 0, 1, 2, and 3. Now substitute each of the 'x' values and find the 'y' values and make the table of values.
Here we have
The linear function given is y = 4x + 1
To find the value table we are taking x values as - 1, 0, 1, 2, 3
At x = - 1 => y = 4(-1) + 1
=> y = - 4 + 1
=> y = - 3
At x = 0 => y = 4(0) + 1
=> y = 0 + 1
=> y = 1
At x = 1 => y = 4(1) + 1
=> y = 4 + 1
=> y = 5
At x = 2 => y = 4(2) + 1
=> y = 8 + 1
=> y = 9
At x = 3 => y = 4(3) + 1
=> y = 12 + 1
=> y = 13
Therefore,
The required value table is
x -1 0 1 2 3
y -3 1 5 9 13
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5+5multiplied 5-5 divided by 5
when I solved that i got no real solutions, is that true? please help tyvm
Answer:
true
Step-by-step explanation:
log2(5x+3)=log2(4x-3)
log2(5x+3)/log2(4x-3)
division turns to minus
log2(5x+3-4x-3)
log2(x)
Logan owns a trucking company. For every truck that goes out, Logan must pay the
driver $16 per hour of driving and also has an expense of $1.25 per mile driven for
gas and maintenance. On one particular day, the driver drove an average of 20 miles
per hour and Logan's total expenses for the driver, gas and truck maintenance were
$205. Write a system of equations that could be used to determine the number of
hours the driver worked and the number of miles the truck drove. Define the
variables that you use to write the system.
Answer:
Let's define the variables:
h: the number of hours the driver worked.
d: the number of miles the truck drove.
We know that the driver is paid $16 per hour, so the cost of the driver's labor is:
16h
We also know that the truck incurs an expense of $1.25 per mile driven, so the cost of gas and maintenance is:
1.25d
The total expenses for the driver, gas, and maintenance were $205, so we can set up the following equation:
16h + 1.25d = 205
We also know that the average speed of the truck was 20 miles per hour, so we can set up the following equation:
d = 20h
So the system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove is:
16h + 1.25d = 205
d = 20h
These two equations can be solved simultaneously to find the values of h and d that satisfy both equations.
Write the given rate as a fraction in simplest form 135 points in 225 minutes
The answer to the question is 17/140 fraction.
What is fraction?A fraction is a numerical expression that represents a part of a whole or a ratio of two numbers. It consists of two parts: a numerator (the number on top) and a denominator (the number on the bottom). For example, 3/4 is a fraction that represents 3 parts out of 4. It can also represent the ratio of 3 to 4.
To move the fraction to each box, you would need to multiply the denominator of the first fraction (10) by the numerator of the second fraction (14). The result is 140. Then, you would add the numerator of the first fraction (3) to the numerator of the second fraction (14), giving you 17. The answer to the question is 17/140.
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how to find p value ti 84
The TI-84 calculator can be used to find the p-value associated with a hypothesis test, given the test statistic and the degrees of freedom (df).
Here are the steps to find the p-value on a TI-84 calculator:
Press the "2nd" button and then the "VARS" button (which is above the "STAT" button). This will open the DISTR menu.
Select "3: tcdf" from the menu by scrolling down with the arrow keys and pressing "ENTER".
Enter the test statistic and degrees of freedom. For a two-tailed test, enter the test statistic with the appropriate sign (positive or negative) and enter a very large number (such as 100 or 999) for the second argument.
For a one-tailed test, enter the test statistic and select "1" or "2" for the third argument, depending on the direction of the test.
Press "ENTER" to calculate the p-value.
The result displayed on the calculator screen will be the p-value associated with the hypothesis test, based on the test statistic and degrees of freedom entered.
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The question is -
How to find the p-value from the TI-84 calculator?
Hannah is getting balloons for her father's birthday party. She wants each balloon strain to be 12 ft long. At the party store string is sold by the yard. If Hannah wants to get 48 balloons how many yards of string was she need.
Explanation:
1 balloon needs 12 ft of string.
48 balloons need 48*12 = 576 ft of string.
Divide by 3 to convert from feet to yards. This is because 1 yard = 3 ft.
576 ft = 576/3 = 192 yards
I Need help plssssssss
Answer: 5, 6, 7, 8, 9, or the numbers 5-9 inclusive.
Step-by-step explanation: The Triangle Inequality Conjecture states that any two sides of a triangle added up will be larger than the third. To easily prove this, you can add the two smaller sides to see if it is bigger than the larger side. Using this conjecture, we can calculate that 5 works, 6 works, 7 works, 8 works (8 is larger than 7 so now we do 3+7), and 9 works.
3.8 Thabo kept a diary of his activities during the week. He then drew up a table to show an average day. Look at his table Activity Sleeping At school PS Doing homework Playing sport Watching TV Eating Time 8 hours 7 hours 1 hour 2 hours 4 hours 2 hours a. What is the ratio of the time spent doing homework to the time spent at school? (1)
The ratio of the time Thabo spent doing homework to the time he spent at school is 2:7.
What is the ratio?Ratio refers to the relative size of a quantity compared to another.
Ratios are expressed as percentages, from 0% to 100%, as fractions, as proportions or decimals, from zero to one, and in ratio forms (:).
To compute the ratio as a decimal, it is the quotient of one quantity and another comparative quantity.
Activity Time
Sleeping 8 hours
At school 7 hours
Doing homework 2 hours
Playing sport 4 hours
Watching TV 2 hours
Eating 1 hour
Total hours = 24 hours
Ratio of time doing homework to the time spent at school = 2:7
The sum of ratios = 9 (2 + 7)
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a mug slides across a horizontal counter with initial speed v. it slides off the 0.86 m high counter and lands 1 m from the base. what was its initial speed?
slides off the 0.86 m high counter and lands 1 m from the base. what was its initial speed ⇒ Ø = 56.87˚ beneath the horizontal
A. Suppose the horizontal component of the velocity is vx and the vertical is vy.
At first at t=0 (as the mug leaves the counter) the components are v0x and v0y.
v0y = 0 since the customer slides it horizontally so applied force is in the x component as it were.
The equations for horizontal and vertical shot movement are:
x = x0 + v0x t
y = y0 + v0y t - 1/2 g t^2 = y0 - 1/2 g t^2
Setting the beginning to be the end corner of the counter so that x0=0 and y0=0, thus:
x = v0x t
y = - 1/2 g t^2
Given esteem are: x=1.50m and y=-1.15m (y is negative since mug is going down)
1.50m = v0x t - - - - > v0x= 1.50/t
-1.15m = - (1/2) (9.81) t^2 - - - - - > t =0.4842 s
Working out for v0x:
v0x = 3.10 m/s
B. v0x is constant since there could be no other horizontal forces so, v0x=vx=3.10m/s
vy can be calculated from the recipe:
vy = v0y + at where a=-g (negative since going down)
vy = - gt = - 9.81 (0.4842)
vy = - 4.75 m/s
Presently to get the point beneath the horizontal, tan(90-Ø) = - vx/vy
tan(90-Ø )= 3.1/4.75
Ø = 56.87˚ beneath the horizontal
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What is the conversion of 152cm in feet ?
The conversied value of 152 centimetres in feet is equals to the 4.98 feet.
Unit conversion, by definition, is the conversion between different units and measurements of the same quantity done in the process of multiplication or division. In mathematics, conversion is the process of changing a value from one form to another, such as converting a value from inches to millimeters, for time minutes to hours, or other units.
How to convert centimeters to feet : 1 meter is a measure of length and equals approximately 3.28 feet.
152 meters = 152×3.28 feet = 498.56 feet --(1)
But we need to convert 152 centimeters to feet. So change meters to centimeters. As you know, 1 meter is 100 centimeters, so 152 meters = 15200 centimeters --(2). Now from equations (1) and (2),
15200 centimeters = 498.56 feet,
Divide both parts by 100,
=> 152 centimetres = 498.56/100 feet
= 4.98 feet
Hence required value is 4.98 feet.
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What is an algebra over a field F?
An algebra over a field F is a vector space over F equipped with a bilinear operation called multiplication.
Let F be a field and let A be a vector space over F. An algebra over F is a triple (A, ×, 1) where × is a bilinear operation A x A -> A, and 1 is an element of A such that:
a × (b × c) = (a × b) × c for all a,b,c in A (associativity)
There exists an element 1 in A such that a × 1 = a = 1 × a for all a in A (existence of identity)
a × (b + c) = (a × b) + (a × c) and (a + b) × c = (a × c) + (b × c) for all a,b,c in A (distributivity)
a × b = b × a for all a,b in A if and only if A is commutative
The operation × is usually referred to as multiplication and the element 1 as the unit or identity element.
Examples of algebras over a field F include the set of n x n matrices over F, the polynomial ring F[x], and the complex numbers C, which can be viewed as an algebra over the field of real numbers R.
Therefore, the algebra over a field F has been explained
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Reflect the figure over the line l
The required reflection of the given figure across the line y = x is shown.
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
A figure on a coordinate plane is shown, and we have to determine the reflection of that figure across the line y = x,
In order to determine the reflection across the line y = x,
The Abscissa inside the line gets interchanged by the ordinate of the corresponding Absciss as.
(x, y) ⇒ (y, x)
Thus, the required reflection of the given figure across the line y = x is shown.
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how to convert 162cm to feet?
We can convert 162 cm to feet by multiplying by the conversion factor to get , 162 cm equivalent to 5.32 feet .
The length or the distance between two points is measured with the help of units such as : meter , centimeter , inches , feet .
We have to convert the length of 162 centimeter to feet ;
We know that , 1 centimeter is approximately equal to 0.0328 feet ;
So , the conversion factor is 0.0328 ;
So , for the conversion we multiply the given length by 0.0328 ;
On multiplication we get ;
⇒ 162 centimeter = 162 × 0.0328 ;
⇒ 162 centimeter = 5.3136 feet .
Therefore , 162 cm is approximately equal to 5.32 feet .
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The measure of each exterior angle of a regular polygon of 12 sides is ______ .
A.45°.
B 75°.
C 60°.
D 30°.
Answer:
Step-by-step explanation:
The sum of exterior angles of a polygon is 360
Each exterior angle = 360/n
where n is the number of sides
360/12 = 30
Answer is D
If the dimensions of a rectangular playground ca be represented as (3x + 16) and (2x + 3), then what is the area of the playground?
Answer:
6x² + 41x + 48
Step-by-step explanation:
Area (A) = l × w
Therefore,
A = (3x + 16)(2x + 3) (distribute)
A = 6x² + 9x + 32x + 48 (combine like terms)
A = 6x² + 41x + 48
Therefore, the area of the playground is 6x² + 41x + 48.
A pets shop amount of rabbits is approximated by R(t)=2t2/3+10 in t weeks. After how many weeks, t, will the pet shop have 18 rabbits.
For a pet shop to approximate 18 rabbits, it would take 6 weeks.
In the question, we have a formula that represents the number of rabbits available with them.
The amount of rabbits is dependent on another variable, Time.
The variables depend on each other, and the number of rabbits with the pet shop relies on the number of weeks.
R(t)= 2t(2/3) + 10
If the number of rabbits is 18, then the value of the equation would be equal to 18. [R(t) = 18]
18= 2t(2/3) +10
18= 4t/3 + 10
8 X 3 = 4t
24/4 = t
6 = t
Therefore, 18 rabbits are approximated by the pet store in 6 weeks.
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what is the surface area of the cylinder? Use 3.14 for π and round to the nearest hundredth.
height=11 Radius=8 in.2
The surface area of the cylinder is approximately 951.44 square inches, rounded to the nearest hundredth.
What is the surface area of the cylinder?
To find the surface area of a cylinder, we need to find the sum of the areas of its curved surface (lateral area) and its two circular bases.
The formula for the lateral area of a cylinder is L = 2πrh, where r is the radius and h is the height. The formula for the area of each circular base is B = πr^2.
We are given that the height of the cylinder is 11 inches and the radius is 8 inches. Therefore, we can calculate:
L = 2πrh = 2 × 3.14 × 8 × 11 = 549.52 in²
B = πr^2 = 3.14 × 8^2 = 200.96 in²
The total surface area is the sum of the lateral area and the two base areas:
Surface area = L + 2B = 549.52 + 2(200.96) = 951.44 in²
Hence, the surface area of the cylinder is approximately 951.44 square inches, rounded to the nearest hundredth.
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Solve. It’s all real numbers are solutions, click on all reels if there’s no solution click on no solution.
Answer:
no solution
Step-by-step explanation:
7 | y + 6 | + 3 < - 18 ( subtract 3 from both sides )
7 | y + 6 | < - 21 ( divide both sides by 7 )
| y + 6 | > - 3
the absolute value function cannot be negative
thus the equation has no solution
Write the solution set of the given homogeneous system in parametric vector form.3x1+3x2+6x3=0−6x1−6x2−12x3=0−4x2+4x3=03x1+3x2+6x3=0−6x1−6x2−12x3=0−4x2+4x3=0 where the solution set is x=⎡⎢⎣x1x2x3⎤⎥⎦x=[x1x2x3]
The solution set of the given homogeneous system in parametric vector form is x = (0, 0, t), where t is a real number
Vectors are an important mathematical tool for representing complex data and equations. In this problem, we are given a homogeneous system of equations and asked to write the solution set in parametric vector form.
The homogeneous system consists of three equations: 3x₁ + 3x₂ + 6x₃ = 0, -6x₁ - 6x₂ - 12x₃ = 0, and -4x₂ + 4x₃ = 0. To solve this system, we need to use linear algebra techniques, such as Gaussian elimination, to find the solution set.
By using Gaussian elimination, we can reduce the system to a simpler system, which has the form x₁ = 0, x₂ = 0, and x₃ = t, where t is a real number. This can be written as a parametric vector form as x = (0, 0, t).
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On a coordinate plane, 2 triangles are shown. The first triangle has points X (2, 5), Y (2, 3), Z (4, 3). The second triangle has points X prime (negative 2, negative 5), Y prime (negative 2, negative 3), Z prime (negative 4, negative 3). What are the vertices for the final image after applying the composition T−2,4 ◦ RO,180° to ΔXYZ?
Herefore, the vertices of the final image after applying the composition T−2,4 ◦ RO,180° to ΔXYZ are X''(-2, -1), Y''(0, -1), and Z''(0, 1).
First, we need to perform a reflection over the x-axis and then a translation of 2 units to the left and 4 units up. This is the transformation T−2,4.
Next, we need to perform a rotation of 180 degrees about the origin. This is the transformation RO,180°.
We can apply these transformations to each vertex of the first triangle ΔXYZ to obtain the coordinates of the final image.
Applying T−2,4 to each vertex:
T−2,4(X) = (2, 5) → reflection over x-axis → (2, -5) → translation 2 units left and 4 units up → (0, -1)
T−2,4(Y) = (2, 3) → reflection over x-axis → (2, -3) → translation 2 units left and 4 units up → (0, 1)
T−2,4(Z) = (4, 3) → reflection over x-axis → (4, -3) → translation 2 units left and 4 units up → (2, 1)
Applying RO,180° to each vertex:
RO,180°(0, -1) = (0 × cos(180°) - (-1) × sin(180°), 0 × sin(180°) + (-1) × cos(180°)) = (0, 1)
RO,180°(0, 1) = (0 × cos(180°) - 1 × sin(180°), 0 × sin(180°) + 1 × cos(180°)) = (0, -1)
RO,180°(2, 1) = (2 × cos(180°) - 1 × sin(180°), 2 × sin(180°) + 1 × cos(180°)) = (-2, -1)
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Answer:
x is (-4,-1)
y is (-4,1)
z is (-6,1)
Step-by-step explanation:
What are the initial and final potition respectively
The initial position is the starting point, and the final position is the endpoint.
We proceed to explain the initial and final position:
The initial position is the starting point or location of an object before any movement or displacement occurs. It is often denoted as x0 or xi. The final position is the ending point or location of an object after it has undergone movement or displacement. It is often denoted as xf.For example, if an object starts at the 2 meter mark (initial position) and moves 3 meters to the right, its final position would be at the 5 meter mark.
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What is 64 times pi?
As per multiplication, the value of 64 times π is 200.96
Multiplication is a fundamental arithmetic operation that involves repeated addition. In this case, we are tasked with finding the result of multiplying 64 and pi. Pi is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is commonly denoted by the Greek letter "π".
To find the product of 64 and pi, we simply need to multiply these two numbers. Multiplication is typically represented using the "×" symbol or the "dot" symbol ( · ). In this case, we can write:
64 × π
Since pi is a mathematical constant, we typically use an approximation of its value in calculations. The commonly used approximation is 3.14, which is accurate to two decimal places. Thus, we can substitute 3.14 for pi and obtain:
64 × 3.14
Using the distributive property of multiplication, we can break down 64 into smaller factors that are easier to multiply with 3.14. For example, we can write:
64 = 60 + 4
Then, we can use the associative property of multiplication to group the factors in a way that makes the calculation easier. For instance, we can write:
64 × 3.14 = (60 × 3.14) + (4 × 3.14)
Now, we can use our knowledge of multiplication tables to calculate the products on the right-hand side. We get:
60 × 3.14 = 188.4
4 × 3.14 = 12.56
Therefore, the final result is:
64 × π = 188.4 + 12.56 = 200.96
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scientists determined that the equation y=0.5x+26 models the amount of shoreline at the beach, y, in feet, x decades after 1950. Which statement is true based on the model
The shoreline is reduced by 0.5 feet every 10 years. Then the correct option is A.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A group of scientists studied the amount of erosion at a beach. The scientist determined that the equation is given below.
y = -0.5 x + 26
Hence, The shoreline is reduced by 0.5 feet every 10 years. Then the correct option is A.
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scientists determined that the equation y=0.5x+26 models the amount of shoreline at the beach, y, in feet, x decades after 1950. Which statement is true based on the model
The shoreline is reduced by 0.5 feet every 10 years.
The shoreline is increased by 0.5 feet every 10 years.
The shoreline is reduced by 26 feet every 10 years.
The shoreline is increased by 26 feet every 10 years.
what is balance chemical equations calculator
A balanced chemical equation calculator is an online tool that assists in the balancing of chemical equations by automatically computing the coefficients for each reactant and product to verify that the equation obeys the rule of mass conservation.
According to the law of conservation of mass, matter cannot be generated or destroyed in a chemical process, just rearranged.
A balanced chemical equation includes the chemical formulae for the reactants and products of a chemical reaction, as well as the factors that balance the amount of atoms of each element on both sides of the equation. Balancing a chemical equation is a necessary step in addressing many sorts of chemistry issues, such as forecasting the quantity of product generated or reactant required in a reaction.
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Assume that births of girls and boys are equally likely. If a family has six children. What the number of outcomes in the sample space?
Group of answer choices
8
12
64
36
The number outcomes in the sample space is option (3) 64
In mathematics, combination is a way of selecting a group of objects from a larger set, where the order in which the objects are selected does not matter.
The number of outcomes in the sample space can be calculated by finding the total number of possible combinations of genders for the six children.
For each child, there are two possible genders: male or female. Therefore, the number of possible outcomes for one child is 2.
To find the total number of outcomes for six children, we need to multiply the number of possible outcomes for each child together:
2 × 2 × 2 × 2 × 2 × 2 = 64
Therefore, the correct option is (3) 64
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