The solutions of the quadratic equation are:
x = (-1 + i√23)/4
x = (-1 - i√23)/4
How to solve the quadratic function?For a general quadratic:
a*x^2 + b*x + c = 0
The solutions are given by the quadratic formula
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Here we have the quadratic equation:
2x^2 + x + 3 = 0
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*2*3} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-23} }{4}[/tex]
So we will have two complex solutions, these are:
x = (-1 + i√23)/4
x = (-1 - i√23)/4
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any p/q combination other than 50%/50% will result in a higher sample size because p times q is in the numerator of the formula. true false
Using the formula of the combination and for the values of 'p' and 'q'. The statement is false.
What do you mean by combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
What is the formula for combination?The formula is:
[tex]C(p,q) = \frac{p!}{q!(p-q)!}[/tex]
p=4 and put q=0 to 4
C(4,2) > C(4,0),C(4,1),C(4,3),C(4,4)
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In a survey of 2000 people who owned a certain type of car, 1300 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
65%
Step-by-step explanation:
65% of 2,000 = 1300
........
Answer:
Step-by-step explanation:
Would buy again customers are people satisfied.
Therefore we have
satisfied overall people surveyed
In numbers, this looks like
1300/2000
Simplifying we get
13/20
If you use a calculator then you can input this equation. However, if you want to be big-brained you can use simple math to get the decimal answer fast.
13/20 = (13•5)/(20•5) = 65/100 = 0.65
But if you need a percent value then you are not done!
0.65 is not a percent. To get a percent you multiply your fraction or decimal by 100. Therefore we get 0.65•100 = 65%
65% of people would buy the car again. Therefore 65% of people are satisfied with that car.
For a family living in Southern Mississippi, the probability of owning a dog is 0.4, the
probability of owning a cat is 0.5, and the probability of owning both a cat and a dog is
0.12.
What is the probability that a family living in Southern Mississippi owns a cat or a dog?
Hence, the probability that a family living in Southern Mississippi owns a cat or a dog is [tex]0.78[/tex].
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.
The meaning of probability is basically the extent to which something is likely to happen.
Here given that,
For a family living in Southern Mississippi, the probability of owning a dog is [tex]0.4[/tex], the probability of owning a cat is [tex]0.5[/tex], and the probability of owning both a cat and a dog is [tex]0.12[/tex].
Probability od owing a dog is
[tex]P(A)=0.4[/tex]
Probability of owing a cat is
[tex]P(B)=0.5[/tex]
Probability pf owing both a cat and a dog is
[tex]P(A[/tex]∩[tex]B)=0.12[/tex]
As we know,
[tex]P(A[/tex]∪[tex]B)=P(A)+P(B)-P(A[/tex]∩[tex]B)[/tex]
[tex]P(A[/tex]∪[tex]B)=0.4+0.5-0.12[/tex]
[tex]P(A[/tex]∪[tex]B)=0.78[/tex]
Hence, the probability that a family living in Southern Mississippi owns a cat or a dog is [tex]0.78[/tex].
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Calculate the size of the following marked angles:
v, w, x and y.
The measures of the angles are v = 80°, y = 100°, w = 45°, and x = 55°.
What is a cyclic quadrilateral?An inscribed four-sided polygon in a circle is known as a cyclic quadrilateral. With the specified side lengths, it has the largest area feasible.
Given the quadrilateral inside a circle.
The angle v is given by:
45° +v + 55°=180°
v + 100° = 180°
v = 180° - 100°
v = 80°
Since the quadrilateral is cyclic, the sum of its opposite angle is 180°.
Therefore,
y + v = 180°
y + 80° = 180°
y = 100°
Using the property of cyclic quadrilateral, it follows:
w = 45° and x = 55°
Hence, the measures of the angles are v = 80°, y = 100°, w = 45°, and x = 55°.
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Temperatures in °F can be converted in °C using the formula
C=5(F-32)/9
Make F the subject of the formula
Give your answer in the form aC+b/c where a,b and c are all positive integers
Answer:
Step-by-step explanation:
To make F the subject of the formula, you need to solve for F in the equation C = 5(F-32)/9.
You can do this by first multiplying both sides of the equation by 9 to get rid of the fraction:
C * 9 = 5(F-32)
Then, you can distribute the 5 on the right side of the equation:
C * 9 = 5F - 160
Then, you can add 160 to both sides of the equation to isolate the F term:
C * 9 + 160 = 5F
Finally, you can divide both sides of the equation by 5 to solve for F:
F = (C * 9 + 160)/5
This gives you the final form of the equation:
F = (9C + 160)/5
In this form, F is the subject of the formula. a = 9, b = 160, and c = 5 are all positive integers.
Answer:
[tex]F=\dfrac{9C+160}{5}[/tex]
Step-by-step explanation:
Given equation:
[tex]C=\dfrac{5(F-32)}{9}[/tex]
Multiply both sides by 9:
[tex]\implies 9C=5(F-32)[/tex]
Divide both sides by 5:
[tex]\implies \dfrac{9C}{5}=F-32[/tex]
Add 32 to both sides:
[tex]\implies \dfrac{9C}{5}+32=F[/tex]
[tex]\implies F=\dfrac{9C}{5}+32[/tex]
Rewrite 32 as a fraction with denominator 5:
[tex]\implies F=\dfrac{9C}{5}+\dfrac{32 \cdot 5}{5}[/tex]
[tex]\implies F=\dfrac{9C}{5}+\dfrac{160}{5}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies F=\dfrac{9C+160}{5}[/tex]
15 = 3t
Joe’s car has a 15 gallon fuel tank and an average fuel economy of 20 miles per gallon. He is planning a road trip where he’ll be driving on the freeway at 60 miles per hour for many hours. The equation above represents the time t (in hours) that it will take for his tank to be empty. What does the 3 represents?
A 3 is the product of his car’s fuel economy and the number of hours
B 3 is the ratio of his speed and his car’s fuel economy.
C 3 is the product of his car’s fuel tank capacity and his speed
D 3 is the ratio of his car’s fuel tank capacity and his fuel economy.
B) 3 is the ratio of his speed and his car's fuel economy.
What is speed?Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is traveling along a path. In other words, velocity is a vector, whereas speed is a scalar value.
Calculation:[tex]\frac{speed}{fuel economy} =\frac{\frac{60 miles}{hour} }{\frac{20 miles}{gallon} } \\\frac{speed}{fuel economy}={\frac{60 miles}{hour} .{\frac{gallon}{20 miles} }\\[/tex]
[tex]\frac{speed}{fuel economy}=\frac{3 gallons}{hour}[/tex]
Inserting this 3 in the given equation 15 = 3t and including each term, we see the units cancel out:
[tex]15 gallons = \frac{3 gallons}{hour}.t(hours)[/tex]
3 is the ratio of his speed and his car's fuel economy.
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#12: A train left Philadelphia at 8 AM on July 1st. It traveled
2,864 miles to Portland, Oregon, arriving at 9AM on July 4th.
What was the average rate of change of the train in miles per
hour?
Round to the nearest hundredth
Answer: 39.23 miles per hour
Step-by-step explanation:
1 day = 24 hour
3 days = 72 hours
Add one more hour for both to get to 9 AM, so it will take 73 hours to get there.
Now we find the average rate of change.
We take 2864 divided by 73 = 39.23 miles per hour
Quanta Indutrie old $325,000 of conumer electronic during July under a nine-month warranty. The cot to repair defect under the warranty i etimated at 4. 5% o-
the ale price. On November 11, a cutomer wa given $220 cah under term of the warranty
The journal entry for the July 31 sales and November 11 cash payment is shown below .
In the question ,
it is given that ,
the amount for which Qantas Industries sold electronics during July under a nine-month warranty is = $325000 ,
cost to repair defects is = 4.5 percent of sales price .
So , the cost to repair is = 4.5% × 325000 = $14625 .
So , the journal entry for July 31 is
Warranty expense Debit 14625
Estimated warranty liability/warranty payable Credit 14625
and the journal entry for November 11 is :
Estimated warranty liability /warranty payable Debit 220 ,
Cash Credit 220 .
Therefore , the Journal entry is shown above .
The given question is incomplete , the complete question is
Qantas Industries sold $325,000 of consumer electronics during July under a nine-month warranty. The cost to repair defects under the warranty is estimated at 4.5% of the sales price. On November 11, a customer was given $220 cash under terms of the warranty. Provide the journal entry for the estimated warranty expense on July 31 for July sales. Provide the journal entry for the November 11 cash payment .
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what is the answer of this question?
Step-by-step explanation:
The given mass of the Earth is 5.972 × 10²⁴
The given mass of the Jupiter is 1.898 × 10²⁷
Now,
1.898 × 10²⁷ ÷ 5.972 × 10²⁴
= 0.3178 × 10³ = 317.8
Thus, Jupiter is 317.8 heavier than Earth
There are 16 triangles and 4 squares. What is the simplest ratio of squares to triangles?
Answer:
4:1
Step-by-step explanation:
find the gcf: 4
divide by the gcf: 16/4 and 4/4
Solve for q.
q=
13
Blank 1:
24
q
Answer: 35
Step-by-step explanation:
Using the trapezoid midsegment theorem,
[tex]\frac{13+q}{2}=24\\\\13+q=48\\\\q=35[/tex]
(-2x + 9) + ( 3x - 4)
Find the slope of the line that passes through \left(10,8\right)(10,8) and \left(1,9\right)(1,9).
-2/3, is the slope of the line that passes.
What is slope?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-
P1 = (x1, y1) and P2 = (x2, y2)
According to our question-
The slope equation is [y2-y1/x2-x1]. For substitution and solution, use the provided points.
12-8/4-10
4/-6
-2/3
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A company sold 7.1 million items in a two-year period. Sales increased by 100,000 the second year. How many were sold the second year?
Answer:
I think it's 3650000
Step-by-step explanation:
7.1 mil ÷ 2 = 3550000
3550000 + 100000 = 3650000
a prestigious program accepts 2 out of every 9 applicants per yer. if the program accepted 360 applicants, how many applicants were not accepted?
If a prestigious program accepts 2 out of every 9 applicants per year than the program will accept 360 applicants out of 1620.
What is ratio math example?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. 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 one boy there are 3 girls)
What is a equation example?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
the ratio is given:
2/9 = 360/x
solving for the value of x;
x/9=360/2
x=(180)9
x=1620
this is the required value of applicants that were not accepted.
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Which statement describes values of x and y such that x/y could be an irrational number?
A. The value of x is zero, and the value of y is an integer less than zero.
B. The value of x is the square root of an integer, and the value of y is an integer greater than zero.
C. The value of x is an integer less than zero, and the value of y is an integer greater than zero.
D. The value of x is a square root that can be simplified to an integer, and the value of y is an integer less than zero.
The statement describes values of x and y such that x/y could be an irrational number is B. The value of x is the square root of an integer, and the value of y is an integer greater than zero.
How to illustrate the irrational number?The square root of an integer for x and a positive integer greater than zero for y are described in the statement as values of x and y that could be irrational numbers.
We have provided x and y values that could be irrational numbers. Any real number that cannot be expressed as the quotient of two integers is considered an irrational number. Positive whole numbers are not considered negative integers, nor are negative integers, or numbers below zero.
Consequently, we can say that A, C, or D do not demonstrate the irrational numbers since they are all expressed as integers.
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how many solutions does the equation 4+3−1=2(2+2)−2 have?
Answer:
1
Step-by-step explanation:
This equation only has 1 solution
Graph the following features: Y intercept = -3 Slope = 4/5
The equation of line where the y intercept is -3 and slope is 4/5 is
y = ( 4/5 )x - 3
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the equation A is y = mx + b
The y intercept of the line b = -3
The value of b = -3
The slope of the line m = 4/5
The value of m = 4/5
Now , substituting the values in the equation of line , we get
y = mx + b
y = ( 4/5 )x + ( -3 )
y = ( 4/5 )x - 3
The graph of the equation y = ( 4/5 )x - 3 is given below
Therefore, the value of the equation of line A is y = ( 4/5 )x - 3
Hence , The equation of line where the y intercept is -3 and slope is 4/5 is
y = ( 4/5 )x - 3
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why does the normal distribution have an importance in statistics of wether or not iut appears in nature
The normal distribution have an importance in statistics of whether or not out appears in nature, because it fits several natural phenomena.
For exa. measurement error, heights, IQ scores, and physical activity measures all follow the normal distribution.
In this question we need to describe why does the normal distribution have an importance in statistics of whether or not out appears in nature.
We know that if we plot the probability distribution and it forms a bell-shaped curve. If the mean, mode, and median of the sample are equal then the variable has normal distribution.
A normal distribution is dependent on two parameters of the data set: mean and the standard deviation of the sample.
This characteristic of the normal distribution makes it extremely simple.
Also, the normal distribution is important because of the Central limit theorem.
It makes math easy - like calculating moments, correlations between variables, and other calculations that are domain specific.
So, the normal distribution have an importance in statistics of whether or not out appears in nature.
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Graph the image of this figure after a dilation with a scale factor of 1/2 centered at the origin.
Use the polygon tool to graph the dilated figure.
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
Polygon with coordinates: (-4, 4), (6, 8), (2, 2), (-4, 4).
The vertices of the dilated triangle are (-2, 2), (3, 4), and (1, 1).
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
The coordinates of the triangle are (-4, 4), (6, 8), and (2, 2).
The scale factor of the triangle is 1/2 centered at the origin. Then the coordinate of the triangle will be given as,
⇒ (-4/2, 4/2), (6/2, 8/2), (2/2, 2/2)
⇒ (-2, 2), (3, 4), (1, 1)
The vertices of the dilated triangle are (-2, 2), (3, 4), and (1, 1).
The image of the triangle and dilated triangle is given below.
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Answer: The other answer is incorrect, the graph below shows the correct answer.
Coordinates of each point
A: (3,4)
B: (-2,2)
C: (1,1)
I know this is late, but I wanted to help those in the future who needed help with the question. Good Luck <3
Jody has 3 red marbles, 6 blue marbles, and 9 yellow marbles. What is the ratio of red marbles to blue marbles?
Answer: The ratio of red marbles to blue marbles is 3:6. This can be written as a fraction as 3/6, which simplifies to 1/2.
Step-by-step explanation:
To find the ratio of two quantities, you can divide the number of one type of item by the number of another type of item. In this case, the ratio of red marbles to blue marbles is 3 marbles / 6 marbles, which simplifies to 1/2.
It's important to note that a ratio is not the same thing as a percentage or a fraction. A ratio is a comparison of two quantities, while a percentage is a measure of a quantity relative to the total amount and a fraction is a division of one number by another.
Si en un Salón hay 25 estudiantes de los cuales 12 son varones ¿Cual es la razón de varones a hembras?
La razón que buscamos para los números de estudiantes es:
12:13
¿Cual es la razón de varones a hembras?Sabemos que si de un numero N podemos separar 2 grupos, de tal forma que hay a elementos del grupo A y b elementos del grupo B, la razon de el grupo A al grupo B es a:b
En este caso sabemos que hay 25 estudiantes y hay 12 varones, entonces hay:
25 - 12 = 13 "hembras"
Entonces la razon que buscamos es:
12:13
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Andrew just started a running plan where he runs 12 miles the first week and then increases the number of miles he runs by 5% each week. If he keeps up this plan for 10 weeks, how many total miles would Andrew have run, to the nearest whole number?
Answer:
18 miles.
Step-by-step explanation:
You start with 12 miles and then you first need to figure out what 5% of that is by doing the equation x/12 = 5/100 and you will then get .6. Then you multiply that number by 10 (one for each week) getting 6. Then you add the 6 to your starting total to get 18.
function rule to find f(7).
Answer: 196
Step-by-step explanation:
[tex]f(7)=(-7-7)^2 =196[/tex]
Add -13[tex]\frac{1}{4}[/tex]+ 4[tex]\frac{3}{4}[/tex] Write your answer as a mixed number in simplest form.
Answer:
Step-by-step explanation:
3 1/4
Rose chin deposited $900 in a new savings account. The amount for $1.00 compounded daily the account earns after 12 years at 5.25% interest is 1.878. Calculate the compound interest earned after 12 years.
The answer to this Question based on Compound Interest is 1690.2$
What is Compound Interest?
Compound interest is a type of interest that is calculated not only on the initial principal but also on the accumulated interest of previous periods. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal plus previously accumulated interest. It is the concept of earning interest on interest, which causes the total balance to grow at a faster rate than simple interest. Compound interest is often referred to as the eighth wonder of the world, as it is a powerful financial concept that can yield impressive results over a long period.
Initial money deposited = 900$
1$ turns into 1.878$ after 12 years of Compound Interest
hence by basic manipulation we can do like
900$ turns into 900 multiplied by 1.878 which comes out to b 1690$
Hence after 12 years final amount will be 1690$
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1.25/0.06 = z−6 /2.4 help quickly
Answer:
z = 56
Step-by-step explanation:
I'll assume 1.25/0.06 = z−6 /2.4 is actuallY: 1.25/0.06 = (z−6)/2.4 (and not 1.25/0.06 = z−(6 /2.4)).
1.25/0.06 = (z−6)/2.4
1.25*(2.4) = (z−6)*(0.06) [Multiply both sides by 0.06 and then 2.4]
3 = 0.06z - 0.36
3.36 = 0.06z
z = (3.36/0.06)
z = 56
the question is in the image
Answer:
1. The negative flips the parabola upside down so there is a maximum
2. The 1/2 means there is a vertical shrink
3. -3 means the graph moves to the RIGHT 3 units (X sign always changes)
4. +12 means the graph shifts up 12 units
Step-by-step explanation:
I need help please help
Answer:
4t + 109.99 = 347.95
Step-by-step explanation:
They bought 4 tickets so that is how we got 4t
they spent altogether $109.99 to make the total
347.95
Bonus : 1 ticket is 59.49
Find the total surface area of this triangular prism 13cm 5cm 12cm 9cm 15cm 20cm.
The surface area of the triangular prism is 924 cm².
What is the triangular prism?
When a prism has three rectangular sides and two triangular bases, the prism is said to be triangular. A pentahedron, that is.
Volume is calculated using the formula volume = 0.5 * b * h * length, where b is the triangle's base length, h is its height, and length is the prism length.
Area is defined as length * (a + b + c) + (2 * base area), where a, b, and c are the triangle's sides and base area is the triangle's base area.
The surface area is equal to the area of the two triangles + area of the three rectangles.
Area of two triangles:
12 × (9+5) × 1/2
= 84
84(2) = 168
Area of the three rectangles:
15 × 20 + 13 × 20 + 14 × 20
= 840
840 + 84
The surface area of the triangular prism is 924 cm².
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