Given in the question:
a.) Base area of music box = 9 1/2 in²
b.) Height of music box = 3 1/5 in.
Let's recall the formula for getting the volume of a rectangular prism:
[tex]\text{ Volume = Length x Width x Height or Base Area x Height}[/tex]Before we plug in the values, let's first transform the mixed numbers into improper fractions.
[tex]\text{ 9 }\frac{1}{2}\text{ = }\frac{1\text{ + (2 x 9)}}{2}\text{ = }\frac{1\text{ + 18}}{2}\text{ = }\frac{19}{2}[/tex][tex]\text{ 3 }\frac{1}{5}\text{ = }\frac{1\text{ + (3 x 5)}}{5}\text{ = }\frac{1\text{ + 15}}{5}\text{ = }\frac{16}{5}[/tex]Let's now plug in the values to get the volume of the music box.
[tex]\text{ Volume = Base Area x Height}[/tex][tex]=\text{ 9 }\frac{1}{2}\text{ x 3 }\frac{1}{5}\text{ = }\frac{19}{2}\text{ x }\frac{16}{5}\text{ = }\frac{304}{10}\text{ }[/tex][tex]\frac{304}{10}\text{ = }\frac{\frac{304}{2}}{\frac{10}{2}}=\frac{152}{5}\text{ or 30 }\frac{2}{5\text{ }}in.^3[/tex]Therefore, the volume of the music box is 30 2/5 in.^3.
Is r = 3 + 3sin θ symmetrical along the y axis?
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
A restaurant offer 7 appetizers and 10 main courses.In how main ways can a person order a two-course meal
Take into account that there are 7 chices for the first course, and there are 10 choices for the entree.
The total number of choices is given bye:
total_choices = Choices_for_first_course x choices_fro_entree
Then, by replacing the values of the previous parameters you get:
total_choices = 7 x 10 = 70
There are 70 ways a person can order a two-course meal
The Connecticut River flows at a rate of 6 km / hour for the length of a popular scenic route. If a cruiser to travels 3 hours with the current to reach a drop-off point, but the return trip against the same current took 7 hours. Find the speed of the boat without a current?The speed of the boat without a current is ____ km/hour. (if needed, round to 2 decimal places).
Given:
Speed of current (y)= 6 km/hour
Distance = d km
Speed of boat in still water = x km/hour
Speed of the cruiser with the current= (x+6) km/hour
Speed of the cruiser against the current= (x-6) km/hour
[tex]\text{Time to travel with the stream=}\frac{d}{x+6}[/tex][tex]3=\frac{d}{x+6}[/tex][tex]3\mleft(x+6\mright)=d[/tex][tex]d=3x+18\ldots.\text{ (1)}[/tex][tex]\text{Time to travel }against\text{ the stream=}\frac{d}{x-6}[/tex][tex]7=\frac{d}{x-6}[/tex][tex]d=7x-42\ldots.\text{ (2)}[/tex]From equation (1) and (2)
[tex]7x-42=3x+18[/tex][tex]7x-3x=18+42[/tex][tex]4x=60[/tex][tex]x=15[/tex]Therefore the speed of the without a current is 15km/hour.
Question 2 1 Simplify. DO NOT PUT ANY SPACES IN YOUR ANSWER. Keep you answer in fraction form. -2/5t - 6+ 2/3t + 15
-2/5t - 6 + 2/3t + 15
Combining similar terms
(-2/5t + 2/3t) + (-6 + 15)
4/15t + 9
Parallel to x = -4 and passing through the point (-3,-5)find the equation of the line
A line of the form x = a, where "a" is a number is a VERTICAL LINE. The graph of the line x = - 4 is shown below:
The line that is parallel to this will also be a vertical line of the form x = a.
The line parallel passes through (-3, -5). So, this will have equation
x = - 3
Answer[tex]x=-3[/tex]
If | m, find the value of x.
1
m
(5x + 9)°
84°
Answer:
15
Step-by-step explanation:
5x + 9 and 84 are alternate interior angles.
Since,
lines l and m are parallel, alternate interior angles are equal.
So,
5x + 9 = 84
Step 1 : Subtract 9 on both sides.
5x = 84 - 9
5x = 75
Step 2 : Divide 5 on both sides.
x = 75/5
x = 15
Hence,
The value of x is 15.
9.) What type of relationship is indicated by the following set of ordered pairs (linear or quadratic)? Explain/Show
how you know by finding successive differences
X
-2
-1
0
1
2
3
Y=-4x-3
Y
14
-1
-6
-1
14
39
10.) Write the equation for question 9 showing all your work for full credit.
11.) Calculate fl-7) for the equation you wrote in Q10. Pls answer all 3 question will mark Brainliest
Step-by-step explanation:
9)
it is not linear, because while x is increasing with every data point by 1, y is decreasing and increasing again, and the differences from one point to the other vary.
for a linear relationship also y has to change in a constant way, and the difference from one point to the next would be the same for all points.
10)
so, since it is not linear, it is quadratic then (since that was our only given alternative).
y = ax² + bx + c
we know c from point (0, -6). c = -6.
for a and b we need to use 2 data points with their x and y coordinates.
let's start with the first (-2, 14)
14 = a×(-2)² + b×-2 - 6 = 4a - 2b - 6
we can simplify that
7 = 2a - b - 3
and then
10 = 2a - b
the next point is (-1, -1)
-1 = a×(-1)² + b×-1 - 6 = a - b - 6
5 = a - b
so, we have the 2 equations
10 = 2a - b
5 = a - b
from the second we get
a = 5 + b
and that we can use in the first equation
10 = 2×(5 + b) - b = 10 + 2b - b
0 = b
therefore
5 = a - b = a - 0 = a
a = 5
and the equation is
y = 5x² - 6
11)
f(-7) = 5×(-7)² - 6 = 5×49 - 6 = 245 - 6 = 239
debbie and tom's bill for dinner was $58. They left a tip of $8.70. what percent of the bill was the tip?
The value of the bill was $58. The tip was $8.7. Percentage is expressed in terms of 100. To determine the percentage of the bill that was the tip, we would find the ratio of the tip to the bill and multiply by 100. It becomes
8.7/58 * 100
= 15%
The tip was 15% of the bill
If the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below A and B, to make this rectangle?
Answer:
C(2,-2), D(-1,-2)
Explanation:
The area of a rectangle is calculated using the formula:
[tex]A=L\times W[/tex]• From the graph, AB = 3 units.
,• Given that the area = 12 square units
[tex]\begin{gathered} 12=3\times L \\ L=\frac{12}{3}=4 \end{gathered}[/tex]This means that the distance from B to C and A to D must be 4 units each.
Count 4 units vertically downwards from A and B.
The coordinates of C and D are:
• C(2,-2)
,• D(-1,-2)
The first option is correct.
use Pythagoras rule to find the slant height of a cone a height of 8 and base radius of 6cm
The Pythagoras rule states that the square hypotenuse is equal to the sum of the squares of the other two sides
In this case, we are given both sides' measures and are asked about the hypotenuse. We leave the hypotenuse on the left side alone by applying the square root on both sides
L = √64+36
L= √100
L = 10
Line segment MN is the image of CD after a dilation by a factor k with a center at point A. Using your ruler, determine the value of k to the nearest hundredth. Show the work that leads to your answer.
Methjod th find the asnswer to thsi question.
First of mark a point on the line segment CD. Then, draw a perpendicular from that point to the a point to the line segment MN.
Then, mesure the length of the line segment.
Thus, the value of k is obtained.
Check picture pls this is geometry work
Answer:
45
scalene
acute
Step-by-step explanation:
Answer: The triangle classified by the sides is 59 degrees. The triangle is classified by the angel is 1
Step-by-step explanation:
I need to find the length x of KL
Answer:
3.6Step-by-step explanation:
We're going to use length DC and ML, along with DA and MJ
[tex]\frac{DC}{ML} = \frac{5}{6}[/tex] which is 0.833333333
now for
[tex]\frac{DA}{MJ} =\frac{7}{8.4}[/tex] which is 0.833333333 (again)
as you can see since the shapes ABCD and JKLM are similar, they have a relationship which in this case is 0.833333333
and we can use this 0.833333333 to help us find the length of KL
knowing that any length for ABCD divided by JKLM is 0.833333333
we can do
[tex]\frac{CB}{LK}=0.833333333[/tex]
since we don't know what KL is, we can switch the spots and enlongate it, to become:
[tex]\frac{CB}{0.833333333} =LK[/tex]
put in the value for CB
[tex]\frac{3}{0.833333333} =LK[/tex]
and we get 3.6
The length of x of KL is...
3.6Which expression is equivalent to ( 43.4-2)-2 ?
EXPLANATION
The expression that is equivalent to (43,4 - 2)-2 is given appyling the distributive property as follows:
-86.8 + 4 = -82.8
I need help finding the area of the sector GPH?I also have to type a exact answer in terms of pi
Let us first change the 80° to radians.
[tex]\text{rad}=80\cdot\frac{\pi}{180}=\frac{4\pi}{9}[/tex]so we get that the area is
[tex]\frac{2}{9}\pi\cdot12^2=144\cdot\frac{2}{9}\pi=32\pi[/tex]so the area is 32pi square yards
Rolls are being prepared to go to grocery stores. Divide 72 rolls into 2 groups so the ratio is 3 to 5
The number of rolls divided in the two groups so that the ratio is 3 to 5 is 27 and 45 respectively.
According to the question,
We have the following information:
Rolls are being prepared to go to grocery stores.
Now, we have to divide 72 rolls into 2 groups so the ratio is 3 to 5.
Now, let's take the number of rolls given to the first group to be 3x and the number of rolls given to the second group to be 5x.
So, we have the following expression:
3x+5x = 72
8x = 72
x = 72/8
x = 9
So, the number of rolls for the first group:
3x
3*9
27
Now, the number of rolls for the second group:
5x
5*9
45
Hence, the number of rolls divided in the given two group is 27 and 45.
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Which phrase best describes the translation from the graph y = 2(x-15)² + 3 to the graph of y = 2(x-11)² + 3?O4 units to the left4 units to the rightO 8 units to the leftO 8 units to the rightMark this and returnSave and ExitNextSubmit
Given:
it is given that a graph of the function y = 2(x-15)^2 + 3 is translated to the graph of the function y =2(x - 11)^2 + 3
Find:
we have to choose the correct option for the given translation.
Explanation:
we will draw the graphs of both the functions as following
The graph of the function y = 2(x - 15)^2 + 3 is represented by red colour and the graph of the translated function y = 2(x - 11)^2 + 3 is represented by blue colour in the above graph.
From, the graphs of both functions, it is concluded that the graph of the translated function is shifted 4 units to the left.
A father is 42 years old and his son is y years old. If the difference of their ages 28 years, what is the value of y?
Answer:
Son's age (y) = 14 years
Step-by-step explanation:
According to the question,
Father's age = 42 years
Son's age = y years
Difference between father's & son's age is 28 years. i.e.
Father's age - son's age = 28
42 - y = 28
42 - 28 = y
y = 42 - 28
y = 14
Use the Law of Sines to solve the triangle. Round your answers to two decimal places. (Let b = 5.1.)
Given:-
An image with triangle.
To find:-
The value of B,a,c.
So the laws of sines are,
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]So now we substitute the known values. we get,
[tex]\frac{\sin16}{a}=\frac{\sin B}{5.1}=\frac{\sin125}{c}[/tex]Now we find the value of B,
Since the sum of angles of the triangle is 180. we get,
[tex]\begin{gathered} A+B+C=180 \\ 16+B+125=180 \\ B+141=180 \\ B=180-141 \\ B=39 \end{gathered}[/tex]So substituting the value we get,
[tex]\frac{\sin16}{a}=\frac{\sin 39}{5.1}=\frac{\sin125}{c}[/tex]Now we find the value of a. we get,
[tex]\begin{gathered} \frac{\sin16}{a}=\frac{\sin 39}{5.1} \\ \frac{0.2756}{a}=\frac{0.6293}{5.1} \\ a=\frac{0.2756\times5.1}{0.6293} \\ a=2.2335 \end{gathered}[/tex]Now we find c. we get,
[tex]\frac{0.2756}{2.2335}=\frac{\sin 125}{c}[/tex]So
The table shows the amount of water used daily to water the fairways at Fairlawn Golf Course. To the nearest tenth,determine the mean absolute deviation of the data. A. 2.3 B. 7.7 C. 10 D. 12.3
Answer:
2.3
Explanation:
The formula for calulating mean deviation is expressed as:
[tex]\frac{1}{n}\sum ^n_{i\mathop=1}|x_i-m|[/tex]where;
m is the mean of the data set
Xi are individual values
n is the total sample space
Get the mean;
n = 7
mean = (10+12+11+15+9+8+5)/7
mean = 70/7
mean = 10
Get the mean deviation:
Mean deviation = (10-10)+(12-10)+(11-10)+(15-10)+(9-10)+(8-10)+(5-10)/7
Since the values is in modulus |xi - m| will give a positive value, hence;
Mean deviation = (0+2+1+5+1+2+5)/7
Mean deviation = 16/7
Mean deviation = 2.28
Mean deviation = 2.3 (to the nearest tenth)
An empty rectangular tank measures 60 cm by 50 cm by 56 cm. It is being filled with water flowing from a tap at rate of 8 liters per minute. (a) Find the capacity of the tank (b) How long will it take to fill up (1 liter = 1000 cm
(a) The capacity of the tank is its volume, which we can calculate by multipling its sides:
[tex]V=abc=60\cdot50\cdot56=168000[/tex]This is, 168000 cm³. It is equivalent to 168 L.
(b) If the tank is being filled at a rate of 8 liters per minute, we can find the time to fill ir by dividing its capacity by the rate:
[tex]t=\frac{168}{8}=21[/tex]That is, it will take 21 minutos to fill it up.
From 2014-2015 to 2024-2025, the number of students enrolled in an associate degree program is projected to increase by 23.1 %. If the enrollment in associate degree programs in 2014-2015 is 6,400,000 , find the increase and the projected number of students in an associate degree program in 2024-2025.
The increase in number will be 1,478,400.
The projected number of students in an associate degree program in 2024-2025 is 7878400.
How to calculate the value?The the number of students enrolled in an associate degree program is projected to increase by 23.1 % and the enrollment in associate degree programs in 2014-2015 is 6,400,000.
The increase will be:
= Percentage increase × Enrollment
= 23.1% × 6,400,000
= 1,478,400
The projected number will be:
= Original number + Increase
= 6400000 + 1478400
= 7878400
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Select all of the expressions approval to c⁶/d⁶:
answers:
(cd-¹)⁶
c¹²d¹⁸/c²d³
c⁸d⁹/c²d³
c⁶d-⁶
c-⁶d⁶
(c‐¹d)-⁶
Answer:
is = c⁸d⁹/c²d³
hope it helps
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solve by square roots: 16k^2-1=24
we have
[tex]16k^2-1=24[/tex]step 1
Adds 1 both sides
[tex]\begin{gathered} 16k^2-1+1=24+1 \\ 16k^2=25 \end{gathered}[/tex]step 2
Divide by 16 both sides
[tex]\begin{gathered} \frac{16}{16}k^2=\frac{25}{16} \\ \text{simplify} \\ k^2=\frac{25}{16} \end{gathered}[/tex]step 3
Applying square root both sides
[tex]k=\pm\frac{5}{4}[/tex]If f(x) = x² is vertically stretched by a factor of 18 to g(x), what is the equation of g(x)?
We need to find the equation of the new function g(x) obtained by vertically stretching the function:
[tex]f\mleft(x\mright)=x²[/tex]Vertically stretching a function by a factor of k corresponds to multiplying the whole expression of function by k:
[tex]g(x)=k\cdot f(x)[/tex]In this problem, we have k = 18. Thus, we obtain:
[tex]g(x)=18\cdot f(x)=18x²[/tex]Answer: C. g(x) = 18x²
you want to buy one pair of pants, one t-shirt, and several pairs of socks. the pants cost $24.95, the t-shirt cost $22.50 and the socks are $5.95 per pair. how many pairs of socks can you buy if you have $80 to spend?*for this question you have to write and inequality solve it and answer the question in words*
ANSWER
5 pairs
EXPLANATION
We have that:
- one pair of pants cost $24.95
- one t-shirt costs $22.50
- one pair of socks cost $5.95
You want to buy one pair of pants, one t-shirt and several pairs of socks and you don't want to spend more than $80.
This means that everything you spend must be less than or equal to $80.
Let the number of pairs of socks you can buy be x.
This therefore means that:
[tex]\begin{gathered} 24.95+22.50+(5.95\cdot x)\text{ }\leq80 \\ \Rightarrow\text{ }24.95\text{ + 22.50 + 5.95x }\leq80 \\ \text{Find x:} \\ 47.45\text{ + 5.95x }\leq80 \\ \Rightarrow\text{ 5.95x }\leq80\text{ - 47.45} \\ 5.95x\text{ }\leq32.55 \\ x\text{ }\leq\frac{32.55}{5.95} \\ x\leq5.47 \end{gathered}[/tex]Because we know that the number of pairs of socks must be a whole number, we have to approximiate to whole number, which will be:
x = 5
Therefore, you can buy at most 5 pairs of socks.
help meeeee pleaseeeee!!!
thank you
The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.
According to the question,
We have the following function:
f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]
Now, in order to find the value of f(0), we will put 0 in place of x.
f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]
f(0) = 0+7*0-0+12
(More to know: when a number is multiplied with 0 then the result is always 0 even the number being multiplied with zero is in lakhs.)
f(0) = 0+0-0+12
f(0) = 12
Now, in order to find the value of f(2), we will put 1 in place of x:
f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]
f(2) = -8+7*4-4+12
f(2) = -8+28-4+12
f(2) = 40 -12
f(2) = 28
Now, in order to find the value of f(2), we will put -2 in place of x:
f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]
f(-2) = -(-8) + 7*4+4+12
f(-2) = 8+28+4+12
f(-2) = 52
Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.
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Allison earns $6,500 per month at her job as a principal the chart below shows the percentages of her budget. how much does Allison pay for her mortgage
Total earning for Allison is $6,500 per year
mortage = 24.6%
he spent 24.6% of his salary on mortgage
24.6 / 100 x 6500
0.246 x 6500
= $ 1599
He spent $1,599 on mortgage
use the number line to find the distance between -3 and -9
Answer:
a) 6
b) 6
-6
c) 6
6
Explanation:
a) For the number line, the distance will be the difference between the endpoint and the initial point as shown;
Distance = -3 - (-9)
Distance = -3 + 9
Distance = 6units
b) -3 - (-9)
= -3 + 9
= 6
c) -9 - (-3)
= -9 + 3
= -6
d) For the modulus
|-3 - (-9)|
= |-3 + 9|
= |6|
Since the modulus of a value returns a positive value, |6| = 6
e) |-9-(-3)|
= |-9+3)|
= |-6|
Since the modulus of a negative value gives a positive value, hence;
|-6| = 6
Answer:
a) 6
b) 6
-6
c) 6
6
Explanation:
a) For the number line, the distance will be the difference between the endpoint and the initial point as shown;
Distance = -3 - (-9)
Distance = -3 + 9
Distance = 6units
b) -3 - (-9)
= -3 + 9
= 6
c) -9 - (-3)
= -9 + 3
= -6
d) For the modulus
|-3 - (-9)|
= |-3 + 9|
= |6|
Since the modulus of a value returns a positive value, |6| = 6
e) |-9-(-3)|
= |-9+3)|
= |-6|
Since the modulus of a negative value gives a positive value, hence;
|-6| = 6
Find the probability of getting 4 aces when 5 cards are drawn from an ordinary deck of cards
First, let's calculate the number of different hands of 5 cards that can be made, using a combination of 52 choose 5:
(a standard deck card has 52 cards)
[tex]C\left(52,5\right)=\frac{52!}{5!\left(52-5\right)!}=\frac{52\cdot51\operatorname{\cdot}50\operatorname{\cdot}49\operatorname{\cdot}48\operatorname{\cdot}47!}{5\operatorname{\cdot}4\operatorname{\cdot}3\operatorname{\cdot}2\operatorname{\cdot}47!}=\frac{52\cdot51\operatorname{\cdot}50\operatorname{\cdot}49\operatorname{\cdot}48}{120}=2,598,960[/tex]Now, let's calculate the number of hands that have 4 aces. Since the fifth card can be any of the remaining 48 cards after picking the 4 aces, there are 48 possible hands that have 4 aces.
Then, the probability of having a hand with 4 aces is given by the division of these 48 possible hands over the total number of possible hands of 5 cards:
[tex]P=\frac{48}{2598960}=\frac{1}{54145}[/tex]The probability is 1/54145.