Using the Pythagorean Theorem, the depth of the lake is 57.24 feet.
What is the depth?According to the Pythagorean Theorem, the depth or height is the difference between the squared root of the hypothenuse and the base.
The Pythagorean Theorem Formula is as follows:
a² + b² = c²
Where:
a = side of the right triangle (height, depth, or perpendicular)
b = side of the right triangle (the base)
c = hypotenuse (the longest part or hypothenuse)
Therefore, the depth is:
a² = c² - b²
a² = 100² - 82²
a² = 10,000 - 6,724
a² = 3,276
a = √3,276
a = 57.24
= 57.24 feet
Thus, assuming a flat-bottom lake, its depth is 57.24 feet.
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A circle has a center point at the coordinates P(3,0) with a diameter line RT where R has the coordinates (-47,25).What is the Coordinates Of T
Given: A circle has a center point at the coordinates P(3,0) with a diameter line RT where R has the coordinates (-47,25).
Required: To determine the coordinates of T.
Explanation: The given circle is-
Let the coordinates of T be (x,y). Then the center of a circle is divided by the diameter in the ratio of 1:1. The section formula for a point (x,y) dividing a line segment in the ratio of 1:1 is-
[tex]\begin{gathered} x=\frac{(x_1+x_2)}{2}, \\ y=\frac{(y_1+y_2)}{2} \end{gathered}[/tex]Hence, for the given line RT, point P divided RT in 1:1. Thus-
[tex]\begin{gathered} 3=\frac{-47+x}{2}, \\ 0=\frac{25+y}{2} \end{gathered}[/tex]Further solving for x and y as-
[tex]\begin{gathered} x=6+47 \\ \Rightarrow x=53 \\ and\text{ }y=-25 \end{gathered}[/tex]Final Answer: The coordinates of T are (53,-25).
y= -2x - 7x - y = -8
Given the system of equations:
[tex]\begin{gathered} y=-2x-7\rightarrow(1) \\ x-y=-8\rightarrow(2) \end{gathered}[/tex]we will find the solution to the system by graphing
To draw the lines, we need to know two points on each line
so, substitute with two values of x and calculate the corresponding value of y
For line (1): y = -2x - 7
[tex]\begin{gathered} x=0\rightarrow y=-2\cdot0-7=-7 \\ x=1\rightarrow y=-2\cdot1-7=-9 \end{gathered}[/tex]so, line (1) passes through the points ( 0, -7) and ( 1, -9)
For line (2): x - y = -8
y = x + 8
[tex]\begin{gathered} x=0\rightarrow y=8 \\ x=1\rightarrow y=1+8=9 \end{gathered}[/tex]So, line 2 passes through the points ( 0, 8) and ( 1, 9)
The graph of the line will be as shown in the following picture
As shown in the figure:
Line (1) is the blue line
Line (2) is the red line
The point of intersection = ( -5, 3)
So, the solution is point ( -5, 3)
Subtract the expressions. (10y - 2) - (8y + 3)
SOLUTION
We want to solve the expression
[tex]\mleft(10y-2\mright)-(8y+3)[/tex]Now, use the minus sign to multiply the other part
That is
[tex]-(8y+3)[/tex]We have
[tex]\begin{gathered} (10y-2)-(8y+3) \\ 10y-2-8y-3 \\ \text{collecting like terms } \\ 10y-8y-2-3 \\ 2y-5 \end{gathered}[/tex]Hence the answer is 2y - 5
the red line equation is y=0.5*2^xthe blue line equation is y=2x+25Compare and contrast this graph
In this question, we are given two lines.
1) y = 0.5*2^x
2) y = 2x + 25
The standard equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
The positive slope moves the line upwards and the negative slope moves the line downwards.
If we compare both the equations, we see the 2nd equation maps with the standard line form. Hence, the second equation is a line with the slope equals to 2 and y-intercept equals 25. As the slope is positive, the line is moving upwards.
The standard equation of an exponential function is y = a*b^x, where b is the base, x is the exponent and a is the y-intercept.
The positive value of the base moves the function upwards and the negative value moves it downwards.
If we compare both the equations, we see the 1st equation maps with the standard exponential form. Hence, the 1st equation is an exponent form with the base to 2 and y-intercept equals 0.5. As the base is positive, the line is moving upwards.
Steps Jeanne has a coupon for $1.95 off a jug of name-brand laundry detergent that normally costs $14.99. The store-brand laundry detergent costs $11.53. How much will Jeanne save if she buys the store-brand detergent instead of using her coupon and buying the name-brand?
we can do a subtraction to calculate the savings
[tex]14.99-11.53=3.46[/tex]will save 3.46 buying store-brand laundry detergent
and your savings from using the coupon are 1.95
We make a subtraction between the savings to know how much you save more with one method than with the other
[tex]3.46-1.95=1.51[/tex]she save $1.51 more buying store-brand
Unit 2: homework 9 shingle proofs
Identify the values of a, b, and c for the quadratic equation given:y=-x2 +9a =b =C=
Question:
Solution:
A quadratic Equation in Standard Form is given by the following formula:
[tex]ax^2+bx\text{ + c = 0}[/tex]now, the given equation is
[tex]y=-x^2+9[/tex]this is equivalent to:
[tex]f(x)=-x^2+9[/tex]According to the Quadratic Equation in Standard Form, we can conclude that
[tex]a\text{ = -1}[/tex][tex]b\text{ = 0}[/tex]
and
[tex]c\text{ = 9}[/tex]A salad recipe requires 3 cups of spinach and 1/2 cup of pecans. At this rate, what amount of pecans should be used with 2 cups of spinach?
We need 3 cups of spinach for each 1/2 cup of pecans.
Then we have:
[tex]\begin{gathered} \frac{2\text{ cups of spinach}}{3\text{ cups of spinach}}=\frac{x\text{ cups of pecans}}{\frac{1}{2}\text{ cups of pecans}} \\ \frac{x}{\frac{1}{2}}=\frac{2}{3} \\ x=\frac{1}{2}\cdot\frac{2}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]Answer: It will be needed 1/3 cup of pecans
Which graph IS a function?
Answer:
Graph A
Step-by-step explanation:
It is a function of f(x) = 2
6 minus 3 times a number is less than 30. Find the number:
x > -8
Explanations:Let the number be represented by x:
Three times the number = 3x
Six minus three times the number = 6 - 3x
Six minus three times the number is less than 30:
That can be interpreted mathematically as:
6 - 3x < 30
To find the value of x:
Step 1: Collect like terms
- 3x < 30 - 6
-3x < 24
Step 2: Divide both sides by 3:
[tex]\frac{-3x}{3}=\text{ }\frac{24}{3}[/tex]-x < 8
Multiply both sides by (-1) and change the < sign to >
(-1) (-x) > 8 x(-1)
x > -8
20% of blank = 100 I suck at math
Answer:
20% means divide by 5 so 100 * 5 = 500
Step-by-step explanation:
because 20% of 500 is 100
Hello!
Original Question: 20% of blank = 100
⇒ 20% = [tex]\dfrac{20}{100} =0.2[/tex]
⇒ 0.2 of blank ⇒ 0.2 * blank = 100
Let's solve:
[tex]0.2 *\text{blank}=100\\\\blank = \dfrac{100}{0.2} = 500[/tex]
Thus blank is 500!
Answer: 500
Hope that helps!
#17 - A bin contains 90 batteries (all size C). There are 30 Eveready, 24 Duracell, 20 Sony,10 Panasonic, and 6 Rayovac batteries. What is the probability that the battery selected is aDuracell?0 27.6%0 26.7%24.6%0 29.2%
According to the basic definition of probability,
[tex]\text{Probability}=\frac{\text{ No. of favorable events}}{\text{ Total no. of events}}[/tex]Given that the bin contains total 90 batteries, out of which 24 are duracell.
So the probability that a randomly selected battery is Duracell, is calculated as,
[tex]\begin{gathered} P(\text{Duracell)}=\frac{\text{ No. of Duracell Batteries}}{\text{ Total no. of batteries}} \\ P(\text{Duracell)}=\frac{24}{90} \\ P(\text{Duracell)}\approx0.267 \\ P(\text{Duracell)}\approx26.7\text{ percent} \end{gathered}[/tex]Thus, the probability that a randomly selected battery is Duracell, is 26.7% approximately.
4. Use the graph below to answer the following questions.
By the concept of set builder notification
(b) 4
(c) 6
(d) -6
What is the set builder notification?In mathematics, the set-builder notation is used to express a set's elements or specify the conditions that each member of the set must meet. for instance The notation for the set builder is A = x Z | x 4 for the supplied set A =..., -3, -2, -1, 0, 1, 2, 3, 4. Sets can also be expressed using an interval or an equation by using the set-builder notation. In many cases, sets with an infinite number of elements have their elements written and represented in this way. These include integers, real numbers, and natural numbers, among other popular forms of numbers. One (or more) variables from these categories are utilized in this.
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Please help quick :/
Answer:
The design fee is $40.
Step-by-step explanation:
The y intercept means the cost when the number of shirts ordered is 0. This means that in the context of this problem the y intercept is the design fee.
Translate to system Grandpa and Grandma are treating their family to the movies. Matineetickets cost $4 per child and $4 per adult. Evening tickets cost $6 per childand $8 per adult. They plan on spending no more than $80 on the matineetickets and no more than $100 on the evening tickets.
Answer:
4x + 4y ≤ 80
6x + 8y ≤ 100
Explanation:
Let's define x as the number of children and y as the number of adults.
For Matinee tickets, they spend $4 per child and $4 per adult, so if the total is no more than 80, we get:
4x + 4y ≤ 80
In the same way, they spend $6 per child and $8 per adult on the evening tickets, so
6x + 8y ≤ 100
Therefore, the system is
4x + 4y ≤ 80
6x + 8y ≤ 100
LaVelle is making a pitcher of caffe mocha. For each ounce of chocolate syrup, she uses 5 ounces of coffee. She wants to make 48 ounces of caffe mocha.
Let c represent the number of ounces of coffee, and let s represent the number of ounces of chocolate syrup used. Which of the following systems of equations models this situation?
The systems of equations which correctly models the situation as described is;
s = 5c ands + c = 48Which systems of equations correctly models the situation as described in the task content?It follows from the task content that the system of equations which models the production process of caffe mocha be determined.
As given in the task content;
Let c represent the number of ounces of coffee.Let s represent the number of ounces of chocolate syrup.Hence, since For each ounce of chocolate syrup, she uses 5 ounces of coffee, the situation can be represented algebraically as;
s = 5c.Also, since she wants to make 48 ounces of caffe mocha; we have;
s + c = 48.Therefore, the required system of equations is;
s = 5c ands + c = 48.Read more on system of equations;
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I can't find the last mark can someone help please
Step-by-step explanation:
right, M = ((xa + xb)/2, (ya + yb)/2) = (3.5, 3.5)
the line through O and M (I assume we need the slope-intercept form) is in general
y = ax + b
"a" is the slope, "b" is the y-intercept (the y-value when x = 0).
the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
so, our 2 points : (0, 0) and (3.5, 3.5).
x changes by +3.5 (from 0 to 3.5).
y changes by +3.5 (from 0 to 3.5).
so, the slope "a" is +3.5/+3.5 = 1.
the point (0, 0) gives us "b" (the y-value when x = 0) directly : 0.
so, the line equation is
y = x
NO LINKS!! Please help me with this probability question
Answer: B) 46.67% approximately
=================================================
Work Shown:
A = it will be cloudy tomorrow
B = it will be rainy tomorrow
P(A) = 0.30
P(B) = 0.15
P(A and B) = 0.14
Apply the conditional probability formula.
P(B given A) = P(A and B)/P(A)
P(B given A) = 0.14/0.30
P(B given A) = 0.4667 approximately
P(B given A) = 46.67% approximately
Answer:
b) About 46.67%.
Step-by-step explanation:
Let event A = being cloudy.
Let even B = being rainy.
Given probabilities:
Probability of being cloudy = 30%.Probability of being rainy = 15%.Probability of being cloudy and rainy = 14%.Therefore:
P(A) = 0.3P(B) = 0.15P(A ∩ B) = 0.14Conditional Probability Formula
[tex]\sf P(B|A)=\dfrac{P(A \cap B)}{P(A)}[/tex]
The probability of being rainy given it is cloudy = P(B | A).
Substitute the given values into the formula:
[tex]\implies \sf P(B|A)=\dfrac{0.14}{0.3}=0.46666...=46.67\%\;(2\;d.p.)[/tex]
Therefore, the probability of it being rainy if you know it will be cloudy is about 46.67%.
What is the area of this triangle?
Pls help :(
Find the volume of the cone. Round to the nearest tenth.27 m-45°O 10,306,0 m320,612.0 m341,224.0 m3763.4 m3
The volume of a cone is given by the formula:
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times r^2\times h \\ r\text{ is the radius} \\ h\text{ is the height} \end{gathered}[/tex]From the question, we are provided with following:
[tex]\begin{gathered} h=27m \\ \theta=45^0 \end{gathered}[/tex]We have to use the given parameters to obtain the radius of the cone.
Thus, we have:
[tex]\begin{gathered} \text{Tan 45}^0=\frac{opposite}{\text{adjacent}} \\ 1=\frac{27}{\text{radius}} \\ \text{Therefore, radius=27m} \end{gathered}[/tex]Therefore, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}\times\frac{22}{7}\times27^2\times27 \\ V=20,611.98m^3 \end{gathered}[/tex]Hence, the correct option is option BH
i need help with this equation please there are two more possible answers that were cut off they are 17,2% and 19,5%
Consider that the experimental probability of an event is based upon the previous trials and observations of the experiment.
The experimental probability of occurrence of an event is given by,
[tex]\text{Probability of an event}=\frac{\text{ Number of outcomes that favoured the event}}{\text{ Total number of trials or outcomes}}[/tex]As per the problem, there are a total of 1230 trials of rolling a dice.
And the favourable event is getting a 2.
The corresponding experimental probability is calculated as,
[tex]\begin{gathered} P(\text{ getting a 2})=\frac{\text{ No. of times 2 occurred}}{\text{ Total no. of times the dice is thrown}} \\ P(\text{ getting a 2})=\frac{172}{1230} \\ P(\text{ getting a 2})\approx0.13984 \\ P(\text{ getting a 2})\approx13.98\text{ percent} \end{gathered}[/tex]Thus, the required probability is 13.98% approximately.
Theref
Write a equation that passes through the points (2,5) (-3,5)
Line equation: y = 5
Slope: 0
Intercept: 5
Formule:
. Equation : y = mx + b
. Slope: m = () / ()
Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph.
Given
A graph of a polynomial with the real coefficients.
To find:
a) The intervals in which the function is increasing is,
[tex]\begin{gathered} (-\infty,-5) \\ (-2,2) \\ (6,\infty) \end{gathered}[/tex]b) The value of x at which the unction has local minima.
From the graph shown in the figure, there is only one local minimum at x=-2.
c) The sign of the functions leading coefficient is positive.
Since the graph is moving upwards.
d) The degree of the function is 5.
how do you simplify this expression to become x ^3 -8
we have the expression
[tex]\begin{gathered} (x^3-4)-4 \\ remove\text{ the parenthesis} \\ x^3-4-4 \\ combine\text{ like terms} \\ x^3-8 \end{gathered}[/tex]Writing about Finding a Percen Explain how to find 27% of 16 using multiplication by a decimal. Then explain how to use estimation to check your answer.
To find 27% of 16 using multiplication by a decimal, we can proceed as follows:
First, convert the number 27 in decimal:
[tex]16\cdot\frac{27}{100}=16\cdot0.27=4.32[/tex]A way to estimate the possible value, we can multiply the number 16 by the nearest tenth, that is, 0.3. We know that the possible value is a little greater than the actual value.
We can do this in the following way:
[tex]16\cdot\frac{30}{100}=\frac{48}{100}=4.8[/tex]Then, after the estimation, we can say that the value must be less than 4.8. Multiplying by 3 or 30 is easier than by 27. This is a way to check the answer.
We can also say that if we multiply 16 by 3 is 48 (equivalently to 4.8, after doing the correct operations), and this is a quick value to know, that, approximately 4.32 is 27% of 16.
I have a practice problem that I need help on.These are included in the problem as well Where did Arjun make errors?Explain his errors and the properties of logarithms that leads to the answer. State the correct answer.
Arjun applied the wrong laws of logarithms.
The question can be solved as shown below:
[tex]\log _7x+\log _7y+\log _7z[/tex]Step 1: Apply the addition rule of logarithm given as
[tex]\log _am+\log _an=\log _a(m\cdot n)[/tex]Thus, we have:
[tex](\log _7x+\log _7y)+\log _7z=\log _7(x\cdot y)+\log _7z[/tex]Step 2: Apply the subtraction rule of logarithm given as
[tex]\log _am-\log _an=\log _a(\frac{m}{n})[/tex]Thus, we have:
[tex]\log _7(x\cdot y)+\log _7z=\log _7(\frac{x\cdot y}{z})[/tex]Therefore, the correct answer is:
[tex]\log _7x+\log _7y+\log _7z=\log _7(\frac{xy}{z})[/tex]Jane, Chau, and Deshaun have a total of $82 in their wallets. Deshaun has 2 times what Jane has. Chau has $6 less than Jane. How much does each have?
Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.
let x represent represent the amount of Jane.
let Y represent represent the amount of chau.
let z represent represent the amount of Deshaun.
Jane, Chau, and Deshaun have a total of $82" can be represented as
x + y + z = $82 .......(1)
Deshaun has 4 times what Jane has. It can be represented mathematically as
y = 2x .......(2)
Chau has $6 less than Jane. It can be represented mathematically as
z= x- 6 .......(3)
we can now solve the equations using the substitution method
substitute equation (2) and (3) into equation (1)
x + y + z = $82
x + 2x + x-6 = $82
4x -6 = $82
4x - 6 = $82
4x = $82 + 6
4x = 88
x = $22
from equation 2
y = 2x
y = 2 x 22 = $44
z = x- 6
z = 22 - 6
z=$16
Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.
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a student teacher is given a guideline that a student should be able to finish a 32 question test in 28 minutes if the student teacher is planning to give a test that contains 160 questions and the average students complete question of the same rate as previously State how many minutes should you plan for the average student to complete the test.
since the student do 32 questions in a time of 28 minutes, then the rate of response is 32/28=8/7 questions/minute ,then the students will be able to complete 160 questions in 20(7)= 140 minutes
I don’t really need explanation just give answer honestly I will rate you a 5star regardless I thankyou so much for the help!
Explanation
The information given directly by the picture is that:
[tex]\begin{gathered} CG\cong CH \\ \angle G\cong\angle H \end{gathered}[/tex]This means we have a pair of congruent sides and a pair of congruent angles.
We need one more information to prove congruency. There is no way of getting side information, by if we see the vertex C, the angles make a pair of vertical angles. Vertical angles are congruent, so:
[tex]\angle FCG\cong\angle JCH[/tex]This means now that we have 2 pairs of congruent angles and one pair of congruent sides, so we will use either AAS or ASA.
To determine which is the case, we can visualize the order in which the angles and side appear going around the triangle.
We can see that we have an Angle then the side then the other Angle, so the order is Angle-Side -Angle, so the rule we need to use is ASA.
Answer
Angle-Side-Anlge, that is ASA.
5 cm5 cmThe surface area of the above figure isA. 208.1 cm2B. 225.6 cm2C. 314.2 cm2D. none of the above
It is a cylinder.
1.- Calculate the area of the base and the top
Area = 2*pi*r^2
Area = 2*3.14*5^2
Area = 157 cm^2
Total area of the base and top = 2 x 157 = 314 cm^2
2.- Calculate the perimeter of the circle.
Perimeter = 2*pi*r
Perimeter = 2*3.14*5
Perimeter = 31.4 cm
3.- Calculate the lateral area
Lateral area = 5 x 31.4
Lateral area = 157 cm^2
4.- Calculate the total area = 157 + 314
= 471 cm^2
5.- Result
D. None of the above
