The probability of answering correctly if you make a random guess is:
P = 1/5 = 0.2
How to find the probability for a random guess?If you make a random guess, then you have no idea of which could (or couldn't) be the correct answer. Thus, all the 5 options have the exact same probability of being the correct one.
From this, the probability of answering correctly the question is given by the quotient between the number of correct answers (we assume is only one) and the total number of options (5).
So the probability is:
P = 1/5 = 0.2
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The heights of the members of a high school class
are normally distributed. If the mean height is 65
inches and a height of 72 inches represents the 84th
percentile, whaķis the standard deviation for this
distribution?
Answer:
the average height is between 65 and 72 inches
Step-by-step explanation:
(SHOW WORK)
Sofia conducted a scientific experiment. For a certain time, the temperature of a compound rose 1 3/4 degrees every 1 2/5 hours. What was the rate, in degrees per hour, that the temperature of the compound rose? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
Answer:
0.8 degrees per hour
Step-by-step explanation:
1 2/5 divided by 1 3/4
7/5 / 7/4
keep, change, flip the fraction
7/5 x 4/7
=4/5= 0.8
how to write 24b^{2}+96b into a equivalent expression
Answer:
See below
Step-by-step explanation:
[tex]24b^2+96b\\\\24(b^2+4b)\\\\24b(b+1)[/tex]
Solve for x, please show work
3(4x-12)+3=3x-7+12x
Answer:
x = - [tex]\frac{26}{3}[/tex]
Step-by-step explanation:
3(4x - 12) + 3 = 3x - 7 + 12x ← distribute parenthesis and simplify left side
12x - 36 + 3 = 15x - 7
12x - 33 = 15x - 7 ( subtract 15x from both sides )
- 3x - 33 = - 7 ( add 33 to both sides )
- 3x = 26 ( divide both sides by - 3 )
x = - [tex]\frac{26}{3}[/tex]
What is the slope of the line that contains the points (-1, 2) and (3, 3)?
Will someone please help me
Answer:
see attached
Step-by-step explanation:
The relationship between time, speed, and distance is ...
distance = speed · time
Stephanie wants her first break before 65 miles, so the time until the break will satisfy the inequality ...
10t < 65 . . . break before 65 miles
t < 6.5 . . . . . divide by 10
On a graph, values less than 6.5 will appear shaded to the left of that point. Since 6.5 is not included in the solution set, the dot at that point is an open circle.
Examine the following diagram:
1
X
Which statement is not true of the given diagram?
Om22+ m23 = 180°
O m2 2 + 24 = 180°
O 23 and 24 are vertical angles
3
4.
N
O 22 = 24
Answer:
The answer is D.
Step-by-step explanation:
Angle two is not congruent to angle four in any way, they are not vertical angles, but they are adjacent, although this doesn't mean they are congruent, rather it means that if added, they will equal 180 degrees.
The lines are intersecting and the angles ∠2 ≅ ∠4 is not true
What are the angles formed by 2 intersecting lines?Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.
Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.
When lines intersect, two angle relationships are formed:
Opposite angles are congruent
Adjacent angles are supplementary
Given data ,
Let the first line be represented as a
Let the second line be represented as b
Now , the lines a and b intersect at point O
where ,
m∠2 + m∠3 = 180° ( angles on a straight line = 180° )
m∠2 + m∠4 = 180° ( angles on a straight line = 180° )
And , ∠3 and ∠4 are congruent ( vertical angles )
Hence , the incorrect statement about intersecting lines is ∠2 ≅ ∠4
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The sum of 2 numbers is 17 and their difference is 29 what are the two numbers
Answer:
23 , -6
Step-by-step explanation:
Let the unknown two numbers be x & y.
According to the question,
The sum of 2 numbers is 17 .
x + y = 17 ⇒ (1)
Their difference is 29 .
x - y = 29 ⇒ (2)
First let us find the value of x.
(1) + (2)
x + y + ( x - y ) = 17 + 29
x + y + x -y = 46
2x = 46
Divide both sides by 2.
x = 23
And now let us find the values of y.
x + y = 17
23 + y = 17
y = 17 - 23
y = -6
There fore, the two numbers are 23 , (-6)
Hope this helps you :-)
Let me know if you have any other questions :-)
Plz help I need so much help
Answer: 28
Step-by-step explanation:
3 to the power of 3 is 3x3= 9 x3 = 27
27 divided by 3 = 9
9-2 = 7 x 4 = 28
A hospital prepares a 100 mg supply of technetium-99m which has a half-life of 6 hours. How much technetium-99m will remain after 72 hours
Notice that 72 hours is 12 times the half-life of 6 hours. So, the starting amount of 100 mg will decay to half, 12 times. In other words
• after 1 hour, 100 mg decays to 50 mg
• after a total 2 hours, 100 mg decays to 25 mg
• after a total 3 hours, 100 mg decays to 12.5 mg
and so on, so that after a total of 72 hours, the hospital is left with
[tex]\dfrac{100\,\rm mg}{2^{12}} = \boxed{0.0244140625 \, \mathrm{mg}}[/tex]
identify the slope for 32+47x=y
Answer:
47
Step-by-step explanation:
The slope for this equation is m=47.
900% of what number is 5,940?
Answer:
660
Step-by-step explanation:
If n represents the number, we are told ...
900% × n = 5940
We know that 900% = 900/100 = 9, so this is ...
9n = 5940
Dividing by the coefficient of n gives ...
n = 5940/9 = 660
The number is 660.
Evaluate: sec(5 pie/4)
Answer:
[tex]sec(\frac{5\pi}{4})=-\sqrt{2}[/tex]
Step-by-step explanation:
[tex]sec(\frac{5\pi}{4})\\\\=\frac{1}{cos(\frac{5\pi}{4})}\\ \\=\frac{1}{-\frac{\sqrt{2}}{2}}\\ \\=-\frac{2}{\sqrt{2}}\\ \\=-\frac{2\sqrt{2}}{2}\\ \\=-\sqrt{2}[/tex]
It really helps to use the unit circle for solving these kinds of problems. I've attached one for your convenience. Note that a point on the unit circle, given the angle in radians, is defined as [tex](cos\theta,sin\theta)[/tex].
The sales tax in your city is 8.8%, and an item costs $63.50. How much tax would you pay on that item?
Step-by-step explanation:
63.5*0.088 =5.588 tax for your answer
ber
4. Mr. Conner purchased 8 liters of eyewash
solution for the science lab. How many
milliliters did Mr. Conner buy?
A 0.8 mL
B 80mL
C 800mL
D 8000mL
So I'm currently doing online school due to external circumstances and haven't done this type of problem before. I need help finding DE and an explanation on how to get it, thanks!
Answer:
DE ≈ 14.91
Step-by-step explanation:
Make use of the relationships between sides and angles in a right triangle. These are summarized by the mnemonic SOH CAH TOA:
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
__
The side DE is opposite the angle 19°, so the sine or tangent relation will be involved. The sine relation requires you know hypotenuse EF. The tangent relation requires you know adjacent side DF.
The only common side between triangles CDF and DEF is side DF. That side is opposite the given 61° angle. The given side length (CF = 24) is adjacent to the 61° angle.
This means you have enough information to use these relations:
tan(61°) = DF/CF = DF/24
DF = 24·tan(61°)
and
tan(19°) = DE/DF
DE = DF·tan(19°) = (24·tan(61°))·tan(19°) . . . . . use DF from above
DE ≈ 24(1.804048)(0.344328) ≈ 14.908
The length of DE is about 14.91.
50 points hellpppppppppppppppppppppppp
Answer:
30
Step-by-step explanation:
Answer:
There will be 25 Toothpicks in the 5th figure. I know this because as the the figures go up the number of toothpicks go up by one.
Step-by-step explanation:
Hope This Helps
Have A great Day
ll~Zero~ll
Answer always, sometimes, or never.
A) The diagonals of a parallelogram are perpendicular
B) The diagonals of a kite bisect each other
C) A polygon is a quadrilateral
D) Thé diagonals of a rectangle are equal
E) Thé opposite angles of a parallelogram are equal
F) A rhombus is a rectangle
Answer:
See belowStep-by-step explanation:
A) The diagonals of a parallelogram are perpendicular
Sometimes (rhombus)B) The diagonals of a kite bisect each other
Sometimes (one of the diagonals is bisected)C) A polygon is a quadrilateral
Sometimes (when it has 4 sides)D) Thé diagonals of a rectangle are equal
Always (definition of rectangle)E) Thé opposite angles of a parallelogram are equal
Always (definition of parallelogram)F) A rhombus is a rectangle
Never (when all interior angles are equal it becomes a square)#1
Rhombus has diagonals perpendicular to each other.
Sometimes#2
Kite is basically a Rhombus hence always.#3
Sometimes , Quadrilateral is counted among polygon with 4sides#4
Always#5
Always#6
All sides of Rhombus are equal where as rectangle has opposite sides equal
NeverSet up but do not evaluate an integral for the length of x^2/16.
Answer:
[tex]L=\int\limits^b_a {\sqrt{1+\frac{x^2}{64}}} \, dx[/tex]
Step-by-step explanation:
Recall the formula for the arc length of a function given a closed interval [tex][a,b][/tex]: [tex]L=\int\limits^b_a {\sqrt{1+(\frac{dy}{dx})^2}} \, dx[/tex]
Given the function [tex]y=\frac{x^2}{16}[/tex], then [tex]\frac{dy}{dx}=\frac{x}{8}[/tex] by the product rule.
Thus, the set-up integral would be:
[tex]L=\int\limits^b_a {\sqrt{1+(\frac{x}{8})^2} } \, dx\\ \\L=\int\limits^b_a {\sqrt{1+\frac{x^2}{64}}} \, dx[/tex]
Which functions have a maximum and are transformed to the left and down of the parent function, f(x) = x2? Check all that apply. P(x) = 14(x 7)2 1 q(x) = –5(x 10)2 – 1 s(x) = –(x – 1)2 0. 5 g(x) = 2x2 10x – 35 t(x) = –2x2 – 4x – 3.
Transformation of a function is shifting the function from its original place in the graph.
The functions have a maximum and are transformed to the left and down of the parent function are,
[tex]q(x) = -5(x +10)^2 -1[/tex]
[tex]t(x) = -2x^2 - 4x - 3[/tex]
Thus the option B and E is correct.
What is transformation of a function?
Transformation of a function is shifting the function from its original place in the graph.
Types of transformation-
Horizontal shift- Let the parent function is [tex]f(x)[/tex]. Thus by replacing parent function with [tex]f(x-b)[/tex] shifts the graph b units right and by replacing parent function with [tex]f(x+b)[/tex] shifts the graph b units left.Vertical shift- Let the parent function is [tex]f(x)[/tex]. Thus by replacing parent function with [tex]f(x)-c[/tex] shifts the graph b units down and by replacing parent function with [tex]f(x)+c[/tex] shifts the graph b units up.
Given information-
The given function in the problem is,
[tex]f(x)=x^2[/tex]
The functions have a maximum and are transformed to the left and down of the parent function.
In the option B the function is shifted 10 units left and 1 units down as,
[tex]q(x) = -5(x +10)^2 -1[/tex]
Thus the option B is the correct option.
In the option E the function is shifted 1 units left and 2 units down as,
[tex]t(x) = -2x^2 - 4x - 3\\t(x)=-2x^2 - 4x - 1-2\\t(x)=-2(x+1)^2-2[/tex]
Thus the option E is the correct option.
Hence, the functions have a maximum and are transformed to the left and down of the parent function are,
[tex]q(x) = -5(x +10)^2 -1[/tex]
[tex]t(x) = -2x^2 - 4x - 3[/tex]
Thus the option B and E is correct.
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Plz help!!! :( Lisa and Susan are driving to college together. They look at a map to find
out how far they have to drive On the map, Lisa measures the distance
to be 4.5 inches. How many miles do they have to drive if the map scale
is 1 in. = 35 min
Which model represents the factors of 4x2 – 9? An algebra tile configuration. 5 tiles are in the Factor 1 spot: 2 x , 3 negative. 5 tiles are in the Factor 2 spot: 2 x, 3 negative. 25 tiles are in the Product spot in 5 columns with 5 rows. First row: 2 x squared, 3 negative x. Second row: 2 x squared, 3 negative x. The last 3 rows are the same: 2 negative x, 3 negative. An algebra tile configuration. 5 tiles are in the Factor 1 spot: 2 x , 3. 5 tiles are in the Factor 2 spot: 2 x, 3. 25 tiles are in the Product spot in 5 columns with 5 rows. First row: 2 x squared, 3 x. Second row: 2 x squared, 3 negative x. The last 3 rows are the same: 1 x, 1 negative x, 3 negative. An algebra tile configuration. 5 tiles are in the Factor 1 spot: 2 x , 3. 5 tiles are in the Factor 2 spot: 2 x, 3 negative. 25 tiles are in the Product spot in 5 columns with 5 rows. First row: 2 x squared, 3 x. Second row: 2 x squared, 3 x. The last 3 rows are the same: 2 negative x, 3 negative. An algebra tile configuration. 5 tiles are in the Factor 1 spot: 2 x , 3. 5 tiles are in the Factor 2 spot: 2 x, 3. 25 tiles are in the Product spot in 5 columns with 5 rows. First row: 2 x squared, 3 x. Second row: 2 x squared, 3 negative x. The last 3 rows are the same: 1 x, 2 negative x, 3.
The correct factor is (2x - 3) and (2x + 3).
Quadratic equationIt is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
Given
4x² -9 = 0 is a quadratic equation.
To findThe factor of the given equation.
How to find the factor of the given equation?4x² -9 = 0 is a quadratic equation.
According to factorization,
4x² - 9 = 0
(2x)² - 3² = 0
( 2x - 3 ) ( 2x + 3 ) = 0
Thus the correct factor is (2x - 3) and (2x + 3).
More about the quadratic equation link is given below.
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Answer:
The answer is C or the third option.
Step-by-step explanation:
Looking at the tiles for the third option, there are the same amount of negative and positive x-tiles. This means that they cancel each other out. What's left are the 4 x^2 tiles and 9 negative tiles. When put together the equation is 4x^2 - 9. This option represents the factors of 4x^2 - 9 accurately.
Esi does an experiment where she picks a block out of a bag without looking 50 times, putting it back each time. She picks a green block 32 times. If the bag has 8 blocks, how many do you think are green
i does an experiment where she picks a block out of a bag without looking 50 times, putting it back each time. She picks a green block 32 times. If the bag has 8 blocks, how many do you think are green
A phone originally priced at $40 is discounted and now sells for $30. What is the percent of discount?
Answer:
25% discount
Step-by-step explanation:
40-30=10
10= 25% of 40
Which model shows the correct factorization of x2 – x – 2? An algebra tile configuration. 3 tiles are in the Factor 1 spot: 1 is labeled x and 2 are labeled. 2 tiles are in the Factor 2 spot: 1 is labeled x and 1 is labeled negative. 6 tiles are in the Product spot: 1 is labeled x squared, 2 are labeled x, 1 is labeled negative x, and 2 are labeled negative. An algebra tile configuration. 3 tiles are in the Factor 1 spot: 1 is labeled x and 2 are labeled negative. 2 tiles are in the Factor 2 spot: 1 is labeled x and 1 is labeled. 6 tiles are in the Product spot: 1 is labeled x squared, 2 are labeled negative x, 1 is labeled x, and 2 are labeled negative. An algebra tile configuration. 3 tiles are in the Factor 1 spot: 1 is labeled x, 1 is labeled , and 1 is labeled negative. 2 tiles are in the Factor 2 spot: 1 is labeled x and 1 is labeled negative. 6 tiles are in the Product spot: 1 is labeled x squared, 1 is labeled x, 2 are labeled negative x, and 2 are labeled negative. An algebra tile configuration. 3 tiles are in the Factor 1 spot: 1 is labeled x and 2 are labeled. 2 tiles are in the Factor 2 spot: 1 is labeled x and 1 is labeled. 6 tiles are in the Product spot: 1 is labeled x squared, 2 are labeled x, 1 is labeled negative x, and 2 are labeled.
The correct factor is (x - 2) and (x + 1).
Quadratic equationIt is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
Given
x² - x - 2 = 0 is a quadratic equation.
To findThe factor of the given equation.
How to find the factor of the given equation?x² - x - 2 = 0 is a quadratic equation.
According to factorization,
x² - x - 2 = 0
x² - 2x + x - 2 = 0
x(x - 2) +1 (x - 2) = 0
( x - 2 ) ( x + 1 ) = 0
Thus the correct factor is (x - 2) and (x + 1).
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Ricky owns a store that sells computers. his profit, in dollars, is represented by the function p(x)=x^3-22x^2-240x where x is the number of computers sold. Ricky hopes to make a profit of at least $10,000 by the time he sells 36 computers. Explain whether or not Ricky will meet his goal. Justify your reasoning.
Ricky's goal is not achievable. This is because selling 36 computers would not yield a profit of at least $10,000.
What is profit?A profit is earned when total revenue is greater than total cost.
Profit = total revenue - total cost.
Is Ricky's goal achievable?Given this function: p(x)=x^3-22x^2-240x substitute for x in the equation
(36)^3 - 22(36^2) - (240 x 36)
46,656 - 28,512 - 8640
=$9504
If he sells 36 computers, he would have a profit of $9504 and would not achieve his goal.
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Solve f(x) = g(x) algebraically. f ( x ) = x 2 − x − 30 g ( x ) = − 2 x + 26
Answer:
x= 7 and -8
Step-by-step explanation:
hope this helps!
Solve for x
please I need the answer the picture shows the question
Answer:
The rounded answer is 11
Step-by-step explanation:
a-squared + b-squared = c-squared
8-squared + 7-squared = c-squared
64 + 49 = c-squared
area-113 (the check mark symbol thing)
Answer:
(d) 10.63
Step-by-step explanation:
You want the length of the hypotenuse of a right triangle with legs 7 in and 8 in.
Pythagorean theoremThe Pythagorean theorem tell you the relationship between legs a, b, and hypotenuse c of a right triangle is ...
c² = a² +b²
ApplicationIn this figure, this means ...
x² = 7² +8² = 49 +64 = 113
x = √113 ≈ 10.63
The length of x is about 10.63.
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Solve the system by substitution.
-2x=y
4x+10y=16
Answer:
x=-1, y=2
Step-by-step explanation:
Plug the y=-2x into the second equation in place of the y to get 4x+10(-2x)=16
Simplify this to 4x-20x=16 then to -16x=16
Divide both side by -16 to get x=-1
Plug x=-1 into the first equation to get -2(-1)=y
Simplify to get y=2
One number is four more than five times another. If their sum is increased by one, the result is thirty-five. Find
the numbers.
Answer:
x=4+5yif sum is increased by 3 (x+y+3), result is 31x+y+3=31minus 3 both sidesx+y=28x=4+5y subsiutute4+5y+y=284+6y=28minus 4 both sides6y=24divide by 6y=4sub backx=4+5yx=4+5(4)x=4+20x=24the numbers are 24 and 4
Step-by-step explanation:
If I helped you
dolphinsproduction on insta
Answer:
29 and 5
Step-by-step explanation:
Given system of equations
[tex]\left \{ {{x=4+5y} \atop {x+y+1=35}} \right.[/tex]
Substitute top equation into bottom equation to determine y
[tex]x+y+1=35\\\\(4+5y)+y+1=35\\\\4+5y+y+1=35\\\\5+6y=35\\\\6y=30\\\\y=5[/tex]
Substitute y=5 into top equation to determine the x-value
[tex]x=4+5y\\\\x=4+5(5)\\\\x=4+25\\\\x=29[/tex]
Therefore, the two numbers are 29 and 5
