Answer:
480 miler per hour
Explanation:
The speed of an object is defined as
[tex]speed\text{ = }\frac{distance\text{ covered}}{time\text{ taken}}[/tex]Now in our case, we are told that
distance
What association does the scatter plot show? у 13 12 11 |-10 9 7. 6 5 4 3 2. 1 1 2 3 4 5 6 7 8 9 10 11 12 13 .
The given scatter plot doesn't shows any association because the points are too dispersed.
Hence, the answer is C. no association.You bought 7 pencils for $2.45. Your friend bought 9 pencils for $3.15. Write an equation in POINT-SLOPE Form to model the total bill (y) in terms of the number of pencils purchased (x).
We can say that we have two points of the graph: (7, 2.45) and (9,3.15)
therefore we can calculate the slope of the function
[tex]m=\frac{3.15-2.45}{9-7}=\frac{0.7}{2}=0.35[/tex]so the equation is
[tex]\begin{gathered} y-2.45=0.35(x-7) \\ y=0.35x-2.45+2.45=0.35x \end{gathered}[/tex]In conclusion we have that the equation is
[tex]y=0.35x[/tex]a cylinder has a volume of approximately 942.48 ft cubed. The height of the cylinder is 12 feet. What is the diameter of the cylinder?
To calculate the volume of a cylinder you have to use the following formula:
[tex]V=\pi r^2h[/tex]Where
V is the volume
r is the radius
h is the height
If we know the value of the volume and the height of the cylinder, we can calculate its radius.
First, let's write the formula in terms of r, that is, isolate r in one side of the expression and all other terms on the other side.
Pi and h are multiplying r, to cancel this multiplication you have to divide it by the same number, that is pi*h. And to keep the equality valid, what's done to one side of the equation has to be done to the other side, so divide the volume by pi*h too
[tex]\begin{gathered} \frac{V}{\pi h}=\frac{\pi hr^2}{\pi h} \\ \frac{V}{\pi h}=r^2 \end{gathered}[/tex]Next, calculate the square root to both sides of the expression to determine it for r
[tex]\begin{gathered} \sqrt[]{\frac{V}{\pi h}}=\sqrt[]{r^2} \\ \sqrt[]{\frac{V}{\pi h}}=r \end{gathered}[/tex]Now that we have an expression to calculate the radius, replace it with the given values of volume and height
V=942.48 ft³
h= 12ft
[tex]\begin{gathered} r=\sqrt[]{\frac{942.48}{12\pi}} \\ r=5 \end{gathered}[/tex]The radius of the cylinder is 5ft, the diameter is by definition twice the radius so
[tex]\begin{gathered} d=r\cdot2 \\ d=5\cdot2 \\ d=10 \end{gathered}[/tex]The diameter of the cylinder is 10ft
find the domain of the function defined in the picture .state answer in interval form.
We will determine the domain of the function as follows:
[tex]\frac{x+7}{x^2-11x+24}=\frac{x+7}{(x-3)(x-8)}[/tex]So, the domain is the following:
[tex]D=\mleft(-\infty,3\mright)\wedge(3,8)\wedge(8,\infty)[/tex]**Explanation***
In order to determine the domain of the function, we factor the denominator and evaluate at which points the denominator will become zero. [When this happens the function is not defined and thus those values do not belong in the domain].
When we factor the denominator, we obtain:
[tex]x^2-11x+24=(x-3)(x-8)[/tex]So, we equal the factor to zero and find which points do not belong in the domain:
[tex](x-3)(x-8)=0\Rightarrow\begin{cases}x=3 \\ x=8\end{cases}[/tex]So, the equation "makes sense" in all of the real numbers, except when x = 3 and x = 8.
Maggie made a scale drawing of a city park. She used the scale 1 centimeter = 1 meter. What is the scale factor of the drawing?Simplify your answer and write it as a ratio, using a colon.
The ratio is the following:
1m:100cm
I need to use the buying binomial distribution formulaI need to find A)Probability 4successesB) Probability 2 successesC) Probability at most 3 successes( HINT When you are finding P( at most 3 successes you need = P(x ≤3)= P(x= 0) + P(x = 1)+ P(x = 2)+ P(x = 3)You need to solve each one individually with the binomial distribution formula then add sum of x=0 + sum of x=1+ sum x=2 + x=0PLEASE HELP ME With EXERCISE ASAP GED PRACTICE Please look at picture for exercise
Given:
There are number of trials and possibility of success
Required:
We need to find the probability by binomial distribution formula
Explanation:
A)
n=15
p=0.4
q=0.6
x=4
Substitute the values in the formula
[tex]P(4)=\frac{15!}{11!4!}(0.4)^4(0.6)^{11}=0.12[/tex]B)
n=12
p=0.2
q=0.8
x=2
Substitute the values in the formula
[tex]P(2)=\frac{12!}{10!2!}(0.2)^2(0.8)^{10}=0.28[/tex]C)
n=20
p=0.05
q=0.95
x=0,1,2,3
Substitute the values in the formula
[tex]\begin{gathered} P(0)=\frac{20!}{20!0!}(0.05)^0(0.95)^{20}=0.35848 \\ \\ P(1)=\frac{20!}{19!1!}(0.05)^1(0.95)^{19}=0.37735 \\ \\ P(2)=\frac{20!}{18!2!}(0.05)^2(0.95)^{18}=0.18867 \\ \\ P(3)=\frac{20!}{17!3!}(0.05)^3(0.95)^{17}=0.0.05958 \end{gathered}[/tex]Now add all
[tex]P(atmost\text{ 3\rparen}=0.98408[/tex]Final answer:
A) 0.12
B) 0.28
C) 0.98408
f(x+h)-f(x)Find the difference quotienthwhere hx0, for the function below.f(x) = -x + 2Simplify your answer as much as possible.[(x + n) - (*)D음h
Given:
[tex]f\mleft(x\mright)=-x^2+2[/tex]Hence, f(x+h) will be;
[tex]\begin{gathered} f(x+h)=-(x+h)^2+2 \\ =-(x^2+2xh+h^2)+2 \\ f(x+h)=-x^2-2xh-h^2+2 \\ \end{gathered}[/tex]The difference quotient of the function will be;
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h} \\ \text{SUbstituting f(x) and f(x+h) in the above formula;} \\ =\frac{-x^2-2xh-h^2+2-(-x^2+2)}{h} \\ =\frac{-x^2-2xh-h^2+2+x^2-2}{h} \\ =\frac{-x^2+x^2-2xh-h^2+2-2}{h} \\ =\frac{-2xh-h^2}{h} \\ \text{Factorizing the common factor out;} \\ =\frac{h(-2x-h)}{h} \\ \frac{f(x+h)-f(x)}{h}=-2x-h \end{gathered}[/tex]Therefore, the difference quotient is;
[tex]\frac{f(x+h)-f(x)}{h}=-2x-h[/tex]Hector's Family Travel 5/8 of the distance to his grandmother's house on Saturday they travel 2/3 ot the remaining distance on Sunday what fraction of the total distance to his grandmother's house was traveled on Sunday
Answer
The fraction of the total distance to his grandmother's house that was travelled on Sunday = ¼
Explanation
Let the whole distance be x
Hector's family travelled (5/8) of the distance to his grandmother's house on Saturday. That is, they travelled (5x/8)
The remaining distance = x - (5x/8) = (3x/8)
They then travelled (2/3) of the remaining distance on Sunday
(2/3) of the rest = (2/3) × (3x/8) = (x/4)
So,
The fraction of the total distance to his grandmother's house that was travelled on Sunday = ¼
Hope this Helps!!!
which of the following represents the characteristic is of the graph x greater than -9
First we need to graph the inequality
because we have ≥ this is a close circle
the shade will be in the right position
1) find the slope of the line tangent to f(x)=6/sq(x) at point (9,2)
First, we need to find the first derivate
[tex]\begin{gathered} f^{}(x)=6x^{-\frac{1}{2}} \\ f^{\prime}(x)=-\frac{1}{2}6x^{-\frac{1}{2}-1}=-3x^{-\frac{3}{2}}=-\frac{3}{\sqrt[]{x^3}} \end{gathered}[/tex]Plug x value of the indicated point into f '(x) to find the slope at x.
[tex]f^{\prime}(9)=-\frac{3}{\sqrt[]{9^3}}[/tex][tex]f^{\prime}(9)=-\frac{1}{9}[/tex]the slope of the line is -1/9
the slope of the tangent line is the inverse of -1/9
the slope of the tangent line is 9
using the distributive property simplify the expression to determine the cost 5(18+3x)= +
5(18+3x)= ( 5 x 18 ) + ( 5 X 3x )
Scalene triangle Isosceles triangle Equilateral triangle (a) T(-8,3), R(-1,0), 1(-1,6) (b) P (2,0), Q(-1, -2), R(2, 6) (c) J(0, 2), K (1,8), L(-5, 8)
The first row is Isosceles
The second row is Scale
The third one es equilateral
what does the value of x have to be to make the lines parallel A. x=14B. x=17C. x=10D x=12
Angle 4 and 5 are alternate interior angles. Therefore, as the horizontal lines are parallel, they will have the same measure.
Then, we can write:
[tex]\begin{gathered} m\angle4=m\angle5 \\ 4x-17=5x-29 \\ 4x-5x=-29+17 \\ -x=-12 \\ x=12 \end{gathered}[/tex]Answer: In order for the angle to have the same measure, then the value for x is x=12.
NOTE: angle 4 is vertical angle with angle 1, which is corresponding to angle 5. Thats why 4 and 5 have the same measure.
What are the domain and range of this relation? 4 2 3 2 1 -5 -3 - 2 -1 0 1 2 3 4 5 -2 -3 --5 Write the numbers in the domain and range with commas between them 3}). Domain: 1
According to the given graph, the relation is (-3, -5), (-1, -4), and (4, 5).
The domain would be all the x-values and the range would be all the y-values.
Therefore, the sets are[tex]\begin{gathered} D\colon\mleft\lbrace-3,-1,4\mright\rbrace \\ R\colon\mleft\lbrace-5,-4,5\mright\rbrace \end{gathered}[/tex]what is 5 3/8 - 1 1/3
Answer
5 3/8 - 1 1/3 = 4 1/24
5 (3/8) - 1 (1/3) = 4 (1/24)
Explanation
The key to solving expressions involving mixed fractions is to convert them to improper fractions first.
5 3/8 = (43/8)
1 1/3 = (4/3)
So,
5 3/8 - 1 1/3 = (43/8) - (4/3)
So, we take the LCM of the denominators, 3 and 8
[tex]\frac{43}{8}-\frac{4}{3}=\frac{129-32}{24}=\frac{97}{24}=4\frac{1}{24}[/tex]Hope this Helps!!!
When Mc.Donalds opened their shakes cost 0.20. today they cost 2.19 what is the percent change?
Let's use the following formula:
[tex]\text{Percent change=}\frac{V2-V1}{V1}\times100[/tex]Where:
V1 = Old value
V2 = New Value
In this case.
Old value = 0.2
New Value = 2.19
Therefore:
[tex]\begin{gathered} \text{Percent change=}\frac{2.19-0.2}{0.2}\times100 \\ \text{Percent change=}9.95\times100 \\ \text{Percent change=}995 \end{gathered}[/tex]Answer:
995%
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.A business owner wants to have the front window of her store painted and is considering two artists for the job. Lena has quoted a flat rate of $191 for the job. Cara's quote is $20 per hour, plus $31 to cover the cost of materials. Depending on how long it takes Cara to paint the window, these two could end up charging the same amount. How long would Cara have to take? How much would it cost?
Given:
A business owner wants to have the front window of her store painted and is considering two artists for the job.
First, Lena has quoted a flat rate of $191 for the job.
so, y = 191
Second, Cara's quote is $20 per hour, plus $31 to cover the cost of materials.
So, y = 20x + 31
where x is the number of hours
so, we have the following system of equations:
[tex]\begin{gathered} y=191\rightarrow(1) \\ y=20x+31\rightarrow(2) \end{gathered}[/tex]solve using substitution,
so substitute with (y) from equation (1) into equation (2)
[tex]191=20x+31[/tex]Solve the equation to find (x)
[tex]\begin{gathered} 20x=191-31 \\ 20x=160 \\ x=\frac{160}{20}=8 \end{gathered}[/tex]so, the answer will be:
The number of hours = 8 hours
and the cost will be $191
Which division problem does the number line below best illustrate?A number line going from 0 to 2. Arrows go from 0 to 2, from 2 to 4, from 4 to 6, from 6 to 8, and from 8 to 10.10 divided by 2 = 515 divided by 3 = 550 divided by 5 = 1020 divided by 10 = 2
We have the following:
The answer is:
[tex]\frac{10}{2}=5[/tex]This is the answer because there are 5 parts divided into 2 units.
A. 10 divided by 2 = 5
Describe all numbers x that are at a distance of 1 from the number 8 . Express this using absolute value notation. The answer field below uses the symbol mode option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then = , the symbol mode will automatically convert that to ≤ . In the same way, if you type in > and then = , the symbol mode will automatically convert that to ≥ .
To solve this, let's think about what are the numbers that are at a distance of 1 from 8. We can take 8 and:
[tex]\begin{gathered} 8+1=9 \\ . \\ 8-1=7 \end{gathered}[/tex]Those are the only two numbers that verify the asked. Now we need to express it using absolute value notation. If two numbers are at a certain 'distance', this means that their difference is that 'distance'. Since we want the distance between a number x and 8 to be 1, we can write:
[tex]\begin{gathered} x-8=\pm1 \\ \\ \end{gathered}[/tex]Because:
[tex]\begin{gathered} 7-8=-1 \\ . \\ 9-8=1 \end{gathered}[/tex]And we can write this plus-minus sign using absolute value:
[tex]|x-8|=1[/tex]Thus, the answer is:
[tex]|x-8|=1[/tex]I need to send picture in session
We need variables to one side and numbers to another, so the first step is to take numbers to left side.
For that, we need to add to both sides.
Next, we will be left with 9x equal some number.
To isolate x, we got to divide both sides by 9.
So, this is the second step.
If we look at the answer choices, we see
fourth answer choice is right
if T is the midpoint of SU findthe values of X and ST the diagram is not drawn to scale.
Problem
Solution
For this problem we know that T is the mudpoint of SU , so then we need to satisfy this equation:
ST + TU= SU
From the figure given we can set up the equation like this:
ST=TU
8x= 5x
State the transformation that makes these different from the parent function, y = xy=2x-2
Answer:
*It has a vertical translation 2 units down.
*Horizontal compression by a factor of 2.
[tex](\frac{x}{2},y-2)[/tex]Step-by-step explanation:
To solve this situation we can use the transformation rules for function, remember these transformations:
*Vertical translation down d units is given by: f(x)-d
*Horizontal compression for b greater than 1 is given by: f(bx)
Therefore, for the following function:
[tex]y=2x-2[/tex]The transformations that make the function above different from the parent function y=x:
*It has a vertical translation 2 units down.
*Horizontal compression by a factor of 2.
What is the equation in slope-intercept form of the line that passes through the point (-1, -1)and is perpendicular to the line represented by y = 1/2x + 5?A. y = -2x - 1B. y = -2x - 3C. y = 1/2x - 3D. y = 1/2x + 1
since we know that the slope of the other line is 1/2, we deduce that the slope of the line that we need to find is -2
then applyind the point-slope formula to the point (-1,-1), the line will be
[tex]y+1=-2(x+1)\Rightarrow y=-2x-3[/tex]Then the answer will be B.
Identify all pairs of lines that appear to be perpendicular D.q,sE. p,mF. q,k
The rest of the options are:
A. k,m
B. k,s
C. q,s
Two pairs of lines are perpendicular when the form to each other an angle of 90 degrees or a right angle.
In this case:
A. The lines k and m appear to form a right angle. They appear to be perpendicular.
B. The lines k and s are not forming a right angle.
C. D. The lines q and s appear to be perpendicular. They appear to form a right angle.
E. The lines p and m do not seem to form a right angle, so they are not perpendicular.
F. The lines q and k do not seem to form a right angle. They are not perpendicular.
Then, the correct answers are A, C, D.
Determine the value of y, if x is 4. y = x + 11
The equation given in the question is,
[tex]y=x+11[/tex]Put 4 for x implies,
[tex]\begin{gathered} y=4+11 \\ y=15 \end{gathered}[/tex]Therefore, the value of y is 15.
If f (x) = 2 + x and g(x) = 3 - X, what is gof(-1) ?206-4
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f (x) = 2 + x
g(x) = 3 - x
gof(-1) = ?
Step 02:
gof(x) = 3 - (2 + x)
= 3 - 2 - x
= 1 - x
gof(-1) = 1 - (-1)
= 1 + 1
= 2
The answer is:
gof(-1) = 2
The volumes of these two cylinders are __.If another cross-section is taken at a different height, the areas of the cross sections will __ be equal.
Notice that both flat surfaces of the cylinders are parallel. Both cylinders have the same radius and the same height, although they don't have the same slant surface.
Nevertheless, since the flat surfaces are parallel, cross sections taken at any height will always result in equal shapes.
Therefore, the volumes of these two cylinders are equal and if another cross section is taken at a different height, the areas of the cross sections will always be equal.
If a sample of gas goes from a temperature of 35 degrees Celsius to a temperature of 100 degrees Fahrenheit, will the average speed of the gas particles (atoms) increase or decrease
In order to being able to compare the temperatures, we want to convert any of the two temperatures of the gas:
35 C and 100 F
so we can have both temperatures in degrees Celsius (C) or both in degrees Fahrenheit (F).
We are going to convert the second to degrees Celsius using following the formula of conversion:
[tex]\frac{5(F-32)}{9}=C[/tex]We want to know how many degrees C correspond to 100F. Then, we just replace it in the equation:
[tex]\begin{gathered} \frac{5(F-32)}{9}=C \\ \frac{5(100-32)}{9}=C \\ \frac{5(68)}{9}=C \\ \frac{340}{9}=C \\ 37.78=C \end{gathered}[/tex]This means that the sample of gas goes from 35° C to 37.78° C. Then, the average speed of the gas particles (atoms) increased
Suppose a $120 pair of Jordan's were now on sale for 20% off. Find the sale price. *
The original price is $120.
The discount is 20% of the original price, that is,
discount = $120x20% = $24
The sale price is calculated as follows:
sale price = original price - discount
sale price = $120 - $24
sale price = $96
Select the equation of the line that passes through the point (3, -1) and is parallel to the line on the graph. y=3y= 3x - 1y=x-1y = -1
ANSWER
y = -1
EXPLANATION
We want to find the line that passes through (3, -1) and is parallel to the line given.
The general form of a linear equation is given as:
y = mx + b
where m = slope
b = y intercept.
The given line is a horizontal line. A horizontal line is given as:
y = b
This means that the slope is 0.
Therefore, since the line we need is parallel to this, it means that its slope is also 0.
Now, we can find the equation of the line using point-slope method. To do that we have:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through
Therefore, since the line passes through (3, -1), we have that the equation is:
y - (-1) = 0(x - 3)
=> y + 1 = 0
=> y = -1
That is the equation of the line.