Answer:
1/6
Step-by-step explanation:
1/2*1/3
1*1/2*3
1/6
Answer:
1/6
Step-by-step explanation:
1/3*1/2 = 1/6
1/3 = 0.33333333 = 3/9 =1/3
1/6 = 0.1666666 = 15/90=1/6
A ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. Use the quadratic function
h(t) = -16t2 + 109t to find how long it will take for the ball to reach its maximum height, and then find the maximum
height. Round your answers to the nearest tenth.
Answer:
Time taken by the ball to reach its maximum height is 3.4 sec
maximum height reached by the ball is 185.6ft
Step-by-step explanation:
h(t) = -16[tex]t^{2}[/tex] + 109t
height is maximum ⇔ [tex]\frac{d}{dt}[/tex](h) = 0 and [tex]\frac{d^{2} }{dt^{2} }[/tex](h) < 0
[tex]\frac{d}{dt}[/tex](h) = 0 ⇒ -32t + 109 = 0
⇒t = [tex]\frac{109}{32}[/tex] ⇒ t = 3.4sec
[tex]\frac{d^{2} }{dt^{2} }[/tex](h) = -32 < 0
∴h(t) is maximum at t = 3.4
and maximum height is h(3.4) = -16×[tex]3.4^{2}[/tex] + 109×3.4 ⇒ h = 185.6ft
Answer:
The maximum height with rounding by the nearest tenth is [tex]280.56\ m[/tex]
Explanation:
Initial velocity of ball [tex]=109\ ft/sec[/tex]
Quadratic function [tex]$h(t)=-16t x^{2} +109t$[/tex]
Maximum height[tex]=?[/tex]
Step 1:
This ball has its height related to time by a parabola with the equation:
[tex]$s=\frac{1}{2} \times a \times t^{2}+v_{0} \times t+s_{0}$[/tex]
where [tex]$s$[/tex] is the height so is the starting height, [tex]v_{0}[/tex] is its starting velocity [tex]$=109 \ {ft} / \mathrm{s}$[/tex]
[tex]$a$[/tex] is the acceleration of gravity, which is [tex]$-16 \ {ft} / \mathrm{s}$[/tex] every second.
Step 2:
Time required to reach its maximum height:
[tex]$v=a^{*} t+v_{0}[/tex] (its velocity is the acceleration of gravity × time [tex]+ v_0[/tex]) [tex]$v$[/tex] will slow down from [tex]$109 \ {ft} / \ s[/tex] to [tex]$0 \mathrm{ft} / \mathrm{s}$[/tex]
And it slowing down at [tex]$16 \mathrm{ft} / \mathrm{s}$[/tex] :
[tex]t(s)=0,1,2,3,4,5,6[/tex]
[tex]V (m/s)=109,93,77,61,45,29,13[/tex]
Before [tex]$7 \mathrm{~s}$[/tex], it will hit the ground.
Exact calculation [tex]$t=\frac{109 f t / s}{16 f t / s}=6.81 s$[/tex]
Thus we can say at the height of,
[tex]$\mathrm{t}_{\max }=\frac{6.81}{2} \\=3.4\ sec[/tex]
Step 3:
Plug the [tex]t_m_a_x[/tex] sec value back into equation:
[tex]$h(t)=t \cdot(-16 t+109)$[/tex]
[tex]$h_{\max }=3.4 \cdot(-16.4 .1875+109)$[/tex]
[tex]$h_{\max }= 185.6\ m[/tex]
Hence, the maximum height is [tex]185\ m[/tex]
To learn more about vertically upward ball, refer:
https://brainly.com/question/17925478https://brainly.com/question/14614888A florist is filling a large order for a client. The client wants no more than 300 roses in vases. The smaller vase will contain 8 roses and the larger vase will contain 12 roses. The client requires that there are at least twice as many small vases as large vases. The client requires that there are at least 6 small vases and no more than 12 large vases.
Let x represent the number of small vases and y represent the number of large vases.
What constraints are placed on the variables in this situation?
Answer:
[tex]8x+12y\leq 300[/tex]
[tex]x\geq 6[/tex]
[tex]y\leq 12[/tex]
[tex]x\geq 2y[/tex]
Step-by-step explanation:
We are given that
x=Number of small vases
y=Number of large vases
Total number of roses not more than 300 in vases.
Number of roses in small vase atleast=8
Number of roses in large vase not more than =12
We have to find the constraints are placed on the variables in the given situation.
According to question
[tex]8x+12y\leq 300[/tex]
[tex]x\geq 6[/tex]
[tex]y\leq 12[/tex]
[tex]x\geq 2y[/tex]
-30=4-8x solve for x
Answer: x=4.25
Step-by-step explanation:
-30=4-8x
subtract 4 from both sides
-8x=-34
divide by -8 on both sides
x=4.25
Jacob knows that 1/20 means “1 divided by 20.” He uses this to find the decimal equivalent for 1/20. Enter a digit into each box to complete his work.
Answer:
0.05
Step-by-step explanation:
1/20=5/100=0.05
Answer:
0.05
Step-by-step explanation:
To find the decimal equivalent of the fraction 1/20, this is shown as shown in the attachment.
1/20 = 0.05
The decimal equivalent of 1/20 is 0.05
2.The diagonals of a rhombus are in the ratio 5:12. If its perimeter is 104 CM, findthe lengths of the sides and the diagonals.
Answer:
Lenghts of the sides: [tex]26\ cm[/tex]
Lenghts of the diagonals: [tex]48\ cm[/tex] and [tex]20\ cm[/tex]
Step-by-step explanation:
Look at the rhombus ABCD shown attached, where AC and BD de diagonals of the rhombus.
The sides of a rhombus have equal lenght. Then, since the perimeter of this one is 104 centimeters, you can find the lenght of each side as following:
[tex]AB=BC=CD=DA=\frac{104\ cm}{4}= 26\ cm[/tex]
You know that the diagonals are in the ratio [tex]5:12[/tex]
Then, let the diagonal AC be:
[tex]AC=12x[/tex]
This means that AE is:
[tex]AE=\frac{12x}{2}=6x[/tex]
And let the diagonal BD be:
[tex]BD=5x[/tex]
So BE is:
[tex]BE=\frac{5x}{2}=2.5x[/tex]
Since the diagonals of a rhombus are perpendicular to each other, four right triangles are formed, so you can use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs.
In this case, you can choose the triangle ABE. Then:
[tex]a=AB=26\\b=AE=6x\\c=BE=2.5x[/tex]
Substituting values and solving for "x", you get:
[tex]26^2=(6x)^2+(2.5x)^2\\\\676=36x^2+6.25x^2\\\\\sqrt{\frac{676}{42.25}}=x\\\\x=4[/tex]
Therefore, the lenghts of the diagonals are:
[tex]AC=12(4)\ cm=48\ cm[/tex]
[tex]BD=5(4)\ cm=20\ cm[/tex]
Solve for
in the equation 2 – 8X+41 = 0.
X=-4 /37
X=-425
X= 4+
37
x = 4 +51
Answer:
x=43/8
Step-by-step explanation:
2-8x+41=0
-8x+43=0
-8x=0-43
-8x=-43
8x=43
x=43/8
A muffin recipe, which yields 12 muffins, calls for 2/3 cup of milk for every 1 3/4 cups of flour. The same recipe calls for 1/4 cup of coconut for every 3/4 cup of chopped apple. To yield a batch of 30 muffins, how much flour will be needed in the mix?
Answer:
[tex]4\dfrac{3}{8}[/tex] cups of flour
Step-by-step explanation:
A muffin recipe, which yields 12 muffins, calls for 2/3 cup of milk for every 1 3/4 cups of flour.
Then this recipe, which yields one muffin, calls for
[tex]\dfrac{2}{3}:12=\dfrac{2}{3}\cdot \dfrac{1}{12}=\dfrac{1}{18}[/tex]
cup of milk for every
[tex]1\dfrac{3}{4}:12=\dfrac{7}{4}\cdot \dfrac{1}{12}=\dfrac{7}{48}[/tex]
cups of flour.
Thus,
this recipe, which yields a batch of 30 muffins, calls for
[tex]\dfrac{1}{18}\cdot 30=\dfrac{5}{3}=1\dfrac{2}{3}[/tex]
cups of milk for every
[tex]\dfrac{7}{48}\cdot 30=\dfrac{210}{48}=\dfrac{35}{8}=4\dfrac{3}{8}[/tex]
cups of flour.
Final answer:
To calculate the amount of flour needed to yield 30 muffins, we first find the amount of flour required for a single muffin and then scale it up to 30 by multiplying. For 30 muffins, approximately 1.094 cups of flour are required based on the original recipe ratios.
Explanation:
The question involves the use of ratios to calculate the amount of a particular ingredient required for a different quantity of the final product. Since the original recipe yields 12 muffins with 1 3/4 cups of flour, we first need to determine how much flour is needed for one muffin by dividing 1 3/4 cups by 12. After finding the flour quantity per muffin, we then multiply that by 30 to find out how much flour is needed for 30 muffins.
Step 1: Calculate the amount of flour for one muffin.
Amount of flour per muffin: 1 3/4 cups / 12 =
7/4 cups / 12 = 7/48 cups per muffin.
Step 2: Calculate the amount of flour needed for 30 muffins.
Amount of flour for 30 muffins: 7/48 cups per muffin x 30 = 7/48 x 30 =
52.5/48 or approximately 1.094 cups of flour.
How do we use graphic technology
Answer:
f light is imagined as a flow of particles, the particles are called photons with each photon carrying a discrete packet of energy.
Sandra wrote p(x) = 30x + 5x2 in vertex form. Her work is below.
1. p(x) = 5x2 + 30x
2. p(x) = 5(x2 + 6x)
3. (six-halves) squared = 9;
4. p(x) = 5(x2 + 6x + 9) – 5(9)
5. p(x) = 5(x + 3)2 – 45
Describe Sandra’s function.
Answer:
p(x) = 5(x + 3)² - 45
Step-by-step explanation:
Sandra wrote the function as p(x) = 30x + 5x².
So, this is a formula of a parabola, and this we have to convert into vertex form.
Now, rearranging the function we get
p(x) = 5(x² + 6x)
⇒ p(x) = 5(x² + 6x + 9) - 45
⇒ p(x) = 5(x + 3)² - 45
So, this is the vertex form and the vertex of the parabola is (-3,-45).
We know the formula of a parabola having vertex at (m,n) and axis parallel to positive y-axis is given by
(x - m)² = 4a(y - n)
⇒ [tex]y = \frac{1}{4a} (x - m)^{2} + n[/tex] (Answer)
Please Help ASAP!! Domain and range of function...
Answer:
Domain: All Real Numbers
Range: All Integers
Step-by-step explanation:
Integers are numbers positive and negative and 0 but cannot be partial numbers. Partial numbers are decimal or fractional numbers when most simplified.
Real numbers are positive and negative and 0 and can be partials, decimal numbers, fractions, radicals, anything considered a number.
The domain is all real numbers. Since the graph has lines that show between the grid lines, decimal numbers are included.
The range is all integers because there are only number on the grid lines. Real numbers would include all of the decimal numbers that not in the white spaces.
Answer:
the bottom right
Step-by-step explanation:
range cannot be all real numbers because they have to be integers(for example, 3/4 is a real number but it is not an integer)as the lines are on integer numbers. But the domain can be all real numbers because the lines go through all real numbers
. A soccer club has 15 players for every team, with the exception of two teams that have 16 players each. Is the number of players proportional to the number of teams?
Answer: No
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
It doesn't tell you how many teams there but if there are two teams that have extra player it is obviously not proportional.
5 million, four thousand, three hundered in standard form
5 million, four thousand, three hundered in standard form is [tex]5.0043 \times 10^{6}[/tex]
Solution:Need to represent 5 million, four thousand, three hundered in standard form
5 million = 5000000
4 thousand = 4000
3 hundred = 300
5 million, four thousand, three hundred = 5000000 + 4000 + 300 = 5004300
In standard form, decimal comes after first digit and multiply to power of 10 dependency on total digits of number.
In our case, given number is 5004300.
So we need decimal after first and after that multiplying it by appropriate power of 10. So,
[tex]5004300=5.0043 \times 10^{6}[/tex]
Hence [tex]5.0043 \times 10^{6}[/tex] is standard form of 5004300 that is standard form of 5 million, four thousand, three hundred.
The number '5 million, four thousand, three hundred' is written in standard form as 5,004,300. Standard form notation uses commas to split up large numbers into thousands, millions, etc.
Explanation:The standard form notation for representing numbers is a helpful way to write large or very small numbers in a more compact format. In this case, the number '5 million, four thousand, three hundred' in standard form would be represented as 5,004,300. This combines all the components: millions, thousands, and hundreds into one concise figure.
In standard form, this value is written by placing commas every three digits, starting from the right. So, '5 million' is written as 5,000,000. 'Four thousand' is written as 4,000 and 'three hundred' as 300. When you add these values together, you get 5,004,300.
Learn more about Standard Form here:https://brainly.com/question/29000730
#SPJ3
18. Find the measure of ZWZX. Show your work.
48 degrees
8x-3
18x+5
<X = 48 degrees, <Y = 8X-3, W = 18X+5
Since it's a triangle we know that it equals 180 degrees.
So take 8X-3+18X+5+48=180
Add your like terms together which makes, 26X+50=180
Now you're going to subtract 50 from 180 which leaves you with 26X=130
Now divide your sums which leaves you X which = 5
You should be able to plug X back into your equation to find <Z. Hope this helps.
The ratio of 15 white paint to 11 black paint and 16
blue paint is......?
Answer:
15 : 11 : 16
Step-by-step explanation:
If A, B, and C are in the ratio x : y : z, then we can say that there is x quantity of A, y quantity of B and z quantity of C.
Therefore, the 15 quantity of white paint. 11 quantity of black paint and 16 quantity of blue paint are in the ratio of 15 : 11 : 16.
Since there is no common factor between 15, 11 and 16 then the ratio is in the simplest form and the ratio is 15 : 11 : 16. (Answer)
Solve for x. 12x-39<9 AND -4x+3<-6
Answer:
1. x<4
2. x>9/4
Step-by-step explanation:
Answer:
the answer is b
Step-by-step explanation:
Interpret the y-intercept of the graph.
Answer:
the y-coordinate of a point where a line, curve, or surface intersects the y-axis.
Step-by-step explanation:
This is the best and easiest way I could put it in.
A rectangular picture has a height that is 5/7 of its width. It’s area is 140 square inches. What are the dimensions of the picture?
The width of the picture is 14 inches and the height is 10 inches, resulting in dimensions of 14 inches by 10 inches.
Explanation:This problem can be solved by using the formula for the area of a rectangle, which is area = length x width. We are given that the area is 140 square inches, and that the height of the picture is 5/7 of its width. Therefore, we can create the equation 140 = width x (5/7)width.
By simplifying this equation, we can then solve for the width:
Multiply both sides of the equation by 7/5: [tex]width^2[/tex] = 140 x (7/5)Simplify the equation: [tex]width^2[/tex] = 196Take the square root of both sides: width = sqrt(196) = 14 inchesSo the width of the picture is 14 inches. To find the height, we multiply the width by 5/7: height = 14 x (5/7) = 10 inches.
Therefore, the dimensions of the picture are 14 inches by 10 inches.
Learn more about Rectangle Area here:https://brainly.com/question/31566854
#SPJ3
If u can help that would be great
Answer:
Step-by-step explanation:
Solved by elim: it is similar (diff size, but not congruent, same size) and B is twice the size of A, not half.
what is the x intercept od this piecewise function? A) (0,2) B) (2,0) C) (0,4) D) (4,0)
Answer: Choice B) (2,0)
======================================
Set the first piece equal to zero and solve for x
x^2 - 4 = 0
x^2 = 4
x = sqrt(4) or x = -sqrt(4)
x = 2 or x = -2
Keep in mind that the first piece y = x^2-4 is only graphed when x = 2 or larger, so we ignore x = -2. This is one x intercept, but there may be more. Let's check the other graph to see what we get.
----------
Set the second piece equal to zero and solve for x
x-2 = 0
x-2+2 = 0+2
x = 2
We get the same result as above in the prior section. Because of this, the two pieces connect at this junction point.
The x intercept x = 2 leads to the location (2,0). The x intercept always occurs when y = 0.
The graph below shows this.
side note: the red piece y = x^2 - 4 looks linear, but it's actually not a straight line. It's just a really stretched out curve.
Which of the following is written as a rational function?
A. P(x)=7x+1
B. G(x)=-4x
C. F(x)=x-5//3x (correct answer
D. Q(x)=x^2+6x-3
Answer:C
Step-by-step explanation:
The required rational function is F(x) = x-5/3x. Option C is correct.
From the options correct rational function is to be determined.
A rational number is defined as the number written in the form of the f ratio.
Here,
The property of rational function is it contains function on both numerator and denominator.
By looking to the property, only function F(x) = x-5/3x seems to rational functions.
Thus, the required rational bis F(x) = x-5/3x.
Learn more about rational numbers here
https://brainly.com/question/17450097
#SPJ5
1=(6/-15)(-5)+b
What is the answer
Answer:
b=-1
Step-by-step explanation:
1=(6/-15)(-5)+b
-6/15=-2/5
(-2/5)(-5)=10/5=2
2+b=1
b=1-2=-1
8,197 rounded to thousand
Answer:
8,000. Hope this helps!
Answer: 8000
Step-by-step explanation: Find the number in the thousand place, 8, and look one place to the right for the rounding digit, 1. Round up if this number is great than or eual to 5 and round down if it is less than 5.
(5 or more, let it sore. 5 or less, let it rest.)
Hope this helps you out! ☺
Yoga classes are offered 2 days a week for 6 weeks at both the community center and the local gym. The cost for the classes at the community center is $72 plus an additional one time fee of $12 to rent the yoga equipment used in class. The cost at the local gym is $8 a class. Regina wants to know which class she can take for less money
Regina can take yoga classes at community center as it would cost her less money.
Step-by-step explanation:
No. of classes per week = 2
Classes in 6 weeks = 2*6 = 12 classes
Cost of classes at community center = $72
Additional one time fee = $12
Total cost at community center = 72+12 = $84
Cost per class at local gym = $8
Cost of 12 classes = 12*8 = $96
Regina can take yoga classes at community center as it would cost her less money.
Keywords: addition, multiplication
Learn more about addition at:
brainly.com/question/3398261brainly.com/question/3614284#LearnwithBrainly
there are 527 students enrolled at school 11% are absent today how many students are absent
Answer:
About 58 students are absent today.
Step-by-step explanation:
11%=0.11
0.11*527=57.97
Two factory plants are making TV panels. Yesterday, Plant A produced 16,000 panels. Five percent of the panels from Plant A and 2% of the panels from Plant B
were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 4%?
Number of panels produced by Plant B????
Answer:
Number of panels produced by Plant B is 8,000.
Step-by-step explanation:
The number of panels produced by Plant A = 16,000
The number of defective panels from A = 5%
Now, 5% of 16,000 = [tex]\frac{5}{100} \times 16,000 = 800[/tex]
So, out of 16,000 panels produced by pant A , 800 are defective. .. (1)
Let us assume number of panels produced by Plant B = m
The number of defective panels from B = 2%
Now, 2% of m = [tex]\frac{2}{100} \times m = 0.02 m[/tex]
So, out of total m panels produced by pant B , 0.02 m are defective. .. (2)
Now, total panels produced over all = Panels by A + Panels by B
= 16,000 + m
The percentage of defected panels over all = 4%
Now, 4% of (16,000 + m) = [tex]\frac{4}{100} \times (16,000+m) = (0.04)(16,000 + m)[/tex]
Also, the total number of defective panels = Defective from A + Defective from B
⇒(0.04)(16,000 + m) = 800 + 0.02 m from (1) and (2)
or, 640 + 0.04 m = 800 + 0.02
or, 0.02 m = 160
⇒ m = 160 /0.02 = 8,000
or, m = 8,000
Hence, Number of panels produced by Plant B is 8,000.
The number of panels produced by Plant B can be calculated by setting up an equation representing the total number of defective panels from both plants. Solving this equation yields a result of 20,000 panels for Plant B.
Explanation:Let's denote the number of panels produced by Plant B as X. According to the problem, 5% of the panels produced by Plant A were defective, which is 0.05*16,000 = 800. Since 2% of the panels produced by Plant B were defective, that's 0.02*X panels.
The total number of defective panels from both plants was 4% of the total production, which means it was equivalent to 0.04 * (16,000+X). Setting this equation equal to the sum of defective panels from both plants, we get the equation 0.04*(16,000+X) = 800 + 0.02*X.
Solving the above equation, we get X = 20,000. Therefore, "Plant B produced 20,000 panels".
Learn more about Problem Solving here:https://brainly.com/question/31606357
#SPJ3
A box of seeds contains p packets. Each packet contains s seeds. Which equation can be used to find the number of seeds in a box (b)?
(A) p= sb
(B) p= s/b
(C) b= ps
(D) b= p/s
The total number of seeds in the box is found by multiplying the number of packets by the number of seeds per packet, yielding the equation b = ps.
Explanation:The equation we are looking for will help us find the total number of seeds in a box, which we will call b. Since the box has p packets and each packet contains s seeds, we can find the total number of seeds by multiplying the number of packets by the number of seeds in each packet. Therefore, the correct equation to represent this relationship is b = ps, which means the total number of seeds in the box (b) is the product of the number of packets (p) and the number of seeds per packet (s).
what is 6–3 simplyified
Answer:
Bro XD lol just simplify it.
the answer is 3
Answer:
3
Step-by-step explanation:
5. A car that travels 20 miles in
a car that travels 30 miles
hour at constant speed is traveling at the same speed as
ar at a constant speed. Explain
Question:
A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles in 3/4 hour at constant speed. Explain
Answer:
Both the car travels at the same speed of 40 miles per hour .
Step-by-step explanation:
Given:
car 1 :
Distance travel car 1 travels =20 miles
Time taken = 1/2 hour
car 2 :
Distance travel car 1 travels =30 miles
Time taken = 3/4 hour
Solution:
Let the speed at which car 1 travels be x
Let the speed at which car 2 travels be y
Finding the speed of car 1 :
Speed of car 1,[tex]x =\frac{distance}{time}[/tex]
=>[tex]x=\frac{20}{(\frac{1}{2})}[/tex]
=>[tex]x=20\times \frac{2}{1}[/tex]
=>x = 40 miles per hour
Finding the speed of car 2 :
Speed of car 2,[tex]y =\frac{distance}{time}[/tex]
=>[tex]y=\frac{30}{(\frac{3}{4})}[/tex]
=>[tex]y=30\times \frac{4}{3}[/tex]
=>[tex]y=\frac{120}{3}[/tex]
=>x = 40 miles per hour
The area of a rectangular room is given by the trinomial 3x^2-13x-30 what are the possible dimensions of the frame? Use factoring.
Answer:
(3x + 5) and (x - 6).
Step-by-step explanation:
3x^2-13x-30
Use the 'ac' method:
a * c = 3*-30 = -90.
We need two numbers whose product is -90 and whose sum is -13. They are -18 and + 5, so we have
3x^2 - 18x + 5x - 30 Factor by grouping:
= 3x(x - 6) + 5(x - 6)
= (3x + 5)(x - 6).
Answer:
A (3x + 5) and (x - 6
Step-by-step explanation:
the three median of a triangle intersect as a point. which measurements could represent the segments of one of the medians? 2 and 3 , 3 and 4.5 , 3 and 6 , 3 and 9
In a triangle, the point where the medians intersect, known as the centroid, divides each median into two segments in a 2:1 ratio. In this context, only the measurement of segments 3 and 6 fit this property.
Explanation:The median of a triangle is a segment joining a vertex to the midpoint of the opposite side. In this question, we are considering segments of a median, so we're considering the vertex of the triangle to the centroid (where medians intersect) and from the centroid to the midpoint of the opposite side.
The key property of medians in a triangle is that the centroid, or point of intersection, divides each median into two segments in the ratio 2:1. This means the distance from a vertex to the centroid is twice the distance from the centroid to the midpoint of the opposite side.
From the provided segments, only 3 and 6 fit this principle. This means the distance from the vertex to the centroid is 3 (representing two-thirds of the median) and the distance from the centroid to the midpoint of the opposite side is 6 (representing one-third of the median).
Learn more about Triangle Medians here:https://brainly.com/question/27844913
#SPJ3