Answer:
Possible solution 1: -4.5 and -8
Solution 2: 4 and 9.
Step-by-step explanation:
Let the two numbers be a and b.
One of them (let it be b) is 1 more than twice the other one. In other words,
b= 1+ 2a.
Their product is 36. Or:
a(b) = 36.
Substitute b:
a(1+2a) = 36
2a^2 + a = 36
2a^2 + a - 36 = 0
This is now a quadratic. We can factor to solve it. Find two numbers that equals 2(-36)=-72 and add to 1. We can use 9 and -8. Thus:
2a^2 - 8a + 9a - 36 = 0
2a(a - 4) +9(a-4) = (2a+9)(a-4) = 0
So, a = -9/2 = -4.5 or a = 4.
Thus, b can equal 1 + 2(-4.5) = -8 or 1 + 2(4) = 9
Given the radius of a circle is 7 cm, what is the circumference?
Answer:
14π or 43.96
Step-by-step explanation:
C = 2πr and we know that r = 7 so C = 14π or 43.96.
What is the next term in the sequence −10,−17,−24,−31,…?
Answer:
-38
Step-by-step explanation:
it's subtracting 7 everytime, and -31-7=-38
A quadratic equation of the form 0=ax2+bx+c has a discriminant value of -16. How many real number solutions does the equation have?
Answer: There will be no real solutions
Explanation: If the discriminant (the part under the radical in the numerator of the quadratic equation) is less than 0, there are no real solutions. If positive, there will be two real solutions. If 0, there will be one.
Please answer this correctly without making mistakes
Answer:
Step-by-step explanation:
2.8 kilometers farther. Subtract 12.1km for Winchester and 9.3 for Stamford to get 2.8 kilometers.
Samuel needs to replace a portion of his rain gutter. The height of the roof is 25 feet and the
length of his ladder is 30 feet. What is the maximum distance away from house that he can place
the ladder? Round your answer to the nearest foot.
Answer:
16.6 ftStep-by-step explanation:
The height of the house, the ground and the ladder forms a right angle triangle, with the following parameters stated below.
1. the hypotenuse is the length of the ladder which is 30 feet
2.the opposite is the height of the house, which is 25 feet
3. the adjacent is the distance of the ladder away from the building, this is the parameter we are solving for.
Since we have two sides of the triangle given, we can employ Pythagoras theorem to solve for the third side of the triangle
let the the opposite be x
we know that
[tex]hyp^2= opp^2+adj^2\\\\ 30^2= x^2+25^2\\\\ 900= 625+x^2\\[/tex]
Solving for x we have
[tex]x^2= 900-625\\\\X^2= 275\\\\x=\sqrt{275} \\\\x= 16.58[/tex]
Hence the maximum distance away from house that he can place
the ladder is 16.6 ft to the nearest foot
Solve application problems using radical equations. A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground?
Answer:
[tex]\large \boxed{\text{5.29 s}}[/tex]
Step-by-step explanation:
The appropriate free fall equation is
y = v₀t + ½gt²
Data:
v₀ = 0
g = 32.17 ft·s⁻²
Calculation:
[tex]\begin{array}{rcl}450 &=& v_{0}t + \dfrac{1}{2}gt^{2}\\\\& = & 0 \times t + \dfrac{1}{2}\times 32.17t^{2}\\\\& = & 16.08t^2\\t^{2}& = & \dfrac{450}{16.08}\\\\& = & 27.97\\t & = & \textbf{5.29 s}\\\end{array}\\\text{It took $\large \boxed{\textbf{5.29 s}}$ for the phone to reach the ground.}[/tex]
Write the equation 0.3x 2 + 5x - 7 = 0 in general form and then choose the value of "b."
Answer:
3x^2 + 50x - 70 = 0
b = 50
Step-by-step explanation:
0.3x^2 + 5x - 7 = 0
Multiply both sides by 10 to get rid of the decimal coefficient.
3x^2 + 50x - 70 = 0
b = 50
Determine the measure of the unknown variables.
Answer:
75
Step-by-step explanation:
x = 75°
yes x = 75°(OPPOSITE ANGLES ARE EQUAL)
..
A cubical container measures 9 ft on each edge. What does it cost to fill the container at $2.58 per cubic ft?
Answer:
1,880.82
Step-by-step explanation:
Need answers ASAP!!!! (due today)
Answer:
6. 156.6 cm
7. 687.7’
Step-by-step explanation:
45 cm and 150 cm are the legs of one triangle.
The longest side is the hypotenuse.
Apply Pythagorean theorem, since the two triangles are right triangles.
a² + b² = c²
a and b are the legs, c is the hypotenuse.
45² + 150² = c²
24525 = c²
√24525 = c
c = 156.604597634...
c ≈ 156.6
Brain hang-glided from a 520’ high cliff. He landed 450’ away from the base of the cliff. Create a right triangle and apply Pythagorean theorem. The distance he travelled is the hypotenuse of the triangle. The 520’ and 450’ are the legs.
a² + b² = c²
450² + 520² = c²
c² = 472900
c = √472900
c = 687.677249878...
c ≈ 687.7
Answer: 6) =approx 156.60 cm
7) =approx 687.68'
Step-by-step explanation:
6. Let the shortest side of the triangle is AB=45 cm ( ∡A=90° so ABCD is a rectangle). The middle side AD=150 cm. The longest side is BD
The length of BD can be calculated using Phitagore theorem because triangle BAD ia right angle.
BD=sqrt(AD²+AB²)=sqrt(2025+22500)=approx 156.60 cm
7. So we can create the model of the situation described in this problem.
The model is right-angle triangle ABC with side AB=520' ,side AC=450', right angle is A. So we have to find the length of side BC .
BC is hypotenuse of triangle ABC. We can find it using Phitagore theorem again.
BC=sqrt(AC²+AB²)=sqrt(450²+520²)=sqrt(472900)=approx 687.68'
The original price of a 2018 Honda Shadow to the dealer is $17,715, but the dealer will pay only $16,985 after rebate. If the dealer pays Honda within 15 days, there is a 2% cash discount.
Answer:
The final price to be paid after the 2% discount has been made will be $ 16,645.30.
Step-by-step explanation:
Since there is a 2% discount on the price of the Honda Shadow in the event that the dealer pays Honda within 15 days, and that after a rebate the price of the vehicle is $ 16,985, to obtain the value of the discount and the final amount to be paid must be calculated as follows:
16,985 x 2/100 = X
33,970 / 100 = X
339.70 = X
Thus, the discount to be made will be $ 339.70, with which the final price to be paid after the 2% discount has been made will be $ 16,645.30.
Help with finding the slope of the line and graph find the slope 1.) (1, 6) (3,8) 2.) (7,10) (5,6) 3.) (1,-2) (3,4) 4.) (10,5) (4,7) 5.) (-2,6) (0,5) 6.) (-9,9) (7,5) 7.) (-3, 5) (0,0) (8, 10) (-7, 14) 9.) (-12, -5) (0, -8)
Answer:
1 is 1.
2 is 2.
3 is 3. (this is not a joke, keep going)
4 is -1/3.
5 is -1/2.
6 is -1/4.
7 is -5/3.
8 is -4/15, if you meant that the points are (8,10) and (-7,14). You might have typed wrong.
9 is -1/4.
10 is 1/3. Take a look at it. It goes up by 1 and it goes over 3. 1 divided by 3 is 1/3.
11 is 1. It rises 2 and goes across by 2. 2 divided by 2 is 1.
12 is -3/4, because it goes down 3 and over 4.
13 is -3/2. Do you see why?
14 is 1. It's super easy, since it only goes up 1 and over 1.
15 is easy. You have to figure this one out, but I'll give you a hint. It goes down by 3 .
A casino offers a game wherein a player can roll one six sided die. If the player rolls a 1or 2, they
win. If the player rolls a 3, 4, 5, or 6, they lose. If a player bets $2.00 and wins, they will be paid out
an additional $3.00. If they lose, they lose their initial $2.00. Find the expected value of the $2.00
bet.
Enter your answer rounded to the nearest cent and don't forget, expected values can be negative!
Answer:
Expected Value of $2:
Expected Value of $2:
Win, 0.3333 x $3 = $1
Plus
Loss, 0.6667 x -$2 = -$1.33
Expected value = ($0.33)
Step-by-step explanation:
Probability of a win = 2/6 = 0.3333
Probability of a loss = 4/6 = 0.6667
Expected Value of $2:
Win, 0.3333 x $3 = $1
Plus
Loss, 0.6667 x -$2 = -$1.33
Expected value = ($0.33)
The casino game player's expected value is computed by multiplying each of the possible outcomes by the likelihood (probability) of each outcome and then adding up the values. The sum of the values is the expected value, which amounts to a loss of $0.33.
4. A bank vault has 3 locks with a key for each lock. Key A is owned by the bank manager. Key B is owned by the senior bank teller. Key C is owned by the trainee bank teller. In order to open the vault door at least two people must insert their keys into the assigned locks at the same time. The trainee bank teller) can only open the vault when the bank manager is present in the opening. X= Bank Manager Y= Senior Bank teller Z= Trainee bank teller. (25 marks) LO 01 a) Construct a truth table for this system
1 means that he is present, 0 means that he is not.
True means that they can open.
[tex]\begin{array}{cccccccccccc} \text{X} &&& \text{Y} &&& \text{Z} &&& \text{True} \\1 &&& 1 &&& 1&&& 1 \\ 1 &&& 1 &&& 0&&&1 \\ 0 &&& 1 &&& 1&&&0 \\ 1 &&& 0 &&& 1&&&1 \\ 0&&& 1 &&& 0&&&0 \\ 0 &&& 0 &&& 1&&&0 \\ 1 &&& 0 &&& 0&&&0 \\ 0 &&& 0 &&& 0&&&0 \\ \end{array}[/tex]
Answer:
police
Step-by-step explanation:
2
A student winds a strip of paper eight times
round a cylindrical pencil of diameter 7 mm.
Use the value 22/7 for pie to find the length of
the paper.
Answer:
176 mm
Step-by-step explanation:
The circumference of a circle is the perimeter of a circle (length of a circle). The circumference of a circle is given as:
Circumference (C) = 2πr = πd, where d is the diameter
The circumference of a circle with diameter 7 mm is:
C = πd = 22/7(7) = 22 mm
The length of the paper to round the cylindrical pencil is the same as the perimeter of the pencil which is 22 mm.
To round the pencil 8 times, the length of the paper needed = 8 × 22 mm = 176 mm
Help me with this please anyone
Answer:
B. [tex] -3x [/tex]
Step-by-step explanation:
In algebra, a term could be a single negative or positive number (constant), a variable or a variable with a coefficient. It could also be 2 variables multiplied together.
The algebraic expression [tex] -3x - 7(x + 4) [/tex] , can be expanded and expressed as:
[tex] -3x - 7(x) -7(+4) [/tex]
[tex] -3x - 7x - 28 [/tex]
The three terms are: [tex]-3x, - 7x, -28[/tex]
Therefore, from the given answer choices, the term that is a term in the expression, [tex] -3x - 7(x + 4) [/tex] , is B. [tex] -3x [/tex]
Find the volume of the figure below. Round to the nearest tenth.
7 cm
7 cm
9 cm
20 cm
11 cm
Answer:
3057.6 cm³
Step-by-step explanation:
You have a cylinder and a rectangular prism. Solve for the area of each separately.
Cylinder
The formula for volume of a cylinder is V = πr²h. The radius is 7, and the height is 7.
V = πr²h
V = π(7)²(7)
V = π(49)(7)
V = 343π
V = 1077.57 cm³
Rectangular Prism
The formula for volume of a rectangular prism is V = lwh. The length is 20, the width is 11, and the height is 9.
V = lwh
V = (20)(11)(9)
V = (220)(9)
V = 1980 cm³
Add the areas of the two shapes.
1077.57 cm³ + 1980 cm³ = 3057.57 cm³
Round to the nearest tenth.
3057.57 cm³ ≈ 3057.6 cm³
A cosine function is graphed below. Use the drop-down menus to describe the graph. The amplitude of the graph is __ . The equation of the midline is __ . The period of the function is __ . The function is shifted __ left. The function is shifted __ units up.
Amplitude:4
Equation of Midline: 2
Period of function:3
Function shifted left:0.5
Function shifted up: 2
From the graphed cosine function we are given, we have;
1) Amplitude = 4
2) Equation of midline; m = 2
3) Period of the function = 3π
4) The function shifted 0.5 units left.
5) The function shifted 2 units up.
1) The amplitude is the distance between the center line and the positive or negative peak of the graph. Now, the positive peak is 6 and the negative one is 2. Thus, Amplitude = 6 - 2 = 42) Equation of the midline is the line that divides the entire sinusoidal curve into 2 equal parts along the x-axis. Since amplitude is 4, then the equation of midline is; m = 4/2 ; m = 2.3) The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3π.4) Looking at the graph, ideally the coordinate (-0.5π, 6) should have been on the y-axis which is at (0π, 6). This means it was shifted by 0.5 units to the left side.5) The positive peak should be equal to the negative peak but in this case, positive is 6 and negative is 2. This means, for them to be equal, they have to each be 4. Thus, the graph was shifted by 2 units upwards .Read more; https://brainly.com/question/16280305
The standard deviation of samples from supplier A is 0.4582, while the standard deviation of samples from supplier B is 0.3358. Which supplier would you be likely to choose based on these data and why
Complete Question
The standard deviation of samples from supplier A is 0.4582, while the standard deviation of samples from supplier B is 0.3358. Which supplier would you be likely to choose based on these data and why?
1 Supplier A, as their standard deviation is higher and, thus easier to fit into our production line
2 Supplier B, as their standard deviation is higher and, thus, easier to fit into our production line
3 supplier B, as their standard deviation is lower and, thus, easier to fit into our production line
4 Supplier A, as their standard deviation is lower and, thus, easier to fit into our production line
Answer:
Option 3 is correct
Step-by-step explanation:
From the question we are told that
The standard deviation of A is [tex]\sigma_a = 0.4582[/tex]
The standard deviation of B is [tex]\sigma _b = 0.3358[/tex]
Generally standard deviation defines the deviation element of a data set with respect to the mean of the set
So sample it mean that samples from A deviates more from it mean(the standard value) than the samples from B so the best supplier to chose is B
Which is steeper: a road with a 12% grade or a road with a pitch of 1 in 8?
Answer:
A road with a pitch of 1 in 8 is steeper.
Step-by-step explanation:
Let us convert these to the same units so that we can better compare them.
[tex]\frac{1}{8} = 0.125[/tex]
0.125=12.5 %
As 12.5% is greater than 12%, the road with a pitch of 1 in 8 will be steeper.
A manager receives 8 applications for a specific position. She wants to narrow it down to 5. In how many ways can she rank 5 applications?
Answer:
56 number of ways
Step-by-step explanation:
This question is a combination question since it involves selection.
Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
If a manager receives 8 applications for a specific position and wants to narrow it down to 5, the number of ways he can do this is 8C5
8C5 = 8!/(8-5)!5!
= 8!/3!5!
= 8*7*6*5!/3*2*5!
= 8*7*6/3*2
= 8*7
= 56 number of ways.
This means that the manager can rank 5 applications in 56 number of ways
The number of ways that can she rank 5 applications should be 6720.
Calculation of the number of ways:Since A manager receives 8 applications for a specific position. She wants to narrow it down to 5.
So here we do apply the permutation here:
[tex]= 8!\div 5!3! \times 5!\div 0!\\\\= 8\times 7\times 6\times 5\times 4[/tex]
= 6720
Hence, The number of ways that can she rank 5 applications should be 6720.
Learn more about ways here: https://brainly.com/question/18988173
Which of these descriptions matches the graph?
Jimmy is walking to a friend's house at a constant
rate.
Jimmy is running late, so he starts to run to school
but needs to take breaks.
Jimmy is riding the bus to school at a decreasing
rate.
Jimmy's bus drives at the same speed for parts A
and C.
Answer:
Step-by-step explanation:
121212121211212 its B
Answer:
answer is B
Step-by-step explanation:
Rolling a 6-sided die and counting the number of each outcome that occurs is a bionomial random variable. True or False? Which option gives the most accurate response?
Answer:
False.
Step-by-step explanation:
This is NOT an example of a binomial random variable, because a binomial random variable can only have TWO possible outcomes: success or failure. In the case of rolling a die, there are SIX possible outcomes: 1, 2, 3, 4, 5, or 6.
So, rolling a 6-sided die and counting the number of each outcome that occurs is NOT a binomial random variable.
Hope this helps!
The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is false.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is not an example of the binomial random variable. This is because the binomial random variable can only have two possible outcomes, which is not true in the case of a die that had six faces and six outcomes for each through.
Although if the probability is needed to be calculated for the same digit occurring or not it can be calculated using the binomial random variable.
Hence, The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is false.
Learn more about Binomial Distribution:
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Examine today’s stock listing for SFT Legal, shown below. 52 wk High 52 wk Low Symbol Div. Close Net Change 74.80 44.61 SFT 8.94 56.11 5.74 What was the price of SFT Legal yesterday? a. $47.17 b. $56.11 c. $50.37 d. $61.85
Answer:
c. $50.37
Step-by-step explanation:
Close price was $56.11 and net change was $5.74. so subtract the net change from the close to get yesterday's price.
Answer:
c.50.37
Step-by-step explanation:
Check whether these statements are wff or not:(a) (p˅q) ∧∼r
Answer:
It is a well formed formula
Step-by-step explanation:
1 - p,q,r are well formed formulas.
2 - [tex]p \ \lor \ q[/tex] is a well formed formula as well.
3 - [tex]\neg r[/tex] is a well formula as well
4 - [tex](\ p \ \lor \ q) \ \land \ \neg r[/tex] is a well formula as well.
please need help with this math question
Answer:
third option
Step-by-step explanation:
We just have to calculate 2x² - 4x - (x² + 6x). 2x² - x² = x² and -4x - 6x = -10x so the answer is x² - 10x.
Answer:
x^2-10x
Step-by-step explanation:
f(x)-g(x)
(2x^2-4x)-(x^2+6x)
carry through the negative
2x^2-4x-x^2-6x
x^2-10x
Solve for x: ( 1/2 )^(x−1)=2^(3x−4)
Answer:
[tex]\huge\boxed{x=\dfrac{5}{4}}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{1}{2}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\\left(2^{-1}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{(-1)(x-1)}=2^{3x-4}\qquad\text{use the distributive property}:\ a(b+c)=ab+ac\\\\2^{(-1)(x)+(-1)(-1)}=2^{3x-4}\\\\2^{-x+1}=2^{3x-4}\iff-x+1=3x-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=3x-4-1\\\\-x=3x-5\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-x-3x=3x-3x-5\\\\-4x=-5\qquad\text{divide both sides by (-4)}[/tex]
[tex]\dfrac{-4x}{-4}=\dfrac{-5}{-4}\\\\x=\dfrac{5}{4}[/tex]
Biologists stock a lake with 160
160
fish, and estimate the carrying capacity of the lake to be 9100
9100
fish. The number of fish tripled in the first year.
(a) Assuming that the fish population satisfies logistic growth, the fish population can be modeled by:()=/[1+55.875−1.13506]
From the given information about this population, determine the constant
that completes the model.
Answer:
[tex]P ( t ) = \frac{9100.024}{1 + 55.875e^-^1^.^1^3^5^0^6^*^t}[/tex]
Step-by-step explanation:
Solution:-
- We are given a logistic growth model of the fish population cultured. The logistic growth of fish population is modeled by the following equation:
[tex]P ( t ) = \frac{c}{1 + 55.875e^-^ 1^.^1^3^5^0^6^t}[/tex]
Where, c: the constant to be evaluated.
- We are given the initial conditions for the model where at t = 0. The initial population was given to be:
t = 0 , Po = 160
N ( carrying capacity ) = 9100
- After a year, t = 1. The population was tripled from the initial value. That is P ( 1 ) = Po*3 = 160*3 = 480.
- We will use the given logistic model and set P ( 1 ) = 480 and determine the constant ( c ) as follows:
[tex]P ( 1 ) = \frac{c}{1 + 55.875e^-^ 1^.^1^3^5^0^6^*^1} = 480\\\\c = 480* [ 1 + 55.875e^-^ 1^.^1^3^5^0^6]\\\\c = 9100.024[/tex]
- The complete model can be written as:
[tex]P ( t ) = \frac{9100.024}{1 + 55.875e^-^1^.^1^3^5^0^6^*^t}[/tex]
What is the missing term that makes these ratios equivalent? 1.5:3, 31.5:____
=========================================
Work Shown:
1.5/3 = 31.5/x
1.5x = 3*31.5 cross multiply
1.5x = 94.5
x = 94.5/1.5 dividing both sides by 1.5
x = 63
-----------
An alternative equation to solve is
1.5/31.5 = 3/x
1.5x = 31.5*3
1.5x = 94.5
The remainder of the steps are the same as in the previous section above.
A system of equations is created by using the line that is created by the equation 3 x minus 2 y = negative 4 and the line that is created by the data in the table below. x y –3 –9 –1 –5 3 3 5 7 What is the y-value of the solution to the system?
Answer:
17
Step-by-step explanation:
A graphing calculator is useful for writing a linear equation from a table of values. The one shown below says the table can be represented by the equation ...
y = 2x -3
The graph of the two equations shows the solution is (10, 17).
The y-value of the solution is 17.
Answer:
17 is correct
Step-by-step explanation: