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Related Questions
10. (01.04 LC)
Your first six-month auto insurance premium was $658.00. Based on your driving record, your renewal premium is $756.70. What percent increase did you see in your premium? (1
12%
15%
28%
35%
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There is 15% in the premium.
How take out percentage?From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.
First six-month auto insurance = $658
Renewal premium = $756
Change in the insurance = $98
percentage of $98 from $658
= 15%
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Hey I need help on this math problem thank you
Answers
Answer:
From the image below we will bring out two coordinates we are going to use to calculate the rate of change of the graph
The coordinates are given below as
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(2,4) \\ (x_2,y_2)\Rightarrow(-2,0) \end{gathered}[/tex]Concept:
The rate of change will be calculated using the formula below
[tex]\begin{gathered} \text{rate of change =}\frac{change\text{ in y}}{\text{change in x}} \\ \text{rate of change}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{rate of change}=\frac{y_2-y_1}{x_2-x_1} \\ \text{rate of change}=\frac{_{}0-4_{}}{-2_{}-2_{}} \\ \text{rate of change}=\frac{-4}{-4} \\ \text{rate of change}=1 \end{gathered}[/tex]Hence,
The rate of change = 1
Which of the following are equations for the line shown below? Check all that apply. 5 (1,2) (3-6) I A. y + 6 = -4(x-3) B. y + 3 = -4(X-6) I C. y1 = -4(x-2) D. y - 2 = -4(x - 1)
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We have the next points (1,2) and (3,-6)
1 pts
4. If line segment AB has coordinates A(-2,4) and B(2,0) and line segment
CD has coordinates C(3,4)and D(-3,-2), how would you describe these two
line segments?
A: neither
B: perpendicular
C: parallel
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Answer:
B
Step-by-step explanation:
[tex]m_{\overline{AB}}=\frac{4-0}{-2-2}=-1 \\ \\ m_{\overline{CD}}=\frac{-2-4}{-3-3}=1 [/tex]
Since the slopes are negative reciprocals of each other, and since they intersect, they are parallel.
Robin is saving money to buy a 720$ phone. she has 105$ saved, and each week she adds 30$ to her savings. write an equation to find the number of weeks (w) until she has enough savings to buy the phone.
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Let call w the number of weeks she has been saving.
Then, we can write the expression for her saving in function of the number of weeks as:
[tex]S(w)=105+30\cdot w[/tex]We now have to find the number of weeks it will take for her savings to reach $720.
We can find it by calculating w for S(w)=720:
[tex]\begin{gathered} S(w)-105+30w=720 \\ 105+30w=720 \\ 30w=720-105 \\ 30w=615 \\ w=\frac{615}{30} \\ w=20.5\approx21 \end{gathered}[/tex]Answer: it will take her 21 weeks to have enough savings.
find the coordinates of the midpoint of the line joining the points and show your work.
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formula of midpoint
[tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]the we replace (7,1) and (-1,3)
[tex](\frac{7+(-1)}{2},\frac{1+3}{2})[/tex]simplify to solve
[tex]\begin{gathered} (\frac{7+1}{2},\frac{4}{2}) \\ \\ (\frac{8}{2},\frac{4}{2}) \\ \\ (4,2) \end{gathered}[/tex]Midpoint is (4,2)
Graph
A bee produce 0,05 ml of honey per day, how many litres of honey can the bee produce in its lifetime if they live for 28 days?
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Given:
A bee produce 0.05 ml of honey per day
We will find how many liters of honey can the bee produce in its lifetime if they live for 28 days
Let it produces x ml
So, using the ratio and proportions
[tex]\frac{0.05}{1}=\frac{x}{28}[/tex]Solve for x:
[tex]x=0.05\times28=1.4ml[/tex]Convert ml to liters
1 liter = 1000 ml
So, 1.4 ml = 0.0014 liters
So, the answer will be
The bee can produce honey in its lifetime = 0.0014 liters
Please help me answer this correctly,
Answers
anywhere you see x, input the value in the brackets.
eg f(-2) = 2(-2)+8
= -4+8
=4
Answer:
if x= -2
then f(x) = 2×(-2)+8
= -4+8
= 4
if x=0
then f(x)=2×0+8
=0+8
=8
if x=5
then f(x)=2×5+8
=10+8
=18
what is the volume of a right triangular pyramid whose base is 5 meters on each side and whose altitude is 4 meters? round to the nearest hundred
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Right triangular pyramid
base = 5 meters
altitude = 4 meters
Volume = ?
Step 02:
The volume of a right triangular pyramid
V = 1/3 B * h
B = 1/2 b * h
[tex]\begin{gathered} B\text{ = }\frac{1}{2}\cdot5m\cdot4m \\ B=\text{ }10m^2 \end{gathered}[/tex][tex]V\text{ = }\frac{1}{3}\cdot10m^2\cdot4m=\text{ }13.3333m^3[/tex]The answer is:
The volume of the pyramid is 13.33 m³.
I'm attempting to solve and linear equation out of ordered pairs in slopes attached
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We know that the equation of a line is given by
y = mx + b,
where m and b are numbers: m is its slope (shows its inclination) and b is its y-intercept.
In order to find the equation we must find m and b.
In all cases, m is given, so we must find b.
We use the equation to find b:
y = mx + b,
↓ taking mx to the left side
y - mx = b
We use this equation to find b.
1We have that the line passes through
(x, y) = (-10, 8)
and m = -1/2
Using this information we replace in the equation we found:
y - mx = b
↓ replacing x = -10, y = 8 and m = -1/2
[tex]\begin{gathered} 8-(-\frac{1}{2})\mleft(-10\mright)=b \\ \downarrow(-\frac{1}{2})(-10)=5 \\ 8-5=b \\ 3=b \end{gathered}[/tex]Then, the equation of this line is:
y = mx + b,
↓
y = -1/2x + 3
Equation 1: y = -1/2x + 3
2Similarly as before, we have that the line passes through
(x, y) = (-1, -10)
and m = 0
we replace in the equation for b,
y - mx = b
↓ replacing x = -1, y = -10 and m = 0
-10 - 0 · (-1) = b
↓ 0 · (-1) = 0
-10 - 0 = b
-10 = b
Then, the equation of this line is:
y = mx + b,
↓
y = 0x - 10
y = -10
Equation 2: y = -10
3Similarly as before, we have that the line passes through
(x, y) = (-6, -9)
and m = 7/6
we replace in the equation for b,
y - mx = b
↓ replacing x = -6, y = -9 and m = 7/6
[tex]\begin{gathered} -9-\frac{7}{6}(-6)=b \\ \downarrow\frac{7}{6}(-6)=-7 \\ -9-(-7)=b \\ -9+7=b \\ -2=b \end{gathered}[/tex]Then, the equation of this line is:
y = mx + b,
↓
y = 7/6x - 2
Equation 3: y = 7/6x - 2
4The line passes through
(x, y) = (6, -4)
and m = does not exist
When m does not exist it means that the line is vertical, and the equation looks like:
x = c
In this case
(x, y) = (6, -4)
then x = 6
Then
Equation 4: x = 6
5The line passes through
(x, y) = (6, -6)
and m = 1/6
we replace in the equation for b,
y - mx = b
↓ replacing x = 6, y = -6 and m = 1/6
[tex]\begin{gathered} -6-\frac{1}{6}(6)=b \\ \downarrow\frac{1}{6}(6)=1 \\ -6-(1)=b \\ -7=b \end{gathered}[/tex]Then, the equation of this line is:
y = mx + b,
↓
y = 1/6x - 7
Equation 5: y = 1/6x - 7
A random survey of 10 students recorded their number of hours of activity each week and their Body Mass Index (BMI). The results are shown in the table below. Student Body Mass Number of Hours of Activity Each Week Index Which of the following best describes the data? O linear positive association linear negative association no association O non-linear association
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According to the given table, the dataset does not describe a linear-relationhip because they do not show a linear relation between the variables, they are too far away from each other.
Hence, the answer is D.Find the slope of the line that passes
through these two points.
Point 1 Point 2
(3,5)
(4,2)
X1 У1
X2 Y2
m =
3
=
y2-91
X2-X1
[?]
Enter
Answers
Answer:
-3
Step-by-step explanation:
The slope of a line is the steepness of the line and is given by the formula below:
[tex]\boxed{\text{Slope} = \frac{y_1 - y_2}{x_1 - x_2} }[/tex], where [tex](x_1,y_1)[/tex] is the 1st coordinate while [tex](x_2,y_2)[/tex] is the 2nd coordinate
The two coordinates given are: (3, 5) and (4, 2)
Slope of line
[tex] = \frac{5 - 2}{3 - 4} [/tex]
[tex] = \frac{3}{ - 1} [/tex]
= -3
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number serieswhat number comes next in the following series 27, 28, 32, 41, 57, 82, ?
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Answer:
The number that comes next is;
[tex]118[/tex]Explanation:
Given the series;
[tex]27,28,32,41,57,82[/tex]From the series, if we observe the series closely we can see a relationship between the difference between consecutive terms.
[tex]\begin{gathered} 28-27=1=1^2 \\ 32-28=4=2^2 \\ 41-32=9=3^2 \\ 57-41=16=4^2 \\ 82-57=25=5^2 \end{gathered}[/tex]We can see that the difference follows the same pattern.
So, the next term would be the sum of the last term and the square of 6;
[tex]\begin{gathered} 82+6^2 \\ =82+36 \\ =118 \end{gathered}[/tex]Therefore, the number that comes next is;
[tex]118[/tex]Kyle has a container of flour in the shape of a cylinder.
Answers
Answer:
Part A:
The volume of a cylinder is given below as
[tex]\begin{gathered} V_{cylinder}=\pi\times r^2\times h \\ r=\frac{d}{2}=\frac{10in}{2}=5in \\ h=8in \end{gathered}[/tex]By substituting the values , we will have
[tex]\begin{gathered} V_{cyl\imaginaryI nder}=\pi r^2h \\ V_{cyl\mathrm{i}nder}=\pi\times5^2\times8 \\ V_{cyl\mathrm{i}nder}=\pi\times200 \\ V_{cyl\mathrm{i}nder}=628.3in^3 \end{gathered}[/tex]Hence,
The volume = 628.3in³
Part B:
To determine the weight of the flour in ounces, we will use the relation below
[tex]\begin{gathered} 0.13ounce=1in^3 \\ x=628.3in^3 \\ cross\text{ multiply, we will have} \\ x=0.13\times628.3 \\ x=81.679 \\ x\approx81.7ounces \end{gathered}[/tex]Hence,
The weight = 81.7 ounces
What is the volume of this triangle right prism 8 cm 15 cm 12 cm
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The volume of a triangle right prism is given by the formula
The resale value V, in thousands of dollars, of a boat is a function of the number of years since the start of 2011, and the formula isV = 10.5 - 1.1t.(a) Calculate V(3).________thousand dollarsExplain in practical terms what your answer means.This means that the resale value of the boat will be______thousand dollars at the start of the year_______(b) In what year will the resale value be 6.1 thousand dollars?______(c) Solve for t in the formula above to obtain a formula expressing t as a function of V. t=______(d) In what year will the resale value be 2.8 thousand dollars?_______
Answers
Answer
a) V (3) = 7.2 thousand dollars.
In practical terms, the resale value of the boat will be 7.2 thousand dollars at the start of the year 2014.
b) t = 4years.
The resale value will be 6.1 thousand dollars in the year 2015.
c) t = 9.545 - 0.909V
d) t = 7 years.
7 years after the start of 2011 = 2018.
Explanation
We are given that the resale value (V), in thousands of dollar, of a boat is given as
V = 10.5 - 1.1t
where t = number of years since the start of 2011.
a) We are told to calculate V(3).
V = 10.5 - 1.1t
t = 3
V = 10.5 - 1.1 (3)
V = 10.5 - 3.3
V = 7.2 thousand dollars.
In practical terms, the resale value of the boat will be 7.2 thousand dollars at the start of the year 2014.
b) In what year will the resale value be 6.1 thousand dollars.
V = 10.5 - 1.1t
what is t when V = 6.1
6.1 = 10.5 - 1.1t
1.1t = 10.5 - 6.1
1.1t = 4.4
Divide both sides by 1.1
(1.1t/1.1) = (4.4/1.1)
t = 4 years.
4 years afther the start of 2011 = 2015.
c) We are asked to solve for t and obtain a formula expressing t as a function of V.
V = 10.5 - 1.1t
1.1t = 10.5 - V
Divide through by 1.1
[tex]\begin{gathered} \frac{1.1t}{1.1}=\frac{10.5}{1.1}-\frac{V}{1.1} \\ t=9.545-\frac{V}{1.1} \\ t=9.545-0.909V \end{gathered}[/tex]t, expressed in terms of V, is t = 9.545 - 0.909V
d) We are now asked to calculate in what year will the resale value be 2.8 thousand dollars.
t = 9.545 - 0.909V
t = 9.545 - 0.909 (2.8)
t = 9.545 - 2.545
t = 7 years.
7 years after the start of 2011 = 2018.
Hope this Helps!!!
10Estimate the solution to the following system of equations by graphingOA (1,7)OB. (-1,1)OC.OD. (-1,-1)
Answers
we have the system of equations
-4x + 5y =8
6x - y = 11
Using a graphing tool
Remember that
the solution is the intersection point of both lines
The answer is the option AFind the measure of angle CDB. Explain your reasoning, including the theorem or postulate you used. (2 pts.) b) Find the measure of angle. (1 pt.)
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The triangle is isosceles, since two of its sides are equal. Besides, the little triangles ABD and CBD are congruent and this can be concluding using the criterion SSS , since they share one side, and the other sides are equal. Then the angles are congruent, and the angles ADB and CDB are congruent and have the same measure. Then
[tex]\begin{gathered} m\angle ADB+m\angle CDB=m\angle ADC \\ 2m\angle CDB=m\angle ADC \\ m\angle CDB=\frac{72}{2} \\ m\angle CDB=32 \end{gathered}[/tex]Then, the measure of angle CDB is 32 degrees.
2. Find the equation ofthe line:through (-5,1) parallel to2y = 2x - 4
Answers
Given data:
The given point is (a,b)=(-5,1).
The given line is 2y=2x-4.
The given line can be written as,
2y=2(x-2)
y=x-2
The standard equation of the line is,
y=mx+c
comapre the given line with the standard form.
m=1
The slope of two parallel lines are always equal.
m'=m
=1
The expression of the line which is parallel to the given line is,
y-b=m'(x-a)
Substitue the given values in the expression.
y-1=1(x-(-5))
y-1=x+5
y=x+6.
Thus, the equation of the line parallel to the given line is y=x+6.
Is r = 3 + 3sin θ symmetrical along the y axis?
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Answer:
Yes. r = 3 + 3sin θ is symmetrical along the y axis
Step-by-step explanation:
Original polar equation is
r = 3 + 3sinθ
If this plot is to be symmetrical about the y axis then replacing Θ with (π-θ) in the original equation should not change the equation and thereby should not change the plot
r = 3 + 3sinθ
Replace θ with π-θ:
==> 3 + 3sin(π-θ)
But sin(π-θ) = sinθ
So the equation is unchanged at 3 + 3sin(π-θ) from the original equation r = 3 + 3sinθ
Hence the equation is symmetrical along the y-axis
This can be also be clearly seen if you plot both the equations, you will see the plot does not change
solve the equation 3x^2 - 5x + 1 = 0 expressing your answer correct to two decimal places
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You have th following equation;
[tex]3x^2-5x+1=0[/tex]In order to find the solution to the previous equation, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, a = 3, b = -5 and c = 1. By replacing these values into the quadratic formula, you obtain:
[tex]\begin{gathered} x=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(3)(1)}}{2(1)} \\ x=\frac{5\pm\sqrt[]{25-12}}{2}=\frac{5\pm\sqrt[]{13}}{2} \\ x=\frac{5\pm3.60}{2}=2.5\pm1.80 \end{gathered}[/tex]Hence, the solutions are:
x = 2.5 + 1.80 = 4.30
x = 2.5 - 1.80 = 0.70
I child drinks 1 1/2 cups of milk twice a day.If a container of milk has 15 cups of milk remaining for the child to drink ,in how many days will the container be empty?
Answers
Data
Milk drank = 1 1/2 twice a day
Volume in a container = 15 cups
Number of days the contaier will be empty = ?
Procedure
To solve this problem just divide the volume of the container by the milk drank by the child.
As the child drinks 1 1/2 twice a day, the total milk drank in a day will be = 2 x 1 1/2 = 3
Division 15/3 = 5
Solution: The container will be empty in 5 days
Solve the following inequality for t. Write your answer in the simplest form.6t + 3 < 7t + 10
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Therefore, the solution is t > -7.
help I'm practicing
Answers
We have the next formula to find the volume of a triangular prism-
[tex]V=B\times h[/tex]where
B= area of the base
h= height
in our case
B=18 square inches
H= 5 inches
[tex]V=18\times5=90in^3[/tex]the volume of the triangular prism is 90 cubic inches
Rearrange the formula y = a-bx² to make x the subject.
Answers
Answer:
x = ± [tex]\sqrt{\frac{a-y}{b} }[/tex]
Step-by-step explanation:
y = a - bx² ( subtract a from both sides )
y - a = - bx² ( multiply through by - 1 )
bx² = a - y ( divide both sides by b )
x² = [tex]\frac{a-y}{b}[/tex] ( take square root of both sides )
x = ± [tex]\sqrt{\frac{a-y}{b} }[/tex]
I’m trying to make a study guide and need step by step explanation on how to solve this question please
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Given:
The dimension of square shape floor is 200 feet by 200 feet.
The area of the square is calculated as,
[tex]\begin{gathered} A=side^2 \\ A=200^2=40000 \end{gathered}[/tex]Now, given that the 1/2 bottle will cover approximately 2000 quare feet.
It gives,
[tex]\begin{gathered} \frac{1}{2}\text{ bottle=2000 square f}ee\text{t} \\ 1\text{ bottle=4000 square fe}et \end{gathered}[/tex]So, the number of bottles required are,
[tex]\frac{A}{4000}=\frac{40000}{4000}=10\text{ bottles}[/tex]Answer: option B)
HeyI need help with this, having trouble solvingIt is from my ACT prep guide
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We will determine the height of the building as follows:
First, we determine the height above her window, that is:
[tex]\tan (56)=\frac{h_u}{150ft}\Rightarrow h_u=(150ft)\tan (56)[/tex][tex]\Rightarrow h_u=222.3841453\ldots ft[/tex]Now, we calculate the height below her window:
[tex]\tan (32)=\frac{h_l}{150ft}\Rightarrow h_l=(150ft)\tan (32)[/tex][tex]\Rightarrow h_l=93.73040279\ldots ft[/tex]Then, we will have that:
[tex]h_T=h_l+h_l\Rightarrow h_T=150(\tan (56)+\tan (32))[/tex][tex]\Rightarrow h_T=316.1145581\ldots ft\Rightarrow h_T\approx316.1ft[/tex]So, the height of the building is approximately 316.1 ft tall.
geometry extra credit- 25 questions
Answers
Given that the triangles are similar, then their corresponding sides are in proportion, that is,
[tex]\frac{AB}{JK}=\frac{BX}{KY}[/tex]Substituting with data and solving for BX:
[tex]\begin{gathered} \frac{32}{10}=\frac{BX}{6} \\ 3.2=\frac{BX}{6} \\ \text{3}.2\cdot6=BX \\ 19.2=BX \end{gathered}[/tex]Identify the segments that are parallel, if any, if ∠ADH≅∠ECK.A. AD¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯B. AC¯¯¯¯¯¯¯¯ || CD¯¯¯¯¯¯¯¯C. AE¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯D. none of these
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Hi there. To solve this question, we have to remember some properties about similar triangle and congruency.
Given the triangles ADH and ECK,
We know that
[tex]\angle ADH\cong\angle ECK[/tex]That is, the angle at D is congruent to the angle at C in the respective triangles.
In this case, we can think of the congruency between the triangles in the following diagram:
Notice that ADCB is a parallelogram and the angles given show that the angles at D and at C are congruent, hence the other angles in the parallelogram must be congruent as well.
This means that opposite sides are parallel and have the same measure (length).
The opposite sides are AD and CB and DC and AB.
In this case, we find that only AD and CB are an option to this question, therefore the correct answer.
In fact, AC is the diagonal of the parallelogram and is not parallel to any segment of the figure.
AE isn't a segment drawn and hence not parallel to any other segment.
The correct answer is the option A).
In an elementary school, 20% of the teachers teach advanced writing skills. If there are 25writing teachers, how many teachers are there in the school?
Answers
Answer:
125 teachers
Explanation:
We were given that:
20% of teachers teach advanced writing skills = 20/100 = 0.2
Number of writing teachers = 25
The total number of teachers = x
We will obtain the number of teachers in the school as shown below:
[tex]\begin{gathered} \frac{No.of.writing.teachers}{Total.number.of.teachers}\times100\text{\%}=20\text{\%} \\ \frac{25}{x}\times100\text{\%}=20\text{\%} \\ \frac{25\times100\text{\%}}{x}=20\text{\%} \\ \text{Cross multiply, we have:} \\ x\cdot20\text{\% }=25\times100\text{\%} \\ \text{Divide both sides by 20\%, we have:} \\ \frac{x\cdot20\text{\%}}{20\text{\%}}=\frac{25\times100\text{\%}}{20\text{\%}} \\ x=\frac{2500}{20} \\ x=125 \\ \\ \therefore x=125 \end{gathered}[/tex]Hence, the total number of teachers in the school is 125
