1 day = 24 hours; then:
37.5 fl oz per hour
37.5 x 24 = 900 fl oz of water in one day
find an equation for the line that passes through the points (-1,-5) and (-5,1)
The equation of line between two points is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]plugging the values into the equation we have:
[tex]\begin{gathered} y-(-5)=\frac{1-(-5)}{-5-(-1)}(x-(-1)) \\ y+5=\frac{1+5}{-5+1}(x+1) \\ y+5=\frac{6}{-4}(x+1) \\ y+5=-\frac{6}{4}(x+1) \end{gathered}[/tex]Therefore the equation is:
[tex]y+5=-\frac{3}{2}(x+1)[/tex]Which of the following equations represents the equation of the circle below ?
Given the graph of a circle
To find the equation of the circle, we need to find the location of the center and the length of the radius
As shown, we can notice that the x-axis bisect the circle
So, the diameter and the center are lying on the x-axis
The diameter is the length between the points of intersection with the x-axis
As shown, the diameter is the line segment with the endpoints:
(3, 0) and (9, 0)
so, the diameter = 9 - 3 = 6
So, the radius = r = 3
And the location of the center = (h, k) = (6, 0)
The equation of the circle will be as follows:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-6)^2+(y-0)^2=3^2 \end{gathered}[/tex]Expand then simplify:
[tex]\begin{gathered} x^2-12x+36+y^2=9 \\ \\ x^2+y^2-12x+27=0 \end{gathered}[/tex]So, the answer will be option 3
[tex]x^2+y^2-12x+27=0[/tex]the diagonal of a rhombus are 14 inches and 28 inches. What is the perimeter of the rhombus in inches. draw a picture
The diagonal of rhombus is:
[tex]\begin{gathered} d_2=\sqrt[]{4a^2-d^2_1} \\ d^2_2=4a^2-d^2_1 \\ d^2_1+d^2_2=4a^2 \end{gathered}[/tex]so side of rombus (a) is:
[tex]\begin{gathered} 14^2+28^2=4a^2 \\ 196+784=4a^2 \\ \frac{980}{4}=a^2 \\ a^2=245 \\ a=\sqrt[]{245} \\ a=15.65247 \end{gathered}[/tex]Perimeter of rombus is:
[tex]\begin{gathered} \text{Perimeter}=4a \\ =4\times15.65247 \\ =62.609 \end{gathered}[/tex]10 The box plots summarize the high temperatures recorded in two different cities. The temperature was recorded for six days. Franklin: Troy: 4 + + 56 58 60 62 64 66 68 70 72 74 High Temperature + 76 78 Which statement best describes the data represented in the box plots? (6.13A, RS, RC4) F For half the days in Franklin, the high temperature was less than 64º. G For half the days in Troy, the high temperature was between 59° and 73°. H The range in high temperatures for Franklin is 18. The interquartile range for Troy is 11.
Here, we are given a box plot.
Given:
Franklin:
Median = 71
Lower quartile = 66
Upper quartile = 76
Lowest value = 63
Highest value = 77
Troy:
Median = 64
Lower quartile = 62
Upper quartile = 73
Lowest value = 59
Highest value = 77
The range is the difference between the lowest value and the highest value.
In a box plot the interquartile range can be said to be the difference between the lower quartile and the upper quartile.
Let's find the interquartile range for both Franklin and Troy.
Interquartile range:
Franklin = 76 - 66 = 10
Troy = 73 - 62 = 11
The interquartile range for Franklin is 10.
The interquartile range for Troy is 11
Therefore, the statement that best describes the data represented in the box plots is:
The interquartile range for Troy is 11
ANSWER:
J. The interquartile range for Troy is 11
What is the volume of the prism? whole unit cubes fit inside the prism. quarter cubic units fit inside the prism. The total volume of the prism is units3 2 units 1 unit 4. units
In the prism there are two rows. In one row there are 4 whole cubes and one quarter cube. So total whole cubes in the prism is 8 and total quarter cubes in the prism is 2.
Determine the volume of prism.
[tex]\begin{gathered} V=2\cdot4\frac{1}{4}\cdot1 \\ =2\cdot\frac{17}{4} \\ =\frac{17}{2} \\ =8.5 \end{gathered}[/tex]So volume of prism is 8.5 units square.
I just need help with how to turn the table into y=Mx+b and f(x). I know how to graph and find R.
Solution:
Given the table as shown below:
Using the equation:
[tex]y=mx+b\text{ ---- equation 1}[/tex]When x = 68, y equals 4.1.
Thus, substitute these values into equation 1
[tex]\begin{gathered} 4.1=m(68)+b \\ \Rightarrow68m+b=4.1\text{ ----- equation 2} \end{gathered}[/tex]When x = 71, y equals 4.6.
Similarly, we have
[tex]\begin{gathered} 4.6=m(71)+b \\ \Rightarrow71m+b=4.6\text{ ----- equation 3} \end{gathered}[/tex]From equation 2, make c the subject of the formula.
[tex]\begin{gathered} 68m+c=4.1\text{ } \\ \Rightarrow c=4.1-68m\text{ ---- equation 4} \end{gathered}[/tex]Substitute equation 4 into equation 3. Thus,
[tex]\begin{gathered} 71m+c=4.6\text{ } \\ \Rightarrow71m+(4.1-68m)=4.6 \\ \text{open parentheses} \\ 71m+4.1-68m=4.6 \\ \text{collect lik terms} \\ 71m-68m=4.6-4.1 \\ 3m=0.5 \\ \text{divide both sides by the coefficient of m, which is 3.} \\ \text{thus,} \\ m=\frac{0.5}{3} \\ \Rightarrow m=\frac{1}{6} \end{gathered}[/tex]Substitute the obtained value of m into equation 4.
thus,
[tex]\begin{gathered} c=4.1-68m \\ \text{where m=}\frac{1}{6} \\ \text{thus,} \\ c=4.1-68(\frac{1}{6}) \\ =4.1-11.33 \\ \Rightarrow c=-7.23 \end{gathered}[/tex]Hence, (x,y) Notation y=mx+c
[tex]undefined[/tex]How many triangles can be constructed with angles measuring 80º, 80º, and 40º?A noneB oneC more than one
One triangle can be formed
Looking at the angles, we can see that we have two angles that are equal
What this mean is that at any point in time, there will be two equal sides
Hence, following definition, we have it that the type of triangle that would be formed will be isosceles
Thus, we have one triangle that can be formed
Number of Workers and Hours to Complete 1 mile of Highway (10, 50) 50 Number of Hours to Complete 1 mile of Highway 30 : (25, 20) 10 10 25 15 20 Number of Workers As the values of x increase, the values of y y :: increase :: decrease : remain the same
In the graph you can see that all the points do not pass through a single line, however, you can obtain the slope of the line that passes through the points.
*If the slope is positive, the values of y increase as the values of x increase.
*If the slope is negative, the values of y decrease as the values of x increase.
The formula for the slope is
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]So, you have
[tex]\begin{gathered} (x_{1,}y_1)=(10,50) \\ (x_{2,}y_2)=(25,20) \end{gathered}[/tex][tex]\begin{gathered} m=\frac{20-50}{25-10} \\ m=\frac{-30}{15} \\ m=-2 \end{gathered}[/tex]Therefore, since the slope of the line that passes through these points is negative then the correct answer is:
As the values of x increase, the values of y decrease.
Points D and E belong to legs AC, that is BC of the triangle ABC and also AB||DE.If |AB|=20cm, |DE|=15cm, |AC|=16cm, find the length of |AD|.
Given that DE || AB, we can think of CDE and CAB as similar triangles.
This means that corresponding sides are proportional.
We have to find AD.
We can find AD as the difference between the length of CA and the length of CD.
We can write the following proportion:
[tex]\frac{CD}{CA}=\frac{DE}{AB}[/tex]Then, we can find CD as:
[tex]\begin{gathered} CD=CA\cdot\frac{DE}{AB} \\ CD=16\cdot\frac{15}{20} \\ CD=16\cdot0.75 \\ CD=12 \end{gathered}[/tex]Then, we can find AD as:
[tex]\begin{gathered} AD+DC=AC \\ AD=AC-DC \\ AD=16-12 \\ AD=4 \end{gathered}[/tex]Answer: AD = 4cm
A certain brand of coffee comes in two sizes. A 12.3-ounce package cost $2.99. A 33.9-ounce package cost $8.74. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent Unit price for the 12.3 ounce?Unit price for 33.9 ounce? What is better buy?
We can find the unit price of each size by dividing their cost by the amount of coffee each size contains.
• For the 12.3 ounce, we get:
[tex]\frac{2.99}{12.3}=0.24[/tex]The unit price for the 12.3 ounce is $0.24 per ounce
• For the 33.9 ounce:
[tex]\frac{8.74}{33.9}=0.26[/tex]The unit price for the 33.9 ounce is $0.26 per ounce
Then, the 12.3-ounce size is the best buy, since its unit price is the lowest.
is it possible to draw a triangle with angles 50°, 65°, and 70°? Explain?
NO.
Explanation
the sum of the internal angles in a triangle must be equal to 180
a+b+c=180
Step 1
check if the given angles satisfy the condition
Let
angle1=50
angle2=65
angle3=70
now
[tex]\begin{gathered} 50+65+70=180 \\ 185=180\rightarrow False \\ \end{gathered}[/tex]so it is NOT possible draw a triangel with angles 50,65 and 70 .
I hope this helps you
Which of the following functions have an average rate of change that is positive on theinterval from x = -3 to x= -1? Select all that apply.f(x) = 3xf(x) = 3f(x) = 3x2f(x) = 3x2 - x
For every function, we will find the average rate of change from x = -3 to x = -1
The average rate of change will be given as follows:
[tex]\frac{f(a)-f(b)}{a-b}[/tex]a) When F(x) = 3x
The average rate will be:
[tex]\frac{f(-3)-f(-1)}{(-3)-(-1)}=\frac{3\cdot-3-(3\cdot-1)}{-3-(-1)}=\frac{-9+3}{-3+1}=\frac{-6}{-2}=3[/tex]So, it will be positive
b) When F(x) = 3
The average rate will be:
[tex]\frac{f(-3)-f(-1)}{(-3)-(-1)}=\frac{3-3}{-3+1}=\frac{0}{2}=0[/tex]So, it will be zero
c) When f(x) = 3x^2
The average rate will be:
[tex]\frac{f(-3)-f(-1)}{(-3)-(-1)}=\frac{3\cdot9-3\cdot1}{(-3)-(-1)}=\frac{24}{-2}=-12[/tex]So, it will be negative
d) when F(X) = 3x^2 - x
The average rate will be:
[tex]\frac{f(-3)-f(-1)}{(-3)-(-1)}=\frac{(3\cdot9+3)-(3\cdot1+1)}{-3+1}=\frac{30-4}{-2}=\frac{26}{-2}=-13[/tex]So, it will be negative
so, the answer will be option a) F(X) = 3x
When is it better to use the sine function and when is it better to use the cosine function when modeling sinusoids behavior
A sine function is as shown below
A cosine function is as shown below
The combination of both sine and cosine function is as shown below
It can be observed from the above combination that:
Cosine is better when the maximum is on the y- axis and sine is better if the midline is at the center.
A spelling test is given to 400 students in Madison County. Those who score in the top 5% will compete in the county spelling bee. How many students will be in the county spelling bee? 80 100 200 20 My Progress 2021 by Curriculum Associates. All rights reserved. These materials, or any portion thereof, may not be reproduced or shared in any manner without express written consent of Curriculu
Answer:
20
Explanation:
To know how many students will be in the country spelling bee, we need to find 5% of 400.
So, we need to multiply 400 by 5 and then divide by 100:
[tex]400\times5\text{ \%=}\frac{400\times5}{100}=\frac{2000}{100}=20[/tex]Therefore, there will be 20 students in the country spelling bee.
Determine whether the following is a trinomial square.x2 - 8x + 64-O NoYes
Explanation:
[tex]x^2\text{ - 8x + 64}[/tex]A trinomial is a polynomial with three terms
[tex]\begin{gathered} x^2\text{ = 1st term} \\ -8x\text{ = 2nd term} \\ 64\text{ = third term} \end{gathered}[/tex][tex]undefined[/tex]Does this table represent a proportional relationship?ху0 22446YesNoMaybe
Answer
NO is the answer.
The table does not represent a proportional relationship.
Explanation
When two quantities x and y are said to be proportional to each other, this is represented by
y ∝ x
Introducing the constant of variation, k, we have
y ∝ x
y = kx
We can then solve for k knowing that for two proportinal quantities, the value of k will remain the same for corresponding values of x and y
x | y
0 | 2
2 | 4
4 | 6
y = kx
when x = 0, y = 2
y = kx
2 = (k) (0)
2 ≠ 0
This first shows that the two quantities aren't proportional
when x = 2, y = 4
y = kx
4 = (k) (2)
2k = 4
k = 2
when x = 4, y = 6
y = kx
6 = (k) (4)
4k = 6
k = (3/2)
The values of k aren't consistent through the values in the table, hence, we cvan see that this data in the table does not represent proportional relationship.
Hope this Helps!!!
The study participants were divided into four groups—two groups received the Power Pill (Group A and Group B) and two groups received a placebo (Group C and Group D). The effects of the Power Pill were measured. One group that received the Power Pill (Group A) and one group that received the placebo (Group C) were told of the anticipated effects of the Power Pill—accelerated hair growth—while the other two groups (Group B and Group D) were not provided with this information. All four groups were told to monitor and report any physical changes during the study.Results were reported and participants were grouped as to either “Saw Results,” meaning that participants reported increased hair growth as part of physical changes during the study, or “No Results,” meaning that increased hair growth was not mentioned as part of physical changes during study.Results are as follows:•6 from 10 people in Group A saw results.•7 from 10 people in Group B saw results.•5 from 10 people in Group C saw results.•4 from 10 people in Group D saw results.Part 1:Create a two-way table for the data and find the probabilities for each group. Describe results in terms of the study.Part 2:What is the probability that a person saw results, given they received the Power Pill? What is the probability that a person saw results, given they received a placebo? Explain in terms of the study.Part 3:What is the probability that a person received the placebo, given that they did not see results? What is the probability that a person received the Power Pill, given that they did not see results? Explain in terms of the study.
Part 1.
First, let's create the two-way table for all the people that saw results:
Part 2:
The number of people that received a power pill is 20, and from these people, only 13 saw results, so the probability is 13/20 = 0.65 = 65%.
The number of people that received a placebo is 20, and from these people, only 9 saw results, so the probability is 9/20 = 0.45 = 45%.
That means if the person received a power pill, the probability of seeing results is greater.
Part 3:
The number of people that didn't see results is 18, and from these people, 11 received a placebo, so the probability is 11/18 = 0.6111 = 61.11%.
The number of people that didn't see results is 18, and from these people, 7 received a power pill, so the probability is 7/18 = 0.3889 = 38.89%.
That means if the person didn't see any results, the probability of having received a placebo is greater.
Find the x-intercepts of y = x2 + 12x + 27.
Given the equation:
[tex]y=x^2+12x+27[/tex]We will find the x-intercepts of the function y
The x-intercept is the value of (x) when y = 0
So, we will substitute with y = 0 then solve the equation to find x
[tex]\begin{gathered} x^2+12x+27=0 \\ \end{gathered}[/tex]Factor the equation to find the roots:
[tex]\begin{gathered} (x+9)(x+3)=0 \\ x+9=0\rightarrow x=-9 \\ x+3=0\rightarrow x=-3 \end{gathered}[/tex]So, the answer will be:
The x-intercepts are the points (-9, 0) and (-3, 0)
Need help for 56 it says solve equation to the nearest tenth use the given restrictions
Problem N 56
we have
sin∅=0.8 ----------> interval [-90,90] ----> that means the angle lie in the I or IV quadrant
∅=sin^-1(0.8)
∅=53.1 degrees
In the IV quadrant, the value of sine is negative (so in the IV quadrant there is no solution)
The answer is
∅=53.1 degreesTranslate the sentence into an equation. Six times the sum of a number and 2 equals 4. Use the variable b for the unknown number.
Given:-
Six times the sum of a number and 2 equals to 4.
Use the variable b for the unknown number.
So the sentence six times the sum of a number and 2 equals to 4 is,
[tex]6(b+2)=4[/tex]So the translated sentence into equation is 6(b+2)=4.
use the slope formula to calcuate the slope (129,110) (300,245) to the nearest hundredth
Given:
The points are (129,110) (300,245).
The slope is calculated as,
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=(129,110)_{} \\ (x_2,y_2)=(300,245) \\ \text{Slope}=\frac{245-110}{300-129} \\ \text{Slope}=\frac{135}{117} \\ \text{Slope}=\frac{15}{19} \end{gathered}[/tex]Answer: slope=15/19
below are a series of statements regarding the number line graph shown below which statements are false? select all that apply
EXPLANATION
-The first statement is FALSE because there is a closed circle, thus the equation should be x ≥ 6
-In the second line, we should isolate x from the inequality -4x - 9 < -29
Adding +9 to both sides:
-4x < -29 + 9
Adding numbers:
-4x < -20
Dividing both sides by -4 and reversing:
x > 20/4
Simplifying:
x > 5
Thus, the inequality is x>5
--> The second statement is TRUE
-The third statement is also TRUE because the number line already includes the number -5 as a possible solution.
-The number line D is also TRUE.
Find the equation of a line passing through (5, -6) parallel to: (a) 2x + y = 12 (b) 3x + 5y = 7 (c) x + 3y = 8 (d) 7x - 12y = 5 2y = 5 (e) r = 7 (f)
ANSWER
y = -2x + 4
EXPLANATION
a. We want to find the equation of the line that is parallel to the given equation and passes through (5, -6):
2x + y = 12
Let us put the equation in the slope-intercept form:
y = -2x + 12
When two lines are parallel, their slopes are equal.
The general form of a linear equation is:
y = mx + c
where m = slope
c = intercept
This means that the slope of the given equation is -2. Therefore, the slope of the equation we need is also -2.
Now, we can apply the point-slope method to find the equation of the line.
We have:
y - y1 = m(x - x1)
where (x1, y1) is a point that lies on the line
m = slope
(x1, y1) => (5, -6).
Therefore:
y - (-6) = -2(x - 5)
y + 6 = -2x + 10
=> y = -2x + 10 - 6
y = -2x + 4
That is the equation of the line that passes through (5, -6) and is parallel to the given equation.
if the value of x and y are negative which of the following values must be positive. (a) x+y (b) x-y (c) x/y
Given data:
Assume the given value of x = -a.
Assume the given value of y= -b.
The expression for the ratio of x/y is,
[tex]\begin{gathered} \frac{x}{y}=\frac{-a}{-b} \\ =\frac{a}{b} \end{gathered}[/tex]Thus, the only ratio of x and y that is x/y is positive.
What is the solution to the following system of equations? A: (-2,3) B: (3, 1)C: (3, -2)D: (1, -3)
The graph shows the lines of two equations, a blue line and a red line.
Note that to solve a system of equations graphically, we would need to identify the point at which they both intersect.
The lines of these two equations intersect at the point where x = -3 and y = 1
ANSWER:
[tex](-3,1)[/tex]The correct answer is option B
Find the z-scores associated with 70 books sold at each locationZ-score (A): Z-score (B):
Z-score (A): -0.6
Z-score (B): -0.67
Explanations:The formula for calculating z-score is expressed as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]For score A:
Given the following parameters
[tex]\begin{gathered} \mu=73 \\ x=70 \\ \sigma=5 \end{gathered}[/tex]Substitute
[tex]\begin{gathered} z=\frac{70-73}{5} \\ z=\frac{-3}{5}=-0.6 \end{gathered}[/tex]For the score B
[tex]\begin{gathered} \mu=80 \\ \sigma=15 \end{gathered}[/tex]Substitute
[tex]\begin{gathered} z=\frac{70-80}{15} \\ z=\frac{-10}{15}=-0.67 \end{gathered}[/tex]Question 41 ptsYou return a book that is 5 days overdue. You have a previous unpaid overbalance of $1.30,and your new balance is $2.05. What is the charge for one book overdue one day?Make sure your answer looks like money. The dollar sign has already been included.$Question 51 pts
According to the given data we have the following:
previous balance=$1.30
new balance=$2.05
new balance-previous balance=$2.05-$1.30
new balance-previous balance=$0.75
Therefore, from the day you rent the book until you return it is $0.75.
Therefore if:
5 days overdue___________$0.75
1 day overdue____________x
x= (1 day overdue*$0.75)/5 days overdue
x=$0.15
The charge for one book overdue one day is $0.15
Find the area of a circle with radius 5 cm.Use the value 3.14 for n, and do not round your answer.Be sure to include the correct unit in your answer.
We use the formula of the area of a circle
[tex]A=\pi\times r^2[/tex]where r is the radious, then replace the values
[tex]\begin{gathered} A=(3.14)\times(5)^2 \\ A=3.14\times25 \\ A=78.5 \end{gathered}[/tex]total area of the circle is 78.5 square centimeter
I just need to know the gosh darn answer I know what I’m supposed to be doing here I ughhh I’ve just been working on this problem for literally 8 minutes because I cannot seem to GET IT. Someone help me please
From the graph
The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry
Hence,
The vertex of the curve is at the point
[tex](3,-2)[/tex]Translate to an algebraic expression. 20 more than yThe translation is ...
Let us consider a number x which is 20 more ethan y.
Then, x can be written as
x=y+20
So, the translation is
[tex]y+20[/tex]