we have the following:
The formula is:
[tex]B=-0.015\cdot t+\frac{2.84\cdot N}{W\cdot g}[/tex]replacing,
where
B is blood alcohol content
t is the time
N is the maximum number of drinks
W is the weight
and g a gender constant (0.55 for wormen)
[tex]\begin{gathered} 0.08=-0.015\cdot2+\frac{2.84\cdot N}{110\cdot0.55} \\ \\ 0.08=-0.03+0.0469N \\ N=\frac{0.08+0.03}{0.0469} \\ N=2.34\cong2 \end{gathered}[/tex]therefor,e th
Solve Einstein's formula E = mc? for c where E. m, and c are greater than zero.
Solve the following equation for c:
[tex]E=mc[/tex]We can divide in both sides by m. Since m is greater than zero, we can do it without problem (because we can not divide by 0).
[tex]\frac{E}{m}=c[/tex]Find the equation of the line that passes through the given points. (Use x as your variable.)(2, 0), (0, −1)
Find the equation of the line that passes through the given points. (Use x as your variable.)
(2, 0), (0, −1)
step 1
Find out the slope
m=(-1-0)/(0-2)
m=-1/-2
m=1/2
step 2
Find out the equation of the line in slope-intercept form
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
we have
m=1/2
the y-intercept is given -----> (0,-1)
so
b=-1
substitute
y=(1/2)x-1How do you do the slope of two triangles on the same line as the hypotenuse?
We can say that the triangles is similar if the slope of the hypotenuse is the same.
The slope is Vertical sides divided by the horizontal side.
The upper triangle has vertical side of 3 and a horizontal side of 2 (By counting)
The slope will be m = 3/2
The lower triangle has a vertical side of 6 and a horizontal side of 4.
The slope will be m = 6/4 = 3/2
Since the slope is the same, the triangles are similar. and the slope is m = 3/2
Which of these best describes the profit Frank makes from selling these cards?
The correct answer is option C.
That is, He makes $1.00 for each 6 boxes he sold.
You hit 9) Consider the set of related x and y values. Which value of g would make it impossible for the set to represent a function? {(8. 67), (5, 28), (g. 19), (9,84)}
Remember that for any value on the domain of a function, there can only be one value on the range that assigns to it.
We have the set:
[tex]\mleft\lbrace(8,67\mright),(5,28),(g,19),(9,84)\}[/tex]therefore, a value of g that make it impossible for the set to represent a function can be 8, 5 or 9, since those values already have another value assigned from the range.
1. **Write the equation of the line that is perpendicular to y = -x + 4 and goes through the point (-8,2)
Write the equation of the line that is perpendicular to y = -x + 4 and goes through the point (-8,2
step 1
Find the slope of the perpendicular line
If two lines are perpendicular, then their slopes are inverse reciprocal
so
the slope of the given line is m=-1/2
therefore
the slope of the perpendicular line is m=2
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=2
point(-8,2)
substitute
2=(2)(-8)+b
solve for b
2=-16+b
b=18
therefore
the equation of the line is
y=2x+18Suppose the population of a town is 5,900 and is growing 2% each year. Write an equation to model the growth in population.
The equation/formula to model population growth can be given below;
[tex]\begin{gathered} P=P_0\times e^{rt} \\ \text{where P = total population after time t} \\ P_0=orig\text{inal or starting population} \\ r=\text{ rate of growth in percentage} \\ t=\text{time in years} \\ e=\text{Euler's constant = }2.71828 \end{gathered}[/tex]Therefore, for the question using the same formula, we have the model equation as;
[tex]\begin{gathered} P_0=5000 \\ r=2\text{ \% = 2/100=0.02} \\ \text{Then the equation will be;} \\ P=5000\times2.71828^{0.02t} \end{gathered}[/tex]Hence, P = 5000 x 2.71828^0.02t
√ is simplified to x4y5y√. What were the values of H and K in the original question?
To solve this problem, we will use the following properties of exponents:
[tex]\begin{gathered} \sqrt{a}=a^{\frac{1}{2}}, \\ \sqrt{a}^n=a^{\frac{n}{2}}, \\ a^na^m=a^{nm}. \end{gathered}[/tex]Using the first and second properties we notice that:
[tex]x^4y^5\sqrt{y}=\sqrt{x^{2*4}y^{2*5}y}.[/tex]Simplifying we get:
[tex]\sqrt{x^8y^{10}y}.[/tex]Finally, applying the last property, we get:
[tex]\sqrt{x^8y^{11}}.[/tex]Answer:
[tex]\begin{gathered} H=8, \\ K=11. \end{gathered}[/tex]1- A given line as a slope of – and y-intercept of 8. Which equation represents a line4that is parallel to the given line and passes through the point (-8,-2)?
Answer:
y=(1/4)x.
Explanation:
Two lines are parallel if their slopes are equal.
The slope of the given line is 1/4, therefore:
• The slope of the new line = 1/4
Thus, the goal is to find the equation of a line with a slope of 1/4 that passes through (-8,-2).
Using the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=\frac{1}{4}(x-(-8)) \\ y+2=\frac{1}{4}(x+8) \\ y+2=\frac{1}{4}x+2 \\ y=\frac{1}{4}x+2-2 \\ y=\frac{1}{4}x \end{gathered}[/tex]The equation of the line is y=(1/4)x.
The 3rd choice is correct.
Luis has a recipe that requires 2 cups of milk. He knows that 1 cup = 8 ounces.How many ounces of milk does Luis need for the recipe?
1 cup is equivalent to 8 ounces.
To find how many ounces are equivalent to 2 cups, we can use the next proportion:
[tex]\frac{1\text{ cup }}{2\text{ cups}}=\frac{8\text{ ounces}}{x\text{ ounces}}[/tex]Solving for x,
[tex]\begin{gathered} 1\cdot x=8\cdot2 \\ x=16\text{ ounces} \end{gathered}[/tex]Justify each step in the equation solution below with either a property of real numbers (associative, commutative, distributive) or a property of equality (addition or multiplication). 5(x+2)=30 Step 1: 5x+10=30 Justification: Justification Step 2: 5x+10+-10 = 30+-10 5x= 20 Step 3: Justification: 5 x 20 5 5 x=4
You have the following equation:
[tex]5(x+2)=30[/tex]with the following steps to find the value of x:
5x + 10 = 30 distributive property
5x = 20 addition property of equality (it has added -10 both sides)
x = 4 division property of equality (it has divided by 5 both sides)
Use the diagram to the night to answer questions 1-4 1. Name two points collinear to point K2. Give another name for line b. 3. Name the intersection of line c and plane R. 4. Name a point non-coplanar to plane R
ANSWER
1. L and J
2.
3.
4.
EXPLANATION
1) We want to name two points that are collinear to K. That is two points that lie on the same line as K.
They are points L and J
2) To name line b,
a spinner with 10 equally sized slices has3 Blue slices2 Yellow slices5 Red slicesthe dial is spun & stop at random what is the Probability that the dial Stops on a slice that is NOT blue? write the fraction in the simplest form
Solution
The number of possible outcomes is 10
We need to find the probability that it is blue
Probability is given as = number of required outcomes/ number of the possible outcome
The probability that the dial Stops on a slice that is blue = 3/10
The probability that the dial Stops on a slice that is NOT blue = 1 - Probability that the dial Stops on a slice that is blue = 1 - 3/10
A river has a current flowing with a velocity of 2.0 meters per second due east. A boat travels at 3.0 meters per second relative to the river and is headed due north. In the adjacent diagram, the vector starting at point P represents the velocity of the boat relative to the river water. What is the direction of the resultant velocity relative to the south riverbank? 12 degrees34 degrees56 degrees78 degrees
First let's draw the vectors that correspond to the boat speed and the river speed.
The river speed is 2 m/s due east, and the boat speed is 3 m/s due north, so we have:
Addind these vectors, the resultant is:
In order to calculate the angle x, we can use the tangent relation, which is the opposite side to the angle over the adjacent side to the angle:
[tex]\begin{gathered} \tan (x)=\frac{3}{2} \\ \tan (x)=1.5 \\ x=56.31\degree \end{gathered}[/tex]So the direction of the resultant is 56 degrees.
State whether the equation has one solution, or infinitely many solutions.
Given:
The expression 8y - 3 = 17 - 2y.
Required:
State whether the equation has one solution, or infinitely many solutions.
Explanation:
The calculation is as:
[tex]\begin{gathered} 8y-3=17-2y \\ 10y=20 \\ y=2 \end{gathered}[/tex]Answer:
System has only one solution.
Find the slope of the line that passes through (10, 10) and (3,1).Simplify your answer and write it as a proper fraction or improper fraction
The formula for the slpe of line passes through point (x_1,y_1) and (x_2,y_2) is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Determine the slope of line passes through the points.
[tex]\begin{gathered} m=\frac{1-10}{3-10} \\ =\frac{-9}{-7} \\ =\frac{9}{7} \end{gathered}[/tex]So answer is 9/7.
A friend tells you that he can run three miles in half an hour. You want to calculate his speed in miles per hour. The ratio is: 3miles------------1---2 hours converts this ratio to a unit cup
Given:
The ratio of speed is given as.
[tex]\frac{3\text{ mies}}{\frac{1}{2}\text{ hours}}[/tex]The objective is to convert the ratio into unit ratio.
The unit ratio can be calculated by multiplying 2 on numerator and denominator, so that the denominator will become one.
[tex]\begin{gathered} \frac{3\times2\text{ miles}}{\frac{1}{2}\times2\text{ hour}} \\ \frac{6\text{ miles}}{1\text{ hour}}\text{ } \\ 6\text{ miles/hour} \end{gathered}[/tex]Hence, the unit ratio is 6 miles/hour.
Find f(8) if f(x) = 5x-1
Answer
f(8) = 39
Explanation
The question asks us to find f(8), that is, f(x) when x = 8 if
f(x) = 5x - 1
Inserting x = 8
f(8) = (5 × 8) - 1
f(8) = 40 - 1
f(8) = 39
Hope this Helps!!!
Consider the data in the table below. Determine the logarithmic regression model for the data. Round the coefficients in the regression equation to 3 decimal places.
Year 1 2 3 4 5 6 7 8
Average Height 7.4 6 4.9 4.4 4 3.6 3.1 2.7
The regression equation is y
=
The regression equation, y = -0.6155x + 7.282
Given,
Year, x ; 1 2 3 4 5 6 7 8
Average height, y ; 7.4 6 4.9 4.4 4 3.6 3.1 2.7
Logarithms of y values;
log 7.4 = 0.869log 6 = 0.778log 4.9 = 0.690log 4.4 = 0.643log 4 = 0.602log 3.6 = 0.556log 3.1 = 0.491log 2.7 = 0.431The order of xy pairs;
(1, 0.869), (2, 0.778), (3, 0.690), (4, 0.643), (5, 0.602), (6, 0.556), (7, 0.491), (8, 0.431)
There are 8 xy pairs
Using online calculator, the regression equation get as;
y = -0.6155x + 7.282
Learn more about regression equation here;
https://brainly.com/question/22294435
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The graph of a function f is shown below.Find one value of x for which f(x)=-3 and find f(0).Hey
One value of x for which f (x ) = -3 is -2 .Therefore,
f(-2) = - 3
f (0) = 1
2. Write an expression that can be used to calculate how many hours are needed for a party. Then use yourexpression to tell the number of hours needed for a party with 16 participants and 4 escape puzzles.• (Replace this text with your expression)I• (Replace this text with your answer and work)
We know that each escape room is scheduled for 20 minutes. So, if there are 8 participants, then they need 160 minutes, which is equivalent to 2.67 hours.
So, the expression would be
[tex]\frac{20\times8}{60}[/tex]On the other hand, if there are 16 participants, then the hours needed are
[tex]2\cdot\frac{20\times8}{60}\approx5.33[/tex]Find the probabilityA box of chocolates contains three milk chocolates, four dark chocolates, and threewhite chocolates. You randomly select a chocolate. It is a milk chocolate or a darkchocolate.O 0.556O None of the other answers are correct0 0.7000363O 0.818
In total the box has 10 chocolates. 7 of them are milk or dark chocolate, hence the probability is:
[tex]P=\frac{7}{10}=0.7[/tex]Therefore the probability is 0.7
please help me I'm not really good with words problem
we know that
The perimeter of rectangle is equal to
In the playing card deck below what is the chance of pulling 5 face cards without replacing the cards in between pulls? Answer in decimal form.
Solve the system of equations by graphing:62 - 7Answer: (2, y) =32 + 11Question Help: Video Message instructorSubmit QuestionJump to Answer
Step 1 : Let's graph the equations, as follows:
y = - 6x - 7
y = 3x + 11
Step 2: Let's find x-intercept and y -intercept for both equations:
y = -6 * 0 - 7
y = -7, therefore, y-intercept = (0, -7)
0 = - 6x - 7
6x = -7
x = -7/6, therefore x-intercept = (-7/6, 0)
y = 3 * 0 + 11
y = 11, therefore, y-intercept = (0, 11)
0 = 3x + 11
-3x = 11
3x = -11
x = -11/3, therefore, x-intercept = (-11/3, 0)
Step 3: Now let's graph the system of equations:
As we can see, the point of intersection is (-2, 5), therefore, the solution is:
x = -2
y = 5
Find the volume of the cone on the left. Use 3.14 for i. The volume is m (Type a whole number or a decimal. Round to the nearest hundredth as needed.) 148 m 19 m
Given data:
The given figure of the cone.
The expression for the volume of the cone is,
[tex]\begin{gathered} V=\frac{1}{3}\pi(r)^2h \\ =\frac{1}{3}\pi(19m)^2(148\text{ m)} \\ \approx55,921.31m^3\text{ } \end{gathered}[/tex]Thus, the volume of the cone is 55,921.31 cubic-m.
5x + 4y if x=3 y=7 ?
In order to evaluate this expression for x = 3 and y = 7, let's use these values in the expression and calculate its final value. So we have:
[tex]\begin{gathered} 5x+4y \\ =5\cdot3+4\cdot7 \\ =15+28 \\ =43 \end{gathered}[/tex]So the value of this expression for x = 3 and y = 7 is 43.
I want to see if I solved a problem correctly
The problem gives us two expressions:
[tex]\begin{gathered} y=9x-18 \\ y=18x \end{gathered}[/tex]And we need to solve for x. For that, the first step is to replace "y" on the first expression by the right side of the second expression:
[tex]18x=9x-18[/tex]Now we need to isolate the "x" variable on the left side:
[tex]\begin{gathered} 18x-9x=-18 \\ 9x=-18 \\ \frac{9x}{9}=\frac{-18}{9} \\ x=-2 \end{gathered}[/tex]We can now find "y" by replacing the value of "x" on the second expression:
[tex]y=18\cdot(-2)=-36[/tex]The value of x is equal to -2, and the value of y is equal to -36.
will swims a total of 45.6 laps iin 2.85 hours how many laps does he swim each hour
Monica, this is the solution to the problem:
Total laps that Will swims = 45.6
Time it takes Will to swim this distance = 2.85 hours
Let's calculate the number of laps Will swims each hour, using Direct Rule of Three, as follows:
Laps Time
45.6 2.85
x 1
____________
2.85 * x = 45.6 * 1
2.85x = 45.6
Dividing by 2.85 at both sides:
2.85x/2.85 = 45.6/2.85
x = 16
Will swims 16 laps per hour
Chase and Heather are traveling towards each other from points that are 469 miles apart. If heather is traveling 7 mph faster than they meet after 7 hours, how fast was each traveling?Chase is traveling ___ mphHeather is traveling ___ mph
The distance between Chase and Heather is 469 miles
They each travel for 7 hours (when they meet)