Answer:
T tof = 2 ( v 0 sin θ 0 ) g . T tof = 2 ( v 0 sin θ 0 ) g . This is the time of flight for a projectile both launched and impacting on a flat horizontal surface.
Find the measure of the indicated angle to the nearest degree.
Answer:
24.315°
Step-by-step explanation:
First use the pythagorean theorem to get the missing side since this is a right triangle.
a^2 + b^2 = c^2 →
b^2 = c^2 – a^2 →
b = (c^2 – a^2)^½
b = (17^2 – 7^2)^½
b = (289 – 49)^½
b = √240.
Then use the law of cosines to find the angle in between.
b^2 = a^2 + c^2 - 2ac * cos(B) →
b^2 - a^2 - c^2 = -2ac * cos(B) →
a^2 + c^2 – b^2 / 2ac = cos(B) →
cos^-1(a^2 + c ^2 – b^2 / 2ac) = C →
B = cos^-1(a^2 + c ^2 – b^2 / 2ac)
B = cos^-1(49 + 289 – √240 / 238)
B ≈ 75.685°.
A = 180 – B
A = 180 – 75.685
A = 24.315°
A plank of wood is 4.6 meters long.
These two lengths of wood are cut from the plank - 88cm and 1630mm
What is the length of the wood left
Step-by-step explanation:
1 meter = 100 centimeter = 1000 millimeter
therefore, 1 cm = 10 mm
4.6 m = 4.6 × 1000 = 4600 mm
88 cm = 880 mm
and so, they cut off
880 mm + 1630 mm = 2510 mm
that means
4600 - 2510 = 2090 mm = 2.09 m
are left.
A study of college freshmen found that students who watched tv for more than one hour each night gained 15 pounds in the first semester, compared to those who watched less than one hour. they concluded that there is an association between watching tv and weight gain in college freshmen. which study design did they most likely use?
Answer:
C. They most likely used an observational study asking students to keep track of their TV habits and weight.
A. This is an experiment because a treatment was applied to a group.
Step-by-step explanation:
According to our question:
1. The study concluded that there is a relation between watching TV and the weight gain in college freshmen.
Now, this is possible when a group of college students were asked to participate to watch TV for more than 1 hour for a specific amount of time and have a record of their weights.
So, the study is an observational study where the habits and weights of college students were observed.
Hence, option C is correct.
2. The students were divided onto two groups where one group used the computer program and the other did not to check the improvement in the reading levels.
This means that the students were given a procedure to follow during the study in order to see the results..
So, the study is an experiment where a treatment is applied to the group of students.
Hence, option A is correct.
Answer: C
For the people who want only one answer and not 2 for the question if you can only submit one answer :)
help i dont feel like doing the math
Answer:
A
Step-by-step explanation:
First, we should put this equation in slope-intercept form by isolating y.
Thus, we have:
[tex]2x-\frac{4}{3}y=4\\ -\frac{4}{3}y=4-2x\\ y=\frac{3}{2}x-3[/tex]
The slope-intercept equation shows that the y-intercept is -3 and the slope is 3/2.
Only answer A meets these requirements.
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=3y2−3x2; 2x y=9
There is a minimum value of -81 located at (x, y) = (6, -3).
The function given to us is f(x, y) = 3y² - 3x².
The constraint given to us is 2x + y = 9.
Rearranging the constraint, we get:
2x + y = 9,
or, y = 9 - 2x.
Substituting this in the function, we get:
f(x, y) = 3y² - 3x²,
or, f(x) = 3(9 - 2x)² - 3x² = 3(81 - 36x + 4x²) - 3x² = 243 - 108x + 12x² - 3x² = 243 - 108x + 9x².
To find the extremum, we differentiate this, with respect to x, and equate that to 0.
f'(x) = - 108 + 18x ... (i)
Equating to 0, we get:
- 108 + 18x = 0,
or, 18x = 108,
or, x = 6.
Differentiating (i), with respect to x again, we get:
f''(x) = 18, which is greater than 0, showing f(x) is minimum at x = 6.
The value of y, when x = 6 is,
y = 9 - 2x,
or, y = 9 - 2*6 = 9 - 12 = -3.
The value of f(x, y) when (x, y) = (6, -3) is,
f(x, y) = 3y² - 3x²,
or, f(x, y) = 3*(-3)² - 3*6² = 3*9 - 3*36 = 27 - 108 = -81.
Thus, there is a minimum value of -81 located at (x, y) = (6, -3).
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Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.
The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.
What is the value of x?
9
10
14
16
The rhombus ABCD has an area of 72 square units. Diagonals AC and BD intersect at E. Given EC = 8 units and DB = x - 1, the value of x is 10 units. The correct option is B).
We are given a rhombus ABCD with area 72 square units. The diagonals AC and BD intersect at point E.
Since all sides of the rhombus are congruent, we can assume that the length of each side is "s" units.
We are also given that EC (a part of diagonal AC) is 8 units long.
As diagonals of a rhombus bisect each other, we can deduce that the other half of diagonal AC is also 8 units. So, the full diagonal AC is 16 units (8 units + 8 units).
Now, we are told that DB (a part of diagonal BD) is x - 1 units long.
To find the value of x, we need to find the length of the other half of diagonal BD, which is also x - 1 units. So, the full diagonal BD is
(x - 1) units + (x - 1) units = 2x - 2 units.
The area of a rhombus is given by the formula:
Area = 1/2 × Product of Diagonals.
Substituting the given values, we have:
72 = 1/2 × 16 × (2x - 2).
Now, we can simplify the equation:
72 = 8x - 8.
Move the constant term to the right side:
8x = 72 + 8.
Combine the constants:
8x = 80.
Finally, solve for x by dividing both sides by 8:
x = 80 / 8 = 10.
So, the value of x is 10 units. The correct answer is B).
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--The given question is incomplete, the complete question is given below " Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.
The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.
What is the value of x?
9
10
14
16 "--
The graph shows a system consisting of a linear equation and a quadratic equation.
What is the solution to the system?
need it kinda asap
The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown.
Quadratic and linear equationQuadratic equation are equation that has a leading degree of 2 while a linear equation has a leading degree of 1.
From the given graph, the curve shown has a two solutions which is the point where the curve intersect the x-axis.
For the graph shows a system consisting of a linear equation and a quadratic equation, the solution will be the points where the line intersects the parabola.
The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown
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Geometry: complete this proof, ASAP!!!!!!!!!!!!!!!! It’s urgent
Answer:
1.ABC is equilateral triangle because all sides are equal
3.because they are the joined figure of a triangle
If a sample of n = 4 scores is obtained from a normal population with µ = 70 and σ = 12. What is the z-score corresponding to a sample mean of m = 69?
The z-score corresponding to a sample mean of m = 69 is -0.167
In this problem, we have been given :
population mean (μ) = 70, standard deviation (σ) = 12, sample size (n) = 4, sample mean (m) = 69
We know that, the Z-score measures how many standard deviations the measure is from the mean.
Also, the formula when calculating the z-score of a sample with known population standard deviation is:
[tex]Z=\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
where z = standard score
μ = population mean
σ = population standard deviation
m = the sample mean
and [tex]\frac{\sigma}{\sqrt{n} }[/tex] is the Standard Error of the Mean for a Population
First we find the Standard Error of the Mean for a Population
σ /√n
= 12 / √4
= 12 / 2
= 6
So, the z-score would be,
⇒ [tex]Z=\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
⇒ [tex]Z=\frac{69-70}{6 }[/tex]
⇒ Z = -1/6
⇒ Z = -0.167
Therefore, the z-score corresponding to a sample mean of m = 69 is -0.167
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product of squre of x and cube of y
Answer:
x²y³
Step-by-step explanation:
(x²) (y³) = x²y³
Hope it helps!
Have a nice day:)
❄ Hi there,
let us find the product of the square of x and the cube of y.
[tex]\sf{The \ square \ of \ x: \ x^2}\\\sf{The \ cube \ of \ y: y^3}\\\sf{The \ product \ of \ the \ two: x^2y^3}[/tex]
The square of x means: x times x, or, as I said earlier, x².
The cube of y means: y times y times y, or, as I said earlier, [tex]\sf{y^3}[/tex].
The product means: you multiply x² times y³.
❄
To pass a particular score a student has to achieve a mean of at least 50% in the ten pieces of work that form the assessment items. In the first nine of these pieces of work the student achieved a mean of 46%. What percentage mark must the student achieve in the tenth item if he is to pass the course?
Step-by-step explanation:
the mean value is the sum of all data points divided by the number of data points.
so, in our case we have after 9 pieces of work
(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) / 9 = 46
that means
(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) = 46×9 =
= 414
now we need to add a p10, so that
(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9 + p10) =
= 50 × 10 = 500
only then do we get
(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9 + p10)/10 =
= 50
so,
(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) + p10 = 500
414 + p10 = 500
p10 = 500 - 414 = 86%
the student must at least achieve 86% for the 10th piece of work.
Anyone know the anwser to this
Answer:
4112
Step-by-step explanation:
When you plug in 3 for x you get 6.
Then you just do 4^6 which is 4096.
Then add 16 which gets you 4112.
The store has a 30% discount on every item in stock. how much is the 5% sales tax reduced on an item that regularly sells for $10?
i need help on this question
For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.
How much money should we pay in sales tax?
In this question we must determine the amount of money needed to pay in taxes by the purchase of an item with a discount. Sales taxes are an example of indirect taxes, this kind of indirect tax is usually calculated on the basis of total costs, including discounts. The amount of money need for the sales tax is described below:
t = (r / 100) · (1 - d / 100) · c (1)
Where:
d - Discount rater - Sales tax ratec - Item pricet - Sales tax totalIf we know that d = 30, r = 5 and c = 10, then the sales tax total is:
t = (5/ 100) · (1 - 30 / 100) · 10
t = 0.35
For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.
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Find the value of x
(4x+10)
108° 67° 3x
Angles in quadrilateral add to 360
108 +67 +10 =185
4x + 3x = 7x
185 + 7x = 360
- 185
7x. = 175
÷ 7
x = 25
Check:
4x25 = 100
100 + 67 + 108 = 275
275 + (3x25) = 350 + extra 10 is 360
Hope this helps!
A triangle is shown.
What is the unknown side length, to the nearest tenth, in the triangle?
Using the Pythagorean Theorem, it is found that the unknown side length of the triangle is of 7.9 cm.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Researching this problem on the internet, we have that:
The unknown side length is of a leg of x.The other leg is of 9 cm.The hypotenuse is of 12 cm.Hence:
x² + 9² = 12²
x = sqrt(12² - 9²)
x = 7.9 cm.
The unknown side length of the triangle is of 7.9 cm.
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Mrs. gomes found that 40% of students at her high school take chemistry. she randomly surveys 12 students. what is the probability that exactly 4 students have taken chemistry? round the answer to the nearest thousandth. p (k successes) = subscript n baseline c subscript k baseline p superscript k baseline (1 minus p) superscript n minus k. subscript n baseline c subscript k baseline = startfraction n factorial over (n minus k) factorial times k factorial endfraction
Answer:
0.213
Step-by-step explanation:
→ Convert into binomial information
x ~ B ( 12 , 0.4 )
→ Write down probability required
p ( x = 4 )
→ Evaluate
0.2128
I need help with this
Answer:
? = 4 units
Step-by-step explanation:
'2' is to ' 7+2 ' as ? is to '14 + ? '
2/ 9 = ? / (14 + ?) cross mutiply
28 + 2? = 9?
28 = 7?
? = 4
A and b are monomials where a = 125 and b = 27p12. what is the factored form of a – b?
The factored form of a - b is [tex]\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)[/tex].
What is monomial factorization ?A monomial is an expression that is the product of constant and non-negative integer powers of x, like [tex]3x^{2}[/tex]..
A monomial is expressed as a product of two or more other monomials when it is factored.
Here,
a = 125
[tex]$b=27 p^{12}$[/tex]
To find: a - b
a - b = 125 - [tex]27 p^{12}$[/tex]
a - b = [tex]5^{3}-\left(3 p^{4}\right)^{3}$[/tex]
We know that,
[tex]$x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$[/tex]
Finding the factored form of a - b using this method:
[tex]$a - b=\left(5-3 p^{4}\right)\left(5^{2}+5\left(3 p^{4}\right)+\left(3 p^{4}\right)^{2}\right)$[/tex]
[tex]$a-b=\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex]
So, factored form of a - b is [tex]$\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex].
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In a set of 10 observations the mean is 20 and the median is 15. There are 2 values that are 6, and all other values are different. What is the mode?
The mode of the set of 10 observations is 2.
What is the mode?
Mode refers to a value that appears most frequently in a data set. Mode is a measure of central tendency of a data set. Other measures of central tendency are mean and median.
According to the information in the question, 6 appears twice in the data set and all other values are different. Thus, 6 has the frequency of 2 which is the highest. 6 is the mode.
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Ashley spent 3x + 2hours on her science project and Adam spent 4x - 6 hours on his science project. If they spent a total of 31 hours on their projects, find the value of x
Answer:
x = 5
Step-by-step explanation:
Ashley and Adam spent a total of 31 hours on their projects so: 3x+2+4x-6 = 31
3x+2+4x-6 = 31
7x-4 = 31
7x = 35
x = 5
1. How much does the glass for region 1 cost?
2. How much does the glass for region 2 cost?
3. What is the total cost for the glass for the sectors in circle B?
4. What is the total cost of the glass for your window?
5. You only have $100 to spend on glass supplies. Do you have enough money to buy your glass?
Answer:
1) 0.10
2) 0.15
3) 0.100
4) No
A locker combination consists of two non-zero digits. the digits in a combination are not repeated and range from 2 through 9. event a = the first digit is less than 5 event b = the second digit is less than 5 if a combination is picked at random, with each possible locker combination being equally likely, what is p(b|a) expressed in simplest form?
Answer:
1/3.
Step-by-step explanation:
P(event a occurs) = 3/9 = 1/3
P(event b occurs) = 3/9 = 1/3
P(a) ∩ P(b) = 1/3 * 1/3 = 1/9
P(b|a) = P(a) ∩ P(b) / P(a)
= 1/9 / 1/3
= 1/3.
perimeter of a quadrilateral is 590m its sides are in ratio 5 ratio 12 ratio 17 ratio 25 find the area of the quadrilateral
Answer:
255,000,000m^2
Step-by-step explanation:
Let 5:12:17:25 be 5x, 12x, 17 x, 25x respectively
So
Perimeter of quadrilateral=5x+12x+17x+25x
590m=59x
590m/59=x
10m=x
So now value
5x= 5*10 =50
12x= 12*10 =120
17x= 17*10 =170
25x= 25*10 =250
Now
Area of quadrilateral=50m*120m* 170m* 250m
=255,000,000m^2
Step-by-step explanation:
if I understand you correctly the sides are in a
5 : 12 : 17 : 25 ratio.
a ratio is basically a fraction. but instead of the denominator telling us the structure of the whole (e.g. 2/5 tells us that the whole is split into 5 equal parts), a ratio tells us this by the sum of its elements :
5 : 12 : 17 : 25
means that the whole perimeter of the quadrilateral has
5 + 12 + 17 + 25 = 59 equal parts.
since the perimeter is 590 m, we know with 59 equal parts, that one part is 590/59 = 10 m.
so, the sides are
50 m, 120 m, 170 m, 250 m
but for the area of the quadrilateral there is at least the information of one angle missing.
to have just the 4 side lengths is not enough. these sides can still have all kinds of angles between them, which creates different areas.
PLS HELLP ITS SO HARD
Answer:
[3,0]
[0,9]
Step-by-step explanation:
9x+3y=27
9x+3(0)=27
9x=27
x=3
9(0)+3y=27
3y=27
y=9
Use the diagram to answer each question.
m/A+m/B=
These are called
1
2 m2D+mz
These are called
= 180°
Use the diagram to answer each question.
3. If m/H=43⁰.
m/E=
m/G=
m/F=
4. If m/G= 132°.
m/H=
m/E=
m/F=
factor this:
18x^2+39x-15
Steps for Factoring:
1) Find CM (common factor) for the expression: 3
Factor out 3 =>
[tex]3(6x^{2}+13x-5)[/tex]
2)Factor the above expression by grouping:
The expression needs to be written as [tex]6x^{2} + ax+ bx -5[/tex]
a and b should add up to 13 and multiply up to -30 (6 × -5)
By Guess & Check we find that the pair is a = -2 and b = 15 (-2+15; -2 × 15)
3) Now we can rewrite [tex](6x^{2}+13x-5)[/tex] as [tex](6x^{2} -2x)+(15x-5)\\[/tex]
Factor out 2x in the first group and 5 in the second group:
[tex]2x(3x-1)+5(3x-1)\\[/tex]
As 3x-1 is on both sides, now we can do the operation: 2x+5 (distributive property)
(3x-1) (2x+5)
The answer is 3(3x-1) (2x+5)
Hope it helps!
PLEASE HELP ASAP……..
Answer:
4x+2y = 14 The original equation
2y = 14-4x Subtract 4x from both sides
2y = -4x+14 Rearrange so x is first
y = -2x+7 Divide everything by 2
Explanation:
The steps above practically explain everything needed, so there's not much to add. The standard form is Ax+By = C while slope intercept form is y = mx+b
In the case of y = -2x+7, we have a slope of m = -2 and y intercept of b = 7. This means (0,7) is one point on the line. Use the slope to move down two and to the right one unit to arrive at (1, 5) as another point on this line.
please help with this i genuinely have no clue how to figure it out
Answer: c = 520
Step-by-step explanation:
f(2) = 578 means that when x = 2, the value is equal to 578. We will plug these knowns in and then solve for c.
Given:
f(x) = 4x³ + 7x² - x + c
Substitute:
578 = 4(2)³ + 7(2)² - (2) + c
Distribute:
578 = 4 * 2³ + 7 * 2² - 2 + c
Raise to the power of 3 and 2:
578 = 4 * 8 + 7 * 4 - 2 + c
Multiply:
578 = 32 + 28 - 2 + c
Add:
578 = 60 - 2 + c
Subtract:
578 = 58 + c
Subtract 58 from both sides:
520 = c
Reflexive property:
c = 520
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:
[tex]\longrightarrow\bold{f(x) = 4x^3 + 7x2 −x + c}[/tex]
[tex]\longrightarrow\sf{578= 32+28 −2+ c}[/tex]
[tex]\longrightarrow\sf{578 =58+ c}[/tex]
[tex]\longrightarrow\sf{c = 578-58}[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\longrightarrow\sf{c= 520}[/tex]
A student is constructing a pair of perpendicular lines using a compass and ruler. Here are her first steps:
Step 1: The student draws her first line and labels it l. She marks a point A (not on the first line) for the second line to pass through.
Step 2: She puts the compass point on A and draws an arc that intersects l at two points. She labels the points B and C.
Step 3: Without changing the compass setting, she puts the compass point on B and draws a large arc.
What should be her next step?
The next step she should take is to use her ruler to join the given point to the point where the arcs intersect.
Steps in constructing perpendicular linesPlace your compass on the given point Draw an arc across the line on each side of the given point. Do not adjust the compass width when drawing the second arcFrom each arc on the line, draw another arc on the opposite side of the line from the given point. The two new arcs will intersect.Use your ruler to join the given point to the point where the arcs intersect.Use your compass and ruler to draw a perpendicular line from each given point to the line segmentFrom this, we can deduce that her next step is to use her ruler to join the given point to the point where the arcs intersect
Thus, the next step she should take is to use her ruler to join the given point to the point where the arcs intersect.
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What is the value of 2√4+3√9
[tex]2 \sqrt{4} + 3 \sqrt{9} \\ 2(2) + 3(3) \\ 4 + 9 = 13[/tex]
Answer:
13
Step-by-step explanation:
2×√4+3×√(9
2x2+3x3
