The shallowest section of an underground tunnel is -50 feet. The deepest section of the tunnel is -135 feet. How many feet below the shallowest section is the deepest section?
A. -95 feet
B. -185 feet
C. 85 feet
D. 195 feet
Answer:
c
Step-by-step explanation:
1) eliminate the negative answers since we need the amount of feet below a section and a negative number below a section doesn't make sense in this context and would result in a distance higher than the shallowest section.
Just find the absolute value or the difference between 135 and 50 resulting in 85
Given that B is the midpoint of the arc AC, find
(i) the length of BD,
(ii) the perimeter of the shaded region
(iii) the area of the shaded region.
Ans:
8.49
21.4
20.5
i. Line BD = 6√2 cm
ii. Perimeter = 3 (π + 4) cm
iii. Area = 18 ( π - 2) cm
How to determine the parametersLet the length of BD = x
Since B is the midpoint of the arc AC, then ∠BOC = 15°
In ΔBDB
Let's use the trigonometric ration, tan
[tex]Tan 45 = \frac{BD}{CD}[/tex]
CD = x
Then, using the Pythagorean theorem
[tex]x^2 + x^2 = 12^2[/tex]
[tex]2x^2 = 144[/tex]
[tex]x^2 = \frac{144}{2}[/tex]
[tex]x = \sqrt{72}[/tex]
[tex]x = \sqrt{36 *2}[/tex]
[tex]x = 6\sqrt{2}[/tex]
Thus, line BD is [tex]6\sqrt{2}[/tex] cm
ii. Perimeter = BC + BD + CD
= 2πr/8 + x + r - x
= π(12)/4 + r
= 3π + 12
= 3 ( π + 4) cm
iii. Area of shaded area = Area of BOC + Area of BOD
⇒ πr^2/8 × 1/2x^2
= π144/8 × 1/2(72)
= 18π - 36
= 18 ( π - 2) cm²
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This table shows values represented by an exponential function x= 0,1,2,3,4,5,6 y=1,3,9,27,64,125,216 what is the average rate of change for this function for the interval from x=2 to x=4?
27.5 is the answer
For this case we know that the average rate of change of a function is given by this general expression:
m = f(b) - f(a)/ b-a
For this special case from the info in the table we have:
a =2 , f(2) = 9
a =4 , f(4) = 64
And replacing the data with the average rate formula we got:
m = 64 - 9/4 - 2 = 27.5
And then the best answer for this case would be:
27.5
The exponential function is a mathematical function represented by f (x) = \ exp or e ^ {x}. Unless otherwise specified, the term generally refers to a function of a positive value of a real variable, but it can also be extended to complex numbers or generalized to other mathematical objects such as matrices and Lie algebras.
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Which expression is equivalent to startroot 8 x superscript 7 baseline y superscript 8 baseline endroot? assume x greater-than-or-equal-to 0.
Expression which is equivalent to [tex]$\sqrt{8 x^{7} y^{8}}[/tex] is [tex]$=2 \sqrt{2} x^{3} y^{4} \sqrt{x}$[/tex].
What are equivalent expressions?
Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).
Solution of the given equation [tex]$\sqrt{8 x^{7} y^{8}}[/tex].
[tex]$\sqrt{8 x^{7} y^{8}}=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]
[tex]$=\sqrt{8} \sqrt{x^{7}} \sqrt{y^{8}}$[/tex]
Simplify [tex]$\sqrt{x^{7}}: x^{3} \sqrt{x}$[/tex]
[tex]$=\sqrt{8} x^{3} \sqrt{x} \sqrt{y^{8}}$[/tex]
Simplify [tex]$\sqrt{y^{8}}: y^{4}$[/tex]
[tex]$=\sqrt{8} x^{3} \sqrt{x} y^{4}$[/tex]
[tex]$\sqrt{8}=2 \sqrt{2}$[/tex]
[tex]$=2 \sqrt{2} x^{3} \sqrt{x} y^{4}$[/tex]
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The complete question is :
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0. x y squared StartRoot 8 x cubed EndRoot 2 x cubed y cubed StartRoot x y squared EndRoot 2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot 4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
In gym class, the students are going to design and build obstacles for an upcoming field day. Before they can start building, each student has to submit a two-dimensional scale drawing of the obstacle they want to build. Barbara's drawing of her obstacle is shown below.
Note: Figure not drawn to scale.
In Barbara's drawing, the obstacle has a total area of______ square feet.
This obstacle will have a width of 4 feet. The volume of the obstacle is____cubic feet.
The obstacle has a total area of 69 square feet and a volume of 276 cubic feet.
The total area of the obstacleTo determine the total area, we calculate and add up the area of each shape.
The shapes in the figure are:
Triangle: Base = 1, Height = 6Triangle: Base = 5, Height = 8Square: Length = 2Rectangle: Length = 7; Width = 6Using the area formula of each shape, the total area is:
Total = 0.5 * 1 * 6 + 0.5 * 5 * 8 + 2 * 2 + 7 * 6
Evaluate
Total = 69
Hence, the obstacle has a total area of 69 square feet.
The volume of the obstacleThis is calculated as:
Volume = Base area * Height
The height is 4.
So, we have:
Volume = 69 * 4
Evaluate
Volume = 276
Hence, the obstacle has a volume of 276 cubic feet.
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Equal amounts of peanuts, cashews, and almonds are packed separately in bags. If 3 bags, one of each kind, cost a total of $3.00 and 2 bags of peanuts and 2 bags of cashews cost a total of $3.50, how much does 1 bag of almond cost
The cost of 1 bag of almond is $1.25
What is linear equation?
An equation in which the highest power of the variable is one is known as linear equation.
We can find the cost of 1 bag of almond as shown below:
Let the cost of 1 bag of peanut be $x
Let the cost of 1 bag of cashews be $y
Let the cost of 1 bag of almonds be $z
x + y + z=3 (1)
2x+2y=3.50
Dividing by 2
x + y=1.75
Putting in equation (1)
1.75+z=3
z=3-1.75
z=1.25
Hence, the cost of 1 bag of almond is $1.25
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Ammonia (NH3) can be made using the reversible reaction shown. Which change would keep this reaction from shifting to form more of the produce Decreasing the pressure in the reaction ? 3H2 + N2 ⇄ 2NH3 + energy A. Decreasing the pressure in the reaction vessel
Decreasing the pressure in the reaction vessel will keep this reaction from shifting to form more of the produce(ammonia).
What is Pressure?This is defined as the force per unit area of a body and the S. I unit is in Pascal.
Ammonia production involves reaction between hydrogen and nitrogen gas in which pressure has an effect on the reaction rate unlike in solids and liquids. An increase in pressure will result in more products being formed and vice versa.
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Find 8. Round to the nearest degree.
OA. 68°
OB. 69°
OC. 22°
OD. 21°
Answer:
A
Step-by-step explanation:
[tex]\cos \theta=\frac{3}{8} \\ \\ \theta=\cos^{-1} \left(\frac{3}{8} \right) \\ \\ \theta \approx 68^{\circ}[/tex]
Identify the function with a period of 4 and an amplitude of 2.
Answer:
it's only 2pi/B because the period of sin and cos is 2pi. If we were dealing with tan it'd be pi/B, since the period of tan is just pi.
Rationalize the denominator:
GRADE 9
CBSE
Answer:
1. a)
[tex] \begin{gathered} \frac{2}{ \sqrt{3} - 1 } = \frac{2}{ \sqrt{3} - 1} \times \ \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1 } \\ = \frac{2 \sqrt{3} + 2 } {( \sqrt{3} ) {}^{2} - 1 {}^{2} } = \frac{2 \sqrt{} 3}{3 - 1} = \frac{2 \sqrt{3} }{2} \\ = \sqrt{3} \end{gathered}[/tex]
[tex]\\[/tex]
b)
[tex]\begin{gathered} = > \: \: \frac{7}{ \sqrt{12} - \sqrt{5} } \\ \\ = > \: \: \frac{7}{ \sqrt{12} - \sqrt{5} } \times \frac{ \sqrt{12} + \sqrt{5} }{ \sqrt{12} + \sqrt{5} } \\ \\ = > \: \: \frac{7( \sqrt{12} + \sqrt{5} ) }{ {( \sqrt{12}) }^{2} - {( \sqrt{5}) }^{2} } \\ \\ = > \: \: \frac{7( \sqrt{12} + \sqrt{5}) }{12 - 5} \\ \\ => \: \: \frac{ \cancel{7}( \sqrt{12} + \sqrt{5} ) }{ \cancel{7}} \\ \\ => \: \: \sqrt{12} + \sqrt{5} \end{gathered}[/tex]
1-:
[tex] \displaystyle \frac{2}{ \sqrt{3} - 1 } [/tex]
[tex] \displaystyle = \frac{2}{( \sqrt{3} - 1)( \sqrt{3} + 1 } \\ [/tex]
[tex] \displaystyle2 \frac{ \sqrt{3} + 1 }{ \sqrt{3 {}^{2} - 1 {}^{2} } } [/tex]
by( a-b×a+b=a²b²)[tex] \displaystyle2 \frac{ \sqrt{3} + 1}{3 - 1} [/tex]
[tex] \displaystyle \: \sqrt{3} + 1[/tex]
[tex] \displaystyle2 - ) \frac{7}{ \sqrt{12} - \sqrt{5} } [/tex]
[tex] \displaystyle\frac{ \sqrt{12} \sqrt{5} }{ \sqrt{12 {}^{2} } \times \sqrt{5 {}^{2} } } [/tex]
[tex] \displaystyle7\frac{ \sqrt{12} + \sqrt{5} }{7} = \sqrt{12} + \sqrt{5} [/tex]
[tex] \displaystyle3) = \frac{8 + 3 \sqrt{5} }{64 - 45} \\ = \frac{8 - 3 \sqrt{5} }{19} [/tex]
bridget went fishing with her dad. Bridget caught the first fish of the day and it weighed f ounces. that day she caught four more fish one was 2 times the weight of the first fish another was 2 more than 3 times the weight of the first fish. next was 1/2 the weight of the first fish and the last was 3/5 the weight of the first fish. bridgets dad caught four fish. the first fish he caught weighed 2 more than 3 times the weight of the first fish that day one fish weighed 4/5 the weight of the first fish caught that day one weighed 4 more than 2 times the weight of the first fish cought that day and the last weighed 1/2 the weight of the first fish caught.
Assuming all the fishes caught by Bridget and her dad have the same total weight, then the first fish Bridget caught would weigh 5 ounces while the first fish caught by her dad weighed 17 ounces.
What is weight?Weight can be defined as the force acting on an object or a physical body due to the effect of gravity. Also, the weight of a physical object (body) is typically measured in Newton or ounces.
How to calculate the weight of the first fish?First of all, we would determine the weight of all of the fishes caught by both Bridget and her father (dad) while translating the word problem into an algebraic equation as follows:
For Bridget, we have:
Bridget's fish = f + 2f + 3f + 2 + ½f + ⅗f
Bridget's fish = 7 f/10 + 2 ......equation 1.
For her dad, we have:
Dad's fish = 3f + 2 + ⅘f + 2f + 4 + ½f
Dad's fish = 6 3f/10 + 6 ......equation 2.
Equating eqn. 1 and eqn. 2, we have:
7 f/10 + 2 = 6 3f/10 + 6
7 f/10 - 6 3f/10 = 6 - 2
8f/10 = 4
8f = 40
f = 40/8
Bridget, f = 5 fishes.
Since her dad's fish weighed 2 more than 3 times, we have:
Dad = 3f + 2
Dad = 3(5) + 2
Dad = 15 +2
Dad = 17 ounces.
In conclusion, the first fish Bridget caught would weigh 5 ounces while the first fish caught by her dad weighed 17 ounces assuming all the fishes caught by Bridget and her dad have the same total weight.
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Complete Question:
Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was 2 times the weight of the first fish, another was 2 more than 3 times the weight of the first fish, the next was 1/2 the weight of the first fish, and the last was 3/5 the weight of the first fish. Bridget’s dad caught four fish. The first fish he caught weighed 2 more than 3 times the weight of the first fish caught that day. One fish weighed 4/5 the weight of the first fish caught that day, one weighed 4 more than 2 times the weight of the first fish caught that day, and the last weighed 1/2 the weight of the first fish caught that day.
If all the fish Bridget caught have the same total weight as all the fish her dad caught, then the first fish Bridget caught weighed___ ounces and the first fish her dad caught___ weighed ounces.
Find a linear inequality with the following solution set. Each grid line represents one unit.
Give your answer in "standard form" ax+by+c>0 or ax+by+c\geq0 where a, b, and c are integers with no common factor greater than 1.)
The linear inequality in standard form is: x + y < -2 or x + y + 2 < 0
How to Write a Linear Inequality?To determine what sign to use, follow these rules:
Use "<" or ">" when the boundary line is dotted or dashed.Use "<" or "≤" when the shaded area is under the boundary line (dotted or dashed).Use "≤" or "≥" when the boundary line is not dotted or dashed.Use ">" or "≥" when the shaded area is above the boundary line (dotted or dashed).The graph given has the following features:
It has a boundary line that is dotted/dashed.It has a shaded area that is under the boundary line.Thus, the inequality sign we would use is, "<".Find the slope:
Slope (m)= rise/run = -(2 units) / (2 units).
Slope (m) = -1.
The y-intercept (b) = -2.
Substitute m = -1 and b = -2 into y < mx + b:
y < (-1)x + (-2)
y < -x - 2
Rewrite
x + y < -2
x + y + 2 < 0
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Out of a sample 650 high school students, 321 take the bus to school every day. construct a 99% confidence interval for the population mean of high school students that take the bus to school every day.
a.ci=(43.23%,51.18%)
b.ci=(44.34%, 54.43%)
c.ci=(45.54%, 53.23%)
d.ci=(46.16%,52.16%)
A 99% confidence interval for the population mean of high school students that take the bus to school every day is b) ci=(44.34%, 54.43%)
We need to find the 99% confidence interval for the population mean of high school students that take the bus to school everyday
A confidence interval is a range of estimates for an unknown parameter. The confidence interval is calculated at the specified confidence level; the most common is the 95% confidence level, but sometimes other levels are used, such as 90% or 99%.
The confidence interval of proportions is given by:
π ± z √(π (1-π) /n)
π is the sample proportion.
z is the critical value.
n is the sample size.
For 99% confidence interval the value of z is 2.58
π = 321/650
The confidence interval is given by
=321/650 ± 2.58 √( (321/650) × [ 1 - (321/650) ] ÷ 650)
= (0.493846 ± 0.050594)
=(0.4434 , 0.5443)
=(44.34 % , 54.43 %)
Hence a 99% confidence interval for the population mean of high school students that take the bus to school every day is ci=(44.34%, 54.43%)
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Ruby buys 24 books and 5 pens.she pays with a 500 rupee note and get rs90 as change.shania bought 12 books and 10 pens for rs280.find the cost of 1 pen.
The cost of one pen is Rs 15.
How to find the cost of one pen?It is given that Ruby paid with a 500 rupee note and got Rs 90 back.
This means that she spent 410 rupees.
Therefore the cost of 24 books and 5 pens is Rs 410.
Let the cost of books be x and the cost of pens be y.
Therefore, we can form the following equations:
24x + 5y = 410 (1)
12x + 10y = 280 (2)
We have to find the value of y.
Multiply the second equation by 2:
24x + 20y = 560 (3)
Now subtract the first equation from the third equation:
24x + 20y - 24x - 5y = 560 - 410
15y = 150
y = 15.
The variable y represents the cost of one pen.
This means that the cost of one pen is Rs 15.
Therefore, we have found that the cost of one pen is Rs 15.
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Define the domain and range of each function. GRAPH IS BELOW :)
Domain:
Range:
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS!
Answer:
Domain: ( Positive infinity, Negative Infinity)
Range: (-3, Positive Infinity )
Step-by-step explanation:
Find the equation of the line that passes through (-1,2) and is perpendicular to y =2x+1 . Leave your answer in the form y = m x + c
Which of the following systems of equations has the solution (1, 6)?
y = –5x – 1
y = –x + 7
y = 5x + 1
y = x – 7
y = 5x + 1
y = –x – 7
y = 5x + 1
y = –x + 7
Answer:
Step-by-step explanation:
hello :
the system is : y = 5x + 1
y = –x + 7
put : x=1 you have y = 6
The radius of a circle is 58 centimeters. enter the circumference of the circle
Answer:
C = 364.24
Step-by-step explanation:
Comment
The circumference and the radius are related to one another. The constant relating them is pi which is a fixed number of 3.14 The formula for the circumference is C = 2*pi * r
Givens
pi = 3.14
r = 58 cm
Circumference = ?
Formula
C = 2*pi * r
C = 2 * 3.14 * 58
C = 364.24
I AM ASKING AGAIN HELP GUYZ
Answer:
[tex]\huge\boxed{\sf C, \ D \ and \ E}[/tex]
Step-by-step explanation:
Given expression:
= 2(4f + 2g)Distribute 2 to both terms.
= 8f + 4gWe can also split 8f into 4f and 4f.
= 4f + 4f + 4gIf we take 4 common
= 4(f + f + g)
= 4(2f + g)[tex]\rule[225]{225}{2}[/tex]
Answer: Heya! ~
8f + 4g also 4(2f + g) and 4f + 4f+ 4gStep-by-step explanation:
Given: Expression 2(4f + 2g)
We have to choose an equivalent expression to the given expression 2(4f + 2g)
Consider the given expression 2(4f + 2g)
Apply Distributive property, a( b + c) =ab + ac
We have,
a = 2, b = 4f and c = 2g
2(4f + 2g) = 8f + 4g
Now, take 4 common from each term, we have,
8f + 4f = 4 (2f + g)
Now, We have,
a = 2, b = 4f and c = 2g
2(4f + 2g) = 8f + 4g
Now, take 4 common from each term, we have,
8f + 4f = 4 (2f + g)
Now, an equivalent expression to the given expression 2(4f + 2g) is 8f + 4g and 4 (2f + g)
- Keira
The science teacher has to write report cards for all her students. It takes 1/8 of an hour to complete one report card. How many report cards can the teacher complete in 14 hours?
Answer:
112
Step-by-step explanation:
If she takes 1/8 of an hour to complete one then she can finish 8 in 1 hour.
8 x 14 = 112
Arrange the tiles on both boards to find the value of x.
Board sum: 3x + (-5) = 1
What x value solves the equation?
3x - 5 = 1
X =
Answer:
3x-5=1
3x=5+1
3x=6
x=6/3
x=2
This question is worth 15 points.
A bedding set that regularly sells for $86
is on sale with a 20% discount. How
much will the total sale be including a 5%
sales tax?
The total sale of the bedding set including 5% sale tax is $69.66
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Discount = 20% of 86 = 0.2 * 86 = 17.2
Selling price of bed = 5% of 17.2 = 0.05 * 17.2 = 0.86
Total sale = 86 - 17.2 + 0.86 = 69.66
The total sale of the bedding set including 5% sale tax is $69.66
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The nth term of a sequence is 2n2² - 4n+4 Work out the 8th term of the sequence. 8th term= Submit Answer Skip for Now
The nth term of a sequence exists 2n2² - 4n+4 is 36.
What is PEMDAS' order of operations?The order of operations exists as a rule that describes the right sequence of measures for estimating a math expression. We can recognize the order utilizing PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition, and Subtraction (from left to right).
[tex]$2*8*2^{2} - 4*8+4[/tex]
Follow the PEMDAS order of operations
Calculating the exponents, we get 2² = 4
[tex]= 2*8*4 - 4*8+4[/tex]
= 64-32 +4
= 36
Therefore, the nth term of a sequence that exists 2n2² - 4n+4 is 36.
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Pack of 100 index cards , 15 cmx 10 cm paper density 200 gsm what is the area of the cards on the table
a)15000 square cm or 1.5 square meter
b)32
c)80 GSM
d)0.405 gram
refer to the following images for solutions :
Index cards are used for a wide range of applications and environments: in the home to record and store recipes, shopping lists, contact information, and other organizational data; in business to record presentation notes, project research and notes, and contact information; in schools as flashcards or other visual.
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Which of these shapes are congruent
Answer:
Option A is probably the answer
If you have any question please contact me
Answer: A is the answer, should be right
At the trial of a contract dispute, the plaintiff has offered to testify to what she heard the defendant say in a private conversation between the two of them, which the plaintiff secretly recorded on an audiotape that she did not offer in evidence. Is the plaintiff's testimony admissible
The plaintiff's testimony is admissible because plaintiff as personal knowledge of the statement of a party-opponent.
How to illustrate the information?The recording is coincidental with firsthand knowledge. The person could testify based upon firsthand knowledge and could also lay the foundation under Article 9 to authenticate the tape.
In this case, the tape is not required as a matter of the original writing rule, giving the proponent options to offer testimony from memory, and/or the opportunity to corroborate the in-court testimony by a demonstrative exhibit
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Put the following equation of a line into slope-intercept form, simplifying all
fractions.
8x +12y = -108
Answer:
y=-(2/3)x -9
Step-by-step explanation:
shuffle the equation so that y is alone in left hand side
The coefficient of x in the right hand side is the slope of line and the other term in right hand side is constant term
The slope-intercept form of the given equation will be y = -2x/3 - 9.
What is slope-intercept form?The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Given an equation, 8x +12y = -108
Converting in slope-intercept form,
12y = -108 - 8x
y = -2x/3 - 9
Hence, the slope-intercept form of the given equation will be
y = -2x/3 - 9.
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3. Which of the following is equivalent to (10a³b³) (5a³b²)?
Answer:
50a^6b^5
Step-by-step explanation:
I don't see answer choices, but this is the simplified version. To do this, multiply 10*5, a^3 * a^3 (which adds the exponents), and then b^3*b^2.
Find the dependent value
for the graph
y = 5x + 30
when the independent value is - 5.
y = [?]
some one help me please
Answer:
(0,3)
Step-by-step explanation:
The y-intercept is the point where the line touches the y-axis and x is 0.
Answer:
(0,3)
Step-by-step explanation:
The y-intercept is when the line crosses the y-axis, in this case the point is at (0,3)