The area of parallelogram with "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches" is 60√3 inch².
What is parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.
Here,
A parallelogram has adjacent angles that add up to 180 degrees.
Since one angle of parallelogram is 120°.
240+2x=360
2x=120
x=60
The other will be 60°
The area of parallelogram= lh
l=15 inch
h=b(sin 60°)
=8*√3/2
h=4√3 inch
area of parallelogram= 15*4√3
= 60√3 inch²
The parallelogram's area is 60√3 inch² when "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches."
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Diego's solar car traveled 3.16 meters farther than Justine's solar car. The equation d=j+3.16 represents this situation. What is the value of j if d=158?
The value of j based on the equation d = j + 3.16 if d = 158 is 154.84 meters.
How to find the missing parameters of an equation?Distance Diego's car traveled farther than Justine's solar car = 3.16 metersd = 158d = j + 3.16
substitute the value of d into the equation
d = j + 3.16
158 = j + 3.16
substract 3.16 from both sides
158 - 3.16 = j
j = 154.84
So therefore, based on the given equation d = j + 3.16, j = 154.84
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The value of j in the equation = 154.84
Distance
Distance is the length of space covered by the car when it moves from one location to another
Given;
Equation d=j+3.16 represent the situation
distance travelled by the car= 3.16meters
d=158
Step 1: Substituting the value of d into the equation d=j+3.16
158= j +3.16
Step 2: Subtract 3.16 from both sides
158-3.16 = j + 3.16 -3.16
Step 3: Add the equation
j= 154.84
Therefore, the value of j in the equation = 154.84
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Divide £72 into.
Ratio 4:5
Thus, 72 is divided into 32 and 40 in a 4:5 ratio. A ratio expresses the number of times one number contains another.
What is meant by Ratio?A ratio is the number of times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six.Similarly, the lemon to orange ratio is 6:8, and the orange to total fruit ratio is 8:14. A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero.A proportion exists as a equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls)Given:
The given ratio is 4:5.
To find: We have to divide 72 in this ratio.
To divide 72 in the 4:5 ratio, we must perform the following steps:
The ratio is 4:5.
We can write the number of the ratio as 4x and 5x by multiplying a constant x.
The total ratio is 4x+5x=9x.
So, 9x is equal to 72.
We can write-
9x=72
x=8.
So, putting the value of x we get-
4×8 and 5×8
So, the numbers are 32 and 40.
Thus 72 divides itself as 32 and 40 in 4:5 ratio.
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suppose that 47% of americans are iphone users. (a) if a random sample of 100 americans are surveyed, what is the probability that the proportion of the sample who are iphone users is between 45% and 50%? (b) if a random sample of 50 americans are surveyed, what is the probability that more than 50% of americans are iphone users?
The probability that the proportion of the sample who are iphone users is between 45% and 50% be 22.87%.
The probability that more than 50% of americans are iphone users be 11.12%.
(a)We know, p = 0.47 and n = 100. First, we should check our conditions for the sampling distribution of the sample proportion.
np = (100)(0.47) = 47 and n(1 - p) = (100)(1 - 0.47) = 53
Since, X will have a sampling distribution that is approximately normal with mean = 0.47
and
standard deviation = √(0.47)(0.53)/100 ≈ 0.05
P(0.45<X<0.50) = P((0.45 - 0.47)/0.05 < Z < (0.50-0.47)/0.05)
P(0.45<X<0.50) ≈ 0.2287
Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 22.87% chance that we would see a sample proportion between 45% and 50% when the sample size is 100.
(b) Now, p = 0.47 and n = 50.
np = (50)(0.47) = 23.5 and n(1 - p) = (50)(1 - 0.47) = 26.5
Since, X will have a sampling distribution that is approximately normal with mean = 0.47
and
standard deviation = √(0.47)(26.5)/50 ≈ 0.25
P(X>0.50) = P(Z > (0.50-0.47)/0.25)
P(X>0.50) ≈ 0.1112
Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 11.12% chance that we would see a sample proportion more than 50% when the sample size is 50.
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Simplify these pls I’ll brainlist.
1) 3b (b+4) - 4 (b-5)
2) 12(3y + 6)
Final answer: 3[tex]b^{2}[/tex] + 8b + 2
12(3y + 6) = 12 x 3(y + 2) // Factor out 12 = 36(y + 2) // Simplify the multiplication Final answer: 36(y + 2)
What is equation?An equation is a statement that two mathematical expressions are equal. It consists of two expressions separated by an equal sign (=), where one expression is on the left side and the other expression is on the right side of the equal sign. An equation represents a balance or equivalence between the two expressions, and it can be solved for the unknown variable(s) by applying mathematical operations to both sides of the equation.
Given by the question.
3b (b+4) - 4 (b-5)
= 3[tex]b^{2}[/tex] + 12b - 4b + 20 // Distribute the terms.
= 3[tex]b^{2}[/tex] + 8b + 20 // Simplify the like terms.
Final answer: 3[tex]b^{2}[/tex]+ 8b + 20
12(3y + 6)
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Solve the inequality for x and identify the graph of its solution.
4|x + 2| < 8
Solution of the inequality 4|x + 2| < 8 is given by x > -4 and x<0.
Solution from the given graph is option B where open interval x<0 and open interval x > -4 is shown.
As given in the question,
Given inequality is :
4|x + 2| < 8
Divide by 4 both the side of inequality we get,
⇒(4|x + 2|)/ 4 < 8/4
⇒|x+2| < 2
⇒ (x+2) < 2 or (x+2) >-2
⇒ x< 2-2 or x > -2 -2
⇒ x < 0 or x > -4
Solution of its graph is shown by option B number line where open interval -4 is greater than and less than open interval 0.
Therefore, solution of the inequality 4|x + 2| < 8 is given by x > -4 and x<0.
Solution from the given graph is option B where open interval x<0 and open interval x > -4 is shown.
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graph y = 1/4 x I dont know how to do
(Excuse me if this doesn't make sense).
Your formula would be (4,1)
Your zero is (0,0)
To graph it:
If your y is 1, your x is 4
If your y is 2, your x is 8.
There's a video for this if my explanation and photo doesn't help
I NEED HELP PLEASEEEEE ASAPPPPPPP
Answer:
7x+40=180
Step-by-step explanation:
(5x+40)+(2x)=180
7x+40=180
if you were to solve
subtract 40 from each side
7x=140
divide both sides by 7
x=20
check your answer
5(20)+40+2(20)=180
100+40+40=180
this is correct
hope this helps..and with future questions if you need to solve it
To find BCD
we know that C is 40 degrees and we know that triangle is also 180
we can also see that B is a right triangle or 90 degree
so 90+40+A=180
130+A=180
subtract 130 from 180
A=50
help me please please please triangle 333333
Answer:
200 cm²
Step-by-step explanation:
Find the areas of all of the faces
17 × 2 = 34 (Top Face)
8 × 15 = 120 (Both Triangles)
15 × 3 = 30 (Bottom Face)
8 × 2 = 16 (Back Face)
Add them all together
120 + 34 + 30 + 16 = 200 cm²
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for y, the length of the room
y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0How do we obtain the relevant equations that can be used for the problem?First and foremost, we can begin solving this equation by noting the formula for calculating the area of a rectangle. This formula is given as follows:
Area of a rectangle = Length × Width
Since the width of the room is 5 feet less than the length of the room, we will have the resulting equation as the area of the rectangle:
y( y - 5) = 750
When this equation is fully expressed, we will get the following equations:
y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0Therefore, options, B, C, and E are correct.
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What is the inverse of f(x)=(5x+2)^2 for x_> -2/5
Answer:
Step-by-step explanation:
f(x)=5x2+xf(x)=5x2+xWrite f(x)=5x2+xf(x)=5x2+x as an equation.y=5x2+xy=5x2+xInterchange the variables.x=5y2+yx=5y2+ySolve for yy.Tap for more steps...y=−1−√1+20x10y=-1-1+20x10y=−1+√20x+110y=-1+20x+110Replace yy with f−1(x)f-1(x) to show the final answer.f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110Verify if f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110 is the inverse of f(x)=5x2+xf(x)=5x2+x.Tap for more steps...f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110
what is the slope of a line that passes through points (7,-5) and (16,7)
Determine the total number of roots of each polynomial function. f (x) = 3x6 2x5 x4 - 2x3 6 g(x) = 5x - 12x2 3
The total number of roots for the given polynomial is for f(x)= 3x^6+2x^5+x^4-2x^3+6 is 6 and for g(x) = 5x-12x^2+3 is 2
Since for finding the number of roots, we just need to see what is the degree fro the given polynomial, where the degree of the polynomial is nothing but the highest exponent.For the function f (x) = 3x6 2x5 x4 - 2x3, here the degree is 6, and the respective function is having 6 numbers of roots, which be real roots and complex roots too.For the function g(x) = 5x-12x^2+3, here the degree is 2, so the respective function has 2 roots.
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Answer:
f (x) = 3x6 + 2x5 + x4 - 2x3 = 6 roots g(x) = 5x - 12x2 + 3 = 2 roots f (x) = (3x4 + 1)2 = 8 roots g(x) = (x - 5)2 + 2x3 = 3 roots
Divide these numbers in the given ratios
36 in the ratio 4:5
we get statistics of 2017-2018 average starting teacher salaries by state measured by nea. given that the salary of arkansas is 33323, the sample size is 3,600 and the standard deviation is 399.876. a. what is the margin of error for a 80% confidence interval in arkansas? symbolic expression b. if we want to get a 80% confidence interval with a small margin of error, say only 7%. how many people do you need to sample?
a) The margin of error for an 80% confidence interval in Arkansas is 0.1041
b) if we want to get an 80% confidence interval with a small margin of error, say only 7%. then the sample size must be 53,599,359
The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.
n = 3600
standard deviation = 399.876
Confidence Interval = 80%
a) α = 0.20
The margin of error = Zα/2 (σ / √n)
Zα/2 = 1.4395 --- (From the tabular value)
The margin of Error = 1.4395 + 399.876 / √3600
Therefore, the Margin of Error = 8.1041
b) Margin of Error = 0.07 = 7%
α = 0.20
Critical Value = 1.2816
Sample Size = (Zc²σ² / ME²) = (Zcσ / ME)²
n = [(1.2816 * 399.876) / 0.07]²
n = 53599358.98
Therefore, Sample size, n = 53599359
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The sum of the first three terms of a G.p is half its sum to infinity.find the positive common ratio
ana and bonita are born on the same date in different years, nn years apart. last year ana was 55 times as old as bonita. this year ana's age is the square of bonita's age. what is nn?
Ana and Bonita were born nn year apart and its value of nn is 12.
Here we have to find nn which difference in the year in which Ana and Bonita were born.
Let x be the age of Ana and y be the age of Bonita.
It is given that last year Ana was 5 times as old as Bonita so from this statement we get the first equation:
x - 1 = 5(y -1)
x -1 = 5y - 5
5y -x = 4--------(1)
The second statement is Ana is square of Bonita's age. From this we get another equation:
x = y²-----------(2)
Putting equation 2 in equation 1 we get:
5y - y² = 4
y² - 5y +4 = 0
y² - 4y - y + 4 = 0
y(y-4) -1(y -4) = 0
(y - 4)(y -1) = 0
y = 4,1
As x = y²
x = 4² = 16 or x = 1² =1
We cannot take 1 as there is a difference in their age
So we get x = 16 and y =4
So the difference in their age = 16-4= 12
Therefore we get the value of nn as 12.
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A scientist is observing two ant colonies. The colonies each have 800 ants when he begins observing them. The population of Colony A increases by 25% each week. The population of Colony B decreases by 25% each week. In each equation, y represents the ant population with respect to a number of weeks, x. Drag each equation to show whether it can be used to represent the ant population of Colony A, Colony B, or neither of these.
In writing the equations that describe each of the colonies A ad B we have;
y = 800e^0.25x (Colony A)y = 800e^-0.25x (colony B )What are the equations?We know that the increase or decrease of population are exponential problems. We such, we must be able to look at the problem form the exponential perspective. This is how we would be able to know how to write the appropriate equation that would be able to be used in each of the cases that have been shown in the problem.
We are told that; a scientist is observing two ant colonies. The colonies each have 800 ants when he begins observing them. The population of Colony A increases by 25% each week. The population of Colony B decreases by 25% each week. In each equation, y represents the ant population with respect to a number of weeks, x.
Thus;
For colony A we can write;
y = 800e^0.25x
For colony B we can write;
y = 800e^-0.25x
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What is the equation of the line that passes through the point (-4, 2) and has a
slope of 1/4?
Answer:
y=1/4x+3
Step-by-step explanation:
To write an equation, let's infer we need to write it in slope-intercept form. We need the y-intercept. We can plug 1/4 and (-4,2) into y=mx+b, to solve for b. We have:
2=1/4*-4+b
2=-1+b
3=b
Since we have the slope, 1/4, we can create our equation:
y=1/4x+3
Solve for b in (y=mx+b):
b=y-mx
b=2-(1/4)(-4)
b=2+1
b=3
So the equation is y= (1/4)x + 3
What is an equation of the line that passes through the points (4, -2) and (2, 3)
The slope-Intercept form of the given line is y=1.5x.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
The given line passes through (4, -2) and (2, 3). Therefore, the slope of the given line can be written as,
Slope of the line, m = (-2 - 3)/(4 - 2)
= 3 / 2
= 1.5
Now, the equation of the line passing through (2, 3) can be written as,
y = mx + c
(3) = 1.5(2) + C
3 = 3 + C
3 - 3 = C
C = 0
Substitute all the value in the equation of the line,
y = m(x) + c
y = 1.5(x) + 0
y = 1.5x
Hence, the equation of the given line is y=1.5x .
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What is the distance between (-5,-6),(-9,-4)
Answer:
The distance between [tex](-5,-6),(-9,-4)[/tex] is [tex]6 units[/tex].
Step-by-step explanation:
Distance Formula :
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Given,
The two points are
[tex](-5,-6),(-9,-4)[/tex]
To calculate the distance between two points, use the distance formula.
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Substitute the actual values of the points into the distance formula.
Distance[tex]=\sqrt{((-9)^{2} -(-5)^{2}) +( (-4)^{2} -(-6)^{2})}[/tex]
[tex]=\sqrt{(81-25)+(16-36)}[/tex]
[tex]=\sqrt{36}[/tex]
[tex]=6[/tex]
Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window.
H
HH represents the height of the tree (in centimeters),
t
tt years since Renata moved in.
H
=
210
+
33
t
H=210+33tH, equals, 210, plus, 33, t
How fast does the tree grow?
The required increasement of height of tree is 33 centimeters annually
What is function of time?Function of time is defined as the change of abject or expression of variables with time. As the time increases, there is change in shape, height, etc. is called function of time.
According to given data in the question:we have given an expression of height of tree,
H = 210 + 33t
Where t represent the time and H is height of tree.
So, Changes in the height of the tree with years,
for t = 1 year
⇒ H = 210 + 33×1 = 210 + 33 = 243 centimeters
Thus, the height of tree in increases by 33 centimeters yearly.
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the sum of three integers is 32. the sum of the first and second integers exceeds the third by 82. the third integer is 16 less than the first. find the three integers.
The values of the three integers are:
x= -9, y=66, z= -25
What is meant by an equation?In French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.
In order to solve an equation with variables, you must first determine which variables' values make the equality true. Unknowns are the variables for which the equation must be solved, and equation solutions are the values of the unknowns that satisfy the equality..
Given,
Sum of three integers= 32
x+ y+ z=32 →1
And also given that,
x+ y= z+82 →2
z+16=x →3
By solving equation 1, we get
z+16+y+z=32
2z+y=16 →4
By solving equation 2, we get
z+16+y= z+82
y=82-16
y=66
By solving equation 4, we get
2z+66=16
2z=-50
z=-25
By solving equation 3, we get
x=z+16
x=-25+16
x=-9
Therefore, the three integers are x=-9, y=66, z=-25
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Doors for the small cabinets are 17.5 inches long. Doors for the large cabinets are 3.5 times as long as the doors for the small cabinets. How many large doors can be cut from a board that is 12 feet long?
Answer:
2
Step-by-step explanation:
If the doors for the small cabinets are 17.5 in long, and the doors for the large cabinets are 3.5 times longer, find the length of the large cabinet doors by multiplying the length of the small cabinet doors by 3.5:
⇒ Length of large cabinet doors = 17.5 × 3.5 = 61.25 in
1 foot = 12 inches
⇒ 12 foot = 12 × 12 = 144 inches
To find how many large doors can be cut from a board that is 12 feet long, divide 144 inches by the found length of the large door:
⇒ 144 ÷ 61.25 = 2 r 21.5
Therefore, 2 large doors can be cut from a board that is 12 feet long.
(There will be 21.5 inches of board left over).
p(x) = (x² - 9) (x² + x - 2)
factor for zeros to plot on a graph
pls help :(
Answer:
P(x) = (x - 3)(x + 3)(x + 2)(x - 1)
Answer:
Step-by-step explanation:
Solution:To write a polynomial in standard form, simplify and then arrange the terms in descending order.Expand ( x2 − 9 )( x + 2 ) using the FOIL Method.Simplify each term.
One day in 2014, 1 euro was worth x rand.
One year later, 1 euro was worth (x+1) rand.
Winston changed 1000 rand into euros in both years.
In 2014 he received 4.50 euros more than in 2015.
Write an equation in terms of x and show that it simplifies to 9x²+9x-2000=0.
1000/x - 1000/(x + 1) = 4.5 is an equation in terms of x that simplifies to this quadratic equation 9x² + 9x - 2000 = 0 as shown below.
What is a quadratic equation?In Mathematics, the standard form of a quadratic equation is given by this mathematical expression:
ax² + bx + c = 0.
Since Winston changed 1000 rand into euros in both 2014 and 2015, this can be represented by this mathematical expression:
1000/x - 1000/(x + 1) = 4.5
Taking the lowest common multiple (lcm), we have:
1000/x(x + 1) = 4.5
1000/(x² + x) = 4.5
Cross-multiplying, we have the following:
1000 = 4.5(x² + x)
1000 = 4.5x² + 4.5x
Multiplying both sides of the equation by 2, we have:
2 × (1000 = 4.5x² + 4.5x)
2000 = 9x² + 9x
Rearranging the terms and equating to zero, we have:
9x² + 9x - 2000 = 0.
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Can somebody please answer these 3 questions please and thank you
[tex]\displaystyle \boxed{\text{First Attachment, 14}}[/tex]
Answer:
x = 30
y = 60
Step-by-step explanation:
First, vertical angles are congruent. This helps us fill in more of the angles so we can find x and y.
Next, supplementary angles add up to 180°, aka a line. We can use this to fill out even more of the diagram given.
Lastly, corresponding angles on parallel lines are congruent.
By using the information above, we can decide that x = 30 and y = 60. See the first attachment for all the angle values filled out.
[tex]\displaystyle \boxed{\text{Second Attachment, 12}}[/tex]
Answer:
x = 65
Step-by-step explanation:
From the above explanation, we will be using vertical angles and supplementary angles to solve this question. See the second attachment.
We also know there are 180 degrees in a triangle.
Lastly, we know that alternate interior angles are congruent.
Using this knowledge, we can decide that x = 65.
[tex]\displaystyle \boxed{\text{Third Attachment, 13}}[/tex]
Answer:
x = 30
Step-by-step explanation:
Again, we will be using vertical angles, supplementary angles, and corresponding angles to solve this question. See the third attachment.
After placing vertical angles down from the given information, we can fill in more using corresponding angles.
Lastly, we know there are 360 degrees in a circle. We can create an equation from this and solve.
Using this information, we can decide that x = 30.
To train for a triathlon, Mr Greg swims, bikes, and runs everyday. Each day he bikes 10 times the distance he swims, and run 1. 5 miles more than half the distance he bikes. If Mr. Greg covers a total of 25. 5 miles on each day of training, how many miles does he swim? Bike? Run?
He covers 15 miles on the bike, 9 miles by running and 1.5 miles while swimming which sum up to 25.5 miles which is his total training distance.
What is distance?Distance is defined as an object's entire movement without regard for direction. Distance may be defined as how much ground an item has traversed regardless of its starting or finishing place. Distance is a scalar number that indicates "how much ground an item has covered" while moving. Displacement is a vector variable that describes "how far out of place an item is"; it represents the total change in position of the object. Distance is the length along a line or line segment between two locations on the line or line segment.
Here,
He rides 15 miles, which is ten times as far as he swims.
He runs 9 miles, which is half the distance he rides (15/2=7.5). Plus the additional 1.5 miles, totaling 9.
He swims.10 of what he bikes, for a total of 15x.10 = 1.5. As a result, he swims 1.5 miles.
15 miles = bike
9 miles= run
1.5 mile =swim
Add them all together and you get 25.5 miles.
He rides his bike for 15 miles, runs for 9 miles, and swims for 1.5 miles, for a total training distance of 25.5 miles.
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Explain c-a, when c = 7 and a=6
Answer:
1
Step-by-step explanation:
7-6=1
Answer:
c-a
replace x with 7 and a with 6
rewrite: 7-6
7-6 = 1
Answer: 1
Here is a set of data
2.4, 1.6, 3.2, 0.3, 1.5
Each piece of data is now doubled
Work out the new mean
Answer:
The new mean is 3.6
Step-by-step explanation:
Since each piece of data is now doubled that means the data is now
4.8, 3.2, 6.4, 0.6, 3
Add up all of the data which comes out to 18
Divide 18 by the number of numbers there are which is 5
This will get you 3.6 which is the new mean of the data
I need help like asap !!!
only numbers and decimal points