Answer:
x = 156/5
Step-by-step explanation:
I'm assuming you want to solve for the value of x in this equation.
With that clarified,
Divide both sides of the equation by 10:
[tex]10x/10 = 312/10[/tex] <- Note that the left side will simplify to just x
[tex]x=312/10[/tex]
Now simplify the fraction:
[tex]x=156/5[/tex]
Therefore, x = 156/5
Let x be a continuous random variable that follows a normal distribution with a mean of 450 and a standard deviation of 80.Find the value of x so that the area under the normal curve between pand x is approximately 0.4591 and the value of x is greater than the mean? Round your answer to the nearest integer.
In order to calculate the value of x, first we need to find the value of z such as the area between the mean and x is 0.4591.
Looking at the z-table, the value of z that gives this area is z = 1.74
Then, using the formula for z, we can calculate the value of x:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ 1.74=\frac{x-450}{80} \\ x-450=139.2 \\ x=589.2 \end{gathered}[/tex]Rounding to the nearest integer, we have x = 589.
Find the value of r, 3/r=12/22
The value of r when 3/r = 12/22 is 5.5 or 11/2.
According to the question,
We have the following information:
3/r = 12/22
Now, we can easily find the value of r using the cross multiplication method:
12r = 22*3
Now, 12 is in the multiplication on the left hand side. So, it will be in the division on the right hand side:
r = 66/12
Now, we will convert this fraction into the simplest form by dividing both the denominator and numerator by 6:
r = 11/2
r = 5.5
Hence, the value of r is 11/2 or 5.5.
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what is the slope of anyas line
Let´s the following line:
[tex]\text{ y-2 = 3(x-1)}[/tex]This is equivalent to say:
[tex]\text{ y-2 = 3x-3}[/tex]resolve for y:
[tex]\text{ y = 3x-}3\text{ +2 = 3x -1}[/tex]So we have the following equation for the line
[tex]\text{ y = 3x -1}[/tex]then we can conclude that the slope is 3.
4ck^2 + 10k^2 − 16ck − 40kPart A: Rewrite the expression by factoring out the greatest common factor. Part B: Factor the entire expression completely. Show the steps of your work.
We have the following polynomial:
[tex]4ck^2+10k^2-16ck-40k[/tex]See that 2k is the greatest common factor, then, let's factor it out
[tex]2k(2kc+5k-8c-20)[/tex]We can still do some small factors inside the parenthesis, like:
[tex]\begin{gathered} 2kc+5k-8c-20 \\ \\ k(2c+5)-4(2c+5) \\ \\ (2c+5)(k-4) \end{gathered}[/tex]Then, inside the parenthesis it's
[tex]2k(2c+5)(k-4)[/tex]Therefore, the expression, completely simplified is
[tex]4ck^2+10k^2−16ck−40k=2k(2c+5)(k-4)[/tex]An object sinks into the river at a rate of -2.5 feet per second and reaches the bottom in t seconds. If the equation -2.5= x/t represents this situation, where x is the depth of the river and t = 39 seconds, how deep is the river? pls help me
The depth of the river is - 97.5 feet.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario
In this case, the object sinks into the river at a rate of -2.5 feet per second.
The equation -2.5= x/t represents this situation, where x is the depth of the river and t = 39 seconds.
The depth will be:
-2.5= x/t
-2.5 = x / 39
Crops multiply
x = 39 × -2.5
x = -97.5
This illustrates the depth.
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Given the explicit formula for an arithmetic sequence find the first five terms and the term named in theproblem.a=65- 100nFind a 39
Given:
a = 65 - 100n
Let's find the first five terms.
[tex]\begin{gathered} \text{First term:} \\ a_1=65-100(1)\text{ = 65-100=-35} \end{gathered}[/tex][tex]\begin{gathered} \text{Second term:} \\ a_2=65-100(2)=65-200=-135 \end{gathered}[/tex][tex]\begin{gathered} \text{Third term:} \\ a_3=65-100(3)\text{ = 65 - 300 = }-235 \end{gathered}[/tex][tex]\begin{gathered} \text{Fourth term:} \\ a_4=65-100(4)\text{ = 65-400=-335} \end{gathered}[/tex][tex]\begin{gathered} \text{Fifth term:} \\ a_5=65-100(5)=65-500=-435 \end{gathered}[/tex]For a39, we have:
[tex]a_{39}=65-100(39)=65\text{ - 3900=}-3835[/tex]ANSWER:
First term = -35
Second term = -135
Third term = -235
Fourth term = -335
Fifth term = -435
39th term = -3835
The data shows the total number of employee medical leave days taken for on-the-job accidents in the first six months of the year.5, 12, 8, 19, 12, 12Find the range of days taken for medical leave for each month.The range of days taken for medical leave for each month isdays
Given:
5, 12, 8, 19, 12, 12
Aim:
We need to find the range of days taken for medical leave for each month.
Explanation:
Rewrite the given data in terms from least to great values
5,8,12,12,12,19
The smallest value is 5.
The highest value is 19.
Recall that the range is the difference between the highest and lowest values in the set.
[tex]Range=\text{ highest value-smallest value}[/tex][tex]Range=19-5=14[/tex]Final answer:
The range of days taken for medical leave for each month is 14 days.
A four-sided figure is resized to create a scaled copy. The proportional relationship . between any given side length in the original figure, f, and the corresponding side length in the scaled copy, s, can be represented by the equation s f. What is the constant of proportionality from side lengths in the original figure to side lengths in the scaled copy?
Step 1. When two variables are related, for example, x and y, there will be a constant of proportionality between the x-values and the y-values, this constant of proportionality ''k'' is represented in the general formula for proportionality:
[tex]y=kx[/tex]Step 2. In this case, we are relating two variables: f and s, through the following equation:
[tex]s=\frac{1}{7}f[/tex]If we compare this with the equation from step 1, we can see that 1/7 represents the constant of proportionality:
[tex]k=\frac{1}{7}[/tex]Answer: The constant of proportionality is 1/7
A particle moves along the x-axis so that at time t> 0 its position is given by x(t) = 3t^3 -27t^2 + 72t. Determine all intervals when the speed of the particle is decreasing.
The time interval when the speed is decreasing 0< t<3
What is instatenous speed?Instatenous speed is the speed of a object in motion at any given moment of time.
When the speed starts deceasing the instatenous acceleration dv/dt<0
differentiating the distance with time with second order
dv/dt= d^2x/dt^2
dv/dt= 18t- 54
dv/dt<0
18t-54<0
18t<54
t<3
Therefore the time interval when the speed start deceasing is 0 to 2
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if you can buy four Bunches of purple grapes for $10 then how many can you buy with $25 select their proportion that correctly represents the situation
If $10 can purchase 4 bunches of purple grapes, then how much can 25 purchase
Mathematically,
$10 is equivalent to 4 bunches
$25 is equivalent to x bunches since we don't know the number of bunches $25 can buy
10 dollars = 4 bunches
25 dollars = x bunches
The proportion is given below by introducing cross multiplication to the above expression
[tex]\frac{4\text{ bunches}}{10\text{ dollars}}\text{ = }\frac{x\text{ bunches}}{25\text{ dollars}}[/tex]A scale drawing of a rectangular swimming pool measures 3 inches long by 1.5 inches wide. The actual width of the swimming pool is 75 feet. What is the actual perimeter of the swimming pool, in feet?
The actual perimeter of the swimming pool is 450 feet.
Given,
The scale drawing measurements;
Length of the pool = 3 inches
Width of the pool = 1.5 inches
Perimeter of the pool = 2(l + w) = 2(3 + 1.5) = 2 x 4.5 = 9 inches
Actual measurements;
Width of the pool = 75 feet
1 feet = 12 inches
So,
75 feet = 75 x 12 = 900 inches
We have to find the actual perimeter of the swimming pool.
Perimeter of the pool = x
Lets take the ratio;
900 ; 1.5 = x ; 9
900/1.5 = x/9
x = (900 x 9) / 1.5 = 8100/1.5 = 5400 inches
5400 inches = 5400/12 = 450 feet.
That is,
The actual perimeter of the swimming pool is 450 feet.
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What is the area of a triangle where the vertices are (-3,-3), (-3,2), and (1,2)
Given:
The vertices of the triangle are (-3,-3), (-3,2), and (1,2).
Required:
We need to find the area of the given triangle.
Explanation:
Mark the points on the graph and join them.
A(-3,2), B(-3,-3), and C(1,2).
The given triangle is a right-angled triangle.
The height of the given triangle is the length of AB.
The base length of the given triangle is the length of AC.
Consider the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Use the distance formula to find the length of the line segments.
Consider the points A(-3,2) and B(-3,-3),
[tex]Substitute\text{ }x_1=-3,y_1=2,x_2=-3\text{ and }y_2=-3\text{ in the formula.}[/tex][tex]AB=\sqrt{(-3-(-3))^2+(-3-2)^2}[/tex][tex]AB=\sqrt{(0)^2+(-5)^2}[/tex][tex]AB=5units[/tex]Consider the points A(-3,2) and C(1,2).
[tex]Substitute\text{ }x_1=-3,y_1=2,x_2=1\text{ and }y_2=2\text{ in the formula.}[/tex][tex]AC=\sqrt{(1-(-3))^2+(2-2)^2}[/tex][tex]AC=\sqrt{(4)^2+(0)^2}[/tex][tex]AC=4[/tex]We get h=AB=5 and b=AC=4.
Consider the area of the triangle formula.
[tex]A=\frac{hb}{2}[/tex]Substitute h=5 and b=4 in the formula.
[tex]A=\frac{5\times4}{2}[/tex][tex]A=10units^2[/tex]Final answer:
[tex]A=10units^2[/tex]Find the slope of each line.
First find the coordinates of the points
(-3, -1) and (3, 3)
The formula for calculating slope is;
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]From the coordinates;
x₁ = -3
y₁=-1
x₂=3
y₂=3
substitute the values into the formula
[tex]\text{slope =}\frac{3+1}{3+3}[/tex][tex]=\frac{4}{6}[/tex][tex]=\frac{2}{3}[/tex]