The expression -3(-3v^3+3-4w^2) after using the distributive property is 9v³ - 9 + 12w²
What is a distributive property?The distributive property of multiplication over addition is a mathematical method of expanding bracket mostly applied when you need to multiply a value by a sum.
This property of multiplication explains how to solve expressions that are in the form of a(b + c).
From the information given, we have the expression;
-3(-3v^3+3-4w^2)
To carry out the distributive multiplication , we need to remove the parentheses of the expression by taking the following steps, we have;
expand the bracket and take note of the mathematical signs, we get
-3(-3v³ + 3 - 4w²)
9v³ - 9 + 12w²
Note that we can no longer add the terms because they are not like terms.
Hence, the expression is 9v³ - 9 + 12w²
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a convex polyhedron $p$ has 26 vertices, 60 edges, and 36 faces, 24 of which are triangular, and 12 of which are quadrilaterals. a space diagonal is a line segment connecting two non-adjacent vertices that do not belong to the same face. how many space diagonals does $p$ have?
A convex polyhedron have 241 space diagonals.
As we know that the every pair of vertices of the convex polyhedron determines either an edge, a face diagonal or a space diagonal.
Here, we have 26 vertices.
so, the total line segments determined by the vertices:
²⁶C₂
= 26! / 2! × (26 - 2)!
= 325
Out of 325 line segments, 60 are edges (Given).
We know that each triangular face has zero face diagonals and each quadrilateral face has two face diagonals.
So there are 2 × 12 = 24 face diagonals.
This means, 325 - 60 - 24 = 241 line segments segments must be the space diagonals.
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Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply
The quadratic equation 4 · x² - 7 · x = 3 · x + 24 has the following roots: x₁ = 19 / 4 and x₂ = - 9 / 4.
How to solve a quadratic equation
In this question we find the case of a quadratic equation, whose form is defined below:
y = a · x² + b · x + c
Where:
a, b, c - Real coefficientsx - Independent variabley - Dependent variableThe procedure find the solutions to the quadratic equations:
Modify the polynomial into standard form.Complete the square.Simplify part of the expression into a perfect binomial.Clear the variable x by algebra properties.Now we proceed to determine the solutions to the quadratic equation:
4 · x² - 7 · x = 3 · x + 24
4 · x² - 10 · x - 24 = 0
4 · [x² - (5 / 2) · x - 6] = 0
4 · [x² - (5 / 2) · x + 25 / 4] = 4 · 6 + 4 · (25 / 4)
4 · (x - 5 / 4)² = 49
(x - 5 / 4)² = 49 / 4
x - 5 / 4 = ± 7 / 2
x = 5 / 4 ± 7 / 2
The solutions to the quadratic equation 4 · x² - 7 · x = 3 · x + 24 are x₁ = 19 / 4 and x₂ = - 9 / 4.
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Please help with the question below
The area of the given image design is; 15 in²
How to find the area of a triangle?The formula to find the area of a triangle is;
Area = ¹/₂(base * height)
Let us divide the image into two triangles and as such;
Area of biggest triangle = ¹/₂(14 * 15)
= 85 in²
We will now deduct the rectangle that was removed by finding its' area to get;
Area of rectangle = length * width
= 10 * 7 = 70 in²
Thus;
Area of image = 85 - 70
Area of image = 15 in²
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Find P(blue and odd).
The probability of getting blue and an odd number will be 1/10.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
The probability of getting blue is 2/10 and the probability of getting odd number is 5/10.
Therefore, the probability of getting blue and an odd number will be:
= 2/10 × 5/10
= 1/10.
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The surface area of a cylinder is 28π m². The distance around the base of the cylinder is 7π meters and the diameter of a base of the cylinder is 4 meters.
What is the height of the cylinder?
Enter your answer, as a simplified fraction, in the box.
m
Answer:
5
Step-by-step explanation:
diameter = 4 so radius =2
open up the cylinder so its top & bottom circle's circumference = 2πr =4π
top & bottom circle's area = πr² = 4π each, 8π for both
total surface = 28π
so lateral surface = 28π - 8π = 20π
so 20π = 4π* height
so height is 5
Two linear equations are represented by using the tables below. A 2-column table with 4 rows is titled Equation A. Column 1 is labeled x with entries negative 5, negative 2, 0, 1. Column 2 is labeled y with entries negative 4, negative 1, 1, 2. A 2-column table with 4 rows is titled Equation B. Column 1 is labeled x with entries negative 6, negative 3, 3, 6. Column 2 is labeled y with entries negative 4, negative 2, 2, 4. The data points for equation A are plotted on the coordinate plane below and are connected by using a straight line. On a coordinate plane, a line goes through points (negative 5, negative 4), (negative 2, negative 1), (0, 1), (1, 2). What is the solution to the system of equations?
Answer:
I need more information
Step-by-step explanation:
The solution to the system of equations cannot be determined from the information provided. The tables provide a set of x and y values for each equation, but they do not provide enough information to determine the equations themselves. In order to find the solution, we would need to know the form of the equations and be able to solve them simultaneously. The information provided is just a set of points that are plotted on a coordinate plane that is connected by using a straight line, but it is not enough to find the solution of the system of equations.
Here are ingredients from recipes for two different banana cakes.
First recipe is in the table shown.
Second recipe is shown in the relationship cups of flour y and cups of sugar x in the second recipe is y=7/4x.
1.if you used 4 cups of sugar, how much flour does each recipe need? Type your answer in the boxes below.
2. What is the constant of proportionality for each situation and what does it mean?
1. The amounts of flour, considering 4 cups of sugar for each recipe, are given as follows:
First recipe: 6 cups.Second recipe: 7 cups.2. The constant for each recipe is given as follows:
First recipe: 3/2, meaning that for each cup of sugar, 3/2 cups of flour are needed.Second recipe: 7/4, meaning that for each cup of sugar, 7/4 cups of flour are needed.How to model the proportional relationship?A proportional relationship is modeled as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
Input x: amount of sugar.Input y: amount of flour.From the table, the constant is given as follows:
k = (3/4)/(1/2)
k = 3/2.
Meaning that for each cup of sugar, 3/2 cups of flour are needed.
Hence the relation is:
y = 3x/2.
The amounts of flour, considering 4 cups of sugar for each recipe, are obtained as follows:
First recipe: 3 x 4/2 = 6 cups.Second recipe: 7 x 4 / 4 = 7 cups.More can be learned about proportional relationships at brainly.com/question/10424180
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Find the domain of y=−9x−26/x+3.
All Real Numbers except x = 9
All Real Numbers except x = -9
All Real Numbers except x = 3
All Real Numbers except x = -3
The domain of the function will be All Real Numbers except x = -9. The correct option is B.
What are a range and domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
Given that the function is y=−9x−26/x+3. As the domain is defined as all the input values going into the function. The domain will be all the real numbers except -9. Because the function is undefined on -9.
The graph of the function is attached with the answer below.
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X
1
2
3
4
5
f(x)
3
9
15
21
27
Linear, exponential, quadratic or neither??
From the data points given, the linear equation is obtained as y = 6x - 3.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The data points given are -
X = 1, 2, 3, 4, 5
f(x) = 3, 9, 15, 21, 27
The slope of the line is given as m.
The slope can be deduced using the formula -
(y2 - y1) / (x2 - x1)
m = (9 - 3) / (2 - 1)
m = 6/1
m = 6
The slope-intercept form of a equation is y = mx + b
Substitute the values of x, y and m in the equation -
3 = 6(1) + b
3 = 6 + b
b = 3 - 6
b = -3
So, the equation becomes -
y = 6x - 3
This equation forms a straight line in the graph.
Therefore, y = 6x - 3 is a linear equation.
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Triangle BCD has vertices B(-8,3), C(-4, 6), and D(2, 0). If the triangle is reflected across the x-axis and dilated by a scale factor of 0. 5 with respect to the origin, what are the coordinates of the vertices of triangle B"C"D"?
If the vertices of the triangle BCD with vertices B(-8,3), C(-4, 6), and D(2, 0) , and if they are reflected across x axis and dilated by a scale factor of 0.5 then the coordinates of B"C"D" are B''(-4 , -1.5) , C"(-2 , 3) and D"(1 , 0) .
If the point (x,y) is reflected across the x axis , then the reflected points are (x,-y) .
the vertices of the triangle BCD are : B(-8,3), C(-4, 6), and D(2, 0) ;
So , the reflected vertices are : B'(-8,-3) , C'(-4,-6) and D'(2,0) ;
if the point (x,y) is dilated by a scale factor of "k" , then the dilated vertices are written as : (kx , ky) .
the dilation factors is = 0.5 ;
So , the vertices B'(-8,-3) , C'(-4,-6) and D'(2,0) after dilation will be written as :
⇒ B''(-8×0.5 , -3×0.5) , C"(-4×0.5 , 6×0.5) and D"(2×0.5 , 0) ;
After simplifying further ,
we have ;
⇒ B''(-4 , -1.5) , C"(-2 , 3) and D"(1 , 0) ;
Therefore , the coordinates of the triangle B"C"D" are B''(-4,-1.5) , C"(-2,3) and D"(1,0) .
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angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
solve an equation to determine the measure of angle x.
Applying the sum of angles on a straight line, we have:
Equation = x + 70 + 60 = 180
Measure of x = 50°.
What is angle ?In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.
A straight line angle equals 180 degrees.
Therefore, the sum of all the angles on a straight line = 180 degrees.
Thus, the equation to solve for x would be:
x + 70 + 60 = 180
Solving for x
x + 130 = 180
x = 180 - 130
x = 50°
Hence, 50° is the measure of angle x.
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A new car is purchased for $23,000 and over time its value depreciates by one half every 3 years. How long, to the nearest tenth of a year, would it take for the value of the car to be $7,800 (25 PTS)
It take for the value of the car is 4.7 years.
Now, According to the question:
A new car is purchased for $23,000
and, over time its value depreciates by one half every 3 years.
It take for the value of the car to be $7,800.
According to the statement :
The equation will be :
y = 23,000 × [tex](\frac{1}{2} )^n[/tex]
7,800 = 23,000 × [tex](\frac{1}{2} )^n[/tex]
By simplification, we get:
n = 1.56
Over time its value depreciates by one half every 3 years.
So, 1.56 × 3 = 4.68 ≈ 4.7 years.
Hence, It take for the value of the car is 4.7 years.
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(n^3+3n^2-15n+19)/(n-2) Synthetic Division
The quotient is n^2+5n-5 and the remainder is 9. The solution has been obtained by using the synthetic division.
What is synthetic division?
Synthetic division is typically used to identify the zeroes of polynomials and is described as "a simplified method of dividing a polynomial with another polynomial equation of degree 1."
We are given the expression as (n^3+3n^2-15n+19)
The expression is to be divided by (n-2)
So, by using the synthetic division, we get
2 | 1 3 -15 19
- 2 10 -10
1 5 -5 9
Quotient = n^2+5n-5
Remainder = 9
Hence, the quotient is n^2+5n-5 and the remainder is 9.
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Segment GM is an altitude of AAGE.
Based on the information in the diagram, what is the length of A-F?
A. O 19.7
B. O 18.4
C. O 17.0
D. O 14.1
The segment lengths in the diagram are given as follows:
GE = 13.AM = 2.083.AG = 5.42.What are the segment lengths?Using the Pythagorean Theorem, the length of segment GE is given as follows:
(GE)² = 5² + 12²
(GE)² = 169
GE = 13.
Applying the geometric mean theorem, the length AM is obtained as follows:
(GM)² = ME x AM
25 = 12 AM
AM = 2.083.
Then, applying the Pythagorean Theorem, the length AG is found as follows:
(AG)² = 2.083² + 5²
AG = 5.42.
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Of the 6 vacant positions to be filled at a company, 3 must be given to men, 2 to woren and can be ether gender. In how many ways can these different positions be filled given that 5 men and o women have applied for these positions?
There are a total of 6 vacant positions to be filled at a company, with 3 of those positions being given to men, 2 to women and 1 being either gender.
How many ways can these different positions be filled given that 5 men and o women have applied for these positions?Given that there are 5 men and 0 women who have applied for these positions, there are a total of 150 ways to fill the 6 positions.Firstly, the 3 positions that must be given to men can be filled in a total of 5 ways, as there are 5 men applying for those positions.Secondly, the 2 positions that must be given to women cannot be filled in this instance, as there are no women applicants for these roles.Finally, the position that must be given to either gender can be filled by any of the 5 men who have applied. This can be done in a total of 5 ways.Combining these three scenarios, the total number of ways to fill the 6 positions is 5 x 5 x 1, or 5 x 5, which is equal to 150.In conclusion, there are a total of 150 different ways to fill the 6 vacant positions at the company, given that 5 men and 0 women have applied for the positions.To learn more about the gender-neutral position refer to:
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what is the distance from y to wx
Step-by-step explanation:
this distance YZ is the height of the triangle WXY.
it splits the main triangle into 2 right-angled triangles WYZ and XYZ.
we can use Pythagoras
c² = a² + b²
with any of the 2 smaller right-angled triangles to get YZ.
remember, "c" is the Hypotenuse (the side opposite to the 90° angle). a and b are the legs.
so, when picking the larger one :
26² = 24² + YZ²
676 = 576 + YZ²
100 = YZ²
YZ = sqrt(100) = 10 = distance of Y to WX.
In triangle MNO, Angle M is congruent to angle O. NO = 12 and OM=14. Find MN
The length of MN is 14 units.
What is isosceles triangle?A type of triangle known as an isosceles triangle has any two sides that are both the same length. The theorem that describes the isosceles triangle states that "if the two sides of a triangle are congruent, then the angle opposite to them are also congruent." This means that the two angles of an isosceles triangle opposite to equal sides are equal in measure. For example, in the triangle ΔABC, if sides AB and AC are equal, then ABC is an isosceles triangle where ∠B = ∠C.
Given;
ΔMNO,
∠M = ∠N
Also, NO=12 and OM=14
The angles are equal then triangle is isosceles and for given triangles the two sides are equal;
Sides opposite to angles are;
NO and MO
MO = NO = 14 units
Therefore, the length of third side of triangle MNO is 14 units.
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Arthur is purchasing ingredients to prepare hotdogs for his school's food fair.
Hotdog buns come in packs of 6 while the sausages come in packs of 10.
What is the least number of packs of each item he should buy to get an equal number of buns
and sausages?
Step-by-step explanation:
To have an equal number of buns and sausages, Arthur needs to find the least common multiple (LCM) of 6 and 10.
The LCM of 6 and 10 is 30.
Therefore, he should buy at least 30 packs of buns and 30 packs of sausages to get an equal number of buns and sausages.
That way, he would have 30/6 = 5 packs of buns and 30/10 = 3 packs of sausages.
Figure 2 is a scale image of Figure 1, as shown below.
What is the scale factor applied to Figure 1 to produce Figure 2?
A.
The scale factor is equivalent to {k} = 4/3.
What is scale factor?Direct variation of {y} with {x} means that as {x} increases, {y} increases uniformly with it. Mathematically - {K} = y/x = constantScale factor is a dimensionless quantity that tells by how much time a specific dimension of a figure is enlarged or reduced. Mathematically, it is the ratio of two similar quantities.Scaling is defined as the process of changing the dimensions of the original figure as per some specific proportional rule.In case of length scaling, we can write -{K} = L{final}/L{initial}
Given is that figure 2 is a scale image of figure 1.
We can write the scale factor as -
K = {y}/{x} = 8/6 = 4/3
Therefore, the scale factor that is applied to figure {1} to get figure {2} is equivalent to {k} = 4/3.
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Which inequality matches the graph? -2x + 3y > 7 02x-3y
the inequality model. 5x-6y <0 is attached below.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
2x + 3y > 7x-3y
5x-6y <0
So we have to plot this inequality.
Hence, the inequality model. 5x-6y <0 is attached below.
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1) b^2 -4=0
2)2x^2 =21+11x
3)5x^2 =3x+92
Answer:
1. b1=-2, b2=2
2. x1= -3/2, x2=7
3. x1=-4, x2= 23/5
Follow formula
b = -b [+][-] sq| b^2-4ac/ 2a
is 3/11 and 17/6 Proportional
The ratios 3/11 and 17/6 is not proportional.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s. If both these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
The given ratios are 3/11 and 17/6.
For two ratios a/b and c/d to be proportional, a/b must be equal to c/d.
If 3/11 and 17/6 are proportional,
3/11 must be equal to 17/6.
Or doing the cross multiplication,
3 × 6 must be equal to 11 × 17.
18 must be equal to 187.
But 18 ≠ 187
So the ratios are not proportional.
Hence 3/11 and 17/6 are not proportional.
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3.
Which is cheaper: 115 plums for $276.00 at Shop ZYX or 198 plums for $633.60 at Shop PWR?
3a What is the cost of a single plum at Shop ZYX?
3b
3c
Enter your next step here
() ba
dollars
The cheaper plan is given as follows:
Shop ZYX.
The cost of a single plum at Shop ZYX is given as follows:
$2.4.
How to obtain the cheaper plan?To obtain the cheaper plan, we must obtain the cost of a single plum for each shop.
The cost of a single plum for each shop is obtained using a proportion, with the division of the total cost by the number of plums.
Hence the cost per plum in each shop is given as follows:
Shop ZYX: 276/115 = $2.4.Shop PWR: 633.6/198 = $3.2.More can be learned about proportions at https://brainly.com/question/24372153
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Ben is considering purchasing a new home. His banker has presented a 10-year mortgage at a fixed rate of 7.6%. The cost of the home is $196000 and Ben will be required to provide a 25% down
payment. If we use Sheets to determine his monthly payment, which of the following Sheets commands could be used to determine his payment? (Choose all that apply!)
-PMT(0.076/12,120,-147000)
PMT(0.076/12,10 12,-$147000)
PMT(7.6,10,-196000)
PMT (7.6% / 12,12 10,-147000)
PMT(7.6/12,12 10,-147000)
-PMT(0.076/12,120,-196000+49000)
Answer: The PMT function in Sheets is used to calculate the monthly payment for a loan. The syntax of the function is PMT(rate, nper, pv, [fv], [type]).
Rate: the interest rate per period
Nper: the total number of payments
Pv: the present value (the total amount of the loan)
Fv: the future value of the loan (optional)
Type: the number 0 or 1 indicating when payments are due (0 = end of period, 1 = beginning of period)
Given the information in the problem, Ben's mortgage is for 10 years, so the total number of payments is 10*12 = 120. The present value of the loan is $196000 and the down payment is 25% of the home's cost so 25%*196000 = $49000. Therefore, the present value of the loan is $196000 - $49000 = $147000
Based on this information, the following commands would be used to determine the monthly payment:
PMT(0.076/12,120,-$147000)
PMT(0.076/12,120,-196000+$49000)
The first command uses the annual interest rate divided by 12 to convert it to a monthly rate, and the total number of payments is 120 (10 years * 12 months/year). The second command also uses the same monthly rate and total payments and the present value which is $147000
The other commands
Step-by-step explanation:
in a candy factory, the nutty chocolate bars contain 18.0 % (by mass) cashews. if 11.3 kg of cashews were used one day, how many pounds of nutty chocolate bars were made?
Answer:
62.8 kg or 128.43 lbs
Step-by-step explanation:
if 18 percent of all the chocolate bars is is cashews at 11.3 kgs, the chocolate makes up the other 82 percent so theres a total of 62.78 kgs of candy total and you can use the eqaution for 1kg equal 2.205 lbs to find a total of 138.43 lbs of total chocolate bars
alfred and bonnie play a game in which they take turns tossing a fair coin. the winner of a game is the first person to obtain a head. alfred and bonnie play this game several times with the stipulation that the loser of a game goes first in the next game. suppose that alfred goes first in the first game, and that the probability that he wins the sixth game is m n , where m and n are relatively prime positive integers. what are the last three digits of m n ? (1993,
So, the last three digits of m*n is 001.
Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.
Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:
p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2
Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.
Therefore, the last three digits of m*n is 001.
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A ring is now reduced to 840 this is saving 40%of the original price .work out the original price of the ring
Answer: 1400
Step-by-step explanation: If it is saving 40% of the original price than it is 60% of the original price. 840=60/100*x, and so we divide both sides by 60/100. 840*100/60=1400. Therefore, 1400 is the original price.
The table shows the number of laps jogged by Cameron last weekend. Day Number of Laps Saturday 21 Sunday 16.5 What was the percent of decrease in the number of laps jogged from Saturday to Sunday? Round the percent to the nearest tenth if necessary.
Answer: To find the percent of the decrease in the number of laps jogged from Saturday to Sunday, we can use the following formula:
percent decrease = (change in value / original value) x 100
In this case, the original value is the number of laps jogged on Saturday, which is 21 laps. The change in value is the difference in the number of laps jogged from Saturday to Sunday, which is 21 - 16.5 = 4.5 laps.
So, substituting these values into the formula:
percent decrease = (4.5 / 21) x 100
percent decrease = 0.214 x 100
percent decrease = 21.4%
Rounded to the nearest tenth, the percent of decrease in the number of laps jogged from Saturday to Sunday is 21.4%.
Step-by-step explanation:
evaluate (8+t power of 3)-6
Answer:
t³+2Step-by-step explanation:
(8+t³)-68+ t³-6t³ +(8 - 6)t³+2- Hope this helps!
The veterinarian orders 15 mg of Vitamin K. The vial is labeled 10mg/mL how many mL is needed?
please explain how to do it
Each ml of the vial contains 10 mg of Vitamin K. So to obtain 15 mg of Vitamin K, we needs a volume 1.5 ml of the solution.
We can calculate the required amount in two ways. We can use either proportions, or we can use the unit value determination.
By using proportions.In 1 ml we have 10mg , to get 15 mg we can use x ml
[tex]\frac{1}{10} = \frac{x}{15}[/tex]
[tex]x = \frac{15* 1}{10}[/tex]
x = 1.5
So, to get 15 mg of Vitamin K, we need 1.5 ml of solution.
By finding the unit valueVolume required to get 10 mg of vitamin K = 1 ml
Volume required to get 1 mg of vitamin K = [tex]\frac{1}{10}[/tex] ml = 0.1 ml
Volume required to get 15 mg of Vitamin K = 15 × 0.1 = 1.5 ml
So volume required to get 15mg = 1.5 ml
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