The preceding polynomial equation has three solutions: z = 0, z = 3/4, and z = -1/5.
First, we can factor out a common factor of z:
z(20z² - 11z - 3) = 0
Now we need to factor the quadratic expression in the parentheses.
We can use the quadratic formula or factor by grouping to do this. Factoring by grouping yields:
z(20z² - 11z - 3) = 0
z(4z - 3)(5z + 1) = 0
Setting each of the factored terms equal to zero, we have:
z = 0, 3/4, -1/5
Therefore, the solutions to the given polynomial equation are z = 0, z = 3/4, and z = -1/5.
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Determine the type of probability:
A spinner has 4 equal-sized spaces labeled A, B, C, and D.
The chance of landing in any of the spaces is 1/4, or 25%.
Answer:
Theoretical Probability
Step-by-step explanation:
Total number of possible outcomes
Mary started a bank account with m dollars. The money increased to 6.2 times the sum of the starting amount and $4. Mary then withdrew 3 times there starting amount. The remaining balance was 348.80. Enter the amount of money, in dollars, Mary used to start the account.
Please be quick I only have an hour to submit. Thank you
The profit made by a shop increases each year. The profit made by the shop in year n is £Pn Given that the profit made by the shop in the next year is £Pn + 1 then Pn + 1 = aPn + 800 where a is a constant. The table shows the profit made by the shop in 2018 and in 2019 Year 2018 2019 Profit £24 000 £29 600 Work out the profit predicted to be made by the shop in 2021
Answer:
£44,384
Step-by-step explanation:
Given the recurrence relation for profit is ...
P[2018] = £24000P[2019] = £29600P[n+1] = a·P[n] +800you want the profit in 2021.
Value of 'a'Using the given relations we have ...
P[2019] = a·P[2018] +800
29600 = a·24000 +800
28800 = a·24000
a = 288/240 = 1.2
Next termsThen the profit for the next two years is ...
P[2020] = 1.2·P[2019] +800 = 1.2·29600 +800 = 36320
P[2021] = 1.2·36320 +800 = 44384
The profit is predicted to be £44,384 in 2021.
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Hello random community i have a question to ask what is 7/8 - 3/4
Answer: 1/8
Step-by-step explanation:
First make the bottom half the same:
3/4*2/2=6/8
We don’t need to change the first portion since they have a common factor
7/8-6/8=1/8
Solve and check the system of equations: 7x-5y=-11, x+2y=-7
A store is having a sale on jelly beans and almonds. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $27. For 9 pounds of jelly beans and
7 pounds of almonds, the total cost is $51. Find the cost for each pound of jelly beans and each pound of almonds.
Cost for each pound of jelly beans:
Cost for each pound of almonds:
Answer:
Cost for each pound of jelly beans: $2.75
Cost for each pound of almonds: $3.75
Step-by-step explanation:
Let J be the cost of one pound of jelly beans.
Let A be the cost of one pound of almonds.
Using the given information, we can create a system of equations.
Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:
[tex]\implies 3J + 5A = 27[/tex]
Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:
[tex]\implies 9J + 7A = 51[/tex]
Therefore, the system of equations is:
[tex]\begin{cases}3J+5A=27\\9J+7A=51\end{cases}[/tex]
To solve the system of equations, multiply the first equation by 3 to create a third equation:
[tex]3J \cdot 3+5A \cdot 3=27 \cdot 3[/tex]
[tex]9J+15A=81[/tex]
Subtract the second equation from the third equation to eliminate the J term.
[tex]\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}[/tex]
Solve the equation for A by dividing both sides by 8:
[tex]\dfrac{8A}{8}=\dfrac{30}{8}[/tex]
[tex]A=3.75[/tex]
Therefore, the cost of one pound of almonds is $3.75.
Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.
Using the first equation:
[tex]3J+5(3.75)=27[/tex]
[tex]3J+18.75=27[/tex]
[tex]3J+18.75-18/75=27-18.75[/tex]
[tex]3J=8.25[/tex]
[tex]\dfrac{3J}{3}=\dfrac{8.25}{3}[/tex]
[tex]J=2.75[/tex]
Therefore, the cost of one pound of jelly beans is $2.75.
A manager of a factory purchases a large number of sheets of aluminium, all of them longer than 100 cm in length. Each piece is then cut so that it is 100 cm long. The length of a sample of the off-cuts, in cm, resulting from cutting the lengths to size are given below: (Hint: Mean = 6, 5)
5,2 6,6 3,5 8,9 7,5 7,3
Using the data above:
Calculate the coefficient of variation rounded to 1 decimal place
The coefficient of variation for the off-cuts lengths is 30.0%, which indicates a relatively high degree of variability in the data.
The coefficient of variation (CV) is a measure of relative variability, which is calculated by dividing the standard deviation by the mean, and expressing the result as a percentage. It is used to compare the variability of different datasets, particularly when they have different units or scales.
To calculate the CV for the off-cuts lengths in this problem, we first need to calculate the mean and the standard deviation. The mean is calculated by adding all the values together and dividing by the number of values:
Mean = (5.2 + 6.6 + 3.5 + 8.9 + 7.5 + 7.3) / 6 = 6.5 cm
Next, we need to calculate the standard deviation, which measures the dispersion of the data points from the mean. We can use the formula:
Standard Deviation = √(Σ(xi - x)² / (n - 1))
where xi is the value of each data point, x is the mean, and n is the number of data points.
Standard Deviation = √[(5.2 - 6.5)² + (6.6 - 6.5)² + (3.5 - 6.5)² + (8.9 - 6.5)² + (7.5 - 6.5)² + (7.3 - 6.5)²] / 5
Standard Deviation = 1.951 cm
Finally, we can calculate the coefficient of variation by dividing the standard deviation by the mean, and multiplying by 100 to express the result as a percentage:
CV = (1.951 / 6.5) x 100 = 30.0%
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Which sequences are geometric? Select three options.
O-2.7, -9, -30, -100, ...
0-1, 2.5, -6.25, 15.625,...
9.1, 9.2, 9.3, 9.4, ...
8, 0.8, 0.08, 0.008, ...
4,-4, -12, -20, ...
Answer:
A. -2.7, -9, -30, -100, ...
B. -1, 2.5, -6.25, 15.625, ...
C. 9.1, 9.2, 9.3, 9.4, ...✔️
D. 8, 0.8, 0.08, 0.008, ...✔️
E. 4, -4, -12, -20, ... ✔️
Hope you understand
Let me know if you need further explaination
I’m not sure what I’m meant to write here if I’ve attached something so yeah how was your day guys
The probability of having regular illness is (0.16) when compared to those with good sleep (0.12).
How to calculate the probabilityLet's calculate the probability of having regular illness given poor sleep:
P(regular illness | poor sleep) = 16% = 0.16
Now, let's calculate the probability of having regular illness given good sleep:
P(regular illness | good sleep) = 24 / (24 + 176) = 0.12
Hence, the probability of having regular illness is (0.16) when compared to those with good sleep (0.12).
This supports the doctor's claim that poor sleep increases the probability of having regular illness.
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Jon has a rectangular picture that is 54 inches wide and 24 inches tall. He wants to hang it on the wall shown so that it is centered both horizontally and vertically.
To center the picture both horizontally and vertically on the wall, Jon should hang it 3.75 feet from the left edge of the wall and 3 feet from the top edge of the wall.
First, we need to convert the dimensions of the picture from inches to feet Width: 54 inches = 4.5 feet and Height: 24 inches = 2 feet
To center the picture horizontally, we need to find the distance between the left edge of the wall and the left edge of the picture, and then subtract this distance from the distance between the right edge of the wall and the right edge of the picture.
The difference should be zero if the picture is centered.
Distance between left edge of wall and left edge of picture = (12 ft - 4.5 ft) / 2 = 3.75 ft
Distance between right edge of wall and right edge of picture = (12 ft - 4.5 ft) / 2 = 3.75 ft
So, the picture is centered horizontally.
To center the picture vertically, we need to find the distance between the top edge of the wall and the top edge of the picture, and then subtract this distance from the distance between the bottom edge of the wall and the bottom edge of the picture.
The difference should be zero if the picture is centered.
Distance between top edge of wall and top edge of picture = (8 ft - 2 ft) / 2 = 3 ft
Distance between bottom edge of wall and bottom edge of picture = (8 ft - 2 ft) / 2 = 3 ft
So, the picture is centered vertically.
Therefore, Jon should hang the picture 3.75 feet from the left edge of the wall and 3 feet from the top edge of the wall to center it both horizontally and vertically.
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Prove Vin 20 + los 20 = 1
The prove of the trig identity gives sin²θ + cos²θ = 1.
What is the proof of the trig identity?The proof of the trig identity is determined as follows;
Let's consider a right triangle with one acute angle θ.
Let the hypotenuse have length 1
Let the length of the adjacent side = cosθ
then, the opposite side length = sinθ
Apply Pythagorean theorem, to determine the hypotenuse side;
(sinθ)² + (cosθ)² = 1²
sin²θ + cos²θ = 1
Thus, we have proved the identity.
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8y^2+6xy
evaluate the given polynomial at:
x=3, y=1
. Replace the variable(s) in the polynomial with the specific value(s) given and determine the value of the polynomial by performing the indicated operations.
Answer:
Putting the values of x and y in the given polynomial
[tex] = 8({1})^{2} + 6(3)(1)[/tex]
[tex] = 8(1) + 18[/tex]
[tex] = 8 + 18[/tex]
[tex] = 26[/tex]
Hence the value of polynomial is 26
Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x? 30° only 90° only 30° or 150° 30°, 90°, or 150°
Answer:
Answer = 30° , 90° , 150°
Step-by-step explanation:
Hope it helps you
Choosing from the binomial factors shown below, write the equation of the parabola to the left in factored form. (please help)
The equation of the parabola to the left in factored form is y = (x - 2)(x - 7).
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factors (zeros or roots) provided as follows;
y = (x - 2)(x - 7)
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Solve for x please and thank you
In the given equation, We can start by isolating the square root term on one side of the equation. The answer is {-2, 10}.
x + 6 - 9 = [tex]\sqrt{2x+29}[/tex]
Simplifying the left-hand side:
x - 3 = root(2x + 29)
Squaring both sides of the equation to eliminate the square root:
(x - 3)^2 = 2x + 29
Expanding the left-hand side:
[tex]x^2[/tex] - 6x + 9 = 2x + 29
Moving all the terms to one side of the equation:
[tex]x^2[/tex] - 8x - 20 = 0
We can now use the quadratic formula to solve for x:
x = (-b ± sqrt([tex]b^2[/tex] - 4ac)) / 2a
where a = 1, b = -8, and c = -20.
Substituting these values into the formula, we get:
x = (-(-8) ± sqrt([tex](-8)^2[/tex] - 4(1)(-20))) / 2(1)
Simplifying the equation:
x = (8 ± sqrt(144)) / 2
x = (8 ± 12) / 2
So, we have two possible solutions:
x1 = 10
x2 = -2
Thus, the answer is {-2, 10}.
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una barra de carbono de radio 0'1 mm se utiliza pára construir una resistencia. La resistividad de este material es 3.5 x 10- 5 Ω. m. Que longitud de la barra de carbono se necesita para obtener una resistencia de 10Ω?
The length of carbon rod is needed to obtain a resistance of 10 ohms is 0.00897 or 8.97 × 10⁻³ meters.
How to determine the length of carbon rod?In Mathematics and Science, the resistance of any conductor (wire) in terms of length can be calculated by using this formula:
Length = RA/ρ
Where:
R is the resistance.A is the area of conductor.ρ is the resistivity.By substituting the parameters, we have:
Length = Rπr²/ρ
Length = [10 × 3.142 × (0.0001)²]/3.5 × 10⁻⁵
Length = 3.142 × 10⁻⁷/3.5 × 10⁻⁵
Length = 0.00897 or 8.97 × 10⁻³ meters.
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Complete Question:
A carbon bar of radius 0.1 mm is used to build a resistor. The resistivity of this material is 3.5 x 10-5 Ω. m. What length of carbon rod is needed to obtain a resistance of 10 ohms?
radioactive technetium-99m is often used in diagnostic medicine because it has a relatively short half life but lasts long enough to get the needed testing done on the patient. if it’s half life is 6 hours, how much of the radioactive material from a 0.5 ml injection will be in the body in 24 hours
Only [tex]0.03125 ml[/tex] of the technetium-99m will be left after 24 hours.
How much will be left in the body after 24 hours?After 6 hours, half of the original amount will decay.
After another, leaves 1/4 of the original amount.
After another, leaves 1/8 of the original amount.
After another, leaves 1/16 of the original amount.
We will below formula calculate the amount of technetium-99m left after 24 hours: N = N0 * (1/2)^(t/T)
N = 0.5 * (1/2)^(24/6)
N = 0.5 * (1/2)^4
N = 0.5 * 1/16
N = 0.03125 ml
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can someone help really fast look at the directions and just do it in a simpler way if you can please hurry somebody
Answer:
The easiest method to remember when dividing fractions is Keep Change Flip (KCF)
Step-by-step explanation:
I wrote out some examples of KCF. Once you use KCF, you just multiply the fractions normally and then don't forget to write the improper fractions (ex: 12/7) as a mixed number (1 5/7)
If you have any questions about the steps just let me know. I hope this helps ^-^
Out of 50 students taking a midterm psychology exam, 26 answered the first of two bonus questions, 33 answered the second bonus question, and 2 didn't bother with either
Answer:
This has no answer. Whats the question? Please tell me so I can help you
Is it probability ???
Which of the points below correctly plots the point (3,7π/6)?
Six plotted points on a coordinate plane.
Select the correct answer below:
A
B
C
D
E
F
Answer: the answer is D
Step-by-step explanation:
Remember that the coordinates (3,7π6) tell us the radius r=3 and the angle θ=7π6. So the point should be on the circle labeled 3 and form an angle of 7π6 with the positive x-axis. Point D is the correct point.
Explain how to simplify this expression: 4a + 19 - 3a - 7
Answer:
1a+12
Step-by-step explanation:
Simplify \sqrt[3]{576000 \cdot 4 \cdot 48}
The simplification of the cube root of the given expression ∛ ( 576000 × 4 × 48 ) is equal to 480.
The expression is equal to ,
∛ ( 576000 × 4 × 48 )
Write all the factors of the given numbers,
576000 = 576 × 1000
⇒ 576000 = 24 × 24 × 10³
Now,
48 = 24 × 2
And 4 = 2 × 2
Simplify this expression,
Use the fact that the cube root of a product is equal to the product of the cube roots of the factors.
∛ (a × b × c) = ∛a × ∛b × ∛c
Using this property, simplify ∛(576000 × 4 × 48) as follows,
∛(576000 × 4 × 48) = ∛(576000) × ∛(4) × ∛(48)
Rewrite the given expression in the factor form,
∛ ( 576000 × 4 × 48 )
= ∛ 24 × 24 × 10³ × 2 × 2 × 2 × 24
= ∛ 24³ × 10³ × 2³
= ∛(24)³ × ∛(10)³ × ∛(2)³
= 24 × 10 × 2
= 480
Therefore, the simplification of the given expression is equal to 480.
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The above question is incomplete, the complete question is:
Simplify ∛ ( 576000 × 4 × 48 )
Solve the following differential equations
Set up and find the meaure of the arc or angle indicated.
Applying the inscribed angle theorem, the measure of the angle is calculated: 35°.
How to Find the Measure of the indicated angle using the Inscribed Angle Theorem?Recall the following based on the inscribed angle theorem:
Measure of an arc = 2(measure of inscribed angle)
Also not that half of a circle is equal to 180 degrees. Therefore, we have:
Measure of arc QR = 180 - 110 = 70 degrees.
Measure of angle QRS = 1/2(measure of arc QR)
Plug in the values:
Measure of angle QRS = 1/2(70)
Measure of angle QRS = 35°
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Can someone help me out these in order please
To find the circumscribed side of a triangle, the steps to follow are:
1. Construct the perpendicular bisector of one of the sides of the triangle.
2. Construct the perpendicular bisector of the second side of the triangle.
3. Identify the point of intersection for the two perpendicular bisectors. This is the circumcenter of the triangle and the center of the circumscribed triangle.
4. Construct a circle that has a radius that is the length from the circumcenter to one of the vertices of the triangle.
What is the circumscription of a triangle?A circumscribed triangle is one in which a circle is drawn in the center of the triangle and the circle goes round while touching only three vertices of the triangle.
To draw the circumscribed side of a triangle, you can start by constructing the perpendicular bisector of one of the sides and then the second side. Next, identify the point of intersection, and finally construct the circle.
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Find the parallelogram
Answer: -14
Step-by-step explanation:
I hope this helps
10. A swimming pool is in the shape of a right rectangular prism. The pool is 40 feet long, 20
feet wide, and 4 feet deep. The cost of repainting the pool is $2.50 per square foot. What is
the total cost of repainting the 4 walls and the floor of the pool?
A. $1,200
B. $3,200
C. $8,000
D. $10,000
The total cost of repainting the 4 walls and floor of the pool would be $2800
Given that;
A swimming pool is in the shape of a right rectangular prism. the pool is 40 feet long,20 feet wide and 4 feet deep the cost of repainting the pool is $2.50 per square foot.
Here, The first step is to calculate the total surface area of the pool, which includes the four walls and the floor.
The area of the floor is simply the length times the width:
Area of floor = 40 ft x 20 ft = 800 square feet
The area of each of the four walls is the height times the width:
Area of each wall = 4 ft x 20 ft = 80 square feet
Since there are four walls, the total area of the walls is:
Total area of walls = 4 x 80 sq ft = 320 square feet
To find the total surface area of the pool, we add the area of the floor to the area of the walls:
Total surface area = Area of floor + Total area of walls
Total surface area = 800 sq ft + 320 sq ft = 1120 square feet
Finally, we can calculate the total cost of repainting the pool by multiplying the total surface area by the cost per square foot:
Total cost = Total surface area x Cost per square foot
Total cost = 1120 sq ft x $2.50/sq ft
Total cost = $2800
Therefore, the total cost of repainting the 4 walls and floor of the pool would be $2800
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Find the 8th term of the geometric sequence with the first term 2 and common ratio -3.
The 8th term of the geometric sequence is -4374.
Given that we need to find the 8th term of the geometric sequence with the first term 2 and common ratio -3.
So,
aₙ = a₁ rⁿ⁻¹
So,
the 8th term of the geometric sequence =
a₈ = 2 (-3)⁸⁻¹
a₈ = 2 × (-3)⁷
a₈ = 2 × (-2187)
a₈ = -4374
Hence, the 8th term of the geometric sequence is -4374.
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5/6 having denominator 35
Answer:( 175/6)
Step-by-step explanation: 5*35/6=175/6 sour our numerator is 175/6. So sour answer is (175/6)/35
Which of the following statements is TRUE?
The volume of a______________
A. prism is thrice the volume of a pyramid.
B. pyramid is thrice the volume of a prism.
C. cylinder is twice the volume of a cone.
D. cone is twice the volume of a cylinder.
The volume of a cylinder is thrice the volume of a cone with the same base and height.
The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height of the cylinder.
The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.
If we take a cone with the same base and height as a cylinder, the radius of the cone's base would be equal to the radius of the cylinder's base. Therefore, we can compare the volumes of a cylinder and a cone with the same base and height as follows:
Vcylinder = πr²h
Vcone = (1/3)πr²h
Dividing the volume of the cylinder by the volume of the cone, we get:
Vcylinder / Vcone = (πr²h) / [(1/3)πr²h]
Vcylinder / Vcone = 3
So the volume of a cylinder is three times the volume of a cone with the same base and height.
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