Answer:
f(x) = 3x - 1
Step-by-step explanation:
The line can be represented in the form f(x) = mx + b, where m is the rate of change of the line and b is the value of the function when x = 0.
Looking at the graph, we can tell that when x = 0 the function = -1. (The point on the line and the y-axis).
We can also tell that when x increases by 1, y increases by 3. The points (0,-1) and (1, 2) are both on the line and their difference in x is 1 and their difference in y is 3.
The formula for slope (rate of change) is [tex]\frac{change\ in\ y}{change\ in\ x}[/tex], so m = [tex]\frac{3}{1}[/tex] or 3.
Now we have the equation for the line is f(x) = 3x - 1
9 grams =
milligrams
Answer:
9000 milligrams
Step-by-step explanation:
1 gram = 1000 milligrams
( × 9 on both sides to get 9 grams )
9 grams = 9000 milligrams
Answer:
9000 milligram
Step-by-step explanation:
multiply the mass value by 1000
Mary tutors english. For each hour that she tutors she earns 40 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H. Then use this equation to find marys earnings after tutoring for 13 hours
Answer:
A.) 40(t) = E
B.) 520
Step-by-step explanation:
t is for time, E is the total, H is the hourly rate.
plug in the numbers to get 40(13) = h and solve for H and you get 520
-- Brainliest answer is much appreciated! :)
An equation is formed of two equal expressions. Mary's earnings after tutoring for 13 hours is $520.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that for each hour that Mary tutors she earns 40 dollars. Therefore, the equation to find marys earnings after tutoring for H hours can be written as,
Earnings = Hourly rate of tutoring × Number of hours
E = 40 × H
E = 40H
Now, Mary's earnings after tutoring for 13 hours will be,
E = 40(13)
E = 520
Hence, Mary's earnings after tutoring for 13 hours is $520.
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The telephone pole is _____ feet tall (Round to the nearest whole number)
14 ft
85 ft
42 ft
33 ft
Answer:
[tex]33\ ft[/tex]
Step-by-step explanation:
Let
y-----> the height of the telephone pole
we know that
In the right triangle of the figure
The sine of angle of 67 degrees is equal to divide the opposite side of angle of 67 degrees by the hypotenuse
[tex]sin(67\°)=\frac{y}{36}[/tex]
solve for y
[tex]y=(36)sin(67\°)=33\ ft[/tex]
The equation for the best fit line is y=5.2x+18. It says if the observed value when x=10 was y=62, then which of the following represents the value of the residual for this point. The options are 52, 8,-8,&-10. i need help please!!
The residual value is -8
What is a residual value?A residual value is the difference between the observed y-value and the predicted y-value( from the regression equation ) .
Here, the given regression equation of the line,
y = 5.2 x +18
Thus, for x = 10, the predicted value of
y = (5.2 × 10) +18
y = 52 + 18
y = 70
Now, by the given question,
For x = 10, the observed value of y = 62,
Hence, the residual for 10 = Observed value of y for 10 - Predicted value of y for 10
= 62 - 70
= -8
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simplify 15c3 please
Answer:
455.
Step-by-step explanation:
Yes. You require the number of combinations of 3 from 15.
15C3
The formula for this is 15! / 12! 3! or you can do itr as follows
15C3 = 15*14*13/3*2*1
= 5*7*13
= 35*13
= 455.
area of this figure please!!! 20 POINTS GUYS FASTTTT
Answer:
15
Step-by-step explanation:
Well first I found the area of the big rectangle which is lxw which will be equal to 12. while the small rectangle the area will be equal to 3. Finally, I added the 2 areas and I got 15. I hope this helped you.
What is a radical equation
Answer:
is an equation in which a variable is under a radical
Answer:
An equation where the radical is under the equation...
Step-by-step explanation:
Right?
7/3x = 2/(x+5) the solution
Hi, if we are using the quadratic formula to solve this, then here is a good answer.
The solution to the equation 7/3x = 2/(x+5) is found by cross-multiplication and simplifying, ending with the result x = -35.
Explanation:To solve the given equation 7/3x = 2/(x+5), the first step is to cross-multiply. This gives us 7*(x+5) = 2*3x. Simplifying this results in 7x + 35 = 6x. Subtract 6x from each side and you get x + 35 = 0. And thus, x = -35 is the solution of the equation.
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Sandra's cell phone plan gives her unlimited minutes for $15.50 per month. She is charged $0.08 for each text message, t. Which equation models the total monthly cost, C, for the cell phone? 10 points
Answer:
c=15.50+0.08t
Step-by-step explanation:
Sandra's total monthly cost for her cell phone, represented by C, consists of a fixed rate of $15.50 for unlimited minutes and an additional $0.08 per text message. The formula to calculate her total cost is C = 15.50 + 0.08t, where t is the number of text messages.
Explanation:The total monthly cost, C, for Sandra's cell phone is composed of a fixed monthly charge plus a variable charge that depends on the number of text messages she sends.
The fixed charge is her unlimited minutes plan which costs $15.50 per month.
On top of that, each text message costs $0.08, so if we let t represent the number of texts she sends, the variable cost will be 0.08t.
Therefore, the equation to model Sandra's total monthly cost would be:
C = 15.50 + 0.08t
We can confidently state that this equation represents how Sandra's monthly expenses on her cell phone will add up depending on the number of texts, t, she sends in a month.
If two sides of a triangle are 9 cm and 15 cm in length, which COULD be the measure of the third side?
A) 23 cm
B) 24 cm
C) 25 cm
D) 26 cm
Answer:
Its A) 23
Step-by-step explanation:
Its right, trust me
The possible value of the third side of the triangle is 23.
What is the range of the third side when two sides of a triangle are known?The range of third side c when two sides a and b of a triangle are known is given by the inequality:
[tex]a-b < c < a+b[/tex]
It is given that:
a =15
b = 9
So, by the triangle inequality
[tex]15-9 < c < 15+9[/tex]
6 <c <24
The third side will take the value between 6 and 24.
so, the possible value of the third side of the triangle i.e. c is 23.
Therefore, the possible value of the third side of the triangle is 23.
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A square has a perimeter of 36 units. One vertex of the square is located at (3,5) on the coordinate grid. What could be the x- and y- coordinates of another vertex of the square?
Answer:
3,-4
Step-by-step explanation:
Answer: (9,11)
Explanation: if you plot (9,11) on a grid you can see that the length between 3 and 9 is 6. And the length between 9 and 11 is 6. 6 times 6 is 36. The two length have to be equal to each other because it is a square.
Tickets to a local circus cost $5 for students and $8 for adults. A group of 9 people spent a total of $60. How many adults were in the group?
Final answer:
By setting up a system of equations based on the provided information and solving them, we can determine that there were 5 adults in the group that attended the circus.
Explanation:
To determine how many adults were in the group at the circus, let's use variables to represent the number of students and adults in the group. Let x be the number of students and y be the number of adults. We know there are a total of 9 people, so we have the equation:
x + y = 9
The total cost for all tickets is $60, and considering the cost for students is $5 and for adults is $8, we have the equation:
5x + 8y = 60
We now have a system of equations that can be solved using the substitution or elimination method. If we solve for x in the first equation (x = 9 - y) and substitute into the second equation:
5(9 - y) + 8y = 60
45 - 5y + 8y = 60
3y = 15
y = 15 / 3
y = 5
There are 5 adults in the group. Now, we can find the number of students by substituting y back into the first equation:
x + 5 = 9
x = 9 - 5
x = 4
So, there are 4 students in the group.
Which of the following represents 3x 5/7
2.14 is the answer!!!
Answer:
Step-by-step explanation:
3*5 / 7 is the way I'm guessing it is.
15/7 one way it can be represented.
2 1/7 is another way.
2.1428 is yet another way.
0. A pill has the shape of a cylinder with a hemisphere at each end. The height of the cylindrical portion 11
mm and the overall height is 18 mm.
(a) Find the volume of the pill in cubic millimeters. Round to the nearest cubic
millimeter.
(b) If the pill is to contain 1,000 milligrams of vitamin C, then how much vitamin C does the pill contain per
cubic millimeter? Round to the nearest tenth of a cubic millimeter.
(c) Another pill that is entirely spherical has a diameter of 10 millimeters and contains 1.5 milligrams of
vitamin C per cubic millimeter. How much less vitamin C does this second pill contain, rounded to the
nearest milligram, than the one pictured?
Answer:
Part a) The volume of the pill is [tex]603\ mm^{3}[/tex]
Part b) [tex]1.7\frac{mg}{mm^{3}}[/tex]
Part c) [tex]215\ mg[/tex]
Step-by-step explanation:
Part a) Find the volume of the pill in cubic millimeters
we know that
The volume of the pill is equal to the volume of the cylinder plus the volume of a sphere (two hemisphere is equal to one sphere)
so
[tex]V=\frac{4}{3}\pi r^{3} +\pi r^{2}h[/tex]
we have
[tex]r= (18-11)/2=3.5\ mm[/tex]
[tex]h=11\ mm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(3.5)^{3} +(3.14)(3.5)^{2}(11)[/tex]
[tex]V=603\ mm^{3}[/tex]
Part b) If the pill is to contain 1,000 milligrams of vitamin C, then how much vitamin C does the pill contain per cubic millimeter?
Divide 1,000 milligrams by the volume
[tex]1,000/603=1.7\frac{mg}{mm^{3}}[/tex]
Part c) Another pill that is entirely spherical has a diameter of 10 millimeters and contains 1.5 milligrams of vitamin C per cubic millimeter. How much less vitamin C does this second pill contain, rounded to the
nearest milligram, than the one pictured?
step 1
Find the volume of the sphere
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=10/2=5\ mm[/tex] ----> the radius is half the diameter
assume
[tex]\pi =3.14[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(5)^{3}[/tex]
[tex]V=523.33\ mm^{3}[/tex]
step 2
Multiply the volume by 1.5 milligrams of vitamin C per cubic millimeter
so
[tex]523.33*1.5=785\ mg[/tex]
step 3
Find the difference
[tex]1,000-785=215\ mg[/tex]
Ms. Giving shared her $500 winnings with friends. She gave Mildred
50%. She gave Bernice 20% of what was left and then gave 40% of
what remained to Alice. She gave 50% of what was left then to Bea.
How much did Ms. Giving keep for herself?
Answer:
50%=250
20%=50
40%=80
50=60
so she kept $60
Step-by-step explanation:
Answer:
$60
Step-by-step explanation:
Winning = $500
Mildred = 50% of $500 = 0.5 x $50 = $250
Left = $500 - $250 = $250
Berice = 20% of $250 = 0.2 x $250 = $50
Left = $250 - $50 = $200
Alice = 40% of $200 = 0.4 x $200 = $80
Left = $200 - $80 = $120
Bea = 50% of $120 = 0.5 x $120 = $60
Left = $120 - $60 = $60
Find the measure of the central angle of an arc if its length is 14pi and 12 is the radius.
[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ s=14\pi \\ r=12 \end{cases}\implies 14\pi =12\theta \implies \cfrac{14\pi }{12}=\theta \\\\\\ \stackrel{\textit{radians}}{\cfrac{7\pi }{6}}=\theta ~\hspace{10em}\stackrel{\textit{in degrees}}{210^o}[/tex]
Which segment is parallel to BC
Line DF is parallel
In triangle ABC with midpoints D, E, and F on sides AB, BC, AC, respectively, segment DF is parallel to BC based on the Midline Theorem
In triangle ABC, if D, E, and F are the midpoints of sides AB, BC, and AC, respectively, then the line segment DE is parallel to BC as per the Midline Theorem.
This theorem states that if a line segment connects the midpoints of two sides of a triangle, that segment is parallel to (and half the length of) the third side of the triangle.
Considering our given scenario, the midpoints of AB and AC are D and F and the line segment formed is DF.
Following the Midline Theorem, this segment DF would be parallel to the third side of the triangle, i.e., BC.
So, the answer to the question 'which segment is parallel to BC?' is DF.
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The probable question may be:
In triangle ABC, Point D, E and F are midpoint of triangle ABC.
which segment us parallel to BC?
A. AB
B. DF
C. AC
D. DE
Help! Help! I need to study for tomorrow's math exam. Plz also explain how u got ur answer
Answer:
5,1 is correct
Step-by-step explanation:
you go over one then up two for G. For H, you go down one and over two.
5,1 because they are both the same distance from F
Select the correct answer. A number is selected at random from the set {2, 3, 4, ... 10}. Which event, by definition, covers the entire sample space of this experiment? A. The number is greater than 2. B. The number is not divisible by 5. C. The number is even or less than 12. D. The number is neither prime nor composite. E. The square root of the number is less than 3.
Answer:
c
Step-by-step explanation:
Answer:
C. The number is even or less than 12.
Step-by-step explanation:
Let's analyze each event:
A. The number is greater than 2.
This doesn't cover the case when we get number 2. Because 2 is equal to 2, not greater.
B. The number is not divisible by 5.
10 and 5 are divisible by 5, so this doesn't cover the entire sample space.
C. The number is even or less than 12.
Let's notice that every number from {2, 3, 4, ... 10} is less than 12, so the even part of the event doesn't play any role. This covers the entire sample space.
D. The number is neither prime nor composite.
The definition of prime number is exactly the opposite of composite number, so there can't be a number that's neither both. This event doesn't cover any number of the set.
E. The square root of the number is less than 3.
This doesn't cover number 10, because the square root of 10 is approx. 3,16 that's greater than 3.
the sum of the series below is 10900 how many numbers n are in the series 19+20.5+22+23.5+...+181
Consecutive terms differ by 1.5, so this is an arithmetic sequence given by
[tex]\begin{cases}a_1=19\\a_n=a_{n-1}+1.5&\text{for }n>1\end{cases}[/tex]
So we have
[tex]a_2=a_1+1.5[/tex]
[tex]a_3=a_2+1.5=a_1+2\cdot1.5[/tex]
[tex]a_4=a_3+1.5=a_1+3\cdot1.5[/tex]
and so on, up to
[tex]a_n=a_1+1.5(n-1)=17.5+1.5n[/tex]
The sum of the first [tex]N[/tex] terms is 10,900:
[tex]\displaystyle\sum_{n=1}^Na_n=\sum_{n=1}^N(17.5+1.5n)=17.5N+1.5\dfrac{N(N+1)}2=10,900[/tex]
[tex]\implies17.5N+0.75N(N+1)=10,900[/tex]
[tex]\implies0.75N^2+18.25N-10,900=0[/tex]
[tex]\implies N=109[/tex] (we ignore the negative solution)
so there are 109 terms in the series.
Answer:
109Step-by-step explanation:
[tex]19,\ 20.5,\ 22,\ 23.5,\ ...,\ 181\\\\\text{It's the arithmetic sequence with:}\\\\a_1=19,\ a_n=181.\\\\\text{The sum of n terms of this sequence is equal to 10,900.}\\\\\text{the formula of a sum of n terms of an arithmetic sequence:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\text{Substitute:}\ S_n=10,900,\ a_1=19,\ a_n=181:\\\\\dfrac{19+181}{2}\cdot n=10,900\\\\\dfrac{200}{2}n=10,900\\\\100n=10,900\qquad\text{divide both sides by 100}\\\\n=109[/tex]
Keiko spent $6 on the fruit at a grocery store. she spent a total of $40 at the store. what percentage of total did she spend on fruit?
Answer:
15%
Step-by-step explanation:
15% of 40 is 6.
What is the median of the data shown in the box plot below?
A:23
B:28
C:30
D:35
Answer:
It has to be 25 it is the middle number
Answer:
C which is 30.
Evaluate the expression when n= 3
what expression?
if you have an expression then I could probably help you.
Solution of 0.5x = -1.
first correct answer gets brainliest!!!
Answer:
x = - 2
Step-by-step explanation:
0.5x = - 1
(0.5/0.5 ) x = -1/0.5
Use your calculator
1
÷
0.5
=
You should get 2. But there is a minus sign on the right. The answer is -2
What is the definition ordered pairs?
Answer:
the definition is two of the same kind
An ordered pair is a set of coordinates or points on a graph. In order, they would be the x coordinate and the y coordinate. The ordered pair would look like this (x, y). For example, on a graph, the ordered pair of a point that is 3 over and 4 up would look like this: (3, 4), as the x value is 3 and y value is 4. The x value always comes before the y value in an ordered pair.
De un triángulo rectángulo se conoce que su hipotenusa mide 20 cm y la suma de los catetos miden 24 cm ¿Cuánto mide su área?
Answer:
The area of the right triangle is [tex]43.88\ cm^{2}[/tex]
Step-by-step explanation:
The question in English is
From a right triangle it is known that its hypotenuse measures 20 cm and the sum of the legs measures 24 cm. How much does its area measure?
Let
x-----> the measure of one leg
y----> the measure of the other leg
Assume x is less than y
we know that
Applying Pythagoras Theorem
[tex]20^{2}=x^{2}+y^{2}[/tex] -----> equation A
[tex]x+y=24[/tex]
[tex]y=24-x[/tex] -----> equation B
Substitute equation B in equation A and solve for x
[tex]20^{2}=x^{2}+(24-x)^{2}\\ \\400=x^{2} + 576-48x+x^{2}\\ \\ 2x^{2} -48x+576-400=0\\ \\2x^{2} -48x+176=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]x=4.5\ cm[/tex]
see the attached figure
[tex]x=4.5\ cm[/tex]
[tex]y=24-4.5=19.5\ cm[/tex]
The area is equal to
[tex]A=xy/2=(4.5)(19.5)/2=43.88\ cm^{2}[/tex]
Please helppp Omg pleaseee
Answer:
3/4 3/6 5/12
Step-by-step explanation:
the bottom goes from least to greatest
Which equation is y = 9x2 + 9x – 1 rewritten in vertex form?
Answer:
[tex]y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
Step-by-step explanation:
An equation in the vertex form is written as
[tex]y = a (x-h) + k[/tex]
Where the point (h, k) is the vertex of the equation.
For an equation in the form [tex]ax ^ 2 + bx + c[/tex] the x coordinate of the vertex is defined as
[tex]x = -\frac{b}{2a}[/tex]
In this case we have the equation [tex]y = 9x^2 + 9x - 1[/tex].
Where
[tex]a = 9\\\\b = 9\\\\c = -1[/tex]
Then the x coordinate of the vertex is:
[tex]x = -\frac{9}{2(9)}\\\\x = -\frac{9}{18}\\\\x = -\frac{1}{2}[/tex]
The y coordinate of the vertex is replacing the value of [tex]x = -\frac{1}{2}[/tex] in the function
[tex]y = 9 (-0.5) ^ 2 + 9 (-0.5) -1\\\\y = -\frac{13}{4}[/tex]
Then the vertex is:
[tex](-\frac{1}{2}, -\frac{13}{4})[/tex]
Therefore The encuacion excrita in the form of vertice is:
[tex]y = a(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
To find the coefficient a we substitute a point that belongs to the function [tex]y = 9x^2 + 9x - 1[/tex]
The point (0, -1) belongs to the function. Thus.
[tex]-1 = a(0 + \frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
[tex]-1 = a(\frac{1}{4}) -\frac{13}{4}\\\\a = \frac{-1 +\frac{13}{4}}{\frac{1}{4}}\\\\a = 9[/tex]
Then the written function in the form of vertice is
[tex]y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}[/tex]
Answer:
The vertex form of a parabolic function has the general formula:
f(x) = a(x-h)^2 + k where (h,k) represent the vertex of the parabola.
Therefore, to write the given equation in vertex form, we will need to transform it to the above formula as follows:
y = 9x^2 + 9x - 1
y = 9(x^2 + x) - 1
y = 9(x^2 + x + 1/4 - 1/4)-1
y = 9((x+1/2)^2 - 1/4)-1
y = 9(x + 1/2)^2 - 9/4 - 1
y = 9(x + 1/2)^2 - 13/4 ..............> The equation in vertex form
Step-by-step explanation:
Hope this helps!!! Have a great day!!! : )
Please help me asap!! 200 points !!!!!!!! Find the area of the trapezoid given the coordinates: -3,3 -1,-3 1,-2 3,-3
Answer:
Area 6
Hope This Helps! Have A Nice Day!!
Area 6
Hope This Helps! Have A Nice Day!!
Which of the following are considered measures of variability?
I. mean
II. interquartile range
III. mean absolute deviation
Answer:
the answers are interquartile range and mean absolute deviation
Step-by-step explanation:
In statistics, measures of variability are Interquartile Range and Mean Absolute Deviation, which indicate the degree of spread in a data set. However, the Mean is a measure of central tendency, not variability.
Explanation:
In the context of statistics, measures of variability are statistical data that highlight the degree of the spread in a data set. These are measures that can help us to identify how much the values in the data set differ from their mean value. Out of the options provided, II. Interquartile Range and III. Mean Absolute Deviation can be classified as measures of variability.
The Interquartile Range (IQR) is a measure of statistical dispersion and is calculated as the difference between the 75th and 25th percentiles. It’s the range within which the center half of a data set lies. The Mean Absolute Deviation (MAD) is the average distance between each data value and the mean.
However, I. Mean is not a measure of variability but rather a measure of central tendency. It helps to identify the central point or typical value of a data set but does not represent the dispersion of data points.
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