To find the value of q, divide both sides of the equation by 8:
[tex]\begin{gathered} 8q=96 \\ \Rightarrow\frac{8q}{8}=\frac{96}{8} \end{gathered}[/tex]Simplify both members of the equation:
[tex]\begin{gathered} \Rightarrow q=\frac{96}{8} \\ \Rightarrow q=12 \end{gathered}[/tex]Therefore:
[tex]q=12[/tex]the Browns build at a restaurant is $60 how much money should mr. Brown leave as a tip if he plans to tip 50%
We need to calculated first the 50% of $60
60*0.5=30
then we calculated the final bill
original bill + tip = money leave by mr Brown
60+30=90
he leave $90
The volume of the cone is 540. Solve for h, the height of the cone, if the radius is 9.
SOLUTION
From the question, we have been given the volume of the cone as 540
Now, volume of a cone is also given by the formula
[tex]V=\frac{1}{3}\pi r^2h[/tex]Now, the volume is 540 and the radius r is 9. Substituting into the formula, we have
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ 540\pi=\frac{1}{3}\times\pi\times9^2\times h \\ 540\pi=\frac{81\pi h}{3} \\ 540\pi=27\pi h \\ cancelling\text{ }\pi\text{ at both sides we have } \\ 540=27h \end{gathered}[/tex]Divide both sides by 27, we have
[tex]\begin{gathered} \frac{540}{27}=\frac{27h}{27} \\ h=\frac{540}{27} \\ h=20 \end{gathered}[/tex]Hence the answer is 20
please help me find ALL of the questions this thing is asking :). Non helping (just to obtain points) questions will be reported.
There were 24 dinner tables with 8 chairs at each table.Each dinner ticket cost $12.50. If 3/4 of thr dinner tables were full,how much money was raised from the dinner ticket sales?
we have the next information
24 dinner tables
each has 8 chairs
First we need to calculate 3/4 of the tables
24 mesas ----- 4/4=1
x ----- 3/4
x = the number of tabl
i need to provide a two column proof. don’t except if you cannot do this. please
Statement Reason
angle P = angle S Given
angle P + angle Q = 180 Given
angle R + angle S = 180 Given
If we substitute angle P = angle S into angle R + angle S = 180, then
angle R + angle P = 180
Which system of equations is represented by the graph?A. y = x + 4 y = x + 4/ x + 2B. y = x - 4 y = x + 4/ x + 2C. y = x + 4 y = x - 4/ x + 2D. y = x - 4 y = x - 4/ x + 2
Step 1. We have two equations represented in the graph. One is the red line and the other is the blue graph.
The red line represents a linear equation,
and the blue segments represent a rational equation.
Step 2. For the linear equations, we have only two options given:
[tex]\begin{gathered} y=x+4 \\ y=x-4 \end{gathered}[/tex]Graphing both lines to pick which one is the line shown in the problem:
The green line is y=x+4,
and the purple line is y=x-4.
Compared with our graph, we have the one that crosses the y-axis at -4, Thus it is the equation y=x-4.
Step 3. For the rational equation, we are given two options to choose from:
[tex]\begin{gathered} y=\frac{x+4}{x+2} \\ or \\ y=\frac{x-4}{x+2} \end{gathered}[/tex]We graph the two equations to check which one is correct:
In the graph, we show in green
[tex]y=\frac{x+4}{x+2}[/tex]and in purple, we have the equation
[tex]y=\frac{x-4}{x+2}[/tex]As you can see, the second one, (the purple one) is the one shown in the graph from this problem, thus, the second equation is:
[tex]y=\frac{x-4}{x+2}[/tex]Answer: D
[tex]\begin{gathered} y=x-4 \\ y=\frac{x-4}{x+2} \end{gathered}[/tex]Solve for x.
3(-3x-3)+2x+4=-33
What would be the new coordinates of the figure below if it is translated the figure 4 units horizontally and -2 units vertically?
Given the coordinates of recatangle ABCD:
A(-3, 1), B(2, 1), C(2, -2), D(-3, -2)
Let's find the new coordinates after the rectangle is translated 4 units horizontally and -2 units vertically.
Let's apply rules of translation.
A translation 4 units horizontally means a shift 4 units to the right.
It is written as: (x + 4)
A translation -2 units vertically means a shift 2 units downwards.
It is written as: (y - 2)
Thus, to find the new coordinates, add 4 to the x-coordinates and subtract 2 from the y-cooridnates.
We have the translation rule: (x + 4, y - 2)
We have:
A(-3, 1) ==> (-3 + 4, 1 - 2) ==> A'(1, -1)
B(2, 1) ==> (2 + 4, 1 - 2) ==> B'(6, -1)
C(2, -2) ==> (2 + 4, -2 - 2) ==> C'(6, -4)
D(-3, -2) ==> (-3 + 4, -2 - 2) ==> (1, -4)
Therefore, the new coordintes of the figure are:
A'(1, -1), B'(6, -1), C'(6, -4), D(1, -4)
ANSWER:
A'(1, -1), B'(6, -1), C'(6, -4), D'(1, -4)
Find the volume of the composite solid. Round your answer to the nearest hundredth,5.1 m5.1 mThe volume is about cubic meters,
The figure shows a cube with a cone shape extracted from it.
Thus, to get the volume of the composite solid, we need to subtract the volume of the cone from the volume of the cube.
i.e. Volume of Solid = Volume of Cube - Volume of Cone
[tex]\begin{gathered} \text{Volume of cube=}l\times l\times l=l^3 \\ l=5.1m\text{ (according to the question)} \end{gathered}[/tex]Therefore the volume of the cube is:
[tex]\text{Volume of cube = 5.1}^3=132.651m^3[/tex]Now we need to get the volume of the cone:
The formula of the volume of a cone is:
[tex]\begin{gathered} \text{Volume of cone = }\frac{1}{3}\times\pi\times r^2\times h \\ \\ r=\text{radius of cone} \\ h=\text{height of cone} \end{gathered}[/tex]The radius of the cone is the same as half the length of one edge of the cube
While the height of the cone is the same as the height of the cube.
A sketch is shown below:
Thus, height (h) of cone = 5.1m
radius (r) of cone = 2.55m
[tex]\text{Volume of cone=}\frac{1}{3}\times\pi\times2.55^2\times5.1=34.728m^3[/tex]Thus, we can now find the volume of the composite solid as:
[tex]\begin{gathered} \text{Volume of Composite Solid=} \\ 132.651m^3-34.728m^3 \\ \\ \therefore\text{Volume of Composite Solid=}97.923m^3\approx97.92m^3\text{ (To nearest Hundredth)} \end{gathered}[/tex]The volume is: 97.92 cubic meters
MATH HELP WILL MARK BRAINLEST
The vertex form of the equation is y = (x - 3)² - 4 , the correct option is (b).
In the question ,
it is given that ,
the equation is y = x² - 6x + 5
we need to write the equation in the vertex form ,
we know that the vertex form of the equation is
y = m(x − a)² + b , where (a,b) is the vertex .
On using the completing the square method for the equation,
y = x² - 6x + 5
Adding and subtracting 9 , in the equation
y = x² - 6x + 9 + 5 - 9
y = x² - 6x + 3² + 5 - 3²
y = (x - 3)² - 4 ....because (x - 3)² = x² - 6x + 3²
Therefore , The vertex form of the equation is y = (x - 3)² - 4 , the correct option is (b).
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Melissa won a week-long cruise in a contest and is working out the details of the trip. She can choose from 4 destinations and 5 departure dates. Since each cruise lets passengers pick one of 5 different day trips, Melissa also needs to choose one of those. How many different cruises can Melissa plan?
To solve this problem, it is necessary to use the fundamental counting principle, which is the multiplication counting rule.
It says that if we have two events, a and b. The total number of possible outcomes will be a times b (a*b).
In this case, a are the destinations she can choose and b are the departure dates. To find how many cruises can she plan, multiply the number of options of a and b, this is 4*5:
[tex]4\cdot5=20[/tex]In this case, she can plan 20 different cruises.
Find the volume of the cylinder in terms of 3.14 and to the nearest tenth.
The volume formula of a cylinder is :
[tex]V=\pi r^2h[/tex]From the problem, we have :
r = 3 in and h = 2 in
Using the formula above, the volume will be :
[tex]\begin{gathered} V=\pi(3)^2(2) \\ V=3.14(9)(2) \\ V=56.52 \end{gathered}[/tex]The answer rounded to the nearest tenth is V = 56.5 in^3
The height of a building is 1497 feet . How long would it take for an object to fall from the top
The function is given as
[tex]S=16t^2[/tex]Given that the height of the building is
[tex]S=1497ft[/tex]To calculate the value for time (t), we will substitute the value of S=1497 ft in the function above
[tex]\begin{gathered} S=16t^2 \\ 1497=16t^2 \\ 16t^2=1497 \\ \text{Divide both sides by 1}6 \\ \frac{16t^2}{16}=\frac{1497}{16} \\ t^2=93.5625 \\ \text{squareroot both sides} \\ t=\sqrt[]{93.5625} \\ t=9.67 \\ t\approx9.7\sec onds \end{gathered}[/tex]Hence,
The final answer is t= 9.7 seconds
Simplify the expression below:\sqrt[]{72}simplifies to a\sqrt[]{b} where:our coefficient a = Answerour radicand b = Answer
√72
Express 72 as 6^2 x 2
√(6^2 * 2 )
Pull terms out from under the radical
6 √2
a = 6
b= 2
A teacher wants to track the number of books students have read each week,encouraging them to increase their reading throughout the school year. Which ofthe following graphs might be most effective to inspire the student?
We have to find which of the graph options is best to track the number of books that the students read each week and encourage them to increase them.
Option 1 (scatter plot): in this case, it is not useful in the sense that we can not compare the evolution in time of each student. We can only see the number of books per student for specific weeks.
Option 2 (time series): in this case, the attendance is not a variable of interest, so it is not suitable.
Option 3: A pie chart is only useful to compare proportions and percentages, and not track an evolution of a variable in time.
Option 4: This aggregation of the data in a Pareto only allows to compare the total number of books per week, but the evolution is not clear, as we sort the columns by the number of books instead of time.
Option 5: A time series with weeks in the x-axis and number of books in the y-axis let the teacher clearly see the evolution of books read in time. So this option is the most suitable.
Answer: Option 5 (time series)
Look at the system of equations shown.y = 3x + 7y = 2x + 8What is the x-coordinate of the solution to the system?Select one:10- 10O- 1o
We have a system of 2 equation (Eq):
y = 3x + 7 (Eq 1)
y = 2x + 8 (Eq 2)
To solve the system, we can match both equations.
3x + 7 = 2x + 8
3x - 2x = 8 - 7
x = 1
You are taking a multiple choice test that has 6 questions. Each of the questions has 3 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?
ANSWER
729
EXPLANATION
Given:
6 question with each question having 3 choices.
Desired Outcome:
Number of ways the questions can be answered.
Now,
The sum of the ways to answer each question is equal to the total number of ways to answer all the questions.
That is:
[tex]3^6=3\times3\times3\times3\times3\times3=729[/tex]Hence, the number of ways the questions can be answered is 729.
When the price of petrol increases by 20%,
a motorist decreases his volume of petrol
consumption by 10%. Find the percentage
increase in his petrol bill.
Answer:
The percentage increase in his petrol bill is 16 2/3%
The percentage increase in his petrol bill would be equal to 16 2/3%
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
Given that When the price of petrol increases by 20%, a motorist decreases his volume of petrol consumption by 10%.
Let the inital price be 100 and consumption be 100t.
Now increased price
= 120 % of 100
= 120
New consumption
= 100 x 100 / 120
= 83.33
Hence, percentage reduction in the consumption will be;
(100 - 83.33)/ 100 x 100
16 and 2/3 %
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Write a two-column proof for the following.
Given: m2 = 30
m21=2m22
Prove: m23 +mZ4=90
(Do not include the degree symbol in your answers.)
Statements
1) m/2=30
2) m1=2m22
3) m/1 = 2(
1) Given
2) Given
3) Substitution
ماد
For the provided two-column proof, the following factors are accordingly absent:
Reason 2: Supplementary Angles' Definition
Reason 3: Equality's Substitution Property
Reason 4: Equality's Subtraction Property
Let we should finish the two-column proof step by step.
We learn that from the two column proof;
m∠2 = m∠3
Now that m∠1 + m∠2 = 180° has been established, we can see that m∠1 and m∠2 are on a straight line and that the sum of the angles on a straight line is 180°. They are hence supplementary angles, which is the explanation.
Similarly, since m∠3 and m∠4 are in a straight line;
So,
m∠3 + m∠4 = 180°
Therefore,
m∠1 + m∠2 = m∠3 + m∠4. The substitution property of equality makes this true.
Last but not least, because m∠2 = m∠3, they will cancel out in statement 3, and as a result, we now have;
m∠1 = m∠4. The equality's subtraction attribute is the cause.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
B
Step-by-step explanation:
x + y = 180
co-interior
co-interior starts with C and x + y make a C shape (easier to remember)
I need help on this practice problem It asks to solve the logarithmic equations. Number 3. And 4.
3) You have the following expression:
[tex]\log _p4096=3[/tex]In order to solve for p, proceed as follow:
- Use the property:
[tex]\log _mn=\frac{\log n}{\log m}[/tex]which applied to the given expression result:
[tex]\frac{\log 4096}{\log p}=3[/tex]- Next, solve for log p and take the complete equation as the exponent of a base 10:
[tex]\begin{gathered} \log p=\frac{1}{3}\log 4096 \\ 10^{\log p}=10^{\frac{1}{3}\log 4096} \end{gathered}[/tex]- By properties of logarithms you obtain:
[tex]\begin{gathered} p=4096^{\frac{1}{3}}=\sqrt[3]{4096^{}} \\ p=16 \end{gathered}[/tex]you earn $3,813.75 in interest by putting $11,300 in the bank at an interest rate of 3.75 % how many years was your money in the bank for
If you consider a simple interest, use the following formula:
I = p x r x t
where p is the initial investment ($11,300), r is the interest rate (3.75%) and t the ime in years. I is the final amount of money ($3,813.75).
Solve the previous equation for t and replace the values of p, I and r:
t = I/(p x r)
t = (3,813.75)/(11,300 x 0.0375)
t = 9
Hence, 9 years allow you to earn $3,813.75
in circle R, mCB=73° and mAD=57° what is M
The measure of the angle ∠CEB is 65°.
We are given a circle. The center of the circle is denoted by R. There are two chords, AB and CD. The point of intersection of the chords is E. The angles subtended by the arcs CB and AD are 73° and 57°, respectively. We have to find the measure of the angle ∠CEB. We can see that there is no direct relationship between the angles, but it is certain that the angle ∠CEB lies between the measures of angles subtended by the two arcs. So, we can write it in the form of an inequality. The measure of the angle ∠CEB is more than 57° but less than 73°. We can take the average value of these angles as an approximation. The average is (57° + 73°)/2 = 65°.
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Find the slope, if it exists, of the line containg the pairs of pointsplease answer them all :(1. ( -4, -1 ) and ( 4, 4 )2. ( 0, 3 ) and ( 4, 0 )3. ( 0, 1 ) and ( 3, 0 )4. ( 7, 8 ) and ( -7, 8 )5. ( 1, 5 ) and ( -8, 5 )
The formula for determine the slope is given by
m = ( y2-y1)/(x2-x1) where ( x1,y1) and (x2,y2) are points on the line
m = ( 4 - -1)/(4 - -4)
Rewriting
m = ( 4+1)/( 4+4)
= 5/8
The slope is 5/8
The length of a 12 foot by 8 foot rectangle is increasing at a rate of 3 feet per second and the width is decreasing at 2 feet per second (a) How fast is the perimeter changing? (b) How fast is the area changing?
The rate of change of the perimeter of this rectangle is equal to 2 feet per second.
The rate of change of the area of this rectangle is equal to 20 feet per second.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2L + 2W
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.The rate of change for the perimeter of this rectangle is given by:
P = 2L + 2W
Differentiating with respect to t, we have:
dP/dt = 2dl/dt + 2dw/dt
Substituting the given parameters into the formula, we have;
dP/dt = 2(3) + 2(-2)
dP/dt = 6 - 4
dP/dt = 2 feet per second.
For the rate of change of the area of this rectangle, we have:
dA/dt = ldw/dt + wdl/dt
dA/dt = 8(-2) + 12(3)
dA/dt = -16 + 36
dA/dt = 20 feet per second.
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a school day is 8 hours how many minutes are in a school day
In order to solve this exercise you need to remember the following:
[tex]1\text{ }hour=60\text{ }minutes[/tex]In this case, based on the information given in the exercise, a school day is 8 hours. Then, you need to make the conversion from hours to minutes.
You can set up the following:
[tex](8\text{ }hours)(\frac{60\text{ }minutes}{1\text{ }hour})[/tex]Therefore, evaluating you get:
[tex]=\frac{(60\text{ }minutes)(8\text{ }hours)}{1\text{ }hour}=480\text{ }minutes[/tex]Hence, the answer is:
[tex]480\text{ }minutes[/tex](a)The perimeter of a rectangular garden is 306m.If the width of the garden is 69m, what is its length?Length of the garden: m (b)The area of a rectangular window is 6364cm2.If the length of the window is 86cm, what is its width?Width of the window: cm
Answer
The length of the garden = 84 m
Explanation
Part (a)
The given parameters are:
Perimeter of the rectangular garden = 306 m
The width of the garden = 69 m
The length of the garden = ?
Solution:
Using the formula for the perimeter of a rectangle:
[tex]\begin{gathered} Perimeter=2(Length+Width \\ \\ 306m=2(L+69m) \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }2 \\ \\ \frac{306m}{2}=\frac{2(L+69m)}{2} \\ \\ 153m=L+69m \\ \\ L=153m-69m \\ \\ L=84\text{ }m \end{gathered}[/tex]The length of the garden = 84 m
Part (b):
The given parameters are:
The area of the rectangular window = 6364 cm²
The length of the window = 86 cm
The width of the window = ?
Solution:
The width of the rectangular window can be calculated using the formula for the area of a rectangle.
[tex]\begin{gathered} Area=Length\times Width \\ \\ 6364cm^2=86cm\times W \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }86cm \\ \\ \frac{6364cm^2}{86cm}=\frac{86cm\times W}{86cm} \\ \\ W=74\text{ }cm \end{gathered}[/tex]The width of the window = 74 cm
Alan needs to manufacture a circular metal plate with a perimeter of `10pi` centimeters. If the allowed error tolerance in the perimeter is `+-1` centimeter, how close to the ideal radius must he control the radius of the plate?
A. `1/(5pi)`
B. `1/(10pi)`
C. `2/pi`
D. `1/(2pi)`
Answer: D. `1/(2pi)`
Your Welcome :)
The ideal radius Alan must control is [tex]\frac{1}{2\pi }[/tex] cm.
Define perimeter of circle.The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The area of a circle determines the space it takes up. A circle's diameter is equal to the length of a straight line traced through its center. Usually, it is stated in terms of units like cm or m.
Given data -
Perimeter of circular plate = 10[tex]\pi[/tex] cm
We know that perimeter of a circle is 2[tex]\pi[/tex]r
Therefore 10[tex]\pi[/tex] = 2[tex]\pi[/tex]r
r = 5 cm
The given error Alan can make is +-1 cm.
Minimum radius is given by
2[tex]\pi[/tex]r = 10[tex]\pi[/tex] - 1
r = [tex]\frac{10\pi - 1 }{2\pi }[/tex]
r = 5 - [tex]\frac{1}{2\pi }[/tex]
Maximum radius is given by
2[tex]\pi[/tex]r = 10[tex]\pi[/tex] + 1
r = [tex]\frac{10\pi + 1 }{2\pi }[/tex]
r = 5 + [tex]\frac{1}{2\pi }[/tex]
The ideal radius Alan must control is [tex]\frac{1}{2\pi }[/tex] cm.
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George invested some money at10% interest. George also invested$169 more than4 times that amount at15 % . How much is invested at each rate if George receives$2427.05 in interest after one year? (Round to two decimal places if necessary.)
The investment is in two places. The first one had a principal of P, with an interest rate of 10% (that is 0.10). The second one had a principal of 169 more than 4 times the first one, which can be translated as;
4P + 169. The interest rate is 15% (that is 0.15)
So, investment X is;
Interest x = PRT
Interest x = P*0.1*1
Interest x = 0.1P
Investment Y is;
Interest y = PRT
Interest y = (4P + 169)*0.15*1
Interest y = 0.6P + 25.35
This means the total interest yielded is given as;
Interest x + interest y = 0.1P + 0.6P + 25.35
Interest x + interest y = 0.7P + 25.35
If however, he receives 2427.05 in interest, then this can be translated as follows;
[tex]\begin{gathered} \text{Interest x+interest y=0.7P+25.35} \\ \text{Similarly;} \\ \text{Interest x+ interest y=2427.05.} \\ \text{Therefore;} \\ 0.7P+25.35=2427.05 \\ 0.7P=2427.05-25.35 \\ 0.7P=2401.7 \\ P=\frac{2401.7}{0.7} \\ P=3431 \end{gathered}[/tex]With P calculated as 3,431, this can be translated as follows;
Investment X had a principal of $3,431. The interest rate was 0.10 and that yielded an interest after a year in the sum of 343.10.
Investment Y had a principal of 4P + 169 which equals;
4 (3431) + 169 = 13,893
And the interest rate was 0.15, which now yielded an interest after a year of 2,083.95.
Therefore, Investment X was $3431 at 10%
Investment Y was $13,893 at 15%
Describe the pattern. Then sketch the next figure in the pattern.
The first figure is a shape of four squares including a shaded square at the bottom left column.
The second figure has 6 squares including a shaded square at the bottom left column.
The third figure has 8 squares including a shaded square at the bottom left column.
The fourth figure has 10 squares including a shaded square at the bottom left column.
Thus, the general pattern is that the number of squares are increasing constantly by 2 but the shaded square remains unchanged.
Thus, the next figure is;
The next figure in the pattern shows a shaded square at the bottom left column with one unshaded square at the top left column. It has 12 squares in total.