Answer:
8
Step-by-step explanation:
is it right?
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
The answer is , (a) For equation 1 Use the quadratic formula , (b) For equation 2 use of Factor out the common factor , (c) For equation 3 use of Complete the square.
What is Quadratic equation?A quadratic equation is a type of equation in algebra that contains a variable of degree 2, meaning that the highest power of the variable is 2.
Quadratic equations can have two real roots, one real root, or two complex roots, depending on the value of the discriminant (b² - 4ac). If discriminant is positive, equation has two real roots, if it is zero, equation has one real root (a "double root"), and if it is negative, equation has two complex roots.
Inga can use the following steps to solve the quadratic equation 2x² + 12x - 3 = 0:
Use the quadratic formula: Inga can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = 12, and c = -3.Factor out the common factor: Inga can factor out the common factor of 2 from the equation to get 2(x² + 6x - 3/2) = 0.Complete the square: Inga can complete the square by adding (6/2)² = 9 to both sides of the equation to get 2(x² +6x +9 -9/2) = 9.Therefore, steps that Inga could use to solve quadratic equation are given:
Use the quadratic formula
Factor out the common factor
Complete the square
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Jeremy and Aksa were finding the volume of this prism. They agreed that 4 layers can be added together to find the volume. Jeremy says that he can see on the end of the prism that each layer will have 16 cubes in it. Aksa says that each layer has 24 cubes in it. Who is right? Explain your answer.
Both Jeremy and Aksa could be right, depending on how they are counting the cubes for finding the volume of a prism.
What is a prism?A prism is a three-dimensional solid shape with a constant cross-section, usually a polygon. It is characterized by two identical end faces, parallel and congruent bases, and straight lateral faces connecting the bases.
According to the given information:Both Jeremy and Aksa could be right, depending on how they are counting the cubes.
If the prism has a square base with 4 cubes along each side, then there would be 16 cubes in each layer. If there are 4 layers, then the total volume would be 16 x 4 = 64 cubic units.
However, if the prism has a rectangular base with 6 cubes along one side and 4 cubes along the other side, then there would be 24 cubes in each layer. If there are 4 layers, then the total volume would be 24 x 4 = 96 cubic units.
Therefore, the answer depends on the shape of the prism and how the layers are counted.
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Elliot read a report from a previous year saying that 6 % 6%6, percent of adults in his city biked to work. He wanted to test whether this had changed, so he took a random sample of 240 240240 adults in his city to test H 0 : p = 0.06 H 0 :p=0.06H, start subscript, 0, end subscript, colon, p, equals, 0, point, 06 versus H a : p ≠ 0.06 H a :p =0.06H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 06, where p pp is the proportion of adults in Elliot's city that bike to work. The sample results showed 21 2121 adults who biked to work, and the corresponding test statistic was z ≈ 1.79 z≈1.79z, approximately equals, 1, point, 79. Assuming that the necessary conditions are met, what is the approximate P-value for Elliot's significance test?
Answer: To find the P-value, we first need to determine the direction of the alternative hypothesis. Since the alternative hypothesis is two-tailed, we need to divide the significance level (α) by 2 before finding the critical values and the rejection region. Therefore, we have:
H0: p = 0.06
Ha: p ≠ 0.06
α = 0.05/2 = 0.025
The test statistic is z = 1.79, which represents the number of standard errors that the sample proportion is from the hypothesized population proportion under the null hypothesis. We can find the P-value by looking up the area in the standard normal distribution table beyond the test statistic in both tails:
P-value = P(Z ≤ -1.79 or Z ≥ 1.79)
= P(Z ≤ -1.79) + P(Z ≥ 1.79)
= 0.0364 + 0.0364
= 0.0728
Therefore, the approximate P-value for Elliot's significance test is 0.0728. Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion of adults who bike to work in Elliot's city has changed significantly from the previous year.
Step-by-step explanation:
The sum of 2 vector forces is <5, -3>. What is the magnitude of the resulting force?
According to the question the magnitude of the resulting force is 5.83.
What is magnitude?Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.
The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.
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How do I solve this problem?
The measure of angle CFE is determined as 29⁰.
What is the measure of angle CFE?The measure of angle CFE is calculated by applying the following formula.
The intersecting chord theorem, also known as the intersecting chords inside and outside theorem, is a geometric property that applies to chords (line segments that connect two points on the circumference of a circle) that intersect inside or outside a circle.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠CFE = ¹/₂( arc angle CE )
arc CE = 360 - 302 (sum of angles in a circle)
arc CE = 58⁰
m∠CFE = ¹/₂ x 58
m∠CFE = 29⁰
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Find the area of a rectangle with length 4.3 cm and breadth 3.9 cm
Answer:
16.77 cm²
Step-by-step explanation:
Area of rectangle = L x W
L = 4.3 cm
Width = 3.9 cm
Let' solve
4.3 x 3.9 = 16.77 cm²
So, the area of the rectangle is 16.77 cm²
Please I need help answer all the questions please
Average Minutes Per Night Spent On Homework
0 20
48 60
190
Average Minutes Per Night Spent Watching TV
0 10
20 30
50
11. What is the median for TV time?
12. What is the range of times that the middle 50% of the sophomores spend on TV per night?
13. What percent of the sophomores spend more than 30 minutes per night watc
Find the area of the polygon
Please help me with this problem
Using the proportions we know that the value of h would be 15 units when b is 10 units.
What are proportions?An online application called a proportion calculator solves two fractions for the parameter x.
It uses cross-multiplication to assess whether two fractions are equivalent.
A proportion is an equation that sets two ratios at the same value.
For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls. (for every boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male. (by dividing 1 by 4).
So, according to the given similar triangle, the proportions would be:
4/b = 6/h
Now, insert the given values:
4/10 = 6/h
Solve as follows:
4/10 = 6/h
4h = 60
h = 60/4
h = 15
Therefore, using the proportions we know that the value of h would be 15 units when b is 10 units.
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HELP ASAP!!!!
The diameter of a circular cookie cake is 14 inches. How many square inches make up half of the cookie cake? Approximate using π = 3.14. 615.44 square inches 307.72 square inches 153.86 square inches 76.93 square inches
The number of square inches to make up half the cookie cake is 76.93 in² area.
How to calculate for the half square inches areaThe diameter of the circular cookie cake is 14 inches, so its radius will be r = 7 inches. Using the formula for area of circle we have:
area of cookies cake = 3.14 × 7 in × 7 in
area of cookies cake = 153.84 in²
half the area of the cookie cake = 153.84 in²/2
half the area of the cookie cake = 76.93 in²
Therefore, the number of square inches to make up half the cookie cake is 76.93 in² area.
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A line has a slope of -4 and passes through the point (-1, 10). Write its equation in slope- intercept form.
Answer:
[tex]10 = -4( - 1) + b[/tex]
[tex]10 = 4 + b[/tex]
[tex]b = 6[/tex]
[tex]y = - 4x + 6[/tex]
The equation of the line in slope-intercept form is y = -4x + 6.
Explanation:The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope is -4 and the line passes through the point (-1, 10), we can substitute these values into the equation.
Using the point-slope formula (y - y1) = m(x - x1), we can rewrite it as (y - 10) = -4(x - (-1)). Simplifying this equation, we get y - 10 = -4x - 4, and rearranging it, we have y = -4x + 6. Therefore, the equation of the line in slope-intercept form is y = -4x + 6.
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How to find the circumference of a circle
Answer: To find the circumference of a circle, there are 2 formulas.
Step-by-step explanation:
The first formula is 2πr and the second formula is πd when solving any math problem. You can use either one but you would use which one is the most helpful to answer your question. Hope this helps!
You want to be able to withdraw $40,000 each year for 15 years. Your account earns 5% interest.
a) How much do you need in your account at the beginning?
b) How much total money will you pull out of the account?
c) How much of that money is interest?
a) you would need $450,332.81 in your account at the beginning. b) the total money that will be pulled out of the account is $600,000.
How to determine How much do you need in your account at the beginninga) To calculate the amount needed in the account at the beginning, we can use the present value formula:
PV = PMT * ((1 - (1 + r)^-n) / r)
Where PV is the present value, PMT is the annual payment, r is the annual interest rate, and n is the number of periods.
Plugging in the values, we get:
PV = 40000 * ((1 - (1 + 0.05)^-15) / 0.05)
PV = $450,332.81
Therefore, you would need $450,332.81 in your account at the beginning.
b) To calculate the total money that will be pulled out of the account, we can simply multiply the annual payment by the number of years:
Total money = PMT * n
Total money = 40000 * 15
Total money = $600,000
Therefore, the total money that will be pulled out of the account is $600,000.
c) To calculate the amount of money that is interest, we can subtract the initial investment from the total money pulled out:
Interest = Total money - Initial investment
Interest = $600,000 - $450,332.81
Interest = $149,667.19
Therefore, $149,667.19 of the money pulled out is interest.
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2À candy company claims that its jelly bean mix contains 15% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 200 jelly beans. What is the probability that a bag will contain more than 20% blue jelly beans?
Answer: To solve this problem, we can use the binomial distribution formula. Let X be the number of blue jelly beans in a bag of 200 jelly beans. Then X follows a binomial distribution with parameters n = 200 and p = 0.15, where p is the probability of drawing a blue jelly bean.
The probability of getting more than 20% blue jelly beans in a bag can be calculated as:
P(X > 0.2*200) = P(X > 40)
We can use the normal approximation to the binomial distribution, since n is large (200) and p is not too close to 0 or 1. Using the mean and variance of the binomial distribution, we can calculate the corresponding mean and standard deviation of the normal distribution as follows:
μ = np = 200 * 0.15 = 30
σ = sqrt(np(1-p)) = sqrt(200 * 0.15 * (1-0.15)) = 4.07
Then, we can standardize the random variable X as:
Z = (X - μ) / σ
So, we have:
P(X > 40) = P((X - μ) / σ > (40 - μ) / σ)
= P(Z > (40 - 30) / 4.07)
= P(Z > 2.46)
Using a standard normal distribution table or a calculator, we find that P(Z > 2.46) is approximately 0.007. Therefore, the probability that a bag will contain more than 20% blue jelly beans is about 0.007 or 0.7%.
Step-by-step explanation:
Gary wants to make a circular pond in his yard and put a low fence around the edge. If Gary has 124 feet of fencing, which is closest to the area of the largest circular pond he can make with the fencing?
In a case whereby Gary wants to make a circular pond in his yard and put a low fence around the edge. If Gary has 124 feet of fencing, the closest to the area of the largest circular pond he can make with the fencing is 1471.61ft^2
How can the area of the largest circular pond be calculated?We were told that he will bw making a pond which is circular in nature, then We can assume that the radius is R, then 2 πR = 136
R= 136/2 π
R= 68/π
The the are of the pond= πR^2
= π * (68/π)^2
=1471.61ft^2
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The sum of a number and three is no more than eight
Answer:5
Step-by-step explanation: hope this helps
Use the following number line to choose the correct statement. R x P > S S > Q × R Q × R > S
Answer:
Looking at the number line, we can see that R is to the left of P, and S is to the right of P. Also, Q is to the left of R, and S is to the right of Q.
So, the first statement "R x P > S" is not true, because S is to the right of both R and P.
The second statement "S > Q x R" is also not true, because Q is to the left of R, and S is to the right of both Q and R.
The third statement "Q x R > S" is true, because Q is to the left of R, and S is to the right of both Q and R. Therefore, the correct statement is:
Q x R > S
While watching a movie, Laila and Thiago shared a
Laila: The amount of surplus corn
Thiago: The amount of corn eaten
How to label each vertical axis on the graph?According to graph the vertical axis of Laila's Graph is surplus popcorn and the vertical axis of Thiago's Graph is popcorn eaten. This can be seen on the graph (graph in image attached below)
Therefore, the correct vertical axis label that accurately represent the situation is:
The amount of surplus popcorn for Laila's graph.
The amount of popcorn eaten for Thiago's graph
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The question is incomplete, complete question in image attached.
The height distributions of two different classes at Dover elementary school are shown below both groups, have the same interquartile range how many times the third quartile range is the difference between the median height of the third grade class in the fourth grade class 1/4 1/2 two or four
The third quartile range is the difference between the median height of the third grade class and the fourth grade class, so the answer is two times.
Please help and hurry
The equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.
What is linear and quadratic equation?A straight line can be used to symbolise a function that is linear, meaning that for each unit change in the input, the output (y) changes by a fixed amount (x). While a parabola can be used to depict a function, a quadratic function has an output (y) that changes by a non-constant amount for each unit change in the input (x). In other words, a quadratic function curves because of the squared term in its equation.
Given, the parabola has vertex at point (2, -11) and passes through the point (0, 5).
Thus, the equation of parabola in vertex form is:
y = a(x - 2)² - 11
Now, the parabola passes through the point (0, 5) we have:
5 = a(0 - 2)² - 11
5 = 4a - 11
16 = 4a
a = 4
Hence, the equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.
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The table contains some points on the graph
of an exponential function. Based on the
table, which function represents the same
relationship?
Answer: 1st one
Step-by-step explanation:
The circle graph represents the hair color of middle-school students. There were 800 middle-school students surveyed. Use the circle graph.
Hair Color
Red
5%
Blonde
30%
Black
25%
Brown
40%
How many students have red hair?
40 students have red hair.
We have,
Red color= 5%
Black = 25%
Brown = 40%
Blonde= 30%
Total middle school students = 800
So, the number of red haired student
= 5% of 800
= 5/100 x 800
= 5 x 8
= 40 students
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1:20 - salesman allows a 5% discount for cash payment. What will be the discount allowed for a ash payment of GH¢5,600.00? A. GH 250.00
The discount allowed for a cash payment of GH 5,600.00 is given as follows:
GHC 280.00.
How to obtain the discount?The discount allowed for a cash payment of GH 5,600.00 is obtained applying the proportions in the context of the problem.
There is a 5% discount, hence the value of the discount is obtained as follows:
0.05 x 5600 = GHC 280.00.
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Choose the expression that correctly compares the numbers 117 and 171.
171 < 117
171 = 117
171 > 117
117 > 171
Answer:
171 > 117
Step-by-step explanation:
171 is greater than 117 meaning the alligator is eating the bigger number, 171.
In triangle BC, point D is on AC such that AD = 12 and CD = 12. If angle ABC = angle BDC = 90 degrees, then what is BD?
Answer:
Step-by-step explanation:
BD is craxking treys and cracking treys is gd dissing bd you can look it up i ffrom o block and bd is the opps im telling so you wont lose yo life so please play right if you gdk be gdk if u gd be gd we aint bd ofn
Choose scales for the coordinate plane shown so that you can graph the points J (5, 50), K(3, 50), L (4, -40), M (-2, 40), and N (-5, -10). on the x-axis use a scale of ____ units for each grid square. on the y-axis use a scale of ____ units of each grid square. complete the explanation for using these scales for each axis. the x-coordinates range from ____ to ____, and the y-coordinates range from ____ to ____.
On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.
What is coordinate plane?In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).
On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.
For the given coordinates the range of x and y coordinates are:
x-coordinates range from -5 to 5
y-coordinates range from -40 to 50.
Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.
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name three solution for h > 8
Answer:
all numbers greater than 8
Step-by-step explanation:
simply pick any number greater than 8, since the > symbol is in front of 8. By the way, you cannot pick 8. :) I hope this helps!
A principal of $1500 is invested at 8.5% interest, compounded annually.
How much will the investment be worth after 14 years?
Use the calculator provided and round your answer to the nearest dollar.
The investment will be worth approximately $4468 after 14 years.
What is annual interest rate?Annual interest rate is the rate at which an investment or loan grows in value over the course of a year, expressed as a percentage. It represents the cost of borrowing or the return on investment over one year.
According to question:The following equation can be used to determine the future value of an investment using compound interest:
FV = P * (r/n + 1)(n*t)
Where:
FV is the investment's future value.
The principal is P. (initial investment)
The annual interest rate is represented by r,
The number of times the interest is compounded annually by n (expressed as a decimal).
t is the time (in years)
In this case:
P = $1500
r = 8.5% = 0.085
n = 1 (compounded annually)
t = 14
With these values entered into the formula, we obtain:
FV = 1500 * [tex](1 + 0.085/1)^(1*14)[/tex]
= $4467.56
Therefore, the investment will be worth approximately $4468 after 14 years.
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Hayley is looking for a job cutting hair. One option is self-employment at The Princeton Salon, where she would pay $774 per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon $9 for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How much would Hayley pay? How many haircuts would that be?
Hayley would pay $ ______ to either salon if she performed _______ haircuts.
Answer:Let's assume the number of haircuts Hayley needs to perform in a month for the total amount paid to either salon to be the same is denoted as 'x'.
For self-employment at The Princeton Salon:
Hayley would pay a fixed monthly rent of $774 to rent a station and keep all of her earnings.
For working at a franchise:
Hayley would have to pay $9 to the salon for every haircut she performs.
Based on the given information, we can set up the following equation to find the value of 'x':
Number of haircuts * Cost per haircut at franchise = Monthly rent at The Princeton Salon
x * 9 = 774
Solving for 'x':
x = 774/9
x ≈ 86.00
So, Hayley would need to perform approximately 86 haircuts in a month for the total amount paid to either salon to be the same.
Now, to calculate the total amount paid to either salon, we can use the following formulas:
Total amount paid at The Princeton Salon = Monthly rent + Earnings (which would be all of her earnings, as mentioned in the prompt)
Total amount paid at the franchise = Cost per haircut * Number of haircuts
Plugging in the values:
Total amount paid at The Princeton Salon = $774 + (Earnings from haircuts)
Total amount paid at the franchise = $9 * 86
Since the total amount paid to either salon is the same, we can equate the two equations:
$774 + Earnings from haircuts = $9 * 86
Solving for Earnings from haircuts:
Earnings from haircuts = $9 * 86 - $774
Earnings from haircuts = $774
So, Hayley would pay a total of $774 in earnings from haircuts, regardless of whether she chooses self-employment at The Princeton Salon or working at the franchise. The number of haircuts she needs to perform to reach this amount is 86.
Step-by-step explanation:
Find the equation of the line tangent to the graph of f(x) = (In x)4 at x = 4.
y =
(Type your answer in slope-intercept form. Do not round until the final answer. Then round to
as needed.)
The equation of the tangent line of f(x) = (ln x)⁴ at x = 4 is y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2.
What is differentiation?We may calculate the derivative of a power function using the power rule of differentiation. Since many functions may be expressed as power functions or can be made simpler using power functions, the power rule is a helpful tool in calculus. We can quickly determine the derivatives of these functions using the power rule and apply them to issues in physics, economics, and engineering.
The slope of the tangent line at x = 4 is determined using the derivative as follows:
f(x) = (ln x)⁴
f'(x) = 4(ln x)³ (1/x)
At x = 4, we have:
f'(4) = 4(ln 4)³ (1/4) = (3/16)ln 2
Now, the equation of the tangent line is:
y - 256ln⁴ 2 = (3/16)ln 2(x - 4)
y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2
Hence, the equation of the tangent line of f(x) = (ln x)⁴ at x = 4 is y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2.
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