We know that RT=36 and that RS=2x+3 and ST=7x+6. We notice that
[tex]RT=RS+ST[/tex]Then, plugging the corresponding values and expressions we have
[tex]36=(2x+3)+(7x+6)[/tex]Solving this equation for x,
[tex]\begin{gathered} 36=(2x+3)+(7x+6) \\ 36=2x+3+7x+6 \\ 36=9x+9 \\ 36-9=9x \\ 27=9x \\ x=\frac{27}{9} \\ x=3 \end{gathered}[/tex]Then te value of x is 3.
Once we have the value of x we are able to find the value of RS and ST, we just have to substitute said value in the expressions. Then
[tex]\begin{gathered} RS=2(3)+3=6+3=9 \\ ST=7(3)+6=21+6=27 \end{gathered}[/tex]Therefore RS=9 and ST=27.
Assume that each circle shown below represents one unit. Express the sha amount as a single fraction and as a mixed number. One Fraction: Mixed Number:
The shaded portions for the first three circles are a total of 15 while for the fourth one is 1. As a fraction it is therefore,
[tex]\frac{16}{5}[/tex]As mixed numbers it is;
[tex]3\frac{1}{5}[/tex]The administrator at your local hospital states that on weekends the average wait time for emergency room visits is 11 minutes. Based on discussions you have had with friends who have complained about how long they wait to be seen in the ER over a weekend, you dispute the administrator's claim. You decide to test your hypothesis. Over the course of a few weekends, you record the wait time for 28 randomly selected patients. The average wait time for these selected patients is 12 minutes with a standard deviation of 2.5 minutes. Do you have enough evidence to support your hypothesis that the average ER wait time is longer than 11 minutes? Conduct your test with a 5% level of significance.
This is a hypothesis test for the population mean.
The claim is that on weekends the average wait time for emergency room visits is more than 11 minutes.
Then, the null and alternative hypothesis are:
[tex]\begin{gathered} H_0\colon\mu=11 \\ H_a\colon\mu>11 \end{gathered}[/tex]The significance level is 0.05.
The sample has a size n=28.
The sample mean is M=12.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.5.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2.5}{\sqrt{28}}=0.4725[/tex]Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{12-11}{0.4725}=\dfrac{1}{0.4725}=2.117[/tex]The degrees of freedom for this sample size are:
[tex]df=n-1=28-1=27[/tex]This test is a right-tailed test, with 27 degrees of freedom and t=2.117, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>2.117)=0.0218[/tex]As the P-value (0.0218) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
Conclusion: at a significance level of 0.05, there is enough evidence to support the claim that, on weekends, the average wait time for emergency room visits is more than 11 minutes.
Explain how rays AB and AC form both a line and an angle.
Answer:
The point from C goes straight until it reaches A and stull continues till it gets ti B and stops. The angle is then given as 180°
Louis borrowed $500 from his bank. His bank will charge Louis 8% simple interest per year to loan him the money. If he paid back the total amount he owed the bank, including interest, in 6 months, how much should he have paid?
The amount that he owed the bank and paid is $520.
What will the interest be?The simple interest is calculated as:
= Principal × Rate × Time / 100
Principal = $500
Rate = 8%
Time = 6 months = 6/12 = 0.5 years
The interest will be:
= PRT / 100
= (500 × 8 × 0.5)/100
= 2000/100
= $20
The amount paid back will be:
= Principal + Interest
= $500 + $20
= $520
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Which ordered pair is a solution to the equation? y=7x-3 O only (14) O neither only (-1,-) both (1, 4) and (-1,-4)
The givenn equation can be written as
[tex]\begin{gathered} 7x-y=3 \\ On\text{ substituting (1,4) in the left hand side of the equation we get:-} \\ 7-4=3 \\ \text{which is equal to RHS} \end{gathered}[/tex][tex]\begin{gathered} \text{Now substitute (-1,-4) in LHS of the equation} \\ -7+4=-3 \\ \text{which is not equal to RHS.} \end{gathered}[/tex]Hence only (1,4) satisfies the given equation.
So the correct option is the first one (1,4).
in slope intercept form what is the line perpendicular to y=2x -5 that passes through the (2, -5) point
The most appropriate choice for equation of line in slope intercept form will be given by-
[tex]y = -\frac{1}{2}x - 4[/tex] is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
The given equation of line is y = 2x-5
Slope of this line = 2
Slope of the line perpendicular to this line = [tex]-\frac{1}{2}[/tex]
The line passes through (2 , -5)
Equation of the required line = [tex]y - (-5) = \frac{1}{2}(x - 2)[/tex]
[tex]y +5=-\frac{1}{2}x+1\\y = -\frac{1}{2}x +1 -5\\y = -\frac{1}{2}x -4[/tex]
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The volume of a rectangular prism is 2 x cubed + 9 x squared minus 8 x minus 36 with height x + 2. Using synthetic division, what is the area of the base?
The base area of the prism is 2x² + 5x - 18
How to determine the area of the base?From the question, the given parameters are
Volume = 2 x cubed + 9 x squared minus 8 x minus 36
Height = x + 2
Rewrite properly as
Volume = 2x³ + 9x² - 8x - 36
Height = x + 2
The base area is calculated as
Base area = Volume/Height
Using the synthetic division, we have
Set the divisor to 0
x + 2 = 0
This gives
x = -2
So, we have the representation to be
-2 | 2 9 - 8 - 36
Write out 2
So, we have
-2 | 2 9 - 8 - 36
2
Multiply 2 and -2
This gives
-2 | 2 9 - 8 - 36
-4
2
So, we have
-2 | 2 9 - 8 - 36
-4
2 5
Repeat the process
So, we have
-2 | 2 9 - 8 - 36
-4 -10
2 5 -18
Repeat the process
So, we have
-2 | 2 9 - 8 - 36
-4 -10 36
2 5 -18 0
This means that
Base area = 2x² + 5x - 18
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Calculate Sy for the arithmetic sequence in which ag = 17 and the common difference is d =-21.O A -46O B.-29.2O C. 32.7O D. 71.3
Given: An arithmetic sequaence has the following parameters
[tex]\begin{gathered} a_9=17 \\ d=-2.1 \end{gathered}[/tex]To Determine: The sum of the first 31st term.
Please note that the sum of the first 31st term is represented as
[tex]S_{31}=\text{ sum of the first 31st term}[/tex]The formula for the finding the n-term of an arithmetic sequence (AP) is
[tex]\begin{gathered} a_n=a+(n-1)d \\ \text{Where} \\ a_n=n-\text{term} \\ a=\text{first term} \\ d=\text{common difference} \end{gathered}[/tex]Since, we are given the 9th term as 17, we can calculate the first term a, as shown below:
[tex]\begin{gathered} a_9=17 \\ \text{Substituting into the formula} \\ a_9=a+(9-1)d \\ a_9=a+8d \\ \text{Therefore:} \\ a+8d=17 \\ d=-2.1 \\ a+8(-2.1)=17 \\ a-16.8=17 \\ a=17+16.8 \\ a=33.8 \end{gathered}[/tex]Calculate the sum of the first 31st term.
The formula for finding the first n-terms of an arithmetic series is given as
[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]We are given the following:
[tex]a=33.8,n=31,d=-2.1[/tex]Substitute the given into the formula:
[tex]\begin{gathered} S_{31}=\frac{31}{2}(2(33.8)+(31-1)-2.1) \\ S_{31}=15.5(67.6)+(30)-2.1) \\ S_{31}=15.5(67.6-63) \end{gathered}[/tex][tex]\begin{gathered} S_{31}=15.5(4.6) \\ S_{31}=71.3 \end{gathered}[/tex]Hence, the sum of the first 31st term of the A.P is 71.3, OPTION D
A. The measure of the angle can not be determined B. 70 degreesC. 110 degreesD. 180 degrees
Okay, here we have this:
Considering the provided graph, we are going to find the measure of the angle "3", so we obtain the following:
Since angle 3 and 4 form a straight angle, that is to say that these two angles are supplementary, then we have:
[tex]\begin{gathered} m\angle3+m\angle4=180 \\ m\angle3+70=180 \\ m\angle3=180-70 \\ m\angle3=110\text{ degre}es \end{gathered}[/tex]Finally we obtain that the correct answer is the option C.
which of the following lines are parallel, skew, intersection, or none of these.
Parallel lines are lines that have the same direction and there is always the same distance between them
Skew lines are lines that are not on the same plane (they are not coplanar) and also they do not intersect.
Intersecting lines are lines that cross at a point, they can be on the same plane or on different planes.
Let's analyze the parts of this problem.
DE and AB.
These two lines are shown in red and blue in the following diagram:
These are not parallel lines because one line is vertical and the other line is horizontal. They are also not intersecting lines because they do not cross at any point. Lines DE and AB are skew lines because they do not intersect and they are on different planes.
--> DE and AB --> skew
CB and
Retest: ProbabilityFor problems 1-3: Johnny Awesome has three red marbles, two blue marbles, five green marbles, and 7 yellowmarbles in a bag. What is the probability that'Johnny.....3) draws a blue marble, does not replace it, and then draws a green marble?
Answer
5/136
Step-by-step explanation
Events
• A: a blue marble is drawn
,• B: without replacing the first marble, a green marble is drawn
There are 17 (= 3 + 2 + 5 + 7) marbles in total in the bag. Two of them are blue, then the probability of drawing a blue marble is:
[tex]P(A)=\frac{2}{17}[/tex]After a blue marble is drawn, 16 marbles are left in the bag. Five of them are green, then the probability of drawing a green marble is:
[tex]P(B)=\frac{5}{16}[/tex]Finally, the probability of drawing a blue marble and then a green marble without replacement is:
[tex]\begin{gathered} P(A\text{ and }B)=P(A)\cdot P(B) \\ P(A\text{ and }B)=\frac{2}{17}\cdot\frac{5}{16} \\ P(A\text{ and }B)=\frac{5}{136} \end{gathered}[/tex]what is the answer help pls
Answer:
1 ½ feet
Step-by-step explanation:
The shortest lizard is ½ a feet
The longest lizard is 2 feet
To find the difference in length:
2-½ = 1½ feet
I need help with geometry!
Basic geometry are formulars and properties of basic shapes like rectangle, square, circle, triangle, and solid shapes like cuboid, cube cylinder etc.
The area, perimeter and volume of solid shape are properties that can be determined from this shape.
Perimeter is the sum of the whole side of the figure. Example the perimeter of a rectangle with 2 length and 2 width can be calculated by adding the whole 2 length and width.
The perimeter of the rectangle above is by adding all the sides.
perimeter = 4 + 4 + 2 + 2 = 12 cm
The area of the figure below is the amount of space of the boundary. The area of the rectangle below is length * width = 4 * 2 = 8 cm squared.
Solve for x: 4 open parentheses 2 x minus 1 close parentheses plus 8 minus 14 x equals negative 8 x plus 4 plus 2 x The solution is X = _________
Answer:
x = 1
Step-by-step explanation:
4(2x-1)+8-14= -8x+ 4+ 2x
THIS IS URGENT
A line includes the points (2,10) and (9,5). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
Step-by-step explanation:
y = 13x -12
Identify an equation in point slope form for the line perpendicular to y=1/4 x-7that passes through -2,-6
The equation in the point slope form for the line perpendicular to y = (1/4)x-7 that passes through the point (-2,-6) is y+6 = -4(x+2)
The given equation of the perpendicular line
y = (1/4)x -7
The equation is in the slope intercept form of the line
y = mx+b
Where m is the slope of the line
By comparing the given equation with the slope intercept form
The slope of the line m = 1/4
The slope of its perpendicular line = -1/m
= -4
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
The point is given that (-2,-6)
Substitute these values in the equation
(y-(-6) = -4(x-(-2)
y+6 = -4(x+2)
Hence, the equation in the point slope form for the line perpendicular to y = (1/4)x-7 that passes through the point (-2,-6) is y+6 = -4(x+2)
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Uptown Tickets charges $7 per baseball game tickets plus a $3 process fee per order. Is the cost of an order proportional to the number of tickets ordered?
The cost of an order is proportional to the number of tickets if the relation between them is constant.
Then, if we order 1 ticket the cost will be $7 + $3 = $10
And if we order 2 tickets, the cost will be $7*2 + $3 = $17
So, the relation between cost and the number of tickets is:
For 1 ticket = $10 / 1 ticket = 10
For 2 tickets = $17/ 2 tickets = 8.5
Since 10 and 8.5 are different, the cost of an order is not proportional to the number of tickets ordered.
Answer: they are not proportional
can you help me please
1. Write the value of the digit in the hundreds place and the value of the digit in the tens place in 440. What is the relationship between the values of those two digits? The ___ in the in the hundreds place has a value _____ times as great as the____in the ____ place.
The ___ in the in the hundreds place has a value _____ times as great as the____in the ____ place.
• We have 440
,• 400 + 40
,• Four hundreds + four tens
The relationship between the values of these two digits is that they are the same, but the four in the hundreds place has a value ten times as great as the four in the tens place.
Determine the rate of change of a line that passes through the coordinates G (-13, -4) andB (7, -12). Reduce when necessary. (Show all work)
EXPLANATION:
-We must first identify the points that correspond to the x-axis and the points that correspond to the y-axis.
-To calculate the slope, then we apply the formula of the slope or rate of change which is the following:
[tex]\begin{gathered} \text{the rate of change :} \\ m=\frac{y2-y1}{x2-x1}\text{ } \end{gathered}[/tex]-now we must correctly locate the points in the formula.
[tex]\begin{gathered} G\text{ }(-13,-4),\text{ X1}=-13\text{ and y1}=-4 \\ B(7,-12);\text{ X2}=7\text{ and y2}=-12 \\ m=\frac{-12-(-4)}{7-(-13)}\text{ }=\frac{-12+4}{7+13}=\frac{-8}{20}=\frac{-4}{10} \\ simplify;\text{ }\frac{-4}{10}=\frac{-2}{5} \end{gathered}[/tex]-
Tan (a) cos (a)= sin (a)Trig: use trigonometric identities to transform the left side of the equation into the right side
hello
the question here relates to trionometric identies and we can easily solve this once we know some of the identities
for example
[tex]undefined[/tex]Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
The amount by which the cost of 1 liter of permimum gasoline is greater is $0.43.
By how much is permimum gasoline greater?The first step is to determine the cost of 1 liter of each type of gasoline. In order to determine the cost of 1 liter, divide the total cost by the number of liters of gasoline bought.
Cost of 1 liter of gasoline = total cost / total liters bought
Cost of 1 liter of regular gasoline = $58.98 / 25 = $2.36
Cost of 1 liter of permimum gasoline = $69.73 / 25 = $2.79
Difference in price = $2.79 - $2.36 = $0.43
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Find the slope of the line that passes through (9, 9) and (6, 7)
The slope of the line passing through the coordinates (9, 9) and (6, 7) is 2/3.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 9, 9 )
x₁ = 9y₁ = 9Point 2( 6, 7 )
x₂ = 6y₂ = 7To determine the slope, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 7 - 9 )/( 6 - 9 )
Slope m = ( -2 )/( -3 )
Slope m = ( 2 )/( 3 )
Slope m = 2/3
Therefore, the slope of the line is 2/3.
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The slope of the required line is 2/3 which passes through points (9, 9) and (6, 7).
What is the slope of the line?The slope is simply expressed as an inclination of the line in the coordinate system.
Slope m = (y₂ - y₁) / (x₂ - x₁)
Given that the line that passes through two points (9, 9) and (6, 7)
Let x₁ = 9, y₁ = 9 and x₂ = 6, y₂ = 7
The slope of the required line is
m = (y₂ - y₁ )/( x₂ - x₁ )
Substitute the values in the formula to get the slope of the line,
m = ( 7 - 9 )/( 6 - 9 )
m = ( -2 )/( -3 )
m = ( 2 )/( 3 )
m = 2/3
Therefore, the slope of the line would be 2/3.
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can (x^4y)^(2/3) be simplified yes or no
Answer:
yes
we are need multiple the exponents in (x^4y)^(2/3).
[tex]x \frac{8y}{3} [/tex]
so hope it help
Answer:
[tex]x^\frac{8}{3} y^\frac{2}{3}[/tex]
Step-by-step explanation:
I'm not sure if you mean
[tex](x^4y)^\frac{2}{3}[/tex]
or
[tex](x^{4y})^\frac{2}{3}[/tex]
but I'll go with the first one
[tex](x^4y)^\frac{2}{3}[/tex]
(distribute the 2/3) (if the y is by it self, it basically is [tex]y^1[/tex])
[tex]x^\frac{8}{3} y^\frac{2}{3}[/tex]
done
Which of these describes the transformation of triangle ABC shown below?A) reflection across the x-axisB) reflection across the y-axisC) reflection across the line y=xD) translation
From the figure, we have the coordinates of the vertices:
ABC ==> A(2, 1), B(5, 1), C(1, 5)
A'B'C' ==> A'(-2, 1), B'(-5, 1), C(-1, 5)
Let's determine the type of transformation that occured here.
Apply the rules of rotation.
For a rotation acorss the y-axis, only the x-coordinates of the points will change to the opposite. i.e from negative to positive or from positive to negative.
For a rotation across the y-axis, we have:
(x, y) ==> (-x, y)
From the given graph, we can see that the only the x-coordinates changed from positive to negative.
Therefore, the transformation that occured here is the reflection across the y-axis.
ANSWER:
B) Reflection across the y-axis.
Suppose that the future price p(t) of a certain item is given by the following exponential function. In this function, p(t) is measured in dollars and t is the number of years from today. p(t) = 3000 * (1.019) ^ t
The growth or decay of an original quantity C that increases or decreases in a p% per year after t years is given by the following equation:
[tex]p(t)=C\cdot(1\pm\frac{p}{100})^t[/tex]If the quantity increases (i.e. it growths) we use the + symbol inside the parenthesis. If the quantity decreases we use the - symbol. This implies that for a growth the term that is raised to t is greater than 1 and for a decay that term is smaller than 1.
Now let's compare that generic equation with the function given by the question:
[tex]3000\cdot(1.019)^t=C\cdot(1\pm\frac{p}{100})^t[/tex]One of the first things you can notice is that C=3000 which means that the initial price was $3000. Just to be sure that this is correct we can evaluate p(t) at t=0:
[tex]p(0)=3000\cdot(1.019)^0=3000[/tex]So the initial price was $3000.
Now let's compare the terms inside parenthesis that are raised to t:
[tex]1.019=1\pm\frac{p}{100}[/tex]As I stated before, if the term raised to t is greater than 1 then we are talking about a growth. 1.019 is greater than 1 so this function represents a growth. What's more, in the right side of the equation we must use the + symbol. This way we have an equation for the yearly percentage of change of the price:
[tex]1.019=1+\frac{p}{100}[/tex]We can substract 1 from both sides of this equation:
[tex]\begin{gathered} 1.019-1=1+\frac{p}{100}-1 \\ 0.019=\frac{p}{100} \end{gathered}[/tex]And we multiply both sides by 100:
[tex]\begin{gathered} 100\cdot0.019=\frac{p}{100}\cdot100 \\ 1.9=p \end{gathered}[/tex]So each year the price increases in a 1.9%.
AnswerThen the answers in order are:
$3000
growth
1.9%
The function y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-1 and x=0. Use the line segment to determine the average rate of change of the function f(x) on the interval −1≤x≤0
Answer:
Aveage Rate of cCanege = 40
Explanation:
The line segment is drawn in the function below:
Using the line segment:
[tex]\begin{gathered} \Delta x=0-(-1)=1 \\ \Delta y=40-0=40 \end{gathered}[/tex]Therefore, the average rate of change will be:
[tex]\text{ Average Rate of Change}=\frac{\Delta y}{\Delta x}=\frac{40}{1}=40[/tex]The average rate of change is 40.
What is the slope and y-intercept?
Answer/Step-by-step explanation:
y = mx + b
Slope = m
y₂ - y₁
---------- = m
x₂ - x₁
----------------------------------------------------------------------------------------------------------
y - intercept = b
y - y₁ = m(x - x₁)
If there's an equation I can solve it, but I hope this helps!
When looking at a graph of a line, there are two things you should look for straight off the bat. First, the y-intercept. And second, the slope.
The equation of a line is y = mx + b, where m is the slope, b is the y-intercept, and x is the input.
What is slope?
Slope is a number that determines how the line changes. It is often referred to as the "rate of change" because it represents how much the y-value of the line changes when the input (x) changes. The formula for slope is:
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Breakdown: This formula represents the change in the line, typically left to right. It shows the change in x-value over the change in corresponding y-value. This is also known as "rise over run," because the y-value is how much the line changes vertically, while the x-value is how much it changes horizontally.
Example: Let's say our line has a slope of 4, or m = 4/1. This means the y-value will change 4 units when the x-value changes by 1.
What is y-intercept?
Y-intercept is a value that determines the location of the line. When x = 0, the value of b will be the y-value. Essentially, when the line crosses the y-axis, that will be the y-value of the line.
Solve for x: 3x + 2 = 11 A : 11/5 B: 3. C : 11/3. D : 13/3. E : 6
Explanation:
The equation is given as:
3x + 2 = 11
The first step is to collect like terms ( Note that if 2 crosses to the other side of the equality sign, it becomes -2)
3x = 11 - 2
3x = 9
The next step is to divide both sides by 3:
3x/3 = 9/3
x = 3
A number multiplied by 2/5 is 3/20, Find the number
Answer:
3/8
Explanation:
Let the number be x.
A number multiplied by 2/5 = (2/5)x
Therefore:
[tex]\frac{2}{5}x=\frac{3}{20}[/tex]To solve for x, first, we cross-multiply.
[tex]\begin{gathered} 2x\times20=3\times5 \\ 40x=15 \end{gathered}[/tex]Next, we divide both sides of the equation by 40.
[tex]\begin{gathered} \frac{40x}{40}=\frac{15}{40} \\ x=\frac{3}{8} \end{gathered}[/tex]The number is 3/8.
