Answer:
a
Step-by-step explanation:
Given a quadratic equation in standard form ax² + bx + c = 0 (a ≠ 0 )
Then the discriminant b² - 4ac determines the nature of the roots.
• If b² - 4ac > 0 then 2 real and distinct roots
• If b² - 4ac = 0 then 2 real and equal roots
• If b² - 4ac < 0 then no real roots
Given
2x² + 8x + 3 = 0 ← in standard form
with a = 2, b = 8, c = 3 , then
b² - 4ac = 8² - (4 × 2 × 3) = 64 - 24 = 40
Since b² - 4ac > 0 then 2 real and distinct roots → a
Answer:
a
Step-by-step explanation:
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3958 grams and a standard deviation of 362 grams. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4320 grams. Round your answer to four decimal places.
Answer:
0.8413 or 84.13%
Step-by-step explanation:
The difference from 4320 grams from the mean is:
[tex]d=4320-3958=362\ grams[/tex]
This is exactly 1 standard deviation.
According to the empirical rule, 68.26% of all data is within 1 standard deviation of the mean, which means that 34.13% of all data is within the mean and 1 standard deviation over the mean. We also know that the mean is at the 50th percent of the normal distribution.
Therefore, the probability that the weight will be less than 4320 grams is:
[tex]P(X\leq 4320) = 0.50+0.3413=0.8413 = 84.13\%[/tex]
The probability is 0.8413 or 84.13%
A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)
y = 18(1.15)x
y = 18(0.15)x
y = 20.7(1.15)x
y = 20.7(0.15)x
Answer: A) 18(1.15)x
Step-by-step explanation:
18 was the original cost, so the price will always be determined with this starting point. Sice there is an increasing value, that makes it 1.15 instead of .15. And it goes up by 15%, making it the coefficient.
Answer:
A) y = 18(1.15)x
Step-by-step explanation:
(1/16)^(x+3) = (1/4)^(x+1)
Answer:
x=-5
Step-by-step explanation:
The answer is x = -5. The explanation and answer is in the image below.
. The sum of the ages of x boys in a class is 84 years. When a new boy aged 8 years, 1 month joins the class, the average age is increased by 1 month
Answer:
The number of boys, x = 12
Step-by-step explanation:
Given that the sum of the ages of the boys in a class = 84 years
The number of boys = x
A new boy aged 8 years 1 month is added and the average age increases by 1 month
We have
Average age = 84/x = y
Age of new boy = 8 years 1 month = [tex]8\frac{1}{12} \ year[/tex]
New average = y + 1/12 = [tex](8\frac{1}{12}+84) /(x + 1)[/tex] which gives;
84/x + 1/12 = [tex](8\frac{1}{12} + 84) /(x + 1)[/tex]
[tex]\dfrac{x +1008}{12 \cdot x} = \dfrac{1105}{12 \cdot x+ 12}[/tex]
(x + 1008)×(12·x + 12) = 1105× 12·x
12·x² -1152·x + 12096 = 0
x² -96·x + 1008 = 0
(x - 84)×(x - 12) = 0
Therefore, x = 12 or 84,
The number of boys are 12 or 84
For there to bee 84 boys, their average age would be one year each
Given that they are boys not babies, then there are only 12 boys.
Find the measure of c. A. 136 B. 144 C. 123 D. 149
Answer:
Option (D)
Step-by-step explanation:
Given quadrilateral in the circle is a cyclic quadrilateral.
By using the property of cyclic quadrilateral,
"Sum of each pair of opposite angles is 180°".
In the given cyclic quadrilateral,
d + 57° = 180°
d = 180 - 57
d = 123°
Similarly, c + 31° = 180°
c = 180° - 31°
c = 149°
Therefore, Option (D) will be the answer.
please help. evaluate 5!.
Answer:
120
Step-by-step explanation:
! means to multiply it by every number less than itself.
Not counting 1, this means 5*4*3*2.
20*3*2
60*2
120
The answer is 120.
Answer:
120
Step-by-step explanation:
A tissue sample is three cells thick. Each cell has a thickness of 0.000004m. What is the thickness of the tissue sample in mm. Give your answer in standard form. PLZ SHOW WORKING NOT IN NANO METERS. IN STANDARD FORM
Answer:
0.012 millimeters
Step-by-step explanation:
First, we solve for 0.000004 m to mm = 0.004 mm x 3 = 0.012 millimeters
One polygon has a side of length 3 feet. A similar polygon has a corresponding side of length 9 feet. The ratio of the perimeter of the smaller polygon to the larger is
Answer:
1:3
Step-by-step explanation:
9/3 = 3
3 is the scale factor
In a small town, there are 4 times as many left-handed males as there are left-handed females, and there are 3 times as many right-handed females as there are right-handed males. There are a total of 204 males and 348 females in the town. Let x represent the number of left-handed females, and let y represent the number of right-handed males. Write a system of equations to represent the situation. What is the value of x, the number of left-handed females? A. 6 B.24 C. 96 D. 108
Answer: 24
Expenation:
Left handed females = x
right handed females = 348 - x
right handed males = y
left handed males = 204 - y
204 - y = 4x
348 - x = 3y
4x + y = 204 . . . . . . . (1)
x + 3y = 348 . . . . . . . (2)
From (2), x = 348 - 3y
subsituting for x in (1), we have
4(348 - 3y) + y = 204
1392 - 12y + y = 204
12y - y = 1392 - 204
11y = 1188
y = 1188/11 = 108
x = 348 - 3y = 348 - 3(108) = 348 - 324 = 24
Answer:
24
Step-by-step explanation:
i got it right
The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units.
Which expression represents the volume of the prism, in cubic units?
x3 + 9
x3 + 3x2
x3 + 3x + 3
x3 + 6x2 + 9x
Answer:
B. x^3 + 3x^2
Step-by-step explanation:
Volume of a rectangular prism=width * length * height
V=w*l*h
h=3 greater than the length of the base
h=x+3
Length of the base=x
Width=x
Substituting values into the formula
V=w*l*h
=(x)*(x)*(x+3)
Multiplying
=(x^2)(x+3)
=x^3 + 3x^2
Option B is the correct answer
The expression [tex]x^3 + 3x^2[/tex] represents the volume of the prism, in cubic units.
We have given that the,
The height of a right rectangular prism is 3 units greater than the length of the base.
The edge length of the square base is x units.
What is the volume of rectangular prism?[tex]Volume of a rectangular prism=width * length * height[/tex]
[tex]V=w*l*h[/tex] ......(1)
We have given that the
h=3 greater than the length of the base
and length of the base is x
Hence, [tex]h=x+3[/tex]
[tex]Length of the base=x[/tex]
[tex]Width=x[/tex]
Substituting values l h and w into the formula (1) we get,
[tex]V=w*l*h[/tex]
[tex]=(x)*(x)*(x+3)[/tex]
[tex]=(x^2)(x+3)[/tex]
[tex]=x^3 + 3x^2[/tex]
Therefore the expression
[tex]x^3 + 3x^2[/tex]
represents the volume of the prism, in cubic units.
To learn more about the volume of the prism visit:
https://brainly.com/question/23963432
The surface area of a cube is 24 square inches What us the side length of the cube ?
A=24in² this th ans because the side of cube is 24 cm
John needs to find out the probability that he will sell all his cars by the end of the
year. He takes a sample of the customers that come in to see if they will buy a car.
How many customers should he sample to get an accurate probability?
a) 3 customers
b) 10 customers
c) 100 customers
d) 1000 customers
Answer:
c) 100
Step-by-step explanation:
This is the best choice because the number is not too low or too high. He will get an accurate probability.
When the variable is on both sides of the equation it is perfectly acceptable to solve each side by itself
True or False
X^4 -33x^2-108 which of the following is equal to the polynomial given above? A. (X+36)(x+v3i)(x-3) B. (X-36)(x+v3i)(x+3)
Answer:
Answer D I believe :)
Step-by-step explanation:
x^4-33x^2-108
rewrite as a difference
x^4+3x^2-36x^2-108
factor out x^2
x^2(x^2+3)-36x^2-108
factor out -36
x^2(x^2+3)-36(x^2+3)
factor out x^2+3
(x^2+3)(x^2-36)
factor x^2-36
(x^2+3)(x-6)(x+6)
set x^2+3 equal to 0
x^2+3=0
solve for x
x=+/-[tex]\sqrt{3}[/tex]i
set at factors
(x+6)(x-6)(x+[tex]\sqrt{3}[/tex]i)(x-[tex]\sqrt{3}[/tex]i)
I hope this helps.
Which graph represents the solution set for the system x+y greater than or equal to 5 and -3x+2y less than or equal than to -2
Step-by-step explanation:
in each equation once substitute the value of x as 0 and again y as zero by this way you will get two values of X and y .
then again find the slope for each equation by the formula
slope= -coefficient of x / coefficient of y
for example,
X+y is greater or equals to 5
or, X+y= 5
or, X=5-y
or, when y is equals to zero
X= 5
and when X is equals to zero
y= 5
then plot the above point in the graph with respect to its slope and the shaded part is the solution
If the blue radius below is perpendicular to the green chord and the segment
AB is 8.5 units long, what is the length of the chord?
A
A. 8.5 units
8.5
B
O B. 17 units
O C. 34 units
O D. 4.25 units
Answer:
O B. 17 units
Step-by-step explanation:
The chord is AC and the radius of the circle is perpendicular to the chord at B. AB = 8.5 units. According to the perpendicular bisector theorem, if the radius of a circle is perpendicular to a chord then the radius bisects the chord. This means that chord AC is bisected by the radius of the circle at point B. The length of the circle is calculated using:
[tex]AB=\frac{AC}{2}\\ AC=2*AB\\cross multiplying:\\AC = 2*8.5\ units\\AC = 17 \ units[/tex]
The length of the chord is 17 units.
Answer:
The answer is 17 units :D
Step-by-step explanation:
A mega-pack of markers contains red markers, black markers, and blue markers. There are 24 red markers in the pack. The probability of randomly choosing a red marker is 1 in 3. If the probability of randomly choosing a blue marker is 1 in 8, how many blue markers are in the pack?
Will mark brainlist
Answer:
Number of blue markers = 9
Step-by-step explanation:
Given that there are 24 red markers.
Probability of randomly choosing a red marker is 1 in 3.
Probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
That means the ratio of red markers to total markers is 1:3.
Here number of favorable cases are 24 i.e. the number of red markers
and Total number of cases are equal to total number of markers.
Let T be the total number of markers.
As per definition of probability:
[tex]\dfrac{1}{3}=\dfrac{24}{T}\\\Rightarrow \bold{T = 72}[/tex]
Also, given that the probability of choosing a blue marker is 1 in 8.
Let the number of blue markers be B.
As per definition of probability:
[tex]\dfrac{1}{8}=\dfrac{B}{72}\\\Rightarrow \bold{B = 9}[/tex]
Hence, the answer is:
Number of blue markers = 9
Evaluate the following expression using the given values: (1 point) Find x − 3y if x = 3 and y = −2.
Answer:
9
Step-by-step explanation:
x − 3y
Let x =3 and y = -2
3 -3(-2)
3 + 6
9
A circle has a radius of 10. An arc in this circle has a central angle of 72 degrees. What is the length of the arc? btw, the arc is aligned with the radius
Answer:
4 Pi
Explanation:
72/360 = 1/5 so the length of the arc is (1/5) the circumference or
(1/5) ( 2 Pi * 10) => C = 2 Pi r
(20/5) Pi =
4 Pi
What is the point-slope form of a line with slope 4/5 that contains the point
(-2, 1)?
Answer:
Y-1=4/5(x-(-2))
Step-by-step explanation:
Point slope form is written as y-y1=M(x-X1)
M is the slope
so replace the variables for the given value
Y-1=4/5(x-(-2))
Answer: y - 1 = 4/5 (x + 2)
Step-by-step explanation:
In how many ways can the letters of the word ``COPYRIGHT'' be arranged?
Answer:
362,880 ways
Step-by-step explanation:
There are 9 letters so 9!
And none of them are repeated so 9!/0!
9! = 362,880
I hope this helps, and plz mark me brainliest!!
Please helpppppppppppp
Answer:
678 ft²
Step-by-step explanation:
The opposite sides of the cuboid are congruent, thus surface area is
2(11 × 9) ← front and back + 2(11 × 12) ← top and base + 2(12 × 9) ← sides
= 2(99) + 2(132) + 2(108)
= 198 + 264 + 216
= 678 ft²
Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1.f(x)=7cos^2x
Answer:
Step-by-step explanation:
Using the double angle formulas,
cos(2x) = cos^2(x) - sin^2(x) ............(1)
1 = cos^2(x) + sin^2(x)............(2)
add (1) and (2)
1 + cos(2x) = 2 cos^2(x)
=> cos^2(x) = (1/2) (1+cos(2x)) ..............(3)
f(x) = 7 cos^2 (x)
substituting (3)
f(x) = (7/2) (1+cos(2x))
Can someone help me with this question (:
I’d appreciate it!
brainliest to the correct answer/explanation) ♀️
Answer:
bet whats the question
Step-by-step explanation:
Rewrite the radical expression as an expression with a rational exponent. the seventh root of x to the third power
Answer:I think it’s 7x^3
Step-by-step explanation:
A set of numbers is shown below: {0, 0.4, 1, 2, 3} Which of the following shows all the numbers from the set that make the inequality 4x + 1 ≥ 5 true? {2, 3} {1, 2, 3} {0, 0.4, 1} {0.4, 1}
Answer:
{1,2,3}
Step-by-step explanation:
The others will not show all the numbers from the set to make the inequality true
Answer:
1,2,3
Step-by-step explanation:
PLEASE HELP ASAP !! Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. QUESTION: Find the average rate of change of each function over the interval [0, 3]. Match each representation with its respective average rate of change 3, -3 ,-2,6,-1,5
Answer:
Average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.
Step-by-step explanation:
The formula for average rate of change of f(x) over [a,b] is
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
The given function is
[tex]r(x)=x^2+2x-5[/tex]
[tex]r(0)=(0)^2+2(0)-5=-5[/tex]
[tex]r(3)=(3)^2+2(3)-5=10[/tex]
Now,
[tex]m_1=\dfrac{r(3)-r(0)}{3-0}[/tex]
[tex]m_1=\dfrac{10-(-5)}{3}=5[/tex]
From the graph it is clear that q(0)=-4 and q(3)=5.
[tex]m_2=\dfrac{q(3)-q(0)}{3-0}[/tex]
[tex]m_2=\dfrac{5-(-4)}{3}=3[/tex]
It is given that function p has as x-intercept at (3,0) and a y-intercept at (0,6). It menas p(0)=6 and p(3)=0.
[tex]m_3=\dfrac{p(3)-p(0)}{3-0}[/tex]
[tex]m_3=\dfrac{0-6}{3}=-2[/tex]
From the given table it is clear that s(0)=-13 and s(3)=5.
[tex]m_4=\dfrac{s(3)-s(0)}{3-0}[/tex]
[tex]m_4=\dfrac{5-(-13)}{3}=6[/tex]
Therefore, the average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.
Please answer this in two minutes
Answer:
R = 21.8° to the nearest tenth
Step-by-step explanation:
To find Angle R we use tan
tan ∅ = opposite / adjacent
From the question
The opposite is 2
The adjacent is 5
So we have
tan R = 2/5
R = tan-¹ 2/5
R = 21.8° to the nearest tenthHope this helps you
Please answer it now in two minutes
Answer:
y = 4
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
y × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 4
Answer:
y=4
Step-by-step explanation:
If we have a triangle with angles A, B, and C. The law of sines says that the proportion between the sin of angle A and its opposite side is equal to the proportion between the sin of angle B and its opposite side and it is equal to the proportion between the sin of angle C and its opposite side.
So, by the law of sines we can say that:
[tex]\frac{sen(60)}{4\sqrt{3} } =\frac{sen(30)}{y}[/tex]
Solving for y, we get:
[tex]sin(60)*y=4\sqrt{3}*sin(30)\\\frac{\sqrt{3} }{2}y=4\sqrt{3}*0.5\\ \frac{1}{2} y=4*0.5\\y = 4[/tex]
Carter bought a bear and paid for a football uniform. The total cost was $38.50. Write and solve an equation to find the cost, x, of buying a bear.
Answer:
Equation:- [tex]x + y = 38.50[/tex]
Solution of x:- [tex]x = 38.50 - y[/tex]
Step-by-step explanation:
Given
Total Purchase = $38.50
Required
Determine the equation for finding the cost of a bear
From the question; we understand that the cost of 1 bear is represented with x
Solving further; by representing the cost of 1 football uniform with y
So;
[tex]1\ bear + 1\ uniform = 38.50[/tex]
Substitute x for 1 bear and y for 1 uniform to give us an equation
[tex]x + y = 38.50[/tex]
Solving for x (Subtract y from both sides)
[tex]x +y - y = 38.50 - y[/tex]
[tex]x = 38.50 - y[/tex]
The equation can't be solved further